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13400 | https://www.mytutor.co.uk/answers/54844/A-Level/Further-Mathematics/Find-the-reflection-of-point-P-2-4-6-in-the-plane-x-2y-z-6/ | Answers
Further Mathematics
A Level
Article
Find the reflection of point P(2,4,-6) in the plane x-2y+z=6
If the point P' is a refection of point P in any plane, then both P and P' line on the line perpendicular to that plane. The equation of such line is easy to find: all we need is a point and the direction vector. The direction vector is given by the coefficients near , and the required point is our point P. These lead us to the following equation of a line in 3D: L=(2,4,-6)+k(1,-2,1), where k is scalar parameter. all we need to do now is to find that parameter. We know that, by definition, points P' and P are equidistant from the plane, therefore, the intersection of that line with the plane will be the middle point. After substituting the equation of the line into our equation of the plane and solving for k, we obtain the result that k=3. But because k=3 only gives us our middle point, we need to double it to get P',therefore k=6. Substituting k=6 into our equation of the line gives the point (8,-8,0), which are the desired coordinates.
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13402 | https://chem.libretexts.org/Courses/Duke_University/CHEM_401L%3A_Analytical_Chemistry_Lab/06%3A_Instrument_Facilities_for_CHEM401L/01%3A_Analytical_Equiptment_and_Methods_for_Calibration/1.03%3A_Methods_of_Calibration | 1.3.3
1.3.4
A400=0.336=15.2CCr+5.60CCo
A400=0187=0.533CCr+5.07CCo
CCo=0.336−15.2CCo5.60
0.187=0.533CCr+5.07×0.336−15.2CCo5.60
0.187=0.3042−13.23CCr
8.86×10−3
3.60×10−2
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1.3: Methods of Calibration
Last updated
: Aug 22, 2023
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1.2: Preparing Solutions
1.4: Uncertainty in values determined from a Calibration Curve
Page ID
: 407714
Kathryn Haas
Duke University
( \newcommand{\kernel}{\mathrm{null}\,})
Single Point Calibration vs Multiple-point Calibration
The simplest calibration is a single-point calibration using a standard. For example, using a standard solution of known concentration of component XX, we could measure its signal (eg absorption), and then calculate the response (eg the εXεX at the wavelength of maximum absorbance).
Limitations to Single-point calibration
A single-point standardization is the least desirable approach for standardizing a method. There are two reasons for this. First, any error in our determination of the response, (eg εXεX), carries over into our calculation of concentratino (CXCX). Second, our experimental value for each response (eg εε) is based on a single concentration of analyte. To extend this value of εε to other concentrations of analyte requires that we assume a linear relationship between the signal and the analyte’s concentration, an assumption that often is not true [Cardone, M. J.; Palmero, P. J.; Sybrandt, L. B. Anal. Chem. 1980, 52, 1187–1191]. Figure 1.3.1
shows how assuming a constant value of response leads to a determinate error in concentration if \the response becomes smaller at higher concentrations of analyte. Despite these limitations, single-point standardizations find routine use when the expected range for the analyte’s concentrations is small.
Multi-point Calibration
The better way to standardize a method is to prepare a series of standards, each of which contains a different concentration of analyte. Standards are chosen such that they bracket the expected range for the analyte’s concentration. A multiple-point standardization should include at least three standards, although more are preferable. A plot of the signal from the standards (SstdSstd versus the concentrations of the standards (CstdCstd)is called a calibration curve. The exact standardization, or calibration relationship, is determined by an appropriate curve-fitting algorithm.
There are two advantages to a multiple-point standardization. First, although a determinate error in one standard introduces a determinate error, its effect is minimized by the remaining standards. Second, because we measure the signal for several concentrations of analyte, we no longer must assume that the response (εε in this case) is independent of the analyte’s concentration. Instead, we can construct a calibration curve similar to the “actual relationship” indicated in Figure 1.3.1
.
External Calibration
The most common method of standardization uses one or more external standards, each of which contains a known concentration of analyte. We call these standards “external” because they are prepared and analyzed separate from the samples.
Figure 1.3.2
shows a typical multiple-point external standardization. The volumetric flask on the left contains a reagent blank and the remaining volumetric flasks contain increasing concentrations of Cu2+. Shown below the volumetric flasks is the resulting calibration curve. Because this is the most common method of standardization, the resulting relationship is called a normal calibration curve.
When a calibration curve is a straight-line, as it is in Figure 1.3.2
, the slope of the line gives the value of bεbε (where bb is path length) This is the most desirable situation because the method’s sensitivity remains constant throughout the analyte’s concentration range. When the calibration curve is not a straight-line, the method’s sensitivity is a function of the analyte’s concentration. In Figure 1.3.1, for example, the value of bεbεis greatest when the analyte’s concentration is small and it decreases continuously for higher concentrations of analyte. The value of bεbε at any point along the calibration curve in Figure 1.3.1 is the slope at that point. In either case, a calibration curve allows us to relate SsampSsamp to the analyte’s concentration.
Limitations to External Calibration
There is a serious limitation, however, to an external standardization. When we determine and analyte's response (\varepsilon) in this case) using external calibration, the analyte is present in the external standard’s matrix; that is usually a much simpler matrix than that of "real" samples. When we use an external standardization we assume the matrix does not affect the value of the response (εε). However, if the matrix does affect the response, we introduce a proportional determinate error into our analysis. This is not the case in Figure 1.3.3
, for instance, where we show calibration curves for an analyte in the sample’s matrix and in the standard’s matrix. In this case, using the calibration curve for the external standards leads to a negative determinate error in analyte’s reported concentration. If we expect that matrix effects are important, then we try to match the standard’s matrix to that of the sample, a process known as matrix matching. If we are unsure of the sample’s matrix, then we must show that matrix effects are negligible or use an alternative method of standardization. Both approaches are discussed in the following section.
Validating an external calibration
Calibration by Standard Additions
We can avoid the complication of matching the matrix of the standards to the matrix of the sample if we carry out the standardization in the sample. This is known as the method of standard additions.
There are several methods of standard addition, and some are described in detail in 5.3: Determining the Sensitivity by David Harvey. We will focus on standard addition by adding standard analyte solution directly to the sample, measuring the signal both before and after the spike (Figure 1.3.5
). In this case the final volume after the standard addition is Vo + Vstdand the relationship between the absorbance and concentration of a analyte "X" becomes (the standard is a standard solution of the analyte X):
Asample=εbCX
Asample=εbCX
Aspiked=εb(CXVoVo+Vstd+CstdVstdVo+Vstd)
Aspiked=εb(CXVoVo+Vstd+CstdVstdVo+Vstd)(1.3.1)
AsampleCX=AspikedCXVoVo+Vstd+CstdVstdVo+Vstd
AsampleCX=AspikedCXVoVo+Vstd+CstdVstdVo+Vstd(1.3.2)
Multiple Standard Additions
We can adapt a single-point standard addition into a multiple-point standard addition by preparing a series of samples that contain increasing amounts of the external standard. Figure 1.3.6
shows two ways to plot a standard addition calibration curve based on equation 1.3.11.3.1. In Figure 1.3.6
, plot (a) we plot Aspike(or more generally Sspike) against the volume of the spikes, Vstd. In plot (b) we plot Cstd×VstdVfCstd×VstdVf on the x axis instead (where Vf=V0+VstdVf=V0+Vstd is total volume after the spike). If kA is constant, then the calibration curve is a straight line in both cases. It is easy to show that the slope is related to the response of the analyte in the given matrix (kAkA and that x-intercept is related to the concentration of the analyte CACA; the x-intercept is equivalent to –CAVoCstd–CAVoCstd in the case of plot (a) or –CAVoVf–CAVoVf in the case of plot (b) (see Figure 1.3.6
).
For Mixtures with overlapping signals: The two-analyte Generalized Standard Addition Method (GSAM)
Suppose we need to determine the concentration of two analytes, X and Y, that are mixed in a sample. If each analyte has a wavelength where the other analyte does not absorb, then we can proceed using Beer's Law to determine the concentration. Unfortunately, UV/Vis absorption bands are so broad that it is sometimes impossible to find suitable wavelengths. Because Beer’s law is additive the mixture’s absorbance, Amix, at a given wavelength will be a sum of the absorbance of each analyte:
(Amix)λ1=(εX)λ1bCX+(εY)λ1bCY
(Amix)λ1=(εX)λ1bCX+(εY)λ1bCY(1.3.3)
where λ1λ1 is the wavelength at which we measure the absorbance. Because Equation 1.3.31.3.3 includes terms for the concentration of both X and Y, the absorbance at one wavelength does not provide enough information to determine either CX or CY. If we measure the absorbance at a second wavelength, λ2λ2
(Amix)λ2=(εx)λ2bCX+(εY)λ2bCY
(Amix)λ2=(εx)λ2bCX+(εY)λ2bCY(1.3.4)
then we can determine CX and CY by solving simultaneously Equation 1.3.31.3.3 and Equation 1.3.41.3.4. Of course, we also must determine the value for εXεXand εYεY at each wavelength. For a mixture of n components, we must measure the absorbance at n different wavelengths.
Example 1.3.1
The concentrations of Fe3+ and Cu2+ in a mixture are determined following their reaction with hexacyanoruthenate (II), Ru(CN)4−6Ru(CN)4−6, which forms a purple-blue complex with Fe3+ (λmaxλmax = 550 nm) and a pale-green complex with Cu2+ (λmaxλmax = 396 nm) [DiTusa, M. R.; Schlit, A. A. J. Chem. Educ. 1985, 62, 541–542]. The molar absorptivities (M–1 cm–1) for the solutions of the individual metal complexes at the two wavelengths are summarized in the following table.
| analyte | ε550ε550 | ε396ε396 |
---
| Fe3+ standard | 9970 | 84 |
| Cu2+ standard | 34 | 856 |
When a sample that contains Fe3+ and Cu2+ is analyzed in a cell with a pathlength of 1.00 cm, the absorbance at 550 nm is 0.183 and the absorbance at 396 nm is 0.109. What are the molar concentrations of Fe3+ and Cu2+ in the sample?
Solution
Substituting known values into Equation 1.3.31.3.3 and Equation 1.3.41.3.4 gives
A550=0.183=9970CFe+34CCuA396=0.109=84CFe+856CCu
A550A396=0.183=9970CFe+34CCu=0.109=84CFe+856CCu
To determine CFe and CCu we solve the first equation for CCu
CCu=0.183−9970CFe34
CCu=0.183−9970CFe34
and substitute the result into the second equation.
0.109=84CFe+856×0.183−9970CFe34=4.607−(2.51×105)CFe
0.109=84CFe+856×0.183−9970CFe34=4.607−(2.51×105)CFe
Solving for CFe gives the concentration of Fe3+ as 1.8×10−51.8×10−5 M. Substituting this concentration back into the equation for the mixture’s absorbance at 396 nm gives the concentration of Cu2+ as 1.3×10−41.3×10−4 M.
Let's consider the example of a mixed Co and Cr solution. To obtain results with good accuracy and precision the two wavelengths should be selected so that εX>εYεX>εY at one wavelength and εX<εYεX<εY at the other wavelength. It is easy to appreciate why this is true. Because the absorbance at each wavelength is dominated by one analyte, any uncertainty in the concentration of the other analyte has less of an impact. Figure 1.3.1
shows the spectra of a Cr standard and a Co standard, as well as a spectrum of the mixture. From the spectra of the standards, we can see that 400 nm is a reasonable choice for one of the wavelengths because it is a point of maximum absorption for Cr3+Cr3+, and εCrεCr > εCoεCo. A reasonable choice for a second wavelength is 505 nm; it is a point of maximum absorbance for Co2+Co2+ where εCoεCo > εCrεCr. These two wavelengths are used in Practice Exercise 1.3.1
(below). When the choice of wavelengths is not obvious, one method for locating the optimum wavelengths is to plot εX/εyεX/εy as function of wavelength, and determine the wavelengths where εX/εyεX/εyreaches maximum and minimum values [Mehra, M. C.; Rioux, J. J. Chem. Educ. 1982, 59, 688–689].
Exercise 1.3.1
The absorbance spectra for Cr3+ and Co2+ overlap significantly. To determine the concentration of these analytes in a mixture, its absorbance is measured at 400 nm and at 505 nm, yielding values of 0.336 and 0.187, respectively. The individual molar absorptivities (M–1 cm–1) for Cr3+ are 15.2 at 400 nm and 0.533 at 505 nm; the values for Co2+ are 5.60 at 400 nm and 5.07 at 505 nm.
Answer
: Substituting into Equation 1.3.3 and Equation 1.3.4 gives
A400=0.336=15.2CCr+5.60CCo
A400=0187=0.533CCr+5.07CCo
To determine CCr and CCo we solve the first equation for CCo
CCo=0.336−15.2CCo5.60
and substitute the result into the second equation.
0.187=0.533CCr+5.07×0.336−15.2CCo5.60
0.187=0.3042−13.23CCr
Solving for CCr gives the concentration of Cr3+ as 8.86×10−3 M. Substituting this concentration back into the equation for the mixture’s absorbance at 400 nm gives the concentration of Co2+ as 3.60×10−2 M.
We can extend the standard addition method to quantitate multiple components of a mixture using the Generalized Standard Addition Method (GSAM). This is the preferred method of calibration when quantitation of multiple components are necessary and matrix effects are suspected. This is the method you will use to quantitate two components of a mixture (eg Co and Cr) that have overlapping spectral features (see Figure 3.4.1) and when matrix effects are suspected. For a sample with components X and Y, the initial absorbance of the sample at λ1λ1 is:
A0λ1=εXλ1bC0X+εYλ1bC0Y
A0λ1=εXλ1bC0X+εYλ1bC0Y(1.3.5)
Where εXλ1εXλ1 is the response factor (aka sensitivity, molar extinction coefficient, or the molar absorptivity) for component X at λ1λ1, and εYλ1εYλ1 is the response factor for component Y at λ1λ1.
In this method, the volume of total sample will change as standard solution of X or Y is added to the sample to create the standard addition calibration for X and Y. When volume changes, concentrations are not additive. But we can correct for this inconvenient truth by multiplying by total volume, VtVt. When C is multiplied by V, the result is total moles (n) of each analyte; this value is additive. Multiplying by V gives the equation below.
V0A0λ1=εXλ1bn0X+εYλ1bn0Y
As standards are added to the sample to create the calibration, the moles of analyte will change by Δnx and Δny, and the new volume-corrected absorption for any point on the calibration would be:
ViAiλ1=εXλ1b(Δnx+n0X)+εYλ1b(ΔnY+n0Y)
where ΔnX is the moles of X added and n0X is the initial amount of analyte in the sample. The same follows for analyte Y.
The initial volume-corrected absorption, V0A0 (Equation 1.3.6) can be factored from Equation 1.3.7 to give the change in absorbance upon standard addition:
Δ(VAλ1)=ViAiλ1−V0A0λ1=εXλ1b(ΔnX)+εYλ1b(ΔnY)
For a mixture of two analytes, absorbance would be measured at two wavelengths as described above. The same model described here for λ1, also applies for λ2:
Δ(VAλ2)=ViAiλ2−V0A0λ2=εXλ2b(ΔnX)+εYλ2b(ΔnY)
Using a known volume of the sample, we can add known amounts of one analyte to the solution to create a calibration line with at least 3 points. For example, suppose we have a sample containing two analytes, X, and Y in a complex matrix where matrix effects are unknown; and suppose we want to determine the concentrations of [X] and [Y] in the sample. This is a problem that can be solved by GSAM. First, we would obtain standard solutions of X and Y, collect their absorption spectra, and select appropriate wavelengths for analysis. Then, we would collect a spectrum of the analyte solution containing unknown amounts of X and Y.
To create a standard curve for X, we could add a standard solution of X into a known quantity of the sample while monitoring the solution mixture at the two wavelengths. Under these conditions, ΔnY is zero, and so equation 1.3.8 is simplified to a Δ(VAλ1)=εXλ1b(ΔnX) ; this is the form of a linear equation with the slope that is εXλ1b. By plotting Δ(VAλ1) at one wavelength vs ΔnX we can determine the molar response factor of X at that wavelength (ελ1). And, by plotting Δ(VAλ2) at the second wavelength vs ΔnX we can determine the molar response factor of X at the second wavelength (ελ2).
Then, using the same sample as above, we can add two aliquots of Y and follow a similar strategy plotting ΔnY against Δ(VAλ1) and Δ(VAλ2) to find the response factors of Y at the two wavelengths.
Once the response factors of both analytes X and Y are determined at the two different wavelengths, the concentrations of each analyte in the original sample can be determined by simultaneously solving equation 1.3.5 and the analogous equation at λ2:
A0λ1=εXλ1bC0X+εYλ1bC0YandA0λ2=εXλ2bC0X+εYbC0Yλ2
1.2: Preparing Solutions
1.4: Uncertainty in values determined from a Calibration Curve |
13403 | https://www.maths.scot/pdf/n5/maths4scotland/Percentage-Appreciation-Depreciation-Notes.pdf | Appreciation & Depreciation Percentage Multipliers: If we wish to increase a quantity by a percentage to a new value, we can: 1. Find the percentage of the quantity 2. Add it on to the original amount to obtain the new value. This requires 2 steps. Example: Peter earns a salary of £12,000 p.a., this year he gets a 10% rise, what will his new salary be? His 10% rise is 10% of £12,000 = £1,200 His new salary will be £12,000 + £1,200 = £13,200 We can however do this calculation in a single step. His original salary corresponds to 100%, he gets a rise of 10%, so he now has 100% + 10% = 110% of his original salary. To find 110% we multiply by 110 100 which is 1.10 So Peter’s new salary is £12,000 × 1.1 = £13,200 Multiplier = 100 + % increase 100 Examples: To obtain an increase of: 5% multiply by 1.05 (105 ÷ 100) 7% multiply by 1.07 (107 ÷ 100) 20% multiply by 1.20 (120 ÷ 100) 2½% multiply by 1.025 (102.5 ÷ 100) Try these: Find the multiplier to give an increase of: 15% [ Ans: 1.15 ] 25% [ Ans: 1.25 ] 3% [ Ans: 1.03 ] 17½% [ Ans: 1.175 ] 8¾% [ Ans: 1.0875 ] 7.3% [ Ans: 1.073 ] Decrease Similarly, to find a decrease, we subtract from 100. For example: To find a decrease of 10% We want 100% − 10% = 90%, so we multiply by 90 100 i.e. 0.9 Multiplier = 100 - % increase 100 Examples: To obtain an decrease of: 5% multiply by 0.95 (95 ÷ 100) 7% multiply by 0.93 (93 ÷ 100) 20% multiply by 0.80 (80 ÷ 100) 2½% multiply by 0.975 (97.5 ÷ 100) Try these: Find the multiplier to give an decrease of: 15% [ Ans: 0.85 ] 25% [ Ans: 0.75 ] 3% [ Ans: 0.97 ] 7½% [ Ans: 0.925 ] 8¾% [ Ans: 0.9125 ] 7.3% [ Ans: 0.927 ] Definitions: Appreciation: A gain or increase in value over time. Items that appreciate in value are: Buildings, Antiques, Paintings, Jewellery, Works of Art. Appreciation is usually expressed as a percentage. Depreciation: A loss or decrease in value over time. Items that depreciate in value are: Cars, Machinery, Technology e.g. computers, Furniture. Depreciation is usually expressed as a percentage. Use of multipliers: If a house is valued today at £80,000 and is expected to appreciate by 3% p.a. (per year). Then we can calculate the value after 3 years. We can calculate year by year. You should note that appreciation is always calculated on the value at the start of each year, so it is compounded. Start Value: Increase Value at end of year. £80,000 £2,400 £82,400 (after 1 year) £82,400 £2,472 £84,872 (after 2 years) £84,872 £2,546.16 £87,418.16 (after 3 years) So value after 3 years is: £ 87, 418.16 An easier way to calculate is to use the multiplier instead: An increase of 3% corresponds to a multiplier of 1.03 After 3 years, the house is worth: £80,000 × 1.03 × 1.03 × 1.03 or £80,000 × 1.033 = £87,418.16 Similarly, we can apply this to depreciation. Example: A car is bought new for £15,000 and depreciates at 20% p.a. What is the value of the car after 4 years. Solution: The car loses 20% of its value each year, so it is worth only 80% So, multiplier = 0.8 After 4 years, car is worth: £15,000 × 0.8 × 0.8 × 0.8 × 0.8 or £15,000 × 0.84 = £6,144 We can have problems involving both appreciation and depreciation: A factory is valued at £120,000 for the building and £60,000 for the machinery. If the building appreciates by 5% p.a. and the machinery depreciates by 8% p.a., calculate the total value of the buildings and machinery after 5 years. Value of building after 5 years: £120,000 × 1.055 = £153,153.79 Value of machinery after 5 years: £ 60,000 × 0.925 = £ 39,544.89 Total value of building and machinery: £153,153.79 + £39,544.89 = £192,698.68 We can have problems involving multiple rates of depreciation: A car is purchased for £20,000. It is assumed to depreciate by 25% in the 1st year, 20% in the 2nd year and 15% in each of the 3rd and 4th years. Calculate the value of the car after 4 years. Value of car after 4 years: £20,000 × 0.75 × 0.8 × 0.85 × 0.85 = £8,670 The same principles apply to growth (increase) and decay (decrease) problems: Example of growth: A colony of bacteria initially contain 25,000 bacteria. It is found that the colony grows at a rate of 35% per hour. What will be the size of the colony after 3 hours. Size of colony after 3 hours: 25,000 × 1.353 = 61509.375 = 61509 bacteria. Example of decay: A flask contains 5 litres of a chemical. If it is left open to the air, it is found that the chemical evaporates at a rate of 15% per hour. How much chemical will be left after 5 hours. After 3 hours: 5,000 × 0.855 = 2218.5 millilitres. Past Paper Questions 1. Bacteria in a test tube increase at the rate of 0.9% per hour. At 12 noon there are 4500 bacteria. At 3 pm, how many bacteria will be present? Give your answer to 3 significant figures. 2. In January 2001, it was estimated that the number of flamingos in a colony was 7000. The number of flamingos is decreasing at the rate of 14% per year. How many flamingos are expected to be in this colony in January 2005 ? Give your answer to the nearest 10. 3. In 1999, a house was valued at £70,000 and the contents were valued at £45,000. The value of the house appreciates by 7% each year. The value of the contents depreciates by 9% each year. What will be the total value of the house and contents in 2002 ? 4. A factory was put on the market in January 2001. The site was in an excellent location so the value of the building has appreciated since then by 5.3% per year. Unfortunately the plant & machinery were poorly maintained and have depreciated by 8⋅5% per year. The value of the building was £435 000 and the value of the plant & machinery was £156 000 in January 2001. What would be the expected value of the complete factory in January 2003 ? 5. How much would the Strachans pay for a new iron, priced £16.50 at Watsons ? Solutions: 1. 4500 × 1.0093 = 4622.59678… 4620 (3 sf) 2. 7000 × 0.864 = 3829.0571… 3830 (nst 10) 3. House: £ 70 000 × 1.073 = £ 85 753.01 Contents: £ 45 000 × 0.913 = £ 33 910.70 Total value: = £ 119 663.71 4. Factory: £ 435 000 × 1.0532 = £ 482 331.92 Plant & Mcy: £ 156 000 × 0.9152 = £ 130 607.10 Total value: = £ 612 939.02 5. 66 2/3 % = 2/3 So, 2/3 off means you pay 1/3 They pay 1/3 of £ 16.50 = £ 5.50 WATSON’S SALE 2 3 % 66 off everything Reversing the change: Quite often we are given the result after a percentage change has been applied, and asked to calculate the original value. Example: A ticket is on sale at 40% discount. Paul paid £9.00 for the ticket. What was the original price before the discount. Solution: A 40% discount means that the ticket was sold for 60% of its price. i.e. 60% is equivalent to £9.00 So, 1% is equivalent to £9.00 ÷ 60 and 100% is equivalent to £9.00 ÷ 60 × 100 = £15 Original price of ticket was £15. (You can check this by taking 40% off it) An alternative (algebraic) solution: Let the original price be £ P Then reduce the price by 40%. → P × 0.6 So: → P × 0.6 = 9.00 Divide both sides by 0.6 → P = £15.00 Examples: 7. A computer is sold for £695. This price includes VAT at 17.5% Calculate the price of the computer without VAT. 8. During the Christmas Sales a shopkeeper sold 60% of his “Santa Claus Dolls” He then found he was left with 50 dolls. How many dolls had he in stock to begin with ? 9. Kerry bought a new car in 1996. When she sold it four years later, she found that it had reduced in value by 60% and she received only £4640. How much had Kerry paid for the car in 1996 ? 10. James bought a car last year. It has lost 12.5 % of its value since then. It is now valued at £14 875. How much did James pay for his car. Solutions: 7. Ex-VAT Price × 1.175 = £695 Ex-VAT Price = £695 ÷ 1.175 = £ 591.49 8. Stock × 0.4 = 50 (60% sold = 40% left) Stock = 50 ÷ 0.4 = 125 9. Original Price × 0.4 = £ 4640 Original Price = £ 4640 ÷ 0.4 = £ 11 600 10. Original Price × 0.875 = £ 14 875 Original Price = £ 14 875 ÷ 0.875 = £ 17 000 |
13404 | https://mathoverflow.net/questions/352891/largest-absolute-value-of-a-polynomial-of-degree-n-on-0-1-ldots-n | real analysis - Largest absolute value of a polynomial of degree $n$ on ${0,1,\ldots,n}$ - MathOverflow
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Largest absolute value of a polynomial of degree n n on {0,1,…,n}{0,1,…,n}
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Consider a polynomial P n(x)∈R[x]P n(x)∈R[x], of degree n≥1 n≥1, of the form
P n(x)=c 0+c 1 x+c 2 x 2+⋯+c n−1 x n−1+x n.P n(x)=c 0+c 1 x+c 2 x 2+⋯+c n−1 x n−1+x n.
To illustrate the question, take P 1(x)=c 0+x P 1(x)=c 0+x so that P 1(0)=c 0 P 1(0)=c 0 and P 1(1)=c 0+1 P 1(1)=c 0+1. If |c 0|<1 2|c 0|<1 2 then |c 0+1|≥1−|c 0|>1−1 2=1 2|c 0+1|≥1−|c 0|>1−1 2=1 2. That means, max max{|P 1(0)|,|P 1(1)|}≥1 2 max max{|P 1(0)|,|P 1(1)|}≥1 2.
In general,
QUESTION. is this true?
max max{|P n(0)|,|P n(1)|,|P n(2)|,…,|P n(n)|}≥n!2 n.max max{|P n(0)|,|P n(1)|,|P n(2)|,…,|P n(n)|}≥n!2 n.
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edited Feb 16, 2020 at 22:33
kodlu
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asked Feb 16, 2020 at 21:13
T. AmdeberhanT. Amdeberhan
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1 you mean P 1(1)=c 0+1 P 1(1)=c 0+1 instead of P 1(x)=c 0+1 P 1(x)=c 0+1, right?AccidentalFourierTransform –AccidentalFourierTransform 2020-02-16 21:18:51 +00:00 Commented Feb 16, 2020 at 21:18
Surely you mean max max and not min min? And also probably an absolute value somewhere in there.Wojowu –Wojowu 2020-02-16 21:29:18 +00:00 Commented Feb 16, 2020 at 21:29
Both of you are correct; edited as such too. Thank you!T. Amdeberhan –T. Amdeberhan 2020-02-16 21:37:23 +00:00 Commented Feb 16, 2020 at 21:37
Just a little remark: the first thing that I thought was trying to link this with the fact that Chebyshev polynomials are those that have the minimum maximum absolute value on [-1,1] and principal coefficient 1.Luis Ferroni –Luis Ferroni 2020-02-16 21:52:29 +00:00 Commented Feb 16, 2020 at 21:52
edited the title, hope you don't mind.kodlu –kodlu 2020-02-16 22:33:33 +00:00 Commented Feb 16, 2020 at 22:33
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You can write your polynomial as
P(x)=∑k=0 n P(k)L n,k(x),P(x)=∑k=0 n P(k)L n,k(x),
where L n,k L n,k are the Lagrange interpolation polynomials with nodes at 0,1,…,n 0,1,…,n. Note that (−1)n−k L n,k(−1)n−k L n,k has positive coefficient at x n x n. Thus, with the constraint
max{|P(k)|:k=0,1,…,n}⩽1,max{|P(k)|:k=0,1,…,n}⩽1,
the largest possible value of the coefficient of P P at x n x n is attained by
P¯(x)=∑k=0 n(−1)n−k L n,k(x),P¯(x)=∑k=0 n(−1)n−k L n,k(x),
and the coefficient of P¯P¯ at x n x n is equal to
∑k=0 n∏0⩽j⩽n j≠k 1|k−j|.∑k=0 n∏0⩽j⩽n j≠k 1|k−j|.
In other words, if the coefficient at x n x n is to be equal to 1 1, the least possible value of max{|P(k)|:k=0,1,…,n}max{|P(k)|:k=0,1,…,n} is
(∑k=0 n∏0⩽j⩽n j≠k 1|k−j|)−1.(∑k=0 n∏0⩽j⩽n j≠k 1|k−j|)−1.
It remains to note that
∑k=0 n∏0⩽j⩽n j≠k 1|k−j|=∑k=0 n 1 k!(n−k)!=1 n!∑k=0 n(n k)=2 n n!.∑k=0 n∏0⩽j⩽n j≠k 1|k−j|=∑k=0 n 1 k!(n−k)!=1 n!∑k=0 n(n k)=2 n n!.
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answered Feb 16, 2020 at 21:41
Mateusz KwaśnickiMateusz Kwaśnicki
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Lagrange interpolation suggested by Mateusz Kwaśnicki is perfectly ok, but in this case it is probably easier to use the finite difference formula
∑i=0 n(−1)i(n i)P(t+n−i)=Δ n P=n!∑i=0 n(−1)i(n i)P(t+n−i)=Δ n P=n!
for t=0 t=0, where Δ:f(t)→f(t+1)−f(t)Δ:f(t)→f(t+1)−f(t) is a finite difference operator.
Also this very statement is well known, in case if you need references.
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answered Feb 17, 2020 at 0:35
Fedor PetrovFedor Petrov
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Nice! It would be good to get any reference.T. Amdeberhan –T. Amdeberhan 2020-02-17 00:54:31 +00:00 Commented Feb 17, 2020 at 0:54
3 It was proposed by Vietnam to IMO 1977 (for arbitrary integers, not consecutive, Mateusz' proof works for this case too), see longlist of 1977 in any edition of IMO Compendium.Fedor Petrov –Fedor Petrov 2020-02-17 01:30:44 +00:00 Commented Feb 17, 2020 at 1:30
I will look it up, thanks.T. Amdeberhan –T. Amdeberhan 2020-02-17 02:10:07 +00:00 Commented Feb 17, 2020 at 2:10
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13405 | https://wujns.edpsciences.org/articles/wujns/pdf/2023/03/wujns-1007-1202-2023-03-0246-11.pdf | 2023, Vol.28 No.3, 246-256 This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Nonlinear Program Construction and Verification Method Based on Partition Recursion and Morgans Refinement Rules □ WANG Changjing1,2, CAO Zhongxiong1, YU Chuling1, WANG Changchang1,2, HUANG Qing1, ZUO Zhengkang1,2† 1. College of Computer Information Engineering, Jiangxi Normal University, Nanchang 330022, Jiangxi, China; 2. College of Digital Industry Academy, Jiangxi Normal University, Shangrao 334000, Jiangxi, China © Wuhan University 2023 Abstract: The traditional program refinement strategy cannot be refined to an executable program, and there are issues such as low verifi‐ cation reliability and automation. To solve the above problems, this paper proposes a nonlinear program construction and verification method based on partition recursion and Morgans refinement rules. First, we use recursive definition technique to characterize the initial specification. The specification is then transformed into GCL(Guarded Command Language) programs using loop invariant derivation and Morgans refinement rules. Furthermore, VCG (Verification Condition Generator) is used in the GCL program to generate the verification condition automatically. The Isabelle theorem prover then validates the GCL programs correctness. Finally, the GCL code generates a C++ executable program automatically via the conversion system. The effectiveness of this method is demonstrated using binary tree preorder traversal program construction and verification as an example. This method addresses the problem that the construction processs loop in‐ variant is difficult to obtain and the refinement process is insufficiently detailed. At the same time, the method improves verification pro‐ cess automation and reduces the manual verification workload.
Key words: program construction; partition recursion; Morgans refinement rules; loop invariant; VCG; Isabelle theorem prover CLC number： TP311 0 Introduction With the continuous progress of computer technol‐ ogy and the expansion of application areas, software se‐ curity has received wide attention from the society. The use of formal methods[1-4] to develop programs can strictly guarantee the correctness and reliability of pro‐ grams. Formal methods also help to better understand the functions and behaviors of programs and meet user requirements. Therefore, formal methods have a wide range of promising applications in software develop‐ ment. Program derivation and verification techniques are the hot spots in the research of formal methods. The more mature techniques are Dijkstras weakest predicate Article ID 1007-1202(2023)03-0246-11 DOI Received date: 2022-05-21 Foundation item: Supported by the National Natural Science Foundation of China (62262031), Science and Technology Key Project of Education Department of Jiangxi Province (GJJ2200302, GJJ210307), and the Graduate Innovative Special Fund Projects of Jiangxi Province (YJS2022064) Biography: WANG Changjing, male, Ph.D., Professor, research direction: software formal method, trustworthy software. E-mail: wcj771006@163.com † To whom correspondence should be addressed. E-mail: zhengkang2005@iscas.ac.cn WANG Changjing et al: Nonlinear Program Construction and Verification … method[5,6], Morgan-based program derivation meth‐ ods[7-9], and PAR(Partition-and-Recur) methods.
Dijkstra s weakest predicate approach defines its own language rules by which programs can be devel‐ oped and verified. The advantage is that the develop‐ ment process is strictly based on mathematical logic and formal verification is performed during the development process. However, the verification process is mostly manual and less automated; and the abstract programs obtained by this method cannot be converted into execut‐ able programs.
The PAR method transforms the initial specifica‐ tion by its own defined rules to obtain recursive equa‐ tions and loop invariant, which eventually lead to an ab‐ stract Apla program. The advantage of this method is that the derivation process is guided by a system with its own derivation patterns and rules, which are more widely applicable. However, the procedure of program derivation using this method is not sufficiently refined and the obtained Apla abstract program is not mechani‐ cally proven and has a low automation procedure.
This paper proposes a program construction and verification method based on partition recursion and Morgans refinement rule. The method first transforms the initial program specification by recursive definition technique, and then obtains recurrence relations and loop invariant by using partitioned recursion rules[10,11]. Then, based on the loop invariant, the program specifica‐ tion is gradually refined using Morgan refinement rules to finally obtain a reliable abstract program. The verifica‐ tion conditions are obtained by VCG12 and then verified by Isabelle[12-14] theo‐ rem provers. After the verification, the obtained abstract program is then generated into a C++ program through the conversion system to realize the whole process from abstract specification to abstract program[15,16], then mechanical verification[16,17], and to executable program.
The paper is organized as follows. Section 1 fo‐ cuses on detailing the program construction and verifica‐ tion methods based on partition recursion and Morgans refinement rule; Section 2 takes the binary tree preorder problem[18,19] as an example to develop and verify the bi‐ nary tree problem using the methods proposed in this pa‐ per as a guide; Section 3 concludes the whole paper.
1 Proposed Method of Nonlinear Program Construction and Verification This section focuses on the method proposed in this paper. The method in this paper contains a complete set of program construction and verification methods, which mainly consists of four steps, as shown in Fig.1.
Fig. 1 Proposed method of nonlinear program construction and verification 247 Wuhan University Journal of Natural Sciences 2023, Vol.28 No.3 1.1 Initial Specification Generation A program specification is a detailed description of a programs functions. It expresses a precise description of the problem in an easy-to-understand manner for the implementer. The program specification consists primar‐ ily of the program s pre-assertion P and post-assertion Q. P and Q are conditions that must be met before and after program input, respectively.
Hoare s formal specification is primarily in the form of triples {P}S{Q}, but this paper primarily uses Morgans specification representation w:[P, Q]. Morgan rewrote the Hoare triples representation to make the specification representation more compact and easier to refine into code.
1.2 Program Refinement and Generation 1.2.1 Initial specification transformation Following the generation of the initial specification, the attributes of first-order logic are typically used to gradually refine the specification transformation from the post-predicate. After the generation of the binary tree preorder specification in Section 1.1, the initial specifica‐ tion transformation needs to be performed on it. The fol‐ lowing is the specific transformation procedure.
Due to the binary trees easy decomposition, this pa‐ per first introduces the recursive function of the binary tree and strengthens the post-prediction of initial specifi‐ cation. Then, Morgan s framework variables are intro‐ duced to convert the initial reductions triple form into a Morgan-specific symbolic form. Figure 2 depicts the en‐ tire initial specification transformation process. This re‐ cursive technique reduces the difficulty of changing the binary tree specification. At the same time, recursion technology provides a foundation for subsequent pro‐ grams to use partition recursion to find loop invariant.
1.2.2 Loop invariant derivation Acquiring loop invariant has always been a difficult point in formal derivation, and acquiring tree structure loop invariant is even more difficult. To address this is‐ sue, this paper proposes the use of partition recursion in conjunction with recursive definition technology to de‐ rive the loop invariant of tree structure.
The basic idea behind partition recursion is to di‐ vide a large, difficult-to-solve problem into some smaller problems of the same scale, and then find the re‐ currence relationship via the relationship between sub-problems.
First, this paper decomposes the original problem using the recursive definition technique. The recurrence relationship between the problems is then determined based on the relationship between the sub-problems in the decomposition process. Finally, the binary trees loop invariant is discovered using the recursive relationship. Figure 3 depicts the specific process flow.
1.2.3 Morgan’s rules refinement The initial statute and loop invariant have been ob‐ tained in Sections 1.2.1 and 1.2.2. Now it is necessary to derive the initial specification to the GCL program based on loop invariant, which are used as Morgan s refine‐ ment rules in this paper. Morgans refinement rules are used to gradually refine the abstract specification into GCL[8,9] code with strong execution, with each refine‐ ment step being small and easy to handle. Using the Morgans refinement rules, each step of the refinement process must be guaranteed to be justified and proven. As a result, the program obtained is extremely reliable.
The rules used in the Morgan refinement method are specified in Table 1 .
1.3 GCL Program Automation Verification The GCL program obtained in Section 1.2 needs to be mechanically verified by generating verification con‐ ditions through VCG and by Isabelle. The specific steps Fig. 3 Loop invariant derivation process Fig. 2 Initial specification conversion process 248 WANG Changjing et al: Nonlinear Program Construction and Verification … are shown as follows.
1.3.1 Verification condition generation The automatic generation of verification conditions is mainly done through VCG, which aims at converting the verification of Hoare triples into the verification of assertions. The advantage of this is that the person or machine verifying the program does not need to know anything about Hoare logic to be able to prove the pro‐ gram.
VCG is a verification condition generator whose working process relies on two conversion functions: pre (this function is different from the following binary tree preorder function Prebt) and vc function. pre function mainly converts the imperative program into specific Hoare logic rules, and vc function mainly converts the result of pre function into specific verification condi‐ tions. The specific VCG working schematic is shown in Fig.4 .
Table 1 Morgans refinement rules Rule 1 2 3 4 5 6 7 8 Name Strengthen postcondition Weaken precondition Skip Assignment Sequential composition Following assignment Selection Repetition Conditions and Rules If Q' Þ Q then w:[PQ]Í w:[PQ'] If P Þ P' then w:[PQ] Í w:[P'Q] If P Þ Q then w:[PQ] Í skip If P Þ Q[\E] then w:[PQ] Í w: = E w:[PQ] Í w:[PM] Í w:[MQ] wx:[ PQ] Í wx:[ PQ[ x\E]] ; x E If P Þ G1 Ú G2 Ú Ú Gn then: w:[PQ]Í If G1 ® w:[G1 Ù PQ] [] [] G1 ® w:[G1 Ù PQ] fi If GG = G1 Ú G2 Ú Ú Gn and V then: w:[PP Ù ØGG]Í do G1 ® w:[G1 Ù PP Ù(0 ≤V < V0 )] [] [] Gn ® w:[Gn Ù PP Ù(0 ≤V < V0 )] od Fig. 4 Working principle of VCG 249 Wuhan University Journal of Natural Sciences 2023, Vol.28 No.3 1.3.2 Isabelle assisted verification Manual and mechanical verification are the two types of formal verification technology. Manual verifica‐ tion is more difficult and prone to errors. Mechanical verification is based on mathematical logic, and it is far more efficient and reliable than manual verification. The mechanical theorem prover is further subdivided into automatic and interactive theorem provers.
Isabelle, an automatic theorem prover, is chosen for auxiliary verification in this paper, primarily because Isa‐ belle has the following advantages.
1)The powerful rule base Isabelle has a powerful rule base, in which every theory contains many related rules and theorems. More importantly, users can add theorems and prove them based on their own proof requirements. If the newly added theorem passes the proof, the Isabelle system will save the newly added lemma and use it in the theorems subsequent proof.
2)The Sledgehammer tool The Isabelle systems Sledgehammer[12,13] tool is ex‐ tremely powerful, and it can invoke several other auto‐ matic theorem provers to find theorems, including E, SPASS, Vampire, and others. In the Isabelle operator in‐ terface, the user only needs to click on the apply applica‐ tion in the Sldgehammer button and Slagehammer can automatically generate the proof process. The user then clicks on the proof process to automatically insert the‐ proof process into the Isabelle script.
1.4 Conversion from GCL Program to Executable Program C++ The GCL programs verified in Section 1.3 are still abstract and cannot be compiled and executed on a com‐ puter. As a result, the GCL program will need to be con‐ verted into an executable file. First, we can convert the GCL program to an Apla program. GCL and Apla can be converted because they are abstract imperative programs with similar syntax. Then, using the teams Apla to C++ program automatic converter, convert the above Apla ab‐ stract program into an imperative C++ program. The team s Apla to C++ conversion system is depicted in Fig.5.
With these four steps, this paper realizes the whole process of program development, verification and trans‐ formation.
2 Example: Binary Tree Preorder Problem (BTPP) 2.1 Initial Specification Generation of BTPP Preorder traversal is a way of traversing a binary tree. By preorder traversal, we mean that when travers‐ ing a binary tree, we first traverse the root node, then the left subtree, and finally the right subtree. In this paper, we use T to represent a binary tree, and the Prebt (T) function to represent the preorder traversal of the entire binary tree T. Therefore, the binary tree preorder tra‐ versal specification can be expressed as follows: [true Prebt(T ) ] (1) 2.2 Program Refinement of BTPP 2.2.1 Initial specification transformation There are two types of binary tree traversal algo‐ rithms: recursive traversal and nonrecursive traversal. The goal of this paper is to deduce the binary trees pre‐ order nonrecursive algorithm program.
This section focuses on the initial specification transformation, which is the transformation of the poste‐ rior assertion Prebt. And we know that the process of bi‐ nary tree preorder traversal is to traverse the root node, then the left subtree, and then the right subtree. So the Prebt function can be written first as follows: Prebt(T ) = ì í î [ ] T = % [ ] T.n Prebt( ) T.l Prebt( ) T.r T ¹ % (2) We decompose this function according to the con‐ tent of the Prebt function, and we can obtain the follow‐ ing derivation process: Prebt(T) = [ ] T.n [ ] T.l [T.r] = [ ] T.n [ ] T.l.n [ ] T.l.l [T.l.r][T.r] = [ ] T.n [ ] T.l.n [ ] T.l.l.n [ ] T.l.l.l [T.l.l.r][T.l.r][T.r] Fig.5 Apla to C++ conversion system 250 WANG Changjing et al: Nonlinear Program Construction and Verification … Figure 6 depicts the binary trees change process as a result of the recursive function Prebt. As shown in the derivation and Fig.6, the root node is retained first when traversing a binary tree recursively. The left subtree of the tree will then be traversed, followed by the right sub‐ tree of the tree. As a result, three variables, X, q, and S, are introduced. The nodes that have been traversed are stored in the sequence X. The sequence S is used to store the nodes to be traversed, while q is used to store the subtree of T that is about to be traversed. The original specification can then be refined as needed: X q S:[true X = Prebt(T ) ] (3) 2.2.2 Loop invariant derivation We have obtained the initial specification after the transformation, next we need to obtain the correspond‐ ing loop invariant. In this paper, the loop invariant are obtained according to the division recursion, i. e., we find the law and obtain the loop invariant in the process of binary tree traversal in the preorder.
As illustrated in Fig.7, for the traversed subtree q, the subtrees head node is always stored in X, and q con‐ tinues to traverse the subtrees left subtree. The right sub‐ tree of the subtree is still in S.
After traversing subtree q, the next round will con‐ tinue to find nodes from sequence S to traverse. The se‐ quence Ss length will be reduced accordingly. The defi‐ nition of the recurrence relation F function can be de‐ rived: F = ì í î ï ï F ( ) [ ] = [ ] F( ) [ ] q S = Prebt( ) q F ( ) S (4) We can see from the previous Prebt and F functions that the binary tree preorder traversal process always places the nodes traversed by q in the sequence X. Then q continues to traverse the subtrees remaining nodes to the left. After traversing the left subtree, q will look for nodes in the sequence S to continue traversing, as shown in Fig. 8. So the loop invariant is inv º Prebt(T ) = X Prebt(q) F(S).
Fig. 6 The process of binary tree change under the action of recursive function Fig. 7 Binary tree traversal node change process diagram 251 Wuhan University Journal of Natural Sciences 2023, Vol.28 No.3 2.2.3 Morgans rules refinement 1) Loop variable initialization Based on loop invariant obtained in Section 2.2.2, the specification can be refined using Strengthen post‐ condition in Table 1, and the specification can then be obtained as: XqS: [true; inv Ù X = Prebt(T ) ] (5) According to the specification, inv is used as an in‐ termediate assertion connecting the pre-predicate and the post-predicate, then (5) is refined using Sequential composition in Table 1: XqS:[true; inv ] (6) XqS: [inv ; inv Ù X = Prebt(T ) ] (7) Assignment in Table 1 is used to refine (6), and the following formula is obtained: XqS:[ true; inv ] ⊑ XSq [] []T (8) Because: true Þ inv[XSq/[] []T] º Prebt( ) T = ( ) X Prebt( ) q F ( ) S [XSq/[] []T º Prebt( ) T =[] Prebt(T) F[] º Prebt( ) T =[] Prebt(T)[] º True So the first part of the refinement is established.
2) Loop process refinement Formula (7) can be refined using Repetition in Table 1, and ¬(X = Pre(T)) is a loop condition and can be equivalently converted to q ¹ % Ú (q = % ÙS ¹[]), then the following equation can be obtained: do q ¹ % Ú(q ¹ % Ù S ¹[]) XqS:[ ] inv Ù ( ) q ¹ % Ú ( ) q = % Ù S ¹[] inv Ù 0 ≤v < v0 od (9) The variable v in the above equation 0 ≤v < v0 is the marker for the terminability proof. v needs to satisfy two conditions: first, it must be guaranteed to be decre‐ mented in each loop, and second, it cannot be decre‐ mented to a negative number. In this paper, we need to find the specific terminability variable v.
We can see here that the variable X stores the nodes that are traversed. And the number of nodes in X keeps increasing. When the loop is completed, the number of nodes stored in X is equal to the number of nodes in the binary tree T. So, we can select (|T|-#X) (|T| is the node value of the whole binary tree and X is the stored tra‐ versed node value) as the variable v.
We can simplify the equation by substituting v=|T|-#X for 0 ≤v < v0: 0 ≤v < v0 º 0 ≤|T | - #X < |T | - #X0 º #X0 < #X ≤|T| Then (9) is simplified to: XqS: inv Ù (q ¹ % Ú (q = ) ) % ÙS ¹[] inv Ù#X0 < #X ≤|T|.
Under the premise of q ¹ % Ú (q = % ÙS ¹[]), the above formula can be further refined according to Selec‐ tion in Table 1.
if q ¹ % ® XqS:[q ¹ % Ù inv Ù ( ] q ¹ % Ú ( ) q = % Ù S ¹[] inv Ù #x0 ≤#x < | |T (10) (q ¹ % Ù S ¹[])® XqS:[(q = % Ù S ¹[])Ù inv Ù (q ¹ % Ú (q = % Ù S ¹[]) inv Ù #x0 <= #x < |T |] (11) fi The above equation (10) can be further refined ac‐ cording to Assignment in Table 1: XqS:[q ¹ % Ù invinv Ù (#x0 < #X ≤|T |)] ⊑ SXq [q.r] SX [q.n]q.l; because Fig. 8 Loop invariant derivation process diagram 252 WANG Changjing et al: Nonlinear Program Construction and Verification … q ¹ % Ù inv Þ inv Ù (#x0 < #X ≤|T |) [SXq\ [q.r] SX [q.n]q.l] According to the definition of inv, Prebt, and F functions, the above formula can be simplified: Left side: q ¹ % Ù inv º q ¹ % Ù(Prebt( ) T = X Prebt(q) F(S)) º Prebt( ) T = X (q.n Prebt( ) q.l Prebt(q.r)) F(S) Right side: Prebt(T ) = X Prebt(q) F(S)Ù (#x0 < #X ≤|T |) º Prebt(T ) = X [q.n] Prebt(q.l F([q.r] S Ù(#x0 < #( ) X [q.n] ≤|T|))) º Prebt(T ) = X [q.n] Prebt(q.l) Prebt(q.r) F(S)Ù true º Prebt(T ) = X [q.n] Prebt(q.l) Prebt(q.r) F(S) So q¹%ÙinvÞinvÙ (#x0<#X≤|T |) [SXq[q.r] SX [ ] q.n q.l]º True Similarly, the above equation (11) can be further re‐ fined according to Assignment in Table 1.
XqS:[(q ¹ % Ù S ¹[])Ù invinv Ù (#x0 < #X ≤|T |)] ⊑qS S [S.h]S[S.h + 1S.t]; According to the above refinement, the program can be replaced by: if q ¹ % ® SXq [q.r] SX [q.n]q.1; (12) (q = % Ù S ¹[])® qS: = S [S.h]S [S.h + 1S.t] ; (13) fi Combined with the above formula, the final GCL program is: XqS []T [] do q ¹ % Ú(q = % Ù S ¹[])® if q ¹ % SXq: =[q.r] SX [q.n]q.1; (q = % Ù S ¹[])® qS: = S[S.h]S[S.h + 1...S.t]; 2.3 GCL Program Automation Verification of BTPP 2.3.1 Verification condition generation In order to verify the GCL code obtained in Section 2.2.3 above, we must first construct the lemma Pre_bt. Then, using the GCL code from above, we must write the corresponding code in Isabelle. The two have the same code structure, and the Isabelle code is as follows: lemma Pre_bt: "VARS X S T q {true} X :=[];q:=T;S :=[]; WHILE (q≠Tnull | q=TnullÙ S≠[]) INV {Prebt(T) =X@Prebt(q)@F(S)} DO IF q≠Tnull THEN X :=X@[data q]; S :=[rtree q]@S ; q :=(ltree q) ELSE IF q=Tnull Ù S≠[] THEN q :=(hd S); S :=(tl S) ELSE SKIP FI OD {X=Prebt(T)}" We then use the apply vcg command to get three verification conditions, as shown in Fig.9.
Fig. 9 Verification condition generation 253 Wuhan University Journal of Natural Sciences 2023, Vol.28 No.3 2.3.2 Isabelle assisted verification Some auxiliary functions and lemmas are required to verify the above three sub-goals. The following are the specific steps: 1) Define two recursive functions Prebt, F: Function 1: primrec Prebt::"'a BTree⇒'a list" where "Prebt Tnull=[]"|"Prebt(BT t1 x t2) =[x]@(Prebt t1) @(Prebt t2)" Function 2: fun F::"'a BTree list⇒'a list" where "F[] =[]"|"F(x#xs) =(Prebt x)@(F xs)" 2) Create the lemmas prebt_rule and F_rule to prove the final program.
Lemma 1: lemma prebt_rule[simp]: "q≠TnullÞPrebt q =data q#Prebt (ltree q)@Prebt(rtree q)" apply (induct q) apply auto done Lemma 2: lemma F_rule[simp]:"xs≠[]ÞF xs=Prebt(hd xs)@F (tl xs)" apply (induct xs) apply auto done 3) Prove the three sub-goals: apply auto With the auto command in 3) above, we can get a successful result of verification. This is shown in Fig.10.
2.4 Conversion from GCL Program to Executable Program C++ of BTPP For the verified GCL program in Section 2.2.3, it is a non-executable abstract program that needs to be con‐ verted to executable C++. First, the GCL program needs to be equivalently converted to an Apla program because their syntax is similar. The resulting Apla program is then passed through our team s conversion system to generate a C++ program, and the conversion result is shown in Fig.11. Finally, the converted C++ program is compiled and run, and the running result is shown in Fig.12.
3 Conclusion This paper proposes a new method for building and verifying nonlinear programs. Using the preorder tra‐ versal of a binary tree as an example, an abstract pro‐ gram GCL is created from the initial specification. Isa‐ belle validates GCL programs before converting them to executables using the C++ conversion platform. The fol‐ lowing are the primary benefits of this paper: 1) Partition recursion is used throughout the pro‐ gram construction process to derive loop invariant. The specification is then gradually refined by Morgans re‐ finement rule based on loop invariant. This method en‐ sures the acquisition of loop invariant while also refin‐ ing the program.
2) The method first employs VCG to generate veri‐ fication conditions automatically. The verification condi‐ tions are then mechanistically verified using Isabelle. This greatly improves verification automation.
Fig.10 Verification success result diagram 254 WANG Changjing et al: Nonlinear Program Construction and Verification … 3) This method improves the methods integrity by converting the obtained abstract program GCL into a C++ executable program using the C++ conversion plat‐ form.
Our next step is to use this approach and combine it with our previous work[20-25] to derive and synthesize more complex algorithms for nonlinear data structures, such as those related to binary trees or graphs.
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Gries D. A note on a standard strategy for developing loop invariant and loops[J]. Science of Computer Programming, 1982, 2(3): 207-214.
Nipkow T, Klein G. Concrete Semantics with Isabelle/HOL [M]. Berlin: Springer International Publishing, 2014.
Nipkow T, Markus W, Lawrence C. Isabelle/HOL: A Proof Fig. 11 Apla to C++ program Fig. 12 Operation result graph 255 Wuhan University Journal of Natural Sciences 2023, Vol.28 No.3 Assistant for Higher-Order Logic[M]. Berlin, Heidelberg: Springer-Verlag, 2002.
Benzmüller C , Claus M , Sultana N. Systematic verification of the modal logic cube in Isabelle / HOL[J] . Electronic Proceedings in Theoretical Computer Science, 2015, 186: 27-41.
Lai Y. Development of APLA to C++ Automatic Program Conversion System [D]. Nanchang : Jiangxi Normal Univer‐ sity, 2002(Ch).
Jiang N, Li Q A, Wang L M, et al. Review of mechanized theorem proof research [J]. Journal of Software, 2020, 31(1): 82-112(Ch).
Tobias N K, Lawrence P S. Auxiliary Proof System for Higher Order Logic[M]. Beijing: Institute of Technology Press, 2013(Ch).
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You Z, Xue J Y. Formal verification of algorithm program based on Isabelle theorem prover[J]. Computer Engineering and Science, 2009, 31(10): 85-89(Ch).
Zhang Q F, Wang C J, Zuo Z K, et al. The formal verifica‐ tion method for smart contract properties based on UPPAAL [J]. Journal of Jiangxi Normal University: Natural Science Edition, 2023, 47(1): 45-51(Ch).
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13407 | https://www.psychiatryadvisor.com/features/agoraphobia-an-evolving-understanding-of-definitions-and-treatment/ | Agoraphobia: An Evolving Understanding of Definitions and Treatment - Psychiatry Advisor
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Anxiety Disorders
Agoraphobia: An Evolving Understanding of Definitions and Treatment
Batya Swift Yasgur, MA, LSW
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Publish Date February 28, 2018
Agoraphobia can be defined as “irrational or disproportionate fear of a range of situations in which a person believes escape or access to help may be impossible, very difficult, or very embarrassing if he or she develops panic-like symptomsor some other incapacitating loss of control.”1
The lifetime prevalence of agoraphobia in the general US population is about 2%,2 with 1 study showing a higher prevalence (10.4%) in adults older than 65 years.3 Despite its high prevalence in older adults, the average age of onset is actually between ages 25 and 30 years.4 Agoraphobia is twice as common in women and is also more disabling in women compared with men.5
During their lifetimes, 87.3% of individuals with agoraphobia will also meet criteria for another psychiatric disorder, including panic disorder, social anxiety disorder, specific phobia, generalized anxiety disorder (GAD),4 and substance use disorder.6
An Evolving Story
Although agoraphobia is very common, it is often misunderstood, according to C. Alec Pollard, PhD, professor emeritus of family and community medicine at Saint Louis University School of Medicine and director of the Center for OCD and Anxiety-Related Disorders at the Saint Louis Behavioral Medicine Institute. For example, a common misconception is that agoraphobia necessarily means fear of going outside or that individuals with agoraphobia are usually homebound.
“The understanding of agoraphobia has been evolving,” Dr Pollard told Psychiatry Advisor, noting that the term was originally coined in 1871 by the German neurologist Westphal, who used the Greek word “agora,” meaning market, to refer to the fear of large, open spaces.7
“The focus was on the external environment, on being away from home or being in public,” Dr Pollard explained, adding that Freud also described agoraphobia, and “foreshadowed the eventual treatment of choice, which is exposure, because insight alone would not be sufficient.”
He described 2 parallel trajectories of research and understanding. “Behavioral therapists were working with exposure therapy and having people gradually face their phobias.”
In this context, “the focus remained on the external situation; for example, going to the mall, being around crowds, and developing a hierarchy of tasks to be exposed, one step at a time, to the object of the fear.”
A second line of approach developed more by the psychiatric community focused on panic attacks, “which were often the center of the fear,” said Dr Pollard, who is the coauthor of The Agoraphobia Workbook: A Comprehensive Program to End Your Fear of Symptom Attacks. 8
“The fear is not of the situation per se, such as being in a crowd, but of having a panic attack in that particular situation,” he said.
Agoraphobia has been reframed as “fear of fear,”9 bringing the 2 lines of thinking into accord. However, Dr Pollard noted that medical research “focused more on stopping the panic attacks and understanding their biological underpinnings,” leading to the investigation of an array of pharmacotherapies to stop the panic attacks.
The approach of cognitive behavioral therapy (CBT) is different. “The goal is not so much to get rid of the attacks but to help patients become less afraid of them because when a person becomes less afraid, he or she has fewer attacks,” Dr Pollard noted.
Agoraphobia and Panic Disorder
The relationship between agoraphobia and panic has gone through some changes and reconceptualization, as evidenced by the diagnostic categories laid out in the Diagnostic and Statistical Manual of Mental Disorders (DSM). In DSM-III,10 agoraphobia without panic attacks was conceptually different from agoraphobia with panic attacks.11 In DSM-III-R,12 however, although the distinction between agoraphobia with and without panic was dropped, agoraphobia without a history of panic disorder still remained a separate diagnosis that could be coded as such.
One of the changes in DSM-5 13 was that panic disorder and agoraphobia were separated again, and criteria were added to distinguish agoraphobia from specific phobia.11 Thus, the situations are feared and avoided because the person believes that escape might be difficult or help might not be available in the event of several distressing symptoms (eg, incontinence), not only panic.11 However, panic attacks are a potential specifier.
DSM-5 Diagnostic Criteria for Agoraphobia include the following:13
Intense fear or anxiety prompted by the actual or predicted exposure to 2 or more of the following situations:
Using public transportation
Being in open areas
Being in closed-off areas
Standing in line or a crowd
Being alone outside of the house
He or she avoids the above situations because the individual believes they may become stuck or help might be unavailable in the event that the individual begins to panic.
The listed situations usually incite fear or anxiety.
The listed situations are avoided, require help from a loved one, or are endured with a strong fear.
The fear the individual has is out of proportion to the possibility of danger.
The fear or avoidance is persistent, as it typically lasts for at least 6 months or longer.
The fear or avoidance causes the individual significant distress.
If another medical condition exists alongside of this disorder, the fear or avoidance is undoubtedly excessive.
The fear of avoidance is not better explained by the symptoms of another medical disorder or a situational circumstance.
“Agoraphobia involves the fear of some type of attack that can come out of the blue, and encompasses not only panic but also fainting, loss of bladder control, vomiting, or even migraine headaches,” Dr Pollack observed, adding that there is still disagreement about “how to best categorize the development of phobic responses around other types of symptom attacks.”
[hmicms_related_articles]
“What these have in common is that they are perceived by the person as overwhelming and unpredictable and very intense, but we tend to see it as another kind of agoraphobia,” he said.
Although incontinence and migraine are medical conditions, the response in agoraphobia is exaggerated in terms of what is medically recommended by a physician.
He noted that what is unique about panic attacks is that they are generally unexpected. “A person with arachnophobia may be afraid of spiders but will panic only when he or she sees a spider and also won’t be worried about the symptoms during the panic, such as lightheadedness or racing heart, in that setting.”
In contrast, someone with agoraphobia does not know why the panic attack suddenly came on; for example, at the grocery store. “The patient thinks, ‘I know I’m not afraid of grocery stores, so why am I having this attack?’ Patients worry that they are losing control or having a heart attack,” Dr Pollack said.
So while they are not afraid of the store per se, they become afraid of having an attack in the store and begin to avoid going shopping.
Behavioral and Pharmacotherapeutic Approaches
Several classes of medication are used for addressing symptoms of panic disorder, including selective serotonin reuptake inhibitors (SSRIs), serotonin-norepinephrine reuptake inhibitors (SNRIs), tricyclic antidepressants, monoamine oxidase inhibitors, and benzodiazepines.14
Table 1: Pharmacotherapies for Panic Disorder in Adults15
ClassAgent
SSRIs Citalopram
Escitalopram
Fluoxetine
Fluvoxamine
Paroxetine
Sertraline
Selective serotonin norepinephrine reuptake inhibitors Duloxetine
Venlafaxine
Tricyclic antidepressants Clomipramine
Calcium modulator Pregabalin
Benzodiazepines Lorazepam melting tablets as needed for acute panic attacks
Azapirone Buspirone
Reversible monoamine oxidase A inhibitor Moclobemide
Consider risk/benefits carefully and use only for limited period; can be used in combination with SSRIs and SNRIs during the first weeks before the onset of antidepressant efficacy.
The most well-researched psychotherapeutic approach is CBT with clinical gains maintained at 2-year follow-up.16 A meta-analysis of 124 studies found that CBT was at least as effective as pharmacotherapy and in some trials even significantly more effective.17 Another review found that CBT is at least as effective as pharmacotherapy for panic.14
The neurobiological effect of CBT can be seen on magnetic resonance imaging. A study 16 comparing CBT with SSRIs and SNRIs found that both treatments led to a significantly greater reduction in panic attacks, depression, and general anxiety than those experienced by the waitlist control group. However, CBT had a significantly greater decrease in avoidance, fear of phobic situations, and anxiety symptoms based on self-report scales. It also yielded great reduction in bilateral amygdala activation, compared with the SSRI/SSNRI and waitlist groups.18
Combining pharmacotherapy with CBT has been found to be superior to either treatment alone during acute-phase treatment. However, long-term studies of treatments that combine pharmacotherapy with CBT for panic disorder with or without agoraphobia have found little benefit for these combinations vs monotherapies.19
“Medication and CBT can both stop panic attacks and reduce avoidance in the short run,” Dr Pollack noted. “But CBT was superior to medication in the long run, with lower rates of relapse.”
Dr Pollack regards CBT as “the frontline treatment” of agoraphobia. “We tell our patients that the preferred treatment is CBT alone, if they can handle it.”
However, if the patient is unwilling or unable to try CBT without medication, “I would not suggest withholding medication,” he emphasized.
CBT plays an important role even in patients who have opted for pharmacotherapy at several particularly critical points in therapy.
“The risk of relapse is highest when patients are tapering off their medications, and CBT can be extremely helpful at that time,” he noted.
It can also be helpful when the person is going through a stressful situation, “since a precursor to the development of panic attacks can be substantially stressful life events, both positive and negative.”
In addition, CBT can be used in the event of “breakthrough” panic attacks that sometimes occur, even when a person has been taking medication successfully. “If the medication has been working but a panic attack happened anyway, this can be a common time for potential relapse.”
Tips for Psychiatrists
In a “fairly mild case” of agoraphobia, whether or not medication is prescribed, psychiatrists can consider recommending books or reliable organizations (eg, the Anxiety and Depression Association of America) to patients who do not wish to attend formal CBT sessions.
He suggested that instead of advising patients to wait until the medication works to begin experimenting with going out, clinicians should encourage them to begin the anti-avoidance process immediately.
Although ultimately, the ideal for patients is to be able to function independently, if they need to bring a family member of friend at first, they can do so, he said.
“You can suggest that they begin gradually, at a pace that they can handle, taking it easy and going one step at a time,” he said.
References
Bienvenu OJ, Wuyek LA, Stein MB. Anxiety disorders diagnosis: some history and controversies. Curr Top Behav Neurosci. 2010;2:3-19.
Kessler RC, Ruscio AM, Shear K, Wittchen HU. Epidemiology of anxiety disorders. Curr Top Behav Neurosci. 2010;2:21-35.
Ritchie K, Norton J, Mann A, Carrière I, Ancelin ML. Late-onset agoraphobia: general population incidence and evidence for a clinical subtype. Am J Psychiatry. 2013;170(7):790-798.
Michael T, Zetsche U, Margraf J. Epidemiology of anxiety disorders.Epidemiol Psychopharmacol. 2007;6(4):136-142.
McLean CP, Asnaani A, Litz BT, Hofmann SG. Gender differences in anxiety disorders: prevalence, course of illness, comorbidity and burden of illness.J Psychiatr Res. 2011;45(8):1027-1035.
Goodwin RD, Stein DJ. Anxiety disorders and drug dependence: evidence on sequence and specificity among adults. Psychiatry Clin Neurosci. 2013;67(3):167-73.
Boyd JH, Crump T. Westphal’s agoraphobia. J Anx Disord. 1991;5(1):77-86.
Pollard CA, Zuercher-White A. _The Agoraphobia Workbook: A Comprehensive Program to End Your Fear of Symptom Attacks_ . Oakland, CA: New Harbinger Publications; 2003.
Goldstein AJ, Chambless DL. A reanalysis of agoraphobia. Behav Ther. 1978;9(1):47-59.
American Psychiatric Association. Diagnostic and Statistical Manual of Mental Disorders, Third Edition (DSM-III). Washington, DC: American Psychiatric Association; 1980.
Asmundson GJ, Taylor S, Smits JA. Panic disorder and agoraphobia: an overview and commentary on DSM-5 changes. Depress Anxiety. 2014 Jun;31(6):480-6.
American Psychiatric Association. Diagnostic and Statistical Manual of Mental Disorders, Third Edition revised (DSM-III-R). Washington, DC: American Psychiatric Association; 1987.
American Psychiatric Association. Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5). Arlington, VA: American Psychiatric Association; 2013.
Pull CB, Damsa C. Pharmacotherapy of panic disorder. Neuropsychiatr Dis Treat. 2008;4(4):779-95.
Bandelow B, Michaelis S, Wedekind D. Treatment of anxiety disorders. Dialogues Clin Neurosci. 2017;19(2):93-107.
Gloster AT, Hauke C, Höfler M, Einsle F, Fydrich T, Hamm A, Sthröhle A, Wittchen HU. Long-term stability of cognitive behavioral therapy effects for panic disorder with agoraphobia: a two-year follow-up study. Behav Res Ther. 2013;51(12):830-839.
Mitte K. A meta-analysis of the efficacy of psycho- and pharmacotherapy in panic disorder with and without agoraphobia. J Affect Disord. 2005 Sep;88(1):27-45.
Liebscher C, Wittmann A, Gechter J, et al. Facing the fear – clinical and neural effects of cognitive behavioural and pharmacotherapy in panic disorder with agoraphobia. Eur Neuropsychopharmacol. 2016;26(3):431-444.
Mavissakalian M. Combined behavioral therapy and pharmacotherapy of agoraphobia. J Psychiatr Res. 1993;27(Suppl 1):179-191.
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Batya Swift Yasgur, MA, LSW
Batya Swift Yasgur, MA, MSW, is a freelance medical writer who writes news, features, CME materials, and books for a variety of venues and target audiences, including healthcare professionals and consumers. She has a passion for human rights activism and is the author of Behind the Burqa (John Wiley, 2002), a memoir of 2 Afghan sisters who escaped Afghanistan. In addition, she holds the 1995 Robert L. Fish Award for Best First Published Mystery Story. Her fiction has appeared in Ellery Queen's Mystery Magazine and several other publications. Beyond her desire to contribute to people's health and wellbeing through her writing, Batya offers emotional/spiritual support to clients in her Teaneck, New Jersey-based counseling practice to facilitate their journeys toward healing.
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13408 | https://www.youtube.com/watch?v=r4bH66vYjss | Vector examples | Vectors and spaces | Linear Algebra | Khan Academy
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117 comments
Transcript:
In the last video I was a little
formal in defining what Rn is, and what a vector is,
and what vector addition or scalar multiplication is. In this video I want to kind of
go back to basics and just give you a lot of examples. And give you a more tangible
sense for what vectors are and how we operate with them. So let me define a couple
of vectors here. And I'm going to do, most of my
vectors I'm going to do in this video are going
to be in R2. And that's because they're
easy to draw. Remember R2 is the set
of all 2-tuples. Ordered 2-tuples where each of
the numbers, so you know you could have x1, my 1 looks like a
comma, x1 and x2, where each of these are real numbers. So you each of them, x1 is a
member of the reals, and x2 is a member of the reals. And just to give you a sense
of what that means, if this right here is my coordinate
axes, and I wanted a plot all my x1's, x2's. You know you could view this
as the first coordinate. We always imagine that
as our x-axis. And then our second coordinate
we plotted on the vertical axis. That traditionally is our
y-axis, but we'll just call that the second number
axis, whatever. You could visually represent all
of R2 by literally every single point on this plane if
we were to continue off to infinity in every direction. That's what R2 is. R1 would just be points
just along one of these number lines. That would be R1. So you could immediately
see that R2 is kind of a bigger space. But anyway, I said that I
wouldn't be too abstract, that I would show you examples. So let's get some vectors
going in R2. So let me define my vector a. I'll make it nice and bold. My vector a is equal to,
I'll make some numbers up, negative 1, 2. And my vector b, make it nice
and bold, let me make that, I don't know, 3, 1. Those are my two vectors. Let's just add them up
and see what we get. Just based on my definition
of vector addition. I'll just stay in one color
for now so I don't have to keep switching back and forth. So a, nice deep a, plus bolded
b is equal to, I just add up each of those terms.
Negative 1 plus 3. And then 2 plus 1. That was my definition
of vector addition. So that is going to be
equal to 2 and 3. Fair enough that just
came out of my definition of vector addition. But how can we represent
this vector? So we already know that if we
have coordinates, you know, if I have the coordinate, and this
is just a convention. It's just the way
that we do it. The way we visualize things. If I wanted to plot the
point 1, 1, I go to my coordinate axes. The first point I go along
the horizontal, what we traditionally call our x-axis. And I go 1 in that direction. And then convention is, the
second point I go 1 in the vertical direction. So the point 1, 1. Oh, sorry, let me
be very clear. This is 2 and 2, so one
is right here, and one is right there. So the point 1, 1 would
be right there. That's just the standard
convention. Now our convention for
representing vectors are, you might be tempted to say, oh,
maybe I just represent this vector at the point
minus 1, 2. And on some level
you can do that. I'll show you in a second. But the convention for vectors
is that you can start at any point. Let's say we're dealing with
two dimensional vectors. You can start at any
point in R2. So let's say that you're
starting at the point x1, and x2. This could be any point in R2. To represent the vector, what
we do is we draw a line from that point to the point x1. And let me call this, let's say
that we wanted to draw a. So x1 minus 1. So this is, I'm representing
a. So this is, I want to represent
the vector a. x1 minus 1, and then
x1 plus 2. Now if that seems confusing to
you, when I draw it, it'll be very obvious. So let's say I just want to
start at the point, let's just say for quirky reasons, I just
pick a random point here. I just pick a point. That one right there. That's my starting point. So minus 4, 4. Now if I want to represent my
vector a, what I just said is that I add the first term
in vector a to my first coordinate. So x1 plus minus 1
or x1 minus 1. So my new one is going to be,
so this is my x1 minus 4. So now it's going to be, let's
see, I'm starting at the point minus 4 comma 4. If I want to represent a, what
I do is, I draw an arrow to minus 4 plus this first
term, minus 1. And then 4 plus the
second term. 4 plus 2. And so this is what? This is minus 5 comma 6. So I go to minus 5 comma 6. So I go to that point right
there and I just draw a line. So my vector will
look like this. I draw a line from
there to there. And I draw an arrow
at the end point. So that's one representation
of the vector minus 1, 2. Actually let me do it
a little bit better. Because minus 5 is actually
more, a little closer to right here. Minus 5 comma 6 Is right
there, so I draw my vector like that. But remember this point minus
4 comma 4 was an arbitrary place to draw my vector. I could have started
at this point here. I could have started at the
point 4 comma 6 and done the same thing. I could have gone minus 1 in
the horizontal direction, that's my movement in the
horizontal direction. And then plus 2 in the
vertical direction. So I could have drawn, so minus
1 in the horizontal and plus 2 in the vertical
gets me right there. So I could have just as easily
drawn my vector like that. These are both interpretations
of the same vector a. I should draw them in the
color of vector a. So vector a was this light
blue color right there. So this is vector a. This is vector a. Sometimes there'll
be a little arrow notation over the vector. But either of those vectors. I could draw an infinite
number of vector a's. I could draw vector a here. I could draw it like that. Vector a, it goes
back 1 and up 2. So vector a could
be right there. Similarly vector b. What does vector b do? I could pick some arbitrary
point for vector b. It goes to the right 3, so it
goes to the right 1, 2, 3 and then it goes up 1. So vector b, one representation
of vector b, looks like this. Another represention. I can start it right here. I could go to the right 3,
1, 2, 3, and then up 1. This would be another
representation of my vector b. There's an infinite number of
representations of them. But the convention is to often
put them in what's called the standard position. And that's to start
them off at 0, 0. So your initial point, let
me write this down. Standard position is just to
start the vectors at 0, 0 and then draw them. So vector a in standard
position, I'd start at 0, 0 like that and I would go
back 1 and then up 2. So this is vector a in standard
position right there. And then vector b in
standard position. Let me write that. That's a. And then vector b in standard
position is 3, go to the 3 right and then up 1. These are the vectors in
standard position, but any of these other things we drew
are just as valid. Now let's see if we can get
an interpretation of what happened when we
added a plus b. Well if I draw that vector in
standard position, I just calculated, it's 2, 3. So I go to the right
2 and I go up 3. So if I just draw it in
standard position it looks like this. This vector right there. And at first when you look at
it, this vector right here is the vector a plus b in
standard position. When you draw it like that,
it's not clear what the relationship is when
we added a and b. But to see the relationship what
you do is, you put a and b head to tails. What that means is, you put
the tail end of b to the front end of a. Because remember, all
of these are valid representations of b. All of the representations
of the vector b. They all have, they're all
parallel to each other, but they can start from anywhere. So another equally valid
representation of vector b is to start at this point right
here, kind of the end point of vector a in standard position,
and then draw vector b starting from there. So you go 3 to the right. So you go 1, 2, 3. And then you go up 1. So vector b could also be
drawn just like that. And then you should
see something interesting had happened. And remember, this vector b
representation is not in standard position, but it's just
an equally valid way to represent my vector. Now what do you see? When I add a, which is right
here, to b what do I get if I connect the starting point of
a with the end point of b? I get the addition. I have added the two vectors. And I could have done
that anywhere. I could have started
with a here. And then I could have
done the end point. I could have started b here and
gone 3 to the right, 1, 2, 3 and then up 1. And I could have drawn b
right there like that. And then if I were to add a plus
b, I go to the starting point of a, and then
the end point of b. And that should also
be the visual representation of a plus b. Just to make sure it confirms
with this number, what I did here was I went 2 to
the right, 1, 2 and then I went 3 up. 1, 2, 3 and I got a plus b. Now let's think about
what happens when we scale our vectors. When we multiply it times
some scalar factor. So let me pick new vectors. Those have gotten monotonous. Let me define vector v. v for vector. Let's say that it is
equal to 1, 2. So if I just wanted to draw
vector v in standard position, I would just go 1 to
the horizontal and then 2 to the vertical. That's it. That's the vector in
standard position. If I wanted to do it in a non
standard position, I could do it right here. 1 to the right up 2,
just like that. Equally valid way of
drawing vector v. Equally valid way of doing it. Now what happens if I
multiply vector v. What if I have, I don't know,
what if I have 2 times v? 2 times my vector v is now going
to be equal to 2 times each of these terms. So it's
going to be 2 times 1 which is 2, and then 2 times
2 which is 4. Now what does 2 times
vector v look like? Well let me just start from
an arbitrary position. Let me just start
right over here. So I'm going to go 2
to the right, 1, 2. And I go up 4. 1, 2, 3, 4. So this is what 2 times
vector v looks like. This is 2 times my vector v. And if you look at it, it's
pointing in the exact same direction but now it's
twice as long. And that makes sense because we
scaled it by a factor of 2. When you multiply it by a
scalar, or you're not changing its direction. Its direction is the exact same
thing as it was before. You're just scaling
it by that amount. And I could draw
this anywhere. I could have drawn
it right here. I could have drawn 2v
right on top of v. Then you would have seen it,
I don't want to cover it. You would have seen that it
goes, it's exactly, in this case when I draw it in standard position, it's colinear. It's along the same line,
it's just twice as far. it's just twice as long
but they have the exact same direction. Now what happens if I were
to multiply minus 4 times our vector v? Well then that will be equal
to minus 4 times 1, which is minus 4. And then minus 4 times
2, which is minus 8. So this is on my new vector. Minus 4, minus 8. This is minus 4 times
our vector v. So let's just start at
some arbitrary point. Let's just do it in
standard position. So you go to the right 4. Or you go to the left 4. So so you go to the left
4, 1, 2, 3, 4. And then down 8. Looks like that. So this new vector is going
to look like this. Let me try and draw a relatively
straight line. There you go. So this is minus 4 times
our vector v. I'll draw a little arrow
on it to make sure you know it's a vector. Now what happened? Well we're kind of in
the same direction. Actually we're in the exact
opposite direction. But we're still along the
same line, right? But we're just in the exact
opposite direction. And it's this negative right
there that flipped us around. If we just multiplied negative
1 times this, we would have just flipped around to
right there, right? But we multiplied it
by negative 4. So we scaled it by 4, so you
make it 4 times as long, and then it's negative, so
then it flips around. It flips backwards. So now that we have that notion,
we can kind of start understanding the idea of
subtracting vectors. Let me make up 2 new
vectors right now. Let's say my vector x, nice and
bold x, is equal to, and I'm doing everything in R2, but
in the last part of this video I'll make a few examples
in R3 or R4. Let's say my vector x
is equal to 2, 4. And let's say I have
a vector y. y, make it nice and bold. And then that is equal to
negative 1, minus 2. And I want to think about
the notion of what x minus y is equal to. Well we can say that this is the
same thing as x plus minus 1 times our vector y. Right? So x plus minus 1 times
our vector y. Now we can use our
definitions. We know how to multiply
by a scalar. So we'll say that this
is equal to, let me switch colors. I don't like this color. This is equal to our
x vector is 2, 4. And then what's minus
1 times y? So minus 1 times y is minus
1 times minus 1 is 1. And then minus 1 times
minus 2 is 2. So x minus y is going to be
these two vectors added to each other, right? I'm just adding the
minus of y. This is minus vector y. So this x minus y is going to
be equal to 3 and 3 and 6. So let's see what that looks
like when we visually represent them. Our vector x was 2, 4. So 2, 4 in standard position
it looks like this. That's my vector x. And then vector y in standard
position, let me do it in a different color, I'll
do y in green. Vector y is minus 1, minus 2. It looks just like this. And actually I ended up
inadvertently doing collinear vectors, but, hey, this
is interesting too. So this is vector y. So then what's their
difference? This is 3, 6. So it's the vector 3, 6. So it's this vector. Let me draw it someplace else. If I start here I go 1, 2, 3. And then I go up 6. So then up 6. It's a vector that
looks like this. That's the difference between
the two vectors. So at first you say,
this is x minus y. Hey, how is this the difference
of these two? Well if you overlay this. If you just shift this over
this, you could actually just start here and go straight up. And you'll see that it's really
the difference between the end points. You're kind of connecting
the end points. I actually didn't want to
draw collinear vectors. Let me do another example. Although that one's kind
of interesting. You often don't see that
one in a book. Let me to define vector x
in this case to be 2, 3. And let me define vector y
to be minus 4, minus 2. So what would be x in
standard position? It would be 2, 3. It'd look like that. That is our vector x if we
start at the origin. So this is x. And then what does vector
y look like? I'll do y in orange. Minus 4, minus 2. So vector y looks like this. Now what is x minus y? Well you know, we could
view this, 2 plus minus 1 times this. We could just say
2 minus minus 4. I think you get the idea now. But we just did it the first
way the last time because I wanted to go from my basic
definitions of scalar multiplication. So x minus y is just going to
be equal to 2 plus minus 1 times minus 4, or
2 minus minus 4. That's the same thing as
2 plus 4, so it's 6. And then it's 3 minus
minus 2, so it's 5. Right? So the difference between the
two is the vector 6, 5. So you could draw it
out here again. So you could go, add 6 to 4, go
up there, then to 5, you'd go like that. So the vector would look
something like this. It shouldn't curve like that,
so that's x minus y. But if we drew them between,
like in the last example, I showed that you could draw it
between their two heads. So if you do it here, what
does it look like? Well if you start at this point
right there and you go 6 to the right and then up 5,
you end up right there. So the difference between the
two vectors, let me make sure I get it, the difference
between the two vectors looks like that. It looks just like that. Which kind of should make
sense intuitively. x minus y. That's the difference between
the two vectors. You can view the difference as,
how do you get from one vector to another
vector, right? Like if, you know, let's go
back to our kind of second grade world of just scalars. If I say what 7 minus 5 is, and
you say it's equal to 2, well that just tells you that
5 plus 2 is equal to 7. Or the difference between
5 and 7 is 2. And here you're saying, look the
difference between x and y is this vector right there. It's equal to that vector
right there. Or you could say look, if I
take 5 and add 2 I get 7. Or you could say, look, if I
take vector y, and I add vector x minus y, then
I get vector x. Now let's do something else
that's interesting. Let's do what y minus
x is equal to. y minus x. What is that equal to? Do it in another color
right here. Well we'll take minus 4, minus
2 which is minus 6. And then you have minus
2, minus 3. It's minus 5. So y minus x is going to be,
let's see, if we start here we're going to go down 6. 1, 2, 3, 4, 5, 6. And then back 5. So back 2, 4, 5. So y minus x looks like this. It's really the exact
same vector. Remember, it doesn't matter
where we start. It's just pointing in the
opposite direction. So if we shifted it here. I could draw it right
on top of this. It would be the exact as x
minus y, but just in the opposite direction. Which is just a general
good thing to know. So you can kind of do them as
the negatives of each other. And actually let me make
that point very clear. You know we drew y. Actually let me draw x, x
we could draw as 2, 3. So you go to the right
2 and then up 3. I've done this before. This is x in non standard
position. That's x as well. What is negative x? Negative x is minus 2 minus 3. So if I were to start here,
I'd go to minus 2, then I'd go minus 3. So minus x would look
just like this. Minus x. It looks just like x. It's parallel. It has the same magnitude. It's just pointing in the exact
opposite direction. And this is just a good thing
to kind of really get seared into your brain is to have an
intuition for these things. Now just to kind of finish up
this kind of idea of adding and subtracting vectors. Everything I did so
far was in R2. But I want to show you that
we can generalize them. And we can even generalize them
to vector spaces that aren't normally intuitive for
us to actually visualize. So let me define a couple
of vectors. Let me define vector a to be
equal to 0, minus 1, 2, and 3. Let me define vector b to be
equal to 4, minus 2, 0, 5. We can do the same addition
and subtraction operations with them. It's just it'll be hard
to visualize. We can keep them in
just vector form. So that it's still useful to
think in four dimensions. So if I were to say 4 times a. This is the vector a
minus 2 times b. What is this going
to be equal to? This is a vector. What is this going
to be equal to? Well we could rewrite this as
4 times this whole column vector, 0, minus 1, 2, and 3. Minus 2 times b. Minus 2 times 4,
minus 2, 0, 5. And what is this going
to be equal to? This term right here, 4 times
this, you're going to get, the pen tablet seems to not work
well there, so I'm going to do it right here. 4 times this, you're going to
get 4 times 0, 0, minus 4, 8. 4 times 2 is 8. 4 times 3 is 12. And then minus, I'll do it in
yellow, minus 2 times 4 is 8. 2 times minus 2 is minus 4. 2 times 0 is 0. 2 times 5 is 10. This isn't a good part of my
board, so let me just. It doesn't write well
right over there. I haven't figured out the
problem, but if I were just right it over here,
what do we get? With 0 minus 8? Minus 8. Minus 4, minus 4. Minus negative 4. So that's minus 4 plus
4, so that's 0. 8 minus 0 is 8. 12 minus, what was this? I can't even read it,
what it says. Oh, this is a 10. Now you can see it again. Something is very bizarre. 2 times 5 is 10. So it's 12 minus
10, so it's 2. So when we take this vector
and multiply it by 4, and subtract 2 times this vector,
we just get this vector. And even though you can't
represent this in kind of an easy kind of graph-able format, this is a useful concept. And we're going to see this
later when we apply some of these vectors to
multi-dimensional spaces. |
13409 | https://www.quora.com/What-can-you-change-in-making-a-parabola-that-intersects-the-x-axis-two-times | What can you change in making a parabola that intersects the x-axis two times? - Quora
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What can you change in making a parabola that intersects the x-axis two times?
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Richard Goldstone
PhD in Mathematics, The Graduate Center, CUNY (Graduated 1995) · Upvoted by
Michael Jørgensen
, PhD in mathematics · Author has 1.8K answers and 3.9M answer views
·10mo
For y=a x 2+b x+c,y=a x 2+b x+c, the quadratic formula for the roots tells us that we must have b 2–4 a c>0.b 2–4 a c>0. But that only accounts for parabolas with axis of symmetry perpendicular to the x x-axis.
The general conic section equation is
a x 2+b x y+c y 2+d x+e y+f=0,a x 2+b x y+c y 2+d x+e y+f=0,
and this is a parabola if and only if b 2–4 a c=0,b 2–4 a c=0, so for a parabola we have
a x 2±2 x y√a c+c y 2+d x+e y+f=0.a x 2±2 x y a c+c y 2+d x+e y+f=0.
If this intersects the x x-axis, then there must be points of the form (t,0)(t,0) that satisfy the equation, and for those points we must have
a t 2+d t+f=0,or t=−d±√d 2−4 a f 2 a.a t 2+d t+f=0,or t=−d±d 2−4 a f 2 a.
In order to have tw
Continue Reading
For y=a x 2+b x+c,y=a x 2+b x+c, the quadratic formula for the roots tells us that we must have b 2–4 a c>0.b 2–4 a c>0. But that only accounts for parabolas with axis of symmetry perpendicular to the x x-axis.
The general conic section equation is
a x 2+b x y+c y 2+d x+e y+f=0,a x 2+b x y+c y 2+d x+e y+f=0,
and this is a parabola if and only if b 2–4 a c=0,b 2–4 a c=0, so for a parabola we have
a x 2±2 x y√a c+c y 2+d x+e y+f=0.a x 2±2 x y a c+c y 2+d x+e y+f=0.
If this intersects the x x-axis, then there must be points of the form (t,0)(t,0) that satisfy the equation, and for those points we must have
a t 2+d t+f=0,or t=−d±√d 2−4 a f 2 a.a t 2+d t+f=0,or t=−d±d 2−4 a f 2 a.
In order to have two values for t,t, we must have d 2–4 a f>0.d 2–4 a f>0.
So that’s it: in the equation
a x 2±2 x y√a c+c y 2+d x+e y+f=0,a x 2±2 x y a c+c y 2+d x+e y+f=0,
choose a a and c c not both zero so that a c≥0,a c≥0, choose e e and f f randomly, and then choose d d so that d 2>4 a f.d 2>4 a f.
For example, we could choose a,c,e,a,c,e, and f f all to be 1 and then choose d d so that d 2>4,d 2>4, say d=3.d=3. The result is two parabolas,
x 2±2 x y+y 2+3 x+y+1=0 x 2±2 x y+y 2+3 x+y+1=0
whose graphs are
Perhaps we want the parabola(s) to pass through two specified points on the x x-axis. Say we want them to go through (−1,0)(−1,0) and (1,0).(1,0). Then since a t 2+d t+f=0,a t 2+d t+f=0, we must have
a+d+f=0 a−d+f=0 a+d+f=0 a−d+f=0
which reduces to f=−a f=−a and d=0.d=0. The equation is thus
a x 2±2 x y√a c+c y 2+e y−a=0,a x 2±2 x y a c+c y 2+e y−a=0,
and, for example, we could take
x 2±2 x y+y 2+y−1=0 x 2±2 x y+y 2+y−1=0
to get
In general, suppose we want our parabolas to pass through (α,0)(α,0) and (β,0)(β,0) with α≠β.α≠β. Then we have to solve the simultaneous equations
α 2 a+α d+f=0 β 2 a+β d+f=0 α 2 a+α d+f=0 β 2 a+β d+f=0
for a,d,a,d, and f.f. We could of course use row reduction techniques, but subtracting one equation from the other quickly leads to
(α−β)((α+β)a+d)=0,(α−β)((α+β)a+d)=0,
and since α≠β,α≠β, we get d=−(α+β)a d=−(α+β)a and
f=−α 2 a−α d=−α 2 a+α(α+β)a=(α β)a.f=−α 2 a−α d=−α 2 a+α(α+β)a=(α β)a.
The result is equations
a x 2±2 x y√a c+c y 2−(α+β)a x+e y+(α β)a=0,a x 2±2 x y a c+c y 2−(α+β)a x+e y+(α β)a=0,
passing through (α,0)(α,0) and (β,0)(β,0) with α≠β.α≠β. The parameters left to choose are a,c,a,c, and e e with a a and c c not both zero and a c≥0.a c≥0.
If we fix a=1=c,a=1=c, then we get the one-parameter family of parabola pairs indexed by e,e,
(x±y)2−(α+β)x+e y+α β=0.(x±y)2−(α+β)x+e y+α β=0.
Here’s what we get for the points (2,0)(2,0) and (3,0)(3,0) with values of e e ranging from −4−4 to 4,4, giving the equations
(x±y)2−5 x+e y+6=0:(x±y)2−5 x+e y+6=0:
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More answers below
Why is a horizontal line called an x-axis?
What are the X axis and the Y axis called?
What is the point of intersection of the x-axis and y-axis called?
Why is the slope of x axis zero?
Why are two different scales in Concordia plot along x-axis and y-axis?
Gopal Menon
B Sc (Hons) in Mathematics, Indira Gandhi National Open University (IGNOU) (Graduated 2010) · Author has 10.2K answers and 15.2M answer views
·7y
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Why does x squared make a parabola?
Why does x 2 x 2 make a parabola?
I presume that the question is “why is it that the equation y=x 2 y=x 2 represents a parabola?”
Let P(x 1,y 1)P(x 1,y 1) be any arbitrary point on the curve y=x 2.y=x 2.
⇒⇒y 1=x 2 1.y 1=x 1 2.
Consider the point A(0,1 4)A(0,1 4) and the line l:y=−1 4 l:y=−1 4
The distance of point P P from point A A is d 1=√(x 1−0)2+(y 1−1 4)2.d 1=(x 1−0)2+(y 1−1 4)2.
⇒d 1=√x 2 1+y 2 1−y 1 2+1 16=√y 1+y 2 1−y 1 2+1 16⇒d 1=x 1 2+y 1 2−y 1 2+1 16=y 1+y 1 2−y 1 2+1 16
=√y 2 1+y 1 2+1 16=y 1+1 4.=y 1 2+y 1 2+1 16=y 1+1 4.
The distance of point P P from line l l is d_2=y_1+\frac{1 d_2=y_1+\frac{1
Continue Reading
Why does x 2 x 2 make a parabola?
I presume that the question is “why is it that the equation y=x 2 y=x 2 represents a parabola?”
Let P(x 1,y 1)P(x 1,y 1) be any arbitrary point on the curve y=x 2.y=x 2.
⇒⇒y 1=x 2 1.y 1=x 1 2.
Consider the point A(0,1 4)A(0,1 4) and the line l:y=−1 4 l:y=−1 4
The distance of point P P from point A A is d 1=√(x 1−0)2+(y 1−1 4)2.d 1=(x 1−0)2+(y 1−1 4)2.
⇒d 1=√x 2 1+y 2 1−y 1 2+1 16=√y 1+y 2 1−y 1 2+1 16⇒d 1=x 1 2+y 1 2−y 1 2+1 16=y 1+y 1 2−y 1 2+1 16
=√y 2 1+y 1 2+1 16=y 1+1 4.=y 1 2+y 1 2+1 16=y 1+1 4.
The distance of point P P from line l l is d 2=y 1+1 4.d 2=y 1+1 4.
It can be seen that d 1=d 2.d 1=d 2.
⇒⇒ Any arbitrary point on the curve y=x 2 y=x 2 is equidistant from point A A and line l.l.
This is precisely the requirement of a parabola with line l l as the directrix and point A A as the focus.
⇒⇒ The equation y=x 2 y=x 2 represents a parabola.
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Buddha Buck
Studied at University at Buffalo · Author has 5.8K answers and 16.9M answer views
·8y
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If a parabola is rotating in the first quadrant such that the X and Y axis are always tangential to it, what is the locus of the focus of the parabola?
Let’s take it from the beginning.
Let’s first look at a simple parabola, and then we can move it around if we want: y=x 2 y=x 2. This has a vertex on the origin, and a focus of (0,1 4)(0,1 4). This happens to be the midpoint of the chord of the parabola from x=−1/2 x=−1/2 to x=1/2 x=1/2
I’m going to parameterize that a bit, to make things a bit easier to work with. In other words, I’m going to introduce a new variable, t t, and rewrite x x and y y in terms of t t, to make some manipulations easier. In this case, I’m going to use the parameterization
x=t,x=t,
y=t 2 y=t 2.
In terms of this parameterization, the focus is at
(\fra(\fra
Continue Reading
Let’s take it from the beginning.
Let’s first look at a simple parabola, and then we can move it around if we want: y=x 2 y=x 2. This has a vertex on the origin, and a focus of (0,1 4)(0,1 4). This happens to be the midpoint of the chord of the parabola from x=−1/2 x=−1/2 to x=1/2 x=1/2
I’m going to parameterize that a bit, to make things a bit easier to work with. In other words, I’m going to introduce a new variable, t t, and rewrite x x and y y in terms of t t, to make some manipulations easier. In this case, I’m going to use the parameterization
x=t,x=t,
y=t 2 y=t 2.
In terms of this parameterization, the focus is at
(x(−1/2)+x(1/2)2,y(−1/2)+y(1/2)2)=(−1/2+1/2 2,1/4+1/4 2)=(0,1/4)(x(−1/2)+x(1/2)2,y(−1/2)+y(1/2)2)=(−1/2+1/2 2,1/4+1/4 2)=(0,1/4),
as expected.
So now let’s rotate the parabola, based on the rotation formulas:
x′=c x−s y=c t−s t 2 x′=c x−s y=c t−s t 2
y′=s x+c y=s t+c t 2 y′=s x+c y=s t+c t 2
where c=cos θ,s=sin θ c=cosθ,s=sinθ.
The focus is now at
(x′(−1/2)+x′(1/2)2,y′(−1/2)+y′(1/2)2)=(−c/2−s/4+c/2−s/4 2,−s/2+c/4+s/2+c/4 2)=(−s 4,c 4)(x′(−1/2)+x′(1/2)2,y′(−1/2)+y′(1/2)2)=(−c/2−s/4+c/2−s/4 2,−s/2+c/4+s/2+c/4 2)=(−s 4,c 4).
For no rotation, that still yields (0,1/4)(0,1/4), so all seems good so far.
We can now find where x′,y′x′,y′ are minimized by finding where the derivatives are zero:
d d t x′=c−2 s t,d d t y′=s+2 c t d d t x′=c−2 s t,d d t y′=s+2 c t.
Setting those to zero and solving for t t yields a minimum x′x′ at
t x=c 2 s t x=c 2 s
and a minimum y′y′ at
t y=−s 2 c t y=−s 2 c.
This gives us
x′m i n=c t x−s t 2 x=c c 2 s−s c 2 4 s 2=c 2 4 s,x m i n′=c t x−s t x 2=c c 2 s−s c 2 4 s 2=c 2 4 s,
and
y′m i n=s t y+c t 2 y=s−s 2 c+c s 2 4 c 2=−s 2 2 c+s 2 4 c=−s 2 4 c y m i n′=s t y+c t y 2=s−s 2 c+c s 2 4 c 2=−s 2 2 c+s 2 4 c=−s 2 4 c.
I think. I’d want to double-check that to be sure, but I think I’m right.
Note that for no rotation, we get x′m i n x m′i n not existing, and for a quarter-turn rotation, we get y′m i n y m′i n not existing. That seems right.
So now we can do x′′=x′+x′m i n,y′′=y′+y′m i n x″=x′+x m′i n,y″=y′+y m′i n, for a focus at (x′′(−1/2)+x′′(1/2)2,y′′(−1/2)+y′′(1/2)2)=(−s 4+c 2 4 s,c 4−s 2 4 c)(x″(−1/2)+x″(1/2)2,y″(−1/2)+y″(1/2)2)=(−s 4+c 2 4 s,c 4−s 2 4 c).
This can be simplified to (c 2−s 2 4 s,c 2−s 2 4 c)(c 2−s 2 4 s,c 2−s 2 4 c).
You can plot that for various values of θ θ to see what sort of shape it takes.
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Gary Russell
Former Professor at University of Iowa (1996–2025) · Upvoted by
Dale Gray
, MA Mathematics, The University of Texas at Arlington (1974) · Author has 6K answers and 3.1M answer views
·4y
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Can a parabola have no x intercepts?
Sure! A quadratic function is a parabola. If f(x) = ax^2 + bx + c has no real roots, then there exists no real-valued number x such that f(x) = 0. That means that f(x) > 0 or f(x) < 0 for all values of x.
Draw a curve like y = x^2 + 1 and take a look:
Continue Reading
Sure! A quadratic function is a parabola. If f(x) = ax^2 + bx + c has no real roots, then there exists no real-valued number x such that f(x) = 0. That means that f(x) > 0 or f(x) < 0 for all values of x.
Draw a curve like y = x^2 + 1 and take a look:
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John Pereira
Former Lecturer, Now Retired · Author has 1.6K answers and 903K answer views
·Feb 4
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Two parabolas having common focus at (4, 3) intersect at points a and b. What is the value of (a b) 2 , given that directrices of these parabola are along x-axis and y-axis respectively?
I understand your question to be:
Two parabolas having common focus at (4,3) intersect at points A and B. in the first quadrant. Find the coordinates of A and B. Given that the directrices of these parabolas are along X-axis and Y-axis respectively.
Kindly draw this diagram. Draw OX, OY, a line parallel to OX and passing through S(4,3) and another line parallel to OY and passing through S(4,3).
The parabola having OY as directrix has vertex at P (2,3), midway between focus and directrix. The distance between vertex and focus is a=2. So, its equation is (y —3) ^2 = 4(2) (x —2).
That is, y^2 —8x —6y
Continue Reading
I understand your question to be:
Two parabolas having common focus at (4,3) intersect at points A and B. in the first quadrant. Find the coordinates of A and B. Given that the directrices of these parabolas are along X-axis and Y-axis respectively.
Kindly draw this diagram. Draw OX, OY, a line parallel to OX and passing through S(4,3) and another line parallel to OY and passing through S(4,3).
The parabola having OY as directrix has vertex at P (2,3), midway between focus and directrix. The distance between vertex and focus is a=2. So, its equation is (y —3) ^2 = 4(2) (x —2).
That is, y^2 —8x —6y = —25………..(1)
The parabola having OX as directrix has vertex at Q (4, 3/2), midway between focus and directrix.
The distance between focus and directrix is b= 3/2
So, its equation is: (x — 4) ^2 = 4 (3/2) ( y —3/2)
That is : (x —4) ^2 = 6( y —3/2)
Or, x^2 —8x —6y =—25…………..(2)
Draw rough sketch of the two parabolas and note that they intersect in two points.
(1) — (2) gives y ^2 — x^2 = 0
So, y = x or y = —x
Take y= x and substitute in (1) to get
x^2 — 14x + 25 = 0
Solving, x =7 + 2sqrt6 = 11.9 and 7 — 2 sqrt6 = 2.1
Take y = —x. Then from (1)
x ^2 —2x + 25 = 0. This does not give any real roots.
Hence the points of intersection are A (11.9, 11.9) and B (2.1, 2.1) Ans
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Zafar Imam
Studied BIT Sindri&Ars Public School (Graduated 2022)
·6y
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If a parabola does not intersect the x-axis, what does it mean?
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Armando Flores
Former Consultant/Senior Engineer, IBM/Lexmark Retired · Author has 2.1K answers and 1.6M answer views
·3y
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How do you find the vertex of a parabola if it doesn't intersect with the y axis?
How do you find the vertex of a parabola if it doesn't intersect with the y axis?
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How do you find the vertex of a parabola if it doesn't intersect with the y axis?
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Philip Lloyd
Specialist Calculus Teacher, Motivator and Baroque Trumpet Soloist. · Author has 6.8K answers and 52.8M answer views
·4y
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How many x intercepts can a parabola have?
This is probably not quite the answer you expected…
But if we include some complex x values but just have real y values, the basic type ...
Continue Reading
This is probably not quite the answer you expected…
But if we include some complex x values but just have real y values, the basic type ...
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Gary Ward
MaEd in Education&Mathematics, Austin Peay State University (Graduated 1997) · Author has 4.9K answers and 7.6M answer views
·3y
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Where does the normal line to the curve y = x – x^2 at the point (1, 0) intersect the curve a second time?
Where does the normal line to the curve y = x – x^2 at the point (1, 0) intersect the curve a second time?
We can take the first derivative of the curve using the power rule to find the slope of the curve at any x-value.
y’=1 - 2x so at x = 1 the slope is -1. The inverse reciprocal of -1 is 1, so the slope of the normal is 1 at the point on the curve (1, 0)
The constant at (1, 0) is 0 = 1(1) + c ; c = -1
The line equation of the normal is y = x - 1
Since both equations equal 1y we can set them equal to each other and solve for x.
x - 1 = x - x² → x² = 1 ; x = ±1
y = 1(-1) - 1 → y = -2
The normal line
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Where does the normal line to the curve y = x – x^2 at the point (1, 0) intersect the curve a second time?
We can take the first derivative of the curve using the power rule to find the slope of the curve at any x-value.
y’=1 - 2x so at x = 1 the slope is -1. The inverse reciprocal of -1 is 1, so the slope of the normal is 1 at the point on the curve (1, 0)
The constant at (1, 0) is 0 = 1(1) + c ; c = -1
The line equation of the normal is y = x - 1
Since both equations equal 1y we can set them equal to each other and solve for x.
x - 1 = x - x² → x² = 1 ; x = ±1
y = 1(-1) - 1 → y = -2
The normal line to the curve at (1, 0) passes through the curve a second time at (-1, -2).
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Navneet Teja
teacher · Author has 699 answers and 412.6K answer views
·4y
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How do you know how many X intercepts a parabola has?
A parabola can have 2,1 or 0 x-intercepts.
If the equation of parabola is given then substitute y=0, and by finding the value of b^2–4ac , we can find numbers of x intercepts, if it’s value is negative then no intercept, if equal to 0 then one intercept and if it is positive great than 0 then 2 intercepts.
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A parabola can have 2,1 or 0 x-intercepts.
If the equation of parabola is given then substitute y=0, and by finding the value of b^2–4ac , we can find numbers of x intercepts, if it’s value is negative then no intercept, if equal to 0 then one intercept and if it is positive great than 0 then 2 intercepts.
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Alireza Shariati
BS from Isfahan University of Technology (Graduated 2025) · Author has 1.4K answers and 972.7K answer views
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Where does the normal line to the curve y = x – x^2 at the point (1, 0) intersect the curve a second time?
I recommend finding the equation of the tangent at the given point first. Using the point-slope formula y−f(x 0)=f′(x 0)(x−x 0)y−f(x 0)=f′(x 0)(x−x 0), the equation would be:
y−f(1)=f′(1)(x−1)y−f(1)=f′(1)(x−1)
⟹y=−(x−1)⟹y=−(x−1)
As the normal is perpendicular to the tangent at the intersection point of the tangent and the curve, the slope of the normal line would be −1/f′(1)=1−1/f′(1)=1, hence the equation is:
y=x−1 y=x−1
Now that we’ve found the equation of the normal, to find the points of intersection with the curve, solve the equation x−1=x−x 2 x−1=x−x 2:
x−1=x−x 2⟹x 2=1⟹x=±1 x−1=x−x 2⟹x 2=1⟹x=±1
So the second point of intersection is
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I recommend finding the equation of the tangent at the given point first. Using the point-slope formula y−f(x 0)=f′(x 0)(x−x 0)y−f(x 0)=f′(x 0)(x−x 0), the equation would be:
y−f(1)=f′(1)(x−1)y−f(1)=f′(1)(x−1)
⟹y=−(x−1)⟹y=−(x−1)
As the normal is perpendicular to the tangent at the intersection point of the tangent and the curve, the slope of the normal line would be −1/f′(1)=1−1/f′(1)=1, hence the equation is:
y=x−1 y=x−1
Now that we’ve found the equation of the normal, to find the points of intersection with the curve, solve the equation x−1=x−x 2 x−1=x−x 2:
x−1=x−x 2⟹x 2=1⟹x=±1 x−1=x−x 2⟹x 2=1⟹x=±1
So the second point of intersection is (−1,−2)(−1,−2).
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Dave Benson
trying to make maths easy. · Upvoted by
BowTangey
, PhD Mathematics, Iowa State University (1988) · Author has 6.1K answers and 2.1M answer views
·2y
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Why do we consider that the x intercepts of a parabola are its solutions? We have many other points that can be the solution for the parabola
We don”t. You are thinking of specific solutions.
But as an example for y² = 4x with one intercept it would not be a solution.
But it would give the vertex (0,0).
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We don”t. You are thinking of specific solutions.
But as an example for y² = 4x with one intercept it would not be a solution.
But it would give the vertex (0,0).
Upvote ·
9 2
Philip Lloyd
Specialist Calculus Teacher, Motivator and Baroque Trumpet Soloist. · Author has 6.8K answers and 52.8M answer views
·1y
Related
Where does the normal line to the curve y = x – x^2 at the point (1, 0) intersect the curve a second time?
I really like teaching problems like this!
Here is all the logic you...
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13410 | https://youglish.com/pronounce/meander/english/us | Meander | 315 pronunciations of Meander in American English
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paths that meander through woodland and plant life, an orangery, several circular stone
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Phonetic:
When you begin to speak English, it's essential to get used to the common sounds of the language, and the best way to do this is to check out the phonetics. Below is the UK transcription for 'meander':
Modern IPA: mɪjándə
Traditional IPA: miːˈændə
3 syllables: "mee" + "AN" + "duh"
Test your pronunciation on words that have sound similarities with 'meander':
meandered
meanders
mander
meandering
manders
mandler
maunder
minder
leander
oleander
madder
man eater
man hour
manda
mandarin
mandi
mandrake
mandrel
mandrill
mandy
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Tips to improve your English pronunciation:
Here are a few tips that should help you perfect your pronunciation of 'meander':
Sound it Out: Break down the word 'meander' into its individual sounds "mee" + "an" + "duh". Say these sounds out loud, exaggerating them at first. Practice until you can consistently produce them clearly.
Self-Record & Review: Record yourself saying 'meander' in sentences. Listen back to identify areas for improvement.
YouTube Pronunciation Guides: Search YouTube for how to pronounce 'meander' in English.
Pick Your Accent: Mixing multiple accents can be confusing, so pick one accent (US or UK) and stick to it for smoother learning.
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Mimic the Experts: Immerse yourself in English by listening to audiobooks, podcasts, or movies with subtitles. Try shadowing—listen to a short sentence and repeat it immediately, mimicking the intonation and pronunciation.
Become Your Own Pronunciation Coach: Record yourself speaking English and listen back. Identify areas for improvement, focusing on clarity, word stress, and intonation.
Train Your Ear with Minimal Pairs: Practice minimal pairs (words that differ by only one sound, like ship vs. sheep) to improve your ability to distinguish between similar sounds.
Explore Online Resources: Websites & apps offer targeted pronunciation exercises. Explore YouTube channels dedicated to pronunciation, like Rachel's English and English with James for additional pronunciation practice and learning.
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13411 | https://www.quora.com/Which-gas-would-behave-more-ideally-among-N2-and-CO-at-the-same-condition-of-pressure-and-temperature | Which gas would behave more ideally among N2 and CO at the same condition of pressure and temperature? - Quora
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Which gas would behave more ideally among N2 and CO at the same condition of pressure and temperature?
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To determine which gas, nitrogen (N₂) or carbon monoxide (CO), would behave more ideally under the same conditions of pressure and temperature, we can consider the following factors:
Molecular Structure: Ideal gas behavior is most closely approximated by gases that are monoatomic or diatomic with minimal intermolecular forces. Both N₂ and CO are diatomic molecules, but CO has a polar bond due to the difference in electronegativity between carbon and oxygen, which can lead to stronger intermolecular attractions (dipole-dipole interactions).
Intermolecular Forces: N₂ is a nonpolar molecule, meanin
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To determine which gas, nitrogen (N₂) or carbon monoxide (CO), would behave more ideally under the same conditions of pressure and temperature, we can consider the following factors:
Molecular Structure: Ideal gas behavior is most closely approximated by gases that are monoatomic or diatomic with minimal intermolecular forces. Both N₂ and CO are diatomic molecules, but CO has a polar bond due to the difference in electronegativity between carbon and oxygen, which can lead to stronger intermolecular attractions (dipole-dipole interactions).
Intermolecular Forces: N₂ is a nonpolar molecule, meaning it has weaker London dispersion forces compared to the dipole-dipole interactions present in CO. This suggests that N₂ would have less deviation from ideal gas behavior at a given temperature and pressure.
Molar Mass: The molar masses of N₂ (approximately 28 g/mol) and CO (approximately 28 g/mol) are similar, so this factor does not significantly influence ideality in this case.
Given these considerations, N₂ would behave more ideally than CO under the same conditions of pressure and temperature due to its nonpolar nature and weaker intermolecular forces.
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Related questions
More answers below
Between N2 and O2, which gas is more ideal?
Which one closely behaves as an ideal gas among O2, N2, NO, Cl2, and CO at the same condition of pressure and temperature?
What happens to a gas while being under extremely high pressure and high temperature at the same time?
A sample of N2O3 has a pressure of 0.024 bar. The temperature in K is doubled and the N2 O3 undergoes complete decomposition to NO2 and NO. What is the total pressure of the mixture of gases?
At the same temperature and pressure, which gas has high density, N2, O2, or H2?
Claudio Giomini
Laurea (M. Sc.) from Sapienza University of Rome (Graduated 1965) · Author has 3.5K answers and 2.1M answer views
·3y
One could look at a and b parameters in van der Waals’ equation for both gases. The gas with lower values for those parameters should have a behaviour that more closely resembles ideal one. We have, for N2, a = 1.370 (L^2)bar/(mol^2) and b = 0.0387 L/mol, while for CO (in the same units), we have a = 1.505 and b = 0.0399 . So, N2 should be just a bit more “ideally-behaving” than CO.
It is to be remarked that, unlike what the formula could suggest, CO has a dipole moment very close to zero, and such that the (very small) negative charge is localized on the carbon atom. The molecules of the two
Continue Reading
One could look at a and b parameters in van der Waals’ equation for both gases. The gas with lower values for those parameters should have a behaviour that more closely resembles ideal one. We have, for N2, a = 1.370 (L^2)bar/(mol^2) and b = 0.0387 L/mol, while for CO (in the same units), we have a = 1.505 and b = 0.0399 . So, N2 should be just a bit more “ideally-behaving” than CO.
It is to be remarked that, unlike what the formula could suggest, CO has a dipole moment very close to zero, and such that the (very small) negative charge is localized on the carbon atom. The molecules of the two gases are very similar; both have identical molar mass, and a triple bond between the two atoms.
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Which are the best AI tools for students?
There are a lot of AI tools out there right now—so how do you know which ones are actually worth your time? Which tools are built for students and school—not just for clicks or content generation? And more importantly, which ones help you sharpen what you already know instead of just doing the work for you?
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There are a lot of AI tools out there right now—so how do you know which ones are actually worth your time? Which tools are built for students and school—not just for clicks or content generation? And more importantly, which ones help you sharpen what you already know instead of just doing the work for you?
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Mark Harder
Ph. D. in Biochemistry, Washington University in St. Louis (Graduated 1975) · Upvoted by
Brian Brady
, Ph. D. Chemistry, Columbia University (1986) · Author has 9.1K answers and 4.2M answer views
·3y
It’s only an ‘educated’ guess, but I think that since CO has a permanent dipole moment, its molecules will have a stronger tendency to interact with each other than molecules of N2, which are symmetric and have no permanent dipole moment. In other words, I expect that N2 is more ideal than CO.
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9 3
NPAsSbBiMc
M.S. in Chemistry, University of Washington (Graduated 2012) · Author has 74 answers and 54.2K answer views
·3y
the ideal gas model assumes that the molecules of the gas are ideal particles, point masses that interact with each other entirely through elastic collisions. so any sort of tendency for the molecules of gas to interact with each other is a departure from the ideal model. carbon monoxide is a molecule with a substantial dipole moment compared to nitrogen, whose electron distribution is symmetrical. hence it’s more likely that carbon monoxide will begin to depart from ideal gas behavior at higher pressures, where the gas molecules are in closer proximity and the CO dipoles will tend to interact
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the ideal gas model assumes that the molecules of the gas are ideal particles, point masses that interact with each other entirely through elastic collisions. so any sort of tendency for the molecules of gas to interact with each other is a departure from the ideal model. carbon monoxide is a molecule with a substantial dipole moment compared to nitrogen, whose electron distribution is symmetrical. hence it’s more likely that carbon monoxide will begin to depart from ideal gas behavior at higher pressures, where the gas molecules are in closer proximity and the CO dipoles will tend to interact with each other. ~Alyx
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Does C02, N2, and H2 gas never behave ideally even when the temperature is high and pressure is lowered?
What happens to the pressure of a gas inside a container if the temperature of the gas decreases?
Why does higher pressure result in higher temperature when adding pressure to gas makes it liquid when liquids are colder than gas?
What happens to the pressure inside a container when more gas is added to it at constant temperature?
Does the gas at the same temperature in lower pressure have more energy?
Jack Leonard
Ph.D. in Chemistry&Biology, California Institute of Technology (Caltech) (Graduated 1971) · Author has 1K answers and 362.7K answer views
·3y
Clearly N2, since its bond is completely nondipolar. while the CO bond is highly polar, leading to “strongish” intermolecular attractions. (That is the primary reason why HF and H20 have such a such low boiling points)..
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Anthony Madden
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·Updated Aug 15
What are the weirdest mistakes people make on the internet right now?
Here are a couple of the worst mistakes I’ve seen people make:
Not using an ad blocker
If you aren’t using an ad blocker yet, you definitely should be.
A good ad blocking app will eliminate virtually all of the ads you’d see on the internet before they load.
No more YouTube ads, no more banner ads, no more pop-up ads, etc.
Most people I know use Total Adblock (link here) - it’s about £2/month, but there are plenty of solid options.
Ads also typically take a while to load, so using an ad blocker reduces loading times (typically by 50% or more). They also block ad tracking pixels to protect your pr
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Here are a couple of the worst mistakes I’ve seen people make:
Not using an ad blocker
If you aren’t using an ad blocker yet, you definitely should be.
A good ad blocking app will eliminate virtually all of the ads you’d see on the internet before they load.
No more YouTube ads, no more banner ads, no more pop-up ads, etc.
Most people I know use Total Adblock (link here) - it’s about £2/month, but there are plenty of solid options.
Ads also typically take a while to load, so using an ad blocker reduces loading times (typically by 50% or more). They also block ad tracking pixels to protect your privacy, which is nice.
More often than not, it saves even more than 50% on load times - here’s a test I ran:
Using an ad blocker saved a whopping 6.5+ seconds of load time.
Here’s a link to Total Adblock, if you’re interested.
Not getting paid for your screentime
Apps like Freecash will pay you to test new games on your phone.
Some testers get paid as much as £270/game. Here are a few examples right now (from Freecash's website):
You don't need any kind of prior experience or degree or anything: all you need is a smartphone (Android or IOS).
If you're scrolling on your phone anyway, why not get paid for it?
I've used Freecash in the past - it’s solid. (They also gave me a £3 bonus instantly when I installed my first game, which was cool).
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Mark Neidorff
Former Chemistry Teacher (retired) (1985–2010) · Author has 9.2K answers and 3.3M answer views
·3y
N2 is non-polar and CO is slightly polar. Their freezing points are close but very slightly different: N2 — -203C and CO — -210 C. I could attribute that slight difference to the different polarity, but I’m not sure if that is correct or not.
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9 1
Aritra Bal
Integrated MSc in Physics, Indian Institute of Technology, Kharagpur (IIT KGP) (Graduated 2022) · Upvoted by
Edward Willhoft
, PhD Physics, King's College London (1966)
·7y
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Why does a real gas behave like an ideal gas only at low pressure and high temperature?
The fallacy of an ideal gas arises from the Kinetic Theory of Gases, in particular, two of its postulates that were later found to be incorrect.
Firstly, it assumed that a gas occupies a volume far larger than that occupied by its molecules. This isn't really a good assumption to make under all possible conditions, especially when the gas is highly compressed. This was the first distinction between a real and ideal gas. The ideal gas molecules occupy a volume negligible in comparison to that occupied by the gas itself, but for a real gas, this is not so. But now, suppose that the pressure is re
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The fallacy of an ideal gas arises from the Kinetic Theory of Gases, in particular, two of its postulates that were later found to be incorrect.
Firstly, it assumed that a gas occupies a volume far larger than that occupied by its molecules. This isn't really a good assumption to make under all possible conditions, especially when the gas is highly compressed. This was the first distinction between a real and ideal gas. The ideal gas molecules occupy a volume negligible in comparison to that occupied by the gas itself, but for a real gas, this is not so. But now, suppose that the pressure is really low. In that case, the volume occupied by the gas must be quite high. Under such circumstances, the assumption is reasonably valid, and indeed, it has been observed that a real gas behaves ideally at low pressure.
Coming to the second error, which was the assumption that the gas molecules exert no influence whatsoever on each other. Clearly, this cannot be so. Electrostatic forces of interaction play a big role in deciding the velocity of, and the pressure exerted by the gas molecules. Here comes the second distinction between a real and ideal gas. The ideal gas molecules do not interact with each other, but the real gas molecules do. However, if the temperature is quite high, then the velocity of the molecules is also high, and at such high velocities, the interactions are negligible. So it's possible to ignore them, and assume that there are no intermolecular interactions at all. Experimental observations seem to support this, as real gases do behave ideally at very high temperatures.
So much for theory! Now, we can use the Van der Waals model for Real Gases to try and validate the points made above.
For one mole of real gas-
(P+a V 2)(V−b)=R T(P+a V 2)(V−b)=R T
P=R T V−b−a V 2 P=R T V−b−a V 2
Multiplying both sides by a factor of V R T,V R T, and noticing that P V R T P V R T is the compressibility factor Z of a real gas, we get-
Z=V V−b−a V R T Z=V V−b−a V R T
⇒Z=1 1−b V−a V R T⇒Z=1 1−b V−a V R T
Now, recall that the summation of an infinite geometric progression is given by-
1 1−x=1+x+x 2+x 3+.....1 1−x=1+x+x 2+x 3+.....
Using the same idea for the first term of our equation, we get:
Z=[1+b V+b 2 V 2+b 3 V 3+......]−a V R T Z=[1+b V+b 2 V 2+b 3 V 3+......]−a V R T
⇒Z=1+(b−a R T)(1 V)+b 2 V 2+b 3 V 3+.....⇒Z=1+(b−a R T)(1 V)+b 2 V 2+b 3 V 3+.....
Now as you can see, the coefficients of 1 V 1 V are all constant, so we can simply replace them by symbols-
Z=1+B V+C V 2+.....Z=1+B V+C V 2+.....
Perhaps you are familiar with this equation, known as the Virial Equation of State
. In this equation, we can see that at very low pressures, implying high volumes, the value of Z is-
lim V→∞Z=1 lim V→∞Z=1
A compressibility factor of 1 implies ideal behaviour, and so, it's reasonable to assume that a real gas will behave ideally at low pressure and high temperature. .
Footnotes
Aritra Bal's answer to Can critical temperatures be more than the Boyle temperature?
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·Updated Sep 18
Which is a good affordable wireless laser printer that prints both sides of paper automatically?
Finding an affordable wireless laser printer that supports automatic duplex printing can be a smart investment if you want to save paper and streamline your workflow. Duplex printing allows the printer to print on both sides of the page without manual intervention, which is especially useful for producing professional documents, reports, or booklets. Wireless connectivity adds convenience by enabling printing from multiple devices, including smartphones, tablets, and laptops. HP offers several models that combine these features with reliable performance and cost-efficiency, making them ideal f
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Finding an affordable wireless laser printer that supports automatic duplex printing can be a smart investment if you want to save paper and streamline your workflow. Duplex printing allows the printer to print on both sides of the page without manual intervention, which is especially useful for producing professional documents, reports, or booklets. Wireless connectivity adds convenience by enabling printing from multiple devices, including smartphones, tablets, and laptops. HP offers several models that combine these features with reliable performance and cost-efficiency, making them ideal for home offices or small businesses.
One strong recommendation is the HP LaserJet Pro MFP 3102fdw. This model is priced around £229 to £329 and includes automatic duplex printing, wireless connectivity, and multifunction capabilities such as scanning and copying. It’s designed for users who need consistent, high-speed printing with minimal maintenance. The compact design makes it suitable for smaller workspaces, while the efficient toner system helps keep running costs low. Its compatibility with the HP Smart app allows for easy mobile printing, adding flexibility to your workflow.
For a more budget-conscious alternative, the HP LaserJet M234sdw is another excellent option. Priced from £136 to £210, it offers automatic duplex printing and wireless functionality, along with fast print speeds of up to 29 pages per minute. This model is ideal for users who primarily need high-volume monochrome printing without the added features of scanning or copying. It supports mobile printing through platforms like Apple AirPrint and the HP Smart app, making it easy to print from various devices. It uses toner really efficiently, so you won’t be spending loads on refills, thus great for everyday printing.
LaserJet Printers - Black & White or Color Document Printers
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Martin Carr
PhD. in Materials Chemistry, Cranfield University (Graduated 1996) · Author has 2.3K answers and 3.7M answer views
·7y
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Between N2 and O2, which gas is more ideal?
No “Real” gas has the perfect “Ideal” gas behaviour although oxygen and nitrogen are close over certain ranges as you can see in the graph below. Nitrogen is closest to ideal gas behaviour at relatively low pressures - up to about 200atm (which is fairly high) but if you want to go above, say 250 atmospheres, then oxygen is the better candidate up to around 600 atmospheres.
This, needless to say, discusses only the physical behaviour of these gases. Depending on the purpose for which you want these gases, it would be important to consider the chemical properties too, since high pressure oxygen
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No “Real” gas has the perfect “Ideal” gas behaviour although oxygen and nitrogen are close over certain ranges as you can see in the graph below. Nitrogen is closest to ideal gas behaviour at relatively low pressures - up to about 200atm (which is fairly high) but if you want to go above, say 250 atmospheres, then oxygen is the better candidate up to around 600 atmospheres.
This, needless to say, discusses only the physical behaviour of these gases. Depending on the purpose for which you want these gases, it would be important to consider the chemical properties too, since high pressure oxygen carries risks that nitrogen does not. For example, on rubber seals, oxygen would cause deterioration due to oxidation whereas nitrogen would not and a leaking, high pressure oxygen system is a serious fire hazard.
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Beny Falkovich
BSc in Chemistry & Mathematics (TAU), 4 years in chemical R&D
·9y
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Why does a real gas behave like an ideal gas only at low pressure and high temperature?
Ideal gas models make a lot of assumptions and neglections, but two things are neglected above all: 1) the non-zero size of each gas molecule (how much space it takes out of V, in virial expansion corrected by V--> V-nb, b is the volume), and 2) the interactions (usually Van der Waals attraction) between the molecules.
If you want to neglect the first one you have to say "oh but there are so few molecules of gas compared to the volume that the effective volume every molecule can bounce around in is almost V, they don't 'feel crowded'". To say that you need to assume a low concentration, or low
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Ideal gas models make a lot of assumptions and neglections, but two things are neglected above all: 1) the non-zero size of each gas molecule (how much space it takes out of V, in virial expansion corrected by V--> V-nb, b is the volume), and 2) the interactions (usually Van der Waals attraction) between the molecules.
If you want to neglect the first one you have to say "oh but there are so few molecules of gas compared to the volume that the effective volume every molecule can bounce around in is almost V, they don't 'feel crowded'". To say that you need to assume a low concentration, or low pressure.
If you want to neglect the second one you have to say "oh but the kinetic energy of each molecule is so large compared to the energy of interactions that they essentially 'don't feel each other, bouncing around so fast'". Well, the kinetic energy of each molecule is proportional to the temperature! So you need a high enough temperature to say that the interaction energy is negligible compared to it.
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Michael Mombourquette
Retired Chemistry Prof, Church member, Knight of Columbus, · Author has 6.8K answers and 17.7M answer views
·3y
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Do gases always behave ideally?
an Ideal gas is one which has molecules that are zero in size and have zero intermolecular forces. no real gas has such molecules so no real gas is perfectly ideal. However, if the molecules are far enough apart from each other, they essentially almost never ‘see’ each other and you can measure their pressure/volume/temperature conditions and use the ideal gas law to correctly predict their behaviours as you adjust their conditions. If you squeeze the molecules closer together then their tiny volumes become noticeable. and you can not ignore them any more. The ideal gas law will not give an ac
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an Ideal gas is one which has molecules that are zero in size and have zero intermolecular forces. no real gas has such molecules so no real gas is perfectly ideal. However, if the molecules are far enough apart from each other, they essentially almost never ‘see’ each other and you can measure their pressure/volume/temperature conditions and use the ideal gas law to correctly predict their behaviours as you adjust their conditions. If you squeeze the molecules closer together then their tiny volumes become noticeable. and you can not ignore them any more. The ideal gas law will not give an accurate prediction of their properties. If the temperature is low enough, their intermolecular forces will become noticeable and for that reason, you will not be able to use the ideal gas law to predict their properties.
Some gases have very low IMFs and are very small so they behave ideally (almost) at room temperature and pressure. All noble gases behave ideally at ambient conditions, as do some simple diatomic gases like H 2 H 2, O 2 O 2, N 2 N 2 . Other gases have larger sizes and start behaving non-ideally at those temperatures. Consider the following alkane molecules and their temperatures. The parameter n is the number of carbons in the alkane. Notice that as n gets bigger, the boiling point gets higher. methane, with a bp of -162 will act nicely as an ideal gas at room temperature and pressure (RTP). Ethane and to a lesser extent, propane as well will be ideal gases at RTP. Butane will be in the range where it does not quite work as well to use the ideal gas law to predict its nature. RTP is pretty close to its boiling point. at that point, the gas can change into a liquid and back again (equilibrium). Clearly, pentane, is not a gas at RTP.
SNIPIT from my own lecture notes
Nomenclature – First Year General Chemistry First Year General Chemistry
So, Size does matter ;)
How about force? consider water, a molecule about the same size as methane but which has very strong IMFs (hydrogen bonding). It has a BP of 100℃ at 1 atm pressure. Clearly, it does not behave ideally at RTP, where it will most likely be found to be a liquid. However, if you have a low enough pressure, the molecules of water will be far apart from each other and will never feel those IMFs. So for low pressure, even at room temperature, water can behave like an ideal gas.
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Alan Humason
Ph.D. in Physical Chemistry, Southern Methodist University (Graduated 2018) · Author has 159 answers and 2.2M answer views
·2y
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Which one of these gases behaves more ideally than others: hydrogen, oxygen, nitrogen or carbon dioxide?
Short Answer: Hydrogen.
Longer Answer: This is a good question. The two approximations in the “ideal” gas are 1) that the individual molecules neither attract nor repel each other, and 2) that molecules have zero volume on their own.
This “ideal behavior” allows from some non-physical results in extreme cases, such as 1) a gas at zero degrees Kelvin (absolute zero) would have zero volume, and 2) a measure of gas under infinite pressure would have zero volume. The key point here is ZERO VOLUME. Molecules consist of matter, and cannot occupy the same space. At some point, the atoms would need to g
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Short Answer: Hydrogen.
Longer Answer: This is a good question. The two approximations in the “ideal” gas are 1) that the individual molecules neither attract nor repel each other, and 2) that molecules have zero volume on their own.
This “ideal behavior” allows from some non-physical results in extreme cases, such as 1) a gas at zero degrees Kelvin (absolute zero) would have zero volume, and 2) a measure of gas under infinite pressure would have zero volume. The key point here is ZERO VOLUME. Molecules consist of matter, and cannot occupy the same space. At some point, the atoms would need to go “closer than possible” to satisfy the equation.
So, the plot of the Ideal Gas Law (pV = nRT) against any two variables (pressure, volume, moles, Kelvin temperature) would be straight lines representing Avogadro’s, Boyle’s, and Charles’ laws. This is very serviceable under usual conditions of temperature and pressure. However, at very low temperature or very high pressure, the observed values will vary. The line representing real gas behavior will bend.
Returning to the question, the first approximation is not troublesome for the non-polar and unreactive (at least to themselves) molecules listed. But, the bigger the molecule, the bigger the problem at low temperature and high pressure. A quick look at the period table shows that HYDROGEN is the smallest molecule, and will deviate least from ideal behavior.
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Rakesh Nellekeri
Engineer and a Dreamer. · Author has 321 answers and 760.5K answer views
·7y
Related
If gases can be liquefied by lowering the temperature and increasing the pressure, can we convert a real gas into an ideal gas by increasing the temperature and lowering the pressure?
Ideal gas is a gas which has zero interference with other molecules and there is no loss of energy on collision with the container.
This happens only when you increase temperature to crazy degree celsius so that the gas expands to the level that the molecules of the gas stop colliding with each other and also the pressure to be extremely low to facilitate expansion.
At high temperatures, the molecules of gas tends to move rapidly, due to that, the intermolecular force decreases and ideal gases are assumed to have no intermolecular forces. So, the temperature has to be raised till the point where
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Ideal gas is a gas which has zero interference with other molecules and there is no loss of energy on collision with the container.
This happens only when you increase temperature to crazy degree celsius so that the gas expands to the level that the molecules of the gas stop colliding with each other and also the pressure to be extremely low to facilitate expansion.
At high temperatures, the molecules of gas tends to move rapidly, due to that, the intermolecular force decreases and ideal gases are assumed to have no intermolecular forces. So, the temperature has to be raised till the point where there is no intermolecular forces exists.
When you attain high temperature, low pressure gas, it wouldn't be fair enough to suggest that, it's one hundred percent ideal. Because of the fact that, ideal doesn't exists. It can be closely compared with the ideal gas because it tends to obey the gas laws, again to some extent. But, this will be close enough to be neglected in general terms.
The other assumption made is, ideal gases don't condense into liquid when cooled. Which gas doesn't condense when cooled? It has to, at some or the other point, right?
In reality, you can't make a gas immune to energy loss on collision in a closed container.
That's why, I consider you can't create an ideal gas by reducing pressure and increasing temperature of a real gas. But, you can bring it as close as possible by that condition.
Hope I have answered you.
Thank you !!!
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Arthur Clarke
Former Chemical Engineer · Author has 1.2K answers and 1.7M answer views
·7y
Related
Between N2 and O2, which gas is more ideal?
The so-called Z factor is used in the ideal gas equation to correct for deviations from no-ideality. A value of Z=1 means perfectly ideal. Here is the table below
As you can see nitrogen’s Z factor is closer to 1.0 than oxygen’s but they are both pretty high on the scale.
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The so-called Z factor is used in the ideal gas equation to correct for deviations from no-ideality. A value of Z=1 means perfectly ideal. Here is the table below
As you can see nitrogen’s Z factor is closer to 1.0 than oxygen’s but they are both pretty high on the scale.
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Between N2 and O2, which gas is more ideal?
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What happens to a gas while being under extremely high pressure and high temperature at the same time?
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At the same temperature and pressure, which gas has high density, N2, O2, or H2?
Does C02, N2, and H2 gas never behave ideally even when the temperature is high and pressure is lowered?
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13412 | https://artofproblemsolving.com/wiki/index.php/Parity?srsltid=AfmBOooF4rotcmngGYP3FY73wSxmAvgNQZqfM7Pz8obWp3oUQFfjd8NM | Art of Problem Solving
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Parity
Parity refers to whether a number is even or odd.
While this may seem highly basic, checking the parity of numbers is often an useful tactic for solving problems, especially with proof by contradictions and casework.
This concept begins with integers. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without remainder; an odd number is an integer that is not evenly divisible by 2. (The old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) A formal definition of an even number is that it is an integer of the form n = 2k, where k is an integer; it can then be shown that an odd number is an integer of the form n = 2k + 1.
This only applies to integers, not fractions or decimals.
Contents
1 Problems
2 Solution 1
3 Solution 2
3.1 Introductory
3.2 Intermediate
3.2.1 Problem
3.2.2 Solution
3.2.3 Problem 2
3.2.4 Solution
Problems
Example from 1997 AJHSME:
Problem: Ten balls numbered to are in a jar. Jack reaches into the jar and randomly removes one of the balls. Then Jill reaches into the jar and randomly removes a different ball. The probability that the sum of the two numbers on the balls removed is even is
Solution 1
For the sum of the two numbers removed to be even, they must be of the same parity. There are five even values and five odd values.
No matter what Jack chooses, the number of numbers with the same parity is four. There are nine numbers total, so the probability Jill chooses a number with the same parity as Jack's is .
Solution 2
We find that it is only possible for the sum to be even if the numbers added are both even or odd. We will get an odd number when we add an even and odd. We can use complementary counting to help solve the problem. There are a total of possibilities since Jack can choose numbers and Jill can pick . There are possibilities for the two numbers to be different since Jack can pick any of the numbers and Jill has to pick from numbers in the set with a different parity than the one that Jack picks. So the probability that the sum will be odd is . Subtracting this by one gets the answer (edited by qkddud)
Introductory
Many AMC 8 problems fit this category, help us out by putting problems here!
Intermediate
2000 AIME II Problem 2:
Problem
A point whose coordinates are both integers is called a lattice point. How many lattice points lie on the hyperbola ?
Solution
Note that and have the same parities, so both must be even. We first give a factor of to both and . We have left. Since there are factors of , and since both and can be negative, this gives us lattice points.
2008 AIME I Problem 3
Problem 2
There exist unique positive integers and that satisfy the equation . Find .
Solution
Completing the square, . Thus by difference of squares.
Since is even, one of the factors is even. A parity check shows that if one of them is even, then both must be even. Since , the factors must be and . Since , we have and ; the latter equation implies that .
Indeed, by solving, we find is the unique solution.
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13413 | https://www.youtube.com/watch?v=rdN1oxtds8U | Small Angle Approximations (1 of 4: Proof)
Eddie Woo
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Transcript:
once we prove this result let me show you where we're going to be going okay we're going to have a result which is very very concise and there are two main applications that we're going to explore in um this is probably worth joining you down in 14f of the year 11 textbook there are two main applications one of them is pure and the other one is can you tell me what the other big branch of mathematics is apart from pure wow we're really asleep this morning okay when we do mass for its own sake that's called pure mass it's like we're not trying to solve any problems we're just like playing around with that to see what happens right but the other kind of math is where you're trying to solve a problem it's applied to a specific context and it's called applied thank you very much so there are some pure problems that we can solve with this result i'm going to show you there are some applied problems we can solve but interestingly and actually this is often the case it's going to be the pure result that becomes more interesting to us because it's going to take us into calculus of trigonometric functions okay so we're gonna focus on those top two because that's where you need to sort of bed things down before you get into calculus but this is just so you know where the trajectory is headed so hopefully by now i've stalled a little bit and you have drawn for you a uh a sector and i've got a triangle within that and because this is a sector it's part of a circle right that's one of the signals to you that even though i'm doing trigonometry as a whole i'm working with these angles right but the angles are not just going to be in any form it's within the context of a circle so when you see circles and you see angles which form of angle are you going to use which method of measuring are you going to use degrees you're going to try and get away from degrees as much as you possibly can sometimes you can't but because this is a circle should indicate to you that everything we're about to do is in radians okay and that's actually very important later on because when we start doing calculus of the trigonometric function one of the key things is hey we're doing this all in radians you'll think why why are we doing this it's some arbitrary thing well all the results on which calculus of trig functions depend we're about to do this morning and because they're based on radians everything following this is also going to be radians okay now you guys know in maths frequently we gain knowledge from looking at a single object from more than one perspective okay um think back to good morning take a seat uh think back to auxiliary angle you guys already covered auxiliary angle right yep so the whole idea is if i give you a function that is the sum of two other trigonometric functions you can write it in a new form you can say okay i'm going to have a new wave function out of these two it's going to have a different amplitude and it's also going to have a different what's the other thing that's going to change so i don't know it starts with a p you guys learned this word yet it's going to have a different phase thank you very much right so when you take your wave function it's the same wave function same amplitude but if you shift it along horizontally we call that the phase right now these are the two same thing they're the same objects right but we like this because you're like oh single trig function i can deal with this much easier so you've got the same object looked at from two different angles and you gain inside right and we're going to do exactly the same thing with this in this within this diagram and you can see the object i'm interested in because i've highlighted with color right this um this h here is what we're interested in and we're going to look at it from two very simple perspectives and therefore gain some information out of this now i've deliberately left some stuff off here which i want you to add along with me okay to get at this h over here to look at it from two different perspectives i want to focus on this guy down here see this little length between our vertical length and our arc over here um this guy is going to be important so we're going to call him x right that little length is x now because along the bottom here this is the edge of a sector right if this is x what does this remaining length end up being uh minus x right it's just that difference there okay so far so good i've done all my setup now i'm ready to actually understand this thing that red object there it exists in a right angle triangle and i know that angle that's subtended at the center of this big circle of which i haven't drawn the whole thing so therefore i can state h in terms of well in terms of a variety of trig functions i've got three to choose from but i'm actually going to be for reasons clear in about 10 minutes i'm only going to focus on sign and turn can someone tell me what statement can i make with h that has sign in it i'll give you a clue it starts with sine tell me what i can write next you've only got one angle in this triangle right so maybe i should take sine of theta wow it's almost as if i've given you information that leans you in this direction particular direction in this right angle triangle sine theta of course is equal to opposite on hypotenuse okay now this is true but remember i told you the object i'm really focusing on is actually that h right so i'm going to change the subject here and i get h equals r sine theta out of that are you so far so good okay so i have a statement for the length of h but that's not the only perspective from which i can look i'm going to write a statement with 10 in it i'm going to give you a second you go ahead you write it down i'm not going to do it together you guys can work this part out okay chester what do we got equals to h over r okay h on r minus x opposite on adjacent or fine but again remember the thing i'm really interested in is h so i'm going to change that to be the subject and this is what i get okay now nothing particularly groundbreaking so far but you notice that i have the same length h and set it in two different ways so i can actually equate those right i can say therefore r sine theta and r minus x tan theta these are the same thing just looked at in two different ways okay now why would i bother doing this well see my diagram see how it's so comically large right the reason it's comically large is because i use this meter rule for this very specific reason okay and if you've got your ruler there also i'm going to pop it down here i'm going to pop it down the end here just so you can see all my actually now put it on top you can still see my x and my minus x there there we go there's one there's my radius in yellow and then here's my other radius now what i've got here no i am going to put it lower what i've got here that's better are these two radii and i'm interested in what happens when the angle gets smaller hence the heading small angle approximations okay so as theta gets smaller as it shrinks down okay this radius is not going to be up here anymore it's going to be at spots like say that there we go that'll do me okay now can you see as theta gets smaller this is like theta which is like half the length okay what's going to happen is this h is going to change isn't its position has changed entirely it's going to be moved over here to the right so it's going to be like so you might like to put this in as well okay i've got a new h but along with that new h i also have a new x where is x in this diagram have a look where would you place it it's like teeny tiny little length over here right and that's actually very important that it's getting teeny tiny this new x over here you can see as theta gets smaller as i move this radius down even further let's go down like this in fact at this point here i'm going to draw one more and probably on your diagram you'll not have much space to do any further than that like that as theta gets small what's happening to x it's just vanishing away right as theta disappears as theta approaches zero so does x so i have a way of stating this right wrong color i can say using my language of limits right i can say but the limit as theta approaches zero of that length x what is that limit what's it approaching what do we just establish also approaching zero right so therefore if i think about this in the context of this statement that we just made over here about h right we've forgotten that it was about h we don't need to know that that's where it came from but that's where we learned this right just simple right angle triangle tree i can take the limit of both sides here as theta as theta approaches zero right in other words for small values of theta this is what happens when theta is approaching zero we say they're getting little right i'm going to have r sine theta on the left hand side what's going to happen over here what's happening to that x we just established this right that x is just vanishing away it's just disappearing right so these things are going to become equal to each other without that x you see what happened that was like r minus 0 and it's just vanishing away okay now you can see here r is just the length of any description so i can divide both sides through by r so i'm getting this like so okay now sine theta and theta what are we saying as theta gets smaller and smaller and smaller the difference between them is really this x and that's getting smaller and smaller and smaller and smaller you can see that these things are approaching each other for small values of theta what does sine theta actually approach when theta gets small think about the graph what does theta sorry what does sine theta approach when theta itself gets small it also approaches zero if you have a look at the graph there right as theta approaches zero as it gets closer and closer into the origin right do you see that theta is getting to zero so is sine theta right what about 10 there's 10 approach when you are getting closer to zero same thing right here's the graph actually not interested in this part over here but this is so you recognize it as tan and as you can see as theta gets closer and closer to zero in this little territory in there right you can see tan is getting closer and closer to zero in other words theta and sine and tan they're all approaching zero does this make sense ok so what we can state is in summary for small values of theta sine theta and theta and tan theta are all basically the same thing this is the small angle approximation after which this entire idea is named for small angles we can approximate these things as all basically equal to each other |
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13415 | https://www.reddit.com/r/math/comments/1gagmeu/which_number_occurs_most_frequently_in/ | Which number occurs most frequently in Pythagorean triples? : r/math
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Which number occurs most frequently in Pythagorean triples?
I'm just wondering if there's a way to figure this outecause I assume some appear more often then others is there a number that is the most common or not?
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13416 | https://math.stackexchange.com/questions/1026144/is-jensens-inequality-an-iff-condition-on-convex-functions | Skip to main content
Is Jensen's inequality an iff condition on convex functions?
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According to wikipedia this is Jensen's inequality:
If X is a random variable and φ is a convex function, then:
φ(E[X])≤E[φ(X)].
Which stated as an implication reads as follows:
If Convex ⟹ φ(E[X])≤E[φ(X)].
However, I was wondering if the converse was also true.
φ(E[X])≤E[φ(X)] ⟹ Convex.
I thought it would be an iff because of the definition of convexity. Recall what convexity means (and let me explain why I thought iff for jensen's):
f is called convex if:
∀x1,x2∈X,∀t∈[0,1]:f(tx1+(1−t)x2)≤tf(x1)+(1−t)f(x2).
Since its a definition, the the word convex and its definition statement are logically equivalent. Therefore, its an iff, i.e.
f is called convex ⇔∀x1,x2∈X,∀t∈[0,1]:f(tx1+(1−t)x2)≤tf(x1)+(1−t)f(x2).
right? Does that logic generalize to Jensen's inequality or am I wrong for both?
Context:
The reason that I care about this is because I wanted to proof that a multivariable function f is convex. My plan of attack was to show Jensen's inequality "worked" on it and since Jensen's inequality and convexity are logically equivalent, then I can conclude that f is convex. But that only works if its an iif. Also, I absolutely wanted to avoid taking the Hessian or derivatives to prove it was convex, I strictly wanted to stick with the "original" definition of convexity to prove this (i.e. the inequality definition).
convex-analysis
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asked Nov 17, 2014 at 15:43
Charlie ParkerCharlie Parker
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If the inequality holds for all random variables (with expectation), then φ is convex.
– Daniel Fischer
Commented
Nov 17, 2014 at 15:57
@DanielFischer how is that not a contradiction to Seyhmus Güngören answer bellow? It seems he said that Jensen's cannot imply convexity but you say it does. I am confused right now.
– Charlie Parker
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Nov 17, 2014 at 16:15
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That answer says that the inequality ψ(E[X])⩽E[ψ(X)] can hold for some random variables X even if ψ is not convex. [Note that in that answer, the chosen ψ is convex on the range of the chosen U.]
– Daniel Fischer
Commented
Nov 17, 2014 at 16:17
Is the random variable for that answer the continuous random variable that takes values in U with any probability distribution?
– Charlie Parker
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Nov 17, 2014 at 16:23
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The convexity of f is equivalent to Jensen's inequality holding for all random variables X. (If it holds for all X, then in particular it holds for the random variable with P(X=x1)=t and P(X=x2)=1−t, where Jensen reduces to the definition of convexity.) So if somehow it's easier to prove Jensen for all X (perhaps because the generality of that statement clears away distractions), then sure, your method is sound.
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answered Nov 17, 2014 at 15:57
user21467user21467
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That is not true take U uniform in [0,1] and consider the function f(x)=x3. Then one can see that E[ψ(X)]≥ψ(E[X]) but f is non-convex.
In general convexity is a much stronger argument than Jensen's inequality.
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answered Nov 17, 2014 at 15:53
Seyhmus GüngörenSeyhmus Güngören
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Sorry if this is a very easy question, but what does it mean that "convexity is a much stronger argument/statement". Are you using the word stronger in a precise way or is it just intuitive? Or both. Either way not sure what it means. Btw, thanx for your response.
– Charlie Parker
Commented
Nov 17, 2014 at 15:58
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Stronger in the sense that in order to imply covexity one needs to do a little bit more that Jensens inequality. More formally, it means that Jensens inequality is not strong enough to imply convexity.
– Seyhmus Güngören
Commented
Nov 17, 2014 at 16:01
Seyhmus, I apologize but a comment on my question confused me. Daniel Fischer in the comments section said: "If the inequality holds for all random variables (with expectation), then φ is convex.", however, you said that jensen's inequality is not strong enough to imply convexity, but he said it can. Currently, I am confused, so can it or can it not imply convexity? Thanks for your time :)
– Charlie Parker
Commented
Nov 17, 2014 at 16:18
there is no contradiction. Hear what he is saying.
– Seyhmus Güngören
Commented
Nov 17, 2014 at 16:24
Oh ok, I think I get it, so its an iff only when its true for all r.vs X. Right? Thanks for your patience :)
– Charlie Parker
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Nov 17, 2014 at 16:27
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It depends on the underlying probability space.
For example, if the measure is δ12 on [0,1], then EX=X(12), Eϕ(X)=ϕ(X(12)), so Jensen's inequality holds whether or not ϕ is convex.
For all t∈[0,1] you need to be able to find a set A such that pA=t.
If you can do this, let X=x1⋅1A+x2⋅1X∖A. Then
EX=tx1+(1−t)x2 and Eϕ(X)=tϕ(x1)+(1−t)ϕ(x2), which implies that ϕ is convex if Jensen's inequality holds.
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edited Nov 17, 2014 at 16:00
answered Nov 17, 2014 at 15:54
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13417 | https://www.me.psu.edu/cimbala/Learning/Fluid/Introductory/descriptions_of_fluid_flows.htm | Descriptions of Fluid Flows
There are two ways to describe fluid flows:
The Lagrangian Description is one in which individual fluid particles are tracked, much like the tracking of billiard balls in a highschool physics experiment.
In the Lagrangian description of fluid flow, individual fluid particles
are "marked," and their positions, velocities, etc. are described as a
function of time. In the example shown, particles A and B have been identified.
Position vectors and velocity vectors are shown at one instant of time for
each of these marked particles. As the particles move in the flow field,
their postions and velocities change with time, as seen in the animated diagram.
The physical laws, such as Newton's laws and conservation of mass and energy,
apply directly to each particle.
If there were only a few particles to consider, as in a high school physics
experiment with billiard balls, the Lagrangian description would
be desirable. However, fluid flow is a continuum phenomenon, at least down
to the molecular level. It is not possible to track each "particle" in a complex
flow field. Thus, the Lagrangian description is rarely used in fluid mechanics.
+ The Eulerian Description is one in which a control volume is defined, within which fluid flow properties of interest are expressed as fields.
In the Eulerian description of fluid flow, individual fluid particles
are not identified. Instead, a control volume is defined, as shown
in the diagram.
Pressure, velocity, acceleration,
and all other flow properties are described as fields within
the control volume.
In other words, each property is expressed as a function of space
and time, as shown for the velocity field in the diagram.
In the Eulerian description of fluid flow, one is not concerned
about the location or velocity of any particular particle, but rather
about the velocity, acceleration, etc. of whatever particle happens
to be at a particular location of interest at a particular time.
Since fluid flow is a continuum phenomenon, at least down
to the molecular level, the Eulerian description is usually
preferred in fluid mechanics. Note, however, that the physical laws
such as Newton's laws and the laws of conservation of mass and
energy apply directly to particles in a Lagrangian description.
Hence, some translation or reformulation of these laws is
required for use with an Eulerian description.
- Example - Pressure field -
An example of a fluid flow variable expressed in Eulerian terms
is the pressure. Rather than following the pressure of an individual
particle, a pressure field is introduced, i.e.
p = p(x,y,z,t).
Note that pressure is a scalar, and is written as a function
of space and time (x,y,z, and t). In other words, at a given point in space
(x,y, and z), and at some particular time (t), the pressure is
defined. In the Eulerian description, it is of no concern which fluid
particle is at that location at that time.
In fact, whatever fluid particle happens to be at that location
at time t experiences the pressure defined above.
- Example - Velocity field -
An example of a fluid flow variable expressed in Eulerian terms
is the velocity. Rather than following the velocity of an individual
particle, a velocity field is introduced, i.e.
Note that since velocity is a vector, it can be split into
three components (u,v, and w), all three of which are functions of space and
time (x,y,z, and t). In other words, at a given point in space
(x,y, and z), and at some particular time (t), the velocity vector is
defined. In the Eulerian description, it is of no concern which fluid
particle is at that location at that time.
In fact, whatever fluid particle happens to be at that location
at time t has the velocity defined above.
- Example - Acceleration field -
An example of a fluid flow variable expressed in Eulerian terms
is the acceleration. Rather than following the acceleration of
an individual
particle, an acceleration field is introduced, i.e.
.
Note that since acceleration is a vector, it can be split into
three components, all three of which are functions of space and
time (x,y,z, and t). In other words, at a given point in space
(x,y, and z), and at some particular time (t), the acceleration vector is
defined. In the Eulerian description, it is of no concern which fluid
particle is at that location at that time.
In fact, whatever fluid particle happens to be at that location
at time t has the acceleration defined above.
+ Either description method is valid in fluid mechanics, but the Eulerian description is usually preferred because there are simply too many particles to keep track of in a Lagrangian description.
The Material Derivative, also called the Total Derivative or Substantial Derivative is useful as a bridge between Lagrangian and Eulerian descriptions.
+ Definition of the material derivative -
The material derivative of some quantity is simply defined as
the rate of change of that quantity following a fluid particle.
It is derived for some arbitrary fluid property Q as follows:
In this derivation, dt/dt = 1 by definition, and since a fluid particle
is being followed, dx/dt = u, i.e. the x-component of the velocity
of the fluid particle. Similarly, dy/dt = v, and dz/dt = w following
a fluid particle.
Note that Q can be any fluid property, scalar or vector.
For example, Q can be a scalar like the pressure, in which
case one gets the material derivative or substantial derivative
of the pressure.
In other words, dp/dt is the rate of change of pressure following
a fluid particle.
Or, using the same equations above, Q can be the velocity vector,
in which case one gets the material derivative of the velocity,
which is defined as the material acceleration,
i.e. the rate of change of velocity following a fluid particle.
Note also the notation, DQ/DT, which is used by some authors to
emphasize that this is a material or total derivative, as
opposed to some partial derivative. DQ/DT is identical to dQ/dt.
The material derivative is a field quantity, i.e. it is expressed in
the Eulerian frame of reference
as a function of space and time (x,y,z,t).
Thus, at some given spatial location (x,y,z) and at some given time (t),
DQ/Dt = dQ/dt = the material derivative of Q, and is defined as
the total rate of change of Q with respect to time
as one follows whatever fluid particle happens to be at that
location at that instant of time. Q changes for two reasons: First,
if the flow is unsteady, Q changes directly with respect to time.
This is called the local or unsteady rate of change of Q.
Second, Q changes as the fluid particle migrates or convects
to a new location in the flow field.
This is called the convective or advective
rate of change of Q.
+ Example - the material acceleration, following a fluid particle -
The material acceleration can be derived as follows:
Note that dt/dt = 1 by definition, and since a fluid particle
is being followed, dx/dt = u, i.e. the x-component of the velocity
of the fluid particle. Similarly, dy/dt = v, and dz/dt = w following
a fluid particle.
The first term on the right hand side is called the local acceleration
or the unsteady acceleration. It is only non-zero in an
unsteady flow.
The last three terms make up the convective acceleration, which
is defined as the acceleration due to convection or movement of the
fluid particle to a different part of the flow field.
The convective acceleration can be non-zero even in a steady flow!
In other words, even when the velocity field is not a function
of time (i.e. a steady flow), a fluid particle is still accelerated
from one location to another.
Methods of Visualizing Fluid Flows
A streamline is a line everywhere tangent to the velocity
vector at a given instant of time.
(A streamline is an instantaneous pattern.)
For example,
consider simple shear flow between parallel plates.
At some instant of time, a streamline can be drawn by connecting
the velocity vector lines such that the streamline is everywhere
parallel to the local velocity vector. In this example, streamlines
are simply horizontal lines.
A streakline is the locus of particles which have earlier
passed through a prescribed point in space.
(A streakline is an integrated pattern.)
For example,
consider simple shear flow between parallel plates.
A streakline is formed by injecting dye into the fluid at a fixed point
in space. As time marches on, the streakline gets longer and longer,
and represents an integrated history of the dye streak.
In this example, streaklines
are simply horizontal lines.
A pathline is the actual path traversed by a given
(marked) fluid particle.
(A pathline is an integrated pattern.)
For example,
consider simple shear flow between parallel plates.
A pathline is the actual path traversed by a given (marked) fluid particle.
A pathline represents an integrated history of where the fluid particle
has been.
In this example, pathlines
are simply horizontal lines.
A timeline is a set of fluid particles that form a line
segment at a given instant of time.
(A timeline is an integrated pattern.)
For example,
consider simple shear flow between parallel plates.
A timeline follows the location of a line of fluid particles.
A timeline represents an integrated flow pattern, since the time line
continually distorts with time, as shown in the sketch.
Notice the no-slip condition in action. The top of the
time line moves with the top plate, i.e. at velocity V to the right.
The bottom of the timeline, however, stays in the same location at all
times, because the bottome plate is not moving.
Note: For steady flow, streamlines, streaklines, and pathlines
are all identical. However, for unsteady flow, these three flow patterns
can be quite different. |
13418 | http://intrologic.stanford.edu/lectures/lecture_02.pdf | Introduction to Logic Propositional Logic Michael Genesereth Computer Science Department Stanford University Propositional Logic (logical operators) If raining and cold, then wet.
Relational Logic (variables and quantifiers) If abby likes x, then bess likes x.
Functional Logic (functional terms) {a, b} is a subset of {a, b, c}.
Multiple Logics If Mary loves Pat, then Mary loves Quincy.
If it is Monday, then Mary loves Pat or Quincy.
If it is Monday, does Mary love Quincy?
If it is Monday, does Mary love Pat?
Example Victor has been murdered, and Art, Bob, and Carl are suspects. Art says he did not do it. He says that Bob was the victim's friend but that Carl hated the victim. Bob says he was out of town the day of the murder, and besides he didn't even know the guy. Carl says he is innocent and he saw Art and Bob with the victim just before the murder. You can assume that everyone is telling the truth - except for the murderer.
Whodunnit? (Answer: Bob) Example Digital Circuits Digital Circuits Example Basics syntactically legal sentences meaning of syntactically legal sentences Evaluation Given truth values for simple sentences, find truth values of complex sentences.
Satisfaction Given truth values for complex sentences, find truth values of simple sentences.
Examples Natural Language Digital Circuits Programme Basics syntactically legal sentences meaning of syntactically legal sentences Evaluation Given truth values for simple sentences, find truth values of complex sentences.
Satisfaction Given truth values for complex sentences, find truth values of simple sentences.
Examples Natural Language Digital Circuits Programme Syntax Proposition Constants express simple facts about the world In English - It is raining. In our language - raining Compound Sentences express relationships between sentences In English - It is raining or it is snowing. In our language - raining ∨ snowing Propositional Sentences By convention (in this course), proposition constants are written as strings of letters, digits, and underscores ("_") beginning with a lower case letter.
Examples: raining rAiNiNg raining_or_snowing Non-Examples: Raining 324567 raining-or-snowing Proposition Constants Negations: (¬raining) The argument of a negation is called the target.
Conjunctions: (raining ∧ snowing) The arguments of a conjunction are called conjuncts.
Disjunctions: (raining ∨ snowing) The arguments of a disjunction are called disjuncts.
Compound Sentences (part I) Implications: (raining ⇒ cloudy) The left argument of an implication is the antecedent. The right argument is the consequent.
Biconditionals: (cloudy ⇔ raining) Compound Sentences (part II) (¬raining) (raining ∧ snowing) (raining ∨ snowing) (raining ⇒ cloudy) (cloudy ⇔ raining) ¬(raining ∧ snowing) ((raining ∧ snowing) ⇒ cloudy) (cloudy ⇒ (raining ∧ snowing)) ((cloudy ∧ wet) ⇔ (raining ∨ snowing)) (¬raining ⇒ (cloudy ⇒ snowing)) Nested Compound Sentences Dropping Parentheses is good: (p ∧ q) → p ∧ q But it can lead to ambiguities: ((p ∨ q) ∧ r) → p ∨ q ∧ r (p ∨ (q ∧ r)) → p ∨ q ∧ r Parentheses Removal Parentheses can be dropped when the structure of an expression can be determined by precedence.
¬ ∧ ∨ ⇒ ⇔ An operand surrounded by operators associates with operator of higher precedence.
¬p ∨ q → ((¬p) ∨ q) p ∨ q ∧ r → (p ∨ (q ∧ r)) p ∧ q ⇒ r → ((p ∧ q) ⇒ r) p ⇒ q ⇔ r → ((p ⇒ q) ⇔ r) Precedence If surrounded by occurrences of ∧ or ∨, the operand associates with the operator to the left.
p ∧ q ∧ r → ((p ∧ q) ∧ r) p ∨ q ∨ r → ((p ∨ q) ∨ r) If surrounded by two occurrences of ⇒ or ⇔, the operand associates with the operator to the right.
p ⇒ q ⇒ r → (p ⇒ (q ⇒ r)) p ⇔ q ⇔ r → (p ⇔ (q ⇔ r)) Precedence (continued) A propositional vocabulary is a set of proposition constants.
Given a propositional vocabulary, a propositional sentence is either (1) a proposition constant or (2) a compound sentence.
A propositional language is the set of all propositional sentences that can be formed from a propositional vocabulary.
Useful Definitions Semantics A propositional interpretation is an association between the propositional constants in a propositional language and the values T or F.
We sometimes write 1 and 0 in place of T and F.
pi = 1 qi = 0 ri = 1 p i ! → ! T pi = T q i ! → ! F qi = F r i ! → ! T ri = T Propositional Interpretation A sentential interpretation is an association between the sentences in a propositional language and truth values.
pi = T (p ∨ q)i = T qi = F (¬q ∨ r)i = T ri = T ((p ∨ q) ∧ (¬q ∨ r))i = T NB: Each distinct propositional interpretation gives rise to a unique sentential interpretation due to operator semantics.
Sentential Interpretation A negation is true if and only if the target is false.
For example, if the interpretation of p is F, then the interpretation of ¬p is T.
For example, if the interpretation of (p∧q) is T, then the interpretation of ¬(p∧q) is F.
φ ¬φ T F F T Semantics of Negations A conjunction is true if and only if both conjuncts are true.
For example, if the interpretation of p is true and q is true, then (p∧q) is true.
φ ψ φ ∧ψ T T T T F F F T F F F F Semantics of Conjunctions A disjunction is true if and only if at least one of the disjuncts is true.
The type of disjunction here is called inclusive or. This contrasts with exclusive or, which says that a disjunction is true if and only if an odd number of disjuncts are true.
φ ψ φ ∨ψ T T T T F T F T T F F F Semantics of Disjunctions A biconditional is true if and only if the truth values of its two constituents are the same.
φ ψ φ ⇔ψ T T T T F F F T F F F T Semantics of Biconditionals An implication is true if and only if the antecedent is false or the consequent is true.
The semantics of implication here is called material implication.
φ ψ φ ⇒ψ T T T T F F F T T F F T Semantics of Implications What Choice Do We Have?
φ ψ φ ⇔ψ T T T T F F F T F F F T φ ψ φ ⇔ψ T T T T F F F T F F F T φ ψ φ ∧ψ T T T T F F F T F F F F φ ψ φ ⇒ψ T T T T F F F T T F F T T F ψ φ ψ φ ⇒ψ T T T T F F F T T F F T Implications and Biconditionals φ ψ φ ⇔ψ T T T T F F F T F F F T φ ψ φ ⇒ψ T T T T F F F T T F F T T T F T ψ ⇒ ϕ ϕ ⇔ ψ is true if and only if ϕ ⇒ ψ and ψ ⇒ ϕ are true.
An implication is true if and only if the antecedent is false or the consequent is true.
A counterfactual is an implication in which the antecedent is false.
Counterfactuals φ ψ φ ⇒ψ T T T T F F F T T F F T A counterfactual is an implication in which the antecedent is false.
NB: Counterfactuals are always true! The truth value of the consequent does not matter.
Examples: It is raining ⇒ I am a billionaire It is raining ⇒ I am a pauper Shakespeare is alive ⇒ Shakespeare is dead 2+2=5 ⇒ 2+2=7 Counterfactuals are Weird Evaluation Interpretation i: pi = T qi = T ri = F Compound Sentence (p ∨ q) ∧ (¬q ∨ r) Evaluation (T ∨ T) ∧ (¬T ∨ F) (T ∨ T) ∧ ( F ∨ F) T ∧ F F Interpretation i: pi = T qi = F ri = T Compound Sentence (p ∨ q) ∧ (¬q ∨ r) Evaluation (T ∨ F) ∧ (¬F ∨ T) (T ∨ F) ∧ (T ∨ T) T ∧ T T Interpretation i: pi = T qi = F ri = T Compound Sentence (p ∧ q) ∨ (¬q ∧ r) Evaluation (T ∧ F) ∨ (¬F ∧ T) (T ∧ F) ∨ (T ∧ T) F ∨ T T Satisfaction Evaluation: Satisfaction: pi = T qi = F (p ∨q)i = T (¬q)i = T (p ∨q)i = T (¬q)i = T pi = T qi = F Evaluation versus Satisfaction Logic does not prescribe which interpretation is “correct”. In the absence of additional information, one interpretation is as good as another.
Interpretation i Interpretation j Examples: Different days of the week Different locations Beliefs of different people pi = T qi = F ri = T p j = F q j = F r j = T Multiple Interpretations p q r T T T T T F T F T T F F F T T F T F F F T F F F A truth table is a table of all possible interpretations for the propositional constants in a language.
One column per constant.
One row per interpretation.
For a language with n constants, there are 2n interpretations.
Truth Tables Method to find all propositional interpretations that satisfy a given set of sentences: (1)Form a truth table for the propositional constants.
(2) For each sentence in the set and each row in the truth table, check whether the row satisfies the sentence. If not, cross out the row.
(3) Any row remaining satisfies all sentences in the set. (Note that there might be more than one.) Truth Table Method Are these sentences satisfiable?
q⇒r p ⇒ q ∧ r ¬r Satisfaction Example p ⇒ q ∧ r p q r T T T T T F T F T T F F F T T F T F F F T F F F q⇒r Satisfaction Example p q r T T T T T F T F T T F F F T T F T F F F T F F F p ⇒ q ∧ r p q r T T T T T F T F T T F F F T T F T F F F T F F F q⇒r Satisfaction Example p q r T T T T T F T F T T F F F T T F T F F F T F F F p ⇒ q ∧ r p q r T T T T T F T F T T F F F T T F T F F F T F F F ¬r p q r T T T T T F T F T T F F F T T F T F F F T F F F Satisfaction Example {q⇒r, p ⇒ q ∧ r, ¬r} p q r T T T T T F T F T T F F F T T F T F F F T F F F Logica Course Website Logica Interleaved Generation and Checking Generation then Evaluation {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Interleaved Generation and Evaluation X X X X X X X X {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Interleaved Generation and Evaluation X X X X X X X X {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Interleaved Generation and Evaluation X X X X X X X X {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Interleaved Generation and Evaluation X X X X X X X X {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Intermediate State Checking {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Intermediate State Checking {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Intermediate State Checking {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Intermediate State Checking {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Intermediate State Checking {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Intermediate State Checking {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Intermediate Checking {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Intermediate Checking {p ∨ q, p ∨ ¬q, ¬p ∨ q, ¬p ∨ ¬q ∨ ¬r, ¬p ∨ r} Simplification and Unit Propagation Simplification Constraints p ∨ q p ∨ ~q ~p ∨ q ~p ∨ ~q ∨ ~r ~p ∨ r Simplification Given p = 1 Original Simplified p ∨ q -p ∨ ~q -~p ∨ q q ~p ∨ ~q ∨ ~r ~q ∨ ~r ~p ∨ r r Unit Propagation Given p = 1, q = 1 Original Simplified p ∨ q -p ∨ ~q -~p ∨ q -~p ∨ ~q ∨ ~r ~r ~p ∨ r r Simplification Original Simplified p ∨ q -p ∨ ~q -~p ∨ q -~p ∨ ~q ∨ ~r x ~p ∨ r -Given p = 1, q = 1, r = 1 More on Computing Satisfaction Digital Circuits Digital Circuits Gates x y x y x y x ∧ y x ∨ y (x ∧ ¬y) ∨ (¬x ∧ y) o ⇔ (x ∧ ¬y) ∨ (¬x ∧ y) a ⇔ z ∧ o b ⇔ x ∧ y s ⇔ (o ∧ ¬z) ∨ (¬o ∧ z) c ⇔ a ∨ b Example xi = 1 yi = 0 zi = 1 ci = ?
Evaluation Example o ⇔ (x ∧ ¬y) ∨ (¬x ∧ y) a ⇔ z ∧ o b ⇔ x ∧ y s ⇔ (o ∧ ¬z) ∨ (¬o ∧ z) c ⇔ a ∨ b c ⇔ (z ∧ ((x ∧ ¬y) ∨ (¬x ∧ y))) ∨ (x ∧ y) Rewriting xi = 1 yi = 0 zi = 1 ci = ?
[(z ∧ ((x ∧ ¬y) ∨ (¬x ∧ y))) ∨ (x ∧ y)]i = ?
Evaluation Example xi = 1 yi = 0 zi = 1 ci = 1 (z ∧ ((x ∧ ¬y) ∨ (¬x ∧ y))) ∨ (x ∧ y) (1 ∧ ((1 ∧ ¬0) ∨ (¬1 ∧ 0))) ∨ (1 ∧ 0) (1 ∧ ((1 ∧ 1) ∨ ( 0 ∧ 1))) ∨ (1 ∧ 0) (1 ∧ ( 1 ∨ 0 )) ∨ 0 (1 ∧ 1 ) ∨ 0 1 ∨ 0 1 Example xi = ?
yi = ?
zi = ? ci = 1 ((z ∧ ((x ∧ ¬y) ∨ (¬x ∧ y))) ∨ (x ∧ y)) i = 1 Satisfaction Example xi = ?
yi = ?
zi = ? ci = 1 ((z ∧ ((x ∧ ¬y) ∨ (¬x ∧ y))) ∨ (x ∧ y)) i = 1 Satisfaction Example xi = 1 yi = 0 zi = 1 ci = 0 Observation: [(z ∧ ((x ∧ ¬y) ∨ (¬x ∧ y))) ∨ (x ∧ y)] i = 0 Problem: Which gate is malfunctioning?
Diagnosis Example o ⇔ (x ∧ ¬y) ∨ (¬x ∧ y) a ⇔ z ∧ o b ⇔ x ∧ y s ⇔ (o ∧ ¬z) ∨ (¬o ∧ z) c ⇔ a ∨ b Example x1 ⇒ (o ⇔ (x ∧ ¬y) ∨ (¬x ∧ y)) a1 ⇒ (a ⇔ z ∧ o) a2 ⇒ (b ⇔ x ∧ y) x2 ⇒ (s ⇔ (o ∧ ¬z) ∨ (¬o ∧ z)) o1 ⇒ (c ⇔ a ∨ b) NB: x1 means that gate x1 is functioning correctly Gate Rules x1 x2 a2 a1 o1 ¬x1 ⇒ x2 ∧ a1 ∧ a2 ∧ o1 ¬x2 ⇒ x1 ∧ a1 ∧ a2 ∧ o1 ¬a1 ⇒ x1 ∧ x2 ∧ a2 ∧ o1 ¬a2 ⇒ x1 ∧ x2 ∧ a1 ∧ o1 ¬o1 ⇒ x1 ∧ x2 ∧ a1 ∧ a2 Single Fault Assumption x1 x2 a2 a1 o1 NB: If a gate is broken, the other gates must be working.
xi = ?
yi = ?
zi = ? ci = ?
Problem: How many inputs must one try to determine whether there is a faulty gate? Hint: fewer than 8.
Testing Example Evaluation, Satisfaction, Diagnosis, Testing Graphical design and simulation Digital Circuits Extras The Big Game Stanford people always tell the truth, and Berkeley people always lie. Unfortunately, by looking at a person, you cannot tell whether he is from Stanford or Berkeley.
You come to a fork in the road and want to get to the football stadium down one fork. However, you do not know which to take. There is a person standing there. What single question can you ask him to help you decide which fork to take?
The Big Game left su Question Response T T T F F T F F Basic Idea left su Question Response T T T F F T F F Desired Response "T" "T" "F" "F" left su Question Response T T T F F T F F Desired Response "T" "T" "F" "F" T F F T Question: The left road is the way to the stadium if and only if you are from Stanford. Is that correct?
left ⇔su The Big Game (solved) Let's Be Careful Out There |
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Statistics
1.3 Frequency, Frequency Tables, and Levels of Measurement
Statistics
1.3
Frequency, Frequency Tables, and Levels of Measurement
Search for key terms or text.
Once you have a set of data, you will need to organize it so that you can analyze how frequently each datum occurs in the set. However, when calculating the frequency, you may need to round your answers so that they are as precise as possible.
Answers and Rounding Off
A simple way to round off answers is to carry your final answer one more decimal place than was present in the original data. Round off only the final answer. Do not round off any intermediate results, if possible. If it becomes necessary to round off intermediate results, carry them to at least twice as many decimal places as the final answer. Expect that some of your answers will vary from the text due to rounding errors.
It is not necessary to reduce most fractions in this course. Especially in Probability Topics, the chapter on probability, it is more helpful to leave an answer as an unreduced fraction.
Levels of Measurement
The way a set of data is measured is called its level of measurement. Correct statistical procedures depend on a researcher being familiar with levels of measurement. Not every statistical operation can be used with every set of data. Data can be classified into four levels of measurement. They are as follows (from lowest to highest level):
Nominal scale level
Ordinal scale level
Interval scale level
Ratio scale level
Data that is measured using a nominal scale is qualitative (categorical). Categories, colors, names, labels, and favorite foods along with yes or no responses are examples of nominal level data. Nominal scale data are not ordered. For example, trying to classify people according to their favorite food does not make any sense. Putting pizza first and sushi second is not meaningful.
Smartphone companies are another example of nominal scale data. The data are the names of the companies that make smartphones, but there is no agreed upon order of these brands, even though people may have personal preferences. Nominal scale data cannot be used in calculations.
Data that is measured using an ordinal scale is similar to nominal scale data but there is a big difference. The ordinal scale data can be ordered. An example of ordinal scale data is a list of the top five national parks in the United States. The top five national parks in the United States can be ranked from one to five but we cannot measure differences between the data.
Another example of using the ordinal scale is a cruise survey where the responses to questions about the cruise are excellent, good, satisfactory, and unsatisfactory. These responses are ordered from the most desired response to the least desired. But the differences between two pieces of data cannot be measured. Like the nominal scale data, ordinal scale data cannot be used in calculations.
Data that is measured using the interval scale is similar to ordinal level data because it has a definite ordering but there is a difference between data. The differences between interval scale data can be measured though the data does not have a starting point.
Temperature scales like Celsius (C) and Fahrenheit (F) are measured by using the interval scale. In both temperature measurements, 40° is equal to 100° minus 60°. Differences make sense. But 0 degrees does not because, in both scales, 0 is not the absolute lowest temperature. Temperatures like –10 °F and –15 °C exist and are colder than 0.
Interval level data can be used in calculations, but one type of comparison cannot be done. 80 °C is not four times as hot as 20 °C (nor is 80 °F four times as hot as 20 °F). There is no meaning to the ratio of 80 to 20 (or four to one).
Data that is measured using the ratio scale takes care of the ratio problem and gives you the most information. Ratio scale data is like interval scale data, but it has a 0 point and ratios can be calculated. For example, four multiple choice statistics final exam scores are 80, 68, 20 and 92 (out of a possible 100 points). The exams are machine-graded.
The data can be put in order from lowest to highest 20, 68, 80, 92.
The differences between the data have meaning. The score 92 is more than the score 68 by 24 points.
Ratios can be calculated. The smallest score is 0. So 80 is four times 20. The score of 80 is four times better than the score of 20.
Frequency
Twenty students were asked how many hours they worked per day. Their responses, in hours, are as follows: 5, 6, 3, 3, 2, 4, 7, 5, 2, 3, 5, 6, 5, 4, 4, 3, 5, 2, 5, 3.
Table 1.12 lists the different data values in ascending order and their frequencies.
| DATA VALUE | FREQUENCY |
--- |
| 2 | 3 |
| 3 | 5 |
| 4 | 3 |
| 5 | 6 |
| 6 | 2 |
| 7 | 1 |
Table
1.12
Frequency Table of Student Work Hours
A frequency is the number of times a value of the data occurs. According to Table 1.12, there are three students who work two hours, five students who work three hours, and so on. The sum of the values in the frequency column, 20, represents the total number of students included in the sample.
A relative frequency is the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes. To find the relative frequencies, divide each frequency by the total number of students in the sample, in this case, 20. Relative frequencies can be written as fractions, percents, or decimals.
| DATA VALUE | FREQUENCY | RELATIVE FREQUENCY |
---
| 2 | 3 | 320 or .15 |
| 3 | 5 | 520 or .25 |
| 4 | 3 | 320 or .15 |
| 5 | 6 | 620 or .30 |
| 6 | 2 | 220 or .10 |
| 7 | 1 | 120 or .05 |
Table
1.13
Frequency Table of Student Work Hours with Relative Frequencies
The sum of the values in the relative frequency column of Table 1.13 is 2020
, or 1.
Cumulative relative frequency is the accumulation of the previous relative
frequencies. To find the cumulative relative frequencies, add all the previous relative frequencies to
the relative frequency for the current row, as shown in Table 1.14.
In the first row, the cumulative frequency is simply .15 because it is the only one. In the second row, the relative frequency was .25, so adding that to .15, we get a relative frequency of .40. Continue adding the relative frequencies in each row to get the rest of the column.
| DATA VALUE | FREQUENCY | RELATIVE FREQUENCY | CUMULATIVE RELATIVE FREQUENCY |
--- --- |
| 2 | 3 | 320 or .15 | .15 |
| 3 | 5 | 520 or .25 | .15 + .25 = .40 |
| 4 | 3 | 320 or .15 | .40 + .15 = .55 |
| 5 | 6 | 620 or .30 | .55 + .30 = .85 |
| 6 | 2 | 220 or .10 | .85 + .10 = .95 |
| 7 | 1 | 120 or .05 | .95 + .05 = 1.00 |
Table
1.14
Frequency Table of Student Work Hours with Relative and Cumulative Relative Frequencies
The last entry of the cumulative relative frequency column is one, indicating that one hundred percent of the data has been accumulated.
NOTE
Because of rounding, the relative frequency column may not always sum to one, and the last entry in the cumulative relative frequency column may not be one. However, they each should be close to one.
The following data are the heights (in inches to the nearest half inch) of 100 male semiprofessional soccer players. The heights are continuous data since height is measured.
60, 60.5, 61, 61, 61.5,
63.5, 63.5, 63.5,
64, 64, 64, 64, 64, 64, 64, 64.5, 64.5, 64.5, 64.5, 64.5, 64.5, 64.5, 64.5,
66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 66.5, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67, 67.5, 67.5, 67.5, 67.5, 67.5, 67.5, 67.5,
68, 68, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69, 69.5, 69.5, 69.5, 69.5, 69.5,
70, 70, 70, 70, 70, 70, 70.5, 70.5, 70.5, 71, 71, 71,
72, 72, 72, 72.5, 72.5, 73, 73.5,
74
Table 1.15 summarizes the heights in this sample. Since heights are expressed in tenths, the frequency table will use labels measured in hundredths. This ensures that no data value will coincide with the upper or lower limit of an interval.
| HEIGHTS (INCHES) | FREQUENCY | RELATIVE FREQUENCY | CUMULATIVE RELATIVE FREQUENCY |
--- --- |
| 59.95–61.95 | 5 | 5100 = .05 | .05 |
| 61.95–63.95 | 3 | 3100 = .03 | .05 + .03 = .08 |
| 63.95–65.95 | 15 | 15100 = .15 | .08 + .15 = .23 |
| 65.95–67.95 | 40 | 40100 = .40 | .23 + .40 = .63 |
| 67.95–69.95 | 17 | 17100 = .17 | .63 + .17 = .80 |
| 69.95–71.95 | 12 | 12100 = .12 | .80 + .12 = .92 |
| 71.95–73.95 | 7 | 7100 = .07 | .92 + .07 = .99 |
| 73.95–75.95 | 1 | 1100 = .01 | .99 + .01 = 1.00 |
| | Total = 100 | Total = 1.00 | |
Table
1.15
Frequency Table of Soccer Player Height
The data in this table have been grouped into the following intervals:
59.95–61.95 inches
61.95–63.95 inches
63.95–65.95 inches
65.95–67.95 inches
67.95–69.95 inches
69.95–71.95 inches
71.95–73.95 inches
73.95–75.95 inches
Note
This example is used again in Descriptive Statistics, where the method used to compute the intervals will be explained.
In this sample, there are five players whose heights fall within the interval 59.95–61.95 inches, three players whose heights fall within the interval 61.95–63.95 inches, 15 players whose heights fall within the interval 63.95–65.95 inches, 40 players whose heights fall within the interval 65.95–67.95 inches, 17 players whose heights fall within the interval 67.95–69.95 inches, 12 players whose heights fall within the interval 69.95–71.95, seven players whose heights fall within the interval 71.95–73.95, and one player whose heights fall within the interval 73.95–75.95. All heights fall between the endpoints of an interval and not at the endpoints.
Example 1.15
Problem
From Table 1.15, find the percentage of heights that are less than 65.95 inches.
Solution
If you look at the first, second, and third rows, the heights are all less than 65.95 inches. There are 5 + 3 + 15 = 23 players whose heights are less than 65.95 inches. The percentage of heights less than 65.95 inches is then 23100 or 23 percent. This percentage is the cumulative relative frequency entry in the third row.
Try It 1.15
Table 1.16 shows the amount, in inches, of annual rainfall in a sample of towns.
| Rainfall (Inches) | Frequency | Relative Frequency | Cumulative Relative Frequency |
--- --- |
| 2.95–4.97 | 6 | 650 = .12 | .12 |
| 4.97–6.99 | 7 | 750 = .14 | .12 + .14 = .26 |
| 6.99–9.01 | 15 | 1550 = .30 | .26 + .30 = .56 |
| 9.01–11.03 | 8 | 850 = .16 | .56 + .16 = .72 |
| 11.03–13.05 | 9 | 950 = .18 | .72 + .18 = .90 |
| 13.05–15.07 | 5 | 550 = .10 | .90 + .10 = 1.00 |
| | Total = 50 | Total = 1.00 | |
Table
1.16
From Table 1.16, find the percentage of rainfall that is less than 9.01 inches.
Example 1.16
Problem
From Table 1.15, find the percentage of heights that fall between 61.95 and 65.95 inches.
Solution
Add the relative frequencies in the second and third rows: .03 + .15 = .18 or 18 percent.
Try It 1.16
From Table 1.16, find the percentage of rainfall that is between 6.99 and 13.05 inches.
Example 1.17
Problem
Use the heights of the 100 male semiprofessional soccer players in Table 1.15. Fill in the blanks and check your answers.
The percentage of heights that are from 67.95–71.95 inches is ________.
The percentage of heights that are from 67.95–73.95 inches is ________.
The percentage of heights that are more than 65.95 inches is ________.
The number of players in the sample who are between 61.95 and 71.95 inches tall is ________.
What kind of data are the heights?
Describe how you could gather this data (the heights) so that the data are characteristic of all male semiprofessional soccer players.
Remember, you count frequencies. To find the relative frequency, divide the frequency by the total number of data values. To find the cumulative relative frequency, add all of the previous relative frequencies to the relative frequency for the current row.
Solution
29 percent
36 percent
77 percent
87
quantitative continuous
get rosters from each team and choose a simple random sample from each
Try It 1.17
From Table 1.16, find the number of towns that have rainfall between 2.95 and 9.01 inches.
Collaborative Exercise
In your class, have someone conduct a survey of the number of siblings (brothers and sisters) each student has. Create a frequency table. Add to it a relative frequency column and a cumulative relative frequency column. Answer the following questions:
What percentage of the students in your class have no siblings?
What percentage of the students have from one to three siblings?
What percentage of the students have fewer than three siblings?
Example 1.18
Nineteen people were asked how many miles, to the nearest mile, they commute to work each day. The data are as follows:
2;
5;
7;
3;
2;
10;
18;
15;
20;
7;
10;
18;
5;
12;
13;
12;
4;
5;
10. Table 1.17 was produced.
| DATA | FREQUENCY | RELATIVE FREQUENCY | CUMULATIVE RELATIVE FREQUENCY |
--- --- |
| 3 | 3 | 319 | .1579 |
| 4 | 1 | 119 | .2105 |
| 5 | 3 | 319 | .1579 |
| 7 | 2 | 219 | .2632 |
| 10 | 3 | 419 | .4737 |
| 12 | 2 | 219 | .7895 |
| 13 | 1 | 119 | .8421 |
| 15 | 1 | 119 | .8948 |
| 18 | 1 | 119 | .9474 |
| 20 | 1 | 119 | 1.0000 |
Table
1.17
Frequency of Commuting Distances
Problem
Is the table correct? If it is not correct, what is wrong?
True or False: Three percent of the people surveyed commute three miles. If the statement is not correct, what should it be? If the table is incorrect, make the corrections.
What fraction of the people surveyed commute five or seven miles?
What fraction of the people surveyed commute 12 miles or more? Less than 12 miles? Between five and 13 miles (not including five and 13 miles)?
Solution
No. The frequency column sums to 18, not 19. Not all cumulative relative frequencies are correct. The table entries for data values 2, 3, 10, and 18 are incorrect. This affects cumulative relative frequency for most values.
False. The frequency for three miles should be one; for two miles (left out), two. The cumulative relative frequency column should read 1052, .1579, .2105, .3684, .4737, .6316, .7368, .7895, .8421, .9474, 1.0000.
519
719, 1219, 719
Try It 1.18
Table 1.16 represents the amount, in inches, of annual rainfall in a sample of towns. What fraction of towns surveyed get between 11.03 and 13.05 inches of rainfall each year?
Example 1.19
Table 1.18 contains the total number of deaths worldwide as a result of earthquakes for the period from 2000 to 2012.
| Year | Total Number of Deaths |
--- |
| 2000 | 231 |
| 2001 | 21,357 |
| 2002 | 11,685 |
| 2003 | 33,819 |
| 2004 | 228,802 |
| 2005 | 88,003 |
| 2006 | 6,605 |
| 2007 | 712 |
| 2008 | 88,011 |
| 2009 | 1,790 |
| 2010 | 320,120 |
| 2011 | 21,953 |
| 2012 | 768 |
| Total | 823,856 |
Table
1.18
Problem
Answer the following questions:
What is the frequency of deaths measured from 2006 through 2009?
What percentage of deaths occurred after 2009?
What is the relative frequency of deaths that occurred in 2003 or earlier?
What is the percentage of deaths that occurred in 2004?
What kind of data are the numbers of deaths?
The Richter scale is used to quantify the energy produced by an earthquake. Examples of Richter scale numbers are 2.3, 4.0, 6.1, and 7.0. What kind of data are these numbers?
Solution
97,118 (11.8 percent)
41.6 percent
67,092/823,356 or 0.081 or 8.1 percent
27.8 percent
quantitative discrete
quantitative continuous
Try It 1.19
Table 1.19 contains the total number of fatal motor vehicle traffic crashes in the United States for the period from 1994–2011.
| Year | Total Number of Crashes | Year | Total Number of Crashes |
--- --- |
| 1994 | 36,254 | 2004 | 38,444 |
| 1995 | 37,241 | 2005 | 39,252 |
| 1996 | 37,494 | 2006 | 38,648 |
| 1997 | 37,324 | 2007 | 37,435 |
| 1998 | 37,107 | 2008 | 34,172 |
| 1999 | 37,140 | 2009 | 30,862 |
| 2000 | 37,526 | 2010 | 30,296 |
| 2001 | 37,862 | 2011 | 29,757 |
| 2002 | 38,491 | Total | 653,782 |
| 2003 | 38,477 | | |
Table
1.19
Answer the following questions:
What is the frequency of deaths measured from 2000 through 2004?
What percentage of deaths occurred after 2006?
What is the relative frequency of deaths that occurred in 2000 or before?
What is the percentage of deaths that occurred in 2011?
What is the cumulative relative frequency for 2006? Explain what this number tells you about the data.
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Authors: Barbara Illowsky, Susan Dean
Publisher/website: OpenStax
Book title: Statistics
Publication date: Mar 27, 2020
Location: Houston, Texas
Book URL:
Section URL:
© Oct 10, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo
are not subject to the Creative Commons license and may not be reproduced without the prior and express written
consent of Rice University. |
13420 | http://www.as.utexas.edu/astronomy/education/fall10/lacy/secure/class02.pdf | AST 301 Introduction to Astronomy John Lacy RLM 16.332 471-1469 lacy@astro.as.utexas.edu Bohua Li RLM 16.212 471-8443 bohuali@astro.as.utexas.edu Myoungwon Jeon RLM 16.216 471-0445 myjeon@astro.as.utexas.edu Watch Venus and Mars move in the sky For the next week or two you can watch Venus and Mars move relative to Spica.
Find a place you can go at about 8:30 PM where no buildings block your view to the west.
Go there at least 3 times in the next 2 weeks.
Sketch the positions of Venus, Mars, and Spica, as well as some landmarks on the horizon.
Write down the date and time, your location, the weather, and the names of any companions.
This assignment is due Friday, Sep. 10.
How long would it take you to walk to the Sun?
The Sun is about 150,000,000 km from the Earth.
If you can walk 40 km in a day, it would take you 150,000,000 / 40 = 3,750,000 days, or about 10,000 years to walk to the Sun (if someone built a bridge you could walk on to get there).
Let’s try running really fast.
What if you could run at the speed of light?
Light travels 300,000 km in a second.
How long would it take to go 150,000,000 km at the speed of light?
What’s the formula?
If you drive at 60 mph (miles/hour) for 10 hours you go 600 miles, or 60 mi/hr x 10 hr = 600 mi.
Or if you want to go 300 miles, it will take you 5 hours.
That is 300 mi / 60 mi/hr = 5 hr.
If you want a formula, it is distance = speed x time.
Or time = distance / speed.
Try using it with a distance of 150,000,000 km and a speed of 300,000 km/s.
Compare your answer with your neighbor’s.
Distance to the Sun in light-seconds The answer is 150,000,000 km / 300,000 km/s = 500 sec.
We sometimes give the distance to astronomical objects by the time it takes light to go that distance.
The distance to the Sun is 500 light-seconds.
This is also known as the astronomical unit or AU.
1 AU = 150,000,000 km = 500 light-seconds.
Pluto is about 40 AU from the Sun.
That’s about 20,000 light-seconds, or 5.5 light-hours.
When the New Horizons spacecraft gets there the messages it sends back will take 5.5 hours to get to us.
More distant objects The nearest star to the Sun is about 4 light years away.
That’s about 7000 times as far away as Pluto is.
We live in a huge collection of stars called the Milky Way.
It is about 100,000 light-years across.
The size of the Milky Way galaxy is about 30,000 times the distance to the nearest star.
The nearest big galaxy to the Milky Way is another factor of 30 farther away, or 1,000,000 times as far as the nearest star.
How big is the Universe?
I don’t know.
We can’t see it all.
It might be infinitely large.
The most distant object we can see is about 14,000,000,000 light-years away (or was when the light left it 14,000,000,000 years ago.
That’s more than 1,000 times as far away as the Andromeda Galaxy.
We can’t see anything more distant because the Universe has only existed for 14,000,000,000 years.
Light from more distant objects couldn’t have gotten here yet.
What should you remember?
Don’t memorize all of the numbers.
But do remember roughly how things compare in size and distance from us.
The Sun is roughly 100 times as big as the Earth.
The astronomical unit is roughly 100 times as big as the Sun.
The solar system is roughly 100 AU across.
The nearest star is more than 1000 times that far away.
The Milky Way galaxy is roughly 10,000 times as big as the distance to the nearest star, so it is more than 10,000,000 times bigger than the solar system.
And the Universe is more than 100,000 times bigger than the Milky Way.
Big numbers Numbers like 1,000,000 are hard to work with.
It is more convenient to use an abbreviation: 1,000,000 = 10 x 10 x 10 x 10 x 10 x 10 = 106 And we write 2,000,000 as 2x106 And sometimes we will write 1/106 as 10-6 We can leave numbers written this way while multiplying and dividing. For example: 2x103 x 3x102 = 2 x 10x10x10 x 3 x 10x10 = 2x3 x 10x10x10x10x10 = 6x105 2x103 / 102 = 2 x 10x10x10 / 10x10 = 2 x 10 = 2x101 = 20 The age of the Universe I gave the age of the Universe as 14,000,000,000 (14x109, or 14 billion years, or 14 Gyr).
How did I know that?
We know the age of the Earth quite well because some rocks change as they age by radioactive decay.
The Earth is about 4.5 Gyr old.
There must be stars older than this since the Earth is made of elements that were made inside of stars that lived before the Earth formed.
We can date some stars from how they change as they age, and some are at least 10 Gyr old.
The age of the Universe The determination of the age of the Universe is more difficult.
Distant galaxies are moving away from us.
From their speeds we can calculate when they were in the same place as we were.
We’ll talk more about that during the last week of classes.
The answer comes out to about 14 Gyr.
We think that was the beginning of the Universe, or at least the part of the Universe we can see.
Our motion through space We aren’t standing still.
The Earth is rotating.
An object at the equator moves 24,000 miles (the circumference of the Earth) every 24 hours, or 1000 mph.
That’s about 0.5 km/s.
In addition, the Earth is orbiting around the Sun.
Can you figure out how fast it’s going?
Use the formula speed = distance / time.
What is the distance around the Earth’s orbit?
Hint: the Earth’s orbit is nearly a circle with a radius of 1 AU, or 150x106 km.
The speed of the Earth The answer comes out to about 9x108 km.
You can do it more accurately on your homework.
We can get the Earth’s speed in km/s by dividing the distance it travels in km by the time in seconds.
There are about 3x107 seconds in a year, and the Earth travels about 9x108 km around the Sun in a year.
Speed = 9x108 km / 3x107 sec = 30 km/s.
The Sun isn’t standing still either.
It is orbiting around the center of the Milky Way at about 200 km/s.
How can the Earth go around the Sun at only 30 km/s while the Sun is moving at 200 km/s? Why doesn’t the Earth get left behind?
The speed of the Milky Way The Milky Way is moving too.
It moves relative to the nearby galaxies at a few 100 km/s.
Is it moving due to the expansion of the Universe?
How can we tell that the distant galaxies are moving away from us rather than us moving away from them?
If they are moving away from us, why are we so special?
We’ll talk more about that later.
Assignment for Monday Read Chapters 1 and 2.
If you haven’t yet, find a place where you can see the western horizon and look for Venus, Mars, and Spica.
If it is clear enough to see them, make a sketch and write down the date, time, place, weather, and names of companions. |
13421 | https://ltcconline.net/greenl/courses/105/derivatives/PRODQUOT.HTM | The Product and Quotient Rules
The Product and Quotient Rules The Product Rule Theorem (The Product Rule) Let f and g be differentiable functions. Then [f(x) g(x)] ' = f(x) g '(x) + f '(x) g(x) Proof: We have Example Find d (2 - x 2)(x 4 - 5) dx Solution: Here f(x) = 2 - x 2 and g(x) = x 4 - 5 The product rule gives d (2 - x 2)(x 4 - 5) = (2 - x 2)(4x 3) + (-2x)(x 4 - 5) dx The Quotient Rule Remember the poem "lo d hi minus hi d lo square the bottom and away you go" This poem is the mnemonic for the taking the derivative of a quotient. Theorem: d f g f ' - f g ' = dx g g 2 Example:Find y' if 2x - 1 y' = x + 1 Solution:Here f(x) = 2x - 1 and g(x) = x + 1 The quotient rule gives (x + 1)(2) - (2x - 1)(1) (x + 1)2 2x + 2 - 2x + 1 = (x + 1)2 3 = (x + 1)2 Other Derivative Sites Visual Calculus Karl's Calculus CyberCalc Derivatives Eric Weisstein's Calculus Dr. Sloan's Calculus Product Rule Problems and Solutions Quotient Rule Problems and Solutions Product Rule by Harvey Mudd Quotient Rule by Harvey Mudd Back to Math 105 Home Page e-mail Questions and Suggestions |
13422 | https://reference.wolfram.com/language/ref/Line.html | Wolfram Language & System Documentation Center
Line
See Also
Arrow
Polygon
BezierCurve
BSplineCurve
Tube
EdgeForm
Thick
Thin
InfiniteLine
ListLinePlot
Point
HilbertCurve
GeometricScene
Related Guides
Graphics Objects
Maps & Cartography
Basic Geometric Regions
Synthetic Geometry
Precollege Education
Solid Geometry
Plane Geometry
Symbolic Graphics Language
Tech Notes
Three-Dimensional Graphics Primitives
Three-Dimensional Graphics Directives
The Structure of Graphics
See Also
Arrow
Polygon
BezierCurve
BSplineCurve
Tube
EdgeForm
Thick
Thin
InfiniteLine
ListLinePlot
Point
HilbertCurve
GeometricScene
Related Guides
Graphics Objects
Maps & Cartography
Basic Geometric Regions
Synthetic Geometry
Precollege Education
Solid Geometry
Plane Geometry
Symbolic Graphics Language
Tech Notes
Three-Dimensional Graphics Primitives
Three-Dimensional Graphics Directives
The Structure of Graphics
Line[{p1,p2,…}]
represents the line segments joining a sequence for points pi.
Line[{{p11,p12,…},{p21,…},…}]
represents a collection of lines.
Details and Options
Background & Context
Examples
Basic Examples
Scope
Graphics
Specification
Styling
Coordinates
Regions
Options
VertexColors
VertexNormals
Applications
Properties & Relations
Possible Issues
Neat Examples
See Also
Tech Notes
Related Guides
Related Links
History
Cite this Page
Line ✖ Line
Line[{p1,p2,…}]
✖
Line[{p1,p2,…}]
represents the line segments joining a sequence for points pi.
Line[{{p11,p12,…},{p21,…},…}]
✖
Line[{{p11,p12,…},{p21,…},…}]
represents a collection of lines.
Details and Options
Line is also known as poly-line or line-segments.
Line can be used as a geometric region or a graphics primitive.
Line represents a piecewise linear curve where the segment from pi to pi+1 is given by .
Line can be used in Graphics and Graphics3D.
In graphics, the points pi can be Scaled, Offset, ImageScaled, and Dynamic expressions.
Graphics rendering is affected by directives such as Thickness, Dashing, JoinForm, CapForm, and color.
The following options and settings can be used in graphics:
| | VertexColors | None | vertex colors to be interpolated |
| | VertexNormals | None | effective vertex normals for shading |
Line can be used with symbolic points in GeometricScene.
Background & Context
Line is a graphics and geometry primitive that represents a geometric line segment or sequence of connected line segments (a "poly-line"). The location of a Line connecting points in -dimensional space is specified as a list argument consisting of sublists, with each sublist containing Cartesian coordinate values. The coordinate sublists of Line objects may consist of exact or approximate values, where RegionEmbeddingDimension can be used to determine the dimension for a given Line expression. A collection of lines (or poly-lines) may be represented as a nested lists of -tuples inside a single Line primitive (a "multiline"). The coordinates of Line objects may have exact or approximate values.
Line objects can be visually formatted in two and three dimensions using Graphics and Graphics3D, respectively. Line objects can also be used in geographical maps using GeoGraphics and GeoPosition (e.g. GeoGraphics[Line[GeoPosition[{{38.9,-77.0},{40.1,-88.3}}]]]). In addition, Line may serve as a region specification over which a computation should be performed.
While lines themselves have dimension 1 (as reported by the RegionDimension function) with zero thickness, Line objects in formatted graphics expressions are by default styled to appear "thicker" than a one-dimensional mathematical line. Furthermore, in graphical visualizations, lines are displayed at the same size regardless of varying distances from the view point. The appearance of Line objects in graphics can be modified by specifying thickness directives such as Thickness, AbsoluteThickness, Thick, and Thin; dashing directives such as Dashing, AbsoluteDashing, Dashed, Dotted, and DotDashed; edge and cap directives EdgeForm and CapForm; color directives such as Red; the transparency directive Opacity; and the style option Antialiasing. In addition, the colors of multilines may be specified using VertexColors, while the shading and simulated lighting of multilines within Graphics3D may be specified using VertexNormals.
GeometricTransformation and more specific transformation functions such as Translate and Rotate can be used to change the coordinates at which a Line object is displayed while leaving the underlying Line expression untouched.
Other graphics primitives such as Tube, Arrow, HalfLine, and InfiniteLine may resemble those of stylized Line objects. While poly-lines consist only of straight line segments, smooth curves may be constructed via splines using BSplineCurve or BezierCurve or via an interpolating function using Interpolation. A function related to Line as a geometric region is Interval, which interprets pairs of numbers as endpoints of a line segment lying on the number line and which can be directly operated on using arithmetic and relational operators.
While the Line primitive explicitly appears in graphics and geometric region specification expressions, it should be noted that coordinates are commonly represented as bare lists in other contexts in the Wolfram Language. However, a number of graphics functions including Plot, ParametricPlot, ParametricPlot3D, and ContourPlot return graphical expressions that explicitly include Line objects.
Examples
open all
close all
Basic Examples (4)Summary of the most common use cases
A line primitive:
In:=1
✖
Out=1
In:=2
✖
Out=2
Differently styled 2D lines:
In:=1
✖
In:=2
✖
Out=2
Differently styled 3D lines:
In:=1
✖
In:=2
✖
Out=2
Compute the ArcLength of a line:
In:=1
✖
Out=1
Centroid:
In:=2
✖
Out=2
Scope (24)Survey of the scope of standard use cases
Graphics (14)
Specification (3)
Single line segment:
In:=2
✖
Out=2
Multiple connected line segments:
In:=1
✖
Out=1
Multiple disconnected line segments:
In:=1
✖
In:=2
✖
Out=2
Styling (8)
Lines with different thicknesses:
In:=3
✖
Out=3
In:=4
✖
Out=4
Thickness in scaled size:
In:=1
✖
Out=1
Thickness in printer's points:
In:=2
✖
Out=2
Dashed lines:
In:=1
✖
Out=1
In:=2
✖
Out=2
Colored lines:
In:=1
✖
Out=1
Line caps can be specified using CapForm:
In:=1
✖
Out=1
In:=2
✖
Out=2
Joining of line segments can be specified using JoinForm:
In:=1
✖
Out=1
In:=2
✖
Out=2
Colors can be specified at vertices using VertexColors:
In:=1
✖
Out=1
In:=2
✖
Out=2
Normals can be specified at vertices using VertexNormals for 3D lines:
In:=1
✖
Out=1
Coordinates (3)
Use Scaled coordinates:
In:=1
✖
Out=1
In:=2
✖
Out=2
Use ImageScaled coordinates in 2D:
In:=1
✖
Out=1
Use Offset coordinates in 2D:
In:=1
✖
Out=1
Regions (10)
Embedding dimension is the dimension of the space in which the line lives:
In:=1
✖
Out=1
In:=2
✖
Out=2
Geometric dimension:
In:=3
✖
Out=3
In:=4
✖
Out=4
Point membership test:
In:=1
✖
In:=2
✖
Out=2
Get conditions for point membership:
In:=3
✖
Out=3
Length:
In:=1
✖
In:=2
✖
Out=2
Centroid:
In:=3
✖
Out=3
In:=4
✖
Out=4
Distance to a line:
In:=1
✖
In:=2
✖
Out=2
Visualize it:
In:=3
✖
Out=3
Signed distance from a line segment:
In:=1
✖
In:=2
✖
Out=2
Signed distance to a line segment:
In:=3
✖
Out=3
Nearest point in the region:
In:=1
✖
In:=2
✖
Out=2
Nearest points:
In:=3
✖
In:=4
✖
Out=4
A line segment is bounded:
In:=1
✖
In:=2
✖
Out=2
Get its range:
In:=3
✖
Out=3
In:=4
✖
Out=4
Integrate over a polygonal curve:
In:=1
✖
In:=2
✖
Out=2
Optimize over a polygonal curve:
In:=1
✖
In:=2
✖
Out=2
Solve equations in a polygonal curve:
In:=1
✖
In:=2
✖
Out=2
In:=3
✖
Out=3
Options (3)Common values & functionality for each option
VertexColors (2)
Line with vertex colors:
In:=1
✖
Out=1
Specify vertex colors for 3D lines:
In:=1
✖
Out=1
VertexNormals (1)
Specify vertex normals for 3D lines:
In:=1
✖
Out=1
Applications (6)Sample problems that can be solved with this function
Complete graph with 11 nodes:
In:=1
✖
In:=2
✖
Out=2
The tangent bundle for a quadratic curve:
In:=1
✖
In:=2
✖
In:=3
✖
Out=3
A vector field:
In:=1
✖
Out=1
2D random walk on a regular lattice:
In:=1
✖
Out=1
3D random walk on a regular lattice:
In:=2
✖
Out=2
Replace Polygon with Line to have special rendering effects:
In:=1
✖
In:=2
✖
Out=2
In:=3
✖
Out=3
Use a random collection of light sources:
In:=4
✖
In:=5
✖
Out=5
In:=6
✖
Out=6
Use lines to estimate the length of a curve:
In:=1
✖
In:=2
✖
In:=3
✖
In:=4
✖
Out=4
In:=5
✖
Out=5
In:=6
✖
Out=6
Increase the number of line segments for a better estimate:
In:=7
✖
Out=7
Properties & Relations (4)Properties of the function, and connections to other functions
Several visualization functions produce Line objects:
In:=1
✖
In:=2
✖
Out=2
Use directive styles appropriate for lines:
In:=3
✖
Out=3
You can also transform the output:
In:=4
✖
Out=4
The same idea applies in 3D:
In:=1
✖
Out=1
This shows the points at which it was sampled:
In:=2
✖
Out=2
ImplicitRegion can be used to represent any Line region:
In:=1
✖
In:=2
✖
Out=2
ParametricRegion can be used to represent any Line region:
In:=1
✖
In:=2
✖
Out=2
Possible Issues (1)Common pitfalls and unexpected behavior
Line objects need to be specified using numbers that can be represented by machine numbers:
In:=1
✖
Out=1
In:=2
✖
Out=2
Neat Examples (4)Surprising or curious use cases
A random collection of lines:
In:=1
✖
Out=1
In:=2
✖
Out=2
Lines with lighting:
In:=1
✖
Out=1
Moiré pattern:
In:=1
✖
Out=1
Tangent vectors along an elliptic curve:
In:=1
✖
Out=1
Wolfram Research (1988), Line, Wolfram Language function, (updated 2014).
✖
Wolfram Research (1988), Line, Wolfram Language function, (updated 2014).
Text
Wolfram Research (1988), Line, Wolfram Language function, (updated 2014).
✖
Wolfram Research (1988), Line, Wolfram Language function, (updated 2014).
CMS
Wolfram Language. 1988. "Line." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014.
✖
Wolfram Language. 1988. "Line." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014.
APA
Wolfram Language. (1988). Line. Wolfram Language & System Documentation Center. Retrieved from
✖
Wolfram Language. (1988). Line. Wolfram Language & System Documentation Center. Retrieved from
BibTeX
@misc{reference.wolfram_2025_line, author="Wolfram Research", title="{Line}", year="2014", howpublished="\url{ note=[Accessed: 28-September-2025]}
✖
@misc{reference.wolfram_2025_line, author="Wolfram Research", title="{Line}", year="2014", howpublished="\url{ note=[Accessed: 28-September-2025]}
BibLaTeX
@online{reference.wolfram_2025_line, organization={Wolfram Research}, title={Line}, year={2014}, url={ note=[Accessed: 28-September-2025]}
✖
@online{reference.wolfram_2025_line, organization={Wolfram Research}, title={Line}, year={2014}, url={ note=[Accessed: 28-September-2025]}
Find out if you already have access to Wolfram tech through your organization |
13423 | https://stackoverflow.com/questions/21896562/recursive-sequence-x-n-sqrt2-x-n1-sqrt2x-n | python - Recursive sequence $x_n = \sqrt{2}$, $x_{n+1} = \sqrt{2x_n}$ - Stack Overflow
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Recursive sequence $x_n = \sqrt{2}$, $x_{n+1} = \sqrt{2x_n}$ [closed]
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How would I create a script it in python late the values from the recursive sequence:
$x_1 = \sqrt{2}$, $x_{n+1} = \sqrt{2x_n}$
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edited Feb 20, 2014 at 2:05
unutbu
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you mean x_0=sqrt(2)?ysakamoto –ysakamoto 2014-02-20 02:02:18 +00:00 Commented Feb 20, 2014 at 2:02
Why is my latex not formatting?spitfiredd –spitfiredd 2014-02-20 02:03:06 +00:00 Commented Feb 20, 2014 at 2:03
It should be $x_1 = sqrt{2}$spitfiredd –spitfiredd 2014-02-20 02:04:47 +00:00 Commented Feb 20, 2014 at 2:04
Unlike math.stackexchange.com, SO does not render latex. I pasted an image using sciweavers.org/free-online-latex-equation-editor.unutbu –unutbu 2014-02-20 02:06:52 +00:00 Commented Feb 20, 2014 at 2:06
3 This question is basic enough that you should probably just go through the Python tutorial. As it is, it's too close to "write me the code".user2357112 –user2357112 2014-02-20 02:10:19 +00:00 Commented Feb 20, 2014 at 2:10
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python
X = [sqrt(2)]
for i in range(1,10):
X.append(sqrt(2X[i-1]))
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answered Feb 20, 2014 at 2:08
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colcarroll
colcarrollOver a year ago
Depending on the use, you might want a generator: x = sqrt(2); while True: yield x; x = sqrt(2 x);
2014-02-20T04:21:23.193Z+00:00
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Here is a slow solution. Assuming n is >=1
python
import math
def recursive(n):
if n = 1:
math.sqrt(2)
return math.sqrt(2recursive(n-1))
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answered Feb 20, 2014 at 2:11
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Systematic Sampling
Systematic sampling is a probability sampling method where researchers select every nth item from a population. This sampling technique creates a systematic pattern for choosing participants or data points. Unlike simple random sampling, systematic sampling follows a structured approach that ensures equal intervals between selections.
The systematic sampling definition involves dividing the total population by the desired sample size. This calculation determines the sampling interval, also called the skip interval. For example, if you need 100 participants from a population of 1,000, you would select every 10th person.
Table of contents
What is Systematic Sampling?
Example Calculation
Basic Formula
Key Features of Systematic Sampling
Systematic Sampling vs. Other Sampling Methods
How to Conduct Systematic Sampling?
Systematic Sampling Example
Another Example: Quality Control
Advantages of Systematic Sampling
Disadvantages of Systematic Sampling
When to Use Systematic Sampling
Systematic Sampling Formula
Real-World Applications of Systematic Sampling
Tips for Effective Systematic Sampling
Common Misconceptions About Systematic Sampling
Final Words
Frequently Asked Questions (FAQs)
Related Articles
What is Systematic Sampling?
Systematic sampling is a probability sampling technique. It involves selecting every kth element from a list. The process starts with a random selection. Then, it follows a fixed interval. This interval, called the sampling interval, ensures uniformity.
For instance, imagine a list of 1000 customers. You want a sample of 100. Divide 1000 by 100 to get a sampling interval of 10. Start with a random number, say 5. Then, select every 10th customer (5, 15, 25, etc.). This is a systematic random sample.
This method is straightforward. It reduces bias compared to non-probability methods. It’s ideal for large populations. Researchers use it in surveys, quality control, and market research.
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Example Calculation
Population size: 800 students
Desired sample: 80 students
Sampling interval: 800 ÷ 80 = 10 Random start: 4 (randomly chosen between 1-10)
Selected students: 4, 14, 24, 34, 44… up to 794
Basic Formula
k = N/n
Where:
k = sampling interval
N = population size
n = desired sample size
Key Features of Systematic Sampling
Structured Selection: Samples are chosen at regular intervals.
Random Start: The first element is randomly selected.
Efficiency: It’s faster than simple random sampling.
Uniform Coverage: Ensures even distribution across the population.
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Systematic Sampling vs. Other Sampling Methods
Systematic sampling differs from other techniques. Let’s compare it with cluster and stratified sampling.
Systematic Sampling vs. Cluster Sampling
Cluster sampling divides a population into groups. These groups, or clusters, are randomly selected. All elements within chosen clusters are studied. For example, a researcher might select entire schools as clusters. This differs from systematic sampling, which selects individuals at intervals.
Cluster sampling is useful for geographically spread populations. It reduces travel costs for researchers. However, it may introduce bias if clusters aren’t diverse. Systematic sampling, conversely, ensures even representation. It’s better for uniform populations.
Systematic Sampling vs. Stratified Sampling
Stratified sampling divides the population into subgroups. These subgroups, or strata, share similar characteristics. Random samples are taken from each stratum. For instance, a survey might group people by age. Then, it randomly selects from each age group.
Systematic sampling doesn’t use subgroups. It treats the population as a whole. Stratified sampling ensures representation of specific groups. Systematic sampling is simpler but may miss subgroup nuances.
Systematic Sampling vs. Simple Random Sampling
Simple random sampling selects elements purely by chance. Every individual has an equal chance of selection. Systematic sampling, however, uses a fixed interval. This makes it less random but more structured. Systematic sampling is faster for large datasets. Simple random sampling can be time-consuming.
Also Read: What is Random Sampling?
How to Conduct Systematic Sampling?
Conducting systematic sampling is straightforward. Follow these steps for accurate results.
Step 1: Define the Population
Identify the entire population to study. For example, a company’s employee list. Ensure the population is well-defined and accessible.
Step 2: Determine Sample Size
Decide how many samples you need. A larger sample increases accuracy. Use statistical tools to calculate the ideal size.
Step 3: Calculate the Sampling Interval
Divide the population size by the sample size. This gives the sampling interval (k). For a population of 500 and a sample of 50, k = 10.
Step 4: Choose a Random Starting Point
Select a random number between 1 and k. This ensures the process remains unbiased. Use a random number generator for fairness.
Step 5: Select Samples
Start with the random number. Then, select every kth element. Continue until you reach the desired sample size.
Step 6: Analyze the Data
Collect data from the selected samples. Analyze it using statistical methods. Ensure the results are representative of the population.
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Systematic Sampling Example
Let’s explore a real-world systematic sampling example. A supermarket wants to survey 200 customers. The store has 2000 customers on its loyalty list. Here’s how they proceed:
Population Size: 2000 customers.
Sample Size: 200 customers.
Sampling Interval: 2000 ÷ 200 = 10.
Random Start: Choose a random number, say 7.
Selection: Select customers 7, 17, 27, 37, and so on.
The supermarket surveys these customers. The method ensures even representation. It’s efficient and cost-effective.
Another Example: Quality Control
A factory produces 10,000 widgets daily. They want to inspect 500 for quality. Using systematic sampling, they calculate a sampling interval of 20. Starting at widget 12, they inspect every 20th widget. This ensures consistent quality checks.
Advantages of Systematic Sampling
Systematic sampling offers several benefits. Here’s why researchers prefer it:
Simplicity: Easy to implement with a clear process.
Time-Saving: Faster than simple random sampling.
Even Distribution: Reduces clustering of samples.
Cost-Effective: Requires fewer resources for large populations.
Also Read: What is Cluster Analysis?
Disadvantages of Systematic Sampling
Despite its strengths, systematic sampling has limitations. Consider these before using it:
Periodicity Bias: If the population has a pattern, bias may occur. For example, if every 10th item is defective, the sample may miss or overrepresent defects.
Requires a List: Needs a complete population list, which isn’t always available.
Less Flexibility: Fixed intervals limit adjustments during sampling.
When to Use Systematic Sampling
Systematic sampling works best in specific scenarios. Use it when:
The population is large and uniform.
A complete list of the population is available.
There’s no hidden pattern in the data.
Time and resources are limited.
It’s ideal for surveys, quality control, and market research. Avoid it if the population has periodic patterns.
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Systematic Sampling Formula
The systematic sampling formula is simple. It calculates the sampling interval (k):
k = Population Size ÷ Sample Size
For example, a population of 1000 and a sample of 100 gives k = 10. This formula ensures consistent intervals.
Real-World Applications of Systematic Sampling
Systematic sampling is versatile. It’s used in various fields:
Market Research: Companies survey customers to understand preferences.
Quality Control: Factories inspect products at regular intervals.
Public Health: Researchers study disease prevalence in populations.
Education: Schools assess student performance using systematic samples.
These applications highlight its efficiency. It’s a go-to method for large-scale studies.
Tips for Effective Systematic Sampling
Maximize accuracy with these tips:
Randomize the Start: Always use a random starting point.
Check for Patterns: Ensure the population has no hidden cycles.
Use a Complete List: Verify the population list is accurate.
Validate Sample Size: Ensure the sample size suits the study’s goals.
Common Misconceptions About Systematic Sampling
Some myths surround systematic sampling. Let’s debunk them:
It’s the Same as Random Sampling: It’s structured, not purely random.
It’s Always Unbiased: Periodic patterns can introduce bias.
It’s Complicated: It’s actually simpler than stratified sampling.
Understanding these clears confusion. It helps researchers choose the right method.
Final Words
Systematic sampling provides researchers with a practical, cost-effective method for selecting representative samples. This sampling technique balances simplicity with statistical validity, making it valuable across numerous research applications.
The systematic sampling method offers clear advantages in terms of implementation ease and resource efficiency. However, researchers must carefully consider population characteristics and potential biases before choosing this approach.
Understanding systematic sampling enables better research design and more reliable results. Whether you’re conducting market research, academic studies, or quality control assessments, this method can provide the structured approach you need.
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Frequently Asked Questions (FAQs)
What is systematic sampling?
Systematic sampling is a probability sampling method where researchers select every nth item from a population using a predetermined interval.
How do you calculate the sampling interval?
The sampling interval equals the population size divided by the desired sample size (k = N/n).
What’s the difference between systematic and random sampling?
Systematic sampling follows a structured pattern, while random sampling selects items without any predetermined order.
When should you avoid systematic sampling?
Avoid systematic sampling when the population has periodic patterns that match your sampling interval.
Is systematic sampling better than stratified sampling?
It depends on your research goals. Systematic sampling is simpler, while stratified sampling provides better subgroup representation.
Can systematic sampling introduce bias?
Yes, if the population has underlying patterns that align with the sampling interval, bias can occur.
What’s the minimum sample size for systematic sampling?
There’s no universal minimum, but ensure your sample size is large enough to meet your statistical requirements.
How do you handle missing participants in systematic sampling?
Develop protocols beforehand for unavailable participants, considering whether substitutions maintain sample integrity.
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Related Articles
Random Sampling
8 Pillars of Total Productive Maintenance (TPM)
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Calculating the Surface Area of a Cone
By stridedevenvNo Comments
Introduction
Cones are not only mathematical shapes but also objects that we encounter in our daily lives. From the delicious ice cream cone to party hats and even traffic cones, understanding the surface area of a cone can have practical applications. In this blog post, we will explore the step-by-step process of calculating the surface area of a cone, providing you with a solid foundation for tackling this mathematical concept.
Understanding the Surface Area Formula
To calculate the surface area of a cone, we use the following formula:
Surface Area = π r (r + l)
In this formula, ‘r’ represents the radius of the base of the cone, and ‘l’ represents the slant height.
Now, let’s dive into the step-by-step guide for calculating the surface area of a cone.
Step 1: Measure the Radius and Height
To begin, measure the radius (r) of the base of the cone. This measurement should be taken from the center of the base to its outer edge. Next, measure the height (h) of the cone, which is the distance from the apex (top point) to the base.
Step 2: Calculate the Slant Height
The slant height (l) of a cone can be found using the Pythagorean theorem. It is the distance from the apex to a point on the circumference of the base. To calculate the slant height, use the formula:
l = √(r^2 + h^2)
Step 3: Calculate the Base Area
The base area (A) of a cone is given by the formula:
A = π r^2
Substitute the value of the radius (r) into the formula to calculate the base area.
Step 4: Calculate the Lateral Surface Area
The lateral surface area (LSA) of a cone refers to the curved surface area excluding the base. It can be calculated using the formula:
LSA = π r l
Substitute the values of the radius (r) and the slant height (l) into the formula to calculate the lateral surface area.
Step 5: Calculate the Total Surface Area
The total surface area (TSA) of a cone is the sum of the base area and the lateral surface area. Use the following formula to calculate the total surface area:
TSA = A + LSA
Substitute the values of the base area (A) and the lateral surface area (LSA) into the formula to calculate the total surface area.
Example Problem
Imagine you have a cone with a radius of 3 cm and a height of 4 cm. Our goal is to calculate the surface area of this cone using the steps outlined above.
Given Values:
Radius (r) = 3 cm
Height (h) = 4 cm
Step 1: Confirming the Given Values
We start with the radius of the base, 3 cm, and the height of the cone, 4 cm, as given.
Step 2: Calculating the Slant Height (l)
Using the Pythagorean theorem:
(l = √(r^2 + h^2) = √(3^2 + 4^2) = √(9 + 16) = √25 = 5) cm
Step 3: Calculating the Base Area (A)
Next, we calculate the base area:
(A = π r^2 = π 3^2 = 9π) cm²
Step 4: Calculating the Lateral Surface Area (LSA)
The lateral surface area is found using the formula:
(LSA = π r l = π 3 5 = 15π) cm²
Step 5: Calculating the Total Surface Area (TSA)
Finally, we calculate the total surface area by adding the base area to the lateral surface area:
(TSA = A + LSA = 9π + 15π = 24π) cm²
Therefore, the total surface area of the cone is (24π) cm², which is approximately (75.36) cm².
Real-Life Applications
Understanding the surface area of a cone has practical applications in various everyday objects. Let’s explore a few examples:
Ice Cream Cone: The surface area calculation helps determine the amount of edible material needed to cover the ice cream cone with chocolate or sprinkles.
Party Hat: Calculating the surface area of a cone can help estimate the amount of paper or fabric required to create a party hat of a specific size.
Traffic Cone: Surface area calculations are used to determine the amount of reflective material needed to ensure visibility and safety on traffic cones.
Conclusion
Calculating the surface area of a cone may seem challenging at first, but by following the step-by-step guide outlined in this blog post, you can master this mathematical concept. Understanding the surface area of a cone has real-life applications in various objects we encounter regularly. From ice cream cones to party hats and traffic cones, the ability to calculate surface area opens doors to practical problem-solving. So, embrace the process, practice your calculations, and enjoy exploring the world of cones from a mathematical perspective.
Looking for more math help? Check out our available math tutors for additional support!
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13426 | http://www.wbuthelp.com/chapter_file/401.pdf | Chapter 4 The Transform 4.1 INTRODUCTION The z-transform is a useful tool in the analysis of discrete-time signals and systems and is the discrete-time counterpart of the Laplace transform for continuous-time signals and systems. The z-transform may be used to solve constant coefficient difference equations, evaluate the response of a linear time-invariant system to a given input, and design linear filters. In this chapter, we will look at the z-transform and examine how it may be used to solve a variety of different problems. 4.2 DEFINITION OF THE Z-TRANSFORM In Chap. 2, we saw that the discrete-time Fourier transform (DTFT) of a sequence .c(n) is equal to the sum However. in order for this series to converge, it is necessary that the signal be absolutely summable. Unfortunately, many of the signals that we would like to consider are not absolutely summable and, therefore, do not have a DTFT. Some examples include x(n) = u(n) x(n) = (OS)"u(-n) x(n) = sin n q The z-transform is a generalization of the DTFT that allows one to deal with such sequences and is defined as follows: Definition: The z-transform of a discrete-time signal x(n) is defined by' where z = reJ" is a complex variable. The values of z for which the sum converges define a region in the z-plane referred to as the region o f convergence (ROC). Notationally, if x(n) has a z-transform X(z), we write The z-transform may be viewed as the DTFT of an exponentially weighted sequence. Specifically, note that with z = rejo, and we see that X(z) is the discrete-time Fourier transform of the sequence r-"x(n). Furthermore, the ROC is determined by the range of values of r for which h he reader should note that in many mathematics books, and in some engineering books, X ( z ) is defined in terms of a sum using positive powers of z. CHAP. 41 THE 2-TRANSFORM 143 Because the z-transform is a function of a complex variable, it is convenient to describe it using the complex z-plane. With z = Re(z) + jIm(z) = rejU the axes of the z-plane are the real and imaginary parts of z as illustrated in Fig. 4- 1, and the contour corresponding to Izl = 1 is a circle of unit radius referred to as the unit circle. The z-transform evaluated on the unit circle corresponds to the DTFT, ~ ( e j " ) = X ( Z ) I ~ = ~ , ~ (4.2) More specifically, evaluating X(z) at points around the unit circle, beginning at z = l(w = 0), through z = j (W = n/2), to z = - 1 ( ~ = n), we obtain the values of X(el") for 0 5 w 5 n . Note that in order for the DTFT of a signal to exist, the unit circle must be within the region of convergence of X(z). Im(z> Unit circle t Fig. 4-1. The unit circle in the complex z-plane. Many of the signals of interest in digital signal processing have z-transforms that are rational functions of z: Factoring the numerator and denominator polynomials, a rational z-transform may be expressed as follows: The roots of the numerator polynomial, Bk, are referred to as the zeros of X(z), and the roots of the denominator polynomial, ak, are referred to as the poles. The poles and zeros uniquely define the functional form of a rational z-transform to within a constant. Therefore, they provide a concise representation for X(z) that is often represented pictorially in terms of apole-zero plot in the z-plane. With a pole-zero plot, the location of each pole is indicated by an "x " and the location of each zero is indicated by an "ow, with the region of convergence indicated by shading the appropriate region of the z-plane. The region of convergence is, in general, an annulus of the form If a = 0, the ROC may also include the point z = 0, and if B = oo, the ROC may also include infinity. For a rational X(z), the region of convergence will contain no poles. Listed below are three properties of the region of convergence: 144 THE Z-TRANSFORM [CHAP. 4 1. A finite-length sequence has a z-transform with a region of convergence that includes the entire z-plane except, possibly, z = 0 and z = ca. The point z = ca will be included if x(n) = 0 for n < 0, and the point z = 0 will be included if x(n) = 0 for n > 0. 2. A right-sided sequence has a z-transform with a region of convergence that is the exterior of a circle: 3. A left-sided sequence has a z-transform with a region of convergence that is the interior of a circle: EXAMPLE 4.2.1 Let us find the z-transform of the sequence x(n) = anu(n). Using the definition of the z-transform and the geometric series given in Table 1 -I, we have with the sum converging if laz-'\ < 1. Therefore the region of convergence is the exterior of a circle defined by the set of points Izl z la. Expressing X ( z ) in terms of positive powers of z, we see that X ( z ) has a zero at z = 0 and a pole at z = a. A pole-zero diagram with the region of convergence is shown in the figure below. Note that if l a 1 < 1, the unit circle is included within the region of convergence, and the DTFT of x(n) exists. Example 4.2.1 considered the z-transform of a right-sided sequence, which led to a region of convergence that is the exterior of a circle. The following example considers the z-transform of a left-sided sequence. EXAMPLE 4.2.2 Let us find the z-transform of the sequence x(n) = -anu(-n - I). Proceeding as in the previous example. we have CHAP. 41 THE z-TRANSFORM 145 with the sum converging if lor-lzl < 1 or lzl < lal. A pole-zero diagram with the region of convergence indicated is given in the figure below. Note that if lor1 5 1, the unit circle is not included within the region of convergence, and the DTFT of x(n) does not exist. Comparing the z-transforms of the signals in Examples 4.2.1 and 4.2.2, we see that they are the same, differing only in their regions of convergence. Thus, the z-transform of a sequence is not uniquely defined until its region of convergence has been specified. EXAMPLE 4.2.3 Find the z-transform of x(n) = (f)"u(n) - 2"u(-n - l), and find another signal that has the same z-transform but a different region of convergence. Here we have a sum of two sequences. Therefore, we may find the z-transform of each sequence separately and add them together. From Example 4.2.1, we know that the z-transform of xl(n) = (i)"u(n) is and from Example 4.2.2 that the z-transform of x2(n) = -2"u(-n - 1) is Therefore, the z-transform of x(n) = xl(n) + x2(n) is with a region of convergence 5 < lzl < 2, which is the set of all points that are in the ROC of both Xl(z) and X2(z). To find another sequence that has the same z-transform, note that because X(z) is a sum of two z-transforms, each term corresponds to the z-transform of either a right-sided or a left-sided sequence, depending upon the region of convergence. Therefore, choosing the right-sided sequences for both terms, it follows that has the same z-transform as x(n), except that the region of convergence is lzl > 2. Listed in Table 4-1 are a few common z-transform pairs. With these z-transform pairs and the z-transform properties described in the following section, most z-transforms of interest may be easily evaluated. THE 2-TRANSFORM Table 4-1 Common z-lkansform Pairs [CHAP. 4 Sequence Region of Convergence 4.3 PROPERTIES Just as with the DTFT, there are a number of important and useful z-transform properties. A few of these properties are described below. Linearity As with the DTFT, the z-transform is a linear operator. Therefore, if x(n) has a z-transform X(z) with a region of convergence R,, and if y(n) has a z-transform Y (z) with a region of convergence R,,, and the ROC of w(n) will include the intersection of R, and R,, that is, R, contains R, n R, However, the region of convergence of W(z) may be larger. For example, if x(n) = u(n) and yin) = u(n - I), the ROC of X(z) and Y(z) is Izl > 1. However, the z-transform of win) = x(n) - y(n) = S(n) is the entire z-plane. Shifting Property Shifting a sequence (delaying or advancing) multiplies the z-transform by a power of z. That is to say, if x(n) has a z-transform X (z), Because shifting a sequence does not affect its absolute summability, shifting does not change the region of convergence. Therefore, the z-transforms of s(n) and x(n - no) have the same region of convergence, with the possible exception of adding or deleting the points z = 0 and z = oo. Time Reversal If x(n) has a z-transform X(z) with a region of convergence R, that is the annulus a < lzl < #I, the z-transform of the time-reversed sequence x(-n) is z x(-n) t -, ~ ( z - I ) and has a region of convergence 1 /#I -= lz 1 < I / a , which is denoted by 1 / R , CHAP. 41 THE z-TRANSFORM Multiplication by an Exponential If a sequence x(n) is multiplied by a complex exponential an, This corresponds to a scaling of the z-plane. If the region of convergence of X(z) is r- < lzl < r,, which will be denoted by R,, the region of convergence of ~ ( a - ' z ) is lair- < IzI < lair+, which is denoted by lalR,. As a special case, note that if x(n) is multiplied by a complex exponential. eJnwcl, which corresponds to a rotation of the z-plane. Convolution Theorem Perhaps the most important z-transform property is the convolution theorem, which states that convolution in the time domain is mapped into multiplication in the frequency domain, that is, y(n) = x(n) h(n) Y(z) = X(z)H(z) The region of convergence of Y(z) includes the intersection of R, and R,, R, contains R, f' R , However, the region of convergence of Y(z) may be larger, if there is a pole-zero cancellation in the product X(z)H(z). EXAMPLE 4.3.1 Consider the two sequences The z-transform of x(n) is 1 X(z) = - 1 -azrl IzI > la1 and the z-transform of h(n) is H(z) = 1 - az-' 0 < l z l However. the z-transform of the convolution of x(n) with h(n) is which, due to a pole-zrro cancellation, has a region of convergence that is the entire z-plane. Conjugation If X(z) is the z-transform of x(n), the z-transform of the complex con.jugate of x(n) is x(n) .Z. x(z) As a corollary, note that if x(n) is real-valued, x(n) = x(n), then X(z) = X(Z) 148 THE Z-TRANSFORM [CHAP. 4 Derivative If X(z) is the z-transform of x(n), the z-transform of nx(n) is Repeated application of this property allows for the evaluation of the z-transform of nkx(n) for any integer k. These properties are summarized in Table 4-2. As illustrated in the following example, these properties are useful in simplifying the evaluation of z-transforms. Table 4-2 Properties of the z-Transform Linearity Shift Time reversal Exponentiation Convolution Conjugation Derivative z-Transform Region of Convergence aX(z) + hY(z) Contains R, n R, z-""x(z) Rx X(z-I) 1/Rx X(a-lz) law, x(z)y(z) Contains R, n R, Nore: Given the z-transforms X(z) and Y ( z ) of x ( n ) and y(n). with regions of convergence R, and R y , respectively, this table lists the z-transforms of sequences that are formed from x(n) and y(n). EXAMPLE 4.3.2 Let us find the z-transform of x(n) = nal'u(-n). To find X(z), we will use the time-reversal and derivative properties. First, as we saw in Example 4.2.1, Therefore. and, using the time-reversal property, 1 anu(-n) A - I - a - ' z I4 < a Finally, using the derivative property, it follows that the z-transform of nanu(-n) is A property that may be used to find the initial value of a causal sequence from its z-transform is the initial value theorem. Initial Value Theorem If x(n) is equal to zero for n < 0, the initial value, x(O), may be found from X(z) as follows: x(0) = lim X(z) Z'OO This property is a consequence of the fact that if x(n) = 0 for n < 0, Therefore, if we let z + o o . each term in X ( z ) goes to zero except the first. CHAP. 4 1 THE z-TRANSFORM 149 4.4 THE INVERSE Z-TRANSFORM The z-transform is a useful tool in linear systems analysis. However, just as important as techniques for finding the z-transform of a sequence are methods that may be used to invert the z-transform and recover the sequence x(n) from X(z). Three possible approaches are described below. 4.4.1 Partial Fraction Expansion For z-transforms thar are rational functions of z, a simple and straightforward approach to find the inverse z-transform is to perform a partial fraction expansion of X(z). Assuming that p > q, and that all of the roots in the denominator are simple, a, # a k for i # k, X(z) may be expanded as follows: for some constants Ak for k = 1,2, . . . , p. The coefficients Ak may be found by multiplying both sides of Eq. (4.5) by (1 - ak?-') and setting z = a k . The result is If p (- q, the partial fraction expansion must include a polynomial in z-I of order ( p -q). The coefficients of this polynomial may be found by long division (i.e., by dividing the numerator polynomial by the denominator). For multiple-order poles, the expansion must be modified. For example, if X(z) has a second-order pole at z = ak, the expansion will include two terms, where B, and B2 are given by EXAMPLE 4.4.1 Suppose that a sequence x ( n ) has a z-transform with a region of convergence lzl z f . Because p = q = 2, and the two poles are simple, the partial fraction expansion has the form 150 THE 2-TRANSFORM [CHAP. 4 The constant C is found by long division: Therefore, C = 2 and we may write X(z) as follows: Next, for the coefficients A , and Az we have and Thus, the complete partial fraction expansion becomes Finally, because the region of convergence is the exterior of the circle Izl > i, x(n) is the right-sided sequence 4.4.2 Power Series The z-transform is a power series expansion, where the sequence values x(n) are the coefficients of z-" in the expansion. Therefore, if we can find the power series expansion for X(z), the sequence values x(n) may be found by simply picking off the coefficients of z-". EXAMPLE 4.4.2 Consider the z-transform X(:) = log(l + a:-') Izl > la1 The power series expansion of this function is Therefore, the sequence x(n) having this z-transform is CHAP. 4 1 THE z-TRANSFORM 151 4.4.3 Contour Integration Another approach that may be used to find the inverse z-transform of X(z) is to use contour integration. This procedure relies on Cauchy's integral theorem, which states that if C is a closed contour that encircles the origin in a counterclockwise direction, w With X(z) = x(n)zPn n=-w Cauchy's integral theorem may be used to show that the coefficients .x(n) may be found from X(z) as follows: where C is a closed contour within the region of convergence of X(z) that encircles the origin in acounterclockwise direction. Contour integrals of this form may often by evaluated with the help of Cauchy's residue theorem, x ( z ) z n l dz = z [residues of x(z)zn'at the poles inside C] If X(z) is a rational function of z with a first-order pole at z = ak, ~es[x(z)z"-l at z = a k ] = [(I - cmz-l)~(z)zn-']z=ak Contour integration is particularly useful if only a few values of x(n) are needed. 4.5 THE ONE-SIDED Z-TRANSFORM The z-transform defined in Sec. 4.2 is the two-sided, or bilateral, z-transform. The one-sided, or unilateral, z-transform is defined by The primary use of the one-sided z-transform is to solve linear constant coefficient difference equations that have initial conditions. Most of the properties of the one-sided z-transform are the same as those for the two-sided z-transform. One that is different, however, is the shift property. Specifically, if x(n) has a one-sided z-transform X 1 ( ~ ) , the one-sided z-transform of x(n - 1) is It is this property that makes the one-sided z-transform useful for solving difference equations with initial conditions. EXAMPLE 4.5.1 Consider the linear constant coefficient difference equation Let us find the solution to this equation assuming that x(n) = S(n - I ) with y(-I) = y(-2) = 1 . We begin by noting that if the one-sided z-transform of y(n) is Yl(z), the one-sided z-transform of y(n - 2) is 152 THE z-TRANSFORM [CHAP. 4 Therefore, taking the z-transform of both sides of the difference equation, we have YI (z) = 0.25[y(-2) + y(-1)z-I + Z - ~ Y ~ ( Z ) ] + XI (z) where X 1 (z) = z-' . Substituting for y ( - 1) and y(-2), and solving for Yl (z), we have To find y(n), note that Yl (z) may be expanded as follow^:^ Therefore. Solved Problems Computing z-'hansforms The z-transform of a sequence x ( n ) is If the region of convergence includes the unit circle, find the DTFT of x ( n ) at w = n. If X(z) is the z-transform of x(n), and the unit circle is within the region of convergence, the DTFT of x(n) may be found by evaluating X(z) around the unit circle: X(eJW) = x(z)J;_-, Therefore. the DTFT at o = 7r is and we have Find the z-transform of each of the following sequences: (a) x(n) = 3S(n)+ S(n - 2 ) + S(n + 2 ) (b) x(n) = u(n) - u(n - 10) (a) Because this sequence is finite in length, the z-transform is a polynomial, and the region of convergence is 0 < Izl < m. Note that because x(n) has nonzero values for n < 0, the region of convergence does not include IzI = co, and because x(n) has nonzero values for n 0, the region of convergence does not include the point z = 0. 2 ~ e e the discussion in Sec. 4.4.1 on partial fraction expansions. CHAP. 41 THE Z-TRANSFORM (h) For this sequence, which converges for all lzl > 0. Note that the roots of the numerator are solutions to the equation z10 = 1 These roots are = ej2nkl10 k = 0 , 1 , ..., 9 which are 10 equally spaced points around the unit circle. Thus, the pole at z = 1 in the denominator of X(z) is canceled by the zero at z = 1 in the numerator, and the z-transform may also be expressed in the form Find the z-transform of each of the following sequences: (a) x(n) = 2"u(n) + 3(;)"u(n) (b) x(n) = cos(noo)u(n). (a) Because x(n) is a sum of two sequences of the form anu(n), using the linearity property of the z-transform, and the z-transform pair 2 1 ffnu(n) - - 1 - az-I IzI > I 4 we have (b) For this sequence we write x(n) = cos(nwo)u(n) = [eJnq + e-jnq M n ) Therefore, the z-transform is with a region of convergence lzl 1. Combining the two terms together, we have 1 - (cos wdz-' X(z) = I - 2(cos wo)z-I + z-2 Izl > 1 Find the z-transform of each of the following sequences. Whenever convenient, use the properties of the z-transform to make the solution easier. (a) x(n) = (+)"u(-n) (b) x(n) = (i)"u(n + 2) + (3)"u(-n - 1 ) (a) Using the definition of the z-transform we have THE 2-TRANSFORM [CHAP. 4 where the sum converges for 1321 < I or 121 i t Alternatively, note that the time-reversed sequence y(n) = x(-n) = (;)-"u(n) has a z-transform given by with a region of convergence given by Izl > 3. Therefore, using the time-reversal property, Y(z) = X(z-I), we obtain the same result. (b) Because x(n) is the sum of two sequences, we will find the z-transform of x(n) by finding the z-transforms of each of these sequences and adding them together. The z-transform of the first sequence may be found easily using the shift property. Specifically, note that because the z-transform of (;)"u(n + 2) is 4.2' times the z-transform of (a)"u(n), that is. which has a region of convergence lzl > i. The second term is a left-sided exponential and has a z-transform that we have seen before, that is, with a region of convergence Izl < 3. Finally, for the z-transform of .u(n). we have with a region of convergence < Izl < 3. (c) As we saw in Problem 4.3(b), the z-transform of cos(nwo)u(n) is I - (cos w")z-I cos(nwo)u(n) 6 ~zl > 1 I - ~ ( C O S O&)z-' + z-2 ' Therefore, using the exponentiation property, we have with a region of convergence lz 1 > f . ( d ) Writing x(n) as s(n) = anu(n) + cr-"u(-n) - S(n) we may use the linearity and time-reversal properties to write 1 X(z) = - 1 +-- 1 ; < 1 z 1 < 2 1 - ffz-' I - ffz which may be simplified to CHAP. 41 THE Z-TRANSFORM 4.5 Without explicitly solving for X(z), find the region of convergence of the z-transform of each of the following sequences: (a, x(n) = [(i)n + ( i ) n ] u ( n - 10, 1 - 1 0 ( n ( 10 (b) x(n) = ( 0 otherwise (a) Because the first sequence is right-sided, the region of convergence is the exterior of a circle. With a pole at z = coming from the term (i)", and a pole at z = coming from the term (:)" it follows that the region of convergence must be Izl > i. (b) This sequence is finite in length. Therefore, the region of convergence is at least 0 < Izl < oo. Because x(n) has nonzero values for n < 0 and for n r 0, z = 0 and z = oo are not included within the ROC. (c) Because this sequence is left-sided, the region of convergence is the interior of a circle. With a pole at z = 2, it follows that the region of convergence is Iz I < 2. 4.6 Find the z-transform of the sequence y(n) = xi=-, x(k) in terms of the z-transform of x(n). There are two ways to approach this problem. The first is to note that x(n) may be written in terms of y(n) as follows: Therefore, if we transform both sides of this equation, and use the shift property of the z-transform, we find X ( z ) = Y ( z ) - z-'y(z) Solving for Y (z), we find Thus. which is referred to as the summation property. The second approach is to note that y(n) is the convolution of x(n) with a unit step, Therefore, using the convolution theorem, we have and, with U ( z ) = I / ( I - z-I), we obtain the same result as before. For the region of convergence, note that because the ROC of l/(z) is Iz( > 1, the ROC of Y ( z ) will be at least R, = R, n ( I Z I > I ) where R, is the ROC of X ( z ) . 4.7 Find the z-transform of the sequence y(n) where and y(n) = 0 for n < 0. Assume that l a 1 < 1. THE Z-TRANSFORM [CHAP. 4 For this sequence, we may use a variation of the summation property derived in Prob. 4.6. Specifically, recall that if then X(z) Y ( z ) = - I - z-' Now consider the two-sided summation, which may be written as Therefore, if we let Therefore, we have Y ( z ) = XI ( z ) + X2W I - z-' - x(0) Finally, with x(n) = a"1, it follows that x l ( n ) = x2(n) = anu(n), and x(0) = I. Thus, with a region of convergence Izl > I. 4.8 Let x(n) be a finite-length sequence that is nonzero only for 0 5 n 5 N - 1, and consider the one-sided periodic sequence, y(n), that is formed by periodically extending x(n) as follows: Express the z-transform of y(n) in terms of X(z) and find the region of convergence of Y(z). The one-sided periodic sequence y(n) may be written as the convolution of x(n) with the pulse train CHAP. 4 1 THE z-TRANSFORM In other words, Therefore, the z-transform of y(n) is the product of the z-transforms of x(n) and pN(n). Because pN(n) is a sum of shifted unit samples, and because the z-transform of S(n - kN) is equal to z - ' ~ , the z-transform of pN(n) is Thus, the z-transform of the one-sided periodic sequence y(n) is Because x(n) is finite in length and zero for n c 0, the region of convergence for X(z) is JzJ > 0. Therefore, the region of convergence of Y (z) is I z 1 > 1. Consider the sequence shown in the figure below. The sequence repeats periodically with a period N = 4 for n 2 0 and is zero for n < 0. Find the z-transform of this sequence along with its region of convergence. This is a problem that may be solved easily using the property derived in Prob. 4.8. Because where N = 4 and w(n) = S(n - I) + 2S(n - 2) + S(n - 3) then W(z) = z-l[l + 2z-' + z - ~ ] and we have Because x(nj is right-sided and X(z) has four poles at lzl = I, the region of convergence is Izl > 1. Properties 4.10 Use the z-transform to perform the convolution of the following two sequences: THE z-TRANSFORM [CHAP. 4 The convolution theorem for z-transforms states that if y(n) = h(n) x(n), the z-transform of y(n) is Y(z) = H(z)X (z). With it follows that Y(z) = H(z)X(z) = ( I + iz-' + :Z-~)(I + z-I + 4z-') Multiplying these two polynomials, we have By inspection, we then have for the sequence y(n), 4.11 Evaluate the convolution of the two sequences h(n) = (OS)"u(n) and x(n) = 3"u(-n) To evaluate this convolution, we will use the convolution property of the z-transform. The z-transform of h(n) is and the z-transform of x(n) may be found from the time-reversal and shift properties, or directly as follows: Therefore, the z-transform of the convolution, y(n) = x(n) h(n), is The region of convergence is the intersection of the regions JzJ > and lzl < 3, which is < lzl < 3. To find the inverse z-transform, we perform a partial fraction expansion of Y (z), A B Y (z) = ----- + - 1 - I,-I 1 - 32-1 2 and B = [(I - 3z-')Y (z)],,~ = - 6 5 Therefore, it follows that Y(.) = ($)(;)"u(n) + (;)3nu(-n - 1) CHAP. 41 THE Z-TRANSFORM Let x(n) be an absolutely summable sequence, with a rational z-transform. If X(z) has a pole at z = and limlzl+m X(z) = 1, what can be said about the extent of x(n) (i.e., finite-in-length, right-sided, etc.)? Because x(n) is an absolutely summable sequence, the ROC of X ( z ) includes the unit circle, Izl = I. With a pole at z = f , the region of convergence will either be an annulus of the form r- < lzl < r,, or it will be the exterior of a circle, r- < Izl. However, because X (z) converges as Izl -+ m, the region of convergence will be the exterior of a circle, and it follows that x(n) is right-sided (infinite in length) with x(n) = 0 for n < 0. Find the z-transform of x(n) = lnl(;)lnl. Using the derivative property and the z-transform pair it follows that the z-transform of w(n) = n(;)"u(n) is Because x(n) may be written as -n x(n) = \nl(f)"' = n(f)"u(n) - n(f) zd-n) using linearity and the time-reversal property, we have which has a region of convergence f < Izl < 2. 4.14 Let y(n) be a sequence that is generated from a sequence x(n) as follows: (a) Show that y(n) satisfies the time-varying difference equation and show that -z2 dX(z) Y (z) = - -- Z - I dz where X(z) and Y (z) are the z-transforms of x(n) and y(n), respectively. (b) Use this property to find the z-transform of THE Z-TRANSFORM [CHAP. 4 (a) From the definition of y(n), we see that and it follows immediately that y(n)- y(n - 1) = nx(n) From this difference equation, we may take the z-transform of both sides. Because then Y(z) - dX(z) z-'Y (z) = -z - dz (b) To find the z-transform of the given sequence, note that where x(n) = (f)"u(n) Because the z-transform of x(n) is 1 X(z) = - 1 - {z-I I4 > : 1 -2 -z2 dX(z) -z2 -:z I - I then Y(z) = -- - - - - 3 2 - z - 1 dz 2 - 1 (1 - iZ-l) (1 - ;z-~)2(l - z - ~ ) Because x(n) is right-sided, then the region of convergence is the exterior of a circle. Having poles at z = 1 and z = i, it follows that the region of convergence is Izl > I. 4.15 Find the value of x(0) for the sequence that has a z-transform X(z) = 1 1 - az-' IzI > a Taking the limit of X(z) as z + oo, we see that X(z) + 1. Because the limit exists, x(n) is causal, and x(0) = 1. 4.16 Find the value of x(0) for the sequence that has a z-transform Because the region of convergence of X(z) is the exterior of a circle, x(n) is right-sided. However, if we write X(z) in terms of positive powers of z, "4 CHAP. 4 4 1 THE z-TRANSFORM 161 we see that X(z) -+ oo as Izl -+ oo. Therefore, x(n) is not causal. However, because x(n) is right-sided, it may be delayed so that it is causal. Specifically, if we delay x(n) by 1 to form the sequence y(n) = x(n - I), Y (z) = (z - ; ) (z2 - ;) which approaches 1 as lzl + m. Thus, y(n) is causal, and we conclude that y(0) = x(-I) = I . Because X(z) - x(-l)z is the z-transform of a causal sequence, and it follows from the initial value theorem that With we have x(0) = lim [X(z) - x(- I )Z 1 = I z l b m 4.17 Generalize the initial value theorem to find the value of a causal sequence x(n) at n = 1 , and find x(1) when If x(n) is causal, X(z) = x(0) + x(1)z-I + , ~ ( 2 ) z - ~ + Therefore, note that if we subtract x(0) from X(z), Multiplying both sides of this equation by z, we have If we let z + m, we obtain the value for x(l), x(l) = lirn (z[X(z) - x(O)]J Izl-rm For the given z-transform we see that x(0) = lim X(z) = $ (21-+m Therefore, and x(1) = lim (z[X(z) - x(0)I) = 3 Izl+m 162 THE z-TRANSFORM [CHAP. 4 4.18 Let x(n) be a left-sided sequence that is equal to zero for n > 0 . If find x(0). For a left-sided sequence that is zero for n > 0, the z-transform is Therefore, it follows that x(0) = lim X(z) 2-0 For the given z-transform, we see that 32-' + 2zp2 32 + 2 x(0) = lim X(z) = lim = lim = 2 i-ro 2-0 3 - z-' + z-2 2-0 3z2 - z + 1 4.19 If x(n) is real and even with a rational z-transform, show that and describe what constraints this places on the poles and zeros of X(z). If x(n) is even, x(n) = x(-n) Therefore, it follows immediately from the time-reversal property that If X(z) has a zero at z = zO, X(z0) = 0 then x (z,') = 0 which implies that X(z) will also have a zero at z = 1/20, The same holds true for poles. That is, if there is a pole at zO, there must also be a pole at z = I /zo. 4.20 Use the derivative property to find the z-transform of the following sequences: (a) x(n) = n(;)"u(n - 2) 1 (b) x(n) = ;(-2)-"4-n - 1 ) (a) The derivative property states that if X(z) is the z-transform of x(n), If we let x(n) = nw(n), where n-2 w(n) = (;)"u(n - 2) = f (i) u(n - 2) from the delay property and the z-transform pair CHAP. 41 THE 2-TRANSFORM it follows that Therefore, using the derivative property, we have the z-transform of x(n), (b) Evaluating the z-transform of this sequence directly is difficult due to the factor of n-I. However, if we define a new sequence, y(n), as follows, y(n) = nx(n) = (-2)-"4-n - I) the z-transform of y(n) is easily determined to be - 1 Y (z) = --- I z I < ; l + ;z-' Noting the relationship between x(n) and y(n), we can apply the derivative property to set up a differential equation for X(z), The solution to this differential equation is X ( z ) = log (z + f ) and the region of convergence is I z 1 < i. 4.21 Up-sampling is an operation that stretches a sequence in time by inserting zeros between the sequence values. For example, up-sampling a sequence x(n) by a factor of L results in the sequence y(n> = otherwise Express the z-transform of y(n) in terms of the z-transform of x(n). Because y(n) isequal to zero for all n + kL, with y(n) equal tox(n/L) forn = kL, the z-transform of the up-sampled signal is If X(z) converges for cu < Izl < /3, Y (z) will converge for cu < lzlL < p, or a'/'. < (zI < pIIL 4 .
2 2 Find the z-transform of the sequence an/10 n = 0, 10,20, . . . x(n) = 0 else where l a 1 -= 1. THE z-TRANSFORM [CHAP. 4 We recognizex(n) as an exponential sequence that has been up-sampled by a factor of 10 (see Prob. 4.21). Therefore, because the z-transform of x(n) is Inverse z-'Ransforms 4.23 Find the inverse of each of the following z-transforms: Because X(z) is a finite-order polynomial, x(n) is a finite-length sequence. Therefore, x(n) is the coefficient that multiplies z-" in X(z). Thus, x(0) = 4 and x(2) = x(-2) = 3. This z-transform is a sum of two first-order rational functions of z. Because the region of convergence of X(z) is the exterior of a circle, x(n) is a right-sided sequence. Using the z-transform pair for a right-sided exponential, we may invert X(z) easily as follows: Here we have a rational function of z with a denominator that is a quadratic in z. Before we can find the inverse z-transform, we need to factor the denominator and perform a partial fraction expansion: Because x(n) is right-sided, the inverse z-transform is One way to invert this z-transform is to perform a partial fraction expansion. With I X(z) = -- - ( I - z - ) ( ~ - z - ~ ( I - the constants A, B I , and B2 are as follows: CHAP. 41 THE z-TRANSFORM Inverse transforming each term, we have x(n) = a[(-1)" + 1 + 2(n .+ I)]u(n) Another way to invert this z-transform is to note that x(n) is the convolution of the two sequences. x(n) = x ~ ( n ) xz(n) where xl (n) = u(n) and x2(n) is a step function that is up-sampled by a factor of 2. Because xl(n) x2(n) = {I, 1,2,2,3,3,4,4,. . .) we have the same result as before. 4.24 Find the inverse z-transform of the second-order system Here we have a second-order pole at z = f . The partial fraction expansion for X(z) is The constant A is and the constant A2 is Therefore, 4.25 Find the inverse of each of the following z-transforms: (a) X ( z ) = log (1 - i z -' ) Izl > $ (b) X(z) = ellZ, with x(n) a right-sided sequence (a) There are several ways to solve this problem. One is to look up or compute the power series expansion of the log function. Another way is to differentiate X(z). Specifically, because if we multiply both sides of this equation by (-z), we have THE z-TRANSFORM [CHAP. 4 Note that the region of convergence for X(z) is Izl > i. Because the region of convergence for Y (z) is the same as it is for X(z), the inverse z-transform of Y (z) is y(n) = -($)"u(n - I ) Now, from the derivative property, y(n) = nx(n), and it follows that x(n) = -i(i)"u(n - I ) (6) For this z-transform, we could determine the inverse by tinding the power series expansion of X(z). However, another approach is to do what we did in part (a) and take the derivative. Differentiating X(z), we find d -X(z) = -z-~x(z) dz Multiplying both sides by (-z), we have and taking the inverse z-transform gives nx(n) = x(n - 1) which is a recursion for x(n). To solve this recursion, we need an initial condition. Because x(n) is a right-sided sequence, we may use the initial value theorem to find x(0). Specifically, x(0) = lim X (z) = I l:+m Thus. the recursion that we want to solve is with x(0) = 1. The solution for n > 0 is and we have 4 .
2 6 Find the inverse z-transform of X(z) = sin z. To find the inverse z-transform of X(z) = sin z, we expand X(z) in a Taylor series about z = 0 as follows: 03 Because ~ ( z ) = ) : x(n)z-" ) I = - N we may associate the coefficients in the Taylor series expansion with the sequence values x(n). Thus, we have I x(n) = (- 1)" n = -1,-3, - 5 , . . . (2lnl+ I)! CHAP. 41 THE Z-TRANSFORM 4.27 Evaluate the following integral: where the contour of integration C is the unit circle. Recall that for a sequence x(n) that has a z-transform X(z), the sequence may be recovered using contour integration as follows: Therefore, the integral that is to be evaluated corresponds to the value of the sequence x(n) at n = 4 that has a z-transform 1 + 2z-I - 2-2 x (z) = - ( I - +z-1)(1 - +-I) Thus, we may find x(n) using a partial fraction expansion of X(z) and then evaluate the sequence at n = 4. With this approach, however, we are finding the values of x(n) for all n. Alternatively, we could perform long division and divide the numerator of X(z) by the denominator. The coefficient multiplying z - ~ would then be the value of x(n) at n = 4, and the value of the integral. However, because we are only interested in the value of the sequence at n = 4, the easiest approach is to evaluate the integral directly using the Cauchy integral theorem. The value of the integral is equal to the sum of the residues of the poles of x(z)z3 inside the unit circle. Because has poles at z = and z = !, and Therefore, we have 4.28 Find the inverse z-transform of Note that the denominator of X(z) is a tenth-order polynomial. Although the roots may be found easily, performing a partial fraction expansion would be time consuming. For this problem, it is much better to exploit the properties of the z-transform. Note, for example, that I X(z) = Y (zJO) where Y(z) = 1 - culoz-l Because THE z-TRANSFORM [CHAP. 4 we may use the up-sampling property (Prob. 4.21) to obtain Therefore, we have a" n = 0, 10,20. x(n) = 0 otherwise 4.29 In many cases one is interested in computing the inverse z-transform of a rational function Because a partial fraction expansion requires knowledge of the roots of A(z), if the order of the denom- inator is large, finding the roots may be difficult. Although a partial fraction expansion would give a closed-form solution for x(n) for all n. if one only wants to plot x(n) for a limited range of values for n, a closed-form expression is not required. Given that x(n) = 0 for n c 0, find a recursion that generates x(n) for n 5 0. If we consider x(n) to be the unit sample response of a linear shift-invariant system, we may straightforwardly specify the filter in terms of a linear constant coefficient difference equation. This leads to a recursively computable difference equation for x(n). Specifically, note that because we may express this in the time domain as follows: Writing out this convolution explicitly, we have Bringing the first term out of the summation and dividing by a(0) gives Therefore, given that x(n) = 0 for n < 0, this recursion allows us to compute s(n) for all n 2 0. For example, Note that h(n) = 0 for n > q. Thus. for n z q, the recursion simplifies to CHAP. 41 THE z-TRANSFORM One-sided z-'hansforms 4.30 Find the one-sided z-transform of the following sequences: (a) x(n) = ({)"u(n + 3) (b) x(n) = S(n - 5 ) + S(n) + 2"-'4-n) In the following, let x+(n) denote the sequence that is formed fromx(n) by setting x(n) equal to zero for n < 0, that is, (a) Because x.,(n) = ( ;lnu(n), the one-sided z-transform of x(n) is (b) For this sequence, because x+(n) = S(n - 5 ) + S(n) + T 1 6 ( n ) then Xl(z) = z-% I + $ = 1.5 + z4 4.31 Let XI(z) be the one-sided z-transform of x(n). Find the one-sided z-transform of y(n) = x(n + 1). The one-sided 2-transform of x(n) is If x(n) is advanced in time by one, y(n) = x(n + I), the one-sided z-transform of y(n) is Therefore. YI(z) = x(1) + x(2)z-' + x(3)z -Z + . Comparing this to XI (z), we see that YI(z) = z[X1(z) - x(0)l 4.32 Consider the LCCDE y ( n ) - i y ( n - 2 ) = S ( n ) n 2 O Find a set of initial conditions on y(n) for n < 0 so that y(n) = 0 for n 2 0. The one-sided z-transform of the LCCDE is Solving for Yl(z), we have 1 + S [ , Y ( - ~ ) + y(- I)z- ll YI(z) = 1 - i z - 2 In order for y(n) to be equal to zero for n 0, Yl(z) must be equal to zero. This will be the case when 170 THE z-TRANSFORM [CHAP. 4 4.33 Consider a system described by the difference equation Find the response of this system to the input with initial conditions y(- 1) = 0.75 and y(-2) = 0.25. This is the same problem as Prob. 1.37. Whereas this difference equation was solved in Chap. 1 by finding the particular and homogeneous solutions, here we will use the one-sided z-transform. First, we take the one-sided z-transform of each term in the difference equation Substituting the given values for the initial conditions, we have Y(z) = z-'Y(z)+ ; - z - ~ Y ( z ) - $2-' - f + ; x ( ~ ) + ; Z - ' ~ ( Z ) Collecting all of the terms that contain Y (z) onto the left side of the equation gives Because x(n) = (i)"u(n). which gives ; - a z - 1 ; + fz-I Y (z) = + 1 - 2-1 + z-2 (1 - iz-l)(l - z-1 + z-2) Expanding the second term using a partial fraction expansion, we have I - 2 ; + ;z-' Y (z) = --- , - Lz-I + 1 - 2-1 + z-2 2 Therefore, the solution is 4.34 A digital filter that is implemented on a DSP chip is described by the linear constant coefficient difference equation 3 y(n) = ?y(n - I) - ky(n - 2) +x(n) In evaluating the performance of the filter, the unit sample response is measured (i.e., the response y(n) to the input x(n) = S(n) is determined). The internal storage registers on the chip, however, are not set to zero prior to applying the input. Therefore, the output of the filter contains the effect of the initial conditions, which are ( - I ) = -1 and y(-2)= 1 CHAP. 41 THE Z-TRANSFORM 171 Determine the response of the filter for all n p 0 and compare it with the zero state response (i.e., the output with y(.-I) = y(-2) = 0). Here we want to solve a difference equation that has initial conditions. Using the one-sided z-transform, we have With X(z) = I and the given initial conditions, this becomes Solving for Y (2). we find Performing a partial fraction expansion gives Thus, with an inverse z-transform we have y(n) = [-;(a)'' + :(;)"]u(n) The zero state response, on the other hand, is simply the unit sample response of the filter. With it follows that Applications 4.35 There are two kinds of particles inside a nuclear reactor. Every second, an cr particle will split into eight B particles and a B particle will split into an a ! particle and two /? particles. If there is a single cr particle in the reactor at time t = 0, how may particles are there altogether at time t = 1 00? In this problern we need to begin by writing down, in mathematical terms, what is happening within the reactor. Let a ( n ) be the number of a particles in the reactor at time n, and let B(n) be the number of / 3 particles. Because there are eight B particles created from each a particle and two from each ~9 particle, we have Also, because one a particle is created from each B particle, Substituting the second equation into the first, we have which is an equation that defines how many B particles there are in the reactor at time n. Because there is one cu particle in the reactor at time n = 0, it follows that there are eight /? particles at time n = 1. Therefore. the initial condition associated with B(n) is B(1) = 8, and this may be incorporated into the equation as follows: THE Z-TRANSFORM [CHAP 4 with B(n) = 0 for n < I. Using z-transforms, we may solve this equation for B(n) as follows: Taking the inverse z-transform, we have Finally, because the number of u particles at time n is equal to the number of B particles at time (n - I), the total number of particles at time n = 100 is 4.36 A $100,000 mortgage is to be paid off in 360 equal monthly payments of d dollars. Interest, compounded monthly. is charged at the rate of 10 percent per annum on the unpaid balance (e.g., after the first month the total debt equals $100,000 + ~$100,000). Find the payment d so that the mortgage is paid in full after 30 years, leaving a net balance of zero. This is the same problem that was solved in Prob. 1.39. Here, however, we will use the z-transform to find the solution. The total unpaid balance at the end of the nth month, in the absence of any additional loans or payments, is equal to the unpaid balance in the previous month plus the interest charged on the unpaid balance for the previous month. Therefore, if y(n) is the balance at the end of the nth month, where B is the interest charged on the unpaid balance. In addition, the balance must be adjusted by the amount of money leaving the bank into your pocket, which is simply the amount borrowed in the nth month and the amount paid to the bank in the nth month. Thus where xh(n) is the amount borrowed in the nth month, and x,(n) is the amount paid in the nth month. Combining terns, we have y(n) - vy(n - 1) = xh(n) - x,(n) = x(n) where v = 1 +B = 1 +O. 10/12, andx(n) is the net amount of money in the nth month that leaves the bank. Because a principal of p dollars is borrowed during month zero, and payments of d dollars begin with month 1, the input x(n) is and the difference equation for y(n) becomes Expressing this difference equation in terms of z-transforms, we have Solving for Y(z), we find Taking the inverse z-transforms yields CHAP. 4 1 THE >TRANSFORM 173 We now want to find the value of d so that the mortgage is retired after 060 equal monthly payments. That is, we want to find d so that I y(360) = -[(p + d - pv)v'60 - dl = 0 I - v Solving for d, we have With v = $ and p = 100,000 we have which is the same as we had previously calculated. 4.37 A generalized Fibonacci sequence is a sequence of numbers, x(n), that satisfies the difference equation x ( n + 2 ) = x ( n ) + x ( n + I ) for n > O That is, x(n) is the sum of the two previous values. The classical Fibonacci sequence results when the initial conditions are x(0) = 0 and x(1) = 1. The Fibonacci numbers occur in such unsuspecting places as the number of ancestors in succeeding generations of the male bee, the input impedance of a resistor ladder network, and the spacing of buds on the branch of a tree. (a) Find a closed-form expression for x(n). (h) Show that the ratio x(n)/x(n + 1) approaches the limit 2/(1 + 8) as n + co. This ratio is known as the golden mean and was said by the ancient Greeks to be the ratio of the sides of the rectangle that has the most pleasing proportions. (c) Show that the Fibonacci sequence has the following properties: (a) Here we have a second-order linear constant coefficient difference equation that we want to solve. Let us begin by rewriting it in a slightly different form. Specifically, consider the following where we assume that x(n) = 0 for n < 0 (i.e, initial rest). Written in this form with the delayed unit sample on the right-hand side, we note that x(0) = 0 and .r(l) = I as desired and x(n + 2) = .r(n) + x(n + 1) for n > 0. The solution to this difference equation may be found using z-transforms as follows: Solving for X(z), we have --I The poles of X(z) are located at z = (I f &)/2, and the partial fraction expansion of X(z) is Taking the inverse z-transform of X(z), we find THE 2-TRANSFORM [CHAP. 4 (h) Starting with the difference equation that defines the Fibonacci sequence, divide both sides by x(n + I): If we define r ( n ) to be the ratio of two successive Fibonacci numbers we have If we let n + m . and define r ( m ) = lim,,,, r ( n ) , we have Solving this quadratic equation for r ( m ) , we find I + & r ( m ) = - 2 However, because ~ ( n ) > 0, it follows that r ( m ) is the positive root, which is Finally, because then (c) For the first property, we may simply substitute the closed-form expression for the Fibonacci sequence into the equation, and verify that it is true. For the second property, from the definition of the Fibonacci sequence we have which we may rewrite as x2(n + 2) - x2(n + I ) = x ( n ) [ x ( n ) + 2x(n + I)] However, note that x ( n + 3) = x(n + I) + x ( n + 2 ) = x ( n ) + 2x(n + I) Substituting this into the previous equation, we have the desired property. 4.38 A savings account pays interest at the rate of 5 percent per year with interest compounded monthly. (a) If $50 is deposited into the account every month for 60 months, find the balance in the account at the end of the 60 months. Assume that the money is deposited on the first day of the month so that, at the end of the month, an entire month's interest has been earned. (b) If no deposits are made for the next 60 months, find the account balance at the end of the next 60- month period. CHAP. 41 THE Z-TRANSFORM 175 (c) Instead of being compounded monthly, suppose that the bank offers to compound the interest daily. Compute the account balance at the end of 60 months and 120 months and compare your balances with those obtained when the interest is compounded monthly. (a) The savirigs account balance at the beginning of the nth month is equal to the balance in the previous month plus the amount deposited in the nth month plus the interest earned on the balance from the previous month. Therefore, if y(n) is the balance at the beginning of the nth month, where j3 is the interest earned on the account, and x(n) is the amount deposited into the savings account in the nth month. Taking z-transforms, and solving for Y (z), we have where v = I + j 3 . With $50 deposits beginning with month number zero, x(n) = 50u(n), and 1 Y (z) = 50 (1 - vz-')(I - z-1) Performing a partial fraction expansion of Y(z), we have Taking the inverse z-transform, we have With v = I + B, and j3 = F. at the end of 60 months. after earning I month's interest, but prior to making the next deposit, the balance is (b) With no deposits for the next 60 months, the balance at the end of the first 60 months simply grows as y(n) = y(60). vn-"' n > 60 Therefore. y( 120) = 4,379.42 (c) With the interest compounded daily, let us compute the effective monthly interest rate. Assuming a balance of $ I at the beginning of the month, the difference equation that describes the daily balance, w(n), is where j3 = g. Using z-transforms as we did in part (a), the solution to this difference equation is where v = 1 + B. Assuming that a month is 30 days long, for I month's interest we have w(30) = v30 = 1.004 175 Using v = 1.004175 in Eq. (4.8), we have 176 THE z-TRANSFORM [CHAR 4 4.39 The deterministic autocorrelation sequence corresponding to a sequence x(n) is defined as (a) Express r , (n) as the convolution of two sequences, and find the z-transform of r,(n) in terms of the z-transform of x(n). (b) If x(n) = anu(n), where la1 < I, find the autocorrelation sequence, r,(n), and its z-transform. (a) From the definition of the deterministic autocorrelation, we see that r,(n) is the convolution of x(n) with x(-n), rx(n) = x(n) x(-n) Therefore, using the time-reversal property of the z-transform, it follows that If the region of convergence of X(z) is R,, the region of convergence of R,(z) will be the intersection of the regions R, and 1/R,,. Therefore, if this intersection is to be nonempty, R, must include the unit circle. (b) With x(n) = anu(n), the z-transform is and the z-transform of the autocorrelation sequence is I I R,(z) = ( I - azr1)(I - az) lal < l z l < - la I The autocorrelation sequence may be found by computing the inverse z-transform of R,(z). Performing a partial fraction expansion of R, (z), we have Thus, because the region of convergence is la\ 4 z < l/laJ, the inverse z-transform is 4.40 In many disciplines, differential equations play a major role in characterizing the behavior of various phe- nomena. Obtaining an approximate solution to a differential equation with the use of a digital computer requires that the differential equation be put into a form that is suitable for digital computation. This prob- lem presents a transformation procedure that will convert a differential equation into a difference equation, which may then be solved by a digital computer. Consider a first-order differential equation of the form where yu(0)=yo. Because numerical techniques are to be used, we will restrict our attention to investi- gating yu(t) at sampling instants nT where T is the sampling period. Evaluating the differential equation at t = nT, we have CHAP. 41 THE z-TRANSFORM 177 From calculus we know that the derivative of a function y,(t) at t = nT is simply the slope of the function at t = nT. This slope may be approximated by the relationship (a) Insert this approximation into the sampled differential equation above and find a difference equation that relates y(n) = y,(nT) and x(n) = x,(nT), and specify the appropriate initial conditions. (b) With x,(t) = u(t) and y,(O-) = I, numerically solve the differential equation using the difference equation approximation obtained above. (c) Compare your approximation to the exact solution. using the approximation d I -Y&W -[y,(n~) - y,(nT - TI] dr T we have I ?[ya(nT) - ya(nT - T)] + crya(nT) = .r,(nT) y,(O-) = yo If we let y(n) = ya(nT) and x(n) = xa(nT), With this becomes ~ ( n ) - ay(n - 1) = aTx(n) ~ ( 0 ) = yo (b) Using the one-sided z-transform to solve this difference equation, we have We must now derive the initial condition on y(n) at time n = - 1 from the initial condition at n = 0. From the difference equation, we have y(0) - ay(-I) = aTx(0) With y(0) = 1 and x(0) = 1, the initial condition becomes With x,(t) = u(t) or x(n) = u(n), Therefore. using the given initial condition, we have THE 2-TRANSFORM [CHAP. 4 Performing a partial fraction expansion gives and we may find v(n) by taking the inverse z-transform: Because this may be written as (c) The solution to the differential equation is a sum of two terms. The first is the homogeneous solution, which is yh(t) = Ae-O1 where A is a constant that is selected in order to satisfy the initial condition ~ ( 0 - ) = 1. The second is the particular solution, which is Thus, the total solution is Evaluating this a1 time I = 0-, we see that in order to match the initial conditions. we must have If we compare this to the approximation in part (h), note that if T < < I, aT - , I C - ~ ~ ) , _ , T = (e ) = Z (I + ( Y T ) - ~ and Supplementary Problems z-'kansforms 4.41 Find the 2-transform of CHAP. 41 THE z-TRANSFORM 4.42 The z-transform of a sequence x(n) is If the region of convergence includes the unit circle, find the DTFT of x(n) at w = r / 2 . 4.43 Find the z-transform of each of the following sequences: (a) x(n) = (--l)"u(n) (b) x(n) = ;u(n - I) (c) x(n) = z cosh (crn)u(n) 4.44 Find the z-transform of the sequence 4.45 Find the z-transform of the sequence 4.46 How many different sequences have a z-transform given by 4.47 The sequence y(n) is formed from x(n) by where X(z) = sinzr'. Find Y(z). 4.48 If x(n) is an absolutely summable sequence with a rational z-transform that has poles at z = f and z = 2, what can be said about the extent of x(n) (i.e., finite in length, right-sided, etc.)? Properties A right-sided sequence x(n) has a z-transform X(z) given by Find the values of x(n) for all n < 0. Use the z-transform to perform the convolution of the following two sequences: Evaluate the following summation: 180 THE z-TRANSFORM 4.52 Find the value of x(0) for the sequence that has a z-transform 4.53 A right-sided sequence has a z-transform Find the index a ~ d the value of the first nonzero value of x(n). Inverse z-Transforms 4.54 Find the inverse z-transform of 4.55 Find the inverse z-transform of X(z) = coszp'. Assume that the ROC includes the unit circle, Izl = 1. 4.56 Find the inverse z-transform of X(z) = e'. Assume that the ROC includes the unit circle, lzl = 1. 4.57 Find the inverse z-transform of z5 - 3 X(z) = - 1 - z-S lzl > I 4.58 Find the inverse z-transform of 4.59 If 1 X(z) = - c 2 2 - 2 find the values of x(n) at n = -2 and n = - I using contour integration. 4.60 Use the residue theorem to find the value of a(n) at n = 10 when 4.61 Find the inverse z-transform of One-sided z-Transforms 4.62 Find the one-sided z-transform of the sequences x(n) = (:)In. [CHAP. 4 4.63 Let Xl(z) be the one-sided z-transform of x(n). (a) Find the one-sided z-transform of y(n) = x(n - I). (b) Find the one-sided z-transform of y ( n ) = x ( n + 3). CHAP. 41 THE :-TRANSFORM 4.64 Find the solution to the following linear constant coefficient difference equations: (a) y(n) = iy(n - 1 ) + x(n) withx(n) = u(n) and y(-I) = $. (b) y(n) = y(n - I ) - y(n - 2) + 2u(n) with y(-1) = 2 and y(-2) = 1. (c) y(n) + y(n - 2) = 6(n) with y(-I) = I and y(-2) = 0. 4.65 The sequence y(n) is the solution to the LCCDE with x(n) = S(n). Find a set of initial conditions on y(n) for n i 0 so that y(n) = 1 for n , 0. 4.66 Consider the following difference equation: y(n) + y(n - 2) = x(n) + x(n - 1 ) If x(n) = IOu(n) and y(-2) = - 10 and y(- I) = 0, find the output sequence y(n) for n 2 0. Applications 4.67 Determine the number of years that are required for an investment of money in a savings account to double if the money is compounded monthly at an annual rate of (a) 5 percent and (b) 10 percent. 4.68 Suppose that x ( n ) has a :-transform with la1 < 1 and I b l < 1 and a region of convergence that includes the unit circle. (a) Find the deterministic autocor- relation sequence r,(n). (b) Find another sequence that has the same autocorrelation. Answers to Supplimentary Problems 1 4.44 Y ( z ) = ( 1 - 2 -I ) " 4.45 X ( : ) = ( 1 + 4.46 Three. 182 THE z-TRANSFORM Two-sided. x(-3) = -1 is the only nonzero value for n < 0. (a) (n + 1)(0.4)"u(n). (b) x(n) = (r.2)"" n even else x ( - I ) = -f and x(-2) = -$, 3-0.6)~[(-0.6)~ - 3 1 + !(0.2)~[(0.2)~ - 31. (a) [2 - :(t)"]u(n). (b) [2 + 5 sin@ + l)n/3]u(n). (c) [cos(nn/2) - sin(nn/2)]u(n). y(-I) = 1 and y(-2) = 3. (a) 167 months. (b) 84 months. I I hin[ - - (a) r,(n) = ----a1"' + - [(an + bn)u(n) + (apn + bpn)u(-n - I ) ] . 1 -a2 I - h2 I -ah (b) x'(n) = aNu(n) - b-"u(-n - 1 ) . [CHAP. 4 |
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Total degree of intersection points of n n lines in the plane
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Here's a conjecture I have. Can anyone prove or disprove it?
Given n n distinct straight lines in the plane, the total degree of any n n (or less) intersection points is O(n)(n) (where the degree of a point is the number of lines containing it).
Update: I meant the question as Justin Smith understood it. Pick any n n or less intersection points (actually they don't even have to be intersection points---just points in the plane). Then for each of these points, count how many lines contain it. Add up these numbers. The conjecture was that the sum will always be O(n)(n). Note that n n is both the number of lines and an upper bound on the number of points you are allowed to select.
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edited Jul 21, 2011 at 8:59
AriAri
asked Jul 20, 2011 at 10:55
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Have you checked Richard Guy's book titled "Unsolved problems in combinatorial geometry" or something like that?Jyrki Lahtonen –Jyrki Lahtonen 2011-07-20 13:41:55 +00:00 Commented Jul 20, 2011 at 13:41
It seems that we all interpret your question differently, could you modify it so as to remove the ambiguities raised in the comments below?Anthony Labarre –Anthony Labarre 2011-07-20 14:03:30 +00:00 Commented Jul 20, 2011 at 14:03
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The sum of "degrees" of a set of points is the total number of "incidences" for those points. There're numerous related bounds, the most famous of which (and applicable to this question) is Szemeredi-Trotter.
This bound applies even when you only select a subset of the lines' intersection points.
And that bound is tight, i.e., there are known arrangements of lines that attain the asymptotic bound.
Tao has a demonstration of points and lines that achieves Omega(n^(4/3)) incidences here:
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edited Jul 20, 2011 at 15:30
answered Jul 20, 2011 at 13:40
Justin W SmithJustin W Smith
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The important part is of course the lower bound, which disproves my conjecture. Thanks for the pointer.Ari –Ari 2011-07-21 09:01:03 +00:00 Commented Jul 21, 2011 at 9:01
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Unless I'm missing something, I don't think this holds: write numbers 1 1 to n n on line A A in the natural order, then the same numbers but in the reverse order on a parallel line B B, and connect i i on A A to i i on B B by a straight line, spacing numbers as required so that all intersections have degree 2 2. Then you have (n 2)(n 2) intersections of degree 2 2.
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answered Jul 20, 2011 at 11:27
Anthony LabarreAnthony Labarre
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I think the question is about a bound on the total degree of the n n highest degree points of intersection. The bound should hold no matter how you draw the lines.Jyrki Lahtonen –Jyrki Lahtonen 2011-07-20 13:40:28 +00:00 Commented Jul 20, 2011 at 13:40
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3Set N N points on plane by intersecting as few lines / conics as possible
1Lines drawn from the intersection of the given lines
1A conjecture about lines and points in the plane
3Say i have n n points in the plane all of which are connected. What is the minimum number of intersections between the connecting lines?
1Points of Intersection of Curves
6Drawing points and straight lines in the plane
5The Maximum number of points of intersection of 4 distinct circles and 8 distinct straight lines is
0If there are n n points in a plane and no three of them are collinear, then find Total no of intersection of the lines joining these n n points.
2Find the number of different lines containing 8 8 points
1Determine the maximum number of points of intersection of these lines.
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13431 | https://pmc.ncbi.nlm.nih.gov/articles/PMC4952057/ | Genetic pleiotropy in complex traits and diseases: implications for genomic medicine - PMC
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. 2016 Jul 19;8:78. doi: 10.1186/s13073-016-0332-x
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Genetic pleiotropy in complex traits and diseases: implications for genomic medicine
Jacob Gratten
Jacob Gratten
1 Queensland Brain Institute, The University of Queensland, Brisbane, QLD 4072 Australia
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1,✉, Peter M Visscher
Peter M Visscher
1 Queensland Brain Institute, The University of Queensland, Brisbane, QLD 4072 Australia
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1 Queensland Brain Institute, The University of Queensland, Brisbane, QLD 4072 Australia
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PMCID: PMC4952057 PMID: 27435222
Editorial summary
Several recent papers have used summary results from genome-wide association studies to characterize genetic overlap between human complex traits and common diseases. The emerging evidence is that individual DNA variants frequently influence multiple phenotypes, often in unexpected ways. This has important implications for genomic medicine and for the application of genome editing.
Pervasive pleiotropy
Pleiotropy is the phenomenon in genetics whereby a DNA variant influences multiple traits. We have known for decades that pleiotropy is widespread because in plant and animal breeding, and in laboratory selection experiments, when selection is applied to one trait, the mean of other traits also changes from generation to generation. The response to selection reflects the genetic correlation between traits, which summarizes the genome-wide average effects of pleiotropy at shared loci. In studies of human traits, estimates of the genetic correlation can be obtained using traditional family-based study designs , or high-dimensional genetic data from genome-wide association studies (GWAS) [2, 3]. These estimates provide no information on where in the genome DNA variants with pleiotropic effects exist, on whether individual shared variants have concordant or discordant effects across traits, or if the effects are causally related as opposed to operating through independent biological pathways. Several new papers have described methods that address these questions using GWAS summary data [4–6]. Here, we review key advances from these papers that enable more in-depth investigations of pleiotropy, and we discuss their implications for genomic medicine.
Understanding pleiotropy using GWAS
GWAS have been applied to hundreds of complex traits and common diseases, yielding thousands of genetic associations that surpass accepted standards for statistical significance . Several studies have used results from GWAS to systematically identify genetic variants associated with multiple traits, both across the breadth of human biomedical traits and disorders [5, 8] and for groups of related diseases with prior evidence for a shared etiology (for example, immune-mediated diseases ). As expected, pleiotropy is commonly found for variants associated with traits in the same “domain”—for example, Parkes and colleagues identified 71 genome-wide significant variants associated with two or more of six immune-mediated diseases—but there are interesting subtleties to this genetic overlap. For instance, although many shared variants have correlated and concordant effects, a surprising number are discordant, insomuch as they increase risk for one disorder (such as ankylosing spondylitis) but are protective for another (such as rheumatoid arthritis ). Conversely, other studies have revealed unexpected associations between traits previously thought to be biologically unrelated. For example, in an analysis of GWAS summary data for 42 traits, Pickrell and coworkers reported the identification of a variant (from among a total of >300 pleiotropic loci) in the ABO gene, which determines blood group, that was associated with both coronary artery disease (CAD) and tonsillectomy (among other traits). A major strength of this approach is that pleiotropy can be investigated without the need to measure phenotypes in the same individuals, meaning that confounding by environmental factors is unlikely.
A genetic correlation between traits or diseases can arise due to pleiotropy, as described above, or because of heterogeneity, which refers to the situation in which a proportion of cases for one disease have been misclassified as another. Han and colleagues recently proposed a method, termed breaking up heterogeneous mixture based on cross-locus correlations (BUHMBOX), for distinguishing between these possibilities. In order to detect heterogeneity involving the misdiagnosis of disease B cases as disease A, the approach tests for an excess of positive correlations between independent disease B risk alleles in individuals with disease A—something that is not expected under pleiotropy. Using this approach, which requires GWAS summary data for individuals with disease B and genotype data for individuals with disease A, the authors reported evidence for heterogeneity between seronegative and seropositive forms of rheumatoid arthritis, presumably due to misclassification of a subset of seropositive cases . Heterogeneity is likely to be widespread in complex traits and common diseases, and may be one explanation for the dearth of genetic associations identified for psychiatric disorders such as major depression. BUHMBOX offers a promising tool to differentiate pleiotropy from heterogeneity, although a caveat is that statistical power is limited when the proportion of heterogeneity is low, and yet high levels of heterogeneity may be more likely if pleiotropy is extensive.
Pleiotropy can involve a genetic variant having effects on two or more traits via independent biological pathways, for instance due to effects in different tissues, or because the effect of the variant on one trait is causally related to variation in another trait. Pickrell and colleagues recently put forward an innovative method to tease apart these possibilities, by testing if variants associated with an increase in one trait are always associated with a proportional increase in the other trait, but not the other way around. Using this approach they confirmed the widely accepted causal relationship between low-density lipoprotein cholesterol and CAD, and identified several other plausible causative relationships, including between body mass index (BMI) and both triglyceride level and risk of type 2 diabetes (that is, BMI-increasing alleles have correlated effects on triglycerides and type 2 diabetes risk, but not vice versa). These are exciting developments because they imply that causal relationships can be uncovered more cheaply and rapidly through statistical analysis of genetic data than by performing randomized controlled trials. However, as the authors note, caution is needed in interpretation because the observed phenotype, which is presumed to be causal, may in fact be genetically correlated with another, unobserved phenotype that is the true causal factor.
A form of pleiotropy commonly encountered in GWAS is that trait- or disease-associated single nucleotide polymorphisms (SNPs) are frequently also associated with variation in gene expression (expression quantitative trait loci (eQTLs)) and/or DNA methylation (methylation quantitative trait loci (meQTLs)). Recently, Zhu and coworkers proposed a novel method termed summary-data-based Mendelian randomization (SMR) for combining GWAS summary data with eQTL and meQTL data in order to isolate the most likely functional gene or regulatory element underlying statistical associations for complex traits and common diseases. They also proposed a method (heterogeneity in dependent instruments (HEIDI)) that can distinguish pleiotropy from linkage, since the observation that a trait- or disease-associated SNP is also a cis-eQTL may actually be due to linkage disequilibrium between the sentinel SNP and other SNPs that are independently causally related to gene expression and the trait or disease under investigation.
We have emphasized evidence for pleiotropy from GWAS here, but pleiotropy is also evident for rare mutations underlying Mendelian disorders. Indeed, specific “syndromes” can be diagnosed on the basis of the combination of phenotypes that arise from the same causal mutation. For example, Rett syndrome, caused by mutations in the MECP2 gene, which encodes a protein important for nerve cell function, is a neurological disorder characterized by intellectual disability and apraxia that frequently presents with short stature and gastrointestinal problems. Another example of a mutation with phenotypic effects spanning different biological “domains” is the cystic fibrosis transmembrane conductance regulator gene (CFTR) ΔF508 mutation causing cystic fibrosis, a disease of the lung that is also associated with male infertility.
Implications for genomic medicine
Pervasive pleiotropy has important implications for genomic medicine, particularly as we move into the era of personalized medicine and genome editing. One issue is that focusing on the effect of a mutation or polymorphism on a single disease may be inadequate, since specific genetic variants may show strong associations with multiple traits but in opposite directions . This is especially salient in the context of identifying molecular targets for drug development , and when contemplating “fixing” mutations using genome editing approaches such as the CRISPR-Cas system, since this might have unexpected genetic, and therefore phenotypic, side effects. We find more evidence for pleiotropy the more we look, and yet the vast majority of phenotypes are never measured. Indeed, one could ask, given the enormous dimensionality of the phenome, how likely it is that functional variants exist without pleiotropic effects. Herein lies a major challenge for the field, as the possibility of detrimental effects (for example, as a consequence of genome editing) may be hard to rule out.
To some extent, this problem will be ameliorated by the availability of GWAS data from very large studies, such as the UK Biobank and US National Institutes of Health Precision Medicine Initiative, in which participants are measured for a large number of phenotypes. In parallel, large-scale genome sequencing studies matching data on rare mutations with deep phenotyping (for example, ) will help to characterize the phenotypic spectrum of gene-disrupting mutations in specific genes, and thus clarify if such events are associated solely with deleterious phenotypic outcomes as opposed to a mix of detrimental and beneficial consequences. We can expect these studies to deliver many new and unexpected discoveries on genome–phenome associations, including plausible causal trait relationships. We anticipate that pleiotropy will come to be recognized as a (near) universal property of genetic variants contributing to human phenotypic variation. The limiting factor in progress towards a more complete understanding of the relationship between genome and phenome will be the availability of high-dimensional phenotype data.
Abbreviations
BMI, body mass index; BUHMBOX, breaking up heterogeneous mixture based on cross-locus correlations; CAD, coronary artery disease; eQTLs, expression quantitative trait loci; GWAS, genome-wide association studies; HEIDI, heterogeneity in dependent instruments; meQTLs, methylation quantitative trait loci; SMR, summary-data-based Mendelian randomization; SNP, single nucleotide polymorphism.
Acknowledgements
We thank members of the Center for Neurogenetics and Statistical Genomics at the University of Queensland for helpful discussions. This work was supported by Australian National Health and Medical Research Council (NHMRC) grants to JG (1087889) and JG and PMV (1067795 and 1103418), and a National Institutes of Health grant (GM099568) to PMV. PMV is supported by an NHMRC Senior Principal Research Fellowship (1078037).
Authors’ contributions
JG and PMV jointly wrote the manuscript. Both authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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13432 | https://leah4sci.com/degree-of-unsaturation-aka-index-of-hydrogen-deficiency/ | MCAT and Organic Chemistry Study Guides, Videos, Cheat Sheets, tutoring and more
Degree of Unsaturation aka Index of Hydrogen Deficiency
By Leah4sci
Degree of unsaturation is typically covered at the start of your organic chemistry course when you learn how to identify constitutional isomers. Yet it amazes me how many advanced orgo students still don't understand or know this concept at the Orgo 2 level.
This concept is CRITICAL for finding isomers, identifying key structures during spectroscopy, and identifying the unknown in a complex reaction roadmap when only a formula is given.
What's more confusing is the way this information is taught. A bunch of letters and numbers to calculate that appear to make little sense overall. This video will show you how to break up the complex ‘Degree of Unsaturation' formula into very simple and easy to understand components.
You will hear this referred to as:
DOU = Degrees of Unsaturation
IHD = Index of Hydrogen Deficiency
DBE = Double Bond Equivalents
(Click HERE to watch this video on YouTube. Transcription coming soon)
Organic Chemistry Reference Material and Cheat Sheets
Alkene Reactions Overview Cheat Sheet – Organic Chemistry
The true key to successful mastery of alkene reactions lies in practice practice practice. However, … [Read More...]
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While the pre-2015 MCAT only tests you on science and verbal, you are still required to perform … [Read More...]
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7
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苫
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舌相線
5
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4
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5
g x `y m
4
舌相線
5
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5
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∐ + 4
8
〇
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：土彠舌
x
軲亨黙皈
x
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x
截跔＝土彠舌
y
軲亨黙皈
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y
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y gx y gx
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,
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(0)
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( ) ( )
7 7 0 0
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y y y y x x x x
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7 7
,
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(
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)
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7
C
舌
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：
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5 5
x x dt y y it
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＃
(
t
∂
)
歡 皈 愂 掫 迗
y
軲 愂 夬 貥 皈 愂 掫 迗
x
軲 愂 夬
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751
誰綷復誾
7-8
冊縴褌翐謝羦
笣丆冊
笣亃童
Khftkh `y mccfi 0576
幸牂
156
?
〇
兦相線皈闓俀＂相線斶稍弎皈觡＆
：
亃允丅欧斶稍絈
7 7 7 0 0 0
5 5
g x y a g x y a
4+ + 4
皈觡
(
x
＃
y
)
仡衢兦相線
7 7 7 7
:5
C g x ` y a
4
＝
0 0 0 0
:5
C g x ` y a
4
皈具吃亨黙＃兿叮胴皈闓俀妀不：
闓俀
盲亨斳丅黙
幱
衃
釄
吂
觡
恵朆丅觡
焧觡
焧陕多絈觡
各稷
盲家斶稍絈
矝盹斶稍絈
盲侔斶稍絈
梔仿
7 7 0 0
g g
≥
7 7 7 0 0 0
g a g a
4 ≥
7 7 7 0 0 0
g a g a
4 4
土彠
<
〇两黙兣弎：訤
7
U
(
7
x
＃
7
y
)
＃
0
U
(
0
x
＃
0
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為坕樖幱靠上盲畵皈兦黙＃剌
7 0
U U
皈两黙坕樖為
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(
7 0
0
x x
+
＃
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0
y y
+
)
2
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：
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皈丆頀黙
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苫
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N
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苫
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‰
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751
誰綷復誾
7-8
冊縴褌翐謝羦
笣丆冊
笣亃童
Khftkh `y mccfi 0576
幸牂
175
(7)
苫
(1,0)
U
〇
(<,1)
W
〇
(7,)
P g
∐
丆黙具線＃汀
g
乍倳
(0)
不土囝梔相線
7018
,,,
C C C C
皈斓玌刏别為
7018
,,,
d d d d
＃詯毘輁兿夬導＞
：
(7) 7
＝
(0)
0781
d d d d
9 9 9
顙顃
：
(7)
訤
U
(1
＃
7)
＃
W
(7
＃
g
)
＃
P
(
;
∐
＃
7
∐
)
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g
皈倳
(0)
訤
G
＃
@
＃
A
＃
H
＃
K
為坕樖幱靠上丅倍歡亘邊彠皈頀黙＃宁 皈两忁舌厞黙釄吂＃丘頀黙
K
圢
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KG
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：
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(0)
AH
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1
∐
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@
(1
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0)
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A
(
m
＃
;)
＃
H
(
7
∐
＃
8)
＃詯汀滾趱不刜合梔 仿皈
m
倳：
畿
G@
//
A H
晀＃汀
m
皈倳
畿
GA
⊫
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m
皈倳
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G
(1
＃
7)
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C
：
0 1 5
x y
4
汀通遉
G
黙丘舌相線
C
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汀 通遉
G
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C
垀相皈相線斶稍弎
：
(7)
;
＝
7
∐
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0 ; 5
x y
∐ 4
＝
0 ; 5
x y
∐ ∐ 4
侍顃 7
侍顃 0
y x
0
C
7
C
1
C
8
C
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751
誰綷復誾
7-8
冊縴褌翐謝羦
笣丆冊
笣亃童
Khftkh `y mccfi 0576
幸牂
177
顙顃
：
(7)
訤
G
(0
＃
7)
＃
@
(1
＃
;)
＃
A
(5
＃
7
∐
)
＃
H
(0
＃
m
)
＃詯尷不刜梔仿刏别汀出
m
倳：
畿
G@
//
AH
晀＃
m
倳
畿
G@
⊫
A H
晀＃
m
倳
(0)
汀通遉兦相線
7
C
：
0 5
x y
4
及
0
C
：
0 1 7 5
x y
∐ ∐ 4
皈亨黙
丘幱衃斳相線
1 8 ; 5
x y
∐ ∐ 4
皈相線斶稍弎
丘垀相斳相線
; 8 <5
x y
∐ + 4
皈相線斶稍弎
：
(7)
<
＝
1 0
∐
(0)
1 8 7 5
x y
∐ ∐ 4
＝
8 ; 6 5
x y
4
(7)
汀綑遉
(0,1)
G
＃
(8, 0)
@
∐
皈相線斶稍弎
(0)
汀綑遉
(0,8)
丘斓玌為
1
皈相線斶稍弎
(1)
苫
C
皈斓玌為
1
＃
y
截跔為
;
＃剌
C
皈斶稍弎為佛＞
(8)
苫
C
相線皈
x
截跔＃
y
截跔刏别為
1, 0
∐
＃汀
C
皈相線斶稍弎＞
：
(7)
; 0 7? 5
x y
∐ 4
＝
(0)
1 0 5
x y
∐ ∐ 4
＝
(1)1;
y x
4 +
＝
(8)
0 1?
x y
∐ 4
侍顃 1
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13434 | https://askfilo.com/chemistry-question-answers/the-number-of-significant-figures-in-000210-isa-fiveb-sixc-fourd-three | Solving time: 2 mins
The number of significant figures in 0.00210 is
Views: 6,166 students
Updated on: Sep 24, 2023
Text SolutionText solutionverified iconVerified
(d) In the given number 0.00210, only last digits 210 are considered as significant figures. Thus the given number has three significant figures.
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| Question Text | The number of significant figures in 0.00210 is |
| Updated On | Sep 24, 2023 |
| Topic | Some Basic Concepts of Chemistry |
| Subject | Chemistry |
| Class | Class 11 |
| Answer Type | Text solution:1 Video solution: 11 |
| Upvotes | 1054 |
| Avg. Video Duration | 4 min |
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13435 | https://en.wikipedia.org/wiki/Insertion_(genetics) | Jump to content
Insertion (genetics)
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From Wikipedia, the free encyclopedia
Type of mutation
In genetics, an insertion (also called an insertion mutation) is the addition of one or more nucleotide base pairs into a DNA sequence. This can often happen in microsatellite regions due to the DNA polymerase slipping. Insertions can be anywhere in size from one base pair incorrectly inserted into a DNA sequence to a section of one chromosome inserted into another. The mechanism of the smallest single base insertion mutations is believed to be through base-pair separation between the template and primer strands followed by non-neighbor base stacking, which can occur locally within the DNA polymerase active site. On a chromosome level, an insertion refers to the insertion of a larger sequence into a chromosome. This can happen due to unequal crossover during meiosis.
N region addition is the addition of non-coded nucleotides during recombination by terminal deoxynucleotidyl transferase.
P nucleotide insertion is the insertion of palindromic sequences encoded by the ends of the recombining gene segments.
Trinucleotide repeats are classified as insertion mutations and sometimes as a separate class of mutations.
Methods
[edit]
Zinc finger nuclease(ZFN), Transcription activator-like effector nucleases (TALEN), and CRISPR gene editing are the three main methods used in the former research to achieve gene insertion. And CRISPR/Cas tools have already become one of the most used methods to present research.[citation needed]
Based on CRISPR/Cas tools, different systems have already been developed to achieve specific functions. For example, one strategy is double-strand nucleases cutting system, using the normal Cas9 protein with single guide RNA (sgRNA) and then achieving the gene insertion through end-joining or dividing cells with the DNA repair system. Another example is the prime editing system, which uses Cas9 nickase and the prime editing guide RNA (pegRNA) carrying the target genes.
One limitation of current technology is that the size for DNA precise insertion is not large enough to meet the demand for genome research. RNA-guided DNA transposition is an emerging area to solve this problem. More efficient methods are expected to be developed and applied in the genome engineering area.
Effects
[edit]
Insertions can be particularly hazardous if they occur in an exon, the amino acid coding region of a gene. A frameshift mutation, an alteration in the normal reading frame of a gene, results if the number of inserted nucleotides is not divisible by three, i.e., the number of nucleotides per codon. Frameshift mutations will alter all the amino acids encoded by the gene following the mutation. Usually, insertions and the subsequent frameshift mutation will cause the active translation of the gene to encounter a premature stop codon, resulting in an end to translation and the production of a truncated protein. Transcripts carrying the frameshift mutation may also be degraded through Nonsense-mediated decay during translation, thus not resulting in any protein product. If translated, the truncated proteins frequently are unable to function properly or at all and can result in any number of genetic disorders depending on the gene in which the insertion occurs.
In-frame insertions occur when the reading frame is not altered as a result of the insertion; the number of inserted nucleotides is divisible by three. The reading frame remains intact after the insertion and translation will most likely run to completion if the inserted nucleotides do not code for a stop codon. However, because of the inserted nucleotides, the finished protein will contain, depending on the size of the insertion, multiple new amino acids that may affect the function of the protein.[citation needed]
See also
[edit]
Indel
Insertional mutagenesis
Loss-of-Function Mutations
Gain-of-Function Mutations
Deletion (genetics)
References
[edit]
^ Banavali, Nilesh K. (2013). "Partial Base Flipping is Sufficient for Strand Slippage near DNA Duplex Termini". Journal of the American Chemical Society. 135 (22): 8274–8282. doi:10.1021/ja401573j. PMID 23692220.
^ "Mechanisms: Genetic Variation: Types of Mutations". Evolution 101: Understanding Evolution For Teachers. University of California Museum of Paleontology. Archived from the original on 2009-04-14. Retrieved 2009-09-19. ] Understanding Evolution For Teachers Home. Retrieved on September 19, 2009
^ Brown, Terence A. (2007). "16 Mutations and DNA Repair". Genomes 3. Garland Science. p. 510. ISBN 978-0-8153-4138-3.
^ Faraone, Stephen V.; Tsuang, Ming T.; Tsuang, Debby W. (1999). "5 Molecular Genetics and Mental Illness: The Search for Disease Mechanisms: Types of Mutations". Genetics of Mental Disorders: A Guide for Students, Clinicians, and Researchers. Guilford Press. p. 145. ISBN 978-1-57230-479-6.
^ Jump up to: a b Anzalone, Andrew V.; Koblan, Luke W.; Liu, David R. (2020). "Genome editing with CRISPR–Cas nucleases, base editors, transposases and prime editors". Nature Biotechnology. 38 (7): 824–844. doi:10.1038/s41587-020-0561-9. PMID 32572269. S2CID 256820370.
^ Sun, Chao; Lei, Yuan; Li, Boshu; Gao, Qiang; Li, Yunjia; Cao, Wen; Yang, Chao; Li, Hongchao; Wang, Zhiwei; Li, Yan; Wang, Yanpeng; Liu, Jun; Zhao, Kevin Tianmeng; Gao, Caixia (2023). "Precise integration of large DNA sequences in plant genomes using PrimeRoot editors". Nature Biotechnology: 1–12. doi:10.1038/s41587-023-01769-w. PMID 37095350. S2CID 258311438.
^ Wang, Joy Y.; Doudna, Jennifer A. (2023). "CRISPR technology: A decade of genome editing is only the beginning". Science. 379 (6629): eadd8643. doi:10.1126/science.add8643. PMID 36656942. S2CID 255966509.{{cite journal}}: CS1 maint: article number as page number (link)
^ Shmilovici, A.; Ben-Gal, I. (2007). "Using a VOM Model for Reconstructing Potential Coding Regions in EST Sequences" (PDF). Journal of Computational Statistics. 22 (1): 49–69. doi:10.1007/s00180-007-0021-8. S2CID 2737235. Archived from the original (PDF) on 2020-05-31. Retrieved 2014-01-10.
Further reading
[edit]
Pierce, Benjamin A. (2013). Genetics: A Conceptual Approach (5th ed.). W. H. Freeman. ISBN 978-1-4641-5084-5.
Wikimedia Commons has media related to Insertion (genetics).
| | |
--- |
| Mechanisms of mutation | Insertion Deletion Substitution + Transversion + Transition |
| Mutation with respect to structure | | | | --- | | Point mutation | Nonsense mutation Missense mutation Conservative mutation Silent mutation Frameshift mutation Dynamic mutation | | Large-scale mutation | Chromosomal translocations Chromosomal inversions | |
| Mutation with respect to overall fitness | Deleterious mutation Advantageous mutation Neutral mutation Nearly neutral mutation Synonymous mutation Nonsynonymous mutation |
Retrieved from "
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Mutation
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13436 | https://www.centrumaudiology.com/hearing-loss-articles/diplacusis-hear-things-in-stereo/ | Skip to content
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Diplacusis: When Your Hearing is in Stereo
| Centrum Hearing & Audiology
The world was very different millions of years ago. This steamy, volcano-laden landscape is where the long-necked Diplacusis roamed. Thanks to its really long neck and tail, Diplacusis was so large that it was afraid of no predator.
Actually, the long-necked dinosaur from the Jurassic Period is known as Diplodocus. Diplacusis is a hearing affliction that causes you to hear two sounds instead of one.
Diplacusis is an affliction which can be frustrating and confusing causing difficulty communicating.
Maybe you’ve been hearing some unusual things
We’re used to thinking of hearing loss as a sort of progressive lowering of the volume knob. Over time, the idea is, we simply hear less and less. But there are some other, not so well recognized, types of hearing loss. One of the most fascinating (or, perhaps, frustrating) such presentations is a condition called diplacusis.
Diplacusis, what is it?
Exactly what is diplacusis? The meaning of the medical term diplacusis is simply “double hearing”. Typically, your brain takes information from the right ear and information from the left ear and marries them harmoniously into one sound. That’s what you hear. The same thing occurs with your eyes. If you put a hand on your right eye and then a hand on your left eye, you see slightly different images, right? It’s the same with your ears, it’s just that usually, you never notice it.
When your brain can’t effectively combine the two sounds from your ears because they are too different, you have this condition of diplacusis. Monaural diplacusis is caused by hearing loss in only one ear while binaural diplacusis is due to hearing loss in both.
Diplacusis comes in two types
Diplacusis does not affect everyone in the same way. Usually, though, people will experience one of the following two types of diplacusis:
Diplacusis dysharmonica: When the pitch of the right and left ear are off it’s an indication of this type of diplacusis. So when your grandkids speak with you, the pitch of their voice will sound distorted. Maybe your right ear thinks the sound is low-pitched and your left ear thinks the sound is high-pitched. Those sounds can be difficult to understand consequently.
Diplacusis echoica: With this, what you hear will sound off because your brain receives the sound from each ear out of sync with the other instead of hearing two different pitches. Artifacts like echoes can be the result. This can also cause challenges when it comes to understanding speech.
Symptoms of diplacusis
Here are some symptoms of diplacusis:
Hearing echoes where they don’t actually exist.
Hearing that seems off (in timing).
Hearing that seems off (in pitch).
The condition of double vision may be a helpful comparison: It’s normally a symptom of something else, but it can produce some of its own symptoms. (It’s the effect, essentially, not the cause.) In these circumstances, diplacusis is almost always a symptom of hearing loss (either in one ear or in both ears). So your best course of action would be to Schedule an appointment with us for a hearing exam.
What causes diplacusis?
In a very general sense (and probably not surprisingly), the causes of diplacusis line up rather well with the causes of hearing loss. But you may develop diplacusis for a number of specific reasons:
Earwax: In some circumstances, an earwax blockage can hinder your hearing. Whether that earwax causes a partial or full blockage, it can cause diplacusis.
Your ears have damage caused by noise: If you’ve experienced hearing loss caused by noise damage, it’s feasible that it could cause diplacusis.
An infection: Swelling of your ear canal can be the result of an ear infection, sinus infection, or even allergies. This swelling, while a natural response, can effect the way sound travels through your inner ear and to your brain.
A tumor: In some extremely rare cases, tumors in your ear canal can cause diplacusis. Don’t panic! In most instances they’re benign. But you still should talk to us about it.
It’s clear that there are many of the same causes of diplacusis and hearing loss. Meaning that you probably have some level of hearing loss if you’re experiencing diplacusis. Which means you have a good reason to see a hearing specialist.
Treatments for diplacusis
The treatments for diplacusis differ based on the underlying cause. If your condition is the result of a blockage, like earwax, then treatment will focus on the removal of that blockage. However, diplacusis is often caused by permanent sensorineural hearing loss. Here are a few treatment options if that’s the situation:
Hearing aids: The right pair of hearing aids can equalize how your ears hear again. Your diplacusis symptoms will slowly fade when you take advantage of hearing aids. It’s essential to get the proper settings on your hearing aids and you’ll need to have us help you with that.
Cochlear implant: In circumstances where the hearing loss at the root of diplacusis is profound, a cochlear implant might be the only way to get relief from the symptoms.
All of this starts with a hearing exam. Here’s how you can think about it: whatever kind of hearing loss is the cause of your diplacusis, a hearing test will be able to determine that (maybe you just think things sound strange at this point and you don’t even recognize it as diplacusis). Modern hearing assessments are quite sensitive, and good at finding discrepancies between how your ears hear the world.
Hearing well is more fun than not
You’ll be better able to enjoy your life when you get the appropriate treatment for your diplacusis, whether that’s hearing aids or something else. It will be easier to carry on conversations. It will be easier to stay in tune with your family.
So there will be no diplacusis symptoms getting in the way of your ability to hear your grandkids telling you all about the Diplodocus.
Call today for an appointment to have your diplacusis symptoms assessed.
Call Today to Set Up an Appointment
The site information is for educational and informational purposes only and does not constitute medical advice. To receive personalized advice or treatment, schedule an appointment.
Centrum Hearing & Audiology
Pocatello, ID
804 Yellowstone AvePocatello, ID 83201
Call or text:208-915-8574
Monday – Friday: 9am – 5pmSaturday: 9am – 12pmClosed 12pm – 1pm for lunch
American Falls, ID
510 Roosevelt StAmerican Falls, ID 83211
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Soda Springs, ID
Visiting SpecialistsCaribou Medical Clinic300 South 3rd WestSoda Springs, ID 83276
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13437 | https://ratiobound.wordpress.com/2021/03/06/the-history-of-hoffmans-ratio-bound/ | The History of Hoffman’s (Ratio) Bound | Ratio Bound – A Combinatorics Blog
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The History of Hoffman’s (Ratio)Bound
Hoffman’s bound (or: ratio bound) on the size of a coclique (or: independent set, stable set) in a graph is one of the most important bounds in spectral graph theory. At the same time it is often misattributed. Primary reason for is that Hoffman never published it, but people want to cite something for it. A few weeks ago, Willem Haemers published a nice article which presents the history of Hoffman’s ratio bound (here is the journal version).
As I have probably misattributed the bound myself in the past and even one of my favorite books, “Distance-Regular Graphs” by Brouwer, Cohen and Neumaier does so too (but they correct it online), I wanted to make this quick post.
The sad occasion of Willem’s article is that Alan J. Hoffman past away on the 18th January 2021 at the age of 96. May he rest in peace.
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13438 | https://www.shaalaa.com/question-bank-solutions/for-the-polynomial-mx2-2x-3-if-p-1-7-then-find-m_77155 | For the polynomial mx2 − 2x + 3 if p(−1) = 7 then find m. - Algebra
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For the polynomial mx2 − 2x + 3 if p(−1) = 7 then find m.
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Let p(x) = mx2 − 2x + 3
∴ p(−1) = 7
⇒ m × (−1)2 − 2 × (−1) + 3 = 7
⇒ m + 2 + 3 = 7
⇒ m = 7 − 5 = 2
Thus the value of m is 2.
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13439 | https://www.ck12.org/assessment/ui/?test/detail/practice/parallel-and-perpendicular-lines-proofs-practice&isPageView=true | Parallel and Perpendicular Lines Proofs | Practice | CK-12 Foundation
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13440 | https://exa.unne.edu.ar/biologia/fisiologia.vegetal/PlantPhysiologyTaiz2002.pdf | Plant Physiology, 3rd ed by Lincoln Taiz and Eduardo Zeiger Hardcover: 690 pages Publisher: Sinauer Associates; 3 edition (Aug 30 2002) Language: English ISBN: 0878938230 Book Description With this Third Edition, the authors and contributors set a new standard for textbooks in the field by tailoring the study of plant physiology to virtually every student—providing the basics for introductory courses without sacrificing the more challenging material sought by upper-division and graduate-level students. Key pedagogical changes to the text will result in a shorter book. Material typically considered prerequisite for plant physiology courses, as well as advanced material from the Second Edition, will be removed and posted at an affiliated Web site, while many new or revised figures and photographs (now in full color), study questions, and a glossary of key terms will be added. Despite the streamlining of the text, the new edition incorporates all the important new developments in plant physiology, especially in cell, molecular, and developmental biology. The Third Edition's interactive Web component is keyed to textbook chapters and referenced from the book. It includes WebTopics (elaborating on selected topics discussed in the text), WebEssays (discussions of cutting-edge research topics, written by those who did the work), additional study questions (by chapter), additional references, and suggestions for further reading. Book Info Plant Physiology textbook covers the transport and translocation of water and solutes, biochemistry and metabolism, and growth and development. Twenty-three scientists contributed to the text. doi:10.1093/aob/mcg079 Plant physiology. 3rd edn.
L. Taiz and E. Zeiger.
Sunderland: Sinauer Associates. $104´95. 690 pp.
Plant physiology is part of the essential core curriculum every botanist has to master.
As usually non-motile organ-isms that are, in most cases, ®xed to a single locality for their entire lifetime, plants have special needs to cope with widely disparate, and often highly changeable environmental conditions.
Physiological adaptations play as great a role in the evolutionary struggle for life of a plant as morphological ones.
Plant physiology by Taiz and Zeiger (and a plethora of contributing expert authors) is a well-received, established textbook aimed at students taking introductory courses in the ®eld. One's ®rst impression of the book is one of excellent craftsmanship: from the eye-catching cover, to the quality of the paper and print, this third edition of Plant physiology is not only comprehensive, it is attractive. A single encounter will turn the ®rst-time user into a potential buyer. The book is subdivided into 25 chapters, grouped into three larger sections (water, metabolism and development) that cover the major topics of modern plant physiology. All topics are treated in a very balanced way, with approxi-mately equal weight being lent to each. Starting with the basics of each subject, the reader is taken to the very forefront of current knowledge. The writing style is succinct and lucid throughout, and the text is arranged in a two-column format that is very reader-friendly. Speci®c topics are easy to ®nd using the detailed table of contents or index.
In the light of the explosive growth of our understanding of physiological processes in plants resulting from techno-logical advances in the ®eld of molecular biology, it is an amazing achievement to ®nd that the authors have managed to keep the book's length to a mere' 690 pages. That this has not been achieved at the expense of including recent literature is borne out throughout the book: ®gures 19±41, for example, have been adopted from a 2001 publication.
The extensive reference lists that conclude each chapter also demonstrate how up-to-date this third edition is, with a large proportion of the references dating from the last 5 years. The transfer of the apprentice from the textbook to the forefront research literature is greatly facilitated in this way. A glossary giving a brief explanation of many technical terms reinforces this impression.
An outstanding feature of this textbook is the large number of crisp ®gures, most of them in full colour.
Although also rendering the ®gures aesthetically pleasing, the use of colour usually serves a didactic purpose (which may well be its primary cause). I found none of the ®gures to be overladen with detail nor of inappropriate (microscop-ically small or in¯ated) size. Full marks for this!
Plant Physiology is a modern textbook with a refreshing style and layout. The overall impression is one of a well-thought-out teaching aid. The authors/editors have achieved a remarkable feat in bringing it up-to-date without allowing any dead wood to accumulate (a symptom of ageing that unfortunately befalls the majority of textbooks as they advance through numerous editions). Let's hope they will be able to retain this phoenix-like rejuvenating potential in future editions. In its third edition, Plant physiology successfully defends its position in the top league of botanical textbooks. It is excellently produced, attractive and fun to use. It can even make an aged botanist wish he were an undergraduate student again!
Thomas Lazar Annals of Botany 91: 750-751, 2003 © 2003 Annals of Botany Company Plant Cells 1 Chapter THE TERM CELL IS DERIVED from the Latin cella, meaning storeroom or chamber. It was first used in biology in 1665 by the English botanist Robert Hooke to describe the individual units of the honeycomb-like structure he observed in cork under a compound microscope. The “cells” Hooke observed were actually the empty lumens of dead cells surrounded by cell walls, but the term is an apt one because cells are the basic building blocks that define plant structure.
This book will emphasize the physiological and biochemical func-tions of plants, but it is important to recognize that these functions depend on structures, whether the process is gas exchange in the leaf, water conduction in the xylem, photosynthesis in the chloroplast, or ion transport across the plasma membrane. At every level, structure and function represent different frames of reference of a biological unity.
This chapter provides an overview of the basic anatomy of plants, from the organ level down to the ultrastructure of cellular organelles. In subsequent chapters we will treat these structures in greater detail from the perspective of their physiological functions in the plant life cycle.
PLANT LIFE: UNIFYING PRINCIPLES The spectacular diversity of plant size and form is familiar to everyone.
Plants range in size from less than 1 cm tall to greater than 100 m. Plant morphology, or shape, is also surprisingly diverse. At first glance, the tiny plant duckweed (Lemna) seems to have little in common with a giant saguaro cactus or a redwood tree. Yet regardless of their specific adaptations, all plants carry out fundamentally similar processes and are based on the same architectural plan. We can summarize the major design elements of plants as follows: • As Earth’s primary producers, green plants are the ultimate solar collectors. They harvest the energy of sunlight by converting light energy to chemical energy, which they store in bonds formed when they synthesize carbohydrates from carbon dioxide and water.
• Other than certain reproductive cells, plants are non-motile. As a substitute for motility, they have evolved the ability to grow toward essential resources, such as light, water, and mineral nutrients, throughout their life span.
• Terrestrial plants are structurally reinforced to sup-port their mass as they grow toward sunlight against the pull of gravity.
• Terrestrial plants lose water continuously by evapo-ration and have evolved mechanisms for avoiding desiccation.
• Terrestrial plants have mechanisms for moving water and minerals from the soil to the sites of photosyn-thesis and growth, as well as mechanisms for moving the products of photosynthesis to nonphotosynthetic organs and tissues.
OVERVIEW OF PLANT STRUCTURE Despite their apparent diversity, all seed plants (see Web Topic 1.1) have the same basic body plan (Figure 1.1). The vegetative body is composed of three organs: leaf, stem, and root. The primary function of a leaf is photosynthesis, that of the stem is support, and that of the root is anchorage and absorption of water and minerals. Leaves are attached to the stem at nodes, and the region of the stem between two nodes is termed the internode. The stem together with its leaves is commonly referred to as the shoot.
There are two categories of seed plants: gymnosperms (from the Greek for “naked seed”) and angiosperms (based on the Greek for “vessel seed,” or seeds contained in a ves-sel). Gymnosperms are the less advanced type; about 700 species are known. The largest group of gymnosperms is the conifers (“cone-bearers”), which include such commercially important forest trees as pine, fir, spruce, and redwood.
Angiosperms, the more advanced type of seed plant, first became abundant during the Cretaceous period, about 100 million years ago. Today, they dominate the landscape, easily outcompeting the gymnosperms. About 250,000 species are known, but many more remain to be character-ized. The major innovation of the angiosperms is the flower; hence they are referred to as flowering plants (see Web Topic 1.2).
Plant Cells Are Surrounded by Rigid Cell Walls A fundamental difference between plants and animals is that each plant cell is surrounded by a rigid cell wall. In animals, embryonic cells can migrate from one location to another, resulting in the development of tissues and organs containing cells that originated in different parts of the organism.
In plants, such cell migrations are prevented because each walled cell and its neighbor are cemented together by a middle lamella. As a consequence, plant development, unlike animal development, depends solely on patterns of cell division and cell enlargement.
Plant cells have two types of walls: primary and sec-ondary (Figure 1.2). Primary cell walls are typically thin (less than 1 µm) and are characteristic of young, growing cells. Secondary cell walls are thicker and stronger than primary walls and are deposited when most cell enlarge-ment has ended. Secondary cell walls owe their strength and toughness to lignin, a brittle, gluelike material (see Chapter 13).
The evolution of lignified secondary cell walls provided plants with the structural reinforcement necessary to grow vertically above the soil and to colonize the land.
Bryophytes, which lack lignified cell walls, are unable to grow more than a few centimeters above the ground.
New Cells Are Produced by Dividing Tissues Called Meristems Plant growth is concentrated in localized regions of cell division called meristems. Nearly all nuclear divisions (mitosis) and cell divisions (cytokinesis) occur in these meristematic regions. In a young plant, the most active meristems are called apical meristems; they are located at the tips of the stem and the root (see Figure 1.1). At the nodes, axillary buds contain the apical meristems for branch shoots. Lateral roots arise from the pericycle, an internal meristematic tissue (see Figure 1.1C). Proximal to (i.e., next to) and overlapping the meristematic regions are zones of cell elongation in which cells increase dramatically in length and width. Cells usually differentiate into spe-cialized types after they elongate.
The phase of plant development that gives rise to new organs and to the basic plant form is called primary growth. Primary growth results from the activity of apical meristems, in which cell division is followed by progres-sive cell enlargement, typically elongation. After elonga-tion in a given region is complete, secondary growth may occur. Secondary growth involves two lateral meristems: the vascular cambium (plural cambia) and the cork cam-bium. The vascular cambium gives rise to secondary xylem (wood) and secondary phloem. The cork cambium pro-duces the periderm, consisting mainly of cork cells.
Three Major Tissue Systems Make Up the Plant Body Three major tissue systems are found in all plant organs: dermal tissue, ground tissue, and vascular tissue. These tis-2 Chapter 1 FIGURE 1.1 Schematic representation of the body of a typi-cal dicot. Cross sections of (A) the leaf, (B) the stem, and (C) the root are also shown. Inserts show longitudinal sections of a shoot tip and a root tip from flax (Linum usitatissi-mum), showing the apical meristems. (Photos © J. Robert Waaland/Biological Photo Service.) L Upper epidermis (dermal tissue) Cuticle Cuticle Palisade parenchyma (ground tissue) Xylem Phloem Phloem Vascular cambium Ground tissues Lower epidermis (dermal tissue) Spongy mesophyll (ground tissue) Guard cell Stomata Lower epidermis Epidermis (dermal tissue) Cortex Pith Xylem Vascular tissues Vascular tissues Leaf primordia Shoot apex and apical meristem Axillary bud with meristem Leaf Node Internode Vascular tissue Soil line Lateral root Taproot Root hairs Root apex with apical meristem Root cap (A) Leaf (B) Stem Mesophyll Bundle sheath parenchyma Root hair (dermal tissue) Epidermis (dermal tissue) Cortex Pericycle (internal meristem) Endodermis Ground tissues Phloem Xylem Vascular tissues (C) Root Vascular cambium Middle lamella Primary wall Simple pit Primary wall Secondary wall Plasma membrane FIGURE 1.2 Schematic representation of primary and secondary cell walls and their relationship to the rest of the cell.
(A) Dermal tissue: epidermal cells (C) Ground tissue: collenchyma cells (D) Ground tissue: sclerenchyma cells (B) Ground tissue: parenchyma cells Primary cell wall Middle lamella Primary cell wall Nucleus Sclereids Fibers Simple pits Vessel elements End wall perforation (E) Vascular tisssue: xylem and phloem Secondary walls Bordered pits Primary walls Tracheids Sieve plate Sieve areas Sieve plate Sieve tube element (angiosperms) Companion cell Nucleus Sieve cell (gymnosperms) Xylem Phloem sues are illustrated and briefly chacterized in Figure 1.3.
For further details and characterizations of these plant tis-sues, see Web Topic 1.3.
THE PLANT CELL Plants are multicellular organisms composed of millions of cells with specialized functions. At maturity, such special-ized cells may differ greatly from one another in their struc-tures. However, all plant cells have the same basic eukary-otic organization: They contain a nucleus, a cytoplasm, and subcellular organelles, and they are enclosed in a mem-brane that defines their boundaries (Figure 1.4). Certain structures, including the nucleus, can be lost during cell maturation, but all plant cells begin with a similar comple-ment of organelles.
Plant Cells 5 FIGURE 1.3 (A) The outer epidermis (dermal tissue) of a leaf of welwischia mirabilis (120×). Diagrammatic representa-tions of three types of ground tissue: (B) parenchyma, (C) collenchyma, (D) sclerenchyma cells, and (E) conducting cells of the xylem and phloem. (A © Meckes/Ottawa/Photo Researchers, Inc.) Chromatin Nuclear envelope Nucleolus Nucleus Vacuole Tonoplast Rough endoplasmic reticulum Ribosomes Smooth endoplasmic reticulum Golgi body Chloroplast Mitochondrion Peroxisome Middle lamella Primary cell wall Plasma membrane Cell wall Intercellular air space Primary cell wall Compound middle lamella FIGURE 1.4 Diagrammatic representation of a plant cell. Various intracellular com-partments are defined by their respective membranes, such as the tonoplast, the nuclear envelope, and the membranes of the other organelles. The two adjacent pri-mary walls, along with the middle lamella, form a composite structure called the compound middle lamella.
L An additional characteristic feature of plant cells is that they are surrounded by a cellulosic cell wall. The following sections provide an overview of the membranes and organelles of plant cells. The structure and function of the cell wall will be treated in detail in Chapter 15.
Biological Membranes Are Phospholipid Bilayers That Contain Proteins All cells are enclosed in a membrane that serves as their outer boundary, separating the cytoplasm from the exter-nal environment. This plasma membrane (also called plas-malemma) allows the cell to take up and retain certain sub-stances while excluding others. Various transport proteins embedded in the plasma membrane are responsible for this selective traffic of solutes across the membrane. The accu-mulation of ions or molecules in the cytosol through the action of transport proteins consumes metabolic energy.
Membranes also delimit the boundaries of the specialized internal organelles of the cell and regulate the fluxes of ions and metabolites into and out of these compartments.
According to the fluid-mosaic model, all biological membranes have the same basic molecular organization.
They consist of a double layer (bilayer) of either phospho-lipids or, in the case of chloroplasts, glycosylglycerides, in which proteins are embedded (Figure 1.5A and B). In most membranes, proteins make up about half of the mem-brane’s mass. However, the composition of the lipid com-ponents and the properties of the proteins vary from mem-brane to membrane, conferring on each membrane its unique functional characteristics.
Phospholipids.
Phospholipids are a class of lipids in which two fatty acids are covalently linked to glycerol, which is covalently linked to a phosphate group. Also attached to this phosphate group is a variable component, called the head group, such as serine, choline, glycerol, or inositol (Figure 1.5C). In contrast to the fatty acids, the head groups are highly polar; consequently, phospholipid mol-ecules display both hydrophilic and hydrophobic proper-ties (i.e., they are amphipathic). The nonpolar hydrocarbon chains of the fatty acids form a region that is exclusively hydrophobic—that is, that excludes water.
Plastid membranes are unique in that their lipid com-ponent consists almost entirely of glycosylglycerides rather than phospholipids. In glycosylglycerides, the polar head group consists of galactose, digalactose, or sulfated galactose, without a phosphate group (see Web Topic 1.4).
The fatty acid chains of phospholipids and glycosyl-glycerides are variable in length, but they usually consist of 14 to 24 carbons. One of the fatty acids is typically satu-rated (i.e., it contains no double bonds); the other fatty acid chain usually has one or more cis double bonds (i.e., it is unsaturated).
The presence of cis double bonds creates a kink in the chain that prevents tight packing of the phospholipids in the bilayer. As a result, the fluidity of the membrane is increased. The fluidity of the membrane, in turn, plays a critical role in many membrane functions. Membrane flu-idity is also strongly influenced by temperature. Because plants generally cannot regulate their body temperatures, they are often faced with the problem of maintaining mem-brane fluidity under conditions of low temperature, which tends to decrease membrane fluidity. Thus, plant phos-pholipids have a high percentage of unsaturated fatty acids, such as oleic acid (one double bond), linoleic acid (two double bonds) and α-linolenic acid (three double bonds), which increase the fluidity of their membranes.
Proteins.
The proteins associated with the lipid bilayer are of three types: integral, peripheral, and anchored. Inte-gral proteins are embedded in the lipid bilayer. Most inte-gral proteins span the entire width of the phospholipid bilayer, so one part of the protein interacts with the outside of the cell, another part interacts with the hydrophobic core of the membrane, and a third part interacts with the inte-rior of the cell, the cytosol. Proteins that serve as ion chan-nels (see Chapter 6) are always integral membrane pro-teins, as are certain receptors that participate in signal transduction pathways (see Chapter 14). Some receptor-like proteins on the outer surface of the plasma membrane rec-ognize and bind tightly to cell wall consituents, effectively cross-linking the membrane to the cell wall.
Peripheral proteins are bound to the membrane surface by noncovalent bonds, such as ionic bonds or hydrogen bonds, and can be dissociated from the membrane with high salt solutions or chaotropic agents, which break ionic and hydrogen bonds, respectively. Peripheral proteins serve a variety of functions in the cell. For example, some are involved in interactions between the plasma membrane and components of the cytoskeleton, such as microtubules and actin microfilaments, which are discussed later in this chapter.
Anchored proteins are bound to the membrane surface via lipid molecules, to which they are covalently attached.
These lipids include fatty acids (myristic acid and palmitic acid), prenyl groups derived from the isoprenoid pathway (farnesyl and geranylgeranyl groups), and glycosylphos-phatidylinositol (GPI)-anchored proteins (Figure 1.6) (Buchanan et al. 2000).
The Nucleus Contains Most of the Genetic Material of the Cell The nucleus (plural nuclei) is the organelle that contains the genetic information primarily responsible for regulating the metabolism, growth, and differentiation of the cell. Collec-tively, these genes and their intervening sequences are referred to as the nuclear genome. The size of the nuclear genome in plants is highly variable, ranging from about 1.2 × 108 base pairs for the diminutive dicot Arabidopsis thaliana to 1 × 1011 base pairs for the lily Fritillaria assyriaca. The 6 Chapter 1 Plant Cells 7 H3C H3C N+ H H H H H H H H H H H H H H H H H H H H C H C O O O O P C C C C C C C C C C C C O O O O H H H H C C H H H H H H H H C C C C C C H H H H C C H H C C H H H H H H H H H H H C C H H H H C C H H H H C C H H H H C C H H H H C C H H H H H C C P O –O O CH H2C O CH2 CH2 O C O CH2 C O O CH H2C O CH2 CH2 O C O CH2 C O O Cytoplasm Outside of cell Cell wall Plasma membrane (A) (C) (B) Hydrophobic region Hydrophilic region Hydrophilic region Carbohydrates Phospholipid bilayer Choline Phosphate Hydrophilic region Hydrophobic region Glycerol Phosphatidylcholine Phosphatidylcholine Galactosylglyceride Choline Galactose Adjoining primary walls 1 mm Plasma membranes Integral protein Peripheral protein FIGURE 1.5 (A) The plasma membrane, endoplasmic retic-ulum, and other endomembranes of plant cells consist of proteins embedded in a phospholipid bilayer. (B) This trans-mission electron micrograph shows plasma membranes in cells from the meristematic region of a root tip of cress (Lepidium sativum). The overall thickness of the plasma mem-brane, viewed as two dense lines and an intervening space, is 8 nm. (C) Chemical structures and space-filling models of typical phospholipids: phosphatidylcholine and galactosyl-glyceride. (B from Gunning and Steer 1996.) remainder of the genetic information of the cell is contained in the two semiautonomous organelles—the chloroplasts and mitochondria—which we will discuss a little later in this chapter.
The nucleus is surrounded by a double membrane called the nuclear envelope (Figure 1.7A). The space between the two membranes of the nuclear envelope is called the perinuclear space, and the two membranes of the nuclear envelope join at sites called nuclear pores (Fig-ure 1.7B). The nuclear “pore” is actually an elaborate struc-ture composed of more than a hundred different proteins arranged octagonally to form a nuclear pore complex (Fig-ure 1.8). There can be very few to many thousands of nuclear pore complexes on an individual nuclear envelope.
The central “plug” of the complex acts as an active (ATP-driven) transporter that facilitates the movement of macro-molecules and ribosomal subunits both into and out of the nucleus. (Active transport will be discussed in detail in Chapter 6.) A specific amino acid sequence called the nuclear localization signal is required for a protein to gain entry into the nucleus.
The nucleus is the site of storage and replication of the chromosomes, composed of DNA and its associated pro-teins. Collectively, this DNA–protein complex is known as 8 Chapter 1 O C HN Gly C S CH2 Cys C N CH2 S C CH3 N O C O H N CH2 S C CH3 N O C O H N HO OH O NH P P Myristic acid (C14) Palmitic acid (C16) Farnesyl (C15) Ceramide Geranylgeranyl (C20) Lipid bilayer Fatty acid–anchored proteins Prenyl lipid–anchored proteins Glycosylphosphatidylinositol (GPI)– anchored protein Ethanolamine Galactose Glucosamine Inositol Mannose OUTSIDE OF CELL CYTOPLASM Amide bond FIGURE 1.6 Different types of anchored membrane proteins that are attached to the membrane via fatty acids, prenyl groups, or phosphatidylinositol. (From Buchanan et al. 2000.) chromatin. The linear length of all the DNA within any plant genome is usually millions of times greater than the diameter of the nucleus in which it is found. To solve the problem of packaging this chromosomal DNA within the nucleus, segments of the linear double helix of DNA are coiled twice around a solid cylinder of eight histone pro-tein molecules, forming a nucleosome. Nucleosomes are arranged like beads on a string along the length of each chromosome.
During mitosis, the chromatin condenses, first by coil-ing tightly into a 30 nm chromatin fiber, with six nucleo-somes per turn, followed by further folding and packing processes that depend on interactions between proteins and nucleic acids (Figure 1.9). At interphase, two types of chromatin are visible: heterochromatin and euchromatin.
About 10% of the DNA consists of heterochromatin, a highly compact and transcriptionally inactive form of chro-matin. The rest of the DNA consists of euchromatin, the dispersed, transcriptionally active form. Only about 10% of the euchromatin is transcriptionally active at any given time. The remainder exists in an intermediate state of con-densation, between heterochromatin and transcriptionally active euchromatin.
Nuclei contain a densely granular region, called the nucleolus (plural nucleoli), that is the site of ribosome syn-thesis (see Figure 1.7A). The nucleolus includes portions of one or more chromosomes where ribosomal RNA (rRNA) genes are clustered to form a structure called the nucleolar organizer. Typical cells have one or more nucleoli per nucleus. Each 80S ribosome is made of a large and a small subunit, and each subunit is a complex aggregate of rRNA and specific proteins. The two subunits exit the nucleus separately, through the nuclear pore, and then unite in the cytoplasm to form a complete ribosome (Figure 1.10A).
Ribosomes are the sites of protein synthesis.
Protein Synthesis Involves Transcription and Translation The complex process of protein synthesis starts with tran-scription—the synthesis of an RNA polymer bearing a base Plant Cells 9 CYTOPLASM Nuclear pore complex 120 nm NUCLEOPLASM Inner nuclear membrane Outer nuclear membrane Cytoplasmic filament Cytoplasmic ring Spoke-ring assembly Central transporter Nuclear basket Nuclear ring FIGURE 1.7 (A) Transmission electron micrograph of a plant cell, showing the nucleolus and the nuclear envelope. (B) Freeze-etched preparation of nuclear pores from a cell of an onion root. (A courtesy of R. Evert; B cour-tesy of D. Branton.) (A) (B) Chromatin Nucleolus Nuclear envelope FIGURE 1.8 Schematic model of the structure of the nuclear pore complex. Parallel rings composed of eight subunits each are arranged octagonally near the inner and outer membranes of the nuclear envelope. Various proteins form the other structures, such as the nuclear ring, the spoke-ring assembly, the central transporter, the cytoplasmic fila-ments, and the nuclear basket.
sequence that is complementary to a specific gene. The RNA transcript is processed to become messenger RNA (mRNA), which moves from the nucleus to the cytoplasm.
The mRNA in the cytoplasm attaches first to the small ribo-somal subunit and then to the large subunit to initiate translation.
Translation is the process whereby a specific protein is synthesized from amino acids, according to the sequence information encoded by the mRNA. The ribosome travels the entire length of the mRNA and serves as the site for the sequential bonding of amino acids as specified by the base sequence of the mRNA (Figure 1.10B).
The Endoplasmic Reticulum Is a Network of Internal Membranes Cells have an elaborate network of internal membranes called the endoplasmic reticulum (ER). The membranes of the ER are typical lipid bilayers with interspersed integral and peripheral proteins. These membranes form flattened or tubular sacs known as cisternae (singular cisterna).
Ultrastructural studies have shown that the ER is con-tinuous with the outer membrane of the nuclear envelope.
There are two types of ER—smooth and rough (Figure 1.11)—and the two types are interconnected. Rough ER (RER) differs from smooth ER in that it is covered with ribosomes that are actively engaged in protein synthesis; in addition, rough ER tends to be lamellar (a flat sheet com-posed of two unit membranes), while smooth ER tends to be tubular, although a gradation for each type can be observed in almost any cell.
The structural differences between the two forms of ER are accompanied by functional differences. Smooth ER functions as a major site of lipid synthesis and membrane assembly. Rough ER is the site of synthesis of membrane proteins and proteins to be secreted outside the cell or into the vacuoles.
Secretion of Proteins from Cells Begins with the Rough ER Proteins destined for secretion cross the RER membrane and enter the lumen of the ER. This is the first step in the 10 Chapter 1 Histones 2 nm 11 nm 30 nm 300 nm 700 nm 1400 nm Highly condensed, duplicated metaphase chromosome of a dividing cell Condensed chromatin Looped domains 30 nm chromatin fiber Nucleosomes ( beads on a string”) DNA double helix Nucleosome Linker DNA Chromatids Nucleosome “ FIGURE 1.9 Packaging of DNA in a metaphase chromo-some. The DNA is first aggregated into nucleosomes and then wound to form the 30 nm chromatin fibers. Further coiling leads to the condensed metaphase chromosome.
(After Alberts et al. 2002.) FIGURE 1.10 (A) Basic steps in gene expression, including transcription, processing, export to the cytoplasm, and translation. Proteins may be synthesized on free or bound ribosomes. Secretory proteins containing a hydrophobic signal sequence bind to the signal recognition particle (SRP) in the cytosol. The SRP–ribosome complex then moves to the endoplasmic reticulum, where it attaches to the SRP receptor. Translation proceeds, and the elongating polypep-tide is inserted into the lumen of the endoplasmic reticu-lum. The signal peptide is cleaved off, sugars are added, and the glycoprotein is transported via vesicles to the Golgi. (B) Amino acids are polymerized on the ribosome, with the help of tRNA, to form the elongating polypeptide chain. L Plant Cells 11 CAG AAA AGG tRNA rRNA mRNA mRNA tRNA tRNA mRNA Translation Transcription Processing Cap Cap Cap Poly-A Poly-A Poly-A Poly-A Cap Poly-A Cap Cap Poly-A Poly-A DNA RNA transcript RNA Nucleus Nuclear pore Nuclear envelope Cytoplasm Exon Intron Ribsomal subunits Amino acids Signal recognition particle (SRP) Signal sequence SRP receptor Ribosome Protein synthesis on ribosomes free in cytoplasm Polypeptides free in cytoplasm Protein synthesis on ribosomes attached to endoplasmic reticulum; polypeptide enters lumen of ER Processing and glycosylation in Golgi body; sequestering and secretion of proteins Cleavage of signal sequence Carbohydrate side chain Release of SRP Rough endoplasmic reticulum Polypeptide Transport vesicle AGC GUC UUU UCC GCC UGA 5’ 3’ Ribosome E site P site A site Phe Val Ser Gly Arg Ser Polypeptide chain (A) (B) m7G secretion pathway that involves the Golgi body and vesi-cles that fuse with the plasma membrane.
The mechanism of transport across the membrane is complex, involving the ribosomes, the mRNA that codes for the secretory protein, and a special receptor in the ER membrane. All secretory proteins and most integral mem-brane proteins have been shown to have a hydrophobic sequence of 18 to 30 amino acid residues at the amino-ter-minal end of the chain. During translation, this hydropho-bic leader, called the signal peptide sequence, is recognized by a signal recognition particle (SRP), made up of protein and RNA, which facilitates binding of the free ribosome to SRP receptor proteins (or “docking proteins”) on the ER (see Figure 1.10A). The signal peptide then mediates the transfer of the elongating polypeptide across the ER mem-brane into the lumen. (In the case of integral membrane proteins, a portion of the completed polypeptide remains embedded in the membrane.) Once inside the lumen of the ER, the signal sequence is cleaved off by a signal peptidase. In some cases, a branched oligosaccharide chain made up of N-acetylglucosamine (GlcNac), mannose (Man), and glucose (Glc), having the stoichiometry GlcNac2Man9Glc3, is attached to the free amino group of a specific asparagine side chain. This car-bohydrate assembly is called an N-linked glycan (Faye et al.
1992). The three terminal glucose residues are then removed by specific glucosidases, and the processed gly-coprotein (i.e., a protein with covalently attached sugars) is ready for transport to the Golgi apparatus. The so-called N-linked glycoproteins are then transported to the Golgi apparatus via small vesicles. The vesicles move through the cytosol and fuse with cisternae on the cis face of the Golgi apparatus (Figure 1.12).
12 Chapter 1 Polyribosome (A) Rough ER (surface view) (B) Rough ER (cross section) (C) Smooth ER Ribosomes FIGURE 1.11 The endoplasmic reticulum. (A) Rough ER can be seen in surface view in this micrograph from the alga Bulbochaete. The polyribosomes (strings of ribosomes attached to messenger RNA) in the rough ER are clearly visible. Polyribosomes are also present on the outer surface of the nuclear envelope (N-nucleus). (75,000×) (B) Stacks of regularly arranged rough endoplasmic reticulum (white arrow) in glandular trichomes of Coleus blumei. The plasma membrane is indicated by the black arrow, and the material outside the plasma membrane is the cell wall. (75,000×) (C) Smooth ER often forms a tubular network, as shown in this transmission electron micrograph from a young petal of Primula kewensis.
(45,000×) (Photos from Gunning and Steer 1996.) Proteins and Polysaccharides for Secretion Are Processed in the Golgi Apparatus The Golgi apparatus (also called Golgi complex) of plant cells is a dynamic structure consisting of one or more stacks of three to ten flattened membrane sacs, or cisternae, and an irregular network of tubules and vesicles called the trans Golgi network (TGN) (see Figure 1.12). Each indi-vidual stack is called a Golgi body or dictyosome.
As Figure 1.12 shows, the Golgi body has distinct func-tional regions: The cisternae closest to the plasma membrane are called the trans face, and the cisternae closest to the cen-ter of the cell are called the cis face. The medial cisternae are between the trans and cis cisternae. The trans Golgi network is located on the trans face. The entire structure is stabilized by the presence of intercisternal elements, protein cross-links that hold the cisternae together. Whereas in animal cells Golgi bodies tend to be clustered in one part of the cell and are interconnected via tubules, plant cells contain up to sev-eral hundred apparently separate Golgi bodies dispersed throughout the cytoplasm (Driouich et al. 1994).
The Golgi apparatus plays a key role in the synthesis and secretion of complex polysaccharides (polymers composed of different types of sugars) and in the assembly of the oligosaccharide side chains of glycoproteins (Driouich et al.
1994). As noted already, the polypeptide chains of future gly-coproteins are first synthesized on the rough ER, then trans-ferred across the ER membrane, and glycosylated on the —NH2 groups of asparagine residues. Further modifications of, and additions to, the oligosaccharide side chains are car-ried out in the Golgi. Glycoproteins destined for secretion reach the Golgi via vesicles that bud off from the RER.
The exact pathway of glycoproteins through the plant Golgi apparatus is not yet known. Since there appears to be no direct membrane continuity between successive cisternae, the con-tents of one cisterna are transferred to the next cisterna via small vesicles budding off from the margins, as occurs in the Golgi apparatus of ani-mals. In some cases, however, entire cisternae may progress through the Golgi body and emerge from the trans face.
Within the lumens of the Golgi cis-ternae, the glycoproteins are enzy-matically modified. Certain sugars, such as mannose, are removed from the oligosaccharide chains, and other sugars are added. In addition to these modifications, glycosylation of the —OH groups of hydroxyproline, ser-ine, threonine, and tyrosine residues (O-linked oligosaccharides) also occurs in the Golgi. After being processed within the Golgi, the gly-coproteins leave the organelle in other vesicles, usually from the trans side of the stack. All of this processing appears to confer on each protein a specific tag or marker that specifies the ultimate destination of that protein inside or outside the cell.
In plant cells, the Golgi body plays an important role in cell wall formation (see Chapter 15). Noncellulosic cell wall polysaccharides (hemicellulose and pectin) are synthesized, and a variety of glycoproteins, including hydroxyproline-rich glycoproteins, are processed within the Golgi.
Secretory vesicles derived from the Golgi carry the poly-saccharides and glycoproteins to the plasma membrane, where the vesicles fuse with the plasma membrane and empty their contents into the region of the cell wall. Secre-tory vesicles may either be smooth or have a protein coat.
Vesicles budding from the ER are generally smooth. Most vesicles budding from the Golgi have protein coats of some type. These proteins aid in the budding process during vesi-cle formation. Vesicles involved in traffic from the ER to the Golgi, between Golgi compartments, and from the Golgi to the TGN have protein coats. Clathrin-coated vesicles (Fig-ure 1.13) are involved in the transport of storage proteins from the Golgi to specialized protein-storing vacuoles. They also participate in endocytosis, the process that brings sol-uble and membrane-bound proteins into the cell.
The Central Vacuole Contains Water and Solutes Mature living plant cells contain large, water-filled central vacuoles that can occupy 80 to 90% of the total volume of the cell (see Figure 1.4). Each vacuole is surrounded by a vacuolar membrane, or tonoplast. Many cells also have cytoplasmic strands that run through the vacuole, but each transvacuolar strand is surrounded by the tonoplast.
Plant Cells 13 cis cisternae trans cisternae trans Golgi network (TGN) medial cisternae FIGURE 1.12 Electron micrograph of a Golgi apparatus in a tobacco (Nicotiana tabacum) root cap cell. The cis, medial, and trans cisternae are indicated. The trans Golgi network is associated with the trans cisterna. (60,000×) (From Gunning and Steer 1996.) In meristematic tissue, vacuoles are less prominent, though they are always present as small provacuoles.
Provacuoles are produced by the trans Golgi network (see Figure 1.12). As the cell begins to mature, the provacuoles fuse to produce the large central vacuoles that are charac-teristic of most mature plant cells. In such cells, the cyto-plasm is restricted to a thin layer surrounding the vacuole.
The vacuole contains water and dissolved inorganic ions, organic acids, sugars, enzymes, and a variety of secondary metabolites (see Chapter 13), which often play roles in plant defense. Active solute accumulation provides the osmotic driving force for water uptake by the vacuole, which is required for plant cell enlargement. The turgor pressure generated by this water uptake provides the structural rigidity needed to keep herbaceous plants upright, since they lack the lignified support tissues of woody plants.
Like animal lysosomes, plant vacuoles contain hydro-lytic enzymes, including proteases, ribonucleases, and gly-cosidases. Unlike animal lysosomes, however, plant vac-uoles do not participate in the turnover of macromolecules throughout the life of the cell. Instead, their degradative enzymes leak out into the cytosol as the cell undergoes senescence, thereby helping to recycle valuable nutrients to the living portion of the plant.
Specialized protein-storing vacuoles, called protein bod-ies, are abundant in seeds. During germination the storage proteins in the protein bodies are hydrolyzed to amino acids and exported to the cytosol for use in protein syn-thesis. The hydrolytic enzymes are stored in specialized lytic vacuoles, which fuse with the protein bodies to ini-tiate the breakdown process (Figure 1.14).
Mitochondria and Chloroplasts Are Sites of Energy Conversion A typical plant cell has two types of energy-producing organelles: mitochondria and chloroplasts. Both types are separated from the cytosol by a double membrane (an outer and an inner membrane). Mitochondria (singular mitochondrion) are the cellular sites of respiration, a process in which the energy released from sugar metabolism is used for the synthesis of ATP (adenosine triphosphate) from ADP (adenosine diphosphate) and inorganic phos-phate (Pi) (see Chapter 11).
Mitochondria can vary in shape from spherical to tubu-lar, but they all have a smooth outer membrane and a highly convoluted inner membrane (Figure 1.15). The infoldings of the inner membrane are called cristae (singular crista).
The compartment enclosed by the inner membrane, the mitochondrial matrix, contains the enzymes of the path-way of intermediary metabolism called the Krebs cycle.
In contrast to the mitochondrial outer membrane and all other membranes in the cell, the inner membrane of a mito-chondrion is almost 70% protein and contains some phos-pholipids that are unique to the organelle (e.g., cardiolipin).
The proteins in and on the inner membrane have special enzymatic and transport capacities.
The inner membrane is highly impermeable to the pas-sage of H+; that is, it serves as a barrier to the movement of protons. This important feature allows the formation of electrochemical gradients. Dissipation of such gradients by the controlled movement of H+ ions through the trans-membrane enzyme ATP synthase is coupled to the phos-phorylation of ADP to produce ATP. ATP can then be released to other cellular sites where energy is needed to drive specific reactions.
14 Chapter 1 FIGURE 1.13 Preparation of clathrin-coated vesicles isolated from bean leaves. (102,000×) (Photo courtesy of D. G.
Robinson.) FIGURE 1.14 Light micrograph of a protoplast prepared from the aleurone layer of seeds. The fluorescent stain reveals two types of vacuoles: the larger protein bodies (V1) and the smaller lytic vacuoles (V2). (Photo courtesy of P.
Bethke and R. L. Jones.) Protein body Lytic vacuole Chloroplasts (Figure 1.16A) belong to another group of double membrane–enclosed organelles called plastids.
Chloroplast membranes are rich in glycosylglycerides (see Web Topic 1.4). Chloroplast membranes contain chlorophyll and its associated proteins and are the sites of photosynthe-sis. In addition to their inner and outer envelope mem-branes, chloroplasts possess a third system of membranes called thylakoids. A stack of thylakoids forms a granum (plural grana) (Figure 1.16B). Proteins and pigments (chloro-phylls and carotenoids) that function in the photochemical events of photosynthesis are embedded in the thylakoid membrane. The fluid compartment surrounding the thy-lakoids, called the stroma, is analogous to the matrix of the mitochondrion. Adjacent grana are connected by unstacked membranes called stroma lamellae (singular lamella).
The different components of the photosynthetic appa-ratus are localized in different areas of the grana and the stroma lamellae. The ATP synthases of the chloroplast are located on the thylakoid membranes (Figure 1.16C). Dur-ing photosynthesis, light-driven electron transfer reactions result in a proton gradient across the thylakoid membrane.
As in the mitochondria, ATP is synthesized when the pro-ton gradient is dissipated via the ATP synthase.
Plastids that contain high concentrations of carotenoid pigments rather than chlorophyll are called chromoplasts.
They are one of the causes of the yellow, orange, or red col-ors of many fruits and flowers, as well as of autumn leaves (Figure 1.17).
Nonpigmented plastids are called leucoplasts. The most important type of leucoplast is the amyloplast, a starch-storing plastid. Amyloplasts are abundant in storage tis-sues of the shoot and root, and in seeds. Specialized amy-loplasts in the root cap also serve as gravity sensors that direct root growth downward into the soil (see Chapter 19).
Mitochondria and Chloroplasts Are Semiautonomous Organelles Both mitochondria and chloroplasts contain their own DNA and protein-synthesizing machinery (ribosomes, transfer RNAs, and other components) and are believed to have evolved from endosymbiotic bacteria. Both plastids and mitochondria divide by fission, and mitochondria can also undergo extensive fusion to form elongated structures or networks.
Plant Cells 15 Cristae Intermembrane space Matrix Outer membrane Inner membrane (A) ADP Pi + ATP H+ H+ H+ H+ H+ H+ (B) FIGURE 1.15 (A) Diagrammatic representation of a mito-chondrion, including the location of the H+-ATPases involved in ATP synthesis on the inner membrane. (B) An electron micrograph of mitochondria from a leaf cell of Bermuda grass, Cynodon dactylon. (26,000×) (Photo by S.
E. Frederick, courtesy of E. H. Newcomb.) ATP H+ H+ H+ H+ H+ H+ H+ H+ H+ ADP Pi + Inner membrane Outer membrane Thylakoid membrane Thylakoids Stroma Stroma Thylakoid lumen Granum (stack of thylakoids) (C) (B) Thylakoid Granum Stroma Stroma lamellae (D) Outer and Inner membranes Stroma lamellae Stroma Grana FIGURE 1.16 (A) Electron micrograph of a chloroplast from a leaf of timothy grass, Phleum pratense. (18,000×) (B) The same preparation at higher magnification.
(52,000×) (C) A three-dimensional view of grana stacks and stroma lamellae, showing the complexity of the organization. (D) Diagrammatic representation of a chloro-plast, showing the location of the H+-ATPases on the thylakoid membranes.
(Micrographs by W. P. Wergin, courtesy of E. H. Newcomb.) (A) The DNA of these organelles is in the form of circular chromosomes, similar to those of bacteria and very differ-ent from the linear chromosomes in the nucleus. These DNA circles are localized in specific regions of the mitochondrial matrix or plastid stroma called nucleoids. DNA replication in both mitochondria and chloroplasts is independent of DNAreplication in the nucleus. On the other hand, the num-bers of these organelles within a given cell type remain approximately constant, suggesting that some aspects of organelle replication are under cellular regulation.
The mitochondrial genome of plants consists of about 200 kilobase pairs (200,000 base pairs), a size considerably larger than that of most animal mitochondria. The mito-chondria of meristematic cells are typically polyploid; that is, they contain multiple copies of the circular chromosome.
However, the number of copies per mitochondrion gradu-ally decreases as cells mature because the mitochondria continue to divide in the absence of DNA synthesis.
Most of the proteins encoded by the mitochondrial genome are prokaryotic-type 70S ribosomal proteins and components of the electron transfer system. The majority of mitochondrial proteins, including Krebs cycle enzymes, are encoded by nuclear genes and are imported from the cytosol.
The chloroplast genome is smaller than the mitochon-drial genome, about 145 kilobase pairs (145,000 base pairs).
Whereas mitochondria are polyploid only in the meris-tems, chloroplasts become polyploid during cell matura-tion. Thus the average amount of DNA per chloroplast in the plant is much greater than that of the mitochondria.
The total amount of DNA from the mitochondria and plas-tids combined is about one-third of the nuclear genome (Gunning and Steer 1996).
Chloroplast DNA encodes rRNA; transfer RNA (tRNA); the large subunit of the enzyme that fixes CO2, ribulose-1,5-bisphosphate carboxylase/oxygenase (rubisco); and sev-eral of the proteins that participate in photosynthesis. Nev-ertheless, the majority of chloroplast proteins, like those of mitochondria, are encoded by nuclear genes, synthesized in the cytosol, and transported to the organelle. Although mitochondria and chloroplasts have their own genomes and can divide independently of the cell, they are charac-terized as semiautonomous organelles because they depend on the nucleus for the majority of their proteins.
Different Plastid Types Are Interconvertible Meristem cells contain proplastids, which have few or no internal membranes, no chlorophyll, and an incomplete com-plement of the enzymes necessary to carry out photosynthe-sis (Figure 1.18A). In angiosperms and some gymnosperms, chloroplast development from proplastids is triggered by light. Upon illumination, enzymes are formed inside the pro-plastid or imported from the cytosol, light-absorbing pig-ments are produced, and membranes proliferate rapidly, giv-ing rise to stroma lamellae and grana stacks (Figure 1.18B).
Seeds usually germinate in the soil away from light, and chloroplasts develop only when the young shoot is exposed to light. If seeds are germinated in the dark, the proplastids differentiate into etioplasts, which contain semicrystalline tubular arrays of membrane known as pro-lamellar bodies (Figure 1.18C). Instead of chlorophyll, the etioplast contains a pale yellow green precursor pigment, protochlorophyllide.
.
Within minutes after exposure to light, the etioplast dif-ferentiates, converting the prolamellar body into thylakoids and stroma lamellae, and the protochlorophyll into chloro-phyll. The maintenance of chloroplast structure depends on the presence of light, and mature chloroplasts can revert to etioplasts during extended periods of darkness.
Chloroplasts can be converted to chromoplasts, as in the case of autumn leaves and ripening fruit, and in some cases Plant Cells 17 Lycopene crystals Vacuole Tonoplast Grana stack FIGURE 1.17 Electron micro-graph of a chromoplast from tomato (Lycopersicon esculen-tum) fruit at an early stage in the transition from chloroplast to chromoplast. Small grana stacks are still visible. Crystals of the carotenoid lycopene are indicated by the stars.
(27,000×) (From Gunning and Steer 1996.) this process is reversible. And amyloplasts can be con-verted to chloroplasts, which explains why exposure of roots to light often results in greening of the roots.
Microbodies Play Specialized Metabolic Roles in Leaves and Seeds Plant cells also contain microbodies, a class of spherical organelles surrounded by a single membrane and special-ized for one of several metabolic functions. The two main types of microbodies are peroxisomes and glyoxysomes.
Peroxisomes are found in all eukaryotic organisms, and in plants they are present in photosynthetic cells (Figure 1.19). Peroxisomes function both in the removal of hydro-gens from organic substrates, consuming O2 in the process, according to the following reaction: RH2 + O2 →R + H2O2 where R is the organic substrate. The potentially harmful peroxide produced in these reactions is broken down in peroxisomes by the enzyme catalase, according to the fol-lowing reaction: H2O2 →H2O + 1⁄2O2 Although some oxygen is regenerated during the catalase reaction, there is a net consumption of oxygen overall.
18 Chapter 1 (B) (A) (C) FIGURE 1.18 Electron micrographs illustrating several stages of plastid development. (A) A higher-magnification view of a proplastid from the root apical meristem of the broad bean (Vicia faba). The internal membrane system is rudimentary, and grana are absent. (47,000×) (B) A meso-phyll cell of a young oat leaf at an early stage of differentia-tion in the light. The plastids are developing grana stacks.
(C) A cell from a young oat leaf from a seedling grown in the dark. The plastids have developed as etioplasts, with elaborate semicrystalline lattices of membrane tubules called prolamellar bodies. When exposed to light, the etio-plast can convert to a chloroplast by the disassembly of the prolamellar body and the formation of grana stacks.
(7,200×) (From Gunning and Steer 1996.) Plastids Etioplasts Prolamellar bodies FIGURE 1.19 Electron micrograph of a peroxisome from a mesophyll cell, showing a crystalline core. (27,000×) This peroxisome is seen in close association with two chloro-plasts and a mitochondrion, probably reflecting the cooper-ative role of these three organelles in photorespiration.
(From Huang 1987.) Microbody Mitochondrion Crystalline core Another type of microbody, the glyoxysome, is present in oil-storing seeds. Glyoxysomes contain the glyoxylate cycle enzymes, which help convert stored fatty acids into sugars that can be translocated throughout the young plant to provide energy for growth (see Chapter 11).
Because both types of microbodies carry out oxidative reactions, it has been suggested they may have evolved from primitive respiratory organelles that were super-seded by mitochondria.
Oleosomes Are Lipid-Storing Organelles In addition to starch and protein, many plants synthesize and store large quantities of triacylglycerol in the form of oil during seed development. These oils accumulate in organelles called oleosomes, also referred to as lipid bod-ies or spherosomes (Figure 1.20A).
Oleosomes are unique among the organelles in that they are surrounded by a “half–unit membrane”—that is, a phospholipid monolayer—derived from the ER (Harwood 1997). The phospholipids in the half–unit membrane are oriented with their polar head groups toward the aqueous phase and their hydrophobic fatty acid tails facing the lumen, dissolved in the stored lipid. Oleosomes are thought to arise from the deposition of lipids within the bilayer itself (Figure 1.20B).
Proteins called oleosins are present in the half–unit mem-brane (see Figure 1.20B). One of the functions of the oleosins may be to maintain each oleosome as a discrete organelle by preventing fusion. Oleosins may also help other proteins bind to the organelle surface. As noted earlier, during seed germination the lipids in the oleosomes are broken down and converted to sucrose with the help of the glyoxysome.
The first step in the process is the hydrolysis of the fatty acid chains from the glycerol backbone by the enzyme lipase.
Lipase is tightly associated with the surface of the half–unit membrane and may be attached to the oleosins.
THE CYTOSKELETON The cytosol is organized into a three-dimensional network of filamentous proteins called the cytoskeleton. This net-work provides the spatial organization for the organelles and serves as a scaffolding for the movements of organelles and other cytoskeletal components. It also plays funda-mental roles in mitosis, meiosis, cytokinesis, wall deposi-tion, the maintenance of cell shape, and cell differentiation.
Plant Cells Contain Microtubules, Microfilaments, and Intermediate Filaments Three types of cytoskeletal elements have been demon-strated in plant cells: microtubules, microfilaments, and intermediate filament–like structures. Each type is fila-mentous, having a fixed diameter and a variable length, up to many micrometers.
Microtubules and microfilaments are macromolecular assemblies of globular proteins. Microtubules are hollow Plant Cells 19 Oil body Oil Oleosin Smooth endoplasmic reticulum (B) (A) Oleosome Peroxisome FIGURE 1.20 (A) Electron micrograph of an oleosome beside a peroxisome. (B) Diagram showing the formation of oleosomes by the synthesis and deposition of oil within the phospholipid bilayer of the ER. After budding off from the ER, the oleosome is surrounded by a phospholipid mono-layer containing the protein oleosin. (A from Huang 1987; B after Buchanan et al. 2000.) cylinders with an outer diameter of 25 nm; they are com-posed of polymers of the protein tubulin. The tubulin monomer of microtubules is a heterodimer composed of two similar polypeptide chains (α- and β-tubulin), each having an apparent molecular mass of 55,000 daltons (Fig-ure 1.21A). A single microtubule consists of hundreds of thousands of tubulin monomers arranged in 13 columns called protofilaments.
Microfilaments are solid, with a diameter of 7 nm; they are composed of a special form of the protein found in muscle: globular actin, or G-actin. Each actin molecule is composed of a single polypeptide with a molecular mass of approximately 42,000 daltons. A microfilament consists of two chains of polymerized actin subunits that intertwine in a helical fashion (Figure 1.21B).
Intermediate filaments are a diverse group of helically wound fibrous elements, 10 nm in diameter. Intermediate filaments are composed of linear polypeptide monomers of various types. In animal cells, for example, the nuclear lamins are composed of a specific polypeptide monomer, while the keratins, a type of intermediate filament found in the cytoplasm, are composed of a different polypeptide monomer.
In animal intermediate filaments, pairs of parallel monomers (i.e., aligned with their —NH2 groups at the same ends) are helically wound around each other in a coiled coil. Two coiled-coil dimers then align in an antipar-allel fashion (i.e., with their —NH2 groups at opposite ends) to form a tetrameric unit. The tetrameric units then assemble into the final intermediate filament (Figure 1.22).
Although nuclear lamins appear to be present in plant cells, there is as yet no convincing evidence for plant ker-atin intermediate filaments in the cytosol. As noted earlier, integral proteins cross-link the plasma membrane of plant cells to the rigid cell wall. Such connections to the wall undoubtedly stabilize the protoplast and help maintain cell shape. The plant cell wall thus serves as a kind of cellular exoskeleton, perhaps obviating the need for keratin-type intermediate filaments for structural support.
Microtubules and Microfilaments Can Assemble and Disassemble In the cell, actin and tubulin monomers exist as pools of free proteins that are in dynamic equilibrium with the poly-merized forms. Polymerization requires energy: ATP is required for microfilament polymerization, GTP (guano-sine triphosphate) for microtubule polymerization. The attachments between subunits in the polymer are nonco-valent, but they are strong enough to render the structure stable under cellular conditions.
Both microtubules and microfilaments are polarized; that is, the two ends are different. In microtubules, the polarity arises from the polarity of the α- and β-tubulin het-erodimer; in microfilaments, the polarity arises from the polarity of the actin monomer itself. The opposite ends of microtubules and microfilaments are termed plus and minus, and polymerization is more rapid at the positive end.
20 Chapter 1 a b a b a b a a b Tubulin subunits (a and b) G-actin subunit 8 nm Protofilament 25 nm 7 nm (A) (B) FIGURE 1.21 (A) Drawing of a microtubule in longitudinal view. Each microtubule is composed of 13 protofilaments.
The organization of the α and β subunits is shown. (B) Diagrammatic representation of a microfilament, showing two strands of G-actin subunits.
(A) Dimer (B) Tetramer (C) Protofilament (D) Filament COOH COOH COOH COOH COOH COOH NH2 NH2 NH2 NH2 NH2 NH2 FIGURE 1.22 The current model for the assembly of inter-mediate filaments from protein monomers. (A) Coiled-coil dimer in parallel orientation (i.e., with amino and carboxyl termini at the same ends). (B) A tetramer of two dimers.
Note that the dimers are arranged in an antiparallel fash-ion, and that one is slightly offset from the other. (C) Two tetramers. (D) Tetramers packed together to form the 10 nm intermediate filament. (After Alberts et al. 2002.) Once formed, microtubules and microfilaments can dis-assemble. The overall rate of assembly and disassembly of these structures is affected by the relative concentrations of free or assembled subunits. In general, microtubules are more unstable than microfilaments. In animal cells, the half-life of an individual microtubule is about 10 minutes.
Thus microtubules are said to exist in a state of dynamic instability.
In contrast to microtubules and microfilaments, inter-mediate filaments lack polarity because of the antiparallel orientation of the dimers that make up the tetramers. In addition, intermediate filaments appear to be much more stable than either microtubules or microfilaments. Although very little is known about intermediate filament–like struc-tures in plant cells, in animal cells nearly all of the interme-diate-filament protein exists in the polymerized state.
Microtubules Function in Mitosis and Cytokinesis Mitosis is the process by which previously replicated chro-mosomes are aligned, separated, and distributed in an orderly fashion to daughter cells (Figure 1.23). Micro-tubules are an integral part of mitosis. Before mitosis begins, microtubules in the cortical (outer) cytoplasm depolymerize, breaking down into their constituent sub-units. The subunits then repolymerize before the start of prophase to form the preprophase band (PPB), a ring of microtubules encircling the nucleus (see Figure 1.23C–F).
The PPB appears in the region where the future cell wall will form after the completion of mitosis, and it is thought to be involved in regulating the plane of cell division.
During prophase, microtubules begin to assemble at two foci on opposite sides of the nucleus, forming the prophase spindle (Figure 1.24). Although not associated with any specific structure, these foci serve the same func-tion as animal cell centrosomes in organizing and assem-bling microtubules.
In early metaphase the nuclear envelope breaks down, the PPB disassembles, and new microtubules polymerize to form the mitotic spindle. In animal cells the spindle microtubules radiate toward each other from two discrete foci at the poles (the centrosomes), resulting in an ellip-soidal, or football-shaped, array of microtubules. The mitotic spindle of plant cells, which lack centrosomes, is more boxlike in shape because the spindle microtubules arise from a diffuse zone consisting of multiple foci at opposite ends of the cell and extend toward the middle in nearly parallel arrays (see Figure 1.24).
Some of the microtubules of the spindle apparatus become attached to the chromosomes at their kinetochores, while others remain unattached. The kinetochores are located in the centromeric regions of the chromosomes. Some of the unattached microtubules overlap with microtubules from the opposite polar region in the spindle midzone.
Cytokinesis is the process whereby a cell is partitioned into two progeny cells. Cytokinesis usually begins late in mitosis. The precursor of the new wall, the cell plate that Plant Cells 21 FIGURE 1.23 Fluorescence micrograph taken with a confocal microscope showing changes in microtubule arrangements at different stages in the cell cycle of wheat root meristem cells. Microtubules stain green and yellow; DNA is blue. (A–D) Cortical microtubules disappear and the preprophase band is formed around the nucleus at the site of the future cell plate. (E–H) The prophase spindle forms from foci of microtubules at the poles. (G, H) The preprophase band disappears in late prophase. (I–K) The nuclear membrane breaks down, and the two poles become more diffuse. The mitotic spindle forms in parallel arrays and the kinetochores bind to spindle microtubules. (From Gunning and Steer 1996.) (A) (B) (C) (D) (E) (F) (G) (H) (I) (J) (K) forms between incipient daughter cells, is rich in pectins (Figure 1.25). Cell plate formation in higher plants is a mul-tistep process (seeWeb Topic 1.5). Vesicle aggregation in the spindle midzone is organized by the phragmoplast, a com-plex of microtubules and ER that forms during late anaphase or early telophase from dissociated spindle subunits.
Microfilaments Are Involved in Cytoplasmic Streaming and in Tip Growth Cytoplasmic streaming is the coordinated movement of par-ticles and organelles through the cytosol in a helical path down one side of a cell and up the other side. Cytoplasmic streaming occurs in most plant cells and has been studied extensively in the giant cells of the green algae Chara and Nitella, in which speeds up to 75 µm s–1 have been measured.
The mechanism of cytoplasmic streaming involves bun-dles of microfilaments that are arranged parallel to the lon-gitudinal direction of particle movement. The forces nec-essary for movement may be generated by an interaction of the microfilament protein actin with the protein myosin in a fashion comparable to that of the protein interaction that occurs during muscle contraction in animals.
Myosins are proteins that have the ability to hydrolyze ATP to ADP and Pi when activated by binding to an actin microfilament. The energy released by ATP hydrolysis pro-pels myosin molecules along the actin microfilament from the minus end to the plus end. Thus, myosins belong to the general class of motor proteins that drive cytoplasmic streaming and the movements of organelles within the cell.
Examples of other motor proteins include the kinesins and dyneins, which drive movements of organelles and other cytoskeletal components along the surfaces of microtubules.
Actin microfilaments also participate in the growth of the pollen tube. Upon germination, a pollen grain forms a tubular extension that grows down the style toward the embryo sac. As the tip of the pollen tube extends, new cell wall material is continually deposited to maintain the integrity of the wall.
A network of microfilaments appears to guide vesicles containing wall precursors from their site of formation in the Golgi through the cytosol to the site of new wall for-mation at the tip. Fusion of these vesicles with the plasma membrane deposits wall precursors outside the cell, where they are assembled into wall material.
Prophase Anaphase Telophase Cytokinesis Prometaphase Metaphase Plasma membrane Cytoplasm Cell wall Nucleus (nucleolus disappears) Condensing chromosomes (sister chromatids held together at centromere) Preprophase band disappears Prophase spindle Spindle pole develops Separated chromatids are pulled toward poles Kinetochore microtubules shorten Decondensing chromosomes Nuclear envelope re-forms Cell plate grows Phragmoplast Nuclear envelope fragment Diffuse spindle pole Chromosomes align at metaphase plate Kinetochore microtubules Polar microtubules Endoplasmic reticulum Two cells formed Nucleolus FIGURE 1.24 Diagram of mitosis in plants.
Intermediate Filaments Occur in the Cytosol and Nucleus of Plant Cells Relatively little is known about plant intermediate fila-ments. Intermediate filament–like structures have been identified in the cytoplasm of plant cells (Yang et al. 1995), but these may not be based on keratin, as in animal cells, since as yet no plant keratin genes have been found.
Nuclear lamins, intermediate filaments of another type that form a dense network on the inner surface of the nuclear membrane, have also been identified in plant cells (Fred-erick et al. 1992), and genes encoding laminlike proteins are present in the Arabidopsis genome. Presumably, plant lamins perform functions similar to those in animal cells as a structural component of the nuclear envelope.
CELL CYCLE REGULATION The cell division cycle, or cell cycle, is the process by which cells reproduce themselves and their genetic material, the nuclear DNA. The four phases of the cell cycle are desig-nated G1, S, G2, and M (Figure 1.26A).
Each Phase of the Cell Cycle Has a Specific Set of Biochemical and Cellular Activities Nuclear DNA is prepared for replication in G1 by the assembly of a prereplication complex at the origins of repli-cation along the chromatin. DNA is replicated during the S phase, and G2 cells prepare for mitosis.
The whole architecture of the cell is altered as cells enter mitosis: The nuclear envelope breaks down, chromatin con-denses to form recognizable chromosomes, the mitotic spindle forms, and the replicated chromosomes attach to the spindle fibers. The transition from metaphase to anaphase of mitosis marks a major transition point when the two chromatids of each replicated chromosome, which were held together at their kinetochores, are separated and the daughter chromosomes are pulled to opposite poles by spindle fibers.
At a key regulatory point early in G1 of the cell cycle, the cell becomes committed to the initiation of DNA synthesis. In yeasts, this point is called START. Once a cell has passed START, it is irre-versibly committed to initiating DNA synthesis and completing the cell cycle through mitosis and cytokinesis. After the cell has completed mitosis, it may initiate another complete cycle (G1 through mitosis), or it may leave the cell cycle and differen-tiate. This choice is made at the critical G1 point, before the cell begins to replicate its DNA.
DNA replication and mitosis are linked in mammalian cells. Often mammalian cells that have stopped dividing can be stimulated to reenter the cell cycle by a variety of hormones and growth factors. When they do so, they reen-ter the cell cycle at the critical point in early G1. In contrast, plant cells can leave the cell division cycle either before or after replicating their DNA (i.e., during G1 or G2). As a con-sequence, whereas most animal cells are diploid (having two sets of chromosomes), plant cells frequently are tetraploid (having four sets of chromosomes), or even poly-ploid (having many sets of chromosomes), after going through additional cycles of nuclear DNA replication with-out mitosis.
The Cell Cycle Is Regulated by Protein Kinases The mechanism regulating the progression of cells through their division cycle is highly conserved in evolution, and plants have retained the basic components of this mecha-nism (Renaudin et al. 1996). The key enzymes that control the transitions between the different states of the cell cycle, and the entry of nondividing cells into the cell cycle, are the cyclin-dependent protein kinases, or CDKs (Figure 1.26B).
Protein kinases are enzymes that phosphorylate proteins using ATP. Most multicellular eukaryotes use several pro-tein kinases that are active in different phases of the cell cycle. All depend on regulatory subunits called cyclins for their activities. The regulated activity of CDKs is essential for the transitions from G1 to S and from G2 to M, and for the entry of nondividing cells into the cell cycle.
CDK activity can be regulated in various ways, but two of the most important mechanisms are (1) cyclin synthe-sis and destruction and (2) the phosphorylation and dephosphorylation of key amino acid residues within the CDK protein. CDKs are inactive unless they are associated Plant Cells 23 Nuclear envelope Vesicles Microtubule Nucleus FIGURE 1.25 Electron micrograph of a cell plate forming in a maple seedling (10,000×). (© E. H. Newcomb and B. A.
Palevitz/Biological Photo Service.) with a cyclin. Most cyclins turn over rapidly. They are syn-thesized and then actively degraded (using ATP) at specific points in the cell cycle. Cyclins are degraded in the cytosol by a large proteolytic complex called the proteasome.
Before being degraded by the proteasome, the cyclins are marked for destruction by the attachment of a small pro-tein called ubiquitin, a process that requires ATP. Ubiquiti-nation is a general mechanism for tagging cellular proteins destined for turnover (see Chapter 14).
The transition from G1 to S requires a set of cyclins (known as G1 cyclins) different from those required in the transition from G2 to mitosis, where mitotic cyclins acti-vate the CDKs (see Figure 1.26B). CDKs possess two tyro-sine phosphorylation sites: One causes activation of the enzyme; the other causes inactivation. Specific kinases carry out both the stimulatory and the inhibitory phos-phorylations.
Similarly, protein phosphatases can remove phosphate from CDKs, either stimulating or inhibiting their activity, depending on the position of the phosphate. The addition or removal of phosphate groups from CDKs is highly reg-ulated and an important mechanism for the control of cell cycle progression (see Figure 1.26B). Cyclin inhibitors play an important role in regulating the cell cycle in animals, and probably in plants as well, although little is known about plant cyclin inhibitors.
Finally, as we will see later in the book, certain plant hormones are able to regulate the cell cycle by regulating the synthesis of key enzymes in the regulatory pathway.
PLASMODESMATA Plasmodesmata (singular plasmodesma) are tubular exten-sions of the plasma membrane, 40 to 50 nm in diameter, that traverse the cell wall and connect the cytoplasms of adjacent cells. Because most plant cells are interconnected in this way, their cytoplasms form a continuum referred to as the symplast. Intercellular transport of solutes through plasmodesmata is thus called symplastic transport (see Chapters 4 and 6).
24 Chapter 1 ATP P P P 2 ATP 2 ADP ADP P P P P (A) (B) G2 G2 G1 G1 S S M it ot ic p h a s e Prophase Metaphase Anaphase Telophase Cytokinesis M i t o s i s M M I N T E R P H A S E G1 cyclin (CG1) Inactive CDK M cyclin degradation Active CDK stimulates mitosis Inactive CDK G1 cyclin degradation Active CDK stimulates DNA synthesis Mitotic cyclin (CM) Activation site Inhibitory site Inactive CDK CDK CDK CDK CDK CDK FIGURE 1.26 (A) Diagram of the cell cycle. (B) Diagram of the regulation of the cell cycle by cyclin-dependent protein kinase (CDK). During G1, CDK is in its inactive form. CDK becomes activated by binding to G1 cyclin (CG1) and by being phosphorylated (P) at the activation site. The activated CDK–cyclin complex allows the transition to the S phase. At the end of the S phase, the G1 cyclin is degraded and the CDK is dephosphorylated, resulting in an inactive CDK.
The cell enters G2. During G2, the inactive CDK binds to the mitotic cyclin (CM), or M cyclin. At the same time, the CDK–cyclin complex becomes phosphorylated at both its activation and its inhibitory sites. The CDK–cyclin complex is still inactive because the inhibitory site is phosphory-lated. The inactive complex becomes activated when the phosphate is removed from the inhibitory site by a protein phosphatase. The activated CDK then stimulates the transi-tion from G2 to mitosis. At the end of mitosis, the mitotic cyclin is degraded and the remaining phosphate at the acti-vation site is removed by the phosphatase, and the cell enters G1 again. There Are Two Types of Plasmodesmata: Primary and Secondary Primary plasmodesmata form during cytokinesis when Golgi-derived vesicles containing cell wall precursors fuse to form the cell plate (the future middle lamella). Rather than forming a continuous uninterrupted sheet, the newly deposited cell plate is penetrated by numerous pores (Fig-ure 1.27A), where remnants of the spindle apparatus, con-sisting of ER and microtubules, disrupt vesicle fusion. Fur-ther deposition of wall polymers increases the thickness of the two primary cell walls on either side of the middle lamella, generating linear membrane-lined channels (Fig-ure 1.27B). Development of primary plasmodesmata thus provides direct continuity and communication between cells that are clonally related (i.e., derived from the same mother cell).
Secondary plasmodesmata form between cells after their cell walls have been deposited. They arise either by evagination of the plasma membrane at the cell surface, or by branching from a primary plasmodesma (Lucas and Wolf 1993). In addition to increasing the communication between cells that are clonally related, secondary plas-modesmata allow symplastic continuity between cells that are not clonally related.
Plasmodesmata Have a Complex Internal Structure Like nuclear pores, plasmodesmata have a complex inter-nal structure that functions in regulating macromolecular traffic from cell to cell. Each plasmodesma contains a nar-row tubule of ER called a desmotubule (see Figure 1.27).
The desmotubule is continuous with the ER of the adjacent cells. Thus the symplast joins not only the cytosol of neigh-boring cells, but the contents of the ER lumens as well.
However, it is not clear that the desmotubule actually rep-resents a passage, since there does not appear to be a space between the membranes, which are tightly appressed.
Globular proteins are associated with both the desmo-tubule membrane and the plasma membrane within the pore (see Figure 1.27B). These globular proteins appear to be interconnected by spokelike extensions, dividing the pore into eight to ten microchannels (Ding et al. 1992).
Some molecules can pass from cell to cell through plas-modesmata, probably by flowing through the microchan-nels, although the exact pathway of communication has not been established.
By following the movement of fluorescent dye mole-cules of different sizes through plasmodesmata connecting leaf epidermal cells, Robards and Lucas (1990) determined Plant Cells 25 Endoplasmic reticulum Central rod Central rod Spokelike filamentous proteins Cytoplasmic sleeve Cell wall Desmotubule Plasma membrane Middle lamella Cytoplasmic sleeve Central cavity Central cavity Cytoplasm Cross sections Cell wall Neck Desmotubule ER Plasma membrane ER FIGURE 1.27 Plasmodesmata between cells. (A) Electron micrograph of a wall separating two adjacent cells, showing the plasmodesmata. (B) Schematic view of a cell wall with two plasmodesmata with different shapes. The desmotubule is continuous with the ER of the adjoining cells. Proteins line the outer surface of the desmotubule and the inner surface of the plasma membrane; the two surfaces are thought to be connected by filamentous proteins. The gap between the pro-teins lining the two membranes apparently controls the mol-ecular sieving properties of plasmodesmata. (A from Tilney et al. 1991; B after Buchanan et al. 2000.) (A) (B) the limiting molecular mass for transport to be about 700 to 1000 daltons, equivalent to a molecular size of about 1.5 to 2.0 nm. This is the size exclusion limit, or SEL, of plas-modesmata. If the width of the cytoplasmic sleeve is approximately 5 to 6 nm, how are molecules larger than 2.0 nm excluded?
The proteins attached to the plasma membrane and the ER within the plasmodesmata appear to act to restrict the size of molecules that can pass through the pore. As we’ll see in Chapter 16, the SELs of plasmodesmata can be regulated.
The mechanism for regulating the SEL is poorly under-stood, but the localization of both actin and myosin within plasmodesmata, possibly forming the “spoke” extensions (see Figure 1.27B), suggests that they may participate in the process (White et al. 1994; Radford and White 1996). Recent studies have also implicated calcium-dependent protein kinases in the regulation of plasmodesmatal SEL.
SUMMARY Despite their great diversity in form and size, all plants carry out similar physiological processes. As primary pro-ducers, plants convert solar energy to chemical energy.
Being nonmotile, plants must grow toward light, and they must have efficient vascular systems for movement of water, mineral nutrients, and photosynthetic products throughout the plant body. Green land plants must also have mechanisms for avoiding desiccation.
The major vegetative organ systems of seed plants are the shoot and the root. The shoot consists of two types of organs: stems and leaves. Unlike animal development, plant growth is indeterminate because of the presence of permanent meristem tissue at the shoot and root apices, which gives rise to new tissues and organs during the entire vegetative phase of the life cycle. Lateral meristems (the vascular cambium and the cork cambium) produce growth in girth, or secondary growth.
Three major tissue systems are recognized: dermal, ground, and vascular. Each of these tissues contains a vari-ety of cell types specialized for different functions.
Plants are eukaryotes and have the typical eukaryotic cell organization, consisting of nucleus and cytoplasm. The nuclear genome directs the growth and development of the organism. The cytoplasm is enclosed by a plasma membrane and contains numerous membrane-enclosed organelles, including plastids, mitochondria, microbodies, oleosomes, and a large central vacuole. Chloroplasts and mitochondria are semiautonomous organelles that contain their own DNA. Nevertheless, most of their proteins are encoded by nuclear DNA and are imported from the cytosol.
The cytoskeletal components—microtubules, microfila-ments, and intermediate filaments—participate in a vari-ety of processes involving intracellular movements, such as mitosis, cytoplasmic streaming, secretory vesicle trans-port, cell plate formation, and cellulose microfibril deposi-tion. The process by which cells reproduce is called the cell cycle. The cell cycle consists of the G1, S, G2, and M phases.
The transition from one phase to another is regulated by cyclin-dependent protein kinases. The activity of the CDKs is regulated by cyclins and by protein phosphorylation.
During cytokinesis, the phragmoplast gives rise to the cell plate in a multistep process that involves vesicle fusion. After cytokinesis, primary cell walls are deposited. The cytosol of adjacent cells is continuous through the cell walls because of the presence of membrane-lined channels called plasmod-esmata, which play a role in cell–cell communication.
Web Material Web Topics 1.1 The Plant Kingdom The major groups of the plant kingdom are surveyed and described.
1.2 Flower Structure and the Angiosperm Life Cycle The steps in the reproductive style of angio-sperms are discussed and illustrated.
1.3 Plant Tissue Systems: Dermal,Ground,and Vascular A more detailed treatment of plant anatomy is given.
1.4 The Structures of Chloroplast Glycosylglycerides The chemical structures of the chloroplast lipids are illustrated.
1.5 The Multiple Steps in Construction of the Cell Plate Following Mitosis Details of the production of the cell plate during cytokinesis in plants are described.
Chapter References Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., and Walter, P. (2002) Molecular Biology of the Cell, 4th ed. Garland, New York.
Buchanan, B. B., Gruissem, W., and Jones, R. L. (eds.) (2000) Bio-chemistry and Molecular Biology of Plants. Amer. Soc. Plant Phys-iologists, Rockville, MD. Ding, B., Turgeon, R., and Parthasarathy, M. V. (1992) Substructure of freeze substituted plasmodesmata. Protoplasma 169: 28–41.
Driouich, A., Levy, S., Staehelin, L. A., and Faye, L. (1994) Structural and functional organization of the Golgi apparatus in plant cells.
Plant Physiol. Biochem. 32: 731–749.
Esau, K. (1960) Anatomy of Seed Plants. Wiley, New York.
Esau, K. (1977) Anatomy of Seed Plants, 2nd ed. Wiley, New York.
Faye, L., Fitchette-Lainé, A. C., Gomord, V ., Chekkafi, A., Delaunay, A. M., and Driouich, A. (1992) Detection, biosynthesis and some functions of glycans N-linked to plant secreted proteins. In Post-translational Modifications in Plants (SEB Seminar Series, no. 53), N. H. Battey, H. G. Dickinson, and A. M. Heatherington, eds., Cambridge University Press, Cambridge, pp. 213–242.
26 Chapter 1 Frederick, S. E., Mangan, M. E., Carey, J. B., and Gruber, P. J. (1992) Intermediate filament antigens of 60 and 65 kDa in the nuclear matrix of plants: Their detection and localization. Exp. Cell Res.
199: 213–222.
Gunning, B. E. S., and Steer, M. W. (1996) Plant Cell Biology: Structure and Function of Plant Cells. Jones and Bartlett, Boston.
Harwood, J. L. (1997) Plant lipid metabolism. In Plant Biochemistry, P. M. Dey and J. B. Harborne, eds., Academic Press, San Diego, CA, pp. 237–272.
Huang, A. H. C. (1987) Lipases in The Biochemistry of Plants: A Com-prehensive Treatise. In Vol. 9, Lipids: Structure and Function, P. K.
Stumpf, ed. Academic Press, New York, pp. 91–119.
Lucas, W. J., and Wolf, S. (1993) Plasmodesmata: The intercellular organelles of green plants. Trends Cell Biol. 3: 308–315.
O’Brien, T. P ., and McCully, M. E. (1969) Plant Structure and Develop-ment: A Pictorial and Physiological Approach. Macmillan, New York.
Radford, J., and White, R. G. (1996) Preliminary localization of myosin to plasmodesmata. Third International Workshop on Basic and Applied Research in Plasmodesmal Biology, Zichron-Takov, Israel, March 10–16, 1996, pp. 37–38.
Renaudin, J.-P., Doonan, J. H., Freeman, D., Hashimoto, J., Hirt, H., Inze, D., Jacobs, T., Kouchi, H., Rouze, P., Sauter, M., et al. (1996) Plant cyclins: Aunified nomenclature for plant A-, B- and D-type cyclins based on sequence organization. Plant Mol. Biol. 32: 1003–1018.
Robards, A. W., and Lucas, W. J. (1990) Plasmodesmata. Annu. Rev.
Plant Physiol. Plant Mol. Biol. 41: 369–420.
Tilney, L. G., Cooke, T. J., Connelly, P . S., and Tilney, M. S. (1991) The structure of plasmodesmata as revealed by plasmolysis, deter-gent extraction, and protease digestion. J. Cell Biol. 112: 739–748.
White, R. G., Badelt, K., Overall, R. L., and Vesk, M. (1994) Actin associated with plasmodesmata. Protoplasma 180: 169–184.
Yang, C., Min, G. W., Tong, X. J., Luo, Z., Liu, Z. F., and Zhai, Z. H.
(1995) The assembly of keratins from higher plant cells. Proto-plasma 188: 128–132.
Plant Cells 27 1 The force that through the green fuse drives the flower Drives my green age; that blasts the roots of trees Is my destroyer.
And I am dumb to tell the crooked rose My youth is bent by the same wintry fever.
The force that drives the water through the rocks Drives my red blood; that dries the mouthing streams Turns mine to wax.
And I am dumb to mouth unto my veins How at the mountain spring the same mouth sucks.
Dylan Thomas, Collected Poems (1952) In these opening stanzas from Dylan Thomas’s famous poem, the poet proclaims the essential unity of the forces that propel animate and inanimate objects alike, from their beginnings to their ultimate decay. Scientists call this force energy. Energy transformations play a key role in all the physical and chemical processes that occur in living systems. But energy alone is insufficient to drive the growth and development of organisms. Protein catalysts called enzymes are required to ensure that the rates of biochemical reactions are rapid enough to support life. In this chapter we will examine basic concepts about energy, the way in which cells transform energy to perform useful work (bioenergetics), and the structure and func-tion of enzymes.
Energy Flow through Living Systems The flow of matter through individual organisms and biological communities is part of everyday experience; the flow of energy is not, even though it is central to the very existence of living things.
Energy and Enzymes 2 CHAPTER 2 2 What makes concepts such as energy, work, and order so elusive is their insubstantial nature: We find it far eas-ier to visualize the dance of atoms and molecules than the forces and fluxes that determine the direction and extent of natural processes. The branch of physical sci-ence that deals with such matters is thermodynamics, an abstract and demanding discipline that most biolo-gists are content to skim over lightly. Yet bioenergetics is so shot through with concepts and quantitative rela-tionships derived from thermodynamics that it is scarcely possible to discuss the subject without frequent reference to free energy, potential, entropy, and the sec-ond law. The purpose of this chapter is to collect and explain, as simply as possible, the fundamental thermodynamic concepts and relationships that recur throughout this book. Readers who prefer a more extensive treatment of the subject should consult either the introductory texts by Klotz (1967) and by Nicholls and Ferguson (1992) or the advanced texts by Morowitz (1978) and by Edsall and Gutfreund (1983).
Thermodynamics evolved during the nineteenth cen-tury out of efforts to understand how a steam engine works and why heat is produced when one bores a can-non. The very name “thermodynamics,” and much of the language of this science, recall these historical roots, but it would be more appropriate to speak of energetics, for the principles involved are universal. Living plants, like all other natural phenomena, are constrained by the laws of thermodynamics. By the same token, thermo-dynamics supplies an indispensable framework for the quantitative description of biological vitality.
Energy and Work Let us begin with the meanings of “energy” and “work.” Energy is defined in elementary physics, as in daily life, as the capacity to do work. The meaning of work is harder to come by and more narrow. Work, in the mechanical sense, is the displacement of any body against an opposing force. The work done is the prod-uct of the force and the distance displaced, as expressed in the following equation: W = f ∆l (2.1) Mechanical work appears in chemistry because whenever the final volume of a reaction mixture exceeds the initial volume, work must be done against the pres-sure of the atmosphere; conversely, the atmosphere per-forms work when a system contracts. This work is cal-culated by the expression P∆V (where P stands for pressure and V for volume), a term that appears fre-quently in thermodynamic formulas. In biology, work is employed in a broader sense to describe displacement against any of the forces that living things encounter or generate: mechanical, electric, osmotic, or even chemical potential.
A familiar mechanical illustration may help clarify the relationship of energy to work. The spring in Figure 2.1 can be extended if force is applied to it over a particular distance—that is, if work is done on the spring. This work can be recovered by an appropriate arrangement of pulleys and used to lift a weight onto the table. The extended spring can thus be said to possess energy that is numerically equal to the work it can do on the weight (neglecting friction). The weight on the table, in turn, can be said to possess energy by virtue of its position in Earth’s gravitational field, which can be utilized to do other work, such as turning a crank. The weight thus illustrates the concept of potential energy, a capacity to do work that arises from the position of an object in a field of force, and the sequence as a whole illustrates the conversion of one kind of energy into another, or energy transduction.
The First Law: The Total Energy Is Always Conserved It is common experience that mechanical devices involve both the performance of work and the produc-Figure 2.1 Energy and work in a mechanical system. (A) A weight resting on the floor is attached to a spring via a string. (B) Pulling on the spring places the spring under tension.
(C) The potential energy stored in the extended spring performs the work of raising the weight when the spring contracts.
We may note in passing that the dimensions of work are complex— ml2t–2 —where m denotes mass, l distance, and t time, and that work is a scalar quantity, that is, the prod-uct of two vectorial terms.
(A) (B) (C) Energy and Enzymes 3 tion or absorption of heat. We are at liberty to vary the amount of work done by the spring, up to a particular maximum, by using different weights, and the amount of heat produced will also vary. But much experimental work has shown that, under ideal circumstances, the sum of the work done and of the heat evolved is con-stant and depends only on the initial and final exten-sions of the spring. We can thus envisage a property, the internal energy of the spring, with the characteristic described by the following equation: ∆U = ∆Q + ∆W (2.2) Here Q is the amount of heat absorbed by the system, and W is the amount of work done on the system. In Figure 2.1 the work is mechanical, but it could just as well be electrical, chemical, or any other kind of work.
Thus ∆U is the net amount of energy put into the sys-tem, either as heat or as work; conversely, both the per-formance of work and the evolution of heat entail a decrease in the internal energy. We cannot specify an absolute value for the energy content; only changes in internal energy can be measured. Note that Equation 2.2 assumes that heat and work are equivalent; its purpose is to stress that, under ideal circumstances, ∆U depends only on the initial and final states of the system, not on how heat and work are partitioned. Equation 2.2 is a statement of the first law of ther-modynamics, which is the principle of energy conser-vation. If a particular system exchanges no energy with its surroundings, its energy content remains constant; if energy is exchanged, the change in internal energy will be given by the difference between the energy gained from the surroundings and that lost to the surroundings.
The change in internal energy depends only on the ini-tial and final states of the system, not on the pathway or mechanism of energy exchange. Energy and work are interconvertible; even heat is a measure of the kinetic energy of the molecular constituents of the system. To put it as simply as possible, Equation 2.2 states that no machine, including the chemical machines that we rec-ognize as living, can do work without an energy source.
An example of the application of the first law to a biological phenomenon is the energy budget of a leaf.
Leaves absorb energy from their surroundings in two ways: as direct incident irradiation from the sun and as infrared irradiation from the surroundings. Some of the energy absorbed by the leaf is radiated back to the sur-roundings as infrared irradiation and heat, while a frac-tion of the absorbed energy is stored, as either photo-synthetic products or leaf temperature changes. Thus we can write the following equation: Total energy absorbed by leaf = energy emitted from leaf + energy stored by leaf Note that although the energy absorbed by the leaf has been transformed, the total energy remains the same, in accordance with the first law.
The Change in the Internal Energy of a System Represents the Maximum Work It Can Do We must qualify the equivalence of energy and work by invoking “ideal conditions”—that is, by requiring that the process be carried out reversibly. The meaning of “reversible” in thermodynamics is a special one: The term describes conditions under which the opposing forces are so nearly balanced that an infinitesimal change in one or the other would reverse the direction of the process.† Under these circumstances the process yields the maximum possible amount of work.
Reversibility in this sense does not often hold in nature, as in the example of the leaf. Ideal conditions differ so little from a state of equilibrium that any process or reac-tion would require infinite time and would therefore not take place at all. Nonetheless, the concept of thermody-namic reversibility is useful: If we measure the change in internal energy that a process entails, we have an upper limit to the work that it can do; for any real process the maximum work will be less.
In the study of plant biology we encounter several sources of energy—notably light and chemical transfor-mations—as well as a variety of work functions, includ-ing mechanical, osmotic, electrical, and chemical work.
The meaning of the first law in biology stems from the certainty, painstakingly achieved by nineteenth-century physicists, that the various kinds of energy and work are measurable, equivalent, and, within limits, inter-convertible. Energy is to biology what money is to eco-nomics: the means by which living things purchase use-ful goods and services.
Each Type of Energy Is Characterized by a Capacity Factor and a Potential Factor The amount of work that can be done by a system, whether mechanical or chemical, is a function of the size of the system. Work can always be defined as the prod-uct of two factors—force and distance, for example. One is a potential or intensity factor, which is independent of the size of the system; the other is a capacity factor and is directly proportional to the size (Table 2.1).
Equation 2.2 is more commonly encountered in the form ∆U = ∆Q – ∆W, which results from the convention that Q is the amount of heat absorbed by the system from the sur-roundings and W is the amount of work done by the sys-tem on the surroundings. This convention affects the sign of W but does not alter the meaning of the equation.
† In biochemistry, reversibility has a different meaning: Usually the term refers to a reaction whose pathway can be reversed, often with an input of energy.
CHAPTER 2 4 In biochemistry, energy and work have traditionally been expressed in calories; 1 calorie is the amount of heat required to raise the temperature of 1 g of water by 1ºC, specifically, from 15.0 to 16.0°C . In principle, one can carry out the same process by doing the work mechanically with a paddle; such experiments led to the establishment of the mechanical equivalent of heat as 4.186 joules per calorie (J cal–1). We will also have occa-sion to use the equivalent electrical units, based on the volt: A volt is the potential difference between two points when 1 J of work is involved in the transfer of a coulomb of charge from one point to another. (A coulomb is the amount of charge carried by a current of 1 ampere [A] flowing for 1 s. Transfer of 1 mole [mol] of charge across a potential of 1 volt [V] involves 96,500 J of energy or work.) The difference between energy and work is often a matter of the sign. Work must be done to bring a positive charge closer to another positive charge, but the charges thereby acquire potential energy, which in turn can do work.
The Direction of Spontaneous Processes Left to themselves, events in the real world take a pre-dictable course. The apple falls from the branch. A mix-ture of hydrogen and oxygen gases is converted into water. The fly trapped in a bottle is doomed to perish, the pyramids to crumble into sand; things fall apart. But there is nothing in the principle of energy conservation that forbids the apple to return to its branch with absorption of heat from the surroundings or that pre-vents water from dissociating into its constituent ele-ments in a like manner. The search for the reason that neither of these things ever happens led to profound philosophical insights and generated useful quantitative statements about the energetics of chemical reactions and the amount of work that can be done by them. Since living things are in many respects chemical machines, we must examine these matters in some detail.
The Second Law: The Total Entropy Always Increases From daily experience with weights falling and warm bodies growing cold, one might expect spontaneous processes to proceed in the direction that lowers the internal energy—that is, the direction in which ∆U is negative. But there are too many exceptions for this to be a general rule. The melting of ice is one exception: An ice cube placed in water at 1°C will melt, yet measure-ments show that liquid water (at any temperature above 0°C) is in a state of higher energy than ice; evidently, some spontaneous processes are accompanied by an increase in internal energy. Our melting ice cube does not violate the first law, for heat is absorbed as it melts.
This suggests that there is a relationship between the capacity for spontaneous heat absorption and the crite-rion determining the direction of spontaneous processes, and that is the case. The thermodynamic function we seek is called entropy, the amount of energy in a system not available for doing work, corresponding to the degree of randomness of a system. Mathematically, entropy is the capacity factor corresponding to temper-ature, Q/T. We may state the answer to our question, as well as the second law of thermodynamics, thus: The direction of all spontaneous processes is to increase the entropy of a system plus its surroundings.
Few concepts are so basic to a comprehension of the world we live in, yet so opaque, as entropy—presum-ably because entropy is not intuitively related to our sense perceptions, as mass and temperature are. The explanation given here follows the particularly lucid exposition by Atkinson (1977), who states the second law in a form bearing, at first sight, little resemblance to that given above: We shall take [the second law] as the concept that any system not at absolute zero has an irre-ducible minimum amount of energy that is an inevitable property of that system at that temper-ature. That is, a system requires a certain amount of energy just to be at any specified temperature.
The molecular constitution of matter supplies a ready explanation: Some energy is stored in the thermal motions of the molecules and in the vibrations and oscil-lations of their constituent atoms. We can speak of it as isothermally unavailable energy, since the system can-not give up any of it without a drop in temperature (assuming that there is no physical or chemical change).
The isothermally unavailable energy of any system increases with temperature, since the energy of molecu-lar and atomic motions increases with temperature.
Quantitatively, the isothermally unavailable energy for a particular system is given by ST, where T is the absolute temperature and S is the entropy.
Table 2.1 Potential and capacity factors in energetics Type of energy Potential factor Capacity factor Mechanical Pressure Volume Electrical Electric potential Charge Chemical Chemical potential Mass Osmotic Concentration Mass Thermal Temperature Entropy In current standard usage based on the meter, kilogram, and second, the fundamental unit of energy is the joule (1 J = 0.24 cal) or the kilojoule (1 kJ = 1000 J).
But what is this thing, entropy? Reflection on the nature of the isothermally unavailable energy suggests that, for any particular temperature, the amount of such energy will be greater the more atoms and molecules are free to move and to vibrate—that is, the more chaotic is the system. By contrast, the orderly array of atoms in a crystal, with a place for each and each in its place, cor-responds to a state of low entropy. At absolute zero, when all motion ceases, the entropy of a pure substance is likewise zero; this statement is sometimes called the third law of thermodynamics. A large molecule, a protein for example, within which many kinds of motion can take place, will have considerable amounts of energy stored in this fashion— more than would, say, an amino acid molecule. But the entropy of the protein molecule will be less than that of the constituent amino acids into which it can dissociate, because of the constraints placed on the motions of those amino acids as long as they are part of the larger structure. Any process leading to the release of these constraints increases freedom of movement, and hence entropy. This is the universal tendency of spontaneous processes as expressed in the second law; it is why the costly enzymes stored in the refrigerator tend to decay and why ice melts into water. The increase in entropy as ice melts into water is “paid for” by the absorption of heat from the surroundings. As long as the net change in entropy of the system plus its surroundings is posi-tive, the process can take place spontaneously. That does not necessarily mean that the process will take place: The rate is usually determined by kinetic factors sepa-rate from the entropy change. All the second law man-dates is that the fate of the pyramids is to crumble into sand, while the sand will never reassemble itself into a pyramid; the law does not tell how quickly this must come about.
A Process Is Spontaneous If DS for the System and Its Surroundings Is Positive There is nothing mystical about entropy; it is a thermo-dynamic quantity like any other, measurable by exper-iment and expressed in entropy units. One method of quantifying it is through the heat capacity of a system, the amount of energy required to raise the temperature by 1°C. In some cases the entropy can even be calculated from theoretical principles, though only for simple mol-ecules. For our purposes, what matters is the sign of the entropy change, ∆S: A process can take place sponta-neously when ∆S for the system and its surroundings is positive; a process for which ∆S is negative cannot take place spontaneously, but the opposite process can; and for a system at equilibrium, the entropy of the system plus its surroundings is maximal and ∆S is zero.
“Equilibrium” is another of those familiar words that is easier to use than to define. Its everyday meaning implies that the forces acting on a system are equally balanced, such that there is no net tendency to change; this is the sense in which the term “equilibrium” will be used here. A mixture of chemicals may be in the midst of rapid interconversion, but if the rates of the forward reaction and the backward reaction are equal, there will be no net change in composition, and equilibrium will prevail. The second law has been stated in many versions.
One version forbids perpetual-motion machines: Because energy is, by the second law, perpetually degraded into heat and rendered isothermally unavail-able (∆S > 0), continued motion requires an input of energy from the outside. The most celebrated yet per-plexing version of the second law was provided by R. J.
Clausius (1879): “The energy of the universe is constant; the entropy of the universe tends towards a maximum.” How can entropy increase forever, created out of nothing? The root of the difficulty is verbal, as Klotz (1967) neatly explains. Had Clausius defined entropy with the opposite sign (corresponding to order rather than to chaos), its universal tendency would be to diminish; it would then be obvious that spontaneous changes proceed in the direction that decreases the capacity for further spontaneous change. Solutes diffuse from a region of higher concentration to one of lower concentration; heat flows from a warm body to a cold one. Sometimes these changes can be reversed by an outside agent to reduce the entropy of the system under consideration, but then that external agent must change in such a way as to reduce its own capacity for further change. In sum, “entropy is an index of exhaustion; the more a system has lost its capacity for spontaneous change, the more this capacity has been exhausted, the greater is the entropy” (Klotz 1967). Conversely, the far-ther a system is from equilibrium, the greater is its capacity for change and the less its entropy. Living things fall into the latter category: A cell is the epitome of a state that is remote from equilibrium.
Free Energy and Chemical Potential Many energy transactions that take place in living organisms are chemical; we therefore need a quantita-tive expression for the amount of work a chemical reac-tion can do. For this purpose, relationships that involve the entropy change in the system plus its surroundings are unsuitable. We need a function that does not depend on the surroundings but that, like ∆S, attains a mini-mum under conditions of equilibrium and so can serve both as a criterion of the feasibility of a reaction and as a measure of the energy available from it for the perfor-Energy and Enzymes 5 CHAPTER 2 6 mance of work. The function universally employed for this purpose is free energy, abbreviated G in honor of the nineteenth-century physical chemist J. Willard Gibbs, who first introduced it.
DG Is Negative for a Spontaneous Process at Constant Temperature and Pressure Earlier we spoke of the isothermally unavailable energy, ST. Free energy is defined as the energy that is available under isothermal conditions, and by the following rela-tionship: ∆H = ∆G + T∆S (2.3) The term H, enthalpy or heat content, is not quite equiv-alent to U, the internal energy (see Equation 2.2). To be exact, ∆H is a measure of the total energy change, including work that may result from changes in volume during the reaction, whereas ∆U excludes this work.
(We will return to the concept of enthalpy a little later.) However, in the biological context we are usually con-cerned with reactions in solution, for which volume changes are negligible. For most purposes, then, ∆U ≅ ∆G + T∆S (2.4) and ∆G ≅ ∆U – T∆S (2.5) What makes this a useful relationship is the demon-stration that for all spontaneous processes at constant tem-perature and pressure, ∆G is negative. The change in free energy is thus a criterion of feasibility. Any chemical reac-tion that proceeds with a negative ∆G can take place spontaneously; a process for which ∆G is positive cannot take place, but the reaction can go in the opposite direc-tion; and a reaction for which ∆G is zero is at equilibrium, and no net change will occur. For a given temperature and pressure, ∆G depends only on the composition of the reaction mixture; hence the alternative term “chemical potential” is particularly apt. Again, nothing is said about rate, only about direction. Whether a reaction having a given ∆G will proceed, and at what rate, is determined by kinetic rather than thermodynamic factors.
There is a close and simple relationship between the change in free energy of a chemical reaction and the work that the reaction can do. Provided the reaction is carried out reversibly, ∆G = ∆Wmax (2.6) That is, for a reaction taking place at constant temperature and pressure, –∆G is a measure of the maximum work the process can perform. More precisely, –∆G is the maximum work possible, exclusive of pressure–volume work, and thus is a quantity of great importance in bioenergetics.
Any process going toward equilibrium can, in principle, do work. We can therefore describe processes for which ∆G is negative as “energy-releasing,” or exergonic. Con-versely, for any process moving away from equilibrium, ∆G is positive, and we speak of an “energy-consuming,” or endergonic, reaction. Of course, an endergonic reac-tion cannot occur: All real processes go toward equilib-rium, with a negative ∆G. The concept of endergonic reactions is nevertheless a useful abstraction, for many biological reactions appear to move away from equilib-rium. A prime example is the synthesis of ATP during oxidative phosphorylation, whose apparent ∆G is as high as 67 kJ mol–1 (16 kcal mol–1). Clearly, the cell must do work to render the reaction exergonic overall. The occur-rence of an endergonic process in nature thus implies that it is coupled to a second, exergonic process. Much of cel-lular and molecular bioenergetics is concerned with the mechanisms by which energy coupling is effected.
The Standard Free-Energy Change, DG0, Is the Change in Free Energy When the Concentration of Reactants and Products Is 1 M Changes in free energy can be measured experimentally by calorimetric methods. They have been tabulated in two forms: as the free energy of formation of a com-pound from its elements, and as ∆G for a particular reac-tion. It is of the utmost importance to remember that, by convention, the numerical values refer to a particular set of conditions. The standard free-energy change, ∆G0, refers to conditions such that all reactants and products are present at a concentration of 1 M; in biochemistry it is more con-venient to employ ∆G0′, which is defined in the same way except that the pH is taken to be 7. The conditions obtained in the real world are likely to be very different from these, particularly with respect to the concentra-tions of the participants. To take a familiar example, ∆G0′ for the hydrolysis of ATP is about –33 kJ mol–1 (–8 kcal mol–1). In the cytoplasm, however, the actual nucleotide concentrations are approximately 3 mM ATP, 1 mM ADP, and 10 mM Pi. As we will see, changes in free energy depend strongly on concentrations, and ∆G for ATP hydrolysis under physiological conditions thus is much more negative than ∆G0′, about –50 to –65 kJ mol–1 (–12 to –15 kcal mol–1). Thus, whereas values of ∆G0′ for many reactions are easily accessible, they must not be used uncritically as guides to what happens in cells.
The Value of ∆G Is a Function of the Displacement of the Reaction from Equilibrium The preceding discussion of free energy shows that there must be a relationship between ∆G and the equi-librium constant of a reaction: At equilibrium, ∆G is zero, and the farther a reaction is from equilibrium, the larger ∆G is and the more work the reaction can do. The quantitative statement of this relationship is ∆G0 = –RT ln K = –2.3RT log K (2.7) where R is the gas constant, T the absolute temperature, and K the equilibrium constant of the reaction. This equation is one of the most useful links between ther-modynamics and biochemistry and has a host of appli-cations. For example, the equation is easily modified to allow computation of the change in free energy for con-centrations other than the standard ones. For the reac-tions shown in the equation (2.8) the actual change in free energy, ∆G, is given by the equation (2.9) where the terms in brackets refer to the concentrations at the time of the reaction. Strictly speaking, one should use activities, but these are usually not known for cel-lular conditions, so concentrations must do.
Equation 2.9 can be rewritten to make its import a lit-tle plainer. Let q stand for the mass:action ratio, [C][D]/[A][B]. Substitution of Equation 2.7 into Equa-tion 2.9, followed by rearrangement, then yields the fol-lowing equation: (2.10) In other words, the value of ∆G is a function of the dis-placement of the reaction from equilibrium. In order to displace a system from equilibrium, work must be done on it and ∆G must be positive. Conversely, a system dis-placed from equilibrium can do work on another sys-tem, provided that the kinetic parameters allow the reaction to proceed and a mechanism exists that couples the two systems. Quantitatively, a reaction mixture at 25°C whose composition is one order of magnitude away from equilibrium (log K/q = 1) corresponds to a free-energy change of 5.7 kJ mol–1 (1.36 kcal mol–1). The value of ∆G is negative if the actual mass:action ratio is less than the equilibrium ratio and positive if the mass:action ratio is greater.
The point that ∆G is a function of the displacement of a reaction (indeed, of any thermodynamic system) from equilibrium is central to an understanding of bioener-getics. Figure 2.2 illustrates this relationship diagram-matically for the chemical interconversion of substances A and B, and the relationship will reappear shortly in other guises.
The Enthalpy Change Measures the Energy Transferred as Heat Chemical and physical processes are almost invariably accompanied by the generation or absorption of heat, which reflects the change in the internal energy of the system. The amount of heat transferred and the sign of the reaction are related to the change in free energy, as set out in Equation 2.3. The energy absorbed or evolved as heat under conditions of constant pressure is desig-nated as the change in heat content or enthalpy, ∆H.
Processes that generate heat, such as combustion, are said to be exothermic; those in which heat is absorbed, such as melting or evaporation, are referred to as endothermic. The oxidation of glucose to CO2 and water is an exergonic reaction (∆G0 = –2858 kJ mol–1 [–686 kcal mol–1] ); when this reaction takes place during respira-tion, part of the free energy is conserved through cou-pled reactions that generate ATP. The combustion of glu-cose dissipates the free energy of reaction, releasing most of it as heat (∆H = –2804 kJ mol–1 [–673 kcal mol–1]). Bioenergetics is preoccupied with energy transduction and therefore gives pride of place to free-energy trans-actions, but at times heat transfer may also carry biolog-ical significance. For example, water has a high heat of vaporization, 44 kJ mol–1 (10.5 kcal mol–1) at 25°C, which plays an important role in the regulation of leaf temper-ature. During the day, the evaporation of water from the leaf surface (transpiration) dissipates heat to the sur-roundings and helps cool the leaf. Conversely, the con-densation of water vapor as dew heats the leaf, since water condensation is the reverse of evaporation, is exothermic. The abstract enthalpy function is a direct measure of the energy exchanged in the form of heat.
Redox Reactions Oxidation and reduction refer to the transfer of one or more electrons from a donor to an acceptor, usually to another chemical species; an example is the oxidation of ferrous iron by oxygen, which forms ferric iron and ∆G RT K q = −2 3 .
log ∆ ∆ G G RT = + 0 C D [A][B] ln [ ][ ] A B C+ D + ⇔ Energy and Enzymes 7 A Pure A Pure B B Free energy 0.1K K 10K 100K 1000K 0.01K 0.001K Figure 2.2 Free energy of a chemical reaction as a function of displacement from equilibrium. Imagine a closed system containing components A and B at concentrations [A] and [B]. The two components can be interconverted by the reac-tion A ↔B, which is at equilibrium when the mass:action ratio, [B]/[A], equals unity. The curve shows qualitatively how the free energy, G, of the system varies when the total [A] + [B] is held constant but the mass:action ratio is dis-placed from equilibrium. The arrows represent schemati-cally the change in free energy, ∆G, for a small conversion of [A] into [B] occurring at different mass:action ratios.
(After Nicholls and Ferguson 1992.) water. Reactions of this kind require special considera-tion, for they play a central role in both respiration and photosynthesis.
The Free-Energy Change of an Oxidation– Reduction Reaction Is Expressed as the Standard Redox Potential in Electrochemical Units Redox reactions can be quite properly described in terms of their change in free energy. However, the par-ticipation of electrons makes it convenient to follow the course of the reaction with electrical instrumentation and encourages the use of an electrochemical notation.
It also permits dissection of the chemical process into separate oxidative and reductive half-reactions. For the oxidation of iron, we can write (2.11) (2.12) (2.13) The tendency of a substance to donate electrons, its “electron pressure,” is measured by its standard reduc-tion (or redox) potential, E0 , with all components pre-sent at a concentration of 1 M. In biochemistry, it is more convenient to employ E′0, which is defined in the same way except that the pH is 7. By definition, then, E′0 is the electromotive force given by a half cell in which the reduced and oxidized species are both present at 1 M, 25°C, and pH 7, in equilibrium with an electrode that can reversibly accept electrons from the reduced species.
By convention, the reaction is written as a reduction.
The standard reduction potential of the hydrogen elec-trode serves as reference: at pH 7, it equals –0.42 V. The standard redox potential as defined here is often referred to in the bioenergetics literature as the mid-point potential, Em. A negative midpoint potential marks a good reducing agent; oxidants have positive midpoint potentials.
The redox potential for the reduction of oxygen to water is +0.82 V; for the reduction of Fe3+ to Fe2+ (the direction opposite to that of Equation 2.11), +0.77 V. We can therefore predict that, under standard conditions, the Fe2+–Fe3+ couple will tend to reduce oxygen to water rather than the reverse. A mixture containing Fe2+, Fe3+, and oxygen will probably not be at equilibrium, and the extent of its displacement from equilibrium can be expressed in terms of either the change in free energy for Equation 2.13 or the difference in redox potential, ∆E′ 0, between the oxidant and the reductant couples (+0.05 V in the case of iron oxidation). In general, ∆G0′ = –nF ∆E′0 (2.14) where n is the number of electrons transferred and F is Faraday’s constant (23.06 kcal V–1 mol–1). In other words, the standard redox potential is a measure, in electrochemical units, of the change in free energy of an oxidation–reduction process.
As with free-energy changes, the redox potential measured under conditions other than the standard ones depends on the concentrations of the oxidized and reduced species, according to the following equation (note the similarity in form to Equation 2.9): (2.15) Here Eh is the measured potential in volts, and the other symbols have their usual meanings. It follows that the redox potential under biological conditions may differ substantially from the standard reduction potential.
The Electrochemical Potential In the preceding section we introduced the concept that a mixture of substances whose composition diverges from the equilibrium state represents a potential source of free energy (see Figure 2.2). Conversely, a similar amount of work must be done on an equilibrium mix-ture in order to displace its composition from equilib-rium. In this section, we will examine the free-energy changes associated with another kind of displacement from equilibrium—namely, gradients of concentration and of electric potential.
Transport of an Uncharged Solute against Its Concentration Gradient Decreases the Entropy of the System Consider a vessel divided by a membrane into two compartments that contain solutions of an uncharged solute at concentrations C1 and C2, respectively. The work required to transfer 1 mol of solute from the first compartment to the second is given by the following equation: (2.16) This expression is analogous to the expression for a chemical reaction (Equation 2.10) and has the same meaning. If C2 is greater than C1, ∆G is positive, and work must be done to transfer the solute. Again, the free-energy change for the transport of 1 mol of solute against a tenfold gradient of concentration is 5.7 kJ, or 1.36 kcal. The reason that work must be done to move a sub-stance from a region of lower concentration to one of ∆G RT = C C 2 1 2 3 .
log E E RT nF h oxidant [reductant] = ′ + 0 2 3 .
log [ ] 2Fe O H Fe H O 2+ 2 + 3+ + + ⇔ + 12 2 2 2 12 2 2 2 O H E H O 2 + ± + + ⇔ Fe Fe e 2+ 3+ ± 2 2 2 ⇔ + CHAPTER 2 8 The standard hydrogen electrode consists of platinum, over which hydrogen gas is bubbled at a pressure of 1 atm. The electrode is immersed in a solution containing hydrogen ions. When the activity of hydrogen ions is 1, approximately 1 M H+, the potential of the electrode is taken to be 0.
higher concentration is that the process entails a change to a less probable state and therefore a decrease in the entropy of the system. Conversely, diffusion of the solute from the region of higher concentration to that of lower concentration takes place in the direction of greater probability; it results in an increase in the entropy of the system and can proceed spontaneously.
The sign of ∆G becomes negative, and the process can do the amount of work specified by Equation 2.16, pro-vided a mechanism exists that couples the exergonic dif-fusion process to the work function.
The Membrane Potential Is the Work That Must Be Done to Move an Ion from One Side of the Membrane to the Other Matters become a little more complex if the solute in question bears an electric charge. Transfer of positively charged solute from compartment 1 to compartment 2 will then cause a difference in charge to develop across the membrane, the second compartment becoming elec-tropositive relative to the first. Since like charges repel one another, the work done by the agent that moves the solute from compartment 1 to compartment 2 is a func-tion of the charge difference; more precisely, it depends on the difference in electric potential across the mem-brane. This difference, called membrane potential for short, will appear again in later pages. The membrane potential, ∆E, is defined as the work that must be done by an agent to move a test charge from one side of the membrane to the other. When 1 J of work must be done to move 1 coulomb of charge, the potential difference is said to be 1 V. The absolute elec-tric potential of any single phase cannot be measured, but the potential difference between two phases can be.
By convention, the membrane potential is always given in reference to the movement of a positive charge. It states the intracellular potential relative to the extracel-lular one, which is defined as zero.
The work that must be done to move 1 mol of an ion against a membrane potential of ∆E volts is given by the following equation: ∆G = zF ∆E (2.17) where z is the valence of the ion and F is Faraday’s con-stant. The value of ∆G for the transfer of cations into a positive compartment is positive and so calls for work.
Conversely, the value of ∆G is negative when cations move into the negative compartment, so work can be done. The electric potential is negative across the plasma membrane of the great majority of cells; therefore cations tend to leak in but have to be “pumped” out.
The Electrochemical-Potential Difference, ~, Includes Both Concentration and Electric Potentials In general, ions moving across a membrane are subject to gradients of both concentration and electric potential.
Consider, for example, the situation depicted in Figure 2.3, which corresponds to a major event in energy trans-duction during photosynthesis. A cation of valence z moves from compartment 1 to compartment 2, against both a concentration gradient (C2 > C1) and a gradient of membrane electric potential (compartment 2 is elec-tropositive relative to compartment 1). The free-energy change involved in this transfer is given by the follow-ing equation: (2.18) ∆G is positive, and the transfer can proceed only if cou-pled to a source of energy, in this instance the absorp-tion of light. As a result of this transfer, cations in com-partment 2 can be said to be at a higher electrochemical potential than the same ions in compartment 1. The electrochemical potential for a particular ion is designated m ~ ion. Ions tend to flow from a region of high electrochemical potential to one of low potential and in so doing can in principle do work. The maximum amount of this work, neglecting friction, is given by the change in free energy of the ions that flow from com-partment 2 to compartment 1 (see Equation 2.6) and is numerically equal to the electrochemical-potential dif-ference, ∆m ~ ion. This principle underlies much of biolog-ical energy transduction.
The electrochemical-potential difference, ∆m ~ ion, is properly expressed in kilojoules per mole or kilocalories per mole. However, it is frequently convenient to ∆ ∆ G zF E RT = + C C 2 1 2 3 .
log Energy and Enzymes 9 2 1 + + + – – – + + + + + + + + + + + + + + + + + + + + + + + Figure 2.3 Transport against an electrochemical-potential gradient. The agent that moves the charged solute (from com-partment 1 to compartment 2) must do work to overcome both the electrochemical-potential gradient and the concen-tration gradient. As a result, cations in compartment 2 have been raised to a higher electrochemical potential than those in compartment 1. Neutralizing anions have been omitted.
Many texts use the term ∆Y for the membrane potential difference. However, to avoid confusion with the use of ∆Y to indicate water potential (see Chapter 3), the term ∆E will be used here and throughout the text.
express the driving force for ion movement in electrical terms, with the dimensions of volts or millivolts. To con-vert ∆m ~ ion into millivolts (mV), divide all the terms in Equation 2.18 by F: (2.19) An important case in point is the proton motive force, which will be considered at length in Chapter 6.
Equations 2.18 and 2.19 have proved to be of central importance in bioenergetics. First, they measure the amount of energy that must be expended on the active transport of ions and metabolites, a major function of biological membranes. Second, since the free energy of chemical reactions is often transduced into other forms via the intermediate generation of electrochemical-poten-tial gradients, these gradients play a major role in descriptions of biological energy coupling. It should be emphasized that the electrical and concentration terms may be either added, as in Equation 2.18, or subtracted, and that the application of the equations to particular cases requires careful attention to the sign of the gradi-ents. We should also note that free-energy changes in chemical reactions (see Equation 2.10) are scalar, whereas transport reactions have direction; this is a subtle but crit-ical aspect of the biological role of ion gradients.
Ion distribution at equilibrium is an important special case of the general electrochemical equation (Equation 2.18). Figure 2.4 shows a membrane-bound vesicle (com-partment 2) that contains a high concentration of the salt K2SO4, surrounded by a medium (compartment 1) con-taining a lower concentration of the same salt; the mem-brane is impermeable to anions but allows the free pas-sage of cations. Potassium ions will therefore tend to diffuse out of the vesicle into the solution, whereas the sulfate anions are retained. Diffusion of the cations gen-erates a membrane potential, with the vesicle interior negative, which restrains further diffusion. At equilib-rium, ∆G and ∆m ~ K+ equal zero (by definition). Equation 2.18 can then be arranged to give the following equation: (2.20) where C2 and C1 are the concentrations of K+ ions in the two compartments; z, the valence, is unity; and ∆E is the membrane potential in equilibrium with the potassium concentration gradient.
This is one form of the celebrated Nernst equation. It states that at equilibrium, a permeant ion will be so dis-tributed across the membrane that the chemical driving force (outward in this instance) will be balanced by the electric driving force (inward). For a univalent cation at 25°C, each tenfold increase in concentration factor cor-responds to a membrane potential of 59 mV; for a diva-lent ion the value is 29.5 mV.
The preceding discussion of the energetic and elec-trical consequences of ion translocation illustrates a point that must be clearly understood—namely, that an electric potential across a membrane may arise by two distinct mechanisms. The first mechanism, illustrated in Figure 2.4, is the diffusion of charged particles down a preexisting concentration gradient, an exergonic process. A potential generated by such a process is described as a diffusion potential or as a Donnan potential. (Donnan potential is defined as the diffusion potential that occurs in the limiting case where the coun-terion is completely impermeant or fixed, as in Figure 2.4.) Many ions are unequally distributed across biolog-ical membranes and differ widely in their rates of diffu-sion across the barrier; therefore diffusion potentials always contribute to the observed membrane potential.
But in most biological systems the measured electric potential differs from the value that would be expected on the basis of passive ion diffusion. In these cases one must invoke electrogenic ion pumps, transport systems that carry out the exergonic process indicated in Figure 2.3 at the expense of an external energy source. Trans-port systems of this kind transduce the free energy of a chemical reaction into the electrochemical potential of an ion gradient and play a leading role in biological energy coupling.
Enzymes: The Catalysts of Life Proteins constitute about 30% of the total dry weight of typical plant cells. If we exclude inert materials, such as the cell wall and starch, which can account for up to 90% of the dry weight of some cells, proteins and amino C C 2 1 ∆E RT zF = −2 3 .
log ∆ ∆ ˜ .
log ion 2 1 C C F z E RT F = + 2 3 CHAPTER 2 10 2 1 – – – + + + + + + + + + + + + + + + + + + + + + + + + + + Figure 2.4 Generation of an electric potential by ion diffu-sion. Compartment 2 has a higher salt concentration than compartment 1 (anions are not shown). If the membrane is permeable to the cations but not to the anions, the cations will tend to diffuse out of compartment 2 into compart-ment 1, generating a membrane potential in which com-partment 2 is negative. acids represent about 60 to 70% of the dry weight of the living cell. As we saw in Chapter 1, cytoskeletal struc-tures such as microtubules and microfilaments are com-posed of protein. Proteins can also occur as storage forms, particularly in seeds. But the major function of proteins in metabolism is to serve as enzymes, biologi-cal catalysts that greatly increase the rates of biochemi-cal reactions, making life possible. Enzymes participate in these reactions but are not themselves fundamentally changed in the process (Mathews and Van Holde 1996).
Enzymes have been called the “agents of life”—a very apt term, since they control almost all life processes. A typical cell has several thousand different enzymes, which carry out a wide variety of actions. The most important features of enzymes are their specificity, which permits them to distinguish among very similar molecules, and their catalytic efficiency, which is far greater than that of ordinary catalysts. The stereospeci-ficity of enzymes is remarkable, allowing them to dis-tinguish not only between enantiomers (mirror-image stereoisomers), for example, but between apparently identical atoms or groups of atoms (Creighton 1983).
This ability to discriminate between similar mole-cules results from the fact that the first step in enzyme catalysis is the formation of a tightly bound, noncova-lent complex between the enzyme and the substrate(s): the enzyme–substrate complex. Enzyme-catalyzed reac-tions exhibit unusual kinetic properties that are also related to the formation of these very specific com-plexes. Another distinguishing feature of enzymes is that they are subject to various kinds of regulatory con-trol, ranging from subtle effects on the catalytic activity by effector molecules (inhibitors or activators) to regu-lation of enzyme synthesis and destruction by the con-trol of gene expression and protein turnover.
Enzymes are unique in the large rate enhancements they bring about, orders of magnitude greater than those effected by other catalysts. Typical orders of rate enhancements of enzyme-catalyzed reactions over the corresponding uncatalyzed reactions are 108 to 1012.
Many enzymes will convert about a thousand molecules of substrate to product in 1 s. Some will convert as many as a million!
Unlike most other catalysts, enzymes function at ambient temperature and atmospheric pressure and usually in a narrow pH range near neutrality (there are exceptions; for instance, vacuolar proteases and ribonu-cleases are most active at pH 4 to 5). A few enzymes are able to function under extremely harsh conditions; examples are pepsin, the protein-degrading enzyme of the stomach, which has a pH optimum around 2.0, and the hydrogenase of the hyperthermophilic (“extreme heat–loving”) archaebacterium Pyrococcus furiosus, which oxidizes H2 at a temperature optimum greater than 95°C (Bryant and Adams 1989). The presence of such remarkably heat-stable enzymes enables Pyrococ-cus to grow optimally at 100°C. Enzymes are usually named after their substrates by the addition of the suffix “-ase”—for example, α-amy-lase, malate dehydrogenase, β-glucosidase, phospho-enolpyruvate carboxylase, horseradish peroxidase.
Many thousands of enzymes have already been discov-ered, and new ones are being found all the time. Each enzyme has been named in a systematic fashion, on the basis of the reaction it catalyzes, by the International Union of Biochemistry. In addition, many enzymes have common, or trivial, names. Thus the common name rubisco refers to D-ribulose-1,5-bisphosphate carboxy-lase/oxygenase (EC 4.1.1.39). The versatility of enzymes reflects their properties as proteins. The nature of proteins permits both the exquis-ite recognition by an enzyme of its substrate and the catalytic apparatus necessary to carry out diverse and rapid chemical reactions (Stryer 1995).
Proteins Are Chains of Amino Acids Joined by Peptide Bonds Proteins are composed of long chains of amino acids (Figure 2.5) linked by amide bonds, known as peptide bonds (Figure 2.6). The 20 different amino acid side chains endow proteins with a large variety of groups that have different chemical and physical properties, including hydrophilic (polar, water-loving) and hydro-phobic (nonpolar, water-avoiding) groups, charged and neutral polar groups, and acidic and basic groups. This diversity, in conjunction with the relative flexibility of the peptide bond, allows for the tremendous variation in protein properties, ranging from the rigidity and inertness of structural proteins to the reactivity of hor-mones, catalysts, and receptors. The three-dimensional aspect of protein structure provides for precise discrim-ination in the recognition of ligands, the molecules that interact with proteins, as shown by the ability of enzymes to recognize their substrates and of antibodies to recognize antigens, for example.
All molecules of a particular protein have the same sequence of amino acid residues, determined by the sequence of nucleotides in the gene that codes for that protein. Although the protein is synthesized as a linear chain on the ribosome, upon release it folds sponta-neously into a specific three-dimensional shape, the native state. The chain of amino acids is called a polypeptide. The three-dimensional arrangement of the atoms in the molecule is referred to as the conformation.
Energy and Enzymes 11 The Enzyme Commission (EC) number indicates the class (4 = lyase) and subclasses (4.1 = carbon–carbon cleavage; 4.1.1 = cleavage of C—COO– bond). CHAPTER 2 12 Alanine [A] (Ala) C H CH3 C H CH CH3 H3C C H CH2 CH CH3 H3C C H C CH3 H CH2 CH3 CH2 C H CH2 C H NH CH2 C H CH2 CH3 S CH2 C H SH C H H Glycine [G] (Gly) Cysteine [C] (Cys) Methionine [M] (Met) Tryptophan [W] (Trp) Phenylalanine [F] (Phe) Proline [P] (Pro) C H CH2 CH2 H2C CH2 C H CH2 C H C C H COO -C C H OH OH CH3 H H H CH2 C H2N O O C H2N C H OH CH2 Tyrosine [Y] (Tyr) Threonine [T] (Thr) Serine [S] (Ser) Glutamine [Q] (Gln) Asparagine [N] (Asn) Hydrophilic (polar) R groups Neutral R groups Hydrophobic (nonpolar) R groups :NH CH HC :N H CH2 C H CH2 C H CH2 CH2 CH2 CH2 CH2 C NH3 NH NH2 H2N CH2 C H CH2 C H CH2 Glutamate [E] (Glu) Aspartate [D] (Asp) Histidine [H] (His) Arginine [R] (Arg) Lysine [K] (Lys) Acidic R groups Basic R groups Valine [V] (Val) Leucine [L] (Leu) Isoleucine [I] (Ile) -COO -COO -COO -COO -COO -COO C CH2 C -COO -COO -COO -COO -COO -COO -COO -COO -COO -COO -COO -COO -COO -COO -COO H3N + H3N + H3N + + + H3N + H3N + H3N + H3N + H3N + H3N + H3N + H3N + H3N + H3N + H3N + H3N + H3N + H3N + H3N + H3N + H2N + Figure 2.5 The structures, names, single-letter codes (in square brackets), three-letter abbreviations, and classification of the amino acids.
Changes in conformation do not involve breaking of covalent bonds. Denaturation involves the loss of this unique three-dimensional shape and results in the loss of catalytic activity.
The forces that are responsible for the shape of a pro-tein molecule are noncovalent (Figure 2.7). These non-covalent interactions include hydrogen bonds; electro-static interactions (also known as ionic bonds or salt bridges); van der Waals interactions (dispersion forces), which are transient dipoles between spatially close atoms; and hydrophobic “bonds”—the tendency of non-polar groups to avoid contact with water and thus to associate with themselves. In addition, covalent disul-fide bonds are found in many proteins. Although each of these types of noncovalent interaction is weak, there are so many noncovalent interactions in proteins that in total they contribute a large amount of free energy to stabilizing the native structure. Protein Structure Is Hierarchical Proteins are built up with increasingly complex organi-zational units. The primary structure of a protein refers to the sequence of amino acid residues. The secondary structure refers to regular, local structural units, usually held together by hydrogen bonding. The most common of these units are the α helix and β strands forming par-allel and antiparallel β pleated sheets and turns (Figure 2.8). The tertiary structure—the final three-dimensional structure of the polypeptide—results from the packing together of the secondary structure units and the exclu-sion of solvent. The quaternary structure refers to the association of two or more separate three-dimensional polypeptides to form complexes. When associated in this manner, the individual polypeptides are called subunits.
Energy and Enzymes 13 H3N R1 O O O– + R2 C H H H C N C C N H O H Rigid unit H O C R1 H R2 C N H N Cα H R3 C C O C φ Peptide bond (A) (B) ψ . . .
. . .
Figure 2.6 (A) The peptide (amide) bond links two amino acids. (B) Sites of free rotation, within the limits of steric hindrance, about the N—Cα and Cα—C bonds (ψ and φ); there is no rotation about the peptide bond, because of its double-bond character. – – + + + – – – + + + – VAN DER WAALS INTERACTIONS ELECTROSTATIC ATTRACTIONS HYDROGEN BONDS N C C H O C R H R NH2 CH2 H N C C H O C R H R H C O CH2 OH Between elements of peptide linkage Between side chains Serine Asparagine CH2 CH2 CH2 CH2 H3N CH2 COO– + Figure 2.7 Examples of noncovalent interactions in proteins. Hydrogen bonds are weak electrostatic interactions involving a hydrogen atom between two electronegative atoms.
In proteins the most important hydrogen bonds are those between the peptide bonds.
Electrostatic interactions are ionic bonds between positively and negatively charged groups. The van der Waals interactions are short-range transient dipole interactions.
Hydrophobic interactions (not shown) involve restructuring of the solvent water around nonpolar groups, minimizing the exposure of nonpolar surface area to polar solvent; these interactions are driven by entropy.
Aprotein molecule consisting of a large single polypep-tide chain is composed of several independently folding units known as domains. Typically, domains have a mol-ecular mass of about 104 daltons. The active site of an enzyme—that is, the region where the substrate binds and the catalytic reaction occurs—is often located at the inter-face between two domains. For example, in the enzyme papain (a vacuolar protease that is found in papaya and is representative of a large class of plant thiol proteases), the active site lies at the junction of two domains (Figure 2.9). Helices, turns, and β sheets contribute to the unique three-dimensional shape of this enzyme.
CHAPTER 2 14 C C C C N N H H H H O R R H H N N C C C O O H N C C C O C H N H N C O H N C C O C H N C O C C O C C O H N H N C C O H N C C O C C O H N C C C N N C H O C C H O C C C N N C H O C C H O C C C N N C H O C C H O C C C N N C H O C C H O N C O H H N O C N C O H H N O C N C O H H N O C N C C C O H H N O C (A) Primary structure (B) Secondary structure (α helix) (R groups not shown) (C) Secondary structure (β pleated sheet) (R groups not shown) (D) Tertiary structure (E) Quaternary structure Figure 2.8 Hierarchy of protein structure. (A) Primary structure: peptide bond. (B and C) Secondary structure: α helix (B) and antiparallel β pleated sheet (C). (D) Tertiary structure: α helices, β pleated sheets, and random coils. (E) Quaternary structure: four subunits.
Determinations of the conformation of proteins have revealed that there are families of proteins that have common three-dimensional folds, as well as common patterns of supersecondary structure, such as β-α-β.
Enzymes Are Highly Specific Protein Catalysts All enzymes are proteins, although recently some small ribonucleic acids and protein–RNA complexes have been found to exhibit enzymelike behavior in the processing of RNA. Proteins have molecular masses ranging from 104 to 106 daltons, and they may be a single folded polypeptide chain (subunit, or protomer) or oligomers of several subunits (oligomers are usually dimers or tetramers). Normally, enzymes have only one type of cat-alytic activity associated with the same protein; isoen-zymes, or isozymes, are enzymes with similar catalytic function that have different structures and catalytic para-meters and are encoded by different genes. For example, various different isozymes have been found for peroxi-dase, an enzyme in plant cell walls that is involved in the synthesis of lignin. An isozyme of peroxidase has also been localized in vacuoles. Isozymes may exhibit tissue specificity and show developmental regulation.
Enzymes frequently contain a nonprotein prosthetic group or cofactor that is necessary for biological activ-ity. The association of a cofactor with an enzyme depends on the three-dimensional structure of the pro-tein. Once bound to the enzyme, the cofactor contributes to the specificity of catalysis. Typical examples of cofac-tors are metal ions (e.g., zinc, iron, molybdenum), heme groups or iron–sulfur clusters (especially in oxida-tion–reduction enzymes), and coenzymes (e.g., nicoti-namide adenine dinucleotide [NAD+/NADH], flavin adenine dinucleotide [FAD/FADH2], flavin mononu-cleotide [FMN], and pyridoxal phosphate [PLP]). Coen-zymes are usually vitamins or are derived from vita-mins and act as carriers. For example, NAD+ and FAD carry hydrogens and electrons in redox reactions, biotin carries CO2, and tetrahydrofolate carries one-carbon fragments. Peroxidase has both heme and Ca2+ pros-thetic groups and is glycosylated; that is, it contains car-bohydrates covalently added to asparagine, serine, or threonine side chains. Such proteins are called glyco-proteins.
A particular enzyme will catalyze only one type of chemical reaction for only one class of molecule—in some cases, for only one particular compound. Enzymes are also very stereospecific and produce no by-products.
For example, β-glucosidase catalyzes the hydrolysis of β-glucosides, compounds formed by a glycosidic bond to D-glucose. The substrate must have the correct anomeric configuration: it must be β-, not α-. Further-more, it must have the glucose structure; no other car-bohydrates, such as xylose or mannose, can act as sub-strates for β-glucosidase. Finally, the substrate must have the correct stereochemistry, in this case the D absolute configuration. Rubisco (D-ribulose-1,5-bisphos-phate carboxylase/oxygenase) catalyzes the addition of carbon dioxide to D-ribulose-1,5-bisphosphate to form two molecules of 3-phospho-D-glycerate, the initial step in the C3 photosynthetic carbon reduction cycle, and is the world’s most abundant enzyme. Rubisco has very strict specificity for the carbohydrate substrate, but it also catalyzes an oxygenase reaction in which O2 replaces CO2, as will be discussed further in Chapter 8.
Enzymes Lower the Free-Energy Barrier between Substrates and Products Catalysts speed the rate of a reaction by lowering the energy barrier between substrates (reactants) and prod-ucts and are not themselves used up in the reaction, but are regenerated. Thus a catalyst increases the rate of a reaction but does not affect the equilibrium ratio of reac-tants and products, because the rates of the reaction in both directions are increased to the same extent. It is important to realize that enzymes cannot make a non-spontaneous (energetically uphill) reaction occur. How-ever, many energetically unfavorable reactions in cells proceed because they are coupled to an energetically more favorable reaction usually involving ATP hydrol-ysis (Figure 2.10).
Enzymes act as catalysts because they lower the free energy of activation for a reaction. They do this by a combination of raising the ground state ∆G of the sub-strate and lowering the ∆G of the transition state of the reaction, thereby decreasing the barrier against the reac-tion (Figure 2.11). The presence of the enzyme leads to Energy and Enzymes 15 Active-site cleft Domain 1 Domain 2 Domain 1 Figure 2.9 The backbone structure of papain, showing the two domains and the active-site cleft between them.
a new reaction pathway that is different from that of the uncatalyzed reaction.
Catalysis Occurs at the Active Site The active site of an enzyme molecule is usually a cleft or pocket on or near the surface of the enzyme that takes up only a small fraction of the enzyme surface. It is con-venient to consider the active site as consisting of two components: the binding site for the substrate (which attracts and positions the substrate) and the catalytic groups (the reactive side chains of amino acids or cofac-tors, which carry out the bond-breaking and bond-form-ing reactions involved).
Binding of substrate at the active site initially involves noncovalent interactions between the substrate and either side chains or peptide bonds of the protein.
The rest of the protein structure provides a means of positioning the substrate and catalytic groups, flexibil-ity for conformational changes, and regulatory control.
The shape and polarity of the binding site account for much of the specificity of enzymes, and there is com-plementarity between the shape and the polarity of the substrate and those of the active site. In some cases, binding of the substrate induces a conformational change in the active site of the enzyme. Conformational change is particularly common where there are two sub-strates. Binding of the first substrate sets up a confor-mational change of the enzyme that results in formation of the binding site for the second substrate. Hexokinase is a good example of an enzyme that exhibits this type of conformational change (Figure 2.12).
The catalytic groups are usually the amino acid side chains and/or cofactors that can function as catalysts.
Common examples of catalytic groups are acids (— COOH from the side chains of aspartic acid or glutamic acid, imidazole from the side chain of histidine), bases (—NH2 from lysine, imidazole from histidine, —S– from cysteine), nucleophiles (imidazole from histidine, —S– from cysteine, —OH from serine), and electrophiles (often metal ions, such as Zn2+). The acidic catalytic groups function by donating a proton, the basic ones by accepting a proton. Nucleophilic catalytic groups form a transient covalent bond to the substrate.
The decisive factor in catalysis is the direct interac-tion between the enzyme and the substrate. In many cases, there is an intermediate that contains a covalent bond between the enzyme and the substrate. Although the details of the catalytic mechanism differ from one type of enzyme to another, a limited number of features are involved in all enzyme catalysis. These features include acid–base catalysis, electrophilic or nucleophilic catalysis, and ground state distortion through electro-static or mechanical strains on the substrate.
A Simple Kinetic Equation Describes an Enzyme-Catalyzed Reaction Enzyme-catalyzed systems often exhibit a special form of kinetics, called Michaelis–Menten kinetics, which are characterized by a hyperbolic relationship between reaction velocity, v, and substrate concentration, [S] (Figure 2.13). This type of plot is known as a saturation plot because when the enzyme becomes saturated with CHAPTER 2 16 A + B C ∆G = +4.0 kcal mol–1 ATP + H2O ADP + Pi + H+ ∆G = –7.3 kcal mol–1 A + ATP A – P + ADP A – P + B + H2O C + H+ + Pi A + B + ATP + H2O C + ADP + Pi + H+ ∆G = –3.3 kcal mol–1 A + B + ATP + H2O C + ADP + Pi + H+ Substrate Product Free energy of activation Enzyme catalyzed Uncatalyzed Transition state Free energy Progress of reaction Figure 2.10 Coupling of the hydrolysis of ATP to drive an energetically unfavorable reaction. The reaction A + B →C is thermodynamically unfavorable, whereas the hydrolysis of ATP to form ADP and inorganic phosphate (Pi) is thermody-namically very favorable (it has a large negative ∆G). Through appropriate intermediates, such as A–P, the two reactions are coupled, yielding an overall reaction that is the sum of the individual reactions and has a favorable free-energy change.
Figure 2.11 Free-energy curves for the same reaction, either uncatalyzed or enzyme catalyzed. As a catalyst, an enzyme lowers the free energy of activation of the transi-tion state between substrates and products compared with the uncatalyzed reaction. It does this by forming various complexes and intermediates, such as enzyme–substrate and enzyme–product complexes. The ground state free energy of the enzyme–substrate complex in the enzyme-catalyzed reaction may be higher than that of the substrate in the uncatalyzed reaction, and the transition state free energy of the enzyme-bound substrate will be signficantly less than that in the corresponding uncatalyzed reaction.
substrate (i.e., each enzyme molecule has a substrate molecule associated with it), the rate becomes inde-pendent of substrate concentration. Saturation kinetics implies that an equilibrium process precedes the rate-limiting step: where E represents the enzyme, S the substrate, P the product, and ES the enzyme–substrate complex. Thus, as the substrate concentration is increased, a point will be reached at which all the enzyme molecules are in the form of the ES complex, and the enzyme is saturated with substrate. Since the rate of the reaction depends on the concentration of ES, the rate will not increase further, because there can be no higher concentration of ES.
When an enzyme is mixed with a large excess of sub-strate, there will be an initial very short time period (usu-ally milliseconds) during which the concentrations of enzyme–substrate complexes and intermediates build up to certain levels; this is known as the pre–steady-state period. Once the intermediate levels have been built up, they remain relatively constant until the substrate is depleted; this period is known as the steady state.
Normally enzyme kinetic values are measured under steady-state conditions, and such conditions usually pre-vail in the cell. For many enzyme-catalyzed reactions the kinetics under steady-state conditions can be described by a simple expression known as the Michaelis–Menten equation: (2.21) where v is the observed rate or velocity (in units such as moles per liter per second), V max is the maximum veloc-ity (at infinite substrate concentration), and Km (usually S S m v V K = + max[ ] [ ] E S ES E P fast slow + ← → → + Energy and Enzymes 17 D-Glucose Active site (A) (B) 1/2Vmax Vmax v = Vmax [S] Km + [S] Km Substrate concentration [S] Initial velocity (v) Figure 2.13 Plot of initial velocity, v, versus substrate con-centration, [S], for an enzyme-catalyzed reaction. The curve is hyperbolic. The maximal rate, V max, occurs when all the enzyme molecules are fully occupied by substrate. The value of Km, defined as the substrate concentration at 1⁄2V max, is a reflection of the affinity of the enzyme for the substrate.
The smaller the value of Km, the tighter the binding.
Figure 2.12 Conformational change in hexokinase, induced by the first substrate of the enzyme, D-glucose. (A) Before glucose binding. (B) After glucose binding. The binding of glucose to hexokinase induces a conformational change in which the two major domains come together to close the cleft that contains the active site. This change sets up the binding site for the second substrate, ATP. In this manner the enzyme prevents the unpro-ductive hydrolysis of ATP by shielding the substrates from the aqueous solvent. The over-all reaction is the phosphorylation of glucose and the formation of ADP.
measured in units of molarity) is a constant that is char-acteristic of the particular enzyme–substrate system and is related to the association constant of the enzyme for the substrate (see Figure 2.13). Km represents the con-centration of substrate required to half-saturate the enzyme and thus is the substrate concentration at Vmax/2. In many cellular systems the usual substrate concentration is in the vicinity of Km. The smaller the value of Km, the more strongly the enzyme binds the substrate. Typical values for Km are in the range of 10–6 to 10–3 M.
We can readily obtain the parameters Vmax and Km by fitting experimental data to the Michaelis–Menten equa-tion, either by computerized curve fitting or by a lin-earized form of the equation. An example of a linearized form of the equation is the Lineweaver–Burk double-reciprocal plot shown in Figure 2.14A. When divided by the concentration of enzyme, the value of Vmax gives the turnover number, the number of molecules of substrate converted to product per unit of time per molecule of enzyme. Typical turnover number values range from 102 to 103 s–1.
Enzymes Are Subject to Various Kinds of Inhibition Any agent that decreases the velocity of an enzyme-cat-alyzed reaction is called an inhibitor. Inhibitors may exert their effects in many different ways. Generally, if inhibition is irreversible the compound is called an inac-tivator. Other agents can increase the efficiency of an enzyme; they are called activators. Inhibitors and acti-vators are very important in the cellular regulation of enzymes. Many agriculturally important insecticides and herbicides are enzyme inhibitors. The study of enzyme inhibition can provide useful information about kinetic mechanisms, the nature of enzyme–substrate intermediates and complexes, the chemical mechanism of catalytic action, and the regulation and control of metabolic enzymes. In addition, the study of inhibitors of potential target enzymes is essential to the rational design of herbicides.
Inhibitors can be classified as reversible or irre-versible. Irreversible inhibitors form covalent bonds with an enzyme or they denature it. For example, iodoacetate (ICH2COOH) irreversibly inhibits thiol pro-teases such as papain by alkylating the active-site —SH group. One class of irreversible inhibitors is called affin-ity labels, or active site–directed modifying agents, because their structure directs them to the active site. An example is tosyl-lysine chloromethyl ketone (TLCK), which irreversibly inactivates papain. The tosyl-lysine part of the inhibitor resembles the substrate structure and so binds in the active site. The chloromethyl ketone part of the bound inhibitor reacts with the active-site histidine side chain. Such compounds are very useful in mechanistic studies of enzymes, but they have limited practical use as herbicides because of their chemical reactivity, which can be harmful to the plant.
Reversible inhibitors form weak, noncovalent bonds with the enzyme, and their effects may be com-petitive, noncompetitive, or mixed. For example, the widely used broad-spectrum herbicide glyphosate (Roundup®) works by competitively inhibiting a key enzyme in the biosynthesis of aromatic amino acids, 5-enolpyruvylshikimate-3-phosphate (EPSP) synthase (see Chapter 13). Resistance to glyphosate has recently been achieved by genetic engineering of plants so that they are capable of overproducing EPSP synthase (Don-ahue et al. 1995).
Competitive inhibition.
Competitive inhibition is the simplest and most common form of reversible inhibi-tion. It usually arises from binding of the inhibitor to the active site with an affinity similar to or stronger CHAPTER 2 18 x-Intercept = – y-Intercept = – 1 Km 1 Vmax Km Vmax 1/v 1/v 1/v Slope = Uninhibited Inhibited 1/[S] 1/[S] 1/[S] (A) Uninhibited enzyme-catalyzed reaction (B) Competitive inhibition (C) Noncompetitive inhibition Uninhibited Inhibited Figure 2.14 Lineweaver–Burk double-reciprocal plots. A plot of 1/v versus 1/[S] yields a straight line. (A) Uninhibited enzyme-catalyzed reaction showing the calculation of Km from the x-intercept and of Vmax from the y-intercept. (B) The effect of a competitive inhibitor on the parameters Km and V max. The apparent Km is increased, but the V max is unchanged. (C) A noncompetitive inhibitor reduces V max but has no effect on Km.
than that of the substrate. Thus the effective concen-tration of the enzyme is decreased by the presence of the inhibitor, and the catalytic reaction will be slower than if the inhibitor were absent. Competitive inhibi-tion is usually based on the fact that the structure of the inhibitor resembles that of the substrate; hence the strong affinity of the inhibitor for the active site.
Competitive inhibition may also occur in allosteric enzymes, where the inhibitor binds to a distant site on the enzyme, causing a conformational change that alters the active site and prevents normal substrate binding. Such a binding site is called an allosteric site.
In this case, the competition between substrate and inhibitor is indirect.
Competitive inhibition results in an apparent increase in Km and has no effect on Vmax (see Figure 2.14B). By measuring the apparent Km as a function of inhibitor concentration, one can calculate Ki, the inhibitor constant, which reflects the affinity of the enzyme for the inhibitor.
Noncompetitive inhibition.
In noncompetitive inhibi-tion, the inhibitor does not compete with the substrate for binding to the active site. Instead, it may bind to another site on the protein and obstruct the substrate’s access to the active site, thereby changing the catalytic properties of the enzyme, or it may bind to the enzyme– substrate complex and thus alter catalysis. Noncom-petitive inhibition is frequently observed in the regula-tion of metabolic enzymes. The diagnostic property of this type of inhibition is that Km is unaffected, whereas V max decreases in the presence of increasing amounts of inhibitor (see Figure 2.14C).
Mixed inhibition.
Mixed inhibition is characterized by effects on both Vmax (which decreases) and Km (which increases). Mixed inhibition is very common and results from the formation of a complex consisting of the enzyme, the substrate, and the inhibitor that does not break down to products. pH and Temperature Affect the Rate of Enzyme-Catalyzed Reactions Enzyme catalysis is very sensitive to pH. This sensitivity is easily understood when one considers that the essen-tial catalytic groups are usually ionizable ones (imida-zole, carboxyl, amino) and that they are catalytically active in only one of their ionization states. For example, imidazole acting as a base will be functional only at pH values above 7. Plots of the rates of enzyme-catalyzed reactions versus pH are usually bell-shaped, corre-sponding to two sigmoidal curves, one for an ionizable group acting as an acid and the other for the group act-ing as a base (Figure 2.15A). Although the effects of pH on enzyme catalysis usually reflect the ionization of the catalytic group, they may also reflect a pH-dependent conformational change in the protein that leads to loss of activity as a result of disruption of the active site.
The temperature dependence of most chemical reac-tions also applies to enzyme-catalyzed reactions. Thus, most enzyme-catalyzed reactions show an exponential increase in rate with increasing temperature. However, because the enzymes are proteins, another major factor comes in to play—namely, denaturation. After a certain temperature is reached, enzymes show a very rapid decrease in activity as a result of the onset of denatur-ation (Figure 2.15B). The temperature at which denatur-ation begins, and hence at which catalytic activity is lost, varies with the particular protein as well as the envi-ronmental conditions, such as pH. Frequently, denatur-ation begins at about 40 to 50°C and is complete over a range of about 10°C. Energy and Enzymes 19 6 5 4 3 7 8 9 30 20 10 0 40 50 60 Initial velocity Initial velocity pH Temperature (°C) (A) (B) Figure 2.15 pH and temperature curves for typical enzyme reactions. (A) Many enzyme-catalyzed reactions show bell-shaped profiles of rate versus pH. The inflection point on each shoulder corresponds to the pKa of an ionizing group (that is, the pH at which the ionizing group is 50% dissoci-ated) in the active site. (B) Temperature causes an exponen-tial increase in the reaction rate until the optimum is reached. Beyond the optimum, thermal denaturation dra-matically decreases the rate.
Cooperative Systems Increase the Sensitivity to Substrates and Are Usually Allosteric Cells control the concentrations of most metabolites very closely. To keep such tight control, the enzymes that con-trol metabolite interconversion must be very sensitive.
From the plot of velocity versus substrate concentration (see Figure 2.13), we can see that the velocity of an enzyme-catalyzed reaction increases with increasing substrate concentration up to V max. However, we can calculate from the Michaelis–Menten equation (Equa-tion 2.21) that raising the velocity of an enzyme-cat-alyzed reaction from 0.1 V max to 0.9 V max requires an enormous (81-fold) increase in the substrate concentra-tion: This calculation shows that reaction velocity is insen-sitive to small changes in substrate concentration. The same factor applies in the case of inhibitors and inhibi-tion. In cooperative systems, on the other hand, a small change in one parameter, such as inhibitor concentra-tion, brings about a large change in velocity. A conse-quence of a cooperative system is that the plot of v ver-sus [S] is no longer hyperbolic, but becomes sigmoidal (Figure 2.16 ). The advantage of cooperative systems is that a small change in the concentration of the critical effector (substrate, inhibitor, or activator) will bring about a large change in the rate. In other words, the sys-tem behaves like a switch.
Cooperativity is typically observed in allosteric enzymes that contain multiple active sites located on multiple subunits. Such oligomeric enzymes usually exist in two major conformational states, one active and one inactive (or relatively inactive). Binding of ligands (substrates, activators, or inhibitors) to the enzyme per-turbs the position of the equilibrium between the two conformations. For example, an inhibitor will favor the inactive form; an activator will favor the active form.
The cooperative aspect comes in as follows: A positive cooperative event is one in which binding of the first lig-and makes binding of the next one easier. Similarly, neg-ative cooperativity means that the second ligand will bind less readily than the first. Cooperativity in substrate binding (homoallostery) occurs when the binding of substrate to a catalytic site on one subunit increases the substrate affinity of an identical catalytic site located on a different subunit.
Effector ligands (inhibitors or activators), in contrast, bind to sites other than the catalytic site (heteroal-lostery). This relationship fits nicely with the fact that the end products of metabolic pathways, which fre-quently serve as feedback inhibitors, usually bear no structural resemblance to the substrates of the first step.
The Kinetics of Some Membrane Transport Processes Can Be Described by the Michaelis–Menten Equation Membranes contain proteins that speed up the move-ment of specific ions or organic molecules across the lipid bilayer. Some membrane transport proteins are enzymes, such as ATPases, that use the energy from the hydrolysis of ATP to pump ions across the membrane.
When these reactions run in the reverse direction, the ATPases of mitochondria and chloroplasts can synthe-size ATP. Other types of membrane proteins function as carriers, binding their substrate on one side of the mem-brane and releasing it on the other side. The kinetics of carrier-mediated transport can be described by the Michaelis–Menten equation in the same manner as the kinetics of enzyme-catalyzed reac-tions are (see Chapter 6). Instead of a biochemical reac-tion with a substrate and product, however, the carrier binds to the solute and transfers it from one side of a membrane to the other. Letting X be the solute, we can write the following equation: Xout + carrier →[X-carrier] →Xin + carrier Since the carrier can bind to the solute more rapidly than it can transport the solute to the other side of the membrane, solute transport exhibits saturation kinetics.
That is, a concentration is reached beyond which adding more solute does not result in a more rapid rate of trans-port (Figure 2.17). V max is the maximum rate of transport of X across the membrane; Km is equivalent to the bind-S S S S 0 1 0 9 0 9 0 1 0 1 0 9 0 01 0 81 2 .
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[ ] [ ] [ ] [ ] .
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= × ′ ′ = = 0.1 S S , 0.9 S S 0.1 = 0.9[S] , 0.9 S max m max m m m V V K V K = + = ′ + ′ = ′ max max [ ] [ ] [ ] [ ] . [ ] V K K 0 1 CHAPTER 2 20 v [S] Inhibitor added Activator added Figure 2.16 Allosteric systems exhibit sigmoidal plots of rate versus substrate concentration. The addition of an acti-vator shifts the curve to the left; the addition of an inhibitor shifts it to the right.
ing constant of the solute for the carrier. Like enzyme-catalyzed reactions, carrier-mediated transport requires a high degree of structural specificity of the protein. The actual transport of the solute across the membrane apparently involves conformational changes, also simi-lar to those in enzyme-catalyzed reactions.
Enzyme Activity Is Often Regulated Cells can control the flux of metabolites by regulating the concentration of enzymes and their catalytic activ-ity. By using allosteric activators or inhibitors, cells can modulate enzymatic activity and obtain very carefully controlled expression of catalysis.
Control of enzyme concentration.
The amount of enzyme in a cell is determined by the relative rates of synthesis and degradation of the enzyme. The rate of synthesis is regulated at the genetic level by a variety of mechanisms, which are discussed in greater detail in the last section of this chapter.
Compartmentalization.
Different enzymes or isozymes with different catalytic properties (e.g., substrate affin-ity) may be localized in different regions of the cell, such as mitochondria and cytosol. Similarly, enzymes associated with special tasks are often compartmental-ized; for example, the enzymes involved in photosyn-thesis are found in chloroplasts. Vacuoles contain many hydrolytic enzymes, such as proteases, ribonucleases, glycosidases, and phosphatases, as well as peroxidases.
The cell walls contain glycosidases and peroxidases.
The mitochondria are the main location of the enzymes involved in oxidative phosphorylation and energy metabolism, including the enzymes of the tricarboxylic acid (TCA) cycle.
Covalent modification.
Control by covalent modifica-tion of enzymes is common and usually involves their phosphorylation or adenylylation, such that the phos-phorylated form, for example, is active and the non-phosphorylated form is inactive. These control mecha-nisms are normally energy dependent and usually involve ATP.
Proteases are normally synthesized as inactive pre-cursors known as zymogens or proenzymes. For exam-ple, papain is synthesized as an inactive precursor called propapain and becomes activated later by cleavage (hydrolysis) of a peptide bond. This type of covalent modification avoids premature proteolytic degradation of cellular constituents by the newly synthesized enzyme.
Feedback inhibition.
Consider a typical metabolic pathway with two or more end products such as that shown in Figure 2.18. Control of the system requires that if the end products build up too much, their rate of formation is decreased. Similarly, if too much reac-tant A builds up, the rate of conversion of A to prod-ucts should be increased. The process is usually regu-lated by control of the flux at the first step of the path-way and at each branch point. The final products, G and J, which might bear no resemblance to the sub-strate A, inhibit the enzymes at A →B and at the branch point.
By having two enzymes at A →B, each inhibited by one of the end metabolites but not by the other, it is pos-sible to exert finer control than with just one enzyme.
The first step in a metabolic pathway is usually called Energy and Enzymes 21 Transport velocity External concentration of solute Km Vmax Vmax 2 Figure 2.17 The kinetics of carrier-mediated transport of a solute across a membrane are analogous to those of enzyme-catalyzed reactions. Thus, plots of transport velocity versus solute concentration are hyperbolic, becoming asymp-totic to the maximal velocity at high solute concentration.
A B C D E F G H I J Figure 2.18 Feedback inhibition in a hypothetical metabolic pathway. The let-ters (A–J) represent metabolites, and each arrow represents an enzyme-cat-alyzed reaction. The boldface arrow for the first reaction indicates that two dif-ferent enzymes with different inhibitor susceptibilities are involved. Broken lines indicate metabolites that inhibit particular enzymes. The first step in the meta-bolic pathway and the branch points are particularly important sites for feed-back control.
Although some texts refer to the conjugation of a com-pound with adenylic acid (AMP) as “adenylation,” the chemically correct term is “adenylylation.” the committed step. At this step enzymes are subject to major control.
Fructose-2,6-bisphosphate plays a central role in the regulation of carbon metabolism in plants. It functions as an activator in glycolysis (the breakdown of sugars to generate energy) and an inhibitor in gluconeogenesis (the synthesis of sugars). Fructose-2,6-bisphosphate is synthesized from fructose-6-phosphate in a reaction requiring ATP and catalyzed by the enzyme fructose-6-phosphate 2-kinase. It is degraded in the reverse reac-tion catalyzed by fructose-2,6-bisphosphatase, which releases inorganic phosphate (Pi). Both of these enzymes are subject to metabolic control by fructose-2,6-bisphos-phate, as well as ATP, Pi, fructose-6-phosphate, dihy-droxyacetone phosphate, and 3-phosphoglycerate. The role of fructose-2,6-bisphosphate in plant metabolism will be discussed further in Chapters 8 and 11.
Summary Living organisms, including green plants, are governed by the same physical laws of energy flow that apply everywhere in the universe. These laws of energy flow have been encapsulated in the laws of thermodynamics.
Energy is defined as the capacity to do work, which may be mechanical, electrical, osmotic, or chemical work. The first law of thermodynamics states the prin-ciple of energy conservation: Energy can be converted from one form to another, but the total energy of the universe remains the same. The second law of thermo-dynamics describes the direction of spontaneous processes: A spontaneous process is one that results in a net increase in the total entropy (∆S), or randomness, of the system plus its surroundings. Processes involving heat transfer, such as the cooling due to water evapora-tion from leaves, are best described in terms of the change in heat content, or enthalpy (∆H), defined as the amount of energy absorbed or evolved as heat under constant pressure.
The free-energy change, ∆G, is a convenient parame-ter for determining the direction of spontaneous processes in chemical or biological systems without ref-erence to their surroundings. The value of ∆G is nega-tive for all spontaneous processes at constant tempera-ture and pressure. The ∆G of a reaction is a function of its displacement from equilibrium. The greater the dis-placement from equilibrium, the more work the reaction can do. Living systems have evolved to maintain their biochemical reactions as far from equilibrium as possi-ble.
The redox potential represents the free-energy change of an oxidation–reduction reaction expressed in electro-chemical units. As with changes in free energy, the redox potential of a system depends on the concentrations of the oxidized and reduced species.
The establishment of ion gradients across membranes is an important aspect of the work carried out by living systems. The membrane potential is a measure of the work required to transport an ion across a membrane.
The electrochemical-potential difference includes both concentration and electric potentials. The laws of thermodynamics predict whether and in which direction a reaction can occur, but they say noth-ing about the speed of a reaction. Life depends on highly specific protein catalysts called enzymes to speed up the rates of reactions. All proteins are composed of amino acids linked together by peptide bonds. Protein structure is hierarchical; it can be classified into primary, secondary, tertiary, and quaternary levels. The forces responsible for the shape of a protein molecule are non-covalent and are easily disrupted by heat, chemicals, or pH, leading to loss of conformation, or denaturation.
Enzymes function by lowering the free-energy bar-rier between the substrates and products of a reaction.
Catalysis occurs at the active site of the enzyme.
Enzyme-mediated reactions exhibit saturation kinetics and can be described by the Michaelis–Menten equa-tion, which relates the velocity of an enzyme-catalyzed reaction to the substrate concentration. The substrate concentration is inversely related to the affinity of an enzyme for its substrate. Since reaction velocity is rela-tively insensitive to small changes in substrate concen-tration, many enzymes exhibit cooperativity. Typically, such enzymes are allosteric, containing two or more active sites that interact with each other and that may be located on different subunits.
Enzymes are subject to reversible and irreversible inhibition. Irreversible inhibitors typically form covalent bonds with the enzyme; reversible inhibitors form non-covalent bonds with the enzyme and may have com-petitive, noncompetitive, or mixed effects. Enzyme activity is often regulated in cells. Regulation may be accomplished by compartmentalization of enzymes and/or substrates; covalent modification; feed-back inhibition, in which the end products of metabolic pathways inhibit the enzymes involved in earlier steps; and control of the enzyme concentration in the cell by gene expression and protein degradation.
General Reading Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., and Watson, J. D.
(1994) Molecular Biology of the Cell, 3rd ed. Garland, New York.
Atchison, M. L. (1988) Enhancers: Mechanisms of action and cell specificity. Annu. Rev. Cell Biol. 4: 127–153.
Atkinson, D. E. (1977) Cellular Energy Metabolism and Its Regulation.
Academic Press, New York.
Creighton, T. E. (1983) Proteins: Structures and Molecular Principles.
W. H. Freeman, New York.
Darnell, J., Lodish, H., and Baltimore, D. (1995) Molecular Cell Biol-ogy, 3rd ed. Scientific American Books, W. H. Freeman, New York.
Edsall, J. T., and Gutfreund, H. (1983) Biothermodynamics: The Study of Biochemical Processes at Equilibrium. Wiley, New York.
CHAPTER 2 22 Fersht, A. (1985) Enzyme Structure and Mechanism, 2nd ed. W. H. Free-man, New York.
Klotz, I. M. (1967) Energy Changes in Biochemical Reactions. Acade-mic Press, New York.
Morowitz, H. J. (1978) Foundations of Bioenergetics. Academic Press, New York.
Walsh, C. T. (1979) Enzymatic Reaction Mechanisms. W. H. Freeman, New York.
Webb, E. ( 1984) Enzyme Nomenclature. Academic Press, Orlando, Fla.
Indicates a reference that is general reading in the field and is also cited in this chapter.
Chapter References Bryant, F. O., and Adams, M. W. W. (1989) Characterization of hydro-genase from the hyperthermophilic archaebacterium? Pyrococcus furiosus. J. Biol. Chem. 264: 5070–5079.
Clausius, R. (1879) The Mechanical Theory of Heat. Tr. by Walter R.
Browne. Macmillan, London. Donahue, R. A., Davis, T. D., Michler, C. H., Riemenschneider, D. E., Carter, D. R., Marquardt, P. E., Sankhla, N., Sahkhla, D. Haissig, B. E., and Isebrands, J. G. (1995) Growth, photosynthesis, and herbicide tolerance of genetically modified hybrid poplar. Can. J.
Forest Res. 24: 2377–2383.
Mathews, C. K., and Van Holde, K. E. (1996) Biochemistry, 2nd ed.
Benjamin/Cummings, Menlo Park, CA. Nicholls, D. G., and Ferguson, S. J. (1992) Bioenergetics 2. Academic Press, San Diego.
Stryer, L. (1995) Biochemistry, 4th ed. W. H. Freeman, New York.
Energy and Enzymes 23 Transport and Translocation of Water and Solutes U N I T I Water and Plant Cells 3 Chapter WATER PLAYS A CRUCIAL ROLE in the life of the plant. For every gram of organic matter made by the plant, approximately 500 g of water is absorbed by the roots, transported through the plant body and lost to the atmosphere. Even slight imbalances in this flow of water can cause water deficits and severe malfunctioning of many cellular processes.
Thus, every plant must delicately balance its uptake and loss of water.
This balancing is a serious challenge for land plants. To carry on photo-synthesis, they need to draw carbon dioxide from the atmosphere, but doing so exposes them to water loss and the threat of dehydration.
A major difference between plant and animal cells that affects virtually all aspects of their relation with water is the existence in plants of the cell wall. Cell walls allow plant cells to build up large internal hydrostatic pressures, called turgor pressure, which are a result of their normal water balance. Turgor pressure is essential for many physiological processes, including cell enlargement, gas exchange in the leaves, transport in the phloem, and various transport processes across membranes. Turgor pres-sure also contributes to the rigidity and mechanical stability of nonligni-fied plant tissues. In this chapter we will consider how water moves into and out of plant cells, emphasizing the molecular properties of water and the physical forces that influence water movement at the cell level. But first we will describe the major functions of water in plant life.
WATER IN PLANT LIFE Water makes up most of the mass of plant cells, as we can readily appre-ciate if we look at microscopic sections of mature plant cells: Each cell contains a large water-filled vacuole. In such cells the cytoplasm makes up only 5 to 10% of the cell volume; the remainder is vacuole. Water typ-ically constitutes 80 to 95% of the mass of growing plant tissues. Com-mon vegetables such as carrots and lettuce may contain 85 to 95% water.
Wood, which is composed mostly of dead cells, has a lower water con-tent; sapwood, which functions in transport in the xylem, contains 35 to 75% water; and heartwood has a slightly lower water con-tent. Seeds, with a water content of 5 to 15%, are among the driest of plant tissues, yet before germinating they must absorb a considerable amount of water.
Water is the most abundant and arguably the best sol-vent known. As a solvent, it makes up the medium for the movement of molecules within and between cells and greatly influences the structure of proteins, nucleic acids, polysaccharides, and other cell constituents. Water forms the environment in which most of the biochemical reac-tions of the cell occur, and it directly participates in many essential chemical reactions.
Plants continuously absorb and lose water. Most of the water lost by the plant evaporates from the leaf as the CO2 needed for photosynthesis is absorbed from the atmo-sphere. On a warm, dry, sunny day a leaf will exchange up to 100% of its water in a single hour. During the plant’s life-time, water equivalent to 100 times the fresh weight of the plant may be lost through the leaf surfaces. Such water loss is called transpiration.
Transpiration is an important means of dissipating the heat input from sunlight. Heat dissipates because the water molecules that escape into the atmosphere have higher-than-average energy, which breaks the bonds holding them in the liquid. When these molecules escape, they leave behind a mass of molecules with lower-than-average energy and thus a cooler body of water. For a typical leaf, nearly half of the net heat input from sunlight is dissipated by transpiration. In addition, the stream of water taken up by the roots is an important means of bringing dissolved soil minerals to the root surface for absorption.
Of all the resources that plants need to grow and func-tion, water is the most abundant and at the same time the most limiting for agricultural productivity (Figure 3.1). The fact that water is limiting is the reason for the practice of crop irrigation. Water availability likewise limits the pro-ductivity of natural ecosystems (Figure 3.2). Thus an understanding of the uptake and loss of water by plants is very important.
We will begin our study of water by considering how its structure gives rise to some of its unique physical proper-ties. We will then examine the physical basis for water movement, the concept of water potential, and the appli-cation of this concept to cell–water relations.
THE STRUCTURE AND PROPERTIES OF WATER Water has special properties that enable it to act as a sol-vent and to be readily transported through the body of the plant. These properties derive primarily from the polar structure of the water molecule. In this section we will examine how the formation of hydrogen bonds contributes to the properties of water that are necessary for life.
The Polarity of Water Molecules Gives Rise to Hydrogen Bonds The water molecule consists of an oxygen atom covalently bonded to two hydrogen atoms. The two O—H bonds form an angle of 105° (Figure 3.3). Because the oxygen atom is more electronegative than hydrogen, it tends to attract the electrons of the covalent bond. This attraction results in a partial negative charge at the oxygen end of the molecule and a partial positive charge at each hydrogen.
Chapter 3 34 10 20 30 40 50 60 2.0 4.0 6.0 8.0 10.0 0 Corn yield (m3 ha–1) Water availability (number of days with optimum water during growing period) 0.5 1.0 1.5 2.0 500 1000 1500 0 Productivity (dry g m–2 yr–1) Annual precipitation (m) FIGURE 3.1 Corn yield as a function of water availability.
The data plotted here were gathered at an Iowa farm over a 4-year period. Water availability was assessed as the num-ber of days without water stress during a 9-week growing period. (Data from Weather and Our Food Supply 1964.) FIGURE 3.2 Productivity of various ecosystems as a func-tion of annual precipitation. Productivity was estimated as net aboveground accumulation of organic matter through growth and reproduction. (After Whittaker 1970.) These partial charges are equal, so the water molecule car-ries no net charge.
This separation of partial charges, together with the shape of the water molecule, makes water a polar molecule, and the opposite partial charges between neighboring water molecules tend to attract each other. The weak elec-trostatic attraction between water molecules, known as a hydrogen bond, is responsible for many of the unusual physical properties of water.
Hydrogen bonds can also form between water and other molecules that contain electronegative atoms (O or N). In aqueous solutions, hydrogen bonding between water mol-ecules leads to local, ordered clusters of water that, because of the continuous thermal agitation of the water molecules, continually form, break up, and re-form (Figure 3.4).
The Polarity of Water Makes It an Excellent Solvent Water is an excellent solvent: It dissolves greater amounts of a wider variety of substances than do other related sol-vents. This versatility as a solvent is due in part to the small size of the water molecule and in part to its polar nature.
The latter makes water a particularly good solvent for ionic substances and for molecules such as sugars and proteins that contain polar —OH or —NH2 groups.
Hydrogen bonding between water molecules and ions, and between water and polar solutes, in solution effectively decreases the electrostatic interaction between the charged substances and thereby increases their solubility. Further-more, the polar ends of water molecules can orient them-selves next to charged or partially charged groups in macromolecules, forming shells of hydration. Hydrogen bonding between macromolecules and water reduces the interaction between the macromolecules and helps draw them into solution.
The Thermal Properties of Water Result from Hydrogen Bonding The extensive hydrogen bonding between water molecules results in unusual thermal properties, such as high specific heat and high latent heat of vaporization. Specific heat is the heat energy required to raise the temperature of a sub-stance by a specific amount.
When the temperature of water is raised, the molecules vibrate faster and with greater amplitude. To allow for this motion, energy must be added to the system to break the hydrogen bonds between water molecules. Thus, com-pared with other liquids, water requires a relatively large energy input to raise its temperature. This large energy input requirement is important for plants because it helps buffer temperature fluctuations.
Latent heat of vaporization is the energy needed to separate molecules from the liquid phase and move them into the gas phase at constant temperature—a process that occurs during transpiration.
For water at 25°C, the heat of vaporization is 44 kJ mol–1—the highest value known for any liq-uid. Most of this energy is used to break hydrogen bonds between water molecules.
The high latent heat of vapor-ization of water enables plants to cool themselves by evaporating water from leaf surfaces, which are prone to heat up because of the radiant input from the sun.
Transpiration is an important component of temperature regu-lation in plants.
Water and Plant Cells 35 H H O 105° d– d+ d+ Net positive charge Attraction of bonding electrons to the oxygen creates local negative and positive partial charges Net negative charge O O O O O O O O O O O H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H O O O O O O O O O O H H O (A) Correlated configuration (B) Random configuration FIGURE 3.3 Diagram of the water molecule. The two intramolecular hydrogen–oxygen bonds form an angle of 105°. The opposite partial charges (δ– and δ+) on the water molecule lead to the formation of intermolecular hydrogen bonds with other water molecules. Oxygen has six elec-trons in the outer orbitals; each hydrogen has one.
FIGURE 3.4 (A) Hydrogen bonding between water molecules results in local aggre-gations of water molecules. (B) Because of the continuous thermal agitation of the water molecules, these aggregations are very short-lived; they break up rapidly to form much more random configurations.
Chapter 3 36 The Cohesive and Adhesive Properties of Water Are Due to Hydrogen Bonding Water molecules at an air–water interface are more strongly attracted to neighboring water molecules than to the gas phase in contact with the water surface. As a consequence of this unequal attraction, an air–water interface minimizes its surface area. To increase the area of an air–water interface, hydrogen bonds must be broken, which requires an input of energy. The energy required to increase the surface area is known as surface tension. Surface tension not only influ-ences the shape of the surface but also may create a pressure in the rest of the liquid. As we will see later, surface tension at the evaporative surfaces of leaves generates the physical forces that pull water through the plant’s vascular system.
The extensive hydrogen bonding in water also gives rise to the property known as cohesion, the mutual attraction between molecules. A related property, called adhesion, is the attraction of water to a solid phase such as a cell wall or glass surface. Cohesion, adhesion, and surface tension give rise to a phenomenon known as capillarity, the move-ment of water along a capillary tube.
In a vertically oriented glass capillary tube, the upward movement of water is due to (1) the attraction of water to the polar surface of the glass tube (adhesion) and (2) the surface tension of water, which tends to minimize the area of the air–water interface. Together, adhesion and surface tension pull on the water molecules, causing them to move up the tube until the upward force is balanced by the weight of the water column. The smaller the tube, the higher the capillary rise. For calculations related to capil-lary rise, see Web Topic 3.1.
Water Has a High Tensile Strength Cohesion gives water a high tensile strength, defined as the maximum force per unit area that a continuous column of water can withstand before breaking. We do not usually think of liquids as having tensile strength; however, such a property must exist for a water column to be pulled up a capillary tube.
We can demonstrate the tensile strength of water by plac-ing it in a capped syringe (Figure 3.5). When we push on the plunger, the water is compressed and a positive hydrosta-tic pressure builds up. Pressure is measured in units called pascals (Pa) or, more conveniently, megapascals (MPa). One MPa equals approximately 9.9 atmospheres. Pressure is equivalent to a force per unit area (1 Pa = 1 N m–2) and to an energy per unit volume (1 Pa = 1 J m–3). A newton (N) = 1 kg m s–1. Table 3.1 compares units of pressure.
If instead of pushing on the plunger we pull on it, a ten-sion, or negative hydrostatic pressure, develops in the water to resist the pull. How hard must we pull on the plunger before the water molecules are torn away from each other and the water column breaks? Breaking the water column requires sufficient energy to break the hydrogen bonds that attract water molecules to one another.
Careful studies have demonstrated that water in small capillaries can resist tensions more negative than –30 MPa (the negative sign indicates tension, as opposed to com-pression). This value is only a fraction of the theoretical ten-sile strength of water computed on the basis of the strength of hydrogen bonds. Nevertheless, it is quite substantial.
The presence of gas bubbles reduces the tensile strength of a water column. For example, in the syringe shown in Figure 3.5, expansion of microscopic bubbles often inter-feres with the ability of the water to resist the pull exerted by the plunger. If a tiny gas bubble forms in a column of water under tension, the gas bubble may expand indefi-nitely, with the result that the tension in the liquid phase collapses, a phenomenon known as cavitation. As we will see in Chapter 4, cavitation can have a devastating effect on water transport through the xylem.
WATER TRANSPORT PROCESSES When water moves from the soil through the plant to the atmosphere, it travels through a widely variable medium (cell wall, cytoplasm, membrane, air spaces), and the mech-anisms of water transport also vary with the type of medium. For many years there has been much uncertainty Cap Force Water Plunger FIGURE 3.5 A sealed syringe can be used to create positive and negative pressures in a fluid like water. Pushing on the plunger compresses the fluid, and a positive pressure builds up. If a small air bubble is trapped within the syringe, it shrinks as the pressure increases. Pulling on the plunger causes the fluid to develop a tension, or negative pressure. Any air bubbles in the syringe will expand as the pressure is reduced.
TABLE 3.1 Comparison of units of pressure 1 atmosphere = 14.7 pounds per square inch = 760 mm Hg (at sea level, 45° latitude) = 1.013 bar = 0.1013 Mpa = 1.013 × 105 Pa A car tire is typically inflated to about 0.2 MPa.
The water pressure in home plumbing is typically 0.2–0.3 MPa.
The water pressure under 15 feet (5 m) of water is about 0.05 MPa.
about how water moves across plant membranes. Specifi-cally it was unclear whether water movement into plant cells was limited to the diffusion of water molecules across the plasma membrane’s lipid bilayer or also involved dif-fusion through protein-lined pores (Figure 3.6).
Some studies indicated that diffusion directly across the lipid bilayer was not sufficient to account for observed rates of water movement across membranes, but the evi-dence in support of microscopic pores was not compelling.
This uncertainty was put to rest with the recent discovery of aquaporins (see Figure 3.6). Aquaporins are integral membrane proteins that form water-selective channels across the membrane. Because water diffuses faster through such channels than through a lipid bilayer, aqua-porins facilitate water movement into plant cells (Weig et al. 1997; Schäffner 1998; Tyerman et al. 1999). Note that although the presence of aquaporins may alter the rate of water movement across the membrane, they do not change the direction of transport or the driving force for water movement. The mode of action of aquaporins is being acitvely investigated (Tajkhorshid et al. 2002).
We will now consider the two major processes in water transport: molecular diffusion and bulk flow.
Diffusion Is the Movement of Molecules by Random Thermal Agitation Water molecules in a solution are not static; they are in con-tinuous motion, colliding with one another and exchang-ing kinetic energy. The molecules intermingle as a result of their random thermal agitation. This random motion is called diffusion. As long as other forces are not acting on the molecules, diffusion causes the net movement of mol-ecules from regions of high concentration to regions of low concentration—that is, down a concentration gradient (Figure 3.7).
In the 1880s the German scientist Adolf Fick discovered that the rate of diffusion is directly proportional to the con-centration gradient (∆cs/∆x)—that is, to the difference in concentration of substance s (∆cs) between two points sep-arated by the distance ∆x. In symbols, we write this rela-tion as Fick’s first law: (3.1) The rate of transport, or the flux density (Js), is the amount of substance s crossing a unit area per unit time (e.g., Js may have units of moles per square meter per sec-ond [mol m–2 s–1]). The diffusion coefficient (Ds) is a pro-portionality constant that measures how easily substance s moves through a particular medium. The diffusion coeffi-cient is a characteristic of the substance (larger molecules have smaller diffusion coefficients) and depends on the medium (diffusion in air is much faster than diffusion in a liquid, for example). The negative sign in the equation indi-cates that the flux moves down a concentration gradient.
Fick’s first law says that a substance will diffuse faster when the concentration gradient becomes steeper (∆cs is large) or when the diffusion coefficient is increased. This equation accounts only for movement in response to a con-centration gradient, and not for movement in response to other forces (e.g., pressure, electric fields, and so on).
Diffusion Is Rapid over Short Distances but Extremely Slow over Long Distances From Fick’s first law, one can derive an expression for the time it takes for a substance to diffuse a particular distance.
If the initial conditions are such that all the solute mole-cules are concentrated at the starting position (Figure 3.8A), then the concentration front moves away from the starting position, as shown for a later time point in Figure 3.8B. As the substance diffuses away from the starting point, the concentration gradient becomes less steep (∆cs decreases), and thus net movement becomes slower.
The average time needed for a particle to diffuse a dis-tance L is equal to L2/Ds, where Ds is the diffusion coeffi-cient, which depends on both the identity of the particle and the medium in which it is diffusing. Thus the average time required for a substance to diffuse a given distance increases in proportion to the square of that distance. The diffusion coefficient for glucose in water is about 10–9 m2 s–1. Thus the average time required for a glucose molecule to diffuse across a cell with a diameter of 50 µm is 2.5 s.
However, the average time needed for the same glucose molecule to diffuse a distance of 1 m in water is approxi-J D c x s s s = − ∆ ∆ Water and Plant Cells 37 fpo CYTOPLASM OUTSIDE OF CELL Water-selective pore (aquaporin) Water molecules Membrane bilayer FIGURE 3.6 Water can cross plant membranes by diffusion of individual water molecules through the membrane bilayer, as shown on the left, and by microscopic bulk flow of water molecules through a water-selective pore formed by integral membrane proteins such as aquaporins.
Chapter 3 38 0 Concentration 0 Concentration (B) Distance Dx Distance Dx (A) Time Dcs Dcs FIGURE 3.8 Graphical representation of the concentration gradient of a solute that is diffusing according to Fick’s law. The solute molecules were initially located in the plane indicated on the x-axis. (A) The distribution of solute molecules shortly after placement at the plane of origin. Note how sharply the concentration drops off as the distance, x, from the origin increases. (B) The solute distribution at a later time point. The average distance of the diffusing molecules from the origin has increased, and the slope of the gradient has flattened out. (After Nobel 1999.) FIGURE 3.7 Thermal motion of molecules leads to diffusion—the gradual mixing of molecules and eventual dissipation of concentration differences. Initially, two mate-rials containing different molecules are brought into contact. The materials may be gas, liquid, or solid. Diffusion is fastest in gases, slower in liquids, and slowest in solids. The initial separation of the molecules is depicted graphically in the upper panels, and the corresponding concentration profiles are shown in the lower panels as a function of position. With time, the mixing and randomization of the molecules diminishes net movement. At equilibrium the two types of molecules are randomly (evenly) distributed.
Initial Intermediate Equilibrium Concentration Position in container Concentration profiles mately 32 years. These values show that diffusion in solu-tions can be effective within cellular dimensions but is far too slow for mass transport over long distances. For addi-tional calculations on diffusion times, see Web Topic 3.2.
Pressure-Driven Bulk Flow Drives Long-Distance Water Transport A second process by which water moves is known as bulk flow or mass flow. Bulk flow is the concerted movement of groups of molecules en masse, most often in response to a pressure gradient. Among many common examples of bulk flow are water moving through a garden hose, a river flowing, and rain falling.
If we consider bulk flow through a tube, the rate of vol-ume flow depends on the radius (r) of the tube, the viscos-ity (h) of the liquid, and the pressure gradient (∆Y p/∆x) that drives the flow. Jean-Léonard-Marie Poiseuille (1797–1869) was a French physician and physiologist, and the relation just described is given by one form of Poiseuille’s equation: (3.2) expressed in cubic meters per second (m3 s–1). This equa-tion tells us that pressure-driven bulk flow is very sensitive to the radius of the tube. If the radius is doubled, the vol-ume flow rate increases by a factor of 16 (24).
Pressure-driven bulk flow of water is the predominant mechanism responsible for long-distance transport of water in the xylem. It also accounts for much of the water flow through the soil and through the cell walls of plant tissues.
In contrast to diffusion, pressure-driven bulk flow is inde-pendent of solute concentration gradients, as long as vis-cosity changes are negligible.
Osmosis Is Driven by a Water Potential Gradient Membranes of plant cells are selectively permeable; that is, they allow the movement of water and other small uncharged substances across them more readily than the movement of larger solutes and charged substances (Stein 1986).
Like molecular diffusion and pressure-driven bulk flow, osmosis occurs spontaneously in response to a driving force. In simple diffusion, substances move down a con-centration gradient; in pressure-driven bulk flow, sub-stances move down a pressure gradient; in osmosis, both types of gradients influence transport (Finkelstein 1987).
The direction and rate of water flow across a membrane are determined not solely by the concentration gradient of water or by the pressure gradient, but by the sum of these two driving forces.
We will soon see how osmosis drives the movement of water across membranes. First, however, let’s discuss the concept of a composite or total driving force, representing the free-energy gradient of water.
The Chemical Potential of Water Represents the Free-Energy Status of Water All living things, including plants, require a continuous input of free energy to maintain and repair their highly organized structures, as well as to grow and reproduce.
Processes such as biochemical reactions, solute accumula-tion, and long-distance transport are all driven by an input of free energy into the plant. (For a detailed discussion of the thermodynamic concept of free energy, see Chapter 2 on the web site.) The chemical potential of water is a quantitative expres-sion of the free energy associated with water. In thermo-dynamics, free energy represents the potential for per-forming work. Note that chemical potential is a relative quantity: It is expressed as the difference between the potential of a substance in a given state and the potential of the same substance in a standard state. The unit of chem-ical potential is energy per mole of substance (J mol–1).
For historical reasons, plant physiologists have most often used a related parameter called water potential, defined as the chemical potential of water divided by the partial molal volume of water (the volume of 1 mol of water): 18 × 10–6 m3 mol–1. Water potential is a measure of the free energy of water per unit volume (J m–3). These units are equivalent to pressure units such as the pascal, which is the common measurement unit for water poten-tial. Let’s look more closely at the important concept of water potential.
Three Major Factors Contribute to Cell Water Potential The major factors influencing the water potential in plants are concentration, pressure, and gravity. Water potential is symbolized by Yw (the Greek letter psi), and the water potential of solutions may be dissected into individual components, usually written as the following sum: (3.3) The terms Ys, Yp, and Yg denote the effects of solutes, pres-sure, and gravity, respectively, on the free energy of water.
(Alternative conventions for components of water poten-tial are discussed in Web Topic 3.3.) The reference state used to define water potential is pure water at ambient pressure and temperature. Let’s consider each of the terms on the right-hand side of Equation 3.3.
Solutes.
The term Ys, called the solute potential or the osmotic potential, represents the effect of dissolved solutes on water potential. Solutes reduce the free energy of water by diluting the water. This is primarily an entropy effect; that is, the mixing of solutes and water increases the dis-order of the system and thereby lowers free energy. This means that the osmotic potential is independent of the spe-cific nature of the solute. For dilute solutions of nondisso-Y Y Y Y w s p g = + + Volume flow rate = x p p h r4 8 ∆ ∆ Y Water and Plant Cells 39 ciating substances, like sucrose, the osmotic potential may be estimated by the van’t Hoff equation: (3.4) where R is the gas constant (8.32 J mol–1 K–1), T is the absolute temperature (in degrees Kelvin, or K), and cs is the solute concentration of the solution, expressed as osmolal-ity (moles of total dissolved solutes per liter of water [mol L–1]). The minus sign indicates that dissolved solutes reduce the water potential of a solution relative to the ref-erence state of pure water. Table 3.2 shows the values of RT at various temperatures and the Ys values of solutions of different solute concen-trations. For ionic solutes that dissociate into two or more particles, cs must be multiplied by the number of dissoci-ated particles to account for the increased number of dis-solved particles.
Equation 3.4 is valid for “ideal” solutions at dilute con-centration. Real solutions frequently deviate from the ideal, especially at high concentrations—for example, greater than 0.1 mol L–1. In our treatment of water potential, we will assume that we are dealing with ideal solutions (Fried-man 1986; Nobel 1999).
Pressure.
The term Yp is the hydrostatic pressure of the solution. Positive pressures raise the water potential; neg-ative pressures reduce it. Sometimes Yp is called pressure potential. The positive hydrostatic pressure within cells is the pressure referred to as turgor pressure. The value of Yp can also be negative, as is the case in the xylem and in the walls between cells, where a tension, or negative hydrostatic pressure, can develop. As we will see, negative pressures outside cells are very important in moving water long dis-tances through the plant.
Hydrostatic pressure is measured as the deviation from ambient pressure (for details, see Web Topic 3.5). Remem-ber that water in the reference state is at ambient pressure, so by this definition Yp = 0 MPa for water in the standard state. Thus the value of Yp for pure water in an open beaker is 0 MPa, even though its absolute pressure is approximately 0.1 MPa (1 atmosphere).
Gravity.
Gravity causes water to move downward unless the force of gravity is opposed by an equal and opposite force. The term Yg depends on the height (h) of the water above the reference-state water, the density of water (rw), and the acceleration due to gravity (g). In sym-bols, we write the following: (3.5) where rwg has a value of 0.01 MPa m–1. Thus a vertical dis-tance of 10 m translates into a 0.1 MPa change in water potential.
When dealing with water transport at the cell level, the gravitational component (Yg) is generally omitted because it is negligible compared to the osmotic potential and the hydrostatic pressure. Thus, in these cases Equation 3.3 can be simplified as follows: (3.6) In discussions of dry soils, seeds, and cell walls, one often finds reference to another component of Yw, the matric potential, which is discussed in Web Topic 3.4.
Water potential in the plant.
Cell growth, photosyn-thesis, and crop productivity are all strongly influenced by water potential and its components. Like the body tem-perature of humans, water potential is a good overall indi-cator of plant health. Plant scientists have thus expended considerable effort in devising accurate and reliable meth-ods for evaluating the water status of plants. Some of the instruments that have been used to measure Yw, Ys, and Yp are described in Web Topic 3.5.
Water Enters the Cell along a Water Potential Gradient In this section we will illustrate the osmotic behavior of plant cells with some numerical examples. First imagine an open beaker full of pure water at 20°C (Figure 3.9A). Because the water is open to the atmosphere, the hydrostatic pressure of the water is the same as atmospheric pressure (Yp = 0 MPa).
There are no solutes in the water, so Ys = 0 MPa; therefore the water potential is 0 MPa (Yw = Ys + Yp).
Y Y Y w s p = + Yg w = r gh Y s s = −RTc Chapter 3 40 TABLE 3.2 Values of RT and osmotic potential of solutions at various temperatures Osmotic potential (MPa) of solution with solute concentration in mol L–1 water Temperature RTa Osmotic potential (°C) (L MPa mol–1) 0.01 0.10 1.00 of seawater (MPa) 0 2.271 −0.0227 −0.227 −2.27 −2.6 20 2.436 −0.0244 −0.244 −2.44 −2.8 25 2.478 −0.0248 −0.248 −2.48 −2.8 30 2.519 −0.0252 −0.252 −2.52 −2.9 aR = 0.0083143 L MPa mol–1 K–1.
Water and Plant Cells 41 FIGURE 3.9 Five examples illustrating the concept of water potential and its com-ponents. (A) Pure water. (B) A solution containing 0.1 M sucrose. (C) A flaccid cell (in air) is dropped in the 0.1 M sucrose solution. Because the starting water poten-tial of the cell is less than the water potential of the solution, the cell takes up water.
After equilibration, the water potential of the cell rises to equal the water potential of the solution, and the result is a cell with a positive turgor pressure. (D) Increasing the concentration of sucrose in the solution makes the cell lose water.
The increased sucrose concentration lowers the solution water potential, draws water out from the cell, and thereby reduces the cell’s turgor pressure. In this case the protoplast is able to pull away from the cell wall (i.e, the cell plasmolyzes) because sucrose molecules are able to pass through the relatively large pores of the cell walls. In contrast, when a cell desiccates in air (e.g., the flaccid cell in panel C) plasmolysis does not occur because the water held by capillary forces in the cell walls prevents air from infiltrating into any void between the plasma membrane and the cell wall. (E) Another way to make the cell lose water is to press it slowly between two plates. In this case, half of the cell water is removed, so cell osmotic potential increases by a factor of 2.
(A) Pure water (B) Solution containing 0.1 M sucrose (C) Flaccid cell dropped into sucrose solution 0.1 M Sucrose solution (D) Concentration of sucrose increased (E) Pressure applied to cell Applied pressure squeezes out half the water, thus doubling s from –0.732 to –1.464 MPa Yp = 0 MPa Ys = 0 MPa Yw = Yp + Ys = 0 MPa Pure water Yp = 0 MPa Ys = –0.244 MPa Yw = Yp + Ys = 0 – 0.244 MPa = –0.244 MPa 0.1 M Sucrose solution Yp = 0 MPa Ys = –0.732 MPa Yw = –0.732 MPa Flaccid cell Cell after equilibrium Yw = –0.244 MPa Ys = –0.732 MPa Yp = Yw – Ys = 0.488 MPa Yp = 0.488 MPa Ys = –0.732 MPa Yw = –0.244 MPa Turgid cell Yw = –0.732 MPa Ys = –0.732 MPa Yp = Yw – Ys = 0 MPa Cell after equilibrium Y Yp = 0 MPa Ys = –0.732 MPa Yw = –0.732 MPa 0.3 M Sucrose solution Yw = –0.244 MPa Ys = –0.732 MPa Yp = Yw – Ys = 0.488 MPa Cell in initial state Yw = –0.244 MPa Ys = –1.464 MPa Yp = Yw – Ys = 1.22 MPa Cell in final state Now imagine dissolving sucrose in the water to a con-centration of 0.1 M (Figure 3.9B). This addition lowers the osmotic potential (Ys) to –0.244 MPa (see Table 3.2) and decreases the water potential (Yw) to –0.244 MPa.
Next consider a flaccid, or limp, plant cell (i.e., a cell with no turgor pressure) that has a total internal solute con-centration of 0.3 M (Figure 3.9C). This solute concentration gives an osmotic potential (Ys) of –0.732 MPa. Because the cell is flaccid, the internal pressure is the same as ambient pressure, so the hydrostatic pressure (Yp) is 0 MPa and the water potential of the cell is –0.732 MPa.
What happens if this cell is placed in the beaker con-taining 0.1 M sucrose (see Figure 3.9C)? Because the water potential of the sucrose solution (Yw = –0.244 MPa; see Fig-ure 3.9B) is greater than the water potential of the cell (Yw = –0.732 MPa), water will move from the sucrose solution to the cell (from high to low water potential).
Because plant cells are surrounded by relatively rigid cell walls, even a slight increase in cell volume causes a large increase in the hydrostatic pressure within the cell.
As water enters the cell, the cell wall is stretched by the contents of the enlarging protoplast. The wall resists such stretching by pushing back on the cell. This phenomenon is analogous to inflating a basketball with air, except that air is compressible, whereas water is nearly incompressible.
As water moves into the cell, the hydrostatic pressure, or turgor pressure (Yp), of the cell increases. Consequently, the cell water potential (Yw) increases, and the difference between inside and outside water potentials (∆Yw) is reduced. Eventually, cell Yp increases enough to raise the cell Yw to the same value as the Yw of the sucrose solution.
At this point, equilibrium is reached (∆Yw = 0 MPa), and net water transport ceases.
Because the volume of the beaker is much larger than that of the cell, the tiny amount of water taken up by the cell does not significantly affect the solute concentration of the sucrose solution. Hence Ys, Yp, and Yw of the sucrose solution are not altered. Therefore, at equilibrium, Yw(cell) = Yw(solution) = –0.244 MPa.
The exact calculation of cell Yp and Ys requires knowl-edge of the change in cell volume. However, if we assume that the cell has a very rigid cell wall, then the increase in cell volume will be small. Thus we can assume to a first approximation that Ys(cell) is unchanged during the equili-bration process and that Ys(solution) remains at –0.732 MPa.
We can obtain cell hydrostatic pressure by rearranging Equation 3.6 as follows: Yp = Yw – Ys = (–0.244) – (–0.732) = 0.488 MPa.
Water Can Also Leave the Cell in Response to a Water Potential Gradient Water can also leave the cell by osmosis. If, in the previous example, we remove our plant cell from the 0.1 M sucrose solution and place it in a 0.3 M sucrose solution (Figure 3.9D), Yw(solution) (–0.732 MPa) is more negative than Yw(cell) (–0.244 MPa), and water will move from the turgid cell to the solution.
As water leaves the cell, the cell volume decreases. As the cell volume decreases, cell Yp and Yw decrease also until Yw(cell) = Yw(solution) = –0.732 MPa. From the water potential equation (Equation 3.6) we can calculate that at equilibrium, Yp = 0 MPa. As before, we assume that the change in cell volume is small, so we can ignore the change in Ys.
If we then slowly squeeze the turgid cell by pressing it between two plates (Figure 3.9E), we effectively raise the cell Yp, consequently raising the cell Yw and creating a ∆Yw such that water now flows out of the cell. If we con-tinue squeezing until half the cell water is removed and then hold the cell in this condition, the cell will reach a new equilibrium. As in the previous example, at equilibrium, ∆Yw = 0 MPa, and the amount of water added to the exter-nal solution is so small that it can be ignored. The cell will thus return to the Yw value that it had before the squeez-ing procedure. However, the components of the cell Yw will be quite different.
Because half of the water was squeezed out of the cell while the solutes remained inside the cell (the plasma membrane is selectively permeable), the cell solution is concentrated twofold, and thus Ys is lower (–0.732 × 2 = –1.464 MPa). Knowing the final values for Yw and Ys, we can calculate the turgor pressure, using Equation 3.6, as Yp = Yw – Ys = (–0.244) – (–1.464) = 1.22 MPa. In our example we used an external force to change cell volume without a change in water potential. In nature, it is typically the water potential of the cell’s environment that changes, and the cell gains or loses water until its Yw matches that of its sur-roundings.
One point common to all these examples deserves emphasis: Water flow is a passive process. That is, water moves in response to physical forces, toward regions of low water poten-tial or low free energy. There are no metabolic “pumps” (reac-tions driven by ATP hydrolysis) that push water from one place to another. This rule is valid as long as water is the only substance being transported. When solutes are trans-ported, however, as occurs for short distances across mem-branes (see Chapter 6) and for long distances in the phloem (see Chapter 10), then water transport may be coupled to solute transport and this coupling may move water against a water potential gradient.
For example, the transport of sugars, amino acids, or other small molecules by various membrane proteins can “drag” up to 260 water molecules across the membrane per molecule of solute transported (Loo et al. 1996). Such trans-port of water can occur even when the movement is against the usual water potential gradient (i.e., toward a larger water potential) because the loss of free energy by the solute more than compensates for the gain of free energy by the water. The net change in free energy remains negative. In the phloem, the bulk flow of solutes and water within sieve tubes occurs along gradients in hydrostatic Chapter 3 42 (turgor) pressure rather than by osmosis. Thus, within the phloem, water can be transported from regions with lower water potentials (e.g., leaves) to regions with higher water potentials (e.g., roots). These situations notwithstanding, in the vast majority of cases water in plants moves from higher to lower water potentials.
Small Changes in Plant Cell Volume Cause Large Changes in Turgor Pressure Cell walls provide plant cells with a substantial degree of volume homeostasis relative to the large changes in water potential that they experience as the everyday consequence of the transpirational water losses associated with photo-synthesis (see Chapter 4). Because plant cells have fairly rigid walls, a change in cell Yw is generally accompanied by a large change in Yp, with relatively little change in cell (protoplast) volume. This phenomenon is illustrated in plots of Yw, Yp, and Ys as a function of relative cell volume. In the example of a hypothetical cell shown in Figure 3.10, as Yw decreases from 0 to about –2 MPa, the cell volume is reduced by only 5%. Most of this decrease is due to a reduction in Yp (by about 1.2 MPa); Ys decreases by about 0.3 MPa as a result of water loss by the cell and consequent increased concen-tration of cell solutes. Contrast this with the volume changes of a cell lacking a wall.
Measurements of cell water potential and cell volume (see Figure 3.10) can be used to quantify how cell walls influence the water status of plant cells.
1. Turgor pressure (Yp > 0) exists only when cells are relatively well hydrated. Turgor pressure in most cells approaches zero as the relative cell volume decreases by 10 to 15%. However, for cells with very rigid cell walls (e.g., mesophyll cells in the leaves of many palm trees), the volume change associated with turgor loss can be much smaller, whereas in cells with extremely elastic walls, such as the water-storing cells in the stems of many cacti, this volume change may be substantially larger.
2. The Yp curve of Figure 3.10 provides a way to measure the relative rigidity of the cell wall, symbolized by e (the Greek letter epsilon): e = ∆Yp/∆(relative volume). e is the slope of the Yp curve. e is not constant but decreases as turgor pressure is lowered because nonlig-nified plant cell walls usually are rigid only when tur-gor pressure puts them under tension. Such cells act like a basketball: The wall is stiff (has high e) when the ball is inflated but becomes soft and collapsible (e = 0) when the ball loses pressure.
3. When e and Yp are low, changes in water potential are dominated by changes in Ys (note how Yw and Ys curves converge as the relative cell volume approaches 85%).
Water Transport Rates Depend on Driving Force and Hydraulic Conductivity So far, we have seen that water moves across a membrane in response to a water potential gradient. The direction of flow is determined by the direction of the Yw gradient, and the rate of water movement is proportional to the magni-tude of the driving gradient. However, for a cell that expe-riences a change in the water potential of its surroundings (e.g., see Figure 3.9), the movement of water across the cell membrane will decrease with time as the internal and external water potentials converge (Figure 3.11). The rate approaches zero in an exponential manner (see Dainty 1976), with a half-time (half-times conveniently character-ize processes that change exponentially with time) given by the following equation: (3.7) where V and A are, respectively, the volume and surface of t A Lp V 1 2 0 693 = ( )( ) − .
e Ys Water and Plant Cells 43 0.9 0.8 –3 –2 –1 0 1 2 1.0 0.95 0.85 Cell water potential (MPa) Relative cell volume (DV/V) Slope = e = DYp DV/V Zero turgor Full turgor pressure Yw = Ys + Yp Ys Yp FIGURE 3.10 Relation between cell water potential (Yw) and its components (Yp and Ys), and relative cell volume (∆V/V). The plots show that turgor pressure (Yp) decreases steeply with the initial 5% decrease in cell volume. In com-parison, osmotic potential (Ys) changes very little. As cell volume decreases below 0.9 in this example, the situation reverses: Most of the change in water potential is due to a drop in cell Ys accompanied by relatively little change in turgor pressure. The slope of the curve that illustrates Y p versus volume relationship is a measure of the cell’s elastic modulus (e) (a measurement of wall rigidity). Note that e is not constant but decreases as the cell loses turgor. (After Tyree and Jarvis 1982, based on a shoot of Sitka spruce.) the cell, and Lp is the hydraulic conductivity of the cell membrane. Hydraulic conductivity describes how readily water can move across a membrane and has units of vol-ume of water per unit area of membrane per unit time per unit driving force (i.e., m3 m–2 s–1 MPa–1). For additional discussion on hydraulic conductivity, see Web Topic 3.6.
A short half-time means fast equilibration. Thus, cells with large surface-to-volume ratios, high membrane hydraulic conductivity, and stiff cell walls (large e) will come rapidly into equilibrium with their surroundings.
Cell half-times typically range from 1 to 10 s, although some are much shorter (Steudle 1989). These low half-times mean that single cells come to water potential equilibrium with their surroundings in less than 1 minute. For multi-cellular tissues, the half-times may be much larger.
The Water Potential Concept Helps Us Evaluate the Water Status of a Plant The concept of water potential has two principal uses: First, water potential governs transport across cell membranes, as we have described. Second, water potential is often used as a measure of the water status of a plant. Because of tran-spirational water loss to the atmosphere, plants are seldom fully hydrated. They suffer from water deficits that lead to inhibition of plant growth and photosynthesis, as well as to other detrimental effects. Figure 3.12 lists some of the physiological changes that plants experience as they become dry.
The process that is most affected by water deficit is cell growth. More severe water stress leads to inhibition of cell division, inhibition of wall and protein synthesis, accumu-Chapter 3 44 Yw (MPa) Time 0 0 –0.2 Transport rate (Jv) slows as Yw increases D w = 0.2 MPa DYw = 0.1 MPa t1/2 = 0.693V (A)(Lp)(e –Ys) (B) Ψ Yw = –0.2 MPa Yw = 0 MPa DYw = 0.2 MPa Initial Jv = Lp (DYw) = 10–6 m s–1 MPa–1 × 0.2 MPa = 0.2 × 10–6 m s–1 (A) Water flow FIGURE 3.11 The rate of water transport into a cell depends on the water potential difference (∆Yw) and the hydraulic conductivity of the cell membranes (Lp). In this example, (A) the initial water potential difference is 0.2 MPa and Lp is 10–6 m s–1 MPa–1. These values give an initial transport rate (Jv) of 0.2 × 10–6 m s–1. (B) As water is taken up by the cell, the water potential difference decreases with time, leading to a slowing in the rate of water uptake. This effect follows an expo-nentially decaying time course with a half-time (t1/ 2) that depends on the following cell parameters: volume (V), surface area (A), Lp, volu-metric elastic modulus (e), and cell osmotic potential (Ys). Abscisic acid accumulation Physiological changes due to dehydration: Solute accumulation Photosynthesis Stomatal conductance Protein synthesis Wall synthesis Cell expansion Water potential (MPa) Well-watered plants Pure water Plants under mild water stress Plants in arid, desert climates –1 –0 –2 –3 –4 FIGURE 3.12 Water potential of plants under various growing conditions, and sensitivity of various physiologi-cal processes to water potential. The intensity of the bar color corresponds to the magnitude of the process. For example, cell expansion decreases as water potential falls (becomes more negative). Abscisic acid is a hormone that induces stomatal closure during water stress (see Chapter 23). (After Hsiao 1979.) lation of solutes, closing of stomata, and inhibition of pho-tosynthesis. Water potential is one measure of how hydrated a plant is and thus provides a relative index of the water stress the plant is experiencing (see Chapter 25).
Figure 3.12 also shows representative values for Yw at various stages of water stress. In leaves of well-watered plants, Yw ranges from –0.2 to about –1.0 MPa, but the leaves of plants in arid climates can have much lower val-ues, perhaps –2 to –5 MPa under extreme conditions.
Because water transport is a passive process, plants can take up water only when the plant Yw is less than the soil Yw. As the soil becomes drier, the plant similarly becomes less hydrated (attains a lower Yw). If this were not the case, the soil would begin to extract water from the plant.
The Components of Water Potential Vary with Growth Conditions and Location within the Plant Just as Yw values depend on the growing conditions and the type of plant, so too, the values of Ys can vary consid-erably. Within cells of well-watered garden plants (exam-ples include lettuce, cucumber seedlings, and bean leaves), Ys may be as high as –0.5 MPa, although values of –0.8 to –1.2 MPa are more typical. The upper limit for cell Ys is set probably by the minimum concentration of dissolved ions, metabolites, and proteins in the cytoplasm of living cells.
At the other extreme, plants under drought conditions sometimes attain a much lower Ys. For instance, water stress typically leads to an accumulation of solutes in the cytoplasm and vacuole, thus allowing the plant to main-tain turgor pressure despite low water potentials.
Plant tissues that store high concentrations of sucrose or other sugars, such as sugar beet roots, sugarcane stems, or grape berries, also attain low values of Ys. Values as low as –2.5 MPa are not unusual. Plants that grow in saline envi-ronments, called halophytes, typically have very low val-ues of Ys. A low Ys lowers cell Yw enough to extract water from salt water, without allowing excessive levels of salts to enter at the same time. Most crop plants cannot survive in seawater, which, because of the dissolved salts, has a lower water potential than the plant tissues can attain while maintaining their functional competence.
Although Ys within cells may be quite negative, the apoplastic solution surrounding the cells—that is, in the cell walls and in the xylem—may contain only low con-centrations of solutes. Thus, Ys of this phase of the plant is typically much higher—for example, –0.1 to 0 MPa. Nega-tive water potentials in the xylem and cell walls are usually due to negative Yp. Values for Yp within cells of well-watered garden plants may range from 0.1 to perhaps 1 MPa, depending on the value of Ys inside the cell.
A positive turgor pressure (Yp) is important for two prin-cipal reasons. First, growth of plant cells requires turgor pressure to stretch the cell walls. The loss of Yp under water deficits can explain in part why cell growth is so sensitive to water stress (see Chapter 25). The second reason positive turgor is important is that turgor pressure increases the mechanical rigidity of cells and tissues. This function of cell turgor pressure is particularly important for young, non-lignified tissues, which cannot support themselves mechan-ically without a high internal pressure. A plant wilts (becomes flaccid) when the turgor pressure inside the cells of such tissues falls toward zero. Web Topic 3.7 discusses plasmolysis, the shrinking of the protoplast away from the cell wall, which occurs when cells in solution lose water.
Whereas the solution inside cells may have a positive and large Yp, the water outside the cell may have negative val-ues for Yp. In the xylem of rapidly transpiring plants, Yp is negative and may attain values of –1 MPa or lower. The magnitude of Yp in the cell walls and xylem varies consid-erably, depending on the rate of transpiration and the height of the plant. During the middle of the day, when transpira-tion is maximal, xylem Yp reaches its lowest, most negative values. At night, when transpiration is low and the plant rehydrates, it tends to increase.
SUMMARY Water is important in the life of plants because it makes up the matrix and medium in which most biochemical processes essential for life take place. The structure and properties of water strongly influence the structure and properties of proteins, membranes, nucleic acids, and other cell constituents.
In most land plants, water is continually lost to the atmosphere and taken up from the soil. The movement of water is driven by a reduction in free energy, and water may move by diffusion, by bulk flow, or by a combination of these fundamental transport mechanisms. Water diffuses because molecules are in constant thermal agitation, which tends to even out concentration differences. Water moves by bulk flow in response to a pressure difference, whenever there is a suitable pathway for bulk movement of water.
Osmosis, the movement of water across membranes, depends on a gradient in free energy of water across the membrane—a gradient commonly measured as a differ-ence in water potential.
Solute concentration and hydrostatic pressure are the two major factors that affect water potential, although when large vertical distances are involved, gravity is also important.
These components of the water potential may be summed as follows: Yw = Ys + Yp + Yg. Plant cells come into water potential equilibrium with their local environment by absorb-ing or losing water. Usually this change in cell volume results in a change in cell Yp, accompanied by minor changes in cell Ys. The rate of water transport across a membrane depends on the water potential difference across the membrane and the hydraulic conductivity of the membrane.
In addition to its importance in transport, water poten-tial is a useful measure of the water status of plants. As we will see in Chapter 4, diffusion, bulk flow, and osmosis all Water and Plant Cells 45 help move water from the soil through the plant to the atmosphere.
Web Material Web Topics 3.1 Calculating Capillary Rise Quantification of capillary rise allows us to assess the functional role of capillary rise in water move-ment of plants.
3.2 Calculating Half-Times of Diffusion The assessment of the time needed for a mole-cule like glucose to diffuse across cells, tissues, and organs shows that diffusion has physiologi-cal significance only over short distances.
3.3 Alternative Conventions for Components of Water Potential Plant physiologists have developed several con-ventions to define water potential of plants. A comparison of key definitions in some of these convention systems provides us with a better understanding of the water relations literature.
3.4 The Matric Potential A brief discussion of the concept of matric poten-tial, used to quantify the chemical potential of water in soils,seeds,and cell walls.
3.5 Measuring Water Potential A detailed description of available methods to measure water potential in plant cells and tissues.
3.6 Understanding Hydraulic Conductivity Hydraulic conductivity, a measurement of the membrane permeability to water, is one of the factors determining the velocity of water move-ments in plants.
3.7 Wilting and Plasmolysis Plasmolysis is a major structural change resulting from major water loss by osmosis.
Chapter References Dainty, J. (1976) Water relations of plant cells. In Transport in Plants, Vol. 2, Part A: Cells (Encyclopedia of Plant Physiology, New Series, Vol. 2.), U. Lüttge and M. G. Pitman, eds., Springer, Berlin, pp. 12–35.
Finkelstein, A. (1987) Water Movement through Lipid Bilayers, Pores, and Plasma Membranes: Theory and Reality. Wiley, New York.
Friedman, M. H. (1986) Principles and Models of Biological Transport.
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Hsiao, T. C. (1979) Plant responses to water deficits, efficiency, and drought resistance. Agricult. Meteorol. 14: 59–84.
Loo, D. D. F., Zeuthen, T., Chandy, G., and Wright, E. M. (1996) Cotransport of water by the Na+/glucose cotransporter. Proc.
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Nobel, P . S. (1999) Physicochemical and Environmental Plant Physiology, 2nd ed. Academic Press, San Diego, CA.
Schäffner, A. R. (1998) Aquaporin function, structure, and expres-sion: Are there more surprises to surface in water relations?
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Stein, W. D. (1986) Transport and Diffusion across Cell Membranes. Aca-demic Press, Orlando, FL.
Steudle, E. (1989) Water flow in plants and its coupling to other processes: An overview. Methods Enzymol. 174: 183–225.
Tajkhorshid, E., Nollert, P ., Jensen, M. Ø., Miercke, L. H. W., O’Con-nell, J., Stroud, R. M., and Schulten, K. (2002) Control of the selec-tivity of the aquaporin water channel family by global orienta-tion tuning. Science 296: 525–530.
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A. C. (1999) Plant aquaporins: Their molecular biology, bio-physics and significance for plant–water relations. J. Exp. Bot. 50: 1055–1071.
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Chapter 3 46 Water Balance of Plants 4 Chapter LIFE IN EARTH’S ATMOSPHERE presents a formidable challenge to land plants. On the one hand, the atmosphere is the source of carbon dioxide, which is needed for photosynthesis. Plants therefore need ready access to the atmosphere. On the other hand, the atmosphere is relatively dry and can dehydrate the plant. To meet the contradictory demands of maximizing carbon dioxide uptake while limiting water loss, plants have evolved adaptations to control water loss from leaves, and to replace the water lost to the atmosphere.
In this chapter we will examine the mechanisms and driving forces operating on water transport within the plant and between the plant and its environment. Transpirational water loss from the leaf is driven by a gradient in water vapor concentration. Long-distance transport in the xylem is driven by pressure gradients, as is water movement in the soil.
Water transport through cell layers such as the root cortex is complex, but it responds to water potential gradients across the tissue. Throughout this journey water transport is passive in the sense that the free energy of water decreases as it moves. Despite its passive nature, water transport is finely regulated by the plant to minimize dehydra-tion, largely by regulating transpiration to the atmosphere. We will begin our examination of water transport by focusing on water in the soil.
WATER IN THE SOIL The water content and the rate of water movement in soils depend to a large extent on soil type and soil structure. Table 4.1 shows that the physical characteristics of different soils can vary greatly. At one extreme is sand, in which the soil particles may be 1 mm or more in diameter.
Sandy soils have a relatively low surface area per gram of soil and have large spaces or channels between particles.
At the other extreme is clay, in which particles are smaller than 2 µm in diameter. Clay soils have much greater surface areas and smaller channels between particles. With the aid of organic sub-stances such as humus (decomposing organic matter), clay particles may aggregate into “crumbs” that help improve soil aeration and infiltration of water.
When a soil is heavily watered by rain or by irrigation, the water percolates downward by gravity through the spaces between soil particles, partly displacing, and in some cases trapping, air in these channels. Water in the soil may exist as a film adhering to the surface of soil particles, or it may fill the entire channel between particles.
In sandy soils, the spaces between particles are so large that water tends to drain from them and remain only on the particle surfaces and at interstices between particles. In clay soils, the channels are small enough that water does not freely drain from them; it is held more tightly (seeWeb Topic 4.1). The moisture-holding capacity of soils is called the field capacity. Field capacity is the water content of a soil after it has been saturated with water and excess water has been allowed to drain away. Clay soils or soils with a high humus content have a large field capacity. A few days after being saturated, they might retain 40% water by vol-ume. In contrast, sandy soils typically retain 3% water by volume after saturation.
In the following sections we will examine how the neg-ative pressure in soil water alters soil water potential, how water moves in the soil, and how roots absorb the water needed by the plant.
A Negative Hydrostatic Pressure in Soil Water Lowers Soil Water Potential Like the water potential of plant cells, the water potential of soils may be dissected into two components, the osmotic potential and the hydrostatic pressure. The osmotic poten-tial (Ys; see Chapter 3) of soil water is generally negligible because solute concentrations are low; a typical value might be –0.02 MPa. For soils that contain a substantial concentration of salts, however, Ys is significant, perhaps –0.2 MPa or lower.
The second component of soil water potential is hydro-static pressure (Yp) (Figure 4.1). For wet soils, Yp is very close to zero. As a soil dries out, Yp decreases and can become quite negative. Where does the negative pressure in soil water come from?
Recall from our discussion of capillarity in Chapter 3 that water has a high surface tension that tends to mini-mize air–water interfaces. As a soil dries out, water is first removed from the center of the largest spaces between par-ticles. Because of adhesive forces, water tends to cling to the surfaces of soil particles, so a large surface area between soil water and soil air develops (Figure 4.2).
As the water content of the soil decreases, the water recedes into the interstices between soil particles, and the air–water surface develops curved air–water interfaces.
48 Chapter 4 Soil line Leaf air spaces (Dcwv) Xylem (DYp) Soil (DYp ) Across root (DYw) FIGURE 4.1 Main driving forces for water flow from the soil through the plant to the atmosphere: differences in water vapor concentration (∆cwv), hydrostatic pressure (∆Yp), and water potential (∆Yw). TABLE 4.1 Physical characteristics of different soils Particle Surface area Soil diameter (µm) per gram (m2) Coarse sand 2000–200 Fine sand 200–20 <1–10 Silt 20–2 10–100 Clay <2 100–1000 Water under these curved surfaces develops a negative pressure that may be estimated by the following formula: (4.1) where T is the surface tension of water (7.28 × 10–8 MPa m) and r is the radius of curvature of the air–water interface.
The value of Yp in soil water can become quite negative because the radius of curvature of air–water surfaces may become very small in drying soils. For instance, a curvature r = 1 µm (about the size of the largest clay particles) corre-sponds to a Yp value of –0.15 MPa. The value of Yp may easily reach –1 to –2 MPa as the air–water interface recedes into the smaller cracks between clay particles.
Soil scientists often describe soil water potential in terms of a matric potential (Jensen et al. 1998). For a discussion of the relation between matric potential and water potential see Web Topic 3.3.
Water Moves through the Soil by Bulk Flow Water moves through soils predominantly by bulk flow driven by a pressure gradient. In addition, diffusion of water vapor accounts for some water movement. As plants absorb water from the soil, they deplete the soil of water near the surface of the roots. This depletion reduces Yp in the water near the root surface and establishes a pressure gradient with respect to neighboring regions of soil that have higher Yp values. Because the water-filled pore spaces in the soil are interconnected, water moves to the root surface by bulk flow through these channels down the pressure gradient.
The rate of water flow in soils depends on two factors: the size of the pressure gradient through the soil, and the hydraulic conductivity of the soil. Soil hydraulic conduc-tivity is a measure of the ease with which water moves through the soil, and it varies with the type of soil and water content. Sandy soils, with their large spaces between particles, have a large hydraulic conductivity, whereas clay soils, with the minute spaces between their particles, have an appreciably smaller hydraulic conductivity.
As the water content (and hence the water potential) of a soil decreases, the hydraulic conductivity decreases dras-tically (see Web Topic 4.2). This decrease in soil hydraulic conductivity is due primarily to the replacement of water in the soil spaces by air. When air moves into a soil chan-nel previously filled with water, water movement through that channel is restricted to the periphery of the channel.
As more of the soil spaces become filled with air, water can flow through fewer and narrower channels, and the hydraulic conductivity falls.
In very dry soils, the water potential (Yw) may fall below what is called the permanent wilting point. At this point the water potential of the soil is so low that plants cannot regain turgor pressure even if all water loss through transpiration ceases. This means that the water potential of the soil (Yw) is less than or equal to the osmotic potential (Ys) of the plant. Because cell Ys varies with plant species, the permanent wilting point is clearly not a unique prop-erty of the soil; it depends on the plant species as well.
WATER ABSORPTION BY ROOTS Intimate contact between the surface of the root and the soil is essential for effective water absorption by the root. This contact provides the surface area needed for water uptake and is maximized by the growth of the root and of root hairs into the soil. Root hairs are microscopic extensions of root epidermal cells that greatly increase the surface area of the root, thus providing greater capacity for absorption of ions and water from the soil. When 4-month-old rye (Secale) plants were examined, their root hairs were found to constitute more than 60% of the surface area of the roots (see Figure 5.6).
Water enters the root most readily in the apical part of the root that includes the root hair zone. More mature regions of the root often have an outer layer of protective tissue, called an exodermis or hypodermis, that contains hydrophobic mate-rials in its walls and is relatively impermeable to water.
The intimate contact between the soil and the root sur-face is easily ruptured when the soil is disturbed. It is for this reason that newly transplanted seedlings and plants Y = −2T r Water Balance of Plants 49 Air Root hair Root Water Sand particle Clay particle FIGURE 4.2 Root hairs make intimate contact with soil particles and greatly amplify the surface area that can be used for water absorption by the plant. The soil is a mixture of particles (sand, clay, silt, and organic material), water, dissolved solutes, and air. Water is adsorbed to the sur-face of the soil particles. As water is absorbed by the plant, the soil solu-tion recedes into smaller pockets, channels, and crevices between the soil particles. At the air–water interfaces, this recession causes the surface of the soil solution to develop concave menisci (curved interfaces between air and water marked in the figure by arrows), and brings the solution into tension (negative pressure) by surface tension. As more water is removed from the soil, more acute menisci are formed, resulting in greater tensions (more negative pressures).
p need to be protected from water loss for the first few days after transplantation. Thereafter, new root growth into the soil reestablishes soil–root contact, and the plant can better withstand water stress.
Let’s consider how water moves within the root, and the factors that determine the rate of water uptake into the root.
Water Moves in the Root via the Apoplast, Transmembrane, and Symplast Pathways In the soil, water is transported predominantly by bulk flow.
However, when water comes in contact with the root sur-face, the nature of water transport becomes more complex.
From the epidermis to the endodermis of the root, there are three pathways through which water can flow (Figure 4.3): the apoplast, transmembrane, and symplast pathways.
1. In the apoplast pathway, water moves exclusively through the cell wall without crossing any mem-branes. The apoplast is the continuous system of cell walls and intercellular air spaces in plant tissues.
2. The transmembrane pathway is the route followed by water that sequentially enters a cell on one side, exits the cell on the other side, enters the next in the series, and so on. In this pathway, water crosses at least two membranes for each cell in its path (the plasma membrane on entering and on exiting).
Transport across the tonoplast may also be involved.
3. In the symplast pathway, water travels from one cell to the next via the plasmodesmata (see Chapter 1).
The symplast consists of the entire network of cell cytoplasm interconnected by plasmodesmata.
Although the relative importance of the apoplast, trans-membrane, and symplast pathways has not yet been clearly established, experiments with the pressure probe technique (see Web Topic 3.6) indicate that the apoplast pathway is particularly important for water uptake by young corn roots (Frensch et al. 1996; Steudle and Frensch 1996).
At the endodermis, water movement through the apoplast pathway is obstructed by the Casparian strip (see Figure 4.3). The Casparian strip is a band of radial cell Apoplast pathway Symplastic and transmembrane pathways Epidermis Cortex Endodermis Casparian strip Pericycle Xylem Phloem FIGURE 4.3 Pathways for water uptake by the root. Through the cortex, water may travel via the apoplast pathway, the transmembrane pathway, and the symplast pathway. In the symplast pathway, water flows between cells through the plasmod-esmata without crossing the plasma membrane. In the transmembrane pathway, water moves across the plasma membranes, with a short visit to the cell wall space.
At the endodermis, the apoplast pathway is blocked by the Casparian strip.
walls in the endodermis that is impregnated with the wax-like, hydrophobic substance suberin. Suberin acts as a bar-rier to water and solute movement. The endodermis becomes suberized in the nongrowing part of the root, sev-eral millimeters behind the root tip, at about the same time that the first protoxylem elements mature (Esau 1953). The Casparian strip breaks the continuity of the apoplast path-way, and forces water and solutes to cross the endodermis by passing through the plasma membrane. Thus, despite the importance of the apoplast pathway in the root cortex and the stele, water movement across the endodermis occurs through the symplast.
Another way to understand water movement through the root is to consider the root as a single pathway having a single hydraulic conductance. Such an approach has led to the development of the concept of root hydraulic con-ductance (see Web Topic 4.3 for details).
The apical region of the root is most permeable to water.
Beyond this point, the exodermis becomes suberized, lim-iting water uptake (Figure 4.4). However, some water absorption may take place through older roots, perhaps through breaks in the cortex associated with the outgrowth of secondary roots.
Water uptake decreases when roots are subjected to low temperature or anaerobic conditions, or treated with respi-ratory inhibitors (such as cyanide). These treatments inhibit root respiration, and the roots transport less water. The exact explanation for this effect is not yet clear. On the other hand, the decrease in water transport in the roots provides an expla-nation for the wilting of plants in waterlogged soils: Sub-merged roots soon run out of oxygen, which is normally pro-vided by diffusion through the air spaces in the soil (diffusion through gas is 104 times faster than diffusion through water).
The anaerobic roots transport less water to the shoots, which consequently suffer net water loss and begin to wilt.
Solute Accumulation in the Xylem Can Generate “Root Pressure” Plants sometimes exhibit a phenomenon referred to as root pressure. For example, if the stem of a young seedling is cut off just above the soil, the stump will often exude sap from the cut xylem for many hours. If a manometer is sealed over the stump, positive pressures can be measured.
These pressures can be as high as 0.05 to 0.5 MPa.
Roots generate positive hydrostatic pressure by absorb-ing ions from the dilute soil solution and transporting them into the xylem. The buildup of solutes in the xylem sap leads to a decrease in the xylem osmotic potential (Ys) and thus a decrease in the xylem water potential (Yw). This lowering of the xylem Yw provides a driving force for water absorption, which in turn leads to a positive hydro-static pressure in the xylem. In effect, the whole root acts like an osmotic cell; the multicellular root tissue behaves as an osmotic membrane does, building up a positive hydro-static pressure in the xylem in response to the accumula-tion of solutes.
Root pressure is most likely to occur when soil water potentials are high and transpiration rates are low. When transpiration rates are high, water is taken up so rapidly into the leaves and lost to the atmosphere that a positive pressure never develops in the xylem.
Plants that develop root pressure frequently produce liq-uid droplets on the edges of their leaves, a phenomenon known as guttation (Figure 4.5). Positive xylem pressure Water Balance of Plants 51 0.4 0 0.8 1.2 1.6 40 80 120 160 200 240 500 Distance from root tip (mm) Rate of water uptake per segment (10–6 L h–1) More suberized Less suberized Growing tip Nongrowing regions of root FIGURE 4.4 Rate of water uptake at various positions along a pumpkin root. (After Kramer and Boyer 1995.) FIGURE 4.5 Guttation in leaves from strawberry (Fragaria grandiflora). In the early morning, leaves secrete water droplets through the hydathodes, located at the margins of the leaves. Young flowers may also show guttation.
(Photograph courtesy of R. Aloni.) causes exudation of xylem sap through specialized pores called hydathodes that are associated with vein endings at the leaf margin. The “dewdrops” that can be seen on the tips of grass leaves in the morning are actually guttation droplets exuded from such specialized pores. Guttation is most noticeable when transpiration is suppressed and the relative humidity is high, such as during the night.
WATER TRANSPORT THROUGH THE XYLEM In most plants, the xylem constitutes the longest part of the pathway of water transport. In a plant 1 m tall, more than 99.5% of the water trans-port pathway through the plant is within the xylem, and in tall trees the xylem represents an even greater frac-tion of the pathway. Compared with the complex pathway across the root tissue, the xylem is a simple pathway of low resistance. In the following sec-tions we will examine how water movement through the xylem is opti-mally suited to carry water from the roots to the leaves, and how negative hydrostatic pressure generated by leaf transpiration pulls water through the xylem.
The Xylem Consists of Two Types of Tracheary Elements The conducting cells in the xylem have a specialized anatomy that enables them to transport large quan-tities of water with great efficiency.
There are two important types of tra-cheary elements in the xylem: tra-cheids and vessel elements (Figure 4.6). Vessel elements are found only in angiosperms, a small group of gym-nosperms called the Gnetales, and perhaps some ferns. Tracheids are pre-sent in both angiosperms and gym-nosperms, as well as in ferns and other groups of vascular plants.
The maturation of both tracheids and vessel elements involves the “death” of the cell. Thus, functional water-conducting cells have no mem-branes and no organelles. What re-52 Chapter 4 (A) Perforation plate (compound) Perforation plate (simple) Pits Vessel elements Tracheids Torus Pit cavity Pit membrane Pit pair Secondary cell walls Primary cell walls (C) (B) mains are the thick, lignified cell walls, which form hollow tubes through which water can flow with relatively little resis-tance.
Tracheids are elongated, spindle-shaped cells (Figure 4.6A) that are arranged in overlapping vertical files. Water flows between tracheids by means of the numerous pits in their lateral walls (Figure 4.6B). Pits are microscopic regions where the secondary wall is absent and the primary wall is thin and porous (Figure 4.6C). Pits of one tracheid are typ-ically located opposite pits of an adjoining tracheid, form-ing pit pairs. Pit pairs constitute a low-resistance path for water movement between tracheids. The porous layer between pit pairs, consisting of two primary walls and a middle lamella, is called the pit membrane.
Pit membranes in tracheids of some species of conifers have a central thickening, called a torus (pl. tori) (see Fig-ure 4.6C). The torus acts like a valve to close the pit by lodging itself in the circular or oval wall thickenings bor-dering these pits. Such lodging of the torus is an effective way of preventing dangerous gas bubbles from invading neighboring tracheids (we will discuss this formation of bubbles, a process called cavitation, shortly).
Vessel elements tend to be shorter and wider than tra-cheids and have perforated end walls that form a perfora-tion plate at each end of the cell. Like tracheids, vessel ele-ments have pits on their lateral walls (see Figure 4.6B).
Unlike tracheids, the perforated end walls allow vessel members to be stacked end to end to form a larger conduit called a vessel (again, see Figure 4.6B). Vessels vary in length both within and between species. Maximum vessel lengths range from 10 cm to many meters. Because of their open end walls, vessels provide a very efficient low-resis-tance pathway for water movement. The vessel members found at the extreme ends of a vessel lack perforations at the end walls and communicate with neighboring vessels via pit pairs.
Water Movement through the Xylem Requires Less Pressure Than Movement through Living Cells The xylem provides a low-resistance pathway for water movement, thus reducing the pressure gradients needed to transport water from the soil to the leaves. Some numeri-cal values will help us appreciate the extraordinary effi-ciency of the xylem. We will calculate the driving force required to move water through the xylem at a typical velocity and compare it with the driving force that would be needed to move water through a cell-to-cell pathway.
For the purposes of this comparison, we will use a figure of 4 mm s–1 for the xylem transport velocity and 40 µm as the vessel radius. This is a high velocity for such a narrow vessel, so it will tend to exaggerate the pressure gradient required to support water flow in the xylem. Using a ver-sion of Poiseuille’s equation (see Equation 3.2), we can cal-culate the pressure gradient needed to move water at a velocity of 4 mm s–1 through an ideal tube with a uniform inner radius of 40 µm. The calculation gives a value of 0.02 MPa m–1. Elaboration of the assumptions, equations, and calculations can be found in Web Topic 4.4.
Of course, real xylem conduits have irregular inner wall surfaces, and water flow through perforation plates and pits adds additional resistance. Such deviations from an ideal tube will increase the frictional drag above that cal-culated from Poiseuille’s equation. However, measure-ments show that the actual resistance is greater by approx-imately a factor of 2 (Nobel 1999). Thus our estimate of 0.02 MPa m–1 is in the correct range for pressure gradients found in real trees.
Let’s now compare this value (0.02 MPa m–1) with the driving force that would be necessary to move water at the same velocity from cell to cell, crossing the plasma mem-brane each time. Using Poiseuille’s equation, as described in Web Topic 4.4, the driving force needed to move water through a layer of cells at 4 mm s–1 is calculated to be 2 × 108 MPa m–1. This is ten orders of magnitude greater than the driving force needed to move water through our 40-µm-radius xylem vessel. Our calculation clearly shows that water flow through the xylem is vastly more efficient than water flow across the membranes of living cells.
What Pressure Difference Is Needed to Lift Water 100 Meters to a Treetop?
With the foregoing example in mind, let’s see how large of a pressure gradient is needed to move water up to the top of a very tall tree. The tallest trees in the world are the coast redwoods (Sequoia sempervirens) of North America and Eucalyptus regnans of Australia. Individuals of both species can exceed 100 m. If we think of the stem of a tree as a long pipe, we can estimate the pressure difference that is needed Water Balance of Plants 53 FIGURE 4.6 Tracheary elements and their interconnections.
(A) Structural comparison of tracheids and vessel elements, two classes of tracheary elements involved in xylem water transport. Tracheids are elongate, hollow, dead cells with highly lignified walls. The walls contain numerous pits— regions where secondary wall is absent but primary wall remains. The shape and pattern of wall pitting vary with species and organ type. Tracheids are present in all vascular plants. Vessels consist of a stack of two or more vessel ele-ments. Like tracheids, vessel elements are dead cells and are connected to one another through perforation plates— regions of the wall where pores or holes have developed.
Vessels are connected to other vessels and to tracheids through pits. Vessels are found in most angiosperms and are lacking in most gymnosperms. (B) Scanning electron micrograph of oak wood showing two vessel elements that make up a portion of a vessel. Large pits are visible on the side walls, and the end walls are open at the perforation plate. (420×) (C) Diagram of a bordered pit with a torus either centered in the pit cavity or lodged to one side of the cavity, thereby blocking flow. (B © G. Shih-R. Kessel/Visuals Unlimited; C after Zimmermann 1983.) L to overcome the frictional drag of moving water from the soil to the top of the tree by multiplying our pressure gra-dient of 0.02 MPa m–1 by the height of the tree (0.02 MPa m–1 × 100 m = 2 MPa).
In addition to frictional resistance, we must consider gravity. The weight of a standing column of water 100 m tall creates a pressure of 1 MPa at the bottom of the water column (100 m × 0.01 MPa m–1). This pressure gradient due to gravity must be added to that required to cause water movement through the xylem. Thus we calculate that a pressure difference of roughly 3 MPa, from the base to the top branches, is needed to carry water up the tallest trees.
The Cohesion–Tension Theory Explains Water Transport in the Xylem In theory, the pressure gradients needed to move water through the xylem could result from the generation of pos-itive pressures at the base of the plant or negative pressures at the top of the plant. We mentioned previously that some roots can develop positive hydrostatic pressure in their xylem—the so-called root pressure. However, root pressure is typically less than 0.1 MPa and disappears when the transpiration rate is high, so it is clearly inadequate to move water up a tall tree.
Instead, the water at the top of a tree develops a large tension (a negative hydrostatic pressure), and this tension pulls water through the xylem. This mechanism, first pro-posed toward the end of the nineteenth century, is called the cohesion–tension theory of sap ascent because it requires the cohesive properties of water to sustain large tensions in the xylem water columns (for details on the history of the research on water movement, see Web Essay 4.1).
Despite its attractiveness, the cohesion–tension theory has been a controversial subject for more than a century and continues to generate lively debate. The main contro-versy surrounds the question of whether water columns in the xylem can sustain the large tensions (negative pres-sures) necessary to pull water up tall trees.
The most recent debate began when researchers modi-fied the cell pressure probe technique to be able to measure directly the tension in xylem vessels (Balling and Zimmer-mann 1990). Prior to this development, estimates of xylem pressures were based primarily on pressure chamber mea-surements of leaves (for a description of the pressure cham-ber method, see Web Topic 3.6). Initially, measurements with the xylem pressure probe failed to find the expected large negative pressures, prob-ably because of cavitation produced by tiny gas bubbles introduced when the xylem walls are punctured with the glass capillary of the pressure probe (Tyree 1997). However, careful refinements of the technique eventually demon-strated good agreement between pressure probe measure-ments and the tensions estimated by the pressure chamber (Melcher et al. 1998; Wei et al. 1999). In addition, indepen-dent studies demonstrated that water in the xylem can sus-tain large negative tensions (Pockman et al. 1995) and that pressure chamber measurements of nontranspiring leaves do reflect tensions in the xylem (Holbrook et al. 1995).
Most researchers have thus concluded that the basic cohesion–tension theory is sound (Steudle 2001) (for alter-native hypotheses, see Canny (1998), and Web Essays 4.1 and 4.2). One can readily demonstrate xylem tensions by puncturing intact xylem through a drop of ink on the sur-face of a stem from a transpiring plant. When the tension in the xylem is relieved, the ink is drawn instantly into the xylem, resulting in visible streaks along the stem.
Xylem Transport of Water in Trees Faces Physical Challenges The large tensions that develop in the xylem of trees (see Web Essay 4.3) and other plants can create some problems.
First, the water under tension transmits an inward force to the walls of the xylem. If the cell walls were weak or pliant, they would collapse under the influence of this tension.
The secondary wall thickenings and lignification of tra-cheids and vessels are adaptations that offset this tendency to collapse.
A second problem is that water under such tensions is in a physically metastable state. We mentioned in Chapter 3 that the experimentally determined breaking strength of degassed water (water that has been boiled to remove gases) is greater than 30 MPa. This value is much larger than the estimated tension of 3 MPa needed to pull water up the tallest trees, so water within the xylem would not normally reach tensions that would destabilize it.
However, as the tension in water increases, there is an increased tendency for air to be pulled through microscopic pores in the xylem cell walls. This phenomenon is called air seeding. A second mode by which bubbles can form in xylem conduits is due to the reduced solubility of gases in ice (Davis et al. 1999): The freezing of xylem conduits can lead to bubble formation. Once a gas bubble has formed within the water column under tension, it will expand because gases cannot resist tensile forces. This phenome-non of bubble formation is known as cavitation or embolism. It is similar to vapor lock in the fuel line of an automobile or embolism in a blood vessel. Cavitation breaks the continuity of the water column and prevents water transport in the xylem (Tyree and Sperry 1989; Hacke et al. 2001).
Such breaks in the water columns in plants are not unusual. With the proper equipment, one can “hear” the water columns break (Jackson et al. 1999). When plants are deprived of water, sound pulses can be detected. The pulses or clicks are presumed to correspond to the formation and rapid expansion of air bubbles in the xylem, resulting in high-frequency acoustic shock waves through the rest of the plant. These breaks in xylem water continuity, if not repaired, would be disastrous to the plant. By blocking the main transport pathway of water, such embolisms would cause the dehydration and death of the leaves.
54 Chapter 4 Plants Minimize the Consequences of Xylem Cavitation The impact of xylem cavitation on the plant is minimized by several means. Because the tracheary elements in the xylem are interconnected, one gas bubble might, in princi-ple, expand to fill the whole network. In practice, gas bub-bles do not spread far because the expanding gas bubble cannot easily pass through the small pores of the pit mem-branes. Since the capillaries in the xylem are interconnected, one gas bubble does not completely stop water flow.
Instead, water can detour around the blocked point by trav-eling through neighboring, connected conduits (Figure 4.7).
Thus the finite length of the tracheid and vessel conduits of the xylem, while resulting in an increased resistance to water flow, also provides a way to restrict cavitation.
Gas bubbles can also be eliminated from the xylem. At night, when transpiration is low, xylem Yp increases and the water vapor and gases may simply dissolve back into the solution of the xylem. Moreover, as we have seen, some plants develop positive pressures (root pressures) in the xylem. Such pressures shrink the gas bubble and cause the gases to dissolve. Recent studies indicate that cavitation may be repaired even when the water in the xylem is under tension (Holbrook et al. 2001). A mechanism for such repair is not yet known and remains the subject of active research (see Web Essay 4.4). Finally, many plants have sec-ondary growth in which new xylem forms each year. The new xylem becomes functional before the old xylem ceases to function, because of occlusion by gas bubbles or by sub-stances secreted by the plant.
Water Evaporation in the Leaf Generates a Negative Pressure in the Xylem The tensions needed to pull water through the xylem are the result of evaporation of water from leaves. In the intact plant, water is brought to the leaves via the xylem of the leaf vas-cular bundle(see Figure 4.1), which branches into a very fine and sometimes intricate network of veins throughout the leaf (Figure 4.8). This venation pattern becomes so finely Water Balance of Plants 55 fpo End wall of vessel element with bordered pits Pit Scalariform perforation plate Gas-filled cavitated vessel Water vapor bubble Gas-filled cavitated tracheid Liquid water FIGURE 4.7 Tracheids (right) and vessels (left) form a series of parallel, interconnected pathways for water movement. Cavitation blocks water movement because of the formation of gas-filled (embolized) conduits.
Because xylem conduits are interconnected through openings (“bor-dered pits”) in their thick secondary walls, water can detour around the blocked vessel by moving through adjacent tracheary elements. The very small pores in the pit membranes help prevent embolisms from spreading between xylem conduits. Thus, in the diagram on the right the gas is contained within a single cavitated tracheid. In the diagram on the left, gas has filled the entire cavitated vessel, shown here as being made up of three vessel elements, each separated by scalariform perfo-ration plates. In nature vessels can be very long (up to several meters in length) and thus made up of many vessel elements.
FIGURE 4.8 Venation of a tobacco leaf, showing ramification of the midrib into finer lateral veins. This venation pattern brings xylem water close to every cell in the leaf. (After Kramer and Boyer 1995.) branched that most cells in a typical leaf are within 0.5 mm of a minor vein. From the xylem, water is drawn into the cells of the leaf and along the cell walls.
The negative pressure that causes water to move up through the xylem develops at the surface of the cell walls in the leaf. The situation is analogous to that in the soil. The cell wall acts like a very fine capillary wick soaked with water.
Water adheres to the cellulose microfibrils and other hydro-philic components of the wall. The mesophyll cells within the leaf are in direct contact with the atmosphere through an extensive system of intercellular air spaces.
Initially water evaporates from a thin film lining these air spaces. As water is lost to the air, the surface of the remain-ing water is drawn into the interstices of the cell wall (Figure 4.9), where it forms curved air–water interfaces. Because of the high surface tension of water, the curvature of these inter-faces induces a tension, or negative pressure, in the water. As more water is removed from the wall, the radius of curvature 56 Chapter 4 Plasma membrane Vacuole Cell wall Air evaporation Chloroplast Cytoplasm Plasma membrane Cytoplasm Cellulose microfibrils in cross section Air–water interface Air Water in wall Cell wall Radius of curvature (µm) Hydrostatic pressure (MPa) (A) 0.5 –0.3 (B) 0.05 –3 (C) 0.01 –15 Evaporation Evaporation Evaporation Water film (A) (B) (C) FIGURE 4.9 Tensions or negative pressures originate in leaves. As water evaporates from the surface film that covers the cell walls of the mesophyll, water withdraws farther into the interstices of the cell wall, and surface tension causes a negative pressure in the liquid phase. As the radius of curvature decreases, the pressure decreases (becomes more negative), as calculated from Equation 4.1.
of the air–water interfaces decreases and the pressure of the water becomes more negative (see Equation 4.1). Thus the motive force for xylem transport is generated at the air– water interfaces within the leaf.
WATER MOVEMENT FROM THE LEAF TO THE ATMOSPHERE After water has evaporated from the cell surface into the intercellular air space, diffusion is the primary means of any further movement of the water out of the leaf. The waxy cuticle that covers the leaf surface is a very effective barrier to water movement. It has been estimated that only about 5% of the water lost from leaves escapes through the cuticle. Almost all of the water lost from typical leaves is lost by diffusion of water vapor through the tiny pores of the stomatal apparatus, which are usually most abundant on the lower surface of the leaf.
On its way from the leaf to the atmosphere, water is pulled from the xylem into the cell walls of the mesophyll, where it evaporates into the air spaces of the leaf (Figure 4.10). The water vapor then exits the leaf through the sto-matal pore. Water moves along this pathway predomi-nantly by diffusion, so this water movement is controlled by the concentration gradient of water vapor.
We will now examine the driving force for leaf transpi-ration, the main resistances in the diffusion pathway from the leaf to the atmosphere, and the anatomical features of the leaf that regulate transpiration.
Water Vapor Diffuses Quickly in Air We saw in Chapter 3 that diffusion in liquids is slow and, thus, effective only within cellular dimensions. How long would it take for a water molecule to diffuse from the cell wall surfaces inside the leaf to the outside atmosphere? In Chapter 3 we saw that the average time needed for a mol-ecule to diffuse a distance L is equal to L2/Ds, where Ds is the diffusion coefficient. The distance through which a water molecule must diffuse from the site of evaporation inside the leaf to the outside air is approximately 1 mm (10–3 m), and the diffusion coefficient of water in air is 2.4 × 10–5 m2 s–1. Thus the average time needed for a water Water Balance of Plants 57 Mesophyll cells Palisade parenchyma Xylem Air boundary layer Cuticle Upper epidermis Air boundary layer Low water vapor content Boundary layer resistance (rb) Leaf stomatal resistance (rs) High CO2 Water vapor CO2 Guard cell Low CO2 High water vapor content Substomatal cavity Lower epidermis Cuticle Stomatal pore FIGURE 4.10 Water pathway through the leaf. Water is pulled from the xylem into the cell walls of the mesophyll, where it evaporates into the air spaces within the leaf. Water vapor then diffuses through the leaf air space, through the stomatal pore, and across the boundary layer of still air found next to the leaf surface. CO2 diffuses in the opposite direction along its concentration gradient (low inside, higher outside).
58 Chapter 4 molecule to escape the leaf is approximately 0.042 s. Thus we see that diffusion is adequate to move water vapor through the gas phase of the leaf. The reason that this time is so much shorter than the 2.5 s calculated in Chapter 3 for a glucose molecule to diffuse across a 50 µm cell, is that dif-fusion is much more rapid in a gas than in a liquid.
Transpiration from the leaf depends on two major fac-tors: (1) the difference in water vapor concentration between the leaf air spaces and the external air and (2) the diffusional resistance (r) of this pathway. We will first dis-cuss how the difference in water vapor concentration con-trols transpiration rates.
The Driving Force for Water Loss Is the Difference in Water Vapor Concentration The difference in water vapor concentration is expressed as cwv(leaf) – cwv(air). The water vapor concentration of bulk air (cwv(air)) can be readily measured, but that of the leaf (cwv(leaf)) is more difficult to assess.
Whereas the volume of air space inside the leaf is small, the wet surface from which water evaporates is compara-tively large. (Air space volume is about 5% of the total leaf volume for pine needles, 10% for corn leaves, 30% for bar-ley, and 40% for tobacco leaves.) In contrast to the volume of the air space, the internal surface area from which water evaporates may be from 7 to 30 times the external leaf area.
This high ratio of surface area to volume makes for rapid vapor equilibration inside the leaf. Thus we can assume that the air space in the leaf is close to water potential equi-librium with the cell wall surfaces from which liquid water is evaporating.
An important point from this relationship is that within the range of water potentials experienced by transpiring leaves (generally <2.0 MPa) the equilibrium water vapor concentration is within a few percentage points of the sat-uration water vapor concentration. This allows one to esti-mate the water vapor concentration within a leaf from its temperature, which is easy to measure. (Web Topic 4.5 shows how we can calculate the water vapor concentration in the leaf air spaces and dis-cusses other aspects of the water relations within a leaf.) The concentration of water vapor, cwv, changes at various points along the transpiration pathway. We see from Table 4.2 that cwv decreases at each step of the pathway from the cell wall surface to the bulk air outside the leaf. The impor-tant points to remember are (1) that the driving force for water loss from the leaf is the absolute concentration differ-ence (difference in cwv, in mol m–3), and (2) that this difference depends on leaf tempera-ture, as shown in Figure 4.11. Water Loss Is Also Regulated by the Pathway Resistances The second important factor governing water loss from the leaf is the diffusional resistance of the transpiration path-way, which consists of two varying components: 1. The resistance associated with diffusion through the stomatal pore, the leaf stomatal resistance (rs).
2. The resistance due to the layer of unstirred air next to the leaf surface through which water vapor must 1 2 3 4 5 0 –10 10 20 30 40 50 Air temperature (°C) Saturation water vapor concentration, cwv(sat.) (mol m–3) Temperature (°C) (mol m–3 ) 0.269 0.378 0.522 0.713 0.961 1.28 1.687 2.201 2.842 3.637 cwv 0 5 10 15 20 25 30 35 40 45 FIGURE 4.11 Concentration of water vapor in saturated air as a function of air temperature.
TABLE 4.2 Representative values for relative humidity, absolute water vapor concentration, and water potential for four points in the pathway of water loss from a leaf Water vapor Relative Concentration Potential Location humidity (mol m–3) (MPa)a Inner air spaces (25°C) 0.99 1.27 −1.38 Just inside stomatal pore (25°C) 0.95 1.21 −7.04 Just outside stomatal pore (25°C) 0.47 0.60 −103.7 Bulk air (20°C) 0.50 0.50 −93.6 Source: Adapted from Nobel 1999.
Note: See Figure 4.10.
aCalculated using Equation 4.5.2 in Web Topic 4.5; with values for RT/V _ w of 135 MPa at 20°C and 137.3 MPa at 25°C.
diffuse to reach the turbulent air of the atmosphere (see Figure 4.10). This second resistance, rb, is called the leaf boundary layer resistance. We will discuss this type of resistance before considering stomatal resistance.
The thickness of the boundary layer is determined pri-marily by wind speed. When the air surrounding the leaf is very still, the layer of unstirred air on the surface of the leaf may be so thick that it is the primary deterrent to water vapor loss from the leaf. Increases in stomatal apertures under such conditions have little effect on transpiration rate (Figure 4.12) (although closing the stomata completely will still reduce transpiration).
When wind velocity is high, the moving air reduces the thickness of the boundary layer at the leaf surface, reducing the resistance of this layer. Under such conditions, the sto-matal resistance will largely control water loss from the leaf.
Various anatomical and morphological aspects of the leaf can influence the thickness of the boundary layer.
Hairs on the surface of leaves can serve as microscopic windbreaks. Some plants have sunken stomata that pro-vide a sheltered region outside the stomatal pore. The size and shape of leaves also influence the way the wind sweeps across the leaf surface. Although these and other factors may influence the boundary layer, they are not char-acteristics that can be altered on an hour-to-hour or even day-to-day basis. For short-term regulation, control of stomatal apertures by the guard cells plays a crucial role in the regulation of leaf transpiration.
Stomatal Control Couples Leaf Transpiration to Leaf Photosynthesis Because the cuticle covering the leaf is nearly impermeable to water, most leaf transpiration results from the diffusion of water vapor through the stomatal pore (see Figure 4.10).
The microscopic stomatal pores provide a low-resistance pathway for diffusional movement of gases across the epi-dermis and cuticle. That is, the stomatal pores lower the diffusional resistance for water loss from leaves. Changes in stomatal resistance are important for the regulation of water loss by the plant and for controlling the rate of car-bon dioxide uptake necessary for sustained CO2 fixation during photosynthesis.
All land plants are faced with competing demands of tak-ing up CO2 from the atmosphere while limiting water loss.
The cuticle that covers exposed plant surfaces serves as an effective barrier to water loss and thus protects the plant from desiccation. However, plants cannot prevent outward diffusion of water without simultaneously excluding CO2 from the leaf. This problem is compounded because the con-centration gradient for CO2 uptake is much, much smaller than the concentration gradient that drives water loss.
When water is abundant, the functional solution to this dilemma is the temporal regulation of stomatal apertures— open during the day, closed at night. At night, when there is no photosynthesis and thus no demand for CO2 inside the leaf, stomatal apertures are kept small, preventing unnecessary loss of water. On a sunny morning when the supply of water is abundant and the solar radiation inci-dent on the leaf favors high photosynthetic activity, the demand for CO2 inside the leaf is large, and the stomatal pores are wide open, decreasing the stomatal resistance to CO2 diffusion. Water loss by transpiration is also substan-tial under these conditions, but since the water supply is plentiful, it is advantageous for the plant to trade water for the products of photosynthesis, which are essential for growth and reproduction.
On the other hand, when soil water is less abundant, the stomata will open less or even remain closed on a sunny morning. By keeping its stomata closed in dry conditions, the plant avoids dehydration. The values for (cwv(leaf) – cwv(air)) and for rb are not readily amenable to biological con-trol. However, stomatal resistance (rs) can be regulated by opening and closing of the stomatal pore. This biological control is exerted by a pair of specialized epidermal cells, the guard cells, which surround the stomatal pore (Figure 4.13).
Water Balance of Plants 59 50 100 150 200 250 300 0 5 10 15 20 Stomatal aperture (mm) Transpirational flux (mg water vapor m–2 leaf surface s–1) Moving air Still air Flux limited by boundary layer resistance FIGURE 4.12 Dependence of transpiration flux on the sto-matal aperture of zebra plant (Zebrina pendula) in still air and in moving air. The boundary layer is larger and more rate limiting in still air than in moving air. As a result, the stomatal aperture has less control over transpiration in still air. (From Bange 1953.) The Cell Walls of Guard Cells Have Specialized Features Guard cells can be found in leaves of all vascular plants, and they are also present in organs from more primitive plants, such as the liverworts and the mosses (Ziegler 1987). Guard cells show considerable morphological diver-sity, but we can distinguish two main types: One is typical of grasses and a few other monocots, such as palms; the other is found in all dicots, in many monocots, and in mosses, ferns, and gymnosperms.
In grasses (see Figure 4.13A), guard cells have a charac-teristic dumbbell shape, with bulbous ends. The pore proper is a long slit located between the two “handles” of the dumbbells. These guard cells are always flanked by a 60 Chapter 4 FIGURE 4.13 Electron micrographs of stomata. (A) A stoma from a grass. The bulbous ends of each guard cell show their cytosolic content and are joined by the heavily thick-ened walls. The stomatal pore separates the two midpor-tions of the guard cells. (2560×) (B) Stomatal complexes of the sedge, Carex, viewed with differential interference con-trast light microscopy. Each complex consists of two guard cells surrounding a pore and two flanking subsidiary cells.
(550×) (C) Scanning electron micrographs of onion epider-mis. The top panel shows the outside surface of the leaf, with a stomatal pore inserted in the cuticle. The bottom panel shows a pair of guard cells facing the stomatal cavity, toward the inside of the leaf. (1640×) (A from Palevitz 1981, B from Jarvis and Mansfield 1981, A and B courtesy of B.
Palevitz; micrographs in C from Zeiger and Hepler 1976 [top] and E. Zeiger and N. Burnstein [bottom].) Cytosol and vacuole Pore Heavily thickened guard cell wall Guard cells Subsidiary cell Epidermal cell Stomatal pore Guard cell (C) (A) (B) pair of differentiated epidermal cells called subsidiary cells, which help the guard cells control the stomatal pores (see Figure 4.13B). The guard cells, subsidiary cells, and pore are collectively called the stomatal complex.
In dicot plants and nongrass monocots, kidney-shaped guard cells have an elliptical contour with the pore at its center (see Figure 4.13C). Although subsidiary cells are not uncommon in species with kidney-shaped stomata, they are often absent, in which case the guard cells are sur-rounded by ordinary epidermal cells.
A distinctive feature of the guard cells is the specialized structure of their walls. Portions of these walls are sub-stantially thickened (Figure 4.14) and may be up to 5 µm across, in contrast to the 1 to 2 µm typical of epidermal cells. In kidney-shaped guard cells, a differential thicken-ing pattern results in very thick inner and outer (lateral) walls, a thin dorsal wall (the wall in contact with epider-mal cells), and a somewhat thickened ventral (pore) wall (see Figure 4.14). The portions of the wall that face the atmosphere extend into well-developed ledges, which form the pore proper.
The alignment of cellulose microfibrils, which reinforce all plant cell walls and are an important determinant of cell shape (see Chapter 15), plays an essential role in the open-ing and closing of the stomatal pore. In ordinary cells hav-ing a cylindrical shape, cellulose microfibrils are oriented transversely to the long axis of the cell. As a result, the cell expands in the direction of its long axis because the cellu-lose reinforcement offers the least resistance at right angles to its orientation. In guard cells the microfibril organization is different.
Kidney-shaped guard cells have cellulose microfibrils fan-ning out radially from the pore (Figure 4.15A). Thus the cell girth is reinforced like a steel-belted radial tire, and the guard cells curve outward during stomatal opening (Sharpe et al. 1987). In grasses, the dumbbell-shaped guard cells function like beams with inflatable ends. As the bul-bous ends of the cells increase in volume and swell, the beams are separated from each other and the slit between them widens (Figure 4.15B).
An Increase in Guard Cell Turgor Pressure Opens the Stomata Guard cells function as multisensory hydraulic valves. Envi-ronmental factors such as light intensity and quality, tem-perature, relative humidity, and intracellular CO2 concentra-Water Balance of Plants 61 Atmosphere Interior of leaf Vacuole Nucleus Pore SUBSTOMATAL CAVITY ATMOSPHERE Plastid Inner cell wall FIGURE 4.14 Electron micrograph showing a pair of guard cells from the dicot Nicotiana tabacum (tobacco). The section was made perpendicular to the main sur-face of the leaf. The pore faces the atmosphere; the bottom faces the substomatal cavity inside the leaf. Note the uneven thickening pattern of the walls, which deter-mines the asymmetric deformation of the guard cells when their volume increases during stomatal opening. (From Sack 1987, courtesy of F. Sack.) 2 µm tions are sensed by guard cells, and these signals are inte-grated into well-defined stomatal responses. If leaves kept in the dark are illuminated, the light stimulus is perceived by the guard cells as an opening signal, triggering a series of responses that result in opening of the stomatal pore.
The early aspects of this process are ion uptake and other metabolic changes in the guard cells, which will be discussed in detail in Chapter 18. Here we will note the effect of decreases in osmotic potential (Ys) resulting from ion uptake and from biosynthesis of organic molecules in the guard cells. Water relations in guard cells follow the same rules as in other cells. As Ys decreases, the water potential decreases and water consequently moves into the guard cells. As water enters the cell, turgor pressure increases. Because of the elastic properties of their walls, guard cells can reversibly increase their volume by 40 to 100%, depending on the species. Because of the differential thickening of guard cell walls, such changes in cell volume lead to opening or closing of the stomatal pore.
The Transpiration Ratio Measures the Relationship between Water Loss and Carbon Gain The effectiveness of plants in moderating water loss while allowing sufficient CO2 uptake for photosynthesis can be assessed by a parameter called the transpiration ratio. This value is defined as the amount of water transpired by the plant, divided by the amount of carbon dioxide assimilated by photosynthesis.
For typical plants in which the first stable product of carbon fixation is a three-carbon compound (such plants are called C3 plants; see Chapter 8), about 500 molecules of water are lost for every molecule of CO2 fixed by photo-synthesis, giving a transpiration ratio of 500. (Sometimes the reciprocal of the transpiration ratio, called the water use efficiency, is cited. Plants with a transpiration ratio of 500 have a water use efficiency of 1/500, or 0.002.) The large ratio of H2O efflux to CO2 influx results from three factors: 1. The concentration gradient driving water loss is about 50 times larger than that driving the influx of CO2. In large part, this difference is due to the low concentra-tion of CO2 in air (about 0.03%) and the relatively high concentration of water vapor within the leaf.
2. CO2 diffuses about 1.6 times more slowly through air than water does (the CO2 molecule is larger than H2O and has a smaller diffusion coefficient).
3. CO2 uptake must cross the plasma membrane, the cytoplasm, and the chloroplast envelope before it is assimilated in the chloroplast. These membranes add to the resistance of the CO2 diffusion pathway.
Some plants are adapted for life in particularly dry envi-ronments or seasons of the year. These plants, designated the C4 and CAM plants, utilize variations in the usual pho-tosynthetic pathway for fixation of carbon dioxide. Plants with C4 photosynthesis (in which a four-carbon compound is the first stable product of photosynthesis; see Chapter 8) generally transpire less water per molecule of CO2 fixed; a typical transpiration ratio for C4 plants is about 250. Desert-adapted plants with CAM (crassulacean acid metabolism) photosynthesis, in which CO2 is initially fixed into four-car-bon organic acids at night, have even lower transpiration ratios; values of about 50 are not unusual.
OVERVIEW: THE SOIL–PLANT–ATMOSPHERE CONTINUUM We have seen that movement of water from the soil through the plant to the atmosphere involves different mechanisms of transport: • In the soil and the xylem, water moves by bulk flow in response to a pressure gradient (∆Yp).
62 Chapter 4 Radially arranged cellulose microfibrils Radially arranged cellulose microfibrils Epidermal cells Guard cells Pore Guard cells (A) (B) Subsidiary cell Stomatal complex Epidermal cells Pore FIGURE 4.15 The radial alignment of the cellulose microfib-rils in guard cells and epidermal cells of (A) a kidney-shaped stoma and (B) a grasslike stoma. (From Meidner and Mansfield 1968.) • In the vapor phase, water moves primarily by diffu-sion, at least until it reaches the outside air, where convection (a form of bulk flow) becomes dominant.
• When water is transported across membranes, the driving force is the water potential difference across the membrane. Such osmotic flow occurs when cells absorb water and when roots transport water from the soil to the xylem.
In all of these situations, water moves toward regions of low water potential or free energy. This phenomenon is illustrated in Figure 4.16, which shows representative values for water potential and its components at various points along the water transport pathway.
Water potential decreases continuously from the soil to the leaves. However, the components of water potential can be quite different at different parts of the pathway. For example, inside the leaf cells, such as in the mesophyll, the water potential is approximately the same as in the neigh-boring xylem, yet the components of Yw are quite differ-ent. The dominant component of Yw in the xylem is the negative pressure (Yp), whereas in the leaf cell Yp is gen-erally positive. This large difference in Yp occurs across the plasma membrane of the leaf cells. Within the leaf cells, water potential is reduced by a high concentration of dis-solved solutes (low Ys).
SUMMARY Water is the essential medium of life. Land plants are faced with potentially lethal desiccation by water loss to the atmosphere. This problem is aggravated by the large sur-face area of leaves, their high radiant-energy gain, and their need to have an open pathway for CO2 uptake. Thus there is a conflict between the need for water conservation and the need for CO2 assimilation.
The need to resolve this vital conflict determines much of the structure of land plants: (1) an extensive root system Water Balance of Plants 63 Outside air (relative humidity = 50%) Leaf internal air space Cell wall of mesophyll (at 10 m) Vacuole of mesophyll (at 10 m) Leaf xylem (at 10 m) Root xylem (near surface) Root cell vacuole (near surface) Soil adjacent to root Soil 10 mm from root –95.2 –0.8 –0.8 –0.8 –0.8 –0.6 –0.6 –0.5 –0.3 –95.2 –0.8 –0.7 0.2 –0.8 –0.5 0.5 –0.4 –0.2 –0.2 –1.1 –0.1 –0.1 –1.1 –0.1 –0.1 0.1 0.1 0.1 0.0 0.0 0.0 0.0 Water potential (Yw) Location Water potential and its components (in MPa) Osmotic potential (Ys) Gravity (Yg) Pressure (Yp) 20 m Water potential in gas phase RT ln [RH] ( ( Vw FIGURE 4.16 Representative overview of water potential and its components at var-ious points in the transport pathway from the soil through the plant to the atmo-sphere. Water potential (Yw) can be measured through this continuum, but the components vary. In the liquid part of the pathway, pressure (Yp), osmotic potential (Ys), and gravity (Yg), determine Yw. In the air, only the relative humidity (RT/V – w × ln[RH]) is important. Note that although the water potential is the same in the vac-uole of the mesophyll cell and in the surrounding cell wall, the components of Yw can differ greatly (e.g., in this case Yp is 0.2 MPa inside the mesophyll cell and –0.7 MPa outside). (After Nobel 1999.) to extract water from the soil; (2) a low-resistance pathway through the xylem vessel elements and tracheids to bring water to the leaves; (3) a hydrophobic cuticle covering the surfaces of the plant to reduce evaporation; (4) microscopic stomata on the leaf surface to allow gas exchange; and (5) guard cells to regulate the diameter (and diffusional resis-tance) of the stomatal aperture.
The result is an organism that transports water from the soil to the atmosphere purely in response to physical forces.
No energy is expended directly by the plant to translocate water, although development and maintenance of the structures needed for efficient and controlled water trans-port require considerable energy input.
The mechanisms of water transport from the soil through the plant body to the atmosphere include diffu-sion, bulk flow, and osmosis. Each of these processes is cou-pled to different driving forces.
Water in the plant can be considered a continuous hydraulic system, connecting the water in the soil with the water vapor in the atmosphere. Transpiration is regulated principally by the guard cells, which regulate the stomatal pore size to meet the photosynthetic demand for CO2 uptake while minimizing water loss to the atmosphere.
Water evaporation from the cell walls of the leaf mesophyll cells generates large negative pressures (or tensions) in the apoplastic water. These negative pressures are transmitted to the xylem, and they pull water through the long xylem conduits.
Although aspects of the cohesion–tension theory of sap ascent are intermittently debated, an overwhelming body of evidence supports the idea that water transport in the xylem is driven by pressure gradients. When transpiration is high, negative pressures in the xylem water may cause cavitation (embolisms) in the xylem. Such embolisms can block water transport and lead to severe water deficits in the leaf. Water deficits are commonplace in plants, neces-sitating a host of adaptive responses that modify the phys-iology and development of plants.
Web Material Web Topics 4.1 Irrigation A discussion of some widely used irrigation methods and their impact on crop yield and soil salinity.
4.2 Soil Hydraulic Conductivity and Water Potential Soil hydraulic conductivity determines the ease with which water moves through the soil, and it is closely related to soil water potential.
4.3 Root Hydraulic Conductance A discussion of root hydraulic conductance and an example of its quantification.
4.4 Calculating Velocities of Water Movement in the Xylem and in Living Cells Calculations of velocities of water movement through the xylem, up a tree trunk, and across cell membranes in a tissue,and their implications for water transport mechanism.
4.5 Leaf Transpiration and Water Vapor Gradients An analysis of leaf transpiration and stomatal conductance,and their relationship with leaf and air water vapor concentrations.
Web Essays 4.1 A Brief History of the Study of Water Movement in the Xylem The history of our understanding of sap ascent in plants, especially in trees, is a beautiful example of how knowledge about plant is acquired.
4.2 The Cohesion–Tension Theory at Work A detailed discussion of the Cohesion–Tension theory on sap ascent in plants,and some alterna-tive explanations.
4.3 How Water Climbs to the Top of a 112-Meter-Tall Tree Measurements of photosynthesis and transpira-tion in 112-meter tall trees show that some of the conditions experienced by the top foliage com-pares to that of extreme deserts.
4.4 Cavitation and Refilling A possible mechanism for cavitation repair is under active investigation.
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Springer, Berlin. Water Balance of Plants 65 Mineral Nutrition 5 Chapter MINERAL NUTRIENTS ARE ELEMENTS acquired primarily in the form of inorganic ions from the soil. Although mineral nutrients continu-ally cycle through all organisms, they enter the biosphere predominantly through the root systems of plants, so in a sense plants act as the “miners” of Earth’s crust (Epstein 1999). The large surface area of roots and their ability to absorb inorganic ions at low concentrations from the soil solu-tion make mineral absorption by plants a very effective process. After being absorbed by the roots, the mineral elements are translocated to the various parts of the plant, where they are utilized in numerous biological functions. Other organisms, such as mycorrhizal fungi and nitrogen-fix-ing bacteria, often participate with roots in the acquisition of nutrients.
The study of how plants obtain and use mineral nutrients is called mineral nutrition. This area of research is central to modern agriculture and environmental protection. High agricultural yields depend strongly on fertilization with mineral nutrients. In fact, yields of most crop plants increase linearly with the amount of fertilizer that they absorb (Loomis and Conner 1992). To meet increased demand for food, world con-sumption of the primary fertilizer mineral elements—nitrogen, phos-phorus, and potassium—rose steadily from 112 million metric tons in 1980 to 143 million metric tons in 1990 and has remained constant through the last decade. Crop plants, however, typically use less than half of the fertilizer applied (Loomis and Conner 1992). The remaining minerals may leach into surface waters or groundwater, become attached to soil particles, or contribute to air pollution. As a consequence of fertilizer leaching, many water wells in the United States no longer meet federal standards for nitrate concentrations in drinking water (Nolan and Stoner 2000). On a brighter note, plants are the traditional means for recycling animal wastes and are proving useful for removing deleterious minerals from toxic-waste dumps (Macek et al. 2000). Because of the complex nature of plant–soil–atmosphere relationships, studies in the area of mineral nutrition involve atmospheric chemists, soil scientists, hydrologists, microbiologists, and ecologists, as well as plant physiologists.
68 Chapter 5 In this chapter we will discuss first the nutritional needs of plants, the symptoms of specific nutritional deficiencies, and the use of fertilizers to ensure proper plant nutrition.
Then we will examine how soil and root structure influence the transfer of inorganic nutrients from the environment into a plant. Finally, we will introduce the topic of mycor-rhizal associations. Chapters 6 and 12 address additional aspects of solute transport and nutrient assimilation, respectively.
ESSENTIAL NUTRIENTS, DEFICIENCIES, AND PLANT DISORDERS Only certain elements have been determined to be essen-tial for plant growth. An essential element is defined as one whose absence prevents a plant from completing its life cycle (Arnon and Stout 1939) or one that has a clear physiological role (Epstein 1999). If plants are given these essential elements, as well as energy from sunlight, they can synthesize all the compounds they need for normal growth. Table 5.1 lists the elements that are considered to be essential for most, if not all, higher plants. The first three elements—hydrogen, carbon, and oxygen—are not con-sidered mineral nutrients because they are obtained primarily from water or carbon dioxide.
Essential mineral elements are usually classified as macronutrients or micronutrients, according to their relative concentration in plant tissue. In some cases, the differ-ences in tissue content of macronu-trients and micronutrients are not as great as those indicated in Table 5.1. For example, some plant tis-sues, such as the leaf mesophyll, have almost as much iron or man-ganese as they do sulfur or magne-sium. Many elements often are pre-sent in concentrations greater than the plant’s minimum requirements.
Some researchers have argued that a classification into macro-nutrients and micronutrients is difficult to justify physiologically. Mengel and Kirkby (1987) have proposed that the essential ele-ments be classified instead accord-ing to their biochemical role and physiological function. Table 5.2 shows such a classification, in which plant nutrients have been divided into four basic groups: 1. The first group of essential ele-ments forms the organic (car-bon) compounds of the plant. Plants assimilate these nutrients via biochemical reactions involving oxida-tion and reduction.
2. The second group is important in energy storage reactions or in maintaining structural integrity.
Elements in this group are often present in plant tis-sues as phosphate, borate, and silicate esters in which the elemental group is bound to the hydroxyl group of an organic molecule (i.e., sugar–phosphate).
3. The third group is present in plant tissue as either free ions or ions bound to substances such as the pec-tic acids present in the plant cell wall. Of particular importance are their roles as enzyme cofactors and in the regulation of osmotic potentials.
4. The fourth group has important roles in reactions involving electron transfer.
Naturally occurring elements, other than those listed in Table 5.1, can also accumulate in plant tissues. For exam-ple, aluminum is not considered to be an essential element, but plants commonly contain from 0.1 to 500 ppm alu-minum, and addition of low levels of aluminum to a nutri-ent solution may stimulate plant growth (Marschner 1995).
TABLE 5.1 Adequate tissue levels of elements that may be required by plants Concentration Relative number of Chemical in dry matter atoms with respect Element symbol (% or ppm)a to molybdenum Obtained from water or carbon dioxide Hydrogen H 6 60,000,000 Carbon C 45 40,000,000 Oxygen O 45 30,000,000 Obtained from the soil Macronutrients Nitrogen N 1.5 1,000,000 Potassium K 1.0 250,000 Calcium Ca 0.5 125,000 Magnesium Mg 0.2 80,000 Phosphorus P 0.2 60,000 Sulfur S 0.1 30,000 Silicon Si 0.1 30,000 Micronutrients Chlorine Cl 100 3,000 Iron Fe 100 2,000 Boron B 20 2,000 Manganese Mn 50 1,000 Sodium Na 10 400 Zinc Zn 20 300 Copper Cu 6 100 Nickel Ni 0.1 2 Molybdenum Mo 0.1 1 Source: Epstein 1972, 1999.
a The values for the nonmineral elements (H, C, O) and the macronutrients are percentages.The values for micronutrients are expressed in parts per million.
Many species in the genera Astragalus, Xylorhiza, and Stan-leya accumulate selenium, although plants have not been shown to have a specific requirement for this element.
Cobalt is part of cobalamin (vitamin B12 and its deriva-tives), a component of several enzymes in nitrogen-fixing microorganisms. Thus cobalt deficiency blocks the devel-opment and function of nitrogen-fixing nodules. Nonethe-less, plants that do not fix nitrogen, as well as nitrogen-fix-ing plants that are supplied with ammonium or nitrate, do not require cobalt. Crop plants normally contain only rela-tively small amounts of nonessential elements.
Special Techniques Are Used in Nutritional Studies To demonstrate that an element is essential requires that plants be grown under experimental conditions in which only the element under investigation is absent. Such condi-tions are extremely difficult to achieve with plants grown in a complex medium such as soil. In the nineteenth century, several researchers, including Nicolas-Théodore de Saus-sure, Julius von Sachs, Jean-Baptiste-Joseph-Dieudonné Boussingault, and Wilhelm Knop, approached this problem by growing plants with their roots immersed in a nutrient solution containing only inorganic salts. Their demonstra-tion that plants could grow normally with no soil or organic matter proved unequivocally that plants can fulfill all their needs from only inorganic elements and sunlight.
The technique of growing plants with their roots immersed in nutrient solution without soil is called solu-tion culture or hydroponics (Gericke 1937). Successful hydroponic culture (Figure 5.1A) requires a large volume of nutrient solution or frequent adjustment of the nutrient solution to prevent nutrient uptake by roots from produc-ing radical changes in nutrient concentrations and pH of the medium. A sufficient supply of oxygen to the root sys-Mineral Nutrition 69 TABLE 5.2 Classification of plant mineral nutrients according to biochemical function Mineral nutrient Functions Group 1 Nutrients that are part of carbon compounds N Constituent of amino acids, amides, proteins, nucleic acids, nucleotides, coenzymes, hexoamines, etc.
S Component of cysteine, cystine, methionine, and proteins. Constituent of lipoic acid, coenzyme A, thiamine pyrophosphate, glutathione, biotin, adenosine-5′-phosphosulfate, and 3-phosphoadenosine.
Group 2 Nutrients that are important in energy storage or structural integrity P Component of sugar phosphates, nucleic acids, nucleotides, coenzymes, phospholipids, phytic acid, etc. Has a key role in reactions that involve ATP.
Si Deposited as amorphous silica in cell walls. Contributes to cell wall mechanical properties, including rigidity and elasticity.
B Complexes with mannitol, mannan, polymannuronic acid, and other constituents of cell walls. Involved in cell elongation and nucleic acid metabolism.
Group 3 Nutrients that remain in ionic form K Required as a cofactor for more than 40 enzymes. Principal cation in establishing cell turgor and maintaining cell electroneutrality.
Ca Constituent of the middle lamella of cell walls. Required as a cofactor by some enzymes involved in the hydrolysis of ATP and phospholipids. Acts as a second messenger in metabolic regulation.
Mg Required by many enzymes involved in phosphate transfer. Constituent of the chlorophyll molecule.
Cl Required for the photosynthetic reactions involved in O2 evolution.
Mn Required for activity of some dehydrogenases, decarboxylases, kinases, oxidases, and peroxidases. Involved with other cation-activated enzymes and photosynthetic O2 evolution.
Na Involved with the regeneration of phosphoenolpyruvate in C4 and CAM plants. Substitutes for potassium in some functions.
Group 4 Nutrients that are involved in redox reactions Fe Constituent of cytochromes and nonheme iron proteins involved in photosynthesis, N2 fixation, and respiration.
Zn Constituent of alcohol dehydrogenase, glutamic dehydrogenase, carbonic anhydrase, etc.
Cu Component of ascorbic acid oxidase, tyrosinase, monoamine oxidase, uricase, cytochrome oxidase, phenolase, laccase, and plastocyanin.
Ni Constituent of urease. In N2-fixing bacteria, constituent of hydrogenases.
Mo Constituent of nitrogenase, nitrate reductase, and xanthine dehydrogenase.
Source: After Evans and Sorger 1966 and Mengel and Kirkby 1987.
tem—also critical—may be achieved by vigorous bubbling of air through the medium. Hydroponics is used in the commercial production of many greenhouse crops. In one form of commercial hydro-ponic culture, plants are grown in a supporting material such as sand, gravel, vermiculite, or expanded clay (i.e., kitty litter). Nutrient solu-tions are then flushed through the supporting material, and old solu-tions are removed by leaching. In another form of hydroponic culture, plant roots lie on the surface of a trough, and nutrient solutions flow in a thin layer along the trough over the roots (Cooper 1979, Asher and Edwards 1983). This nutrient film growth system ensures that the roots receive an ample supply of oxygen (Figure 5.1B).
Another alternative, which has sometimes been heralded as the medium of the future, is to grow the plants aeroponically (Weathers and Zobel 1992). In this technique, plants are grown with their roots sus-pended in air while being sprayed continuously with a nutrient solu-tion (Figure 5.1C). This approach provides easy manipulation of the gaseous environment around the root, but it requires higher levels of nutrients than hydroponic culture does to sustain rapid plant growth.
For this reason and other technical difficulties, the use of aeroponics is not widespread.
Nutrient Solutions Can Sustain Rapid Plant Growth Over the years, many formulations have been used for nutrient solu-tions. Early formulations developed by Knop in Germany included only KNO3, Ca(NO3)2, KH2PO4, MgSO4, and an iron salt. At the time this nutrient solution was believed to contain all the minerals required by the plant, but these experiments were carried out with chemicals that were contaminated with other ele-ments that are now known to be essential (such as boron or molyb-denum). Table 5.3 shows a more modern formulation for a nutrient solution. This formulation is called a modified Hoagland solution, named after Dennis R. Hoagland, a researcher who was prominent in the development of modern mineral nutri-tion research in the United States.
70 Chapter 5 Nutrient recovery chamber Pump Air Air bubbles Plant support system Nutrient solution Nutrient solution Plant holdings cover seals chamber Motor-driven rotor generates mist Nutrient solution Nutrient mist chamber (A) Hydroponic growth system (B) Nutrient film growth system (C) Aeroponic growth system FIGURE 5.1 Hydroponic and aeroponic systems for growing plants in nutrient solu-tions in which composition and pH can be automatically controlled. (A) In a hydro-ponic system, the roots are immersed in the nutrient solution, and air is bubbled through the solution. (B) An alternative hydroponic system, often used in commer-cial production, is the nutrient film growth system, in which the nutrient solution is pumped as a thin film down a shallow trough surrounding the plant roots. In this system the composition and pH of the nutrient solution can be controlled automati-cally. (C) In the aeroponic system, the roots are suspended over the nutrient solu-tion, which is whipped into a mist by a motor-driven rotor. (C after Weathers and Zobel 1992.) A modified Hoagland solution contains all of the known mineral elements needed for rapid plant growth. The con-centrations of these elements are set at the highest possible levels without producing toxicity symptoms or salinity stress and thus may be several orders of magnitude higher than those found in the soil around plant roots. For example, whereas phosphorus is present in the soil solution at con-centrations normally less than 0.06 ppm, here it is offered at 62 ppm (Epstein 1972). Such high initial levels permit plants to be grown in a medium for extended periods without replenishment of the nutrients. Many researchers, however, dilute their nutrient solutions severalfold and replenish them frequently to minimize fluctuations of nutrient concentra-tion in the medium and in plant tissue.
Another important property of the modified Hoagland formulation is that nitrogen is supplied as both ammonium (NH4 +) and nitrate (NO3 –). Supplying nitrogen in a balanced mixture of cations and anions tends to reduce the rapid rise in the pH of the medium that is commonly observed when the nitrogen is supplied solely as nitrate anion (Asher and Edwards 1983). Even when the pH of the medium is kept neutral, most plants grow better if they have access to both NH4 + and NO3 – because absorption and assimilation of the two nitrogen forms promotes cation–anion balance within the plant (Raven and Smith 1976; Bloom 1994).
A significant problem with nutrient solutions is main-taining the availability of iron. When supplied as an inor-ganic salt such as FeSO4 or Fe(NO3)2, iron can precipitate out of solution as iron hydroxide. If phosphate salts are present, insoluble iron phosphate will also form. Precipi-tation of the iron out of solution makes it physically unavailable to the plant, unless iron salts are added at fre-quent intervals. Earlier researchers approached this prob-lem by adding iron together with citric acid or tartaric acid.
Compounds such as these are called chelators because they form soluble complexes with cations such as iron and cal-Mineral Nutrition 71 TABLE 5.3 Composition of a modified Hoagland nutrient solution for growing plants Concentration Concentration Volume of stock Final Molecular of stock of stock solution per liter concentration Compound weight solution solution of final solution Element of element g mol–1 mM g L–1 mL mM ppm Macronutrients KNO3 101.10 1,000 101.10 6.0 N 16,000 224 Ca(NO3)2⋅4H2O 236.16 1,000 236.16 4.0 K 6,000 235 NH4H2PO4 115.08 1,000 115.08 2.0 Ca 4,000 160 MgSO4⋅7H2O 246.48 1,000 246.49 1.0 P 2,000 62 S 1,000 32 Mg 1,000 24 Micronutrients KCl 74.55 25 1.864 Cl 50 1.77 H3BO3 61.83 12.5 0.773 B 25 0.27 MnSO4⋅H2O 169.01 1.0 0.169 Mn 2.0 0.11 ZnSO4⋅7H2O 287.54 1.0 0.288 2.0 Zn 2.0 0.13 CuSO4⋅5H2O 249.68 0.25 0.062 Cu 0.5 0.03 H2MoO4 (85% MoO3) 161.97 0.25 0.040 Mo 0.5 0.05 NaFeDTPA (10% Fe) 468.20 64 30.0 0.3–1.0 Fe 16.1–53.7 1.00–3.00 Optionala NiSO4⋅6H2O 262.86 0.25 0.066 2.0 Ni 0.5 0.03 Na2SiO3⋅9H2O 284.20 1,000 284.20 1.0 Si 1,000 28 Source: After Epstein 1972.
Note:The macronutrients are added separately from stock solutions to prevent precipitation during preparation of the nutrient solution. A com-bined stock solution is made up containing all micronutrients except iron. Iron is added as sodium ferric diethylenetriaminepentaacetate (NaFeDTPA, trade name Ciba-Geigy Sequestrene 330 Fe; see Figure 5.2); some plants, such as maize, require the higher level of iron shown in the table.
aNickel is usually present as a contaminant of the other chemicals, so it may not need to be added explicitly. Silicon, if included, should be added first and the pH adjusted with HCl to prevent precipitation of the other nutrients.
cium in which the cation is held by ionic forces, rather than by covalent bonds. Chelated cations thus are physically more available to a plant.
More modern nutrient solutions use the chemicals eth-ylenediaminetetraacetic acid (EDTA) or diethylenetri-aminepentaacetic acid (DTPA, or pentetic acid) as chelat-ing agents (Sievers and Bailar 1962). Figure 5.2 shows the structure of DTPA. The fate of the chelation complex dur-ing iron uptake by the root cells is not clear; iron may be released from the chelator when it is reduced from Fe3+ to Fe2+ at the root surface. The chelator may then diffuse back into the nutrient (or soil) solution and react with another Fe3+ ion or other metal ions. After uptake, iron is kept sol-uble by chelation with organic compounds present in plant cells. Citric acid may play a major role in iron chelation and its long-distance transport in the xylem.
Mineral Deficiencies Disrupt Plant Metabolism and Function Inadequate supply of an essential element results in a nutritional disorder manifested by characteristic deficiency symptoms. In hydroponic culture, withholding of an essen-tial element can be readily correlated with a given set of symptoms for acute deficiencies. Diagnosis of soil-grown plants can be more complex, for the following reasons: • Both chronic and acute deficiencies of several ele-ments may occur simultaneously.
• Deficiencies or excessive amounts of one element may induce deficiencies or excessive accumulations of another.
• Some virus-induced plant diseases may produce symptoms similar to those of nutrient deficiencies.
Nutrient deficiency symptoms in a plant are the expres-sion of metabolic disorders resulting from the insufficient supply of an essential element. These disorders are related to the roles played by essential elements in normal plant metabolism and function. Table 5.2 lists some of the roles of essential elements.
Even though each essential element participates in many different metabolic reactions, some general statements about the functions of essential elements in plant metabo-lism are possible. In general, the essential elements function in plant structure, metabolic function, and osmoregulation of plant cells. More specific roles may be related to the abil-ity of divalent cations such as calcium or magnesium to modify the permeability of plant membranes. In addition, research continues to reveal specific roles of these elements in plant metabolism; for example, calcium acts as a signal to regulate key enzymes in the cytosol (Hepler and Wayne 1985; Sanders et al. 1999). Thus, most essential elements have multiple roles in plant metabolism.
When relating acute deficiency symptoms to a particu-lar essential element, an important clue is the extent to which an element can be recycled from older to younger leaves. Some elements, such as nitrogen, phosphorus, and potassium, can readily move from leaf to leaf; others, such as boron, iron, and calcium, are relatively immobile in most plant species (Table 5.4). If an essential element is mobile, deficiency symptoms tend to appear first in older leaves.
Deficiency of an immobile essential element will become evident first in younger leaves. Although the precise mech-anisms of nutrient mobilization are not well understood, 72 Chapter 5 –O C O CH2 CH2 NCH2CH2NCH2CH2N O– C O CH2 O– C CH2 O– C –O C O CH2 O O –O O– C O CH2 N N C CH2 O O– C O CH2CH2 N CH2CH2 CH2 Fe3+ CH2 CH2 C C O– O– O O (A) (B) FIGURE 5.2 Chemical structure of the chelator DTPA by itself (A) and chelated to an Fe3+ ion (B). Iron binds to DTPA through interaction with three nitrogen atoms and the three ionized oxygen atoms of the carboxylate groups (Sievers and Bailar 1962). The resulting ring structure clamps the metallic ion and effectively neutralizes its reac-tivity in solution. During the uptake of iron at the root sur-face, Fe3+ appears to be reduced to Fe2+, which is released from the DTPA–iron complex. The chelator can then bind to other available Fe3+ ions.
TABLE 5.4 Mineral elements classified on the basis of their mobility within a plant and their tendency to retranslocate during deficiencies Mobile Immobile Nitrogen Calcium Potassium Sulfur Magnesium Iron Phosphorus Boron Chlorine Copper Sodium Zinc Molybdenum Note: Elements are listed in the order of their abundance in the plant.
plant hormones such as cytokinins appear to be involved (see Chapter 21). In the discussion that follows, we will describe the specific deficiency symptoms and functional roles for the mineral essential elements as they are grouped in Table 5.2.
Group 1: Deficiencies in mineral nutrients that are part of carbon compounds.
This first group consists of nitro-gen and sulfur. Nitrogen availability in soils limits plant productivity in most natural and agricultural ecosystems.
By contrast, soils generally contain sulfur in excess.
Nonetheless, nitrogen and sulfur share the property that their oxidation–reduction states range widely (see Chapter 12). Some of the most energy-intensive reactions in life con-vert the highly oxidized, inorganic forms absorbed from the soil into the highly reduced forms found in organic compounds such as amino acids.
NITROGEN. Nitrogen is the mineral element that plants require in greatest amounts. It serves as a constituent of many plant cell components, including amino acids and nucleic acids. Therefore, nitrogen deficiency rapidly inhibits plant growth. If such a deficiency persists, most species show chlorosis (yellowing of the leaves), especially in the older leaves near the base of the plant (for pictures of nitro-gen deficiency and the other mineral deficiencies described in this chapter, see Web Topic 5.1). Under severe nitrogen deficiency, these leaves become completely yellow (or tan) and fall off the plant. Younger leaves may not show these symptoms initially because nitrogen can be mobilized from older leaves. Thus a nitrogen-deficient plant may have light green upper leaves and yellow or tan lower leaves. When nitrogen deficiency develops slowly, plants may have markedly slender and often woody stems. This wood-iness may be due to a buildup of excess carbohydrates that cannot be used in the synthesis of amino acids or other nitrogen compounds. Carbohydrates not used in nitrogen metabolism may also be used in anthocyanin synthesis, leading to accumulation of that pigment. This condition is revealed as a purple coloration in leaves, petioles, and stems of some nitrogen-deficient plants, such as tomato and certain varieties of corn.
SULFUR. Sulfur is found in two amino acids and is a con-stituent of several coenzymes and vitamins essential for metabolism. Many of the symptoms of sulfur deficiency are similar to those of nitrogen deficiency, including chlorosis, stunting of growth, and anthocyanin accumulation. This similarity is not surprising, since sulfur and nitrogen are both constituents of proteins. However, the chlorosis caused by sulfur deficiency generally arises initially in mature and young leaves, rather than in the old leaves as in nitrogen deficiency, because unlike nitrogen, sulfur is not easily remobilized to the younger leaves in most species.
Nonetheless, in many plant species sulfur chlorosis may occur simultaneously in all leaves or even initially in the older leaves.
Group 2: Deficiencies in mineral nutrients that are impor-tant in energy storage or structural integrity.
This group consists of phosphorus, silicon, and boron. Phosphorus and silicon are found at concentrations within plant tissue that warrant their classification as macronutrients, whereas boron is much less abundant and considered a micronutri-ent. These elements are usually present in plants as ester linkages to a carbon molecule.
PHOSPHORUS. Phosphorus (as phosphate, PO4 3–) is an inte-gral component of important compounds of plant cells, including the sugar–phosphate intermediates of respiration and photosynthesis, and the phospholipids that make up plant membranes. It is also a component of nucleotides used in plant energy metabolism (such as ATP) and in DNA and RNA. Characteristic symptoms of phosphorus deficiency include stunted growth in young plants and a dark green coloration of the leaves, which may be mal-formed and contain small spots of dead tissue called necrotic spots (for a picture, see Web Topic 5.1).
As in nitrogen deficiency, some species may produce excess anthocyanins, giving the leaves a slight purple col-oration. In contrast to nitrogen deficiency, the purple col-oration of phosphorus deficiency is not associated with chlorosis. In fact, the leaves may be a dark greenish purple.
Additional symptoms of phosphorus deficiency include the production of slender (but not woody) stems and the death of older leaves. Maturation of the plant may also be delayed.
SILICON. Only members of the family Equisetaceae—called scouring rushes because at one time their ash, rich in gritty silica, was used to scour pots—require silicon to complete their life cycle. Nonetheless, many other species accumu-late substantial amounts of silicon within their tissues and show enhanced growth and fertility when supplied with adequate amounts of silicon (Epstein 1999). Plants deficient in silicon are more susceptible to lodg-ing (falling over) and fungal infection. Silicon is deposited primarily in the endoplasmic reticulum, cell walls, and intercellular spaces as hydrated, amorphous silica (SiO2·nH2O). It also forms complexes with polyphenols and thus serves as an alternative to lignin in the reinforcement of cell walls. In addition, silicon can ameliorate the toxicity of many heavy metals.
BORON. Although the precise function of boron in plant metabolism is unclear, evidence suggests that it plays roles in cell elongation, nucleic acid synthesis, hormone responses, and membrane function (Shelp 1993). Boron-deficient plants may exhibit a wide variety of symptoms, depending on the species and the age of the plant. Mineral Nutrition 73 A characteristic symptom is black necrosis of the young leaves and terminal buds. The necrosis of the young leaves occurs primarily at the base of the leaf blade. Stems may be unusually stiff and brittle. Apical dominance may also be lost, causing the plant to become highly branched; how-ever, the terminal apices of the branches soon become necrotic because of inhibition of cell division. Structures such as the fruit, fleshy roots, and tubers may exhibit necro-sis or abnormalities related to the breakdown of internal tissues.
Group 3: Deficiencies in mineral nutrients that remain in ionic form.
This group includes some of the most familiar mineral elements: The macronutrients potassium, calcium, and magnesium, and the micronutrients chlorine, manganese, and sodium. They may be found in solution in the cytosol or vacuoles, or they may be bound electrostati-cally or as ligands to larger carbon-containing compounds.
POTASSIUM. Potassium, present within plants as the cation K+, plays an important role in regulation of the osmotic potential of plant cells (see Chapters 3 and 6). It also acti-vates many enzymes involved in respiration and photo-synthesis. The first observable symptom of potassium defi-ciency is mottled or marginal chlorosis, which then develops into necrosis primarily at the leaf tips, at the mar-gins, and between veins. In many monocots, these necrotic lesions may initially form at the leaf tips and margins and then extend toward the leaf base. Because potassium can be mobilized to the younger leaves, these symptoms appear initially on the more mature leaves toward the base of the plant. The leaves may also curl and crinkle. The stems of potassium-deficient plants may be slender and weak, with abnormally short internodal regions. In potassium-deficient corn, the roots may have an increased susceptibility to root-rotting fungi present in the soil, and this susceptibility, together with effects on the stem, results in an increased tendency for the plant to be easily bent to the ground (lodging).
CALCIUM. Calcium ions (Ca2+) are used in the synthesis of new cell walls, particularly the middle lamellae that sepa-rate newly divided cells. Calcium is also used in the mitotic spindle during cell division. It is required for the normal functioning of plant membranes and has been implicated as a second messenger for various plant responses to both environmental and hormonal signals (Sanders et al. 1999).
In its function as a second messenger, calcium may bind to calmodulin, a protein found in the cytosol of plant cells.
The calmodulin–calcium complex regulates many meta-bolic processes. Characteristic symptoms of calcium deficiency include necrosis of young meristematic regions, such as the tips of roots or young leaves, where cell division and wall forma-tion are most rapid. Necrosis in slowly growing plants may be preceded by a general chlorosis and downward hook-ing of the young leaves. Young leaves may also appear deformed. The root system of a calcium-deficient plant may appear brownish, short, and highly branched. Severe stunting may result if the meristematic regions of the plant die prematurely.
MAGNESIUM. In plant cells, magnesium ions (Mg2+) have a specific role in the activation of enzymes involved in respi-ration, photosynthesis, and the synthesis of DNA and RNA.
Magnesium is also a part of the ring structure of the chloro-phyll molecule (see Figure 7.6A). A characteristic symptom of magnesium deficiency is chlorosis between the leaf veins, occurring first in the older leaves because of the mobility of this element. This pattern of chlorosis results because the chlorophyll in the vascular bundles remains unaffected for longer periods than the chlorophyll in the cells between the bundles does. If the deficiency is extensive, the leaves may become yellow or white. An additional symptom of mag-nesium deficiency may be premature leaf abscission.
CHLORINE. The element chlorine is found in plants as the chloride ion (Cl–). It is required for the water-splitting reac-tion of photosynthesis through which oxygen is produced (see Chapter 7) (Clarke and Eaton-Rye 2000). In addition, chlorine may be required for cell division in both leaves and roots (Harling et al. 1997). Plants deficient in chlorine develop wilting of the leaf tips followed by general leaf chlorosis and necrosis. The leaves may also exhibit reduced growth. Eventually, the leaves may take on a bronzelike color (“bronzing”). Roots of chlorine-deficient plants may appear stunted and thickened near the root tips. Chloride ions are very soluble and generally available in soils because seawater is swept into the air by wind and is delivered to soil when it rains. Therefore, chlorine defi-ciency is unknown in plants grown in native or agricultural habitats. Most plants generally absorb chlorine at levels much higher than those required for normal functioning.
MANGANESE. Manganese ions (Mn2+) activate several enzymes in plant cells. In particular, decarboxylases and dehydrogenases involved in the tricarboxylic acid (Krebs) cycle are specifically activated by manganese. The best-defined function of manganese is in the photosynthetic reaction through which oxygen is produced from water (Marschner 1995). The major symptom of manganese defi-ciency is intervenous chlorosis associated with the devel-opment of small necrotic spots. This chlorosis may occur on younger or older leaves, depending on plant species and growth rate.
SODIUM. Most species utilizing the C4 and CAM pathways of carbon fixation (see Chapter 8) require sodium ions (Na+). In these plants, sodium appears vital for regenerat-ing phosphoenolpyruvate, the substrate for the first car-74 Chapter 5 boxylation in the C4 and CAM pathways (Johnstone et al.
1988). Under sodium deficiency, these plants exhibit chloro-sis and necrosis, or even fail to form flowers. Many C3 species also benefit from exposure to low levels of sodium ions. Sodium stimulates growth through enhanced cell expansion, and it can partly substitute for potassium as an osmotically active solute.
Group 4: Deficiencies in mineral nutrients that are involved in redox reactions.
This group of five micronu-trients includes the metals iron, zinc, copper, nickel, and molybdenum. All of these can undergo reversible oxidations and reductions (e.g., Fe2+ ~ Fe3+) and have important roles in electron transfer and energy transformation. They are usu-ally found in association with larger molecules such as cytochromes, chlorophyll, and proteins (usually enzymes).
IRON. Iron has an important role as a component of enzymes involved in the transfer of electrons (redox reac-tions), such as cytochromes. In this role, it is reversibly oxi-dized from Fe2+ to Fe3+ during electron transfer. As in mag-nesium deficiency, a characteristic symptom of iron deficiency is intervenous chlorosis. In contrast to magne-sium deficiency symptoms, these symptoms appear ini-tially on the younger leaves because iron cannot be readily mobilized from older leaves. Under conditions of extreme or prolonged deficiency, the veins may also become chlorotic, causing the whole leaf to turn white. The leaves become chlorotic because iron is required for the synthesis of some of the chlorophyll–protein complexes in the chloroplast. The low mobility of iron is probably due to its precipitation in the older leaves as insoluble oxides or phosphates or to the formation of complexes with phyto-ferritin, an iron-binding protein found in the leaf and other plant parts (Oh et al. 1996). The precipitation of iron dimin-ishes subsequent mobilization of the metal into the phloem for long-distance translocation.
ZINC. Many enzymes require zinc ions (Zn2+) for their activity, and zinc may be required for chlorophyll biosyn-thesis in some plants. Zinc deficiency is characterized by a reduction in internodal growth, and as a result plants dis-play a rosette habit of growth in which the leaves form a circular cluster radiating at or close to the ground. The leaves may also be small and distorted, with leaf margins having a puckered appearance. These symptoms may result from loss of the capacity to produce sufficient amounts of the auxin indoleacetic acid. In some species (corn, sorghum, beans), the older leaves may become inter-venously chlorotic and then develop white necrotic spots.
This chlorosis may be an expression of a zinc requirement for chlorophyll biosynthesis.
COPPER. Like iron, copper is associated with enzymes involved in redox reactions being reversibly oxidized from Cu+ to Cu2+. An example of such an enzyme is plasto-cyanin, which is involved in electron transfer during the light reactions of photosynthesis (Haehnel 1984). The ini-tial symptom of copper deficiency is the production of dark green leaves, which may contain necrotic spots. The necrotic spots appear first at the tips of the young leaves and then extend toward the leaf base along the margins.
The leaves may also be twisted or malformed. Under extreme copper deficiency, leaves may abscise prematurely.
NICKEL. Urease is the only known nickel-containing enzyme in higher plants, although nitrogen-fixing microor-ganisms require nickel for the enzyme that reprocesses some of the hydrogen gas generated during fixation (hydrogen uptake hydrogenase) (see Chapter 12). Nickel-deficient plants accumulate urea in their leaves and, con-sequently, show leaf tip necrosis. Plants grown in soil sel-dom, if ever, show signs of nickel deficiency because the amounts of nickel required are minuscule.
MOLYBDENUM. Molybdenum ions (Mo4+ through Mo6+) are components of several enzymes, including nitrate reductase and nitrogenase. Nitrate reductase catalyzes the reduction of nitrate to nitrite during its assimilation by the plant cell; nitrogenase converts nitrogen gas to ammonia in nitrogen-fixing microorganisms (see Chapter 12). The first indication of a molybdenum deficiency is general chloro-sis between veins and necrosis of the older leaves. In some plants, such as cauliflower or broccoli, the leaves may not become necrotic but instead may appear twisted and sub-sequently die (whiptail disease). Flower formation may be prevented, or the flowers may abscise prematurely. Because molybdenum is involved with both nitrate assimilation and nitrogen fixation, a molybdenum defi-ciency may bring about a nitrogen deficiency if the nitrogen source is primarily nitrate or if the plant depends on sym-biotic nitrogen fixation. Although plants require only small amounts of molybdenum, some soils supply inadequate levels. Small additions of molybdenum to such soils can greatly enhance crop or forage growth at negligible cost.
Analysis of Plant Tissues Reveals Mineral Deficiencies Requirements for mineral elements change during the growth and development of a plant. In crop plants, nutri-ent levels at certain stages of growth influence the yield of the economically important tissues (tuber, grain, and so on). To optimize yields, farmers use analyses of nutrient levels in soil and in plant tissue to determine fertilizer schedules.
Soil analysis is the chemical determination of the nutri-ent content in a soil sample from the root zone. As dis-cussed later in the chapter, both the chemistry and the biol-ogy of soils are complex, and the results of soil analyses vary with sampling methods, storage conditions for the Mineral Nutrition 75 samples, and nutrient extraction techniques. Perhaps more important is that a particular soil analysis reflects the lev-els of nutrients potentially available to the plant roots from the soil, but soil analysis does not tell us how much of a particular mineral nutrient the plant actually needs or is able to absorb. This additional information is best deter-mined by plant tissue analysis.
Proper use of plant tissue analysis requires an under-standing of the relationship between plant growth (or yield) and the mineral concentration of plant tissue sam-ples (Bouma 1983). As the data plot in Figure 5.3 shows, when the nutrient concentration in a tissue sample is low, growth is reduced. In this deficiency zone of the curve, an increase in nutrient availability is directly related to an increase in growth or yield. As the nutrient availability con-tinues to increase, a point is reached at which further addi-tion of nutrients is no longer related to increases in growth or yield but is reflected in increased tissue concentrations.
This region of the curve is often called the adequate zone.
The transition between the deficiency and adequate zones of the curve reveals the critical concentration of the nutrient (see Figure 5.3), which may be defined as the min-imum tissue content of the nutrient that is correlated with maximal growth or yield. As the nutrient concentration of the tissue increases beyond the adequate zone, growth or yield declines because of toxicity (this is the toxic zone).
To evaluate the relationship between growth and tissue nutrient concentration, researchers grow plants in soil or nutrient solution in which all the nutrients are present in adequate amounts except the nutrient under consideration.
At the start of the experiment, the limiting nutrient is added in increasing concentrations to different sets of plants, and the concentrations of the nutrient in specific tis-sues are correlated with a particular measure of growth or yield. Several curves are established for each element, one for each tissue and tissue age. Because agricultural soils are often limited in the ele-ments nitrogen, phosphorus, and potassium, many farm-ers routinely use, at a minimum, curves for these elements.
If a nutrient deficiency is suspected, steps are taken to cor-rect the deficiency before it reduces growth or yield. Plant analysis has proven useful in establishing fertilizer sched-ules that sustain yields and ensure the food quality of many crops.
TREATING NUTRITIONAL DEFICIENCIES Many traditional and subsistence farming practices pro-mote the recycling of mineral elements. Crop plants absorb the nutrients from the soil, humans and animals consume locally grown crops, and crop residues and manure from humans and animals return the nutrients to the soil. The main losses of nutrients from such agricultural systems ensue from leaching that carries dissolved ions away with drainage water. In acid soils, leaching may be decreased by the addition of lime—a mix of CaO, CaCO3, and Ca(OH)2—to make the soil more alkaline because many mineral elements form less soluble compounds when the pH is higher than 6 (Figure 5.4).
In the high-production agricultural systems of industrial countries, the unidirectional removal of nutrients from the soil to the crop can become significant because a large por-tion of crop biomass leaves the area of cultivation. Plants synthesize all their components from basic inorganic sub-stances and sunlight, so it is important to restore these lost nutrients to the soil through the addition of fertilizers.
Crop Yields Can Be Improved by Addition of Fertilizers Most chemical fertilizers contain inorganic salts of the macronutrients nitrogen, phosphorus, and potassium (see Table 5.1). Fertilizers that contain only one of these three nutrients are termed straight fertilizers. Some examples of straight fertilizers are superphosphate, ammonium nitrate, and muriate of potash (a source of potassium). Fertilizers that contain two or more mineral nutrients are called com-pound fertilizers or mixed fertilizers, and the numbers on the package label, such as 10-14-10, refer to the effective per-centages of N, P2O5, and K2O, respectively, in the fertilizer.
With long-term agricultural production, consumption of micronutrients can reach a point at which they, too, must be added to the soil as fertilizers. Adding micronutrients to the soil may also be necessary to correct a preexisting defi-ciency. For example, some soils in the United States are 76 Chapter 5 Critical concentration Concentration of nutrient in tissue (mmol/g dry weight) Growth or yield (percent of maximum) Deficiency zone Toxic zone 100 50 0 Adequate zone FIGURE 5.3 Relationship between yield (or growth) and the nutrient content of the plant tissue. The yield parameter may be expressed in terms of shoot dry weight or height.
Three zones—deficiency, adequate, and toxic—are indi-cated on the graph. To yield data of this type, plants are grown under conditions in which the concentration of one essential nutrient is varied while all others are in adequate supply. The effect of varying the concentration of this nutri-ent during plant growth is reflected in the growth or yield.
The critical concentration for that nutrient is the concentra-tion below which yield or growth is reduced. deficient in boron, copper, zinc, manganese, molybdenum, or iron (Mengel and Kirkby 1987) and can benefit from nutrient supplementation.
Chemicals may also be applied to the soil to modify soil pH. As Figure 5.4 shows, soil pH affects the availability of all mineral nutrients. Addition of lime, as mentioned previ-ously, can raise the pH of acidic soils; addition of elemental sulfur can lower the pH of alkaline soils. In the latter case, microorganisms absorb the sulfur and subsequently release sulfate and hydrogen ions that acidify the soil.
Organic fertilizers, in contrast to chemical fertilizers, originate from the residues of plant or animal life or from natural rock deposits. Plant and animal residues contain many of the nutrient elements in the form of organic com-pounds. Before crop plants can acquire the nutrient ele-ments from these residues, the organic compounds must be broken down, usually by the action of soil microorgan-isms through a process called mineralization. Mineraliza-tion depends on many factors, including temperature, water and oxygen availability, and the type and number of microorganisms present in the soil.
As a consequence, the rate of mineralization is highly variable, and nutrients from organic residues become avail-able to plants over periods that range from days to months to years. The slow rate of mineralization hinders efficient fertilizer use, so farms that rely solely on organic fertilizers may require the addition of substantially more nitrogen or phosphorus and suffer even higher nutrient losses than farms that use chemical fertilizers. Residues from organic fertilizers do improve the physical structure of most soils, enhancing water retention during drought and increasing drainage in wet weather.
Some Mineral Nutrients Can Be Absorbed by Leaves In addition to nutrients being added to the soil as fertiliz-ers, some mineral nutrients can be applied to the leaves as sprays, in a process known as foliar application, and the leaves can absorb the applied nutrients. In some cases, this method can have agronomic advantages over the applica-tion of nutrients to the soil. Foliar application can reduce the lag time between application and uptake by the plant, which could be important during a phase of rapid growth.
It can also circumvent the problem of restricted uptake of a nutrient from the soil. For example, foliar application of mineral nutrients such as iron, manganese, and copper may be more efficient than application through the soil, where they are adsorbed on soil particles and hence are less available to the root system.
Nutrient uptake by plant leaves is most effective when the nutrient solution remains on the leaf as a thin film (Mengel and Kirkby 1987). Production of a thin film often requires that the nutrient solutions be supplemented with surfactant chemicals, such as the detergent Tween 80, that reduce surface tension. Nutrient movement into the plant seems to involve diffusion through the cuticle and uptake by leaf cells. Although uptake through the stomatal pore could provide a pathway into the leaf, the architecture of the pore (see Figures 4.13 and 4.14) largely prevents liquid penetration (Ziegler 1987).
For foliar nutrient application to be successful, damage to the leaves must be minimized. If foliar sprays are applied on a hot day, when evaporation is high, salts may accumulate on the leaf surface and cause burning or scorching. Spraying on cool days or in the evening helps to alleviate this problem. Addition of lime to the spray dimin-ishes the solubility of many nutrients and limits toxicity.
Foliar application has proved economically successful mainly with tree crops and vines such as grapes, but it is also used with cereals. Nutrients applied to the leaves could save an orchard or vineyard when soil-applied nutri-ents would be too slow to correct a deficiency. In wheat, nitrogen applied to the leaves during the later stages of growth enhances the protein content of seeds.
Mineral Nutrition 77 Nitrogen Phosphorus Potassium Sulfur Calcium Magnesium Iron Manganese Boron Copper Zinc Molybdenum 4.0 4.5 5.0 5.5 6.0 6.5 pH Neutral Acid Alkaline 7.0 7.5 8.0 8.5 9.0 FIGURE 5.4 Influence of soil pH on the availability of nutri-ent elements in organic soils. The width of the shaded areas indicates the degree of nutrient availability to the plant root. All of these nutrients are available in the pH range of 5.5 to 6.5. (From Lucas and Davis 1961.) SOIL, ROOTS, AND MICROBES The soil is a complex physical, chemical, and biological substrate. It is a heterogeneous material containing solid, liquid, and gaseous phases (see Chapter 4). All of these phases interact with mineral elements. The inorganic par-ticles of the solid phase provide a reservoir of potassium, calcium, magnesium, and iron. Also associated with this solid phase are organic compounds containing nitrogen, phosphorus, and sulfur, among other elements. The liquid phase of the soil constitutes the soil solution, which con-tains dissolved mineral ions and serves as the medium for ion movement to the root surface. Gases such as oxygen, carbon dioxide, and nitrogen are dissolved in the soil solu-tion, but in roots gases are exchanged predominantly through the air gaps between soil particles.
From a biological perspective, soil constitutes a diverse ecosystem in which plant roots and microorganisms com-pete strongly for mineral nutrients. In spite of this compe-tition, roots and microorganisms can form alliances for their mutual benefit (symbioses, singular symbiosis). In this section we will discuss the importance of soil properties, root structure, and mycorrhizal symbiotic relationships to plant mineral nutrition. Chapter 12 addresses symbiotic relationships with nitrogen-fixing bacteria.
Negatively Charged Soil Particles Affect the Adsorption of Mineral Nutrients Soil particles, both inorganic and organic, have predomi-nantly negative charges on their surfaces. Many inorganic soil particles are crystal lattices that are tetrahedral arrange-ments of the cationic forms of aluminum and silicon (Al3+ and Si4+) bound to oxygen atoms, thus forming aluminates and silicates. When cations of lesser charge replace Al3+ and Si4+, inorganic soil particles become negatively charged.
Organic soil particles originate from the products of the microbial decomposition of dead plants, animals, and microorganisms. The negative surface charges of organic particles result from the dissociation of hydrogen ions from the carboxylic acid and phe-nolic groups present in this component of the soil. Most of the world’s soil particles, however, are inorganic.
Inorganic soils are catego-rized by particle size: • Gravel has particles larger than 2 mm.
• Coarse sand has particles between 0.2 and 2 mm.
• Fine sand has particles between 0.02 and 0.2 mm.
• Silt has particles between 0.002 and 0.02 mm.
• Clay has particles smaller than 0.002 mm (see Table 4.1).
The silicate-containing clay materials are further divided into three major groups—kaolinite, illite, and montmoril-lonite—based on differences in their structure and physi-cal properties (Table 5.5). The kaolinite group is generally found in well-weathered soils; the montmorillonite and illite groups are found in less weathered soils.
Mineral cations such as ammonium (NH4 +) and potas-sium (K+) adsorb to the negative surface charges of inor-ganic and organic soil particles. This cation adsorption is an important factor in soil fertility. Mineral cations adsorbed on the surface of soil particles are not easily lost when the soil is leached by water, and they provide a nutri-ent reserve available to plant roots. Mineral nutrients adsorbed in this way can be replaced by other cations in a process known as cation exchange (Figure 5.5). The degree to which a soil can adsorb and exchange ions is termed its cation exchange capacity (CEC) and is highly dependent on the soil type. A soil with higher cation exchange capacity generally has a larger reserve of mineral nutrients.
Mineral anions such as nitrate (NO3 –) and chloride (Cl–) tend to be repelled by the negative charge on the surface of soil particles and remain dissolved in the soil solution.
Thus the anion exchange capacity of most agricultural soils is small compared to the cation exchange capacity. Among anions, nitrate remains mobile in the soil solution, where it is susceptible to leaching by water moving through the soil. Phosphate ions (H2PO2 –) may bind to soil particles con-taining aluminum or iron because the positively charged iron and aluminum ions (Fe2+, Fe3+, and Al3+) have hydroxyl (OH–) groups that exchange with phosphate. As a result, phosphate can be tightly bound, and its mobility and availability in soil can limit plant growth. Sulfate (SO4 2–) in the presence of calcium (Ca2+) forms gypsum (CaSO4). Gypsum is only slightly soluble, but it releases sufficient sulfate to support plant growth. Most 78 Chapter 5 TABLE 5.5 Comparison of properties of three major types of silicate clays found in the soil Type of clay Property Montmorillonite Illite Kaolinite Size (µm) 0.01–1.0 0.1–2.0 0.1–5.0 Shape Irregular flakes Irregular flakes Hexagonal crystals Cohesion High Medium Low Water-swelling capacity High Medium Low Cation exchange capacity 80–100 15–40 3–15 (milliequivalents 100 g−1) Source: After Brady 1974.
nonacid soils contain substantial amounts of calcium; con-sequently, sulfate mobility in these soils is low, so sulfate is not highly susceptible to leaching.
Soil pH Affects Nutrient Availability, Soil Microbes, and Root Growth Hydrogen ion concentration (pH) is an important property of soils because it affects the growth of plant roots and soil microorganisms. Root growth is generally favored in slightly acidic soils, at pH values between 5.5 and 6.5.
Fungi generally predominate in acidic soils; bacteria become more prevalent in alkaline soils. Soil pH deter-mines the availability of soil nutrients (see Figure 5.4).
Acidity promotes the weathering of rocks that releases K+, Mg2+, Ca2+, and Mn2+ and increases the solubility of car-bonates, sulfates, and phosphates. Increasing the solubility of nutrients facilitates their availability to roots.
Major factors that lower the soil pH are the decomposi-tion of organic matter and the amount of rainfall. Carbon dioxide is produced as a result of the decomposition of organic material and equilibrates with soil water in the fol-lowing reaction: CO2 + H2O ~ H+ + HCO3 – This reaction releases hydrogen ions (H+), lowering the pH of the soil. Microbial decomposition of organic material also produces ammonia and hydrogen sulfide that can be oxidized in the soil to form the strong acids nitric acid (HNO3) and sulfuric acid (H2SO4), respectively. Hydrogen ions also displace K+, Mg2+, Ca2+, and Mn2+ from the cation exchange complex in a soil. Leaching then may remove these ions from the upper soil layers, leaving a more acid soil. By contrast, the weathering of rock in arid regions releases K+, Mg2+, Ca2+, and Mn2+ to the soil, but because of the low rainfall, these ions do not leach from the upper soil layers, and the soil remains alkaline.
Excess Minerals in the Soil Limit Plant Growth When excess minerals are present in the soil, the soil is said to be saline, and plant growth may be restricted if these min-eral ions reach levels that limit water availability or exceed the adequate zone for a particular nutrient (see Chapter 25).
Sodium chloride and sodium sulfate are the most common salts in saline soils. Excess minerals in soils can be a major problem in arid and semiarid regions because rainfall is insufficient to leach the mineral ions from the soil layers near the surface. Irrigated agriculture fosters soil salinization if insufficient water is applied to leach the salt below the root-ing zone. Irrigation water can contain 100 to 1000 g of min-erals per cubic meter. An average crop requires about 4000 m3 of water per acre. Consequently, 400 to 4000 kg of min-erals may be added to the soil per crop (Marschner 1995).
In saline soil, plants encounter salt stress. Whereas many plants are affected adversely by the presence of rel-atively low levels of salt, other plants can survive high lev-els (salt-tolerant plants) or even thrive (halophytes) under such conditions. The mechanisms by which plants tolerate salinity are complex (see Chapter 25), involving molecular synthesis, enzyme induction, and membrane transport. In some species, excess minerals are not taken up; in others, minerals are taken up but excreted from the plant by salt glands associated with the leaves. To prevent toxic buildup of mineral ions in the cytosol, many plants may sequester them in the vacuole (Stewart and Ahmad 1983). Efforts are under way to bestow salt tolerance on salt-sensitive crop species using both classic plant breeding and molecular biology (Hasegawa et al. 2000).
Another important problem with excess minerals is the accumulation of heavy metals in the soil, which can cause severe toxicity in plants as well as humans (see Web Essay 5.1). Heavy metals include zinc, copper, cobalt, nickel, mer-cury, lead, cadmium, silver, and chromium (Berry and Wal-lace 1981).
Plants Develop Extensive Root Systems The ability of plants to obtain both water and mineral nutrients from the soil is related to their capacity to develop an extensive root system. In the late 1930s, H. J. Dittmer examined the root system of a single winter rye plant after 16 weeks of growth and estimated that the plant had 13 × 106 primary and lateral root axes, extending more than 500 km in length and providing 200 m2 of surface area (Dittmer 1937). This plant also had more than 1010 root hairs, pro-viding another 300 m2 of surface area.
Mineral Nutrition 79 – – – – – – – – – K+ K+ K+ K+ K+ K+ K+ Ca2+ Ca2+ Ca2+ Ca2+ Ca2+ Ca2+ Mg2+ H+ H+ Soil particle FIGURE 5.5 The principle of cation exchange on the surface of a soil particle. Cations are bound to the surface of soil particles because the surface is negatively charged.
Addition of a cation such as potassium (K+) can displace another cation such as calcium (Ca2+) from its binding on the surface of the soil particle and make it available for uptake by the root.
In the desert, the roots of mesquite (genus Prosopis) may extend down more than 50 m to reach groundwater. Annual crop plants have roots that usually grow between 0.1 and 2.0 m in depth and extend laterally to distances of 0.3 to 1.0 m. In orchards, the major root systems of trees planted 1 m apart reach a total length of 12 to 18 km per tree. The annual production of roots in natural ecosystems may easily sur-pass that of shoots, so in many respects, the aboveground portions of a plant represent only “the tip of an iceberg.” Plant roots may grow continuously throughout the year.
Their proliferation, however, depends on the availability of water and minerals in the immediate microenvironment surrounding the root, the so-called rhizosphere. If the rhi-zosphere is poor in nutrients or too dry, root growth is slow. As rhizosphere conditions improve, root growth increases. If fertilization and irrigation provide abundant nutrients and water, root growth may not keep pace with shoot growth. Plant growth under such conditions becomes carbohydrate limited, and a relatively small root system meets the nutrient needs of the whole plant (Bloom et al. 1993). Roots growing below the soil surface are stud-ied by special techniques (see Web Topic 5.2).
Root Systems Differ in Form but Are Based on Common Structures The form of the root system differs greatly among plant species. In monocots, root development starts with the emergence of three to six primary (or seminal) root axes from the germinating seed. With further growth, the plant extends new adventitious roots, called nodal roots or brace roots. Over time, the primary and nodal root axes grow and branch extensively to form a complex fibrous root system (Figure 5.6). In fibrous root systems, all the roots generally have the same diameter (except where environmental con-ditions or pathogenic interactions modify the root struc-ture), so it is difficult to distinguish a main root axis.
In contrast to monocots, dicots develop root systems with a main single root axis, called a taproot, which may thicken as a result of secondary cambial activity. From this main root axis, lateral roots develop to form an extensively branched root system (Figure 5.7).
The development of the root system in both monocots and dicots depends on the activity of the root apical meri-stem and the production of lateral root meristems. Figure 5.8 shows a generalized diagram of the apical region of a plant root and identifies the three zones of activity: meri-stematic, elongation, and maturation.
In the meristematic zone, cells divide both in the direc-tion of the root base to form cells that will differentiate into the tissues of the functional root and in the direction of the root apex to form the root cap. The root cap protects the delicate meristematic cells as the root moves through the soil. It also secretes a gelatinous material called mucigel, which commonly surrounds the root tip. The precise func-tion of the mucigel is uncertain, but it has been suggested that it lubricates the penetration of the root through the soil, protects the root apex from desiccation, promotes the transfer of nutrients to the root, or affects the interaction between roots and soil microorganisms (Russell 1977). The root cap is central to the perception of gravity, the signal that directs the growth of roots downward. This process is termed the gravitropic response (see Chapter 19).
Cell division at the root apex proper is relatively slow; thus this region is called the quiescent center. After a few generations of slow cell divisions, root cells displaced from the apex by about 0.1 mm begin to divide more rapidly.
Cell division again tapers off at about 0.4 mm from the apex, and the cells expand equally in all directions.
The elongation zone begins 0.7 to 1.5 mm from the apex (see Figure 5.8). In this zone, cells elongate rapidly and undergo a final round of divisions to produce a central ring of cells called the endodermis. The walls of this endoder-mal cell layer become thickened, and suberin (see Chapter 13) deposited on the radial walls forms the Casparian strip, a hydrophobic structure that prevents the apoplastic move-ment of water or solutes across the root (see Figure 4.3).
The endodermis divides the root into two regions: the cor-tex toward the outside and the stele toward the inside. The stele contains the vascular elements of the root: the phloem, which transports metabolites from the shoot to the root, and the xylem, which transports water and solutes to the shoot.
80 Chapter 5 (A) Dry soil (B) Irrigated soil 30 cm FIGURE 5.6 Fibrous root systems of wheat (a monocot). (A) The root system of a mature (3-month-old) wheat plant growing in dry soil. (B) The root system of a wheat plant growing in irrigated soil. It is apparent that the morphol-ogy of the root system is affected by the amount of water present in the soil. In a fibrous root system, the primary root axes are no longer distinguishable. (After Weaver 1926.) Phloem develops more rapidly than xylem, attesting to the fact that phloem function is critical near the root apex.
Large quantities of carbohydrates must flow through the phloem to the growing apical zones in order to support cell division and elongation. Carbohydrates provide rapidly growing cells with an energy source and with the carbon skeletons required to synthesize organic compounds. Six-carbon sugars (hexoses) also function as osmotically active solutes in the root tissue. At the root apex, where the phloem is not yet developed, carbohydrate movement depends on symplastic diffusion and is relatively slow (Bret-Harte and Silk 1994). The low rates of cell division in the quiescent center may result from the fact that insuffi-cient carbohydrates reach this centrally located region or that this area is kept in an oxidized state (see Web Essay 5.2).
Root hairs, with their large surface area for absorption of water and solutes, first appear in the maturation zone (see Figure 5.8), and it is here that the xylem develops the capacity to translocate substantial quantities of water and solutes to the shoot.
Mineral Nutrition 81 30 cm Sugar beet Alfalfa FIGURE 5.7 Taproot system of two adequately watered dicots: sugar beet and alfalfa. The sugar beet root system is typical of 5 months of growth; the alfalfa root system is typ-ical of 2 years of growth. In both dicots, the root system shows a major vertical root axis. In the case of sugar beet, the upper portion of the taproot system is thickened because of its function as storage tissue. (After Weaver 1926.) Maturation zone Elongation zone Meristematic zone Root hair Cortex Xylem Phloem Stele Endodermis with Casparian strip Epidermis Region of rapid cell division Quiescent center (few cell divisions) Root cap Mucigel sheath Apex FIGURE 5.8 Diagrammatic longitudinal section of the apical region of the root. The meristematic cells are located near the tip of the root. These cells generate the root cap and the upper tissues of the root. In the elongation zone, cells dif-ferentiate to produce xylem, phloem, and cortex. Root hairs, formed in epidermal cells, first appear in the matura-tion zone.
Different Areas of the Root Absorb Different Mineral Ions The precise point of entry of minerals into the root system has been a topic of considerable interest. Some researchers have claimed that nutrients are absorbed only at the apical regions of the root axes or branches (Bar-Yosef et al. 1972); others claim that nutrients are absorbed over the entire root surface (Nye and Tinker 1977). Experimental evidence sup-ports both possibilities, depending on the plant species and the nutrient being investigated: • Root absorption of calcium in barley appears to be restricted to the apical region.
• Iron may be taken up either at the apical region, as in barley (Clarkson 1985), or over the entire root sur-face, as in corn (Kashirad et al. 1973).
• Potassium, nitrate, ammonium, and phosphate can be absorbed freely at all locations of the root surface (Clarkson 1985), but in corn the elongation zone has the maximum rates of potassium accumulation (Sharp et al. 1990) and nitrate absorption (Taylor and Bloom 1998).
• In corn and rice, the root apex absorbs ammonium more rapidly than the elongation zone does (Colmer and Bloom 1998).
• In several species, root hairs are the most active in phosphate absorption (Fohse et al. 1991).
The high rates of nutrient absorption in the apical root zones result from the strong demand for nutrients in these tissues and the relatively high nutrient availability in the soil surrounding them. For example, cell elongation depends on the accumulation of solutes such as potassium, chloride, and nitrate to increase the osmotic pressure within the cell (see Chapter 15). Ammonium is the pre-ferred nitrogen source to support cell division in the meri-stem because meristematic tissues are often carbohydrate limited, and the assimilation of ammonium consumes less energy than that of nitrate (see Chapter 12). The root apex and root hairs grow into fresh soil, where nutrients have not yet been depleted.
Within the soil, nutrients can move to the root surface both by bulk flow and by diffusion (see Chapter 3). In bulk flow, nutrients are carried by water moving through the soil toward the root. The amount of nutrient provided to the root by bulk flow depends on the rate of water flow through the soil toward the plant, which depends on tran-spiration rates and on nutrient levels in the soil solution.
When both the rate of water flow and the concentrations of nutrients in the soil solution are high, bulk flow can play an important role in nutrient supply. In diffusion, mineral nutrients move from a region of higher concentration to a region of lower concentration.
Nutrient uptake by the roots lowers the concentration of nutrients at the root surface, generating concentration gra-dients in the soil solution surrounding the root. Diffusion of nutrients down their concentration gradient and bulk flow resulting from transpiration can increase nutrient availability at the root surface.
When absorption of nutrients by the roots is high and the nutrient concentration in the soil is low, bulk flow can supply only a small fraction of the total nutrient require-ment (Mengel and Kirkby 1987). Under these conditions, diffusion rates limit the movement of nutrients to the root surface. When diffusion is too slow to maintain high nutri-ent concentrations near the root, a nutrient depletion zone forms adjacent to the root surface (Figure 5.9). This zone extends from about 0.2 to 2.0 mm from the root surface, depending on the mobility of the nutrient in the soil.
The formation of a depletion zone tells us something important about mineral nutrition: Because roots deplete the mineral supply in the rhizosphere, their effectiveness in mining minerals from the soil is determined not only by the rate at which they can remove nutrients from the soil solution, but by their continuous growth. Without growth, roots would rapidly deplete the soil adjacent to their surface.
Optimal nutrient acquisition therefore depends both on the capac-ity for nutrient uptake and on the ability of the root system to grow into fresh soil.
Mycorrhizal Fungi Facilitate Nutrient Uptake by Roots Our discussion thus far has centered on the direct acqui-sition of mineral elements by the root, but this process may be modified by the association of mycorrhizal fungi with the root system. Mycorrhizae (singular mycorrhiza, from the Greek words for “fungus” and “root”) are not unusual; in fact, they are widespread under natural conditions. Much of the world’s vegetation appears to have roots associated 82 Chapter 5 Distance from the root surface Nutrient concentration in the soil solution High nutrient level Low nutrient level Depletion zones FIGURE 5.9 Formation of a nutrient depletion zone in the region of the soil adjacent to the plant root. A nutrient depletion zone forms when the rate of nutrient uptake by the cells of the root exceeds the rate of replacement of the nutrient by diffusion in the soil solution. This depletion causes a localized decrease in the nutrient concentration in the area adjacent to the root surface. (After Mengel and Kirkby 1987.) with mycorrhizal fungi: 83% of dicots, 79% of monocots, and all gymnosperms regularly form mycorrhizal associa-tions (Wilcox 1991).
On the other hand, plants from the families Cruciferae (cabbage), Chenopodiaceae (spinach), and Proteaceae (macadamia nuts), as well as aquatic plants, rarely if ever have mycorrhizae. Mycorrhizae are absent from roots in very dry, saline, or flooded soils, or where soil fertility is extreme, either high or low. In particular, plants grown under hydroponics and young, rapidly growing crop plants seldom have mycorrhizae.
Mycorrhizal fungi are composed of fine, tubular fila-ments called hyphae (singular hypha). The mass of hyphae that forms the body of the fungus is called the mycelium (plural mycelia). There are two major classes of mycorrhizal fungi: ectotrophic mycorrhizae and vesicular-arbuscular mycorrhizae (Smith et al. 1997). Minor classes of mycor-rhizal fungi include the ericaceous and orchidaceous myc-orrhizae, which may have limited importance in terms of mineral nutrient uptake.
Ectotrophic mycorrhizal fungi typically show a thick sheath, or “mantle,” of fungal mycelium around the roots, and some of the mycelium penetrates between the cortical cells (Figure 5.10). The cortical cells themselves are not pen-etrated by the fungal hyphae but instead are surrounded by a network of hyphae called the Hartig net. Often the amount of fungal mycelium is so extensive that its total mass is comparable to that of the roots themselves. The fungal mycelium also extends into the soil, away from this compact mantle, where it forms individual hyphae or strands containing fruiting bodies.
The capacity of the root system to absorb nutrients is improved by the presence of external fungal hyphae that are much finer than plant roots and can reach beyond the areas of nutrient-depleted soil near the roots (Clarkson 1985). Ectotrophic mycorrhizal fungi infect exclusively tree species, including gymnosperms and woody angiosperms.
Unlike the ectotrophic mycorrhizal fungi, vesicular-arbuscular mycorrhizal fungi do not produce a compact mantle of fungal mycelium around the root. Instead, the hyphae grow in a less dense arrangement, both within the root itself and extending outward from the root into the surrounding soil (Figure 5.11). After entering the root through either the epidermis or a root hair, the hyphae not only extend through the regions between cells but also pen-etrate individual cells of the cortex. Within the cells, the hyphae can form oval structures called vesicles and branched structures called arbuscules. The arbuscules appear to be sites of nutrient transfer between the fungus and the host plant.
Mineral Nutrition 83 Xylem Phloem Hartig net Fungal sheath 100 mm Epidermis Cortex FIGURE 5.10 Root infected with ectotrophic mycorrhizal fungi. In the infected root, the fungal hyphae surround the root to produce a dense fungal sheath and penetrate the intercellular spaces of the cortex to form the Hartig net. The total mass of fungal hyphae may be comparable to the root mass itself. (From Rovira et al. 1983.) Reproductive chlamydospore Epidermis Arbuscule Endodermis Vesicle Root hair External mycelium Cortex Root FIGURE 5.11 Association of vesicular-arbuscular mycor-rhizal fungi with a section of a plant root. The fungal hyphae grow into the intercellular wall spaces of the cortex and penetrate individual cortical cells. As they extend into the cell, they do not break the plasma membrane or the tonoplast of the host cell. Instead, the hypha is surrounded by these membranes and forms structures known as arbus-cules, which participate in nutrient ion exchange between the host plant and the fungus. (From Mauseth 1988.) Outside the root, the external mycelium can extend sev-eral centimeters away from the root and may contain spore-bearing structures. Unlike the ectotrophic mycor-rhizae, vesicular-arbuscular mycorrhizae make up only a small mass of fungal material, which is unlikely to exceed 10% of the root weight. Vesicular-arbuscular mycorrhizae are found in association with the roots of most species of herbaceous angiosperms (Smith et al. 1997).
The association of vesicular-arbuscular mycorrhizae with plant roots facilitates the uptake of phosphorus and trace metals such as zinc and copper. By extending beyond the depletion zone for phosphorus around the root, the external mycelium improves phosphorus absorption. Cal-culations show that a root associated with mycorrhizal fungi can transport phosphate at a rate more than four times higher than that of a root not associated with myc-orrhizae (Nye and Tinker 1977). The external mycelium of the ectotrophic mycorrhizae can also absorb phosphate and make it available to the plant. In addition, it has been sug-gested that ectotrophic mycorrhizae proliferate in the organic litter of the soil and hydrolyze organic phosphorus for transfer to the root (Smith et al. 1997).
Nutrients Move from the Mycorrhizal Fungi to the Root Cells Little is known about the mechanism by which the mineral nutrients absorbed by mycorrhizal fungi are transferred to the cells of plant roots. With ectotrophic mycorrhizae, inor-ganic phosphate may simply diffuse from the hyphae in the Hartig net and be absorbed by the root cortical cells.
With vesicular-arbuscular mycorrhizae, the situation may be more complex. Nutrients may diffuse from intact arbus-cules to root cortical cells. Alternatively, because some root arbuscules are continually degenerating while new ones are forming, degenerating arbuscules may release their internal contents to the host root cells.
A key factor in the extent of mycorrhizal association with the plant root is the nutritional status of the host plant.
Moderate deficiency of a nutrient such as phosphorus tends to promote infection, whereas plants with abundant nutrients tend to suppress mycorrhizal infection.
Mycorrhizal association in well-fertilized soils may shift from a symbiotic relationship to a parasitic one in that the fungus still obtains carbohydrates from the host plant, but the host plant no longer benefits from improved nutrient uptake efficiency. Under such conditions, the host plant may treat mycorrhizal fungi as it does other pathogens (Brundrett 1991; Marschner 1995).
SUMMARY Plants are autotrophic organisms capable of using the energy from sunlight to synthesize all their components from carbon dioxide, water, and mineral elements. Studies of plant nutrition have shown that specific mineral ele-ments are essential for plant life. These elements are clas-sified as macronutrients or micronutrients, depending on the relative amounts found in plant tissue.
Certain visual symptoms are diagnostic for deficiencies in specific nutrients in higher plants. Nutritional disorders occur because nutrients have key roles in plant metabolism.
They serve as components of organic compounds, in energy storage, in plant structures, as enzyme cofactors, and in electron transfer reactions. Mineral nutrition can be studied through the use of hydroponics or aeroponics, which allow the characterization of specific nutrient requirements. Soil and plant tissue analysis can provide information on the nutritional status of the plant–soil sys-tem and can suggest corrective actions to avoid deficien-cies or toxicities.
When crop plants are grown under modern high-pro-duction conditions, substantial amounts of nutrients are removed from the soil. To prevent the development of defi-ciencies, nutrients can be added back to the soil in the form of fertilizers. Fertilizers that provide nutrients in inorganic forms are called chemical fertilizers; those that derive from plant or animal residues are considered organic fertilizers.
In both cases, plants absorb the nutrients primarily as inor-ganic ions. Most fertilizers are applied to the soil, but some are sprayed on leaves.
The soil is a complex substrate—physically, chemically, and biologically. The size of soil particles and the cation exchange capacity of the soil determine the extent to which a soil provides a reservoir for water and nutrients. Soil pH also has a large influence on the availability of mineral ele-ments to plants.
If mineral elements, especially sodium or heavy metals, are present in excess in the soil, plant growth may be adversely affected. Certain plants are able to tolerate excess mineral elements, and a few species—for example, halo-phytes in the case of sodium—grow under these extreme conditions.
To obtain nutrients from the soil, plants develop exten-sive root systems. Roots have a relatively simple structure with radial symmetry and few differentiated cell types.
Roots continually deplete the nutrients from the immedi-ate soil around them, and such a simple structure may per-mit rapid growth into fresh soil.
Plant roots often form associations with mycorrhizal fungi. The fine hyphae of mycorrhizae extend the reach of roots into the surrounding soil and facilitate the acquisition of mineral elements, particularly those like phosphorus that are relatively immobile in the soil. In return, plants provide carbohydrates to the mycorrhizae. Plants tend to suppress mycorrhizal associations under conditions of high nutrient availability.
84 Chapter 5 Web Material Web Topics 5.1 Symptoms of Deficiency in Essential Minerals Defficiency symptoms are characteristic of each essential element and can be used as diagnostic for the defficiency.These color pictures illustrate defficiency symptoms for each essential element in a tomato.
5.2 Observing Roots below Ground The study of roots growing under natural condi-tions requires means to observe roots below ground.State-of-the-art techniques are described in this essay.
Web Essays 5.1 From Meals to Metals and Back Heavy metal accumulation by plants is toxic.
Understanding of the involved molecular process is helping to develop better phytoreme-diation crops.
5.2 Redox Control of the Root Quiescent Center The redox status of the quiescent center seems to control the cell cycle of these cells.
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86 Chapter 5 Solute Transport 6 Chapter PLANT CELLS ARE SEPARATED from their environment by a plasma membrane that is only two lipid molecules thick. This thin layer sepa-rates a relatively constant internal environment from highly variable external surroundings. In addition to forming a hydrophobic barrier to diffusion, the membrane must facilitate and continuously regulate the inward and outward traffic of selected molecules and ions as the cell takes up nutrients, exports wastes, and regulates its turgor pressure. The same is true of the internal membranes that separate the various com-partments within each cell.
As the cell’s only contact with its surroundings, the plasma mem-brane must also relay information about its physical environment, about molecular signals from other cells, and about the presence of invading pathogens. Often these signal transduction processes are mediated by changes in ion fluxes across the membrane.
Molecular and ionic movement from one location to another is known as transport. Local transport of solutes into or within cells is regulated mainly by membranes. Larger-scale transport between plant and envi-ronment, or between leaves and roots, is also controlled by membrane transport at the cellular level. For example, the transport of sucrose from leaf to root through the phloem, referred to as translocation, is driven and regulated by membrane transport into the phloem cells of the leaf, and from the phloem to the storage cells of the root (see Chapter 10).
In this chapter we will consider first the physical and chemical prin-ciples that govern the movements of molecules in solution. Then we will show how these principles apply to membranes and to biological sys-tems. We will also discuss the molecular mechanisms of transport in liv-ing cells and the great variety of membrane transport proteins that are responsible for the particular transport properties of plant cells. Finally, we will examine the pathway that ions take when they enter the root, as well as the mechanism of xylem loading, the process whereby ions are released into the vessel elements and tracheids of the stele.
PASSIVE AND ACTIVE TRANSPORT According to Fick’s first law (see Equation 3.1), the move-ment of molecules by diffusion always proceeds sponta-neously, down a gradient of concentration or chemical potential (see Chapter 2 on the web site), until equilibrium is reached. The spontaneous “downhill” movement of mol-ecules is termed passive transport. At equilibrium, no fur-ther net movements of solute can occur without the appli-cation of a driving force.
The movement of substances against or up a gradient of chemical potential (e.g., to a higher concentration) is termed active transport. It is not spontaneous, and it requires that work be done on the system by the applica-tion of cellular energy. One way (but not the only way) of accomplishing this task is to couple transport to the hydrol-ysis of ATP.
Recall from Chapter 3 that we can calculate the driving force for diffusion, or, conversely, the energy input neces-sary to move substances against a gradient, by measuring the potential-energy gradient, which is often a simple func-tion of the difference in concentration. Biological transport can be driven by four major forces: concentration, hydro-static pressure, gravity, and electric fields. (However, recall from Chapter 3 that in biological systems, gravity seldom contributes substantially to the force that drives transport.) The chemical potential for any solute is defined as the sum of the concentration, electric, and hydrostatic poten-tials (and the chemical potential under standard condi-tions): Here m ~ j is the chemical potential of the solute species j in joules per mole (J mol–1), mj is its chemical potential under standard conditions (a correction factor that will cancel out in future equations and so can be ignored), R is the uni-versal gas constant, T is the absolute temperature, and Cj is the concentration (more accurately the activity) of j.
The electrical term, zjFE, applies only to ions; z is the electrostatic charge of the ion (+1 for monovalent cations, –1 for monovalent anions, +2 for divalent cations, and so on), F is Faraday’s constant (equivalent to the electric charge on 1 mol of protons), and E is the overall electric potential of the solution (with respect to ground). The final term, V – jP, expresses the contribution of the partial molal volume of j (V – j) and pressure (P) to the chemical potential of j. (The partial molal volume of j is the change in volume per mole of substance j added to the system, for an infini-tesimal addition.) This final term, V – jP, makes a much smaller contribution to m ~ j than do the concentration and electrical terms, except in the very important case of osmotic water movements. As discussed in Chapter 3, the chemical potential of water (i.e., the water potential) depends on the concentration of dis-solved solutes and the hydrostatic pressure on the system.
The importance of the concept of chemical potential is that it sums all the forces that may act on a molecule to drive net trans-port (Nobel 1991).
In general, diffusion (or passive transport) always moves molecules from areas of higher chemical potential downhill to areas of lower chemical potential. Movement against a chemical-potential gradient is indicative of active transport (Figure 6.1).
If we take the diffusion of sucrose across a permeable membrane as an example, we can accurately approximate the chemical potential of sucrose in any compartment by the concentration term alone (unless a solution is very con-centrated, causing hydrostatic pressure to build up). From Equation 6.1, the chemical potential of sucrose inside a cell can be described as follows (in the next three equations, the subscript s stands for sucrose, and the superscripts i and o stand for inside and outside, respectively): The chemical potential of sucrose outside the cell is calcu-lated as follows: m ~ s o = ms + RT ln Cs o (6.3) We can calculate the difference in the chemical potential of sucrose between the solutions inside and outside the cell, ∆m ~ s, regardless of the mechanism of transport. To get the signs right, remember that for inward transport, sucrose is being removed (–) from outside the cell and added (+) to the inside, so the change in free energy in joules per mole of sucrose transported will be as follows: (6.4) Substituting the terms from Equations 6.2 and 6.3 into Equation 6.4, we get the following: ∆˜ ln ln m m m s s s i s s o s i s o s i s o ln ln ln = + ( ) − + ( ) = − ( ) = RT C RT C RT C C RT C C ∆ σ σ ι σ ο ˜ ˜ ˜ m m m = − Chemical potential of sucrose solution inside the cell µsi ~ Chemical potential of sucrose solution under standard conditions Concentration component µs = + RT ln Csi Chemical potential for a given solute, j µj ~ Chemical potential of j under standard conditions Concentration (activity) component µj = + RT ln Cj Electric-potential component + zjFE Hydrostatic-pressure component + VjP – 88 Chapter 6 (6.1) (6.2) (6.5) If this difference in chemical potential is negative, sucrose could diffuse inward spontaneously (provided the mem-brane had a finite permeability to sucrose; see the next sec-tion). In other words, the driving force (∆m ~ s) for solute dif-fusion is related to the magnitude of the concentration gradient (Cs i/Cs o).
If the solute carries an electric charge (as does the potas-sium ion), the electrical component of the chemical poten-tial must also be considered. Suppose the membrane is per-meable to K+ and Cl– rather than to sucrose. Because the ionic species (K+ and Cl–) diffuse independently, each has its own chemical potential. Thus for inward K+ diffusion, (6.6) Substituting the appropriate terms from Equation 6.1 into Equation 6.6, we get ∆m ~ s = (RT ln [K+]i + zFEi) – (RT ln [K+]o + zFEo) (6.7) and because the electrostatic charge of K+ is +1, z = +1 and (6.8) The magnitude and sign of this expression will indicate the driving force for K+ diffusion across the membrane, and its direction. A similar expression can be written for Cl– (but remember that for Cl–, z = –1).
Equation 6.8 shows that ions, such as K+, diffuse in re-sponse to both their concentration gradients ([K+]i /[K+]o) and any electric-potential difference between the two compartments (Ei – Eo). One very important implication of this equation is that ions can be driven passively against their concentration gradients if an appropriate voltage (electric field) is applied between the two com-partments. Because of the importance of electric fields in biological transport, m ~ is often called the electrochemical potential, and ∆m ~ is the difference in electrochemical potential between two compartments.
TRANSPORT OF IONS ACROSS A MEMBRANE BARRIER If the two KCl solutions in the previous example are sep-arated by a biological membrane, diffusion is complicated by the fact that the ions must move through the membrane as well as across the open solutions. The extent to which a membrane permits the movement of a substance is called membrane permeability. As will be discussed later, per-meability depends on the composition of the membrane, as well as on the chemical nature of the solute. In a loose sense, permeability can be expressed in terms of a diffusion coefficient for the solute in the membrane. However, per-meability is influenced by several additional factors, such = + F(Ei – Eo) RT ln [K+]i [K+]o ∆µK ~ ∆ Κ Κ ι Κ ο ˜ ˜ ˜ m m m = − Solute Transport 89 Chemical potential in compartment A Chemical potential in compartment B Description Passive transport (diffusion) occurs spontaneously down a chemical-potential gradient.
Semipermeable membrane > Active transport occurs against a chemical potential gradient.
At equilibrium, . If there is no active transport, steady state occurs.
= ∆G per mole for movement of j from A to B is equal to – . For an overall negative ∆G, the reaction must be coupled to a process that has a ∆G more negative than –( – ).
< mj A ˜ mj A ˜ mj A ˜ mj B ˜ mj A ˜ mj A ˜ mj A ˜ mj B ˜ mj B ˜ mj B ˜ mj B ˜ mj B ˜ mj B ˜ mj B ˜ mj A ˜ mj A ˜ FIGURE 6.1 Relationship between the chemical poten-tial, m ~, and the transport of molecules across a permeabil-ity barrier. The net movement of molecular species j between compartments A and B depends on the relative magnitude of the chemical potential of j in each com-partment, represented here by the size of the boxes.
Movement down a chemical gradient occurs sponta-neously and is called passive transport; movement against or up a gradient requires energy and is called active transport.
as the ability of a substance to enter the membrane, that are difficult to measure.
Despite its theoretical complexity, we can readily mea-sure permeability by determining the rate at which a solute passes through a membrane under a specific set of condi-tions. Generally the membrane will hinder diffusion and thus reduce the speed with which equilibrium is reached.
The permeability or resistance of the membrane itself, how-ever, cannot alter the final equilibrium conditions. Equilib-rium occurs when ∆m ~ j = 0. In the sections that follow we will discuss the factors that influence the passive distribution of ions across a membrane. These parameters can be used to predict the relationship between the electrical gradient and the con-centration gradient of an ion.
Diffusion Potentials Develop When Oppositely Charged Ions Move across a Membrane at Different Rates When salts diffuse across a membrane, an electric mem-brane potential (voltage) can develop. Consider the two KCl solutions separated by a membrane in Figure 6.2. The K+ and Cl– ions will permeate the membrane indepen-dently as they diffuse down their respective gradients of electrochemical potential. And unless the membrane is very porous, its permeability for the two ions will differ.
As a consequence of these different permeabilities, K+ and Cl– initially will diffuse across the membrane at dif-ferent rates. The result will be a slight separation of charge, which instantly creates an electric potential across the membrane. In biological systems, membranes are usually more permeable to K+ than to Cl–. Therefore, K+ will dif-fuse out of the cell (compartment A in Figure 6.2) faster than Cl–, causing the cell to develop a negative electric charge with respect to the medium. A potential that devel-ops as a result of diffusion is called a diffusion potential.
An important principle that must always be kept in mind when the movement of ions across membranes is considered is the principle of electrical neutrality. Bulk solutions always contain equal numbers of anions and cations. The existence of a membrane potential implies that the distribution of charges across the membrane is uneven; however, the actual number of unbalanced ions is negligi-ble in chemical terms. For example, a membrane potential of –100 mV (millivolts), like that found across the plasma membranes of many plant cells, results from the presence of only one extra anion out of every 100,000 within the cell—a concentration difference of only 0.001%!
As Figure 6.2 shows, all of these extra anions are found immediately adjacent to the surface of the membrane; there is no charge imbalance throughout the bulk of the cell. In our example of KCl diffusion across a membrane, electri-cal neutrality is preserved because as K+ moves ahead of Cl– in the membrane, the resulting diffusion potential retards the movement of K+ and speeds that of Cl–. Ulti-mately, both ions diffuse at the same rate, but the diffusion potential persists and can be measured. As the system moves toward equilibrium and the concentration gradient collapses, the diffusion potential also collapses.
The Nernst Equation Relates the Membrane Potential to the Distribution of an Ion at Equilibrium Because the membrane is permeable to both K+ and Cl– ions, equilibrium in the preceding example will not be reached for either ion until the concentration gradients decrease to zero. However, if the membrane were perme-able to only K+, diffusion of K+ would carry charges across the membrane until the membrane potential balanced the concentration gradient. Because a change in potential requires very few ions, this balance would be reached instantly. Transport would then be at equilibrium, even though the concentration gradients were unchanged.
When the distribution of any solute across a membrane reaches equilibrium, the passive flux, J (i.e., the amount of solute crossing a unit area of membrane per unit time), is the same in the two directions—outside to inside and inside to outside: Jo→i = Ji→o 90 Chapter 6 Compartment A Compartment B – + Membrane K+ Cl– Initial conditions: [KCl]A > [KCl]B Equilibrium conditions: [KCl]A = [KCl]B Diffusion potential exists until chemical equilibrium is reached.
At chemical equilibrium, diffusion potential equals zero.
FIGURE 6.2 Development of a diffusion potential and a charge separation between two compartments separated by a membrane that is preferentially permeable to potassium.
If the concentration of potassium chloride is higher in com-partment A ([KCl]A > [KCl]B), potassium and chloride ions will diffuse at a higher rate into compartment B, and a dif-fusion potential will be established. When membranes are more permeable to potassium than to chloride, potassium ions will diffuse faster than chloride ions, and charge sepa-ration (+ and –) will develop.
Fluxes are related to ∆m ~ (for a discussion on fluxes and ∆m ~, see Chapter 2 on the web site); thus at equilibrium, the electrochemical potentials will be the same: m ~ j o = m ~ j i and for any given ion (the ion is symbolized here by the subscript j): mj + RT ln Cj o + zjFEo = mj + RT ln Cj i + zjFEi (6.9) By rearranging Equation 6.9, we can obtain the difference in electric potential between the two compartments at equi-librium (Ei – Eo): This electric-potential difference is known as the Nernst potential (∆Ej) for that ion: ∆Ej = Ei – Eo and or This relationship, known as the Nernst equation, states that at equilibrium the difference in concentration of an ion between two compartments is balanced by the voltage dif-ference between the compartments. The Nernst equation can be further simplified for a univalent cation at 25°C: (6.11) Note that a tenfold difference in concentration corresponds to a Nernst potential of 59 mV (Co/Ci = 10/1; log 10 = 1).
That is, a membrane potential of 59 mV would maintain a tenfold concentration gradient of an ion that is transported by passive diffusion. Similarly, if a tenfold concentration gradient of an ion existed across the membrane, passive diffusion of that ion down its concentration gradient (if it were allowed to come to equilibrium) would result in a dif-ference of 59 mV across the membrane.
All living cells exhibit a membrane potential that is due to the asymmetric ion distribution between the inside and outside of the cell. We can readily determine these mem-brane potentials by inserting a microelectrode into the cell and measuring the voltage difference between the inside of the cell and the external bathing medium (Figure 6.3).
The Nernst equation can be used at any time to determine whether a given ion is at equilibrium across a membrane.
However, a distinction must be made between equilibrium and steady state. Steady state is the condition in which influx and efflux of a given solute are equal and therefore the ion concentrations are constant with respect to time. Steady state is not the same as equilibrium (see Figure 6.1); in steady state, the existence of active transport across the membrane pre-vents many diffusive fluxes from ever reaching equilibrium.
The Nernst Equation Can Be Used to Distinguish between Active and Passive Transport Table 6.1 shows how the experimentally measured ion con-centrations at steady state for pea root cells compare with predicted values calculated from the Nernst equation (Hig-inbotham et al. 1967). In this example, the external concen-tration of each ion in the solution bathing the tissue, and the measured membrane potential, were substituted into the Nernst equation, and a predicted internal concentration was calculated for that ion.
Notice that, of all the ions shown in Table 6.1, only K+ is at or near equilibrium. The anions NO3 –, Cl–, H2PO4 –, and SO4 2– all have higher internal concentrations than pre-dicted, indicating that their uptake is active. The cations ∆ µς ϕ ϕ ο ϕ ι E C C = 59 log ∆ϕ ϕ ϕ ο ϕ ι E RT z F C C = 2 3 .
log ∆ϕ ϕ ϕ ο ϕ ι E RT z F C C = ln E E RT z F C C i o j j o j i − = ln Solute Transport 91 – + Voltmeter Microelectrode Conducting nutrient solution Plant tissue Ag/AgCl junctions to permit reversible electric current Salt solution Glass pipette Cell wall Plasma membrane seals to glass Open tip (<1 mm diameter) FIGURE 6.3 Diagram of a pair of microelectrodes used to measure membrane potentials across cell membranes. One of the glass micropipette electrodes is inserted into the cell compartment under study (usually the vacuole or the cyto-plasm), while the other is kept in an electrolytic solution that serves as a reference. The microelectrodes are con-nected to a voltmeter, which records the electric-potential difference between the cell compartment and the solution.
Typical membrane potentials across plant cell membranes range from –60 to –240 mV. The insert shows how electrical contact with the interior of the cell is made through the open tip of the glass micropipette, which contains an elec-trically conducting salt solution.
Na+, Mg2+, and Ca2+ have lower internal concentrations than predicted; therefore, these ions enter the cell by diffu-sion down their electrochemical-potential gradients and then are actively exported.
The example shown in Table 6.1 is an oversimplification: Plant cells have several internal compartments, each of which can differ in its ionic composition. The cytosol and the vacuole are the most important intracellular compart-ments that determine the ionic relations of plant cells. In mature plant cells, the central vacuole often occupies 90% or more of the cell’s volume, and the cytosol is restricted to a thin layer around the periphery of the cell.
Because of its small volume, the cytosol of most angiosperm cells is difficult to assay chemically. For this rea-son, much of the early work on the ionic relations of plants focused on certain green algae, such as Chara and Nitella, whose cells are several inches long and can contain an appre-ciable volume of cytosol. Figure 6.4 diagrams the conclusions from these studies and from related work with higher plants.
• Potassium is accumulated passively by both the cytosol and the vacuole, except when extracellular K+ concentrations are very low, in which case it is taken up actively.
• Sodium is pumped actively out of the cytosol into the extracellular spaces and vacuole.
• Excess protons, generated by intermediary metabo-lism, are also actively extruded from the cytosol. This process helps maintain the cytosolic pH near neutral-ity, while the vacuole and the extracellular medium are generally more acidic by one or two pH units.
• All the anions are taken up actively into the cytosol.
• Calcium is actively transported out of the cytosol at both the cell membrane and the vacuolar membrane, which is called the tonoplast (see Figure 6.4).
Many different ions permeate the membranes of living cells simultane-ously, but K+, Na+, and Cl– have the high-est concentrations and largest permeabil-ities in plant cells. A modified version of the Nernst equation, the Goldman equa-tion, includes all three of these ions and therefore gives a more accurate value for the diffusion potential in these cells. The diffusion potential calculated from the Goldman equation is termed the Goldman diffusion potential (for a detailed discus-sion of the Goldman equation, see Web Topic 6.1).
Proton Transport Is a Major Determinant of the Membrane Potential When permeabilities and ion gradients are known, it is possible to calculate a diffusion potential for the membrane from the Goldman equation. In most cells, K+ has both the greatest internal concentration and the highest membrane permeability, so the diffusion potential may approach EK, the Nernst potential for K+.
In some organisms, or in tissues such as nerves, the nor-mal resting potential of the cell may be close to EK. This is not 92 Chapter 6 TABLE 6.1 Comparison of observed and predicted ion concentrations in pea root tissue Concentration in external medium Internal concentration (mmol L–1) Ion (mmol L–1) Predicted Observed K+ 1 74 75 Na+ 1 74 8 Mg2+ 0.25 1340 3 Ca2+ 1 5360 2 NO3 – 2 0.0272 28 Cl– 1 0.0136 7 H2PO4 – 1 0.0136 21 SO4 2– 0.25 0.00005 19 Source: Data from Higinbotham et al. 1967.
Note:The membrane potential was measured as –110 mV.
Plasma membrane Tonoplast K+ Na+ H+ K+ K+ Na+ Na+ Ca2+ Ca2+ Ca2+ H+ H+ H2PO4 – H2PO4 – H2PO4 – NO3 – NO3 – NO3 – Cl– Cl– Cl– Vacuole Cytosol Cell wall FIGURE 6.4 Ion concentrations in the cytosol and the vac-uole are controlled by passive (dashed arrows) and active (solid arrows) transport processes. In most plant cells the vacuole occupies up to 90% of the cell’s volume and con-tains the bulk of the cell solutes. Control of the ion concen-trations in the cytosol is important for the regulation of metabolic enzymes. The cell wall surrounding the plasma membrane does not represent a permeability barrier and hence is not a factor in solute transport.
the case with plants and fungi, which may show experimen-tally measured membrane potentials (often –200 to –100 mV) that are much more negative than those calculated from the Goldman equation, which are usually only –80 to –50 mV.
Thus, in addition to the diffusion potential, the membrane potential has a second component. The excess voltage is pro-vided by the plasma membrane electrogenic H+-ATPase.
Whenever an ion moves into or out of a cell without being balanced by countermovement of an ion of opposite charge, a voltage is created across the membrane. Any active transport mechanism that results in the movement of a net electric charge will tend to move the membrane potential away from the value predicted by the Goldman equation. Such a transport mechanism is called an electro-genic pump and is common in living cells.
The energy required for active transport is often pro-vided by the hydrolysis of ATP. In plants we can study the dependence of the membrane potential on ATP by observ-ing the effect of cyanide (CN–) on the membrane potential (Figure 6.5). Cyanide rapidly poisons the mitochondria, and the cell’s ATP consequently becomes depleted. As ATP synthesis is inhibited, the membrane potential falls to the level of the Goldman diffusion potential, which, as dis-cussed in the previous section, is due primarily to the pas-sive movements of K+, Cl–, and Na+ (see Web Topic 6.1).
Thus the membrane potentials of plant cells have two components: a diffusion potential and a component result-ing from electrogenic ion transport (transport that results in the generation of a membrane potential) (Spanswick 1981). When cyanide inhibits electrogenic ion transport, the pH of the external medium increases while the cytosol becomes acidic because H+ remains inside the cell. This is one piece of evidence that it is the active transport of H+ out of the cell that is electrogenic.
As discussed earlier, a change in the membrane poten-tial caused by an electrogenic pump will change the driv-ing forces for diffusion of all ions that cross the membrane.
For example, the outward transport of H+ can create a driv-ing force for the passive diffusion of K+ into the cell. H+ is transported electrogenically across the plasma membrane not only in plants but also in bacteria, algae, fungi, and some animal cells, such as those of the kidney epithelia.
ATP synthesis in mitochondria and chloroplasts also depends on a H+-ATPase. In these organelles, this transport protein is sometimes called ATP synthase because it forms ATP rather than hydrolyzing it (see Chapter 11). The struc-ture and function of membrane proteins involved in active and passive transport in plant cells will be discussed later.
MEMBRANE TRANSPORT PROCESSES Artificial membranes made of pure phospholipids have been used extensively to study membrane permeability.
When the permeability of artificial phospholipid bilayers for ions and molecules is compared with that of biological membranes, important similarities and differences become evident (Figure 6.6).
Both biological and artificial membranes have similar permeabilities for nonpolar molecules and many small polar molecules. On the other hand, biological membranes are much more permeable to ions and some large polar molecules, such as sugars, than artificial bilayers are. The reason is that, unlike artificial bilayers, biological mem-branes contain transport proteins that facilitate the passage of selected ions and other polar molecules.
Transport proteins exhibit specificity for the solutes they transport, hence their great diversity in cells. The simple prokaryote Haemophilus influenzae, the first organism for which the complete genome was sequenced, has only 1743 genes, yet more than 200 of these genes (greater than 10% of the genome) encode various proteins involved in mem-NH2 P O O O O O O O P CH2 – P O O O – – O – H OH H H N C C C N N N HC OH H CH Adenosine-5′-triphosphate (ATP 4– ) Solute Transport 93 20 Time (minutes) 0 40 60 80 –50 –30 –70 –90 –110 –130 –150 Cell membrane potential (mV) 0.1 mM CN– added CN– removed FIGURE 6.5 The membrane potential of a pea cell collapses when cyanide (CN–) is added to the bathing solution.
Cyanide blocks ATP production in the cells by poisoning the mitochondria. The collapse of the membrane potential upon addition of cyanide indicates that an ATP supply is necessary for maintenance of the potential. Washing the cyanide out of the tissue results in a slow recovery of ATP production and restoration of the membrane potential.
(From Higinbotham et al. 1970.) brane transport. In Arabidopsis, 849 genes, or 4.8% of all genes, code for proteins involved in membrane transport.
Although a particular transport protein is usually highly specific for the kinds of substances it will transport, its specificity is not absolute: It generally also transports a small family of related substances. For example, in plants a K+ transporter on the plasma membrane may transport Rb+ and Na+ in addition to K+, but K+ is usually preferred. On the other hand, the K+ transporter is completely ineffective in transporting anions such as Cl– or uncharged solutes such as sucrose. Similarly, a protein involved in the trans-port of neutral amino acids may move glycine, alanine, and valine with equal ease but not accept aspartic acid or lysine.
In the next several pages we will consider the structures, functions, and physiological roles of the various membrane transporters found in plant cells, especially on the plasma membrane and tonoplast. We begin with a discussion of the role of certain transporters (channels and carriers) in promoting the diffusion of solutes across membranes. We then distinguish between primary and secondary active transport, and we discuss the roles of the electrogenic H+-ATPase and various symporters (proteins that transport two substances in the same direction simultaneously) in driving proton-coupled secondary active transport.
Channel Transporters Enhance Ion and Water Diffusion across Membranes Three types of membrane transporters enhance the move-ment of solutes across membranes: channels, carriers, and pumps (Figure 6.7). Channels are transmembrane proteins 94 Chapter 6 High Low Electrochemical potential gradient Transported molecule Channel protein Carrier protein Pump Plasma membrane Energy Primary active transport (against the direction of electrochemical gradient) Simple diffusion Passive transport (in the direction of electrochemical gradient) FIGURE 6.7 Three classes of membrane transport proteins: channels, carriers, and pumps. Channels and carriers can mediate the passive transport of solutes across membranes (by simple diffusion or facilitated diffusion), down the solute’s gradient of electrochemical potential. Channel proteins act as membrane pores, and their specificity is determined primarily by the biophysical properties of the channel.
Carrier proteins bind the transported molecule on one side of the membrane and release it on the other side. Primary active transport is carried out by pumps and uses energy directly, usually from ATP hydrolysis, to pump solutes against their gradient of electrochemical potential.
FIGURE 6.6 Typical values for the permeability, P, of a bio-logical membrane to various substances, compared with those for an artificial phospholipid bilayer. For nonpolar molecules such as O2 and CO2, and for some small uncharged molecules such as glycerol, P values are similar in both systems. For ions and selected polar molecules, including water, the permeability of biological membranes is increased by one or more orders of magnitude, because of the presence of transport proteins. Note the logarithmic scale.
10–10 10–10 10–8 10–6 10–4 10–2 1 102 10–8 10–6 10–4 10–2 1 102 Permeability of lipid bilayer (cm s–1) Permeability of biological membrane (cm s–1) K+ Na+ Cl– H2O CO2 O2 Glycerol that function as selective pores, through which molecules or ions can diffuse across the membrane. The size of a pore and the density of surface charges on its interior lining determine its transport specificity. Transport through chan-nels is always passive, and because the specificity of trans-port depends on pore size and electric charge more than on selective binding, channel transport is limited mainly to ions or water (Figure 6.8).
Transport through a channel may or may not involve transient binding of the solute to the channel protein. In any case, as long as the channel pore is open, solutes that can penetrate the pore diffuse through it extremely rapidly: about 108 ions per second through each channel protein.
Channels are not open all the time: Channel proteins have structures called gates that open and close the pore in response to external signals (see Figure 6.8B). Signals that can open or close gates include voltage changes, hormone binding, or light. For example, voltage-gated channels open or close in response to changes in the membrane potential.
Individual ion channels can be studied in detail by the technique of patch clamp electrophysiology (seeWeb Topic 6.2), which can detect the electric current carried by ions diffusing through a single channel. Patch clamp studies reveal that, for a given ion, such as potassium, a given membrane has a variety of different channels. These chan-nels may open in different voltage ranges, or in response to different signals, which may include K+ or Ca2+ concen-trations, pH, protein kinases and phosphatases, and so on.
This specificity enables the transport of each ion to be fine-tuned to the prevailing conditions. Thus the ion perme-ability of a membrane is a variable that depends on the mix of ion channels that are open at a particular time.
As we saw in the experiment of Table 6.1, the distribu-tion of most ions is not close to equilibrium across the membrane. Anion channels will always function to allow anions to diffuse out of the cell, and other mechanisms are needed for anion uptake. Similarly, calcium channels can function only in the direction of calcium release into the cytosol, and calcium must be expelled by active transport.
The exception is potassium, which can diffuse either inward or outward, depending on whether the membrane potential is more negative or more positive than EK, the potassium equilibrium potential. K+ channels that open only at more negative potentials are specialized for inward diffusion of K+ and are known as inward-rectifying, or simply inward, K+ channels. Con-versely, K+ channels that open only at more positive poten-tials are outward-rectifying, or outward, K+ channels (see Web Essay 6.1). Whereas inward K+ channels function in the accumulation of K+ from the environment, or in the opening of stomata, various outward K+ channels function in the closing of stomata, in the release of K+ into the xylem or in regulation of the membrane potential.
Carriers Bind and Transport Specific Substances Unlike channels, carrier proteins do not have pores that extend completely across the membrane. In transport mediated by a carrier, the substance being transported is Solute Transport 95 Plasma membrane OUTSIDE OF CELL CYTOPLASM S1 S2 S3 S4 S5 S6 + + + + + Voltage-sensing region Pore-forming region (P-domain or H5) N C K+ (A) (B) FIGURE 6.8 Models of K+ channels in plants. (A) Top view of channel, looking through the pore of the protein. Membrane-spanning helices of four subunits come together in an inverted teepee with the pore at the center. The pore-forming regions of the four subunits dip into the membrane, with a K+ selectivity finger region formed at the outer (near) part of the pore (more details on the struc-ture of this channel can be found in Web Essay 6.1). (B) Side view of the inward rectifying K+ chan-nel, showing a polypeptide chain of one subunit, with six membrane-spanning helices. The fourth helix contains positively-charged amino acids and acts as a voltage-sensor. The pore-forming region is a loop between helices 5 and 6. (A after Leng et al. 2002; B after Buchanan et al. 2000.) initially bound to a specific site on the carrier protein. This requirement for binding allows carriers to be highly selec-tive for a particular substrate to be transported. Carriers therefore specialize in the transport of specific organic metabolites. Binding causes a conformational change in the protein, which exposes the substance to the solution on the other side of the membrane. Transport is complete when the substance dissociates from the carrier’s binding site.
Because a conformational change in the protein is required to transport individual molecules or ions, the rate of transport by a carrier is many orders of magnitude slower than through a channel. Typically, carriers may transport 100 to 1000 ions or molecules per second, which is about 106 times slower than transport through a channel.
The binding and release of a molecule at a specific site on a protein that occur in carrier-mediated transport are sim-ilar to the binding and release of molecules from an enzyme in an enzyme-catalyzed reaction. As will be dis-cussed later in the chapter, enzyme kinetics has been used to characterize transport carrier proteins (for a detailed dis-cussion on kinetics, see Chapter 2 on the web site).
Carrier-mediated transport (unlike transport through channels) can be either passive or active, and it can transport a much wider range of possible substrates. Passive transport on a carrier is sometimes called facilitated diffusion, although it resembles diffusion only in that it transports sub-stances down their gradient of electrochemical potential, without an additional input of energy. (This term might seem more appropriately applied to transport through chan-nels, but historically it has not been used in this way.) Primary Active Transport Is Directly Coupled to Metabolic or Light Energy To carry out active transport, a carrier must couple the uphill transport of the solute with another, energy-releas-ing, event so that the overall free-energy change is negative.
Primary active transport is coupled directly to a source of energy other than ∆m ~ j, such as ATP hydrolysis, an oxida-tion–reduction reaction (the electron transport chain of mitochondria and chloroplasts), or the absorption of light by the carrier protein (in halobacteria, bacteriorhodopsin).
The membrane proteins that carry out primary active transport are called pumps (see Figure 6.7). Most pumps transport ions, such as H+ or Ca2+. However, as we will see later in the chapter, pumps belonging to the “ATP-binding cassette” family of transporters can carry large organic molecules.
Ion pumps can be further characterized as either elec-trogenic or electroneutral. In general, electrogenic trans-port refers to ion transport involving the net movement of charge across the membrane. In contrast, electroneutral transport, as the name implies, involves no net movement of charge. For example, the Na+/K+-ATPase of animal cells pumps three Na+ ions out for every two K+ ions in, result-ing in a net outward movement of one positive charge. The Na+/K+-ATPase is therefore an electrogenic ion pump. In contrast, the H+/K+-ATPase of the animal gastric mucosa pumps one H+ out of the cell for every one K+ in, so there is no net movement of charge across the membrane. There-fore, the H+/K+-ATPase is an electroneutral pump.
In the plasma membranes of plants, fungi, and bacteria, as well as in plant tonoplasts and other plant and animal endomembranes, H+ is the principal ion that is electro-genically pumped across the membrane. The plasma mem-brane H+-ATPase generates the gradient of electrochemi-cal potentials of H+ across the plasma membranes, while the vacuolar H+-ATPase and the H+-pyrophosphatase (H+-PPase) electrogenically pump protons into the lumen of the vacuole and the Golgi cisternae.
In plant plasma membranes, the most prominent pumps are for H+ and Ca2+, and the direction of pumping is out-ward. Therefore another mechanism is needed to drive the active uptake of most mineral nutrients. The other impor-tant way that solutes can be actively transported across a membrane against their gradient of electrochemical poten-tial is by coupling of the uphill transport of one solute to the downhill transport of another. This type of carrier-mediated cotransport is termed secondary active transport, and it is driven indirectly by pumps.
Secondary Active Transport Uses the Energy Stored in Electrochemical-Potential Gradients Protons are extruded from the cytosol by electrogenic H+-ATPases operating in the plasma membrane and at the vac-uole membrane. Consequently, a membrane potential and a pH gradient are created at the expense of ATP hydroly-sis. This gradient of electrochemical potential for H+, ∆m ~ H+, or (when expressed in other units) the proton motive force (PMF), or ∆p, represents stored free energy in the form of the H+ gradient (see Web Topic 6.3).
The proton motive force generated by electrogenic H+ transport is used in secondary active transport to drive the transport of many other substances against their gradient of electrochemical potentials. Figure 6.9 shows how sec-ondary transport may involve the binding of a substrate (S) and an ion (usually H+) to a carrier protein, and a confor-mational change in that protein.
There are two types of secondary transport: symport and antiport. The example shown in Figure 6.9 is called symport (and the protein involved is called a symporter) because the two substances are moving in the same direc-tion through the membrane (see also Figure 6.10A).
Antiport (facilitated by a protein called an antiporter) refers to coupled transport in which the downhill movement of protons drives the active (uphill) transport of a solute in the opposite direction (Figure 6.10B).
In both types of secondary transport, the ion or solute being transported simultaneously with the protons is mov-ing against its gradient of electrochemical potential, so its transport is active. However, the energy driving this trans-port is provided by the proton motive force rather than directly by ATP hydrolysis.
96 Chapter 6 Solute Transport 97 High Low Electrochemical potential gradient OUTSIDE OF CELL CYTOPLASM High Low Electrochemical potential gradient of substrate A High Low Electrochemical potential gradient of substrate B H+ A H+ A H+ H+ B B (A) Symport (B) Antiport FIGURE 6.10 Two examples of secondary active transport coupled to a primary pro-ton gradient. (A) In a symport, the energy dissipated by a proton moving back into the cell is coupled to the uptake of one molecule of a substrate (e.g., a sugar) into the cell. (B) In an antiport, the energy dis-sipated by a proton moving back into the cell is coupled to the active transport of a substrate (for example, a sodium ion) out of the cell. In both cases, the substrate under consideration is moving against its gradient of electrochemical potential. Both neutral and charged substrates can be transported by such secondary active transport processes.
Plasma membrane OUTSIDE OF CELL CYTOPLASM H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S Concentration gradients for S and H+ S H+ (A) (B) (C) (D) FIGURE 6.9 Hypothetical model for secondary active transport. The energy that drives the process has been stored in a ∆m ~ H+ (symbolized by the red arrow on the right in A) and is being used to take up a substrate (S) against its concentration gra-dient (left-hand red arrow). (A) In the initial conformation, the binding sites on the protein are exposed to the outside environment and can bind a proton. (B) This binding results in a conformational change that permits a molecule of S to be bound. (C) The binding of S causes another conformational change that exposes the binding sites and their substrates to the inside of the cell. (D) Release of a proton and a molecule of S to the cell’s interior restores the original conformation of the carrier and allows a new pumping cycle to begin.
98 Chapter 6 Tonoplast ADP + Pi ADP + Pi ADP + Pi PPi 2 Pi IP3 ATP ATP ATP GS VACUOLE OUTSIDE OF CELL CYTOSOL H+ H+ H+ H+ H+,Na+ K+ H+ H+ H+ Na+ H+ H+ Na+ H+ H+ H+ H+ H+ 2H+ Mg2+ Cd2+ NO3 – PO43– Ca2+ Ca2+ 3 H+ Anthocyanin PC-Cd2+ Sucrose Hexose Slow vacuolar (SV) channel Fast vacuolar (FV) channel Channels Channels Antiporters H+ pumps H+ pumps ABC transporters pH 7.2 ∆E = –120 mV ADP + Pi ATP ADP + Pi ATP ADP + Pi ATP Plasma membrane pH 5.5 Sucrose Amino acid Efflux carrier Antiporter Symporters Sucrose Ca2+ Ca2+ pump ADP + Pi ATP K+ K+ Ca2+ Cl– Inward rectifying Inward rectifying Outward rectifying Outward rectifying Anions, cations pH 5.5 ∆E = –90 mV Anions (malate2–, Cl–, NO3 –) ABC ABC FIGURE 6.11 Overview of the various transport processes on the plasma membrane and tonoplast of plant cells.
Typically, transport across a biological membrane is energized by one primary active transport system coupled to ATP hydrolysis. The transport of that ion—for example, H+—generates an ion gradient and an electrochemical potential. Many other ions or organic substrates can then be transported by a variety of secondary active-transport proteins, which energize the transport of their respective substrates by simultaneously carrying one or two H+ ions down their energy gradient. Thus H+ ions circulate across the membrane, outward through the primary active trans-port proteins, and back into the cell through the secondary transport proteins. In plants and fungi, sugars and amino acids are taken up by symport with protons.
Most of the ionic gradients across membranes of higher plants are generated and maintained by electrochemical-potential gradients of H+ (Tazawa et al. 1987). In turn, these H+ gradients are generated by the electrogenic proton pumps. Evidence suggests that in plants, Na+ is trans-ported out of the cell by a Na+–H+ antiporter and that Cl–, NO3 –, H2PO4 –, sucrose, amino acids, and other substances enter the cell via specific proton symporters.
What about K+? At very low external concentrations, K+ can be taken up by active symport proteins, but at higher concentrations it can enter the cell by diffusion through spe-cific K+ channels. However, even influx through channels is driven by the H+-ATPase, in the sense that K+ diffusion is driven by the membrane potential, which is maintained at a value more negative than the K+ equilibrium potential by the action of the electrogenic H+ pump. Conversely, K+ efflux requires the membrane potential to be maintained at a value more positive than EK, which can be achieved if efflux of Cl– through Cl– channels is allowed. Several rep-resentative transport processes located on the plasma mem-brane and the tonoplast are illustrated in Figure 6.11.
MEMBRANE TRANSPORT PROTEINS We have seen in preceding sections that some transmem-brane proteins operate as channels for the controlled dif-fusion of ions. Other membrane proteins act as carriers for other substances (mostly molecules and ions). Active trans-port utilizes carrier-type proteins that are energized directly by ATP hydrolysis or indirectly as symporters and antiporters. The latter systems use the energy of ion gradi-ents (often a H+ gradient) to drive the uphill transport of another ion or molecule. In the pages that follow we will examine in more detail the molecular properties, cellular locations, and genetic manipulations of some of these transport proteins.
Kinetic Analyses Can Elucidate Transport Mechanisms Thus far, we have described cellular transport in terms of its energetics. However, cellular transport can also be stud-ied by use of enzyme kinetics because transport involves the binding and dissociation of molecules at active sites on transport proteins. One advantage of the kinetic approach is that it gives new insights into the regulation of transport.
In kinetic experiments the effects of external ion (or other solute) concentrations on transport rates are mea-sured. The kinetic characteristics of the transport rates can then be used to distinguish between different transporters.
The maximum rate (Vmax) of carrier-mediated transport, and often channel transport as well, cannot be exceeded, regardless of the concentration of substrate (Figure 6.12).
Vmax is approached when the substrate-binding site on the carrier is always occupied. The concentration of carrier, not the concentration of solute, becomes rate limiting. Thus Vmax is a measure of the number of molecules of the spe-cific carrier protein that are functioning in the membrane.
The constant Km (which is numerically equal to the solute concentration that yields half the maximal rate of transport) tends to reflect the properties of the particular binding site (for a detailed discussion on Km and Vmax see Chapter 2 on the web site). Low Km values indicate high affinity of the transport site for the transported substance.
Such values usually imply the operation of a carrier sys-tem. Higher values of Km indicate a lower affinity of the transport site for the solute. The affinity is often so low that in practice Vmax is never reached. In such cases, kinetics alone cannot distinguish between carriers and channels.
Usually transport displays both high-affinity and low-affinity components when a wide range of solute concen-trations are studied. Figure 6.13 shows sucrose uptake by soybean cotyledon protoplasts as a function of the external Solute Transport 99 (Km) 1/2 Vmax Vmax External concentration of transported molecule Rate Simple diffusion Carrier transport FIGURE 6.12 Carrier transport often shows saturation kinetics (Vmax) (see Chapter 2 on the web site), because of saturation of a binding site. Ideally, diffusion through chan-nels is directly proportional to the concentration of the transported solute, or for an ion, to the difference in electro-chemical potential across the membrane.
sucrose concentration (Lin et al. 1984). Uptake increases sharply with concentration and begins to saturate at about 10 mM. At concentrations above 10 mM, uptake becomes linear and nonsaturable. Inhibition of ATP synthesis with metabolic poisons blocks the saturable component but not the linear one. The interpretation is that sucrose uptake at low concentrations is an active carrier-mediated process (sucrose–H+ symport). At higher concentrations, sucrose enters the cells by diffusion down its concentration gradi-ent and is therefore insensitive to metabolic poisons. How-ever, additional information is needed to investigate whether the nonsaturating component represents uptake by a carrier with very low affinity, or by a channel. (Trans-port by a carrier is more likely in the case of a molecular solute such as sucrose.) The Genes for Many Transporters Have Been Cloned Transporter gene identification, isolation, and cloning have greatly aided in the elucidation of the molecular properties of transporter proteins. Nitrate transport is an example that is of interest not only because of its nutritional importance, but also because of its complexity. Kinetic analysis shows that nitrate transport, like the sucrose transport shown in Figure 6.13, has both high-affinity (low Km) and low-affinity (high Km) components. In contrast with sucrose, nitrate is negatively charged, and such an electric charge imposes an energy requirement for the transport of the nitrate ion at all concentrations. The energy is provided by symport with H+.
Nitrate transport is also strongly regulated according to nitrate availability: The enzymes required for nitrate trans-port, as well as nitrate assimilation (see Chapter 12), are induced in the presence of nitrate in the environment, and uptake can also be repressed if nitrate accumulates in the cells.
Mutants in nitrate transport or nitrate reduction can be selected by growth in the presence of chlorate (ClO3 –).
Chlorate is a nitrate analog that is taken up and reduced in wild-type plants to the toxic product chlorite. If plants resistant to chlorate are selected, they are likely to show mutations that block nitrate transport or reduction.
Several such mutations have been identified in Ara-bidopsis, a small crucifer that is ideal for genetic studies. The first transport gene identified in this way encodes a low-affinity inducible nitrate–proton symporter. As more genes for nitrate transport have been identified and character-ized, the picture has become more complex. Each compo-nent of transport may involve more than one gene product, and at least one gene encodes a dual-affinity carrier that contributes to both high-affinity and low-affinity transport (Chrispeels et al. 1999).
The emerging picture of plant transporter genes shows that a family of genes, rather than an individual gene, exists in the plant genome for each transport function.
Within a gene family, variations in transport characteristics such as Km, in mode of regulation, and in differential tissue expression give plants a remarkable plasticity to acclimate to a broad range of environmental conditions.
The identification of regions of sequence similarity between plant transport genes and the transport genes of other organisms, such as yeast, has enabled the cloning of plant transport genes (Kochian 2000). In some cases, it has been possible to identify the gene after purifying the trans-port protein, but often sequence similarity is limited, and individual transport proteins represent too small a fraction of total protein. Another way to identify transport genes is to screen plant cDNA (complementary DNA) libraries for genes that complement (i.e., compensate for) transport defi-ciencies in yeast. Many yeast transport mutants are known and have been used to identify corresponding plant genes by complementation.
In the case of genes for ion channels, researchers have studied the behavior of the channel proteins by express-ing the genes in oocytes of the toad Xenopus, which, because of their large size, are convenient for electro-physiological studies. Genes for both inward- and out-ward-rectifying K+ channels have been cloned and stud-ied in this way. Of the inward K+ channel genes identified so far, one is expressed strongly in stomatal guard cells, another in roots, and a third in leaves. These channels are considered to be responsible for low-affinity K+ uptake into plant cells.
An outward K+ channel responsible for K+ flux from root stelar cells into the dead xylem vessels has been 100 Chapter 6 0 10 20 30 40 50 25 50 75 100 125 0 Sucrose concentration (mM) Rate of sucrose uptake (nmol per 106 cells per hour) Predicted by Michaelis–Menten kinetics Observed FIGURE 6.13 The transport properties of a solute can change at different solute concentrations. For example, at low concentrations (1 to 10 mM), the rate of uptake of sucrose by soybean cells shows saturation kinetics typical of carriers. A curve fit-ted to these data is predicted to approach a maximal rate (Vmax) of 57 nmol per 106 cells per hour. Instead, at higher sucrose concentrations the uptake rate continues to increase linearly over a broad range of concentrations, suggesting the existence of other sucrose transporters, which might be carriers with very low affinity for the substrate. (From Lin et al. 1984.) cloned, and several genes for high-affinity K+ carriers have been identified. Further research is needed to determine to what extent they each contribute to K+ uptake, and how they obtain their energy (see Web Topic 6.4). Genes for plant vacuolar H+–Ca2+ antiporters and genes for the pro-ton symport of several amino acids and sugars have also been identified through various genetic techniques (Hirshi et al. 1996; Tanner and Caspari 1996; Kuehn et al. 1999).
Genes for Specific Water Channels Have Been Identified Aquaporins are a class of proteins that is relatively abun-dant in plant membranes (see Chapter 3). Aquaporins reveal no ion currents when expressed in oocytes, but when the osmolarity of the external medium is reduced, expres-sion of these proteins results in swelling and bursting of the oocytes. The bursting results from rapid influx of water across the oocyte plasma membrane, which normally has a very low water permeability. These results show that aqua-porins form water channels in membranes (see Figure 3.6). The existence of aquaporins was a surprise at first because it was thought that the lipid bilayer is itself suffi-ciently permeable to water. Nevertheless, aquaporins are common in plant and animal membranes, and their expres-sion and activity appear to be regulated, possibly by pro-tein phosphorylation, in response to water availability (Tyerman et al. 2002).
The Plasma Membrane H+-ATPase Has Several Functional Domains The outward, active transport of H+ across the plasma membrane creates gradients of pH and electric potential that drive the transport of many other substances (ions and molecules) through the various secondary active-transport proteins. Figure 6.14 illustrates how a membrane H+-ATPase might work.
Plant and fungal plasma membrane H+-ATPases and Ca2+-ATPases are members of a class known as P-type ATPases, which are phosphorylated as part of the catalytic cycle that hydrolyzes ATP. Because of this phosphorylation step, the plasma membrane ATPases are strongly inhibited by orthovanadate (HVO4 2–), a phosphate (HPO4 2–) analog that competes with phosphate from ATP for the aspartic acid phosphorylation site on the enzyme. The high affinity of the enzyme for vanadate is attributed to the fact that vanadate can mimic the transitional structure of phosphate during hydrolysis.
Plasma membrane H+-ATPases are encoded by a family of about ten genes. Each gene encodes an isoform of the enzyme (Sussman 1994). The isoforms are tissue specific, and they are preferentially expressed in the root, the seed, the phloem, and so on. The functional specificity of each isoform is not yet understood; it may alter the pH optimum of some isoforms and allow transport to be regulated in dif-ferent ways for each tissue.
Solute Transport 101 OUTSIDE OF CELL CYTOPLASM M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ M+ (A) (B) (C) (D) ATP ADP P P P Pi FIGURE 6.14 Hypothetical steps in the transport of a cation (the hypothetical M+) against its chemical gradient by an electrogenic pump. The protein, embedded in the membrane, binds the cation on the inside of the cell (A) and is phosphorylated by ATP (B). This phosphorylation leads to a conformational change that exposes the cation to the outside of the cell and makes it possible for the cation to diffuse away (C). Release of the phosphate ion (P) from the protein into the cytosol (D) restores the initial con-figuration of the membrane protein and allows a new pumping cycle to begin.
Figure 6.15 shows a model of the functional domains of the plasma membrane H+-ATPase of yeast, which is similar to that of plants.
The protein has ten membrane-spanning domains that cause it to loop back and forth across the mem-brane. Some of the membrane-span-ning domains make up the pathway through which protons are pumped.
The catalytic domain, including the aspartic acid residue that becomes phosphorylated during the catalytic cycle, is on the cytosolic face of the membrane.
Like other enzymes, the plasma membrane ATPase is regulated by the concentration of substrate (ATP), pH, temperature, and other factors.
In addition, H+-ATPase molecules can be reversibly activated or deac-tivated by specific signals, such as light, hormones, pathogen attack, and the like. This type of regulation is mediated by a specialized autoin-hibitory domain at the C-terminal end of the polypeptide chain, which acts to regulate the activity of the proton pump (see Figure 6.15). If the autoinhibitory domain is removed through the action of a protease, the enzyme becomes irreversibly activated (Palmgren 2001).
The autoinhibitory effect of the C-terminal domain can also be regulated through the action of protein kinases and phosphatases that add or remove phosphate groups to ser-ine or threonine residues on the autoinhibitory domain of the enzyme. For example, one mechanism of response to pathogens in tomato involves the activation of protein phos-phatases that dephosphorylate residues on the plasma membrane H+-ATPase, thereby activating it (Vera-Estrella et al. 1994). This is one step in a cascade of responses that activate plant defenses.
The Vacuolar H+-ATPase Drives Solute Accumulation into Vacuoles Because plant cells increase their size primarily by taking up water into large, central vacuoles, the osmotic pressure of the vacuole must be maintained sufficiently high for water to enter from the cytoplasm. The tonoplast regulates the traffic of ions and metabolites between the cytosol and the vacuole, just as the plasma membrane regulates uptake into the cell. Tonoplast transport became a vigorous area of research following the development of methods for the iso-lation of intact vacuoles and tonoplast vesicles (see Web Topic 6.5). These studies led to the discovery of a new type of proton-pumping ATPase, which transports protons into the vacuole (see Figure 6.11).
The vacuolar H+-ATPase (also called V-ATPase) differs both structurally and functionally from the plasma mem-brane H+-ATPase. The vacuolar ATPase is more closely related to the F-ATPases of mitochondria and chloroplasts (see Chapter 11). Because the hydrolysis of ATP by the vac-uolar ATPase does not involve the formation of a phos-phorylated intermediate, vacuolar ATPases are insensitive to vanadate, the inhibitor of plasma membrane ATPases discussed earlier. Vacuolar ATPases are specifically inhib-ited by the antibiotic bafilomycin, as well as by high con-centrations of nitrate, neither of which inhibit plasma mem-brane ATPases. Use of these selective inhibitors makes it possible to identify different types of ATPases, and to assay their activity.
Vacuolar ATPases belong to a general class of ATPases that are present on the endomembrane systems of all FIGURE 6.15 Two-dimensional rep-resentation of the plasma membrane H+-ATPase. The H+-ATPase has 10 transmembrane segments. The regu-latory domain is the autoinhibitory domain. (From Palmgren 2001.) COOH Regulatory domain Transmembrane domains Plasma membrane OUTSIDE OF CELL CYTOPLASM eukaryotes. They are large enzyme complexes, about 750 kDa, composed of at least ten different subunits (Lüttge and Ratajczak 1997). These subunits are organized into a peripheral catalytic complex, V1, and an integral membrane channel complex, V0 (Figure 6.16). Because of their simi-larities to F-ATPases, vacuolar ATPases are assumed to operate like tiny rotary motors (see Chapter 11).
Vacuolar ATPases are electrogenic proton pumps that trans-port protons from the cytoplasm to the vacuole and generate a proton motive force across the tonoplast. The electrogenic proton pumping accounts for the fact that the vacuole is typ-ically 20 to 30 mV more positive than the cytoplasm, although it is still negative relative to the external medium. To maintain bulk electrical neutrality, anions such as Cl– or malate2– are transported from the cytoplasm into the vacuole through channels in the membrane (Barkla and Pantoja 1996). Without the simultaneous movement of anions along with the pumped protons, the charge buildup across the tonoplast would make the pumping of additional protons energetically impossible.
The conservation of bulk electrical neutrality by anion transport makes it possible for the vacuolar H+-ATPase to generate a large concentration (pH) gradient of protons across the tonoplast. This gradient accounts for the fact that the pH of the vacuolar sap is typically about 5.5, while the cytoplasmic pH is 7.0 to 7.5. Whereas the electrical compo-nent of the proton motive force drives the uptake of anions into the vacuole, the electrochemical-potential gradient for H+ (∆m m ~ H+) is harnessed to drive the uptake of cations and sugars into the vacuole via secondary transport (antiporter) systems (see Figure 6.11).
Although the pH of most plant vacuoles is mildly acidic (about 5.5), the pH of the vacuoles of some species is much lower—a phenomenon termed hyperacidification. Vacuolar hyperacidification is the cause of the sour taste of certain fruits (lemons) and vegetables (rhubarb). Some extreme examples are listed in Table 6.2. Biochemical studies with lemon fruits have suggested that the low pH of the lemon fruit vacuoles (specifically, those of the juice sac cells) is due to a combination of factors: • The low permeability of the vacuolar membrane to protons permits a steeper pH gradient to build up.
• A specialized vacuolar ATPase is able to pump pro-tons more efficiently (with less wasted energy) than normal vacuolar ATPases can (Müller et al. 1997).
Solute Transport 103 V1 V0 CYTOPLASM LUMEN OF VACUOLE H+ H+ B A A A B B C E H D c d F a a G Tonoplast FIGURE 6.16 Model of the V-ATPase rotary motor. Many polypep-tide subunits come together to make this complex enzyme. The V1 catalytic complex is easily dissociated from the membrane, and contains the nucleotide-binding and catalytic sites. Components of V1 are designated by uppercase letters. The intrinsic membrane complex mediating H+ transport is designated V0, and its subunits are given lowercase letters. It is proposed that ATPase reactions catalyzed by each of the A subunits, acting in sequence, drive the rotation of the shaft D and the six c subunits. The rotation of the c subunits relative to subunit a is thought to drive the transport of H+ across the membrane. (Based on an illustration courtesy of M.
F. Manolson.) TABLE 6.2 The vacuolar pH of some hyperacidifying plant species Tissue Species pHa Fruits Lime (Citrus aurantifolia) 1.7 Lemon (Citrus limonia) 2.5 Cherry (Prunus cerasus) 2.5 Grapefruit (Citrus paradisi) 3.0 Leaves Rosette oxalis (Oxalis deppei) 1.3 Wax begonia 1.5 (Begonia semperflorens) Begonia ‘Lucerna’ 0.9 – 1.4 Oxalis sp.
1.9 – 2.6 Sorrel (Rumex sp.) 2.6 Prickly Pear 1.4 (6:45 A.M.) (Opuntia phaeacantha)b 5.5 (4:00 P.M.) Source: Data from Small 1946.
a The values represent the pH of the juice or expressed sap of each tissue, usually a good indicator of vacuolar pH.
b The vacuolar pH of the cactus Opuntia phaeacantha varies with the time of day. As will be discussed in Chapter 8, many desert succu-lents have a specialized type of photosynthesis, called crassulacean acid metabolism (CAM), that causes the pH of the vacuoles to decrease during the night.
• The accumulation of organic acids such as citric, malic, and oxalic acids helps maintain the low pH of the vacuole by acting as buffers.
Plant Vacuoles Are Energized by a Second Proton Pump, the H+-Pyrophosphatase Another type of proton pump, an H+-pyrophosphatase (H+-PPase) (Rea et al. 1998), appears to work in parallel with the vacuolar ATPase to create a proton gradient across the tonoplast (see Figure 6.11). This enzyme consists of a single polypeptide that has a molecular mass of 80 kDa.
The H+-PPase harnesses its energy from the hydrolysis of inorganic pyrophosphate (PPi).
The free energy released by PPi hydrolysis is less than that from ATP hydrolysis. However, the vacuolar H+-PPase trans-ports only one H+ ion per PPi molecule hydrolyzed, whereas the vacuolar ATPase appears to transport two H+ ions per ATP hydrolyzed. Thus the energy available per H+ ion trans-ported appears to be the same, and the two enzymes appear to be able to generate comparable H+ gradients.
In some plants the synthesis of the vacuolar H+-PPase is induced by low O2 levels (hypoxia) or by chilling. This indicates that the vacuolar H+-PPase might function as a backup system to maintain essential cell metabolism under conditions in which ATP supply is depleted because of the inhibition of respiration by hypoxia or chilling. It is of inter-est that the plant vacuolar H+-PPase is not found in ani-mals or yeast, although a similar enzyme is present in some bacteria and protists.
Large metabolites such as flavonoids, anthocyanins and secondary products of metabolism are sequestered in the vacuole. These large molecules are transported into vac-uoles by ATP-binding cassette (ABC) transporters. Trans-port processes by the ABC transporters consume ATP and do not depend on a primary electrochemical gradient (see Web Topic 6.6). Recent studies have shown that ABC trans-porters can also be found at the plasma membrane and in mitochondria (Theodoulou 2000).
Calcium Pumps, Antiports, and Channels Regulate Intracellular Calcium Calcium is another important ion whose concentration is strongly regulated. Calcium concentrations in the cell wall and the apoplastic (extracellular) spaces are usually in the millimolar range; free cytosolic Ca2+ concentrations are maintained at the micromolar (10–6 M) range, against the large electrochemical-potential gradient that drives Ca2+ diffusion into the cell. Small fluctuations in cytosolic Ca2+ concentration dras-tically alter the activities of many enzymes, making cal-cium an important second messenger in signal transduc-tion. Most of the calcium in the cell is stored in the central vacuole, where it is taken up via Ca2+–H+ antiporters, which use the electrochemical potential of the proton gra-dient to energize the accumulation of calcium into the vac-uole (Bush 1995). Mitochondria and the endoplasmic retic-ulum also store calcium within the cells.
Calcium efflux from the vacuole into the cytosol may in some cells be triggered by inositol trisphosphate (IP3). IP3, which appears to act as a “second messenger” in certain sig-nal transduction pathways, induces the opening of IP3-gated calcium channels on the tonoplast and endoplasmic reticu-lum (ER). (For a more detailed description of these sensory transduction pathways see Chapter 14 on the web site.) Calcium ATPases are found at the plasma membrane (Chung et al. 2000) and in some endomembranes of plant cells (see Figure 6.11). Plant cells regulate cytosolic Ca2+ con-centrations by controlling the opening of Ca2+ channels that allow calcium to diffuse in, as well as by modulating the activity of pumps that drive Ca2+ out of the cytoplasm back into the extracellular spaces. Whereas the plasma membrane calcium pumps move calcium out of the cell, the calcium pumps on the ER transport calcium into the ER lumen.
ION TRANSPORT IN ROOTS Mineral nutrients absorbed by the root are carried to the shoot by the transpiration stream moving through the xylem (see Chapter 4). Both the initial uptake of nutrients and the subsequent movement of mineral ions from the root surface across the cortex and into the xylem are highly specific, well-regulated processes.
Ion transport across the root obeys the same biophysi-cal laws that govern cellular transport. However, as we have seen in the case of water movement (see Chapter 4), the anatomy of roots imposes some special constraints on the pathway of ion movement. In this section we will dis-cuss the pathways and mechanisms involved in the radial movement of ions from the root surface to the tracheary elements of the xylem.
Solutes Move through Both Apoplast and Symplast Thus far, our discussion of cellular ion transport has not included the cell wall. In terms of the transport of small molecules, the cell wall is an open lattice of polysaccharides through which mineral nutrients diffuse readily. Because all plant cells are separated by cell walls, ions can diffuse across a tissue (or be carried passively by water flow) entirely through the cell wall space without ever entering a living cell. This continuum of cell walls is called the extra-cellular space, or apoplast (see Figure 4.3).
We can determine the apoplastic volume of a slice of plant tissue by comparing the uptake of 3H-labeled water and 14C-labeled mannitol. Mannitol is a nonpermeating sugar alcohol that diffuses within the extracellular space but cannot enter the cells. Water, on the other hand, freely penetrates both the cells and the cell walls. Measurements of this type usually show that 5 to 20% of the plant tissue volume is occupied by cell walls.
104 Chapter 6 Just as the cell walls form a continuous phase, so do the cytoplasms of neighboring cells, collectively referred to as the symplast. Plant cells are interconnected by cytoplasmic bridges called plasmodesmata (see Chapter 1), cylindrical pores 20 to 60 nm in diameter (see Figure 1.27). Each plas-modesma is lined with a plasma membrane and contains a narrow tubule, the desmotubule, that is a continuation of the endoplasmic reticulum.
In tissues where significant amounts of intercellular transport occur, neighboring cells contain large numbers of plasmodesmata, up to 15 per square micrometer of cell sur-face (Figure 6.17). Specialized secretory cells, such as floral nectaries and leaf salt glands, appear to have high densi-ties of plasmodesmata; so do the cells near root tips, where most nutrient absorption occurs.
By injecting dyes or by making electrical-resistance mea-surements on cells containing large numbers of plasmod-esmata, investigators have shown that ions, water, and small solutes can move from cell to cell through these pores. Because each plasmodesma is partly occluded by the desmotubule and associated proteins (see Chapter 1), the movement of large molecules such as proteins through the plasmodesmata requires special mechanisms (Ghoshroy et al. 1997). Ions, on the other hand, appear to move from cell to cell through the entire plant by simple diffusion through the symplast (see Chapter 4).
Ions Moving through the Root Cross Both Symplastic and Apoplastic Spaces Ion absorption by the roots (see Chapter 5) is more pro-nounced in the root hair zone than in the meristem and elongation zones. Cells in the root hair zone have com-pleted their elongation but have not yet begun secondary growth. The root hairs are simply extensions of specific epi-dermal cells that greatly increase the surface area available for ion absorption.
An ion that enters a root may immediately enter the symplast by crossing the plasma membrane of an epider-mal cell, or it may enter the apoplast and diffuse between the epidermal cells through the cell walls. From the apoplast of the cortex, an ion may either cross the plasma membrane of a cortical cell, thus entering the symplast, or diffuse radi-ally all the way to the endodermis via the apoplast. In all cases, ions must enter the symplast before they can enter the stele, because of the presence of the Casparian strip.
The apoplast forms a continuous phase from the root surface through the cortex. At the boundary between the vascular cylinder (the stele) and the cortex is a layer of spe-cialized cells, the endodermis. As discussed in Chapters 4 and 5, a suberized cell layer in the endodermis, known as the Casparian strip, effectively blocks the entry of water and mineral ions into the stele via the apoplast.
Once an ion has entered the stele through the symplas-tic connections across the endodermis, it continues to dif-fuse from cell to cell into the xylem. Finally, the ion reen-ters the apoplast as it diffuses into a xylem tracheid or vessel element. Again, the Casparian strip prevents the ion from diffusing back out of the root through the apoplast.
The presence of the Casparian strip allows the plant to maintain a higher ionic concentration in the xylem than exists in the soil water surrounding the roots.
Xylem Parenchyma Cells Participate in Xylem Loading Once ions have been taken up into the symplast of the root at the epidermis or cortex, they must be loaded into the tra-cheids or vessel elements of the stele to be translocated to the shoot. The stele consists of dead tracheary elements and Solute Transport 105 Plasma membrane Middle lamella Cell wall Tonoplast Cytoplasm Vacuole Plasmodesma Protein particles on outer leaflet of ER Protein particles on inner leaflet of ER Protein particles on inner leaflet of plasma membrane Desmotubule with appressed ER Endoplasmic reticulum FIGURE 6.17 Diagram illustrating how plasmodesmata con-nect the cytoplasms of neighboring cells. Plasmodesmata are about 40 nm in diameter and allow diffusion of water and small molecules from one cell to the next. In addition, the size of the opening can be regulated by rearrange-ments of the internal proteins to allow the passage of larger molecules.
the living xylem parenchyma. Because the xylem tracheary elements are dead cells, they lack cytoplasmic continuity with surrounding xylem parenchyma. To enter the tra-cheary elements, the ions must exit the symplast by cross-ing a plasma membrane a second time. The process whereby ions exit the symplast and enter the conducting cells of the xylem is called xylem loading.
The mechanism of xylem loading has long baffled scien-tists. Ions could enter the tracheids and vessel elements of the xylem by simple passive diffusion. In this case, the movement of ions from the root surface to the xylem would take only a single step requiring metabolic energy.
The site of this single-step, energy-dependent uptake would be the plasma membrane surfaces of the root epi-dermal, cortical, or endodermal cells. According to the pas-sive-diffusion model, ions move passively into the stele via the symplast down a gradient of electrochemical potential, and then leak out of the living cells of the stele (possibly because of lower oxygen availability in the interior of the root) into the nonliving conducting cells of the xylem.
Support for the passive-diffusion model was provided by use of ion-specific microelectrodes to measure the elec-trochemical potentials of various ions across maize roots (Figure 6.18) (Dunlop and Bowling 1971). Data from this and other studies indicate that K+, Cl–, Na+, SO4 2–, and NO3 – are all taken up actively by the epidermal and corti-cal cells and are maintained in the xylem against a gradi-ent of electrochemical potential when compared with the external medium (Lüttge and Higinbotham 1979). How-ever, none of these ions is at a higher electrochemical potential in the xylem than in the cortex or living portions of the stele. Therefore, the final movement of ions into the xylem could be due to passive diffusion.
However, other observations have led to the view that this final step of xylem loading may also involve active processes within the stele (Lüttge and Higinbotham 1979).
With the type of apparatus shown in Figure 6.19, it is pos-sible to make simultaneous measurements of ion uptake into the epidermal or cortical cytoplasm and of ion loading into the xylem.
By using treatments with inhibitors and plant hormones, investigators have shown that ion uptake by the cortex and ion loading into the xylem operate independently. For example, treatment with the protein synthesis inhibitor cycloheximide or with the cytokinin benzyladenine inhibits xylem loading without affecting uptake by the cortex. This result indicates that efflux from the stelar cells is regulated independently from uptake by the cortical cells.
Recent biochemical studies have supported a role for the xylem parenchyma cells in xylem loading. The plasma 106 Chapter 6 Outside solution Epidermis Cortex Endodermis Xylem parenchyma Xylem tracheary Electrochemical potential High Low Chloride (Cl–) Potassium (K+) Stele Casparian strip FIGURE 6.18 Diagram showing electrochemical potentials of K+ and Cl– across a maize root. To determine the electro-chemical potentials, the root was bathed in a solution con-taining 1 mM KCl and 0.1 mM CaCl2. A reference electrode was positioned in the bathing solution, and an ion-sensitive measuring electrode was inserted in different cells of the root. The horizontal axis shows the different tissues found in a root cross section. The substantial increase in electro-chemical potential for both K+ and Cl– between the bathing medium and the epidermis indicates that ions are taken up into the root by an active transport process. In contrast, the potentials decrease at the xylem vessels, suggesting that ions are transported into the xylem by passive diffusion down the gradient of electrochemical potential. (After Dunlop and Bowling 1971.) membranes of xylem parenchyma cells contain proton pumps, water channels, and a variety of ion channels spe-cialized for influx or efflux (Maathuis et al. 1997). In barley xylem parenchyma, two types of cation efflux channels have been identified: K+-specific efflux channels and non-selective cation efflux channels. These channels are regu-lated by both the membrane potential and the cytosolic cal-cium concentration (De Boer and Wegner 1997). This finding suggests that the flux of ions from the xylem parenchyma cells into the xylem tracheary elements, rather than being due to simple leakage, is under tight metabolic control through regulation of the plasma membrane H+-ATPase and ion efflux channels.
SUMMARY The movement of molecules and ions from one location to another is known as transport. Plants exchange solutes and water with their environment and among their tissues and organs. Both local and long-distance transport processes in plants are controlled largely by cellular membranes.
Forces that drive biological transport, which include concentration gradients, electric-potential gradients, and hydrostatic pressures, are integrated by an expression called the electrochemical potential. Transport of solutes down a chemical gradient (e.g., by diffusion) is known as passive transport. Movement of solutes against a chemical-potential gradient is known as active transport and requires energy input.
The extent to which a membrane permits or restricts the movement of a substance is called membrane permeabil-ity. The permeability depends on the chemical properties of the particular solute and on the lipid composition of the membrane, as well as on the membrane proteins that facil-itate the transport of specific substances.
When cations and anions move passively across a mem-brane at different rates, the electric potential that develops is called the diffusion potential. For each ion, the relation-ship between the voltage difference across the membrane and the distribution of the ion at equilibrium is described by the Nernst equation. The Nernst equation shows that at equilibrium the difference in concentration of an ion between two compartments is balanced by the voltage dif-ference between the compartments. That voltage difference, or membrane potential, is seen in all living cells because of the asymmetric ion distributions between the inside and outside of the cells. The electrical effects of different ions diffusing simul-taneously across a cell membrane are summed by the Goldman equation. Electrogenic pumps, which carry out active transport and carry a net charge, change the mem-brane potential from the value created by diffusion.
Membranes contain specialized proteins—channels, car-riers, and pumps—that facilitate solute transport. Channels are transport proteins that span the membrane, forming pores through which solutes diffuse down their gradient of electrochemical potentials. Carriers bind a solute on one side of the membrane and release it on the other side.
Transport specificity is determined largely by the proper-ties of channels and carriers.
A family of H+-pumping ATPases provides the primary driving force for transport across the plasma membrane of plant cells. Two other kinds of electrogenic proton pumps serve this purpose at the tonoplast. Plant cells also have cal-cium-pumping ATPases that participate in the regulation of intracellular calcium concentrations, as well as ATP-binding cassette transporters that use the energy of ATP to transport large anionic molecules. The gradient of electro-chemical potential generated by H+ pumping is used to drive the transport of other substances in a process called secondary transport. Genetic studies have revealed many genes, and their corresponding transport proteins, that account for the ver-satility of plant transport. Patch clamp electrophysiology provides unique information on ion channels, and it enables measurement of the permeability and gating of individual channel proteins.
Solutes move between cells either through the extra-cellular spaces (the apoplast) or from cytoplasm to cyto-plasm (via the symplast). Cytoplasms of neighboring cells are connected by plasmodesmata, which facilitate sym-plastic transport. When an ion enters the root, it may be taken up into the cytoplasm of an epidermal cell, or it may diffuse through the apoplast into the root cortex and enter the symplast through a cortical cell. From the symplast, the ion is loaded into the xylem and transported to the shoot.
Solute Transport 107 Compartment A Compartment B Root segment Ion uptake measurement Xylem-loading measurement Radioactive tracer added FIGURE 6.19 We can measure the relationship between ion uptake into the root and xylem loading by placing a root seg-ment across two compartments and adding a radioactive tracer to one of them (in this case compartment A). The rate of disap-pearance of the tracer from compartment A gives a measure of ion uptake, and the rate of appearance in compartment B pro-vides a measurement of xylem loading. (From Lüttge and Higinbotham 1979.) Web Material Web Topics 6.1 Relating the Membrane Potential to the Distribution of Several Ions across the Membrane:The Goldman Equation A brief explanation of the use of the Goldman equation to calculate the membrane permeabil-ity of more than one ion.
6.2 Patch Clamp Studies in Plant Cells The electrophysiological method of patch clamping as applied to plant cells is described, with some specific examples.
6.3 Chemiosmosis in Action The chemiosmotic theory explains how electrical and concentration gradients are used to perform cellular work.
6.4 Kinetic Analysis of Multiple Transporter Systems Application of principles on enzyme kinetics to transport systems provides an effective way to characterize different carriers.
6.5 Transport Studies with Isolated Vacuoles and Membrane Vesicles Certain experimental techniques enable the iso-lation of tonoplasts and plasma membranes for study.
6.6 ABC Transporters in Plants ATP-binding cassette (ABC) transporters are a large family of active transport proteins ener-gized directly by ATP.
Web Essay 6.1 Potassium Channels Several plant K+ channels have been characterized.
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108 Chapter 6 Biochemistry and Metabolism U N I T II Photosynthesis: The Light Reactions 7 Chapter LIFE ON EARTH ULTIMATELY DEPENDS ON ENERGY derived from the sun. Photosynthesis is the only process of biological importance that can harvest this energy. In addition, a large fraction of the planet’s energy resources results from photosynthetic activity in either recent or ancient times (fossil fuels). This chapter introduces the basic physical principles that underlie photosynthetic energy storage and the current understanding of the structure and function of the photosynthetic appa-ratus (Blankenship 2002).
The term photosynthesis means literally “synthesis using light.” As we will see in this chapter, photosynthetic organisms use solar energy to synthesize carbon compounds that cannot be formed without the input of energy. More specifically, light energy drives the synthesis of carbo-hydrates from carbon dioxide and water with the generation of oxygen: 6 CO2 + 6 H2O → C6H12O6 + 6 O2 Carbon Water Carbohydrate Oxygen dioxide Energy stored in these molecules can be used later to power cellular processes in the plant and can serve as the energy source for all forms of life.
This chapter deals with the role of light in photosynthesis, the struc-ture of the photosynthetic apparatus, and the processes that begin with the excitation of chlorophyll by light and culminate in the synthesis of ATP and NADPH.
PHOTOSYNTHESIS IN HIGHER PLANTS The most active photosynthetic tissue in higher plants is the mesophyll of leaves. Mesophyll cells have many chloroplasts, which contain the specialized light-absorbing green pigments, the chlorophylls. In photo-synthesis, the plant uses solar energy to oxidize water, thereby releasing oxygen, and to reduce carbon dioxide, thereby forming large carbon compounds, primarily sugars. The complex series of reactions that cul-minate in the reduction of CO2 include the thylakoid reac-tions and the carbon fixation reactions.
The thylakoid reactions of photosynthesis take place in the specialized internal membranes of the chloroplast called thylakoids (see Chapter 1). The end products of these thylakoid reactions are the high-energy compounds ATP and NADPH, which are used for the synthesis of sug-ars in the carbon fixation reactions. These synthetic processes take place in the stroma of the chloroplasts, the aqueous region that surrounds the thylakoids. The thy-lakoid reactions of photosynthesis are the subject of this chapter; the carbon fixation reactions are discussed in Chapter 8.
In the chloroplast, light energy is converted into chem-ical energy by two different functional units called photo-systems. The absorbed light energy is used to power the transfer of electrons through a series of compounds that act as electron donors and electron acceptors. The majority of electrons ultimately reduce NADP+ to NADPH and oxi-dize H2O to O2. Light energy is also used to generate a pro-ton motive force (see Chapter 6) across the thylakoid mem-brane, which is used to synthesize ATP.
GENERAL CONCEPTS In this section we will explore the essential concepts that provide a foundation for an understanding of photosyn-thesis. These concepts include the nature of light, the prop-erties of pigments, and the various roles of pigments.
Light Has Characteristics of Both a Particle and a Wave A triumph of physics in the early twentieth century was the realization that light has properties of both particles and waves. A wave (Figure 7.1) is characterized by a wave-length, denoted by the Greek letter lambda (l), which is the distance between successive wave crests. The frequency, represented by the Greek let-ter nu (n), is the number of wave crests that pass an observer in a given time. A simple equation relates the wavelength, the frequency, and the speed of any wave: c = ln (7.1) where c is the speed of the wave—in the present case, the speed of light (3.0 × 108 m s–1). The light wave is a trans-verse (side-to-side) electro-magnetic wave, in which both electric and magnetic fields oscillate perpendicularly to the direction of propagation of the wave and at 90° with respect to each other.
Light is also a particle, which we call a photon. Each photon contains an amount of energy that is called a quan-tum (plural quanta). The energy content of light is not con-tinuous but rather is delivered in these discrete packets, the quanta. The energy (E) of a photon depends on the fre-quency of the light according to a relation known as Planck’s law: E = hn (7.2) where h is Planck’s constant (6.626 × 10–34 J s).
Sunlight is like a rain of photons of different frequencies.
Our eyes are sensitive to only a small range of frequen-cies—the visible-light region of the electromagnetic spec-trum (Figure 7.2). Light of slightly higher frequencies (or 112 Chapter 7 Electric-field component Magnetic-field component Direction of propagation Wavelength (l) FIGURE 7.1 Light is a transverse electromagnetic wave, consisting of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propa-gation of the light. Light moves at a speed of 3 × 108 m s–1.
The wavelength (l) is the distance between successive crests of the wave.
10–3 10–1 10 103 105 107 109 1011 1013 1015 1020 1018 1016 1014 1012 1010 108 106 104 102 Gamma ray High energy Low energy Radio wave Ultra-violet X-ray Infrared Microwave Wavelength, l (nm) Frequency, n (Hz) Type of radiation 400 700 Visible spectrum FIGURE 7.2 Electromagnetic spectrum. Wavelength (λ) and frequency (ν) are inversely related. Our eyes are sensitive to only a narrow range of wavelengths of radiation, the visible region, which extends from about 400 nm (violet) to about 700 nm (red). Short-wavelength (high-frequency) light has a high energy content; long-wavelength (low-frequency) light has a low energy content.
shorter wavelengths) is in the ultravi-olet region of the spectrum, and light of slightly lower frequencies (or longer wavelengths) is in the infrared region.
The output of the sun is shown in Fig-ure 7.3, along with the energy density that strikes the surface of Earth. The absorption spectrum of chlorophyll a (curve C in Figure 7.3) indicates ap-proximately the portion of the solar output that is utilized by plants.
An absorption spectrum (plural spectra) displays the amount of light energy taken up or absorbed by a mol-ecule or substance as a function of the wavelength of the light. The absorp-tion spectrum for a particular substance in a nonabsorbing solvent can be determined by a spectrophotometer as illus-trated in Figure 7.4. Spectrophotometry, the technique used to measure the absorption of light by a sample, is more completely discussed in Web Topic 7.1.
When Molecules Absorb or Emit Light,They Change Their Electronic State Chlorophyll appears green to our eyes because it absorbs light mainly in the red and blue parts of the spectrum, so only some of the light enriched in green wavelengths (about 550 nm) is reflected into our eyes (see Figure 7.3).
The absorption of light is represented by Equation 7.3, in which chlorophyll (Chl) in its lowest-energy, or ground, state absorbs a photon (represented by hn) and makes a transition to a higher-energy, or excited, state (Chl): Chl + hn →Chl (7.3) The distribution of electrons in the excited molecule is somewhat different from the distribution in the ground-state molecule (Figure 7.5) Absorption of blue light excites the chlorophyll to a higher energy state than absorption of red light because the energy of photons is higher when their wavelength is shorter. In the higher excited state, chlorophyll is extremely unstable, very rapidly gives up some of its energy to the surroundings as heat, and enters the lowest excited state, where it can be stable for a maxi-mum of several nanoseconds (10–9 s). Because of this inher-ent instability of the excited state, any process that captures its energy must be extremely rapid.
In the lowest excited state, the excited chlorophyll has four alternative pathways for disposing of its available energy.
1. Excited chlorophyll can re-emit a photon and thereby return to its ground state—a process known as fluo-rescence. When it does so, the wavelength of fluores-cence is slightly longer (and of lower energy) than the wavelength of absorption because a portion of the excitation energy is converted into heat before the flu-orescent photon is emitted. Chlorophylls fluoresce in the red region of the spectrum.
2. The excited chlorophyll can return to its ground state by directly converting its excitation energy into heat, with no emission of a photon.
Photosynthesis: The Light Reactions 113 FIGURE 7.3 The solar spectrum and its relation to the absorption spectrum of chlorophyll. Curve A is the energy output of the sun as a function of wavelength. Curve B is the energy that strikes the surface of Earth. The sharp val-leys in the infrared region beyond 700 nm represent the absorption of solar energy by molecules in the atmosphere, chiefly water vapor. Curve C is the absorption spectrum of chlorophyll, which absorbs strongly in the blue (about 430 nm) and the red (about 660 nm) portions of the spectrum.
Because the green light in the middle of the visible region is not efficiently absorbed, most of it is reflected into our eyes and gives plants their characteristic green color.
1.0 1.5 2.0 0.5 400 800 1200 Wavelength, l Irradiance W m–2 nm–1 1600 2000 Visible spectrum Solar output Energy at Earth‘s surface Absorption of chlorophyll I0 I Light Prism Monochromator Sample Transmitted light Monochromatic incident light Photodetector Recorder or computer l(nm) A FIGURE 7.4 Schematic diagram of a spectrophotometer. The instrument consists of a light source, a monochromator that contains a wavelength selection device such as a prism, a sample holder, a photodetector, and a recorder or computer.
The output wavelength of the monochromator can be changed by rotation of the prism; the graph of absorbance (A) versus wavelength (λ) is called a spectrum.
114 Chapter 7 Wavelength, l Ground state (lowest energy state) Red Blue 400 500 600 700 900 800 Energy Absorption of blue light Absorption of red light Fluorescence Absorption Fluorescence (loss of energy by emission of light of longer l) Heat loss Lowest excited state Higher excited state (A) (B) FIGURE 7.5 Light absorption and emis-sion by chlorophyll. (A) Energy level diagram. Absorption or emission of light is indicated by vertical lines that connect the ground state with excited electron states. The blue and red absorption bands of chlorophyll (which absorb blue and red photons, respectively) corre-spond to the upward vertical arrows, signifying that energy absorbed from light causes the molecule to change from the ground state to an excited state. The downward-pointing arrow indicates fluorescence, in which the molecule goes from the lowest excited state to the ground state while re-emitting energy as a photon. (B) Spectra of absorption and fluorescence. The long-wavelength (red) absorption band of chlorophyll corre-sponds to light that has the energy required to cause the transition from the ground state to the first excited state.
The short-wavelength (blue) absorption band corresponds to a transition to a higher excited state. H H H CH3 CH2 CH2 COOCH3 CH3 H3C H3C CH2 H H C H H H H H O C2H5 C2H5 C2H5 H3C C O O CH2 CH C (CH2)3 (CH2)3 (CH2)3 CH3 CH3 CH3 HC HC CH CH3 CH3 H3C NH CH O H N N N N N N A A B B B D E C CHO H3C O H H CH3 C H NH N O NH H3C H3C H3C H3C CH2 HOOC CH2 CH2 HOOC CH2 CH H3C CH HC C HC CH HC C HC CH HC CH HC H3C CH HC CH HC CH HC CH3 H3C H3C H3C CH3 CH3 CH3 CH3 CH3 CH3 Mg H (C) Bilin pigments (B) Carotenoids Phycoerythrobilin Chlorophyll a Chlorophyll b Bacteriochlorophyll a β-Carotene (A) Chlorophylls 3. Chlorophyll may participate in energy transfer, dur-ing which an excited chlorophyll transfers its energy to another molecule.
4. A fourth process is photochemistry, in which the energy of the excited state causes chemical reactions to occur. The photochemical reactions of photosyn-thesis are among the fastest known chemical reac-tions. This extreme speed is necessary for photo-chemistry to compete with the three other possible reactions of the excited state just described.
Photosynthetic Pigments Absorb the Light That Powers Photosynthesis The energy of sunlight is first absorbed by the pigments of the plant. All pigments active in photosynthesis are found in the chloroplast. Structures and absorption spectra of sev-eral photosynthetic pigments are shown in Figures 7.6 and 7.7, respectively. The chlorophylls and bacteriochloro-phylls (pigments found in certain bacteria) are the typical pigments of photosynthetic organisms, but all organisms contain a mixture of more than one kind of pigment, each serving a specific function.
Chlorophylls a and b are abundant in green plants, and c and d are found in some protists and cyanobacteria. A number of different types of bacteriochlorophyll have been found; type a is the most widely distributed. Web Topic 7.2 shows the distribution of pigments in different types of photosynthetic organisms.
All chlorophylls have a complex ring structure that is chemically related to the porphyrin-like groups found in hemoglobin and cytochromes (see Figure 7.6A). In addition, a long hydrocarbon tail is almost always attached to the ring structure. The tail anchors the chlorophyll to the hydropho-bic portion of its environment. The ring structure contains some loosely bound electrons and is the part of the molecule involved in electron transitions and redox reactions.
The different types of carotenoids found in photosyn-thetic organisms are all linear molecules with multiple con-jugated double bonds (see Figure 7.6B). Absorption bands in the 400 to 500 nm region give carotenoids their charac-teristic orange color. The color of carrots, for example, is due to the carotenoid β-carotene, whose structure and absorp-tion spectrum are shown in Figures 7.6 and 7.7, respectively.
Carotenoids are found in all photosynthetic organisms, except for mutants incapable of living outside the labora-tory. Carotenoids are integral constituents of the thylakoid membrane and are usually associated intimately with both antenna and reaction center pigment proteins. The light absorbed by the carotenoids is transferred to chlorophyll for photosynthesis; because of this role they are called accessory pigments.
KEY EXPERIMENTS IN UNDERSTANDING PHOTOSYNTHESIS Establishing the overall chemical equation of photosyn-thesis required several hundred years and contributions by many scientists (literature references for historical developments can be found on the web site). In 1771, Joseph Priestley observed that a sprig of mint growing in air in which a candle had burned out improved the air so that another candle could burn. He had discovered oxygen evolution by plants. A Dutchman, Jan Ingenhousz, documented the essential role of light in photosynthesis in 1779.
Other scientists established the roles of CO2 and H2O and showed that organic Photosynthesis: The Light Reactions 115 FIGURE 7.6 Molecular structure of some photosynthetic pigments. (A) The chlorophylls have a porphyrin-like ring structure with a magnesium atom (Mg) coordinated in the center and a long hydrophobic hydrocarbon tail that anchors them in the photosynthetic membrane. The porphyrin-like ring is the site of the electron rearrangements that occur when the chlorophyll is excited and of the unpaired electrons when it is either oxidized or reduced.
Various chlorophylls differ chiefly in the substituents around the rings and the pattern of double bonds. (B) Carotenoids are linear polyenes that serve as both antenna pigments and photoprotective agents. (C) Bilin pigments are open-chain tetrapyrroles found in antenna structures known as phyco-bilisomes that occur in cyanobacteria and red algae.
400 500 600 700 800 1 5 2 4 3 Absorption Wavelength (nm) Visible spectrum Infrared FIGURE 7.7 Absorption spectra of some photosynthetic pigments. Curve 1, bacteriochlorophyll a; curve 2, chlorophyll a; curve 3, chlorophyll b; curve 4, phycoerythrobilin; curve 5, β-carotene. The absorption spectra shown are for pure pig-ments dissolved in nonpolar solvents, except for curve 4, which represents an aqueous buffer of phycoerythrin, a pro-tein from cyanobacteria that contains a phycoerythrobilin chromophore covalently attached to the peptide chain. In many cases the spectra of photosynthetic pigments in vivo are substantially affected by the environment of the pigments in the photosynthetic membrane. (After Avers 1985.) L matter, specifically carbohydrate, is a product of photo-synthesis along with oxygen. By the end of the nineteenth century, the balanced overall chemical reaction for photo-synthesis could be written as follows: (7.4) where C6H12O6 represents a simple sugar such as glucose.
As will be discussed in Chapter 8, glucose is not the actual product of the carbon fixation reactions. However, the ener-getics for the actual products is approximately the same, so the representation of glucose in Equation 7.4 should be regarded as a convenience but not taken literally.
The chemical reactions of photosynthesis are complex. In fact, at least 50 intermediate reaction steps have now been identified, and undoubtedly additional steps will be discov-ered. An early clue to the chemical nature of the essential chemical process of photosynthesis came in the 1920s from investigations of photosynthetic bacteria that did not produce oxygen as an end product. From his studies on these bacte-ria, C. B. van Niel concluded that photosynthesis is a redox (reduction–oxidation) process. This conclusion has been con-firmed, and it has served as a fundamental concept on which all subsequent research on photosynthesis has been based.
We now turn to the relationship between photosynthetic activity and the spectrum of absorbed light. We will discuss some of the critical experiments that have contributed to our present understanding of photosynthesis, and we will consider equations for essential chemical reactions of pho-tosynthesis.
Action Spectra Relate Light Absorption to Photosynthetic Activity The use of action spectra has been central to the develop-ment of our current understanding of photosynthesis. An action spectrum depicts the magnitude of a response of a biological system to light, as a function of wavelength. For example, an action spectrum for photosynthesis can be con-structed from measurements of oxygen evolution at dif-ferent wavelengths (Figure 7.8). Often an action spectrum can identify the chromophore (pigment) responsible for a particular light-induced phenomenon.
Some of the first action spectra were measured by T. W.
Engelmann in the late 1800s (Figure 7.9). Engelmann used a prism to disperse sunlight into a rainbow that was allowed to fall on an aquatic algal filament. A population of O2-seeking bacteria was introduced into the system. The 6 6 6 2 2 6 12 2 CO H O C H O O Light, plant 6 + → + 116 Chapter 7 Absorbance ( ) or O2 evolution rate ( ) Absorption spectrum Action spectrum 400 500 600 700 800 Wavelength (nm) Visible spectrum Infrared FIGURE 7.8 Action spectrum compared with an absorption spectrum. The absorption spectrum is measured as shown in Figure 7.4. An action spectrum is measured by plotting a response to light such as oxygen evolution, as a function of wavelength. If the pigment used to obtain the absorption spectrum is the same as those that cause the response, the absorption and action spectra will match. In the example shown here, the action spectrum for oxygen evolution matches the absorption spectrum of intact chloroplasts quite well, indicating that light absorption by the chlorophylls mediates oxygen evolution. Discrepancies are found in the region of carotenoid absorption, from 450 to 550 nm, indi-cating that energy transfer from carotenoids to chlorophylls is not as effective as energy transfer between chlorophylls.
Wavelength of light (nm) 400 500 600 700 Aerotactic bacteria Spiral chloroplast Spirogyra cell Prism Light FIGURE 7.9 Schematic diagram of the action spectrum measurements by T. W.
Engelmann. Engelmann projected a spectrum of light onto the spiral chloroplast of the filamentous green alga Spirogyra and observed that oxygen-seeking bacteria introduced into the system collected in the region of the spectrum where chloro-phyll pigments absorb. This action spectrum gave the first indication of the effec-tiveness of light absorbed by accessory pigments in driving photosynthesis.
bacteria congregated in the regions of the filaments that evolved the most O2. These were the regions illuminated by blue light and red light, which are strongly absorbed by chlorophyll. Today, action spectra can be measured in room-sized spectrographs in which a huge monochroma-tor bathes the experimental samples in monochromatic light. But the principle of the experiment is the same as that of Engelmann’s experiments.
Action spectra were very important for the discovery of two distinct photosystems operating in O2-evolving pho-tosynthetic organisms. Before we introduce the two pho-tosystems, however, we need to describe the light-gather-ing antennas and the energy needs of photosynthesis.
Photosynthesis Takes Place in Complexes Containing Light-Harvesting Antennas and Photochemical Reaction Centers A portion of the light energy absorbed by chlorophylls and carotenoids is eventually stored as chemical energy via the formation of chemical bonds. This conversion of energy from one form to another is a complex process that depends on cooperation between many pigment molecules and a group of electron transfer proteins.
The majority of the pigments serve as an antenna com-plex, collecting light and transferring the energy to the reaction center complex, where the chemical oxidation and reduction reactions leading to long-term energy storage take place (Figure 7.10). Molecular structures of some of the antenna and reaction center complexes are discussed later in the chapter.
How does the plant benefit from this division of labor between antenna and reaction center pigments? Even in bright sunlight, a chlorophyll molecule absorbs only a few photons each second. If every chlorophyll had a complete reaction center associated with it, the enzymes that make up this system would be idle most of the time, only occa-sionally being activated by photon absorption. However, if many pigments can send energy into a common reaction center, the system is kept active a large fraction of the time.
In 1932, Robert Emerson and William Arnold performed a key experiment that provided the first evidence for the cooperation of many chlorophyll molecules in energy con-version during photosynthesis. They delivered very brief (10–5 s) flashes of light to a suspension of the green alga Chlorella pyrenoidosa and measured the amount of oxygen produced. The flashes were spaced about 0.1 s apart, a time that Emerson and Arnold had determined in earlier work was long enough for the enzymatic steps of the process to be completed before the arrival of the next flash. The inves-tigators varied the energy of the flashes and found that at high energies the oxygen production did not increase when a more intense flash was given: The photosynthetic system was saturated with light (Figure 7.11).
In their measurement of the relationship of oxygen pro-duction to flash energy, Emerson and Arnold were sur-prised to find that under saturating conditions, only one molecule of oxygen was produced for each 2500 chloro-phyll molecules in the sample. We know now that several hundred pigments are associated with each reaction cen-ter and that each reaction center must operate four times Photosynthesis: The Light Reactions 117 Reaction center e– e– Acceptor Donor Pigment molecules Energy transfer Electron transfer Antenna complex Light FIGURE 7.10 Basic concept of energy transfer during photo-synthesis. Many pigments together serve as an antenna, collecting light and transferring its energy to the reaction center, where chemical reactions store some of the energy by transferring electrons from a chlorophyll pigment to an electron acceptor molecule. An electron donor then reduces the chlorophyll again. The transfer of energy in the antenna is a purely physical phenomenon and involves no chemical changes. Flash energy (number of photons) Maximum yield = 1 O2 / 2500 chlorophyll molecules O2 produced per flash Initial slope = quantum yield 1 O2 / 9–10 absorbed quanta Low intensity High intensity FIGURE 7.11 Relationship of oxygen production to flash energy, the first evidence for the interaction between the antenna pigments and the reaction center. At saturating energies, the maximum amount of O2 produced is 1 mole-cule per 2500 chlorophyll molecules. to produce one molecule of oxygen—hence the value of 2500 chlorophylls per O2.
The reaction centers and most of the antenna complexes are integral components of the photosynthetic membrane.
In eukaryotic photosynthetic organisms, these membranes are found within the chloroplast; in photosynthetic prokaryotes, the site of photosynthesis is the plasma mem-brane or membranes derived from it.
The graph shown in Figure 7.11 permits us to calculate another important parameter of the light reactions of pho-tosynthesis, the quantum yield. The quantum yield of pho-tosynthesis ( )is defined as follows: (7.5) In the linear portion (low light intensity) of the curve, an increase in the number of photons stimulates a propor-tional increase in oxygen evolution. Thus the slope of the curve measures the quantum yield for oxygen production.
The quantum yield for a particular process can range from 0 (if that process does not respond to light) to 1.0 (if every photon absorbed contributes to the process). A more detailed discussion of quantum yields can be found in Web Topic 7.3.
In functional chloroplasts kept in dim light, the quan-tum yield of photochemistry is approximately 0.95, the quantum yield of fluorescence is 0.05 or lower, and the quantum yields of other processes are negligible. The vast majority of excited chlorophyll molecules therefore lead to photochemistry.
The Chemical Reaction of Photosynthesis Is Driven by Light It is important to realize that equilibrium for the chemical reaction shown in Equation 7.4 lies very far in the direction of the reactants. The equilibrium constant for Equation 7.4, calculated from tabulated free energies of formation for each of the compounds involved, is about 10–500. This num-ber is so close to zero that one can be quite confident that in the entire history of the universe no molecule of glucose has formed spontaneously from H2O and CO2 without external energy being provided. The energy needed to drive the photosynthetic reaction comes from light. Here’s a simpler form of Equation 7.4: (7.6) where (CH2O) is one-sixth of a glucose molecule. About nine or ten photons of light are required to drive the reac-tion of Equation 7.6.
Although the photochemical quantum yield under optimum conditions is nearly 100%, the efficiency of the conversion of light into chemical energy is much less. If red light of wavelength 680 nm is absorbed, the total energy input (see Equation 7.2) is 1760 kJ per mole of oxygen formed. This amount of energy is more than enough to drive the reaction in Equation 7.6, which has a standard-state free-energy change of +467 kJ mol–1. The efficiency of conversion of light energy at the optimal wavelength into chemical energy is therefore about 27%, which is remark-ably high for an energy conversion system. Most of this stored energy is used for cellular maintenance processes; the amount diverted to the formation of biomass is much less (see Figure 9.2).
There is no conflict between the fact that the photo-chemical quantum efficiency (quantum yield) is nearly 1 (100%) and the energy conversion efficiency is only 27%.
The quantum efficiency is a measure of the fraction of absorbed photons that engage in photochemistry; the energy efficiency is a measure of how much energy in the absorbed photons is stored as chemical products. The numbers indicate that almost all the absorbed photons engage in photochemistry, but only about a fourth of the energy in each photon is stored, the remainder being con-verted to heat.
Light Drives the Reduction of NADP and the Formation of ATP The overall process of photosynthesis is a redox chemical reaction, in which electrons are removed from one chemi-cal species, thereby oxidizing it, and added to another species, thereby reducing it. In 1937, Robert Hill found that in the light, isolated chloroplast thylakoids reduce a vari-ety of compounds, such as iron salts. These compounds serve as oxidants in place of CO2, as the following equation shows: 4 Fe3+ + 2 H2O → 4 Fe2+ + O2 + 4 H+ (7.7) Many compounds have since been shown to act as artifi-cial electron acceptors in what has come to be known as the Hill reaction. Their use has been invaluable in elucidating the reactions that precede carbon reduction.
We now know that during the normal functioning of the photosynthetic system, light reduces nicotinamide adenine dinucleotide phosphate (NADP), which in turn serves as the reducing agent for carbon fixation in the Calvin cycle (see Chapter 8). ATP is also formed during the electron flow from water to NADP, and it, too, is used in carbon reduction.
The chemical reactions in which water is oxidized to oxygen, NADP is reduced, and ATP is formed are known as the thylakoid reactions because almost all the reactions up to NADP reduction take place within the thylakoids. The carbon fixation and reduction reactions are called the stroma reactions because the carbon reduction reactions take place in the aqueous region of the chloroplast, the stroma.
CO H O CH O O Light, plant 2 2 2 2 + → ( ) + F = Number of photochemical products Total number of quanta absorbed F 118 Chapter 7 Although this division is somewhat arbitrary, it is concep-tually useful.
Oxygen-Evolving Organisms Have Two Photosystems That Operate in Series By the late 1950s, several experiments were puzzling the scientists who studied photosynthesis. One of these exper-iments carried out by Emerson, measured the quantum yield of photosynthesis as a function of wavelength and revealed an effect known as the red drop (Figure 7.12).
If the quantum yield is measured for the wavelengths at which chlorophyll absorbs light, the values found through-out most of the range are fairly constant, indicating that any photon absorbed by chlorophyll or other pigments is as effective as any other photon in driving photosynthesis.
However, the yield drops dramatically in the far-red region of chlorophyll absorption (greater than 680 nm).
This drop cannot be caused by a decrease in chlorophyll absorption because the quantum yield measures only light that has actually been absorbed. Thus, light with a wave-length greater than 680 nm is much less efficient than light of shorter wavelengths.
Another puzzling experimental result was the enhance-ment effect, also discovered by Emerson. He measured the rate of photosynthesis separately with light of two differ-ent wavelengths and then used the two beams simultane-ously (Figure 7.13). When red and far-red light were given together, the rate of photosynthesis was greater than the sum of the individual rates. This was a startling and sur-prising observation.
These observations were eventually explained by exper-iments performed in the 1960s (see Web Topic 7.4) that led to the discovery that two photochemical complexes, now known as photosystems I and II (PSI and PSII), operate in series to carry out the early energy storage reactions of pho-tosynthesis.
Photosystem I preferentially absorbs far-red light of wavelengths greater than 680 nm; photosystem II prefer-entially absorbs red light of 680 nm and is driven very poorly by far-red light. This wavelength dependence explains the enhancement effect and the red drop effect.
Another difference between the photosystems is that • Photosystem I produces a strong reductant, capable of reducing NADP+, and a weak oxidant.
• Photosystem II produces a very strong oxidant, capa-ble of oxidizing water, and a weaker reductant than the one produced by photosystem I.
The reductant produced by photosystem II re-reduces the oxidant produced by photosystem I. These properties of the two photosystems are shown schematically in Figure 7.14.
The scheme of photosynthesis depicted in Figure 7.14, called the Z (for zigzag) scheme, has become the basis for understanding O2-evolving (oxygenic) photosynthetic organisms. It accounts for the operation of two physically and chemically distinct photosystems (I and II), each with its own antenna pigments and photochemical reaction cen-ter. The two photosystems are linked by an electron trans-port chain.
Photosynthesis: The Light Reactions 119 0 0.1 0.05 400 500 600 700 Wavelength (nm) Quantum yield of photosynthesis Absorption spectrum Visible spectrum Quantum yield FIGURE 7.12 Red drop effect. The quantum yield of photo-synthesis (black curve) falls off drastically for far-red light of wavelengths greater than 680 nm, indicating that far-red light alone is inefficient in driving photosynthesis. The slight dip near 500 nm reflects the somewhat lower efficiency of photosynthesis using light absorbed by accessory pigments, carotenoids. Far-red light on Off Off Off Red light on Both lights on Time Relative rate of photosynthesis FIGURE 7.13 Enhancement effect. The rate of photosynthe-sis when red and far-red light are given together is greater than the sum of the rates when they are given apart. The enhancement effect provided essential evidence in favor of the concept that photosynthesis is carried out by two pho-tochemical systems working in tandem but with slightly different wavelength optima.
ORGANIZATION OF THE PHOTOSYNTHETIC APPARATUS The previous section explained some of the physical prin-ciples underlying photosynthesis, some aspects of the func-tional roles of various pigments, and some of the chemical reactions carried out by photosynthetic organisms. We now turn to the architecture of the photosynthetic apparatus and the structure of its components.
The Chloroplast Is the Site of Photosynthesis In photosynthetic eukaryotes, photosynthesis takes place in the subcellular organelle known as the chloroplast. Fig-ure 7.15 shows a transmission electron micrograph of a thin section from a pea chloroplast. The most striking aspect of the structure of the chloroplast is the extensive system of internal membranes known as thylakoids. All the chloro-phyll is contained within this membrane system, which is the site of the light reactions of photosynthesis.
The carbon reduction reactions, which are catalyzed by water-soluble enzymes, take place in the stroma (plural stromata), the region of the chloroplast outside the thy-lakoids. Most of the thylakoids appear to be very closely associated with each other. These stacked membranes are known as grana lamellae (singular lamella; each stack is called a granum), and the exposed membranes in which stacking is absent are known as stroma lamellae.
Two separate membranes, each composed of a lipid bilayer and together known as the envelope, surround most types of chloroplasts (Figure 7.16). This double-membrane system contains a variety of metabolite transport systems.
120 Chapter 7 Oxidizing Reducing Redox potential Photosystem II Photosystem I Weak reductant Red light Far-red light Electron transport chain Strong reductant Weak oxidant Strong oxidant P680 P680 P700 P700 e– e– e– e– e– e– NADPH NADP+ H2O O2 + H+ FIGURE 7.14 Z scheme of photosynthesis. Red light absorbed by photosystem II (PSII) produces a strong oxidant and a weak reductant. Far-red light absorbed by photosystem I (PSI) produces a weak oxidant and a strong reductant. The strong oxidant generated by PSII oxidizes water, while the strong reductant produced by PSI reduces NADP+. This scheme is basic to an understanding of photosyn-thetic electron transport. P680 and P700 refer to the wavelengths of maximum absorption of the reaction center chlorophylls in PSII and PSI, respectively. Stroma Stroma lamellae (not stacked) Outer and inner membranes Thylakoid Grana lamellae (stacked) FIGURE 7.15 Transmission electron micrograph of a chloro-plast from pea (Pisum sativum), fixed in glutaraldehyde and OsO4, embedded in plastic resin, and thin-sectioned with an ultramicrotome. (14,500×) (Courtesy of J. Swafford.) The chloroplast also contains its own DNA, RNA, and ribosomes.
Many of the chloroplast proteins are products of transcription and translation within the chloroplast itself, whereas others are encoded by nuclear DNA, synthesized on cytoplasmic ribosomes, and then imported into the chloroplast. This remarkable division of labor, extending in many cases to differ-ent subunits of the same enzyme complex, will be discussed in more detail later in this chapter. For some dynamic structures of chloroplasts see Web Essay 7.1.
Thylakoids Contain Integral Membrane Proteins A wide variety of proteins essential to photo-synthesis are embedded in the thylakoid membranes. In many cases, portions of these proteins extend into the aqueous regions on both sides of the thylakoids. These integral membrane proteins contain a large propor-tion of hydrophobic amino acids and are therefore much more stable in a nonaqueous medium such as the hydrocarbon portion of the membrane (see Figure 1.5A).
The reaction centers, the antenna pig-ment–protein complexes, and most of the electron trans-port enzymes are all integral membrane proteins. In all known cases, integral membrane proteins of the chloro-plast have a unique orientation within the membrane. Thy-lakoid membrane proteins have one region pointing toward the stromal side of the membrane and the other ori-ented toward the interior portion of the thylakoid, known as the lumen (see Figures 7.16 and 7.17).
The chlorophylls and accessory light-gathering pig-ments in the thylakoid membrane are always associated in a noncovalent but highly specific way with proteins. Both antenna and reaction center chlorophylls are associated with proteins that are organized within the membrane so as to optimize energy transfer in antenna complexes and electron transfer in reaction centers, while at the same time minimizing wasteful processes.
Photosynthesis: The Light Reactions 121 Intermembrane space Outer envelope Stroma lamellae (site of PSI) Stroma lamella Thylakoid Thylakoid Thylakoid lumen Grana lamellae (stack of thylakoids and site of PSII) Stroma Inner envelope Granum (stack of thylakoids) FIGURE 7.16 Schematic picture of the overall organization of the mem-branes in the chloroplast. The chloroplast of higher plants is surrounded by the inner and outer membranes (envelope). The region of the chloro-plast that is inside the inner membrane and surrounds the thylakoid membranes is known as the stroma. It contains the enzymes that cat-alyze carbon fixation and other biosynthetic pathways. The thylakoid membranes are highly folded and appear in many pictures to be stacked like coins, although in reality they form one or a few large intercon-nected membrane systems, with a well-defined interior and exterior with respect to the stroma. The inner space within a thylakoid is known as the lumen. (After Becker 1986.) Carboxyl terminus (COOH) Amino terminus (NH2) Thylakoid membrane Stroma Thylakoid lumen Thylakoid Thylakoid lumen FIGURE 7.17 Predicted folding pattern of the D1 protein of the PSII reaction center. The hydrophobic portion of the membrane is traversed five times by the peptide chain rich in hydrophobic amino acid residues. The protein is asym-metrically arranged in the thylakoid membrane, with the amino (NH2) terminus on the stromal side of the membrane and the carboxyl (COOH) terminus on the lumen side.
(After Trebst 1986.) Photosystems I and II Are Spatially Separated in the Thylakoid Membrane The PSII reaction center, along with its antenna chloro-phylls and associated electron transport proteins, is located predominantly in the grana lamellae (Figure 7.18) (Allen and Forsberg 2001). The PSI reaction center and its associated antenna pig-ments and electron transfer proteins, as well as the cou-pling-factor enzyme that catalyzes the formation of ATP, are found almost exclusively in the stroma lamellae and at the edges of the grana lamellae. The cytochrome b6 f com-plex of the electron transport chain that connects the two photosystems (see Figure 7.21) is evenly distributed between stroma and grana.
Thus the two photochemical events that take place in O2-evolving photosynthesis are spatially separated. This separation implies that one or more of the electron carriers that function between the photosystems diffuses from the grana region of the membrane to the stroma region, where electrons are delivered to photosystem I.
In PSII, the oxidation of two water molecules produces four electrons, four protons, and a single O2 (see Equation 7.8). The protons produced by this oxidation of water must also be able to diffuse to the stroma region, where ATP is synthesized. The functional role of this large separation (many tens of nanometers) between photosystems I and II is not entirely clear but is thought to improve the efficiency of energy distribution between the two photosystems (Trissl and Wilhelm 1993; Allen and Forsberg 2001).
The spatial separation between photosystems I and II indicates that a strict one-to-one stoichiometry between the two photosystems is not required. Instead, PSII reaction centers feed reducing equivalents into a common interme-diate pool of soluble electron carriers (plastoquinone), which will be described in detail later in the chapter. The PSI reaction centers remove the reducing equivalents from the common pool, rather than from any specific PSII reac-tion center complex.
Most measurements of the relative quantities of photo-systems I and II have shown that there is an excess of pho-tosystem II in chloroplasts. Most commonly, the ratio of PSII to PSI is about 1.5:1, but it can change when plants are grown in different light conditions.
Anoxygenic Photosynthetic Bacteria Have a Reaction Center Similar to That of Photosystem II Non-O2-evolving (anoxygenic) organisms, such as the pur-ple photosynthetic bacteria of the genera Rhodobacter and Rhodopseudomonas, contain only a single photosystem.
These simpler organisms have been very useful for detailed structural and functional studies that have contributed to a better understanding of oxygenic photosynthesis.
Hartmut Michel, Johann Deisenhofer, Robert Huber, and coworkers in Munich resolved the three-dimensional struc-ture of the reaction center from the purple photosynthetic bacterium Rhodopseudomonas viridis (Deisenhofer and Michel 1989). This landmark achievement, for which a Nobel Prize was awarded in 1988, was the first high-reso-122 Chapter 7 Cytochrome b6f dimer PSII LHCII trimer PSI ATP synthase STROMA Thylakoid membrane LUMEN FIGURE 7.18 Organization of the protein complexes of the thy-lakoid membrane. Photosystem II is located predominantly in the stacked regions of the thylakoid membrane; photosystem I and ATP synthase are found in the unstacked regions protruding into the stroma. Cytochrome b6 f complexes are evenly distributed. This lateral separation of the two photosystems requires that electrons and protons produced by photosystem II be transported a consid-erable distance before they can be acted on by photosystem I and the ATP-coupling enzyme. (After Allen and Forsberg 2001.) lution, X-ray structural determination for an integral mem-brane protein, and the first structural determination for a reaction center complex (see Figures 7.5.A and 7.5.B in Web Topic 7.5). Detailed analysis of these structures, along with the characterization of numerous mutants, has revealed many of the principles involved in the energy storage processes carried out by all reaction centers.
The structure of the bacterial reaction center is thought to be similar in many ways to that found in photosystem II from oxygen-evolving organisms, especially in the electron acceptor portion of the chain. The proteins that make up the core of the bacterial reaction center are relatively simi-lar in sequence to their photosystem II counterparts, imply-ing an evolutionary relatedness.
ORGANIZATION OF LIGHT-ABSORBING ANTENNA SYSTEMS The antenna systems of different classes of photosynthetic organisms are remarkably varied, in contrast to the reaction centers, which appear to be similar in even distantly related organisms. The variety of antenna complexes reflects evo-lutionary adaptation to the diverse environments in which different organisms live, as well as the need in some organ-isms to balance energy input to the two photosystems (Grossman et al. 1995; Green and Durnford 1996).
Antenna systems function to deliver energy efficiently to the reaction centers with which they are associated (van Grondelle et al. 1994; Pullerits and Sundström 1996). The size of the antenna system varies considerably in different organisms, ranging from a low of 20 to 30 bacteriochloro-phylls per reaction center in some photosynthetic bacteria, to generally 200 to 300 chlorophylls per reaction center in higher plants, to a few thousand pigments per reaction cen-ter in some types of algae and bacteria. The molecular structures of antenna pigments are also quite diverse, although all of them are associated in some way with the photosynthetic membrane.
The physical mechanism by which excitation energy is conveyed from the chlorophyll that absorbs the light to the reaction center is thought to be resonance transfer. By this mechanism the excitation energy is transferred from one molecule to another by a nonradiative process.
A useful analogy for resonance transfer is the transfer of energy between two tuning forks. If one tuning fork is struck and properly placed near another, the second tuning fork receives some energy from the first and begins to vibrate. As in resonance energy transfer in antenna complexes, the effi-ciency of energy transfer between the two tuning forks depends on their distance from each other and their relative orientation, as well as their pitches or vibrational frequencies.
Energy transfer in antenna complexes is very efficient: Approximately 95 to 99% of the photons absorbed by the antenna pigments have their energy transferred to the reac-tion center, where it can be used for photochemistry. There is an important difference between energy transfer among pigments in the antenna and the electron transfer that occurs in the reaction center: Whereas energy transfer is a purely physical phenomenon, electron transfer involves chemical changes in molecules.
The Antenna Funnels Energy to the Reaction Center The sequence of pigments within the antenna that funnel absorbed energy toward the reaction center has absorption maxima that are progressively shifted toward longer red wavelengths (Figure 7.19). This red shift in absorption max-imum means that the energy of the excited state is some-what lower nearer the reaction center than in the more peripheral portions of the antenna system.
As a result of this arrangement, when excitation is trans-ferred, for example, from a chlorophyll b molecule absorbing maximally at 650 nm to a chlorophyll a molecule absorbing maximally at 670 nm, the difference in energy between these two excited chlorophylls is lost to the environment as heat.
For the excitation to be transferred back to the chloro-phyll b, the energy lost as heat would have to be resup-plied. The probability of reverse transfer is therefore smaller simply because thermal energy is not sufficient to make up the deficit between the lower-energy and higher-energy pigments. This effect gives the energy-trapping process a degree of directionality or irreversibility and makes the delivery of excitation to the reaction center more efficient. In essence, the system sacrifices some energy from each quantum so that nearly all of the quanta can be trapped by the reaction center.
Many Antenna Complexes Have a Common Structural Motif In all eukaryotic photosynthetic organisms that contain both chlorophyll a and chlorophyll b, the most abundant antenna proteins are members of a large family of structurally related proteins. Some of these proteins are associated pri-marily with photosystem II and are called light-harvesting complex II (LHCII) proteins; others are associated with photosystem I and are called LHCI proteins. These antenna complexes are also known as chlorophyll a/b antenna pro-teins (Paulsen 1995; Green and Durnford 1996).
The structure of one of the LHCII proteins has been determined by a combination of electron microscopy and electron crystallography (Figure 7.20) (Kühlbrandt et al.
1994). The protein contains three α-helical regions and binds about 15 chlorophyll a and b molecules, as well as a few carotenoids. Only some of these pigments are visible in the resolved structure. The structure of the LHCI pro-teins has not yet been determined but is probably similar to that of the LHCII proteins. All of these proteins have sig-nificant sequence similarity and are almost certainly descendants of a common ancestral protein (Grossman et al. 1995; Green and Durnford 1996).
Light absorbed by carotenoids or chlorophyll b in the LHC proteins is rapidly transferred to chlorophyll a and Photosynthesis: The Light Reactions 123 then to other antenna pigments that are intimately asso-ciated with the reaction center. The LHCII complex is also involved in regulatory processes, which are discussed later in the chapter.
MECHANISMS OF ELECTRON TRANSPORT Some of the evidence that led to the idea of two photochem-ical reactions operating in series was discussed earlier in this chapter. Here we will consider in detail the chemical reac-tions involved in electron transfer during photosynthesis. We will discuss the excitation of chlorophyll by light and the reduction of the first electron acceptor, the flow of electrons through photosystems II and I, the oxi-dation of water as the primary source of electrons, and the reduction of the final electron acceptor (NADP+). The chemios-motic mechanism that mediates ATP syn-thesis will be discussed in detail later in the chapter (see “Proton Transport and ATP Synthesis in the Chloroplast”).
124 Chapter 7 Light High Low Energy gradient Energy Photon absorption P680 Carotenoids Chlorophyll b Chlorophyll a Carotenoids Chlorophyll b Chlorophyll a Reaction center Energy lost as heat during excitation transfer Antenna complexes Energy of reaction center excited state available for storage P680 (A) (B) Ground-state energy FIGURE 7.19 Funneling of excitation from the antenna sys-tem toward the reaction center. (A) The excited-state energy of pigments increases with distance from the reaction cen-ter; that is, pigments closer to the reaction center are lower in energy than those farther from the reaction center. This energy gradient ensures that excitation transfer toward the reaction center is energetically favorable and that excitation transfer back out to the peripheral portions of the antenna is energetically unfavorable. (B) Some energy is lost as heat to the environment by this process, but under optimal con-ditions almost all the excitations absorbed in the antenna complexes can be delivered to the reaction center. The asterisks denote an excited state.
Chlorophyll a Chlorophyll b Carotenoid Thylakoid membrane STROMA LUMEN FIGURE 7.20 Two-dimensional view of the structure of the LHCII antenna complex from higher plants, determined by a combination of electron microscopy and electron crystallography. Like X-ray crystallography, electron crystallography uses the diffraction patterns of soft-energy electrons to resolve macromolecule structures. The antenna complex is a transmembrane pigment protein, with three helical regions that cross the nonpolar part of the mem-brane. Approximately 15 chlorophyll a and b molecules are associated with the complex, as well as several carotenoids. The positions of several of the chloro-phylls are shown, and two of the carotenoids form an X in the middle of the complex. In the membrane, the complex is trimeric and aggregates around the periphery of the PSII reaction center complex. (After Kühlbrandt et al. 1994.) Electrons Ejected from Chlorophyll Travel Through a Series of Electron Carriers Organized in the “Z Scheme” Figure 7.21 shows a current version of the Z scheme, in which all the electron carriers known to function in elec-tron flow from H2O to NADP+ are arranged vertically at their midpoint redox potentials (see Web Topic 7.6 for fur-ther detail). Components known to react with each other are connected by arrows, so the Z scheme is really a syn-thesis of both kinetic and thermodynamic information. The large vertical arrows represent the input of light energy into the system.
Photons excite the specialized chlorophyll of the reac-tion centers (P680 for PSII, and P700 for PSI), and an elec-tron is ejected. The electron then passes through a series of electron carriers and eventually reduces P700 (for electrons from PSII) or NADP+ (for electrons from PSI). Much of the following discussion describes the journeys of these elec-trons and the nature of their carriers.
Almost all the chemical processes that make up the light reactions of photosynthesis are carried out by four major protein complexes: photosystem II, the cytochrome b6 f com-plex, photosystem I, and the ATP synthase. These four inte-gral membrane complexes are vectorially oriented in the thylakoid membrane to function as follows (Figure 7.22): • Photosystem II oxidizes water to O2 in the thylakoid lumen and in the process releases protons into the lumen.
• Cytochrome b6 f receives electrons from PSII and delivers them to PSI. It also transports additional protons into the lumen from the stroma.
• Photosystem I reduces NADP+ to NADPH in the stroma by the action of ferredoxin (Fd) and the flavo-protein ferredoxin–NADP reductase (FNR).
• ATP synthase produces ATP as protons diffuse back through it from the lumen into the stroma.
Photosynthesis: The Light Reactions 125 Photosystem II Photosystem I P680 P680 P700 P700 H2O O2 + H+ Pheo QA QB PC Oxygen-evolving complex –0.5 –1.0 –1.5 –2.0 0.5 1.0 1.5 0 m Cytochrome b6f complex Cyt b Cyt b Cyt f Q FeSR FNR Fd A0 A1 FeSX FeSA FeSB Yz Light Light NADP+ NADPH 1 2 3 4 1 6 5 FIGURE 7.21 Detailed Z scheme for O2-evolving photosyn-thetic organisms. The redox carriers are placed at their mid-point redox potentials (at pH 7). (1) The vertical arrows rep-resent photon absorption by the reaction center chloro-phylls: P680 for photosystem II (PSII) and P700 for photo-system I (PSI). The excited PSII reaction center chlorophyll, P680, transfers an electron to pheophytin (Pheo). (2) On the oxidizing side of PSII (to the left of the arrow joining P680 with P680), P680 oxidized by light is re-reduced by Yz, that has received electrons from oxidation of water. (3) On the reducing side of PSII (to the right of the arrow join-ing P680 with P680), pheophytin transfers electrons to the acceptors QA and QB, which are plastoquinones. (4) The cytochrome b6 f complex transfers electrons to plastocyanin (PC), a soluble protein, which in turn reduces P700+ (oxi-dized P700). (5) The acceptor of electrons from P700 (A0) is thought to be a chlorophyll, and the next acceptor (A1) is a quinone. A series of membrane-bound iron–sulfur proteins (FeSX, FeSA, and FeSB) transfers electrons to soluble ferre-doxin (Fd). (6) The soluble flavoprotein ferredoxin–NADP reductase (FNR) reduces NADP+ to NADPH, which is used in the Calvin cycle to reduce CO2 (see Chapter 8). The dashed line indicates cyclic electron flow around PSI. (After Blankenship and Prince 1985.) Energy Is Captured When an Excited Chlorophyll Reduces an Electron Acceptor Molecule As discussed earlier, the function of light is to excite a spe-cialized chlorophyll in the reaction center, either by direct absorption or, more frequently, via energy transfer from an antenna pigment. This excitation process can be envisioned as the promotion of an electron from the highest-energy filled orbital of the chlorophyll to the lowest-energy unfilled orbital (Figure 7.23). The electron in the upper orbital is only loosely bound to the chlorophyll and is eas-ily lost if a molecule that can accept the electron is nearby.
The first reaction that converts electron energy into chemical energy—that is, the primary photochemical event—is the transfer of an electron from the excited state of a chlorophyll in the reaction center to an acceptor mole-cule. An equivalent way to view this process is that the absorbed photon causes an electron rearrangement in the reaction center chlorophyll, followed by an electron trans-fer process in which part of the energy in the photon is cap-tured in the form of redox energy.
Immediately after the photochemical event, the reaction center chlorophyll is in an oxidized state (electron deficient, or positively charged) and the nearby electron acceptor mol-126 Chapter 7 High Low Electrochemical potential gradient FNR STROMA (low H+) LUMEN (high H+) Cytochrome b6f O2 + H2O ATP synthase Plastocyanin PC Fd P680 PSII P700 PSI Light NADPH + NADP+ ATP ADP Pi Light e– e– e– Plastoquinone PQ PQH2 + Oxidation of water H+ H+ H+ H+ H+ H+ FIGURE 7.22 The transfer of electrons and protons in the thylakoid membrane is carried out vectorially by four pro-tein complexes. Water is oxidized and protons are released in the lumen by PSII. PSI reduces NADP+ to NADPH in the stroma, via the action of ferredoxin (Fd) and the flavopro-tein ferredoxin–NADP reductase (FNR). Protons are also transported into the lumen by the action of the cytochrome b6 f complex and contribute to the electrochemical proton gradient. These protons must then diffuse to the ATP syn-thase enzyme, where their diffusion down the electrochem-ical potential gradient is used to synthesize ATP in the stroma. Reduced plastoquinone (PQH2) and plastocyanin transfer electrons to cytochrome b6 f and to PSI, respec-tively. Dashed lines represent electron transfer; solid lines represent proton movement. Redox properties of ground and excited states of reaction center chlorophyll Acceptor orbital Light Donor orbital Good reducing agent Poor oxidizing agent Good oxidizing agent Poor reducing agent Donor orbital Ground-state chlorophyll Excited-state chlorophyll Acceptor orbital FIGURE 7.23 Orbital occupation diagram for the ground and excited states of reaction center chlorophyll. In the ground state the molecule is a poor reducing agent (loses electrons from a low-energy orbital) and a poor oxidizing agent (accepts electrons only into a high-energy orbital). In the excited state the situation is reversed, and an electron can be lost from the high-energy orbital, making the molecule an extremely powerful reducing agent. This is the reason for the extremely negative excited-state redox potential shown by P680 and P700 in Figure 7.21. The excited state can also act as a strong oxidant by accepting an electron into the lower-energy orbital, although this pathway is not significant in reaction centers. (After Blankenship and Prince 1985.) ecule is reduced (electron rich, or negatively charged). The system is now at a critical juncture. The lower-energy orbital of the positively charged oxidized reaction center chloro-phyll shown in Figure 7.23 has a vacancy and can accept an electron. If the acceptor molecule donates its electron back to the reaction center chlorophyll, the system will be returned to the state that existed before the light excitation, and all the absorbed energy will be converted into heat.
This wasteful recombination process, however, does not appear to occur to any substantial degree in functioning reaction centers. Instead, the acceptor transfers its extra electron to a secondary acceptor and so on down the elec-tron transport chain. The oxidized reaction center of the chlorophyll that had donated an electron is re-reduced by a secondary donor, which in turn is reduced by a tertiary donor. In plants, the ultimate electron donor is H2O, and the ultimate electron acceptor is NADP+ (see Figure 7.21).
The essence of photosynthetic energy storage is thus the initial transfer of an electron from an excited chlorophyll to an acceptor molecule, followed by a very rapid series of secondary chemical reactions that separate the positive and negative charges. These secondary reactions separate the charges to opposite sides of the thylakoid membrane in approximately 200 picoseconds (1 picosecond = 10–12 s).
With the charges thus separated, the reversal reaction is many orders of magnitude slower, and the energy has been captured. Each of the secondary electron transfers is accom-panied by a loss of some energy, thus making the process effectively irreversible. The quantum yield for the produc-tion of stable products in purified reaction centers from photosynthetic bacteria has been measured as 1.0; that is, every photon produces stable products, and no reversal reactions occur.
Although these types of measurements have not been made on purified reaction centers from higher plants, the measured quantum requirements for O2 production under optimal conditions (low-intensity light) indicate that the values for the primary photochemical events are very close to 1.0. The structure of the reaction center appears to be extremely fine-tuned for maximal rates of productive reac-tions and minimal rates of energy-wasting reactions.
The Reaction Center Chlorophylls of the Two Photosystems Absorb at Different Wavelengths As discussed earlier in the chapter, PSI and PSII have dis-tinct absorption characteristics. Precise measurements of absorption maxima were made possible by optical changes in the reaction center chlorophylls in the reduced and oxi-dized states. The reaction center chlorophyll is transiently in an oxidized state after losing an electron and before being re-reduced by its electron donor.
In the oxidized state, the strong light absorbance in the red region of the spectrum that is characteristic of chloro-phylls is lost, or bleached. It is therefore possible to mon-itor the redox state of these chlorophylls by time-resolved optical absorbance measurements in which this bleaching is monitored directly (see Web Topic 7.1).
Using such techniques, Bessel Kok found that the reac-tion center chlorophyll of photosystem I absorbs maximally at 700 nm in its reduced state. Accordingly, this chlorophyll is named P700 (the P stands for pigment). H. T. Witt and coworkers found the analogous optical transient of photo-system II at 680 nm, so its reaction center chlorophyll is known as P680. Earlier, Louis Duysens had identified the reaction center bacteriochlorophyll from purple photosyn-thetic bacteria as P870.
The X-ray structure of the bacterial reaction center (see Figures 7.5.A and 7.5.B in Web Topic 7.5) clearly indicates that P870 is a closely coupled pair or dimer of bacteri-ochlorophylls, rather than a single molecule. The primary donor of photosystem I, P700, is a dimer of chlorophyll a molecules. Photosystem II also contains a dimer of chloro-phylls, although the primary donor, P680, may not reside entirely on these pigments. In the oxidized state, reaction center chlorophylls contain an unpaired electron. Mole-cules with unpaired electrons often can be detected by a magnetic-resonance technique known as electron spin res-onance (ESR). ESR studies, along with the spectroscopic measurements already described, have led to the discov-ery of many intermediate electron carriers in the photo-synthetic electron transport system.
The Photosystem II Reaction Center Is a Multisubunit Pigment–Protein Complex Photosystem II is contained in a multisubunit protein supercomplex (Figure 7.24) (Barber et al. 1999). In higher plants, the multisubunit protein supercomplex has two complete reaction centers and some antenna complexes.
The core of the reaction center consists of two membrane proteins known as D1 and D2, as well as other proteins, as shown in Figure 7.25 (Zouni et al. 2001).
The primary donor chlorophyll (P680), additional chloro-phylls, carotenoids, pheophytins, and plastoquinones (two electron acceptors described in the following section) are bound to the membrane proteins D1 and D2. These proteins have some sequence similarity to the L and M peptides of purple bacteria. Other proteins serve as antenna complexes or are involved in oxygen evolution. Some, such as cytochrome b559, have no known function but may be involved in a protective cycle around photosystem II.
Water Is Oxidized to Oxygen by Photosystem II Water is oxidized according to the following chemical reac-tion (Hoganson and Babcock 1997): 2 H2O →O2 + 4 H+ + 4 e– (7.8) This equation indicates that four electrons are removed from two water molecules, generating an oxygen molecule and four hydrogen ions. (For more on oxidation–reduction reac-tions, see Chapter 2 on the web site and Web Topic 7.6.) Photosynthesis: The Light Reactions 127 Water is a very stable molecule. Oxidation of water to form molecular oxygen is very difficult, and the photo-synthetic oxygen-evolving complex is the only known bio-chemical system that carries out this reaction. Photosyn-thetic oxygen evolution is also the source of almost all the oxygen in Earth’s atmosphere.
The chemical mechanism of photosynthetic water oxi-dation is not yet known, although many studies have pro-vided a substantial amount of information about the process (see Web Topic 7.7 and Figure 7.26). The protons produced by water oxidation are released into the lumen of the thylakoid, not directly into the stromal compartment (see Figure 7.22). They are released into the lumen because of the vectorial nature of the membrane and the fact that the oxygen-evolving complex is localized on the interior surface of the thylakoid. These protons are eventually transferred from the lumen to the stroma by translocation through ATP synthase. In this way the protons released during water oxidation contribute to the electrochemical potential driving ATP formation.
It has been known for many years that manganese (Mn) is an essential cofactor in the water-oxidizing process (see Chapter 5), and a classic hypothesis in photosynthesis research postulates that Mn ions undergo a series of oxida-tions—which are known as S states, and are labeled S0, S1, S2, S3, and S4 (see Web Topic 7.7)—that are perhaps linked to H2O oxidation and the generation of O2 (see Figure 7.26).
This hypothesis has received strong support from a variety of experiments, most notably X-ray absorption and ESR stud-ies, both of which detect the manganese directly (Yachandra 128 Chapter 7 (A) CP43 CP43 CP43 CP47 CP47 CP47 CP47 CP43 CP26 CP26 CP29 CP29 (B) (C) D2 D2 D2 D1 D1 D1 D2 D1 LHCII LHCII 23 33 FIGURE 7.24 Structure of dimeric multisubunit protein supercomplex of photosystem II from higher plants, as deter-mined by electron microscopy. The figure shows two com-plete reaction centers, each of which is a dimeric complex.
(A) Helical arrangement of the D1 and D2 (red) and CP43 and CP47 (green) core subunits. (B) View from the lumenal side of the supercomplex, including additional antenna com-plexes, LHCII, CP26 and CP29, and extrinsic oxygen-evolv-ing complex, shown as orange and yellow circles.
Unassigned helices are shown in gray. (C) Side view of the complex illustrating the arrangement of the extrinsic proteins of the oxygen-evolving complex. (After Barber et al. 1999.) PsbH CP47 ChlzD1 D2 D1 Nonheme iron Heme iron of Cyt b559 Heme iron of Cyt c550 PsbX α β CP43 Mn cluster 10 Å CP47 PsbO Mn cluster CP43 Fe Cyt c550/PsbV Fe(Cyt b559) PsbK/ PsbL (A) (B) ChlzD2 Psbl Cyt b559 CP43 Stroma Lumen FIGURE 7.25 Structure of the photosystem II reaction center from the cyanobacterium Synechococcus elongatus, resolved at 3.8 Å. The structure includes the D1 and D1 core reaction center proteins, the CP43 and CP47 antenna proteins, cytochromes b559 and c550, the extrinsic 33 kDa oxygen evolution protein PsbO, and the pigments and other cofactors. Seven unassigned helices are shown in gray.
(A) View from the lumenal surface, perpendicular to the plane of the membrane. (B) Side view parallel to the membrane plane. (After Zouni et al. 2001.) e– O O O O O O O O O O O O O O O O Mn Mn Mn Mn H H H H H Cl Ca S0 S4 S3 S2 S1 Yz Yz Yz O H O O O O O O O O O O O O O O O O Mn Mn Mn Mn H H H H Cl Ca O O O O O O O O O O O O O O O Mn Mn Mn Mn H H Cl Ca O O O O O O O O O O O O O O O Mn Mn Mn Mn Ca O H Yz O O O O O O O O O O O O O O O Mn Mn Mn Mn H Cl Ca O O O O O O O O O O O O O O O Mn Mn Mn Mn H H Cl Ca S2 H+ , e– H+ , e– H+ , e– H+ , O2 2 H2O FIGURE 7.26 Model of the S state cycle of oxygen evolution in PSII. Successive stages in the oxidation of water via the Mn oxygen-evolving complex are shown. Yz is a tyrosine radical that is an intermediate electron carrier between P680 and the Mn cluster. (After Tommos and Babcock 1998.) et al. 1996). Analytical experiments indicate that four Mn ions are associated with each oxygen-evolving complex. Other experiments have shown that Cl– and Ca2+ ions are essential for O2 evolution (see Figure 7.26 and Web Topic 7.7). One electron carrier, generally identified as Yz, functions between the oxygen-evolving complex and P680 (see Fig-ures 7.21 and 7.26). To function in this region, Yz needs to have a very strong tendency to retain its electrons. This species has been identified as a radical formed from a tyro-sine residue in the D1 protein of the PSII reaction center.
Pheophytin and Two Quinones Accept Electrons from Photosystem II Evidence from spectral and ESR studies indicates that pheo-phytin acts as an early acceptor in photosystem II, followed by a complex of two plastoquinones in close proximity to an iron atom. Pheophytin is a chlorophyll in which the cen-tral magnesium atom has been replaced by two hydrogen atoms. This chemical change gives pheophytin chemical and spectral properties that are slightly different from those of chlorophyll. The precise arrangement of the carriers in the electron acceptor complex is not known, but it is prob-ably very similar to that of the reaction center of purple bac-teria (for details, see Figure 7.5.B in Web Topic 7.5).
Two plastoquinones (QA and QB) are bound to the reac-tion center and receive electrons from pheophytin in a sequential fashion (Okamura et al. 2000). Transfer of the two electrons to QB reduces it to QB 2–, and the reduced QB 2– takes two protons from the stroma side of the medium, yielding a fully reduced plastohydroquinone (QH2) (Figure 7.27). The plastohydroquinone then dissociates from the reaction center complex and enters the hydrocarbon portion of the membrane, where it in turn transfers its electrons to the cytochrome b6 f complex. Unlike the large protein com-plexes of the thylakoid membrane, hydroquinone is a small, nonpolar molecule that diffuses readily in the nonpolar core of the membrane bilayer.
Electron Flow through the Cytochrome b6f Complex Also Transports Protons The cytochrome b6 f complex is a large multisubunit pro-tein with several prosthetic groups (Cramer et al. 1996; Berry et al. 2000). It contains two b-type hemes and one c-type heme (cytochrome f ). In c-type cytochromes the heme is covalently attached to the peptide; in b-type cytochromes the chemically similar protoheme group is not covalently attached (Figure 7.28). In addition, the complex contains a Rieske iron–sulfur protein (named for the scientist who discovered it), in which two iron atoms are bridged by two sulfur atoms.
The structures of cytochrome f and the related cyto-chrome bc1 complex have been determined and suggest a mechanism for electron and proton flow. The precise way by which electrons and protons flow through the cytochrome b6 f complex is not yet fully understood, but a mechanism known as the Q cycle accounts for most of the observations. In this mechanism, plastohydroquinone (QH2) is oxidized, and one of the two electrons is passed along a linear electron transport chain toward photosystem I, while the other electron goes through a cyclic process that increases the number of protons pumped across the mem-brane (Figure 7.29).
In the linear electron transport chain, the oxidized Rieske protein (FeSR) accepts an electron from plastohydroquinone (QH2) and transfers it to cytochrome f (see Figure 7.29A).
Cytochrome f then transfers an electron to the blue-colored copper protein plastocyanin (PC), which in turn reduces oxidized P700 of PSI. In the cyclic part of the process (see Figure 7.29B), the plastosemiquinone (see Figure 7.27) trans-fers its other electron to one of the b-type hemes, releasing both of its protons to the lumenal side of the membrane.
The b-type heme transfers its electron through the sec-ond b-type heme to an oxidized quinone molecule, reduc-ing it to the semiquinone form near the stromal surface of 130 Chapter 7 O O (CH2 C CH H3C H3C CH2)9 H O O R H3C H3C O– O• R H3C H3C OH OH R H3C H3C + e– + 1 e– + 2 H+ CH3 _ Plastoquinone (A) (B) Quinone (Q) Plastosemiquinone (Q– • ) Plastohydroquinone (QH2) FIGURE 7.27 Structure and reactions of plastoquinone that operate in photosystem II. (A) The plastoquinone consists of a quinoid head and a long non-polar tail that anchors it in the membrane. (B) Redox reactions of plastoquinone. The fully oxi-dized quinone (Q), anionic semiquinone (Q• −), and reduced hydroquinone (QH2) forms are shown; R represents the side chain.
CH3 CH3 CH3 CH2 CH CH2 CH3 CH2 CH H H H H CH2 –OOC CH2 COO– N N N N Fe CH3 CH3 H3C CH2 CH S CH3 CH2 CH H H H H CH3 CH2 –OOC CH2 S CH2 CH2 COO– N N N N Fe CH2 CH3 Protein Protoheme of b-type cytochromes Heme c of c-type cytochromes FIGURE 7.28 Structure of prosthetic groups of b- and c-type cytochromes. The pro-toheme group (also called protoporphyrin IX) is found in b-type cytochromes, the heme c group in c-type cytochromes. The heme c group is covalently attached to the protein by thioether linkages with two cysteine residues in the protein; the proto-heme group is not covalently attached to the protein. The Fe ion is in the 2+ oxida-tion state in reduced cytochromes and in the 3+ oxidation state in oxidized cytochromes.
Thylakoid membrane STROMA LUMEN Plastocyanin PC PSII PSI P700 PSI P700 e– e– e– e– e– e– Cytochrome b6f complex (A) First QH2 oxidized Q 2 H+ QH2 Q Q– Cyt b Cyt f Cyt b FeSR Thylakoid membrane STROMA LUMEN Plastocyanin PC e– e– e– e– e– e– Cytochrome b6f complex (B) Second QH2 oxidized Q 2 H+ 2 H+ QH2 QH2 Q– Cyt b Cyt f Cyt b FeSR PSII FIGURE 7.29 Mechanism of electron and proton transfer in the cytochrome b6 f complex. This complex contains two b-type cytochromes (Cyt b), a c-type cytochrome (Cyt c, historically called cytochrome f ), a Rieske Fe–S protein (FeSR), and two quinone oxidation–reduction sites. (A) The noncyclic or linear processes: A plastohy-droquinone (QH2) molecule produced by the action of PSII (see Figure 7.27) is oxidized near the lumenal side of the complex, transferring its two electrons to the Rieske Fe–S protein and one of the b-type cytochromes and simultane-ously expelling two protons to the lumen. The electron transferred to FeSR is passed to cytochrome f (Cyt f ) and then to plastocyanin (PC), which reduces P700 of PSI. The reduced b-type cytochrome transfers an electron to the other b-type cytochrome, which reduces a quinone (Q) to the semiquinone (Q• • −) state (see Figure 7.27). (B) The cyclic processes: A second QH2 is oxidized, with one electron going from FeSR to PC and finally to P700. The second elec-tron goes through the two b-type cytochromes and reduces the semiquinone to the plastohy-droquinone, at the same time picking up two protons from the stroma. Overall, four protons are transported across the membrane for every two electrons delivered to P700.
the complex. Another similar sequence of electron flow fully reduces the plastoquinone, which picks up protons from the stromal side of the membrane and is released from the b6 f complex as plastohydroquinone.
The net result of two turnovers of the complex is that two electrons are transferred to P700, two plastohydro-quinones are oxidized to the quinone form, and one oxi-dized plastoquinone is reduced to the hydroquinone form.
In addition, four protons are transferred from the stromal to the lumenal side of the membrane.
By this mechanism, electron flow connecting the acceptor side of the PSII reaction center to the donor side of the PSI reaction center also gives rise to an electrochemical potential across the membrane, due in part to H+ concentration differ-ences on the two sides of the membrane. This electrochemi-cal potential is used to power the synthesis of ATP . The cyclic electron flow through the cytochrome b and plastoquinone increases the number of protons pumped per electron beyond what could be achieved in a strictly linear sequence.
Plastoquinone and Plastocyanin Carry Electrons between Photosystems II and I The location of the two photosystems at different sites on the thylakoid membranes (see Figure 7.18) requires that at least one component be capable of moving along or within the membrane in order to deliver electrons produced by photosystem II to photosystem I. The cytochrome b6 f com-plex is distributed equally between the grana and the stroma regions of the membranes, but its large size makes it unlikely that it is the mobile carrier. Instead, plasto-quinone or plastocyanin or possibly both are thought to serve as mobile carriers to connect the two photosystems.
Plastocyanin is a small (10.5 kDa), water-soluble, cop-per-containing protein that transfers electrons between the cytochrome b6 f complex and P700. This protein is found in the lumenal space (see Figure 7.29). In certain green algae and cyanobacteria, a c-type cytochrome is sometimes found instead of plastocyanin; which of these two proteins is syn-thesized depends on the amount of copper available to the organism.
The Photosystem I Reaction Center Reduces NADP+ The PSI reaction center complex is a large multisubunit complex (Figure 7.30) (Jordan et al. 2001). In contrast to PSII, a core antenna consisting of about 100 chlorophylls is a part of the PSI reaction center, P700. The core antenna and P700 are bound to two proteins, PsaA and PsaB, with molecular masses in the range of 66 to 70 kDa (Brettel 1997; Chitnis 2001; see also Web Topic 7.8). The antenna pigments form a bowl sur-rounding the electron transfer cofactors, which are in the center of the complex. In 132 Chapter 7 Lumen Stroma PC– PC Fd Fd– e– e– e– e– Light D C A0 A1 FeSB E K J L I G H N F PsaA PsaB ++ + + +++ + ++ – – – – – –– – – – (A) (B) P700 PsaC PsaD PsaE Lumen Stroma (B) FeSA FeSX FIGURE 7.30 Structure of photosystem I. (A) Structural model of the PSI reaction center. Components of the PSI reaction center are organized around two major proteins, PsaA and PsaB. Minor proteins PsaC to PsaN are labelled C to N. Electrons are transferred from plastocyanin (PC) to P700 (see Figures 7.21 and 7.22) and then to a chlorophyll molecule, A0, to phylloquinone, A1, to the FeSX, FeSA, and FeSB Fe–S centers, and finally to the soluble iron–sulfur protein, ferrodoxin (Fd). (B) Side view of one monomer of PSI from the cyanobacterium Synechococcus elongatus, at 2.5 Å resolution. The stromal side of the membrane is at the top, and the lumenal side is at the bottom of the figure. Transmembrane α-helices of PsaA and PsaB are shown as blue and red cylinders, respectively. (A after Buchanan et al. 2000; B from Jordan et al. 2001.) their reduced form, the electron carriers that function in the acceptor region of photosystem I are all extremely strong reducing agents. These reduced species are very unstable and thus difficult to identify. Evidence indicates that one of these early acceptors is a chlorophyll molecule, and another is a quinone species, phylloquinone, also known as vitamin K1.
Additional electron acceptors include a series of three membrane-associated iron–sulfur proteins, or bound ferre-doxins, also known as Fe–S centers FeSX, FeSA, and FeSB (see Figure 7.30). Fe–S center X is part of the P700-binding protein; centers A and B reside on an 8 kDa protein that is part of the PSI reaction center complex. Electrons are trans-ferred through centers A and B to ferredoxin (Fd), a small, water-soluble iron–sulfur protein (see Figures 7.21 and 7.30).
The membrane-associated flavoprotein ferredoxin–NADP reductase (FNR) reduces NADP+ to NADPH, thus com-pleting the sequence of noncyclic electron transport that begins with the oxidation of water (Karplus et al. 1991).
In addition to the reduction of NADP+, reduced ferre-doxin produced by photosystem I has several other func-tions in the chloroplast, such as the supply of reductants to reduce nitrate and the regulation of some of the carbon fix-ation enzymes (see Chapter 8).
Cyclic Electron Flow Generates ATP but no NADPH Some of the cytochrome b6 f complexes are found in the stroma region of the membrane, where photosystem I is located. Under certain conditions cyclic electron flow from the reducing side of photosystem I, through the b6 f com-plex and back to P700, is known to occur. This cyclic elec-tron flow is coupled to proton pumping into the lumen, which can be utilized for ATP synthesis but does not oxi-dize water or reduce NADP+. Cyclic electron flow is espe-cially important as an ATP source in the bundle sheath chloroplasts of some plants that carry out C4 carbon fixa-tion (see Chapter 8).
Some Herbicides Block Electron Flow The use of herbicides to kill unwanted plants is widespread in modern agriculture. Many different classes of herbicides have been developed, and they act by blocking amino acid, carotenoid, or lipid biosynthesis or by disrupting cell divi-sion. Other herbicides, such as DCMU (dichlorophenyl-dimethylurea) and paraquat, block photosynthetic electron flow (Figure 7.31). DCMU is also known as diuron.
Paraquat has acquired public notoriety because of its use on marijuana crops.
Many herbicides, DCMU among them, act by blocking electron flow at the quinone acceptors of photosystem II, by competing for the binding site of plastoquinone that is normally occupied by QB. Other herbicides, such as paraquat, act by accepting electrons from the early accep-tors of photosystem I and then reacting with oxygen to form superoxide, O2 –, a species that is very damaging to chloroplast components, especially lipids.
PROTON TRANSPORT AND ATP SYNTHESIS IN THE CHLOROPLAST In the preceding sections we learned how captured light energy is used to reduce NADP+ to NADPH. Another frac-tion of the captured light energy is used for light-dependent ATP synthesis, which is known as photophosphorylation.
This process was discovered by Daniel Arnon and his coworkers in the 1950s. In normal cellular conditions, pho-tophosphorylation requires electron flow, although under some conditions electron flow and photophosphorylation can take place independently of each other. Electron flow with-out accompanying phosphorylation is said to be uncoupled.
It is now widely accepted that photophosphorylation works via the chemiosmotic mechanism, first proposed in the 1960s by Peter Mitchell. The same general mechanism drives phosphorylation during aerobic respiration in bac-teria and mitochondria (see Chapter 11), as well as the transfer of many ions and metabolites across membranes (see Chapter 6). Chemiosmosis appears to be a unifying aspect of membrane processes in all forms of life.
Photosynthesis: The Light Reactions 133 Cl Cl– Cl– Cl N H C O N(CH3)2 CH3 CH3 N+ N+ P680 P680 P700 P700 H2O O2 QA QB DCMU Paraquat NADPH NADP+ DCMU (diuron) (dichlorophenyl-dimethylurea) Paraquat (methyl viologen) (A) (B) FIGURE 7.31 Chemical structure and mechanism of action of two important herbicides. (A) Chemical structure of dichlorophenyl-dimethylurea (DCMU) and methyl violo-gen (paraquat), two herbicides that block photosynthetic electron flow. DCMU is also known as diuron. (B) Sites of action of the two herbicides. DCMU blocks electron flow at the quinone acceptors of photosystem II, by competing for the binding site of plastoquinone. Paraquat acts by accept-ing electrons from the early acceptors of photosystem I.
In Chapter 6 we discussed the role of ATPases in chemiosmosis and ion transport at the cell’s plasma mem-brane. The ATP used by the plasma membrane ATPase is synthesized by photophosphorylation in the chloroplast and oxidative phosphorylation in the mitochondrion. Here we are concerned with chemiosmosis and transmembrane proton concentration differences used to make ATP in the chloroplast.
The basic principle of chemiosmosis is that ion concen-tration differences and electric-potential differences across membranes are a source of free energy that can be utilized by the cell. As described by the second law of thermody-namics (see Chapter 2 on the web site for a detailed dis-cussion), any nonuniform distribution of matter or energy represents a source of energy. Differences in chemical potential of any molecular species whose concentrations are not the same on opposite sides of a membrane provide such a source of energy.
The asymmetric nature of the photosynthetic membrane and the fact that proton flow from one side of the mem-brane to the other accompanies electron flow were dis-cussed earlier. The direction of proton translocation is such that the stroma becomes more alkaline (fewer H+ ions) and the lumen becomes more acidic (more H+ ions) as a result of electron transport (see Figures 7.22 and 7.29).
Some of the early evidence supporting a chemiosmotic mechanism of photosynthetic ATP formation was provided by an elegant experiment carried out by André Jagendorf and coworkers (Figure 7.32). They suspended chloroplast thylakoids in a pH 4 buffer, and the buffer diffused across the membrane, causing the interior, as well as the exterior, of the thylakoid to equilibrate at this acidic pH. They then rapidly transferred the thylakoids to a pH 8 buffer, thereby creating a pH difference of 4 units across the thylakoid membrane, with the inside acidic relative to the outside.
They found that large amounts of ATP were formed from ADP and Pi by this process, with no light input or electron transport. This result supports the predictions of the chemiosmotic hypothesis, described in the paragraphs that follow.
Mitchell proposed that the total energy available for ATP synthesis, which he called the proton motive force (∆p), is the sum of a proton chemical potential and a trans-membrane electric potential. These two components of the proton motive force from the outside of the membrane to the inside are given by the following equation: ∆p = ∆E −59(pΗi − pΗο) (7.9) where ∆E is the transmembrane electric potential, and pHi – pHo (or ∆pH) is the pH difference across the membrane.
The constant of proportionality (at 25°C) is 59 mV per pH unit, so a transmembrane pH difference of 1 pH unit is equivalent to a membrane potential of 59 mV.
Under conditions of steady-state electron transport in chloroplasts, the membrane electric potential is quite small because of ion movement across the membrane, so ∆p is built almost entirely by ∆pH. The stoichiometry of pro-tons translocated per ATP synthesized has recently been found to be four H+ ions per ATP (Haraux and De Kouchkovsky 1998).
In addition to the need for mobile electron carriers dis-cussed earlier, the uneven distribution of photosystems II and I, and of ATP synthase at the thylakoid membrane (see Figure 7.18), poses some challenges for the formation of ATP. ATP synthase is found only in the stroma lamellae and at the edges of the grana stacks. Protons pumped 134 Chapter 7 Buffered medium Equilibration Thylakoids transferred Chloroplast thylakoids pH 4 pH 4 pH 8 pH8 ATP ADP Pi + ADP Pi + In the dark FIGURE 7.32 Summary of the experiment carried out by Jagendorf and coworkers. Isolated chloroplast thylakoids kept previously at pH 8 were equilibrated in an acid medium at pH 4. The thylakoids were then transferred to a buffer at pH 8 that contained ADP and Pi. The proton gra-dient generated by this manipulation provided a driving force for ATP synthesis in the absence of light. This experi-ment verified a prediction of the chemiosmotic theory stat-ing that a chemical potential across a membrane can pro-vide energy for ATP synthesis.
across the membrane by the cytochrome b6 f complex or protons produced by water oxidation in the middle of the grana must move laterally up to several tens of nanometers to reach ATP synthase.
The ATP is synthesized by a large (400 kDa) enzyme com-plex known by several names: ATP synthase, ATPase (after the reverse reaction of ATP hydrolysis), and CFo–CF1 (Boyer 1997). This enzyme consists of two parts: a hydrophobic membrane-bound portion called CFo and a portion that sticks out into the stroma called CF1 (Figure 7.33).
CFo appears to form a channel across the membrane through which protons can pass. CF1 is made up of several peptides, including three copies of each of the α and β pep-tides arranged alternately much like the sections of an orange. Whereas the catalytic sites are located largely on the β polypeptide, many of the other peptides are thought to have primarily regulatory functions. CF1 is the portion of the complex that synthesizes ATP.
The molecular structure of the mitochondrial ATP syn-thase has been determined by X-ray crystallography (Stock et al. 1999). Although there are significant differences between the chloroplast and mitochondrial enzymes, they have the same overall architecture and probably nearly identical catalytic sites. In fact, there are remarkable simi-larities in the way electron flow is coupled to proton translocation in chloroplasts, mitochondria, and purple bacteria (Figure 7.34). Another remarkable aspect of the mechanism of the ATP synthase is that the internal stalk and probably much of the CFo portion of the enzyme rotate during catalysis (Yasuda et al. 2001). The enzyme is actu-ally a tiny molecular motor (see Web Topics 7.9 and 11.4).
REPAIR AND REGULATION OF THE PHOTOSYNTHETIC MACHINERY Photosynthetic systems face a special challenge. They are designed to absorb large amounts of light energy and process it into chemical energy. At the molecular level, the energy in a photon can be damaging, particularly under unfavorable conditions. In excess, light energy can lead to the production of toxic species, such as superoxide, singlet oxygen, and peroxide, and damage can occur if the light energy is not dissipated safely (Horton et al. 1996; Asada 1999; Müller et al. 2001). Photosynthetic organisms there-fore contain complex regulatory and repair mechanisms.
Some of these mechanisms regulate energy flow in the antenna system, to avoid excess excitation of the reaction centers and ensure that the two photosystems are equally driven. Although very effective, these processes are not entirely fail-safe, and sometimes toxic compounds are pro-duced. Additional mechanisms are needed to dissipate these compounds—in particular, toxic oxygen species.
Despite these protective and scavenging mechanisms, damage can occur, and additional mechanisms are required to repair the system. Figure 7.35 provides an overview of the several levels of the regulation and repair systems.
Carotenoids Serve as Photoprotective Agents In addition to their role as accessory pigments, carotenoids play an essential role in photoprotection. The photosyn-thetic membrane can easily be damaged by the large amounts of energy absorbed by the pigments if this energy cannot be stored by photochemistry; this is why a protec-tion mechanism is needed. The photoprotection mecha-nism can be thought of as a safety valve, venting excess energy before it can damage the organism. When the energy stored in chlorophylls in the excited state is rapidly dissipated by excitation transfer or photochemistry, the excited state is said to be quenched.
If the excited state of chlorophyll is not rapidly quenched by excitation transfer or photochemistry, it can react with molecular oxygen to form an excited state of oxygen known as singlet oxygen (1O2). The extremely reactive singlet oxy-gen goes on to react with and damage many cellular com-ponents, especially lipids. Carotenoids exert their photo-protective action by rapidly quenching the excited state of chlorophyll. The excited state of carotenoids does not have Photosynthesis: The Light Reactions 135 STROMA LUMEN Thylakoid membrane a c α α β β β α ATP ADP Pi + CF1 CFo b δ ε γ H+ H+ FIGURE 7.33 Structure of ATP synthase. This enzyme con-sists of a large multisubunit complex, CF1, attached on the stromal side of the membrane to an integral membrane por-tion, known as CFo. CF1 consists of five different polypep-tides, with a stoichiometry of α3, β3, γ, δ, ε. CFo contains probably four different polypeptides, with a stoichiometry of a, b, b′, c12.
sufficient energy to form singlet oxygen, so it decays back to its ground state while losing its energy as heat.
Mutant organisms that lack carotenoids cannot live in the presence of both light and molecular oxygen—a rather difficult situation for an O2-evolving photosynthetic organ-ism. For non-O2-evolving photosynthetic bacteria, mutants that lack carotenoids can be maintained under labora-tory conditions if oxygen is excluded from the growth medium.
Recently carotenoids were found to play a role in non-photochemical quenching, which is a second protective and regulatory mechanism.
Some Xanthophylls Also Participate in Energy Dissipation Nonphotochemical quenching, a major process regulating the delivery of excitation energy to the reaction center, can be thought of as a “volume knob” that adjusts the flow of 136 Chapter 7 STROMA LUMEN MATRIX INTERMEMBRANE SPACE Cyt bc1 complex ATP synthase Q Cyt c (A) Purple bacteria Cyt b6f complex O2 + H2O CFo CF1 F1 Fo Q PC (B) Chloroplasts Cyt bc1 complex Fo F1 Q (C) Mitochondria NADH dehydrogenase Cyt c Cytochrome oxidase H2O O2 CYTOSOL PERIPLASM ATP ATP ADP Pi + ADP Pi + ATP ADP Pi + ATP synthase ATP synthase NADPH NADH NADP+ NAD+ Light Light Light H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ Reaction center PSII Reaction center PSI Reaction center FIGURE 7.34 Similarities of photosynthetic and respira-tory electron flow in bacteria, chloroplasts, and mitochon-dria. In all three, electron flow is coupled to proton transloca-tion, creating a transmem-brane proton motive force (∆p). The energy in the proton motive force is then used for the synthesis of ATP by ATP synthase. (A) A reaction center (RC) in purple photosynthetic bacteria carries out cyclic elec-tron flow, generating a proton potential by the action of the cytochrome bc1 complex. (B) Chloroplasts carry out non-cyclic electron flow, oxidizing water and reducing NADP+.
Protons are produced by the oxidation of water and by the oxidation of PQH2 (Q) by the cytochrome b6 f complex. (C) Mitochondria oxidize NADH to NAD+ and reduce oxygen to water. Protons are pumped by the enzyme NADH dehy-drogenase, the cytochrome bc1 complex, and cytochrome oxi-dase. The ATP synthases in the three systems are very similar in structure.
excitations to the PSII reaction center to a manageable level, depending on the light intensity and other conditions. The process appears to be an essential part of the regulation of antenna systems in most algae and plants.
Nonphotochemical quenching is the quenching of chlorophyll fluorescence (see Figure 7.5) by processes other than photochemistry. As a result of nonphotochemical quenching, a large fraction of the excitations in the antenna system caused by intense illumination are quenched by conversion into heat (Krause and Weis 1991). Nonphoto-chemical quenching is thought to be involved in protecting the photosynthetic machinery against overexcitation and subsequent damage.
The molecular mechanism of nonphotochemical quenching is not well understood, although it is clear that the pH of the thylakoid lumen and the state of aggregation of the antenna com-plexes are important factors. Three carotenoids, called xanthophylls, are involved in nonpho-tochemical quenching: violaxanthin, antherax-anthin, and zeaxanthin (Figure 7.36).
In high light, violaxanthin is converted into zeaxanthin, via the intermediate antheraxan-thin, by the enzyme violaxanthin de-epoxidase.
When light intensity decreases, the process is reversed. Binding of protons and zeaxanthin to light-harvesting antenna proteins is thought to cause conformational changes that lead to quenching and heat dissipation (Demmig-Photosynthesis: The Light Reactions 137 Photon intensity Excess photons Toxic photoproducts Damage to D1 of PSII Oxidized D1 Photoinhibition Photon used for photosynthesis First line of defense: Suppression mechanisms Second line of defense: Scavenging systems (e.g., carotenoids, superoxide dismutase, ascorbate) Heat Repair, de novo synthesis Triplet state of Chl (3Chl) Superoxide (O2 −) Singlet oxygen (1O2 ) Hydrogen peroxide (H2O2) Hydroxyl radical (•OH) FIGURE 7.35 Overall picture of the regulation of photon capture and the protection and repair of photodamage.
Protection against photodamage is a multilevel process.
The first line of defense is suppression of damage by quenching of excess excitation as heat. If this defense is not sufficient and toxic photoproducts form, a variety of scav-enging systems eliminate the reactive photoproducts. If this second line of defense also fails, the photoproducts can damage the D1 protein of photosystem II. This damage leads to photoinhibition. The D1 protein is then excised from the PSII reaction center and degraded. A newly syn-thesized D1 is reinserted into the PSII reaction center to form a functional unit. (After Asada 1999.) H2O 2 H + O2 H2O 2 H Ascorbate NADPH O HO O OH O HO OH H2O 2 H + O2 H2O 2 H Ascorbate NADPH HO OH Violaxanthin Antheraxanthin Zeaxanthin Low light High light FIGURE 7.36 Chemical structure of violaxan-thin, antheraxanthin, and zeaxanthin. The highly quenched state of photosystem II is asso-ciated with zeaxanthin, the unquenched state with violaxanthin. Enzymes interconvert these two carotenoids, with antheraxanthin as the intermediate, in response to changing condi-tions, especially changes in light intensity.
Zeaxanthin formation uses ascorbate as a cofac-tor, and violaxanthin formation requires NADPH. (After Pfündel and Bilger 1994.) Adams and Adams 1992; Horton et al. 1996). Nonphoto-chemical quenching appears to be preferentially associated with a peripheral antenna complex of photosystem II, the PsbS protein (Li et al. 2000).
The Photosystem II Reaction Center Is Easily Damaged Another effect that appears to be a major factor in the sta-bility of the photosynthetic apparatus is photoinhibition, which occurs when excess excitation arriving at the PSII reaction center leads to its inactivation and damage (Long et al. 1994). Photoinhibition is a complex set of molecular processes, defined as the inhibition of photosynthesis by excess light.
As will be discussed in detail in Chapter 9, photoinhi-bition is reversible in early stages. Prolongued inhibition, however, results in damage to the system such that the PSII reaction center must be disassembled and repaired (Melis 1999). The main target of this damage is the D1 protein that makes up part of the PSII reaction center complex (see Fig-ure 7.24). When D1 is damaged by excess light, it must be removed from the membrane and replaced with a newly synthesized molecule. The other components of the PSII reaction center are not damaged by excess excitation and are thought to be recycled, so the D1 protein is the only component that needs to be synthesized.
Photosystem I Is Protected from Active Oxygen Species Photosystem I is particularly vulnerable to damage from active oxygen species. The ferredoxin acceptor of PSI is a very strong reductant that can easily reduce molecular oxygen to form superoxide (O2 –). This reduction competes with the nor-mal channeling of electrons to the reduction of NADP+ and other processes. Superoxide is one of a series of active oxy-gen species that can be very damaging to biological mem-branes. Superoxide formed in this way can be eliminated by the action of a series of enzymes, including superoxide dis-mutase and ascorbate peroxidase (Asada 1999).
Thylakoid Stacking Permits Energy Partitioning between the Photosystems The fact that photosynthesis in higher plants is driven by two photosystems with different light-absorbing properties poses a special problem. If the rate of delivery of energy to PSI and PSII is not precisely matched and conditions are such that the rate of photosynthesis is limited by the avail-able light (low light intensity), the rate of electron flow will be limited by the photosystem that is receiving less energy.
In the most efficient situation, the input of energy would be the same to both photosystems. However, no single arrangement of pigments would satisfy this requirement because at different times of day the light intensity and spectral distribution tend to favor one photosystem or the other (Trissl and Wilhelm 1993; Allen and Forsberg 2001).
This problem can be solved by a mechanism that shifts energy from one photosystem to the other in response to different conditions. Such a regulating mechanism has been shown to operate in different experimental conditions. The observation that the overall quantum yield of photosyn-thesis is nearly independent of wavelength (see Figure 7.12) strongly suggests that such a mechanism exists.
Thylakoid membranes contain a protein kinase that can phosphorylate a specific threonine residue on the surface of LHCII, one of the membrane-bound antenna pigment pro-teins described earlier in the chapter (see Figure 7.20). When LHCII is not phosphorylated, it delivers more energy to photosystem II, and when it is phosphorylated, it delivers more energy to photosystem I (Haldrup et al. 2001).
The kinase is activated when plastoquinone, one of the electron carriers between PSI and PSII, accumulates in the reduced state. Reduced plastoquinone accumulates when PSII is being activated more frequently than PSI. The phos-phorylated LHCII then migrates out of the stacked regions of the membrane into the unstacked regions (see Figure 7.18), probably because of repulsive interactions with neg-ative charges on adjacent membranes.
The lateral migration of LHCII shifts the energy balance toward photosystem I, which is located in the stroma lamellae, and away from photosystem II, which is located in the stacked membranes of the grana. This situation is called state 2. If plastoquinone becomes more oxidized because of excess excitation of photosystem I, the kinase is deactivated and the level of phosphorylation of LHCII is decreased by the action of a membrane-bound phos-phatase. LHCII then moves back to the grana, and the sys-tem is in state 1. The net result is a very precise control of the energy distribution between the photosystems, allow-ing the most efficient use of the available energy.
GENETICS, ASSEMBLY, AND EVOLUTION OF PHOTOSYNTHETIC SYSTEMS Chloroplasts have their own DNA, mRNA, and protein synthesis machinery, but some chloroplast proteins are encoded by nuclear genes and imported into the chloro-plast. In this section we will consider the genetics, assem-bly, and evolution of the main chloroplast components.
Chloroplast, Cyanobacterial, and Nuclear Genomes Have Been Sequenced The complete chloroplast genomes of several organisms have been sequenced. Chloroplast DNA is circular and ranges in size from 120 to 160 kilobases. The chloroplast genome contains coding sequences for approximately 120 proteins. Some of these DNA sequences code for proteins that are yet to be characterized. It is uncertain whether all these genes are transcribed into mRNA and translated into protein, but it seems likely that some chloroplast proteins remain to be identified.
138 Chapter 7 The complete genome of the cyanobacterium Syne-chocystis (strain PCC 6803) and the higher plant Arabidopsis have been sequenced, and genomes of important crop plants such as rice and maize have been completed (Kotani and Tabata 1998; Arabidopsis Genome Initiative 2000).
Genomic data for both chloroplast and nuclear DNA will provide new insights into the mechanism of photosynthe-sis, as well as many other plant processes.
Chloroplast Genes Exhibit Non-Mendelian Patterns of Inheritance Chloroplasts and mitochondria reproduce by division rather than by de novo synthesis. This mode of reproduc-tion is not surprising, since these organelles contain genetic information that is not present in the nucleus. During cell division, chloroplasts are divided between the two daugh-ter cells. In most sexual plants, however, only the maternal plant contributes chloroplasts to the zygote. In these plants the normal Mendelian pattern of inheritance does not apply to chloroplast-encoded genes because the offspring receive chloroplasts from only one parent. The result is non-Mendelian, or maternal, inheritance. Numerous traits are inherited in this way; one example is the herbicide resistance trait discussed in Web Topic 7.10.
Many Chloroplast Proteins Are Imported from the Cytoplasm Chloroplast proteins can be encoded by either chloroplas-tic or nuclear DNA. The chloroplast-encoded proteins are synthesized on chloroplast ribosomes; the nucleus-encoded proteins are synthesized on cytoplasmic ribosomes and then transported into the chloroplast. Many nuclear genes contain introns—that is, base sequences that do not code for protein. The mRNA is processed to remove the introns, and the proteins are then synthesized in the cytoplasm.
The genes needed for chloroplast function are distrib-uted in the nucleus and in the chloroplast genome with no evident pattern, but both sets are essential for the viability of the chloroplast. Some chloroplast genes are necessary for other cellular functions, such as heme and lipid synthesis.
Control of the expression of the nuclear genes that code for chloroplast proteins is complex, involving light-dependent regulation mediated by both phytochrome (see Chapter 17) and blue light (see Chapter 18), as well as other factors (Bruick and Mayfield 1999; Wollman et al. 1999).
The transport of chloroplast proteins that are synthe-sized in the cytoplasm is a tightly regulated process (Chen and Schnell 1999). For example, the enzyme rubisco (see Chapter 8), which functions in carbon fixation, has two types of subunits, a chloroplast-encoded large subunit and a nucleus-encoded small subunit. Small subunits of rubisco are synthesized in the cytoplasm and transported into the chloroplast, where the enzyme is assembled.
In this and other known cases, the nucleus-encoded chloroplast proteins are synthesized as precursor proteins containing an N-terminal amino acid sequence known as a transit peptide. This terminal sequence directs the precur-sor protein to the chloroplast, facilitates its passage through both the outer and the inner envelope membranes, and is then clipped off. The electron carrier plastocyanin is a water-soluble protein that is encoded in the nucleus but functions in the lumen of the chloroplast. It therefore must cross three membranes to reach its destination in the lumen. The transit peptide of plastocyanin is very large and is processed in more than one step.
The Biosynthesis and Breakdown of Chlorophyll Are Complex Pathways Chlorophylls are complex molecules exquisitely suited to the light absorption, energy transfer, and electron transfer functions that they carry out in photosynthesis (see Figure 7.6). Like all other biomolecules, chlorophylls are made by a biosynthetic pathway in which simple molecules are used as building blocks to assemble more complex molecules (Porra 1997; Beale 1999). Each step in the biosynthetic path-way is enzymatically catalyzed.
The chlorophyll biosynthetic pathway consists of more than a dozen steps (see Web Topic 7.11). The process can be divided into several phases (Figure 7.37), each of which can be considered separately, but which in the cell are highly coordinated and regulated. This regulation is essen-tial because free chlorophyll and many of the biosynthetic intermediates are damaging to cellular components. The damage results largely because chlorophylls absorb light efficiently, but in the absence of accompanying proteins, they lack a pathway for disposing of the energy, with the result that toxic singlet oxygen is formed.
The breakdown pathway of chlorophyll in senescent leaves is quite different from the biosynthetic pathway (Matile et al. 1996). The first step is removal of the phytol tail by an enzyme known as chlorophyllase, followed by removal of the magnesium by magnesium de-chelatase.
Next the porphyrin structure is opened by an oxygen-dependent oxygenase enzyme to form an open-chain tetrapyrrole.
The tetrapyrrole is further modified to form water-sol-uble, colorless products. These colorless metabolites are then exported from the senescent chloroplast and trans-ported to the vacuole, where they are permanently stored.
The chlorophyll metabolites are not further processed or recycled, although the proteins associated with them in the chloroplast are subsequently recycled into new proteins.
The recycling of proteins is thought to be important for the nitrogen economy of the plant.
Complex Photosynthetic Organisms Have Evolved from Simpler Forms The complicated photosynthetic apparatus found in plants and algae is the end product of a long evolutionary sequence. Much can be learned about this evolutionary Photosynthesis: The Light Reactions 139 140 Chapter 7 COOH CH2 CH2 CHNH2 COOH COOH CH2 CH2 C O CH2NH2 N H HOOC COOH NH2 NH N N HN COOH COOH E O COOH N Mg N N N CH2 Mg2+ CH3 CH3 CH3 CH3 CO2CH3 CH3 A B D C E O H H COOH N Mg N N N CH2 CH3 CH3 CH3 CH3 CO2CH3 CH3 A B D C N Mg N N O O H H H O N A B D E C H3C CO2CH3 CH2CH3 CH CH3 CH3 CH2 H3C Reduction site Phase I Phase II Phase III Phase IV Glutamic acid 5-Aminolevulinic acid (ALA) Porphobilinogen (PBG) Protoporphyrin IX NADPH, light Protochlorophyllide oxidoreductase Chlorophyllide a Monovinyl protochlorophyllide a Chlorophyll a Phytol tail Phytol tail FIGURE 7.37 The biosynthetic pathway of chloro-phyll. The pathway begins with glutamic acid, which is converted to 5-aminolevulinic acid (ALA). Two molecules of ALA are condensed to form porphobilinogen (PBG). Four PBG mole-cules are linked to form protoporphyrin IX. The magnesium (Mg) is then inserted, and the light-dependent cyclization of ring E, the reduction of ring D, and the attachment of the phytol tail com-plete the process. Many steps in the process are omitted in this figure. process from analysis of simpler prokaryotic photosyn-thetic organisms, including the anoxygenic photosynthetic bacteria and the cyanobacteria.
The chloroplast is a semiautonomous cell organelle, with its own DNA and a complete protein synthesis apparatus.
Many of the proteins that make up the photosynthetic appa-ratus, as well as all the chlorophylls and lipids, are synthe-sized in the chloroplast. Other proteins are imported from the cytoplasm and are encoded by nuclear genes. How did this curious division of labor come about? Most experts now agree that the chloroplast is the descendant of a sym-biotic relationship between a cyanobacterium and a simple nonphotosynthetic eukaryotic cell. This type of relationship is called endosymbiosis (Cavalier-Smith 2000).
Originally the cyanobacterium was capable of indepen-dent life, but over time much of its genetic information needed for normal cellular functions was lost, and a sub-stantial amount of information needed to synthesize the photosynthetic apparatus was transferred to the nucleus.
So the chloroplast was no longer capable of life outside its host and eventually became an integral part of the cell.
In some types of algae, chloroplasts are thought to have arisen by endosymbiosis of eukaryotic photosynthetic organisms (Palmer and Delwiche 1996). In these organisms the chloroplast is surrounded by three and in some cases four membranes, which are thought to be remnants of the plasma membranes of the earlier organisms. Mitochondria are also thought to have originated by endosymbiosis in a separate event much earlier than chloroplast formation.
The answers to other questions related to the evolution of photosynthesis are less clear. These include the nature of the earliest photosynthetic systems, how the two photo-systems became linked, and the evolutionary origin of the oxygen evolution complex (Blankenship and Hartman 1998; Xiong et al. 2000).
SUMMARY Photosynthesis is the storage of solar energy carried out by plants, algae, and photosynthetic bacteria. Absorbed pho-tons excite chlorophyll molecules, and these excited chloro-phylls can dispose of this energy as heat, fluorescence, energy transfer, or photochemistry. Light is absorbed mainly in the antenna complexes, which comprise chloro-phylls, accessory pigments, and proteins and are located at the thylakoid membranes of the chloroplast.
Photosynthetic antenna pigments transfer the energy to a specialized chlorophyll–protein complex known as a reaction center. The reaction center contains multisubunit protein complexes and hundreds or, in some organisms, thousands of chlorophylls. The antenna complexes and the reaction centers are integral components of the thylakoid membrane. The reaction center initiates a complex series of chemical reactions that capture energy in the form of chem-ical bonds.
The relationship between the amount of absorbed quanta and the yield of a photochemical product made in a light-dependent reaction is given by the quantum yield.
The quantum yield of the early steps of photosynthesis is approximately 0.95, indicating that nearly every photon that is absorbed yields a charge separation at the reaction center.
Plants and some photosynthetic prokaryotes have two reaction centers, photosystem I and photosystem II, that function in series. The two photosystems are spatially sep-arated: PSI is found exclusively in the nonstacked stroma membranes, PSII largely in the stacked grana membranes.
The reaction center chlorophylls of PSI absorb maximally at 700 nm, those of PSII at 680 nm. Photosystems II and I carry out noncyclic electron transport, oxidize water to molecular oxygen, and reduce NADP+ to NADPH. It is energetically very difficult to oxidize water to form molec-ular oxygen, and the photosynthetic oxygen-evolving sys-tem is the only known biochemical system that can oxidize water, thus providing almost all the oxygen in Earth’s atmosphere. The photooxidation of water is modeled by the five-step S state mechanism. Manganese is an essential cofactor in the water-oxidizing process, and the five S states appear to represent successive oxidized states of a man-ganese-containing enzyme.
A tyrosine residue of the D1 protein of the PSII reaction center functions as an electron carrier between the oxygen-evolving complex and P680. Pheophytin and two plasto-quinones are electron carriers between P680 and the large cytochrome b6 f complex. Plastocyanin is the electron car-rier between cytochrome b6 f and P700. The electron car-riers that accept electrons from P700 are very strong reduc-ing agents, and they include a quinone and three membrane-bound iron–sulfur proteins known as bound ferredoxins. The electron flow ends with the reduction of NADP+ to NADPH by a membrane-bound, ferro-doxin–NADP reductase.
A portion of the energy of photons is also initially stored as chemical-potential energy, largely in the form of a pH difference across the thylakoid membrane. This energy is quickly converted into chemical energy during ATP for-mation by action of an enzyme complex known as the ATP synthase. The photophosphorylation of ADP by the ATP synthase is driven by a chemiosmotic mechanism. Photo-synthetic electron flow is coupled to proton translocation across the thylakoid membrane, and the stroma becomes more alkaline and the lumen more acidic. This proton gra-dient drives ATP synthesis with a stoichiometry of four H+ ions per ATP. NADPH and ATP formed by the light reac-tions provide the energy for carbon reduction.
Excess light energy can damage photosynthetic systems, and several mechanisms minimize such damage.
Carotenoids work as photoprotective agents by rapidly quenching the excited state of chlorophyll. Changes in the phosphorylated state of antenna pigment proteins can Photosynthesis: The Light Reactions 141 change the energy distribution between photosystems I and II when there is an imbalance between the energy absorbed by each photosystem. The xanthophyll cycle also contributes to the dissipation of excess energy by nonpho-tochemical quenching.
Chloroplasts contain DNA and encode and synthesize some of the proteins that are essential for photosynthesis.
Additional proteins are encoded by nuclear DNA, synthe-sized in the cytosol, and imported into the chloroplast.
Chlorophylls are synthesized in a biosynthetic pathway involving more than a dozen steps, each of which is very carefully regulated. Once synthesized, proteins and pig-ments are assembled into the thylakoid membrane.
Web Material Web Topics 7.1 Principles of Spectrophotometry Spectroscopy is a key technique to study light reactions.
7.2 The Distribution of Chlorophylls and Other Photosynthetic Pigments The content of chlorophylls and other photo-synthetic pigments varies among plant king-doms.
7.3 Quantum Yield Quantum yields measure how effectively light drives a photobiological process.
7.4 Antagonistic Effects of Light on Cytochrome Oxidation Photosystems I and II were discovered in some ingenious experiments.
7.5 Structures of Two Bacterial Reaction Centers X-ray diffraction studies resolved the atomic structure of the reaction center of photosystem II.
7.6 Midpoint Potentials and Redox Reactions The measurement of midpoint potentials is useful for analyzing electron flow through pho-tosystem II.
7.7 Oxygen Evolution The S state mechanism is a valuable model for water splitting in PSII.
7.8 Photosystem I The PSI reaction is a multiprotein complex.
7.9 ATP Synthase The ATP synthase functions as a molecular motor.
7.10 Mode of Action of Some Herbicides Some herbicides kill plants by blocking photo-synthetic electron flow.
7.11 Chlorophyll Biosynthesis Chlorophyll and heme share early steps of their biosynthetic pathways.
Web Essay 7.1 A novel view of chloroplast structure Stromules extend the reach of the chloroplasts.
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Photosynthesis: The Light Reactions 143 Photosynthesis: Carbon Reactions 8 Chapter IN CHAPTER 5 WE DISCUSSED plants’ requirements for mineral nutri-ents and light in order to grow and complete their life cycle. Because liv-ing organisms interact with one another and their environment, mineral nutrients cycle through the biosphere. These cycles involve complex interactions, and each cycle is critical in its own right. Because the amount of matter in the biosphere remains constant, energy must be supplied to keep the cycles operational. Otherwise increasing entropy dictates that the flow of matter would ultimately stop.
Autotrophic organisms have the ability to convert physical and chemical sources of energy into carbohydrates in the absence of organic substrates. Most of the external energy is consumed in transforming CO2 to a reduced state that is compatible with the needs of the cell (—CHOH—).
Recent estimates indicate that about 200 billion tons of CO2 are con-verted to biomass each year. About 40% of this mass originates from the activities of marine phytoplankton. The bulk of the carbon is incorpo-rated into organic compounds by the carbon reduction reactions associ-ated with photosynthesis.
In Chapter 7 we saw how the photochemical oxidation of water to molecular oxygen is coupled to the generation of ATP and reduced pyri-dine nucleotide (NADPH) by reactions taking place in the chloroplast thylakoid membrane. The reactions catalyzing the reduction of CO2 to carbohydrate are coupled to the consumption of NADPH and ATP by enzymes found in the stroma, the soluble phase of chloroplasts.
These stroma reactions were long thought to be independent of light and, as a consequence, were referred to as the dark reactions. However, because these stroma-localized reactions depend on the products of the photochemical processes, and are also directly regulated by light, they are more properly referred to as the carbon reactions of photosynthesis.
In this chapter we will examine the cyclic reactions that accomplish fixation and reduction of CO2, then consider how the phenomenon of photorespiration catalyzed by the carboxylating enzyme alters the effi-ciency of photosynthesis. This chapter will also describe biochemical mechanisms for concentrating carbon dioxide that allow plants to mitigate the impact of photorespira-tion: CO2 pumps, C4 metabolism, and crassulacean acid metabolism (CAM). We will close the chapter with a con-sideration of the synthesis of sucrose and starch.
THE CALVIN CYCLE All photosynthetic eukaryotes, from the most primitive alga to the most advanced angiosperm, reduce CO2 to carbohy-drate via the same basic mechanism: the photosynthetic car-bon reduction cycle originally described for C3 species (the Calvin cycle, or reductive pentose phosphate [RPP] cycle).
Other metabolic pathways associated with the photosyn-thetic fixation of CO2, such as the C4 photosynthetic carbon assimilation cycle and the photorespiratory carbon oxida-tion cycle, are either auxiliary to or dependent on the basic Calvin cycle.
In this section we will examine how CO2 is fixed by the Calvin cycle through the use of ATP and NADPH generated by the light reactions (Figure 8.1), and how the Calvin cycle is regulated.
The Calvin Cycle Has Three Stages: Carboxylation, Reduction, and Regeneration The Calvin cycle was elucidated as a result of a series of elegant experiments by Melvin Calvin and his colleagues in the 1950s, for which a Nobel Prize was awarded in 1961 (see Web Topic 8.1). In the Calvin cycle, CO2 and water from the environment are enzymatically combined with a five-carbon acceptor molecule to generate two molecules of a three-carbon intermediate. This intermediate (3-phos-phoglycerate) is reduced to carbohydrate by use of the ATP and NADPH generated photochemically. The cycle is com-pleted by regeneration of the five-carbon acceptor (ribu-lose-1,5-bisphosphate, abbreviated RuBP).
The Calvin cycle proceeds in three stages (Figure 8.2): 1. Carboxylation of the CO2 acceptor ribulose-1,5-bispho-sphate, forming two molecules of 3-phosphoglycerate, the first stable intermediate of the Calvin cycle 2. Reduction of 3-phosphoglycerate, forming gyceralde-hyde-3-phosphate, a carbohydrate 3. Regeneration of the CO2 acceptor ribulose-1,5-bisphos-phate from glyceraldehyde-3-phosphate The carbon in CO2 is the most oxidized form found in nature (+4). The carbon of the first stable intermediate, 3-phosphoglycerate, is more reduced (+3), and it is further reduced in the glyceraldehyde-3-phosphate product (+1).
Overall, the early reactions of the Calvin cycle complete the reduction of atmospheric carbon and, in so doing, facilitate its incorporation into organic compounds.
The Carboxylation of Ribulose Bisphosphate Is Catalyzed by the Enzyme Rubisco CO2 enters the Calvin cycle by reacting with ribulose-1,5-bisphosphate to yield two molecules of 3-phosphoglycerate (Figure 8.3 and Table 8.1), a reaction catalyzed by the chloro-plast enzyme ribulose bisphosphate carboxylase/oxy-genase, referred to as rubisco (see Web Topic 8.2). As indi-146 Chapter 8 Light Light reactions Chlorophyll Carbon reactions Triose phosphates O2 H2O CO2 + H2O (CH2O)n NADP+ ADP Pi NADPH ATP + + FIGURE 8.1 The light and carbon reactions of photosynthe-sis. Light is required for the generation of ATP and NADPH. The ATP and NADPH are consumed by the car-bon reactions, which reduce CO2 to carbohydrate (triose phosphates).
ADP NADPH ATP ATP + NADP+ ADP Pi + CO2 + H2O Start of cycle 3-phosphoglycerate Ribulose-1,5-bisphosphate Glyceraldehyde-3-phosphate Sucrose, starch Regeneration Carboxylation Reduction FIGURE 8.2 The Calvin cycle proceeds in three stages: (1) carboxylation, during which CO2 is covalently linked to a carbon skeleton; (2) reduction, during which carbohydrate is formed at the expense of the photochemically derived ATP and reducing equivalents in the form of NADPH; and (3) regeneration, during which the CO2 acceptor ribulose-1,5-bisphosphate re-forms.
H C C CH2OP OH O H OH C CH2OPO3 2– COO– C H OH CH2OP C H OH CH2OP CH2OPO3 2– CH2OP O C HO C O H OH OH H H C C C CH2OH C O 3 CO2 3 H2O 6 H+ Ribulose 1,5-bisphosphate 1,3-bisphosphoglycerate 3-phosphoglycerate Rubisco Phosphoglycerate kinase Glyceraldehyde 3-phosphate dehydrogenase Glyceraldehyde 3-phosphate NADPH NADP+ ADP 6 ATP 3 ADP 3 ATP Pi Pi 6 OP CH2OP C H OH CH2OP O C H C H OH C H OH CH2OP O C H 6 + 6 H+ + 6 6 Triose phosphate G3P DHAP Dihydroxy-acetone phosphate Dihydroxy-acetone phosphate CH2OH C O CH2OP Triose phosphate isomerase CH2OPO3 2– CH2OP HO C O H OH OH H H C C C OH H C Fructose 1,6-bisphosphate Fructose 1,6-bisphosphatase CH2OH CH2OP HO C O H OH OH H H C C C Fructose 6-phosphate CH2OH CH2OP HO C O H OH H C C Xylulose 5-phosphate CH2OH CH2OP HO C O H OH H C C Xylulose 5-phosphate CH2OH CH2OP H C O OH OH H C C Ribulose 5-phosphate CH2OH CH2OP H C O OH OH H C C Ribulose 5-phosphate O C H CH2OP H OH OH H C H OH C C Ribose 5-phosphate Aldolase H2O Pi H2O Transketolase Transketolase Aldolase Erythrose 4-phosphate Ribulose 5-phosphate 3-epimerase Phosphoribulokinase Sedoheptulose 1,7-bisphosphate Sedoheptulose 1,7-bisphosphatase CH2OH CH2OP HO C O H OH OH H H C C C OH H C Sedoheptulose 7-phosphate CH2OH CH2OP H C O OH OH H C C Ribulose 5-phosphate Ribulose 5-phosphate isomerase Ribulose 5-phosphate 3-epimerase FIGURE 8.3 The Calvin cycle. The carboxylation of three molecules of ribulose-1,5-bisphosphate leads to the net synthesis of one molecule of glyceraldehyde-3-phos-phate and the regeneration of the three molecules of starting material. This process starts and ends with three molecules of ribulose-1,5-bisphosphate, reflecting the cyclic nature of the pathway.
cated by the full name, the enzyme also has an oxygenase activity in which O2 competes with CO2 for the common substrate ribulose-1,5-bisphosphate (Lorimer 1983). As we will discuss later, this property limits net CO2 fixation.
As shown in Figure 8.4, CO2 is added to carbon 2 of ribu-lose-1,5-bisphosphate, yielding an unstable, enzyme-bound intermediate, which is hydrolyzed to yield two molecules of the stable product 3-phosphoglycerate (see Table 8.1, reac-tion 1). The two molecules of 3-phosphoglycerate—labeled “upper” and “lower” on the figure—are distinguished by the fact that the upper molecule contains the newly incor-porated carbon dioxide, designated here as CO2.
Two properties of the carboxylase reaction are especially important: 1. The negative change in free energy (see Chapter 2 on the web site for a discussion of free energy) associated with the carboxylation of ribulose-1,5-bisphosphate is large; thus the forward reaction is strongly favored.
2. The affinity of rubisco for CO2 is sufficiently high to ensure rapid carboxylation at the low concentrations of CO2 found in photosynthetic cells.
Rubisco is very abundant, representing up to 40% of the total soluble protein of most leaves. The concentration of rubisco active sites within the chloroplast stroma is calcu-lated to be about 4 mM, or about 500 times greater than the concentration of its CO2 substrate (see Web Topic 8.3).
Triose Phosphates Are Formed in the Reduction Step of the Calvin Cycle Next in the Calvin cycle (Figure 8.3 and Table 8.1), the 3-phosphoglycerate formed in the carboxylation stage under-goes two modifications: 1. It is first phosphorylated via 3-phosphoglycerate kinase to 1,3-bisphosphoglycerate through use of the ATP generated in the light reactions (Table 8.1, reac-tion 2).
2. Then it is reduced to glyceraldehyde-3-phosphate through use of the NADPH generated by the light reactions (Table 8.1, reaction 3). The chloroplast enzyme NADP:glyceraldehyde-3-phosphate dehy-drogenase catalyzes this step. Note that the enzyme is similar to that of glycolysis (which will be dis-148 Chapter 8 TABLE 8.1 Reactions of the Calvin cycle Enzyme Reaction 1. Ribulose-1,5-bisphosphate carboxylase/oxygenase 6 Ribulose-1,5-bisphosphate + 6 CO2 + 6 H2O → 12 (3-phosphoglycerate) + 12 H+ 2. 3-Phosphoglycerate kinase 12 (3-Phosphoglycerate) + 12 ATP → 12 (1,3-bisphosphoglycerate) + 12 ADP 3. NADP:glyceraldehyde-3-phosphate dehydrogenase 12 (1,3-Bisphosphoglycerate) + 12 NADPH + 12 H+ → 12 glyceraldehye-3-phosphate + 12 NADP+ + 12 Pi 4. Triose phosphate isomerase 5 Glyceraldehyde-3-phosphate → 5 dihydroxyacetone-3-phosphate 5. Aldolase 3 Glyceraldehyde-3-phosphate + 3 dihydroxyacetone-3-phosphate → 3 fructose-1,6-bisphosphate 6. Fructose-1,6-bisphosphatase 3 Fructose-1,6-bisphosphate + 3 H2O → 3 fructose-6-phosphate + 3 Pi 7. Transketolase 2 Fructose-6-phosphate + 2 glyceraldehyde-3-phosphate → 2 erythrose-4-phosphate + 2 xylulose-5-phosphate 8. Aldolase 2 Erythrose-4-phosphate + 2 dihydroxyacetone-3-phosphate → 2 sedoheptulose-1,7-bisphosphate 9. Sedoheptulose-1,7,bisphosphatase 2 Sedoheptulose-1,7-bisphosphate + 2 H2O → 2 sedoheptulose-7-phosphate + 2 Pi 10. Transketolase 2 Sedoheptulose-7-phosphate + 2 glyceraldehyde-3-phosphate → 2 ribose-5-phosphate + 2 xylulose-5-phosphate 11a. Ribulose-5-phosphate epimerase 4 Xylulose-5-phosphate → 4 ribulose-5-phosphate 11b. Ribose-5-phosphate isomerase 2 Ribose-5-phosphate → 2 ribulose-5-phosphate 12. Ribulose-5-phosphate kinase 6 Ribulose-5-phosphate + 6 ATP → 6 ribulose-1,5-bisphosphate + 6 ADP + 6 H+ Net: 6 CO2 + 11 H2O + 12 NADPH + 18 ATP → Fructose-6-phosphate + 12 NADP+ + 6 H+ + 18 ADP + 17 Pi Note: Pi stands for inorganic phosphate.
cussed in Chapter 11), except that NADP rather than NAD is the coenzyme. An NADP-linked form of the enzyme is synthesized during chloroplast develop-ment (greening), and this form is preferentially used in biosynthetic reactions.
Operation of the Calvin Cycle Requires the Regeneration of Ribulose-1,5-Bisphosphate The continued uptake of CO2 requires that the CO2 accep-tor, ribulose-1,5-bisphosphate, be constantly regenerated.
To prevent depletion of Calvin cycle intermediates, three molecules of ribulose-1,5-bisphosphate (15 carbons total) are formed by reactions that reshuffle the carbons from the five molecules of triose phosphate (5 × 3 = 15 carbons). This reshuffling consists of reactions 4 through 12 in Table 8.1 (see also Figure 8.3): 1. One molecule of glyceraldehyde-3-phosphate is con-verted via triose phosphate isomerase to dihydroxy-acetone-3-phosphate in an isomerization reaction (reaction 4).
2. Dihydroxyacetone-3-phosphate then undergoes aldol condensation with a second molecule of glyceralde-hyde-3-phosphate, a reaction catalyzed by aldolase to give fructose-1,6-bisphosphate (reaction 5).
3. Fructose-1,6-bisphosphate occupies a key position in the cycle and is hydrolyzed to fructose-6-phosphate (reaction 6), which then reacts with the enzyme trans-ketolase.
4. A two-carbon unit (C-1 and C-2 of fructose-6-phos-phate) is transferred via transketolase to a third mol-ecule of glyceraldehyde-3-phosphate to give ery-throse-4-phosphate (from C-3 to C-6 of the fructose) and xylulose-5-phosphate (from C-2 of the fructose and the glyceraldehyde-3-phosphate) (reaction 7).
5. Erythrose-4-phosphate then combines via aldolase with a fourth molecule of triose phosphate (dihy-droxyacetone-3-phosphate) to yield the seven-carbon sugar sedoheptulose-1,7-bisphosphate (reaction 8).
6. This seven-carbon bisphosphate is then hydrolyzed by way of a specific phosphatase to give sedoheptu-lose-7-phosphate (reaction 9).
7. Sedoheptulose-7-phosphate donates a two-carbon unit to the fifth (and last) molecule of glyceralde-hyde-3-phosphate via transketolase and produces ribose-5-phosphate (from C-3 to C-7 of sedoheptu-lose) and xylulose-5-phosphate (from C-2 of the sedo-heptulose and the glyceraldehyde-3-phosphate) (reaction 10).
8. The two molecules of xylulose-5-phosphate are con-verted to two molecules of ribulose-5-phosphate sug-ars by a ribulose-5-phosphate epimerase (reaction 11a). The third molecule of ribulose-5-phosphate is formed from ribose-5-phosphate by ribose-5-phos-phate isomerase (reaction 11b).
9. Finally, ribulose-5-phosphate kinase catalyzes the phos-phorylation of ribulose-5-phosphate with ATP, thus regenerating the three needed molecules of the initial CO2 acceptor, ribulose-1,5-bisphosphate (reaction 12).
The Calvin Cycle Regenerates Its Own Biochemical Components The Calvin cycle reactions regenerate the biochemical inter-mediates that are necessary to maintain the operation of the cycle. But more importantly, the rate of operation of the Calvin cycle can be enhanced by increases in the concentra-tion of its intermediates; that is, the cycle is autocatalytic. As a consequence, the Calvin cycle has the metabolically desir-able feature of producing more substrate than is consumed, as long as triose phosphate is not being diverted elsewhere: 5 RuBP4– + 5 CO2 + 9 H2O + 16 ATP4– + 10 NADPH → 6 RuBP4– + 14 Pi + 6 H+ + 16 ADP3– + 10 NADP+ The importance of this autocatalytic property is shown by experiments in which previously darkened leaves or isolated chloroplasts are illuminated. In such experiments, CO2 fixation starts only after a lag, called the induction period, and the rate of photosynthesis increases with time in the first few minutes after the onset of illumination. The Photosynthesis: Carbon Reactions 149 1CH2OPO3 2– CO2 CO2 – 5CH2OPO3 2– 2C O 3C OH H 4C OH H Ribulose-1,5-bisphosphate 3-Phosphoglycerate 1CH2OPO3 2– 5CH2OPO3 2– 2C 3C O HO CO2 – 1CH2OPO3 2– 2C OH H OH 3CO2 – 4C 5CH2OPO3 2– H 4C OH H 2-Carboxy-3-ketoarabinitol-1,5-bisphosphate (a transient, unstable, enzyme-bound intermediate) Carboxylation H2O Hydrolysis + “Upper” “Lower” FIGURE 8.4 The carboxyla-tion of ribulose-1,5-bisphos-phate by rubisco.
increase in the rate of photosynthesis during the induction period is due in part to the activation of enzymes by light (discussed later), and in part to an increase in the concen-tration of intermediates of the Calvin cycle.
Calvin Cycle Stoichiometry Shows That Only One-Sixth of the Triose Phosphate Is Used for Sucrose or Starch The synthesis of carbohydrates (starch, sucrose) provides a sink ensuring an adequate flow of carbon atoms through the Calvin cycle under conditions of continuous CO2 uptake. An important feature of the cycle is its overall sto-ichiometry. At the onset of illumination, most of the triose phosphates are drawn back into the cycle to facilitate the buildup of an adequate concentration of metabolites. When photosynthesis reaches a steady state, however, five-sixths of the triose phosphate contributes to regeneration of the ribulose-1,5-bisphosphate, and one-sixth is exported to the cytosol for the synthesis of sucrose or other metabolites that are converted to starch in the chloroplast.
An input of energy, provided by ATP and NADPH, is required in order to keep the cycle functioning in the fixa-tion of CO2. The calculation at the end of Table 8.1 shows that in order to synthesize the equivalent of 1 molecule of hexose, 6 molecules of CO2 are fixed at the expense of 18 ATP and 12 NADPH. In other words, the Calvin cycle con-sumes two molecules of NADPH and three molecules of ATP for every molecule of CO2 fixed into carbohydrate.
We can compute the maximal overall thermodynamic efficiency of photosynthesis if we know the energy content of the light, the minimum quantum requirement (moles of quanta absorbed per mole of CO2 fixed; see Chapter 7), and the energy stored in a mole of carbohydrate (hexose).
Red light at 680 nm contains 175 kJ (42 kcal) per quan-tum mole of photons. The minimum quantum requirement is usually calculated to be 8 photons per molecule of CO2 fixed, although the number obtained experimentally is 9 to 10 (see Chapter 7). Therefore, the minimum light energy needed to reduce 6 moles of CO2 to a mole of hexose is approximately 6 × 8 × 175 kJ = 8400 kJ (2016 kcal). How-ever, a mole of a hexose such as fructose yields only 2804 kJ (673 kcal) when totally oxidized.
Comparing 8400 and 2804 kJ, we see that the maximum overall thermodynamic efficiency of photosynthesis is about 33%. However, most of the unused light energy is lost in the generation of ATP and NADPH by the light reac-tions (see Chapter 7) rather than during operation of the Calvin cycle.
We can calculate the efficiency of the Calvin cycle more directly by computing the changes in free energy associated with the hydrolysis of ATP and the oxidation of NADPH, which are 29 and 217 kJ (7 and 52 kcal) per mole, respec-tively. We saw in the list summarizing the Calvin cycle reac-tions that the synthesis of 1 molecule of fructose-6-phos-phate from 6 molecules of CO2 uses 12 NADPH and 18 ATP molecules. Therefore the Calvin cycle consumes (12 × 217) + (18 × 29) = 3126 kJ (750 kcal) in the form of NADPH and ATP, resulting in a thermodynamic efficiency close to 90%.
An examination of these calculations shows that the bulk of the energy required for the conversion of CO2 to carbohydrate comes from NADPH. That is, 2 mol NADPH × 52 kcal mol–1 = 104 kcal, but 3 mol ATP × 7 kcal mol–1 = 21 kcal. Thus, 83% (104 of 125 kcal) of the energy stored comes from the reductant NADPH.
The Calvin cycle does not occur in all autotrophic cells.
Some anaerobic bacteria use other pathways for auto-trophic growth: • The ferredoxin-mediated synthesis of organic acids from acetyl– and succinyl– CoA derivatives via a reversal of the citric acid cycle (the reductive car-boxylic acid cycle of green sulfur bacteria) • The glyoxylate-producing cycle (the hydroxypropi-onate pathway of green nonsulfur bacteria) • The linear route (acetyl-CoA pathway) of acetogenic, methanogenic bacteria Thus although the Calvin cycle is quantitatively the most important pathway of autotrophic CO2 fixation, others have been described.
REGULATION OF THE CALVIN CYCLE The high energy efficiency of the Calvin cycle indicates that some form of regulation ensures that all intermediates in the cycle are present at adequate concentrations and that the cycle is turned off when it is not needed in the dark. In general, variation in the concentration or in the specific activity of enzymes modulates catalytic rates, thereby adjusting the level of metabolites in the cycle.
Changes in gene expression and protein biosynthesis regulate enzyme concentration. Posttranslational modifi-cation of proteins contributes to the regulation of enzyme activity. At the genetic level the amount of each enzyme present in the chloroplast stroma is regulated by mecha-nisms that control expression of the nuclear and chloroplast genomes (Maier et al. 1995; Purton 1995).
Short-term regulation of the Calvin cycle is achieved by several mechanisms that optimize the concentration of intermediates. These mechanisms minimize reactions oper-ating in opposing directions, which would waste resources (Wolosiuk et al. 1993). Two general mechanisms can change the kinetic properties of enzymes: 1. The transformation of covalent bonds such as the reduction of disulfides and the carbamylation of amino groups, which generate a chemically modified enzyme.
2. The modification of noncovalent interactions, such as the binding of metabolites or changes in the composi-150 Chapter 8 tion of the cellular milieu (e.g., pH). In addition, the binding of the enzymes to the thylakoid membranes enhances the efficiency of the Calvin cycle, thereby achieving a higher level of organization that favors the channeling and protection of substrates.
Light-Dependent Enzyme Activation Regulates the Calvin Cycle Five light-regulated enzymes operate in the Calvin cycle: 1. Rubisco 2. NADP:glyceraldehyde-3-phosphate dehydrogenase 3. Fructose-1,6-bisphosphatase 4. Sedoheptulose-1,7-bisphosphatase 5. Ribulose-5-phosphate kinase The last four enzymes contain one or more disulfide (—S—S—) groups. Light controls the activity of these four enzymes via the ferredoxin–thioredoxin system, a cova-lent thiol-based oxidation–reduction mechanism identified by Bob Buchanan and colleagues (Buchanan 1980; Wolo-siuk et al. 1993; Besse and Buchanan 1997; Schürmann and Jacquot 2000). In the dark these residues exist in the oxi-dized state (—S—S—), which renders the enzyme inactive or subactive. In the light the —S—S— group is reduced to the sulfhydryl state (—SH HS—). This redox change leads to activation of the enzyme (Figure 8.5). The resolution of the crystal structure of each member of the ferredoxin– thioredoxin system and of the target enzymes fructose-1,6-bisphosphatase and NADP:malate dehydrogenase (Dai et al. 2000) have provided valuable information about the mechanisms involved.
This sulfhydryl (also called dithiol) signal of the regula-tory protein thioredoxin is transmitted to specific target enzymes, resulting in their activation (see Web Topic 8.4).
In some cases (such as fructose-1,6-bisphosphatase), the thioredoxin-linked activation is enhanced by an effector (e.g., fructose-1,6-bisphosphate substrate).
Inactivation of the target enzymes observed upon darkening appears to take place by a reversal of the reduc-tion (activation) pathway. That is, oxygen converts the thioredoxin and target enzyme from the reduced state (—SH HS—) to the oxidized state (—S—S—) and, in so doing, leads to inactivation of the enzyme (see Figure 8.5; see also Web Topic 8.4). The last four of the enzymes listed here are regulated directly by thioredoxin; the first, rubisco, is regulated indirectly by a thioredoxin accessory enzyme, rubisco activase (see the next section).
Rubisco Activity Increases in the Light The activity of rubisco is also regulated by light, but the enzyme itself does not respond to thioredoxin. George Lorimer and colleagues found that rubisco is activated when activator CO2 (a different molecule from the sub-strate CO2 that becomes fixed) reacts slowly with an uncharged ε-NH2 group of lysine within the active site of the enzyme. The resulting carbamate derivative (a new anionic site) then rapidly binds Mg2+ to yield the activated complex (Figure 8.6).
Two protons are released during the formation of the ternary complex rubisco–CO2–Mg2+, so activation is pro-moted by an increase in both pH and Mg2+ concentration.
Thus, light-dependent stromal changes in pH and Mg2+ (see the next section) appear to facilitate the observed acti-vation of rubisco by light.
In the active state, rubisco binds another molecule of CO2, which reacts with the 2,3-enediol form of ribulose-1,5-bisphosphate (P—O—CH2—COH— —COH—CHOH— CH2O—P) yielding 2-carboxy-3-ketoribitol 1,5-bisphos-Photosynthesis: Carbon Reactions 151 Light Photosystem I Ferredoxin Ferredoxin H+ (oxidized) (reduced) Inactive Active (oxidized) (reduced) (oxidized) (reduced) Ferredoxin: thioredoxin reductase Thioredoxin Thioredoxin SH HS SH HS S S S S Target enzyme Target enzyme FIGURE 8.5 The ferredoxin–thioredoxin system reduces specific enzymes in the light. Upon reduction, biosynthetic enzymes are converted from an inactive to an active state.
The activation process starts in the light by a reduction of ferredoxin by photosystem I (see Chapter 7). The reduced ferredoxin plus two protons are used to reduce a catalyti-cally active disulfide (—S—S—) group of the iron–sulfur enzyme ferredoxin:thioredoxin reductase, which in turn reduces the highly specific disulfide (—S—S—) bond of the small regulatory protein thioredoxin (see Web Topic 8.4 for details). The reduced form (—SH HS—) of thioredoxin then reduces the critical disulfide bond (converts —S—S— to —SH HS—) of a target enzyme and thereby leads to activa-tion of that enzyme. The light signal is thus converted to a sulfhydryl, or —SH, signal via ferredoxin and the enzyme ferredoxin:thioredoxin reductase.
phate. The extreme instability of the latter intermediate leads to the cleavage of the bond that links carbons 2 and 3 of ribulose-1,5-bisphosphate, and as a consequence, rubisco releases two molecules of 3-phosphoglycerate.
The binding of sugar phosphates, such as ribulose-1,5-bisphosphate, to rubisco prevents carbamylation. The sugar phosphates can be removed by the enzyme rubisco activase, in a reaction that requires ATP. The primary role of rubisco activase is to accelerate the release of bound sugar phosphates, thus preparing rubisco for carbamyla-tion (Salvucci and Ogren 1996, see also Web Topic 8.5).
Rubisco is also regulated by a natural sugar phosphate, carboxyarabinitol-1-phosphate, that closely resembles the six-carbon transition intermediate of the carboxylation reaction. This inhibitor is present at low concentrations in leaves of many species and at high concentrations in leaves of legumes such as soybean and bean. Carboxyarabinitol-1-phosphate binds to rubisco at night, and it is removed by the action of rubisco activase in the morning, when photon flux density increases.
Recent work has shown that in some plants rubisco acti-vase is regulated by the ferredoxin–thioredoxin system (Zhang and Portis 1999). In addition to connecting thiore-doxin to all five regulatory enzymes of the Calvin cycle, this finding provides a new mechanism for linking light to the regulation of enzyme activity.
Light-Dependent Ion Movements Regulate Calvin Cycle Enzymes Light causes reversible ion changes in the stroma that influ-ence the activity of rubisco and other chloroplast enzymes.
Upon illumination, protons are pumped from the stroma into the lumen of the thylakoids. The proton efflux is cou-pled to Mg2+ uptake into the stroma. These ion fluxes decrease the stromal concentration of H+ (pH 7 →8) and increase that of Mg2+. These changes in the ionic composi-tion of the chloroplast stroma are reversed upon darkening.
Several Calvin cycle en-zymes (rubisco, fructose-1,6-bisphosphatase, sedoheptu-lose-1,7-bisphosphatase, and ribulose-5-phosphate kinase) are more active at pH 8 than at pH 7 and require Mg2+ as a cofactor for catalysis. Hence these light-dependent ion fluxes enhance the activity of key enzymes of the Calvin cycle (Heldt 1979).
Light-Dependent Membrane Transport Regulates the Calvin Cycle The rate at which carbon is ex-ported from the chloroplast plays a role in regulation of the Calvin cycle. Carbon is exported as triose phosphates in exchange for orthophosphate via the phosphate translocator in the inner membrane of the chloroplast envelope (Flügge and Heldt 1991). To ensure continued operation of the Calvin cycle, at least five-sixths of the triose phosphate must be recycled (see Table 8.1 and Figure 8.3). Thus, at most one-sixth can be exported for sucrose synthesis in the cytosol or diverted to starch syn-thesis within the chloroplast. The regulation of this aspect of photosynthetic carbon metabolism will be discussed fur-ther when the syntheses of sucrose and starch are consid-ered in detail later in this chapter.
THE C2 OXIDATIVE PHOTOSYNTHETIC CARBON CYCLE An important property of rubisco is its ability to catalyze both the carboxylation and the oxygenation of RuBP. Oxy-genation is the primary reaction in a process known as photorespiration. Because photosynthesis and photores-piration work in diametrically opposite directions, pho-torespiration results in loss of CO2 from cells that are simul-taneously fixing CO2 by the Calvin cycle (Ogren 1984; Leegood et al. 1995).
In this section we will describe the C2 oxidative photo-synthetic carbon cycle—the reactions that result in the par-tial recovery of carbon lost through oxidation.
Photosynthetic CO2 Fixation and Photorespiratory Oxygenation Are Competing Reactions The incorporation of one molecule of O2 into the 2,3-ene-diol isomer of ribulose-1,5-bisphosphate generates an unstable intermediate that rapidly splits into 2-phospho-glycolate and 3-phosphoglycerate (Figure 8.7 and Table 8.2, reaction 1). The ability to catalyze the oxygenation of ribu-lose-1,5-bisphosphate is a property of all rubiscos, regard-152 Chapter 8 Rubisco Rubisco Rubisco Rubisco Lys NH3 + Lys NH2 Lys NH CO2 H+ H+ COO– Lys NH COO– Mg2+ Mg2+ Mg2+ H+ H+ Carbamylation Inactive Active FIGURE 8.6 One way in which rubisco is activated involves the formation of a car-bamate–Mg2+ complex on the ε-amino group of a lysine within the active site of the enzyme. Two protons are released. Activation is enhanced by the increase in Mg2+ concentration and higher pH (low H+ concentration) that result from illumination.
The CO2 involved in the carbamate–Mg2+ reaction is not the same as the CO2 involved in the carboxylation of ribulose-1,5-bisphosphate.
2 POCH2 — (CHOH)3 — H2COP Ribulose-1,5-bisphosphate 2 POCH2 — CHOH — CO2 – 3-phosphoglycerate POCH2 — CHOH — CO2 – 3-phosphoglycerate HOCH2 — HOCH — CO2 – Glycerate HOCH2 — CO — CO2 – Hydroxypyruvate Serine HOCH2 — H2 NCH — CO2 – Serine 2 POCH2 — CO2 – 2-phosphoglycolate 2 HOCH2 — CO2 – Glycolate 2 Glycolate 2 H2 N CH2 — CO2 – Glycine 2 Glycine HO2C — (CH2)2 — CH N H2 — CO2 Gluta mate HO2C — (CH2)2 — CO — CO2 a-ketoglutarate Glutamate Glutamate HO2C — (CH2)2 — CO — CO2 a-ketoglutarate a-ketoglutarate Calvin cycle 2 O2 2 H2O 2 OCH — CO2 – Glyoxylate NADH NAD+ ATP ADP Pi 2 2 O2 2 H2O2 2 H2O H2O CO2 O2 O2 NADH NAD+ PEROXISOME MITOCHONDRION CHLOROPLAST (2.1) (2.2) (2.10) (2.3) (2.4) (2.5) (2.9) (2.8) (2.6, 2.7) + NH4 + Glycerate FIGURE 8.7 The main reactions of the photorespiratory cycle. Operation of the C2 oxidative photosynthetic cycle involves the cooperative interaction among three organelles: chloroplasts, mitochondria, and peroxisomes.
Two molecules of glycolate (four carbons) transported from the chloroplast into the peroxisome are converted to glycine, which in turn is exported to the mitochondrion and transformed to serine (three carbons) with the concur-rent release of carbon dioxide (one carbon). Serine is trans-ported to the peroxisome and transformed to glycerate. The latter flows to the chloroplast where it is phosphorylated to 3-phosphoglycerate and incorporated into the Calvin cycle.
Inorganic nitrogen (ammonia) released by the mitochon-drion is captured by the chloroplast for the incorporation into amino acids by using appropiate skeletons (α-ketoglu-tarate). The heavy arrow in red marks the assimilation of ammonia into glutamate catalyzed by glutamine syn-thetase. In addition, the uptake of oxygen in the peroxi-some supports a short oxygen cycle coupled to oxidative reactions. The flow of carbon, nitrogen and oxygen are indi-cated in black, red and blue, respectively. See Table 8.2 for a description of each numbered reaction.
less of taxonomic origin. Even the rubisco from anaerobic, autotrophic bacteria catalyzes the oxygenase reaction when exposed to oxygen.
As alternative substrates for rubisco, CO2 and O2 com-pete for reaction with ribulose-1,5-bisphosphate because carboxylation and oxygenation occur within the same active site of the enzyme. Offered equal concentrations of CO2 and O2 in a test tube, angiosperm rubiscos fix CO2 about 80 times faster than they oxygenate. However, an aqueous solution in equilibrium with air at 25°C has a CO2:O2 ratio of 0.0416 (see Web Topics 8.2 and 8.3). At these concentrations, carboxylation in air outruns oxy-genation by a scant three to one.
The C2 oxidative photosynthetic carbon cycle acts as a scavenger operation to recover fixed carbon lost during photorespiration by the oxygenase reaction of rubisco (Web Topic 8.6). The 2-phosphoglycolate formed in the chloro-plast by oxygenation of ribulose-1,5-bisphosphate is rapidly hydrolyzed to glycolate by a specific chloroplast phosphatase (Figure 8.7 and Table 8.2, reaction 2). Subse-quent metabolism of the glycolate involves the cooperation of two other organelles: peroxisomes and mitochondria (see Chapter 1) (Tolbert 1981).
Glycolate leaves the chloroplast via a specific trans-porter protein in the envelope membrane and diffuses to the peroxisome. There it is oxidized to glyoxylate and hydrogen peroxide (H2O2) by a flavin mononucleotide-dependent oxidase: glycolate oxidase (Figure 8.7 and Table 8.2, reaction 3). The vast amounts of hydrogen peroxide released in the peroxisome are destroyed by the action of catalase (Table 8.2, reaction 4) while the glyoxylate under-goes transamination (reaction 5). The amino donor for this transamination is probably glutamate, and the product is the amino acid glycine.
Glycine leaves the peroxisome and enters the mito-chondrion (see Figure 8.7). There the glycine decarboxylase multienzyme complex catalyzes the conversion of two mol-ecules of glycine and one of NAD+ to one molecule each of serine, NADH, NH4 + and CO2 (Table 8.2, reactions 6 and 7). This multienzyme complex, present in large concentra-tions in the matrix of plant mitochondria, comprises four proteins, named H-protein (a lipoamide-containing polypeptide), P-protein (a 200 kDa, homodimer, pyridoxal phosphate-containing protein), T-protein (a folate-de-pendent protein), and L-protein (a flavin adenine nucleotide–containing protein).
The ammonia formed in the oxidation of glycine dif-fuses rapidly from the matrix of mitochondria to chloro-plasts, where glutamine synthetase combines it with car-bon skeletons to form amino acids. The newly formed serine leaves the mitochondria and enters the peroxisome, where it is converted first by transamination to hydrox-ypyruvate (Table 8.2, reaction 8) and then by an NADH-dependent reduction to glycerate (reaction 9).
154 Chapter 8 TABLE 8.2 Reactions of the C2 oxidative photosynthetic carbon cycle Enzyme Reaction 1. Ribulose-1,5-bisphosphate carboxylase/oxygenase 2 Ribulose-1,5-bisphosphate + 2 O2 →2 phosphoglycolate + (chloroplast) 2 3-phosphoglycerate + 4 H+ 2. Phosphoglycolate phosphatase (chloroplast) 2 Phosphoglycolate + 2 H2O →2 glycolate + 2 Pi 3. Glycolate oxidase (peroxisome) 2 Glycolate + 2 O2 →2 glyoxylate + 2 H2O2 4. Catalase (peroxisome) 2 H2O2 →2 H2O + O2 5. Glyoxylate:glutamate aminotransferase (peroxisome) 2 Glyoxylate + 2 glutamate →2 glycine + 2 α-ketoglutarate 6. Glycine decarboxylase (mitochondrion) Glycine + NAD+ + H+ + H4-folate →NADH + CO2 + NH4 + + methylene-H4-folate 7. Serine hydroxymethyltransferase (mitochondrion) Methylene-H4-folate + H2O + glycine →serine + H4-folate 8. Serine aminotransferase (peroxisome) Serine + α-ketoglutarate → hydroxypyruvate + glutamate 9. Hydroxypyruvate reductase (peroxisome) Hydroxypyruvate + NADH + H+ →glycerate + NAD+ 10. Glycerate kinase (chloroplast) Glycerate + ATP →3-phosphoglycerate + ADP + H+ Note: Upon the release of glycolate from the chloroplast (reactions 2 →3), the interplay of this organelle with the peroxisome and the mitochon-drion drives the following overall reaction: 2 Glycolate + glutamate + O2 →glycerate + α-ketoglutarate + NH4 + + CO2 + H2O The 3-phosphoglycerate formed in the chloroplast (reaction 10) is converted to ribulose-1,5-bisphosphate via the reductive and regenerative reactions of the Calvin cycle.The ammonia and α-ketoglutarate are converted to glutamate in the chloroplast by ferrodoxin-linked glutamate synthase (GOGAT).
Pi stands for inorganic phosphate.
A malate-oxaloacetate shuttle transfers NADH from the cytoplasm into the peroxisome, thus maintaining an ade-quate concentration of NADH for this reaction. Finally, glycerate reenters the chloroplast, where it is phosphory-lated to yield 3-phosphoglycerate (Table 8.2, reaction 10).
In photorespiration, various compounds are circulated in concert through two cycles. In one of the cycles, carbon exits the chloroplast in two molecules of glycolate and returns in one molecule of glycerate. In the other cycle, nitrogen exits the chloroplast in one molecule of glutamate and returns in one molecule of ammonia (together with one molecule of α-ketoglutarate) (see Figure 8.7).
Thus overall, two molecules of phosphoglycolate (four carbon atoms), lost from the Calvin cycle by the oxygenation of RuBP, are converted into one molecule of 3-phospho-glycerate (three carbon atoms) and one CO2. In other words, 75% of the carbon lost by the oxygenation of ribulose-1,5-bis-phosphate is recovered by the C2 oxidative photosynthetic carbon cycle and returned to the Calvin cycle (Lorimer 1981).
On the other hand, the total organic nitrogen remains unchanged because the formation of inorganic nitrogen (NH4 +) in the mitochondrion is balanced by the synthesis of glutamine in the chloroplast. Similarly, the use of NADH in the peroxisome (by hydroxypyruvate reductase) is bal-anced by the reduction of NAD+ in the mitochondrion (by glycine decarboxylase).
Competition between Carboxylation and Oxygenation Decreases the Efficiency of Photosynthesis Because photorespiration is concurrent with photosyn-thesis, it is difficult to measure the rate of pho-torespiration in intact cells. Two molecules of 2-phosphoglycolate (four carbon atoms) are needed to make one molecule of 3-phospho-glycerate, with the release of one molecule of CO2; so theoretically one-fourth of the carbon entering the C2 oxidative photosynthetic carbon cycle is released as CO2.
Measurements of CO2 release by sunflower leaves support this calculated value. This result indicates that the actual rate of photosynthesis is approximately 120 to 125% of the measured rate.
The ratio of carboxylation to oxygenation in air at 25°C is computed to be between 2.5 and 3.
Further calculations indicate that photorespira-tion lowers the efficiency of photosynthetic car-bon fixation from 90% to approximately 50%.
This decreased efficiency can be measured as an increase in the quantum requirement for CO2 fixation under photorespiratory conditions (air with high O2 and low CO2) as opposed to non-photorespiratory conditions (low O2 and high CO2).
Carboxylation and Oxygenation Are Closely Interlocked in the Intact Leaf Photosynthetic carbon metabolism in the intact leaf reflects the integrated balance between two mutually opposing and interlocking cycles (Figure 8.8). The Calvin cycle can operate independently, but the C2 oxidative photosynthetic carbon cycle depends on the Calvin cycle for a supply of ribulose-1,5-bisphosphate. The balance between the two cycles is determined by three factors: the kinetic properties of rubisco, the concentrations of the substrates CO2 and O2, and temperature.
As the temperature increases, the concentration of CO2 in a solution in equilibrium with air decreases more than the concentration of O2 does (see Web Topic 8.3). Conse-quently, the concentration ratio of CO2 to O2 decreases as the temperature rises. As a result of this property, pho-torespiration (oxygenation) increases relative to photosyn-thesis (carboxylation) as the temperature rises. This effect is enhanced by the kinetic properties of rubisco, which also result in a relative increase in oxygenation at higher tem-peratures (Ku and Edwards 1978). Overall, then, increas-ing temperatures progressively tilt the balance away from the Calvin cycle and toward the oxidative photosynthetic carbon cycle (see Chapter 9).
The Biological Function of Photorespiration Is Unknown Although the C2 oxidative photosynthetic carbon cycle recovers 75% of the carbon originally lost from the Calvin cycle as 2-phosphoglycolate, why does 2-phosphoglycolate form at all? One possible explanation is that the formation Photosynthesis: Carbon Reactions 155 Electron transport and the Calvin cycle C2 oxidative photosynthetic carbon cycle Ribulose 1,5-bisphosphate 3-Phosphoglycerate 2-Phosphoglycolate CO2 CO2 O2 O2 (Net carbon gain) (Net carbon loss) FIGURE 8.8 The flow of carbon in the leaf is determined by the balance between two mutually opposing cycles. Whereas the Calvin cycle is capable of independent operation in the presence of adequate sub-strates generated by photosynthetic electron transport, the C2 oxidative photosynthetic carbon cycle requires continued operation of the Calvin cycle to regenerate its starting material, ribulose-1,5-bisphosphate.
of 2-phosphoglycolate is a consequence of the chemistry of the carboxylation reaction, which requires an intermediate that can react with both CO2 and O2.
Such a reaction would have had little consequence in early evolutionary times if the ratio of CO2 to O2 in air were higher than it is today. However, the low CO2:O2 ratios prevalent in modern times are conducive to photorespira-tion, with no other function than the recovery of some of the carbon present in 2-phosphoglycolate.
Another possible explanation is that photorespiration is important, especially under conditions of high light inten-sity and low intercellular CO2 concentration (e.g., when stomata are closed because of water stress), to dissipate excess ATP and reducing power from the light reactions, thus preventing damage to the photosynthetic apparatus.
Arabidopsis mutants that are unable to photorespire grow normally under 2% CO2, but they die rapidly if transferred to normal air. There is evidence from work with transgenic plants that photorespiration protects C3 plants from pho-tooxidation and photoinhibition (Kozaki and Takeba 1996).
Further work is needed to improve our understanding of the function of photorespiration.
CO2-CONCENTRATING MECHANISMS I: ALGAL AND CYANOBACTERIAL PUMPS Many plants either do not photorespire at all, or they do so to only a limited extent. These plants have normal rubis-cos, and their lack of photorespiration is a consequence of mechanisms that concentrate CO2 in the rubisco environ-ment and thereby suppress the oxygenation reaction.
In this and the two following sections we will discuss three mechanisms for concentrating CO2 at the site of car-boxylation: 1. C4 photosynthetic carbon fixation (C4) 2. Crassulacean acid metabolism (CAM) 3. CO2 pumps at the plasma membrane The first two of these CO2-concentrating mechanisms are found in some angiosperms and involve “add-ons” to the Calvin cycle. Plants with C4 metabolism are often found in hot environments; CAM plants are typical of desert envi-ronments. We will examine each of these two systems after we consider the third mechanism: a CO2 pump found in aquatic plants that has been studied extensively in unicel-lular cyanobacteria and algae.
When algal and cyanobacterial cells are grown in air enriched with 5% CO2 and then transferred to a low-CO2 medium, they display symptoms typical of photorespira-tion (O2 inhibition of photosynthesis at low concentration of CO2). But if the cells are grown in air containing 0.03% CO2, they rapidly develop the ability to concentrate inor-ganic carbon (CO2 plus HCO3 –) internally. Under these low-CO2 conditions, the cells no longer photorespire.
At the concentrations of CO2 found in aquatic environ-ments, rubisco operates far below its maximal specific activity. Marine and freshwater organisms overcome this drawback by accumulating inorganic carbon by the use of CO2 and HCO3 – pumps at the plasma membrane. ATP derived from the light reactions provides the energy nec-essary for the active uptake of CO2 and HCO3 –. Total inor-ganic carbon inside some cyanobacterial cells can reach concentrations of 50 mM (Ogawa and Kaplan 1987). Recent work indicates that a single gene encoding a transcription factor can regulate the expression of genes that encode the components of the CO2-concentrating mechanism in algae (Xiang et al. 2001).
The proteins that function as CO2–HCO3 – pumps are not present in cells grown in high concentrations of CO2 but are induced upon exposure to low concentrations of CO2. The accumulated HCO3 – is converted to CO2 by the enzyme car-bonic anhydrase, and the CO2 enters the Calvin cycle.
The metabolic consequence of this CO2 enrichment is suppression of the oxygenation of ribulose bisphosphate and hence also suppression of photorespiration. The ener-getic cost of this adaptation is the additional ATP needed for concentrating the CO2.
CO2-CONCENTRATING MECHANISMS II: THE C4 CARBON CYCLE There are differences in leaf anatomy between plants that have a C4 carbon cycle (called C4 plants) and those that pho-tosynthesize solely via the Calvin photosynthetic cycle (C3 plants). A cross section of a typical C3 leaf reveals one major cell type that has chloroplasts, the mesophyll. In contrast, a typical C4 leaf has two distinct chloroplast-containing cell types: mesophyll and bundle sheath (or Kranz, German for “wreath”) cells (Figure 8.9).
There is considerable anatomic variation in the arrange-ment of the bundle sheath cells with respect to the meso-phyll and vascular tissue. In all cases, however, operation of the C4 cycle requires the cooperative effort of both cell types. No mesophyll cell of a C4 plant is more than two or three cells away from the nearest bundle sheath cell (see Figure 8.9A). In addition, an extensive network of plas-modesmata (see Figure 1.27) connects mesophyll and bun-dle sheath cells, thus providing a pathway for the flow of metabolites between the cell types.
Malate and Aspartate Are Carboxylation Products of the C4 Cycle Early labeling of C4 acids was first observed in 14CO2 label-ing studies of sugarcane by H. P. Kortschack and colleagues and of maize by Y. Karpilov and coworkers. When leaves were exposed for a few seconds to 14CO2 in the light, 70 to 80% of the label was found in the C4 acids malate and aspartate—a pattern very different from the one observed in leaves that photosynthesize solely via the Calvin cycle.
156 Chapter 8 Photosynthesis: Carbon Reactions 157 Bundle sheath cells Mesophyll cells (D) (B) (A) (C) (E) Plasmodesmata FIGURE 8.9 Cross-sections of leaves, showing the anatomic differences between C3 and C4 plants. (A) A C4 monocot, saccharum officinarum (sugarcane). (135×) (B) A C3 monocot, Poa sp. (a grass). (240×) (C) A C4 dicot, Flaveria australasica (Asteraceae). (740×) The bundle sheath cells are large in C4 leaves (A and C), and no mesophyll cell is more than two or three cells away from the nearest bundle sheath cell.
These anatomic features are absent in the C3 leaf (B). (D) Three-dimensional model of a C4 leaf. (A and B © David Webb; C courtesy of Athena McKown; D after Lüttge and Higinbotham; E from Craig and Goodchild 1977.) (E) Scanning electon micrograph of a C leaf from Triodia irritans, showing the plasmodesmata pits in the bundle sheath heath cell walls through which metabolites of the C carbon cycle are thought to be transported.
4 4 In pursuing these initial observations, M. D. Hatch and C. R. Slack elucidated what is now known as the C4 pho-tosynthetic carbon cycle (C4 cycle) (Figure 8.10). They established that the C4 acids malate and aspartate are the first stable, detectable intermediates of photosynthesis in leaves of sugarcane and that carbon atom 4 of malate sub-sequently becomes carbon atom 1 of 3-phosphoglycerate (Hatch and Slack 1966). The primary carboxylation in these leaves is catalyzed not by rubisco, but by PEP (phos-phoenylpyruvate) carboxylase (Chollet et al. 1996).
The manner in which carbon is transferred from car-bon atom 4 of malate to carbon atom 1 of 3-phospho-glycerate became clear when the involvement of meso-phyll and bundle sheath cells was elucidated. The participating enzymes occur in one of the two cell types: PEP carboxylase and pyruvate–orthophosphate dikinase are restricted to mesophyll cells; the decarboxylases and the enzymes of the complete Calvin cycle are confined to the bundle sheath cells. With this knowledge, Hatch and Slack were able to formulate the basic model of the cycle (Figure 8.11 and Table 8.3).
The C4 Cycle Concentrates CO2 in Bundle Sheath Cells The basic C4 cycle consists of four stages: 1. Fixation of CO2 by the carboxylation of phosphoenolpyruvate in the mesophyll cells to form a C4 acid (malate and/or aspartate) 2. Transport of the C4 acids to the bundle sheath cells 3. Decarboxylation of the C4 acids within the bundle sheath cells and generation of CO2, which is then reduced to carbo-hydrate via the Calvin cycle 158 Chapter 8 Carboxylation Decarboxylation Regeneration HCO3– Phosphoenol-pyruvate C4 acid C4 acid C3 acid C3 acid CO2 Calvin cycle Atmospheric CO2 Mesophyll cell Bundle sheath cell Plasma membrane Cell wall FIGURE 8.10 The basic C4 photosynthetic carbon cycle involves four stages in two different cell types: (1) Fixation of CO2 into a four-carbon acid in a mesophyll cell; (2) Transport of the four-carbon acid from the mesophyll cell to a bundle sheath cell; (3) Decarboxylation of the four-car-bon acid, and the generation of a high CO2 concentration in the bundle sheath cell. The CO2 released is fixed by rubisco and converted to carbo-hydrate by the Calvin cycle.(4) Transport of the residual three-carbon acid back to the mesophyll cell, where the original CO2 acceptor, phospho-enolpyruvate, is regenerated.
TABLE 8.3 Reactions of the C4 photosynthetic carbon cycle Enzyme Reaction 1. Phosphoenolpyruvate (PEP) carboxylase Phosphoenolpyruvate + HCO3 – →oxaloacetate + Pi 2. NADP:malate dehydrogenase Oxaloacetate + NADPH + H+ →malate + NADP+ 3. Aspartate aminotransferase Oxaloacetate + glutamate →aspartate + α-ketoglutarate 4. NAD(P) malic enzyme Malate + NAD(P)+ →pyruvate + CO2 + NAD(P)H + H+ 5. Phosphoenolpyruvate carboxykinase Oxaloacetate + ATP →phosphoenolpyruvate + CO2 + ADP 6. Alanine aminotransferase Pyruvate + glutamate ↔alanine + α-ketoglutarate 7. Adenylate kinase AMP + ATP →2 ADP 8. Pyruvate–orthophosphate dikinase Pyruvate + Pi + ATP →phosphoenolpyruvate + AMP + PPi 9. Pyrophosphatase PPi + H2O →2 Pi Note: Pi and PPi stand for inorganic phosphate and pyrophosphate, respectively.
4. Transport of the C3 acid (pyruvate or alanine) that is formed by the decarboxylation step back to the meso-phyll cell and regeneration of the CO2 acceptor phos-phoenolpyruvate One interesting feature of the cycle is that regeneration of the primary acceptor—phosphoenolpyruvate—con-sumes two “high-energy” phosphate bonds: one in the reaction catalyzed by pyruvate–orthophosphate dikinase (Table 8.3, reaction 8) and another in the conversion of PPi to 2Pi catalyzed by pyrophosphatase (reaction 9; see also Figure 8.11).
Shuttling of metabolites between mesophyll and bundle sheath cells is driven by diffusion gradients along numer-ous plasmodesmata, and transport within the cells is reg-ulated by concentration gradients and the operation of spe-cialized translocators at the chloroplast envelope. The cycle thus effectively shuttles CO2 from the atmosphere into the bundle sheath cells. This transport process generates a much higher concentration of CO2 in the bundle sheath cells than would occur in equilibrium with the external atmos-phere. This elevated concentration of CO2 at the carboxyla-tion site of rubisco results in suppression of the oxygenation of ribulose-1,5-bisphosphate and hence of photorespiration.
Discovered in the tropical grasses, sugarcane, and maize, the C4 cycle is now known to occur in 16 families of both monocotyledons and dicotyledons, and it is particu-larly prominent in Gramineae (corn, millet, sorghum, sugarcane), Chenopodiaceae (Atriplex), and Cyperaceae (sedges). About 1% of all known species have C4 metabo-lism (Edwards and Walker 1983).
There are three variations of the basic C4 pathway that occur in different species (see Web Topic 8.7). The varia-tions differ principally in the C4 acid (malate or aspartate) transported into the bundle sheath cells and in the manner of decarboxylation.
The Concentration of CO2 in Bundle Sheath Cells Has an Energy Cost The net effect of the C4 cycle is to convert a dilute solution of CO2 in the mesophyll cells into a concentrated CO2 solu-tion in cells of the bundle sheath. Studies of a PEP car-boxylase–deficient mutant of Amaranthus edulis clearly showed that the lack of an effective mechanism for con-centrating CO2 in the bundle sheath markedly enhances photorespiration in a C4 plant (Dever et al. 1996).
Thermodynamics tells us that work must be done to establish and maintain the CO2 concentration gradient in the bundle sheath (for a detailed discussion of theomody-namics, see Chapter 2 on the web site). This principle also applies to the operation of the C4 cycle. From a summation COO¯ OPO3 2– HCO3 – Atmospheric CO2 C CH2 NADPH NADP+ ATP Pi Pi Pi + PPi + 2 Pyruvate-phosphate dikinase PEP carboxylase Malate dehydrogenase Malic enzyme Phosphoenol-pyruvate (PEP) COO¯ O C CH3 Pyruvate COO¯ O C CH2 CO2 – CO2 Oxaloacetate COO¯ C H OH CH2 CO2 – Malate NADPH NADP+ Carbonic anhydrase Mesophyll cell Bundle sheath cell Calvin cycle AMP + ATP 2 ADP Adenylate kinase FIGURE 8.11 The C4 photosynthetic pathway. The hydrolysis of two ATP drives the cycle in the direction of the arrows, thus pumping CO2 from the atmosphere to the Calvin cycle of the chloroplasts from bundle sheath cells.
of the reactions involved, we can calculate the energy cost to the plant (Table 8.4). The calculation shows that the CO2-concentrating process consumes two ATP equivalents (2 “high-energy” bonds) per CO2 molecule transported. Thus the total energy requirement for fixing CO2 by the com-bined C4 and Calvin cycles (calculated in Tables 8.4 and 8.1, respectively) is five ATP plus two NADPH per CO2 fixed.
Because of this higher energy demand, C4 plants pho-tosynthesizing under nonphotorespiratory conditions (high CO2 and low O2) require more quanta of light per CO2 than C3 leaves do. In normal air, the quantum requirement of C3 plants changes with factors that affect the balance between photosynthesis and photorespiration, such as temperature.
By contrast, owing to the mechanisms built in to avoid photorespiration, the quantum requirement of C4 plants remains relatively constant under different environmental conditions (see Figure 9.23).
Light Regulates the Activity of Key C4 Enzymes Light is essential for the operation of the C4 cycle because it regulates several specific enzymes. For example, the activities of PEP carboxylase, NADP:malate dehydroge-nase, and pyruvate–orthophosphate dikinase (see Table 8.3) are regulated in response to variations in photon flux den-sity by two different processes: reduction–oxidation of thiol groups and phosphorylation–dephosphorylation.
NADP:malate dehydrogenase is regulated via the thiore-doxin system of the chloroplast (see Figure 8.5). The enzyme is reduced (activated) upon illumination of leaves and is oxidized (inactivated) upon darkening. PEP carboxylase is activated by a light-dependent phosphorylation–dephos-phorylation mechanism yet to be characterized.
The third regulatory member of the C4 pathway, pyru-vate–orthophosphate dikinase, is rapidly inactivated by an unusual ADP-dependent phosphorylation of the enzyme when the photon flux density drops (Burnell and Hatch 1985). Activation is accomplished by phosphorolytic cleav-age of this phosphate group. Both reactions, phosphory-lation and dephosphorylation, appear to be catalyzed by a single regulatory protein.
In Hot, Dry Climates, the C4 Cycle Reduces Photorespiration and Water Loss Two features of the C4 cycle in C4 plants overcome the dele-terious effects of higher temperature on photosynthesis that were noted earlier. First, the affinity of PEP carboxylase for its substrate, HCO3 –, is sufficiently high that the enzyme is saturated by HCO3 – in equlibrium with air levels of CO2.
Furthermore, because the substrate is HCO3 –, oxygen is not a competitor in the reaction. This high activity of PEP car-boxylase enables C4 plants to reduce the stomatal aperture and thereby conserve water while fixing CO2 at rates equal to or greater than those of C3 plants. The second beneficial feature is the suppression of photorespiration resulting from the concentration of CO2 in bundle sheath cells (Marocco et al. 1998).
These features enable C4 plants to photosynthesize more efficiently at high temperatures than C3 plants, and they are probably the reason for the relative abundance of C4 plants in drier, hotter climates. Depending on their natural envi-ronment, some plants show properties intermediate between strictly C3 and C4 species.
CO2-CONCENTRATING MECHANISMS III: CRASSULACEAN ACID METABOLISM A third mechanism for concentrating CO2 at the site of rubisco is found in crassulacean acid metabolism (CAM).
Despite its name, CAM is not restricted to the family Cras-sulaceae (Crassula, Kalanchoe, Sedum); it is found in numer-ous angiosperm families. Cacti and euphorbias are CAM plants, as well as pineapple, vanilla, and agave.
The CAM mechanism enables plants to improve water use efficiency. Typically, a CAM plant loses 50 to 100 g of water for every gram of CO2 gained, compared with val-ues of 250 to 300 g and 400 to 500 g for C4 and C3 plants, 160 Chapter 8 TABLE 8.4 Energetics of the C4 photosynthetic carbon cycle Phosphoenolpyruvate + H2O + NADPH + CO2 (mesophyll) → malate + NADP+ + Pi (mesophyll) Malate + NADP+ → pyruvate + NADPH + CO2 (bundle sheath) Pyruvate + Pi+ ATP → phosphoenolpyruvate + AMP + PPi (mesophyll) PPi + H2O → 2 Pi (mesophyll) AMP + ATP → 2ADP Net: CO2 (mesophyll) + ATP + 2 H2O → CO2 (bundle sheath) + 2ADP + 2 Pi Cost of concentrating CO2 within the bundle sheath cell = 2 ATP per CO2 Note: As shown in reaction 1 of Table 8.3, the H2O and CO2 shown in the first line of this table actually react with phospho-enolpyruvate as HCO3 –.
Pi and PPi stand for inorganic phosphate and pyrophosphate, respectively.
respectively (see Chapter 4). Thus, CAM plants have a competitive advantage in dry environments.
The CAM mechanism is similar in many respects to the C4 cycle. In C4 plants, formation of the C4 acids in the mes-ophyll is spatially separated from decarboxylation of the C4 acids and from refixation of the resulting CO2 by the Calvin cycle in the bundle sheath. In CAM plants, forma-tion of the C4 acids is both temporally and spatially sepa-rated. At night, CO2 is captured by PEP carboxylase in the cytosol, and the malate that forms from the oxaloacetate product is stored in the vacuole (Figure 8.12). During the day, the stored malate is transported to the chloroplast and decarboxylated by NADP-malic enzyme, the released CO2 is fixed by the Calvin cycle, and the NADPH is used for converting the decarboxylated triose phosphate product to starch.
The Stomata of CAM Plants Open at Night and Close during the Day CAM plants such as cacti achieve their high water use effi-ciency by opening their stomata during the cool, desert nights and closing them during the hot, dry days. Closing the stomata during the day minimizes water loss, but because H2O and CO2 share the same diffusion pathway, CO2 must then be taken up at night.
CO2 is incorporated via carboxylation of phospho-enolpyruvate to oxaloacetate, which is then reduced to malate. The malate accumulates and is stored in the large vacuoles that are a typical, but not obligatory, anatomic fea-ture of the leaf cells of CAM plants (see Figure 8.12). The accumulation of substantial amounts of malic acid, equiv-alent to the amount of CO2 assimilated at night, has long been recognized as a nocturnal acidification of the leaf (Bonner and Bonner 1948).
With the onset of day, the stomata close, preventing loss of water and further uptake of CO2. The leaf cells deacid-ify as the reserves of vacuolar malic acid are consumed.
Decarboxylation is usually achieved by the action of NADP-malic enzyme on malate (Drincovich et al. 2001).
Because the stomata are closed, the internally released CO2 cannot escape from the leaf and instead is fixed and con-verted to carbohydrate by the Calvin cycle.
Photosynthesis: Carbon Reactions 161 CO2 Dark: Stomata opened Light: Stomata closed CO2 uptake and fixation: leaf acidification Open stoma permits entry of CO2 and loss of H2O Atmospheric Decarboxylation of stored malate and refixation of internal CO2: deacidification Closed stoma prevents H2O loss and CO2 uptake HCO3 – Phosphoenol-pyruvate PEP carboxylase Oxaloacetate Malate Malic acid Triose phosphate Starch Pi NADH NAD+ NAD+ malic dehydrogenase Chloroplast Vacuole Chloroplast Vacuole CO2 Malic acid Malate Starch Pyruvate Calvin cycle NADP+ malic enzyme FIGURE 8.12 Crassulacean acid metabolism (CAM). Temporal separation of CO2 uptake from photosynthetic reactions: CO2 uptake and fixation take place at night, and decar-boxylation and refixation of the internally released CO2 occur during the day. The adap-tive advantage of CAM is the reduction of water loss by transpiration, achieved by the stomatal opening during the night. The elevated internal concentration of CO2 effectively suppresses the photorespiratory oxygenation of ribulose bisphosphate and favors carboxylation. The C3 acid result-ing from the decarboxylation is thought to be converted first to triose phosphate and then to starch or sucrose, thus regenerating the source of the original carbon acceptor.
Phosphorylation Regulates the Activity of PEP Carboxylase in C4 and CAM Plants The CAM mechanism that we have outlined in this discus-sion requires separation of the initial carboxylation from the subsequent decarboxylation, to avoid a futile cycle. In addi-tion to the spatial and temporal separation exhibited by C4 and CAM plants, respectively, a futile cycle is avoided by the regulation of PEP carboxylase (Figure 8.13). In C4 plants the carboxylase is “switched on,” or active, during the day and in CAM plants during the night. In both C4 and CAM plants, PEP carboxylase is inhibited by malate and activated by glucose-6-phosphate (see Web Essay 8.1 for a detailed discussion of the regulation of PEP carboxylase). Phosphorylation of a single serine residue of the CAM enzyme diminishes the malate inhibition and enhances the action of glucose-6-phosphate so that the enzyme becomes catalytically more active (Chollet et al. 1996; Vidal and Chollet 1997) (see Figure 8.13). The phosphorylation is cat-alyzed by a PEP carboxylase-kinase. The synthesis of this kinase is stimulated by the efflux of Ca2+ from the vacuole to the cytosol and the resulting activation of a Ca2+/calmodulin protein kinase (Giglioli-Guivarc’h et al.
1996; Coursol et al. 2000; Nimmo 2000; Bakrim et al. 2001).
Some Plants Adjust Their Pattern of CO2 Uptake to Environmental Conditions Plants have many mechanisms that maximize water and CO2 supply during development and reproduction. C3 plants regulate the stomatal aperture of their leaves during the day, and stomata close during the night. C4 and CAM plants utilize PEP carboxylase to fix CO2, and they separate that enzyme from rubisco either spatially (C4 plants) or temporally (CAM plants).
Some CAM plants show longer-term regulation and are able to adjust their pattern of CO2 uptake to environmental conditions. Facultative CAM plants such as the ice plant (Mesembryanthemum crystallinum) carry on C3 metabolism under unstressed conditions, and they shift to CAM in response to heat, water, or salt stress. This form of regulation requires the expression of numerous CAM genes in response to stress signals (Adams et al. 1998; Cushman 2001).
In aquatic environments, cyanobacteria and green algae have abundant water but find low CO2 concentrations in their surroundings and actively concentrate inorganic CO2 intracellularly. In diatoms, which abound in the phyto-plankton, a CO2-concentrating mechanism operates simul-taneously with a C4 pathway (Reinfelder et al. 2000).
Diatoms are a fine example of photosynthetic organisms that have the capacity to use different CO2-concentrating mechanisms in response to environmental fluctuations.
SYNTHESIS OF STARCH AND SUCROSE In most species, sucrose is the principal form of carbohydrate translocated throughout the plant by the phloem. Starch is an insoluble stable carbohydrate reserve that is present in almost all plants. Both starch and sucrose are synthesized from the triose phosphate that is generated by the Calvin cycle (see Table 8.1) (Beck and Ziegler 1989). The pathways for the syn-thesis of starch and sucrose are shown in Figure 8.14.
Starch Is Synthesized in the Chloroplast Electron micrographs showing prominent starch deposits, as well as enzyme localization studies, leave no doubt that the chloroplast is the site of starch synthesis in leaves (Fig-ure 8.15). Starch is synthesized from triose phosphate via fructose-1,6-bisphosphate (Table 8.5 and Figure 8.14). The glucose-1-phosphate intermediate is converted to ADP-glu-cose via ADP-glucose pyrophosphorylase (Figure 8.14 and Table 8.5, reaction 5) in a reaction that requires ATP and generates pyrophosphate (PPi, or H2P2O7 2–).
As in many biosynthetic reactions, the pyrophosphate is hydrolyzed via a specific inorganic pyrophosphatase to two orthophosphate (Pi) molecules (Table 8.5, reaction 6), thereby driving reaction 5 toward ADP-glucose synthesis.
Finally, the glucose moiety of ADP-glucose is transferred to the nonreducing end (carbon 4) of the terminal glucose of a growing starch chain (Table 8.5, reaction 7), thus com-pleting the reaction sequence.
Sucrose Is Synthesized in the Cytosol The site of sucrose synthesis has been studied by cell frac-tionation, in which the organelles are isolated and sepa-rated from one another. Enzyme analyses have shown that sucrose is synthesized in the cytosol from triose phosphates 162 Chapter 8 PEP carboxylase Inactive day form PEP carboxylase Active night form Kinase Phosphatase H2O Inhibited by malate Insensitive to malate OH Ser O P Ser Pi ATP ADP FIGURE 8.13 Diurnal regulation of CAM phosphoenolpyru-vate (PEP) carboxylase. Phosphorylation of the serine residue (Ser-OP) yields a form of the enzyme which is active during the night and relatively insensitive to malate.
During the day, dephosphorylation of the serine (Ser-OH) gives a form of the enzyme which is inhibited by malate.
by a pathway similar to that of starch—that is, by way of fructose-1,6-bisphosphate and glucose-1-phosphate (Fig-ure 8.14 and Table 8.6, reactions 2–6).
In sucrose synthesis, the glucose-1-phosphate is con-verted to UDP-glucose via a specific UDP-glucose pyrophosphorylase (Table 8.6, reaction 7) that is analogous to the ADP-glucose pyrophosphorylase of chloroplasts. At this stage, two consecutive reactions complete the synthe-sis of sucrose (Huber and Huber 1996). First, sucrose-6-phosphate synthase catalyzes the reaction of UDP-glucose with fructose-6-phosphate to yield sucrose-6-phosphate and UDP (Table 8.6, reaction 9). Second, the sucrose-6-phosphate phosphatase (phosphohydrolase) cleaves the phosphate from sucrose-6-phosphate, yielding sucrose (Table 8.6, reaction 10). The latter reaction, which is essen-tially irreversible, pulls the former in the direction of sucrose synthesis.
As in starch synthesis, the pyrophosphate formed in the reaction catalyzed by UDP-glucose pyrophosphorylase (Table 8.6, reaction 7) is hydrolyzed, but not immediately as in the chloroplasts. Because of the absence of an inor-ganic pyrophosphatase, the pyrophosphate can be used by other enzymes, in transphosphorylation reactions. One example is fructose-6-phosphate phosphotransferase, an enzyme that catalyzes a reaction like the one catalyzed by phosphofructokinase (Table 8.6, reaction 4a) except that pyrophosphate replaces ATP as the phosphoryl donor.
A comparison of the reactions in Tables 8.5 and 8.6 (as illustrated in Figure 8.14) reveals that the conversion of triose phosphates to glucose-1-phosphate in the pathways Triose phosphates Sucrose phosphate UDP-glucose Sucrose Pi translocator Triose phosphates UTP ADP-glucose CHLOROPLAST CYTOSOL Glucose-1-phosphate Glucose-6-phosphate Glucose-1-phosphate Glucose-6-phosphate Fructose-6-phosphate Fructose-6-phosphate Fructose-1,6-bisphosphate Fructose-1,6-bisphosphate Starch H2O ATP Pi Pi Pi Pi Pi Pi PPi PPi Calvin cycle Glucose-6-phosphate Starch synthase (5-7) Hexose phosphate isomerase (5-3) Phospho-glucomutase (5-4) Fructose-1, 6-biphosphatase (5-2) Sucrose phosphate phosphatase (6-10) Sucrose phosphate synthase (6-9) UDP-glucose pyrophosphorylase (6-7) Phospho-glucomutase (6-6) Hexose phosphate isomerase (6-5) Fructose-1, 6-bisphosphatase (6-4a) Aldolase (6-3) ADP glucose pyro-phosphorylase (5-5) Pyrophosphatase (5-6) Aldolase (5-1) (6-1) FIGURE 8.14 The syntheses of starch and sucrose are compet-ing processes that occur in the chloroplast and the cytosol, respectively. When the cytosolic Pi concentration is high, chloroplast triose phosphate is exported to the cytosol via the Pi in exchange for Pi, and sucrose is synthesized. When the cytosolic Pi concentration is low, triose phosphate is retained within the chloroplast, and starch is synthesized. The num-bers facing the arrows are keyed to Tables 8.5 and 8.6.
leading to the synthesis of starch and sucrose have several steps in common. However, these pathways utilize isozymes (different forms of enzymes catalyzing the same reaction) that are unique to the chloroplast or cytosol.
The isozymes show markedly different properties. For example, the chloroplastic fructose-1,6-bisphosphatase is regulated by the thioredoxin system but not by fructose-2,6-bisphosphate and AMP. Conversely, the cytosolic form of the enzyme is regulated by fructose-2,6-bisphosphate (see the next section), is sensitive to AMP especially in the presence of fructose-2,6-bisphosphate, and is unaffected by thioredoxin.
Aside from the cytosolic fructose-1,6-bisphosphatase, sucrose synthesis is regulated at the level of sucrose phos-phate synthase, an allosteric enzyme that is activated by glucose-6-phosphate and inhibited by orthophosphate. The enzyme is inactivated in the dark by phosphorylation of a specific serine residue via a protein kinase and activated in the light by dephosphorylation via a protein phos-phatase. Glucose-6-phosphate inhibits the kinase, and Pi inhibits the phosphatase.
The recent purification and cloning of sucrose-6-phos-phate phosphatase from rice leaves (Lund et al. 2000) is providing new information on the molecular and func-tional properties of this enzyme. These studies indicate that sucrose-6-phosphate synthase and sucrose-6-phosphatase exist as a supramolecular complex showing an enzymatic activity that is higher than that of the isolated constituent enzymes (Salerno et al. 1996). This noncovalent interaction of the two enzymes involved in the last two steps of sucrose synthesis points to a novel regulatory feature of carbohydrate metabolism in plants.
The Syntheses of Sucrose and Starch Are Competing Reactions The relative concentrations of ortho-phosphate and triose phosphate are major factors that control whether photosynthetically fixed carbon is partitioned as starch in the chloro-plast or as sucrose in the cytosol.
The two compartments communi-cate with one another via the phos-phate/triose phosphate translocator, also called the phosphate transloca-tor (see Table 8.6, reaction 1), a strict stoichiometric antiporter.
The phosphate translocator cat-alyzes the movement of orthophos-phate and triose phosphate in oppo-site directions between chloroplast and cytosol. A low concentration of orthophosphate in the cytosol limits the export of triose phosphate from the chloroplast through the translo-cator, thereby promoting the synthesis of starch. Con-versely, an abundance of orthophosphate in the cytosol inhibits starch synthesis within the chloroplast and pro-motes the export of triose phosphate into the cytosol, where it is converted to sucrose.
Orthophosphate and triose phosphate control the activ-ity of several regulatory enzymes in the sucrose and starch biosynthetic pathways. The chloroplast enzyme ADP-glu-cose pyrophosphorylase (see Table 8.5, reaction 5) is the key enzyme that regulates the synthesis of starch from glucose-1-phosphate. This enzyme is stimulated by 3-phospho-glycerate and inhibited by orthophosphate. A high con-centration ratio of 3-phosphoglycerate to orthophosphate is typically found in illuminated chloroplasts that are actively synthesizing starch. Reciprocal conditions prevail in the dark.
Fructose-2,6-bisphosphate is a key control molecule that allows increased synthesis of sucrose in the light and decreased synthesis in the dark. It is found in the cytosol in minute concentrations, and it exerts a regulatory effect on the cytosolic interconversion of fructose-1,6-bisphosphate and fructose-6-phosphate (Huber 1986; Stitt 1990): CH2OH –2O3POCH2 OH HO OPO3 2– H H H O Fructose-2,6-bisphosphate (a regulatory metabolite) OH CH2OPO3 2– –2O3POCH2 HO OH H H H O Fructose-1,6-bisphosphate (an intermediary metabolite) 164 Chapter 8 Thylakoid Starch grain FIGURE 8.15 Electron micrograph of a bundle sheath cell from maize, showing the starch grains in the chloroplasts. (15,800×) (Photo by S. E. Frederick, courtesy of E.
H. Newcomb.) Photosynthesis: Carbon Reactions 165 TABLE 8.5 Reactions of starch synthesis from triose phosphate in chloroplasts 1. Fructose-1,6,bisphosphate aldolase Dihydroxyacetone-3-phosphate + glyceraldehyde-3-phosphate→ fructose-1,6-bisphosphate 2. Fructose-1,6-bisphosphatase Fructose-1,6-bisphosphate + H2O → fructose-6-phosphate + Pi 3. Hexose phosphate isomerase Fructose-6-phosphate → glucose-6-phosphate 4. Phosphoglucomutase Glucose-6-phosphate →glucose-1-phosphate 5. ADP-glucose pyrophosphorylase Glucose-1-phosphate + ATP →ADP-glucose + PPi 6. Pyrophosphatase PPi + H2O →2 Pi + 2H+ 7. Starch synthase ADP-glucose + (1,4-α-D-glucosyl)n → ADP + (1,4-α-D-glucosyl)n+1 Note: Reaction 6 is irreversible and “pulls”the preceding reaction to the right.
Pi and PPi stand for inorganic phosphate and pyrophosphate, respectively.
C O CH2OPO3 2– CH2OH C C HO O H H CH2OPO3 2– CH2OPO3 2– 2–O3POH2C HO HO OH H H H O CH2OPO3 2– 2–O3POH2C HO HO OH H H H O CH2OH OH 2–O3POH2C HO HO OH H H H O CH2OH 2–O3POH2C HO HO OH H H H O CH2OPO3 2– OH OH HO H H H H H O OH CH2OPO3 2– OH OH HO H H H H H O OPO3 2– CH2OH HO OH HO H H H H H O OPO3 2– CH2OH HO OH HO H H H H H O O CH2OH HO OH HO H H H H O P O O O– O O– P O Adenosine O CH2OH HO OH HO H H H H O P O O O– O O– P O Adenosine O CH2OH OH OH OH H H H H H O O CH2OH OH OH O H H H H H O O CH2OH OH OH H H H H O Nonreducing end of a starch chain with n residues Elongated starch with n + 1 residues 166 Chapter 8 C O CH2OPO3 2– CH2OH C C HO O H H CH2OPO3 2– C O CH2OPO3 2– CH2OH C C HO O H H CH2OPO3 2– CH2OPO3 2– 2–O3POH2C HO HO OH H H H O CH2OPO3 2– 2–O3POH2C HO HO OH H H H O CH2OH 2–O3POH2C HO HO OH H H H O CH2OH 2–O3POH2C HO HO OH H H H O CH2OPO3 2– 2–O3POH2C HO HO OH H H H O CH2OH 2–O3POH2C HO HO OH H H H O CH2OPO3 2– OH OH OH HO H H H H H O CH2OPO3 2– OH OH OH HO H H H H H O CH2OH HO OPO3 2– OH HO H H H H H O CH2OH HO OPO3 2– OH HO H H H H H O O P O O –O –O P O –O O –O P O Uridine CH2OH OH OH HO H H H H H O P O O O– O O– P O O Uridine TABLE 8.6 Reactions of sucrose synthesis from triose phosphate in the cytosol 1. Phosphate/triose phosphate translocator Triose phosphate (chloroplast) + Pi (cytosol) → triose phosphate (cytosol) + Pi (chloroplast) 2. Triose phosphate isomerase Dihydroxyacetone-3-phosphate →glyceraldehyde-3-phosphate 3. Fructose-1,6-bisphosphate aldolase Dihydroxyacetone-3-phosphate + glyceraldehyde-3-phosphate → fructose-1,6-bisphosphate 4a. Fructose-1,6-phosphatase Fructose-1,6-bisphosphate + H2O →fructose-6-phosphate + Pi 4b. PPi-linked phosphofructokinase Fructose-6-phosphate + PPi →fructose-1,6-bisphosphate + Pi 5. Hexose phosphate isomerase Fructose-6-phosphate → glucose-6-phosphate 6. Phosphoglucomutase Glucose-6-phosphate → glucose-1-phosphate 7. UDP-glucose pyrophosphorylase Glucose-1-phosphate + UTP → UDP-glucose + PPi Increased cytosolic fructose-2,6-bisphosphate is associated with decreased rates of sucrose synthesis because fructose-2,6-bisphosphate is a powerful inhibitor of cytosolic fructose-1,6-bisphosphatase (see Table 8.6, reaction 4a) and an activa-tor of the pyrophosphate-dependent (PPi-linked) phospho-fructokinase (reaction 4b). But what, in turn, controls the cytosolic concentration of fructose-2,6-bisphosphate?
Fructose-2,6-bisphosphate is synthesized from fructose-6-phosphate by a special fructose-6-phosphate 2-kinase (not to be confused with the fructose-6-phosphate 1-kinase of glycolysis) and is degraded specifically by fructose-2,6-bisphosphatase (not to be confused with fructose-1,6-bis-phosphatase of the Calvin cycle). Recent evidence suggests that, as in animal cells, both plant activities reside on a sin-gle polypeptide chain.
The kinase and phosphatase activities are controlled by orthophosphate and triose phosphate. Orthophosphate stimulates fructose-6-phosphate 2-kinase and inhibits fruc-tose-2,6-bisphosphatase; triose phosphate inhibits the 2-kinase (Figure 8.16). Consequently, a low cytosolic ratio of triose phosphate to orthophosphate promotes the forma-tion of fructose-2,6-bisphosphate, which in turn inhibits the hydrolysis of cytosolic fructose-1,6-bisphosphate and slows the rate of sucrose synthesis. A high cytosolic ratio of triose phosphate to orthophosphate has the opposite effect.
Light regulates the concentration of these activators and inhibitors through the reactions associated with photo-synthesis and thereby controls the concentration of fruc-tose-2,6-bisphosphate in the cytosol. The glycolytic enzyme phosphofructokinase also functions in the con-version of fructose-6-phosphate to fructose-1,6-bisphos-phate, but in plants it is not appreciably affected by fruc-tose-2,6-bisphosphate.
The activity of phosphofructokinase in plants appears to be regulated by the relative concentrations of ATP, ADP, and AMP. The remarkable plasticity of plants was once again illustrated by recent gene deletion experiments with transformed tobacco plants. This experiment shows that the transformed plants can grow without a functional pyrophosphate-dependent fructose-6-phosphate kinase enzyme. In this case the conversion of fructose-6-phosphate to fructose-1,6-bisphosphate is apparently catalyzed exclu-sively by phosphofructokinase (Paul et al. 1995).
Photosynthesis: Carbon Reactions 167 TABLE 8.6 (continued) Reactions of sucrose synthesis from triose phosphate in the cytosol 8. Pyrophosphatase PPi +H2O → 2 Pi + 2 H+ 9. Sucrose phosphate synthase UDP-glucose + fructose-6-phosphate → UDP + sucrose-6-phosphate 10. Sucrose phosphate phosphatase Sucrose-6-phosphate + H2O →sucrose + Pi Note: Reaction 1 takes place on the chloroplast inner envelope membrane. Reactions 2 through 10 take place in the cytosol. Reaction 8 is irre-versible and “pulls”the preceding reaction to the right.
Pi and PPi stand for inorganic phosphate and pyrophosphate, respectively .
CH2OH OH OH HO H H H H H O O P O O O– O O– P O Uridine CH2OH 2–O3PO CH2 HO HO OH H H H O CH2OH HO HO O H H H O CH2OH OH OH HO H H H H H 2–O3PO CH2 O CH2OH HO HO O H H H O CH2OH OH OH HO H H H H H O 2–O3PO CH2 CH2OH HO HO O H H H O CH2OH OH OH HO H H H H H O HOH2C SUMMARY The reduction of CO2 to carbohydrate via the carbon-linked reactions of photosynthesis is coupled to the consumption of NADPH and ATP synthesized by the light reactions of thy-lakoid membranes. Photosynthetic eukaryotes reduce CO2 via the Calvin cycle that takes place in the stroma, or soluble phase, of chloroplasts. Here, CO2 and water are combined with ribulose-1,5-bisphosphate to form two molecules of 3-phosphoglycerate, which are reduced and converted to car-bohydrate. The continued operation of the cycle is ensured by the regeneration of ribulose-1,5-bisphosphate. The Calvin cycle consumes two molecules of NADPH and three mole-cules of ATP for every CO2 fixed and, provided these sub-strates, has a thermodynamic efficiency close to 90%.
Several light-dependent systems act jointly to regulate the Calvin cycle: changes in ions (Mg2+ and H+), effector metabolites (enzyme substrates), and protein-mediated sys-tems (rubisco activase, ferredoxin–thioredoxin system).
The ferredoxin–thioredoxin control system plays a ver-satile role by linking light to the regulation of other chloro-plast processes, such as carbohydrate breakdown, pho-tophosphorylation, fatty acid biosynthesis, and mRNA translation. Control of these reactions by light separates opposing biosynthetic from degradative processes and thereby minimizes the waste of resources that would occur if the processes operated concurrently.
Rubisco, the enzyme that catalyzes the carboxylation of ribulose-1,5-bisphosphate, also acts as an oxygenase. In both cases the enzyme must be carbamylated to be fully active. The carboxylation and oxygenation reactions take place at the active site of rubisco. When reacting with oxy-gen, rubisco produces 2-phosphoglycolate and 3-phos-phoglycerate from ribulose-1,5-bisphosphate rather than two 3-phosphoglycerates as with CO2, thereby decreasing the efficiency of photosynthesis.
The C2 oxidative photosynthetic carbon cycle rescues the carbon lost as 2-phosphoglycolate by rubisco oxyge-nase activity. The dissipative effects of photorespiration are avoided in some plants by mechanisms that concentrate CO2 at the carboxylation sites in the chloroplast. These mechanisms include a C4 photosynthetic carbon cycle, CAM metabolism, and “CO2 pumps” of algae and cyanobacteria.
The carbohydrates synthesized by the Calvin cycle are converted into storage forms of energy and carbon: sucrose and starch. Sucrose, the transportable form of carbon and energy in most plants, is synthesized in the cytosol, and its synthesis is regulated by phosphorylation of sucrose phos-phate synthase. Starch is synthesized in the chloroplast.
The balance between the biosynthetic pathways for sucrose and starch is determined by the relative concentrations of metabolite effectors (orthophosphate, fructose-6-phosphate, 3-phosphoglycerate, and dihydroxyacetone phosphate).
These metabolite effectors function in the cytosol by way of the enzymes synthesizing and degrading fructose-2,6-bis-phosphate, the regulatory metabolite that plays a primary role in controlling the partitioning of photosynthetically fixed carbon between sucrose and starch. Two of these effec-tors, 3-phosphoglycerate and orthophosphate, also act on 168 Chapter 8 Pi Pi Pi ATP ADP Sucrose synthesis Fructose-1,6-bisphosphate Fructose-6-phosphate Glycolysis PP-Fructose-6-phosphate kinase Fructose-1,6-bisphosphatase Fructose-6-phosphate Fructose-2, 6-bisphosphate PP Activates Inhibits Activated by: Orthophosphate (Pi) Fructose-6-phosphate Inhibited by: Dihydroxyacetone phosphate 3-phosphoglycerate Inhibited by: Orthophosphate (Pi) Fructose-6-phosphate Fructose-2,6-bisphosphatase Fructose-6-phosphate 2-kinase (A) (B) FIGURE 8.16 Regulation of the cytosolic interconversion of fructose-6-phosphate and fructose-1,6-bisphosphate. (A) The key metabolites in the allocation between glycolysis and sucrose synthesis. The regulatory metabolite fructose 2,6-bisphosphate regulates the interconversion by inhibiting the phosphatase and activating the kinase, as shown.
(B) The synthesis of fructose-2,6-bisphosphate itself is under strict regulation by the activators and inhibitors shown in the figure. starch synthesis in the chloroplast by allosterically regulat-ing the activity of ADP-glucose pyrophosphorylase. In this way the synthesis of starch from triose phosphates during the day can be separated from its breakdown, which is required to provide energy to the plant at night.
Web Material Web Topics 8.1 How the Calvin Cycle Was Elucidated Experiments carried out in the 1950s led to the discovery of the path of CO2 fixation.
8.2 Rubisco: A Model Enzyme for Studying Struc-ture and Function As the most abundant enzyme on Earth, rubisco was obtained in quantities sufficient for elucidat-ing its structure and catalytic properties.
8.3 Carbon Dioxide: Some Important Physico-chemical Properties Plants have adapted to the properties of CO2 by altering the reactions catalyzing its fixation.
8.4 Thioredoxins First found to regulate chloroplast enzymes, thioredoxins are now known to play a regulatory role in all types of cells.
8.5 Rubisco Activase Rubisco is unique among Calvin cycle enzymes in its regulation by a specific protein, rubisco activase.
8.6 Operation of the C2 Oxidative Photosynthetic Carbon Cycle The enzymes of the C2 oxidative photosynthetic carbon cycle are localized in three different organelles.
8.7 Three Variations of C4 Metabolism Certain reactions of the C4 photosynthetic path-way differ among plant species.
Web Essay 8.1 Modulation of Phosphoenolpyruvate Car-boxylase in C4 and CAM Plants The CO2-fixing enzyme, phosphoenolpyruvate carboxylase is regulated differently in C4 and CAM species.
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170 Chapter 8 Photosynthesis: Physiological and Ecological Considerations 9 Chapter THE CONVERSION OF SOLAR ENERGY to the chemical energy of organic compounds is a complex process that includes electron trans-port and photosynthetic carbon metabolism (see Chapters 7 and 8). Ear-lier discussions of the photochemical and biochemical reactions of pho-tosynthesis should not overshadow the fact that, under natural conditions, the photosynthetic process takes place in intact organisms that are continuously responding to internal and external changes. This chapter addresses some of the photosynthetic responses of the intact leaf to its environment. Additional photosynthetic responses to different types of stress are covered in Chapter 25.
The impact of the environment on photosynthesis is of interest to both plant physiologists and agronomists. From a physiological stand-point, we wish to understand how photosynthesis responds to envi-ronmental factors such as light, ambient CO2 concentrations, and tem-perature. The dependence of photosynthetic processes on environment is also important to agronomists because plant productivity, and hence crop yield, depends strongly on prevailing photosynthetic rates in a dynamic environment.
In studying the environmental dependence of photosynthesis, a cen-tral question arises: How many environmental factors can limit photo-synthesis at one time? The British plant physiologist F. F. Blackman hypothesized in 1905 that, under any particular conditions, the rate of photosynthesis is limited by the slowest step, the so-called limiting factor.
The implication of this hypothesis is that at any given time, photo-synthesis can be limited either by light or by CO2 concentration, but not by both factors. This hypothesis has had a marked influence on the approach used by plant physiologists to study photosynthesis—that is, varying one factor and keeping all other environmental conditions con-stant.
In the intact leaf, three major metabolic steps have been identified as important for optimal photosynthetic perfor-mance: 1. Rubisco activity 2. Regeneration of ribulose bisphosphate (RuBP) 3. Metabolism of the triose phosphates The first two steps are the most prevalent under natural conditions. Table 9.1 provides some examples of how light and CO2 can affect these key metabolic steps. In the fol-lowing sections, biophysical, biochemical, and environ-mental aspects of photosynthesis in leaves are discussed in detail.
LIGHT, LEAVES, AND PHOTOSYNTHESIS Scaling up from the chloroplast (the focus of Chapters 7 and 8) to the leaf adds new levels of complexity to photosyn-thesis. At the same time, the structural and functional prop-erties of the leaf make possible other levels of regulation.
We will start by examining how leaf anatomy, and movements by chloroplasts and leaves, control the absorp-tion of light for photosynthesis. Then we will describe how chloroplasts and leaves adapt to their light environment and how the photosynthetic response of leaves grown under low light reflects their adaptation to a low-light envi-ronment. Leaves also adapt to high light conditions, illus-trating that plants are physiologically flexible and that they adapt to their immediate environment.
Both the amount of light and the amount of CO2 deter-mine the photosynthetic response of leaves. In some situa-tions, photosynthesis is limited by an inadequate supply of light or CO2. In other situations, absorption of too much light can cause severe problems, and special mechanisms protect the photosynthetic system from excessive light.
Multiple levels of control over photosynthesis allow plants to grow successfully in a constantly changing environment and different habitats.
CONCEPTS AND UNITS IN THE MEASUREMENT OF LIGHT Three light parameters are especially important in the mea-surement of light: (1) spectral quality, (2) amount, and (3) direction. Spectral quality was discussed in Chapter 7 (see Figures 7.2 and 7.3, and Web Topic 7.1). A discussion of the amount and direction of light reaching the plant requires consideration of the geometry of the part of the plant that receives the light: Is the plant organ flat or cylindrical?
Flat, or planar, light sensors are best suited for flat leaves. The light reaching the plant can be measured as energy, and the amount of energy that falls on a flat sensor of known area per unit time is quantified as irradiance (see Table 9.2). Units can be expressed in terms of energy, such as watts per square meter (W m–2). Time (seconds) is con-tained within the term watt: 1 W = 1 joule (J) s–1.
Light can also be measured as the number of incident quanta (singular quantum). In this case, units can be expressed in moles per square meter per second (mol m–2 s–1), where moles refers to the num-ber of photons (1 mol of light = 6.02 × 1023 photons, Avogadro’s number).
This measure is called photon irra-diance. Quanta and energy units can be interconverted relatively easily, provided that the wavelength of the light, l, is known. The energy of a photon is related to its wavelength as follows: where c is the speed of light (3 × 108 m s–1), h is Planck’s constant (6.63 × 10–34 J s), and l is the wavelength E hc = l 172 Chapter 9 TABLE 9.1 Some characteristics of limitations to the rate of photosynthesis Conditions that Response of photosynthesis lead to this limitation under this limitation to Limiting factor CO2 Light CO2 O2 Light Rubisco activity Low High Strong Strong Absent RuBP regeneration High Low Moderate Moderate Strong TABLE 9.2 Concepts and units for the quantification of light Energy measurements Photon measurements (W m–2) (mol m–2s–1) Flat light sensor Irradiance Photon irradiance Photosynthetically PAR (quantum units) active radiation (PAR, 400-700 nm, energy units) — Photosynthetic photon flux density (PPFD) Spherical light sensor Fluence rate (energy units) Fluence rate (quantum units) Scalar irradiance Quantum scalar irradiance of light, usually expressed in nm (1 nm = 10–9 m). From this equation it can be shown that a photon at 400 nm has twice the energy of a photon at 800 nm (see Web Topic 9.1).
Now let’s turn our attention to the direction of light.
Light can strike a flat surface directly from above or obliquely. When light deviates from perpendicular, irradi-ance is proportional to the cosine of the angle at which the light rays hit the sensor (Figure 9.1).
There are many examples in nature in which the light-intercepting object is not flat (e.g., complex shoots, whole plants, chloroplasts). In addition, in some situations light can come from many directions simultaneously (e.g., direct light from the sun plus the light that is reflected upward from sand, soil, or snow). In these situations it makes more sense to measure light with a spherical sensor that takes measurements omnidirectionally (from all directions).
The term for this omnidirectional measurement is flu-ence rate (see Table 9.2) (Rupert and Letarjet 1978), and this quantity can be expressed in watts per square meter (W m–2) or moles per square meter per second (mol m–2 s–1).
The units clearly indicate whether light is being measured as energy (W) or as photons (mol).
In contrast to a flat sensor’s sensitivity, the sensitivity to light of a spherical sensor is independent of direction (see Figure 9.1). Depending on whether the light is collimated (rays are parallel) or diffuse (rays travel in random direc-tions), values for fluence rate versus irradiance measured with a flat or a spherical sensor can provide different val-ues (see Figure 9.1) (for a detailed discussion, see Björn and Vogelmann 1994).
Photosynthetically active radiation (PAR, 400–700 nm) may also be expressed in terms of energy (W m–2) or quanta (mol m–2 s–1) (McCree 1981). Note that PAR is an irradiance-type measurement. In research on photosyn-thesis, when PAR is expressed on a quantum basis, it is given the special term photosynthetic photon flux density (PPFD). However, it has been suggested that the term den-sity be discontinued because within the International Sys-tem of Units (SI units, where SI stands for Système Interna-tional), density can mean area or volume.
In summary, when choosing how to quantify light, it is important to match sensor geometry and spectral response with that of the plant. Flat, cosine-corrected sensors are ide-ally suited to measure the amount of light that strikes the surface of a leaf; spherical sensors are more appropriate in other situations, such as in studies of a chloroplast sus-pension or a branch from a tree (see Table 9.2).
How much light is there on a sunny day, and what is the relationship between PAR irradiance and PAR fluence rate?
Under direct sunlight, PAR irradiance and fluence rate are both about 2000 µmol m–2 s–1, though higher values can be measured at high altitudes. The corresponding value in energy units is about 400 W m–2.
Leaf Anatomy Maximizes Light Absorption Roughly 1.3 kW m–2 of radiant energy from the sun reaches Earth, but only about 5% of this energy can be converted into carbohydrates by a photosynthesizing leaf (Figure 9.2).
The reason this percentage is so low is that a major fraction of the incident light is of a wavelength either too short or too long to be absorbed by the photosynthetic pigments (see Figure 7.3). Of the absorbed light energy, a significant fraction is lost as heat, and a smaller amount is lost as flu-orescence (see Chapter 7).
Recall from Chapter 7 that radiant energy from the sun consists of many different wavelengths of light. Only pho-tons of wavelengths from 400 to 700 nm are utilized in pho-tosynthesis, and about 85 to 90% of this PAR is absorbed by the leaf; the remainder is either reflected at the leaf surface or transmitted through the leaf (Figure 9.3). Because chloro-phyll absorbs very strongly in the blue and the red regions of the spectrum (see Figure 7.3), the transmitted and reflected light are vastly enriched in green—hence the green color of vegetation.
The anatomy of the leaf is highly specialized for light absorption (Terashima and Hikosaka 1995). The outermost cell layer, the epidermis, is typically transparent to visible light, and the individual cells are often convex. Convex epidermal cells can act as lenses and can focus light so that the amount reaching some of the chloroplasts can be many times greater than the amount of ambient light (Vogel-Photosynthesis: Physiological and Ecological Considerations 173 Equal irradiance values (A) (B) (C) (D) Light Light Sensor Sensor Sensor Sensor a Irradiance = (A) × cosine a FIGURE 9.1 Flat and spherical light sensors. Equivalent amounts of collimated light strike a flat irradiance-type sen-sor (A) and a spherical sensor (B) that measure fluence rate.
With collimated light, A and B will give the same light read-ings. When the light direction is changed 45°, the spherical sensor (D) will measure the same quantity as in B. In con-trast, the flat irradiance sensor (C) will measure an amount equivalent to the irradiance in A multiplied by the cosine of the angle α in C. (After Björn and Vogelmann 1994.) mann et al. 1996). Epidermal focusing is common among herbaceous plants and is especially prominent among tropical plants that grow in the forest understory, where light levels are very low.
Below the epidermis, the top layers of photosynthetic cells are called palisade cells; they are shaped like pillars that stand in parallel columns one to three layers deep (Fig-ure 9.4). Some leaves have several layers of columnar pal-isade cells, and we may wonder how efficient it is for a plant to invest energy in the development of multiple cell layers when the high chlorophyll content of the first layer would appear to allow little transmission of the incident light to the leaf interior. In fact, more light than might be expected penetrates the first layer of palisade cells because of the sieve effect and light channeling.
The sieve effect is due to the fact that chlorophyll is not uniformly distributed throughout cells but instead is con-fined to the chloroplasts. This packaging of chlorophyll results in shading between the chlorophyll molecules and creates gaps between the chloroplasts, where light is not absorbed—hence the reference to a sieve. Because of the sieve effect, the total absorption of light by a given amount of chlorophyll in a palisade cell is less than the light absorbed by the same amount of chlorophyll in a solution.
Light channeling occurs when some of the incident light is propagated through the central vacuole of the pal-isade cells and through the air spaces between the cells, an arrangement that facilitates the transmission of light into the leaf interior (Vogelmann 1993).
Below the palisade layers is the spongy mesophyll, where the cells are very irregular in shape and are sur-rounded by large air spaces (see Figure 9.4). The large air spaces generate many interfaces between air and water that reflect and refract the light, thereby randomizing its direc-tion of travel. This phenomenon is called light scattering.
Light scattering is especially important in leaves because the multiple reflections between cell–air interfaces greatly increase the length of the path over which photons travel, thereby increasing the probability for absorption. In fact, photon path lengths within leaves are commonly four times or more longer than the thickness of the leaf (Richter and Fukshansky 1996). Thus the palisade cell properties that allow light to pass through, and the spongy mesophyll cell properties that are conducive to light scattering, result in more uniform light absorption throughout the leaf.
Some environments, such as deserts, have so much light that it is potentially harmful to leaves. In these environ-ments leaves often have special anatomic features, such as 174 Chapter 9 Total solar energy (100%) Nonabsorbed wavelengths (60% loss) Reflection and transmission (8% loss) Heat dissipation (8% loss) Metabolism (19% loss) 5% 24% 32% 40% Carbohydrate FIGURE 9.2 Conversion of solar energy into carbohydrates by a leaf. Of the total incident energy, only 5% is converted into carbohydrates.
20 40 500 600 700 800 400 0 60 80 100 80 100 60 40 20 0 Percentage of transmitted light Percentage of reflected light Wavelength (nm) Photosynthetically active radiation Absorbed light Transmitted light Reflected light Visible spectrum FIGURE 9.3 Optical properties of a bean leaf. Shown here are the percentages of light absorbed, reflected, and transmitted, as a function of wavelength. The transmitted and reflected green light in the wave band at 500 to 600 nm gives leaves their green color. Note that most of the light above 700 nm is not absorbed by the leaf. (From Smith 1986.) hairs, salt glands, and epicuticular wax that increase the reflection of light from the leaf surface, thereby reducing light absorption (Ehleringer et al. 1976). Such adaptations can decrease light absorption by as much as 40%, mini-mizing heating and other problems associated with the absorption of too much light.
Chloroplast Movement and Leaf Movement Can Control Light Absorption Chloroplast movement is widespread among algae, mosses, and leaves of higher plants (Haupt and Scheuer-lein 1990). If chloroplast orientation and location are con-trolled, leaves can regulate how much of the incident light is absorbed. Under low light (Figure 9.5B), chloroplasts gather at the cell surfaces parallel to the plane of the leaf so that they are aligned perpendicularly to the incident light— a position that maximizes absorption of light.
Under high light (Figure 9.5C), the chloroplasts move to the cell surfaces that are parallel to the incident light, thus avoiding excess absorption of light. Such chloroplast rearrangement can decrease the amount of light absorbed by the leaf by about 15% (Gorton et al. 1999). Chloroplast movement in leaves is a typical blue-light response (see Chapter 18). Blue light also controls chloroplast orientation Photosynthesis: Physiological and Ecological Considerations 175 FIGURE 9.4 Scanning electron micrographs of the leaf anatomy from a legume (Thermopsis montana) grown in different light environments. Note that the sun leaf (A) is much thicker than the shade leaf (B) and that the palisade (columnlike) cells are much longer in the leaves grown in sunlight. Layers of spongy mesophyll cells can be seen below the palisade cells.
(Micrographs courtesy of T. Vogelmann.) Leaf grown in sun Leaf grown in shade (A) Epidermis Palisade cells Spongy mesophyll Epidermis 100 mm Guard cells (B) (A) Darkness (B) Weak blue light (C) Strong blue light FIGURE 9.5 Chloroplast distribution in photosynthesizing cells of the duckweed Lemna. These surface views show the same cells under three conditions: (A) darkness, (B) weak blue light, and (C) strong blue light. In A and B, chloro-plasts are positioned near the upper surface of the cells, where they can absorb maximum amounts of light. When the cells were irradiated with strong blue light (C), the chloroplasts move to the side walls, where they shade each other, thus minimizing the absorption of excess light.
(Micrographs courtesy of M. Tlalka and M. D. Fricker.) 176 Chapter 9 in many of the lower plants, but in some algae, chloroplast movement is controlled by phytochrome (Haupt and Scheuerlein 1990). In leaves, chloroplasts move along actin microfilaments in the cytoplasm, and calcium regulates their movement (Tlalka and Fricker 1999).
Leaves have the highest light absorption when the leaf blade, or lamina, is perpendicular to the incident light.
Some plants control light absorption by solar tracking (Koller 2000); that is, their leaves continuously adjust the orientation of their laminae such that they remain perpen-dicular to the sun’s rays (Figure 9.6). Alfalfa, cotton, soy-bean, bean, lupine, and some wild species of the mallow family (Malvaceae) are examples of the numerous plant species that are capable of solar tracking.
Solar-tracking leaves keep a nearly vertical position at sunrise, facing the eastern horizon, where the sun will rise.
The leaf blades then lock on to the rising sun and follow its movement across the sky with an accuracy of ±15° until sunset, when the laminae are nearly vertical, facing the west, where the sun will set. During the night the leaf takes a horizontal position and reorients just before dawn so that it faces the eastern horizon in anticipation of another sun-rise. Leaves track the sun only on clear days, and they stop when a cloud obscures the sun. In the case of intermittent cloud cover, some leaves can reorient as rapidly as 90° per hour and thus can catch up to the new solar position when the sun emerges from behind a cloud (Koller 1990).
Solar tracking is another blue-light response, and the sensing of blue light in solar-tracking leaves occurs in spe-cialized regions. In species of Lavatera (Malvaceae), the pho-tosensitive region is located in or near the major leaf veins (Koller 1990). In lupines, (Lupinus, Fabaceae), leaves con-sist of five or more leaflets, and the photosensitive region is located in the basal part of each leaflet lamina.
In many cases, leaf orientation is controlled by a spe-cialized organ called the pulvinus (plural pulvini), found at the junction between the blade and petiole. The pulvinus contains motor cells that change their osmotic potential and generate mechanical forces that determine laminar orien-tation. In other plants, leaf orientation is controlled by small mechanical changes along the length of the petiole and by movements of the younger parts of the stem.
Some solar-tracking plants can also move their leaves such that they avoid full exposure to sunlight, thus mini-mizing heating and water loss. Building on the term heliotropism (bending toward the sun), which is often used to describe sun-induced leaf movements, these sun-avoiding leaves are called paraheliotropic, and leaves that maximize light interception by solar tracking are called dia-heliotropic. Some plant species can display diaheliotropic movements when they are well watered and parahe-liotropic movements when they experience water stress.
Since full sunlight usually exceeds the amount of light that can be utilized for photosynthesis, what advantage is gained by solar tracking? By keeping leaves perpendicular to the sun, solar-tracking plants maintain maximum pho-tosynthetic rates throughout the day, including early morn-ing and late afternoon. Moreover, air temperature is lower during the early morning and late afternoon, so water stress is lower. Solar tracking therefore gives an advantage to plants that grow in arid regions.
Plants Adapt to Sun and Shade Some plants have enough developmental plasticity to adapt to a range of light regimes, growing as sun plants in sunny areas and as shade plants in shady habitats. Some shady habitats receive less than 1% of the PAR available in an exposed habitat. Leaves that are adapted to very sunny (A) (B) FIGURE 9.6 Leaf movement in sun-tracking plants. (A) Initial leaf orientation in the lupine Lupinus succulentus. (B) Leaf orientation 4 hours after exposure to oblique light. The direction of the light beam is indicated by the arrows. Movement is gen-erated by asymmetric swelling of a pulvinus, found at the junction between the lamina and the petiole. In natural conditions, the leaves track the sun’s trajectory in the sky. (From Vogelmann and Björn 1983, courtesy of T. Vogelmann.) or very shady environments are often unable to survive in the other type of habitat (see Figure 9.10). Sun and shade leaves have some contrasting characteristics: • Shade leaves have more total chlorophyll per reaction center, have a higher ratio of chlorophyll b to chloro-phyll a, and are usually thinner than sun leaves.
• Sun leaves have more rubisco, and a larger pool of xanthophyll cycle components than shade leaves (see Chapter 7).
Contrasting anatomic characteristics can also be found in leaves of the same plant that are exposed to different light regimes. Figure 9.4 shows some anatomic differences between a leaf grown in the sun and a leaf grown in the shade. Sun-grown leaves are thicker and have longer pal-isade cells than leaves growing in the shade. Even different parts of a single leaf show adaptations to their light microenvironment. Cells in the upper surface of the leaf, which are exposed to the highest prevailing photon flux, have characteristics of cells from leaves grown in full sun-light; cells in the lower surface of the leaf have characteris-tics of cells found in shade-grown leaves (Terashima 1992).
These morphological and biochemical modifications are associated with specific functions. Far-red light is absorbed primarily by PSI, and altering the ratio of PSI to PSII or changing the light-harvesting antennae associated with the photosystems makes it possible to maintain a better bal-ance of energy flow through the two photosystems (Melis 1996). These adaptations are found in nature; some shade plants show a 3:1 ratio of photosystem II to photosystem I reaction centers, compared with the 2:1 ratio found in sun plants (Anderson 1986). Other shade plants, rather than altering the ratio of PSI to PSII, add more antennae chloro-phyll to PSII. These adaptations appear to enhance light absorption and energy transfer in shady environments, where far-red light is more abundant.
Sun and shade plants also differ in their respiration rates, and these differences alter the relationship between respiration and photosynthesis, as we’ll see a little later in this chapter.
Plants Compete for Sunlight Plants normally compete for sunlight. Held upright by stems and trunks, leaves configure a canopy that absorbs light and influences photosynthetic rates and growth beneath them.
Leaves that are shaded by other leaves have much lower photosynthetic rates. Some plants have very thick leaves that transmit little, if any, light. Other plants, such as those of the dandelion (Taraxacum sp.), have a rosette growth habit, in which leaves grow radially very close to each other and to the stem, thus preventing the growth of any leaves below them.
Trees represent an outstanding adaptation for light inter-ception. The elaborate branching structure of trees vastly increases the interception of sunlight. Very little PAR pen-etrates the canopy of many forests; almost all of it is absorbed by leaves (Figure 9.7).
Another feature of the shady habitat is sunflecks, patches of sunlight that pass through small gaps in the leaf canopy and move across shaded leaves as the sun moves.
In a dense forest, sunflecks can change the photon flux impinging on a leaf in the forest floor more than tenfold within seconds. For some of these leaves, a sunfleck con-tains nearly 50% of the total light energy available during the day, but this critical energy is available for only a few minutes in a very high dose.
Sunflecks also play a role in the carbon metabolism of lower leaves in dense crops that are shaded by the upper leaves of the plant. Rapid responses of both the photosyn-thetic apparatus and the stomata to sunflecks have been of substantial interest to plant physiologists and ecologists (Pearcy et al. 1997) because they represent unique physio-logical responses specialized for capturing a short burst of sunlight.
PHOTOSYNTHETIC RESPONSES TO LIGHT BY THE INTACT LEAF Light is a critical resource for plants that can often limit growth and reproduction. The photosynthetic properties Photosynthesis: Physiological and Ecological Considerations 177 In sun at top of canopy In shade beneath canopy 1 2 3 4 5 6 0.05 0.10 0.15 0.20 0.25 500 400 600 700 800 0 0.00 Spectral irradiance, sun (µmol m–2 s–1 nm–1) Spectral irradiance, shade (µmol m–2 s–1 nm–1) Far red and infrared Wavelength (nm) Visible spectrum FIGURE 9.7 The spectral distribution of sunlight at the top of a canopy and under the canopy. For unfiltered sunlight, the total irradiance was 1900 µmol m–2 s–1; for shade, 17.7 µmol m–2 s–1. Most of the photosynthetically active radiation was absorbed by leaves in the canopy. (From Smith 1994.) of the leaf provide valuable information about plant adap-tations to their light environment.
In this section we describe typical photosynthetic responses to light as measured in light-response curves. We also consider how an important feature of light-response curves, the light compensation point, explains contrasting physiological properties of sun and shade plants. We then describe quantum yields of photosynthesis in the intact leaf, and the differences in quantum yields between C3 and C4 plants. The section closes with descriptions of leaf adap-tations to excess light, and the different pathways of heat dissipation in the leaf.
Light-Response Curves Reveal Photosynthetic Properties Measuring CO2 fixation in intact leaves at increasing pho-ton flux allows us to construct light-response curves (Fig-ure 9.8) that provide useful information about the photo-synthetic properties of leaves. In the dark there is no photosynthetic carbon assimilation, and CO2 is given off by the plant because of respiration (see Chapter 11). By con-vention, CO2 assimilation is negative in this part of the light-response curve. As the photon flux increases, photo-synthetic CO2 assimilation increases until it equals CO2 release by mitochondrial respiration. The point at which CO2 uptake exactly balances CO2 release is called the light compensation point.
The photon flux at which different leaves reach the light compensation point varies with species and developmen-tal conditions. One of the more interesting differences is found between plants grown in full sunlight and those grown in the shade (Figure 9.9). Light compensation points of sun plants range from 10 to 20 µmol m–2 s–1; corre-sponding values for shade plants are 1 to 5 µmol m–2 s–1.
The values for shade plants are lower because respira-tion rates in shade plants are very low, so little net photo-synthesis suffices to bring the net rates of CO2 exchange to zero. Low respiratory rates seem to represent a basic adap-tation that allows shade plants to survive in light-limited environments.
Increasing photon flux above the light compensation point results in a proportional increase in photosynthetic rate (see Figure 9.8), yielding a linear relationship between photon flux and photosynthetic rate. Such a linear rela-178 Chapter 9 –5 0 5 10 15 20 25 200 400 Absorbed light (µmol m–2 s–1) Photosynthetic CO2 assimilation (µmol m–2 s–1) 600 800 1000 0 CO2 limited Light limited Light compensation point (CO2 uptake = CO2 evolution) Dark respiration rate FIGURE 9.8 Response of photosynthesis to light in a C3 plant. In darkness, respiration causes a net efflux of CO2 from the plant. The light compensation point is reached when photosynthetic CO2 assimilation equals the amount of CO2 evolved by respiration. Increasing light above the light compensation point proportionally increases photo-synthesis indicating that photosynthesis is limited by the rate of electron transport, which in turn is limited by the amount of available light. This portion of the curve is referred to as light-limited. Further increases in photosyn-thesis are eventually limited by the carboxylation capacity of rubisco or the metabolism of triose phosphates. This part of the curve is referred to as CO2 limited.
0 –4 4 8 12 16 20 24 28 32 400 800 Irradiance (µmol m–2 s–1) Photosynthetically active radiation Photosynthetic CO2 assimilation (µmol m–2 s–1) 1200 1600 2000 0 Atriplex triangularis (sun plant) Asarum caudatum (shade plant) FIGURE 9.9 Light–response curves of photosynthetic car-bon fixation in sun and shade plants. Atriplex triangularis (triangle orache) is a sun plant, and Asarum caudatum (a wild ginger) is a shade plant. Typically, shade plants have a low light compensation point and have lower maximal photosynthetic rates than sun plants. The dashed line has been extrapolated from the measured part of the curve.
(From Harvey 1979.) tionship comes about because photosynthesis is light lim-ited at those levels of incident light, so more light stimulates more photosynthesis.
In this linear portion of the curve, the slope of the line reveals the maximum quantum yield of photosynthesis for the leaf. Recall that quantum yield is the relation between a given light-dependent product (in this case CO2 assimilation) and the number of absorbed photons (see Equation 7.5).
Quantum yields vary from 0, where none of the light energy is used in photosynthesis, to 1, where all the absorbed light is used. Recall from Chapter 7 that the quan-tum yield of photochemistry is about 0.95, and the quan-tum yield of oxygen evolution by isolated chloroplasts is about 0.1 (10 photons per molecule of O2).
In the intact leaf, measured quantum yields for CO2 fix-ation vary between 0.04 and 0.06. Healthy leaves from many species of C3 plants, kept under low O2 concentra-tions that inhibit photorespiration, usually show a quan-tum yield of 0.1. In normal air, the quantum yield of C3 plants is lower, typically 0.05.
Quantum yield varies with temperature and CO2 con-centration because of their effect on the ratio of the carboxy-lase and oxygenase reactions of rubisco (see Chapter 8).
Below 30°C, quantum yields of C3 plants are generally higher than those of C4 plants; above 30°C, the situation is usually reversed (see Figure 9.23). Despite their different growth habitats, sun and shade plants show similar quantum yields.
At higher photon fluxes, the photosynthetic response to light starts to level off (see Figure 9.8) and reaches saturation.
Once the saturation point is reached, further increases in photon flux no longer affect photosynthetic rates, indicat-ing that factors other than incident light, such as electron transport rate, rubisco activity, or the metabolism of triose phosphates, have become limiting to photosynthesis.
After the saturation point, photosynthesis is commonly referred to as CO2 limited, reflecting the inability of the Calvin cycle enzymes to keep pace with the absorbed light energy. Light saturation levels for shade plants are sub-stantially lower than those for sun plants (see Figure 9.9).
These levels usually reflect the maximal photon flux to which the leaf was exposed during growth (Figure 9.10).
The light-response curve of most leaves saturates between 500 and 1000 µmol m–2 s–1, photon fluxes well below full sunlight (which is about 2000 µmol m–2 s–1).
Although individual leaves are rarely able to utilize full sunlight, whole plants usually consist of many leaves that shade each other. For example, only a small fraction of a tree’s leaves are exposed to full sun at any given time of the day. The rest of the leaves receive subsaturating photon fluxes in the form of small patches of light that pass through gaps in the leaf canopy or in the form of light transmitted through other leaves. Because the photosyn-thetic response of the intact plant is the sum of the photo-synthetic activity of all the leaves, only rarely is photosyn-thesis saturated at the level of the whole plant.
Light-response curves of individual trees and of the for-est canopy show that photosynthetic rate increases with photon flux and photosynthesis usually does not saturate, even in full sunlight (Figure 9.11). Along these lines, crop productivity is related to the total amount of light received during the growing season, and given enough water and nutrients, the more light a crop receives, the higher the bio-mass (Ort and Baker 1988).
Leaves Must Dissipate Excess Light Energy When exposed to excess light, leaves must dissipate the surplus absorbed light energy so that it does not harm the photosynthetic apparatus (Figure 9.12). There are several routes for energy dissipation involving nonphotochemical quenching (see Chapter 7), which is the quenching of chloro-phyll fluorescence by mechanisms other than photochem-istry. The most important example involves the transfer of absorbed light energy away from electron transport toward heat production. Although the molecular mechanisms are not yet fully understood, the xanthophyll cycle appears to be an important avenue for dissipation of excess light energy (see Web Essay 9.1).
Photosynthesis: Physiological and Ecological Considerations 179 0 10 20 30 40 500 1000 Irradiance (µmol m–2 s–1) Photosynthetically active radiation 1500 Grown at 920 µmol m–2 s–1 irradiance (sun) Grown at 92 µmol m–2 s–1 irradiance (shade) 2000 2500 0 Atriplex triangularis (sun plant) Photosynthetic CO2 assimilation (µmol m–2 s–1) FIGURE 9.10 Light–response of photosynthesis of a sun plant gown under sun or shade conditions. The upper curve represents an Atriplex triangularis leaf grown at an irradiance ten times higher than that of the lower curve. In the leaf grown at the lower light levels, photosynthesis sat-urates at a substantially lower irradiance, indicating that the photosynthetic properties of a leaf depend on its grow-ing conditions. The dashed line has been extrapolated from the measured part of the curve. (From Björkman 1981.) The xanthophyll cycle.
Recall from Chapter 7 that the xanthophyll cycle, which comprises the three carotenoids violaxanthin, antheraxanthin, and zeaxanthin, is involved in the dissipation of excess light energy in the leaf (see Fig-ure 7.36). Under high light, violaxanthin is converted to antheraxanthin and then to zeaxanthin. Note that the two aromatic rings of violaxanthin have a bound oxygen atom in them, antheraxanthin has one, and zeaxanthin has none (again, see Figure 7.36). Experiments have shown that zeax-anthin is the most effective of the three xanthophylls in heat dissipation, and antheraxanthin is only half as effective.
Whereas the levels of antheraxanthin remain relatively con-stant throughout the day, the zeaxanthin content increases at high irradiances and decreases at low irradiances.
In leaves growing under full sunlight, zeaxanthin and antheraxanthin can make up 60% of the total xanthophyll cycle pool at maximal irradiance levels attained at midday (Figure 9.13). In these conditions a substantial amount of excess light energy absorbed by the thylakoid membranes can be dissipated as heat, thus preventing damage to the photosynthetic machinery of the chloroplast (see Chapter 7).
The fraction of light energy that is dissipated depends on irradiance, species, growth conditions, nutrient status, and ambient temperature (Demmig-Adams and Adams 1996).
The xanthophyll cycle in sun and shade leaves. Leaves that grow in full sunlight contain a substantially larger xan-thophyll pool than shade leaves, so they can dissipate higher amounts of excess light energy. Nevertheless, the xanthophyll cycle also operates in plants that grow in the low light of the forest understory, where they are only occasionally exposed to high light when sunlight passes through gaps in the overlying leaf canopy, forming sun-flecks (which were described earlier in the chapter). Expo-sure to one sunfleck results in the conversion of much of the violaxanthin in the leaf to zeaxanthin. In contrast to typical leaves, in which violaxanthin levels increase again when irradiances drop, the zeaxanthin formed in shade leaves of the forest understory is retained and protects the leaf against exposure to subsequent sunflecks.
The xanthophyll cycle is also found in species such as conifers, the leaves of which remain green during winter, when photosynthetic rates are very low yet light absorp-tion remains high. Contrary to the diurnal cycling of the xanthophyll pool observed in the summer, zeaxanthin lev-180 Chapter 9 0 10 20 30 40 500 1000 1500 0 Forest canopy Shoot Individual needles Irradiance (µmol m–2 s–1) Photosynthetically active radiation Photosynthetic CO2 assimilation (µmol m–2 s–1) FIGURE 9.11 Changes in photosynthesis (expressed on a per-square-meter basis) in individual needles, a complex shoot, and a forest canopy of Sitka spruce (Picea sitchensis) as a function of irradiance. Complex shoots consist of groupings of needles that often shade each other, similar to the situation in a canopy where branches often shade other branches. As a result of shading, much higher irradiance levels are needed to saturate photosynthesis. The dashed line has been extrapolated from the measured part of the curve. (From Jarvis and Leverenz 1983.) 0 10 20 30 40 50 60 70 200 400 600 Absorbed light (µmol m–2 s–1) Photosynthetic oxygen evolution Photosynthetic O2 evolution (µmol m–2 s–1) Excess light energy FIGURE 9.12 Excess light energy in relation to a light–response curve of photosynthetic evolution. The bro-ken line shows theoretical oxygen evolution in the absence of any rate limitation to photosynthesis. At levels of photon flux up to 150 µmol m–2 s–1, a shade plant is able to utilize the absorbed light. Above 150 µmol m–2 s–1, however, photo-synthesis saturates, and an increasingly larger amount of the absorbed light energy must be dissipated. At higher irradi-ances there is a large difference between the fraction of light used by photosynthesis versus that which must be dissi-pated (excess light energy). The differences are much higher in a shade plant than in a sun plant. (After Osmond 1994.) els remain high all day during the winter. Presumably this mechanism maximizes dissipation of light energy, thereby protecting the leaves against photooxidation during win-ter (Adams et al. 2001).
In addition to protecting the photosynthetic system against high light, the xanthophyll cycle may help protect against high temperatures. Chloroplasts are more tolerant of heat when they accumulate zeaxanthin (Havaux et al.
1996). Thus, plants may employ more than one biochemi-cal mechanism to guard against the deleterious effect of excess heat.
Leaves Must Dissipate Vast Quantities of Heat The heat load on a leaf exposed to full sunlight is very high.
In fact, a leaf with an effective thickness of water of 300 µm would warm up by 100°C every minute if all available solar energy were absorbed and no heat were lost. However, this enormous heat load is dissipated by the emission of long-wave radiation, by sensible (i.e., perceptible) heat loss, and by evaporative (or latent) heat loss (Figure 9.14): • Air circulation around the leaf removes heat from the leaf surfaces if the temperature of the leaf is higher than that of the air; this phenomenon is called sensi-ble heat loss.
• Evaporative heat loss occurs because the evaporation of water requires energy. Thus as water evaporates from a leaf, it withdraws heat from the leaf and cools it. The human body is cooled by the same principle, through perspiration.
Sensible heat loss and evaporative heat loss are the most important processes in the regulation of leaf temperature, and the ratio of the two is called the Bowen ratio (Camp-bell 1977): In well-watered crops, transpiration (see Chapter 4), and hence water evaporation from the leaf, is high, so the Bowen ratio is low (see Web Topic 9.2). On the other hand, when evaporative cooling is limited, the Bowen ratio is large. For example, in some cacti, stomata closure prevents evaporative cooling; all the heat is dissipated by sensible heat loss, and the Bowen ratio is infinite.
Plants with very high Bowen ratios conserve water but have to endure very high leaf temperatures in order to maintain a sufficient temperature gradient between the leaf and the air. Slow growth is usually correlated with these adaptations.
Isoprene Synthesis Helps Leaves Cope with Heat We have seen how the xanthophyll cycle can protect against high light, but how do chloroplasts cope with the Bowen ratio Sensible heat loss Evaporative heat loss = Photosynthesis: Physiological and Ecological Considerations 181 20 6:00 12:00 18:00 0 40 60 80 500 0 1000 1500 2000 100 Xanthophylls (mmol [mol Chl a + b]–1) Irradiance, PAR (µmol m–2 s–1) Time of day Zeaxanthin + Antheraxanthin Violaxanthin Light FIGURE 9.13 Diurnal changes in xanthophyll content as a function of irradiance in sunflower (Helianthus annuus). As the amount of light incident to a leaf increases, a greater proportion of violaxanthin is converted to antheraxanthin and zeaxanthin, thereby dissipating excess excitation energy and protecting the photosynthetic apparatus. (After Demmig-Adams and Adams 1996.) Energy input Heat dissipation Sunlight absorbed by leaf Long-wavelength radiation Conduction and convection to cool air (sensible heat loss) Evaporative cooling from water loss FIGURE 9.14 The absorption and dissipation of energy from sunlight by the leaf. The imposed heat load must be dissi-pated in order to avoid damage to the leaf. The heat load is dissipated by emission of long-wavelength radiation, by sensible heat loss to the air surrounding the leaf, and by the evaporative cooling caused by transpiration. high leaf temperatures that usually accompany high light?
Isoprene synthesis appears to confer stability to photosyn-thetic membranes at high light and temperatures. Many plants, including American oak (Quercus sp.), aspen (Pop-ulus sp.), and kudzu (Pueraria lobata) emit gaseous five-car-bon molecules such as isoprene (2-methyl-1,3-butadiene; see Chapter 13).
On a global scale, these emissions amount to 5 × 1014 g released to the atmosphere each year. These gaseous hydro-carbons are responsible for the pine scent (α- and β-pinene) in coniferous forests and can form a blue haze above forests on hot days. Because isoprene and related hydrocarbons play an important role in atmospheric chemistry, they have attracted much attention from atmospheric scientists.
Isoprene emission from leaves can constitute a signifi-cant fraction of the carbon assimilated in photosynthesis.
For example, up to 2% of the carbon fixed by photosyn-thesis in aspen and oak leaves at 30°C is released as iso-prene (Sharkey 1996). Sun leaves synthesize more isoprene than shade leaves, and synthesis is proportional to leaf temperature and water stress.
Evidence that isoprene confers stability to photosyn-thetic membranes under high temperatures comes from three types of experimental results: 1. Whereas preventing isoprene emission with an inhibitor increases susceptibility to damage by heat, adding isoprene to plants that do not produce iso-prene confers heat stability (Sharkey et al. 2001).
2. Mutant plants unable to emit isoprene are more eas-ily damaged by high temperatures than are wild-type plants (Sharkey and Singsaas 1995).
3. Isoprene is rapidly synthesized enzymatically in response to elevated leaf temperatures.
Absorption of Too Much Light Can Lead to Photoinhibition Recall from Chapter 7 that when leaves are exposed to more light than they can utilize (see Figure 9.12), the reac-tion center of PSII is inactivated and damaged, in a phe-nomenon called photoinhibition. The characteristics of photoinhibition in the intact leaf depend on the amount of light to which the plant is exposed (Figure 9.15), and two types of photoinhibition are identified: dynamic photoin-hibition and chronic photoinhibition (Osmond 1994).
Under moderate excess light, dynamic photoinhibition is observed. Quantum efficiency decreases (contrast the slopes of the curves in Figure 9.15), but the maximum pho-tosynthetic rate remains unchanged. Dynamic photoinhi-bition is caused by the diversion of absorbed light energy toward heat dissipation—hence the decrease in quantum efficiency. This decrease is often temporary, and quantum efficiency can return to its initial higher value when pho-ton flux decreases below saturation levels.
Chronic photoinhibition results from exposure to high levels of excess light that damage the photosynthetic sys-tem and decrease both quantum efficiency and maximum photosynthetic rate (see Figure 9.15). Chronic photoinhibi-tion is associated with damage and replacement of the D1 protein from the reaction center of PSII (see Chapter 7). In contrast to dynamic photoinhibition, these effects are rela-tively long-lasting, persisting for weeks or months.
Early researchers of photoinhibition interpreted all decreases in quantum efficiency as damage to the photo-synthetic apparatus. It is now recognized that short-term decreases in quantum efficiency seem to reflect protective mechanisms (see Chapter 7), whereas chronic photoinhibi-tion represents actual damage to the chloroplast resulting from excess light, or a failure of the protective mechanisms.
How significant is photoinhibition in nature? Dynamic photoinhibition appears to occur normally at midday, when leaves are exposed to maximum amounts of light and there is a corresponding reduction in carbon fixation. Photoinhi-bition is more pronounced at low temperatures, and it becomes chronic under more extreme climatic conditions.
182 Chapter 9 0 5 10 15 20 25 500 1000 Absorbed light (µmol m–2 s–1) Photosynthetic O2 evolution (µmol m–2 s–1) 1500 Optimal photosynthesis Dynamic photoinhibition (moderate excess light) Chronic photoinhibition (high excess light) FIGURE 9.15 Changes in the light–response curves of pho-tosynthesis caused by photoinhibition. Exposure to moder-ate levels of excess light can decrease quantum efficiency (reduced slope of curve) without reducing maximum pho-tosynthetic rate, a condition called dynamic photoinhibi-tion. Exposure to high levels of excess light leads to chronic photoinhibition, where damage to the chloroplast decreases both quantum efficiency and maximum photosynthetic rate. (After Osmond 1994.) Studies of natural willow populations, and crops of Brassica napus (oilseed rape) and Zea mays (maize), have shown that the cumulative effects of a daily depression in photosynthetic rates caused by photoinhibition decrease biomass by 10% at the end of the growing season (Long et al. 1994). This may not seem a particularly large effect, but it could be significant in natural plant populations com-peting for limited resources—conditions under which any reduction in carbon allocated to reproduction can adversely affect reproductive success and survival.
PHOTOSYNTHETIC RESPONSES TO CARBON DIOXIDE We have discussed how plant growth and leaf anatomy are influenced by light. Now we turn our attention to how CO2 concentration affects photosynthesis. CO2 diffuses from the atmosphere into leaves—first through stomata, then through the intercellular air spaces, and ultimately into cells and chloroplasts. In the presence of adequate amounts of light, higher CO2 concentrations support higher photo-synthetic rates. The reverse is also true; that is, low CO2 concentration can limit the amount of photosynthesis.
In this section we will discuss the concentration of atmospheric CO2 in recent history, and its availability for carbon-fixing processes. Then we’ll consider the limitations that CO2 places on photosynthesis and the impact of the CO2-concentrating mechanisms of C4 plants.
Atmospheric CO2 Concentration Keeps Rising Carbon dioxide is a trace gas in the atmosphere, presently accounting for about 0.037%, or 370 parts per million (ppm), of air. The partial pressure of ambient CO2 (Ca) varies with atmospheric pressure and is approximately 36 pascals (Pa) at sea level (see Web Topic 9.3). Water vapor usually accounts for up to 2% of the atmosphere and O2 for about 20%. The bulk of the atmosphere, nearly 80%, is nitrogen.
The current atmospheric concentration of CO2 is almost twice the concentration that has prevailed during most of the last 160,00 years, as measured from air bubbles trapped in glacial ice in Antarctica (Figure 9.16A). Except for the last 200 years, CO2 concentrations during the recent geological past have been low, fluctuating between 180 and 260 ppm.
These low concentrations were typical of times extending back to the Cretaceous, when Earth was much warmer and the CO2 concentration may have been as high as 1200 to 2800 ppm (Ehleringer et al. 1991).
The current CO2 concentration of the atmosphere is increasing by about 1 ppm each year, primarily because of the burning of fossil fuels (see Figure 9.16C). Since 1958, when systematic measurements of CO2 began at Mauna Loa, Hawaii, atmospheric CO2 concentrations have increased by more than 17% (Keeling et al. 1995), and by 2020 the atmos-pheric CO2 concentration could reach 600 ppm.
Photosynthesis: Physiological and Ecological Considerations 183 Year 1000 1500 2000 260 280 300 320 340 360 150,000 100,000 50,000 0 1960 1970 1980 1990 2000 Years ago Year 200 160 240 280 320 360 360 380 370 350 340 330 320 310 CO2 concentration (ppm) (A) (C) (B) FIGURE 9.16 Concentration of atmospheric CO2 from the present to 160,000 years ago. (A) Past atmospheric CO2 con-centrations, determined from bubbles trapped in glacial ice in Antarctica, were much lower than current levels. (B) In the last 1000 years, the rise in CO2 concentration coincides with the Industrial Revolution and the increased burning of fossil fuels. (C) Current atmospheric concentrations of CO2 measured at Mauna Loa, Hawaii, continue to rise. The wavy nature of the trace is caused by change in atmospheric CO2 concentrations associated with the growth of agricultural crops. Each year the highest CO2 concentration is observed in May, just before the Northern Hemisphere growing sea-son, and the lowest concentration is observed in October.
(After Barnola et al. 1994, Keeling and Whorf 1994, Neftel et al. 1994, and Keeling et al. 1995.) The greenhouse effect.
The consequences of this increase in atmospheric CO2 are under intense scrutiny by scientists and government agencies, particularly because of predic-tions that the greenhouse effect is altering the world’s cli-mate. The term greenhouse effect refers to the resulting warm-ing of Earth’s climate, which is caused by the trapping of long-wavelength radiation by the atmosphere.
A greenhouse roof transmits visible light, which is absorbed by plants and other surfaces inside the green-house. The absorbed light energy is converted to heat, and part of it is re-emitted as long-wavelength radiation.
Because glass transmits long-wavelength radiation very poorly, this radiation cannot leave the greenhouse through the glass roof, and the greenhouse heats up.
Certain gases in the atmosphere, particularly CO2 and methane, play the same role as the glass roof in a greenhouse.
The increased CO2 concentration and temperature associated with the greenhouse effect can influence photosynthesis. At current atmospheric CO2 concentrations, photosynthesis in C3 plants is CO2 limited (as we will discuss later in the chap-ter), but this situation could change as atmospheric CO2 con-centrations continue to rise. Under laboratory conditions, most C3 plants grow 30 to 60% faster when CO2 concentra-tion is doubled (to 600–700 ppm), and the growth rate changes depend on nutrient status (Bowes 1993). In some plants the enhanced growth is only temporary.
For many crops, such as tomatoes, lettuce, cucumbers, and roses growing in greenhouses under optimal nutrition, carbon dioxide enrichment in the greenhouse environment results in increased productivity. The photosynthetic per-formance of C3 plants under elevated CO2 is enhanced because photorespiration decreases (see Chapter 8).
Diffusion of CO2 to the Chloroplast Is Essential to Photosynthesis For photosynthesis to occur, carbon dioxide must diffuse from the atmosphere into the leaf and into the carboxyla-tion site of rubisco. Because diffusion rates depend on con-centration gradients (see Chapters 3 and 6), appropriate gradients are needed to ensure adequate diffusion of CO2 from the leaf surface to the chloroplast.
The cuticle that covers the leaf is nearly impermeable to CO2, so the main port of entry of CO2 into the leaf is the stomatal pore. CO2 diffuses through the pore into the sub-stomatal cavity and into the intercellular air spaces between the mesophyll cells. This portion of the diffusion path of CO2 into the chloroplast is a gaseous phase. The remainder of the diffusion path to the chloroplast is a liq-uid phase, which begins at the water layer that wets the walls of the mesophyll cells and continues through the plasma membrane, the cytosol, and the chloroplast. (For the properties of CO2 in solution, see Web Topic 8.3.) Each portion of this diffusion pathway imposes a resis-tance to CO2 diffusion, so the supply of CO2 for photosyn-thesis meets a series of different points of resistance (Fig-ure 9.17). An evaluation of the magnitude of each point of resistance is helpful for understanding CO2 limitations to photosynthesis.
Carbon dioxide enters the intercellular air spaces of the leaf through the stomatal pores. From the air spaces it dis-solves in the water of wet cell walls and diffuses into the cell and chloroplast. The same path is traveled in the reverse direction by H2O.
The sharing of this pathway by CO2 and water presents the plant with a functional dilemma. In air of high relative humidity, the diffusion gradient that drives water loss is about 50 times larger than the gradient that drives CO2 uptake. In drier air, this gradient can be even larger. There-fore, a decrease in stomatal resistance through the opening of stomata facilitates higher CO2 uptake but is unavoidably accompanied by substantial water loss.
Recall from Chapter 4 that the gas phase of CO2 diffu-sion into the leaf can be divided into three components— the boundary layer, the stomata, and the intercellular spaces of the leaf—each of which imposes a resistance to CO2 diffusion (see Figure 9.17).
The boundary layer consists of relatively unstirred air at the leaf surface, and its resistance to diffusion is called the boundary layer resistance. The magnitude of the bound-ary layer resistance decreases with leaf size and wind speed. The boundary layer resistance to water and CO2 dif-fusion is physically related to the boundary layer resistance to sensible heat loss discussed earlier.
Smaller leaves have a lower boundary layer resistance to CO2 and water diffusion, and to sensible heat loss. Leaves 184 Chapter 9 CO2 Boundary layer resistance Boundary layer Stomatal resistance Stoma Intercellular air space resistance Liquid phase resistance Stomatal pore FIGURE 9.17 Points of resistance to the diffusion of CO2 from outside the leaf to the chloroplasts. The stomatal pore is the major point of resistance to CO2 diffusion.
of desert plants are usually small, facilitating sensible heat loss. The large leaves often found in the humid Tropics can have large boundary layer resistances, but these leaves can dissipate the radiation heat load by evaporative cooling because of the high transpiration rates made possible by the abundant water supply in these habitats.
After diffusing through the boundary layer, CO2 enters the leaf through the stomatal pores, which impose the next type of resistance in the diffusion pathway, the stomatal resistance. Under most conditions in nature, in which the air around a leaf is seldom completely still, the boundary layer resistance is much smaller than the stomatal resis-tance, and the main limitation to CO2 diffusion is imposed by the stomatal resistance.
There is also a resistance to CO2 diffusion in the air spaces that separate the substomatal cavity from the walls of the mesophyll cells, called the intercellular air space resistance. This resistance is also usually small—causing a drop of 0.5 Pa or less in partial pressure of CO2, compared with the 36 Pa outside the leaf.
The resistance to CO2 diffusion of the liquid phase—the liquid phase resistance, also called mesophyll resistance— encompasses diffusion from the intercellular leaf spaces to the carboxylation sites in the chloroplast. This point of resis-tance to CO2 diffusion has been calculated as approximately one-tenth of the combined boundary layer resistance and stomatal resistance when the stomata are fully open. This low resistance value can be attributed in part to the large surface area of mesophyll cells exposed to the intercellular air spaces, which can be as much as 10 to 30 times the projected leaf area (Syvertsen et al. 1995). In addition, the localization of chloro-plasts near the cell periphery minimizes the distance that CO2 diffuses to carboxylation sites within the chloroplast.
The positioning of chloroplasts and the relatively large percentage of intercellular air space (about 20–40%) are special anatomic features that facilitate the internal diffu-sion and uptake of CO2by leaves (Evans 1999). Because the stomatal pores usually impose the largest resistance to CO2 uptake and water loss in the diffusion pathway, this regu-lation provides the plant with an effective way to control gas exchange between the leaf and the atmosphere. In experimental measurements of gas exchange from leaves, the boundary layer resistance and the intercellular air space resistance are usually ignored, and the stomatal resistance is used as the single parameter describing the gas phase resistance to CO2 (see Web Topic 9.4).
Patterns of Light Absorption Generate Gradients of CO2 Fixation within the Leaf We have discussed how leaf anatomy is specialized for cap-turing light and how it also facilitates the internal diffusion of CO2, but where in the leaf do maximum rates of photo-synthesis occur? In most leaves, light is preferentially absorbed at the upper surface, whereas CO2enters through the lower surface. Given that light and CO2 enter from opposing sides of the leaf, does photosynthesis occur uni-formly within the leaf tissues, or is there a gradient in pho-tosynthesis across the leaf? The photosynthetic properties of a leaf are determined by the following: • Profiles of light absorption across the mesophyll • Photosynthetic capacity of those tissues • Internal CO2 supply For most leaves, internal CO2 diffusion is rapid, so lim-itations on photosynthetic performance within the leaf are imposed by factors other than CO2 supply. When white light enters the upper surface of a leaf, blue and red pho-tons are preferentially absorbed by chloroplasts near the irradiated surface (Figure 9.18), owing to the strong absorp-tion bands of chlorophyll in the blue and red regions of the spectrum (see Figure 7.5). Green light, on the other hand, penetrates deeper into the leaf. Compared to blue and red, Photosynthesis: Physiological and Ecological Considerations 185 0 20 40 60 80 100 20 0 40 60 80 100 Tissue depth (%) Absorbed light (%) Chlorophyll Green (550 nm) Red (650 nm) Blue (450 nm) Light Epidermis Epidermis Palisade cells 0 20 40 60 80 100 Spinach leaf cross-section Tissue depth Mesophyll cells FIGURE 9.18 Distribution of absorbed light in spinach sun leaves. Irradiation with blue, green or red light results in different profiles of absorbed light in the leaf. The micro-graph above the graph shows a cross-section of a spinach leaf, with rows of palisade cells occupying nearly half of the leaf thickness. The shapes of the curves are in part a result of the unequal distribution of chlorophyll within the leaf tissues. (From Nishio et al. 1993 and Vogelmann and Han 2000; micrograph courtesy of T. Vogelmann.) chlorophyll absorbs poorly in the green (again, see Figure 7.5), yet green light is very effective in supplying energy for photosynthesis in the tissues within the leaf depleted from blue and red photons.
The capacity of the leaf tissue for photosynthetic CO2 assimilation depends to a large extent on its rubisco con-tent. In spinach and the faba bean (Vicia faba), rubisco con-tent starts out low at the top of the leaf, increases toward the middle, and then decreases again toward the bottom.
As a result, the distribution of carbon fixation within the leaf is bell shaped (Figure 9.19). The spongy mesophyll (see Figure 9.4) fixes about 40% of the total carbon in spinach.
The functional significance of the rubisco distribution and the profiles of carbon assimilation within leaves is not yet known, although it is likely that photosynthesis profiles vary in leaves with different anatomy and in leaves adapted to different environments.
CO2 Imposes Limitations on Photosynthesis Expressing photosynthetic rate as a function of the partial pressure of CO2 in the intercellular air space (Ci) within the leaf (see Web Topic 9.4) makes it possible to evaluate limi-tations to photosynthesis imposed by CO2 supply. At very low intercellular CO2 concentrations, photosynthesis is strongly limited by the low CO2, while respiratory rates are unaffected. As a result, there is a negative balance between CO2 fixed by photosynthesis and CO2 produced by respi-ration, and a net efflux of CO2 from the plant.
Increasing intercellular CO2 to the concentration at which these two processes balance each other defines the CO2 compensation point, at which the net efflux of CO2 from the plant is zero (Figure 9.20A). This concept is anal-ogous to that of the light compensation point discussed earlier in the chapter: The CO2 compensation point reflects the balance between photosynthesis and respiration as a function of CO2 concentration, and the light compensation point reflects that balance as a function of photon flux.
In C3 plants, increasing CO2 above the compensation point stimulates photosynthesis over a wide concentration 186 Chapter 9 0 20 40 60 80 100 20 0 40 60 80 100 Tissue depth (%) Carbon fixation (%) Vicia faba Rubisco Spinacia oleracea FIGURE 9.19 Distribution of rubisco and carbon fixation within leaves. Carbon fixation (solid line) within spinach leaves closely follows the internal distribution of rubisco (dashed line). Carbon fixation profiles are similar between Vicia and spinach. (From Nishio et al. 1993 and Jeje and Zimmermann 1983.) 20 40 60 80 20 40 60 80 100 100 Ambient CO2 concentration, Ca (Pa) Intercellular CO2 partial pressure, Ci (Pa) 10 0 20 30 40 50 60 CO2 assimilation (µmol m–2 s–1) 10 0 20 30 40 50 60 CO2 assimilation (µmol m–2 s–1) C4 plant C4 plant C3 plant C3 plant CO2 compensation points (A) (B) FIGURE 9.20 Changes in photosynthesis as a function of ambient intercellular CO2 concentrations in Tidestromia oblongifolia (Arizona honeysweet), a C4 plant, and Larrea divaricata (creosote bush), a C3 plant. Photosynthetic rate is plotted against (A) partial pressure of CO2 in ambient air and (B) calculated intercellular partial pressure of CO2 inside the leaf (see Equation 5 in Web Topic 9.4). The partial pressure at which CO2 assimilation is zero defines the CO2 compensation point. (From Berry and Downton 1982.) range (see Figure 9.20A). At low to intermediate CO2 con-centrations, photosynthesis is limited by the carboxylation capacity of rubisco. At high CO2 concentrations, photosyn-thesis is limited by the capacity of Calvin cycle to regener-ate the acceptor molecule ribulose-1,5-bisphosphate, which depends on electron transport rates. By regulating stomatal conductance, most leaves appear to regulate their Ci (inter-nal partial pressure for CO2) such that it is intermediate between limitations imposed by carboxylation capacity and the capacity to regenerate ribulose-1,5-bisphosphate.
A plot of CO2 assimilation as a function intercellular partial pressures of CO2 tells us how photosynthesis is reg-ulated by CO2, independent of the functioning of stomata (Figure 9.20B). Inspection of such a plot for C3 and C4 plants reveals interesting differences between the two types of carbon metabolism: • In C4 plants, photosynthetic rates saturate at Ci values of about 15 Pa, reflecting the effective CO2-concentrat-ing mechanisms operating in these plants (see Chapter 8).
• In C3 plants, increasing Ci levels continue to stimulate photosynthesis over a much broader range.
These results indicate that C3 plants may benefit more from ongoing increases in atmospheric CO2 concentrations (see Figure 9.16). In contrast, photosynthesis in C4 plants is CO2 saturated at low concentrations, and as a result C4 plants do not benefit from increases in atmospheric CO2 concentrations. Figure 9.20 also shows that plants with C4 metabolism have a CO2 compensation point of zero or nearly zero, reflecting their very low levels of photorespi-ration (see Chapter 8). This difference between C3 and C4 plants is not seen when the experiments are conducted at low oxygen concentrations because oxygenation is also suppressed in C3 plants.
CO2-Concentrating Mechanisms Affect Photosynthetic Responses of Leaves Because of the operating CO2-concentrating mechanisms in C4 plants, CO2 concentration at the carboxylation sites within C4 chloroplasts is often saturating for rubisco activ-ity. As a result, plants with C4 metabolism need less rubisco than C3 plants need to achieve a given rate of photosynthe-sis, and require less nitrogen to grow (von Caemmerer 2000).
In addition, the CO2-concentrating mechanism allows the leaf to maintain high photosynthetic rates at lower Ci values, which require lower rates of stomatal conductance for a given rate of photosynthesis. Thus, C4 plants can use water and nitrogen more efficiently than C3 plants can. On the other hand, the additional energy cost of the concen-trating mechanism (see Chapter 8) makes C4 plants less efficient in their utilization of light. This is probably one of the reasons that most shade-adapted plants are C3 plants.
Many cacti and other succulent plants with CAM metabolism open their stomata at night and close them during the day (Figure 9.21). The CO2 taken up during the night is fixed into malate (see Chapter 8). Because air tem-peratures are much lower at night than during the day, water loss is low and a significant amount of water is saved relative to the amount of CO2 fixed.
The main constraint on CAM metabolism is that the capacity to store malic acid is limited, and this limitation restricts the amount of CO2 uptake. However, many CAM plants can fix CO2 via the Calvin cycle at the end of the day, when temperature gradients are less extreme.
Cladodes (flattened stems) of cacti can survive after detachment from the plant for several months without Photosynthesis: Physiological and Ecological Considerations 187 0 –2 4 8 12 0 6 12 18 24 CO2 assimilation (µmol m–2 s–1) 0.0 0.2 0.4 0.6 0 6 12 18 24 H2O evaporation (mmol m–2 s–1) 0 20 40 60 80 100 0 6 12 18 24 Time (hours) Stomatal conductance (mmol m–2 s–1) (C) (B) (A) Dark Dark Light FIGURE 9.21 Photosynthetic carbon assimilation, evapora-tion, and stomatal conductance of a CAM plant, the cactus Opuntia ficus-indica, during a 24-hour period. The whole plant was kept in a gas exchange chamber in the laboratory.
The dark period is indicated by shaded areas. In contrast to plants with C3 or C4 metabolism, CAM plants open their stomata and fix CO2 at night. (From Gibson and Nobel 1986.) water. Their stomata are closed all the time, and the CO2 released by respiration is refixed into malate. This process, which has been called CAM idling, allows the plant to sur-vive for prolonged periods of time while losing remarkably little water.
Discrimination of Carbon Isotopes Reveals Different Photosynthetic Pathways Atmospheric CO2 contains the naturally occurring carbon isotopes 12C, 13C, and 14C in the proportions 98.9%, 1.1%, and 10–10%, respectively. 14CO2 is present in such small quantities that it has no physiological relevance, but 13CO2 is different. The chemical properties of 13CO2 are identical to those of 12CO2, but because of the slight difference in mass (2.3%), most plants assimilate less 13CO2 than 12CO2.
In other words, plants discriminate against the heavier iso-tope of carbon, and they have smaller ratios of 13C to 12C than are found in atmospheric CO2. How effective are plants at distinguishing between the two carbon isotopes?
Although discrimination against 13C is subtle, the isotope composition of plants reveals a wealth of information.
Carbon isotope composition is measured by use of a mass spectrometer, which yields the following ratio: (9.1) The isotope composition of plants, δ13C, is quantified on a per mil (–‰) basis: (9.2) where the standard represents the carbon isotopes con-tained in a fossil belemnite from the Pee Dee limestone for-mation of South Carolina. The δ13C of atmospheric CO2 has a value of –8 ‰, meaning that there is less 13C in the atmos-pheric CO2 than is found in the carbonate of the belemnite standard. What are some typical values for carbon isotope ratios of plants? C3 plants have a δ13C of about –28 ‰; C4 plants have an average value of –14 ‰ (Farquhar et al.
1989). Both C3 and C4 plants have less 13C than the isotope standard, which means that there has been a discrimination against 13C during the photosynthetic process. Because the per mil calculation involves multiplying by 1000, the actual isotope discrimination is small. Nonethe-less, differences in carbon isotope discrimination are easily detectable with mass spectrometers. For example, measur-ing the δ13C of table sugar (sucrose) makes it possible to determine if the sucrose came from sugar beet (a C3 plant) or sugarcane (a C4 plant).
What is the physiological basis for 13C depletion in plants? One reason in both C3 and C4 plants is diffusion.
CO2 diffuses from air outside of the leaf to the carboxyla-tion sites within leaves. Because 12CO2 is lighter than 13CO2, it diffuses slightly faster toward the carboxylation site, cre-ating an effective diffusion discrimination of –4.4 ‰. How-ever, the largest isotope discrimination step is the carboxy-lation reaction catalyzed by rubisco (Farquhar et al. 1989).
Rubisco has an intrinsic discrimination value against 13C of –30 ‰. By contrast, PEP carboxylase, the primary CO2 fixation enzyme of C4 plants, has a much smaller isotope discrimination effect (about –2 to –6 ‰). Thus the inherent difference between the discrimination effects of the two car-boxylating enzymes causes the different isotope composi-tions observed in C3 and C4 plants (Farquhar et al. 1989).
Other physiological characteristics of plants affect isotope composition. One factor is the partial pressure of CO2 in the intercellular air spaces of leaves (Ci). In C3 plants the poten-tial discrimination by rubisco of –30 ‰ is not fully expressed because the availability of CO2 at the carboxylation site becomes a limiting factor restricting the discrimination by rubisco. More discrimination occurs when Ci is high, as when stomata are open. Open stomata also facilitate water loss. Thus, lower water use efficiency is correlated with greater discrimination against 13C (Farquhar et al. 1989).
Fossil fuels have a δ13C of about –26 ‰ because the car-bon in these deposits came from organisms that had a C3 carbon fixation pathway. Furthermore, measuring δ13C in fossil, carbonate-containing soils and fossil teeth makes it possible to determine that C4 photosynthesis developed and became prevalent relatively recently (see Web Topic 9.5).
CAM plants can have δ13C values that are intermediate between those of C3 and C4 plants. In CAM plants that fix CO2 at night via PEP carboxylase, δ13C is similar to that of C4 plants. However, when some CAM plants are well watered, they switch to C3 mode by opening their stomata and fixing CO2 during the day via rubisco. Under these conditions the isotope composition shifts more toward that of C3 plants. Thus the 13C/12C values of CAM plants reflect how much carbon is fixed via the C3 pathway versus the C4 pathway (see Web Topic 9.5).
Plants also fractionate other isotopes, such as 18O/16O and 15N/14N, and the various patterns of isotope enrich-ment or depletion can be used as indicators of particular metabolic pathways or features. PHOTOSYNTHETIC RESPONSES TO TEMPERATURE When photosynthetic rate is plotted as a function of tem-perature, the curve has a characteristic bell shape (Figure 9.22). The ascending arm of the curve represents a tempera-ture-dependent stimulation of photosynthesis up to an opti-mum; the descending arm is associated with deleterious effects, some of which are reversible while others are not.
Temperature affects all biochemical reactions of photo-synthesis, so it is not surprising that the responses to tem-perature are complex. We can gain insight into the under-lying mechanisms by comparing photosynthetic rates in air at normal and at high CO2 concentrations. At high CO2 (see Figure 9.22A), there is an ample supply of CO2 at the car-d13 1 1000 C = 0 00 sample standard R R − × R = 13 2 12 2 CO CO 188 Chapter 9 boxylation sites, and the rate of photosynthesis is limited primarily by biochemical reactions connected with electron transport (see Chapter 7). In these conditions, temperature changes have large effects on fixation rates.
At ambient CO2 concentrations (see Figure 9.22B), pho-tosynthesis is limited by the activity of rubisco, and the response reflects two conflicting processes: an increase in carboxylation rate with temperature and a decrease in the affinity of rubisco for CO2 as the temperature rises (see Chapter 8). These opposing effects dampen the temperature response of photosynthesis at ambient CO2 concentrations.
Respiration rates also increase as a function of temper-ature, and the interaction between photorespiration and photosynthesis becomes apparent in temperature re-sponses. Figure 9.23 shows changes in quantum yield as a function of temperature in a C3 plant and in a C4 plant. In the C4 plant the quantum yield remains constant with tem-perature, reflecting typical low rates of photorespiration.
In the C3 plant the quantum yield decreases with temper-ature, reflecting a stimulation of photorespiration by tem-perature and an ensuing higher energy demand per net CO2 fixed.
At low temperatures, photosynthesis is often limited by phosphate availability at the chloroplast (Sage and Sharkey 1987). When triose phosphates are exported from the chloroplast to the cytosol, an equimolar amount of inor-ganic phosphate is taken up via translocators in the chloro-plast membrane.
If the rate of triose phosphate utilization in the cytosol decreases, phosphate uptake into the chloroplast is inhib-ited and photosynthesis becomes phosphate limited (Geiger and Servaites 1994). Starch synthesis and sucrose synthesis decrease rapidly with temperature, reducing the demand for triose phosphates and causing the phosphate limitation observed at low temperatures.
The highest photosynthetic rates seen in temperature responses represent the so-called optimal temperature response. When these temperatures are exceeded, photo-synthetic rates decrease again. It has been argued that this optimal temperature is the point at which the capacities of the various steps of photosynthesis are optimally balanced, with some of the steps becoming limiting as the tempera-ture decreases or increases.
Optimal temperatures have strong genetic and physio-logical components. Plants of different species growing in habitats with different temperatures have different optimal temperatures for photosynthesis, and plants of the same Photosynthesis: Physiological and Ecological Considerations 189 0 10 20 30 40 10 20 30 Temperature (°C) CO2 assimilation (µmol m–2 s–1) 40 50 50 Saturating CO2 concentrations Ambient CO2 concentrations (A) (B) FIGURE 9.22 Changes in photosynthesis as a function of temperature at CO2 concentrations that saturate photosyn-thetic CO2 assimilation (A) and at normal atmospheric CO2 concentrations (B). Photosynthesis depends strongly on temperature at saturating CO2 concentrations. Note the sig-nificantly higher photosynthetic rates at saturating CO2 concentrations. (Redrawn from Berry and Björkman 1980.) 0.02 0.00 0.04 0.06 0.08 0.10 15 20 25 30 35 Leaf temperature (°C) Quantum yield (mol CO2 per absorbed quantum) 40 10 Atriplex rosea (C4 plant) Encelia californica (C3 plant) FIGURE 9.23 The quantum yield of photosynthetic carbon fixation in a C3 plant and in a C4 plant as a function of leaf temperature. In normal air, photorespiration increases with temperature in C3 plants, and the energy cost of net CO2 fixation increases accordingly. This higher energy cost is expressed in lower quantum yields at higher temperatures.
Because of the CO2 concentrating mechanisms of C4 plants, photorespiration is low in these plants, and the quantum yield does not show a temperature dependence. Note that at lower temperatures the quantum yield of C3 plants is higher than that of C4 plants, indicating that photosynthesis in C3 plants is more efficient at lower temperatures. (From Ehleringer and Björkman 1977.) species, grown at different temperatures and then tested for their photosynthetic responses, show temperature optima that correlate with the temperature at which they were grown. Plants growing at low temperatures maintain higher photosynthetic rates at low temperatures than plants grown at high temperatures.
These changes in photosynthetic properties in response to temperature play an important role in plant adaptations to different environments. Plants are remarkably plastic in their adaptations to temperature. In the lower temperature range, plants growing in alpine areas are capable of net CO2 uptake at temperatures close to 0°C; at the other extreme, plants living in Death Valley, California, have optimal rates of photosynthesis at temperatures approaching 50°C.
SUMMARY Photosynthetic activity in the intact leaf is an integral process that depends on many biochemical reactions. Dif-ferent environmental factors can limit photosynthetic rates.
Leaf anatomy is highly specialized for light absorption, and the properties of palisade and mesophyll cells ensure uniform light absorption throughout the leaf. In addition to the anatomic features of the leaf, chloroplast movements within cells and solar tracking by the leaf blade help max-imize light absorption. Light transmitted through upper leaves is absorbed by leaves growing beneath them.
Many properties of the photosynthetic apparatus change as a function of the available light, including the light compensation point, which is higher in sun leaves than in shade leaves. The linear portion of the light-response curve for photosynthesis provides a measure of the quantum yield of photosynthesis in the intact leaf. In temperate areas, quantum yields of C3 plants are generally higher than those of C4 plants.
Sunlight imposes a substantial heat load on the leaf, which is dissipated back into the air by long-wavelength radiation, by sensible heat loss, or by evaporative heat loss.
Increasing CO2 concentrations in the atmosphere are increas-ing the heat load on the biosphere. This process could cause damaging changes in the world’s climate, but it could also reduce the CO2 limitations on photosynthesis. At high pho-ton flux, photosynthesis in most plants is CO2 limited, but the limitation is substantially lower in C4 and CAM plants because of their CO2-concentrating mechanisms.
Diffusion of CO2 into the leaf is constrained by a series of different points of resistance. The largest resistance is usually that imposed by the stomata, so modulation of stomatal apertures provides the plant with an effective means of controlling water loss and CO2 uptake. Both stomatal and nonstomatal factors affect CO2 limitations on photosynthesis.
Temperature responses of photosynthesis reflect the temperature sensitivity of the biochemical reactions of pho-tosynthesis and are most pronounced at high CO2 concen-trations. Because of the role of photorespiration, the quan-tum yield is strongly dependent on temperature in C3 plants but is nearly independent of temperature in C4 plants.
Leaves growing in cold climates can maintain higher photosynthetic rates at low temperatures than leaves grow-ing in warmer climates. Leaves grown at high tempera-tures perform better at high temperatures than leaves grown at low temperatures do. Functional changes in the photosynthetic apparatus in response to prevailing tem-peratures in their environment have an important effect on the capacity of plants to live in diverse habitats.
Web Material Web Topics 9.1 Working with Light Amount, direction, and spectral quality are important parameters for the measurement of light.
9.2 Heat Dissipation from Leaves:The Bowen Ratio Sensible heat loss and evaporative heat loss are the most important processes in the regulation of leaf temperature.
9.3 Working with Gases This web topic explains how to work with mole fractions and other physical parameters of gases.
9.4 Calculating Important Parameters in Leaf Gas Exchange Gas exchange methods allow us to measure pho-tosynthesis and stomatal conductance in the intact leaf.
9.5 Isotope Discrimination The carbon isotope composition of plants reveals a wealth of information.
Web Essay 9.1 The Xanthophyll Cycle Molecular and biophysical studies are revealing the role of the xanthophyll cycle on the photo-protection of leaves.
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192 Chapter 9 Translocation in the Phloem 10 Chapter SURVIVAL ON LAND POSES SOME SERIOUS CHALLENGES to ter-restrial plants, foremost of which is the need to acquire and retain water.
In response to these environmental pressures, plants evolved roots and leaves. Roots anchor the plant and absorb water and nutrients; leaves absorb light and exchange gases. As plants increased in size, the roots and leaves became increasingly separated from each other in space.
Thus, systems evolved for long-distance transport that allowed the shoot and the root to efficiently exchange products of absorption and assimilation.
You will recall from Chapters 4 and 6 that the xylem is the tissue that transports water and minerals from the root system to the aerial portions of the plant. The phloem is the tissue that translocates the products of photosynthesis from mature leaves to areas of growth and storage, including the roots. As we will see, the phloem also redistributes water and various compounds throughout the plant body. These compounds, some of which initially arrive in the mature leaves via the xylem, can be either transferred out of the leaves without modification or metabolized before redistribution.
The discussion that follows emphasizes translocation in the phloem of angiosperms because most of the research has been conducted on that group of plants. Gymnosperms will be compared briefly to angiosperms in terms of the anatomy of their conducting cells and possible differences in their mechanism of translocation. First we will examine some aspects of translocation in the phloem that have been researched extensively and are thought to be well understood. These include the pathway and pat-terns of translocation, materials translocated in the phloem, and rates of movement.
In the second part of the chapter we will explore aspects of transloca-tion in the phloem that need further investigation. Some of these areas, such as phloem loading and unloading and the allocation and partition-ing of photosynthetic products, are being studied intensively at present.
PATHWAYS OF TRANSLOCATION The two long-distance transport pathways—the phloem and the xylem—extend throughout the plant body. The phloem is generally found on the outer side of both pri-mary and secondary vascular tissues (Figures 10.1 and 10.2). In plants with secondary growth the phloem consti-tutes the inner bark.
The cells of the phloem that conduct sugars and other organic materials throughout the plant are called sieve ele-ments. Sieve element is a comprehensive term that includes both the highly differentiated sieve tube elements typical of the angiosperms and the relatively unspecialized sieve cells of gymnosperms. In addition to sieve elements, the phloem tissue contains companion cells (discussed below) and parenchyma cells (which store and release food mole-cules). In some cases the phloem tissue also includes fibers and sclereids (for protection and strengthening of the tis-sue) and laticifers (latex-containing cells). However, only the sieve elements are directly involved in translocation.
The small veins of leaves and the primary vascular bun-dles of stems are often surrounded by a bundle sheath (see Figure 10.1), which consists of one or more layers of com-pactly arranged cells. (You will recall the bundle sheath cells involved in C4 metabolism discussed in Chapter 8.) In the vascular tissue of leaves, the bundle sheath surrounds the small veins all the way to their ends, isolating the veins from the intercellular spaces of the leaf.
We will begin our discussion of translocation pathways with the experimental evidence demonstrating that the sieve elements are the conducting cells in the phloem. Then we will examine the structure and physiology of these unusual plant cells.
Sugar Is Translocated in Phloem Sieve Elements Early experiments on phloem transport date back to the nineteenth century, indicating the importance of long-dis-tance transport in plants (see Web Topic 10.1). These clas-sical experiments demonstrated that removal of a ring of bark around the trunk of a tree, which removes the phloem, effectively stops sugar transport from the leaves to the roots without altering water transport through the xylem. When radioactive compounds became available, radiolabeled 14CO2 was used to show that sugars made in the photosynthetic process are translocated through the phloem sieve elements (see Web Topic 10.1).
Mature Sieve Elements Are Living Cells Highly Specialized for Translocation Detailed knowledge of the ultrastructure of sieve elements is critical to any discussion of the mechanism of transloca-tion in the phloem. Mature sieve elements are unique among living plant cells (Figures 10.3 and 10.4). They lack 194 Chapter 10 Secondary phloem Vascular cambium Pith 3 2 1 Secondary xylem FIGURE 10.1 Transverse section of a vascular bundle of trefoil, a clover (Trifolium). (130×) The primary phloem is toward the outside of the stem. Both the primary phloem and the primary xylem are surrounded by a bundle sheath of thick-walled sclerenchyma cells, which isolate the vascular tissue from the ground tissue. (© J. N. A.
Lott/Biological Photo Service.) Primary phloem Primary xylem Bundle sheath FIGURE 10.2 Transverse section of a 3-year-old stem of an ash (Fraxinus excelsior) tree. (27×) The numbers 1, 2, and 3 indicate growth rings in the secondary xylem. The old sec-ondary phloem has been crushed by expansion of the xylem. Only the most recent (innermost) layer of secondary phloem is functional. (© P. Gates/Biological Photo Service.) many structures normally found in living cells, even the undifferentiated cells from which mature sieve elements are formed. For example, sieve elements lose their nuclei and tonoplasts (vacuolar membrane) during development.
Microfilaments, microtubules, Golgi bodies, and ribosomes are also absent from the mature cells. In addition to the plasma membrane, organelles that are retained include somewhat modified mitochondria, plastids, and smooth endoplasmic reticulum. The walls are nonlignified, though they are secondarily thickened in some cases.
Translocation in the Phloem 195 Cytoplasm Modified plastid Plasma membrane Thickened primary wall Sieve plate Mitochondrion Nucleus Companion cell Sieve tube element Vacuole Branched plasmodesmata Smooth endoplasmic reticulum P-protein (B) Chloroplast Sieve plate pore Sieve tube element (A) Sieve plate Sieve plate pore Lateral sieve area FIGURE 10.3 Schematic drawings of mature sieve elements (sieve tube elements). (A) External view, showing sieve plates and lateral sieve areas. (B) Longitudinal section, showing two sieve tube ele-ments joined together to form a sieve tube. The pores in the sieve plates between the sieve tube ele-ments are open channels for transport through the sieve tube. The plasma membrane of a sieve tube element is continuous with that of its neighboring sieve tube element. Each sieve tube element is asso-ciated with one or more companion cells, which take over some of the essential metabolic functions that are reduced or lost during differentiation of the sieve tube elements. Note that the companion cell has many cytoplasmic organelles, whereas the sieve tube element has relatively few organelles. An ordi-nary companion cell is depicted here.
Companion cell Sieve tube elements FIGURE 10.4 Electron micrograph of a transverse section of ordinary companion cells and mature sieve tube elements.
(3600×) The cellular components are distributed along the walls of the sieve tube elements. (From Warmbrodt 1985.) Thus the sieve elements have a cellular structure differ-ent from that of tracheary elements of the xylem, which are dead at maturity, lack a plasma membrane, and have lig-nified secondary walls. As we will see, living cells are crit-ical to the mechanism of translocation in the phloem.
Sieve Areas Are the Prominent Feature of Sieve Elements Sieve elements (sieve cells and sieve tube elements) have characteristic sieve areas in their cell walls, where pores interconnect the conducting cells (see Figure 10.5). The sieve area pores range in diameter from less than 1 µm to approximately 15 µm. Unlike sieve areas of gymnosperms, the sieve areas of angiosperms can differentiate into sieve plates (see Figure 10.5 and Table 10.1).
Sieve plates have larger pores than the other sieve areas in the cell and are generally found on the end walls of sieve tube elements, where the individual cells are joined together to form a longitudinal series called a sieve tube (see Figure 10.3). Furthermore, the sieve plate pores of sieve tube elements are open channels that allow transport between cells (see Figure 10.5).
In contrast, all of the sieve areas are more or less the same in gymnosperms such as conifers. The pores of gymnosperm sieve areas meet in large median cavities in the middle of the wall. Smooth endoplasmic reticulum (SER) covers the sieve areas (Figure 10.6) and is continuous through the sieve pores and median cavity, as indicated by ER-specific staining.
Observation of living material with confocal laser scanning microscopy confirms that the observed distribution of SER is not an artifact of fixation (Schulz 1992).
Deposition of P-Protein and Callose Seals Off Damaged Sieve Elements The sieve tube elements of most angiosperms are rich in a phloem protein called P-protein (see Figure 10.3B) (Clark et al. 1997). (In classical literature, P-protein was called slime.) P-protein is found in all dicots and in many mono-cots, and it is absent in gymnosperms. It occurs in several different forms (tubular, fibrillar, granular, and crystalline) depending on the species and maturity of the cell.
In immature cells, P-protein is most evident as discrete bodies in the cytosol known as P-protein bodies. P-protein bodies may be spheroidal, spindle-shaped, or twisted and coiled. They generally disperse into tubular or fibrillar forms during cell maturation.
P-proteins have been characterized at the molecular level. For example, P-proteins from the genus Cucurbita consist of two major proteins: PP1, the phloem filament protein, and PP2, the phloem lectin. The gene that encodes PP1 in pumpkin (Cucurbita maxima) has sequence similar-ity to genes encoding cysteine proteinase inhibitors, sug-gesting a possible role in defense against phloem-feeding insects. Both PP1 and PP2 are thought to be synthesized in companion cells (discussed in the next section) and trans-ported via the plasmodesmata to the sieve elements, where they associate to form P-protein filaments and P-protein bodies (Clark et al. 1997).
P-protein appears to function in sealing off damaged sieve elements by plugging up the sieve plate pores. Sieve tubes are under very high internal turgor pressure, and the sieve elements in a sieve tube are connected through open sieve plate pores. When a sieve tube is cut or punctured, 196 Chapter 10 Unobstructed sieve plate pores Sieve element Wall between sieve elements Companion cell Parenchyma cell FIGURE 10.5 Sieve elements and open sieve plate pores. (A) Electron micrograph of a longitudinal section of two mature sieve elements (sieve tube elements), showing the wall between the sieve elements (called a sieve plate) in the hypocotyl of winter squash (Cucurbita maxima). (3685×) (B) The inset shows sieve plate pores in face view (4280×). In both images A and B, the sieve plate pores are open—that is, unobstructed by P-protein. (From Evert 1982.) TABLE 10.1 Characteristics of the two types of sieve elements in seed plants Sieve tube elements found in angiosperms 1. Some sieve areas are differentiated into sieve plates; individual sieve tube elements are joined together into a sieve tube.
2. Sieve plate pores are open channels.
3. P-protein is present in all dicots and many monocots.
4. Companion cells are sources of ATP and perhaps other compounds and, in some species, are transfer cells or intermediary cells.
Sieve cells found in gymnosperms 1. There are no sieve plates; all sieve areas are similar.
2. Pores in sieve areas appear blocked with membranes 3. There is no P-protein.
4. Albuminous cells sometimes function as companion cells.
Parenchyma cell Sieve element (B) (A) the release of pressure causes the contents of the sieve ele-ments to surge toward the cut end, from which the plant could lose much sugar-rich phloem sap if there were no sealing mechanism. (Sap is a general term used to refer to the fluid contents of plant cells.) When surging occurs, however, P-protein and other cellular inclusions are trapped on the sieve plate pores, helping to seal the sieve element and to prevent further loss of sap.
A longer-term solution to sieve tube damage is the pro-duction of callose in the sieve pores. Callose, a β-1,3-glu-can, is synthesized by an enzyme in the plasma membrane and is deposited between the plasma membrane and the cell wall. Callose is synthesized in functioning sieve ele-ments in response to damage and other stresses, such as mechanical stimulation and high temperatures, or in prepa-ration for normal developmental events, such as dormancy.
The deposition of wound callose in the sieve pores effi-ciently seals off damaged sieve elements from surrounding intact tissue. As the sieve elements recover from damage, the callose disappears from these pores.
Companion Cells Aid the Highly Specialized Sieve Elements Each sieve tube element is associated with one or more companion cells (see Figures 10.3B, 10.4, and 10.5). The division of a single mother cell forms the sieve tube ele-ment and the companion cell. Numerous plasmodesmata (see Chapter 1) penetrate the walls between sieve tube ele-ments and their companion cells, suggesting a close func-tional relationship and a ready exchange of solutes between the two cells. The plasmodesmata are often com-plex and branched on the companion cell side.
Companion cells play a role in the transport of photo-synthetic products from producing cells in mature leaves to the sieve elements in the minor (small) veins of the leaf.
They are also thought to take over some of the critical metabolic functions, such as protein synthesis, that are reduced or lost during differentiation of the sieve elements (Bostwick et al. 1992). In addition, the numerous mito-chondria in companion cells may supply energy as ATP to the sieve elements.
There are at least three different types of companion cells in the minor veins of mature, exporting leaves: “ordi-nary” companion cells, transfer cells, and intermediary cells. All three cell types have dense cytoplasm and abun-dant mitochondria.
Ordinary companion cells (Figure 10.7A) have chloro-plasts with well-developed thylakoids and a cell wall with a smooth inner surface. Of most significance, relatively few plasmodesmata connect this type of companion cell to any of the surrounding cells except its own sieve element. As a result, the symplast of the sieve element and its compan-ion cell is relatively, if not entirely, symplastically isolated from that of surrounding cells.
Transfer cells are similar to ordinary companion cells, except for the development of fingerlike wall ingrowths, particularly on the cell walls that face away from the sieve element (Figure 10.7B). These wall ingrowths greatly increase the surface area of the plasma membrane, thus increasing the potential for solute transfer across the mem-brane.
Because of the scarcity of cytoplasmic connections to surrounding cells and the wall ingrowths in transfer cells, the ordinary companion cell and the transfer cell are thought to be specialized for taking up solutes from the apoplast or cell wall space. Xylem parenchyma cells can also be modified as transfer cells, probably serving to retrieve and reroute solutes moving in the xylem, which is also part of the apoplast.
Though ordinary companion cells and transfer cells are relatively isolated symplastically from surrounding cells, there are some plasmodesmata in the walls of these cells.
The function of these plasmodesmata is not known. The fact that they are present indicates that they must have a function, and an important one, since the cost of having them is high: They are the avenues by which viruses become systemic in the plant. They are, however, difficult to study because they are so inaccessible.
Intermediary cells appear well suited for taking up solutes via cytoplasmic connections (Figure 10.7C). Inter-mediary cells have numerous plasmodesmata connecting them to surrounding cells, particularly to the bundle sheath cells. Although the presence of many plasmodesmatal con-nections to surrounding cells is their most characteristic feature, intermediary cells are also distinctive in having Translocation in the Phloem 197 FIGURE 10.6 Electron micrograph showing a sieve area (sa) linking two sieve cells of a conifer (Pinus resinosa). Smooth endoplasmic reticulum (SER) covers the sieve area on both sides and is also found within the pores and the extended median cavity. Plastids (P) are enclosed by the SER. (From Schulz 1990.) SER P P sa 1 µm Sieve cell Sieve cell numerous small vacuoles, as well as poorly developed thy-lakoids and a lack of starch grains in the chloroplasts.
In general, ordinary companion cells and transfer cells are found in plants that feature an apoplastic step in the transfer of sugars from mesophyll cells to sieve elements.
Companion cells and transfer cells transfer sugars from the apoplast to the symplast of the sieve elements and com-panion cells in the source. Intermediary cells, on the other hand, function in symplastic transport of sugars from mes-ophyll cells to sieve elements in plants where no apoplas-tic step appears to occur in the source leaf.
PATTERNS OF TRANSLOCATION: SOURCE TO SINK Sap in the phloem is not translocated exclusively in either an upward or a downward direction, and translocation in the phloem is not defined with respect to gravity. Rather, sap is translocated from areas of supply, called sources, to areas of metabolism or storage, called sinks.
Sources include any exporting organs, typically mature leaves, that are capable of producing photosynthate in excess of their own needs. The term photosynthate refers to products of photosynthesis. Another type of source is a storage organ during the exporting phase of its develop-ment. For example, the storage root of the biennial wild beet (Beta maritima) is a sink during the growing season of the first year, when it accumulates sugars received from the source leaves. During the second growing season the same root becomes a source; the sugars are remobilized and uti-lized to produce a new shoot, which ultimately becomes reproductive.
It is noteworthy that cultivated varieties of beets have been selected for the capacity of their roots to act as sinks during all phases of development. Thus, roots of the cul-tivated sugar beet (Beta vulgaris) can increase in dry mass during both the first and the second growing seasons, so 198 Chapter 10 (C) (A) Vascular parenchyma cell Ordinary companion cell Sieve elements Intermediary cell Bundle sheath cells (B) Sieve element Plasmodesmata Transfer cell Intermediary cell Sieve elements Parenchyma cell Wall ingrowths FIGURE 10.7 Electron micrographs of companion cells in minor veins of mature leaves. (A) Three sieve elements abut two intermediary cells and a more lightly stained ordi-nary companion cell in a minor vein from Mimulus cardi-nalis. (6585×) (B) A sieve element adjacent to a transfer cell with numerous wall ingrowths in pea (Pisum sativum).
(8020×) Such ingrowths greatly increase the surface area of the transfer cell’s plasma membrane, thus increasing the transfer of materials from the mesophyll to the sieve ele-ments. (C) A typical intermediary cell with numerous fields of plasmodesmata (arrows) connecting it to neighboring bundle sheath cells. These plasmodesmata are branched on both sides, but the branches are longer and narrower on the intermediary cell side. Minor-vein phloem was taken from heartleaf maskflower (Alonsoa warscewiczii). (4700×) (A and C from Turgeon et al. 1993, courtesy of R. Turgeon; B from Brentwood 1978.) the leaves serve as sources during both flowering and fruit-ing stages.
Sinks include any nonphotosynthetic organs of the plant and organs that do not produce enough photosyn-thetic products to support their own growth or storage needs. Roots, tubers, developing fruits, and immature leaves, which must import carbohydrate for normal devel-opment, are all examples of sink tissues. Both girdling and labeling studies support the source-to-sink pattern of translocation in the phloem.
Source-to-Sink Pathways Follow Anatomic and Developmental Patterns Although the overall pattern of transport in the phloem can be stated simply as source-to-sink movement, the specific pathways involved are often more complex. Not all sources supply all sinks on a plant; rather, certain sources prefer-entially supply specific sinks. In the case of herbaceous plants, such as sugar beet and soybean, the following gen-eralizations can be made.
Proximity.
The proximity of the source to the sink is a significant factor. The upper mature leaves on a plant usu-ally provide photosynthates to the growing shoot tip and young, immature leaves; the lower leaves supply predom-inantly the root system. Intermediate leaves export in both directions, bypassing the intervening mature leaves.
Development.
The importance of various sinks may shift during plant development. Whereas the root and shoot apices are usually the major sinks during vegetative growth, fruits generally become the dominant sinks dur-ing reproductive development, particularly for adjacent and other nearby leaves.
Vascular connections.
Source leaves preferentially sup-ply sinks with which they have direct vascular connections.
In the shoot system, for example, a given leaf is generally connected via the vascular system to other leaves directly above or below it on the stem. Such a vertical row of leaves is called an orthostichy. The number of internodes between leaves on the same orthostichy varies with the species. Fig-ure 10.8A shows the three-dimensional structure of the phloem in an internode of dahlia (Dahlia pinnata).
Modification of translocation pathways.
Interference with a translocation pathway by wounding or pruning can alter the patterns established by proximity and vascular Translocation in the Phloem 199 14 9 4 1 12 7 15 10 2 5 13 8 11 3 6 (B) 14CO2 10 2 4 7 9 6 11 8 3 1 5 (C) 14CO2 FIGURE 10.8 (A) Longitudinal view of a typical three-dimensional structure of the phloem in a thick section (from an internode of dahlia [Dahlia pinnata]). View here after clearing, staining with aniline blue, and observing under an epifluorescent microscope; the sieve plates are seen as numerous small dots because of the yellow staining of callosa in the sieve areas. Two large longitudinal vascu-lar bundles are prominent. This staining reveals the delicate sieve tubes forming the phloem network; two phloem anas-tomoses are marked by arrows. (B) Distribution of radioac-tivity from a single labeled source leaf in an intact plant.
The distribution of radioactivity in leaves of a sugar beet plant (Beta vulgaris) was determined 1 week after 14CO2 was supplied for 4 hours to a single source leaf (arrow). The degree of radioactive labeling is indicated by the intensity of shading of the leaves. Leaves are numbered according to their age; the youngest, newly emerged leaf is designated 1.
The 14C label was translocated mainly to the sink leaves directly above the source leaf (that is, sink leaves on the same orthostichy as the source; for example, leaves 1 and 6 are sink leaves directly above source leaf 14). (C) Same as B, except all source leaves on the side of the plant opposite the labeled leaf were removed 24 hours before labeling. Sink leaves on both sides of the plant now receive 14C-labeled assimilates from the source. (A courtesy of R. Aloni; B and C based on data from Joy 1964.) (A) connections that have been outlined here. In the absence of direct connections between source and sink, vascular inter-connections, called anastomoses (singular anastomosis) (see Figure 10.8A), can provide an alternative pathway. In sugar beet, for example, removing source leaves from one side of the plant can bring about cross-transfer of photosynthates to young leaves (sink leaves) on the pruned side (Figure 10.8C). Removal of the lower source leaves on a plant can force the upper source leaves to translocate materials to the roots, and removal of the upper source leaves can force lower source leaves to translocate materials to the upper parts of the plant.
The plasticity of the translocation pathway depends on the extent of the interconnections between vascular bun-dles and thus on the species and organs studied. In some species the leaves on a branch with no fruits cannot trans-port photosynthate to the fruits on an adjacent defoliated branch. But in other plants, such as soybean (Glycine max), photosynthate is transferred readily from a partly defruited side to a partly defoliated side.
MATERIALS TRANSLOCATED IN THE PHLOEM: SUCROSE, AMINO ACIDS, HORMONES, AND SOME INORGANIC IONS Water is the most abundant substance transported in the phloem. Dissolved in the water are the translocated solutes, mainly carbohydrates (Table 10.2). Sucrose is the sugar most commonly transported in sieve elements. There is always some sucrose in sieve element sap, and it can reach concentrations of 0.3 to 0.9 M.
Nitrogen is found in the phloem largely in amino acids and amides, especially glutamate and aspartate and their respective amides, glutamine and asparagine. Reported levels of amino acids and organic acids vary widely, even for the same species, but they are usually low compared with carbohydrates.
Almost all the endogenous plant hormones, including auxin, gibberellins, cytokinins, and abscisic acid (see Chap-ters 19, 20, 21, and 23), have been found in sieve elements.
The long-distance transport of hormones is thought to occur at least partly in the sieve elements. Nucleotide phos-phates and proteins have also been found in phloem sap.
Proteins found in the phloem include filamentous P-proteins (which are involved in the sealing of wounded sieve elements), protein kinases (protein phosphorylation), thioredoxin (disulfide reduction), ubiquitin (protein turnover), chaperones (protein folding), and protease inhibitors (protection of phloem proteins from degradation and defense against phloem-feeding insects) (Schobert et al. 1995; Yoo et al. 2000).
Inorganic solutes that move in the phloem include potassium, magnesium, phosphate, and chloride (see Table 10.2). In contrast, nitrate, calcium, sulfur, and iron are rela-tively immobile in the phloem.
We will begin the discussion of phloem content with a look at the methods used to identify materials translocated in the phloem. We will then examine the translocated sug-ars and the complexities of nitrogen transport in the plant.
Phloem Sap Can Be Collected and Analyzed The collection of phloem sap has been experimentally chal-lenging (see Web Topic 10.2). A few species exude phloem sap from wounds that sever sieve elements, making it pos-sible to collect relatively pure samples of phloem sap.
Another approach is to use the stylet of an aphid as a “nat-ural syringe.” Aphids are small insects that feed by inserting their mouthparts, consisting of four tubular stylets, into a single sieve element of a leaf or stem. Sap can be collected from aphid stylets cut from the body of the insect, usually with a laser, after the aphid has been anesthetized with CO2. The high turgor pressure in the sieve element forces the cell contents through the stylet to the cut end, where they can be collected. Exudate from severed stylets provides a fairly accurate picture of the composition of phloem sap (see Web Topic 10.2). Exudation from severed stylets can continue for hours, suggesting that the aphid prevents the plant’s normal sealing mechanisms from operating.
Sugars Are Translocated in Nonreducing Form Results from analyses of collected sap indicate that the translocated carbohydrates are all nonreducing sugars.
Reducing sugars, such as glucose and fructose, contain an exposed aldehyde or ketone group (Figure 10.9A). In a nonreducing sugar, such as sucrose, the ketone or aldehyde group is reduced to an alcohol or combined with a simi-lar group on another sugar (Figure 10.9B). Most researchers believe that the nonreducing sugars are the major com-pounds translocated in the phloem because they are less reactive than their reducing counterparts.
Sucrose is the most commonly translocated sugar; many of the other mobile carbohydrates contain sucrose bound to varying numbers of galactose molecules. Raffinose consists 200 Chapter 10 TABLE 10.2 The composition of phloem sap from castor bean (Ricinus communis), collected as an exudate from cuts in the phloem Component Concentration (mg mL–1) Sugars 80.0–106.0 Amino acids 5.2 Organic acids 2.0–3.2 Protein 1.45–2.20 Potassium 2.3–4.4 Chloride 0.355–0.675 Phosphate 0.350–0.550 Magnesium 0.109–0.122 Source: Hall and Baker 1972.
Translocation in the Phloem 201 H C C C OH H O HO C H H C OH H CH2OH OH D-Glucose C CH2OH C O HO C H H C OH H CH2OH OH D-Fructose HO C C C H H O HO C H H C OH H CH2OH OH D-Mannose OH HO HO O O CH2 CH2OH OH HO HO O O CH2 OH HO HO O O CH2 OH OH HO O O OH HO O CH2OH HOH2C C CH2OH C H HO C H HO H C OH H CH2OH OH D-Mannitol C HO O C C C C OH H H H H H H H N O C H2N O C C C C OH H H H H H H H N O C C H2N O N C OH H H N C H2N O H O C HN C N H C NH2 NH O O H C N COOH CH2CH2CH2C H2N H O H C O NH2 Aldehyde The reducing groups are aldehyde (glucose and mannose) and ketone (fructose) groups.
Ketone Aldehyde (A) Reducing sugars, which are not generally translocated in the phloem (B) Compounds commonly translocated in the phloem Sugar alcohol Nonreducing sugar Amino acid Glutamic acid Allantoic acid Allantoin Ureides Citrulline Amide Glutamine Galactose Galactose Galactose Glucose Fructose Sucrose is a disaccharide made up of one glucose and one fructose molecule. Raffinose, stachyose, and verbascose contain sucrose bound to one, two, or three galactose molecules, respectively.
Glutamic acid, an amino acid, and glutamine, its amide, are important nitrogenous compounds in the phloem, in addition to aspartate and asparagine.
Species with nitrogen-fixing nodules also utilize ureides as transport forms of nitrogen.
Mannitol is a sugar alcohol formed by the reduction of the aldehyde group of mannose. Stachyose Verbascose Raffinose Sucrose FIGURE 10.9 Structures of com-pounds not normally translo-cated in the phloem (A) and of compounds commonly translo-cated in the phloem (B).
of sucrose and one galactose molecule, stachyose consists of sucrose and two galactose molecules, and verbascose consists of sucrose and three galactose molecules (see Figure 10.9B).
Translocated sugar alcohols include mannitol and sorbitol.
Phloem and Xylem Interact to Transport Nitrogenous Compounds Nitrogen is transported throughout the plant in either inorganic or organic form, with the predominant form depending on several factors, including the transport path-way. Whereas nitrogen is transported in the phloem almost entirely in organic form, in the xylem it can be transported either as nitrate or as part of an organic molecule. (see Chapter 12). Usually the same group of organic molecules carries nitrogen in both the xylem and the phloem.
The form in which nitrogen is transported in the xylem depends on the species studied. Species that do not form a glutamine (see Figure 10.9B).
Species with nitrogen-fixing nodules on their roots (see Chapter 12) depend on atmospheric nitrogen, rather than on soil nitrate, as their major nitrogen source. After being converted to an organic form, this nitrogen is transported in the xylem to the shoot, usually in the form of amides or ureides such as allantoin, allantoic acid, or citrulline (see Figure 10.9B).
Whenever nitrogen is assimilated into organic com-pounds in the roots, both the energy and the carbon skele-tons required for assimilation are derived from photosyn-thates transported to the roots via the phloem. Nitrogen levels in mature leaves are quite stable, indicating that at least some of the excess nitrogen continuously arriving via the xylem is redistributed via the phloem to fruits or younger leaves. (See Web Topic 10.3 for information on nitrogen transport in the soybean.) Finally, levels of nitrogenous compounds in the phloem are quite high during leaf senescence. In woody species, senescing leaves mobilize and export nitrogenous com-pounds to the woody tissues for storage; in herbaceous plants nitrogen is exported generally to the seeds. Other solutes, such as mineral ions, are redistributed from senesc-ing leaves in the same manner.
RATES OF MOVEMENT The rate of movement of materials in the sieve elements can be expressed in two ways: as velocity, the linear distance traveled per unit time, or as mass transfer rate, the quantity of material passing through a given cross section of phloem or sieve elements per unit time. Mass transfer rates based on the cross-sectional area of the sieve elements are pre-ferred because the sieve elements are the conducting cells of the phloem. Values for mass transfer rate range from 1 to 15 g h–1 cm–2 of sieve elements (see Web Topic 10.4).
In early publications reporting on rates of transport in the phloem, the units of velocity were centimeters per hour (cm h–1), and the units of mass transfer were grams per hour per square centimeter (g h–1 cm–2) of phloem or sieve elements. The currently preferred units (SI units) are meters (m) or millimeters (mm) for length, seconds (s) for time, and kilograms (kg) for mass.
Velocities of Phloem Transport Far Exceed the Rate of Diffusion Both velocities and mass transfer rates can be measured with radioactive tracers. (Methods of measuring mass transfer rates are described in Web Topic 10.4.) In the sim-plest type of experiment for measuring velocity, 11C- or 14C-labeled CO2 is applied for a brief period of time to a source leaf (pulse labeling), and the arrival of label at a sink tissue or at a particular point along the pathway is monitored with an appropriate detector.
The length of the translocation pathway divided by the time interval required for label to be first detected at the sink yields a measure of velocity. A more accurate mea-surement of velocity is obtained from monitoring the arrival of label at two points along the pathway. This method excludes from the measurement the time required for fixation of labeled carbon by photosynthesis, for its incorporation into transport sugar, and for accumulation of sugar in the sieve elements of the source leaf.
In general, velocities measured by a variety of tech-niques average about 1 m h–1 and range from 0.3 to 1.5 m h–1 (30–150 cm h–1). Transport velocities in the phloem are clearly quite high, well in excess of the rate of diffusion over long distances. Any proposed mechanism of phloem translocation must account for these high velocities.
THE MECHANISM OF TRANSLOCATION IN THE PHLOEM: THE PRESSURE-FLOW MODEL The mechanism of phloem translocation in angiosperms is best explained by the pressure-flow model, which accounts for most of the experimental and structural data currently available. We will see in this discussion that the pressure-flow model explains phloem translocation as a flow of solu-tion (bulk flow) driven by an osmotically generated pres-sure gradient between source and sink.
In early research on phloem translocation, both active and passive mechanisms were considered. All theories, both active and passive, assume an energy requirement in both sources and sinks. In sources, energy is necessary to move photosynthate from producing cells into the sieve elements.
This movement of photosynthate is called phloem loading, and it is discussed in detail later in the chapter. In sinks, energy is 202 Chapter 10 symbiotic association with nitrogen-fixing microorganisms usually depend on soil nitrate as their major nitrogen source (see Chapter 12). In the xylem of these species, nitrogen is usually present in the form of both nitrate and nitrogen-rich organic molecules, particularly the amides asparagine and essential for some aspects of movement from sieve elements to sink cells, which store or metabolize the sugar. This move-ment of photosynthate from sieve elements to sink cells is called phloem unloading and will also be discussed later.
The passive mechanisms of phloem transport further assume that energy is required in the sieve elements of the path between sources and sinks simply to maintain struc-tures such as the cell plasma membrane and to recover sug-ars lost from the phloem by leakage. The pressure-flow model is an example of a passive mechanism. The active theories, on the other hand, postulate an additional expen-diture of energy by path sieve elements in order to drive translocation itself (Zimmermann and Milburn 1975).
A Pressure Gradient Drives Translocation Diffusion is far too slow to account for the velocities of solute movement observed in the phloem. Translocation velocities average 1 m h–1; the rate of diffusion is 1 m per 32 years! (See Chapter 3 for a discussion of diffusion veloc-ities and the distances over which diffusion is an effective transport mechanism.) The pressure-flow model, first proposed by Ernst Münch in 1930, states that a flow of solution in the sieve elements is driven by an osmotically generated pressure gra-dient between source and sink (∆Yp). The pressure gradi-ent is established as a consequence of phloem loading at the source and phloem unloading at the sink.
Recall from Chapter 3 (Equation 3.6) that Yw = Ys + Yp; that is, Yp = Yw − Ys. In source tissues, energy-driven phloem loading leads to an accumulation of sugars in the sieve elements, generating a low (negative) solute poten-tial (∆Ys) and causing a steep drop in the water potential (∆Yw). In response to the water potential gradient, water enters the sieve elements and causes the turgor pressure (Yp) to increase.
At the receiving end of the translocation pathway, phloem unloading leads to a lower sugar concentration in the sieve elements, generating a higher (more positive) solute potential in the sieve elements of sink tissues. As the water potential of the phloem rises above that of the xylem, water tends to leave the phloem in response to the water potential gradient, causing a decrease in turgor pressure in the sieve elements of the sink. Figure 10.10 illustrates the pressure-flow hypothesis.
If no cross-walls were present in the translocation path-way—that is, if the entire pathway were a single mem-brane-enclosed compartment—the different pressures at the source and sink would rapidly equilibrate. The pres-ence of sieve plates greatly increases the resistance along the pathway and results in the generation and mainte-nance of a substantial pressure gradient in the sieve ele-ments between source and sink. The sieve element con-tents are physically pushed along the translocation pathway as a bulk flow, much like water flowing through a garden hose.
Close inspection of the water potential values shown in Figure 10.10 shows that water in the phloem is moving against a water potential gradient from source to sink. Such water movement does not violate the laws of thermodynamics because the water is moving by bulk flow rather than by osmosis. That is, no membranes are crossed during trans-port from one sieve tube to another, and solutes are mov-ing at the same rate as the water molecules.
Under these conditions, the solute potential, Ys, cannot contribute to the driving force for water movement, although it still influences the water potential. Water move-ment in the translocation pathway is therefore driven by the pressure gradient rather than by the water potential gradi-ent. Of course, the passive, pressure-driven, long-distance translocation in the sieve tubes ultimately depends on the active, short-distance transport mechanisms involved in phloem loading and unloading. These active mechanisms are responsible for setting up the pressure gradient.
The Predictions of the Pressure-Flow Model Have Been Confirmed Some important predictions emerge from the pressure-flow model: • The sieve plate pores must be unobstructed. If P-pro-tein or other materials blocked the pores, the resistance to flow of the sieve element sap would be too great.
• True bidirectional transport (i.e., simultaneous transport in both directions) in a single sieve element cannot occur. A mass flow of solution precludes such bidirec-tional movement because a solution can flow in only one direction in a pipe at any one time. Solutes within the phloem can move bidirectionally, but in different sieve elements or at different times.
• Great expenditures of energy are not required in order to drive translocation in the tissues along the path, although energy is required to maintain the structure of the sieve elements and to reload any sug-ars lost to the apoplast by leakage. Therefore, treat-ments that restrict the supply of ATP in the path, such as low temperature, anoxia, and metabolic inhibitors, should not stop translocation.
• The pressure-flow hypothesis demands the presence of a positive pressure gradient. Turgor pressure must be higher in sieve elements of sources than in sieve elements of sinks, and the pressure difference must be large enough to overcome the resistance of the path-way and to maintain flow at the observed velocities.
The available evidence testing these predictions supports the pressure-flow hypothesis.
Sieve Plate Pores Are Open Channels Ultrastructural studies of sieve elements are challenging because of the high internal pressure in these cells. When Translocation in the Phloem 203 the phloem is excised or killed slowly with chemical fixa-tives, the turgor pressure in the sieve elements is released.
The contents of the cell, including P-protein, surge toward the point of pressure release and, in the case of sieve tube elements, accumulate on the sieve plates. This accumula-tion is probably the reason that many earlier electron micrographs show sieve plates that are obstructed.
Newer, rapid freezing and fixation techniques provide reliable pictures of undisturbed sieve elements. Electron micrographs of sieve tube elements prepared by such tech-niques show that P-protein is usually found along the periphery of the sieve tube elements (see Figures 10.3, 10.4, and 10.5), or it is evenly distributed throughout the lumen of the cell. Furthermore, the pores contain P-protein in sim-ilar positions, lining the pore or in a loose network. The open condition of the pores, seen in many species, such as cucurbits, sugar beet, and bean (e.g., see Figure 10.5), sup-ports the pressure-flow model.
In addition to obtaining the structural evidence provided by electron microscopy, it is important to determine whether the sieve plate pores are open in the intact tissue. The use of confocal laser scanning microscopy, which allows for the direct observation of translocation through living sieve ele-ments, addresses this question (Knoblauch and van Bel 1998). Such experiments show that the sieve plate pores of living, translocating sieve elements are open (Figure 10.11).
Bidirectional Transport Cannot Be Seen in Single Sieve Elements Researchers have investigated bidirectional transport by applying two different radiotracers to two source leaves, one above the other (Eschrich 1975). Each leaf receives one 204 Chapter 10 Xylem vessel elements Phloem sieve elements Companion cell Yw = –0.8 MPa Yp = –0.7 MPa Ys = –0.1 MPa H2O H2O H2O H2O Yw = –0.6 MPa Yp = –0.5 MPa Ys = –0.1 MPa Active phloem unloading increases the solute potential, water flows out, and a lower turgor pressure results.
Active phloem loading into sieve elements decreases the solute potential, water enters, and high turgor pressure results.
Yw = –0.4 MPa Yp = 0.3 MPa Ys = –0.7 MPa H2O Source cell H2O Sink cell Pressure-driven bulk flow of water and solute from source to sink Sucrose Sucrose Transpiration stream Yw = –1.1 MPa Yp = 0.6 MPa Ys = –1.7 MPa Sugar at the source, illustrated here by sucrose (red spheres) is actively loaded into the sieve element–companion cell complex.
At the sink, sugars are unloaded.
FIGURE 10.10 Pressure-flow model of translocation in the phloem. Possible values for Yw, Yp, and Ys in the xylem and phloem are illustrated. (After Nobel 1991.) Translocation in the Phloem 205 Main vein Translocation to intact plant Confocal microscope objective Basal window Apical window Phloem-mobile dye added here Direction of translocation Leaf blade (A) 15 µm of the tracers, and a point between the two sources is mon-itored for the presence of both tracers. Transport in two directions has often been detected in sieve elements of different vascular bundles in stems.
Transport in two directions has also been seen in adjacent sieve elements of the same bundle in petioles. Bidirectional transport in adjacent sieve elements can occur in the peti-ole of a leaf that is undergoing the transition from sink to source and simultaneously importing and exporting pho-tosynthates through its petiole. However, simultaneous bidirectional transport in a single sieve element has never been demonstrated.
Translocation Rate Is Typically Insensitive to the Energy Supply of the Path Tissues In plants that can survive periods of low temperature, such as sugar beet, rapidly chilling a short segment of the peti-ole of a source leaf to approximately 1°C does not cause sustained inhibition of mass transport out of the leaf (Fig-ure 10.12). Rather, there is a brief period of inhibition, after which transport slowly returns to the control rate. Chilling reduces respiration rate and both the synthesis and the con-sumption of ATP in the petiole by about 90%, at a time when translocation has recovered and is proceeding nor-mally. These experiments show that the energy require-ment for transport through the pathway of these plants is small, consistent with the pressure-flow hypothesis.
Extreme treatments that inhibit all energy metabolism do inhibit translocation. For example, in bean (Phaseolus vulgaris), treating the petiole of a source leaf with a meta-bolic inhibitor (cyanide) inhibited translocation out of the FIGURE 10.11 Translocation in living, functional sieve ele-ments of a leaf attached to an intact broad bean (Vicia faba) plant. (A) Two windows were sliced parallel to the epider-mis on the lower side of the main vein of a mature leaf, exposing the phloem tissue. The objective of the laser con-focal microscope was positioned over the basal window. A phloem-mobile fluorescent dye was added at the apical window. If translocation occurred, the dye would become visible in the microscope at the basal window of the leaf. In this way it could be demonstrated that the sieve elements being observed were alive and functional. (B,C) Phloem tis-sue of bean doubly stained with a locally applied fluores-cent dye (red) that primarily stains membranes, and a translocated fluorescent dye (green). Protein (arrows) deposited against the plasma membrane and the sieve plate does not impede translocation. A crystalline P-protein body (asterisk) is stained by the green dye. Plastids (arrowheads) are evenly distributed around the periphery of the sieve element. CC = companion cell, SP = sieve plate. See also Web Topic 10.8. (From Knoblauch and van Bel 1998; cour-tesy of A. van Bel.) 15 µm (C) SE SE SE CC CC CC SP (B) SE SE SE SP CC leaf. However, examination of the treated tissue by electron microscopy revealed blockage of the sieve plate pores by cellular debris (Giaquinta and Geiger 1977). Clearly, these results do not bear on the question of whether energy is required for translocation along the pathway.
Pressure Gradients Are Sufficient to Drive a Mass Flow of Solution Turgor pressure in sieve elements can be either calculated from the water potential and solute potential (Yp = Yw − Ys) or measured directly. The most effective technique uses micromanometers or pressure transducers sealed over exuding aphid stylets (see Figure 10.2.A in Web Topic 10.2) (Wright and Fisher 1980). The data obtained are accurate because aphids pierce only a single sieve element, and the plasma membrane apparently seals well around the aphid stylet. When the turgor pressure of sieve elements is mea-sured by this technique, the pressure at the source is higher than that at the sink.
In soybean, the observed pressure difference between source and sink has been shown to be sufficient to drive a mass flow of solution through the pathway, taking into account the path resistance (caused mainly by the sieve plate pores), the path length, and the velocity of translocation (Fisher 1978). The actual pressure difference between source and sink was calculated from the water potential and solute potential to be 0.41 MPa, and the pressure difference required for translocation by pressure flow was calculated to be 0.12 to 0.46 MPa. Thus the observed pressure difference appears to be sufficient to drive mass flow through the phloem.
We can therefore conclude that all the experiments and data described here support the operation of pressure flow in angiosperm phloem. The lack of an energy requirement in the pathway and the presence of open sieve plate pores provide definitive evidence for a mechanism in which the path phloem is relatively passive. The failure to detect bidi-rectional transport or motility proteins, as well as the pos-itive data on pressure gradients, is in accord with the pres-sure-flow hypothesis.
The Mechanism of Phloem Transport in Gymnosperms May Be Different Although pressure flow explains translocation in angio-sperms, it may not be sufficient for gymnosperms. Very lit-tle physiological information on gymnosperm phloem is available, and speculation about translocation in these species is based almost entirely on interpretations of elec-tron micrographs. As discussed previously, the sieve cells of gymnosperms are similar in many respects to sieve tube elements of angiosperms, but the sieve areas of sieve cells are relatively unspecialized and do not appear to consist of open pores (see Figure 10.6).
The pores in gymnosperms are filled with numerous membranes that are continuous with the smooth endoplas-mic reticulum adjacent to the sieve areas. Such pores are clearly inconsistent with the requirements of the pressure-flow hypothesis. Although these electron micrographs might be artifactual and fail to show conditions in the intact tissue, translocation in gymnosperms might involve a different mechanism—a possibility that requires further investigation.
PHLOEM LOADING: FROM CHLOROPLASTS TO SIEVE ELEMENTS Several transport steps are involved in the movement of photosynthate from the mesophyll chloroplasts to the sieve elements of mature leaves, which is called phloem loading (Oparka and van Bel 1992): 1. Triose phosphate formed by photosynthesis during the day (see Chapter 8) is transported from the chloroplast to the cytosol, where it is converted to sucrose. During the night, carbon from stored starch exits the chloroplast probably in the form of glucose and is converted to sucrose. (Other transport sugars are later synthesized from sucrose in some species.) 2. Sucrose moves from the mesophyll cell to the vicinity of the sieve elements in the smallest veins of the leaf (Figure 10.13). This short-distance transport pathway usually covers a distance of only two or three cell diameters.
3. In a process called sieve element loading, sugars are transported into the sieve elements and companion cells. In most of the species studied so far, sugars become more concentrated in the sieve elements and 206 Chapter 10 60 40 20 50 30 10 80 120 160 200 240 280 320 360 400 440 460 Time (minutes) Translocation rate (µg C min–1 dm2) 30°C 1°C 25°C FIGURE 10.12 Loss of metabolic energy resulting from the chilling of the leaf petiole partially reduces the rate of translocation in sugar beet (Beta vulgaris), although translo-cation rates recover with time. The fact that translocation recovers when ATP production and utilization are largely inhibited by chilling indicates that the energy requirement for translocation is small. 14CO2 was supplied to a source leaf, and a 2 cm portion of its petiole was chilled to 1°C.
Translocation was monitored by the arrival of 14C at a sink leaf. (dm [decimeter] = 0.1 meter) (Data from Geiger and Sovonick 1975.) companion cells than in the mesophyll. Note that with respect to loading, the sieve elements and companion cells are often considered a functional unit, called the sieve element–companion cell complex. Once inside the sieve elements, sucrose and other solutes are translo-cated away from the source, a process known as export. Translocation through the vascular system to the sink is referred to as long-distance transport.
As discussed earlier, the processes of loading at the source and unloading at the sink provide the driving force that generates the pressure gradient pushing phloem sap in long-distance transport and are thus of considerable basic, as well as agricultural, importance. A thorough understanding of these mechanisms should provide the basis of technology aimed at enhancing crop productivity by increasing the accumulation of photosynthate by edible sink tissues, such as cereal grains.
Photosynthate Can Move from Mesophyll Cells to the Sieve Elements via the Apoplast or the Symplast We have seen that solutes (mainly sugars) in source leaves must move from the photosynthesizing cells in the meso-phyll to the veins. Sugars might move entirely through the symplast (cytoplasm) via the plasmodesmata, or they might enter the apoplast at some point en route to the phloem (Fig-ure 10.14). (See Figure 4.3 for a general description of the symplast and apoplast.) In the latter case, the sugars are actively loaded from the apoplast into the sieve elements and companion cells by an energy-driven, selective transporter located in the plasma membranes of these cells. In fact, the apoplastic and symplastic routes are used in different species.
Early research on phloem loading focused on the apoplastic pathway. Apoplastic phloem loading leads to three basic predictions (Grusak et al. 1996): (1) Transported sugars should be found in the apoplast; (2) in experiments in which sugars are supplied to the apoplast, the exoge-nously supplied sugars should accumulate in sieve ele-ments and companion cells; and (3) inhibition of sugar uptake from the apoplast should result in inhibition of export from the leaf. Many studies devoted to testing these predictions have provided solid evidence for apoplastic loading in several species (see Web Topic 10.5).
Sucrose Uptake in the Apoplastic Pathway Requires Metabolic Energy In source leaves, sugars become more concentrated in the sieve elements and companion cells than in the mesophyll.
This difference in solute concentration, found in most of the species studied, can be demonstrated through measure-ment of the osmotic potential (Ys) of the various cell types in the leaf (see Chapter 3).
In sugar beet, the osmotic potential of the mesophyll is approximately –1.3 MPa, and the osmotic potential of the sieve elements and companion cells is about –3.0 MPa (Geiger et al. 1973). Most of this difference in osmotic potential is thought to result from accumulated sugar, specifically sucrose because sucrose is the major transport sugar in this species. Experimental studies have also demonstrated that both externally supplied sucrose and sucrose made from photosynthetic products accumulate in the sieve elements and companion cells of the minor veins of sugar beet source leaves (Figure 10.15).
The fact that sucrose is at a higher concentration in the sieve element–companion cell complex than in surround-ing cells indicates that sucrose is actively transported against its chemical-potential gradient. The dependence of sucrose accumulation on active transport is supported by the fact that treating source tissue with respiratory inhibitors both decreases ATP concentration and inhibits loading of exogenous sugar. On the other hand, other metabolites, such as organic acids and hormones, may enter sieve elements passively (see Web Topic 10.6).
In the Apoplastic Pathway, Sieve Element Loading Involves a Sucrose–H+ Symporter A sucrose–H+ symporter is thought to mediate the trans-port of sucrose from the apoplast into the sieve element–companion cell complex. Recall from Chapter 6 Translocation in the Phloem 207 Vascular parenchyma cell Phloem parenchyma cell Part of tracheary element in the xylem Sieve element Ordinary companion cell Bundle sheath cell FIGURE 10.13 Electron micrograph showing the relation-ship between the various cell types of a small vein in a source leaf of sugar beet (Beta vulgaris). Photosynthetic cells (mesophyll cells) surround the compactly arranged cells of the bundle sheath layer. Photosynthate from the mesophyll must move a distance equivalent to several cell diameters before being loaded into the sieve elements.
(From Evert and Mierzwa 1985, courtesy of R. Evert.) that symport is a secondary transport process that uses the energy generated by the proton pump (see Figure 6.10A).
The energy dissipated by protons moving back into the cell is coupled to the uptake of a substrate, in this case sucrose (Figure 10.16).
High pH (low H+ concentration) in the apoplast reduces the uptake of exogenous sucrose into the sieve elements and companion cells of broad bean. This effect occurs because a low proton concentration in the apoplast reduces the driving force for proton diffusion into the symplast and for the sucrose–H+ symporter.
Data from molecular studies support the operation of a sucrose–H+ symporter in sieve element loading. Proton-pumping ATPases, localized by immunological techniques, have been found in the plasma membranes of companion cells of Arabidopsis and in transfer cells of broad bean. In transfer cells, the H+-ATPase molecules are most concen-trated in the plasma membrane infoldings that face the bundle sheath and phloem parenchyma cells (for details, see Web Topic 10.7).
Such localization suggests that the function of these H+-ATPases is to energize the transport of photosynthate from 208 Chapter 10 FIGURE 10.15 This autoradiograph shows that labeled sugar moves from the apoplast into sieve elements and compan-ion cells against its concentration gradient. A solution of 14C-labeled sucrose was applied for 30 minutes to the upper surface of a sugar beet (Beta vulgaris) leaf that had previ-ously been kept in darkness for 3 hours. The leaf cuticle was removed to allow penetration of the solution to the interior of the leaf. Label accumulates in the small veins, sieve ele-ments, and companion cells of the source leaf, indicating the ability of these cells to transport sucrose against its concen-tration gradient. (From Fondy 1975, courtesy of D. Geiger.) Sugar Sugar Sugar Plasma membrane Plasmodesma Mesophyll cell Bundle sheath cell Phloem parenchyma cell Companion cells Sieve elements CO2 Cell wall–apoplast pathway Small vein Cytoplasm–symplast pathway Active loading FIGURE 10.14 Schematic diagram of pathways of phloem loading in source leaves. In the totally symplastic pathway, sugars move from one cell to another in the plasmodes-mata, all the way from the mesophyll to the sieve elements.
In the partly apoplastic pathway, sugars enter the apoplast at some point. For simplicity, sugars are shown here enter-ing the apoplast near the sieve element–companion cell complex, but they could also enter the apoplast earlier in the path and then move to the small veins. In any case, the sugars are actively loaded into the companion cells and sieve elements from the apoplast. Sugars loaded into the companion cells are thought to move through plasmodes-mata into the sieve elements.
the apoplast to the sieve elements (Bouche-Pillon et al.
1994). Furthermore, the distribution of the H+-ATPases in companion cells of Arabidopsis appears to be correlated with the distribution of a sucrose–H+ symporter called SUC2 (DeWitt and Sussman 1995; Truernit and Sauer 1995). The SUC2 transporter has also been localized in companion cells of broad-leaved plantain, Plantago major (see Web Topic 10.7). H+-ATPases and sucrose–H+ symporters are some-times co-localized in the plasma membranes of sieve ele-ments (Langhans et al. 2001) rather than companion cells.
SUC2 is one of several sucrose–H+ symporters that have been cloned and localized in the phloem (Table 10.3). The carriers are found in plasma membranes of either sieve ele-ments (SUT1, SUT2, and SUT4) or companion cells (SUC2).
Work with SUT1 has shown that the messenger RNAs for symporters found in the sieve element membrane are syn-thesized in the companion cells (Kuhn et al. 1997). This finding agrees with the fact that sieve elements lack nuclei.
The symporter protein is probably also synthesized in the companion cells, since ribosomes do not appear to persist in mature sieve elements.
The roles played by the various carriers listed in Table 10.3 are still being elucidated. Most of the transporters are found in source, path, and sink tissues. SUT1, characterized as a high-affinity/low-capacity transporter found in the minor veins of source tissues, appears to be important in phloem loading. Potato plants transformed with antisense DNA to SUT1 showed reduced transporter activity, a reduction in root and tuber growth, and accumulation of starch and lipids in source leaves (Schulz et al. 1998).
SUT1 is also thought to play a role in the retrieval of sucrose lost in transit. The important role of SUT1 in phloem loading appears to be complemented by SUT4, a low-affinity/high-capacity carrier (Weise et al. 2000). SUT2, on the other hand, appears to function as a sucrose sensor.
This is indicated by findings showing that SUT2 is more highly expressed in sink and path tissues than in source leaves, and by the similarity between many structural fea-tures of SUT2 and yeast sugar sensors (Lalonde et al. 1999; Barker et al. 2000). Finally, uptake into companion cells appears to be the function of SUC2.
Regulating sucrose loading.
The mechanisms that reg-ulate the loading of sucrose from the apoplast to the sieve elements by the sucrose–H+ symporter await characteri-zation. Possible regulatory factors include the following: • The solute potential or, more likely, the turgor pressure of the sieve elements. A decrease in sieve element turgor below a certain threshold would lead to a compen-satory increase in loading.
Translocation in the Phloem 209 H+ H+ H+-ATPase H+ Sucrose H+ Sucrose Sucrose–H+ symporter Low H+ concentration High H+ concentration ATP ADP Pi + Sieve element–companion cell complex FIGURE 10.16 ATP-dependent sucrose transport in sieve element loading. In the cotransport model of sucrose load-ing into the symplast of the sieve element–companion cell complex, the plasma membrane ATPase pumps protons out of the cell into the apoplast, establishing a high proton con-centration there. The energy in this proton gradient is then used to drive the transport of sucrose into the symplast of the sieve element–companion cell complex through a sucrose–H+ symporter.
TABLE 10.3 Sucrose–H+ symporters in the phloem Carrier Location Species Affinity Source SUT1 Sieve elements Tobacco, tomato, potato High Kuhn et al. 1997 SUT2 Sieve elements Tomato Sensor Barker et al. 2000 SUT4 Sieve elements Arabidopsis, tomato, potato Low Weise et al. 2000 SUC2 Companion cells Arabidopsis, plantain — Truernit and Sauer, 1995; Stadler et al. 1995 • Sucrose concentration in the apoplast. High sucrose con-centrations in the apoplast would increase phloem loading.
• The available number of symporter protein molecules. The levels of SUT1 transporter mRNA and protein have been shown to be lower after 15 hours of darkness than after a light treatment. These data suggest that the concentration of SUT1 transporter molecules could regulate loading.
Other studies have shown that sucrose efflux into the apoplast is enhanced by potassium availability in the apoplast, suggesting that a better nutrient supply increases translocation to sinks and enhances sink growth.
Phloem Loading Appears to Be Symplastic in Plants with Intermediary Cells As discussed earlier, many results point to apoplastic phloem loading in species that have ordinary companion cells or transfer cells in the minor veins, and that transport only sucrose. On the other hand, a symplastic pathway has become evident in species that transport raffinose and stachyose in the phloem, in addition to sucrose, and that have intermediary cells in the minor veins. Some examples of such species are common coleus (Coleus blumei), squash (Cucurbita pepo), and melon (Cucumis melo) (see Web Topic 10.8).
The operation of a symplastic pathway requires the pres-ence of open plasmodesmata between the different cells in the pathway. Many species have numerous plasmodesmata at the interface between the sieve element–companion cell complex and the surrounding cells (see Figure 10.7C), and experimental studies have demonstrated symplastic conti-nuity in source leaves of some species (see Web Topic 10.8).
The Polymer-Trapping Model Explains Symplastic Loading in Source Leaves The composition of sieve element sap is generally different from the solute composition in tissues surrounding the phloem. This difference indicates that certain sugars are specifically selected for transport in the source leaf. The involvement of symporters in apoplastic phloem loading provides a clear mechanism for selectivity because sym-porters are specific for certain sugar molecules. Symplastic loading, on the other hand, depends on the diffusion of sugars from the mesophyll to the sieve elements via the plasmodesmata. It is more difficult to envision how diffu-sion through plasmodesmata during symplastic loading could be selective for certain sugars.
Furthermore, data from several species showing sym-plastic loading indicate that sieve elements and companion cells have a higher osmotic content than the mesophyll.
How could diffusion-dependent symplastic loading account for the observed selectivity for transported mole-cules and the accumulation of sugars against a concentra-tion gradient?
The polymer-trapping model (Figure 10.17) has been developed to address these questions (Turgeon and Gowan 210 Chapter 10 Plasmodesma Bundle sheath cell Intermediary cell Sieve element Glucose Fructose Sucrose Sucrose Raffinose Galactose Sucrose, synthesized in the mesophyll, diffuses from the bundle sheath cells into the intermediary cells through the abundant plasmodesmata.
In the intermediary cells, raffinose (and stachyose) are synthesized from sucrose and galactose, thus maintaining the diffusion gradient for sucrose. Because of their larger sizes, they are not able to diffuse back into the mesophyll.
Raffinose and stachyose are able to diffuse into the sieve elements. As a result, the concentration of transport sugar rises in the intermediary cells and the sieve elements. FIGURE 10.17 Polymer-trap-ping model of phloem load-ing. For simplicity, the trisac-charide stachyose is omitted.
(After van Bel 1992.) 1990). This model states that the sucrose synthesized in the mesophyll diffuses from the bundle sheath cells into the intermediary cells through the abundant plasmodesmata that connect the two cell types. In the intermediary cells, raffinose and stachyose (polymers made of three and four hexose sugars, respectively; see Figure 10.9B) are synthe-sized from the transported sucrose and from galactose.
Because of the anatomy of the tissue and the relatively large size of raffinose and stachyose, the polymers cannot diffuse back into the bundle sheath cells, but they can dif-fuse into the sieve element. Sucrose can continue to diffuse into the intermediary cells because its synthesis in the mes-ophyll and its utilization in the intermediary cells maintain the concentration gradient (see Figure 10.17).
The polymer-trapping model makes three predictions: 1. Sucrose should be more concentrated in the meso-phyll than in the intermediary cells.
2. The enzymes for raffinose and stachyose synthesis should be preferentially located in the intermediary cells.
3. The plasmodesmata linking the bundle sheath cells and the intermediary cells should exclude molecules larger than sucrose.
Many studies support the polymer-trapping model. For instance, all of the enzymes required to synthesize stachyose from sucrose have been found in intermediary cells. In melon, raffinose and stachyose are present in high concen-trations in intermediary cells, but not in mesophyll cells.
The Type of Phloem Loading Is Correlated with Plant Family and with Climate As discussed earlier, the operation of apoplastic and sym-plastic phloem-loading pathways is correlated with the transport sugar, the type of companion cell in the minor veins, and the number of plasmodesmata connecting the sieve elements and companion cells to the surrounding photosynthetic cells (Table 10.4) (van Bel et al. 1992): • Species showing apoplastic phloem loading translo-cate sucrose almost exclusively, have either ordinary companion cells or transfer cells in the minor veins, and possess few connections between the sieve ele-ment–companion cell complex and the surrounding cells.
• Species having symplastic phloem loading translo-cate oligosaccharides such as raffinose in addition to sucrose, have intermediary-type companion cells in the minor veins, and possess abundant connections between the sieve element–companion cell complex and the surrounding cells.
Plants that have abundant plasmodesmata between the phloem and surrounding cells are often trees, shrubs, or vines. Plants with few plasmodesmata at this interface are more typically herbaceous plants. In general, plants with abundant plasmodesmata between the phloem and sur-rounding cells tend to be found in tropical and subtropical regions, and plants with few plasmodesmata at this inter-face tend to be found in temperate and arid climates.
Translocation in the Phloem 211 TABLE 10.4 Patterns in apoplastic and symplastic loading Apoplastic loading Symplastic loading Transport sugar Sucrose Oligosaccharides in addition to sucrose Type of companion Ordinary companion cells Intermediary cells cell in the minor veins or transfer cells Number of plasmodesmata Few Abundant connecting the sieve elements and companion cells to surrounding cells Source: Drawings after van Bel et al. 1992.
Note: Some species may load both apoplastically and symplastically, since different types of companion cells can be found within the veins of a single species.
Xylem vessel Phloem parenchyma Sieve element Intermediary cell Companion cell Plasmodesmata There are, of course, intermediate cases and exceptions to these generalizations. Some species with apoplastic load-ing have more plasmodesmata linking their companion cells to surrounding cells than might be predicted from known apoplastically loading species (Goggin et al. 2001).
A number of species have more than one type of compan-ion cell in their minor veins. For example, coleus has both intermediary cells and ordinary companion cells. It has been suggested that the symplastic and apoplastic pathways may coexist in some species, simultaneously or at different times, in different sieve elements in the same vein or in sieve ele-ments in veins of different sizes (Turgeon et al. 2001).
Future research may reveal new loading pathways or combinations of pathways (Flora and Madore 1996). Cer-tainly, the evolution of different loading types and how these types adapt species to their environment will be important research areas in the future, as loading pathways are clarified in more species.
PHLOEM UNLOADING AND SINK-TO-SOURCE TRANSITION Now that we have learned about the events leading up to the export of sugars from sources, let’s take a look at phloem unloading. In many ways the events in sink tissues are simply the reverse of the events in sources. Transport into sink organs, such as developing roots, tubers, and reproductive structures, is termed import. The following steps are involved in the import of sugars into sink cells.
1. Sieve element unloading. This is the process by which imported sugars leave the sieve elements of sink tis-sues.
2. Short-distance transport. After sieve element unloading, the sugars are transported to cells in the sink by means of a short-distance transport pathway. This pathway has also been called post–sieve element transport.
3. Storage and metabolism. In the final step, sugars are stored or metabolized in sink cells.
These three transport steps together constitute phloem unloading, the movement of photosynthates from the sieve elements and their distribution to the sink cells that store or metabolize them (Oparka and van Bel 1992).
In this section we will discuss the following questions: Is phloem unloading symplastic or apoplastic? Is sucrose hydrolyzed during the process? Does phloem unloading require energy? Finally, we will examine the transition process by which a young, importing leaf becomes an exporting source leaf.
Phloem Unloading Can Occur via Symplastic or Apoplastic Pathways In sink organs, sugars move from the sieve elements to the cells that store or metabolize them. Sinks vary widely from growing vegetative organs (root tips and young leaves) to storage tissues (roots and stems) to organs of reproduction and dispersal (fruits and seeds). Because sinks vary so greatly in structure and function, there is no single scheme of phloem unloading. As in sources, the sugars may move entirely through the symplast via the plasmodesmata, or they may enter the apoplast at some point.
Figure 10.18 diagrams several possible phloem-unloading pathways. The unloading pathway appears to be completely symplastic in some young dicot leaves, such as sugar beet and tobacco (Figure 10.18A). Evidence for the symplastic pathway of unloading includes insensitivity to PCMBS (p-chloromercuribenzenesulfonic acid), a reagent that inhibits the transport of sucrose across plasma membranes but does not permeate the symplastic pathway. Meristematic and elon-gating regions of primary root tips also appear to unload symplastically. Sufficient plasmodesmata exist in these path-ways to support symplastic unloading.
In some sink organs, part of the phloem-unloading pathway is apoplastic (Figure 10.18B). In principle, the apoplastic step could be located at the site of the sieve ele-ment–companion cell complex (type 1 in Figure 10.18B), although this pattern has yet to receive experimental sup-port. The apoplastic step could also be farther removed from the sieve elements (type 2). This arrangement, typical of developing seeds, appears to be the most common in apoplastic phloem unloading.
An apoplastic step is required in developing seeds because there are no symplastic connections between the maternal tissues and the tissues of the embryo. Sugars exit the sieve elements (sieve element unloading) via a sym-plastic pathway and are transferred from the symplast to the apoplast at some point removed from the sieve ele-ment–companion cell complex (type 2 in Figure 10.18B).
The apoplastic step permits membrane control over the substances that enter the embryo because two membranes must be crossed in the process.
When phloem unloading is apoplastic, the transport sugar can be partly metabolized in the apoplast, or it can cross the apoplast unchanged (see Web Topic 10.9). For example, sucrose can be hydrolyzed into glucose and fruc-tose in the apoplast by invertase, a sucrose-splitting enzyme, and glucose and/or fructose would then enter the sink cells. As we will discuss later, such sucrose-cleaving enzymes play a role in the control of phloem transport by sink tissues.
Transport into Sink Tissues Requires Metabolic Energy Inhibitor studies have shown that import into sink tissues is energy dependent. Growing leaves, roots, and storage sinks in which carbon is stored in starch or protein utilize sym-plastic phloem unloading. Transport sugars are used as sub-strate for respiration and are metabolized into storage poly-mers and into compounds needed for growth. Sucrose 212 Chapter 10 metabolism results in a low sucrose concentration in the sink cells, thus maintaining a concentration gradient for sugar uptake. No membranes are crossed during sugar uptake into the sink cells, and unloading through the plasmodesmata is passive because transport sugars move from a high concen-tration in the sieve elements to a low concentration in the sink cells. Metabolic energy is thus required in these sink organs for respiration and for biosynthesis reactions.
In apoplastic phloem unloading, sugars must cross at least two membranes: the plasma membrane of the cell that is exporting the sugar, and the plasma membrane of the sink cell. When sugars are transported into the vacuole of the sink cell, they must also traverse the tonoplast.
As discussed earlier, transport across membranes in an apoplastic pathway may be energy dependent. Developing seeds are valuable experimental systems for studying unloading processes. In legumes such as soybean, the embryo can be removed from the seed, and unloading from the seed coat into the apoplast can be studied with-out the influence of the embryo. Uptake into the embryo can also be investigated separately. Such studies have shown that energy-requiring transporters mediate both unloading of sucrose into the apoplast and uptake of sucrose into the embryo in soybean (see Web Topic 10.10).
The Transition of a Leaf from Sink to Source Is Gradual Leaves of dicots such as tomato or bean begin their devel-opment as sink organs. A transition from sink to source sta-tus occurs later in development, when the leaf is approxi-mately 25% expanded, and it is usually complete when the leaf is 40 to 50% expanded.
Export from the leaf begins at the tip or apex of the blade and progresses toward the base until the whole leaf becomes a sugar exporter. During the transition period, the tip exports sugar while the base imports it from the other source leaves (Figure 10.19).
The maturation of leaves is accompanied by a large number of functional and anatomic changes, many of which are needed for the export of photosynthate. The sink-to-source transition is quite different in species with apoplastic versus symplastic loading. In leaves with apoplastic phloem loading, a drastic switch from a sym-plastic unloading pathway to an apoplastic loading path-way must be made.
In the development of a leaf that will load apoplastically, the cessation of import and the initiation of export are inde-pendent events (Turgeon 1984). In albino leaves of tobacco, which have no chlorophyll and therefore are incapable of Translocation in the Phloem 213 Phloem unloading pathway Symplastic SE unloading Type 1 Apoplastic SE unloading Type 2A Symplastic SE unloading Type 2B Symplastic SE unloading (A) Symplastic phloem unloading (B) Apoplastic phloem unloading Plasmodesma Sink cell CC/SE Cell wall Type 1: This phloem unloading pathway is designated apoplastic because one step, transport from the sieve element–companion cell complex to the successive sink cells, occurs in the apoplast. Once the sugars are taken back up into the symplast of adjoining cells, transport is symplastic. This route has not yet been demonstrated in any sink type.
Type 2: This pathway also has an apoplastic step. However, the exit from the sieve element-companion cell complex—that is, sieve element unloading—is symplastic. The apoplastic step occurs later in the pathway. The upper figure (2A) shows an apoplastic step close to the sieve element–companion cell complex; the lower figure (2B), an apoplastic step that is further removed.
FIGURE 10.18 Pathways for phloem unloading. The sieve element–companion cell complex (CC/SE) is considered a single functional unit. The presence of plasmo-desmata is assumed to provide functional symplastic continuity. An absence of plasmodesmata between cells indicates an apoplastic transport step. (A) Symplastic phloem unloading. (B) Three types of apoplastic phloem unloading. (After Oparka and van Bel 1992.) photosynthesis, import stops at the same developmental stage as in green leaves, even though export is not possible.
Therefore some other change must occur in developing leaves of tobacco that causes them to cease importing sugars.
Such a change could involve blockage of the unloading pathway at some point in the development of mature leaves. In dicot sink leaves with symplastic unloading, fac-tors that could account for the cessation of unloading include plasmodesmatal closure, a decrease in plasmodes-matal frequency, or another change in symplastic continu-ity. Experimental data have shown that the unloading path-way is blocked in mature leaves of apoplastic loaders.
Export of sugars begins when phloem loading has accu-mulated sufficient photosynthate in the sieve elements to drive translocation out of the leaf. In normal leaves with apoplastic loading, export is initiated when • The symplastic unloading pathway is closed.
• The leaf is synthesizing photosynthate in sufficient quantity that some is available for export.
• The sucrose-synthesizing genes are being expressed.
• The sucrose–H+ symporter is in place in the plasma-lemma of the sieve element–companion cell complex.
In leaves of plants like sugar beet and tobacco, the abil-ity to accumulate exogenous [14C]sucrose in the sieve ele-ment–companion cell complex is acquired as the leaves undergo the sink-to-source transition, suggesting that the symporter required for loading has become functional. In developing leaves of Arabidopsis, expression of the sym-porter that is thought to transport sugars during loading begins in the tip and proceeds to the base during a sink-to-source transition. The same basipetal pattern is seen in the development of export capacity.
In tobacco and other Nicotiana species, the minor veins that are eventually responsible for most of the loading do not mature until about the time import ceases. Thus, sug-ars are unloaded and loaded almost entirely via different veins (Roberts et al. 1997).
In leaves in which the symplastic route for unloading is maintained for loading, the transition from import to export is to some extent reversible. In variegated leaves of coleus that have both green and albino regions, the albino portions of mature leaves retain many sinklike character-istics. The green regions of the leaves can export photo-synthate to the albino regions; if the green regions are removed, the albino regions can import and unload sugars from other mature leaves. PHOTOSYNTHATE ALLOCATION AND PARTITIONING The photosynthetic rate determines the total amount of fixed carbon available to the leaf. However, the amount of fixed carbon available for translocation depends on subse-quent metabolic events. The regulation of the diversion of fixed carbon into the various metabolic pathways is termed allocation.
The vascular bundles in a plant form a system of pipes that can direct the flow of photosynthates to various sinks: young leaves, stems, roots, fruits, or seeds. However, the vas-cular system is often highly interconnected, forming an open network that allows source leaves to communicate with mul-tiple sinks. Under these conditions, what determines the vol-ume of flow to any given sink? The differential distribution of photosynthates within the plant is termed partitioning.
After giving an overview of allocation and partitioning, we will examine the coordination of starch and sucrose 214 Chapter 10 (A) (B) (D) (C) FIGURE 10.19 Autoradiographs of a leaf of summer squash (Cucurbita pepo), showing the transition of the leaf from sink to source status. In each case, the leaf imported 14C from the source leaf on the plant for 2 hours. Label is visible as black accumulations. (A) The entire leaf is a sink, importing sugar from the source leaf. (B–D) The base is still a sink. As the tip of the leaf loses the ability to unload and stops importing sugar (as shown by the loss of black accumula-tions), it gains the ability to load and to export sugar. (From Turgeon and Webb 1973.) synthesis. We will conclude by discussing how sinks com-pete, how sink demand might regulate photosynthetic rate in the source leaf, and how sources and sinks communicate with each other.
Allocation Includes the Storage, Utilization, and Transport of Fixed Carbon The carbon fixed in a source cell can be used for storage, metabolism, and transport: • Synthesis of storage compounds. Starch is synthesized and stored within chloroplasts and, in most species, is the primary storage form that is mobilized for translo-cation during the night. Plants that store carbon pri-marily as starch are called starch storers.
• Metabolic utilization. Fixed carbon can be utilized within various compartments of the photosynthesiz-ing cell to meet the energy needs of the cell or to pro-vide carbon skeletons for the synthesis of other com-pounds required by the cell.
• Synthesis of transport compounds. Fixed carbon can be incorporated into transport sugars for export to vari-ous sink tissues. A portion of the transport sugar can also be stored temporarily in the vacuole (see Web Topic 10.9).
Allocation is also a key process in sink tissues. Once the transport sugars have been unloaded and enter the sink cells, they can remain as such or can be transformed into various other compounds. In storage sinks, fixed carbon can be accumulated as sucrose or hexose in vacuoles or as starch in amyloplasts. In growing sinks, sugars can be uti-lized for respiration and for the synthesis of other mole-cules required for growth.
Transport Sugars Are Partitioned among the Various Sink Tissues The greater the ability of a sink to store or metabolize imported sugars (the process of allocation), the greater its ability to compete for photosynthate being exported by the sources. Such competition determines the distribution of transport sugars among the various sink tissues of the plant (photosynthate partitioning), at least in the short term.
Of course, events in sources and sinks must be syn-chronized. Partitioning determines the patterns of growth, and such growth must be balanced between shoot growth (photosynthetic productivity) and root growth (water and mineral uptake). So an additional level of control lies in the interaction between areas of supply and demand.
Turgor pressure in the sieve elements could be an important means of communication between sources and sinks, acting to coordinate rates of loading and unloading.
Chemical messengers are also important in signaling to one organ the status of the other. Such chemical messengers include plant hormones and nutrients, such as potassium and phosphate and even the transport sugars themselves.
Attainment of higher yields of crop plants is one goal of research on photosynthate allocation and partitioning.
Whereas grains and fruits are examples of edible yields, total yield includes inedible portions of the shoot. An under-standing of partitioning enables plant breeders to select and develop varieties that have improved transport to edible por-tions of the plant. Significant improvements have been made in the ratio of commercial or edible yield to total shoot yield.
Allocation and partitioning in the whole plant must be coordinated such that increased transport to edible tissues does not occur at the expense of other essential processes and structures. Crop yield will also be improved if photosyn-thates that are normally “lost” by the plant are retained. For example, losses due to nonessential respiration or exudation from roots could be reduced. In the latter case, care must be taken not to disrupt essential processes outside the plant, such as growth of beneficial microbial species in the vicin-ity of the root that obtain nutrients from the root exudate.
Allocation in Source Leaves Is Regulated Increases in the rate of photosynthesis in a source leaf gen-erally result in an increase in the rate of translocation from the source. Control points for the allocation of photosyn-thate (Figure 10.20) include the allocation of triose phos-phates to the following processes: • Regeneration of intermediates in the C3 photosyn-thetic carbon reduction cycle (the Calvin cycle; see Chapter 8) • Starch synthesis • Sucrose synthesis, as well as distribution of sucrose between transport and temporary storage pools Various enzymes operate in the pathways that process the photosynthate, and the control of these steps is complex (Geiger and Servaites 1994.) During the day the rate of starch synthesis in the chloro-plast must be coordinated with sucrose synthesis in the cytosol. Triose phosphates (glyceraldehyde-3-phosphate and dihydroxyacetone phosphate) produced in the chloro-plast by the C3 Calvin cycle (see Chapter 8) can be used for either starch or sucrose synthesis. Sucrose synthesis in the cytoplasm diverts triose phosphate away from starch syn-thesis and storage. For example, it has been shown that when the demand for sucrose by other parts of a soybean plant is high, less carbon is stored as starch by the source leaves. The key enzymes involved in the regulation of sucrose synthesis in the cytoplasm and of starch synthesis in the chloroplast are sucrose phosphate synthase and fruc-tose-1,6-bisphosphatase in the cytoplasm and ADP-glucose pyrophosphorylase in the chloroplast (see Chapter 8, Fig-ure 10.20, and Web Topic 10.9).
Translocation in the Phloem 215 However, there is a limit to the amount of carbon that normally can be diverted from starch synthesis in species that store carbon primarily as starch. Studies of allocation between starch and sucrose under different conditions sug-gest that a fairly steady rate of translocation throughout the 24-hour period is a priority for most plants.
The use of mutants and transgenic plants enables us to ask a new set of questions about allocation. For example, what happens when one of the competing processes, such as starch synthesis, is inhibited or even eliminated? The results have revealed the amazing flexibility of plants. For example, starch-deficient tobacco mutants synthesize only trace amounts of starch but are able to compensate for a lack of stored carbon by doubling the rate of sucrose synthesis and export during the day and by switching most of their growth to the day (Geiger et al. 1995). On the other hand, plants with enhanced starch synthesis during the day often export more of their fixed carbon during the night.
Sink Tissues Compete for Available Translocated Photosynthate As discussed earlier, translocation to sink tissues depends on the position of the sink in relation to the source and on the vascular connections between source and sink. Another factor determining the pattern of transport is competition between sinks. For example, reproductive tissues (seeds) might compete with growing vegetative tissues (young leaves and roots) for photosynthates in the translocation stream. Competition has been shown by numerous exper-iments in which removal of a sink tissue from a plant gen-erally results in increased translocation to alternative, and hence competing, sinks.
In the reverse type of experiment, the source supply can be altered while the sink tissues are left intact. When the supply of photosynthates from sources to competing sinks is suddenly and drastically reduced by shading of all the source leaves but one, the sink tissues become dependent on a single source. In sugar beet and bean plants, the rates of photosynthesis and export from the single remaining source leaf usually do not change over the short term (approximately 8 hours; Fondy and Geiger 1980). However, the roots receive less sugar from the single source, while the young leaves receive relatively more. Thus the young leaves are stronger sinks than the roots in these conditions.
A stronger sink can deplete the sugar content of the sieve elements more readily and thus increase the pressure gra-dient and the rate of translocation toward itself.
An effect on the pressure gradient is also indicated indi-rectly by experiments in which investigators enhance trans-port to a sink by making the sink water potential more neg-ative. Treatment of the root tips of pea seedlings with 350 mM mannitol solutions increased the import of [14C]sucrose by more than 300%, presumably because of a turgor decrease in the sink cells (Schulz 1994).
Sink Strength Is a Function of Sink Size and Sink Activity Various experiments indicate that the ability of a sink to mobilize photosynthate toward itself, the sink strength, depends on two factors—sink size and sink activity—as follows: Sink strength = sink size × sink activity Sink size is the total weight of the sink tissue, and sink activity is the rate of uptake of photosynthates per unit weight of sink tissue. Altering either the size or the activ-ity of the sink results in changes in translocation patterns.
For example, the ability of a pea pod to import carbon depends on the dry weight of that pod as a proportion of the total number of pods (Jeuffroy and Warembourg 1991).
Changes in sink activity can be complex because vari-ous activities in sink tissues can potentially limit the rate of uptake by the sink. These activities include unloading from the sieve elements, metabolism in the cell wall, uptake from 216 Chapter 10 Inner chloroplast membrane Antiport system (phosphate translocator) Fructose-1,6-bisphosphate Fructose-6-phosphate Transport CHLOROPLAST STROMA CYTOSOL Calvin cycle intermediates CO2 Triose phosphate Triose phosphate ADPG Storage Starch Storage Sucrose Sucrose phosphate UDPG 1 3 2 Pi Pi Pi FIGURE 10.20 A simplified scheme for starch and sucrose synthesis during the day. Triose phosphate, formed in the Calvin cycle, can either be utilized in starch formation in the chloroplast or transported into the cytosol in exchange for inorganic phosphate (Pi) via the phosphate translocator in the inner chloroplast membrane. The outer chloroplast membrane is porous to small molecules and is omitted here for clarity. In the cytosol, triose phosphate can be converted to sucrose for either storage in the vacuole or transport.
Key enzymes involved are starch synthetase (1), fructose-1,6-bisphosphatase (2), and sucrose phosphate synthase (3).
The second and third enzymes, along with ADP-glucose pyrophosphorylase, which forms adenosine diphosphate glucose (ADPG), are regulated enzymes in sucrose and starch synthesis (see Chapter 8). UDPG, uridine diphos-phate glucose. (After Preiss 1982.) the apoplast, and metabolic processes that use the photo-synthate in either growth or storage.
Cooling a sink tissue inhibits activities that require metabolic energy and results in a decrease in the speed of transport toward the sink. In corn, a mutant that has a defective enzyme for starch synthesis in the kernels trans-ports less material to the kernels than does its normal coun-terpart (Koch et al. 1982). In this mutant, a deficiency in photosynthate storage leads to an inhibition of transport.
Sink activity and thus sink strength are also thought to be related to the presence and activity of the sucrose-splitting enzymes acid invertase and sucrose synthase because they catalyze the first step in sucrose utilization. Whether these enzymes control sink strength or are simply correlated with sink metabolism and growth is currently an active topic of research. Interestingly, the genes for sucrose synthase and invertase are among those regulated by carbohydrate sup-ply. In general, carbohydrate depletion enhances the expres-sion of genes for photosynthesis, reserve mobilization, and export processes, while abundant carbon resources favor genes for storage and utilization (Koch 1996).
However, the finding that different isoforms of sucrose synthase, encoded by different genes, respond in opposite ways to carbohydrate supply, indicates that the overall pic-ture is complex. For example, the mRNA for one gene for sucrose synthase in corn roots is widely distributed in root tissues and is maximally expressed when sugars are abun-dant. The mRNA of a second sucrose synthase gene is most abundant in the epidermis and outer tissues of the root and is maximally expressed under conditions of sugar depletion. Thus, utilization of imported sugars is broadly maximized when sugars are abundant, but when sugar supply is low, utilization is increasingly restricted to sites that are crucial for uptake of water and minerals (Koch et al. 1996).
In addition, genes for invertase and sucrose synthase are often expressed at different times during sink develop-ment. In bean pods and corn kernels, changes in invertase activity are found to precede changes in photosynthate import. These results point to a key role of invertase and sucrose synthase in controlling import patterns, both dur-ing the genetic program of sink development and during responses to environmental stresses (see Web Topic 10.9).
Changes in the Source-to-Sink Ratio Cause Long-Term Alterations in the Source If all but one of the source leaves of a soybean plant are shaded for an extended period (e.g., 8 days), many changes occur in the single remaining source leaf. These changes include a decrease in starch concentration and increases in photosynthetic rate, rubisco activity, sucrose concentration, transport from the source, and orthophosphate concentra-tion (Thorne and Koller 1974). These data indicate that, besides the observed short-term changes in the distribution of photosynthate among different sinks, the metabolism of the source adjusts to the altered conditions in long-term experiments.
Photosynthetic rate (the net amount of carbon fixed per unit leaf area per unit time) often increases over several days when sink demand increases, and it decreases when sink demand decreases. Photosynthesis is most strongly inhibited under conditions of reduced sink demand in plants that normally store starch, rather than sucrose, dur-ing the day. Perhaps an accumulation of photosynthate (starch, sucrose, or hexoses) in the source leaf could account for the linkage between sink demand and photo-synthetic rate in starch-storing plants (see Web Topic 10.11).
Long-Distance Signals May Coordinate the Activities of Sources and Sinks Besides having a major function in the long-distance trans-port of photosynthate, the phloem is a conduit for the transport of signal molecules from one part of the organ-ism to another. Signals between sources and sinks might be physical (such as turgor pressure) or chemical (such as plant hormones and carbohydrates). Signals indicating tur-gor change could be transmitted rapidly via the intercon-necting system of sieve elements.
For example, if phloem unloading were rapid under conditions of rapid sugar utilization at the sink tissue, tur-gor pressures in the sieve elements of sinks would be reduced, and this reduction would be transmitted to the sources. If loading were controlled in part by turgor in the sieve elements of the source, it would increase in response to this signal from the sinks. The opposite response would be seen when unloading was slow in the sinks. Some data suggest that cell turgor can modify the activity of the pro-ton-pumping ATPase at the plasma membrane and there-fore alter transport rates.
Shoots produce growth regulators such as auxin (see Chapter 19), which can be rapidly transported to the roots via the phloem; and roots produce cytokinins (see Chapter 21), which move to the shoots through the xylem. Gib-berellins (GA) and abscisic acid (ABA) (see Chapters 20 and 23) are also transported throughout the plant in the vascular system. Plant hormones play a role in regulating source–sink relationships. They affect photosynthate par-titioning by controlling sink growth, leaf senescence, and other developmental processes.
Loading of sucrose in castor bean is stimulated by exogenous auxin but inhibited by ABA, while exogenous ABA enhances, and auxin inhibits, sucrose uptake by sugar beet taproot tissue. Active transporters in plasma mem-branes are obvious targets for regulation of apoplastic load-ing and unloading by hormones. Other potential sites of hormone regulation of unloading include tonoplast trans-porters, enzymes for metabolism of incoming sucrose, wall extensibility, and plasmodesmatal permeability in the case of symplastic unloading (see the next section).
Translocation in the Phloem 217 As indicated earlier, carbohydrate levels can influence the expression of encoding photosynthesis component genes, as well as genes involved in sucrose hydrolysis.
Many genes have been shown to be responsive to sugar depletion and abundance (Koch 1996). Thus, not only is sucrose transported in the phloem, but sucrose or its metabolites can act as signals that modify the activities of sources and sinks. In sugar beet, for example, proton–sucrose symporter activity declines in plasma membrane vesicles isolated from source leaves fed exoge-nous sucrose through the xylem.
The loss of symporter activity is accompanied by a decline in symporter mRNA, suggesting an effect on tran-scription or mRNA stability. A working model includes the following steps: (1) Decreased sink demand leads to high sucrose levels in the vascular tissue; (2) high sucrose levels lead to down-regulation of the symporter in the source; (3) decreased loading results in increased sucrose concentra-tions in the source (Chiou and Bush 1998). Increased sucrose concentrations in the source can result in a lower photosynthetic rate (see Web Topic 10.11). An increase of starch accumulation in source leaves of plants transformed with antisense DNA to the sucrose symporter SUT1 also supports this model (Schulz et al. 1998).
In some source–sink systems, sugars and other metabo-lites have been shown to interact with hormonal signals to control gene expression (Thomas and Rodriguez 1994).
Long-Distance Signals May Also Regulate Plant Growth and Development It has long been known that viruses can move in the phloem, traveling as complexes of proteins and nucleic acids or as intact virus particles. More recently, endogenous mRNA molecules and proteins have been found in phloem sap, and at least some of these are thought to be signal molecules.
The following pathway appears to be open to the move-ment of macromolecules over long distances: from com-panion cells of sources to source sieve elements, through the path to sink sieve elements, to companion cells of the sink, and finally to cells of the sink itself.
Proteins synthesized in companion cells can clearly enter the sieve elements through the plasmodesmata that connect the two cell types. As noted earlier, both the SUT1 transporter in the plasma membrane of the sieve element and P-proteins in cucurbit sap (PP1 and PP2) appear to be synthesized in companion cells. The plasmodesmata con-necting the companion cells and sieve elements must thus allow these macromolecules to move across them. Viral particles have been observed in the plasmodesmata.
Some of the proteins that enter sieve elements may sim-ply diffuse through the plasmodesmata into the sieve ele-ments, others may mediate their own cell-to-cell transport, and yet others may be aided by specific control proteins (Mezitt and Lucas 1996). Passive movement of proteins from companion cells to sieve elements has been demon-strated in Arabidopsis and tobacco plants, transformed with the gene for a green fluorescent protein (GFP) from jellyfish, under the control of the SUC2 promoter from Arabidopsis.
The SUC2 sucrose–H+ symporter is synthesized within the companion cells, so proteins expressed under the con-trol of its promoter are also synthesized in the companion cells. GFP, which is localized by its fluorescence after exci-tation with blue light, moves through plasmodesmata from companion cells into sieve elements and migrates within the phloem to sink tissues. Because jellyfish GFP is unlikely to possess specific sequences for interaction with plas-modesmatal structures, its movement into sieve elements is likely to occur by passive diffusion (Imlau et al. 1999).
Once in the sieve elements, some proteins (e.g., SUT1) are targeted to the plasma membrane or other cellular loca-tions, while other proteins move with the translocation stream to sink tissues. Proteins moving to sinks in the phloem include the P-proteins PP1 and PP2. Subunits of P-proteins from cucumber (Cucumis sativus) can move across graft unions from the cucumber stock (basal graft partner) to a pumpkin (Cucurbita maxima) scion (upper graft part-ner). One experiment showed that the smaller PP2 protein is able to move from the sieve elements to companion cells of the scion stem; the larger PP1 was not detected in the companion cells. Neither protein was able to move beyond the sieve element–companion cell complex (Golecki et al.
1999). These proteins may be too large to pass through the plasmodesmata that surround the sieve element–compan-ion cell complex, or they may lack recognition factors allow-ing interaction with the plasmodesmata (Oparka and Santa Cruz 2000). In contrast, the jellyfish green fluorescent pro-tein is unloaded symplastically through the plasmodesmata into sink tissues, such as seed coats, anthers, root tips, and mesophyll cells in importing leaves (Imlau et al. 1999).
Clearly, proteins can be transported from the compan-ion cells in the source through the intervening sieve ele-ments to sink companion cells. However, little evidence exists for a similar movement of proteins synthesized out-side the companion cells. Other signals from outside the sieve element–companion cell complex may give rise to the production of mobile proteins in the companion cells. Evi-dence also exists for the translocation via the phloem of mRNA molecules that are involved in sink tissue develop-ment (Oparka and Santa Cruz 2000). To be assigned a sig-naling role in plants, a macromolecule must be able to leave the sieve element–companion cell complex in sink tis-sues, and perhaps most importantly, it must be able to modify the functions of specific cells in the sink (Oparka and Santa Cruz 2000). Such demonstrations await the results of future experimentation.
Plasmodesmata can exercise dynamic control of the intercellular diffusion of small molecules (Lucas et al. 1993; Baluska et al. 2001). RNA and protein also move from cell to cell in plants via plasmodesmata. Virally encoded 218 Chapter 10 “movement proteins” interact directly with plasmodes-mata to allow the passage of viral nucleic acids. Potato plants transformed with the tobacco mosaic virus move-ment protein show altered allocation patterns in source leaves (Olesinski et al. 1996) and modified whole-plant par-titioning patterns (Almon et al. 1997). The modification of source leaf allocation depends on whether the movement protein is expressed in mesophyll and bundle sheath cells or in phloem parenchyma and companion cells.
Plasmodesmata have been implicated in nearly every aspect of phloem translocation, from loading to long-dis-tance transport (remember that pores in sieve areas and sieve plates are modified plasmodesmata) to allocation and partitioning. Future research on phloem translocation and on the roles of plasmodesmata in plant growth and devel-opment will surely go hand in hand.
SUMMARY Translocation in the phloem is the movement of the prod-ucts of photosynthesis from mature leaves to areas of growth and storage. The phloem also redistributes water and various compounds throughout the plant body.
Some aspects of phloem translocation have been well established by extensive research over many years. These include the following: • The pathway of translocation. Sugars and other organic materials are conducted throughout the plant in the phloem, specifically in cells called sieve elements.
Sieve elements display a variety of structural adapta-tions that make them well suited for transport.
• Patterns of translocation. Materials are translocated in the phloem from sources (areas of photosynthate supply) to sinks (areas of metabolism or storage of photosynthate). Sources are usually mature leaves.
Sinks include organs such as roots and immature leaves and fruits.
• Materials translocated in the phloem. The translocated solutes are mainly carbohydrates, and sucrose is the most commonly translocated sugar. Phloem sap also contains other organic molecules, such as amino acids, proteins, and plant hormones, as well as inor-ganic ions.
• Rates of movement. Rates of movement in the phloem are quite rapid, well in excess of rates of diffusion.
Velocities average 1 m h–1, and mass transfer rates range from 1 to 15 g h–1 cm–2 of sieve elements.
Other aspects of phloem translocation require further investigation, and most of these are being studied intensively at the present time. These aspects include the following: • Phloem loading and unloading. Transport of sugars into and out of the sieve elements is called sieve element loading and unloading, respectively. In some species, sugars must enter the apoplast of the source leaf before loading. In these plants, loading into the sieve elements requires metabolic energy, provided in the form of a proton gradient. In other species, the whole pathway from the photosynthesizing cells to the sieve elements occurs in the symplast of the source leaf. In either case, phloem loading is specific for the trans-ported sugar. Phloem unloading requires metabolic energy, but the transport pathway, the site of metabo-lism of transport sugars, and the site where energy is expended vary with the organ and species.
• Mechanism of translocation. Pressure flow is well accepted as the most probable mechanism of phloem translocation. In this model the bulk flow of phloem sap occurs in response to an osmotically generated pressure gradient. A variety of structural and physio-logical data indicate that materials are translocated in the phloem of angiosperms by pressure flow. The mechanism of translocation in gymnosperms requires further investigation.
• Photosynthate allocation and partitioning. Allocation is the regulation of the quantities of fixed carbon that are channeled into various metabolic pathways. In sources, the regulatory mechanisms of allocation determine the quantities of fixed carbon that will be stored (usually as starch), metabolized within the cells of the source, or immediately transported to sink tis-sues. In sinks, transport sugars are allocated to growth processes or to storage. Partitioning is the differential distribution of photosynthates within the whole plant.
Partitioning mechanisms determine the quantities of fixed carbon delivered to specific sink tissues. Phloem loading and unloading, and photosynthate allocation and partitioning, are of great research interest because of their roles in crop productivity.
Web Material Web Topics 10.1 Classical Studies on Phloem Transport Classical experiments illustrate some basic properties of phloem transport.
10.2 Sampling Phloem Sap Aphid stylets are optimally suited to sample phloem sap.
10.3 Nitrogen Transport in Soybean Nitrogen compounds synthesized in the roots are transferred from the xylem to the phloem.
10.4 Monitoring Traffic on the Sugar Freeway Sugar transport rates in the phloem are mea-sured with radioactive tracers.
Translocation in the Phloem 219 10.5 Evidence for Apoplastic Loading of Sieve Elements Transgenic plants have provided experimental support for apoplastic loading.
10.6 Some Substances Enter the Phloem by Diffusion Substances such as plant hormones might enter the phloem by diffusion.
10.7 Localization of the Sucrose–H+ Symporter in the Phloem of Apoplastic Loaders The sucrose H+ symporter of companion cells has been localized using fluorescent dyes.
10.8 Physiological Evidence for Symplastic Continuity in Source Leaves Fluorescent dyes have also been used to show symplastic continuity in source leaves.
10.9 Sugars in the Phloem The transport, allocation, and metabolism of phloem sugars are tightly regulated.
10.10 Energy Requirements for Unloading in Developing Seeds and Storage Organs Unloading of seed storage sugars into the embryo is mediated by active transporters.
10.11 Possible Mechanisms Linking Sink Demand and Photosynthetic Rate in Starch Storers Photosynthate accumulation increases sink demand.
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Zimmermann, M. H., and Milburn, J. A., eds. (1975) Transport in Plants, 1: Phloem Transport (Encyclopedia of Plant Physiology, New Series, Vol. 1). Springer, New York. Translocation in the Phloem 221 Respiration and Lipid Metabolism 1 1 Chapter PHOTOSYNTHESIS PROVIDES the organic building blocks that plants (and nearly all other life) depend on. Respiration, with its associated car-bon metabolism, releases the energy stored in carbon compounds in a controlled manner for cellular use. At the same time it generates many carbon precursors for biosynthesis. In the first part of this chapter we will review respiration in its metabolic context, emphasizing the inter-connections and the special features that are peculiar to plants. We will also relate respiration to recent developments in our understanding of the biochemistry and molecular biology of plant mitochondria.
In the second part of the chapter we will describe the pathways of lipid biosynthesis that lead to the accumulation of fats and oils, which many plants use for storage. We will also examine lipid synthesis and the influence of lipids on membrane properties. Finally, we will discuss the catabolic pathways involved in the breakdown of lipids and the con-version of the degradation products to sugars that occurs during seed germination.
OVERVIEW OF PLANT RESPIRATION Aerobic (oxygen-requiring) respiration is common to nearly all eukary-otic organisms, and in its broad outlines, the respiratory process in plants is similar to that found in animals and lower eukaryotes. However, some specific aspects of plant respiration distinguish it from its animal coun-terpart. Aerobic respiration is the biological process by which reduced organic compounds are mobilized and subsequently oxidized in a con-trolled manner. During respiration, free energy is released and tran-siently stored in a compound, ATP, which can be readily utilized for the maintenance and development of the plant.
Glucose is most commonly cited as the substrate for respiration. How-ever, in a functioning plant cell the reduced carbon is derived from sources such as the disaccharide sucrose, hexose phosphates and triose phosphates from starch degradation and photosynthesis, fructose-con-taining polymers (fructans), and other sugars, as well as lipids (primar-ily triacylglycerols), organic acids, and on occasion, proteins (Figure 11.1).
From a chemical standpoint, plant respiration can be expressed as the oxidation of the 12-carbon molecule sucrose and the reduction of 12 molecules of O2: C12H22O11 + 13 H2O →12 CO2 + 48 H+ + 48 e– 12 O2 + 48 H+ + 48 e– →24 H2O giving the following net reaction: C12H22O11 + 12 O2 →12 CO2 + 11 H2O This reaction is the reversal of the photosynthetic process; it represents a coupled redox reaction in which sucrose is completely oxidized to CO2 while oxygen serves as the ultimate electron acceptor, being reduced to water.
The standard free-energy decrease for the reaction as writ-ten is 5760 kJ (1380 kcal) per mole (342 g) of sucrose oxi-dized. The controlled release of this free energy, along with its coupling to the synthesis of ATP, is the primary, though by no means only, role of respiratory metabolism.
To prevent damage (incineration) of cellular structures, the cell mobilizes the large amount of free energy released in the oxidation of sucrose in a series of step-by-step reactions.
These reactions can be grouped into four major processes: glycolysis, the citric acid cycle, the reactions of the pentose phosphate pathway, and oxidative phosphorylation. The sub-strates of respiration enter the respiratory process at different points in the pathways, as summarized in Figure 11.1: • Glycolysis involves a series of reactions carried out by a group of soluble enzymes located in both the cytosol and the plastid. A sugar—for example, sucrose—is partly oxidized via six-carbon sugar phos-phates (hexose phosphates) and three-carbon sugar phosphates (triose phosphates) to produce an organic acid—for example, pyruvate. The process yields a small amount of energy as ATP, and reducing power in the form of a reduced pyridine nucleotide, NADH.
• In the pentose phosphate pathway, also located both in the cytosol and the plastid, the six-carbon glucose-6-phosphate is initially oxidized to the five-carbon ribulose-5-phosphate. The carbon is lost as CO2, and reducing power is conserved in the form of two mol-ecules of another reduced pyridine nucleotide, NADPH. In the following near-equilibrium reactions, ribulose-5-phosphate is converted into three- to seven-carbon sugars.
FIGURE 11.1 Overview of respira-tion. Substrates for respiration are generated by other cellular processes and enter the respiratory pathways. Glycolysis and the pen-tose phosphate pathways in the cytosol and plastid convert sugars to organic acids, via hexose phos-phates and triose phosphates, gen-erating NADH or NADPH and ATP. The organic acids are oxi-dized in the mitochondrial citric acid cycle, and the NADH and FADH2 produced provide the energy for ATP synthesis by the electron transport chain and ATP synthase in oxidative phosphoryla-tion. In gluconeogenesis, carbon from lipid breakdown is broken down in the glyoxysomes, metabo-lized in the citric acid cycle, and then used to synthesize sugars in the cytosol by reverse glycolysis.
NADPH ATP ATP NADH NADH FADH2 NADPH Sucrose Starch Storage, phloem transport CYTOSOL PLASTID MITOCHONDRION Hexose-P Hexose-P Triose-P Triose-P Photosynthesis Organic acids Pentose phosphate pathway Glycolysis Oxidative phosphorylation Citric acid cycle Lipid breakdown Pentose-P CO2 CO2 O2 Pentose phosphate pathway Pentose-P CO2 Storage 224 Chapter 11 • In the citric acid cycle, pyruvate is oxidized com-pletely to CO2, and a considerable amount of reduc-ing power (16 NADH + 4 FADH2 equivalents per sucrose) is generated in the process. With one excep-tion (succinate dehydrogenase), these reactions involve a series of enzymes located in the internal aqueous compartment, or matrix, of the mitochon-drion (see Figure 11.5). As we will discuss later, suc-cinate dehydrogenase is localized in the inner of the two mitochondrial membranes.
• In oxidative phosphorylation, electrons are trans-ferred along an electron transport chain, consisting of a collection of electron transport proteins bound to the inner of the two mitochondrial membranes. This system transfers electrons from NADH (and related species)—produced during glycolysis, the pentose phosphate pathway, and the citric acid cycle—to oxy-gen. This electron transfer releases a large amount of free energy, much of which is conserved through the synthesis of ATP from ADP and Pi (inorganic phos-phate) catalyzed by the enzyme ATP synthase. Col-lectively the redox reactions of the electron transport chain and the synthesis of ATP are called oxidative phosphorylation. This final stage completes the oxi-dation of sucrose.
Nicotinamide adenine dinucleotide (NAD+/NADH) is an organic cofactor (coenzyme) associated with many enzymes that catalyze cellular redox reactions. NAD+ is the oxidized form of the cofactor, and it undergoes a reversible two-electron reaction that yields NADH (Figure 11.2): H P O OCH2 O H2CO O O O P O – – H O H H H HO H H— H H NH2 H H H CONH2 N N N N (2–O3P—) O HO OH H H H N + H H O H3C H3C N N N H H H H H CONH2 N P O O H2CO O O P O CH2 CH2 HCOH HCOH HCOH O – – H O H H HO H H— H H NH2 + 2 e– + 2H+ N N N N NH O H H H H O H3C CH2 HCOH H3C N N N NH O + 2 e– + 2H+ NAD+ (NADP+) NAD(P)H FAD FMN FADH2 (A) (B) FIGURE 11.2 Structures and reactions of the major electron-carrying cofactors involved in respiratory bioenergetics. (A) Reduction of NAD(P)+ to NAD(P)H; (B) Reduction of FAD to FADH2. FMN is identical to the flavin part of FAD and is shown in the dashed box. Blue shaded areas show the por-tions of the molecules that are involved in the redox reaction.
Respiration and Lipid Metabolism 225 NAD+ + 2 e– + H+ →NADH The standard reduction potential for this redox couple is about –320 mV, which makes it a relatively strong reduc-tant (i.e., electron donor). NADH is thus a good molecule in which to conserve the free energy carried by electrons released during the stepwise oxidations of glycolysis and the citric acid cycle. A related compound, nicotinamide adenine dinucleotide phosphate (NADP+/NADPH), func-tions in redox reactions of photosynthesis (see Chapter 8) and of the oxidative pentose phosphate pathway; it also takes part in mitochondrial metabolism (Møller and Ras-musson 1998). This will be discussed later in the chapter.
The oxidation of NADH by oxygen via the electron transport chain releases free energy (220 kJ mol–1, or 52 kcal mol–1) that drives the synthesis of ATP. We can now for-mulate a more complete picture of respiration as related to its role in cellular energy metabolism by coupling the fol-lowing two reactions: C12H22O11 + 12 O2 →12 CO2 + 11 H2O 60 ADP + 60 Pi → 60 ATP + 60 H2O Keep in mind that not all the carbon that enters the res-piratory pathway ends up as CO2. Many respiratory inter-mediates are the starting points for pathways that assimi-late nitrogen into organic form, pathways that synthesize nucleotides and lipids, and many others (see Figure 11.13).
GLYCOLYSIS: A CYTOSOLIC AND PLASTIDIC PROCESS In the early steps of glycolysis (from the Greek words glykos, “sugar,” and lysis, “splitting”), carbohydrates are converted to hexose phosphates, which are then split into two triose phosphates. In a subsequent energy-conserving phase, the triose phosphates are oxidized and rearranged to yield two molecules of pyruvate, an organic acid.
Besides preparing the substrate for oxidation in the citric acid cycle, glycolysis yields a small amount of chemical energy in the form of ATP and NADH.
When molecular oxygen is unavailable—for example, in plant roots in flooded soils—glycolysis can be the main source of energy for cells. For this to work, the fermenta-tion pathways, which are localized in the cytosol, reduce pyruvate to recycle the NADH produced by glycolysis. In this section we will describe the basic glycolytic and fer-mentative pathways, emphasizing features that are specific for plant cells. We will end by discussing the pentose phos-phate pathway.
Glycolysis Converts Carbohydrates into Pyruvate, Producing NADH and ATP Glycolysis occurs in all living organisms (prokaryotes and eukaryotes). The principal reactions associated with the classic glycolytic and fermentative pathways in plants are almost identical with those of animal cells (Figure 11.3).
However, plant glycolysis has unique regulatory features, as well as a parallel partial glycolytic pathway in plastids and alternative enzymatic routes for several cytosolic steps.
In animals the substrate of glycolysis is glucose and the end product pyruvate. Because sucrose is the major translo-cated sugar in most plants and is therefore the form of car-bon that most nonphotosynthetic tissues import, sucrose (not glucose) can be argued to be the true sugar substrate for plant respiration. The end products of plant glycolysis include another organic acid, malate.
In the early steps of glycolysis, sucrose is broken down into the two monosaccharides—glucose and fructose— which can readily enter the glycolytic pathway. Two path-ways for the degradation of sucrose are known in plants, both of which also take part in the unloading of sucrose from the phloem (see Chapter 10).
In most plant tissues sucrose synthase, localized in the cytosol, is used to degrade sucrose by combining sucrose with UDP to produce fructose and UDP-glucose. UDP-glu-cose pyrophosphorylase then converts UDP-glucose and pyrophosphate (PPi) into UTP and glucose-6-phosphate (see Figure 11.3). In some tissues, invertases present in the cell wall, vacuole, or cytosol hydrolyze sucrose to its two component hexoses (glucose and fructose). The hexoses are then phosphorylated in a reaction that uses ATP. Whereas the sucrose synthase reaction is close to equilibrium, the invertase reaction releases sufficient energy to be essentially irreversible.
Plastids such as chloroplasts or amyloplasts (see Chap-ter 1) can also supply substrates for glycolysis. Starch is synthesized and catabolized only in plastids (see Chapter 8), and carbon obtained from starch degradation enters the glycolytic pathway in the cytosol primarily as hexose phos-phate (which is translocated out of amyloplasts) or triose phosphate (which is translocated out of chloroplasts). Pho-tosynthetic products can also directly enter the glycolytic pathway as triose phosphate (Hoefnagel et al. 1998).
Plastids convert starch into triose phosphates using a separate set of glycolytic isozymes that convert hexose phosphates to triose phosphates. All the enzymes shown in Figure 11.3 have been measured at levels sufficient to sup-port the respiration rates observed in intact plant tissues.
In the initial phase of glycolysis, each hexose unit is phosphorylated twice and then split, eventually producing two molecules of triose phosphate. This series of reactions consumes two to four molecules of ATP per sucrose unit, depending on whether the sucrose is split by sucrose syn-thase or invertase. These reactions also include two of the three essentially irreversible reactions of the glycolytic pathway that are catalyzed by hexokinase and phospho-fructokinase (see Figure 11.3). The phosphofructokinase reaction is one of the control points of glycolysis in both plants and animals.
226 Chapter 11 The energy-conserving phase of glycolysis.
The reac-tions discussed thus far transfer carbon from the various substrate pools into triose phosphates. Once glyceralde-hyde-3-phosphate is formed, the glycolytic pathway can begin to extract usable energy in the energy-conserving phase. The enzyme glyceraldehyde-3-phosphate dehydro-genase catalyzes the oxidation of the aldehyde to a car-boxylic acid, reducing NAD+ to NADH. This reaction releases sufficient free energy to allow the phosphorylation (using inorganic phosphate) of glyceraldehyde-3-phos-phate to produce 1,3-bisphosphoglycerate. The phospho-rylated carboxylic acid on carbon 1 of 1,3-bisphosphoglyc-erate (see Figure 11.3) has a large standard free energy of hydrolysis (–49.3 kJ mol–1, or –11.8 kcal mol–1). Thus, 1,3-bisphosphoglycerate is a strong donor of phosphate groups.
In the next step of glycolysis, catalyzed by phospho-glycerate kinase, the phosphate on carbon 1 is transferred to a molecule of ADP, yielding ATP and 3-phosphoglycer-ate. For each sucrose entering the pathway, four ATPs are generated by this reaction—one for each molecule of 1,3-bisphosphoglycerate.
This type of ATP synthesis, traditionally referred to as substrate-level phosphorylation, involves the direct trans-fer of a phosphate group from a substrate molecule to ADP, to form ATP. As we will see, ATP synthesis by substrate-level phosphorylation is mechanistically distinct from ATP synthesis by ATP synthases involved in the oxidative phos-phorylation in mitochondria (which will be described later in this chapter) or photophosphorylation in chloroplasts (see Chapter 7).
In the following reaction, the phosphate on 3-phospho-glycerate is transferred to carbon 2 and a molecule of water is removed, yielding the compound phosphoenylpyruvate (PEP). The phosphate group on PEP has a high standard free energy of hydrolysis (–61.9 kJ mol–1, or –14.8 kcal mol–1), which makes PEP an extremely good phosphate donor for ATP formation. Using PEP as substrate, the enzyme pyruvate kinase catalyzes a second substrate-level phosphorylation to yield ATP and pyruvate. This final step, which is the third essentially irreversible step in glycolysis, yields four additional molecules of ATP for each sucrose that enters the pathway.
Plants Have Alternative Glycolytic Reactions The sequence of reactions leading to the formation of pyru-vate from glucose occurs in all organisms that carry out glycolysis. In addition, organisms can operate this pathway in the opposite direction to synthesize sugar from organic acids. This process is known as gluconeogenesis.
Gluconeogenesis is not common in plants, but it does operate in the seeds of some plants, such as castor bean and sunflower, that store a significant quantity of their carbon reserves in the form of oils (triacylglycerols). After the seed germinates, much of the oil is converted by gluconeogene-sis to sucrose, which is then used to support the growing seedling. In the initial phase of glycolysis, gluconeogenesis overlaps with the pathway for synthesis of sucrose from photosynthetic triose phosphate described in Chapter 8, which is typical for plants.
Because the glycolytic reaction catalyzed by ATP-dependent phosphofructokinase is essentially irreversible (see Figure 11.3), an additional enzyme, fructose-1,6-bis-phosphatase, converts fructose-1,6-bisphosphate to fruc-tose-6-phosphate and Pi during gluconeogenesis. ATP-dependent phosphofructokinase and fructose-1,6-bis-phosphatase represent a major control point of carbon flux through the glycolytic/gluconeogenic pathways in both plants and animals, as well as in sucrose synthesis in plants (see Chapter 8).
In plants, the interconversion of fructose-6-phosphate and fructose-1,6-bisphosphate is made more complex by the presence of an additional (cytosolic) enzyme, a PPi-dependent phosphofructokinase (pyrophosphate:fructose-6-phosphate 1-phosphotransferase), which catalyzes the following reversible reaction (see Figure 11.3): Fructose-6-P + PPi ↔fructose-1,6-P2 + Pi where P represents phosphate and P2 bisphosphate. PPi-dependent phosphofructokinase is found in the cytosol of most plant tissues at levels that are considerably higher than those of the ATP-dependent phosphofructokinase (Kruger 1997). Suppression of the PPi-dependent phos-phofructokinase in transgenic potato has indicated that it contributes to glycolytic flux, but that it is not essential for plant survival, indicating that other enzymes can take over its function.
The reaction catalyzed by the PPi-dependent phospho-fructokinase is readily reversible, but it is unlikely to oper-ate in sucrose synthesis (Dennis and Blakely 2000). Like ATP-dependent phosphofructokinase and fructose bis-phosphatase, this enzyme appears to be regulated by fluc-tuations in cell metabolism (discussed later in the chapter), suggesting that under some circumstances operation of the glycolytic pathway in plants differs from that in many other organisms (see Web Essay 11.1).
At the end of the glycolytic sequence, plants have alter-native pathways for metabolizing PEP. In one pathway PEP is carboxylated by the ubiquitous cytosolic enzyme PEP carboxylase to form the organic acid oxaloacetate (OAA). The OAA is then reduced to malate by the action of malate dehydrogenase, which uses NADH as the source of electrons, and this performs a role similar to that of the dehydrogenases during fermentative metabolism (see Fig-ure 11.3). The resulting malate can be stored by export to the vacuole or transported to the mitochondrion, where it can enter the citric acid cycle. Thus the operation of pyru-vate kinase and PEP carboxylase can produce alternative organic acids—pyruvate or malate—for mitochondrial res-piration, though pyruvate dominates in most tissues.
Respiration and Lipid Metabolism 227 228 Chapter 11 ATP ATP ATP ATP CYTOSOL PLASTID Starch Glucose-1-P Glucose-6-P Triose phosphates Glucose Fructose Glucose UDP-Glucose Fructose-6-P Fructose-1,6-bisphosphate Glyceraldehyde-3-phosphate 1,3-Bisphosphoglycerate 3-Phosphoglycerate Dihydroxyacetone phosphate Glucose-6-P Glucose-6-P Glucose-1-P UDP (A) Sucrose synthase Hexokinase Hexose phosphate isomerase PPi-dependent phosphofructokinase Hexose phosphate isomerase Triose phosphate isomerase Glyceraldehyde-3-phosphate dehydrogenase Phosphoglycerate kinase Pyruvate kinase Lactate dehydrogenase Pyruvate decarboxylase Alcohol dehydrogenase Phosphoglycerate mutase ATP-dependent phosphofructokinase Hexokinase Invertase UDP-Glucose pyrophosphorylase PPi UTP NAD+ H2O CO2 2-Phosphoglycerate Phosphoenolpyruvate Oxaloacetate Malate Pyruvate Lactate Ethanol Fermentation reactions Acetaldehyde Enolase HCO3 – Malate dehydrogenase To MITOCHONDRION H2O Starch phosphorylase Amylase Glucose kinase AMYLOPLASTS CHLOROPLASTS Phospho-gluco-mutase Phosphoglucomutase Aldolase Sucrose Glycolysis ADP ADP ADP ADP ATP ATP ADP ADP Triose phosphates Hexose phosphates NAD+ NAD+ NADH NADH NAD+ NADH NAD+ NADH PEP carboxylase Initial phase of glycolysis Substrates from different sources are channeled into triose phosphate. For each molecule of sucrose that is metabolized, four molecules of triose phosphate are formed. The process requires an input of up to 4 ATP.
Energy-conserving phase of glycoysis Triose phosphate is converted to pyruvate. NAD+ is reduced to NADH by glyceraldehyde-3-phosphate dehydrogenase. ATP is synthesized in the reactions catalyzed by phosphoglycerate kinase and pyruvate kinase. An alternative end product, phosphoenolpyruvate, can be converted to malate for mitochondrial oxidation; NADH can be reoxidized during fermentation by either lactate dehydrogenase or alcohol dehydrogenase. Pi Pi Pi Pi PPi In the Absence of O2, Fermentation Regenerates the NAD+ Needed for Glycolysis In the absence of oxygen, the citric acid cycle and oxida-tive phosphorylation cannot function. Glycolysis thus can-not continue to operate because the cell’s supply of NAD+ is limited, and once all the NAD+ becomes tied up in the reduced state (NADH), the reaction catalyzed by glycer-aldehyde-3-phosphate dehydrogenase cannot take place.
To overcome this problem, plants and other organisms can further metabolize pyruvate by carrying out one or more forms of fermentative metabolism (see Figure 11.3).
In alcoholic fermentation (common in plants, but more widely known from brewer’s yeast), the two enzymes pyruvate decarboxylase and alcohol dehydrogenase act on pyruvate, ultimately producing ethanol and CO2 and oxi-dizing NADH in the process. In lactic acid fermentation (common to mammalian muscle but also found in plants), the enzyme lactate dehydrogenase uses NADH to reduce pyruvate to lactate, thus regenerating NAD+.
Under some circumstances, plant tissues may be sub-jected to low (hypoxic) or zero (anoxic) concentrations of ambient oxygen, forcing them to carry out fermentative metabolism. The best-studied example involves flooded or waterlogged soils in which the diffusion of oxygen is sufficiently reduced to cause root tissues to become hypoxic.
In corn the initial response to low oxygen is lactic acid fermentation, but the subsequent response is alcoholic fer-mentation. Ethanol is thought to be a less toxic end prod-uct of fermentation because it can diffuse out of the cell, whereas lactate accumulates and promotes acidification of the cytosol. In numerous other cases plants function under near-anaerobic conditions by carrying out some form of fermentation.
Fermentation Does Not Liberate All the Energy Available in Each Sugar Molecule Before we leave the topic of glycolysis, we need to con-sider the efficiency of fermentation. Efficiency is defined here as the energy conserved as ATP relative to the energy potentially available in a molecule of sucrose. The stan-dard free-energy change (∆G0′) for the complete oxidation of sucrose is –5760 kJ mol–1 (1380 kcal mol–1). The value of ∆G0′ for the synthesis of ATP is 32 kJ mol–1 (7.7 kcal mol–1).
However, under the nonstandard conditions that normally exist in both mammalian and plant cells, the synthesis of ATP requires an input of free energy of approximately 50 kJ mol–1 (12 kcal mol–1). (For a discussion of free energy, see Chapter 2 on the web site.) Given the net synthesis of four molecules of ATP for each sucrose molecule that is converted to ethanol (or lac-tate), the efficiency of anaerobic fermentation is only about 4%. Most of the energy available in sucrose remains in the reduced by-product of fermentation: lactate or ethanol.
During aerobic respiration, the pyruvate produced by gly-colysis is transported into mitochondria, where it is fur-ther oxidized, resulting in a much more efficient conver-sion of the free energy originally available in the sucrose.
Because of the low efficiency of energy conservation under fermentation, an increased rate of glycolysis is needed to sustain the ATP production necessary for cell survival. This is called the Pasteur effect after the French microbiologist Louis Pasteur, who first noted it when yeast switched from aerobic respiration to anaerobic alcoholic fermentation. The higher rates of glycolysis result from changes in glycolytic metabolite levels, as well as from increased expression of genes encoding enzymes of gly-colysis and fermentation (Sachs et al. 1996).
Respiration and Lipid Metabolism 229 O CH2OH CH2OH OH H H H H OH OH HO HO H H O OH2C OH H OH OH HO O O HOCH2 CH2OH OH OH O P P OH2C HO CH2O OH OH O P P OH2C C H O HCOH H2CO P C O– O HCOH H2CO P C O– O HCO H2COH P C O– O CO H2C P C O– O C O CH3 C O– O HCOH CH3 O CH CH3 CH2OH CH3 CO O HCOH H2CO P P C O H2COH H2CO P H H H H H H H HO H (B) Sucrose Glucose-6-P Fructose-6-P Glyceraldehyde-3-P 3-P-Glycerate 2-P-Glycerate Pyruvate Lactate Acetaldehyde Ethanol Phosphoenol-pyruvate Dihydroxy-acetone-P 1,3-P2-Glycerate Fructose-1,6-P2 FIGURE 11.3 Reactions of plant glycolysis and fermenta-tion. (A) In the main pathway, sucrose is oxidized to the organic acid pyruvate. The double arrows denote reversible reactions; the single arrows, essentially irreversible reac-tions. (B) The structures of the intermediates. P, phosphate; P2, bisphosphate.
Plant Glycolysis Is Controlled by Its Products In vivo, glycolysis appears to be regulated at the level of fruc-tose-6-phosphate phosphorylation and PEP turnover (see Web Essay 11.1). In contrast to animals, AMP and ATP are not major effectors of plant phosphofructokinase and pyru-vate kinase. The cytosolic concentration of PEP, which is a potent inhibitor of the plant ATP-dependent phosphofruc-tokinase, is a more important regulator of plant glycolysis.
This inhibitory effect of PEP on phosphofructokinase is strongly decreased by inorganic phosphate, making the cytosolic ratio of PEP to Pi a critical factor in the control of plant glycolytic activity. Pyruvate kinase and PEP car-boxylase, the enzymes that metabolize PEP in the last steps of glycolysis (see Figure 11.3), are in turn sensitive to feed-back inhibition by citric acid cycle intermediates and their derivatives, including malate, citrate, 2-oxoglutarate, and glutamate.
In plants, therefore, the control of glycolysis comes from the “bottom up” (see Figure 11.12), with primary regula-tion at the level of PEP metabolism by pyruvate kinase and PEP carboxylase and secondary regulation exerted by PEP at the conversion of fructose-6-phosphate to fructose-1,6-bisphosphate (see Figure 11.3). In animals, the primary con-trol operates at the phosphofructokinase, and secondary control at the pyruvate kinase.
One conceivable benefit of bottom-up control of glyco-lysis is that it permits plants to control net glycolytic flux to pyruvate independently of related metabolic processes such as the Calvin cycle and sucrose–triose phosphate– starch interconversion (Plaxton 1996). Another benefit of this control mechanism is that glycolysis may adjust to the demand for biosynthetic precursors.
The presence of two enzymes metabolizing PEP in plant cells—pyruvate kinase and PEP carboxylase—has conse-quences for the control of glycolysis that are not quite clear.
Though the two enzymes are inhibited by similar metabo-lites, the PEP carboxylase can under some conditions per-form a bypass reaction around the pyruvate kinase. The resulting malate can then enter the mitochondrial citric acid cycle. Hence, the bottom-up regulation enables a high flex-ibility in the control of plant glycolysis.
Experimental support for multiple pathways of PEP metabolism comes from the study of transgenic tobacco plants with less than 5% of the normal level of cytosolic pyruvate kinase in their leaves (Plaxton 1996). In these plants, rates of both leaf respiration and photosynthesis were unaffected relative to controls having wild-type lev-els of pyruvate kinase. However, reduced root growth in the transgenic plants indicated that the pyruvate kinase reaction could not be circumvented without some detri-mental effects.
The regulation of the conversion of fructose-6-phos-phate to fructose-1,6-bisphosphate is also complex. Fruc-tose-2,6-bisphosphate, another hexose bisphosphate, is pre-sent at varying levels in the cytosol (see Chapter 8). It markedly inhibits the activity of cytosolic fructose-1,6-bis-phosphatase but stimulates the activity of PPi-dependent phosphofructokinase. These observations suggest that fruc-tose-2,6-bisphosphate plays a central role in partitioning flux between ATP-dependent and PPi-dependent pathways of fructose phosphate metabolism at the crossing point between sucrose synthesis and glycolysis.
Understanding of the fine levels of glycolysis regulation requires the study of temporal changes in metabolite lev-els (Givan 1999). Methods are now available by rapid extraction and simultaneous analyses of many metabo-lites—for example, by mass spectrometry—an approach called metabolic profiling (see Web Essay 11.2).
The Pentose Phosphate Pathway Produces NADPH and Biosynthetic Intermediates The glycolytic pathway is not the only route available for the oxidation of sugars in plant cells. Sharing common metabolites, the oxidative pentose phosphate pathway (also known as the hexose monophosphate shunt) can also accomplish this task (Figure 11.4). The reactions are carried out by soluble enzymes present in the cytosol and in plas-tids. Generally, the pathway in plastids predominates over the cytosolic pathway (Dennis et al. 1997).
The first two reactions of this pathway involve the oxidative events that convert the six-carbon glucose-6-phosphate to a five-carbon sugar, ribulose-5-phosphate, with loss of a CO2 molecule and generation of two mole-cules of NADPH (not NADH). The remaining reactions of the pathway convert ribulose-5-phosphate to the glycolytic intermediates glyceraldehyde-3-phosphate and fructose-6-phosphate. Because glucose-6-phosphate can be regener-ated from glyceraldehyde-3-phosphate and fructose-6-phosphate by glycolytic enzymes, for six turns of the cycle we can write the reaction as follows: 6 glucose-6-P + 12 NADP+ + 7 H2O → 5 glucose-6-P + 6 CO2 + Pi + 12 NADPH + 12 H+ The net result is the complete oxidation of one glucose-6-phosphate molecule to CO2 with the concomitant synthe-sis of 12 NADPH molecules.
Studies of the release of 14CO2 from isotopically labeled glucose indicate that glycolysis is the more dominant breakdown pathway, accounting for 80 to 95% of the total carbon flux in most plant tissues. However, the pentose phosphate pathway does contribute to the flux, and devel-opmental studies indicate that its contribution increases as plant cells develop from a meristematic to a more differ-entiated state (Ap Rees 1980). The oxidative pentose phos-phate pathway plays several roles in plant metabolism: • The product of the two oxidative steps is NADPH, and this NADPH is thought to drive reductive steps associated with various biosynthetic reactions that occur in the cytosol. In nongreen plastids, such as amyloplasts, and in chloroplasts functioning in the 230 Chapter 11 Respiration and Lipid Metabolism 231 NADPH H H H H H OH OH OH O COOH HCOH HO CH2O Glucose-6-phosphate 6-Phosphogluconate Glucose-6-phosphate dehydrogenase HOCH HCOH HCOH CH2O CH2OH C O Ribulose-5-phosphate Ribulose-5-phosphate Gluconate-6-phosphate dehydrogenase HCOH HCOH CH2O CO2 CHO Ribose-5-phosphate HCOH HCOH HCOH CH2O CH2OH Xylulose-5-phosphate HOCH HCOH CH2O C O Fructose-6-phosphate HOCH CH2OH HCOH HCOH CH2O Erythrose-4-phosphate HCOH HCOH CH2O CHO CHO Glyceraldehyde-3-phosphate HCOH CH2O CH2OH Sedoheptulose-7-phosphate HOCH HCOH HCOH HCOH CH2O C O C O Glyceraldehyde-3-phosphate HCOH CH2O CHO Pentose phosphate epimerase Transketolase Transaldolase Transketolase NADP+ NADPH NADP+ —P —P —P —P —P —P —P —P —P —P NADPH is generated in the first two reactions of the pathway, where glucose-6-phosphate is oxidized to ribulose-5-phosphate. These reactions are essentially irreversible.
The ribulose-5-phosphate is converted to the glycolytic intermediates fructose-6-phosphate and glyceraldehyde-3-phosphate through a series of metabolic interconversions. These reactions are freely reversible.
Pentose phosphate isomerase Hexose phosphate isomerase FIGURE 11.4 Reactions of the oxidative pentose phosphate pathway in higher plants. P, phosphate.
dark, the pathway may also supply NADPH for biosynthetic reactions such as lipid biosynthesis and nitrogen assimilation.
• Because plant mitochondria are able to oxidize cytosolic NADPH via an NADPH dehydrogenase localized on the external surface of the inner mem-brane, some of the reducing power generated by this pathway may contribute to cellular energy metabo-lism; that is, electrons from NADPH may end up reducing O2 and generating ATP.
• The pathway produces ribose-5-phosphate, a precur-sor of the ribose and deoxyribose needed in the syn-thesis of RNA and DNA, respectively.
• Another intermediate in this pathway, the four-car-bon erythrose-4-phosphate, combines with PEP in the initial reaction that produces plant phenolic com-pounds, including the aromatic amino acids and the precursors of lignin, flavonoids, and phytoalexins (see Chapter 13).
• During the early stages of greening, before leaf tis-sues become fully photoautotrophic, the oxidative pentose phosphate pathway is thought to be involved in generating Calvin cycle intermediates.
Control of the oxidative pathway.
The oxidative pen-tose phosphate pathway is controlled by the initial reaction of the pathway catalyzed by glucose-6-phosphate dehy-drogenase, the activity of which is markedly inhibited by a high ratio of NADPH to NADP+.
In the light, however, little operation of the oxidative pathway is likely to occur in the chloroplast because the end products of the pathway, fructose-6-phosphate and glyceraldehyde-3-phosphate, are being synthesized by the Calvin cycle. Thus, mass action will drive the nonoxidative interconversions of the pathway in the direction of pentose synthesis. Moreover, glucose-6-phosphate dehydrogenase will be inhibited during photosynthesis by the high ratio of NADPH to NADP+ in the chloroplast, as well as by a reductive inactivation involving the ferredoxin–thioredoxin system (see Chapter 8).
THE CITRIC ACID CYCLE: A MITOCHONDRIAL MATRIX PROCESS During the nineteenth century, biologists discovered that in the absence of air, cells produce ethanol or lactic acid, whereas in the presence of air, cells consume O2 and pro-duce CO2 and H2O. In 1937 the German-born British bio-chemist Hans A. Krebs reported the discovery of the cit-ric acid cycle—also called the tricarboxylic acid cycle or Krebs cycle. The elucidation of the citric acid cycle not only explained how pyruvate is broken down to CO2 and H2O; it also highlighted the key concept of cycles in metabolic pathways. For his discovery, Hans Krebs was awarded the Nobel Prize in physiology and medicine in 1953.
Because the citric acid cycle is localized in the matrix of mitochondria, we will begin with a general description of mitochondrial structure and function, knowledge obtained mainly through experiments on isolated mitochondria (see Web Topic 11.1). We will then review the steps of the citric acid cycle, emphasizing the features that are specific to plants. For all plant-specific properties, we will consider how they affect respiratory function.
Mitochondria Are Semiautonomous Organelles The breakdown of sucrose to pyruvate releases less than 25% of the total energy in sucrose; the remaining energy is stored in the two molecules of pyruvate. The next two stages of respiration (the citric acid cycle and oxidative phosphorylation—i.e., electron transport coupled to ATP synthesis) take place within an organelle enclosed by a dou-ble membrane, the mitochondrion (plural mitochondria).
In electron micrographs, plant mitochondria—whether in situ or in vitro—usually look spherical or rodlike (Fig-ure 11.5), ranging from 0.5 to 1.0 µm in diameter and up to 3 µm in length (Douce 1985). With some exceptions, plant cells have a substantially lower number of mitochondria than that found in a typical animal cell. The number of mitochondria per plant cell varies, and it is usually directly related to the metabolic activity of the tissue, reflecting the mitochondrial role in energy metabolism. Guard cells, for example, are unusually rich in mitochondria.
The ultrastructural features of plant mitochondria are similar to those of mitochondria in nonplant tissues (see Figure 11.5). Plant mitochondria have two membranes: a smooth outer membrane that completely surrounds a highly invaginated inner membrane. The invaginations of the inner membrane are known as cristae (singular crista).
As a consequence of the greatly enlarged surface area, the inner membrane can contain more than 50% of the total mitochondrial protein. The aqueous phase contained within the inner membrane is referred to as the mitochon-drial matrix (plural matrices), and the region between the two mitochondrial membranes is known as the intermem-brane space.
Intact mitochondria are osmotically active; that is, they take up water and swell when placed in a hypo-osmotic medium. Most inorganic ions and charged organic mole-cules are not able to diffuse freely into the matrix space.
The inner membrane is the osmotic barrier; the outer mem-brane is permeable to solutes that have a molecular mass of less than approximately 10,000 Da (i.e., most cellular metabolites and ions, but not proteins). The lipid fraction of both membranes is primarily made up of phospholipids, 80% of which are either phosphatidylcholine or phos-phatidylethanolamine.
Like chloroplasts, mitochondria are semiautonomous organelles because they contain ribosomes, RNA, and 232 Chapter 11 DNA, which encodes a limited number of mitochondrial proteins. Plant mitochondria are thus able to carry out the various steps of protein synthesis and to transmit their genetic information. Mitochondria proliferate through the division by fission of preexisting mitochondria and not through de novo biogenesis of the organelle.
Pyruvate Enters the Mitochondrion and Is Oxidized via the Citric Acid Cycle As already noted, the citric acid cycle is also known as the tricarboxylic acid cycle, because of the importance of the tricarboxylic acids citric acid (citrate) and isocitric acid (isocitrate) as early intermediates (Figure 11.6). This cycle constitutes the second stage in respiration and takes place in the mitochondrial matrix. Its operation requires that the pyruvate generated in the cytosol during glycolysis be transported through the impermeable inner mitochondrial membrane via a specific transport protein (as will be described shortly).
Once inside the mitochondrial matrix, pyruvate is decar-boxylated in an oxidation reaction by the enzyme pyruvate dehydrogenase. The products are NADH (from NAD+), CO2, and acetic acid in the form of acetyl-CoA, in which a thioester bond links the acetic acid to a sulfur-containing cofactor, coenzyme A (CoA) (see Figure 11.6). Pyruvate dehydrogenase exists as a large complex of several enzymes that catalyze the overall reaction in a three-step process: decarboxylation, oxidation, and conjugation to CoA.
In the next reaction the enzyme citrate synthase com-bines the acetyl group of acetyl-CoA with a four-carbon dicarboxylic acid (oxaloacetate, OAA) to give a six-carbon tricarboxylic acid (citrate). Citrate is then isomerized to isocitrate by the enzyme aconitase.
The following two reactions are successive oxidative decarboxylations, each of which produces one NADH and releases one molecule of CO2, yielding a four-carbon mol-ecule, succinyl-CoA. At this point, three molecules of CO2 have been produced for each pyruvate that entered the mitochondrion, or 12 CO2 for each molecule of sucrose oxi-dized.
During the remainder of the citric acid cycle, succinyl-CoA is oxidized to OAA, allowing the continued operation of the cycle. Initially the large amount of free energy avail-able in the thioester bond of succinyl-CoA is conserved through the synthesis of ATP from ADP and Pi via a sub-strate-level phosphorylation catalyzed by succinyl-CoA synthetase. (Recall that the free energy available in the thioester bond of acetyl-CoA was used to form a car-bon–carbon bond in the step catalyzed by citrate synthase.) The resulting succinate is oxidized to fumarate by succinate dehydrogenase, which is the only membrane-associated enzyme of the citric acid cycle and also part of the electron transport chain (which is the next major topic to be dis-cussed in this chapter).
The electrons and protons removed from succinate end up not on NAD+ but on another cofactor involved in redox reactions: FAD (flavin adenine dinucleotide). FAD is cova-lently bound to the active site of succinate dehydrogenase and undergoes a reversible two-electron reduction to pro-duce FADH2 (see Figure 11.2).
(B) Cristae Intermembrane space (A) Outer membrane Inner membrane Matrix FIGURE 11.5 Structure of plant mitochondria. (A) Three-dimensional representa-tion of a mitochondrion, showing the invaginations of the inner membrane that are called cristae, as well as the location of the matrix and intermembrane spaces (see also Figure 11.10). (B) Electron micrograph of mitochondria in a mesophyll cell of Vicia faba. (Photo from Gunning and Steer 1996.) 0.5 mm Respiration and Lipid Metabolism 233 In the final two reactions of the citric acid cycle, fumarate is hydrated to produce malate, which is subse-quently oxidized by malate dehydrogenase to regenerate OAA and produce another molecule of NADH. The OAA produced is now able to react with another acetyl-CoA and continue the cycling.
The stepwise oxidation of one mole-cule of pyruvate in the mitochondrion gives rise to three molecules of CO2, and much of the free energy released during these oxidations is conserved in the form of four NADH and one FADH2. In addition, one molecule of ATP is produced by a substrate-level phosphorylation during the citric acid cycle.
All the enzymes associated with the citric acid cycle are found in plant mitochondria. Some of them may be asso-ciated in multienzyme complexes, which would facilitate movement of metabolites between the enzymes.
CH3 O O OH C C C C C CH2 C H H OH OH C O –O O O O– O– C C C CH2 C H H C O –O O O O– O– O C CH3 CoA C CH2 CH2 C O C O –O O O– C CH2 CH2 O –O C C C H H H H C O –O O O– C C C C O –O O O– H H C C H OH CH2 C O –O O O– C C CH2 C O O O O– O– ATP ADP FADH2 FAD Acetyl-CoA Pyruvate Pyruvate dehydrogenase Citrate synthase Aconitase CoA CO2 CO2 CO2 CoA Citrate Isocitrate Oxaloacetate Malate Succinate Succinyl-CoA C CoA CoA O 2-Oxoglutarate Fumarate Isocitrate dehydrogenase 2-Oxoglutarate dehydrogenase CoA Succinyl-CoA synthetase H2O Succinate dehydrogenase Fumarase H2O Malate dehydrogenase Citric acid cycle NADH NADH NADH NADH NADH NAD+ NAD+ NAD+ NAD+ NAD+ One molecule of ATP is synthesized by a substrate-level phosphorylation during the reaction catalyzed by succinyl-CoA synthetase.
Malic enzyme decarboxylates malate to pyruvate and enables plant mitochondria to oxidize malate.
Malic enzyme CO2 FIGURE 11.6 Reactions and enzymes of the plant citric acid cycle. Pyruvate is completely oxidized to three molecules of CO2. The electrons released during these oxidations are used to reduce four molecules of NAD+ to NADH and one molecule of FAD to FADH2.
234 Chapter 11 The Citric Acid Cycle of Plants Has Unique Features The citric acid cycle reactions outlined in Figure 11.6 are not all identical with those carried out by animal mitochondria.
For example, the step catalyzed by succinyl-CoA syn-thetase produces ATP in plants and GTP in animals.
A feature of the plant citric acid cycle that is absent in many other organisms is the significant activity of NAD+ malic enzyme, which has been found in the matrix of all plant mitochondria analyzed to date. This enzyme cat-alyzes the oxidative decarboxylation of malate: Malate + NAD+ →pyruvate + CO2 + NADH The presence of NAD+ malic enzyme enables plant mitochondria to operate alternative pathways for the metabolism of PEP derived from glycolysis. As already described, malate can be synthesized from PEP in the cytosol via the enzymes PEP carboxylase and malate dehy-drogenase (see Figure 11.3). Malate is then transported into the mitochondrial matrix, where NAD+ malic enzyme can oxidize it to pyruvate. This reaction makes possible the complete net oxidation of citric acid cycle intermediates such as malate (Figure 11.7A) or citrate (Figure 11.7B) (Oliver and McIntosh 1995).
Alternatively, the malate produced via the PEP car-boxylase can replace citric acid cycle intermediates used in biosynthesis. Reactions that can replenish intermediates in a metabolic cycle are known as anaplerotic. For example, export of 2-oxoglutarate for nitrogen assimilation in the chloroplast will cause a shortage of malate needed in the citrate synthase reaction. This malate can be replaced through the PEP carboxylase pathway (Figure 11.7C).
The presence of an alternative pathway for the oxidation of malate is consistent with the observation that many plants, in addition to those that carry out crassulacean acid metabolism (see Chapter 8), store significant levels of malate in their central vacuole.
ELECTRON TRANSPORT AND ATP SYNTHESIS AT THE INNER MITOCHONDRIAL MEMBRANE ATP is the energy carrier used by cells to drive living processes, and chemical energy conserved during the cit-ric acid cycle in the form of NADH and FADH2 (redox equivalents with high-energy electrons) must be converted to ATP to perform useful work in the cell. This O2-depen-dent process, called oxidative phosphorylation, occurs in the inner mitochondrial membrane.
In this section we will describe the process by which the energy level of the electrons is lowered in a stepwise fash-ion and conserved in the form of an electrochemical proton gradient across the inner mitochondrial membrane.
Although fundamentally similar in all aerobic cells, the electron transport chain of plants (and fungi) contains mul-1 Malate 1 Malate 1 Oxaloacetate 1 Pyruvate (A) 1 Citrate 1 Isocitrate 1 Acetyl-CoA From cytosol: 2 Malate 1 Pyruvate (B) 1 Citrate 2 Isocitrate 1 Acetyl-CoA 1 Citrate From cytosol: 1 Malate 1 Pyruvate 2 PEP (C) 1 Citrate 1 Isocitrate 2-Oxoglutarate Nitrogen assimilation 1 Acetyl-CoA 1 Oxaloacetate 1 Oxaloacetate + FIGURE 11.7 Malic enzyme and PEP carboxylase provide plants with metabolic flexibility for the metabolism of phosphoenolpyruvate. Malic enzyme makes it possible for plant mitochondria to oxidize both malate (A) and citrate (B) to CO2 without involving pyruvate delivered by glycol-ysis. The joint action of PEP carboxylase and pyruvate kinase can convert glycolytic PEP to 2-oxoglutarate, which is used for nitrogen assimilation (C).
Respiration and Lipid Metabolism 235 tiple NAD(P)H dehydrogenases and an alternative oxidase not found in mammalian mitochondria.
We will also examine the enzyme that uses the energy of the proton gradient to synthesize ATP: the FoF1-ATP syn-thase. After examining the various stages in the production of ATP, we will summarize the energy conservation steps at each stage, as well as the regulatory mechanisms that coordinate the different pathways.
The Electron Transport Chain Catalyzes a Flow of Electrons from NADH to O2 For each molecule of sucrose oxidized through glycolysis and the citric acid cycle pathways, 4 molecules of NADH are generated in the cytosol and 16 molecules of NADH plus 4 molecules of FADH2 (associated with succinate dehydrogenase) are generated in the mitochondrial matrix.
These reduced compounds must be reoxidized or the entire respiratory process will come to a halt.
The electron transport chain catalyzes an electron flow from NADH (and FADH2) to oxygen, the final electron acceptor of the respiratory process. For the oxidation of NADH, the overall two-electron transfer can be written as follows: NADH + H+ + 1⁄2 O2 →NAD+ + H2O From the reduction potentials for the NADH–NAD+ pair (–320 mV) and the H2O–1⁄2O2 pair (+810 mV), it can be calculated that the standard free energy released during this overall reaction (–nF∆E0′ ) is about 220 kJ mol–1 (52 kcal mol–1) per two electrons (for a detailed discussion on standard free energy see Chapter 2 on the web site).
Because the succinate–fumarate reduction potential is higher (+30 mV), only 152 kJ mol–1 (36 kcal mol–1) of energy is released for each two electrons generated during the oxidation of succinate. The role of the electron transport chain is to bring about the oxidation of NADH (and FADH2) and, in the process, utilize some of the free energy released to generate an electrochemical proton gradient, ∆m ~ Η+, across the inner mitochondrial membrane.
The electron transport chain of plants contains the same set of electron carriers found in mitochondria from other organisms (Figure 11.8) (Siedow 1995; Siedow and Umbach 1995). The individual electron transport proteins are orga-nized into four multiprotein complexes (identified by Roman numerals I through IV), all of which are localized in the inner mitochondrial membrane: Complex I (NADH dehydrogenase).
Electrons from NADH generated in the mitochondrial matrix during the citric acid cycle are oxidized by complex I (an NADH dehydrogenase). The electron carriers in complex I include a tightly bound cofactor (flavin mononucleotide [FMN], which is chemically similar to FAD; see Figure 11.2B) and several iron–sulfur centers. Complex I then transfers these electrons to ubiquinone. Four protons are pumped from the matrix to the intermembrane space for every electron pair passing through the complex.
Ubiquinone, a small lipid-soluble electron and proton carrier, is located within the inner membrane. It is not tightly associated with any protein, and it can diffuse within the hydrophobic core of the membrane bilayer.
Complex II (succinate dehydrogenase).
Oxidation of succinate in the citric acid cycle is catalyzed by this com-plex, and the reducing equivalents are transferred via the FADH2 and a group of iron–sulfur proteins into the ubiquinone pool. This complex does not pump protons.
Complex III (cytochrome bc1 complex).
This complex oxidizes reduced ubiquinone (ubiquinol) and transfers the electrons via an iron–sulfur center, two b-type cytochromes (b565 and b560), and a membrane-bound cytochrome c1 to cytochrome c. Four protons per electron pair are pumped by complex III.
Cytochrome c is a small protein loosely attached to the outer surface of the inner membrane and serves as a mobile carrier to transfer electrons between complexes III and IV.
Complex IV (cytochrome c oxidase).
This complex con-tains two copper centers (CuA and CuB) and cytochromes a and a3. Complex IV is the terminal oxidase and brings about the four-electron reduction of O2 to two molecules of H2O.
Two protons are pumped per electon pair (see Figure 11.8).
Both structurally and functionally, ubiquinone and the cytochrome bc1 complex are very similar to plastoquinone and the cytochrome b6 f complex, respectively, in the pho-tosynthetic electron transport chain (see Chapter 7).
Some Electron Transport Enzymes Are Unique to Plant Mitochondria In addition to the set of electron carriers described in the previous section, plant mitochondria contain some com-ponents not found in mammalian mitochondria (see Fig-ure 11.8). Note that none of these additional enzymes pump protons and that energy conservation is therefore lower whenever they are used: • Two NAD(P)H dehydrogenases, both Ca2+-depen-dent, attached to the outer surface of the inner mem-brane facing the intermembrane space can oxidize cytosolic NADH and NADPH. Electrons from these external NAD(P)H dehydrogenases—NDex(NADH) and NDex(NADPH)—enter the main electron trans-port chain at the level of the ubiquinone pool (see Web Topic 11.2) (Møller 2001).
• Plant mitochondria have two pathways for oxidizing matrix NADH. Electron flow through complex I, described in the previous section, is sensitive to inhi-bition by several compounds, including rotenone and piericidin. In addition, plant mitochondria have a rotenone-resistant dehydrogenase, NDin(NADH), for 236 Chapter 11 the oxidation of NADH derived from citric acid cycle substrates. The role of this pathway may well be as a bypass being engaged when complex I is overloaded (Møller and Rasmusson 1998; Møller 2001), such as under photorespiratory conditions, as we will see shortly (see also Web Topic 11.2).
• An NADPH dehydrogenase, NDin(NADPH), is pre-sent on the matrix surface. Very little is known about this enzyme.
• Most, if not all, plants have an “alternative” respira-tory pathway for the reduction of oxygen. This path-way involves the so-called alternative oxidase that, unlike cytochrome c oxidase, is insensitive to inhibi-tion by cyanide, azide, or carbon monoxide (see Web Topic 11.3).
The nature and physiological significance of these plant-specific enzymes will be considered more fully later in the chapter.
ATP Synthesis in the Mitochondrion Is Coupled to Electron Transport In oxidative phosphorylation, the transfer of electrons to oxygen via complexes I to IV is coupled to the synthesis of ATP from ADP and Pi via the ATP synthase (complex V).
The number of ATPs synthesized depends on the nature of the electron donor.
In experiments conducted with the use of isolated mitochondria, electrons derived from internal (matrix) NADH give ADP:O ratios (the number of ATPs synthe-sized per two electrons transferred to oxygen) of 2.4 to 2.7 (Table 11.1). Succinate and externally added NADH each give values in the range of 1.6 to 1.8, while ascorbate, which serves as an artificial electron donor to cytochrome c, gives values of 0.8 to 0.9. Results such as these (for both plant and animal mitochondria) have led to the gen-eral concept that there are three sites of energy conserva-tion along the electron transport chain, at complexes I, III, and IV.
ATP e– e– e– e– e– e– e– e– e– External (rotenone-insensitive) NAD(P)H dehydrogenases can accept electrons directly from NAD(P)H produced in the cytosol. The ubiquinone (UQ) pool diffuses freely within the inner membrane and serves to transfer electrons from the dehydrogenases to either complex III or the alternative oxidase.
Cytochrome c is a peripheral protein that transfers electrons from complex III to complex IV. Rotenone-insensitive NAD(P)H dehydrogenases exist on the matrix side of the membrane. An alternative oxidase (AOX) accepts electrons directly from ubiquinone. Inner membrane INTERMEMBRANE SPACE MATRIX NADH NAD+ NADH NAD+ Ca2+ NADPH NADP+ AOX NADH NAD+ Ca2+ Ca2+ NADPH NADP+ Succinate Fumarate O2 H2O O2 H2O UQ Cyt c ADP Pi + Complex I NADH dehydrogenase Complex II Succinate dehydrogenase Complex III Cytochrome bc1 complex Complex IV Cytochrome oxidase Complex V ATP synthase FO F1 4 H+ 4 H+ 2 H+ 3 H+ 3 H+ FIGURE 11.8 Organization of the electron transport chain and ATP synthesis in the inner membrane of plant mito-chondria. In addition to the five standard protein com-plexes found in nearly all other mitochondria, the electron transport chain of plant mitochondria contains five addi-tional enzymes marked in green. None of these additional enzymes pumps protons. Specific inhibitors, rotenone for complex I, antimycin for complex III, cyanide for complex IV, and salicylhydroxamic acid (SHAM) for the alternative oxidase, are important tools to investigate the electron transport chain of plant mitochondria.
Respiration and Lipid Metabolism 237 The experimental ADP:O ratios agree quite well with the values calculated on the basis of the number of H+ pumped by complexes I, III, and IV and the cost of 4 H+ for synthesizing one ATP (see next section and Table 11.1). For instance, electrons from external NADH pass only com-plexes III and IV, so a total of 6 H+ are pumped, giving 1.5 ATP (when the alternative oxidase pathway is not used).
The mechanism of mitochondrial ATP synthesis is based on the chemiosmotic hypothesis, described in Web Topic 6.3 and Chapter 7, which was first proposed in 1961 by Nobel laureate Peter Mitchell as a general mechanism of energy conservation across biological membranes (Nicholls and Ferguson 2002). According to the chemiosmotic theory, the orientation of electron carriers within the mitochon-drial inner membrane allows for the transfer of protons (H+) across the inner membrane during electron flow.
Numerous studies have confirmed that mitochondrial elec-tron transport is associated with a net transfer of protons from the mitochondrial matrix to the intermembrane space (see Figure 11.8) (Whitehouse and Moore 1995).
Because the inner mitochondrial membrane is imperme-able to H+, an electrochemical proton gradient can build up.
As discussed in Chapters 6 and 7, the free energy associated with the formation of an electrochemical proton gradient (∆m ~ Η+, also referred to as a proton motive force, ∆p, when expressed in units of volts) is made up of an electric trans-membrane potential component (∆E) and a chemical-poten-tial component (∆pH) according to the following equation: ∆p = ∆E – 59∆pH where ∆E = Einside – Eoutside and ∆pH = pHinside – pHoutside ∆E results from the asymmetric distribution of a charged species (H+) across the membrane, and ∆pH is due to the proton concentration difference across the membrane.
Because protons are translocated from the mitochondrial matrix to the intermembrane space, the resulting ∆E across the inner mitochondrial membrane is negative.
As this equation shows, both ∆E and ∆pH contribute to the proton motive force in plant mitochondria, although ∆E is consistently found to be of greater magnitude, probably because of the large buffering capacity of both cytosol and matrix, which prevent large pH changes. This situation contrasts to that in the chloroplast, where almost all of the proton motive force across the thylakoid membrane is made up by a proton gradient (see Chapter 7).
The free-energy input required to generate ∆m ~ Η+ comes from the free energy released during electron transport.
How electron transport is coupled to proton translocation is not well understood in all cases. Because of the low per-meability (conductance) of the inner membrane to protons, the proton electrochemical gradient is reasonably stable, once generated, and the free energy ∆m ~ Η+ can be utilized to carry out chemical work (ATP synthesis). The ∆m ~ Η+ is cou-pled to the synthesis of ATP by an additional protein com-plex associated with the inner membrane, the FoF1-ATP synthase.
The FoF1-ATP synthase (also called complex V) consists of two major components, F1 and Fo (see Figure 11.8). F1 is a peripheral membrane protein complex that is composed of at least five different subunits and contains the catalytic site for converting ADP and Pi to ATP. This complex is attached to the matrix side of the inner membrane. Fo is an integral membrane protein complex that consists of at least three different polypeptides that form the channel through which protons cross the inner membrane.
The passage of protons through the channel is coupled to the catalytic cycle of the F1 component of the ATP syn-thase, allowing the ongoing synthesis of ATP and the simul-taneous utilization of the ∆m ~ Η+. For each ATP synthesized, 3 H+ pass through the Fo from the intermembrane space to the matrix down the electrochemical proton gradient.
A high-resolution X-ray structure of most of the F1 com-plex of the mammalian mitochondrial ATP synthase sup-ports a “rotational model” for the catalytic mechanism of ATP synthesis (see Web Topic 11.4) (Abrahams et al. 1994).
The structure and function of the mitochondrial ATP syn-thase is similar to that of the CFo–CF1 ATP synthase in pho-tophosphorylation (see Chapter 7).
The operation of a chemiosmotic mechanism of ATP synthesis has several implications. First, the true site of ATP formation on the mitochondrial inner membrane is the ATP synthase, not complex I, III, or IV. These complexes serve as sites of energy conservation whereby electron transport is coupled to the generation of a ∆m ~ Η+.
Second, the chemiosmotic theory explains the action mechanism of uncouplers, a wide range of chemically TABLE 11.1 Theoretical and experimental ADP:O ratios in isolated plant mitochondria ADP:O ratio Substrate Theoreticala Experimental Malate 2.5 2.4–2.7 Succinate 1.5 1.6–1.8 NADH (external) 1.5 1.6–1.8 Ascorbate 1.0b 0.8–0.9 aIt is assumed that complexes I, III, and IV pump 4, 4, and 2 H+ per 2 electrons, respectively; that the cost of synthesizing one ATP and exporting it to the cytosol is 4 H+ (Brand 1994); and that the non-phosphorylating pathways are not active.
bCytochrome c oxidase pumps only two protons when it is mea-sured with ascorbate as electron donor. However, two electrons move from the outer surface of the inner membrane (where the electrons are donated) across the inner membrane to the inner, matrix side. As a result, 2 H+ are consumed on the matrix side.This means that the net movement of H+ and charges is equivalent to the movement of a total of 4 H+, giving an ADP:O ratio of 1.0.
238 Chapter 11 unrelated compounds (including 2,4-dinitrophenol and FCCP [p-trifluoromethoxycarbonylcyanide phenylhydra-zone]) that decreases mitochondrial ATP synthesis but often stimulates the rate of electron transport (see Web Topic 11.5). All of these compounds make the inner mem-brane leaky to protons, which prevents the buildup of a sufficiently large ∆m ~ Η+ to drive ATP synthesis.
In experiments on isolated mitochondria, higher rates of electron flow (measured as the rate of oxygen uptake in the presence of a substrate such as succinate) are observed upon addition of ADP (referred to as state 3) than in its absence (Figure 11.9). ADP provides a substrate that stim-ulates dissipation of the ∆m ~ Η+ through the FoF1-ATP syn-thase during ATP synthesis. Once all the ADP has been converted to ATP, the ∆m ~ Η+ builds up again and reduces the rate of electron flow (state 4). The ratio of the rates with and without ADP (state 3:state 4) is referred to as the respiratory control ratio.
Transporters Exchange Substrates and Products The electrochemical proton gradient also plays a role in the movement of the organic acids of the citric acid cycle and of substrates and products of ATP synthesis in and out of mitochondria. Although ATP is synthesized in the mito-chondrial matrix, most of it is used outside the mitochon-drion, so an efficient mechanism is needed for moving ADP in and ATP out of the organelle.
Adenylate transport involves another inner-membrane protein, the ADP/ATP (adenine nucleotide) transporter, which catalyzes an exchange of ADP and ATP across the inner membrane (Figure 11.10). The movement of the more negatively charged ATP4– out of the mitochondria in exchange for ADP3–—that is, one net negative charge out— is driven by the electric-potential gradient (∆E, positive out-side) generated by proton pumping.
The uptake of inorganic phosphate (Pi) involves an active phosphate transporter protein that uses the proton gradient component (∆pH) of the proton motive force to drive the electroneutral exchange of Pi – (in) for OH– (out).
As long as a ∆pH is maintained across the inner mem-brane, the Pi content within the matrix will remain high.
Similar reasoning applies to the uptake of pyruvate, which is driven by the electroneutral exchange of pyruvate for OH–, leading to continued uptake of pyruvate from the cytosol (see Figure 11.10).
The total cost of taking up a phosphate (1 OH– out, which is the same as 1 H+ in) and exchanging ADP for ATP (one negative charge out, which is the same as one positive charge in) is 1 H+. This proton should also be included in calculation of the cost of synthesizing one ATP.
Thus the total cost is 3 H+ used by the ATP synthase plus 1 H+ for the exchange across the membrane, or a total of 4 H+.
The inner membrane also contains transporters for dicarboxylic acids (malate or succinate) exchanged for Pi 2– and for the tricarboxylic acid citrate exchanged for malate (see Figure 11.10 and Web Topic 11.5).
Aerobic Respiration Yields about 60 Molecules of ATP per Molecule of Sucrose The complete oxidation of a sucrose molecule leads to the net formation of • 8 molecules of ATP by substrate-level phosphoryla-tion (4 during glycolysis and 4 in the citric acid cycle) • 4 molecules of NADH in the cytosol • 16 molecules of NADH plus 4 molecules of FADH2 (via succinate dehydrogenase) in the mitochondrial matrix On the basis of theoretical ADP:O values (see Table 11.1), a total of approximately 52 molecules of ATP will be generated 150 125 100 75 50 25 0 1 2 3 4 5 6 7 Time (minutes) Percentage initial oxygen Mitochondria Succinate ADP ADP State 3 KCN SHAM 68 175 State 4 257 71 0 112 1. Addition of succinate initiates mitochondrial electron transfer, which is measured with an oxygen electrode as the rate of oxygen reduction (to H2O).
2. Addition of cyanide inhibits electron flow through the main cytochrome pathway and only allows electron flow to oxygen through the alternative, cyanide-resistant pathway, which is subsequently inhibited by the addition of SHAM.
3. Addition of ADP stimulates electron transfer (state 3) by facilitating dissipation of the electrochemical proton gradient. The rate is higher after the second ADP addition because of activation of succinate dehydrogenase.
4. When all the ADP has been converted to ATP, electron transfer reverts to a lower rate (state 4).
FIGURE 11.9 Regulation of respiratory rate by ADP during succinate oxidation in isolated mitochondria from mung bean (Vigna radiata). The numbers below the traces are the rates of oxygen uptake expressed as O2 consumed (nmol min–1 mg protein–1). (Data courtesy of Steven J. Stegink.) Respiration and Lipid Metabolism 239 The membrane potential component (∆E) of the proton gradient drives the electrogenic exchange of ADP from the cytosol for ATP from the mitochondrion via the adenine nucleotide transporter.
The tricarboxylic acid citrate is exchanged for a dicarboxylic acid such as malate or succinate.
Uptake of dicarboxylic acids such as malate or succinate in exchange for a phosphate ion is mediated by the dicarb-oxylate transporter.
Uncouplers (and the uncoupling protein) permit the rapid movement of protons across the inner membrane, preventing buildup of the electrochemical proton gradient and reducing the rate of ATP synthesis but not the rate of electron transfer.
The ∆pH drives the electroneutral uptake of Pi through the phosphate transporter.
Free energy released by the dissipation of the proton gradient is coupled to the synthesis of ATP4– from ADP3– and Pi via the many FoF1-ATP synthase complexes that span the inner membrane.
Uptake of pyruvate in exchange for a hydroxyl ion is mediated by the pyruvate transporter.
Pyruvate transporter OH– OH– Phosphate transporter I II III IV Electron transport complexes ATP synthase (complex V) Uncouplers Dicarboxylate transporter Low [H+] High Adenine nucleotide transporter F1 Fo Malate2– ADP3– ATP4– ADP3– Pi – Pi2– Pi– Pyruvate– ATP4– Inner membrane Intermembrane space Pore Outer membrane CYTOSOL MATRIX pH 7.5 pH 8.0 Citrate2– Malate2– F1 F1 Fo Fo H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ H+ Tricarboxylate transporter [H+] 240 Chapter 11 per sucrose by oxidative phosphorylation. The result is a total of about 60 ATPs synthesized per sucrose (Table 11.2).
Using 50 kJ mol–1 (12 kcal mol–1) as the actual free energy of formation of ATP in vivo, we find that about 3010 kJ mol–1 (720 kcal mol–1) of free energy is conserved in the form of ATP per mole of sucrose oxidized during aerobic respiration. This amount represents about 52% of the standard free energy available from the complete oxi-dation of sucrose; the rest is lost as heat. This is a vast improvement over the conversion of only 4% of the energy available in sucrose to ATP that is associated with fer-mentative metabolism.
Several Subunits of Respiratory Complexes Are Encoded by the Mitochondrial Genome With the first complete sequencing of plant mitochond-rial DNA (mtDNA) in Arabidopsis thaliana (Marienfeld et al.
1999), our knowledge about the mitochondrial genome has taken a great leap forward.
Some characteristics of the plant mitochondrial genetic system are not generally found in the mitochondria of ani-mals, protozoans, or even fungi. Most notably, RNA pro-cessing differs between plant mitochondria and mitochon-dria from most other organisms. Several plant mito-chondrial genes contain introns, and some genes are even split between separate transcript molecules, which must be joined by splicing. Plant mtDNA also lacks strict comple-mentarity to translated mRNA (see Web Topic 11.6).
Another characteristic feature of the plant mitochondrial genetic system is that it strictly observes the universal genetic code, showing none of the deviations found in mtDNA in all other kingdoms.
Plant mitochondrial genomes are generally much larger than those of animals. The plant mtDNA is in the range of 200 to 2400 kilobase pairs (kb) in size, with large variations even between closely related plant species. This size com-pares with the compact and uniform 16 kb genome found in mammalian mitochondria. The size differences are due mainly to the presence of much noncoding sequence, including numerous introns, in plant mtDNA. Mammalian mtDNA encodes only 13 proteins, in contrast to the 35 known proteins encoded by the Arabidopsis mtDNA. Both plant and mammalian mitochondria encode rRNAs and tRNAs.
The genes of the mtDNA can be divided into two main groups: those needed for expression of mitochondrial genes (tRNA, rRNA, and ribosome proteins) and those for oxida-tive phosphorylation complexes. Plant mtDNAencodes nine subunits for complex I, one for complex III, three for com-plex IV, three for ATP synthase, and five proteins for bio-genesis of cytochromes (Marienfeld et al. 1999). The mito-chondrially encoded subunits are essential for the activity of the respiratory complexes, a feature also evident in the sequence conservation to their bacterial homologs. The nuclear genome encodes all proteins not encoded in mtDNA, and the nuclear-encoded proteins are the large majority—for example, all proteins in the citric acid cycle.
The nuclear-encoded mitochondrial proteins are synthesized by cytosolic ribosomes and imported via translocators in the outer and inner mitochondrial membrane. Therefore, oxida-tive phosphorylation is dependent on expression of genes located in two separate genomes. Any change in expression in response to a stimulus or for develop-mental reasons must be coordinated.
Whereas the expression of nuclear genes for mitochondrial proteins appears to be regulated as other nuclear genes, much less is known about the expression of mitochondrial genes. The master circle of plant mtDNA is normally split into several smaller subgenomic segments, and genes can be down-regulated by decreased copy number for a segment of the mtDNA (Leon et al. 1998). The gene promoters in mtDNA are of several kinds and show different transcriptional activ-ity. However, a main control of mito-chondrial gene expression appears to take place at the posttranslational level, by degradation of excess polypeptides (McCabe et al. 2000).
FIGURE 11.10 Transmembrane transport in plant mitochon-dria. An electrochemical proton gradient (∆m ~ Η+) consisting of a membrane potential (∆E, –200mV, negative inside) and a ∆pH (alkaline inside) is established across the inner mito-chondrial membrane during electron transport as outlined in the text. Specific metabolites are moved across the inner membrane by specialized proteins, called transporters or carriers (After Douce 1985).
L TABLE 11.2 The maximum yield of cytosolic ATP from the complete oxidation of sucrose to CO2 via aerobic glycolysis and the citric acid cycle Part reaction ATP per sucrosea Glycolysis 4 substrate-level phosphorylations 4 4 NADH 4 ×1.5 6 Citric acid cycle 4 substrate level phosphorylations 4 4 FADH2 4 × 1.5 6 16 NADH 16 × 2.5 40 Total 60 Source: Adapted from Brand 1994.
Note: Cytosolic NADH is assumed oxidized by the external NADH dehydrogenase.The nonphosphorylating pathways are assumed not to be engaged.
aCalculated using the theoretical values from Table 11.1 Respiration and Lipid Metabolism 241 Plants Have Several Mechanisms That Lower the ATP Yield As we have seen, a complex machinery is required for a high efficiency of energy conservation in oxidative phos-phorylation. So it is perhaps surprising that plant mito-chondria have several functional proteins that reduce this efficiency. Probably plants are less limited by the energy supply (sunlight) than by other factors in the environment (e.g., access to nitrogen or phosphate). As a consequence, adaptational flexibility may be more important than ener-getic efficiency.
In the following subsections we will discuss the role of the nonphosphorylating mechanisms and their possible usefulness in the life of the plant.
The alternative oxidase.
If cyanide (1 mM) is added to actively respiring animal tissues, cytochrome c oxidase is inhibited and the respiration rate quickly drops to less than 1% of its initial level. However, most plant tissues display a level of cyanide-resistant respiration that can represent 10 to 25%, and in some tissues up to 100%, of the uninhibited control rate. The enzyme responsible for this oxygen uptake has been identified as a cyanide-resistant oxidase compo-nent of the plant mitochondrial electron transport chain called the alternative oxidase (see Figure 11.8 and Web Topic 11.3) (Vanlerberghe and McIntosh 1997).
Electrons feed off the main electron transport chain into the alternative pathway at the level of the ubiquinone pool (see Figure 11.8). The alternative oxidase, the only compo-nent of the alternative pathway, catalyzes a four-electron reduction of oxygen to water and is specifically inhibited by several compounds, most notably salicylhydroxamic acid (SHAM).
When electrons pass to the alternative pathway from the ubiquinone pool, two sites of proton pumping (at com-plexes III and IV) are bypassed. Because there is no energy conservation site in the alternative pathway between ubiquinone and oxygen, the free energy that would nor-mally be conserved as ATP is lost as heat when electrons are shunted through the alternative pathway.
How can a process as seemingly energetically wasteful as the alternative pathway contribute to plant metabolism?
One example of the functional usefulness of the alternative oxidase is its activity during floral development in certain members of the Araceae (the arum family)—for example, the voodoo lily (Sauromatum guttatum). Just before pollina-tion, tissues of the clublike inflorescence, called the appen-dix, which bears male and female flowers, exhibit a dra-matic increase in the rate of respiration via the alternative pathway. As a result, the temperature of the upper appen-dix increases by as much as 25°C over the ambient tem-perature for a period of about 7 hours.
During this extraordinary burst of heat production, cer-tain amines, indoles, and terpenes are volatilized, and the plant therefore gives off a putrid odor that attracts insect pollinators. Salicylic acid, a phenolic compound related to aspirin (see Chapter 13), has been identified as the chemi-cal signal responsible for initiating this thermogenic event in the voodoo lily (Raskin et al. 1989) (see Web Essay 11.3).
In most plants, however, both the respiratory rates and the rate of cyanide-resistant respiration are too low to generate sufficient heat to raise the temperature significantly, so what other role(s) does the alternative pathway play?
It has been suggested that the alternative pathway can function as an “energy overflow” pathway, oxidizing res-piratory substrates that accumulate in excess of those needed for growth, storage, or ATP synthesis (Lambers 1985). This view suggests that electrons flow through the alternative pathway only when the activity of the main pathway is saturated. Such saturation is reached in the test tube in state 4 (see Figure 11.9); in vivo, saturation may occur if the respiration rate exceeds the cell’s demand for ATP (i.e., if ADP levels are very low). However, it is now clear that the alternative oxidase can be active before the cytochrome pathway is saturated. Thus the alternative oxi-dase makes it possible for the mitochondrion to adjust the relative rates of ATP production and synthesis of carbon skeletons for use in biosynthetic reactions.
Another possible function of the alternative pathway is in the response of plants to a variety of stresses (phosphate deficiency, chilling, drought, osmotic stress, and so on), many of which can inhibit mitochondrial respiration (see Chapter 25 and Web Essay 11.1) (Wagner and Krab 1995).
By draining off electrons from the electron transport chain, the alternative pathway prevents a potential overre-duction of the ubiquinone pool (see Figure 11.8), which, if left unchecked, can lead to the generation of destructive reactive oxygen species such as superoxide anions and hydroxyl radicals. In this way the alternative pathway may lessen the detrimental effects of stress on respiration (see Web Essay 11.4) (Wagner and Krab 1995; Møller 2001).
The uncoupling protein.
A protein found in the inner membrane of mammalian mitochondria, the uncoupling protein, can dramatically increase the proton permeability of the membrane and thus act as an uncoupler. As a result, less ATP and more heat is generated. Heat production appears to be one of the uncoupling protein’s main func-tions in mammalian cells.
It has long been thought that the alternative oxidase in plants and the uncoupling protein in mammals were sim-ply two different means of achieving the same end. It was therefore surprising when a protein similar to the uncou-pling protein was discovered in plant mitochondria (Vercesi et al. 1995; Laloi et al. 1997). This protein is stress induced and, like the alternative oxidase, may function to prevent overreduction of the electron transport chain (see Web Topic 11.3 and Web Essay 11.4). It remains unclear, however, why plant mitochondria require both mechanisms.
242 Chapter 11 The internal, rotenone-insensitive NADH dehydroge-nase, NDin(NADH).
This is one of the multiple NAD(P)H dehydrogenases found in plant mitochondria (see Figure 11.8). It has been suggested to work as a non-proton-pumping bypass when complex I is overloaded.
Complex I has a higher affinity for NADH (ten times lower Km), than NDin(NADH). At lower NADH levels in the matrix, typically when ADP is available (state 3), complex I will dominate, whereas when ADP is rate limiting (state 4), NADH levels will increase and NDin(NADH) will be more active. The physiological importance of this enzyme is, however, still unclear.
Mitochondrial Respiration Is Controlled by Key Metabolites The substrates of ATP synthesis—ADP and Pi—appear to be key regulators of the rates of glycolysis in the cytosol, as well as the citric acid cycle and oxidative phosphorylation in the mitochondria. Control points exist at all three stages of respiration; here we will give just a brief overview of some major features.
The best-characterized site of regulation of the citric acid cycle is at the pyruvate dehydrogenase complex, which is reversibly phosphorylated by a regulatory kinase and a phos-phatase. Pyruvate dehydrogenase is inactive in the phos-phorylated state, and the regulatory kinase is inhibited by pyruvate, allowing the enzyme to be active when substrate is available (Figure 11.11). In addition, several citric acid cycle enzymes, including pyruvate dehydrogenase and 2-oxoglu-tarate dehydrogenase, are directly inhibited by NADH.
ATP ADP P Pi PDH Inactive PDH Active H2O PDH kinase PDH phosphatase Pyruvate + CoA + NAD+ Acetyl-CoA + CO2 + NADH Effect on PDH activity Activating Inhibits kinase Inhibits kinase Stimulates phosphatase Mechanism Inhibits PDH Stimulates kinase Inhibits PDH Stimulates kinase Inhibits PDH Stimulates kinase Pyruvate ADP Mg2+ (or Mn2+) Inactivating NADH Acetyl CoA NH4 + FIGURE 11.11 Regulation of pyruvate dehydrogenase (PDH) activity by reversible phosphorylation and by other metabolites.
Malate Oxaloacetate Pyruvate Phosphoenolpyruvate Fructose-1,6-bisphosphate Fructose-6-phosphate Citrate Isocitrate 2-Oxoglutarate Acetyl-CoA Citric acid cycle Electron transport chain ATP ADP NADH NAD+ Pi + FIGURE 11.12 Concept of bottom-up regulation of plant res-piration. Several substrates for respiration (e.g., ADP) stimu-late enzymes in early steps of the pathways (green arrows .
In contrast, accumulation of products (e.g., ATP) inhibits (red squares) earlier reactions in a stepwise fashion. For instance, ATP inhibits the electron transport chain leading to an accumulation of NADH. NADH inhibits citric acid enzymes such as isocitrate dehydrogenase and 2-oxoglu-tarate dehydrogenase. Then, citric acid cycle intermediates like citrate inhibit the PEP-metabolizing enzymes in the cytosol. Finally, PEP inhibits the conversion of fructose-6-phosphate to fructose-1,6-biphosphate and restricts carbon feeding into glycolysis.
Respiration and Lipid Metabolism 243 The citric acid cycle oxidations, and subsequently res-piration, are dynamically controlled by the cellular level of adenine nucleotides. As the cell’s demand for ATP in the cytosol decreases relative to the rate of synthesis of ATP in the mitochondria, less ADP will be available, and the elec-tron transport chain will operate at a reduced rate (see Fig-ure 11.10). This slowdown could be signaled to citric acid cycle enzymes through an increase in matrix NADH, inhibiting the activity of several citric acid cycle dehydro-genases (Oliver and McIntosh 1995).
The buildup of citric acid cycle intermediates and their derivates, such as citrate and glutamate, inhibits the action of cytosolic pyruvate kinase, increasing the cytosolic PEP concentration, which in turn reduces the rate of conversion of fructose-6-phosphate to fructose-1,6-bisphosphate, thus inhibiting glycolysis.
In summary, plant respiratory rates are controlled from the “bottom up” by the cellular level of ADP (Figure 11.12).
ADP initially regulates the rate of electron transfer and ATP synthesis, which in turn regulates citric acid cycle activity, which, finally, regulates the rate of the glycolytic reactions.
Respiration Is Tightly Coupled to Other Pathways Glycolysis, the pentose phosphate pathway, and the citric acid cycle are linked to several other important metabolic pathways, some of which will be covered in greater detail in Chapter 13. The respiratory pathways are central to the pro-duction of a wide variety of plant metabolites, including amino acids, lipids and related compounds, isoprenoids, and porphyrins (Figure 11.13). Indeed, much of the reduced car-bon that is metabolized by glycolysis and the citric acid cycle is diverted to biosynthetic purposes and not oxidized to CO2.
ADP ATP NAD NADP FMN CoA Cytokinins Alkaloids Flavonoids Lignin Tryptophan Tyrosine Phenylalanine Proteins Aspartate Alanine Pyruvate Acetyl-CoA Oxaloacetate Citric acid cycle Nucleotides Nucleic acids Indoleacetic acid (auxin) Shikimic acid Erythrose-4-phosphate Pentose phosphate Glucose-6-phosphate Cellulose Glyceraldehyde-3-phosphate Phosphoenolpyruvate Dihydroxyacetone phosphate Glycerol-3-phosphate Lipids and related substances Glutamate Other amino acids Citrate Isocitrate Malate Fumarate Succinate 2-Oxoglutarate Proteins Fatty acids Gibberellins Carotenoids Sterols Abscisic acid Chlorophylls Phycocyanins Phytochrome Cytochrome Catalase Glucose-1-phosphate Starch FIGURE 11.13 Glycolysis, the pentose phosphate pathway and the citric acid cycle contribute precursors to many biosynthetic pathways in higher plants. The pathways shown illustrate the extent to which plant biosynthesis depends on the flux of carbon through these pathways and emphasize the fact that not all the carbon that enters the glycolytic pathway is oxidized to CO2.
244 Chapter 11 RESPIRATION IN INTACT PLANTS AND TISSUES Many rewarding studies of plant respiration and its regu-lation have been carried out on isolated organelles and on cell-free extracts of plant tissues. But how does this knowl-edge relate to the function of the whole plant in a natural or agricultural setting?
In this section we’ll examine respiration and mitochon-drial function in the context of the whole plant under a variety of conditions. First, when green tissues are exposed to light, respiration and photosynthesis operate simulta-neously and interact in complex ways. Next we will dis-cuss different rates of tissue respiration, which may be under developmental control, as well as the very interest-ing case of cytoplasmic male sterility. Finally, we will look at the influence of various environmental factors on respi-ration rates.
Plants Respire Roughly Half of the Daily Photosynthetic Yield Many factors can affect the respiration rate of an intact plant or of its individual organs. Relevant factors include the species and growth habit of the plant, the type and age of the specific organ, and environmental variables such as the external oxygen concentration, temperature, and nutri-ent and water supply (see Chapter 25, Web Topic 11.7, and Web Essay 11.5).
Whole-plant respiration rates, particularly when con-sidered on a fresh-weight basis, are generally lower than respiration rates reported for animal tissues. This difference is due in large part to the presence, in plant cells, of a large central vacuole and cell wall compartments, neither of which contains mitochondria. Nonetheless, respiration rates in some plant tissues are as high as those observed in actively respiring animal tissues, so the plant respiratory process is not inherently slower than respiration in animals.
In fact, isolated plant mitochondria respire faster than mammalian mitochondria, when expressed on a per mg protein basis.
Even though plants generally have low respiration rates, the contribution of respiration to the overall carbon econ-omy of the plant can be substantial (see Web Topic 11.7).
Whereas only green tissues photosynthesize, all tissues respire, and they do so 24 hours a day. Even in photosyn-thetically active tissues, respiration, if integrated over the entire day, can represent a substantial fraction of gross pho-tosynthesis. A survey of several herbaceous species indi-cated that 30 to 60% of the daily gain in photosynthetic car-bon was lost to respiration, although these values tended to decrease in older plants (Lambers 1985).
Young trees lose roughly a third of their daily photo-synthate as respiration, and this loss can double in older trees as the ratio of photosynthetic to nonphotosynthetic tissue decreases. In tropical areas, 70 to 80% of the daily photosynthetic gain can be lost to respiration because of the high dark respiration rates associated with elevated night temperatures.
Respiration Operates during Photosynthesis Mitochondria are involved in the metabolism of photo-synthesizing leaves. The glycine generated by photorespi-ration is oxidized to serine in the mitochondrion (see Chap-ter 8). At the same time, mitochondria in photosynthesizing tissue also carry out respiration via the citric acid cycle (often called dark respiration because it does not require light). Relative to the maximum rate of photosynthesis, dark respiration rates measured in green tissues are far slower, generally by a factor ranging from 6- to 20-fold.
Given that rates of photorespiration can often reach 20 to 40% of the gross photosynthetic rate, citric acid cycle-medi-ated mitochondrial respiration operates at rates also well below the rate of photorespiration.
A question that has not been adequately answered is how much mitochondrial respiration (apart from the involvement of mitochondria in the photorespiratory car-bon oxidation cycle) operates simultaneously with photo-synthesis in illuminated green tissues. The activity of pyru-vate dehydrogenase, one of the ports of entry into the citric acid cycle, decreases in the light to 25% of the dark activity (Budde and Randall 1990). The overall rate of respiration decreases in the light, but the extent of the decrease remains uncertain at present. It is clear, however, that the mitochondrion is a major supplier of ATP to the cytosol even in illuminated leaves (Krömer 1995).
Another role of mitochondrial respiration during pho-tosynthesis is to supply carbon metabolites for biosynthetic reactions—for example, by formation of 2-oxoglutarate needed for nitrogen assimilation. Leaf mitochondria typi-cally have high capacities of nonphosphorylating pathways in the electron transport chain. By oxidizing NADH with lower ATP yield, mitochondria can maintain a higher 2-oxoglutarate production by the respiratory pathways with-out being restricted by the cytosolic demand for ATP (see Figures 11.7C and 11.12) (Hoefnagel et al. 1998; Noctor and Foyer 1998).
Additional evidence for the involvement of mitochon-drial respiration in photosynthesizing leaves has been obtained in studies with mitochondrial mutants defective in respiratory complexes, showing that leaf development and photosynthesis are negatively affected (Vedel et al.
1999).
Different Tissues and Organs Respire at Different Rates A useful rule of thumb is that the greater the overall meta-bolic activity of a given tissue, the higher its respiration rate. Developing buds usually show very high rates of res-piration (on a dry-weight basis), and respiration rates of vegetative tissues usually decrease from the point of Respiration and Lipid Metabolism 245 growth (e.g., the leaf tip in dicotyledons and the leaf base in monocotyledons) to more differentiated regions. A well-studied example is the growing barley leaf (Thompson et al. 1998). In mature vegetative tissues, stems generally have the lowest respiration rates, and leaf and root respiration varies with the plant species and the conditions under which the plants are growing.
When a plant tissue has reached maturity, its respiration rate will either remain roughly constant or decrease slowly as the tissue ages and ultimately senesces. An exception to this pattern is the marked rise in respiration, known as the climacteric, that accompanies the onset of ripening in many fruits (avocado, apple, banana) and senescence in detached leaves and flowers. Both ripening and the climacteric res-piratory rise are triggered by the endogenous production of ethylene, as well as by an exogenous application of eth-ylene (see Chapter 22). In general, ethylene-induced respi-ration is associated with an active cyanide-resistant alter-native pathway, but the role of this pathway in ripening is not clear (Tucker 1993).
Mitochondrial Function Is Crucial during Pollen Development A physiological feature directly linked to the plant mito-chondrial genome is a phenomenon known as cytoplasmic male sterility, or cms. Plant lines that display cms do not form viable pollen—hence the designation male sterility.
The term cytoplasmic here refers to the fact that this trait is transmitted in a non-Mendelian fashion; the cms genotype is always maternally inherited with the mitochondrial genome. cms is a very important trait in plant breeding because a stable male sterile line can facilitate the produc-tion of hybrid seed stock. For this use, cms traits that pro-duce no major effects throughout the plant’s life cycle, except for male sterility, have been found for many species.
All plants carrying the cms trait that have been charac-terized at the molecular level show the presence of distinct rearrangements in their mtDNA, relative to wild-type plants. These rearrangements create novel open reading frames and have been strongly correlated with cms pheno-types in various systems. Nuclear restorer genes can over-come the effects of the mtDNA rearrangements and restore fertility to plants with the cms genotype. Such restorer genes are essential for the commercial utilization of cms if seeds are the harvested product.
An interesting consequence of the use of the cms gene occurred in the late 1960s, at which time 85% of the hybrid feed corn grown in the United States was derived from the use of a cms line of maize called cms-T (Texas). In cms-T maize, the mtDNA rearrangements give rise to a unique 13 kDa protein, URF13 (Levings and Siedow 1992). How the URF13 protein acts to bring about male sterility is not known, but in the late 1960s a disease appeared, caused by a race of the fungus Bipolaris maydis (also called Cochliobolus heterostrophus). This specific race synthesizes a compound (HmT-toxin) that specifically interacts with the URF13 pro-tein to produce pores in the inner mitochondrial membrane, with the result that selective permeability is lost.
The interaction between HmT-toxin and URF13 made Bipolaris maydis race T a particularly virulent pathogen on cms-T maize and led to an epidemic in the corn-growing regions of the United States that was known as southern corn leaf blight. As a result of this epidemic, the use of cms-T in the production of hybrid maize was discontinued. No other cms maize has been found to be a suitable replacement, so current production of hybrid corn seed has reverted to manual detasseling that prevents self-pollination.
As compared to other organs, the amount of mitochon-dria per cell and the expression of respiratory proteins are very high in developing anthers, where pollen develop-ment is an energy-demanding process (Huang et al. 1994).
Male sterility is a common phenotype of mutations in mito-chondrial genes for subunits of the complexes of oxidative phosphorylation (Vedel et al. 1999). Such mutants can be viable because of the existence of the alternative nonphos-phorylating respiratory pathways.
Programmed cell death (PCD) is part of normal anther development. There are now indications that mitochondria are involved in plant PCD and that PCD is premature in anthers of cms sunflower (see Web Essay 11.6).
Environmental Factors Alter Respiration Rates Many environmental factors can alter the operation of metabolic pathways and respiratory rates. Here we will examine the roles of environmental oxygen (O2), tempera-ture, and carbon dioxide (CO2).
Oxygen.
Oxygen can affect plant respiration because of its role as a substrate in the overall process. At 25°C, the equilibrium concentration of O2 in an air-saturated (21% O2), aqueous solution is about 250 µM. The Km value for oxygen in the reaction catalyzed by cytochrome c oxidase is well below 1 µM, so there should be no apparent depen-dence of the respiration rate on external O2 concentrations (see Chapter 2 on the web site for a discussion of Km).
However, respiration rates decrease if the atmospheric oxy-gen concentration is below 5% for whole tissues or below 2 to 3% for tissue slices. These findings show that oxygen diffusion through the aqueous phase in the tissue imposes a limitation on plant respiration.
The diffusion limitation imposed by an aqueous phase emphasizes the importance of the intercellular air spaces found in plant tissues for oxygen availability in the mito-chondria. If there were no gaseous diffusion pathway throughout the plant, the cellular respiration rates of many plants would be limited by an insufficient oxygen supply (see Web Essay 11.3).
Water saturation/low O2.
Diffusion limitation is even more significant when plant organs are growing in an 246 Chapter 11 aqueous medium. When plants are grown hydroponically, the solutions must be aerated vigorously to keep oxygen levels high in the vicinity of the roots. The problem of oxy-gen supply also arises with plants growing in very wet or flooded soils (see Chapter 25).
Some plants, particularly trees, have a restricted geo-graphic distribution because of the need to maintain a sup-ply of oxygen to their roots. For instance, dogwood and tulip tree poplar can survive only in well-drained, aerated soils because their roots cannot tolerate more than a limited exposure to a flooded condition. On the other hand, many plant species are adapted to grow in flooded soils. Herba-ceous species such as rice and sunflower often rely on a network of intercellular air spaces (aerenchyma) running from the leaves to the roots to provide a continuous, gaseous pathway for the movement of oxygen to the flooded roots.
Limitation in oxygen supply can be more severe for trees having very deep roots that grow in wet soils. Such roots must survive on anaerobic (fermentative) metabolism or develop structures that facilitate the movement of oxy-gen to the roots. Examples of such structures are out-growths of the roots, called pneumatophores, that protrude out of the water and provide a gaseous pathway for oxy-gen diffusion into the roots. Pneumatophores are found in Avicennia and Rhizophora, trees that grow in mangrove swamps under continuously flooded conditions.
Temperature.
Respiration typically increases with tem-perature (see, however, Web Essay 11.3). Between 0 and 30°C, the increase in respiration rate for every 10°C increase in ambient temperature (commonly referred to as the dimensionless, temperature coefficient, Q10) is about 2.
Above 30°C the respiration rate often increases more slowly, reaches a plateau at 40 to 50°C and decreases at even higher temperatures. High night temperatures are thought to account for the high respiratory rates of tropical plants.
Low temperatures are utilized to retard postharvest res-piration rates during the storage of fruits and vegetables.
However, complications may arise from such storage. For instance, when potato tubers are stored at temperatures above 10°C, respiration and ancillary metabolic activities are sufficient to allow sprouting. Below 5°C, respiration rates and sprouting are reduced in most tissues, but the breakdown of stored starch and its conversion to sucrose impart an unwanted sweetness to the tubers. As a com-promise, potatoes are stored at 7 to 9°C, which prevents the breakdown of starch while minimizing respiration and ger-mination.
CO2 concentration.
It is common practice in the com-mercial storage of fruits to take advantage of the effects of atmospheric oxygen and temperature on respiration, and to store fruits at low temperatures under 2 to 3% oxygen and 3 to 5% CO2. The reduced temperature lowers the res-piration rate, as does the reduced oxygen. Low levels of oxygen are used instead of anoxic conditions to avoid low-ering tissue oxygen tensions to the point that stimulates fer-mentative metabolism.
Carbon dioxide has a limited direct inhibitory effect on the respiration rate at a concentration of 3 to 5%, which is well in excess of the 0.036% (360 ppm) normally found in the atmosphere. The atmospheric CO2 concentration is increasing rapidly as a result of human activities, and it is projected to double, to 700 ppm, before the end of the twenty-first century (see Chapter 9).
Compared to plants grown at 350 ppm CO2, plants grown at 700 ppm CO2 have been reported to have a 15 to 20% slower dark respiration rate (on a dry-weight basis) (Drake et al. 1999), but this has been questioned (Jahnke 2001; Bruhn et al. 2002). The number of mitochondria per unit cell area actually doubles in the high CO2 environ-ment. These data imply that the respiratory activity in the light instead may increase at higher ambient CO2 concen-trations (Griffin et al. 2001). Thus it is presently a matter of debate how plants growing at an increased CO2 concen-tration will contribute to the global carbon cycle.
LIPID METABOLISM Whereas animals use fats for energy storage, plants use them mainly for carbon storage. Fats and oils are important storage forms of reduced carbon in many seeds, including those of agriculturally important species such as soybean, sunflower, peanut, and cotton. Oils often serve a major storage function in nondomesticated plants that produce small seeds. Some fruits, such as olives and avocados, also store fats and oils.
In this final part of the chapter we describe the biosyn-thesis of two types of glycerolipids: the triacylglycerols (the fats and oils stored in seeds) and the polar glycerolipids (which form the lipid bilayers of cellular membranes) (Fig-ure 11.14). We will see that the biosynthesis of triacylglyc-erols and polar glycerolipids requires the cooperation of two organelles: the plastids and the endoplasmic reticulum.
Plants can also use fats and oils for energy production. We will thus examine the complex process by which germi-nating seeds obtain metabolic energy from the oxidation of fats and oils.
Fats and Oils Store Large Amounts of Energy Fats and oils belong to the general class lipids, a structurally diverse group of hydrophobic compounds that are soluble in organic solvents and highly insoluble in water. Lipids represent a more reduced form of carbon than carbohy-drates, so the complete oxidation of 1 g of fat or oil (which contains about 40 kJ, or 9.3 kcal, of energy ) can produce considerably more ATP than the oxidation of 1 g of starch (about 15.9 kJ, or 3.8 kcal). Conversely, the biosynthesis of Respiration and Lipid Metabolism 247 fats, oils, and related molecules, such as the phospholipids of membranes, requires a correspondingly large investment of metabolic energy.
Other lipids are important for plant structure and func-tion but are not used for energy storage. These include waxes, which make up the protective cuticle that reduces water loss from exposed plant tissues, and terpenoids (also known as isoprenoids), which include carotenoids involved in photosynthesis and sterols present in many plant membranes (see Chapter 13).
Triacylglycerols Are Stored in Oleosomes Fats and oils exist mainly in the form of triacylglycerols (acyl refers to the fatty acid portion), or triglycerides, in which fatty acid molecules are linked by ester bonds to the three hydroxyl groups of glycerol (see Figure 11.14).
The fatty acids in plants are usually straight-chain car-boxylic acids having an even number of carbon atoms. The carbon chains can be as short as 12 units and as long as 20, but more commonly they are 16 or 18 carbons long. Oils are liquid at room temperature, primarily because of the pres-ence of unsaturated bonds in their component fatty acids; fats, which have a higher proportion of saturated fatty acids, are solid at room temperature. The major fatty acids in plant lipids are shown in Table 11.3.
The composition of fatty acids in plant lipids varies with the species. For example, peanut oil is about 9% palmitic acid, 59% oleic acid, and 21% linoleic acid, and cottonseed oil is 20% palmitic acid, 30% oleic acid, and 45% linoleic acid. The biosynthesis of these fatty acids will be discussed shortly.
Triacylglycerols in most seeds are stored in the cyto-plasm of either cotyledon or endosperm cells in organelles known as oleosomes (also called spherosomes or oil bodies) (see Chapter 1). Oleosomes have an unusual membrane barrier that separates the triglycerides from the aqueous cytoplasm. A single layer of phospholipids (i.e., a half-bilayer) surrounds the oil body with the hydrophilic ends of the phospholipids exposed to the cytosol and the hydrophobic acyl hydrocarbon chains facing the triacyl-glycerol interior (see Chapter 1). The oleosome is stabilized 248 Chapter 11 TABLE 11.3 Common fatty acids in higher plant tissues Namea Structure Saturated Fatty Acids Lauric acid (12:0) CH3(CH2)10CO2H Myristic acid (14:0) CH3(CH2)12CO2H Palmitic acid (16:0) CH3(CH2)14CO2H Stearic acid (18:0) CH3(CH2)16CO2H Unsaturated Fatty Acids Oleic acid (18:1) CH3(CH2)7CH — — CH(CH2)7CO2H Linoleic acid (18:2) CH3(CH2)4CH — — CH—CH2—CH— — CH(CH2)7CO2H Linolenic acid (18:3) CH3CH2CH — — CH—CH2—CH— — CH—CH2—CH — — CH—(CH2)7CO2H aEach fatty acid has a numerical abbreviation.The number before the colon represents the total number of carbons; the num-ber after the colon is the number of double bonds.
CHOH CH2OH CH2OH HC H2C H2C O O O O O O C C C (CH2)n (CH2)n (CH2)n CH3 CH3 CH3 HC H2C H2C O O O O O C X C (CH2)n (CH2)n CH3 CH3 Diacylglycerol (DAG) Phosphatidic acid Phosphatidylcholine Phosphatidylethanolamine Galactolipids X = H X = HPO3 2– X = PO3 2– X = PO3 2– X = galactose Glycerol Triacylglycerol (the major stored lipid) Glycerolipid CH2 CH2 CH2 CH2 N(CH3)3 NH2 + FIGURE 11.14 Structural features of triacylglycerols and polar glyc-erolipids in higher plants. The car-bon chain lengths of the fatty acids, which always have an even number of carbons, range from 12 to 20 but are typically 16 or 18. Thus, the value of n is usually 14 or 16.
by the presence of specific proteins, called oleosins, that coat the surface and prevent the phospholipids of adjacent oil bodies from coming in contact and fusing.
This unique membrane structure for oleosomes results from the pattern of triacylglycerol biosynthesis. Triacyl-glycerol synthesis is completed by enzymes located in the membranes of the endoplasmic reticulum (ER), and the resulting fats accumulate between the two monolayers of the ER membrane bilayer. The bilayer swells apart as more fats are added to the growing structure, and ulti-mately a mature oil body buds off from the ER (Napier et al. 1996).
Polar Glycerolipids Are the Main Structural Lipids in Membranes As outlined in Chapter 1, each membrane in the cell is a bilayer of amphipathic (i.e., having both hydrophilic and hydrophobic regions) lipid molecules in which a polar head group interacts with the aqueous phase while hydrophobic fatty acid chains form the center of the mem-brane. This hydrophobic core prevents random diffusion of solutes between cell compartments and thereby allows the biochemistry of the cell to be organized.
The main structural lipids in membranes are the polar glycerolipids (see Figure 11.14), in which the hydrophobic portion consists of two 16-carbon or 18-carbon fatty acid chains esterified to positions 1 and 2 of a glycerol backbone.
The polar head group is attached to position 3 of the glyc-erol. There are two categories of polar glycerolipids: 1. Glyceroglycolipids, in which sugars form the head group (Figure 11.15A) 2. Glycerophospholipids, in which the head group contains phosphate (Figure 11.15B) Plant membranes have additional structural lipids, including sphingolipids and sterols (see Chapter 13), but these are minor components. Other lipids perform specific roles in photosynthesis and other processes. Included among these lipids are chlorophylls, plastoquinone, carotenoids, and tocopherols, which together account for about one-third of the lipids in plant leaves.
Figure 11.15 shows the nine major glycerolipid classes in plants, each of which can be associated with many different fatty acid combinations. The structures shown in Figure 11.15 illustrate some of the more common molecular species.
Chloroplast membranes, which account for 70% of the membrane lipids in photosynthetic tissues, are dominated by glyceroglycolipids; other membranes of the cell contain glycerophospholipids (Table 11.4). In nonphotosynthetic tissues, phospholipids are the major membrane glyc-erolipids.
Fatty Acid Biosynthesis Consists of Cycles of Two-Carbon Addition Fatty acid biosynthesis involves the cyclic condensation of two-carbon units in which acetyl-CoA is the precursor. In plants, fatty acids are synthesized exclusively in the plas-tids; in animals, fatty acids are synthesized primarily in the cytosol.
The enzymes of the pathway are thought to be held together in a complex that is collectively referred to as fatty acid synthase. The complex probably allows the series of reactions to occur more efficiently than it would if the enzymes were physically separated from each other. In addition, the growing acyl chains are covalently bound to a low-molecular-weight, acidic protein called acyl carrier protein (ACP). When conjugated to the acyl carrier protein, the fatty acid chain is referred to as acyl-ACP.
The first committed step in the pathway (i.e., the first step unique to the synthesis of fatty acids) is the synthesis of malonyl-CoA from acetyl-CoA and CO2 by the enzyme acetyl-CoA carboxylase (Figure 11.16) (Sasaki et al. 1995).
The tight regulation of acetyl-CoA carboxylase appears to control the overall rate of fatty acid synthesis (Ohlrogge and Jaworski 1997). The malonyl-CoA then reacts with ACP to yield malonyl-ACP: 1. In the first cycle of fatty acid synthesis, the acetate group from acetyl-CoA is transferred to a specific cys-Respiration and Lipid Metabolism 249 TABLE 11.4 Glycerolipid components of cellular membranes Lipid composition (percentage of total) Endoplasmic Chloroplast reticulum Mitochondrion Phosphatidylcholine 4 47 43 Phosphatidylethanolamine — 34 35 Phosphatidylinositol 1 17 6 Phosphatidylglycerol 7 2 3 Diphosphatidylglycerol — — 13 Monogalactosyldiacylglycerol 55 — — Digalactosyldiacylglycerol 24 — — Sulfolipid 8 — — 250 Chapter 11 CH2OH O O O O O O CH2OH O O CH2OH O O O O O O CH2SO3 – O O O O O O O O O O CH2OH O P O O– O CH3 CH3 CH3 O– N+ O O O P O O O O H3N H2 H2 C C O P O O O– O O O O + O O O O C C C C C C O OH OH OH H H OH H H OH P O O– O H3N H H2 C C O P O O O– COO– O O O O + O P O H2C HC O O– O O O O O O OH O OH O P O H2C O O– O O H Monogalactosyldiacylglycerol (18:3 16:3) Digalactosyldiacylglycerol (16:0 18:3) Sulfolipid (sulfoquinovosyldiacylglycerol) (18:3 16:0) Phosphatidylglycerol (18:3 16:0) Phosphatidylcholine (16:0 18:3) Phosphatidylethanolamine (16:0 18:2) Phosphatidylinositol (16:0 18:2) Phosphatidylserine (16:0 18:2) Diphosphatidylglycerol (cardiolipin) (18:2 18:2) (A) Glyceroglycolipids (B) Glycerophospholipids Respiration and Lipid Metabolism 251 CH3 C O SCoA CH2 C O SCoA –OOC CH2 C O SACP –OOC CH2 C O SACP CH3 C O CH2 C O SACP CH2 CH3 Completed fatty acid Acetyl-CoA Malonyl-CoA Malony-ACP Acetoacetyl-ACP Butyryl-ACP ACP, CO2 CO2 ACP 2 2 CO2 Condensing enzyme Condensing enzyme (Continues to 16- to 18-carbon chain length) (acyl-ACP) ACP Acetyl-CoA carboxylase Decarboxylation step Decarboxylation step 6. The cycle continues multiple times adding acetate (2-carbon) units from malonyl-ACP.
4. The keto group at carbon 3 is removed in three steps.
5. The second cycle of fatty acid synthesis begins here.
7. ACP is removed from completed fatty acid in a transferase reaction.
2. Malonyl group is transferred to acyl carrier protein.
1. First committed step in fatty acid biosynthetic pathway.
3. The first cycle of fatty acid synthesis begins here.
NADPH NADPH+ ATP ADP Pi + FIGURE 11.15 Major polar lipids of plant membranes: (A) glyceroglycol-ipids and (B) glycerophospholipids. At least six different fatty acids may be attached to the glycerol backbone. One of the more common molecular species is shown for each lipid. The numbers given below each name refer to the number of carbons (number before the colon) and the number of double bonds (number after the colon).
L FIGURE 11.16 Cycle of fatty acid synthesis in plastids of plant cells.
teine of condensing enzyme (3-ketoacyl-ACP synthase) and then combined with malonyl-ACP to form ace-toacetyl-ACP.
2. Next the keto group at carbon 3 is removed (reduced) by the action of three enzymes to form a new acyl chain (butyryl-ACP), which is now four carbons long (see Figure 11.16).
3. The four-carbon acid and another molecule of mal-onyl-ACP then become the new substrates for con-densing enzyme, resulting in the addition of another two-carbon unit to the growing chain, and the cycle continues until 16 or 18 carbons have been added.
4. Some 16:0-ACP is released from the fatty acid syn-thase machinery, but most molecules that are elon-gated to 18:0-ACP are efficiently converted to 18:1-ACP by a desaturase enzyme. The repetition of this sequence of events makes 16:0-ACP and 18:1-ACP the major products of fatty acid synthesis in plastids (Figure 11.17).
Fatty acids may undergo further modification after they are linked with glycerol to form glycerolipids. Additional double bonds are placed in the 16:0 and 18:1 fatty acids by a series of desaturase isozymes. Desaturase isozymes are integral membrane proteins found in the chloroplast and the endoplasmic reticulum (ER). Each desaturase inserts a double bond at a specific position in the fatty acid chain, and the enzymes act sequentially to produce the final 18:3 and 16:3 products (Ohlrogge and Browse 1995).
Glycerolipids Are Synthesized in the Plastids and the ER The fatty acids synthesized in the plastid are next used to make the glycerolipids of membranes and oleosomes. The first steps of glycerolipid synthesis are two acylation reac-tions that transfer fatty acids from acyl-ACP or acyl-CoA to glycerol-3-phosphate to form phosphatidic acid.
The action of a specific phosphatase produces diacyl-glycerol (DAG) from phosphatidic acid. Phosphatidic acid can also be converted directly to phosphatidylinositol or phosphatidylglycerol; DAG can give rise to phos-phatidylethanolamine or phosphatidylcholine (see Figure 11.17).
The localization of the enzymes of glycerolipid synthe-sis reveals a complex and highly regulated interaction between the chloroplast, where fatty acids are synthesized, and other membrane systems of the cell. In simple terms, the biochemistry involves two pathways referred to as the prokaryotic (or chloroplast) pathway and the eukaryotic (or ER) pathway.
1. In chloroplasts, the prokaryotic pathway utilizes the 16:0- and 18:1-ACP products of chloroplast fatty acid synthesis to synthesize phosphatidic acid and its derivatives. Alternatively, the fatty acids may be exported to the cytoplasm as CoA esters.
2. In the cytoplasm, the eukaryotic pathway uses a sep-arate set of acyltransferases in the ER to incorporate the fatty acids into phosphatidic acid and its deriva-tives.
A simplified version of this model is depicted in Figure 11.17.
In some higher plants, including Arabidopsis and spinach, the two pathways contribute almost equally to chloroplast lipid synthesis. In many other angiosperms, however, phosphatidylglycerol is the only product of the prokaryotic pathway, and the remaining chloroplast lipids are synthesized entirely by the eukaryotic pathway.
The biochemistry of triacylglycerol synthesis in oilseeds is generally the same as described for the glycerolipids.
252 Chapter 11 Chloroplast (Prokaryotic pathway) Endoplasmic Reticulum (Eukaryotic pathway) Fatty acid synthase and 18:0-ACP Desaturase 16:0-ACP 18:1-ACP 16:0-CoA 18:1-CoA Phosphatidylglycerol Phosphatidic acid (PA) Phosphatidic acid (PA) Digalactosyldiacyl-glycerol Diacylglycerol (DAG) Diacylglycerol (DAG) Phosphatidyl-inositol Phophatidyl-glycerol Phosphatidyl-ethanolamine Phosphatidylcholine Monogalactosyl-diacylglycerol Sulfolipid FIGURE 11.17 The two path-ways for glycerolipid synthesis in the chloroplast and ER of Arabidopsis leaf cells. The major membrane components are shown in boxes. Glycerolipid desaturates in the chloroplast, and enzymes in the endoplas-mic reticulum convert 16:0 and 18:1 fatty acids to the more highly unsaturated fatty acids shown in Figure 11.15.
16:0- and 18:1-ACP are synthesized in the plastids of the cell and exported as CoA thioesters for incorporation into DAG in the endoplasmic reticulum (see Figure 11.17).
The key enzymes in oilseed metabolism (not shown in Figure 11.17), are acyl-CoA:DAG acyltransferase and PC:DAG acyltransferase, which catalyze triacylglycerol synthesis (Dahlqvist et al. 2000). As noted earlier, triacyl-glycerol molecules accumulate in specialized subcellular structures—the oleosomes—from which they can be mobi-lized during germination and converted to sugar.
Lipid Composition Influences Membrane Function A central question in membrane biology is the functional reason behind lipid diversity. Each membrane system of the cell has a characteristic and distinct complement of lipid types, and within a single membrane each class of lipids has a distinct fatty acid composition. Our under-standing of a membrane is one in which lipids make up the fluid, semipermeable bilayer that is the matrix for the func-tional membrane proteins.
Since this bulk lipid role could be satisfied by a single unsaturated species of phosphatidylcholine, obviously such a simple model is unsatisfactory. Why is lipid diver-sity needed? One aspect of membrane biology that might offer answers to this central question is the relationship between lipid composition and the ability of organisms to adjust to temperature changes (Wolter et al. 1992). For example, chill-sensitive plants experience sharp reductions in growth rate and development at temperatures between 0 and 12°C (see Chapter 25). Many economically important crops, such as cotton, soybean, maize, rice, and many trop-ical and subtropical fruits, are classified as chill sensitive.
In contrast, most plants that originate from temperate regions are able to grow and develop at chilling tempera-tures and are classified as chill-resistant plants.
It has been suggested that because of the decrease in lipid fluidity at lower temperatures, the primary event of chilling injury is a transition from a liquid-crystalline phase to a gel phase in the cellular membranes. According to this proposal, this transition would result in alterations in the metabolism of chilled cells and lead to injury and death of the chill-sensitive plants. The degree of unsaturation of the fatty acids would determine the temperature at which such damage occurred.
Recent research, however, suggests that the relationship between membrane unsaturation and plant responses to temperature is more subtle and complex (see Web Topic 11.8). The responses of Arabidopsis mutants with increased saturation of fatty acids to low temperature appear quite distinct from what is predicted by the chilling sensitivity hypothesis, suggesting that normal chilling injury may not be strictly related to the level of unsaturation of membrane lipids.
On the other hand, experiments with transgenic tobacco plants that are chill sensitive show opposite results. The transgenic expression of exogenous genes in tobacco has been used specifically to decrease the level of saturated phosphatidylglycerol or to bring about a general increase in membrane unsaturation. In each case, damage caused by chilling was alleviated to some extent.
These new findings make it clear that the extent of membrane unsaturation or the presence of particular lipids, such as disaturated phosphatidylglycerol, can affect the responses of plants to low temperature. As discussed in Web Topic 11.8, more work is required to fully understand the relationship between lipid composition and membrane function.
Membrane Lipids Are Precursors of Important Signaling Compounds Plants, animals, and microbes all use membrane lipids as precursors for compounds that are used for intracellular or long-range signaling. For example, jasmonate derived from linolenic acid (18:3) activates plant defenses against insects and many fungal pathogens. In addition, jasmonate regu-lates other aspects of plant growth, including the develop-ment of anthers and pollen (Stintzi and Browse 2000).
Phosphatidylinositol-4,5-bisphosphate (PIP2) is the most important of several phosphorylated derivatives of phos-phatidylinositol known as phosphoinositides. In animals, receptor-mediated activation of phospholipase C leads to the hydrolysis of PIP2 to inositol trisphosphate (IP3) and diacylglycerol, which both act as intracellular secondary messengers.
The action of IP3 in releasing Ca2+ into the cytoplasm (through calcium-sensitive channels in the tonoplast and other membranes) and thereby regulating cellular processes has been demonstrated in several plant systems, including the stomatal guard cells (Schroeder et al. 2001).
Information about other types of lipid signaling in plants is becoming available through biochemical and molecular genetic studies of phospholipases (Wang 2001) and other enzymes involved in the generation of these signals.
Storage Lipids Are Converted into Carbohydrates in Germinating Seeds After germinating, oil-containing seeds metabolize stored triacylglycerols by converting lipids to sucrose. Plants are not able to transport fats from the endosperm to the root and shoot tissues of the germinating seedling, so they must convert stored lipids to a more mobile form of carbon, gen-erally sucrose. This process involves several steps that are located in different cellular compartments: oleosomes, gly-oxysomes, mitochondria, and cytosol.
Overview: Lipids to sucrose.
The conversion of lipids to sucrose in oilseeds is triggered by germination and begins with the hydrolysis of triacylglycerols stored in the oil bodies to free fatty acids, followed by oxidation of the fatty acids to produce acetyl-CoA (Figure 11.18). The fatty Respiration and Lipid Metabolism 253 254 Chapter 11 Triacylglycerols are hydrolyzed to yield fatty acids.
Fatty acids are metabolized by β-oxidation to acetyl-CoA in the glyoxysome. Every two molecules of acetyl-CoA produced are metabolized by the glyoxylate cycle to generate one succinate.
Succinate moves into the mitochondrion and is converted to malate.
Malate is transported into the cytosol and oxidized to oxaloacetate, which is converted to phosphoenolpyruvate by the enzyme PEP carboxykinase. The resulting PEP is then metabolized to produce sucrose via the gluconeogenic pathway.
Malate Malate Fumarate Succinate MITOCHONDRION (A) OLEOSOME Fatty acid Acetyl-CoA Citrate Citrate Aconitase Malate Oxaloacetate Phosphoenolpyruvate Fructose-6-P Sucrose Isocitrate Isocitrate Succinate Glyoxylate Triacylglycerols CoA CoA CoA Acyl-CoA (Cn) Fatty-acid-CoA synthase Isocitrate lyase Citrate synthase Malate dehydrogenase Malate synthase O2 CO2 nH2O n n n n CHO COOH Oxaloacetate Malate dehydrogenase PEP carboxykinase CYTOSOL n 2 GLYOXYSOME β-oxidation Glyoxylate cycle Lipase ATP ADP NADH NADH NAD+ NADH NAD+ NAD+ FADH2 FAD (B) Glyoxysomes Oleosomes Mitochondria FIGURE 11.18 The conversion of fats to sugars during ger-mination in oil-storing seeds. (A) Carbon flow during fatty acid breakdown and gluconeogenesis (refer to Figures 11.2, 11.3, and 11.6 for structures). (B) Electron micrograph of a cell from the oil-storing cotyledon of a cucumber seedling, showing glyoxysomes, mitochondria, and oleosomes.
(Photo courtesy of R. N. Trelease.) acids are oxidized in a type of peroxisome called a gly-oxysome, an organelle enclosed by a single bilayer mem-brane that is found in the oil-rich storage tissues of seeds.
Acetyl-CoA is metabolized in the glyoxysome (see Figure 11.18A) to produce succinate, which is transported from the glyoxysome to the mitochondrion, where it is converted first to oxaloacetate and then to malate. The process ends in the cytosol with the conversion of malate to glucose via gluconeogenesis, and then to sucrose.
Although some of this fatty acid–derived carbon is diverted to other metabolic reactions in certain oilseeds, in castor bean (Ricinus communis) the process is so efficient that each gram of lipid metabolized results in the forma-tion of 1 g of carbohydrate, which is equivalent to a 40% recovery of free energy in the form of carbon bonds ([15.9 kJ/40 kJ] × 100 = 40%).
Lipase hydrolysis.
The initial step in the conversion of lipids to carbohydrate is the breakdown of triglycerides stored in the oil bodies by the enzyme lipase, which, at least in castor bean endosperm, is located on the half-mem-brane that serves as the outer boundary of the oil body. The lipase hydrolyzes triacylglycerols to three molecules of fatty acid and glycerol. Corn and cotton also contain a lipase activity in the oil body, but peanut, soybean, and cucumber show lipase activity in the glyoxysome instead.
During the breakdown of lipids, oil bodies and gly-oxysomes are generally in close physical association (see Figure 11.18B).
β-Oxidation of fatty acids.
After hydrolysis of the tria-cylglycerols, the resulting fatty acids enter the glyoxysome, where they are activated by conversion to fatty-acyl-CoA by the enzyme fatty-acyl-CoA synthase. Fatty-acyl-CoA is the initial substrate for the β-oxidation series of reactions, in which Cn fatty acids (fatty acids composed of n number of carbons) are sequentially broken down to n/2 molecules of acetyl-CoA (see Figure 11.18A). This reaction sequence involves the reduction of 1⁄2 O2 to H2O and the formation of 1 NADH and 1 FADH2 for each acetyl-CoA produced.
In mammalian tissues, the four enzymes associated with β-oxidation are present in the mitochondrion; in plant seed storage tissues, they are localized exclusively in the gly-oxysome. Interestingly, in plant vegetative tissues (e.g., mung bean hypocotyl and potato tuber), the β-oxidation reactions are localized in a related organelle, the peroxi-some (see Chapter 1).
The glyoxylate cycle.
The function of the glyoxylate cycle is to convert two molecules of acetyl-CoA to succi-nate. The acetyl-CoA produced by β-oxidation is further metabolized in the glyoxysome through a series of reac-tions that make up the glyoxylate cycle (see Figure 11.18A).
Initially, the acetyl-CoA reacts with oxaloacetate to give cit-rate, which is then transferred to the cytoplasm for iso-merization to isocitrate by aconitase. Isocitrate is reim-ported into the peroxisome and converted to malate by two reactions that are unique to the glyoxylate pathway.
1. First isocitrate (C6) is cleaved by the enzyme isocitrate lyase to give succinate (C4) and glyoxylate (C2). This succinate is exported to the motochondria.
2. Next malate synthase combines a second molecule of acetyl-CoA with glyoxylate to produce malate.
Malate is then oxidized by malate dehydrogenase to oxaloacetate, which can combine with another acetyl-CoA to continue the cycle (see Figure 11.18A). The glyoxylate produced keeps the cycle operating in the glyoxysome, but the succinate is exported to the mitochondria for further processing.
The mitochondrial role.
Moving from the glyoxysomes to the mitochondria, the succinate is converted to malate by the normal citric acid cycle reactions. The resulting malate can be exported from the mitochondria in exchange for succinate via the dicarboxylate transporter located in the inner mitochondrial membrane. Malate is then oxidized to oxaloacetate by malate dehydrogenase in the cytosol, and the resulting oxaloacetate is converted to carbohydrate.
This conversion requires circumventing the irreversibil-ity of the pyruvate kinase reaction (see Figure 11.3) and is facilitated by the enzyme PEP carboxykinase, which uti-lizes the phosphorylating ability of ATP to convert oxaloac-etate to PEP and CO2 (see Figure 11.18A). From PEP, glu-coneogenesis can proceed to the production of glucose, as described earlier. Sucrose is the final product of this process, and the primary form of reduced carbon translo-cated from the cotyledons to the growing seedling tissues.
Not all seeds quantitatively convert fat to sugar (see Web Topic 11.9).
SUMMARY In plant respiration, reduced cellular carbon generated dur-ing photosynthesis is oxidized to CO2 and water, and this oxidation is coupled to the synthesis of ATP. Respiration takes place in three main stages: glycolysis, the citric acid cycle, and oxidative phosphorylation. The latter comprises the electron transport chain and ATP synthesis.
In glycolysis, carbohydrate is converted in the cytosol to pyruvate, and a small amount of ATP is synthesized via substrate-level phosphorylation. Pyruvate is subsequently oxidized within the mitochondrial matrix through the cit-ric acid cycle, generating a large number of reducing equiv-alents in the form of NADH and FADH2.
In the third stage, oxidative phosphorylation, electrons from NADH and FADH2 pass through the electron trans-port chain in the inner mitochondrial membrane to reduce oxygen. The chemical energy is conserved in the form of an electrochemical proton gradient, which is created by the Respiration and Lipid Metabolism 255 coupling of electron flow to proton pumping from the matrix to the intermembrane space. This energy is then converted into chemical energy in the form of ATP by the FoF1-ATP synthase, also located in the inner membrane, which couples ATP synthesis from ADP and Pi to the flow of protons back into the matrix down their electrochemical gradient.
Aerobic respiration in plants has several unique fea-tures, including the presence of a cyanide-resistant alter-native oxidase and multiple NAD(P)H dehydrogenases, none of which pumps protons. Substrate oxidation during respiration is regulated at control points in glycolysis, the citric acid cycle, and the electron transport chain, but ulti-mately substrate oxidation is controlled by the level of cel-lular ADP. Carbohydrates can also be oxidized via the oxidative pentose phosphate pathway, in which the reduc-ing power is produced in the form of NADPH mainly for biosynthetic purposes. Numerous glycolytic and citric acid cycle intermediates also provide the starting material for a multitude of biosynthetic pathways.
More than 50% of the daily photosynthetic yield can be respired by a plant, but many factors can affect the respi-ration rate observed at the whole-plant level. These factors include the nature and age of the plant tissue, as well as environmental factors such as light, oxygen concentration, temperature, and CO2 concentration.
Lipids play a major role in plants: Amphipathic lipids serve as the primary nonprotein components of plant membranes; fats and oils are an efficient storage form of reduced carbon, particularly in seeds. Glycerolipids play important roles as structural components of membranes.
Fatty acids are synthesized in plastids using acetyl-CoA.
Fatty acids from the plastid can be transported to the ER, where they are further modified.
Membrane function may be influenced by the lipid composition. The degree of unsaturation of the fatty acids influences the sensitivity of plants to cold but does not seem to be involved in normal chilling injury. On the other hand, certain membrane lipid breakdown products, such as jasmonic acid, can act as signaling agents in plant cells.
Triacylglycerol is synthesized in the ER and accumulates within the phospholipid bilayer, forming oil bodies. Dur-ing germination in oil-storing seeds, the stored lipids are metabolized to carbohydrate in a series of reactions that involve a metabolic sequence known as the glyoxylate cycle. This cycle takes place in glyoxysomes, and subse-quent steps occur in the mitochondria. The reduced carbon generated during lipid breakdown in the glyoxysomes is ultimately converted to carbohydrate in the cytosol by glu-coneogenesis.
Web Material Web Topics 11.1 Isolation of Mitochondria Methods for the isolation of intact, functional mitochondria have been developed.
11.2 The Electron Transport Chain of Plant Mitochondria Contains Multiple NAD(P)H Dehydrogenases Mitochondrial NAD(P)H dehydrogenases oxi-dize NADH or NADPH and pass the electrons to ubiquinone.
11.3 The Alternative Oxidase The alternative oxidase is an oxidoreductase localized at the inner membrane of plant mito-chondria.
11.4 FoF1-ATP Synthases:The World’s Smallest Rotary Motors Rotation of the g subunit brings about the con-formational changes that allow the release of ATP from the enzyme.
11.5 Transport In and Out of Plant Mitochondria Plant mitochondria operate different transport mechanisms.
11.6 The Genetic System of Plant Mitochondria Has Some Special Features The mitochondrial genome encodes about 40 mitochondrial proteins.
11.7 Does Respiration Reduce Crop Yields?
Empirical relations between plant respiration rates and crop yield have been established.
11.8 The Lipid Composition of Membranes Affects the Cell Biology and Physiology of Plants Lipid mutants are expanding our understand-ing of the ability of organisms to adapt to tem-perature changes.
11.9 Utilization of Oil Reserves in Cotyledons In some species, only part of the stored lipid in the cotyledons is exported as carbohydrate.
Web Essays 11.1 Metabolic Flexibility Helps Plants Survive Stress The ability of plants to carry out a metabolic step in different ways increases plant survival under stress.
256 Chapter 11 11.2 Metabolic Profiling of Plant Cells Metabolic profiling complements genomics and proteomics.
11.3 Temperature Regulation by Thermogenic Flowers In thermogenic flowers, such as the Arum lilies, temperature can increase up to 20°C above their surroundings.
11.4 Reactive Oxygen Species (ROS) and Plant Mitochondria The production of damaging reactive oxygen species is an unavoidable consequence of aero-bic respiration.
11.5 The Role of Respiration in Desiccation Tolerance Respiration has both positive and negative effects on the survival of plant cells under water stress.
11.6 Balancing Life and Death;The Role of Mito-chondria in Programmed Cell Death Programmed cell death is an integral part of the life cycle of plants, directly involving mito-chondria.
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258 Chapter 11 Assimilation of Mineral Nutrients 12 Chapter HIGHER PLANTS ARE AUTOTROPHIC ORGANISMS that can syn-thesize their organic molecular components out of inorganic nutrients obtained from their surroundings. For many mineral nutrients, this process involves absorption from the soil by the roots (see Chapter 5) and incorporation into the organic compounds that are essential for growth and development. This incorporation of mineral nutrients into organic substances such as pigments, enzyme cofactors, lipids, nucleic acids, and amino acids is termed nutrient assimilation.
Assimilation of some nutrients—particularly nitrogen and sulfur— requires a complex series of biochemical reactions that are among the most energy-requiring reactions in living organisms: • In nitrate (NO3 –) assimilation, the nitrogen in NO3 – is converted to a higher-energy form in nitrite (NO2 –), then to a yet higher-energy form in ammonium (NH4 +), and finally into the amide nitrogen of glutamine. This process consumes the equivalent of 12 ATPs per nitrogen (Bloom et al. 1992).
• Plants such as legumes form symbiotic relationships with nitro-gen-fixing bacteria to convert molecular nitrogen (N2) into ammo-nia (NH3). Ammonia (NH3) is the first stable product of natural fixation; at physiological pH, however, ammonia is protonated to form the ammonium ion (NH4 +). The process of biological nitro-gen fixation, together with the subsequent assimilation of NH3 into an amino acid, consumes about 16 ATPs per nitrogen (Pate and Layzell 1990; Vande Broek and Vanderleyden 1995).
• The assimilation of sulfate (SO4 2–) into the amino acid cysteine via the two pathways found in plants consumes about 14 ATPs (Hell 1997).
For some perspective on the enormous energies involved, consider that if these reactions run rapidly in reverse—say, from NH4NO3 (ammo-nium nitrate) to N2—they become explosive, liberating vast amounts of energy as motion, heat, and light. Nearly all explosives are based on the rapid oxidation of nitrogen or sulfur compounds.
Assimilation of other nutrients, especially the macronu-trient and micronutrient cations (see Chapter 5), involves the formation of complexes with organic compounds. For example, Mg2+ associates with chlorophyll pigments, Ca2+ associates with pectates within the cell wall, and Mo6+ associates with enzymes such as nitrate reductase and nitrogenase. These complexes are highly stable, and removal of the nutrient from the complex may result in total loss of function.
This chapter outlines the primary reactions through which the major nutrients (nitrogen, sulfur, phosphate, cations, and oxygen) are assimilated. We emphasize the physiological implications of the required energy expendi-tures and introduce the topic of symbiotic nitrogen fixation.
NITROGEN IN THE ENVIRONMENT Many biochemical compounds present in plant cells con-tain nitrogen (see Chapter 5). For example, nitrogen is found in the nucleoside phosphates and amino acids that form the building blocks of nucleic acids and proteins, respectively. Only the elements oxygen, carbon, and hydro-gen are more abundant in plants than nitrogen. Most nat-ural and agricultural ecosystems show dramatic gains in productivity after fertilization with inorganic nitrogen, attesting to the importance of this element.
In this section we will discuss the biogeochemical cycle of nitrogen, the crucial role of nitrogen fixation in the con-version of molecular nitrogen into ammonium and nitrate, and the fate of nitrate and ammonium in plant tissues.
Nitrogen Passes through Several Forms in a Biogeochemical Cycle Nitrogen is present in many forms in the biosphere. The atmosphere contains vast quantities (about 78% by vol-ume) of molecular nitrogen (N2) (see Chapter 9). For the most part, this large reservoir of nitrogen is not directly available to living organisms. Acquisition of nitrogen from the atmosphere requires the breaking of an exceptionally stable triple covalent bond between two nitrogen atoms (N— — —N) to produce ammonia (NH3) or nitrate (NO3 –).
These reactions, known as nitrogen fixation, can be accom-plished by both industrial and natural processes.
Under elevated temperature (about 200°C) and high pressure (about 200 atmospheres), N2 combines with hydrogen to form ammonia. The extreme conditions are required to overcome the high activation energy of the reaction. This nitrogen fixation reaction, called the Haber–Bosch process, is a starting point for the manufacture of many industrial and agricultural products. Worldwide industrial production of nitrogen fertilizers amounts to more than 80 × 1012 g yr–1 (FAOSTAT 2001).
Natural processes fix about 190 × 1012 g yr–1 of nitrogen (Table 12.1) through the following processes (Schlesinger 1997): • Lightning. Lightning is responsible for about 8% of the nitrogen fixed. Lightning converts water vapor and TABLE 12.1 The major processes of the biogeochemical nitrogen cycle Rate Process Definition (1012 g yr–1)a Industrial fixation Industrial conversion of molecular nitrogen to ammonia 80 Atmospheric fixation Lightning and photochemical conversion of molecular nitrogen to nitrate 19 Biological fixation Prokaryotic conversion of molecular nitrogen to ammonia 170 Plant acquisition Plant absorption and assimilation of ammonium or nitrate 1200 Immobilization Microbial absorption and assimilation of ammonium or nitrate N/C Ammonification Bacterial and fungal catabolism of soil organic matter to ammonium N/C Nitrification Bacterial (Nitrosomonas sp.) oxidation of ammonium to nitrite and subsequent bacterial (Nitrobacter sp.) oxidation of nitrite to nitrate N/C Mineralization Bacterial and fungal catabolism of soil organic matter to mineral nitrogen through ammonification or nitrification N/C Volatilization Physical loss of gaseous ammonia to the atmosphere 100 Ammonium fixation Physical embedding of ammonium into soil particles 10 Denitrification Bacterial conversion of nitrate to nitrous oxide and molecular nitrogen 210 Nitrate leaching Physical flow of nitrate dissolved in groundwater out of the topsoil and eventually into the oceans 36 Note: Terrestrial organisms, the soil, and the oceans contain about 5.2 × 1015 g, 95 × 1015 g, and 6.5 x 1015 g, respectively, of organic nitrogen that is active in the cycle. Assuming that the amount of atmospheric N2 remains constant (inputs = outputs), the mean residence time (the average time that a nitrogen molecule remains in organic forms) is about 370 years [(pool size)/(fixation input) = (5.2 × 1015 g + 95 × 1015 g)/(80 × 1012 g yr–1 + 19 × 1012 g yr–1+ 170 × 1012 g yr–1)] (Schlesinger 1997).
aN/C, not calculated.
260 Chapter 12 oxygen into highly reactive hydroxyl free radicals, free hydrogen atoms, and free oxygen atoms that attack molecular nitrogen (N2) to form nitric acid (HNO3). This nitric acid subsequently falls to Earth with rain.
• Photochemical reactions. Approximately 2% of the nitrogen fixed derives from photochemical reactions between gaseous nitric oxide (NO) and ozone (O3) that produce nitric acid (HNO3).
• Biological nitrogen fixation. The remaining 90% results from biological nitrogen fixation, in which bacteria or blue-green algae (cyanobacteria) fix N2 into ammo-nium (NH4 +). From an agricultural standpoint, biological nitrogen fixa-tion is critical because industrial production of nitrogen fer-tilizers seldom meets agricultural demand (FAOSTAT 2001).
Once fixed in ammonium or nitrate, nitrogen enters a biogeochemical cycle and passes through several organic or inorganic forms before it eventually returns to molecu-lar nitrogen (Figure 12.1; see also Table 12.1). The ammo-nium (NH4 +) and nitrate (NO3 –) ions that are generated through fixation or released through decomposition of soil organic matter become the object of intense competition among plants and microorganisms. To remain competitive, plants have developed mechanisms for scavenging these ions from the soil solution as quickly as possible (see Chap-ter 5). Under the elevated soil concentrations that occur after fertilization, the absorption of ammonium and nitrate by the roots may exceed the capacity of a plant to assimi-late these ions, leading to their accumulation within the plant’s tissues.
Stored Ammonium or Nitrate Can Be Toxic Plants can store high levels of nitrate, or they can translo-cate it from tissue to tissue without deleterious effect. How-ever, if livestock and humans consume plant material that is high in nitrate, they may suffer methemoglobinemia, a disease in which the liver reduces nitrate to nitrite, which combines with hemoglobin and renders the hemoglobin unable to bind oxygen. Humans and other animals may also convert nitrate into nitrosamines, which are potent car-cinogens. Some countries limit the nitrate content in plant materials sold for human consumption.
In contrast to nitrate, high levels of ammonium are toxic to both plants and animals. Ammonium dissipates trans-membrane proton gradients (Figure 12.2) that are required for both photosynthetic and respiratory electron transport (see Chapters 7 and 11) and for sequestering metabolites in Atmospheric nitrogen (N2) Mineralization (ammonification) Ammonium (NH4 +) Nitrite (NO2 –) Nitrate (NO3 –) Loss by leaching Denitrifiers Immobilization by bacteria and fungi Industrial fixation Biological fixation Nitrogen compounds in rain Excreta and dead bodies Dead organic matter Free-living N2 fixers FIGURE 12.1 Nitrogen cycles through the atmosphere as it changes from a gaseous form to reduced ions before being incorporated into organic compounds in living organisms. Some of the steps involved in the nitrogen cycle are shown.
Assimilation of Mineral Nutrients 261 the vacuole (see Chapter 6). Because high levels of ammo-nium are dangerous, animals have developed a strong aver-sion to its smell. The active ingredient in smelling salts, a medicinal vapor released under the nose to revive a person who has fainted, is ammonium carbonate. Plants assimilate ammonium near the site of absorption or generation and rapidly store any excess in their vacuoles, thus avoiding toxic effects on membranes and the cytosol.
In the next section we will discuss the process by which the nitrate absorbed by the roots via an H+–NO3 – sym-porter (see Chapter 6 for a discussion of symport) is assim-ilated into organic compounds, and the enzymatic processes mediating the reduction of nitrate first into nitrite and then into ammonium.
NITRATE ASSIMILATION Plants assimilate most of the nitrate absorbed by their roots into organic nitrogen compounds. The first step of this process is the reduction of nitrate to nitrite in the cytosol (Oaks 1994). The enzyme nitrate reductase catalyzes this reaction: NO3 – + NAD(P)H + H+ + 2 e– → NO2 – + NAD(P)+ + H2O (12.1) where NAD(P)H indicates NADH or NADPH. The most common form of nitrate reductase uses only NADH as an electron donor; another form of the enzyme that is found predominantly in nongreen tissues such as roots can use either NADH or NADPH (Warner and Kleinhofs 1992).
The nitrate reductases of higher plants are composed of two identical subunits, each containing three prosthetic groups: FAD (flavin adenine dinucleotide), heme, and a molybdenum complexed to an organic molecule called a pterin (Mendel and Stallmeyer 1995; Campbell 1999).
Nitrate reductase is the main molybdenum-containing pro-tein in vegetative tissues, and one symptom of molybde-num deficiency is the accumulation of nitrate that results from diminished nitrate reductase activity.
Comparison of the amino acid sequences for nitrate reductase from several species with those of other well-characterized proteins that bind FAD, heme, or molybde-num has led to the three-domain model for nitrate reduc-tase shown in Figure 12.3. The FAD-binding domain accepts two electrons from NADH or NADPH. The elec-trons then pass through the heme domain to the molybde-num complex, where they are transferred to nitrate.
Nitrate, Light, and Carbohydrates Regulate Nitrate Reductase Nitrate, light, and carbohydrates influence nitrate reductase at the transcription and translation levels (Sivasankar and Oaks 1996). In barley seedlings, nitrate reductase mRNA was detected approximately 40 minutes after addition of nitrate, and maximum levels were attained within 3 hours (Figure 12.4). In contrast to the rapid mRNA accumulation, N N N HN H2N O A pterin (fully oxidized) OH– OH– OH– OH– OH– OH– OH– OH– NH4 + + OH– NH3 H2O H+ H+ H+ H+ H+ H+ H+ H+ NH3 + H+ NH4 + + High pH: Low pH: Membrane At high pH, NH4 + reacts with OH– to produce NH3.
NH3 is membrane permeable and diffuses across the membrane along its concentration gradient.
NH3 reacts with H+ to form NH4 +.
Lumen, intermembrane space, or vacuole Stroma, matrix, or cytoplasm FIGURE 12.2 NH4 + toxicity can dissipate pH gradients. The left side represents the stroma, matrix, or cytoplasm, where the pH is high; the right side represents the lumen, inter-membrane space, or vacuole, where the pH is low; and the membrane represents the thylakoid, inner mitochondrial, or tonoplast membrane for a chloroplast, mitochondrion, or root cell, respectively. The net result of the reaction shown is that both the OH– concentration on the left side and the H+ concentration on the right side have been diminished; that is, the pH gradient has been dissipated. (After Bloom 1997.) NO3 – NO3 – 2 MoCo Heme 2 MoCo Heme Nitrate reductase e– e– NADH FAD FAD NADH Hinge regions N terminus C terminus FIGURE 12.3 A model of the nitrate reductase dimer, illus-trating the three binding domains whose polypeptide sequences are similar in eukaryotes: molybdenum complex (MoCo), heme, and FAD. The NADH binds at the FAD-binding region of each subunit and initiates a two-electron transfer from the carboxyl (C) terminus, through each of the electron transfer components, to the amino (N) termi-nus. Nitrate is reduced at the molybdenum complex near the amino terminus. The polypeptide sequences of the hinge regions are highly variable among species.
262 Chapter 12 there was a gradual linear increase in nitrate reductase activity, reflecting the slower synthesis of the protein.
In addition, the protein is subject to posttranslational modulation (involving a reversible phosphorylation) that is analogous to the regulation of sucrose phosphate syn-thase (see Chapters 8 and 10). Light, carbohydrate levels, and other environmental factors stimulate a protein phos-phatase that dephosphorylates several serine residues on the nitrate reductase protein and thereby activates the enzyme.
Operating in the reverse direction, darkness and Mg2+ stimulate a protein kinase that phosphorylates the same serine residues, which then interact with a 14-3-3 inhibitor protein, and thereby inactivate nitrate reductase (Kaiser et al. 1999). Regulation of nitrate reductase activity through phos-phorylation and dephosphorylation provides more rapid control than can be achieved through synthesis or degradation of the enzyme (minutes versus hours).
Nitrite Reductase Converts Nitrite to Ammonium Nitrite (NO2 –) is a highly reactive, potentially toxic ion.
Plant cells immediately transport the nitrite generated by nitrate reduction (see Equation 12.1) from the cytosol into chloroplasts in leaves and plastids in roots. In these organelles, the enzyme nitrite reductase reduces nitrite to ammonium according to the following overall reaction: NO2 – + 6 Fdred + 8 H+ + 6 e– → NH4 + + 6 Fdox + 2 H2O (12.2) where Fd is ferredoxin, and the subscripts red and ox stand for reduced and oxi-dized, respectively. Reduced ferredoxin derives from pho-tosynthetic electron transport in the chloroplasts (see Chap-ter 7) and from NADPH generated by the oxidative pen-tose phosphate pathway in nongreen tissues (see Chapter 11).
Chloroplasts and root plastids contain different forms of the enzyme, but both forms consist of a single polypeptide containing two prosthetic groups: an iron–sulfur cluster (Fe4S4) and a specialized heme (Siegel and Wilkerson 1989).
These groups acting together bind nitrite and reduce it directly to ammonium, without accumulation of nitrogen compounds of intermediate redox states. The electron flow through ferredoxin, Fe4S4, and heme can be represented as in Figure 12.5.
Nitrite reductase is encoded in the nucleus and synthe-sized in the cytoplasm with an N-terminal transit peptide that targets it to the plastids (Wray 1993). Whereas NO3 – and light induce the transcription of nitrite reductase mRNA, the end products of the process—asparagine and glutamine—repress this induction.
Plants Can Assimilate Nitrate in Both Roots and Shoots In many plants, when the roots receive small amounts of nitrate, nitrate is reduced primarily in the roots. As the supply of nitrate increases, a greater proportion of the 100 80 60 40 20 5 10 15 20 0 4 8 12 Time after induction (hours) 16 20 24 Relative nitrate reductase mRNA (%) Nitrate reductase activity (µmol gfw–1 h–1) Root mRNA Shoot mRNA Shoot nitrate reductase Root nitrate reductase FIGURE 12.4 Stimulation of nitrate reduc-tase activity follows the induction of nitrate reductase mRNA in shoots and roots of barley; gfw, grams fresh weight.
(From Kleinhofs et al. 1989.) Light Light reactions in photosynthesis Ferredoxin (reduced) Ferredoxin (oxidized) Nitrite reductase Heme NO2 – Nitrite NH4 + Ammonia H+ (Fe4S4) e– e– FIGURE 12.5 Model for coupling of photosynthetic electron flow, via ferredoxin, to the reduction of nitrite by nitrite reductase. The enzyme contains two prosthetic groups, Fe4S4 and heme, which participate in the reduction of nitrite to ammonium.
Assimilation of Mineral Nutrients 263 absorbed nitrate is translocated to the shoot and assimi-lated there (Marschner 1995). Even under similar condi-tions of nitrate supply, the balance between root and shoot nitrate metabolism—as indicated by the proportion of nitrate reductase activity in each of the two organs or by the relative concentrations of nitrate and reduced nitrogen in the xylem sap—varies from species to species.
In plants such as the cocklebur (Xanthium strumarium), nitrate metabolism is restricted to the shoot; in other plants, such as white lupine (Lupinus albus), most nitrate is metab-olized in the roots (Figure 12.6). Generally, species native to temperate regions rely more heavily on nitrate assimila-tion by the roots than do species of tropical or subtropical origins.
AMMONIUM ASSIMILATION Plant cells avoid ammonium toxicity by rapidly converting the ammonium generated from nitrate assimilation or pho-torespiration (see Chapter 8) into amino acids. The primary pathway for this conversion involves the sequential actions of glutamine synthetase and glutamate synthase (Lea et al.
1992). In this section we will discuss the enzymatic processes that mediate the assimilation of ammonium into essential amino acids, and the role of amides in the regu-lation of nitrogen and carbon metabolism.
Conversion of Ammonium to Amino Acids Requires Two Enzymes Glutamine synthetase (GS) combines ammonium with glutamate to form glutamine (Figure 12.7A): Glutamate + NH4 + + ATP →glutamine + ADP + Pi (12.3) This reaction requires the hydrolysis of one ATP and involves a divalent cation such as Mg2+, Mn2+, or Co2+ as a cofactor. Plants contain two classes of GS, one in the cytosol and the other in root plastids or shoot chloroplasts. The cytosolic forms are expressed in germinating seeds or in the vascular bundles of roots and shoots and produce gluta-mine for intracellular nitrogen transport. The GS in root plastids generates amide nitrogen for local consumption; the GS in shoot chloroplasts reassimilates photorespiratory NH4 + (Lam et al. 1996). Light and carbohydrate levels alter the expression of the plastid forms of the enzyme, but they have little effect on the cytosolic forms.
Elevated plastid levels of glutamine stimulate the activ-ity of glutamate synthase (also known as glutamine:2-oxo-glutarate aminotransferase, or GOGAT). This enzyme trans-fers the amide group of glutamine to 2-oxoglutarate, yield-ing two molecules of glutamate (see Figure 12.7A). Plants contain two types of GOGAT: One accepts electrons from NADH; the other accepts electrons from ferredoxin (Fd): Glutamine + 2-oxoglutarate + NADH + H+ → 2 glutamate + NAD+ (12.4) Glutamine + 2-oxoglutarate + Fdred → 2 glutamate + Fdox (12.5) The NADH type of the enzyme (NADH-GOGAT) is located in plastids of nonphotosynthetic tissues such as roots or vascular bundles of developing leaves. In roots, NADH-GOGAT is involved in the assimilation of NH4 + absorbed from the rhizosphere (the soil near the surface of the roots); in vascular bundles of developing leaves, NADH-GOGAT assimilates glutamine translocated from roots or senescing leaves.
The ferredoxin-dependent type of glutamate synthase (Fd-GOGAT) is found in chloroplasts and serves in photorespi-ratory nitrogen metabolism. Both the amount of protein and its activity increase with light levels. Roots, particularly those under nitrate nutrition, have Fd-GOGAT in plastids. Fd-GOGAT in the roots presumably functions to incorporate the glutamine generated during nitrate assimilation.
Ammonium Can Be Assimilated via an Alternative Pathway Glutamate dehydrogenase (GDH) catalyzes a reversible reaction that synthesizes or deaminates glutamate (Figure 12.7B): 2-Oxoglutarate + NH4 + + NAD(P)H ↔ glutamate + H2O + NAD(P)+ (12.6) Cocklebur Stellaria media White clover Perilla fruticosa Oat Corn Impatiens Sunflower Barley Bean Broad bean Pea Radish White lupine 10 0 20 30 40 50 60 70 80 90 100 Nitrogen in xylem exudate (%) Nitrate Amino acids Amides Ureides FIGURE 12.6 Relative amounts of nitrate and other nitrogen compounds in the xylem exudate of various plant species.
The plants were grown with their roots exposed to nitrate solutions, and xylem sap was collected by severing of the stem. Note the presence of ureides, specialized nitrogen compounds, in bean and pea (which will be discussed later in the text). (After Pate 1983.) 264 Chapter 12 HC COOH CH2 NH2 NH4 + CH2 O– C O HC COOH CH2 NH2 CH2 NH2 C O C COOH CH2 O CH2 O– C O Glutamine synthetase (GS) + + HC COOH CH2 NH2 CH2 O– C O HC COOH CH2 NH2 CH2 O– C O NADH + H+ or Fdred NAD+ or Fdox Glutamate synthase (GOGAT) + ATP ADP Pi + + C COOH CH2 O NH4 + CH2 O– C O HC COOH CH2 NH2 CH2 O– C O Glutamate dehydrogenase (GDH) NAD(P)H NAD(P)+ C COOH CH2 O CH2 O O– C O HC COOH CH2 NH2 CH2 O– C O C COOH CH2 O– C O NH2 C COOH CH2 O– C O + + HC COOH CH2 NH2 CH2 NH2 C O HC COOH CH2 NH2 CH2 O– C O C COOH CH2 O– C O NH2 HC COOH CH2 NH2 C O + + NH2 ATP ADP PPi + + H2O (A) Glutamate Glutamine 2-Oxoglutarate Ammonium 2 Glutamates (B) 2-Oxoglutarate Glutamate Ammonium (C) 2-Oxoglutarate Glutamate Oxaloacetate Aspartate (D) Glutamine Glutamate Aspartate Asparagine Asparagine synthetase (AS) Aspartate aminotransferase (Asp-AT) FIGURE 12.7 Structure and pathways of compounds involved in ammonium metabolism. Ammonium can be assimilated by one of several processes. (A) The GS-GOGAT pathway that forms glutamine and glutamate. A reduced cofactor is required for the reaction: ferredoxin in green leaves and NADH in nonphotosyn-thetic tissue. (B) The GDH pathway that forms glutamate using NADH or NADPH as a reductant. (C) Transfer of the amino group from glutamate to oxaloacetate to form aspartate (cat-alyzed by aspartate aminotransferase). (D) Synthesis of asparagine by transfer of an amino acid group from glutamine to aspartate (catalyzed by asparagine synthesis).
Assimilation of Mineral Nutrients 265 An NADH-dependent form of GDH is found in mito-chondria, and an NADPH-dependent form is localized in the chloroplasts of photosynthetic organs. Although both forms are relatively abundant, they cannot substitute for the GS–GOGAT pathway for assimilation of ammonium, and their primary function is to deaminate glutamate (see Figure 12.7B).
Transamination Reactions Transfer Nitrogen Once assimilated into glutamine and glutamate, nitrogen is incorporated into other amino acids via transamination reactions. The enzymes that catalyze these reactions are known as aminotransferases. An example is aspartate aminotransferase (Asp-AT), which catalyzes the following reaction (Figure 12.7C): Glutamate + oxaloacetate → aspartate + 2-oxoglutarate (12.7) in which the amino group of glutamate is transferred to the carboxyl atom of aspartate. Aspartate is an amino acid that participates in the malate–aspartate shuttle to transfer reducing equivalents from the mitochondrion and chloro-plast into the cytosol (see Chapter 11) and in the transport of carbon from mesophyll to bundle sheath for C4 carbon fixation (see Chapter 8). All transamination reactions require pyridoxal phosphate (vitamin B6) as a cofactor.
Aminotransferases are found in the cytoplasm, chloro-plasts, mitochondria, glyoxysomes, and peroxisomes. The aminotransferases localized in the chloroplasts may have a significant role in amino acid biosynthesis because plant leaves or isolated chloroplasts exposed to radioactively labeled carbon dioxide rapidly incorporate the label into glutamate, aspartate, alanine, serine, and glycine.
Asparagine and Glutamine Link Carbon and Nitrogen Metabolism Asparagine, isolated from asparagus as early as 1806, was the first amide to be identified (Lam et al. 1996). It serves not only as a protein precursor, but as a key compound for nitrogen transport and storage because of its stability and high nitrogen-to-carbon ratio (2 N to 4 C for asparagine, versus 2 N to 5 C for glutamine or 1 N to 5 C for gluta-mate).
The major pathway for asparagine synthesis involves the transfer of the amide nitrogen from glutamine to asparagine (Figure 12.7D): Glutamine + aspartate + ATP → asparagine + glutamate + AMP + PPi (12.8) Asparagine synthetase (AS), the enzyme that catalyzes this reaction, is found in the cytosol of leaves and roots and in nitrogen-fixing nodules (see the next section). In maize roots, particularly those under potentially toxic levels of ammonia, ammonium may replace glutamine as the source of the amide group (Sivasankar and Oaks 1996).
High levels of light and carbohydrate—conditions that stimulate plastid GS and Fd-GOGAT—inhibit the expres-sion of genes coding for AS and the activity of the enzyme.
The opposing regulation of these competing pathways helps balance the metabolism of carbon and nitrogen in plants (Lam et al. 1996). Conditions of ample energy (i.e., high lev-els of light and carbohydrates) stimulate GS and GOGAT, inhibit AS, and thus favor nitrogen assimilation into gluta-mine and glutamate, compounds that are rich in carbon and participate in the synthesis of new plant materials.
By contrast, energy-limited conditions inhibit GS and GOGAT, stimulate AS, and thus favor nitrogen assimilation into asparagine, a compound that is rich in nitrogen and sufficiently stable for long-distance transport or long-term storage.
BIOLOGICAL NITROGEN FIXATION Biological nitrogen fixation accounts for most of the fixation of atmospheric N2 into ammonium, thus representing the key entry point of molecular nitrogen into the biogeochem-ical cycle of nitrogen (see Figure 12.1). In this section we will describe the properties of the nitrogenase enzymes that fix nitrogen, the symbiotic relations between nitrogen-fixing organisms and higher plants, the specialized structures that form in roots when infected by nitrogen-fixing bacteria, and the genetic and signaling interactions that regulate nitrogen fixation by symbiotic prokaryotes and their hosts.
Free-Living and Symbiotic Bacteria Fix Nitrogen Some bacteria, as stated earlier, can convert atmospheric nitrogen into ammonium (Table 12.2). Most of these nitro-gen-fixing prokaryotes are free-living in the soil. A few form symbiotic associations with higher plants in which the prokaryote directly provides the host plant with fixed nitrogen in exchange for other nutrients and carbohydrates (top portion of Table 12.2). Such symbioses occur in nod-ules that form on the roots of the plant and contain the nitrogen-fixing bacteria.
The most common type of symbiosis occurs between members of the plant family Leguminosae and soil bacte-ria of the genera Azorhizobium, Bradyrhizobium, Photorhizo-bium, Rhizobium, and Sinorhizobium (collectively called rhi-zobia; Table 12.3 and Figure 12.8). Another common type of symbiosis occurs between several woody plant species, such as alder trees, and soil bacteria of the genus Frankia.
Still other types involve the South American herb Gunnera and the tiny water fern Azolla, which form associations with the cyanobacteria Nostoc and Anabaena, respectively (see Table 12.2 and Figure 12.9).
Nitrogen Fixation Requires Anaerobic Conditions Because oxygen irreversibly inactivates the nitrogenase enzymes involved in nitrogen fixation, nitrogen must be fixed under anaerobic conditions. Thus each of the nitro-266 Chapter 12 gen-fixing organisms listed in Table 12.2 either functions under natural anaerobic conditions or can create an inter-nal anaerobic environment in the presence of oxygen.
In cyanobacteria, anaerobic conditions are created in spe-cialized cells called heterocysts (see Figure 12.9). Heterocysts are thick-walled cells that differentiate when filamentous cyanobacteria are deprived of NH4 +. These cells lack photo-system II, the oxygen-producing photosystem of chloro-plasts (see Chapter 7), so they do not generate oxygen (Bur-ris 1976). Heterocysts appear to represent an adaptation for nitrogen fixation, in that they are widespread among aero-bic cyanobacteria that fix nitrogen.
Cyanobacteria that lack heterocysts can fix nitrogen only under anaerobic conditions such as those that occur in flooded fields. In Asian countries, nitrogen-fixing cyano-bacteria of both the heterocyst and nonheterocyst types are a major means for maintaining an adequate nitrogen sup-ply in the soil of rice fields. These microorganisms fix nitro-gen when the fields are flooded and die as the fields dry, releasing the fixed nitrogen to the soil. Another important TABLE 12.2 Examples of organisms that can carry out nitrogen fixation Symbiotic nitrogen fixation Host plant N-fixing symbionts Leguminous: legumes, Parasponia Azorhizobium, Bradyrhizobium, Photorhizobium, Rhizobium, Sinorhizobium Actinorhizal: alder (tree), Ceanothus (shrub), Frankia Casuarina (tree), Datisca (shrub) Gunnera Nostoc Azolla (water fern) Anabaena Sugarcane Acetobacter Free-living nitrogen fixation Type N-fixing genera Cyanobacteria (blue-green algae) Anabaena, Calothrix,Nostoc Other bacteria Aerobic Azospirillum, Azotobacter,Beijerinckia, Derxia Facultative Bacillus, Klebsiella Anaerobic Nonphotosynthetic Clostridium, Methanococcus (archaebacterium) Photosynthetic Chromatium,Rhodospirillum TABLE 12.3 Associations between host plants and rhizobia Plant host Rhizobial symbiont Parasponia (a nonlegume, formerly called Trema) Bradyrhizobium spp.
Soybean (Glycine max) Bradyrhizobium japonicum (slow-growing type); Sinorhizobium fredii (fast-growing type) Alfalfa (Medicago sativa) Sinorhizobium meliloti Sesbania (aquatic) Azorhizobium (forms both root and stem nodules; the stems have adventitious roots) Bean (Phaseolus) Rhizobium leguminosarum bv. phaseoli; Rhizobium tropicii; Rhizobium etli Clover (Trifolium) Rhizobium leguminosarum bv. trifolii Pea (Pisum sativum) Rhizobium leguminosarum bv. viciae Aeschenomene (aquatic) Photorhizobium (photosynthetically active rhizobia that form stem nodules, probably associated with adventitious roots) Assimilation of Mineral Nutrients 267 source of available nitrogen in flooded rice fields is the water fern Azolla, which associates with the cyanobac-terium Anabaena. The Azolla–Anabaena association can fix as much as 0.5 kg of atmospheric nitrogen per hectare per day, a rate of fertilization that is sufficient to attain moder-ate rice yields.
Free-living bacteria that are capable of fixing nitrogen are aerobic, facultative, or anaerobic (see Table 12.2, bottom): • Aerobic nitrogen-fixing bacteria such as Azotobacter are thought to maintain reduced oxygen conditions (microaerobic conditions) through their high levels of respiration (Burris 1976). Others, such as Gloeothece, evolve O2 photosynthetically during the day and fix nitrogen during the night.
• Facultative organisms, which are able to grow under both aerobic and anaerobic conditions, generally fix nitrogen only under anaerobic conditions.
• For anaerobic nitrogen-fixing bacteria, oxygen does not pose a problem, because it is absent in their habi-tat. These anaerobic organisms can be either photo-synthetic (e.g., Rhodospirillum), or nonphotosynthetic (e.g., Clostridium).
Symbiotic Nitrogen Fixation Occurs in Specialized Structures Symbiotic nitrogen-fixing prokaryotes dwell within nod-ules, the special organs of the plant host that enclose the nitrogen-fixing bacteria (see Figure 12.8). In the case of Gunnera, these organs are existing stem glands that develop independently of the symbiont. In the case of legumes and actinorhizal plants, the nitrogen-fixing bacteria induce the plant to form root nodules.
Grasses can also develop symbiotic relationships with nitrogen-fixing organisms, but in these associations root nodules are not produced. Instead, the nitrogen-fixing bac-teria seem to colonize plant tissues or anchor to the root surfaces, mainly around the elongation zone and the root hairs (Reis et al. 2000). For example, the nitrogen-fixing FIGURE 12.8 Root nodules on soybean. The nodules are a result of infection by Rhizobium japonicum. (© Wally Eberhart/Visuals Unlimited.) Vegetative cells Heterocyst FIGURE 12.9 A heterocyst in a fila-ment of the nitrogen-fixing cyanobac-terium Anabaena. The thick-walled heterocysts, interspaced among vege-tative cells, have an anaerobic inner environment that allows cyano-bacteria to fix nitrogen in aerobic conditions. (© Paul W. Johnson/ Biological Photo Service.) 268 Chapter 12 bacterium Acetobacter diazotrophicus lives in the apoplast of stem tissues in sugarcane and may provide its host with sufficient nitrogen to grant independence from nitrogen fertilization (Dong et al. 1994). The potential for applying Azospirillum to corn and other grains has been explored, but Azospirillum seems to fix little nitrogen when associated with plants (Vande Broek and Vanderleyden 1995).
Legumes and actinorhizal plants regulate gas perme-ability in their nodules, maintaining a level of oxygen within the nodule that can support respiration but is suffi-ciently low to avoid inactivation of the nitrogenase (Kuzma et al. 1993). Gas permeability increases in the light and decreases under drought or upon exposure to nitrate. The mechanism for regulating gas permeability is not yet known.
Nodules contain an oxygen-binding heme protein called leghemoglobin. Leghemoglobin is present in the cyto-plasm of infected nodule cells at high concentrations (700 µM in soybean nodules) and gives the nodules a pink color.
The host plant produces the globin portion of leghemo-globin in response to infection by the bacteria (Marschner 1995); the bacterial symbiont produces the heme portion.
Leghemoglobin has a high affinity for oxygen (a Km of about 0.01 µM), about ten times higher than the β chain of human hemoglobin.
Although leghemoglobin was once thought to provide a buffer for nodule oxygen, recent studies indicate that it stores only enough oxygen to support nodule respiration for a few seconds (Denison and Harter 1995). Its function is to help transport oxygen to the respiring symbiotic bac-terial cells in a manner analogous to hemoglobin trans-porting oxygen to respiring tissues in animals (Ludwig and de Vries 1986).
Establishing Symbiosis Requires an Exchange of Signals The symbiosis between legumes and rhizobia is not oblig-atory. Legume seedlings germinate without any association with rhizobia, and they may remain unassociated through-out their life cycle. Rhizobia also occur as free-living organ-isms in the soil. Under nitrogen-limited conditions, how-ever, the symbionts seek out one another through an elaborate exchange of signals. This signaling, the subse-quent infection process, and the development of nitrogen-fixing nodules involve specific genes in both the host and the symbionts.
Plant genes specific to nodules are called nodulin (Nod) genes; rhizobial genes that participate in nodule formation are called nodulation (nod) genes (Heidstra and Bisseling 1996). The nod genes are classified as common nod genes or host-specific nod genes. The common nod genes—nodA, nodB, and nodC—are found in all rhizobial strains; the host-specific nod genes—such as nodP, nodQ, and nodH; or nodF, nodE, and nodL—differ among rhizobial species and determine the host range. Only one of the nod genes, the regulatory nodD, is constitutively expressed, and as we will explain in detail, its protein product (NodD) regulates the transcription of the other nod genes.
The first stage in the formation of the symbiotic rela-tionship between the nitrogen-fixing bacteria and their host is migration of the bacteria toward the roots of the host plant. This migration is a chemotactic response mediated by chemical attractants, especially (iso)flavonoids and betaines, secreted by the roots. These attractants activate the rhizobial NodD protein, which then induces transcrip-tion of the other nod genes (Phillips and Kapulnik 1995).
The promoter region of all nod operons, except that of nodD, contains a highly conserved sequence called the nod box. Binding of the activated NodD to the nod box induces transcription of the other nod genes.
Nod Factors Produced by Bacteria Act as Signals for Symbiosis The nod genes activated by NodD code for nodulation pro-teins, most of which are involved in the biosynthesis of Nod factors. Nod factors are lipochitin oligosaccharide sig-nal molecules, all of which have a chitin β-1→4-linked N-acetyl-D-glucosamine backbone (varying in length from three to six sugar units) and a fatty acyl chain on the C-2 position of the nonreducing sugar (Figure 12.10).
Three of the nod genes (nodA, nodB, and nodC) encode enzymes (NodA, NodB, and NodC, respectively) that are required for synthesizing this basic structure (Stokkermans et al. 1995): 1. NodA is an N-acyltransferase that catalyzes the addi-tion of a fatty acyl chain.
2. NodB is a chitin-oligosaccharide deacetylase that removes the acetyl group from the terminal nonre-ducing sugar.
CH2OH CH3 HO HO NH O CH2OH O HO N O C O CH3 CH2 O O O HO N O C O n Fatty acid Hydrogen or glycerol Hydrogen, sulfate, fucose, or 2-O-methyl fucose FIGURE 12.10 Nod factors are lipochitin oligosaccharides.
The fatty acid chain typically has 16 to 18 carbons. The number of repeated middle sections (n) is usually 2 to 3.
(After Stokkermans et al. 1995.) Assimilation of Mineral Nutrients 269 3. NodC is a chitin-oligosaccharide synthase that links N-acetyl-D-glucosamine monomers.
Host-specific nod genes that vary among rhizobial species are involved in the modification of the fatty acyl chain or the addition of groups important in determining host specificity (Carlson et al. 1995): • NodE and NodF determine the length and degree of saturation of the fatty acyl chain; those of Rhizobium leguminosarum bv. viciae and R. meliloti result in the synthesis of an 18:4 and a 16:2 fatty acyl group, respectively. (Recall from Chapter 11 that the number before the colon gives the total number of carbons in the fatty acyl chain, and the number after the colon gives the number of double bonds.) • Other enzymes, such as NodL, influence the host specificity of Nod factors through the addition of specific substitutions at the reducing or nonreducing sugar moieties of the chitin backbone.
A particular legume host responds to a specific Nod fac-tor. The legume receptors for Nod factors appear to be spe-cial lectins (sugar-binding proteins) produced in the root hairs (van Rhijn et al. 1998; Etzler et al. 1999). Nod factors activate these lectins, increasing their hydrolysis of phos-phoanhydride bonds of nucleoside di- and triphosphates.
This lectin activation directs particular rhizobia to appro-priate hosts and facilitates attachment of the rhizobia to the cell walls of a root hair.
Nodule Formation Involves Several Phytohormones Two processes—infection and nodule organogenesis— occur simultaneously during root nodule formation. Dur-ing the infection process, rhizobia that are attached to the root hairs release Nod factors that induce a pronounced curling of the root hair cells (Figure 12.11A and B). The rhi-zobia become enclosed in the small compartment formed by the curling. The cell wall of the root hair degrades in these regions, also in response to Nod factors, allowing the bacterial cells direct access to the outer surface of the plant plasma membrane (Lazarowitz and Bisseling 1997).
The next step is formation of the infection thread (Fig-ure 12.11C), an internal tubular extension of the plasma membrane that is produced by the fusion of Golgi-derived membrane vesicles at the site of infection. The thread grows at its tip by the fusion of secretory vesicles to the end of the tube. Deeper into the root cortex, near the xylem, cortical cells dedifferentiate and start dividing, forming a distinct area within the cortex, called a nodule primordium, from which the nodule will develop. The nodule primordia form opposite the protoxylem poles of the root vascular bundle (Timmers et al. 1999) (See Web Topic 12.1).
Different signaling compounds, acting either positively or negatively, control the position of nodule primordia. The nucleoside uridine diffuses from the stele into the cortex in the protoxylem zones of the root and stimulates cell division (Lazarowitz and Bisseling 1997). Ethylene is synthesized in the region of the pericycle, diffuses into the cortex, and blocks cell division opposite the phloem poles of the root.
The infection thread filled with proliferating rhizobia elongates through the root hair and cortical cell layers, in the direction of the nodule primordium. When the infection thread reaches specialized cells within the nodule, its tip fuses with the plasma membrane of the host cell, releasing bacterial cells that are packaged in a membrane derived from the host cell plasma membrane (see Figure 12.11D).
Branching of the infection thread inside the nodule enables the bacteria to infect many cells (see Figure 12.11E and F) (Mylona et al. 1995).
At first the bacteria continue to divide, and the sur-rounding membrane increases in surface area to accom-modate this growth by fusing with smaller vesicles. Soon thereafter, upon an undetermined signal from the plant, the bacteria stop dividing and begin to enlarge and to differ-entiate into nitrogen-fixing endosymbiotic organelles called bacteroids. The membrane surrounding the bacteroids is called the peribacteroid membrane.
The nodule as a whole develops such features as a vas-cular system (which facilitates the exchange of fixed nitro-gen produced by the bacteroids for nutrients contributed by the plant) and a layer of cells to exclude O2 from the root nodule interior. In some temperate legumes (e.g., peas), the nodules are elongated and cylindrical because of the pres-ence of a nodule meristem. The nodules of tropical legumes, such as soybeans and peanuts, lack a persistent meristem and are spherical (Rolfe and Gresshoff 1988).
The Nitrogenase Enzyme Complex Fixes N2 Biological nitrogen fixation, like industrial nitrogen fixa-tion, produces ammonia from molecular nitrogen. The overall reaction is N2 + 8 e– + 8 H+ + 16 ATP → 2 NH3 + H2 + 16 ADP + 16 Pi (12.9) FIGURE 12.11 The infection process during nodule organo-genesis. (A) Rhizobia bind to an emerging root hair in response to chemical attractants sent by the plant. (B) In response to factors produced by the bacteria, the root hair exhibits abnormal curling growth, and rhizobia cells prolif-erate within the coils. (C) Localized degradation of the root hair wall leads to infection and formation of the infection thread from Golgi secretory vesicles of root cells. (D) The infection thread reaches the end of the cell, and its mem-brane fuses with the plasma membrane of the root hair cell.
(E) Rhizobia are released into the apoplast and penetrate the compound middle lamella to the subepidermal cell plasma membrane, leading to the initiation of a new infec-tion thread, which forms an open channel with the first. (F) The infection thread extends and branches until it reaches target cells, where vesicles composed of plant membrane that enclose bacterial cells are released into the cytosol.
L 270 Chapter 12 (A) (C) (E) (B) (D) (F) Rhizobia Root hair Infection thread Golgi body Golgi vesicle Curling growth Infection thread membrane fuses with cell membrane Vesicle containing rhizobia Note that the reduction of N2 to 2 NH3, a six-electron transfer, is coupled to the reduction of two protons to evolve H2. The nitrogenase enzyme complex catalyzes this reaction.
The nitrogenase enzyme complex can be separated into two components—the Fe protein and the MoFe protein— neither of which has catalytic activity by itself (Figure 12.12): • The Fe protein is the smaller of the two components and has two identical subunits of 30 to 72 kDa each, depending on the organism. Each subunit contains an iron–sulfur cluster (4 Fe and 4 S2– ) that participates in the redox reactions involved in the conversion of N2 to NH3. The Fe protein is irreversibly inactivated by O2 with typical half-decay times of 30 to 45 seconds (Dixon and Wheeler 1986).
• The MoFe protein has four subunits, with a total mol-ecular mass of 180 to 235 kDa, depending on the species. Each subunit has two Mo–Fe–S clusters. The MoFe protein is also inactivated by oxygen, with a half-decay time in air of 10 minutes.
In the overall nitrogen reduction reaction (see Figure 12.12), ferredoxin serves as an electron donor to the Fe pro-tein, which in turn hydrolyzes ATP and reduces the MoFe protein. The MoFe protein then can reduce numerous sub-strates (Table 12.4), although under natural conditions it reacts only with N2 and H+. One of the reactions catalyzed by nitrogenase, the reduction of acetylene to ethylene, is used in estimating nitrogenase activity (see Web Topic 12.2).
The energetics of nitrogen fixation is complex. The pro-duction of NH3 from N2 and H2 is an exergonic reaction Assimilation of Mineral Nutrients 271 (see Chapter 2 on the website for a discussion of exergonic reactions), with a ∆G0′ (change in free energy) of –27 kJ mol–1. However, industrial production of NH3 from N2 and H2 is endergonic, requiring a very large energy input because of the activation energy needed to break the triple bond in N2. For the same reason, the enzymatic reduction of N2 by nitrogenase also requires a large investment of energy (see Equation 12.9), although the exact changes in free energy are not yet known.
Calculations based on the carbohydrate metabolism of legumes show that a plant consumes 12 g of organic car-bon per gram of N2 fixed (Heytler et al. 1984). On the basis of Equation 12.9, the ∆G0′ for the overall reaction of bio-logical nitrogen fixation is about –200 kJ mol–1. Because the overall reaction is highly exergonic, ammonium produc-tion is limited by the slow operation (number of N2 mole-cules reduced per unit time) of the nitrogenase complex (Ludwig and de Vries 1986).
Under natural conditions, substantial amounts of H+ are reduced to H2 gas, and this process can compete with N2 reduction for electrons from nitrogenase. In rhizobia, 30 to 60% of the energy supplied to nitrogenase may be lost as H2, diminishing the efficiency of nitrogen fixation. Some rhizobia, however, contain hydrogenase, an enzyme that can split the H2 formed and generate electrons for N2 reduction, thus improving the efficiency of nitrogen fixa-tion (Marschner 1995).
Amides and Ureides Are the Transported Forms of Nitrogen The symbiotic nitrogen-fixing prokaryotes release ammo-nia that, to avoid toxicity, must be rapidly converted into organic forms in the root nodules before being transported to the shoot via the xylem. Nitrogen-fixing legumes can be divided into amide exporters or ureide exporters on the basis of the composition of the xylem sap. Amides (princi-pally the amino acids asparagine or glutamine) are exported by temperate-region legumes, such as pea (Pisum), clover (Trifolium), broad bean (Vicia), and lentil (Lens).
Ureides are exported by legumes of tropical origin, such as soybean (Glycine), kidney bean (Phaseolus), peanut (Arachis), and southern pea (Vigna). The three major urei-des are allantoin, allantoic acid, and citrulline (Figure 12.13). Allantoin is synthesized in peroxisomes from uric acid, and allantoic acid is synthesized from allantoin in the endoplasmic reticulum. The site of citrulline synthesis from the amino acid ornithine has not yet been determined. All three compounds are ultimately released into the xylem and transported to the shoot, where they are rapidly catab-olized to ammonium. This ammonium enters the assimi-lation pathway described earlier.
SULFUR ASSIMILATION Sulfur is among the most versatile elements in living organ-isms (Hell 1997). Disulfide bridges in proteins play struc-tural and regulatory roles (see Chapter 8). Sulfur partici-pates in electron transport through iron–sulfur clusters (see Chapters 7 and 11). The catalytic sites for several enzymes and coenzymes, such as urease and coenzyme A, contain sulfur. Secondary metabolites (compounds that are not involved in primary pathways of growth and develop-Ferredoxinox Ferredoxinred Fered Fered MoFered Feox MoFeox MoFeox Products 2 NH3, H2 Substrate N2, 8 H+ Nitrogenase enzyme complex Fe protein MoFe protein 16 ATP 16 ADP + Pi 16 FIGURE 12.12 The reaction cat-alyzed by nitrogenase. Ferredoxin reduces the Fe protein. Binding and hydrolysis of ATP to the Fe protein is thought to cause a con-formational change of the Fe pro-tein that facilitates the redox reac-tions. The Fe protein reduces the MoFe protein, and the MoFe pro-tein reduces the N2. (After Dixon and Wheeler 1986, and Buchanan et al. 2000.) TABLE 12.4 Reactions catalyzed by nitrogenase N2 →NH3 Molecular nitrogen fixation N2O →N2 + H2O Nitrous oxide reduction N3 - →N2 + NH3 Azide reduction C2H2 → C2H4 Acetylene reduction 2 H+ →H2 H2 production ATP →ADP + Pi ATP hydrolytic activity Source: After Burris 1976.
272 Chapter 12 ment) that contain sulfur range from the rhizobial Nod fac-tors discussed in the previous section to antiseptic alliin in garlic and anticarcinogen sulforaphane in broccoli.
The versatility of sulfur derives in part from the prop-erty that it shares with nitrogen: multiple stable oxidation states. In this section we discuss the enzymatic steps that mediate sulfur assimilation, and the biochemical reactions that catalyze the reduction of sulfate into the two sulfur-containing amino acids, cysteine and methionine.
Sulfate Is the Absorbed Form of Sulfur in Plants Most of the sulfur in higher-plant cells derives from sulfate (SO4 2–) absorbed via an H+–SO4 2– symporter (see Chapter 6) from the soil solution. Sulfate in the soil comes predom-inantly from the weathering of parent rock material. Indus-trialization, however, adds an additional source of sulfate: atmospheric pollution. The burning of fossil fuels releases several gaseous forms of sulfur, including sulfur dioxide (SO2) and hydrogen sulfide (H2S), which find their way to the soil in rain.
When dissolved in water, SO2 is hydrolyzed to become sulfuric acid (H2SO4), a strong acid, which is the major source of acid rain. Plants can also metabolize sulfur diox-ide taken up in the gaseous form through their stomata.
Nonetheless, prolonged exposure (more than 8 hours) to high atmospheric concentrations (greater than 0.3 ppm) of SO2 causes extensive tissue damage because of the forma-tion of sulfuric acid.
Sulfate Assimilation Requires the Reduction of Sulfate to Cysteine The first step in the synthesis of sulfur-containing organic compounds is the reduction of sulfate to the amino acid cysteine (Figure 12.14). Sulfate is very stable and thus needs to be activated before any subsequent reactions may pro-ceed. Activation begins with the reaction between sulfate and ATP to form 5′-adenylylsulfate (which is sometimes referred to as adenosine-5′-phosphosulfate and thus is abbreviated APS) and pyrophosphate (PPi) (see Figure 12.14): SO4 2– + Mg-ATP →APS + PPi (12.10) The enzyme that catalyzes this reaction, ATP sulfury-lase, has two forms: The major one is found in plastids, and a minor one is found in the cytoplasm (Leustek et al. 2000).
The activation reaction is energetically unfavorable. To drive this reaction forward, the products APS and PPi must be converted immediately to other compounds. PPi is hydrolyzed to inorganic phosphate (Pi) by inorganic pyrophosphatase according to the following reaction: PPi + H2O →2 Pi (12.11) The other product, APS, is rapidly reduced or sulfated.
Reduction is the dominant pathway (Leustek et al. 2000).
The reduction of APS is a multistep process that occurs exclusively in the plastids. First, APS reductase transfers two electrons apparently from reduced glutathione (GSH) to produce sulfite (SO3 2–): APS + 2 GSH →SO3 2– + 2 H+ + GSSG + AMP (12.12) where GSSG stands for oxidized glutathione. (The SH in GSH and the SS in GSSG stand for S—H and S—S bonds, respectively.) Second, sulfite reductase transfers six electrons from ferredoxin (Fdred) to produce sulfide (S2–): SO3 2– + 6 Fdred →S2– + 6 Fdox (12.13) The resultant sulfide then reacts with O-acetylserine (OAS) to form cysteine and acetate. The O-acetylserine that reacts with S2– is formed in a reaction catalyzed by serine acetyl-transferase: Serine + acetyl-CoA →OAS + CoA (12.14) The reaction that produces cysteine and acetate is catalyzed by OAS thiol-lyase: OAS + S2– →cysteine + acetate (12.15) The sulfation of APS, localized in the cytosol, is the alter-native pathway. First, APS kinase catalyzes a reaction of APS with ATP to form 3′-phosphoadenosine-5′-phospho-sulfate (PAPS).
APS + ATP →PAPS + ADP (12.16) H2N C O C H H N H H2N C N C OH O O C HN NH C N C NH2 C H H O O H2N CH2CH2CH2C H C COOH N H O NH2 Allantoic acid Allantoin Citrulline O FIGURE 12.13 The major ureide compounds used to trans-port nitrogen from sites of fixation to sites where their deamination will provide nitrogen for amino acid and nucleoside synthesis.
Assimilation of Mineral Nutrients 273 Sulfotransferases then may transfer the sulfate group from PAPS to various compounds, including choline, brassinos-teroids, flavonol, gallic acid glucoside, glucosinolates, pep-tides, and polysaccharides (Leustek and Saito 1999).
Sulfate Assimilation Occurs Mostly in Leaves The reduction of sulfate to cysteine changes the oxidation number of sulfur from +6 to –4, thus entailing the transfer of 10 electrons. Glutathione, ferredoxin, NAD(P)H, or O-acetylserine may serve as electron donors at various steps of the pathway (see Figure 12.14).
Leaves are generally much more active than roots in sul-fur assimilation, presumably because photosynthesis pro-vides reduced ferredoxin and photorespiration generates serine that may stimulate the production of O-acetylserine (see Chapter 8). Sulfur assimilated in leaves is exported via the phloem to sites of protein synthesis (shoot and root apices, and fruits) mainly as glutathione (Bergmann and Rennenberg 1993): Glutathione also acts as a signal that coordinates the absorption of sulfate by the roots and the assimilation of sulfate by the shoot.
H O O O– H H3N+ C N C C N C CH2 CH2 SH CH2 C C C H H H H O O O– Glycine Cysteine Glutamate Reduced glutathione H OH O O CH2 P H H H O O– O– O– P O O S O– O O O R O S O– O O H OH OH CH2 H H H O O– P O O S O– O O O SO4 2– H2O ATP ATP ADP PPi 2 Pi H H H CH2 CH2 S C O S O– C NH C O NH COO– CH2 CH2 C H H3N+ COO– O O O S S2– O– O– S2– O C O CH2 CH COOH CH3 NH2 HO CH2 CH COOH NH2 CH2 CH COOH SH NH2 O-Acetylserine thio-lyase H H Adenine R-OH 3´-Phosphoadenylate Sulfotransferase 3´-Phosphoadenosine-5´-phosphosulfate (PAPS) O-Sulfated metabolite GSH 5´-AMP APS sulfo-transferase ATP sulfurylase APS kinase Non-enzymatic Adenosine-5´-phosphosulfate (APS) S-Sulfoglutathione Sulfite Sulfide Sulfate Acetyl-CoA CoA Serine acetyltransferase O-Acetylserine Serine Cysteine Inorganic pyrophosphatase GSH GSSG Sulfite reductase 6Fdred 6Fdox Acetate Adenine FIGURE 12.14 Structure and pathways of compounds involved in sulfur assimilation. The enzyme ATP sulfurylase cleaves pyrophosphate from ATP and replaces it with sulfate. Sulfide is produced from APS through reactions involving reduction by glutathione and ferredoxin. The sulfide or thiosulfide reacts with O-acetylserine to form cysteine. Fd, ferredoxin; GSH, glutathione, reduced; GSSG, glutathione, oxidized.
Methionine Is Synthesized from Cysteine Methionine, the other sulfur-containing amino acid found in proteins, is synthesized in plastids from cysteine (see Web Topic 12.3 for further detail). After cysteine and methionine are synthesized, sulfur can be incorporated into proteins and a variety of other compounds, such as acetyl-CoA and S-adenosylmethionine. The latter compound is important in the synthesis of ethylene (see Chapter 22) and in reactions involving the transfer of methyl groups, as in lignin synthesis (see Chapter 13).
PHOSPHATE ASSIMILATION Phosphate (HPO4 2–) in the soil solution is readily absorbed by plant roots via an H+–HPO4 2– symporter (see Chapter 6) and incorporated into a variety of organic compounds, including sugar phosphates, phospholipids, and nucleotides.
The main entry point of phosphate into assimilatory path-ways occurs during the formation of ATP, the energy “cur-rency” of the cell. In the overall reaction for this process, inor-ganic phosphate is added to the second phosphate group in adenosine diphosphate to form a phosphate ester bond.
In mitochondria, the energy for ATP synthesis derives from the oxidation of NADH by oxidative phosphorylation (see Chapter 11). ATP synthesis is also driven by light-depen-dent photophosphorylation in the chloroplasts (see Chapter 7). In addition to these reactions in mitochondria and chloro-plasts, reactions in the cytosol also assimilate phosphate.
Glycolysis incorporates inorganic phosphate into 1,3-bis-phosphoglyceric acid, forming a high-energy acyl phosphate group. This phosphate can be donated to ADP to form ATP in a substrate-level phosphorylation reaction (see Chapter 11). Once incorporated into ATP, the phosphate group may be transferred via many different reactions to form the var-ious phosphorylated compounds found in higher-plant cells.
CATION ASSIMILATION Cations taken up by plant cells form complexes with organic compounds in which the cation becomes bound to the complex by noncovalent bonds (for a discussion of non-covalent bonds, see Chapter 2 on the web site). Plants assimilate macronutrient cations such as potassium, mag-nesium, and calcium, as well as micronutrient cations such as copper, iron, manganese, cobalt, sodium, and zinc, in this manner. In this section we will describe coordination bonds and electrostatic bonds, which mediate the assimi-lation of several cations that plants require as nutrients, and the special requirements for the absorption of iron by roots and subsequent assimilation of iron within plants.
Cations Form Noncovalent Bonds with Carbon Compounds The noncovalent bonds formed between cations and car-bon compounds are of two types: coordination bonds and electrostatic bonds. In the formation of a coordination com-plex, several oxygen or nitrogen atoms of a carbon com-pound donate unshared electrons to form a bond with the cation nutrient. As a result, the positive charge on the cation is neutralized.
Coordination bonds typically form between polyvalent cations and carbon molecules—for example, complexes between copper and tartaric acid (Figure 12.15A) or mag-nesium and chlorophyll a (Figure 12.15B). The nutrients that are assimilated as coordination complexes include cop-per, zinc, iron, and magnesium. Calcium can also form coordination complexes with the polygalacturonic acid of cell walls (Figure 12.15C).
Electrostatic bonds form because of the attraction of a pos-itively charged cation for a negatively charged group such as carboxylate (—COO–) on a carbon compound. Unlike the situation in coordination bonds, the cation in an electrosta-tic bond retains its positive charge. Monovalent cations such as potassium (K+) can form electrostatic bonds with the car-boxylic groups of many organic acids (Figure 12.16A).
Nonetheless, much of the potassium that is accumulated by plant cells and functions in osmotic regulation and enzyme activation remains in the cytosol and the vacuole as the free ion. Divalent ions such as calcium form electrostatic bonds with pectates (Figure 12.16B) and the carboxylic groups of polygalacturonic acid (see Chapter 15).
In general, cations such as magnesium (Mg2+) and cal-cium (Ca2+) are assimilated by the formation of both coor-dination complexes and electrostatic bonds with amino acids, phospholipids, and other negatively charged mole-cules.
Roots Modify the Rhizosphere to Acquire Iron Iron is important in iron–sulfur proteins (see Chapter 7) and as a catalyst in enzyme-mediated redox reactions (see Chapter 5), such as those of nitrogen metabolism discussed earlier. Plants obtain iron from the soil, where it is present primarily as ferric iron (Fe3+) in oxides such as Fe(OH)2+, Fe(OH)3, and Fe(OH)4 –. At neutral pH, ferric iron is highly insoluble. To absorb sufficient amounts of iron from the soil solution, roots have developed several mechanisms that increase iron solubility and thus its availability. These mechanisms include: • Soil acidification that increases the solubility of ferric iron.
• Reduction of ferric iron to the more soluble ferrous form (Fe2+).
• Release of compounds that form stable, soluble com-plexes with iron (Marschner 1995). Recall from Chapter 5 that such compounds are called iron chela-tors (see Figure 5.2).
Roots generally acidify the soil around them. They extrude protons during the absorption and assimilation of Assimilation of Mineral Nutrients 275 cations, particularly ammonium, and release organic acids such as malic acid and citric acid that enhance iron and phosphate availability (see Figure 5.4). Iron deficiencies stimulate the extrusion of protons by roots. In addition, plasma membranes in roots contain an enzyme, called iron-chelating reductase, that reduces ferric iron to the ferrous form, with NADH or NADPH serving as the electron donor. The activity of this enzyme increases under iron deprivation.
Several compounds secreted by roots form stable chelates with iron. Examples include malic acid, citric acid, phenolics, and piscidic acid. Grasses produce a special class + Cu2+ Mg N N N N H2C CH3 CH3 CH3 CH2 CH3 OCH3 H39C20OOC O C O C2H5 CH CH2 COOH HC HC OH Cu OH COOH ..
..
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COOH HC HC OH OH COOH ..
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O O O O O O O O H H H H H H H CO2 – H H H H HO HO Ca ..
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Chlorophyll a Polygalacturonic acid Tartaric acid Copper–tartaric acid complex (A) (C) (B) Polygalacturonic acid chain Calcium ions are held in the spaces between two polygalacturonic acid chains.
Much of the calcium in the cell wall is thought to be bound in this fashion.
FIGURE 12.15 Examples of coordination complexes.
Coordination complexes form when oxygen or nitrogen atoms of a carbon compound donate unshared electron pairs (represented by dots) to form a bond with a cation.
(A) Copper ions share electrons with the hydroxyl oxygens of tartaric acid. (B) Magnesium ions share electrons with nitrogen atoms in chlorophyll a. Dashed lines represent a coordination bond between unshared electrons from the nitrogen atoms and the magnesium cation. (C) The “egg box” model of the interaction of polygalacturonic acid, a major constituent of pectins in cell walls, and calcium ions.
At right is an enlargement of a single calcium ion forming a coordination complex with the hydroxyl oxygens of the galacturonic acid residues. (After Rees 1977.) 2 H+ HCOH COOH CH2 COOH HCOH COO– CH2 COO– HCOH COO– K+ CH2 COO– K+ 2 K+ C O O– C O –O Ca2+ C O O– C O –O Ca2+ (A) Monovalent cation (B) Divalent cation Dissociation of H+ Malic acid Malate Potassium malate Calcium pectate Complex formation FIGURE 12.16 Examples of electrostatic (ionic) complexes. (A) The mono-valent cation K+ and malate form the complex potassium malate. (B) The divalent cation Ca2+ and pectate form the complex calcium pectate.
Divalent cations can form cross-links between parallel strands that contain negatively charged carboxyl groups. Calcium cross-links play a structural role in the cell walls.
276 Chapter 12 of iron chelators called phytosiderophores. Phytosiderophores are made of amino acids that are not found in proteins, such as mugineic acid, and form highly stable complexes with Fe3+. Root cells of grasses have Fe3+–phytosiderophore transport systems in their plasma membrane that bring the chelate into the cytoplasm. Under iron deficiency, grass roots release more phytosiderophores into the soil and increase the capacity of their Fe3+–phytosiderophore trans-port system.
Iron Forms Complexes with Carbon and Phosphate Once the roots absorb iron or an iron chelate, they oxidize it to a ferric form and translocate much of it to the leaves as an electrostatic complex with citrate.
Most of the iron in the plant is found in the heme mole-cule of cytochromes within the chloroplasts and mito-chondria (see Chapter 7). An important assimilatory reac-tion for iron is its insertion into the porphyrin precursor of heme. This reaction is catalyzed by the enzyme ferrochelatase (Figure 12.17) (Jones 1983). In addition, iron–sulfur proteins of the electron transport chain (see Chapter 7) contain nonheme Fe covalently bound to the sulfur atoms of cysteine residues in the apoprotein. Iron is also found in Fe2S2 centers, which contain two irons (each complexed with the sulfur atoms of cysteine residues) and two inorganic sulfides.
Free iron (iron that is not complexed with carbon com-pounds) may interact with oxygen to form superoxide anions (O2 –), which can damage membranes by degrading unsaturated lipid components. Plant cells may limit such damage by storing surplus iron in an iron–protein complex called phytoferritin (Bienfait and Van der Mark 1983).
Phytoferritin consists of a protein shell with 24 identical subunits forming a hollow sphere that has a molecular mass of about 480 kDa. Within this sphere is a core of 5400 to 6200 iron atoms present as a ferric oxide–phosphate complex.
How iron is released from phytoferritin is uncertain, but breakdown of the protein shell appears to be involved. The level of free iron in plant cells regulates the de novo biosyn-thesis of phytoferritin (Lobreaux et al. 1992).
OXYGEN ASSIMILATION Respiration accounts for the bulk (about 90%) of the oxy-gen (O2) assimilated by plant cells (see Chapter 11).
Another major pathway for the assimilation of O2 into organic compounds involves the incorporation of O2 from water (see reaction 1 in Table 8.1). A small proportion of oxygen can be directly assimilated into organic compounds in the process of oxygen fixation.
In oxygen fixation, molecular oxygen is added directly to an organic compound in reactions carried out by enzymes known as oxygenases. Recall from Chapter 8 that oxygen is directly incorporated into an organic compound during photorespiration in a reaction that involves the oxy-genase activity of ribulose-1,5-bisphosphate carboxy-lase/oxygenase (rubisco), the enzyme of CO2 fixation (Ogren 1984). The first stable product that contains oxygen originating from molecular oxygen is 2-phosphoglycolate.
In general, oxygenases are classified as dioxygenases or monooxygenases, according to the number of atoms of oxygen that are transferred to a carbon compound in the catalyzed reaction. In dioxygenase reactions, both oxygen atoms are incorporated into one or two carbon compounds (Figure 12.18A and B). Examples of dioxygenases in plant cells are lipoxygenase, which catalyzes the addition of two atoms of oxygen to unsaturated fatty acids (see Figure 12.18A), and prolyl hydroxylase, the enzyme that converts proline to the less common amino acid hydroxyproline (see Figure 12.18B).
Hydroxyproline is an important component of the cell wall protein extensin (see Chapter 15). The synthesis of hydroxyproline from proline differs from the synthesis of all other amino acids in that the reaction occurs after the proline has been incorporated into protein and is therefore a posttranslational modification reaction. Prolyl hydroxy-lase is localized in the endoplasmic reticulum, suggesting that most proteins containing hydroxypro-line are found in the secretory pathway.
Monooxygenases add one of the atoms in molecular oxygen to a carbon com-pound; the other oxygen atom is converted into water. Monooxygenases are some-times referred to as mixed-function oxidases because of their ability to catalyze simulta-neously both the oxygenation reaction and the oxidase reaction (reduction of oxygen to water). The monooxygenase reaction also requires a reduced substrate (NADH or NADPH) as an electron donor, accord-ing to the following equation: A + O2 + BH2 →AO + H2O + B Porphyrin ring + Fe2+ Fe N N N N N N N N Ferrochelatase FIGURE 12.17 The ferrochelatase reaction. The enzyme ferrochelatase cat-alyzes the insertion of iron into the porphyrin ring to form a coordination complex. See Figure 7.37 for illustration of the biosynthesis of the porphyrin ring. Assimilation of Mineral Nutrients 277 where A represents an organic compound and B represents the electron donor.
An important monooxygenase in plants is the family of heme proteins collectively called cytochrome P450, which catalyzes the hydroxylation of cinnamic acid to p-coumaric acid (Figure 12.18C). In monooxygenases, the oxygen is first activated by being combined with the iron atom of the heme group; NADPH serves as the electron donor. The mixed-function oxidase system is localized on the endo-plasmic reticulum and is capable of oxidizing a variety of substrates, including mono- and diterpenes and fatty acids.
THE ENERGETICS OF NUTRIENT ASSIMILATION Nutrient assimilation generally requires large amounts of energy to convert stable, low-energy inorganic compounds into high-energy organic compounds. For example, the reduction of nitrate to nitrite and then to ammonium requires the transfer of about ten electrons and accounts for about 25% of the total energy expenditures in both roots and shoots (Bloom 1997). Consequently, a plant may use one-fourth of its energy to assimilate nitrogen, a constituent that accounts for less than 2% of the total dry weight of the plant.
Many of these assimilatory reactions occur in the stroma of the chloroplast, where they have ready access to power-ful reducing agents such as NADPH, thioredoxin, and ferredoxin generated during photosynthetic electron trans-port. This process—coupling nutrient assimilation to pho-tosynthetic electron transport—is called photoassimilation (Figure 12.19).
Photoassimilation and the Calvin cycle occur in the same compartment but only when photosynthetic electron transport generates reductant in excess of the needs of the Calvin cycle (e.g., under conditions of high light and low CO2), does photoassimilation proceed (Robinson 1988).
High levels of CO2 inhibit photoassimilation (Figure 12.20 see Web Essay 12.1). As a result, C4 plants (see Chapter 8) conduct the majority of their photoassimilation in meso-phyll cells, where the CO2 concentrations are lower (Becker et al. 1993).
The mechanisms that regulate the partitioning of reduc-tant between the Calvin cycle and photoassimilation war-rant investigation because atmospheric levels of CO2 are Lipoxygenase C H H H H N H H R1 R2 CH2 O2 + + C H CH2 COOH C O COOH 4 C O O H H H H N OH H R1 R2 CH2 CO2 + + C H COOH CH2 COOH 4 CH O2 + NADPH + H+ + CH COOH CH H2O + NADP+ + CH OH COOH C H R1 H R2 C H H H H C C C C H CH R1 H H R2 C O O H C C cis O2 trans Prolyl hydroxylase Fe2+, ascorbate Proline (in polypeptide) a-Ketoglutarate 4-trans-L-Hydroxyproline (in polypeptide) Succinate Cinnamic acid p-Coumaric acid Cytochrome P450 (A) Dioxygenase reaction (B) Dioxygenase reaction (C) Monooxygenase reaction Fatty acid The dioxygenase lipoxygenase catalyzes the addition of two atoms of oxygen to the conjugated fatty acid to form a hydroperoxide with a pair of cis–trans conjugated double bonds. The hydroxy peroxy fatty acid may then be enzymatically converted to hydroxy fatty acids and other metabolites.
The dioxygenase prolyl hydroxylase catalyzes the addition of one oxygen from O2 to proline in a polypeptide chain to produce hydroxyproline, and the addition of one oxygen to α-ketoglutarate to produce succinate and CO2.
The monooxygenase cytochrome P450 uses one oxygen from O2 to hydroxylate cinnamic acid (and other substrates) and the other oxygen to produce water. NAD(P)H serves as the electron donor for monooxygenase reactions.
FIGURE 12.18 Examples of the two types of oxygenase reactions in cells of higher plants.
278 Chapter 12 expected to double during the next century (see Chapter 9), so this phenomenon may affect plant–nutrient relations.
SUMMARY Nutrient assimilation is the process by which nutrients acquired by plants are incorporated into the carbon con-stituents necessary for growth and development. These processes often involve chemical reactions that are highly energy intensive and thus may depend directly on reduc-tant generated through photosynthesis.
For nitrogen, assimilation is but one in a series of steps that constitute the nitrogen cycle. The nitrogen cycle encom-passes the various states of nitrogen in the biosphere and their interconversions. The principal sources of nitrogen available to plants are nitrate (NO3 –) and ammonium (NH4 +).
The nitrate absorbed by roots is assimilated in either roots or shoots, depending on nitrate availability and plant ATP ATP ATP 3 ATP 7 ATP 2 ATP 2 ATP NADH NO3 – H+ NRT NO2 – NO2 – NH4 + Glutamate Glutamate Aspartate Asparagine Other amino acids Proteins, nucleic acids H+ NiR GS/ GOGAT Asp-AT AS NO3 – NR Fdred Fdred MESOPHYLL CELL CHLOROPLAST FIGURE 12.19 Summary of the processes involved in the assimilation of mineral nitrogen in the leaf. Nitrate translo-cated from the roots through the xylem is absorbed by a mesophyll cell via one of the nitrate–proton symporters (NRT) into the cytoplasm. There it is reduced to nitrite via nitrate reductase (NR). Nitrite is translocated into the stroma of the chloroplast along with a proton. In the stroma, nitrite is reduced to ammonium via nitrite reduc-tase (NiR) and this ammonium is converted into glutamate via the sequential action of glutamine synthetase (GS) and glutamate synthase (GOGAT). Once again in the cytoplasm, the glutamate is transaminated to aspartate via aspartate aminotransferase (Asp-AT). Finally, asparagine synthetase (AS) converts aspartate into asparagine. The approximate amounts of ATP equivalents are given above each reaction.
0.6 0.4 0.8 1.0 400 0 800 1200 1600 2000 CO2 assimilated/O2 evolved Photosynthetic active radiation (mmol m–2s–1) Measurement conditions 700 mmol mol–1 CO2 360 mmol mol–1 CO2 FIGURE 12.20 The assimilatory quotient (AQ = CO2 assimi-lated/O2 evolved) of wheat seedlings as a function of light level (photosynthetic active radiation). Nitrate photoassimi-lation is directly related to assimilatory quotient because transfer of electrons to nitrate and nitrite during photoas-similation increases O2 evolution from the light-dependent reactions of photosynthesis, while CO2 assimilation by the light-independent reactions continues at similar rates.
Therefore, plants that are photoassimilating nitrate exhibit a lower AQ. In measurements carried out at ambient, 360 µmol mol–1 CO2 concentrations (red trace), the AQ decreased as a function of incident radiation, indicating that photoassimilation rates increased. At elevated (700 µmol mol–1 CO2, blue trace) the AQ remains constant at all light levels used, indicating that the CO2-fixing reactions are competing for reductant, and inhibit photoassimilation.
(After Bloom et al. 2002.) Assimilation of Mineral Nutrients 279 species. In nitrate assimilation, nitrate is reduced to nitrite (NO2 –) in the cytosol via the enzyme nitrate reductase; then nitrite is reduced to ammonium in root plastids or chloro-plasts via the enzyme nitrite reductase.
Ammonium, derived either from root absorption or generated through nitrate assimilation or photorespiration, is converted to glutamine and glutamate through the sequential actions of glutamine synthetase and glutamate synthase, which are located in the cytosol and root plastids or chloroplasts.
Once assimilated into glutamine or glutamate, nitrogen may be transferred to many other organic compounds through various reactions, including the transamination reactions. Interconversion between glutamine and asparagine by asparagine synthetase balances carbon metabolism and nitrogen metabolism within a plant.
Many plants form a symbiotic relationship with nitro-gen-fixing bacteria that contain an enzyme complex, nitro-genase, that can reduce atmospheric nitrogen to ammonia.
Legumes and actinorhizal plants form associations with rhizobia and Frankia, respectively. These associations result from a finely tuned interaction between the symbiont and host plant that involves the recognition of specific signals, the induction of a specialized developmental program within the plant, the uptake of the bacteria by the plant, and the development of nodules, unique organs that house the bacteria within plant cells. Some nitrogen-fixing prokaryotic microorganisms do not form symbiotic rela-tionships with higher plants but benefit plants by enrich-ing the nitrogen content of the soil.
Like nitrate, sulfate (SO4 2–) must be reduced by assim-ilation. In sulfate reduction, an activated form of sulfate called 5′-adenylylsulfate (APS) forms. Sulfide (S2–), the end product of sulfate reduction, does not accumulate in plant cells, but is instead rapidly incorporated into the amino acids cysteine and methionine.
Phosphate (HPO4 2–) is present in a variety of com-pounds found in plant cells, including sugar phosphates, lipids, nucleic acids, and free nucleotides. The initial prod-uct of its assimilation is ATP, which is produced by sub-strate-level phosphorylations in the cytosol, oxidative phosphorylation in the mitochondria, and photophospho-rylation in the chloroplasts.
Whereas the assimilation of nitrogen, sulfur, and phos-phorus requires the formation of covalent bonds with car-bon compounds, many macro- and micronutrient cations (e.g., K+, Mg2+, Ca2+, Cu2+, Fe3+, Mn2+, Co2+, Na+, Zn2+) simply form complexes. These complexes may be held together by electrostatic bonds or coordination bonds.
Iron assimilation may involve chelation, oxidation– reduction reactions, and the formation of complexes. In order to store large amounts of iron, plant cells synthesize phyto-ferritin, an iron storage protein. An important function of iron in plant cells is to act as a redox component in the active site f enzymes, often as an iron–porphyrin complex. Iron is inserted into a porphyrin group in the ferrochelatase reaction.
In addition to being utilized in respiration, molecular oxygen can be assimilated in the process of oxygen fixation, the direct addition of oxygen to organic compounds. This process is catalyzed by enzymes known as oxygenases, which are classified as monooxygenases or dioxygenases.
Nutrient assimilation requires large amounts of energy to convert stable, low-energy, inorganic compounds into high-energy organic compounds. A plant may use one-fourth of its energy to assimilate nitrogen. Plants use energy from photosynthesis to assimilate inorganic com-pounds in a process called photoassimilation.
Web Material Web Topics 12.1 Development of a Root Nodule Nodule primordia form opposite to the pro-toxylem poles of the root vascular bundles.
12.2 Measurement of Nitrogen Fixation Acetylene reduction is used as an indirect measurement of nitrogen reduction.
12.3 The Synthesis of Methionine Methionine is synthesized in plastids from cysteine.
Web Essay 12.1 Elevated CO2 and Nitrogen Photoassimilation In leaves grown under high CO2 concentrations, CO2 inhibits nitrogen photoassimilation be-cause it competes for reductant.
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282 Chapter 12 Secondary Metabolites and Plant Defense 1 3 Chapter IN NATURAL HABITATS, plants are surrounded by an enormous num-ber of potential enemies. Nearly all ecosystems contain a wide variety of bacteria, viruses, fungi, nematodes, mites, insects, mammals, and other herbivorous animals. By their nature, plants cannot avoid these herbivores and pathogens simply by moving away; they must protect themselves in other ways.
The cuticle (a waxy outer layer) and the periderm (secondary pro-tective tissue), besides retarding water loss, provide barriers to bacterial and fungal entry. In addition, a group of plant compounds known as secondary metabolites defend plants against a variety of herbivores and pathogenic microbes. Secondary compounds may serve other important functions as well, such as structural support, as in the case of lignin, or pigments, as in the case of the anthocyanins.
In this chapter we will discuss some of the mechanisms by which plants protect themselves against both herbivory and pathogenic organ-isms. We will begin with a discussion of the three classes of compounds that provide surface protection to the plant: cutin, suberin, and waxes.
Next we will describe the structures and biosynthetic pathways for the three major classes of secondary metabolites: terpenes, phenolics, and nitrogen-containing compounds. Finally, we will examine specific plant responses to pathogen attack, the genetic control of host–pathogen inter-actions, and cell signaling processes associated with infection.
CUTIN, WAXES, AND SUBERIN All plant parts exposed to the atmosphere are coated with layers of lipid material that reduce water loss and help block the entry of pathogenic fungi and bacteria. The principal types of coatings are cutin, suberin, and waxes. Cutin is found on most aboveground parts; suberin is present on underground parts, woody stems, and healed wounds. Waxes are asso-ciated with both cutin and suberin.
Cutin,Waxes, and Suberin Are Made Up of Hydrophobic Compounds Cutin is a macromolecule, a polymer consisting of many long-chain fatty acids that are attached to each other by ester linkages, creating a rigid three-dimensional net-work. Cutin is formed from 16:0 and 18:1 fatty acids1 with hydroxyl or epoxide groups situated either in the middle of the chain or at the end opposite the carboxylic acid function (Figure 13.1A).
Cutin is a principal constituent of the cuticle, a mul-tilayered secreted structure that coats the outer cell walls of the epidermis on the aerial parts of all herba-ceous plants (Figure 13.2). The cuticle is com-posed of a top coating of wax, a thick middle layer containing cutin embedded in wax (the cuticle proper), and a lower layer formed of cutin and wax blended with the cell wall sub-stances pectin, cellulose, and other carbohydrates (the cuticular layer). Recent research suggests that, in addi-tion to cutin, the cuticle may contain a second lipid poly-mer, made up of long-chain hydrocarbons, that has been named cutan (Jeffree 1996).
Waxes are not macromolecules, but complex mixtures of long-chain acyl lipids that are extremely hydrophobic. The most common components of wax are straight-chain alka-nes and alcohols of 25 to 35 carbon atoms (see Figure 13.1B).
Long-chain aldehydes, ketones, esters, and free fatty acids are also found. The waxes of the cuticle are synthesized by epidermal cells. They leave the epidermal cells as droplets that pass through pores in the cell wall by an unknown mechanism. The top coating of cuticle wax often crystallizes in an intricate pattern of rods, tubes, or plates (Figure 13.3).
Suberin is a polymer whose structure is very poorly understood. Like cutin, suberin is formed from hydroxy or epoxy fatty acids joined by ester linkages. However, suberin differs from cutin in that it has dicarboxylic acids (see Fig-ure 13.1C), more long-chain components, and a significant proportion of phenolic compounds as part of its structure.
284 Chapter 13 (A) Hydroxy fatty acids that polymerize to make cutin: HOCH2(CH2)14COOH CH3(CH2)8CH(CH2)5COOH (B) Common wax components: Straight-chain alkanes CH3(CH2)27CH3 CH3(CH2)29CH3 Fatty acid ester CH3(CH2)22C — O(CH2)25CH3 Long-chain fatty acid CH3(CH2)22COOH Long-chain alcohol CH3(CH2)24CH2OH (C) Hydroxy fatty acids that polymerize along with other constituents to make suberin: HOCH2(CH2)14COOH HOOC(CH2)14COOH (a dicarboxylic acid) O OH FIGURE 13.1 Constituents of (A) cutin, (B) waxes, and (C) suberin.
1 Recall from Chapter 11 that the nomenclature for fatty acids is X:Y, where X is the number of carbon atoms and Y is the number of cis double bonds.
Surface wax Cuticle proper (cutin embedded in wax) Cuticular layer (cutin, wax, and carbohydrates) Cell wall Plasma membrane Epidermal cell Tonoplast Middle lamella Vacuole (B) Cuticle Cuticular layer Primary cell wall Plasma membrane FIGURE 13.2 (A) Schematic drawing of the structure of the plant cuticle, the protective covering on the epidermis of leaves and young stems at the stage of full leaf expansion.
(B) Electron micrograph of the cuticle of a glandular cell from a young leaf (Lamium sp.), showing the presence of the cuticle layers indicated in A, except for surface waxes, which are not visible. (51,000×) (A, after Jeffree 1996; B, from Gunning and Steer 1996.) (A) Suberin is a cell wall constituent found in many loca-tions throughout the plant. We have already noted its pres-ence in the Casparian strip of the root endodermis, which forms a barrier between the apoplast of the cortex and the stele (see Chapter 4). Suberin is a principal component of the outer cell walls of all underground organs and is asso-ciated with the cork cells of the periderm, the tissue that forms the outer bark of stems and roots during secondary growth of woody plants. Suberin also forms at sites of leaf abscission and in areas damaged by disease or wounding.
Cutin,Waxes, and Suberin Help Reduce Transpiration and Pathogen Invasion Cutin, suberin, and their associated waxes form barriers between the plant and its environment that function to keep water in and pathogens out. The cuticle is very effective at limiting water loss from aerial parts of the plant but does not block transpiration completely because even with the stom-ata closed, some water is lost. The thickness of the cuticle varies with environmental conditions. Plant species native to arid areas typically have thicker cuticles than plants from moist habitats have, but plants from moist habitats often develop thick cuticles when grown under dry conditions.
The cuticle and suberized tissue are both important in excluding fungi and bacteria, although they do not appear to be as important in pathogen resistance as some of the other defenses we will discuss in this chapter. Many fungi penetrate directly through the plant surface by mechanical means. Others produce cutinase, an enzyme that hydrolyzes cutin and thus facilitates entry into the plant.
SECONDARY METABOLITES Plants produce a large, diverse array of organic compounds that appear to have no direct function in growth and devel-opment. These substances are known as secondary metabolites, secondary products, or natural products. Sec-ondary metabolites have no generally recognized, direct roles in the processes of photosynthesis, respiration, solute transport, translocation, protein synthesis, nutrient assim-ilation, differentiation, or the formation of carbohydrates, proteins, and lipids discussed elsewhere in this book.
Secondary metabolites also differ from primary metabo-lites (amino acids, nucleotides, sugars, acyl lipids) in hav-ing a restricted distribution in the plant kingdom. That is, particular secondary metabolites are often found in only one plant species or related group of species, whereas pri-mary metabolites are found throughout the plant kingdom.
Secondary Metabolites Defend Plants against Herbivores and Pathogens For many years the adaptive significance of most plant sec-ondary metabolites was unknown. These compounds were thought to be simply functionless end products of metab-olism, or metabolic wastes. Study of these substances was pioneered by organic chemists of the nineteenth and early twentieth centuries who were interested in these sub-stances because of their importance as medicinal drugs, poisons, flavors, and industrial materials.
More recently, many secondary metabolites have been suggested to have important ecological functions in plants: Secondary Metabolites and Plant Defense 285 10 mm FIGURE 13.3 Surface wax deposits, which form the top layer of the cuticle, adopt dif-ferent forms. These scanning electron micrographs show the leaf surfaces of two different lines of Brassica oleracea, which differ in wax crystal structure.
(From Eigenbrode et al. 1991, courtesy of S. D. Eigenbrode, with permission from the Entomological Society of America.) • They protect plants against being eaten by herbivores (herbivory) and against being infected by microbial pathogens.
• They serve as attractants for pollinators and seed-dispersing animals and as agents of plant–plant competition.
In the remainder of this chapter we will discuss the major types of plant secondary metabolites, their biosynthesis, and what is known about their functions in the plant, par-ticularly their roles in defense.
Plant Defenses Are a Product of Evolution We can begin by asking how plants came to have defenses.
According to evolutionary biologists, plant defenses must have arisen through heritable mutations, natural selection, and evolutionary change. Random mutations in basic metabolic pathways led to the appearance of new com-pounds that happened to be toxic or deterrent to herbi-vores and pathogenic microbes.
As long as these compounds were not unduly toxic to the plants themselves and the metabolic cost of producing them was not excessive, they gave the plants that pos-sessed them greater reproductive fitness than undefended plants had. Thus the defended plants left more descen-dants than undefended plants, and they passed their defen-sive traits on to the next generation.
Interestingly, the very defense compounds that increase the reproductive fitness of plants by warding off fungi, bac-teria, and herbivores may also make them undesirable as food for humans. Many important crop plants have been artificially selected for producing relatively low levels of these compounds, which of course can make them more susceptible to insects and disease.
Secondary Metabolites Are Divided into Three Major Groups Plant secondary metabolites can be divided into three chemically distinct groups: terpenes, phenolics, and nitro-gen-containing compounds. Figure 13.4 shows in simpli-286 Chapter 13 Erythrose-4-phosphate 3-Phosphoglycerate (3-PGA) Phosphoenolpyruvate Pyruvate Acetyl CoA Tricarboxylic acid cycle Aliphatic amino acids Aromatic amino acids Shikimic acid pathway Terpenes Nitrogen-containing secondary products Phenolic compounds Malonic acid pathway MEP pathway Mevalonic acid pathway SECONDARY CARBON METABOLISM CO2 Photosynthesis PRIMARY CARBON METABOLISM FIGURE 13.4 A simplified view of the major pathways of secondary-metabolite biosynthesis and their interrelationships with primary metabolism.
fied form the pathways involved in the biosynthesis of sec-ondary metabolites and their interconnections with pri-mary metabolism.
TERPENES The terpenes, or terpenoids, constitute the largest class of secondary products. The diverse substances of this class are generally insoluble in water. They are biosynthesized from acetyl-CoA or glycolytic intermediates. After discussing the biosynthesis of terpenes, we’ll examine how they act to repel herbivores and how some herbivores circumvent the toxic effects of terpenes.
Terpenes Are Formed by the Fusion of Five-Carbon Isoprene Units All terpenes are derived from the union of five-carbon ele-ments that have the branched carbon skeleton of isopentane: The basic structural elements of terpenes are sometimes called isoprene units because terpenes can decompose at high temperatures to give isoprene: Thus all terpenes are occasionally referred to as isoprenoids.
Terpenes are classified by the number of five-carbon units they contain, although extensive metabolic modifi-cations can sometimes make it difficult to pick out the orig-inal five-carbon residues. Ten-carbon terpenes, which con-tain two C5 units, are called monoterpenes; 15-carbon terpenes (three C5 units) are sesquiterpenes; and 20-carbon terpenes (four C5 units) are diterpenes. Larger terpenes include triterpenes (30 carbons), tetraterpenes (40 carbons), and polyterpenoids ([C5]n carbons, where n > 8).
There Are Two Pathways for Terpene Biosynthesis Terpenes are biosynthesized from primary metabolites in at least two different ways. In the well-studied mevalonic acid pathway, three molecules of acetyl-CoA are joined together stepwise to form mevalonic acid (Figure 13.5).
This key six-carbon intermediate is then pyrophosphory-lated, decarboxylated, and dehydrated to yield isopentenyl diphosphate (IPP2).
IPP is the activated five-carbon building block of ter-penes. Recently, it was discovered that IPP also can be formed from intermediates of glycolysis or the photosyn-thetic carbon reduction cycle via a separate set of reactions called the methylerythritol phosphate (MEP) pathway that operates in chloroplasts and other plastids (Lichten-thaler 1999). Although all the details have not yet been elu-cidated, glyceraldehyde-3-phosphate and two carbon atoms derived from pyruvate appear to combine to generate an intermediate that is eventually converted to IPP.
Isopentenyl Diphosphate and Its Isomer Combine to Form Larger Terpenes Isopentenyl diphosphate and its isomer, dimethylallyl diphosphate (DPP), are the activated five-carbon building blocks of terpene biosynthesis that join together to form larger molecules. First IPP and DPP react to give geranyl diphosphate (GPP), the 10-carbon precursor of nearly all the monoterpenes (see Figure 13.5). GPP can then link to another molecule of IPP to give the 15-carbon compound farnesyl diphosphate (FPP), the precursor of nearly all the sesquiterpenes. Addition of yet another molecule of IPP gives the 20-carbon compound geranylgeranyl diphos-phate (GGPP), the precursor of the diterpenes. Finally, FPP and GGPP can dimerize to give the triterpenes (C30) and the tetraterpenes (C40), respectively.
Some Terpenes Have Roles in Growth and Development Certain terpenes have a well-characterized function in plant growth or development and so can be considered pri-mary rather than secondary metabolites. For example, the gibberellins, an important group of plant hormones, are diterpenes. Sterols are triterpene derivatives that are essen-tial components of cell membranes, which they stabilize by interacting with phospholipids (see Chapter 11). The red, orange, and yellow carotenoids are tetraterpenes that func-tion as accessory pigments in photosynthesis and protect photosynthetic tissues from photooxidation (see Chapter 7). The hormone abscisic acid (see Chapter 23) is a C15 ter-pene produced by degradation of a carotenoid precursor.
Long-chain polyterpene alcohols known as dolichols function as carriers of sugars in cell wall and glycoprotein synthesis (see Chapter 15). Terpene-derived side chains, such as the phytol side chain of chlorophyll (see Chapter 7), help anchor certain molecules in membranes. Thus var-ious terpenes have important primary roles in plants. How-ever, the vast majority of the different terpene structures produced by plants are secondary metabolites that are pre-sumed to be involved in defense.
Terpenes Defend against Herbivores in Many Plants Terpenes are toxins and feeding deterrents to many plant-feeding insects and mammals; thus they appear to play important defensive roles in the plant kingdom (Gershen-zon and Croteau 1992). For example, the monoterpene esters called pyrethroids that occur in the leaves and flow-H3C H2C CH — CH CH2 H3C H3C CH — CH2 — CH3 Secondary Metabolites and Plant Defense 287 2 IPP is the abbreviation for isopentenyl pyrophosphate, an earlier name for this compound. The other pyrophosphory-lated intermediates in the pathway are also now referred to as diphosphates.
ers of Chrysanthemum species show very striking insecti-cidal activity. Both natural and synthetic pyrethroids are popular ingredients in commercial insecticides because of their low persistence in the environment and their negligi-ble toxicity to mammals.
In conifers such as pine and fir, monoterpenes accumu-late in resin ducts found in the needles, twigs, and trunk.
These compounds are toxic to numerous insects, including bark beetles, which are serious pests of conifer species throughout the world. Many conifers respond to bark bee-tle infestation by producing additional quantities of monoterpenes (Trapp and Croteau 2001).
Many plants contain mixtures of volatile monoterpenes and sesquiterpenes, called essential oils, that lend a char-288 Chapter 13 C H OH CH2OP O C H CH3 O O OH C C CH3 C O S CoA HO CH3 C COOH CH2 CH2 CH2 OH CH2 O P P CH2 O P P CH2 O P P CH2 O P P CH2 O P P CH2 O P P OH H3C CH2 CH O C CH2 OH OH P 2× 2× Glyceraldehyde 3-phosphate (C3) Pyruvate (C3) 3× Acetyl-CoA (C2) Mevalonic acid Isopentenyl diphosphate (IPP, C5) Dimethyallyl diphosphate (DMAPP, C5) Geranyl diphosphate (GPP, C10) Farnesyl diphosphate (FPP, C15) Geranylgeranyl diphosphate (GGPP, C20 ) Methylerythritol phosphate (MEP) Methylerythritol phosphate pathway Mevalonate pathway Isoprene (C5) Sesquiterpenes (C15) Triterpenes (C30) Polyterpenoids Monoterpenes (C10) Diterpenes (C20) Tetraterpenes (C40) FIGURE 13.5 Outline of terpene biosynthesis. The basic 5-carbon units of terpenes are synthesized by two different pathways. The phosphorylated intermediates, IPP and DMAPP, are combined to make 10-carbon, 15-carbon and larger terpenes.
acteristic odor to their foliage. Peppermint, lemon, basil, and sage are examples of plants that contain essential oils.
The chief monoterpene constituent of peppermint oil is menthol; that of lemon oil is limonene (Figure 13.6).
Essential oils have well-known insect repellent proper-ties. They are frequently found in glandular hairs that pro-ject outward from the epidermis and serve to “advertise” the toxicity of the plant, repelling potential herbivores even before they take a trial bite. In the glandular hairs, the ter-penes are stored in a modified extracellular space in the cell wall (Figure 13.7). Essential oils can be extracted from plants by steam distillation and are important commer-cially in flavoring foods and making perfumes.
Recent research has revealed an interesting twist on the role of volatile terpenes in plant protection. In corn, cotton, wild tobacco, and other species, certain monoterpenes and sesquiterpenes are produced and emitted only after insect feeding has already begun. These substances repel ovipositing herbivores and attract natural enemies, includ-ing predatory and parasitic insects, that kill plant-feeding insects and so help minimize further damage (Turlings et al. 1995; Kessler and Baldwin 2001). Thus, volatile terpenes are not only defenses in their own right, but also provide a way for plants to call for defensive help from other organ-isms. The ability of plants to attract natural enemies of plant-feeding insects shows promise as a new, ecologically sound means of pest control (see Web Essay 13.1).
Among the nonvolatile terpene antiherbivore com-pounds are the limonoids, a group of triterpenes (C30) well known as bitter substances in citrus fruit. Perhaps the most powerful deterrent to insect feeding known is azadirachtin (Figure 13.8A), a complex limonoid from the neem tree (Azadirachta indica) of Africa and Asia. Azadirachtin is a feeding deterrent to some insects at doses as low as 50 parts per billion, and it exerts a variety of toxic effects (Aerts and Mordue 1997). It has considerable potential as a commer-cial insect control agent because of its low toxicity to mam-mals, and several preparations containing azadirachtin are now being marketed in North America and India. The phytoecdysones, first isolated from the common fern, Polypodium vulgare, are a group of plant steroids that have the same basic structure as insect molting hormones (Figure 13.8B). Ingestion of phytoecdysones by insects dis-rupts molting and other developmental processes, often with lethal consequences.
Triterpenes that are active against vertebrate herbivores include cardenolides and saponins. Cardenolides are gly-cosides (compounds containing an attached sugar or sug-ars) that taste bitter and are extremely toxic to higher ani-mals. In humans, they have dramatic effects on the heart muscle through their influence on Na+/K+-activated ATPases.
In carefully regulated doses, they slow and strengthen the heartbeat. Cardenolides extracted from species of foxglove Secondary Metabolites and Plant Defense 289 H3C CH2 CH3 Limonene H3C CH3 CH3 OH Menthol (A) (B) FIGURE 13.6 Structures of limonene (A) and menthol (B).
These two well-known monoterpenes serve as defenses against insects and other organisms that feed on these plants. (A, photo © Calvin Larsen/Photo Researchers, Inc.; B, photo © David Sieren/Visuals Unlimited.) FIGURE 13.7 Monoterpenes and sesquiterpenes are commonly found in glandular hairs on the plant surface. This scanning electron micrograph shows a glandular hair on a young leaf of spring sunflower (Balsamorhiza sagittata). Terpenes are thought to be synthesized in the cells of the hair and are stored in the rounded cap at the top. This “cap” is an extracellular space that forms when the cuticle and a portion of the cell wall pull away from the remainder of the cell. (1105×) (© J. N. A. Lott/Biological Photo Service.) (Digitalis) are prescribed to millions of patients for the treat-ment of heart disease (see Web Topic 13.1).
Saponins are steroid and triterpene glycosides, so named because of their soaplike properties. The presence of both lipid-soluble (the steroid or triterpene) and water-soluble (the sugar) elements in one molecule gives saponins detergent properties, and they form a soapy lather when shaken with water. The toxicity of saponins is thought to be a result of their ability to form complexes with sterols. Saponins may interfere with sterol uptake from the digestive system or disrupt cell membranes after being absorbed into the bloodstream.
PHENOLIC COMPOUNDS Plants produce a large variety of secondary products that contain a phenol group—a hydroxyl functional group on an aromatic ring: These substances are classified as phenolic compounds.
Plant phenolics are a chemically heterogeneous group of nearly 10,000 individual compounds: Some are soluble only in organic solvents, some are water-soluble carboxylic acids and glycosides, and others are large, insoluble polymers.
In keeping with their chemical diversity, phenolics play a variety of roles in the plant. After giving a brief account of phenolic biosynthesis, we will discuss several principal groups of phenolic compounds and what is known about their roles in the plant. Many serve as defense compounds against herbivores and pathogens. Others function in mechanical support, in attracting pollinators and fruit dis-persers, in absorbing harmful ultraviolet radiation, or in reducing the growth of nearby competing plants.
Phenylalanine Is an Intermediate in the Biosynthesis of Most Plant Phenolics Plant phenolics are biosynthesized by several different routes and thus constitute a heterogeneous group from a metabolic point of view. Two basic pathways are involved: the shikimic acid pathway and the malonic acid pathway (Figure 13.9). The shikimic acid pathway participates in the biosynthesis of most plant phenolics. The malonic acid pathway, although an important source of phenolic sec-ondary products in fungi and bacteria, is of less signifi-cance in higher plants.
The shikimic acid pathway converts simple carbohydrate precursors derived from glycolysis and the pentose phos-phate pathway to the aromatic amino acids (see Web Topic 13.2) (Herrmann and Weaver 1999). One of the pathway intermediates is shikimic acid, which has given its name to this whole sequence of reactions. The well-known, broad-spectrum herbicide glyphosate (available commercially as Roundup) kills plants by blocking a step in this pathway (see Chapter 2 on the web site). The shikimic acid pathway is pre-sent in plants, fungi, and bacteria but is not found in animals.
Animals have no way to synthesize the three aromatic amino acids—phenylalanine, tyrosine, and tryptophan—which are therefore essential nutrients in animal diets.
The most abundant classes of secondary phenolic com-pounds in plants are derived from phenylalanine via the OH 290 Chapter 13 CH3CO CH3 CH3 CH3 H3C O O O O OH O OH HO O O O O C CH3OC CH3OC O (A) Azadirachtin, a limonoid HO O OH OH HO CH3 CH3 CH3 OH CH3 H3C (B) a-Ecdysone, an insect molting hormone FIGURE 13.8 Structure of two triterpenes, azadirachtin (A), and α-ecdysone (B), which serve as powerful feeding deterrents to insects. (A, photo © Inga Spence/Visuals Unlimited; B, photo ©Wally Eberhart/Visuals Unlimited.) elimination of an ammonia molecule to form cinnamic acid (Figure 13.10). This reaction is catalyzed by phenylalanine ammonia lyase (PAL), perhaps the most studied enzyme in plant secondary metabolism. PAL is situated at a branch point between primary and secondary metabolism, so the reaction that it catalyzes is an important regulatory step in the formation of many phenolic compounds.
The activity of PAL is increased by environmental fac-tors, such as low nutrient levels, light (through its effect on phytochrome), and fungal infection. The point of control appears to be the initiation of transcription. Fungal inva-sion, for example, triggers the transcription of messenger RNA that codes for PAL, thus increasing the amount of PAL in the plant, which then stimulates the synthesis of phenolic compounds.
The regulation of PAL activity in plants is made more complex by the existence in many species of multiple PAL-encoding genes, some of which are expressed only in spe-cific tissues or only under certain environmental conditions (Logemann et al. 1995).
Reactions subsequent to that catalyzed by PAL lead to the addition of more hydroxyl groups and other sub-stituents. Trans-cinnamic acid, p-coumaric acid, and their derivatives are simple phenolic compounds called phenyl-propanoids because they contain a benzene ring: and a three-carbon side chain. Phenylpropanoids are important building blocks of the more complex phenolic compounds discussed later in this chapter.
Now that the biosynthetic pathways leading to most widespread phenolic compounds have been determined, researchers have turned their attention to studying how these pathways are regulated. In some cases, specific enzymes, such as PAL, are important in controlling flux through the pathway. Several transcription factors have been shown to regulate phenolic metabolism by binding to the promoter regions of certain biosynthetic genes and activating tran-scription. Some of these factors activate the transcription of large groups of genes (Jin and Martin 1999).
Some Simple Phenolics Are Activated by Ultraviolet Light Simple phenolic compounds are widespread in vascular plants and appear to function in different capacities. Their structures include the following: • Simple phenylpropanoids, such as trans-cinnamic acid, p-coumaric acid, and their derivatives, such as caffeic acid, which have a basic phenylpropanoid car-bon skeleton (Figure 13.11A): • Phenylpropanoid lactones (cyclic esters) called coumarins, also with a phenylpropanoid skeleton (see Figure 13.11B) • Benzoic acid derivatives, which have a skeleton: which is formed from phenylpropanoids by cleavage of a two-carbon fragment from the side chain (see Figure 13.11C) (see also Figure 13.10) As with many other secondary products, plants can elabo-rate on the basic carbon skeleton of simple phenolic com-pounds to make more complex products.
Many simple phenolic compounds have important roles in plants as defenses against insect herbivores and fungi.
Of special interest is the phototoxicity of certain coumarins called furanocoumarins, which have an attached furan ring (see Figure 13.11B).
C1 C6 C6 C3 C6 Secondary Metabolites and Plant Defense 291 Shikimic acid pathway Erythrose-4 phosphate (from pentose phosphate pathway) Phosphoenolpyruvic acid (from glycolysis) Acetyl-CoA Miscellaneous phenolics Malonic acid pathway Phenylalanine Cinnamic acid Simple phenolics Flavonoids Lignin Hydrolyzable tannins Gallic acid C3 C6 [ ] C3 C6 [ ]n C3 C6 [ ] C3 C6 [ ] C1 C6 [ ] C3 C6 C6 [ ] Condensed tannins n C3 C6 C6 [ ] FIGURE 13.9 Plant phenolics are biosynthesized in several differ-ent ways. In higher plants, most phenolics are derived at least in part from phenylalanine, a prod-uct of the shikimic acid pathway.
Formulas in brackets indicate the basic arrangement of carbon skeletons: indicates a benzene ring, and C3 is a three-carbon chain. More detail on the pathway from phenylalanine onward is given in Figure 13.10.
C6 These compounds are not toxic until they are activated by light. Sunlight in the ultra-violet A (UV-A) region (320–400 nm) causes some furanocoumarins to become activated to a high-energy electron state. Activated furanocoumarins can insert themselves into the double helix of DNA and bind to the pyrimidine bases cytosine and thymine, thus blocking transcription and repair and leading eventually to cell death.
Phototoxic furanocoumarins are espe-cially abundant in members of the Umbel-liferae family, including celery, parsnip, and parsley. In celery, the level of these com-pounds can increase about 100-fold if the plant is stressed or diseased. Celery pickers, and even some grocery shoppers, have been known to develop skin rashes from han-dling stressed or diseased celery. Some insects have adapted to survive on plants that contain furanocoumarins and other phototoxic compounds by living in silken webs or rolled-up leaves, which screen out the activating wavelengths (Sandberg and Berenbaum 1989).
The Release of Phenolics into the Soil May Limit the Growth of Other Plants From leaves, roots, and decaying litter, plants release a variety of primary and secondary metabolites into the environment. Investiga-tion of the effects of these compounds on neighboring plants is the study of allelopa-thy. If a plant can reduce the growth of nearby plants by releasing chemicals into the soil, it may increase its access to light, water, and nutrients and thus its evolutionary fit-ness. Generally speaking, the term allelopathy has come to be applied to the harmful effects of plants on their neighbors, although a pre-cise definition also includes beneficial effects.
Simple phenylpropanoids and benzoic acid derivatives are frequently cited as hav-ing allelopathic activity. Compounds such as caffeic acid and ferulic acid (see Figure 13.11A) occur in soil in appreciable amounts and have been shown in laboratory experi-ments to inhibit the germination and growth of many plants (Inderjit et al. 1995).
292 Chapter 13 NH2 COOH COOH COSCoA COOH HO OH O OH HO OH O HO OH O OH OH O HO O OH HO OH O HO OH O OH O HO OH OH O HO OH O OH O Phenylalanine trans-Cinnamic acid p-Coumaric acid Phenylalanine ammonia lyase (PAL) 3 Malonyl-CoA molecules Chalcone synthase Benzoic acid derivatives (Figure 13.11C) Anthocyanins (Figure 13.13B) Condensed tannins (Figure 13.15A) Lignin precursors (Web Topic 13.3) NH3 p-Coumaroyl-CoA Chalcones Flavanones OH Flavones Isoflavones (isoflavonoids) Flavonols Dihydroflavonols Caffeic acid and other simple phenylpropanoids (Figure 13.11A) Coumarins (Figure 13.11B) CoA-SH FIGURE 13.10 Outline of phenolic biosynthesis from phenylalanine. The formation of many plant phenolics, including simple phenylpropanoids, coumarins, benzoic acid derivatives, lignin, anthocyanins, isoflavones, condensed tannins, and other flavonoids, begins with phenylalanine. In spite of results such as these, the importance of allelopathy in natural ecosystems is still controversial.
Many scientists doubt that allelopathy is a significant fac-tor in plant–plant interactions because good evidence for this phenomenon has been hard to obtain. It is easy to show that extracts or purified compounds from one plant can inhibit the growth of other plants in laboratory exper-iments, but it has been very difficult to demonstrate that these compounds are present in the soil in sufficient con-centration to inhibit growth. Furthermore, organic sub-stances in the soil are often bound to soil particles and may be rapidly degraded by microbes.
In spite of the lack of supporting evidence, allelopathy is currently of great interest because of its potential agri-cultural applications. Reductions in crop yields caused by weeds or residues from the previous crop may in some cases be a result of allelopathy. An exciting future prospect is the development of crop plants genetically engineered to be allelopathic to weeds.
Lignin Is a Highly Complex Phenolic Macromolecule After cellulose, the most abundant organic substance in plants is lignin, a highly branched polymer of phenyl-propanoid groups that plays both primary and secondary roles. The precise structure of lignin is not known because it is difficult to extract lignin from plants, where it is covalently bound to cellulose and other polysaccharides of the cell wall.
Lignin is generally formed from three different phenyl-propanoid alcohols: coniferyl, coumaryl, and sinapyl, alco-hols which are synthesized from phenylalanine via various cinnamic acid derivatives. The phenylpropanoid alcohols are joined into a polymer through the action of enzymes that generate free-radical intermediates. The proportions of the three monomeric units in lignin vary among species, plant organs, and even layers of a single cell wall. In the polymer, there are often multiple C—C and C—O—C bonds in each phenylpropanoid alcohol unit, resulting in a complex struc-ture that branches in three dimensions. Unlike polymers such as starch, rubber, or cellulose, the units of lignin do not appear to be linked in a simple, repeating way. However, recent research suggests that a guiding protein may bind the individual phenylpropanoid units during lignin biosynthe-sis, giving rise to a scaffold that then directs the formation of a large, repeating unit (Davin and Lewis 2000; Hatfield and Vermerris 2001). (See Web Topic 13.3 for the partial structure of a hypothetical lignin molecule.) Lignin is found in the cell walls of various types of sup-porting and conducting tissue, notably the tracheids and vessel elements of the xylem. It is deposited chiefly in the thickened secondary wall but can also occur in the primary wall and middle lamella in close contact with the celluloses and hemicelluloses already present. The mechanical rigid-ity of lignin strengthens stems and vascular tissue, allow-ing upward growth and permitting water and minerals to be conducted through the xylem under negative pressure without collapse of the tissue. Because lignin is such a key component of water transport tissue, the ability to make lignin must have been one of the most important adapta-tions permitting primitive plants to colonize dry land.
Besides providing mechanical support, lignin has signif-icant protective functions in plants. Its physical toughness deters feeding by animals, and its chemical durability makes it relatively indigestible to herbivores. By bonding to cellu-lose and protein, lignin also reduces the digestibility of these substances. Lignification blocks the growth of pathogens and is a frequent response to infection or wounding.
C6 C3 Secondary Metabolites and Plant Defense 293 H OH HO C C COOH H OCH3 HO C C COOH H H HO O O O O O OCH3 CH O HO OH COOH Caffeic acid C3 C6 [ ] Ferulic acid Furan ring Umbelliferone, a simple coumarin C3 C6 [ ] Vanillin Salicylic acid C1 C6 [ ] Psoralen, a furanocoumarin (A) (B) (C) Simple phenylpropanoids Coumarins Benzoic acid derivatives FIGURE 13.11 Simple phenolic compounds play a great diversity of roles in plants. (A) Caffeic acid and ferulic acid may be released into the soil and inhibit the growth of neighboring plants. (B) Psoralen is a furanocoumarin that exhibits phototoxicity to insect herbivores. (C) Salicylic acid is a plant growth regulator that is involved in systemic resistance to plant pathogens. There Are Four Major Groups of Flavonoids The flavonoids are one of the largest classes of plant phe-nolics. The basic carbon skeleton of a flavonoid contains 15 carbons arranged in two aromatic rings connected by a three-carbon bridge: This structure results from two separate biosynthetic path-ways: the shikimic acid pathway and the malonic acid pathway (Figure 13.12).
Flavonoids are classified into different groups, primar-ily on the basis of the degree of oxidation of the three-car-bon bridge. We will discuss four of the groups shown in Figure 13.10: the anthocyanins, the flavones, the flavonols, and the isoflavones.
The basic flavonoid carbon skeleton may have numer-ous substituents. Hydroxyl groups are usually present at positions 4, 5, and 7, but they may also be found at other positions. Sugars are very common as well; in fact, the majority of flavonoids exist naturally as glycosides.
Whereas both hydroxyl groups and sugars increase the water solubility of flavonoids, other substituents, such as methyl ethers or modified isopentyl units, make flavonoids lipophilic (hydrophobic). Different types of flavonoids per-form very different functions in the plant, including pig-mentation and defense.
Anthocyanins Are Colored Flavonoids That Attract Animals In addition to predator–prey interactions, there are mutual-istic associations among plants and animals. In return for the reward of ingesting nectar or fruit pulp, animals perform extremely important services for plants as carriers of pollen and seeds. Secondary metabolites are involved in these plant–animal interactions, helping to attract animals to flow-ers and fruit by providing visual and olfactory signals.
The colored pigments of plants are of two principal types: carotenoids and flavonoids. Carotenoids, as we have already seen, are yellow, orange, and red terpenoid com-pounds that also serve as accessory pigments in photo-synthesis (see Chapter 7). Flavonoids are phenolic com-pounds that include a wide range of colored substances.
The most widespread group of pigmented flavonoids is the anthocyanins, which are responsible for most of the red, pink, purple, and blue colors observed in plant parts. By col-oring flowers and fruits, the anthocyanins are vitally impor-tant in attracting animals for pollination and seed dispersal.
Anthocyanins are glycosides that have sugars at position 3 (Figure 13.13B) and sometimes elsewhere. Without their sugars, anthocyanins are known as anthocyanidins (Figure 13.13A). Anthocyanin color is influenced by many factors, including the number of hydroxyl and methoxyl groups in ring B of the anthocyanidin (see Figure 13.13A), the presence of aromatic acids esterified to the main skeleton, and the pH of the cell vacuole in which these compounds are stored.
Anthocyanins may also exist in supramolecular complexes along with chelated metal ions and flavone copigments. The blue pigment of dayflower (Commelina communis) was found C3 C6 C6 294 Chapter 13 A 8 5 4 6 3 2 7 C 3′ 6′ 1′ 2′ 5′ 4′ B O 1 Basic flavonoid skeleton From shikimic acid pathway via phenylalanine From malonic acid pathway The three-carbon bridge C3 C6 [ ] C6 [ ] FIGURE 13.12 Basic flavonoid carbon skeleton. Flavonoids are biosynthesized from products of the shikimic acid and malonic acid pathways. Positions on the flavonoid ring sys-tem are numbered as shown. FIGURE 13.13 The structures of anthocyanidins (A) and anthocyanin (B). The colors of anthocyanidins depend in part on the substituents attached to ring B (see Table 13.1).
An increase in the number of hydroxyl groups shifts absorption to a longer wavelength and gives a bluer color.
Replacement of a hydroxyl group with a methoxyl group (OCH3) shifts absorption to a slightly shorter wavelength, resulting in a redder color.
+ OH HO OH A C 3′ 2′ 6′ 1′ 5′ 4′ B A C B OH OH HO O O + O Anthocyanidin Anthocyanin Sugar (A) (B) to consist of a large complex of six anthocyanin molecules, six flavones, and two associated magnesium ions (Kondo et al. 1992). The most common anthocyanidins and their colors are shown in Figure 13.13 and Table 13.1.
Considering the variety of factors affecting anthocyanin coloration and the possible presence of carotenoids as well, it is not surprising that so many different shades of flower and fruit color are found in nature. The evolution of flower color may have been governed by selection pressures for different sorts of pollinators, which often have different color preferences.
Color, of course, is just one type of signal used to attract pollinators to flowers. Volatile chemicals, particularly monoterpenes, frequently provide attractive scents.
Flavonoids May Protect against Damage by Ultraviolet Light Two other major groups of flavonoids found in flowers are flavones and flavonols (see Figure 13.10). These flavonoids generally absorb light at shorter wavelengths than anthocyanins do, so they are not visible to the human eye. However, insects such as bees, which see farther into the ultraviolet range of the spectrum than humans do, may respond to flavones and flavonols as attractant cues (Figure 13.14). Flavonols in a flower often form sym-metric patterns of stripes, spots, or concentric circles called nectar guides (Lunau 1992). These patterns may be conspicuous to insects and are thought to help indicate the location of pollen and nectar.
Flavones and flavonols are not restricted to flowers; they are also present in the leaves of all green plants. These two classes of flavonoids function to protect cells from exces-sive UV-B radiation (280–320 nm) because they accumulate in the epidermal layers of leaves and stems and absorb light strongly in the UV-B region while allowing the visible (photosynthetically active) wavelengths to pass through uninterrupted. In addition, exposure of plants to increased UV-B light has been demonstrated to increase the synthe-sis of flavones and flavonols.
Arabidopsis thaliana mutants that lack the enzyme chal-cone synthase produce no flavonoids. Lacking flavonoids, these plants are much more sensitive to UV-B radiation than wild-type individuals are, and they grow very poorly under normal conditions. When shielded from UV light, however, they grow normally (Li et al. 1993). A group of simple phenylpropanoid esters are also important in UV protection in Arabidopsis.
Secondary Metabolites and Plant Defense 295 TABLE 13.1 Effects of ring substituents on anthocyanidin color Anthocyanidin Substituents Color Pelargonidin 4′— OH Orange red Cyanidin 3′— OH, 4′— OH Purplish red Delphinidin 3′— OH,4′— OH,5′— OH Bluish purple Peonidin 3′— OCH3, 4′— OH Rosy red Petunidin 3′— OCH3, 4′— OH, 5′— OCH3 Purple FIGURE 13.14 Black-eyed Susan (Rudbeckia sp.) as seen by humans (A) and as it might appear to honeybees (B). (A) To humans, the golden-eye has yellow rays and a brown central disc. (B) To bees, the tips of the rays appear “light yellow,” the inner portion of the rays “dark yellow,” and the central disc “black.” Ultraviolet-absorbing flavonols are found in the inner parts of the rays but not in the tips. The distribution of flavonols in the rays and the sensitivity of insects to part of the UV spectrum contribute to the “bull’s-eye” pattern seen by honeybees, which presumably helps them locate pollen and nectar. Special lighting was used to simulate the spectral sensitivity of the honeybee visual system. (Courtesy of Thomas Eisner.) (B) (A) Other functions of flavonoids have recently been dis-covered. For example, flavones and flavonols secreted into the soil by legume roots mediate the interaction of legumes and nitrogen-fixing symbionts, a phenomenon described in Chapter 12. As will be discussed in Chapter 19, recent work suggests that flavonoids also play a regulatory role in plant development as modulators of polar auxin transport.
Isoflavonoids Have Antimicrobial Activity The isoflavonoids (isoflavones) are a group of flavonoids in which the position of one aromatic ring (ring B) is shifted (see Figure 13.10). Isoflavonoids are found mostly in legumes and have several different bio-logical activities. Some, such as the rotenoids, have strong insecticidal actions; others have anti-estrogenic effects. For example, sheep grazing on clover rich in isoflavonoids often suffer from infertility. The isoflavonoid ring sys-tem has a three-dimensional structure similar to that of steroids (see Figure 13.8B), allowing these substances to bind to estrogen receptors. Isoflavonoids may also be responsible for the anticancer benefits of food prepared from soybeans.
In the past few years, isoflavonoids have become best known for their role as phytoalexins, antimicrobial compounds synthesized in response to bacterial or fungal infection that help limit the spread of the invading pathogen. Phytoalexins are discussed in more detail later in this chapter.
Tannins Deter Feeding by Herbivores A second category of plant phenolic polymers with defensive properties, besides lignins, is the tannins. The term tannin was first used to describe com-pounds that could convert raw animal hides into leather in the process known as tanning. Tannins bind the collagen proteins of animal hides, increasing their resistance to heat, water, and microbes.
There are two categories of tannins: condensed and hydrolyzable. Con-densed tannins are compounds formed by the polymerization of flavonoid units (Figure 13.15A). They are frequent con-stituents of woody plants. Because con-densed tannins can often be hydrolyzed to anthocyanidins by treatment with strong acids, they are sometimes called pro-anthocyanidins.
Hydrolyzable tannins are heterogeneous polymers con-taining phenolic acids, especially gallic acid, and simple sugars (see Figure 13.15B). They are smaller than con-densed tannins and may be hydrolyzed more easily; only dilute acid is needed. Most tannins have molecular masses between 600 and 3000.
Tannins are general toxins that significantly reduce the growth and survivorship of many herbivores when added to their diets. In addition, tannins act as feeding repellents to a great diversity of animals. Mammals such as cattle, deer, and apes characteristically avoid plants or parts of plants with high tannin contents. Unripe fruits, for 296 Chapter 13 OH HO OH OH OH A C B O OH HO OH OH OH O OH HO OH OH OH O n O OH OH C O OH C O OH OH OH HO OH OH O C CH2O O OH OH OH HO O C O HO C O O H O OH H O CO HO HO HO OH OH HO C O C O O H O H (A) Condensed tannin (B) Hydrolyzable tannin Gallic acid FIGURE 13.15 Structure of some tannins formed from phenolic acids or flavonoid units. (A) The general structure of a condensed tannin, where n is usually 1 to 10. There may also be a third —OH group on ring B. (B) The hydrolyzable tannin from sumac (Rhus semialata) consists of glucose and eight molecules of gallic acid. instance, frequently have very high tannin levels, which may be concentrated in the outer cell layers. Interestingly, humans often prefer a certain level of astringency in tannin-containing foods, such as apples, blackberries, tea, and red wine. Recently, polyphenols (tan-nins) in red wine were shown to block the formation of endothelin-1, a signaling molecule that makes blood ves-sels constrict (Corder et al. 2001). This effect of wine tan-nins may account for the often-touted health benefits of red wine, especially the reduction in the risk of heart disease associated with moderate red wine consumption.
Although moderate amounts of specific polyphenolics may have health benefits for humans, the defensive prop-erties of most tannins are due to their toxicity, which is gen-erally attributed to their ability to bind proteins nonspecif-ically. It has long been thought that plant tannins complex proteins in the guts of herbivores by forming hydrogen bonds between their hydroxyl groups and electronegative sites on the protein (Figure 13.16A).
More recent evidence indicates that tannins and other phenolics can also bind to dietary protein in a covalent fash-ion (see Figure 13.16B). The foliage of many plants contains enzymes that oxidize phenolics to their corresponding quinone forms in the guts of herbivores (Felton et al. 1989).
Quinones are highly reactive electrophilic molecules that readily react with the nucleophilic —NH2 and —SH groups of proteins (see Figure 13.16B). By whatever mechanism protein–tannin binding occurs, this process has a negative impact on herbivore nutrition. Tannins can inactivate her-bivore digestive enzymes and create complex aggregates of tannins and plant proteins that are difficult to digest.
Herbivores that habitually feed on tannin-rich plant material appear to possess some interesting adaptations to remove tannins from their digestive systems. For example, some mammals, such as rodents and rabbits, produce sali-vary proteins with a very high proline content (25–45%) that have a high affinity for tannins. Secretion of these proteins is induced by ingestion of food with a high tannin content and greatly diminishes the toxic effects of tannins (Butler 1989). The large number of proline residues gives these pro-teins a very flexible, open conformation and a high degree of hydrophobicity that facilitates binding to tannins.
Plant tannins also serve as defenses against microor-ganisms. For example, the nonliving heartwood of many trees contains high concentrations of tannins that help pre-vent fungal and bacterial decay.
NITROGEN-CONTAINING COMPOUNDS A large variety of plant secondary metabolites have nitro-gen in their structure. Included in this category are such well-known antiherbivore defenses as alkaloids and cyanogenic glycosides, which are of considerable interest because of their toxicity to humans and their medicinal properties. Most nitrogenous secondary metabolites are biosynthesized from common amino acids.
In this section we will examine the structure and biolog-ical properties of various nitrogen-containing secondary metabolites, including alkaloids, cyanogenic glycosides, glu-cosinolates, and nonprotein amino acids. In addition, we will discuss the ability of systemin, a protein released from dam-aged cells, to serve as a wound signal to the rest of the plant.
Alkaloids Have Dramatic Physiological Effects on Animals The alkaloids are a large family of more than 15,000 nitro-gen-containing secondary metabolites found in approxi-mately 20% of the species of vascular plants. The nitrogen atom in these substances is usually part of a heterocyclic ring, a ring that contains both nitrogen and carbon atoms.
As a group, alkaloids are best known for their striking pharmacological effects on vertebrate animals.
As their name would suggest, most alkaloids are alka-line. At pH values commonly found in the cytosol (pH 7.2) Secondary Metabolites and Plant Defense 297 O H N H2 OH OH HN H2N O (A) Hydrogen bonding between tannins and protein (B) Covalent bonding to protein after oxidation Polyphenol oxidase Tannin in phenol form Tannin in quinone form Tannin linked to protein Tannin Protein Protein Protein Covalent bond d+ d− FIGURE 13.16 Proposed mechanisms for the interaction of tannins with proteins. (A) Hydrogen bonds may form between the phenolic hydroxyl groups of tannins and elec-tronegative sites on the protein. (B) Phenolic hydroxyl groups may bind covalently to proteins following activa-tion by oxidative enzymes, such as polyphenol oxidase. or the vacuole (pH 5 to 6), the nitrogen atom is protonated; hence, alkaloids are positively charged and are generally water soluble.
Alkaloids are usually synthesized from one of a few common amino acids—in particular, lysine, tyrosine, and tryptophan. However, the carbon skeleton of some alka-loids contains a component derived from the terpene pathway. Table 13.2 lists the major alkaloid types and their amino acid precursors. Several different types, including nicotine and its relatives (Figure 13.17), are derived from ornithine, an intermediate in arginine biosynthesis. The B vitamin nicotinic acid (niacin) is a precursor of the pyridine (six-membered) ring of this alkaloid; the pyrrolidine (five-membered) ring of nicotine arises from ornithine (Figure 13.18). Nicotinic acid is also a constituent of NAD+ and NADP+, which serve as electron carriers in metabolism.
The role of alkaloids in plants has been a subject of spec-ulation for at least 100 years. Alkaloids were once thought to be nitrogenous wastes (analogous to urea and uric acid in animals), nitrogen storage compounds, or growth regu-lators, but there is little evidence to support any of these functions. Most alkaloids are now believed to function as defenses against predators, especially mammals, because 298 Chapter 13 TABLE 13.2 Major types of alkaloids, their amino acid precursors, and well-known examples of each type Biosynthetic Alkaloid class Structure precursor Examples Human uses Pyrrolidine Ornithine (aspartate) Nicotine Stimulant, depressant, tranquilizer Tropane Ornithine Atropine Prevention of intestinal spasms, antidote to other poisons, dilation of pupils for examination Cocaine Stimulant of the central nervous system, local anesthetic Piperidine Lysine (or acetate) Coniine Poison (paralyzes motor neurons) Pyrrolizidine Ornithine Retrorsine None Quinolizidine Lysine Lupinine Restoration of heart rhythm Isoquinoline Tyrosine Codeine Analgesic (pain relief), treatment of coughs Morphine Analgesic Indole Tryptophan Psilocybin Halucinogen Reserpine Treatment of hypertension, treatment of psychoses Strychnine Rat poison, treatment of eye disorders N N N N N N N C N N N H3C N N N O O O O CH3 CH3 CH3 CH3 OCH3 N OC CH3 HO N HO O Cocaine Morphine Representative alkaloids Caffeine Nicotine FIGURE 13.17 Examples of alkaloids, a diverse group of secondary metabolites that contain nitrogen, usually as part of a heterocyclic ring. Caffeine is a purine-type alkaloid similar to the nucleic acid bases adenine and guanine. The pyrrolidine (five-membered) ring of nicotine arises from ornithine; the pyridine (six-membered) ring is derived from nicotinic acid. of their general toxicity and deter-rence capability (Hartmann 1992).
Large numbers of livestock deaths are caused by the ingestion of alkaloid-containing plants. In the United States, a significant per-centage of all grazing livestock animals are poisoned each year by consumption of large quantities of alkaloid-containing plants such as lupines (Lupinus), larkspur (Del-phinium), and groundsel (Senecio).
This phenomenon may be due to the fact that domestic animals, unlike wild animals, have not been subjected to natural selection for the avoidance of toxic plants.
Indeed, some livestock actually seem to prefer alkaloid-containing plants to less harmful forage.
Nearly all alkaloids are also toxic to humans when taken in sufficient quantity. For example, strychnine, atropine, and coniine (from poison hemlock) are classic alkaloid poison-ing agents. At lower doses, however, many are useful phar-macologically. Morphine, codeine, and scopolamine are just a few of the plant alkaloids currently used in medicine.
Other alkaloids, including cocaine, nicotine, and caffeine (see Figure 13.17), enjoy widespread nonmedical use as stimu-lants or sedatives.
On a cellular level, the mode of action of alkaloids in animals is quite variable. Many alkaloids interfere with components of the nervous system, especially the chemi-cal transmitters; others affect membrane transport, protein synthesis, or miscellaneous enzyme activities.
One group of alkaloids, the pyrrolizidine alkaloids, illus-trates how herbivores can become adapted to tolerate plant defensive substances and even use them in their own defense (Hartmann 1999). Within plants, pyrrolizidine alka-loids occur naturally as nontoxic N-oxides. In herbivore digestive tracts, however, they are quickly reduced to uncharged, hydrophobic tertiary alkaloids (Figure 13.19), which easily pass through membranes and are toxic. Nev-ertheless, some herbivores, such as cinnabar moth (Tyria jacobeae), have developed the ability to reconvert tertiary pyrrolizidine alkaloids to the nontoxic N-oxide form imme-diately after its absorption from the digestive tract. These herbivores may then store the N-oxides in their bodies as defenses against their own predators.
Not all of the alkaloids that appear in plants are pro-duced by the plant itself. Many grasses harbor endogenous fungal symbionts that grow in the apoplast and synthesize a variety of different types of alkaloids. Grasses with fun-gal symbionts often grow faster and are better defended Secondary Metabolites and Plant Defense 299 CH2 NH2 CH NH2 COOH N CH3 + N N CH3 P OH2C H OH O H HO N COOH + N COOH H2C H2C Nicotinic acid mononucleotide (NADP+) Nicotinic acid Ornithine N-Methyl pyrrolinium Nicotine FIGURE 13.18 Nicotine biosynthesis begins with the biosyn-thesis of the nicotinic acid (niacin) from aspartate and glyc-eraldehyde-3-phosphate. Nicotinic acid is also a component of NAD+ and NADP+, important participants in biological oxidation–reduction reactions. The five-membered ring of nicotine is derived from ornithine, an intermediate in argi-nine biosynthesis.
H3C O O N+ O– CH3 O O HO CH3 H3C O O N CH3 O O HO CH3 N-oxide (nontoxic form, stored in plants) Tertiary alkaloid (toxic form) Reduced in digestive tracts of most herbivores to toxic form Oxidized to nontoxic form by certain adapted herbivores FIGURE 13.19 Two forms of pyrrolizidine alkaloids occur in nature: the N-oxide form and the tertiary alkaloid. The nontoxic N-oxide found in plants is reduced to the toxic tertiary form in the digestive tracts of most herbivores. However, some adapted herbivores can convert the toxic tertiary alkaloid back to the nontoxic N-oxide. These forms are illustrated here for the alkaloid senecionine, found in species of ragwort (Senecio).
against insect and mammalian herbivores than those with-out symbionts. Unfortunately, certain grasses with sym-bionts, such as tall fescue, are important pasture grasses that may become toxic to livestock when their alkaloid con-tent is too high. Efforts are under way to breed tall fescue with alkaloid levels that are not poisonous to livestock but still provide protection against insects (see Web Essay 13.2).
Like monoterpenes in conifer resin and many other anti-herbivore defense compounds, alkaloids increase in response to initial herbivore damage, fortifying the plant against subsequent attack (Karban and Baldwin 1997). For example, Nicotiana attenuata, a wild tobacco that grows in the deserts of the Great Basin, produces higher levels of nicotine following herbivory. When it is attacked by nico-tine-tolerant caterpillars, however, there is no increase in nicotine. Instead, volatile terpenes are released that attract enemies of the caterpillars. Clearly, wild tobacco and other plants must have ways of determining what type of herbi-vore is damaging their foliage. Herbivores might signal their presence by the type of damage they inflict or the dis-tinctive chemical compounds they release. Recently, the oral secretions of caterpillars feeding on corn leaves were shown to contain a fatty acid–amino acid conjugate that induced the plant to produce defensive terpenes when applied to cut leaves.
Cyanogenic Glycosides Release the Poison Hydrogen Cyanide Various nitrogenous protective compounds other than alkaloids are found in plants. Two groups of these sub-stances—cyanogenic glycosides and glucosinolates—are not in themselves toxic but are readily broken down to give off volatile poisons when the plant is crushed. Cyanogenic glycosides release the well-known poisonous gas hydrogen cyanide (HCN).
The breakdown of cyanogenic glycosides in plants is a two-step enzymatic process. Species that make cyanogenic glycosides also make the enzymes necessary to hydrolyze the sugar and liberate HCN: 1. In the first step the sugar is cleaved by a glycosidase, an enzyme that separates sugars from other mole-cules to which they are linked (Figure 13.20).
2. In the second step the resulting hydrolysis product, called an α-hydroxynitrile or cyanohydrin, can decompose spontaneously at a low rate to liberate HCN. This second step can be accelerated by the enzyme hydroxynitrile lyase.
Cyanogenic glycosides are not normally broken down in the intact plant because the glycoside and the degrada-tive enzymes are spatially separated, in different cellular compartments or in different tissues. In sorghum, for exam-ple, the cyanogenic glycoside dhurrin is present in the vac-uoles of epidermal cells, while the hydrolytic and lytic enzymes are found in the mesophyll (Poulton 1990).
Under ordinary conditions this compartmentation pre-vents decomposition of the glycoside. When the leaf is damaged, however, as during herbivore feeding, the cell contents of different tissues mix and HCN forms.
Cyanogenic glycosides are widely distributed in the plant kingdom and are frequently encountered in legumes, grasses, and species of the rose family.
Considerable evidence indicates that cyanogenic glyco-sides have a protective function in certain plants. HCN is a fast-acting toxin that inhibits metalloproteins, such as the iron-containing cytochrome oxidase, a key enzyme of mito-chondrial respiration. The presence of cyanogenic glycosides deters feeding by insects and other herbivores, such as snails and slugs. As with other classes of secondary metabolites, however, some herbivores have adapted to feed on cyanogenic plants and can tolerate large doses of HCN.
The tubers of cassava (Manihot esculenta), a high-carbo-hydrate, staple food in many tropical countries, contain high levels of cyanogenic glycosides. Traditional process-ing methods, such as grating, grinding, soaking, and dry-ing, lead to the removal or degradation of a large fraction of the cyanogenic glycosides present in cassava tubers.
However, chronic cyanide poisoning leading to partial paralysis of the limbs is still widespread in regions where cassava is a major food source because the traditional detoxification methods employed to remove cyanogenic glycosides from cassava are not completely effective. In addition, many populations that consume cassava have poor nutrition, which aggravates the effects of the cyanogenic glycosides.
300 Chapter 13 C O— C R′ R N C OH C R′ R N N C O + HC R′ R Glycosidase Sugar Sugar Cyanogenic glycoside Hydrogen cyanide Cyanohydrin Hydroxynitrile lyase or spontaneous Ketone FIGURE 13.20 Enzyme-catalyzed hydrolysis of cyanogenic glycosides to release hydro-gen cyanide. R and R′ represent various alkyl or aryl substituents. For example, if R is phenyl, R′ is hydrogen, and the sugar is the disaccharide β-gentiobiose, the compound is amygdalin (the common cyanogenic glycoside found in the seeds of almonds, apri-cots, cherries, and peaches).
Efforts are currently under way to reduce the cyanogenic glycoside content of cassava through both conventional breeding and genetic engineering approaches. However, the complete elimination of cyanogenic glycosides may not be desirable because these substances are probably responsi-ble for the fact that cassava can be stored for very long peri-ods of time without being attacked by pests.
Glucosinolates Release Volatile Toxins A second class of plant glycosides, called the glucosino-lates, or mustard oil glycosides, break down to release volatile defensive substances. Found principally in the Brassicaceae and related plant families, glucosinolates give off the compounds responsible for the smell and taste of vegetables such as cabbage, broccoli, and radishes.
The release of these mustard-smelling volatiles from glucosinolates is catalyzed by a hydrolytic enzyme, called a thioglucosidase or myrosinase, that cleaves glucose from its bond with the sulfur atom (Figure 13.21). The resulting aglycone, the nonsugar portion of the molecule, rearranges with loss of the sulfate to give pungent and chemically reactive products, including isothiocyanates and nitriles, depending on the conditions of hydrolysis. These products function in defense as herbivore toxins and feeding repel-lents. Like cyanogenic glycosides, glucosinolates are stored in the intact plant separately from the enzymes that hydrolyze them, and they are brought into contact with these enzymes only when the plant is crushed.
As with other secondary metabolites, certain animals are adapted to feed on glucosinolate-containing plants without ill effects. For adapted herbivores, such as the cabbage butterfly, glucosinolates often serve as stimulants for feeding and egg laying, and the isothiocyanates produced after glucosinolate hydrolysis act as volatile attractants (Renwick et al. 1992).
Most of the recent research on glucosinolates in plant defense has concentrated on rape, or canola (Brassica napus), a major oil crop in both North America and Europe.
Plant breeders have tried to lower the glucosinolate levels of rapeseed so that the high-protein seed meal remaining after oil extraction can be used as animal food. The first low-glucosinolate varieties tested in the field were unable to survive because of severe pest problems. However, more recently developed varieties with low glucosinolate levels in seeds but high glucosinolate levels in leaves are able to hold their own against pests and still provide a protein-rich seed residue for animal feeding.
Nonprotein Amino Acids Defend against Herbivores Plants and animals incorporate the same 20 amino acids into their proteins. However, many plants also contain unusual amino acids, called nonprotein amino acids, that are not incorporated into proteins but are present instead in the free form and act as protective substances. Nonpro-tein amino acids are often very similar to common protein amino acids. Canavanine, for example, is a close analog of arginine, and azetidine-2-carboxylic acid has a structure very much like that of proline (Figure 13.22).
Nonprotein amino acids exert their toxicity in various ways. Some block the synthesis or uptake of protein amino Secondary Metabolites and Plant Defense 301 Glucose C S N R O SO3 – Glucose C SH N R O SO3 – SO4 2– R N C S R C N Glucosinolate Aglycone Nitrile Thioglucosidase Spontaneous Isothiocyanate FIGURE 13.21 Hydrolysis of glucosinolates to mustard-smelling volatiles. R repre-sents various alkyl or aryl substituents. For example, if R is CH2 — — CH—CH2 –, the compound is sinigrin, a major glucosinolate of black mustard seeds and horserad-ish roots. CH CH2 HOOC COOH CH2 O NH NH CH2 CH2 CH NH2 CH NH NH2 CH CH2 HOOC COOH CH2 CH2 CH2 CH CH2 NH CH2 NH2 CH NH NH2 NH Canavanine Nonprotein amino acid Protein amino acid analog Arginine Proline Azetidine-2-carboxylic acid FIGURE 13.22 Nonprotein amino acids and their pro-tein amino acid analogs.
The nonprotein amino acids are not incorporated into proteins but are defen-sive compounds found in free form in plant cells. acids; others, such as canavanine, can be mistakenly incor-porated into proteins. After ingestion, canavanine is recog-nized by the herbivore enzyme that normally binds arginine to the arginine transfer RNA molecule, so it becomes incor-porated into proteins in place of arginine. The usual result is a nonfunctional protein because either its tertiary struc-ture or its catalytic site is disrupted. Canavanine is less basic than arginine and may alter the ability of an enzyme to bind substrates or catalyze chemical reactions (Rosenthal 1991).
Plants that synthesize nonprotein amino acids are not susceptible to the toxicity of these compounds. The jack bean (Canavalia ensiformis), which synthesizes large amounts of canavanine in its seeds, has protein-synthesizing machin-ery that can discriminate between canavanine and arginine, and it does not incorporate canavanine into its own pro-teins. Some insects that specialize on plants containing non-protein amino acids have similar biochemical adaptations.
Some Plant Proteins Inhibit Herbivore Digestion Among the diverse components of plant defense arsenals are proteins that interfere with herbivore digestion. For example, some legumes synthesize α-amylase inhibitors that block the action of the starch-digesting enzyme α-amy-lase. Other plant species produce lectins, defensive proteins that bind to carbohydrates or carbohydrate-containing pro-teins. After being ingested by an herbivore, lectins bind to the epithelial cells lining the digestive tract and interfere with nutrient absorption (Peumans and Van Damme 1995).
The best-known antidigestive proteins in plants are the proteinase inhibitors. Found in legumes, tomatoes, and other plants, these sub-stances block the action of herbivore proteolytic enzymes. After entering the herbivore’s diges-tive tract, they hinder protein digestion by bind-ing tightly and specifically to the active site of protein-hydrolyzing enzymes such as trypsin and chymotrypsin. Insects that feed on plants containing proteinase inhibitors suffer reduced rates of growth and development that can be offset by supplemental amino acids in their diet.
The defensive role of proteinase inhibitors has been confirmed by experiments with transgenic tobacco. Plants that had been transformed to accumulate increased levels of proteinase inhibitors suffered less damage from insect her-bivores than did untransformed control plants (Johnson et al. 1989).
Herbivore Damage Triggers a Complex Signaling Pathway Proteinase inhibitors and certain other defenses are not continuously present in plants, but are synthesized only after initial herbivore or pathogen attack. In tomatoes, insect feeding leads to the rapid accumulation of proteinase inhibitors throughout the plant, even in undamaged areas far from the initial feeding site. The systemic production of proteinase inhibitors in young tomato plants is triggered by a complex sequence of events: 1. Wounded tomato leaves synthesize prosystemin, a large (200 amino acid) precursor protein.
2. Prosystemin is proteolytically processed to produce the short (18 amino acid) polypeptide called sys-temin, the first (and so far only) polypeptide hor-mone discovered in plants (Pearce et al. 1991) (Figure 13.23).
3. Systemin is released from damaged cells into the apoplast.
4. Systemin is then transported out of the wounded leaf via the phloem.
5. In target cells, systemin is believed to bind to a site on the plasma membrane and initiate the biosynthe-sis of jasmonic acid, a plant growth regulator that has wide-ranging effects (Creelman and Mullet 1997).
6. Jasmonic acid eventually activates the expression of genes that encode proteinase inhibitors (see Figure 13.23). Other signals, such as ABA (abscisic acid), sal-icylic acid, and pectin fragments from damaged plant cell walls also appear to participate in this wound-signaling cascade, but their specific roles are still unclear.
302 Chapter 13 O COOH Herbivory Systemin (polypeptide hormone) Transported through phloem to target cells in other organs Receptor Lipase Membrane lipids Free linolenic acid Jasmonic acid biosynthesis (see Figure 13.24) Jasmonic acid Activation of proteinase inhibitor genes Plasma membrane OUTSIDE OF CELL CYTOPLASM Wounded leaf releases hormone Signaling pathway FIGURE 13.23 Proposed signaling pathway for the rapid induction of proteinase inhibitor biosynthesis in wounded tomato plants. Jasmonic Acid Is a Plant Stress Hormone That Activates Many Defense Responses Jasmonic acid levels rise steeply in response to damage caused by a variety of different herbivores and trigger the formation of many different kinds of plant defenses besides proteinase inhibitors, including terpenes and alkaloids. The structure and biosynthesis of jasmonic acid have intrigued plant biologists because of the parallels to some eicosanoids that are central to inflammatory responses and other phys-iological processes in mammals (see Chapter 14 on the web site). In plants, jasmonic acid is synthesized from linolenic acid (18:3), which is released from membrane lipids and then converted to jasmonic acid as outlined in Figure 13.24.
Jasmonic acid is known to induce the transcription of a host of genes involved in plant defense metabolism. The mechanisms for this gene activation are slowly becoming clear. For example, recent research on the Madagascar peri-winkle (Catharanthus roseus), which makes some valuable anticancer alkaloids, identified a transcription factor that responds to jasmonic acid by activating the expression of several genes encoding alkaloid biosynthetic genes (van der Fits and Memelink 2000). Interestingly, this transcription factor also activates the genes of certain primary metabolic pathways that provide precursors for alkaloid formation, so it appears to be a master regulator of metabolism in Mada-gascar periwinkle.
Direct demonstration of the role of jasmonic acid in insect resistance has come from research with mutant lines of Arabidopsis that produce only low levels of jasmonic acid (McConn et al. 1997). Such mutants are easily killed by insect pests, such as fungus gnats, that normally do not damage Arabidopsis. However, application of exogenous jasmonic acid can restore resistance nearly to the levels of the wild-type plant.
PLANT DEFENSE AGAINST PATHOGENS Even though they lack an immune system, plants are sur-prisingly resistant to diseases caused by the fungi, bacteria, viruses, and nematodes that are ever present in the envi-ronment. In this section we will examine the diverse array of mechanisms that plants have evolved to resist infection, including the production of antimicrobial agents and a type of programmed cell death (see Chapter 16) called the hyper-sensitive response. Finally, we will discuss a special type of plant immunity called systemic acquired resistance.
Some Antimicrobial Compounds Are Synthesized before Pathogen Attack Several classes of secondary metabolites that we have already discussed have strong antimicrobial activity when tested in vitro; thus they have been proposed to function as defenses against pathogens in the intact plant. Among these are saponins, a group of triterpenes thought to dis-rupt fungal membranes by binding to sterols.
Experiments performed in the laboratory of Anne Osbourn at the John Innes Centre (Norwich, England) uti-lized genetic approaches to demonstrate the role of saponins in defense against pathogens of oat (Papadopoulou et al.
1999). Mutant oat lines with reduced saponin levels had much less resistance to fungal pathogens than wild-type oats. Interestingly, one fungal strain that normally grows on oats was able to detoxify one of the principal saponins in the plant. However, mutants of this strain that could no longer detoxify saponins failed to infect oats, but could grow suc-cessfully on wheat that did not contain any saponins.
Infection Induces Additional Antipathogen Defenses Some defenses are induced by herbivore attack or micro-bial infection. Defenses that are produced only after initial herbivore damage theoretically require a smaller invest-ment of plant resources than defenses that are always pre-sent, but they must be activated quickly to be effective. Like proteinase inhibitors, other induced defenses appear to be triggered by complex signal transduction networks, which often involve jasmonic acid.
After being infected by a pathogen, plants deploy a broad spectrum of defenses against invading microbes. A common defense is the hypersensitive response, in which cells immediately surrounding the infection site die rapidly, Secondary Metabolites and Plant Defense 303 COOH O COOH O COOH Linolenic acid 12-Oxophytodienoic acid Jasmonic acid FIGURE 13.24 Steps in the pathway for conversion of linolenic acid (18:3) to jasmonic acid.
depriving the pathogen of nutrients and preventing its spread. After a successful hypersensitive response, a small region of dead tissue is left at the site of the attempted inva-sion, but the rest of the plant is unaffected.
The hypersensitive response is often preceded by the pro-duction of reactive oxygen species. Cells in the vicinity of the infection synthesize a burst of toxic compounds formed by the reduction of molecular oxygen, including the superoxide anion (O2•–), hydrogen peroxide (H2O2) and the hydroxyl radical (•OH). An NADPH-dependent oxidase located on the plasma membrane (Figure 13.25) is thought to produce O2 •–, which in turn is converted to •OH and H2O2.
The hydroxyl radical is the strongest oxidant of these active oxygen species and can initiate radical chain reac-tions with a range of organic molecules, leading to lipid peroxidation, enzyme inactivation, and nucleic acid degra-dation (Lamb and Dixon 1997). Active oxygen species may contribute to cell death as part of the hypersensitive response or act to kill the pathogen directly.
Many species react to fungal or bacterial invasion by synthesizing lignin or callose (see Chapter 10). These poly-mers are thought to serve as barriers, walling off the pathogen from the rest of the plant and physically block-ing its spread. A related response is the modification of cell wall proteins. Certain proline-rich proteins of the wall become oxidatively cross-linked after pathogen attack in an H2O2-mediated reaction (see Figure 13.25) (Bradley et al. 1992). This process strengthens the walls of the cells in the vicinity of the infection site, increasing their resistance to microbial digestion.
Another defensive response to infection is the formation of hydrolytic enzymes that attack the cell wall of the pathogen. An assortment of glucanases, chitinases, and other hydrolases are induced by fungal invasion. Chitin, a polymer of N-acetylglucosamine residues, is a principal component of fungal cell walls. These hydrolytic enzymes belong to a group of proteins that are closely associated with pathogen infection and so are known as pathogene-sis-related (PR) proteins.
Phytoalexins. Perhaps the best-studied response of plants to bacterial or fungal invasion is the synthesis of phy-toalexins. Phytoalexins are a chemically diverse group of secondary metabolites with strong antimicrobial activity that accumulate around the site of infection.
Phytoalexin production appears to be a common mech-anism of resistance to pathogenic microbes in a wide range of plants. However, different plant families employ differ-ent types of secondary products as phytoalexins. For exam-ple, isoflavonoids are common phytoalexins in the legume family, whereas in plants of the potato family (Solanaceae), such as potato, tobacco, and tomato, various sesquiterpenes are produced as phytoalexins (Figure 13.26).
Phytoalexins are generally undetectable in the plant before infection, but they are synthesized very rapidly after microbial attack because of the activation of new biosyn-thetic pathways. The point of control is usually the initia-tion of gene transcription. Thus, plants do not appear to store any of the enzymatic machinery required for phy-toalexin synthesis. Instead, soon after microbial invasion 304 Chapter 13 Receptor (R gene product) Ion fluxes, change in membrane potential Activation of genes for: Plasma membrane Cell wall OUTSIDE OF CELL CYTOPLASM Pathogen Elicitor (product of an avr gene) NADPH oxidase O2 Reactive oxygen species Cell wall cross-linking Systemic acquired resistance ?
?
Hypersensitive response Phytoalexin biosynthesis Lignin biosynthesis Salicylic acid biosynthesis Biosynthesis of hydrolytic enzymes FIGURE 13.25 Many modes of antipathogen defense are induced by infection.
Fragments of pathogen molecules called elicitors initiate a complex signaling path-way leading to the activation of defensive responses. Some bacterial protein elici-tors are injected directly into the cell, where they interact with R gene products.
they begin transcribing and translating the appropriate mRNAs and synthesizing the enzymes de novo.
Although phytoalexins accumulate in concentrations that have been shown to be toxic to pathogens in bioassays, the defensive significance of these compounds in the intact plant is not fully known. Recent experiments on genetically mod-ified plants and pathogens have provided the first direct proof of phytoalexin function in vivo. For example, when tobacco was transformed with a gene catalyzing the biosyn-thesis of the phenylpropanoid phytoalexin resveratrol, it became much more resistant to a fungal pathogen than non-transformed control plants were (Hain et al. 1993). In con-trast, Arabidopsis mutants deficient in the tryptophan-derived phytoalexin camalexin were more susceptible than the wild-type to a fungal pathogen. In other experiments, pathogens that had been transformed with genes encoding phytoalexin-degrading enzymes were then able to infect plants that were normally resistant to them (Kombrink and Somssich 1995).
Some Plants Recognize Specific Substances Released from Pathogens Within a species, individual plants often differ greatly in their resistance to microbial pathogens. These differences often lie in the speed and intensity of a plant’s reactions.
Resistant plants respond more rapidly and more vigor-ously to pathogens than susceptible plants. Hence it is important to learn how plants sense the presence of pathogens and initiate defense.
In the last few years, researchers have isolated over 20 different plant resistance genes, known as R genes, that function in defense against fungi, bacteria, and nematodes. Most of the R genes are thought to encode protein receptors that rec-ognize and bind specific molecules originat-ing from pathogens. This binding alerts the plant to the pathogen’s presence (see Figure 13.25). The specific pathogen molecules rec-ognized are referred to as elicitors, and they include proteins, peptides, sterols, and poly-saccharide fragments arising from the pathogen cell wall, outer membrane, or a secretion process (Boller 1995). The R gene products themselves are nearly all proteins with a leucine-rich domain that is repeated inexactly several times in the amino acid sequence (see Chapter 14 on the web-site). Such domains may be involved in elic-itor binding and pathogen recognition. In addition, the R gene product is equipped to initiate signaling pathways that activate the various modes of antipathogen defense. Some R genes encode a nucleotide-binding site that binds ATP or GTP; others encode a protein kinase domain (Young 2000).
R gene products are distributed in more than one place in the cell. Some appear to be situated on the outside of the plasma membrane, where they could rapidly detect elici-tors; others are cytoplasmic to detect either pathogen mol-ecules that are injected into the cell or other metabolic changes indicating pathogen infection. R genes constitute one of the largest gene families in plants and are often clus-tered together in the genome. The structures of R gene clus-ters may help generate R gene diversity by promoting exchange between chromosomes.
Studies of plant disease have revealed complex patterns of host relationships between plants and pathogen strains.
Plant species are generally susceptible to the attack of certain pathogen strains, but resistant to others. This specificity is thought to be determined by interaction between the prod-ucts of host R genes and pathogen avr (avirulence) genes believed to encode specific elicitors. According to current thinking, successful resistance requires the elicitor, a product of the pathogen avr gene, to be rapidly recognized by a host plant receptor, the product of an R gene. Despite their name, avr genes appear to encode factors that promote infection.
Exposure to Elicitors Induces a Signal Transduction Cascade Within a few minutes after pathogen elicitors have been recognized by an R gene, complex signaling pathways are Secondary Metabolites and Plant Defense 305 O HO O OCH3 OH O CH3 H3C O O OH HO HO CH3 CH3 CH2 OH HO CH3 CH3 CH3 CH2 Medicarpin (from alfalfa) Isoflavonoids from the Leguminosae (the pea family) Glyceollin I (from soybean) Rishitin (from potato and tomato) Sesquiterpenes from the Solanaceae (the potato family) Capsidiol (from pepper and tobacco) Additional ring formed from a C5 unit from the terpene pathway FIGURE 13.26 Structure of some phytoalex-ins—secondary metabolites with antimicrobial properties that are rapidly synthesized after microbial infection. set in motion that lead eventually to defense responses (see Figure 13.25). A common early element of these cascades is a transient change in the ion permeability of the plasma membrane. R gene activation stimulates an influx of Ca2+ and H+ ions into the cell and an efflux of K+ and Cl– ions (Nürn-berger and Scheel 2001). The influx of Ca2+ activates the oxidative burst that may act directly in defense (as already described), as well as signaling other defense reactions. Other components of pathogen-stimulated signal transduction pathways include nitric oxide, mitogen-activated protein (MAP) kinases, calcium-dependent protein kinases, jasmonic acid, and salicylic acid (see the next section).
A Single Encounter with a Pathogen May Increase Resistance to Future Attacks When a plant survives the infection of a pathogen at one site, it often develops increased resistance to subsequent attacks at sites throughout the plant and enjoys protection against a wide range of pathogen species. This phenome-non, called systemic acquired resistance (SAR), develops over a period of several days following initial infection (Ryals et al. 1996). Systemic acquired resistance appears to result from increased levels of certain defense compounds that we have already mentioned, including chitinases and other hydrolytic enzymes.
Although the mechanism of SAR induction is still unknown, one of the endogenous signals is likely to be sal-icylic acid. The level of this benzoic acid derivative, a compound rises dramatically in the zone of infection after initial attack, and it is thought to establish SAR in other parts of the plant, although salicylic acid itself is not the mobile signal (Figure 13.27).
In addition to salicylic acid, recent studies suggest that its methyl ester, methyl salicylate, acts as a volatile SAR-inducing signal transmitted to distant parts of the plant and even to neighboring plants (Shulaev et al. 1997). Thus, even though plants lack immune systems like those present in many animals, they have developed elaborate mecha-nisms to protect themselves from disease-causing microbes.
SUMMARY Plants produce an enormous diversity of substances that have no apparent roles in growth and development processes and so are classified under the heading of sec-ondary metabolites. Scientists have long speculated that these compounds protect plants from predators and pathogens on the basis of their toxicity and repellency to herbivores and microbes when tested in vitro. Recent experiments on plants whose secondary-metabolite expres-sion has been altered by modern molecular methods have begun to confirm these defensive roles.
There are three major groups of secondary metabolites: terpenes, phenolics, and nitrogen-containing compounds.
Terpenes, composed of five-carbon isoprene units, are tox-ins and feeding deterrents to many herbivores. Phenolics, which are synthesized primarily from prod-ucts of the shikimic acid pathway, have several important roles in plants. Lignin mechanically strengthens cell walls.
Flavonoid pigments function as shields against harmful ultraviolet radiation and as attractants for pollinators and fruit dispersers. Finally, lignin, flavonoids, and other phe-nolic compounds serve as defenses against herbivores and pathogens. Members of the third major group, nitrogen-containing secondary metabolites, are synthesized principally from common amino acids. Compounds such as alkaloids, cyanogenic glycosides, glucosinolates, nonprotein amino acids, and proteinase inhibitors protect plants from a vari-ety of herbivorous animals.
Plants have evolved multiple defense mechanisms against microbial pathogens. Besides antimicrobial sec-ondary metabolites, some of which are preformed and some of which are induced by infection, other modes of defense include the construction of polymeric barriers to pathogen penetration and the synthesis of enzymes that degrade pathogen cell walls. In addition, plants employ specific recognition and signaling systems enabling the rapid detection of pathogen invasion and initiation of a vigorous defensive response. Once infected, some plants also develop an immunity to subsequent microbial attacks.
C1 C6 306 Chapter 13 COOH OH COOCH3 OH Accumulation of salicylic acid Infection of one leaf Synthesis and release of volatile methyl salicylate Airborne transmission of signal to other parts of plant (and neighboring plants) Transmission of signal to other parts of plant via vascular system, resulting in increased systemic resistance to pathogens FIGURE 13.27 Initial pathogen infection may increase resis-tance to future pathogen attack through development of systemic acquired resistance.
For millions of years, plants have produced defenses against herbivory and microbial attack. Well-defended plants have tended to leave more survivors than poorly defended plants, so the capacity to produce effective defen-sive products has become widely established in the plant kingdom. In response, many species of herbivores and microbes have evolved the ability to feed on or infect plants containing secondary products without being adversely affected, and this herbivore and pathogen pressure has in turn selected for new defensive products in plants.
The study of plant secondary metabolites has many practical applications. By virtue of their biological activi-ties against herbivorous animals and microbes, many of these substances are employed commercially as insecti-cides, fungicides, and pharmaceuticals, while others find uses as fragrances, flavorings, medicinal drugs, and indus-trial materials. The breeding of increased levels of sec-ondary metabolites into crop plants has made it possible to reduce the need for certain costly and potentially harmful pesticides. In some cases, however, it has been necessary to reduce the levels of naturally occurring secondary metabo-lites to minimize toxicity to humans and domestic animals.
Web Material Web Topics 13.1 Structure of Various Triterpenes The structures of several triterpenes are given.
13.2 The Shikimic Acid Pathway The biochemical pathway for the synthesis of aromatic amino acids, the precursors of pheno-lic compounds, is presented.
13.3 Detailed Chemical Structure of a Portion of a Lignin Molecule The partial structure of a hypothetical lignin molecule from European beech (Fagus sylvat-ica) is described.
Web Essays 13.1 Unraveling the Function of Secondary Metabolites Wild tobacco plants use alkaloids and terpenes to defend themselves against herbivores.
13.2 Alkaloid-Making Fungal Symbionts Fungal endophytes can enhance plant growth, increase resistance to various stresses, and act as “defensive mutualists”against herbivores.
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308 Chapter 13 1 PLANT BIOLOGISTS MAY BE FORGIVEN for taking abiding sat-isfaction in the fact that Mendel’s classic studies on the role of her-itable factors in development were carried out on a flowering plant: the garden pea. The heritable factors that Mendel discovered, which control such characters as flower color, flower position, pod shape, stem length, seed color, and seed shape, came to be called genes.
Genes are the DNA sequences that encode the RNA molecules directly involved in making the enzymes and structural proteins of the cell. Genes are arranged linearly on chromosomes, which form linkage groups—that is, genes that are inherited together. The total amount of DNA or genetic information contained in a cell, nucleus, or organelle is termed its genome.
Since Mendel’s pioneering discoveries in his garden, the princi-ple has become firmly established that the growth, development, and environmental responses of even the simplest microorganism are determined by the programmed expression of its genes. Among multicellular organisms, turning genes on (gene expression) or off alters a cell’s complement of enzymes and structural proteins, allowing cells to differentiate. In the chapters that follow, we will discuss various aspects of plant development in relation to the reg-ulation of gene expression. Various internal signals are required for coordinating the expres-sion of genes during development and for enabling the plant to respond to environmental signals. Such internal (as well as external) signaling agents typically bring about their effects by means of sequences of biochemical reactions, called signal transduction path-ways, that greatly amplify the original signal and ultimately result in the activation or repression of genes. Much progress has been made in the study of signal transduction pathways in plants in recent years. However, before describing what Gene Expression and Signal Transduction 14 CHAPTER 14 2 is known about these pathways in plants, we will provide background information on gene expression and signal transduction in other organisms, such as bacteria, yeasts, and animals, making reference to plant systems wherever appropriate. These models will provide the framework for the recent advances in the study of plant development that are discussed in subsequent chapters.
Genome Size, Organization, and Complexity As might be expected, the size of the genome bears some relation to the complexity of the organism. For example, the genome size of E. coli is 4.7 × 106 bp (base pairs), that of the fruit fly is 2 × 108 bp per haploid cell, and that of a human is 3 × 109 bp per haploid cell. However, genome size in eukaryotes is an unreliable indicator of complex-ity because not all of the DNA encodes genes. In prokaryotes, nearly all of the DNA consists of unique sequences that encode proteins or functional RNA molecules. In addition to unique sequences, how-ever, eukaryotic chromosomes contain large amounts of noncoding DNA whose main functions appear to be chromosome organization and structure. Much of this noncoding DNA consists of multicopy sequences, called repetitive DNA. The remainder of the noncoding DNA is made up of single-copy sequences called spacer DNA.
Together, repetitive and spacer DNA can make up the majority of the total genome in some eukaryotes. For example, in humans only about 5% of the total DNA consists of genes, the unique sequences that encode for RNA and protein synthesis. The genome size in plants is more variable than in any other group of eukaryotes. In angiosperms, the hap-loid genome ranges from about 1.5 × 108 bp for Ara-bidopsis thaliana (smaller than that of the fruit fly) to 1 × 1011 bp for the monocot Trillium, which is considerably larger than the human genome. Even closely related beans of the genus Vicia exhibit genomic DNA contents that vary over a 20-fold range. Why are plant genomes so variable in size? Studies of plant molecular biology have shown that most of the DNA in plants with large genomes is repet-itive DNA. Arabidopsis has the smallest genome of any plant because only 10% of its nuclear DNA is repetitive DNA. The genome size of rice is estimated to be about five times that of Arabidopsis, yet the total amount of unique sequence DNA in the rice genome is about the same as in Arabidopsis. Thus the difference in genome size between Arabidopsis and rice is due mainly to repet-itive and spacer DNA. Most Plant Haploid Genomes Contain 20,000 to 30,000 Genes Until recently, the total number of genes in an organ-ism’s genome was difficult to assess. Thanks to recent advances in many genomic sequencing projects, such numbers are now becoming available, although precise values are still lacking. According to Miklos and Rubin (1996), the number of genes in bacteria varies from 500 to 8,000 and overlaps with the number of genes in many simple unicellular eukaryotes. For example, the yeast genome appears to contain about 6,000 genes. More complex eukaryotes, such as protozoans, worms, and flies, all seem to have gene numbers in the range of 12,000 to 14,000. The Drosophila (fruit fly) genome con-tains about 12,000 genes. Thus, the current view is that it takes roughly 12,000 basic types of genes to form a eukaryotic organism, although values as high as 43,000 genes are common, as a result of multiple copies of cer-tain genes, or multigene families. The best-studied plant genome is that of Arabidop-sis thaliana. Chris Somerville and his colleagues at Stan-ford University have estimated that the Arabidopsis genome contains roughly 20,000 genes (Rounsley et al.
1996). This estimate is based on more than one approach. For example, since large regions of the genome have been sequenced, we know there is one gene for every 5 kb (kilobases) of DNA. Since the entire genome contains about 100,000 kb, there must be about 20,000 genes. However, 6% of the genome encodes ribosomal RNA, and another 2% consists of highly repetitive sequences, so the number could be lower.
Similar values likely will be found for the genomes of other plants as well. The current consensus is that the genomes of most plants will be found to contain from 20,000 to 30,000 genes. Some of these genes encode proteins that perform housekeeping functions, basic cellular processes that go on in all the different kinds of cells. Such genes are per-manently turned on; that is, they are constitutively expressed. Other genes are highly regulated, being turned on or off at specific stages of development or in response to specific environmental stimuli. Prokaryotic Gene Expression The first step in gene expression is transcription, the synthesis of an mRNA copy of the DNA template that encodes a protein (Alberts et al. 1994; Lodish et al. 1995).
Transcription is followed by translation, the synthesis of the protein on the ribosome. Developmental studies have shown that each plant organ contains large num-bers of organ-specific mRNAs. Transcription is con-trolled by proteins that bind DNA, and these DNA-binding proteins are themselves subject to various types of regulation. Much of our understanding of the basic elements of transcription is derived from early work on bacterial systems; hence we precede our discussion of eukaryotic gene expression with a brief overview of transcriptional regulation in prokaryotes. However, it is now clear that Gene Expression and Signal Transduction 3 gene regulation in eukaryotes is far more complex than in prokaryotes. The added complexity of gene expres-sion in eukaryotes is what allows cells and tissues to dif-ferentiate and makes possible the diverse life cycles of plants and animals.
DNA-Binding Proteins Regulate Transcription in Prokaryotes In prokaryotes, genes are arranged in operons, sets of contiguous genes that include structural genes and reg-ulatory sequences. A famous example is the E. coli lac-tose (lac) operon, which was first described in 1961 by François Jacob and Jacques Monod of the Pasteur Insti-tute in Paris. The lac operon is an example of an inducible operon—that is, one in which a key metabolic intermediate induces the transcription of the genes.
The lac operon is responsible for the production of three proteins involved in utilization of the disaccharide lactose. This operon consists of three structural genes and three regulatory sequences. The structural genes (z, y, and a) code for the sequence of amino acids in three proteins: β-galactosidase, the enzyme that catalyzes the hydrolysis of lactose to glucose and galactose; perme-ase, a carrier protein for the membrane transport of lac-tose into the cell; and transacetylase, the significance of which is unknown.
The three regulatory sequences (i, p, and o) control the transcription of mRNA for the synthesis of these proteins (Figure 14.1). Gene i is responsible for the syn-thesis of a repressor protein that recognizes and binds to a specific nucleotide sequence, the operator. The operator, o, is located downstream (i.e., on the 3′ side) of Gene z DNA mRNA Gene y Gene a Operator o Transcription is blocked when repressor protein binds to operator; z y a mRNA is not made, and therefore enzymes are not produced Transcription initiation site Structural genes Lactose operon Translation Transcription mRNA Translation β-Galactosidase Acetylase Permease Lactose inducer Transcription Repressor protein binds to the operator gene RNA polymerase attaches to promoter 5′ DNA Gene y Gene z Repressor–inducer (inactive) Repressor protein Gene a Promoter p Operator o 5′ 3′ 3′ (A) (B) RNA polymerase mRNA Transcription occurs Regulatory gene i Regulatory gene i Promoter p Figure 14.1 The lac operon of E. coli uses negative control. (A) The regulatory gene i, located upstream of the operon, is transcribed to produce an mRNA that encodes a repressor protein. The repressor protein binds to the operator gene o. The operator is a short stretch of DNA located between the promoter sequence p (the site of RNA poly-merase attachment to the DNA) and the three structural genes, z, y, and a. Upon binding to the operator, the repressor prevents RNA polymerase from binding to the transcription initiation site. (B) When lactose (inducer) is added to the medium and is taken up by the cell, it binds to the repressor and inactivates it. The inactivated repressor is unable to bind to o, and transcription and translation can proceed. The mRNA produced is termed “poly-cistronic” because it encodes multiple genes. Note that translation begins while transcrip-tion is still in progress. CHAPTER 14 4 the promoter sequence, p, where RNA polymerase attaches to the operon to initiate transcription, and immediately upstream (i.e., on the 5′ side) of the tran-scription start site, where transcription begins. (The ini-tiation site is considered to be at the 5′ end of the gene, even though the RNA polymerase transcribes from the 3′ end to the 5′ end along the opposite strand. This con-vention was adopted so that the sequence of the mRNA would match the DNA sequence of the gene.) In the absence of lactose, the lactose repressor forms a tight complex with the operator sequence and blocks the interaction of RNApolymerase with the transcription start site, effectively preventing transcription (see Figure 14.1A).
When present, lactose binds to the repressor, causing it to undergo a conformational change (see Figure 14.1B). The lac repressor is thus an allosteric protein whose confor-mation is determined by the presence or absence of an effector molecule, in this case lactose. As a result of the conformational change due to binding lactose, the lac repressor detaches from the operator. When the operator sequence is unobstructed, the RNApolymerase can move along the DNA, synthesizing a continuous mRNA. The translation of this mRNA yields the three proteins, and lactose is said to induce their synthesis.
The lac repressor is an example of negative control, since the repressor blocks transcription upon binding to the operator region of the operon. The lac operon is also regulated by positive control, which was discovered in connection with a phenomenon called the glucose effect.
If glucose is added to a nutrient medium that includes lactose, the E. coli cells metabolize the glucose and ignore the lactose. Glucose suppresses expression of the lac operon and prevents synthesis of the enzymes needed to degrade lactose. Glucose exerts this effect by lowering the cellular concentration of cyclic AMP (cAMP). When glucose levels are low, cAMP levels are high. Cyclic AMP binds to an activator protein, the catabolite activator pro-tein (CAP), which recognizes and binds to a specific nucleotide sequence immediately upstream of the lac operator and promoter sites (Figure 14.2).
In contrast to the behavior of the lactose repressor pro-tein, when the CAP is complexed with its effector, cAMP, its affinity for its DNA-binding site is dramatically increased (hence the reference to positive control). The ternary complex formed by CAP, cAMP, and the lactose operon DNA sequences induces bending of the DNA, which activates transcription of the lactose operon struc-tural genes by increasing the affinity of RNA polymerase for the neighboring promoter site. Bacteria synthesize cyclic AMP when they exhaust the glucose in their growth medium. The lactose operon genes are thus under opposing regulation by the absence of glucose (high lev-els of cyclic AMP) and the presence of lactose, since glu-cose is a catabolite of lactose.
In bacteria, metabolites can also serve as corepressors, activating a repressor protein that blocks transcription.
Repression of enzyme synthesis is often involved in the regulation of biosynthetic pathways in which one or Gene z DNA Gene y Gene a Operator o Lactose operon CAP–cAMP complex RNA polymerase 5′ 3′ (A) CAP Cyclic AMP (cAMP) Gene z DNA Gene y Gene a Operator o Transcription occurs mRNA 5′ 3′ (B) Regulatory gene i Promoter p Regulatory gene i Promoter p Catabolite activator protein Figure 14.2 Stimulation of transcription by the catabolite activator protein (CAP) and cyclic AMP (cAMP). CAP has no effect on transcription until cAMP binds to it. (A) The CAP– cAMP complex binds to a specific DNA sequence near the promoter region of the lac operon. (B) Binding of the CAP– cAMP complex makes the promoter region more accessible to RNA polymerase, and transcription rates are enhanced. more enzymes are synthesized only if the end product of the pathway—an amino acid, for example—is not available. In such a case the amino acid acts as a core-pressor: It complexes with the repressor protein, and this complex attaches to the operator DNA, preventing transcription. The tryptophan (trp) operon in E. coli is an example of an operon that works by corepression (Fig-ure 14.3).
Eukaryotic Gene Expression The study of bacterial gene expression has provided models that can be tested in eukaryotes. However, the details of the process are quite different and more com-plex in eukaryotes. In prokaryotes, translation is cou-pled to transcription: As the mRNA transcripts elongate, they bind to ribosomes and begin synthesizing proteins (translation). In eukaryotes, however, the nuclear enve-lope separates the genome from the translational machinery. The transcripts must first be transported to the cytoplasm, adding another level of control. Eukaryotic Nuclear Transcripts Require Extensive Processing Eukaryotes differ from prokaryotes also in the organi-zation of their genomes. In most eukaryotic organisms, each gene encodes a single polypeptide. The eukaryotic nuclear genome contains no operons, with one notable exception. Furthermore, eukaryotic genes are divided into coding regions called exons and noncoding regions Gene Expression and Signal Transduction 5 Gene E DNA mRNA Gene D Gene C Gene B Gene A Gene E Gene D Gene C Gene B Gene A Tryptophan operon Translation Transcription mRNA Translation Transcription Repressor (inactive) RNA polymerase 5′ DNA Repressor protein Corepressor (tryptophan) 5′ 3′ 3′ (A) (B) RNA polymerase mRNA Transcription occurs Repressor–corepressor complex (active) Transcription is blocked Enzymes for tryptophan synthesis Regulatory gene i Promoter p Operator o Regulatory gene i Promoter p Operator o Figure 14.3 The tryptophan (trp) operon of E. coli. Tryptophan (Trp) is the end product of the pathway catalyzed by tryptophan synthetase and other enzymes. Transcription of the repressor genes results in the production of a repressor protein. However, the repres-sor is inactive until it forms a complex with its corepressor, Trp. (A) In the absence of Trp, transcription and translation proceed. (B) In the presence of Trp, the activated repres-sor–corepressor complex blocks transcription by binding to the operator sequence.
About 25% of the genes in the nematode Caenorhabditis ele-gans are in operons. The operon pre-mRNAs are processed into individual mRNAs that encode single polypeptides (monocistronic mRNAs) by a combination of cleavage, polyadenylation, and splicing (Kuersten et al. 1997).
CHAPTER 14 6 called introns (Figure 14.4). Since the primary tran-script, or pre-mRNA, contains both exon and intron sequences, the pre-mRNA must be processed to remove the introns. RNA processing involves multiple steps. The newly synthesized pre-mRNA is immediately packaged into a string of small protein-containing particles, called het-eronuclear ribonucleoprotein particles, or hnRNP par-ticles. Some of these particles are composed of proteins and small nuclear RNAs, and are called small nuclear ribonucleoproteins, or snRNPs (pronounced “snurps”).
Various snRNPs assemble into spliceosome complexes at exon–intron boundaries of the pre-mRNA and carry out the splicing reaction. In some cases, the primary transcript can be spliced in different ways, a process called alternative RNA splicing. For example, an exon that is present in one version of a processed transcript may be spliced out of another version. In this way, the same gene can give rise to different polypeptide chains. Approximately 15% of human genes are processed by alternative splicing.
Although alternative splicing is rare in plants, it is involved in the synthesis of rubisco activase, RNA poly-merase II, and the gene product of a rice homeobox gene (discussed later in the chapter), as well as other proteins (Golovkin and Reddy 1996).
Before splicing, the pre-mRNA is modified in two important ways. First it is capped by the addition of 7-methylguanylate to the 5′ end of the transcript via a 5′-to-5′ linkage. The pre-mRNA is capped almost immedi-ately after the initiation of mRNA synthesis. One of the functions of the 5′ cap is to protect the growing RNA transcript from degradation by RNases. At a later stage in the synthesis of the primary transcript, the 3′ end is Intron Intron DNA Promoter Exon Exon Exon Translational stop site AUG (Translational start site) Transcription starts here RNA polymerase II 5′ 3′ mRNA Polysome Released polypeptides Pre-mRNA m7G cap Transcription occurs Transcription (+ capping and polyadenylation) Translation Transport out of nucleus to cytoplasm Processing of precursor AAAAn AAAAn AAAAn Figure 14.4 Gene expression in eukaryotes. RNA polymerase II binds to the promoter of genes that encode proteins. Unlike prokaryotic genes, eukaryotic genes are not clustered in operons, and each is divided into introns and exons. Transcription from the template strand proceeds in the 3′-to-5′ direction at the transcription start site, and the growing RNA chain extends one nucleotide at a time in the 5′-to-3′ direction. Translation begins with the first AUG encoding methionine, as in prokaryotes, and ends with the stop codon. The pre-mRNA transcript is first “capped” by the addition of 7-methylguanylate (m7G) to the 5′ end. The 3′ end is shortened slightly by cleavage at a specific site, and a poly-A tail is added. The capped and polyadenylated pre-mRNA is then spliced by a spliceosome complex, and the introns are removed. The mature mRNA exits the nucleus through the pores and initiates translation on ribosomes in the cytosol. As each ribosome progresses toward the 3′ end of the mRNA, new ribosomes attach at the 5′ end and begin translating, leading to the formation of polysomes. cleaved at a specific site, and a poly-A tail, usually con-sisting of about 100 to 200 adenylic acid residues, is added by the enzyme poly-A polymerase (see Figure 14.4).
The poly-A tail has several functions: (1) It protects against RNases and therefore increases the stability of mRNA molecules in the cytoplasm, (2) both it and the 5′ cap are required for transit through the nuclear pore, and (3) it increases the efficiency of translation on the ribosomes. The requirement of eukaryotic mRNAs to have both a 5′ cap and a poly-A tail ensures that only properly processed transcripts will reach the ribosome and be translated.
Each step in eukaryotic gene expression can poten-tially regulate the amount of gene product in the cell at any given time (Figure 14.5). Like transcription initia-tion, splicing may be regulated. Export from the nucleus is also regulated. For example, to exit the nucleus an mRNA must possess a 5′ cap and a poly-A tail, and it must be properly spliced. Incompletely processed tran-scripts remain in the nucleus and are degraded.
Various Posttranscriptional Regulatory Mechanisms Have Been Identified The stabilities or turnover rates of mRNA molecules dif-fer from one another, and may vary from tissue to tis-sue, depending on the physiological conditions. For example, in bean (Vicia faba), fungal infection causes the rapid degradation of the mRNA that encodes the pro-line-rich protein PvPRP1 of the bean cell wall. Another example of the regulation of gene expression by RNA degradation is the regulation of expression of one of the genes for the small subunit of rubisco in roots of the aquatic duckweed Lemna gibba. Lemna roots are photo-synthetic and therefore express genes for the small sub-unit of rubisco, but the expression of one of the genes (SSU5B) is much lower in roots than in the fronds (leaves). Jane Silverthorne and her colleagues at the Uni-versity of California, Santa Cruz, showed that the low level of SSU5B in the roots is due to a high rate of turnover of the SSU5B pre-mRNA in the nucleus (Peters and Silverthorne 1995).
In addition to RNA turnover, the translatability of mRNA molecules is variable. For example, RNAs fold into molecules with varying secondary and tertiary structures that can influence the accessibility of the translation initiation codon (the first AUG sequence) to the ribosome. Another factor that can influence trans-latability of an mRNA is codon usage. There is redun-dancy in the triplet codons that specify a given amino acid during translation, and each cell has a characteris-tic ratio of the different aminoacylated tRNAs available, known as codon bias. If a message contains a large number of triplet codons that are rare for that cell, the small number of charged tRNAs available for those codons will slow translation. Finally, the cellular loca-tion at which translation occurs seems to affect the rate of gene expression. Free polysomes may translate mRNAs at very different rates from those at which polysomes bound to the endoplasmic reticulum do; even within the endoplasmic reticulum, there may be differential translation rates.
Although examples of posttranscriptional regulation have been demonstrated for each of the steps described above and summarized in Figure 14.5, the expression of most eukaryotic genes, like their prokaryotic counterparts, appears to be regulated at the level of transcription. Gene Expression and Signal Transduction 7 The levels for control of gene expression Genome Transcription RNA processing and translocation Translation Posttranslation Chromatin DNA available for expression NUCLEUS CYTOPLASM Gene amplification (rare) DNA rearrangements (rare) Chromatin decondensation DNA methylation RNA polymerase II Primary RNA transcript Processing (5′ capping, addition of poly-A tail, excision of introns, splicing together of exons) and turnover mRNA in nucleus Transport of mRNA across nuclear envelope mRNA in cytosol mRNA degradation (turnover) Functional protein Protein degradation (turnover) Translation Possible targeting to ER Polypeptide product in cytosol or ER Protein folding and assembly Possible polypeptide cleavage Possible modification Possible import into organelles 1 2 3 4 5 Figure 14.5 Eukaryotic gene expression can be regulated at multiple levels. (1) genomic regulation, by gene amplifi-cation, DNA rearrangements, chromatin decondensation or condensation, or DNA methylation; (2) transcriptional regu-lation; (3) RNA processing, and RNA turnover in the nucleus and translocation out of the nucleus; (4) translational con-trol (including binding to ER in some cases); (5) posttransla-tional control, including mRNA turnover in the cytosol, and the folding, assembly, modification, and import of proteins into organelles. (After Becker et al. 1996.) Transcription in Eukaryotes Is Modulated by cis-Acting Regulatory Sequences The synthesis of most eukaryotic proteins is regulated at the level of transcription. However, transcription in eukaryotes is much more complex than in prokaryotes.
First, there are three different RNA polymerases in eukaryotes: I, II, and III. RNA polymerase I is located in the nucleolus and functions in the synthesis of most ribosomal RNAs. RNA polymerase II, located in the nucleoplasm, is responsible for pre-mRNA synthesis.
RNA polymerase III, also located in the nucleoplasm, synthesizes small RNAs, such as tRNA and 5S rRNA. A second important difference between transcription in prokaryotes and in eukaryotes is that the RNA poly-merases of eukaryotes require additional proteins called general transcription factors to position them at the cor-rect start site. While prokaryotic RNA polymerases also require accessory polypeptides called sigma factors (σ), these polypeptides are considered to be subunits of the RNA polymerase. In contrast, eukaryotic general tran-scription factors make up a large, multisubunit tran-scription initiation complex. For example, seven gen-eral transcription factors constitute the initiation complex of RNA polymerase II, each of which must be added in a specific order during assembly (Figure 14.6). According to one current model, transcription is ini-tiated when the final transcription factor, TFIIH (tran-scription factor for RNA polymerase II protein H), joins the complex and causes phosphorylation of the RNA polymerase. RNA polymerase II then separates from the initiation complex and proceeds along the antisense strand in the 3′-to-5′ direction. While some of the gen-eral transcription factors dissociate from the complex at this point, others remain to bind another RNA poly-merase molecule and initiate another round of tran-scription. A third difference between transcription in prokary-otes and in eukaryotes is in the complexity of the pro-moters, the sequences upstream (5′) of the initiation site that regulate transcription. We can divide the structure of the eukaryotic promoter into two parts, the core or minimum promoter, consisting of the minimum up-stream sequence required for gene expression, and the additional regulatory sequences, which control the activity of the core promoter.
Each of the three RNA polymerases has a different type of promoter. An example of a typical RNA poly-merase II promoter is shown schematically in Figure 14.7A. The minimum promoter for genes transcribed by RNA polymerase II typically extends about 100 bp upstream of the transcription initiation site and includes several sequence elements referred to as proximal pro-moter sequences. About 25 to 35 bp upstream of the transcriptional start site is a short sequence called the TATA box, consisting of the sequence TATAAA(A). The TATA box plays a crucial role in transcription because it serves as the site of assembly of the transcription initia-tion complex. Approximately 85% of the plant genes sequenced thus far contain TATA boxes. In addition to the TATA box, the minimum promot-ers of eukaryotes also contain two additional regulatory sequences: the CAAT box and the GC box (see Figure 14.7A). These two sequences are the sites of binding of transcription factors, proteins that enhance the rate of transcription by facilitating the assembly of the initia-tion complex. The DNA sequences themselves are CHAPTER 14 8 1 P P P P Transcription Begins Protein kinase (TFIIH) activity Start of transcription TFIID TATA TFIIB TFIIF TFIIE TFIIH RNA polymerase II 2 3 4 Figure 14.6 Ordered assembly of the general transcription factors required for transcription by RNA polymerase II. (1) TFIID, a multisubunit complex, binds to the TATA box via the TATA-binding protein. (2) TFIIB joins the complex. (3) TFIIF bound to RNA polymerase II associates with the com-plex, along with TFIIE and TFIIH. The assembly of proteins is referred to as the transcription initiation complex. (4) TFIIH, a protein kinase, phosphorylates the RNA polymerase, some of the general transcription factors are released, and tran-scription begins. (From Alberts et al. 1994.) termed cis-acting sequences, since they are adjacent to the transcription units they are regulating. The tran-scription factors that bind to the cis-acting sequences are called trans-acting factors, since the genes that encode them are located elsewhere in the genome.
Numerous other cis-acting sequences located farther upstream of the proximal promoter sequences can exert either positive or negative control over eukaryotic pro-moters. These sequences are termed the distal regula-tory sequences and they are usually located within 1000 bp of the transcription initiation site. As with prokary-otes, the positively acting transcription factors that bind to these sites are called activators, while those that inhibit transcription are called repressors.
As we will see in Chapters 19 and 20, the regulation of gene expression by the plant hormones and by phyto-chrome is thought to involve the deactivation of repres-sor proteins. Cis-acting sequences involved in gene reg-ulation by hormones and other signaling agents are called response elements. As will be discussed in Chap-ters 17 and 19 through 23 (on phytochrome and the plant hormones), numerous response elements that reg-ulate gene expression have been identified in plants. In addition to having regulatory sequences within the promoter itself, eukaryotic genes can be regulated by control elements located tens of thousands of base pairs away from the start site. Distantly located positive reg-ulatory sequences are called enhancers. Enhancers may be located either upstream or downstream from the pro-moter. In plants, many developmentally important plant genes have been shown to be regulated by enhancers (Sundaresan et al. 1995). How do all the DNA-binding proteins on the cis-act-ing sequences regulate transcription? During formation Gene Expression and Signal Transduction 9 GGGCGG GC box CAAT box Gene X Promoter DNA GCCCAATCT TATAAA TATA RNA polymerase II and general transcription factors Spacer DNA The gene control region for gene X Silent assembly of regulatory proteins Strongly activating assembly Strongly inhibiting protein Weakly activating protein assembly Gene regulatory proteins RNA polymerase II Regulatory sequence Proximal control element General transcription factors RNA transcript (A) (B) –100 –80 TATA box –25 Figure 14.7 Organization and regulation of a typical eukaryotic gene. (A) Features of a typical eukaryotic RNA polymerase II minimum promoter and proteins that regulate gene expression. RNA polymerase II is situated at the TATA box in association with the general transcription factors about 25 bp upstream of the transcription start site. Two cis-acting regulatory sequences that enhance the activity of RNA polymerase II are the CAAT box and the GC box, located at about 80 and 100 bp upstream, respectively, of the transcrip-tion start site. The DNA proteins that bind to these elements are indicated. (B) Regulation of transcription by distal regulatory sequences and trans-acting factors. trans-acting fac-tors bound to distal regulatory sequences can act in concert to activate transcription by making direct physical contact with the transcription initiation complex. The details of this process are not well understood. (A after Alberts et al. 1994; B from Alberts et al 1994.) of the initiation complex, the DNA between the core promoter and the most distally located control elements loops out in such a way as to allow all of the transcrip-tion factors bound to that segment of DNA to make physical contact with the initiation complex (see Figure 14.7B). Through this physical contact the transcription factor exerts its control, either positive or negative, over transcription. Given the large number of control ele-ments that can modify the activity of a single promoter, the possibilities for differential gene regulation in eukaryotes are nearly infinite. Transcription Factors Contain Specific Structural Motifs Transcription factors generally have three structural fea-tures: a DNA-binding domain, a transcription-activat-ing domain, and a ligand-binding domain. To bind to a specific sequence of DNA, the DNA-binding domain must have extensive interactions with the double helix through the formation of hydrogen, ionic, and hydro-phobic bonds. Although the particular combination and spatial distribution of such interactions are unique for each sequence, analyses of many DNA-binding proteins have led to the identification of a small number of highly conserved DNA-binding structural motifs, which are summarized in Table 14.1.
Most of the transcription factors characterized thus far in plants belong to the basic zipper (bZIP) class of DNA-binding proteins. DNA-binding proteins contain-ing the zinc finger domain are relatively rare in plants. Homeodomain Proteins Are a Special Class of Helix-Turn-Helix Proteins The term “homeodomain protein” is derived from a group of Drosophila (fruit fly) genes called selector genes or homeotic genes. Drosophila homeotic genes encode transcription factors that determine which structures develop at specific locations on the fly’s body; that is, they act as major developmental switches that activate a large number of genes that constitute the entire genetic CHAPTER 14 10 Table 14.1 DNA-Binding Motifs Name Examples of proteins Key structural features Illustration Helix-turn-helix Transcription factors that Two α helices separated regulate genes in antho-by a turn in the polypep-cyanin biosynthesis tide chain; function as pathway dimers Zinc finger COP1 in Arabidopsis Various structures in which zinc plays an important structural role; bind to DNA either as monomers or as dimers Helix-loop-helix GT element–binding protein A short α helix connected of phytochrome-regulated by a loop to a longer α helix; genes function as dimers Leucine zipper Fos and Jun An α helix of about 35 amino acids containing leucine at every seventh position; dimerization occurs along the hydrophobic surface Basic zipper Opaque 2 protein in maize, Variation of the leucine zipper (bZip) G box factors of phyto-motif in which other hydro-chrome-regulated genes, phobic amino acids substitute transcription factors that for leucine and the DNA-bind ABA response binding domain contains elements amino acids COOH NH2 NH+ 3 H+ 3N Zn His His Cys Cys Zn Cys Cys Cys Cys + + + + + + + + Leu Leu Leu Leu Leu Leu NH+ 3 H+ 3N COO– COO– COO– COO– Ala Leu Val Ise Ala Val program for a particular structure. Mutations in homeotic genes cause homeosis, the transformation of one body part into another. For example, a homeotic mutation in the ANTENNAPEDIA gene causes a leg to form in place of an antenna. When the sequences of var-ious homeotic genes in Drosophila were compared, the proteins were all found to contain a highly conserved stretch of 60 amino acids called the homeobox. Homologous homeobox sequences have now been identified in developmentally important genes of verte-brates and plants. As will be discussed in Chapter 16, the KN1 (KNOTTED) gene of maize encodes a home-odomain protein that can affect cell fate during devel-opment. Maize plants with the kn1 mutation exhibit abnormal cell divisions in the vascular tissues, giving rise to the “knotted” appearance of the leaf surface.
However, the kn1 mutation is not a homeotic mutation, since it does not involve the substitution of one entire structure for another. Rather, the plant homeodomain protein, KN1, is involved in the regulation of cell divi-sion. Thus, not all genes that encode homeodomain pro-teins are homeotic genes, and vice versa. As will be dis-cussed in Chapter 24, four of the floral homeotic genes in plants encode proteins with the DNA-binding helix-turn-helix motif called the MADS domain. Eukaryotic Genes Can Be Coordinately Regulated Although eukaryotic nuclear genes are not arranged into operons, they are often coordinately regulated in the cell. For example, in yeast, many of the enzymes involved in galactose metabolism and transport are inducible and coregulated, even though the genes are located on different chromosomes. Incubation of wild-type yeast cells in galactose-containing media results in more than a thousandfold increase in the mRNA levels for all of these enzymes.
The six yeast genes that encode the enzymes in the galactose metabolism pathway are under both positive and negative control (Figure 14.8). Most yeast genes are regulated by a single proximal control element called an upstream activating sequence (UAS). The GAL4 gene encodes a transcription factor that binds to UAS ele-ments located about 200 bp upstream of the transcrip-tion start sites of all six genes. The UAS of each of the six genes, while not identical, consists of one or more copies of a similar 17 bp repeated sequence. The GAL4 protein can bind to each of them and activate transcription. In this way a single transcription factor can control the expres-sion of many genes. Protein–protein interactions can modify the effects of DNA-binding transcription factors. Another gene on a different yeast chromosome, GAL80, encodes a negative transcription regulator that forms a complex with the GAL4 protein when it is bound to the UAS. When the GAL80 protein is complexed with GAL4, transcription is blocked. In the presence of galactose, however, the meta-bolite formed by the enzyme that is encoded by the GAL3 gene acts as an inducer by causing the dissociation of GAL80 from GAL4 (Johnston 1987; Mortimer et al. 1989). There are many other examples of coordinate regu-lation of genes in eukaryotes. In plants, the develop-mental effects induced by light and hormones (see Chapters 17 through 23), as well as the adaptive responses caused by various types of stress (see Chap-ter 25), involve the coordinate regulation of groups of genes that share a common response element upstream of the promoter. In addition, genes that act as major developmental switches, such as the homeotic genes, encode transcription factors that bind to a common reg-ulatory sequence that is present on dozens, or even hun-dreds, of genes scattered throughout the genome (see Chapters 16 and 24). The Ubiquitin Pathway Regulates Protein Turnover An enzyme molecule, once synthesized, has a finite life-time in the cell, ranging from a few minutes to several hours. Hence, steady-state levels of cellular enzymes are attained as the result of an equilibrium between enzyme synthesis and enzyme degradation, or turnover. Protein turnover plays an important role in development. In eti-olated seedlings, for example, the red-light photorecep-tor, phytochrome, is regulated by proteolysis. The phy-tochrome synthesized in the dark is highly stable and accumulates in the cells to high concentrations. Upon exposure to red light, however, the phytochrome is con-verted to its active form and simultaneously becomes highly susceptible to degradation by proteases (see Chapter 17). In animal cells there are two distinct pathways of pro-tein turnover, one in specialized digestive vacuoles called lysosomes and the other in the cytosol. Proteins destined to be digested in lysosomes appear to be specifically targeted to these organelles. Upon entering the lysosomes, the proteins are rapidly degraded by lysosomal proteases. Lysosomes are also capable of engulfing and digesting entire organelles by an auto-phagic process. The central vacuole of plant cells is rich in proteases and is the plant equivalent of lysosomes, but as yet there is no clear evidence that plant vacuoles either engulf organelles or participate in the turnover of cytosolic proteins, except during senescence. The nonlysosomal pathway of protein turnover involves the ATP-dependent formation of a covalent bond to a small, 76-amino-acid polypeptide called ubiq-uitin. Ubiquitination of an enzyme molecule apparently marks it for destruction by a large ATP-dependent pro-teolytic complex (26S proteasome) that specifically rec-ognizes the “tagged” molecule (Coux et al. 1996). More than 90% of the short-lived proteins in eukaryotic cells are degraded via the ubiquitin pathway (Lam 1997). The ubiquitin pathway regulates cytosolic protein turnover in plant cells as well (Shanklin et al. 1987). Gene Expression and Signal Transduction 11 Before it can take part in protein tagging, free ubiq-uitin must be activated (Figure 14.9). The enzyme E1 cat-alyzes the ATP-dependent adenylylation of the C ter-minus of ubiquitin. The adenylylated ubiquitin is then transferred to a second enzyme, called E2. Proteins des-tined for ubiquitination form complexes with a third protein, E3. Finally, the E2–ubiquitin conjugate is used to transfer ubiquitin to the lysine residues of proteins bound to E3. This process can occur multiple times to form a polymer of ubiquitin. The ubiquitinated protein is then targeted to the proteasome for degradation. As we shall see in Chapter 19, recent evidence suggests that CHAPTER 14 12 E1 E1 E2 E2 E3 AMP ATP + U U U U U U U U U U U U Target Target Degradation Target Ubiquitin activation 26S proteasome Figure 14.9 Diagram of the ubiquitin (U) pathway of pro-tein degradation in the cytosol. ATP is required for the ini-tial activation of E1. E1 tranfers ubiquitin to E2. E3 medi-ates the final transfer of ubiquitin to a target protein, which may be ubiquinated multiple times. The ubiquinated target protein is then degraded by the 26S proteasome.
EXTRACELLULAR SPACE NUCLEUS CYTOSOL Galactose Galactose Melibiose α-Galactosidase GAL3 protein GAL2 (transport enzyme) Inducer Glucose-1-phosphate MEL1 GAL1 GAL7 GAL10 GAL7 Chromosome XIII Chromosome XVI Chromosome II Chromosome XII Chromosome IV GAL80 Translation GAL80 protein Blocks GAL4 protein Removes GAL80 Activates GAL80 mRNA GAL4 GAL4 mRNA GAL7 GAL10 GAL1 MEL1 GAL2 GAL3 UAS Figure 14.8 Model for eukaryotic gene induction: the galactose metabolism pathway of the yeast Saccharomyces cerevisiae. Several enzymes involved in galactose transport and metabolism are induced by a metabolite of galactose.
The genes GAL7, GAL10, GAL1, and MEL1 are located on chromosome II; GAL2 is on chromosome XII; GAL3 is on chromosome IV. GAL4 and GAL80, located on two other chromosomes, encode positive and negative trans-acting regulatory proteins, respectively. The GAL4 protein binds to an upstream activating sequence located upstream of each of the genes in the pathway, indicated by the hatched lines. The GAL80 protein forms an inhibitory complex with the GAL4 protein. In the presence of galactose, the metabolite formed by the GAL3 gene product diffuses to the nucleus and stimulates transcription by causing dissoci-ation of the GAL80 protein from the complex. (After Darnell et al. 1990.) the regulation of gene expression by the phytohormone, auxin, may be mediated in part by the activation of the ubiquitin pathway.
Signal Transduction in Prokaryotes Prokaryotic cells could not have survived billions of years of evolution without an exquisitely developed ability to sense their environment. As we have seen, bac-teria respond to the presence of a nutrient by synthesiz-ing the proteins involved in the uptake and metabolism of that nutrient. Bacteria can also respond to nonnutri-ent signals, both physical and chemical. Motile bacteria can adjust their movements according to the prevailing gradients of light, oxygen, osmolarity, temperature, and toxic chemicals in the medium. The basic mechanisms that enable bacteria to sense and to respond to their environment are common to all cell sensory systems, and include stimulus detection, sig-nal amplification, and the appropriate output responses.
Many bacterial signaling pathways have been shown to consist of modular units called transmitters and receivers.
These modules form the basis of the so-called two-com-ponent regulatory systems. Bacteria Employ Two-Component Regulatory Systems to Sense Extracellular Signals Bacteria sense chemicals in the environment by means of a small family of cell surface receptors, each involved in the response to a defined group of chemicals (here-after referred to as ligands). A protein in the plasma membrane of bacteria binds directly to a ligand, or binds to a soluble protein that has already attached to the ligand, in the periplasmic space between the plasma membrane and the cell wall. Upon binding, the mem-brane protein undergoes a conformational change that is propagated across the membrane to the cytosolic domain of the receptor protein. This conformational change initiates the signaling pathway that leads to the response. A broad spectrum of responses in bacteria, including osmoregulation, chemotaxis, and sporulation, are regu-lated by two-component systems. Two-component reg-ulatory systems are composed of a sensor protein and a response regulator protein (Figure 14.10) (Parkinson 1993). The function of the sensor is to receive the signal and to pass the signal on to the response regulator, which brings about the cellular response, typically gene expression. Sensor proteins have two domains, an input domain, which receives the environmental signal, and a transmitter domain, which transmits the signal to the response regulator. The response regulator also has two domains, a receiver domain, which receives the signal from the transmitter domain of the sensor protein, and an output domain, such as a DNA-binding domain, which brings about the response. The signal is passed from transmitter domain to re-ceiver domain via protein phosphorylation. Transmitter domains have the ability to phosphorylate themselves, using ATP, on a specific histidine residue near the amino terminus (Figure 14.11A). For this reason, sensor proteins containing transmitter domains are called autophos-phorylating histidine kinases. These proteins normally Gene Expression and Signal Transduction 13 Sensor protein Response regulator Input signal Output signal Input Output Transmitter Receiver P + – Figure 14.10 Signaling via bacterial two-component sys-tems. The sensor protein detects the stimulus via the input domain and transfers the signal to the transmitter domain by means of a conformational change (indicated by the first dashed arrow). The transmitter domain of the sensor then communicates with the response regulator by protein phosphorylation of the receiver domain. Phosphorylation of the receiver domain induces a conformational change (second dashed arrow) that activates the output domain and brings about the cellular response. (After Parkinson 1993.) P R R H H Transmitter (T): (A) (B) Receiver (R): H Phosphorylation sites D T T Autophosphorylation Phosphorylation ATP ADP P D D Conformational change of response regulator ∫ ∫ Figure 14.11 Phosphorylation signaling mechanism of bac-terial two-component systems. (A) The transmitter domain of the sensor protein contains a conserved histidine (H) at its N-terminal end, while the receiver domain of the re-sponse regulator contains a conserved aspartate (D). (B) The transmitter phosphorylates itself at its conserved histidine and transfers the phosphate to the aspartate of the response regulator. The response regulator then under-goes a conformational change leading to the response.
(After Parkinson 1993.) function as dimers in which the catalytic site of one sub-unit phosphorylates the acceptor site on the other. Immediately after the transmitter domain becomes autophosphorylated on a histidine residue, the phos-phate is transferred to a specific aspartate residue near the middle of the receiver domain of the response regu-lator protein (see Figure 14.11A). As a result, a specific aspartate residue of the response regulator becomes phosphorylated (Figure 14.11B). Phosphorylation of the aspartate residue causes the response regulator to undergo a conformational change that results in its acti-vation. Osmolarity Is Detected by a Two-Component System An example of a relatively simple bacterial two-compo-nent system is the signaling system involved in sensing osmolarity in E. coli. E. coli is a Gram-negative bacterium and thus has two cell membranes, an inner membrane and an outer membrane, separated by a cell wall. The inner membrane is the primary permeability barrier of the cell. The outer membrane contains large pores com-posed of two types of porin proteins, OmpF and OmpC.
Pores made with OmpF are larger than those made with OmpC. When E. coli is subjected to high osmolarity in the medium, it synthesizes more OmpC than OmpF, result-ing in smaller pores on the outer membrane. These smaller pores filter out the solutes from the periplasmic space, shielding the inner membrane from the effects of the high solute concentration in the external medium.
When the bacterium is placed in a medium with low osmolarity, more OmpF is synthesized, and the average pore size increases. As Figure 14.12 shows, expression of the genes that encode the two porin proteins is regulated by a two-component system. The sensor protein, EnvZ, is located on the inner membrane. It consists of an N-terminal periplasmic input domain that detects the osmolarity changes in the medium, flanked by two membrane-spanning segments, and a C-terminal cytoplasmic trans-mitter domain. When the osmolarity of the medium increases, the input domain undergoes a conformational change that is transduced across the membrane to the transmitter domain. The transmitter then autophosphorylates its histidine residue. The phosphate is rapidly transferred to an aspartate residue of the receiver domain of the response regulator, OmpR. The N terminus of OmpR consists of a DNA-binding domain. When activated by phosphorylation, this domain interacts with RNA poly-merase at the promoters of the porin genes, enhancing the expression of ompC and repressing the expression of ompF. Under conditions of low osmolarity in the medium, the nonphosphorylated form of OmpR stimu-lates ompF expression and represses ompC expression. In this way the osmolarity stimulus is communicated to the genes. Related Two-Component Systems Have Been Identified in Eukaryotes Recently, combination sensor–response regulator pro-teins related to the bacterial two-component systems have been discovered in yeast and in plants. For exam-ple, The SLN1 gene of the yeast Saccharomyces cerevisiae encodes a 134-kilodalton protein that has sequence sim-ilarities to both the transmitter and the receiver domains of bacteria and appears to function in osmoregulation (Ota and Varshavsky 1993). There is increasing evidence that several plant sig-naling systems evolved from bacterial two-component systems. For example, the red/far-red–absorbing pig-ment, phytochrome, has now been demonstrated in CHAPTER 14 14 PERIPLASMIC SPACE CYTOPLASMIC MEMBRANE P ATP P P Medium osmolarity Control of porin expression High Low EnvZ OmpR DNA-binding domain Figure 14.12 E. coli two-component system for osmoregu-lation. When the osmolarity of the medium is high, the membrane sensor protein, EnvZ (in the form of a dimer), acts as an autophosphorylating histidine kinase. The phos-phorylated EnvZ then phosphorylates the response regula-tor, OmpR, which has a DNA-binding domain. Phosphory-lated OmpR binds to the promoters of the two porin genes, ompC and ompF, enhancing expression of the former and repressing expression of the latter. When the osmolarity of the medium is low, EnvZ acts as a protein phosphatase instead of a kinase and dephosphorylates OmpR. When the nonphosphorylated form of OmpR binds to the promoters of the two porin genes, ompC expression is repressed and ompF expression is stimulated. (From Parkinson 1993.) cyanobacteria, and it appears to be related to bacterial sensor proteins (see Chapter 17). In addition, the genes that encode putative receptors for two plant hormones, cytokinin and ethylene, both contain autophosphory-lating histidine kinase domains, as well as contiguous response regulator motifs. These proteins will be dis-cussed further in Chapters 21 and 22. Signal Transduction in Eukaryotes Many eukaryotic microorganisms use chemical signals in cell–cell communication. For example, in the slime mold Dictyostelium, starvation induces certain cells to secrete cyclic AMP (cAMP). The secreted cAMP diffuses across the substrate and induces nearby cells to aggre-gate into a sluglike colony. Yeast mating-type factors are another example of chemical communication between the cells of simple microorganisms. Around a billion years ago, however, cell signaling took a great leap in complexity when eukaryotic cells began to associate together as multicellular organisms. After the evolution of multicellularity came a trend toward ever-increasing cell specialization, as well as the development of tissues and organs to perform specific functions. Coordination of the development and environmental responses of complex multicellular organisms required an array of signaling mechanisms. Two main systems evolved in animals: the nervous system and the endo-crine system. Plants, lacking motility, never developed a nervous system, but they did evolve hormones as chem-ical messengers. As photosynthesizing organisms, plants also evolved mechanisms for adapting their growth and development to the amount and quality of light.
In the sections that follow we will explore some of the basic mechanisms of signal transduction in animals, emphasizing pathways that may have some parallel in plants. However, keep in mind that plant signal trans-duction pathways may differ in significant ways from those of animals. To illustrate this point, we end the chapter with an overview of some of the known plant-specific transmembrane receptors.
Two Classes of Signals Define Two Classes of Receptors Hormones fall into two classes based on their ability to move across the plasma membrane: lipophilic hormones, which diffuse readily across the hydrophobic bilayer of the plasma membrane; and water-soluble hormones, which are unable to enter the cell. Lipophilic hormones bind mainly to receptors in the cytoplasm or nucleus; water-soluble hormones bind to receptors located on the cell surface. In either case, ligand binding alters the receptor, typically by causing a conformational change. Some receptors, such as the steroid hormone recep-tors (see the next section), can regulate gene expression directly. In the vast majority of cases, however, the receptor initiates one or more sequences of biochemical reactions that connect the stimulus to a cellular response. Such a sequence of reactions is called a signal transduction pathway. Typically, the end result of sig-nal transduction pathways is to regulate transcription factors, which in turn regulate gene expression. Signal transduction pathways often involve the gen-eration of second messengers, transient secondary sig-nals inside the cell that greatly amplify the original sig-nal. For example, a single hormone molecule might lead to the activation of an enzyme that produces hundreds of molecules of a second messenger. Among the most common second messengers are 3′,5′-cyclic AMP (cAMP); 3′,5′-cyclic GMP (cGMP); nitric oxide (NO); cyclic ADP-ribose (cADPR); 1,2-diacylglycerol (DAG); inositol 1,4,5-trisphosphate (IP3); and Ca2+ (Figure 14.13).
Hormone binding normally causes elevated levels of one or more of these second messengers, resulting in the activation or inactivation of enzymes or regulatory pro-teins. Protein kinases and phosphatases are nearly always involved. Most Steroid Receptors Act as Transcription Factors The steroid hormones, thyroid hormones, retinoids, and vitamin D all pass freely across the plasma membrane because of their hydrophobic nature and they bind to intracellular receptor proteins. When activated by bind-ing to their ligand, these proteins function as transcrip-tion factors. All such steroid receptor proteins have sim-ilar DNA-binding domains. Steroid response elements are typically located in enhancer regions of steroid-stim-ulated genes. Most steroid receptors are localized in the nucleus, where they are anchored to nuclear proteins in an inactive form. When the receptor binds to the steroid, it is released from the anchor protein and becomes activated as a transcription factor. The activated transcription factor then binds to the enhancer and stimulates transcription.
The receptor for thyroid hormone deviates from this pattern in that it is already bound to the DNA but is unable to stimulate transcription in the absence of the hormone. Binding to the hormone converts the receptor to an active transcription factor. Not all intracellular steroid receptors are localized in the nucleus. The receptor for glucocorticoid hormone (cortisol) differs from the others in that it is located in the cytosol, anchored in an inactive state to a cytosolic protein. Binding of the hormone causes the release of the receptor from its cytosolic anchor, and the recep-tor–hormone complex then migrates into the nucleus, where it binds to the enhancer and stimulates tran-scription (Figure 14.14).
Although most studies on animal steroid hormones Gene Expression and Signal Transduction 15 have focused on their roles in regulating gene expres-sion via receptors that act as transcription factors, increasing evidence suggests that steroids can also inter-act with proteins on the cell surface (McEwen 1991). As will be discussed in Chapter 17, brassinosteroid has recently been demonstrated to be an authentic steroid hormone in plants, and the gene for a brassinosteroid receptor has recently been cloned and sequenced. It encodes a type of transmembrane receptor called a leucine-rich repeat receptor, which is described at the end of this chapter.
Cell Surface Receptors Can Interact with G Proteins All water-soluble mammalian hormones bind to cell surface receptors. Members of the largest class of mam-malian cell surface receptors interact with signal-trans-ducing, GTP-binding regulatory proteins called het-erotrimeric G proteins. The activated G proteins, in turn, activate an effector enzyme. The activated effector enzyme generates an intracellular second messenger, which stimulates a variety of cellular processes. Receptors using heterotrimeric G proteins are struc-turally similar and functionally diverse. Their overall structure is similar to that of bacteriorhodopsin, the pur-ple pigment involved in photosynthesis in bacteria of the genus Halobacterium, and to that of rhodopsin, the visual pigment of the vertebrate eye. The recently char-acterized olfactory receptors of the vertebrate nose also belong to this group. The receptor proteins consist of seven transmembrane a helices (Figure 14.15). These receptors are sometimes referred to as seven-spanning, seven-pass, or serpentine receptors. Heterotrimeric G Proteins Cycle between Active and Inactive Forms The G proteins that transduce the signals from the seven-spanning receptors are called heterotrimeric G pro-teins because they are composed of three different sub-units: α, β, and γ (gamma). They are distinct from the monomeric G proteins, which will be discussed later.
Heterotrimeric G proteins cycle between active and inactive forms, thus acting as molecular switches. The β and γ subunits form a tight complex that anchors the trimeric G protein to the membrane on the cytoplasmic side (Figure 14.16). The G protein becomes activated upon binding to the ligand-activated seven-spanning receptor. In its inactive form, G exists as a trimer with GDP bound to the α subunit. Binding to the receptor–ligand complex induces the α subunit to exchange GDP for GTP. This exchange causes the α sub-unit to dissociate from β and γ, allowing α to associate instead with an effector enzyme.
The α subunit has a GTPase activity that is activated when it binds to the effector enzyme, in this case adeny-lyl cyclase (also called adenylate cyclase) (see Figure 14.16). GTP is hydrolyzed to GDP, thereby inactivating the α subunit, which in turn inactivates adenylyl CHAPTER 14 16 N N N N O O P –O OH CH2 NH2 O O 3′,5′-Cyclic AMP 2′ 1′ 4′ 3′ 5′ N N N N O O OH CH2 NH2 3′,5′-Cyclic GMP 2′ 1′ 4′ 3′ 5′ O CH3 C (CH2)n CH2 O CH3 C (CH2)n O 1 CH 2 CH2OH 3 Fatty acyl groups Glycerol O O 1,2-Diacylglycerol Inositol 1,4,5-trisphosphate Calcium ion PO3 2– O OH OH HO 3 4 1 2 5 6 OPO3 2– OPO3 2– Ca2+ N O HO OH Cyclic ADP-Ribose (cADPR) H H H CH2 C N C H N HC N C C NH H O OH H H H HO H CH2 O O P O P HO O O HO N O Nitric oxide P –O O O Figure 14.13 Structure of seven eukaryotic second messengers. cyclase. The α subunit bound to GDP reassociates with the β and γ subunits and can then be reactivated by associating with the hormone–receptor complex. Activation of Adenylyl Cyclase Increases the Level of Cyclic AMP Cyclic AMP is an important signaling molecule in both prokaryotes and animal cells, and increasing evidence suggests that cAMP plays a similar role in plant cells.
In vertebrates, adenylyl cyclase is an integral mem-brane protein that contains two clusters of six mem-brane-spanning domains separating two catalytic domains that extend into the cytoplasm. Activation of adenylyl cyclase by heterotrimeric G proteins raises the concentration of cAMP in the cell, which is normally maintained at a low level by the action of cyclic AMP phosphodiesterase, which hydrolyzes cAMP to 5′-AMP.
Nearly all the effects of cAMP in animal cells are mediated by the enzyme protein kinase A (PKA). In unstimulated cells, PKA is in the inactive state because of the presence of a pair of inhibitory subunits. Cyclic AMP binds to these inhibitory subunits, causing them to dissociate from the two catalytic subunits, thereby activating the catalytic subunits. The activated catalytic subunits then are able to phosphorylate specific serine or threonine residues of selected proteins, which may also be protein kinases. An example of an enzyme that is phosphorylated by PKA is glycogen phosphorylase kinase. When phosphorylated by PKA, glycogen phos-phorylase kinase phosphorylates (activates) glycogen phosphorylase, the enzyme that breaks down glycogen in muscle cells to glucose-1-phosphate. In cells in which cAMP regulates gene expression, PKA phosphorylates a transcription factor called CREB (cyclic AMP response element–binding protein). Upon activation by PKA, CREB binds to the cAMP response element (CRE), which is located in the promoter regions of genes that are regulated by cAMP. In addition to activating PKA, cAMP can interact with specific cAMP-gated cation channels. For example, in olfactory receptor neurons, cAMP binds to and opens Na+ channels on the plasma membrane, resulting in Na+ influx and membrane depolarization.
Because of the extremely low levels of cyclic AMP that have been detected in plant tissue extracts, the role of cAMP in plant signal transduction has been highly controversial (Assmann 1995). Nevertheless, various lines of evidence supporting a role of cAMP in plant cells have accumulated. For example, genes that encode homologs of CREB have been identified in plants (Kate-giri et al. 1989). Pollen tube growth in lily has been shown to be stimulated by concentrations of cAMP as low as 10 nM (Tezuka et al. 1993). Li and colleagues (1994) showed that cAMP activates K+ channels in the plasma membrane of fava bean (Vicia faba) mesophyll cells. And Ichikawa and coworkers (1997) recently iden-tified possible genes for adenylyl cyclase in tobacco (Nicotiana tabacum) and Arabidopsis. Thus, despite years of doubt, the role of cAMP as a universal signaling agent in living organisms, including plants, seems likely.
Gene Expression and Signal Transduction 17 +++ EXTRACELLULAR SPACE CYTOSOL NUCLEUS Plasma membrane Steroid hormone +++ Receptor Inhibitory protein Hormone– receptor complex DNA-binding site Gene activation site Inhibitor Enhancer region mRNA +++ Coding region DNA 4 5 6 3 2 1 Figure 14.14 Glucocorticoid steroid receptors are transcrip-tion factors. (1) Glucocorticoid hormone is lipophilic and diffuses readily through the membrane to the cytosol. (2) Once in the cytosol, the hormone binds to its cytosolic receptor, (3) causing the release of an inhibitory protein from the receptor. (4) The activated receptor then diffuses into the nucleus. (5) In the nucleus, the receptor–hormone complex binds to the enhancer regions of steroid-regulated genes. (6) Transcription of the genes is stimulated. (From Becker et al. 1996.) Activation of Phospholipase C Initiates the IP3 Pathway Calcium serves as a second messenger for a wide vari-ety of cell signaling events. This role of calcium is well established in animal cells, and as we will see in later chapters, circumstantial evidence suggests a role for cal-cium in signal transduction in plants as well. The con-centration of free Ca2+ in the cytosol normally is main-tained at extremely low levels (1 × 10–7 M). Ca2+-ATPases on the plasma membrane and on the endo-plasmic reticulum pump calcium ions out of the cell and into the lumen of the ER, respectively. In plant cells, most of the calcium of the cell accumulates in the vac-uole. The proton electrochemical gradient across the vacuolar membrane that is generated by tonoplast pro-ton pumps drives calcium uptake via Ca2+–H+ anti-porters (see Chapter 6). In animal cells, certain hormones can induce a tran-sient rise in the cytosolic Ca2+ concentration to about 5 × 10–6 M. This increase may occur even in the absence of extracellular calcium, indicating that the Ca2+ is being released from intracellular compartments by the open-ing of intracellular calcium channels. However, the cou-pling of hormone binding to the opening of intracellu-lar calcium channels is mediated by yet another second messenger, inositol trisphosphate (IP3). Phosphatidylinositol (PI) is a minor phospholipid component of cell membranes (see Chapter 11). PI can be converted to the polyphosphoinositides PI phosphate (PIP) and PI bisphosphate (PIP2) by kinases (Figure 14.17). Although PIP2 is even less abundant in the mem-brane than PI is, it plays a central role in signal trans-duction. In animal cells, binding of a hormone, such as vasopressin, to its receptor leads to the activation of het-erotrimeric G proteins. The α subunit then dissociates from G and activates a phosphoinositide-specific phos-pholipase, phospholipase C (PLC). The activated PLC rapidly hydrolyzes PIP2, generating inositol trisphos-phate (IP3) and diacylglycerol (DAG) as products. Each of these two molecules plays an important role in cell signaling.
IP3 Opens Calcium Channels on the ER and on the Tonoplast The IP3 generated by the activated phospholipase C is water soluble and diffuses through the cytosol until it encounters IP3-binding sites on the ER and (in plants) on the tonoplast. These binding sites are IP3-gated Ca2+ channels that open when they bind IP3 (Figure 14.18).
Since these organelles maintain internal Ca2+ concen-trations in the millimolar range, calcium diffuses rapidly into the cytosol down a steep concentration gradient.
The response is terminated when IP3 is broken down by specific phosphatases or when the released calcium is pumped out of the cytoplasm by Ca2+-ATPases. Studies with Ca2+-sensitive fluorescent indicators, such as fura-2 and aequorin, have shown that the cal-cium signal often originates in a localized region of the cell and propagates as a wave throughout the cytosol.
Repeated waves called calcium oscillations can follow the original signal, each lasting from a few seconds to sev-eral minutes. The biological significance of calcium oscillation is still unclear, although it has been suggested that it is a mechanism for avoiding the toxicity that might result from a sustained elevation in cytosolic lev-els of free calcium. Such wavelike oscillations have recently been detected in plant stomatal guard cells (McAinsh et al. 1995). Cyclic ADP-Ribose Mediates Intracellular Ca2+ Release Independently of IP3 Signaling Cyclic ADP-Ribose (cADPR) acts as a second messenger CHAPTER 14 18 NH2 NH2 COOH COOH CYTOSOL EXTRACELLULAR SPACE Ligand-binding domain (A) (B) G protein– binding domains G protein– binding domains Plasma membrane Ligand-binding domains Figure 14.15 Schematic draw-ing of two types of seven-spanning receptors. (A) Large extracellular ligand-binding domains are characteristic of seven-spanning receptors that bind proteins. The region of the intracellular domain that interacts with the hetero-trimeric G protein is indicated.
(B) Small extracellular domains are characteristic of seven-spanning receptors that bind to small ligands such as epi-nephrine. The ligand-binding site is usually formed by sev-eral of the transmembrane helices within the bilayer.
(After Alberts et al. 1994.) that can release calcium from intracellular stores, inde-pendent of the IP3 signaling pathway. Like cAMP, cADPR is a cyclic nucleotide, but whereas cAMP brings about its effects by activating protein kinase A, cADPR binds to and activates specific calcium channels, called type-3 ryanodine receptors (ryanodine is a calcium channel blocker). These ryanodine receptor/calcium channels are located on the membranes of calcium-stor-ing organelles, such as sarcoplasmic reticulum of animal cells or the vacuoles of plant cells. By stimulating the release of calcium into the cytosol, cADPR helps to reg-ulate calcium oscillations that bring about physiological effects. Abscisic acid-induced stomatal closure is an example of the roles of cADPR and calcium oscillations in plants (see Chapter 23).
Some Protein Kinases Are Activated by Calcium–Calmodulin Complexes As we have seen with IP3-gated channels, calcium can activate some proteins, such as channels, by binding directly to them. However, most of the effects of calcium result from the binding of calcium to the regulatory pro-tein calmodulin (Figure 14.19). Calmodulin is a highly conserved protein that is abundant in all eukaryotic cells, but it appears to be absent from prokaryotic cells.
The same calcium-binding site is found in a wide vari-ety of calcium-binding proteins and is called an EF hand. The name is derived from the two α helices, E and F, that are part of the calcium-binding domain of the protein parvalbumin (Kretsinger 1980). Each calmodulin molecule binds four Ca2+ ions and changes conformation, enabling it to bind to and acti-vate other proteins. The Ca2+–calmodulin complex can stimulate some enzymes directly, such as the plasma membrane Ca2+-ATPase, which pumps calcium out of the cell. Most of the effects of calcium, however, are brought about by activation of Ca2+–calmodulin-depen-dent protein kinases (CaM kinases). CaM kinases phosphorylate serine or threonine residues of their tar-get enzymes, causing enzyme activation. Thus, the effect Gene Expression and Signal Transduction 19 GDP Receptor protein Hormone Heterotrimeric G protein Adenylyl cyclase R C γ β α R C γ β α R C γ β α R C γ β α R C γ β α R C γ β α Binding of hormone produces conformational change in receptor Binding of hormone produces conformational change in recepto 1 GDP Receptor binds to G protein GDP GDP GTP GDP bound to G protein is replaced by GTP, and subunits of G protein dissociate 3 GTP α Subunit binds to adenylyl cyclase, activating synthesis of cAMP; hormone tends to dissociate GTP GDP ATP cAMP + PPi EXTRACELLULAR SPACE CYTOSOL Plasma membrane Pi Hydrolysis of GTP to GDP causes α subunit to dissociate from adenylyl cyclase and bind to β–γ, regenerating a conformation of G protein that can be activated by a receptor– hormone complex 2 4 5 Figure 14.16 Hormone-induced activation of an effector enzyme is mediated by the α subunit of a heterotrimeric G protein. (1) Upon binding to its hormonal ligand, the seven-spanning receptor undergoes a conformational change. (2) The receptor binds to the heterotrimeric G protein. (3) Contact with the receptor induces the α subunit of the het-erotrimeric G protein to exchange GDP for GTP, and the α subunit then dissociates from the complex. (4) The G pro-tein α subunit associates with the effector protein (adenylyl cyclase) in the membrane, causing its activation. At the same time the hormone is released from its receptor. (5) The effector enzyme becomes inactivated when GTP is hydrolyzed to GDP. The α subunit then reassociates with the heterotrimeric G protein and is ready to be reactivated by a second hormonal stimulus. (From Lodish et al. 1995.) that calcium has on a particular cell depends to a large extent on which CaM kinases are expressed in that cell. Calcium signaling has been strongly implicated in many developmental processes in plants, ranging from the regulation of development by phytochrome (see Chapter 17) to the regulation of stomatal guard cells by abscisic acid (see Chapter 23). Thus far, however, there have been few reports of CaM kinase activity in plants.
Recently, however, a gene that codes for a CaM kinase has been cloned from lily and shown to be specifically expressed in anthers. The lily CaM kinase is a serine/threonine kinase that phosphorylates various protein substrates in vitro in a Ca2+–calmodulin-depen-dent manner (Takezawa et al. 1996). The occurrence and regulatory roles of such plant CaM kinases remain to be determined.
Plants Contain Calcium-Dependent Protein Kinases The most abundant calcium-regulated protein kinases in plants appear to be the calcium-dependent protein kinases (CDPKs) (Harper et al. 1991; Roberts and Har-mon 1992). CDPKs are strongly activated by calcium, but are insensitive to calmodulin. The proteins are char-acterized by two domains: a catalytic domain that is similar to those of the animal CaM kinases, and a calmodulin-like domain. The presence of a calmodulin-like domain may explain why the enzyme does not require calmodulin for activity. CDPKs are widespread in plants and are encoded by multigene families. A CDPK has also been identified in Chara, the giant freshwater green alga thought to be a precursor of land plants (McCurdy and Harmon 1992). In Chara the enzyme was shown to be associated with the actin microfilaments that line the outer cortex of the cytoplasm along the inner surface of the plasma mem-brane. The function of these microfilaments is to drive cytoplasmic streaming around the cell. The rate of cyto-plasmic streaming is inhibited by increases in cytosolic CHAPTER 14 20 Phosphatidylinositol (Pl) Pl 4-phosphate (PIP) Pl 4,5-bisphosphate (PIP2) P O– O O– O CH2 CH2 CH P O O O –O OH OH HO O O C C O O P O– O– O P O– O– O CH2 CH2 CH OH O O C C O O CH2 CH2 CH P O O O –O OH OH HO O O C C O O 3 4 1 2 5 6 OH OH OH Inositol O CH2 CH2 CH P O O O –O OH OH HO O O C C O O P O O– O– O Activates protein kinase C Releases Ca2+ from the endoplasmic reticulum and vacuole ADP PI kinase ATP ADP PIP kinase ATP Phospholipase C (PLC) Diacylglycerol (DAG) Inositol 1,4,5-trisphosphate (IP3) O P O O O –O OH OH HO P O O O– O CYTOSOL Fatty acid chains of outer lipid monolayer of plasma membrane Fatty acid chains of inner lipid monolayer of plasma membrane Figure 14.17 Phospholipase C pathway of membrane hydrolysis. The rare phospholipid phosphatidylinositol (PI) is the starting point for the pathway.
The phosphoinositol head group of PI is phosphorylated twice, producing first PI 4-phosphate (PIP) and then PI 4,5-bisphosphate (PIP2). PIP2 is then hydrolyzed by phospholipase C to diacylglycerol (DAG) and inositol 1,4,5-trisphosphate (IP3). (After Alberts et al. 1994.) Gene Expression and Signal Transduction 21 Cellular response EXTRACELLULAR SPACE CYTOSOL Hormone Receptor G protein Phospholipase C Gβγ Gα P P P P P Protein (inactive) Cellular response Protein kinase C DAG PIP2 IP3 Protein (active) Ca2+ IP3-sensitive Ca2+ channel Endoplasmic reticulum or vacuole P P Plasma membrane Ca2+ Bound IP3 Figure 14.18 Summary diagram of the events in the inositol–lipid signal trans-duction pathway coupled to seven-spanning G protein–linked receptors.
The binding of hormone to its receptor triggers activation of the α subunit of the heterotrimeric G protein, which activates the effector enzyme phos-pholipase C (PLC). PLC cleaves PIP2 in the membrane to yield IP3 and DAG.
IP3 diffuses into the cytosol and binds to IP3-gated calcium channels on the ER or vacuolar membrane, causing the release of calcium into the cytosol from intracellular stores. The increase in cytosolic calcium concentration leads to a cellular response. DAG remains in the membrane and activates protein kinase C. The activated protein kinase C then phosphorylates other proteins, leading to a cellular response. In ani-mal cells the inositol–lipid pathway may also be coupled to receptor tyro-sine kinases. (From Lodish et al. 1995.) COOH COOH COOH 2 nm HOOC NH2 H2N Ca2+ H2N H2N (A) (B) Figure 14.19 Structure of calmodulin. (A) Calmodulin con-sists of two globular ends separated by a flexible α helix.
Each globular end has two calcium-binding sites. (B) When the calcium–calmodulin complex associates with a protein, it literally wraps around it. (From Alberts et al. 1994.) calcium, and it has been proposed that CDPKs mediate the effects of calcium by phosphorylating the heavy chain of myosin, a component of the microfilaments (McCurdy and Harmon 1992).
CDPKs may also mediate the effects of calcium in guard cells. Abscisic acid–induced stomatal closure involves calcium as a second messenger (see Chapter 23). Recent studies using isolated vacuoles from guard cells of Vicia faba (fava bean) suggest that CDPKs can regulate anion channels on the tonoplast (Pei et al. 1996).
Thus, CDPKs may be a component of the abscisic acid signaling pathway.
Diacylglycerol Activates Protein Kinase C Cleavage of PIP2 by phospholipase C produces diacyl-gycerol (DAG) in addition to IP3 (see Figure 14.17).
Whereas IP3 is hydrophilic and diffuses rapidly into the cytoplasm, DAG is a lipid and remains in the mem-brane. In animal cells, DAG can associate with and acti-vate the serine/threonine kinase protein kinase C (PKC). The inactive form of PKC is a soluble enzyme that is located in the cytosol. Upon binding to calcium, the soluble, inactive PKC undergoes a conformational change and associates with a PKC receptor protein that transports it to the inner surface of the plasma mem-brane, where it encounters DAG.
PKCs have been shown to phosphorylate ion chan-nels, transcription factors, and enzymes in animal cells.
One of the enzymes phosphorylated by PKC is another protein kinase that regulates cell proliferation and dif-ferentiation, MAP kinase kinase kinase (discussed later in the chapter). G proteins, phospholipase C, and various protein kinases have been identified in plant mem-branes (Millner and Causier 1996). PKC activity has also been detected in plants (Elliott and Kokke 1987; Chen et al. 1996), and a plant gene encoding the PKC receptor protein that transports the soluble enzyme to the mem-brane has recently been cloned (Kwak et al. 1997). How-ever, there is as yet no evidence that activation of PKC by DAG plays a role in plant signal transduction. Phospholipase A2 Generates Other Membrane-Derived Signaling Agents In animals, the endocrine system is involved in signal-ing between hormone-producing cells at one location of the body and hormone-responding cells at another loca-tion; in contrast, the autocrine system involves cells sending signals to themselves and their immediate neighbors. One type of autocrine signaling system that plays important roles in pain and inflammatory re-sponses, as well as platelet aggregation and smooth-muscle contraction, is called the eicosanoid pathway. There are four major classes of eicosanoids: prostaglandins, prostacyclins, thromboxanes, and leuko-CHAPTER 14 22 OH COOH COOH O COOH C CH OH Oxidation steps O O P O X O O O– C CH2 O O CH2 Phospholipase A2 Membrane phospholipid Arachidonic acid (20 carbons), extended conformation Arachidonic acid, folded conformation Prostaglandin (A) (B) Arachidonic acid Cyclooxygenase-dependent pathway Lipoxygenase-dependent pathway Prostaglandins Prostacyclins Thromboxanes Leukotrienes Figure 14.20 Eicosanoid biosynthetic pathway. (A) The first step is the hydrolysis of 20-carbon fatty acid chains contain-ing at least three double bonds from a membrane phos-pholipid by the enzyme phospholipase A2, producing arachidonic acid, which can be oxidized by prostaglandin.
(B) Arachidonic acid is further metabolized by two path-ways: one cyclooxygenase dependent, the other lipoxyge-nase dependent. (From Alberts et al. 1994.) trienes. All are derived from the breakdown of mem-brane phospholipids, and in this respect the eicosanoid pathway resembles the IP3 pathway. There the resem-blance ends, however. For whereas the IP3 pathway begins with the cleavage of IP3 from PIP2 by phospholi-pase C, the eicosanoid pathway is initiated by the cleav-age of the 20-carbon fatty acid arachidonic acid from the intact phospholipid by the enzyme phospholipase A2 (PLA2) (Figure 14.20A). Two oxidative pathways—one cyclooxygenase dependent, the other lipoxygenase dependent—then convert arachidonic acid to the four eicosanoids (Figure 14.20B). As we will see in Chapter 19, there is some indirect evidence for the possible involvement of prostaglandins in the regulation of the plant cell cycle, although direct evidence is lacking.
Higher plants generally have negligible amounts of arachidonic acid in their membranes, although the level is higher in certain mosses.
In addition to generating arachidonic acid, PLA2 pro-duces lysophosphatidylcholine (LPC) as a breakdown product of phosphatidylcholine. LPC has detergent properties, and it has been shown to regulate ion chan-nels through its effects on protein kinases. For example, LPC has been shown to modulate the sodium currents in cardiac-muscle cells by signal transduction pathways that involve the activation of both protein kinase C and a tyrosine kinase (Watson and Gold 1997). Protein kinase C is activated by LPC independently of the phos-pholipase C pathway. In recent years plant biologists have become increas-ingly interested in the eicosanoid pathway because it now appears that an important signaling agent in plant defense responses, jasmonic acid, is produced by a sim-ilar pathway, which was described in Chapter 13. In addition, LPC has been shown to activate plant protein kinases in vitro. As we will see in Chapter 19, LPC is one of many candidates for a second messenger in the rapid responses of plant cells to auxin.
In Vertebrate Vision, a Heterotrimeric G Protein Activates Cyclic GMP Phosphodiesterase The human eye contains two types of photoreceptor cells: rods and cones. Rods are responsible for mono-chromatic vision in dim light; cones are involved in color vision in bright light. Signal transduction in response to light has been studied more intensively in rods. The rod is a highly specialized tubular cell that contains an elongated stack of densely packed mem-brane sacs called discs at the tip, or outer segment, reminiscent of the grana stacks of chloroplasts. The disc membranes of rod cells contain the photosensitive pro-tein pigment rhodopsin, a member of the seven-span-ning transmembrane family of receptors. Rhodopsin consists of the protein opsin covalently bound to the light-absorbing molecule 11-cis-retinal. When 11-cis-reti-nal absorbs a single photon of light (400 to 600 nm) it immediately isomerizes to all-trans-retinal (Figure 14.21). This change causes a slower conformational change in the protein, converting it to meta-rhodopsin II, or activated opsin. Gene Expression and Signal Transduction 23 CH3 CH3 CH3 C O H H3C H3C (CH2)4 + H2N + H2O C R H H N+ (CH2)4 CH3 CH3 CH3 H3C CH3 1 4 2 3 6 8 10 11 12 13 14 15 7 9 5 cis double bond Lysine side chain on opsin cis-Retinal moiety trans-Retinal portion of rhodopsin trans double bond 11-cis-Retinal Opsin Rhodopsin Opsin Opsin C N Opsin 15 Meta-rhodopsin II (activated opsin) Transducin (CH2)4 Light-induced isomerization H+ Figure 14.21 Transduction of the light sig-nal in vertebrate vision. The photoreceptor pigment is rhodopsin, a transmembrane protein composed of the protein opsin and the chromophore 11-cis-retinal. Light absorption causes the rapid isomerization of cis-retinal to trans-retinal. The formation of trans-retinal then causes a conforma-tional change in the protein opsin, forming meta-rhodopsin II, the activated form of opsin. The activated opsin then interacts with the heterotrimeric G protein trans-ducin. (After Lodish et al. 1995.) Activated opsin, in turn, lowers the concentration of the cyclic nucleotide 3′5′-cGMP. Cyclic GMP is synthe-sized from GTP by the enzyme guanylate cyclase. In the dark, guanylate cyclase activity results in the buildup of a high concentration of cGMP in the rod cells. Because the plasma membrane contains cGMP-gated Na+ chan-nels, the high cGMP concentration in the cytosol main-tains the Na+ channels in the open position in the absence of light. When the Na+ channels are open, Na+ can enter the cell freely, and this passage of Na+ tends to depolarize the membrane potential.
When opsin becomes activated by light, however, it binds to the heterotrimeric G protein transducin. This binding causes the α subunit of transducin to exchange GDP for GTP and dissociate from the complex. The α subunit of transducin then activates the enzyme cyclic GMP phosphodiesterase, which breaks down 3′5′-cGMP to 5′-GMP (Figure 14.22). Light therefore has the effect of decreasing the concentration of cGMP in the rod cell.
A lower concentration of cGMP has the effect of closing the cGMP-gated Na+ channels on the plasma mem-brane, which are kept open in the dark by a high cGMP concentration. To give some idea of the signal amplifi-cation provided, a single photon may cause the closure of hundreds of Na+ channels, blocking the uptake of about 10 million Na+ ions. By preventing the influx of Na+, which tends to depolarize the membrane, the membrane polarity increases—that is, becomes hyperpolarized. In this way a light signal is converted into an electric signal. Mem-brane hyperpolarization, in turn, inhibits neurotrans-mitter release from the synaptic body of the rod cell.
Paradoxically, the nervous system detects light as an inhibition rather than a stimulation of neurotransmitter release. Cyclic GMP, which regulates ion channels and pro-tein kinases in animal cells, appears to be an important regulatory molecule in plant cells as well. Cyclic GMP has been definitively identified in plant extracts by gas chromatography combined with mass spectrometry (Janistyn 1983; Newton and Brown 1992). Moreover, cGMP has been implicated as a second messenger in the responses of phytochrome (see Chapter 17) and gib-berellin (see Chapter 20).
Nitric Oxide Gas Stimulates the Synthesis of cGMP The level of 3′,5′-cyclic GMP in cells is controlled by the balance between the rate of cGMP synthesis by the enzyme, guanylyl (or guanylate) cyclase, and the rate of cGMP degradation by the enzyme cGMP phosphodi-esterase. We have seen how light activation of rhodopsin leads to the activation of cGMP phosphodi-esterase in vertebrate rod cells, resulting in a reduction in cGMP. In smooth muscle tissue of animal cells, cGMP levels can be increased via the direct activation of guanylyl cyclase by the signaling intermediate, nitric CHAPTER 14 24 Depolarization of plasma membrane Opens Na+ channels Increase in cytosolic Ca2+ Hyperpolarization of plasma membrane Decrease in cytosolic Ca2+ Opens Ca2+ channels Closes Na+ channels Closes Ca2+ channels cGMP (active) GTP Stimulates 5′-GMP (inactive) Guanylate cyclase cGMP phosphodiesterase (active) Activated transducin High Ca2+ inhibits Low Ca2+ stimulates Ca2+-sensing protein Figure 14.22 The role of cyclic GMP (cGMP) and calcium as second messengers in vertebrate vision. Activation of the heterotrimeric G protein transducin by activated opsin causes the activation of cGMP phosphodiesterase, which lowers the concentration of cGMP in the cell. The reduction in cGMP closes cGMP-activated Na+ channels. Closure of the Na+ channels blocks the influx of Na+, causing membrane hyperpolarization. Cyclic GMP also regulates calcium chan-nels. When the cGMP concentration in the cell is high, the calcium channels open, raising the cytosolic calcium concen-tration. Guanylate cyclase, the enzyme that synthesizes cGMP from GTP, is inhibited by high levels of calcium.
Conversely, when cGMP levels are low, closure of calcium channels lowers the cytosolic calcium concentration. This lowering of the calcium concentration stimulates guanylate cyclase. Calcium thus provides a feedback system for regu-lating cGMP levels in the cell.
oxide (NO). NO is synthesized from arginine by the enzyme, NO synthase, in a reaction involving oxygen: NO synthase Arginine + O2→Citrulline + NO Once produced in animal endothelial cells, dissolved NO passes rapidly across membranes and acts locally on neighboring smooth muscle cells, with a half-life of 5–10 seconds. Guanylyl cyclase contains a heme group that binds NO tightly, and binding of NO causes a con-formational change which activates the enzyme. The NO-induced increase in cGMP causes smooth muscle cells to relax. Nitroglycerine, which can be metabolized to yield NO, has long been administered to heart patients to prevent the coronary artery spasms respon-sible for variant angina. In plants, NO has recently been implicated as an intermediate in ABA-induced stomatal closure (see Chapter 23).
Cell Surface Receptors May Have Catalytic Activity Some cell surface receptors are enzymes themselves or are directly associated with enzymes. Unlike the seven-spanning receptors, the catalytic receptors, as these enzyme or enzyme-associated receptors are called, are typically attached to the membrane via a single trans-membrane helix and do not interact with heterotrimeric G proteins. The six main categories of catalytic receptors in animals include: (1) receptor tyrosine kinases, (2) receptor tyrosine phosphatases, (3) receptor serine/thre-onine kinases, (4) tyrosine kinase–linked receptors, (5) receptor guanylate cyclases, and (6) cell surface pro-teases. Of these, the receptor tyrosine kinases are prob-ably the most abundant in animal cells. Thus far, no receptor tyrosine kinases (RTKs) have been identified in plants. However, plant cells do con-tain a class of receptors called receptorlike kinases (RLKs) that are structurally similar to the animal RTKs.
In addition, some of the components of the RTK signal-ing pathway of animals have been identified in plants.
After first reviewing the animal RTK pathway, we will examine the RLK receptors of plants. Ligand Binding to Receptor Tyrosine Kinases Induces Autophosphorylation The receptor tyrosine kinases (RTKs) make up the most important class of enzyme-linked cell surface receptors in animal cells, although so far they have not been found in either plants or fungi. Their ligands are soluble or membrane-bound peptide or protein hormones, including insulin, epidermal growth factor (EGF), platelet-derived growth factor (PDGF), and several other protein growth factors.
Since the transmembrane domain that separates the hormone-binding site on the outer surface of the mem-brane from the catalytic site on the cytoplasmic surface consists of only a single α helix, the hormone cannot transmit a signal directly to the cytosolic side of the membrane via a conformational change. Rather, bind-ing of the ligand to its receptor induces dimerization of adjacent receptors, which allows the two catalytic domains to come into contact and phosphorylate each other on multiple tyrosine residues (autophosphoryla-tion) (Figure 14.23). Dimerization may be a general mechanism for activating cell surface receptors that con-tain single transmembrane domains. Intracellular Signaling Proteins That Bind to RTKs Are Activated by Phosphorylation Once autophosphorylated, the catalytic site of the RTKs binds to a variety of cytosolic signaling proteins. After binding to the RTK, the inactive signaling protein is itself phosphorylated on specific tyrosine residues. Some tran-scription factors are activated in this way, after which they migrate to the nucleus and stimulate gene expres-sion directly. Other signaling molecules take part in a sig-naling cascade that ultimately results in the activation of transcription factors. The signaling cascade initiated by RTKs begins with the small, monomeric G protein Ras. The Ras superfamily.
In addition to possessing het-erotrimeric G proteins, eukaryotic cells contain small monomeric G proteins that are related to the α sub-units of the heterotrimeric G proteins. The three fami-lies, Ras, Rab, and Rho/Rac, all belong to the Ras superfamily of monomeric GTPases. Rho and Rac relay signals from surface receptors to the actin cyto-skeleton; members of the Rab family of GTPases are involved in regulating intracellular membrane vesicle traffic; the Ras proteins, which are located on the inner surface of the membrane, play a crucial role in initiat-ing the kinase cascade that relays signals from RTKs to the nucleus. The RAS gene was originally discovered as a viral oncogene (cancer-causing gene) and was later shown to be present as a normal gene in animal cells. Ras is a G protein that cycles between an inactive GDP-binding form and an active GTP-binding form. Ras also pos-sesses GTPase activity that hydrolyzes bound GTP to GDP, thus terminating the response. The RAS oncogene is a mutant form of the protein that is unable to hydrolyze GTP . As a result, the molecular switch remains in the on position, triggering uncontrolled cell division.
The study of small GTP-binding proteins in plants is still in its infancy. Thus far, about 30 genes encoding members of monomeric G protein families have been cloned, including homologs of RAB and RHO. Surpris-ingly, RAS itself has so far not yet been identified in plants (Terryn et al. 1996). Ras Recruits Raf to the Plasma Membrane The initial steps in the Ras signaling pathway are illus-Gene Expression and Signal Transduction 25 trated in Figure 14.23. First, binding of the hormone to the RTK induces dimerization followed by autophos-phorylation of the catalytic domain. Autophosphoryla-tion of the receptor causes binding to the Grb2 protein, which is tightly associated with another protein, called Sos. As a result, the Grb2–Sos complex attaches to the RTK at the phosphorylation site. The Sos protein then binds to the inactive form of Ras, which is associated with the inner surface of the plasma membrane. Upon binding to Sos, Ras releases GDP and binds GTP instead, which converts Ras to the active form. The acti-vated Ras, in turn, provides a binding site for the solu-ble serine/threonine kinase Raf. The primary function of the activated Ras is thus to recruit Raf to the plasma membrane. Binding to Ras activates Raf and initiates a chain of phosphorylation reactions called the MAPK cascade (see the next section). As we will see in later chapters, increasing evidence suggests that plant signaling pathways also employ the MAPK cascade. For example, the ethylene receptor, ETR1, probably passes its signal to CTR1, a protein kinase of the Raf family (see Chapter 22). The Activated MAP Kinase Enters the Nucleus The MAPK (mitogen-activated protein kinase) cascade owes its name to a series of protein kinases that phos-phorylate each other in a specific sequence, much like runners in a relay race passing a baton (Figure 14.24).
The first kinase in the sequence is Raf, referred to in this context as MAP kinase kinase kinase (MAPKKK).
MAPKKK passes the phosphate baton to MAP kinase kinase (MAPKK), which hands it off to MAP kinase (MAPK). MAPK, the “anchor” of the relay team, enters the nucleus, where it activates still other protein kinases, specific transcription factors, and regulatory proteins. The transcription factors that are activated by MAPK are called serum response factors (SRFs) because all of the growth factors that bind to RTKs are transported in the serum. Serum response factors bind to specific nucleotide sequences on the genes they regulate called serum response elements (SREs). The entire process from binding of the growth factor to the receptor to tran-scriptional activation of gene expression can be very rapid, taking place in a few minutes. Some of the genes that are activated encode other transcription factors that regulate the expression of other genes. Because these genes are important for cell prolif-eration and growth, many of them are proto-oncogenes.
For example, one of the genes whose expression is stim-ulated by MAPK is the proto-oncogene FOS. A proto-oncogene is a normal gene that potentially can cause malignant tumors when mutated. When the Fos protein combines with the phosphorylated Jun protein (one of the nuclear proteins that is phosphorylated by MAPK), it forms a heterodimeric transcription factor called AP-1, which turns on other genes. Other important proto-oncogenes that encode nuclear transcription factors include MYC and MYB. Both phytochrome (see Chap-CHAPTER 14 26 P P P P P P P P P Sos Grb2 Ras GTP Raf Grb2 Phosphotyrosines P Sos Ras GTP Extracellular domain Ligand Cytosolic domain Transmembrane domain Kinase catalytic site CYTOSOL Ligand binding Ligand-binding site Receptor dimerization Autophosphory-lation on tyrosines Active Ras P P P P P P Raf binds to activated Ras Grb2–Sos associates with activated RTK and activates Ras P P P ATP ADP ATP ADP P EXTRACELLULAR SPACE Figure 14.23 Hormone-induced activation of receptor tyrosine kinases. Binding of the hormone to the monomeric receptors induces receptor dimerization.
Dimerization leads to autophosphorylation of the cytosolic domains at multiple tyrosine residues. The phosphorylated cytoplasmic domains then serve as bind-ing sites for various regulatory proteins. Among these are the Grb2–Sos het-erodimer. When Grb2–Sos associates with the activated RTK, the Sos polypep-tide binds to the small monomeric G protein Ras, which is bound to the inner surface of the plasma membrane. Binding of Grb2–Sos to Ras induces Ras to exchange GTP for GDP, and Ras becomes active. The activated Ras then acts as a binding site for the protein kinase Raf. Once localized at the plasma membrane, Raf triggers a series of phosphorylation reactions called the MAP kinase cascade (see Figure 14.24). (After Lodish et al. 1995 and Karp 1996.) ter 17) and gibberellin (see Chapter 20) are believed to regulate gene expression via the up-regulation of MYB-like transcription factors.
Plant Receptorlike Kinases Are Structurally Similar to Animal Receptor Tyrosine Kinases Because of the recent progress in sequencing the genomes of plants such as Arabidopsis and rice, it is pos-sible to use computers to search for DNA nucleotide sequences that correspond to the amino acid sequences of proteins identified in other organisms. Such database searches of plant DNA sequences have successfully iden-tified a large family of receptorlike protein kinases (RLKs) by homology to animal receptor tyrosine kinases.
These plant RLKs are structurally similar to the animal RTKs. They have a large extracellular domain, span the membrane only once, and contain a catalytic domain on the cytoplasmic side. Although they resemble the RTKs in their general structure, they differ in catalytic activity.
Whereas RTKs of animals are autophosphorylating tyro-sine kinases, the plant RLKs are autophosphorylating serine/threonine kinases (Walker 1994).
Three types of RLKs have been identified in plants, primarily on the basis of their extracellular domains.
The first class is characterized by an extracellular S domain and is called S receptor kinase or SRK. The S domain was first identified in a group of secreted gly-coproteins, called S locus glycoproteins (SLGs), which regulate self-incompatibility in Brassica species. Self-incompatibility is characterized by the failure of pollen tubes to grow when placed on pistils from the same plant, and self-incompatibility loci are genes that regu-late this phenotype. The S domain consists of ten cysteines in a particular arrangement with other amino acids. The high degree of homology between the S domains of SRKs and those of SLGs suggests that they are functionally related and are involved in the recognition pathways involved in pollen tube growth. Consistent with this idea, SRK genes are expressed predominantly in pistils. Several other S domain RLKs with highly divergent sequences have been identified in other species, and each of these may play unique roles in plant cell signaling. The leucine-rich repeat (LRR) family of receptors constitute the second group of RLKs. They were first identified as disease resistance genes that may play key roles in the cell surface recognition of ligands produced by pathogens and the subsequent activation of the intra-cellular defense response (Bent 1996; Song et al. 1995).
However, plant LRR receptors have been implicated in normal developmental functions as well. For example, a pollen-specific LRR receptor has been identified in sunflower that may be involved in cell–cell recognition during pollination (Reddy et al. 1995), and the Ara-bidopsis ERECTA gene, which regulates the shape and size of organs originating from the shoot apical meris-tem, encodes an LRR receptor (Torii et al. 1996). More recently, the receptor for the plant steroid hormone brassinosteroid has been identified as an LRR receptor (see Web Topic 19.14). The LRR receptors are members of a larger family of LRR proteins that includes soluble forms with lower molecular mass that are widespread in plants and ani-mals. The most conserved element of the LRR domain forms a β sheet with an exposed face that participates in protein–protein interactions (Buchanan and Gay 1996).
Gene Expression and Signal Transduction 27 P P P TF MAPK MAPKK TF MAPK MAPKK MAPKKK (Raf) P P P P Ras-GTP Ras-GDP RTK RTK Transcription Nucleus Gene Cytoplasm Grb2 + Sos Growth factor Binding of growth factor activates RTK Ras binds GTP and is activated MAPKKK (Raf) phosphorylates MAP kinase kinase (MAPKK) MAPKK phosphorylates MAP kinase (MAPK) The activated MAPK enters the nucleus and activates transcription factors The activated transcription factors stimulate gene expression Figure 14.24 The MAPK cascade. Hormonal stimulation of the receptor tyrosine kinase leads to the activation of Raf (see Figure 14.23), also known as MAP kinase kinase kinase (MAPKKK). (1) MAPKKK phosphorylates MAP kinase kinase (MAPKK). (2) MAPKK phosphorylates MAP kinase (MAPK).
(3) The activated MAPK enters the nucleus. and activates transcription factors (TF). (4) The activated transcription fac-tors stimulate gene expression. (After Karp 1996.) The small soluble LRR proteins may participate in cell signaling by hydrophobic binding to LRR receptors. For example, in tomato a protein that contains four tandem repeats of a canonical 24-amino-acid leucine-rich repeat motif is up-regulated during virus infection. This pro-tein is apparently secreted into the apoplast along with a protease that digests it to lower molecular weight pep-tides (Tornero et al. 1996). These peptides could form part of a signaling pathway by interacting with cell sur-face LRR receptors.
Finally, a third type of RLK that contains an epider-mal growth factor–like repeat has been identified in Ara-bidopsis. Interestingly, the receptor, called PRO25, is localized in the chloroplast and interacts with a light-harvesting chlorophyll a/b–binding protein (LHCP) (Walker 1994). Little or nothing is known about signal-ing within plastids, which undoubtedly will be an important area for future research. Summary The size of the genome (the total amount of DNA in a cell, a nucleus, or an organelle) is related to the com-plexity of the organism. However, not all of the DNA in a genome codes for genes. Prokaryotic genomes consist mainly of unique sequences (genes). Much of the genome in eukaryotes, however, consists of repetitive DNA and spacer DNA. The genome size in plants is highly variable, ranging from 1.5 × 108 bp in Arabidopsis to 1 × 1011 bp in Trillium. Plant genomes contain about 25,000 genes; by comparison, the Drosophila genome contains about 12,000 genes. In prokaryotes, structural genes involved in related functions are organized into operons, such as the lac operon. Regulatory genes encode DNA-binding pro-teins that may repress or activate transcription. In inducible systems, the regulatory proteins are them-selves activated or inactivated by binding to small effec-tor molecules. Similar control systems are present in eukaryotic genomes. However, related genes are not clustered in operons, and genes are subdivided into exons and introns. Pre-mRNA transcripts must be processed by splicing, capping, and addition of poly-A tails to pro-duce the mature mRNA, and the mature mRNA must then exit the nucleus to initiate translation in the cytosol.
Despite these differences, most eukaryotic genes are reg-ulated at the level of transcription, as in prokaryotes.
Transcription in eukaryotes is characterized by three different RNA polymerases whose activities are modu-lated by a diverse group of cis-acting regulatory sequences. RNA polymerase II is responsible for the synthesis of pre-mRNA. General transcription factors assemble into a transcription initiation complex at the TATA box of the minimum promoter, which lies within 100 bp of the transcription start site of the gene. Addi-tional cis-acting regulatory sequences, such as the CAAT box and GC box, bind transcription factors that enhance expression of the gene. Distal regulatory sequences located farther upstream bind to other transcription fac-tors called activators or repressors. Many plant genes are also regulated by enhancers, distantly located posi-tive regulatory sequences. Despite being scattered throughout the genome, many eukaryotic genes are both inducible and coregu-lated. Genes that are coordinately regulated have com-mon cis-acting regulatory sequences in their promoters.
Most transcription factors in plants contain the basic zip-per (bZIP) motif. An important group of transcription factors in plants, the floral homeotic genes, contain the MADS domain. Enzyme concentration is also regulated by protein degradation, or turnover. As yet there is no evidence that plant vacuoles function like animal lysosomes in protein turnover, except during senescence, when the contents of the vacuole are released. However, protein turnover via the covalent attachment of the short polypeptide ubiquitin and subsequent proteolysis is an important mechanism for regulating the cytosolic pro-tein concentration in plants.
Signal transduction pathways coordinate gene expres-sion with environmental conditions and with develop-ment. Prokaryotes employ two-component regulatory systems that include a sensor protein and a response reg-ulator protein that facilitates the response, typically gene expression. The sensor and the response regulator com-municate via protein phosphorylation. Receptor proteins related to the bacterial two-component systems have recently been identified in yeast and plants.
In multicellular eukaryotes, lipophilic hormones usu-ally bind to intracellular receptors, while water-soluble hormones bind to cell surface receptors. Binding to a receptor initiates a signal transduction pathway, often involving the generation of second messengers, such as cyclic nucleotides, inositol trisphosphate, and calcium, which greatly amplify the original signal and bring about the cellular response. Such pathways normally lead to changes in gene expression. In plants, the recep-tor for the phytohormone brassinosteroid is a cell sur-face receptor. The seven-spanning receptors of animal cells interact with heterotrimeric G proteins, which act as molecular switches by cycling between active (GTP-binding) forms and inactive (GDP-binding) forms. Dissociation of the α subunit from the complex allows it to activate the effec-tor enzyme. Activation of adenylyl cyclase increases cAMP levels, resulting in the activation of protein kinase A. Cyclic AMP can also regulate cation channels directly. When heterotrimeric G proteins activate phospholi-pase C, it initiates the IP3 pathway. IP3 released from the CHAPTER 14 28 membrane opens intracellular calcium channels, releas-ing calcium from the ER and vacuole into the cytosol.
The increase in calcium concentration, in turn, activates protein kinases and other enzymes. In plants, calcium dependent protein kinases, which have a calmodulin domain, are activated by calcium directly. The other by-product of phospholipase C, diacylglycerol, can also act as a second messenger by activating protein kinase C.
There is increasing evidence that cyclic GMP operates as a second messenger in plant cells as it does in animal cells. In animal cells, cyclic GMP has been shown to reg-ulate ion channels and protein kinases.
The most common family of cell surface catalytic receptors in animals consists of the receptor tyrosine kinases. RTKs dimerize upon binding to the hormone; then their multiple tyrosine residues are autophospho-rylated. The phosphorylated receptor then acts as an assembly site for various protein complexes, including the Ras superfamily of monomeric GTPases. Binding of Ras leads to recruitment of the protein kinase Raf to the membrane. Raf initiates the MAPK cascade. The last kinase to be phosphorylated (activated) is MAP kinase, which enters the nucleus and activates various tran-scription factors (serum response factors), which bind to cis-acting regulatory sequences called serum response elements. Plants appear to lack RTKs, but they have struc-turally similar receptors called receptorlike kinases, which are serine/threonine kinases. The three main cat-egories of plant RLKs are the S receptor kinases, the leucine-rich repeat receptors, and a receptor on the chloroplast called PRO25. Little is known about the sig-naling pathways used by these receptors, although enzymes of the MAPK cascade have been identified in plants.
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Cell Walls: Structure, Biogenesis,and Expansion 1 5 Chapter PLANT CELLS, UNLIKE ANIMAL CELLS, are surrounded by a rela-tively thin but mechanically strong cell wall. This wall consists of a com-plex mixture of polysaccharides and other polymers that are secreted by the cell and are assembled into an organized network linked together by both covalent and noncovalent bonds. Plant cell walls also contain struc-tural proteins, enzymes, phenolic polymers, and other materials that modify the wall’s physical and chemical characteristics.
The cell walls of prokaryotes, fungi, algae, and plants are distinctive from each other in chemical composition and microscopic structure, yet they all serve two common primary functions: regulating cell volume and determining cell shape. As we will see, however, plant cell walls have acquired additional functions that are not apparent in the walls of other organisms. Because of these diverse functions, the structure and composition of plant cell walls are complex and variable.
In addition to these biological functions, the plant cell wall is impor-tant in human economics. As a natural product, the plant cell wall is used commercially in the form of paper, textiles, fibers (cotton, flax, hemp, and others), charcoal, lumber, and other wood products. Another major use of plant cell walls is in the form of extracted polysaccharides that have been modified to make plastics, films, coatings, adhesives, gels, and thickeners in a huge variety of products.
As the most abundant reservoir of organic carbon in nature, the plant cell wall also takes part in the processes of carbon flow through ecosys-tems. The organic substances that make up humus in the soil and that enhance soil structure and fertility are derived from cell walls. Finally, as an important source of roughage in our diet, the plant cell wall is a significant factor in human health and nutrition.
We begin this chapter with a description of the general structure and composition of cell walls and the mechanisms of the biosynthesis and secretion of cell wall materials. We then turn to the role of the primary cell wall in cell expansion. The mechanisms of tip growth will be con-trasted with those of diffuse growth, particularly with respect to the establishment of cell polarity and the control of the rate of cell expansion. Finally, we will describe the dynamic changes in the cell wall that often accompany cell differ-entiation, along with the role of cell wall fragments as sig-naling molecules.
THE STRUCTURE AND SYNTHESIS OF PLANT CELL WALLS Without a cell wall, plants would be very different organ-isms from what we know. Indeed, the plant cell wall is essential for many processes in plant growth, development, maintenance, and reproduction: • Plant cell walls determine the mechanical strength of plant structures, allowing those structures to grow to great heights.
• Cell walls glue cells together, preventing them from sliding past one another. This constraint on cellular movement contrasts markedly to the situation in ani-mal cells, and it dictates the way in which plants develop (see Chapter 16).
• A tough outer coating enclosing the cell, the cell wall acts as a cellular “exoskeleton” that controls cell shape and allows high turgor pressures to develop.
• Plant morphogenesis depends largely on the control of cell wall properties because the expansive growth of plant cells is limited prin-cipally by the ability of the cell wall to expand.
• The cell wall is required for normal water relations of plants because the wall determines the relationship between the cell turgor pressure and cell volume (see Chapter 3).
• The bulk flow of water in the xylem requires a mechanically tough wall that resists collapse by the negative pressure in the xylem.
• The wall acts as a diffusion barrier that limits the size of macromole-cules that can reach the plasma membrane from outside, and it is a major structural barrier to pathogen invasion.
Much of the carbon that is assimilated in photosynthesis is channeled into poly-saccharides in the wall. During specific phases of development, these polymers may be hydrolyzed into their constituent sugars, which may be scavenged by the cell and used to make new polymers. This phenomenon is most notable in many seeds, in which wall polysaccharides of the endosperm or cotyledons function primarily as food reserves. Furthermore, oligosaccharide components of the cell wall may act as important signaling molecules during cell differentiation and during recogni-tion of pathogens and symbionts.
The diversity of functions of the plant cell wall requires a diverse and complex plant cell wall structure. In this sec-tion we will begin with a brief description of the morphol-ogy and basic architecture of plant cell walls. Then we will discuss the organization, composition, and synthesis of pri-mary and secondary cell walls.
Plant Cell Walls Have Varied Architecture Stained sections of plant tissues reveal that the cell wall is not uniform, but varies greatly in appearance and compo-sition in different cell types (Figure 15.1). Cell walls of the cortical parenchyma are generally thin and have few dis-tinguishing features. In contrast, the walls of some spe-cialized cells, such as epidermal cells, collenchyma, phloem fibers, xylem tracheary elements, and other forms of scle-renchyma have thicker, multilayered walls. Often these walls are intricately sculpted and are impregnated with specific substances, such as lignin, cutin, suberin, waxes, silica, or structural proteins.
314 Chapter 15 FIGURE 15.1 Cross section of a stem of Trifolium (clover), showing cells with varying wall morphology. Note the highly thickened walls of the phloem fibers. (Photo © James Solliday/Biological Photo Service.) Epidermis Cortex Phloem fibers Phloem Cambium Xylem Pith The individual sides of a wall surrounding a cell may also vary in thickness, embedded substances, sculpting, and fre-quency of pitting and plasmodesmata. For example, the outer wall of the epidermis is usually much thicker than the other walls of the cell; moreover, this wall lacks plasmodesmata and is impregnated with cutin and waxes. In guard cells, the side of the wall adjacent to the stomatal pore is much thicker than the walls on the other sides of the cell. Such variations in wall architecture for a single cell reflect the polarity and differentiated functions of the cell and arise from targeted secretion of wall components to the cell surface.
Despite this diversity in cell wall morphology, cell walls commonly are classified into two major types: primary walls and secondary walls. Primary walls are formed by growing cells and are usually considered to be relatively unspecialized and similar in molecular architecture in all cell types. Nevertheless, the ultrastructure of primary walls also shows wide variation. Some primary walls, such as those of the onion bulb parenchyma, are very thin (100 nm) and architecturally simple (Figure 15.2). Other primary walls, such as those found in collenchyma or in the epidermis (Figure 15.3), may be much thicker and con-sist of multiple layers.
Secondary walls are the cell walls that form after cell growth (enlargement) has ceased. Secondary walls may become highly specialized in structure and composition, reflecting the differentiated state of the cell. Xylem cells, such as those found in wood, are notable for possessing highly thickened secondary walls that are strengthened by lignin (see Chapter 13).
A thin layer of material, the middle lamella (plural lamellae), can usually be seen at the junction where the walls of neighboring cells come into contact. The composi-tion of the middle lamella differs from the rest of the wall in that it is high in pectin and contains different proteins compared with the bulk of the wall. Its origin can be traced to the cell plate that formed during cell division.
As we saw in Chapter 1, the cell wall is usually pene-trated by tiny membrane-lined channels, called plasmo-desmata (singular plasmodesma), which connect neighbor-ing cells. Plasmodesmata function in communication between cells, by allowing passive transport of small mol-ecules and active transport of proteins and nucleic acids between the cytoplasms of adjacent cells.
The Primary Cell Wall Is Composed of Cellulose Microfibrils Embedded in a Polysaccharide Matrix In primary cell walls, cellulose microfibrils are embedded in a highly hydrated matrix (Figure 15.4). This structure provides both strength and flexibility. In the case of cell walls, the matrix (plural matrices) consists of two major groups of polysaccharides, usually called hemicelluloses and pectins, plus a small amount of structural protein. The matrix polysaccharides consist of a variety of polymers that may vary according to cell type and plant species (Table 15.1).
Cell Walls: Structure, Biogenesis, and Expansion 315 FIGURE 15.2 Primary cell walls from onion parenchyma. (A) This surface view of cell wall fragments was taken through the use of Nomarski optics. Note that the wall looks like a very thin sheet with small surface depressions; these depressions may be pit fields, places where plasmodesmatal connections between cells are con-centrated. (B) This surface view of a cell wall was prepared by a freeze-etch replica technique. It shows the fibrillar nature of the cell wall. (From McCann et al. 1990, courtesy of M. McCann.) (A) (B) 200 nm 200 nm Outer wall layers Inner wall layers Cuticle 316 Chapter 15 FIGURE 15.3 Electron micro-graph of the outer epidermal cell wall from the growing region of a bean hypocotyl.
Multiple layers are visible within the wall. The inner lay-ers are thicker and more defined than the outer layers because the outer layers are the older regions of the wall and have been stretched and thinned by cell expansion.
(From Roland et al. 1982.) Hemicelluloses Pectins Rhamnogalacturonan I (a pectin) Structural protein Cellulose microfibril FIGURE 15.4 Schematic diagram of the major structural components of the primary cell wall and their likely arrangement. Cellulose microfibrils are coated with hemi-celluloses (such as xyloglucan), which may also cross-link the microfibrils to one another. Pectins form an interlocking matrix gel, perhaps interacting with structural proteins. (From Brett and Waldron 1996.) These polysaccharides are named after the principal sugars they contain. For example, a glucan is a polymer made up of glucose, a xylan is a polymer made up of xylose, a galactan is made from galactose, and so on. Glycan is the general term for a polymer made up of sugars. For branched polysaccharides, the backbone of the polysac-charide is usually indicated by the last part of the name. For example, xyloglucan has a glucan backbone (a linear chain of glucose residues) with xylose sugars attached to it in the side chains; glucuronoarabinoxylan has a xylan back-bone (made up of xylose subunits) with glucuronic acid and arabinose side chains. However, a compound name does not necessarily imply a branched structure. For exam-ple, glucomannan is the name given to a polymer contain-ing both glucose and mannose in its backbone.
Cellulose microfibrils are relatively stiff structures that contribute to the strength and structural bias of the cell wall.
The individual glucans that make up the microfibril are closely aligned and bonded to each other to make a highly ordered (crystalline) ribbon that excludes water and is rel-atively inaccessible to enzymatic attack. As a result, cellu-lose is very strong and very stable and resists degradation.
Hemicelluloses are flexible polysaccharides that char-acteristically bind to the surface of cellulose. They may form tethers that bind cellulose microfibrils together into a cohesive network (see Figure 15.4), or they may act as a slippery coating to prevent direct microfibril–microfibril contact. Another term for these molecules is cross-linking glucans, but in this chapter we’ll use the more traditional term, hemicelluloses. As described later, the term hemicellu-lose includes several different kinds of polysaccharides.
Pectins form a hydrated gel phase in which the cellu-lose–hemicellulose network is embedded. They act as hydrophilic filler, to prevent aggregation and collapse of the cellulose network. They also determine the porosity of the cell wall to macromolecules. Like hemicelluloses, pectins include several different kinds of polysaccharides.
The precise role of wall structural proteins is uncertain, but they may add mechanical strength to the wall and assist in the proper assembly of other wall components.
The primary wall is composed of approximately 25% cellulose, 25% hemicelluloses, and 35% pectins, with per-haps 1 to 8% structural protein, on a dry-weight basis.
However, large deviations from these values may be found.
For example, the walls of grass coleoptiles consist of 60 to 70% hemicelluloses, 20 to 25% cellulose, and only about 10% pectins. Cereal endosperm walls are mostly (about 85%) hemicelluloses. Secondary walls typically contain much higher cellulose contents.
In this chapter we will present a basic model of the pri-mary wall, but be aware that plant cell walls are more diverse than this model suggests. The composition of matrix poly-saccharides and structural proteins in walls varies signifi-cantly among different species and cell types (Carpita and McCann 2000). Most notably, in grasses and related species the major matrix polysaccharides differ from those that make up the matrix of most other land plants (Carpita 1996).
The primary wall also contains much water. This water is located mostly in the matrix, which is perhaps 75 to 80% water. The hydration state of the matrix is an important determinant of the physical properties of the wall; for example, removal of water makes the wall stiffer and less extensible. This stiffening effect of dehydration may play a role in growth inhibition by water deficits. We will exam-ine the structure of each of the major polymers of the cell wall in more detail in the sections that follow.
Cellulose Microfibrils Are Synthesized at the Plasma Membrane Cellulose is a tightly packed microfibril of linear chains of (1→4)-linked β-D-glucose (Figure 15.5 and Web Topic 15.1).
Because of the alternating spatial configuration of the glu-cosidic bonds linking adjacent glucose residues, the repeat-ing unit in cellulose is considered to be cellobiose, a (1→4)-linked β-D-glucose disaccharide.
Cellulose microfibrils are of indeterminate length and vary considerably in width and in degree of order, depending on the source. For instance, cellulose microfibrils in land plants appear under the electron microscope to be 5 to 12 nm wide, whereas those formed by algae may be up to 30 nm wide and more crystalline. This variety in width corresponds to a vari-ation in the number of parallel chains that make up the cross section of a microfibril—estimated to consist of about 20 to 40 individual chains in the thinner microfibrils.
The precise molecular structure of the cellulose microfib-ril is uncertain. Current models of microfibril organization suggest that it has a substructure consisting of highly crys-talline domains linked together by less organized “amor-Cell Walls: Structure, Biogenesis, and Expansion 317 TABLE 15.1 Structural components of plant cell walls Class Examples Cellulose Microfibrils of (1→4)β-D-glucan Matrix Polysaccharides Pectins Homogalacturonan Rhamnogalacturonan Arabinan Galactan Hemicelluloses Xyloglucan Xylan Glucomannan Arabinoxylan Callose (1→3)β-D-glucan (1→3,1→4)β-D-glucan [grasses only] Lignin (see Chapter 13) Structural proteins (see Table 15.2) phous” regions (Figure 15.6). Within the crystalline domains, adjacent glucans are highly ordered and bonded to each other by noncovalent bonding, such as hydrogen bonds and hydrophobic interactions. The individual glucan chains of cellulose are composed of 2000 to more than 25,000 glucose residues (Brown et al.
1996). These chains are long enough (about 1 to 5 µm long) to extend through multiple crystalline and amorphous regions within a microfibril. When cellulose is degraded— for example, by fungal cellulases—the amorphous regions are degraded first, releasing small crystallites that are thought to correspond to the crystalline domains of the microfibril.
The extensive noncovalent bonding between adjacent glucans within a cellulose microfibril gives this structure remarkable properties. Cellulose has a high tensile strength, equivalent to that of steel. Cellulose is also insol-uble, chemically stable, and relatively immune to chemical and enzymatic attack. These properties make cellulose an excellent structural material for building a strong cell wall.
Evidence from electron microscopy indicates that cellu-lose microfibrils are synthesized by large, ordered protein complexes, called particle rosettes or terminal complexes, that are embedded in the plasma membrane (Figure 15.7) (Kimura et al. 1999). These structures contain many units of cellulose synthase, the enzyme that synthesizes the individual (1→4)β-D-glucans that make up the microfib-ril (see Web Topic 15.2).
Cellulose synthase, which is located on the cytoplasmic side of the plasma membrane, transfers a glucose residue from a sugar nucleotide donor to the growing glucan chain. Sterol-glucosides (sterols linked to a chain of two or three glucose residues) serve as the primers, or initial acceptors, to start the growth of the glucan chain (Peng et al. 2002). The sterol is clipped from the glucan by an endoglucanase, and the growing glucan chain is then extruded through the membrane to the exterior of the cell, where, together with other glucan chains, it crystallizes into a microfibril and interacts with xyloglucans and other matrix polysaccharides. The sugar nucleotide donor is probably uridine diphos-phate D-glucose (UDP-glucose). Recent evidence suggests that the glucose used for the synthesis of cellulose may be obtained from sucrose (a disaccharide composed of fructose and glucose) (Amor et al. 1995; Salnikov et al. 2001). Accord-ing to this hypothesis, the enzyme sucrose synthase acts as a metabolic channel to transfer glucose taken from sucrose, via UDP-glucose, to the growing cellulose chain (Figure 15.8). After many years of fruitless searching, the genes for cellulose synthase in higher plants have now been isolated (Pear et al. 1996; Arioli et al. 1998; Holland et al. 2000; Rich-mond and Somerville 2000). In Arabidopsis, the cellulose synthases are part of a large family of proteins whose func-tion may be to synthesize the backbones of many cell wall polysaccharides.
318 Chapter 15 CH2OH O HO HO OH OH H H H H H CH2OH O HO HO OH OH H H H H H CH2OH O HO HO H OH H OH H H H H O H HO OH OH H H H H HO O H HO OH H OH H H H H HO HOCH2 O OH OH H OH H H H O HO HO OH H OH H H H H O C O O H HO OH H OH H H H OH O– H H H H H HO CH3 OH OH OH O H H H OH HO H CH3 OH H OH HO H H H H H H H H H H HO OH O CH2OH CH2OH O O HO OH OH C O O– b-D-Galactose (A) Hexoses (B) Pentoses b-D-Glucose b-D-Mannose b-D-Xylose b-L-Arabinose a-D-Apiose a-D-Galacturonic acid (GalA) a-D-Glucuronic acid (GlcA) Glucosyl Glucose (C) Uronic acids (E) Cellobiose (D) Deoxy sugars a-L-Rhamnose (Rha) a-L-Fucose (Fuc) FIGURE 15.5 Conformational structures of sugars com-monly found in plant cell walls. (A) Hexoses (six-carbon sugars). (B) Pentoses (five-carbon sugars). (C) Uronic acids (acidic sugars). (D) Deoxy sugars. (E) Cellobiose (showing the (1→4)β-D-linkage between two glucose residues in inverted orientation).
The formation of cellulose involves not only the syn-thesis of the glucan, but also the crystallization of multiple glucan chains into a microfibril. Little is known about the control of this process, except that the direction of microfib-ril deposition may be guided by microtubules adjacent to the membrane.
When the cellulose microfibril is synthesized, it is deposited into a milieu (the wall) that contains a high con-centration of other polysaccharides that are able to interact with and perhaps modify the growing microfibril. In vitro binding studies have shown that hemicelluloses such as xyloglucan and xylan may bind to the surface of cellulose.
Some hemicelluloses may also become physically en-trapped within the microfibril during its formation, thereby reducing the crystallinity and order of the microfibril (Hayashi 1989).
Matrix Polymers Are Synthesized in the Golgi and Secreted in Vesicles The matrix is a highly hydrated phase in which the cellu-lose microfibrils are embedded. The major polysaccharides of the matrix are synthesized by membrane-bound enzymes in the Golgi apparatus and are delivered to the cell wall via exocytosis of tiny vesicles (Figure 15.9 and Web Topic 15.3). The enzymes responsible for synthesis are sugar-nucleotide polysaccharide glycosyltransferases. These Cell Walls: Structure, Biogenesis, and Expansion 319 O O O O O HO H H H H H H H H H O O OH O CH2OH CH2OH O O O HO OH H H H H H CH2OH O HO OH H O O O O O O O O O O O O O O O HO H H H H H OH O CH2OH O O O O O O Cell wall Cellulose microfibril Hemicelluloses bound to the surface and entrapped within the microfibril Crystalline domains 4 nm (1→4)b-Glucan chains Cellobiose repeating unit b-1→4 Glycosidic linkage Amorphous regions FIGURE 15.6 Structural model of a cellulose microfibril. The microfibril has regions of high crystallinity intermixed with less orga-nized glucans. Some hemicelluloses may also be trapped within the microfibril and bound to the surface. Wall matrix in which microfibrils are embedded (C) Cellulose-synthesizing complex in the plasma membrane (1→4)b-glucan chains in a cellulose microfibril Microfibrils linked by xyloglucans Outer leaflet of lipid bilayer Intermicrotubule bridge Microtubule Microtubule bridged to plasma membrane (and cell wall) Cellulose microfibril emerging from rosette Lipid bilayer of plasma membrane Microfibril emerging from plasma membrane Inner leaflet of lipid bilayer Cell wall FIGURE 15.7 Cellulose synthesis by the cell. (A) Electron micrograph showing newly synthe-sized cellulose microfibrils immediately exterior to the plasma membrane. (B) Freeze-fracture labeled replicas showing reactions with antibod-ies against cellulose synthase. A field of labeled rosettes (arrows) with seven clearly labeled rosettes and one unlabeled rosette. The inset shows an enlarged view of two selected rosettes (terminal complexes) with immunogold labels. (C) Schematic diagram showing cellulose being synthesized by membrane synthase complex (“rosette”) and its presumed guidance by the underlying microtubules in the cyto-plasm. (A and C from Gunning and Steer 1996 B from Kimura et al. 1999.) (A) Microfibril in the cell wall Microfilament bundle Microtubule (B) 0.1 µm 30 nm enzymes transfer monosaccharides from sugar nucleotides to the growing end of the polysaccharide chain.
Unlike cellulose, which forms a crystalline microfibril, the matrix polysaccharides are much less ordered and are often described as amorphous. This noncrystalline charac-ter is a consequence of the structure of these polysaccha-rides—their branching and their nonlinear conformation.
Nevertheless, spectroscopy studies indicate that there is partial order in the orientation of hemicelluloses and pectins in the cell wall, probably as a result of a physical tendency for these polymers to become aligned along the long axis of cellulose (Séné et al. 1994; Wilson et al. 2000).
Hemicelluloses Are Matrix Polysaccharides That Bind to Cellulose Hemicelluloses are a heterogeneous group of polysaccharides (Figure 15.10) that are bound tightly in the wall. Typically they are solubilized from depectinated walls by the use of a strong alkali (1–4 M NaOH). Several kinds of hemicelluloses are found in plant cell walls, and walls from different tissues and different species vary in their hemicellulose composition.
In the primary wall of dicotyledons (the best-studied example), the most abundant hemicellulose is xyloglucan (see Figure 15.10A). Like cellulose, this polysaccharide has a backbone of (1→4)-linked β-D-glucose residues. Unlike cellulose, however, xyloglucan has short side chains that contain xylose, galactose, and often, though not always, a terminal fucose. By interfering with the linear alignment of the glucan backbones with one another, these side chains prevent the Cell Walls: Structure, Biogenesis, and Expansion 321 CELL WALL CYTOPLASM Cellulose synthase Fructose Sucrose (glucose– fructose) Sucrose synthase Glucan chains UDP-G UDP Plasma membrane FIGURE 15.8 Model of cellulose synthesis by a multisubunit complex containing cellulose synthase. Glucose residues are donated to the growing glucan chains by UDP-glucose (UDP-G). Sucrose synthase may act as a metabolic channel to transfer glucose taken from sucrose to UDP-glucose, or UDP-glucose may be obtained directly from the cytoplasm.
(After Delmer and Amor 1995.) Cell wall Plasma membrane Rough endoplasmic reticulum Golgi body Vesicle from Golgi body Vesicle from ER Matrix polysaccharides FIGURE 15.9 Scheme for the synthe-sis and delivery of matrix polysac-charides to the cell wall. Polysaccha-rides are synthesized by enzymes in the Golgi apparatus and then secreted to the wall by fusion of membrane vesicles to the plasma membrane. 322 Chapter 15 4)b-D-Glc-(1 4)b-D-Glc-(1 4)b-D-Glc-(1 4)b-D-Glc-(1 4)b-D-Glc-(1 4)b-D-Glc a-D-Xyl-(1 6) a-D-Xyl-(1 6) a-D-Xyl-(1 6) a-D-Xyl-(1 6) (A) Xyloglucan (B) Glucuronoarabinoxylan b-D-Xyl-(1 4)b-D-Xyl-(1 4)b-D-Xyl-(1 4)b-D-Xyl-(1 4)b-D-Xyl-(1 4)b-D-Xyl a-D-GlcA-(1 2) a-L-Ara-(1 2) a-L-Ara-(1 2) a-L-Ara-(1 2) 4) HO HO HO HO OH OH OH O CH2 CH2 O O O O O O HO HO OH O O HO HO HO HO OH OH OH O CH2 HO HO OH O O CH2 HOCH2 O O O O HO HO OH OH O HOCH2 CH2 O O O O HO OH O O O HO HO HO OH OH O— O OH O O O HO HO O O O HO O O O O OH O HO OH O O HO OH CH2OH O OH HOCH2 O HO OH HOCH2 O FIGURE 15.10 Partial structures of common hemicelluloses. (For details on carbohydrate nomenclature, see Web Topic 15.1.) (A) Xyloglucan has a backbone of (1→4)-linked β-D-glu-cose (Glc), with (1→6)-linked branches containing β-D-xylose (Xyl).
In some cases galactose (Gal) and fucose (Fuc) are added to the xylose side chains. (B) Glucuronoarabinoxy-lans have a (1→4)-linked backbone of β-D-xylose (Xyl). They may also have side chains containing arabinose (Ara), 4-O-methyl-glucuronic acid (4-O-Me-α−D−GlcA), or other sugars.
(From Carpita and McCann 2000.) assembly of xyloglucan into a crystalline microfibril.
Because xyloglucans are longer (about 50–500 nm) than the spacing between cellulose microfibrils (20–40 nm), they have the potential to link several microfibrils together. Varying with the developmental state and plant species, the hemicellulose fraction of the wall may also contain large amounts of other important polysaccharides—for example, glucuronoarabinoxylans (see Figure 15.10B) and gluco-mannans. Secondary walls typically contain less xyloglu-can and more xylans and glucomannans, which also bind tightly to cellulose. The cell walls of grasses contain only small amounts of xyloglucan and pectin, which are replaced by glucuronoarabinoxylan and (1→3,1→4)β-D-glucan.
Pectins Are Gel-Forming Components of the Matrix Like the hemicelluloses, pectins constitute a heterogeneous group of polysaccharides (Figure 15.11), characteristically containing acidic sugars such as galacturonic acid and neu-tral sugars such as rhamnose, galactose, and arabinose.
Pectins are the most soluble of the wall polysaccharides; they can be extracted with hot water or with calcium chela-tors. In the wall, pectins are very large and complex mole-cules composed of different kinds of pectic polysaccharides.
Some pectic polysaccharides have a relatively simple primary structure, such as homogalacturonan (see Figure 15.11A). This polysaccharide, also called polygalacturonic acid, is a (1→4)-linked polymer of α-D-glucuronic acid residues. Figure 15.12 shows a triple-fluorescence-labeled section of tobacco stem parenchyma cells showing the dis-tribution of cellulose and pectic homogalacturonan.
One of the most abundant of the pectins is the complex polysaccharide rhamnogalacturonan I (RG I), which has a long backbone and a variety of side chains (see Figure 15.11B). This molecule is very large and is believed to con-tain highly branched (“hairy”) regions (i.e., with arabinan, Cell Walls: Structure, Biogenesis, and Expansion 323 HO HO OH OH H3CO OCH3 OCH3 C C O O O O O O H3CO C O HO HO HO OH OH OH O– C O O O O C O O O O O O O– O O O O O OH OH OH C HO CH3 O O– O O O O O OH OH O—CCH3 C HO CH3 O O– O O O O OH OH OH C HO CH3 O O O O HO HO OH OH CH2OH O O OH CH2OH O O OH CH2OH O O HO OH CH2OH HOCH2 O O HO OH HOCH2 O O OH HO CH2 O O O OH OH OH OH HO HO HO HO CH2 CH2 CH2 CH2 O O O O O O O O OH HO CH2 O O (B) Rhamnogalacturonan I (RG I) (C) 5-Arabinan (D) Type I arabinogalactan (A) Homogalacturonan (HGA) FIGURE 15.11 Partial structures of the most common pectins.
(A) Homogalacturonan, also known as polygalacturonic acid or pectic acid, is made up of (1→4)-linked α-D-galacturonic acid (GalA) with occasional rhamnosyl residues that put a kink in the chain. The carboxyl residues are often methyl esterified. (B) Rhamnogalacturonan I (RG I) is a very large and heterogeneous pectin, with a backbone of alternating (1→4)α-D-galacturonic acid (GalA) and (1→2)α-D-rhamnose (Rha). Side chains are attached to rhamnose and are composed principally of arabi-nans (C), galactans, and arabinogalactans (D). These side chains may be short or quite long. The galacturonic acid residues are often methyl esterified. (From Carpita and McCann 2000.) FIGURE 15.12 Triple-fluorescence-labeled section of tobacco stem show-ing the primary cell walls of three adjacent parenchyma cells bordering an intercellular space. The blue color is calcofluor (staining of cellulose), and the red and green colors indicate the binding of two monoclonal antibodies to different epitopes (immunologically distinct regions) of pectic homogalacturonan. (Courtesy of W. Willats.) 324 Chapter 15 and galactan side shains) interspersed with unbranched (“smooth”) regions of homogalacturonan (Figure 15.13A).
Pectic polysaccharides may be very complex. A striking example is a highly branched pectic polysaccharide called rhamnogalacturonan II (RG II) (see Figure 15.13C), which con-tains at least ten different sugars in a complicated pattern of linkages. Although RG I and RG II have similar names, they have very different structures. RG II units may be cross-linked by borate diesters (Ishi et al. 1999) and are important for wall structure. For example, Arabidopsis mutants that synthesize an altered RG II that is unable to be cross-linked by borate show substantial growth abnormalities (O’Neill et al. 2001).
Pectins typically form gels—loose networks formed by highly hydrated polymers. Pectins are what make fruit jams and jellies “gel,” or solidify. In pectic gels, the charged car-boxyl (COO–) groups of neighboring pectin chains are linked O O O C O O– O OH OH OH OH OH HO O C O O O C C H3CO O O O O O O O O O C O O– O– Ca2+ O O C O O– O OH OH OH HO HO HO HO HO O C O O O Ca2+ OH C O O O O C O HO HO HO O– O O C O O– O OH OH OH OH HO HO O C C O O O Ca2+ O O O OCH3 OH C O O O O O C O HO HO HO O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B (B) Ionic bonding of pectin network by calcium (C) Rhamnogalacturonan II (RG II) dimer cross-linked by borate diester bonds Methyl ester (A) Rhamnogalacturonan I structure Side chains of arabinan, galactan or arabinogalactan Rhamnose–galacturonic acid backbone Homogalacturonan Nonbranched segments Highly branched segments FIGURE 15.13 Pectin structure. (A) Proposed structure of rhamnogalacturonan I, containing highly branched segments interspersed with nonbranched segments, and a backbone of rhamnose and galactur-onic acid. (B) Formation of a pectin net-work involves ionic bridging of the nones-terified carboxyl groups (COO–) by calcium ions. When blocked by methyl-esterified groups, the carboxyl groups cannot partici-pate in this type of interchain network for-mation. Likewise, the presence of side chains on the backbone interferes with net-work formation. (C) Structure of rhamno-galacturonan II (RG II). (B and C from Carpita and McCann 2000.) together via Ca2+, which forms a tight complex with pectin. A large calcium-bridged net-work may thus form, as illus-trated in Figure 15.13B.
Pectins are subject to mod-ifications that may alter their conformation and linkage in the wall. Many of the acidic residues are esterified with methyl, acetyl, and other unidentified groups during biosynthesis in the Golgi appa-ratus. Such esterification masks the charges of carboxyl groups and prevents calcium bridging between pectins, thereby reducing the gel-forming character of the pectin. Once the pectin has been secreted into the wall, the ester groups may be removed by pectin esterases found in the wall, thus unmasking the charges of the carboxyl groups and increasing the ability of the pectin to form a rigid gel. By cre-ating free carboxyl groups, de-esterification also increases the electric-charge density in the wall, which in turn may influ-ence the concentration of ions in the wall and the activities of wall enzymes. In addition to being connected by calcium bridging, pectins may be linked to each other by various covalent bonds, including ester linkages between phenolic residues such as ferulic acid (see Chapter 13).
Structural Proteins Become Cross-Linked in the Wall In addition to the major polysaccharides described in the previous section, the cell wall contains several classes of structural proteins. These proteins usually are classified according to their predominant amino acid composition— for example, hydroxyproline-rich glycoprotein (HRGP), glycine-rich protein (GRP), proline-rich protein (PRP), and so on (Table 15.2). Some wall proteins have sequences that are characteristic of more than one class. Many structural proteins of walls have highly repetitive primary structures and sometimes are highly glycosylated (Figure 15.14).
In vitro extraction studies have shown that newly secreted wall structural proteins are relatively soluble, but they become more and more insoluble during cell matu-ration or in response to wounding. The biochemical nature of the insolubilization process is uncertain, how-ever.
Wall structural proteins vary greatly in their abundance, depending on cell type, maturation, and previous stimula-tion. Wounding, pathogen attack, and treatment with elic-itors (molecules that activate plant defense responses; see Chapter 13) increase expression of the genes that code for many of these proteins. In histological studies, wall struc-tural proteins are often localized to specific cell and tissue types. For example, HRGPs are associated mostly with cambium, phloem parenchyma, and various types of scle-renchyma. GRPs and PRPs are most often localized to xylem vessels and fibers and thus are more characteristic of a differentiated cell wall.
In addition to the structural proteins already listed, cell walls contain arabinogalactan proteins (AGPs) which usu-ally amount to less than 1% of the dry mass of the wall.
These water-soluble proteins are very heavily glycosylated: More than 90% of the mass of AGPs may be sugar residues—primarily galactose and arabinose (Figure 15.15) (Gaspar et al. 2001). Multiple AGP forms are found in plant tissues, either in the wall or associated with the plasma membrane, and they display tissue- and cell-specific expression patterns.
Cell Walls: Structure, Biogenesis, and Expansion 325 TABLE 15.2 Structural proteins of the cell wall Percentage Class of cell wall proteins carbohydrate Localization typically in: HRGP (hydroxyproline-rich glycoprotein) ~55 Phloem, cambium, sclereids PRP (proline-rich protein) ~0–20 Xylem, fibers, cortex GRP (glycine-rich protein) 0 Xylem Ser Hyp Hyp Hyp Hyp Ser Hyp Ser Hyp Hyp Hyp Hyp Val Tyr Isodityrosine Tomato extensin (extensive glycosylation) Lys Tyr X X X X O FIGURE 15.14 A repeated hydroxyproline-rich motif from a molecule of extensin from tomato, showing extensive glycosylation and the formation of intramolecular isodity-rosine bonds. (From Carpita and McCann 2000.) AGPs may function in cell adhesion and in cell signal-ing during cell differentiation. As evidence for the latter idea, treatment of suspension cultures with exogenous AGPs or with agents that specifically bind AGPs is reported to influence cell proliferation and embryogenesis.
AGPs are also implicated in the growth, nutrition, and guidance of pollen tubes through stylar tissues, as well as in other developmental processes (Cheung et al. 1996; Gas-par et al. 2001). Finally, AGPs may also function as a kind of polysaccharide chaperone within secretory vesicles to reduce spontaneous association of newly synthesized poly-saccharides until they are secreted to the cell wall.
New Primary Walls Are Assembled during Cytokinesis Primary walls originate de novo during the final stages of cell division, when the newly formed cell plate separates the two daughter cells and solidifies into a stable wall that is capable of bearing a physical load from turgor pressure.
The cell plate forms when Golgi vesicles and ER cisternae aggregate in the spindle midzone area of a dividing cell. This aggregation is organized by the phragmoplast, a complex assembly of microtubules, membranes, and vesicles that forms during late anaphase or early telophase (see Chapter 1). The membranes of the vesicles fuse with each other, and with the lateral plasma membrane, to become the new plasma membrane separating the daughter cells. The con-tents of the vesicles are the precursors from which the new middle lamella and the primary wall are assembled.
After a wall forms, it can grow and mature through a process that may be outlined as follows: Synthesis →secretion →assembly → expansion (in growing cells) → cross-linking and secondary wall formation The synthesis and secretion of the major wall polymers were described earlier. Here we will consider the assembly and expansion of the wall.
After their secretion into the extracellular space, the wall polymers must be assembled into a cohesive structure; that is, the individual polymers must attain the physical arrangement and bonding relationships that are character-istic of the wall. Although the details of wall assembly are not understood, the prime candidates for this process are self-assembly and enzyme-mediated assembly.
Self-assembly.
Self-assembly is attractive because it is mechanistically simple. Wall polysaccharides possess a marked tendency to aggregate spontaneously into orga-nized structures. For example, isolated cellulose may be dissolved in strong solvents and then extruded to form sta-ble fibers, called rayon.
Similarly, hemicelluloses may be dissolved in strong alkali; when the alkali is removed, these polysaccharides aggregate into concentric, ordered networks that resemble the native wall at the ultrastructural level. This tendency to aggregate can make the separation of hemicellulose into its component polymers technically difficult. In contrast, pectins are more soluble and tend to form dispersed, isotropic networks (gels). These observations indicate that the wall polymers have an inherent ability to aggregate into partly ordered structures.
Enzyme-mediated assembly.
In addition to self-assem-bly, wall enzymes may take part in putting the wall together. A prime candidate for enzyme-mediated wall assembly is xyloglucan endotransglycosylase (XET). This enzyme has the ability to cut the backbone of a xyloglucan and to join one end of the cut xyloglucan with the free end of an acceptor xyloglucan (Figure 15.16). Such a transfer reaction integrates newly synthesized xyloglucans into the wall (Nishitani 1997; Thompson and Fry 2001).
Other wall enzymes that might aid in assembly of the wall include glycosidases, pectin methyl esterases, and various oxidases. Some glycosidases remove the side chains of hemicelluloses. This “debranching” activity increases the tendency of hemicelluloses to adhere to the surface of cellulose microfibrils. Pectin methyl esterases hydrolyze the methyl esters that block the carboxyl groups of pectins. By unblocking the carboxyl groups, these enzymes increase the concentration of acidic groups on the pectins and enhance the ability of pectins to form a Ca2+-bridged gel network.
Oxidases such as peroxidase may catalyze cross-linking between phenolic groups (tyrosine, phenylalanine, ferulic 326 Chapter 15 Protein Arabinogalactan side chains FIGURE 15.15 A highly branched arabinogalactan molecule.
(From Carpita and McCann 2000.) acid) in wall proteins, pectins, and other wall polymers.
Such phenolic coupling is clearly important for the forma-tion of lignin cross-links, and it may likewise link diverse components of the wall together.
Secondary Walls Form in Some Cells after Expansion Ceases After wall expansion ceases, cells sometimes continue to syn-thesize a wall, known as a secondary wall. Secondary walls are often quite thick, as in tracheids, fibers, and other cells that serve in mechanical support of the plant (Figure 15.17).
Often such secondary walls are multilayered and differ in structure and composition from the primary wall. For example, the secondary walls in wood contain xylans rather than xyloglucans, as well as a higher proportion of cellulose. The orientation of the cellulose microfibrils may be more neatly aligned parallel to each other in secondary walls than in primary walls. Secondary walls are often (but not always) impregnated with lignin.
Lignin is a phenolic polymer with a complex, irregular pattern of linkages that link the aromatic alcohol subunits together (see Chapter 13). These subunits are synthesized from phenylalanine and are secreted to the wall, where they are oxidized in place by the enzymes peroxidase and laccase. As lignin forms in the wall, it displaces water from the matrix and forms a hydrophobic network that bonds tightly to cellulose and prevents wall enlargement (Figure 15.18).
Lignin adds significant mechanical strength to cell walls and reduces the susceptibility of walls to attack by pathogens.
Cell Walls: Structure, Biogenesis, and Expansion 327 Xyloglucan endotransglycosylase (XET) (A) Xyloglucans (B) (C) (D) (E) (F) FIGURE 15.16 Action of xyloglucan endotransglycosylase (XET) to cut and stitch xyloglucan polymers into new con-figurations. Two xyloglucan chains are shown in (A) with two distinct patterns to emphasize their rearrangement.
XET binds to the middle of one xyloglucan (B), cuts it (C), and transfers one end to the end of a second xyloglucan (D, E), resulting in one shorter and one longer xyloglucan (F). (After Smith and Fry 1991.) (B) S3 S2 S1 S1 S2 S3 Secondary wall Primary wall Middle lamella FIGURE 15.17 (A) Cross section of a Podocarpus sclereid, in which multiple layers in the secondary wall are visible. (B) Diagram of the cell wall organization often found in tra-cheids and other cells with thick secondary walls. Three distinct layers (S1, S2, S3) are formed interior to the primary wall. (Photo ©David Webb.) (A) Lignin also reduces the digestibility of plant material by ani-mals. Genetic engineering of lignin content and structure may improve the digestibility and nutritional content of plants used as animal fodder.
PATTERNS OF CELL EXPANSION During plant cell enlargement, new wall polymers are con-tinuously synthesized and secreted at the same time that the preexisting wall is expanding. Wall expansion may be highly localized (as in the case of tip growth) or evenly dis-tributed over the wall surface (diffuse growth) (Figure 15.19). Whereas tip growth is characteristic of root hairs and pollen tubes (see Web Essay 15.1), most of the other cells in the plant body exhibit diffuse growth. Cells such as fibers, some sclereids, and trichomes grow in a pattern that is intermediate between diffuse growth and tip growth.
Even in cells with diffuse growth, however, different parts of the wall may enlarge at different rates or in differ-ent directions. For example, in cortical cells of the stem, the end walls grow much less than side walls. This difference may be due to structural or enzymatic variations in specific walls or variations in the stresses borne by different walls.
As a consequence of this uneven pattern of wall expansion, plant cells may assume irregular forms.
Microfibril Orientation Determines Growth Directionality of Cells with Diffuse Growth During growth, the loosened cell wall is extended by physical forces generated from cell turgor pressure. Turgor pres-sure creates an outward-directed force, equal in all directions. The directionality of growth is determined largely by the structure of the cell wall—in particular, the orientation of cellulose microfibrils.
When cells first form in the meristem, they are isodiametric; that is, they have equal diameters in all directions. If the orientation of cellulose microfibrils in the primary cell wall were isotropic (ran-domly arranged), the cell would grow equally in all directions, expanding radi-ally to generate a sphere (Figure 15.20A).
In most plant cell walls, however, the arrangement of cel-lulose microfibrils is anisotropic (nonrandom).
Cellulose microfibrils are synthesized mainly in the lat-eral walls of cylindrical, enlarging cells such as cortical and vascular cells of stems and roots, or the giant internode cells of the filamentous green alga Nitella. Moreover, the cellulose microfibrils are deposited circumferentially (transversely) in these lateral walls, at right angles to the long axis of the cell.
The circumferentially arranged cellulose microfibrils have been likened to hoops in a barrel, restricting growth in girth and promoting growth in length (see Figure 15.20B). How-ever, because individual cellulose microfibrils do not actu-ally form closed hoops around the cell, a more accurate anal-ogy would be the glass fibers in fiberglass.
Fiberglass is a complex composite material, composed of an amorphous resin matrix reinforced by discontinuous strengthening elements, in this case glass fibers. In complex composites, rod-shaped crystalline elements exert their maximum reinforcement of the matrix in the direction par-allel to their orientation, and their minimum reinforcement perpendicular to their orientation. The reinforcement of the wall is greater in the parallel direction because the matrix must physically scrape along the entire length of the fibers for lateral displacement to occur. 328 Chapter 15 Cellulose microfibril (cross section) Lignin formed by cross-linking phenolic compounds Phenolic subunit FIGURE 15.18 Diagram illustrating how the phenolic subunits of lignin infil-trate the space between cellulose microfibrils, where they become cross-linked. (Other components of the matrix are omitted from this diagram.) (A) Tip growth (B) Diffuse growth Cell expansion Marks on cell surface FIGURE 15.19 The cell surface expands differently during tip growth and diffuse growth. (A) Expansion of a tip-growing cell is confined to an apical dome at one end of the cell. If marks are placed on the cell surface and the cell is allowed to continue to grow, only the marks that were ini-tially within the apical dome grow farther apart. Root hairs and pollen tubes are examples of plant cells that exhibit tip growth. (B) If marks are placed on the surface of a diffuse-growing cell, the distance between all the marks increases as the cell grows. Most cells in multicellular plants grow by diffuse growth.
In contrast, when the material is stretched in the perpen-dicular direction, the matrix polymers need only slip over the diameters of the fibrous elements, resulting in little or no strengthening of the matrix. Because the glass fibers in fiber-glass are randomly arranged, fiberglass is equally strong in all directions; that is, it is mechanically isotropic.
Plant cell walls, like fiberglass, are complex composite materials, composed of an amorphous phase and crys-talline elements (Darley et al. 2001). Unlike fiberglass, how-ever, the microfibril strengthening elements of a typical pri-mary cell wall are transversely oriented, rendering the wall structurally and mechanically anisotropic. For this reason growing plant cells tend to elongate, and they increase only minimally in girth.
Cell wall deposition continues as cells enlarge. Accord-ing to the multinet hypothesis, each successive wall layer is stretched and thinned during cell expansion, so the microfibrils become passively reoriented in the longitudi-nal direction—that is, in the direction of growth. Successive layers of microfibrils thus show a gradation in their degree of reorientation across the thickness of the wall, and those in the outer layers are longitudinally oriented as a result of wall stretching (Figure 15.21).
Because of thinning and fragmentation, these outer lay-ers have much less influence on the direction of cell expan-sion than do the newly deposited inner layers. The inner one-fourth of the wall bears nearly all the stress due to tur-gor pressure and determines the directionality of cell expansion (see Web Topic 15.4).
Cortical Microtubules Determine the Orientation of Newly Deposited Microfibrils Newly deposited cellulose microfibrils and cytoplasmic microtubules in cell walls usually are coaligned, suggest-ing that microtubules determine the orientation of cellu-lose microfibril deposition. The orientation of microtubules in the cortical cytoplasm, the cytoplasm immediately adja-cent to the plasma membrane, usually mirrors that of the newly deposited microfibrils in the adjacent cell wall, and both are usually coaligned in the transverse direction, at right angles to the axis of polarity (Figure 15.22). In some cell types, such as tracheids, the microfibrils in the wall alternate between transverse and longitudinal orientations, and in such cases the microtubules are parallel to the microfibrils of the most recently deposited wall layer.
The main evidence for the involvement of microtubules in the deposition of cellulose microfibrils is that the orien-tation of the microfibrils can be perturbed by genetic muta-tions and certain drugs that disrupt cytoplasmic micro-tubules. For example, several drugs bind to tubulin, the subunit protein of microtubules, causing them to depoly-merize. When growing roots are treated with a micro-tubule-depolymerizing drug, such as oryzalin, the region of elongation expands laterally, becoming bulbous and tumorlike (Figure 15.23).
This disrupted growth is due to the isotropic expansion of the cells; that is, they enlarge like a sphere instead of elongating. The drug-induced destruction of microtubules Cell Walls: Structure, Biogenesis, and Expansion 329 (A) Randomly oriented cellulose microfibrils (B) Transverse cellulose microfibrils FIGURE 15.20 The orientation of newly deposited cellulose microfibrils determines the direction of cell expansion. (A) If the cell wall is reinforced by randomly oriented cellulose microfibrils, the cell will expand equally in all directions, forming a sphere. (B) When most of the reinforcing cellu-lose microfibrils have the same orientation, the cell expands at right angles to the microfibril orientation and is con-strained in the direction of the reinforcement. Here the microfibril orientation is transverse, so cell expansion is longitudinal. FIGURE 15.21 The multinet hypothesis for wall extension.
Newly synthesized cellulose microfibrils are continually deposited on the inner surface of the wall in the transverse orientation. As cell elongation proceeds, the older outer wall layers are progressively thinned and weakened, and their cellulose microfibrils are passively rearranged to a longitudinal orientation. The wall mechanical properties are determined by the inner layers. 330 Chapter 15 FIGURE 15.22 The orientation of microtubules in the cortical cytoplasm mir-rors the orientation of newly deposited cellulose microfibrils in the cell wall of cells that are elongating. (A) The arrangement of microtubules can be revealed with fluorescently labeled antibodies to the microtubule protein tubulin. In this differentiating tracheary element from a Zinnia cell suspen-sion culture, the pattern of microtubules (green) mirrors the orientation of the cellulose microfibrils in the wall, as shown by calcofluor staining (blue).
(B) The alignment of cellulose microfibrils in the cell wall can sometimes be seen in grazing sections prepared for electron microscopy, as in this micro-graph of a developing sieve tube element in a root of Azolla (a water fern).
The longitudinal axis of the root and the sieve tube element runs vertically.
Both the wall microfibrils (double-headed arrows) and the cortical micro-tubules (single-headed arrows) are aligned transversely. (A courtesy of Robert W. Seagull; B courtesy of A. Hardham.) 5 µm (A) (B) FIGURE 15.23 The disruption of cortical microtubules results in a dramatic increase in radial cell expansion and a concomitant decrease in elongation. (A) Root of Arabidopsis seedling treated with the microtubule-depolymerizing drug oryzalin (1 mM) for 2 days before this photomicrograph was taken. The drug has altered the polarity of growth. (B) Microtubules were visualized by means of an indirect immunofluorescence technique and an antitubulin anti-body. Whereas cortical microtubules in the control are ori-ented at right angles to the direction of cell elongation, very few microtubules remain in roots treated with 1 mM oryza-lin. (From Baskin et al. 1994, courtesy of T. Baskin.) (A) (B) Control (no drug treatment) 1 mM Oryzalin Control (no drug treatment) 1 mM Oryzalin in the growing cells also disrupts the transverse orientation of cellulose microfibrils in the most recently deposited lay-ers of the wall. Cell wall deposition continues in the absence of microtubules, but the cellulose microfibrils are deposited randomly and the cells expand equally in all directions. Since the antimicrotubule drugs specifically tar-get the microtubules, these results suggest that micro-tubules act as guides for the orientation of cellulose microfibril deposition.
THE RATE OF CELL ELONGATION Plant cells typically expand 10- to 100-fold in volume before reaching maturity. In extreme cases, cells may enlarge more than 10,000-fold in volume (e.g., xylem ves-sel elements). The cell wall typically undergoes this pro-found expansion without losing its mechanical integrity and without becoming thinner. Thus, newly synthesized polymers are integrated into the wall without destabilizing it. Exactly how this integration is accomplished is uncer-tain, although self-assembly and xyloglucan endotransg-lycosylase (XET) play important roles, as already described.
This integrating process may be particularly critical for rapidly growing root hairs, pollen tubes, and other special-ized cells that exhibit tip growth, in which the region of wall deposition and surface expansion is localized to the hemi-spherical dome at the apex of the tubelike cell, and cell expansion and wall deposition must be closely coordinated.
In rapidly growing cells with tip growth, the wall dou-bles its surface area and is displaced to the nonexpanding part of the cell within minutes. This is a much greater rate of wall expansion than is typically found in cells with dif-fuse growth, and tip-growing cells are therefore suscepti-ble to wall thinning and bursting. Although diffuse growth and tip growth appear to be different growth patterns, both types of wall expansion must have analogous, if not iden-tical, processes of polymer integration, stress relaxation, and wall polymer creep.
Many factors influence the rate of cell wall expansion.
Cell type and age are important developmental factors. So, too, are hormones such as auxin and gibberellin. Environ-mental conditions such as light and water availability may likewise modulate cell expansion. These internal and exter-nal factors most likely modify cell expansion by loosening the cell wall so that it yields (stretches irreversibly). In this context we speak of the yielding properties of the cell wall.
In this section we will first examine the biomechanical and biophysical parameters that characterize the yielding prop-erties of the wall. For cells to expand at all, the rigid cell wall must be loosened in some way. The type of wall loosening involved in plant cell expansion is termed stress relaxation.
According to the acid growth hypothesis for auxin action (see Chapter 19), one mechanism that causes wall stress relaxation and wall yielding is cell wall acidification, result-ing from proton extrusion across the plasma membrane.
Cell wall loosening is enhanced at acidic pH. A little later we will explore the biochemical basis for acid-induced wall loosening and stress relaxation, including the role of a spe-cial class of wall-loosening proteins called expansins.
As the cell approaches its maximum size, its growth rate diminishes and finally ceases altogether. At the end of this section we will consider the process of cell wall rigidifica-tion that leads to the cessation of growth.
Stress Relaxation of the Cell Wall Drives Water Uptake and Cell Elongation Because the cell wall is the major mechanical restraint that limits cell expansion, much attention has been given to its physical properties. As a hydrated polymeric material, the plant cell wall has physical properties that are intermedi-ate between those of a solid and those of a liquid. We call these viscoelastic, or rheological (flow), properties. Grow-ing-cell walls are generally less rigid than walls of non-growing cells, and under appropriate conditions they exhibit a long-term irreversible stretching, or yielding, that is lacking or nearly lacking in nongrowing walls.
Stress relaxation is a crucial concept for understanding how cell walls enlarge (Cosgrove 1997). The term stress is used here in the mechanical sense, as force per unit area. Wall stresses arise as an inevitable consequence of cell turgor. The turgor pressure in growing plant cells is typically between 0.3 and 1.0 MPa. Turgor pressure stretches the cell wall and gen-erates a counterbalancing physical stress or tension in the wall. Because of cell geometry (a large pressurized volume contained by a thin wall), this wall tension is equivalent to 10 to 100 MPa of tensile stress—a very large stress indeed.
This simple fact has important consequences for the mechanics of cell enlargement. Whereas animal cells can change shape in response to cytoskeleton-generated forces, such forces are negligible compared with the turgor-gener-ated forces that are resisted by the plant cell wall. To change shape, plant cells must thus control the direction and rate of wall expansion, which they do by depositing cellulose in a biased orientation (which determines the directionality of cell wall expansion) and by selectively loosening the bond-ing between cell wall polymers. This biochemical loosening enables the wall polymers to slip by each other, thereby increasing the wall surface area. At the same time, such loosening reduces the physical stress in the wall.
Wall stress relaxation is crucial because it allows growing plant cells to reduce their turgor and water potentials, which enables them to absorb water and to expand. Without stress relaxation, wall synthesis would only thicken the wall, not expand it. During secondary-wall deposition in nongrow-ing cells, for example, stress relaxation does not occur.
The Rate of Cell Expansion Is Governed By Two Growth Equations When plant cells enlarge before maturation, the increase in volume is generated mostly by water uptake. This water Cell Walls: Structure, Biogenesis, and Expansion 331 ends up mainly in the vacuole, which takes up an ever larger proportion of the cell volume as the cell grows. Here we will describe how growing cells regulate their water uptake and how this uptake is coordinated with wall yielding.
Water uptake by growing cells is a passive process.
There are no active water pumps; instead the growing cell is able to lower the water potential inside the cell so that water is taken up spontaneously in response to a water potential difference, without direct energy expenditure.
We define the water potential difference, ∆Yw (expressed in megapascals), as the water potential outside the cell minus the water potential inside (see Chapters 3 and 4). The rate of uptake also depends on the surface area of the cell (A, in square meters) and the permeability of the plasma membrane to water (Lp, in meters per second per megapascal). Membrane Lp is a measure of how readily water crosses the membrane, and it is a function of the physical structure of the membrane and the activity of aquaporins (see Chap-ter 3). Thus we have the rate of water uptake in volume units: ∆V/∆t, expressed in cubic meters per second.
Assuming that a growing cell is in contact with pure water (with zero water potential), then Rate of water uptake = A × Lp (∆Yw) = A × Lp (Yo – Yi) (15.1) This equation states that the rate of water uptake depends only on the cell area, membrane permeability to water, cell turgor, and osmotic potential.
Equation 15.1 is valid for both growing and nongrow-ing cells in pure water. But how can we account for the fact that growing cells can continue to take up water for a long time, whereas nongrowing cells soon cease water uptake?
In a nongrowing cell, water absorption increases cell vol-ume, causing the protoplast to push harder against the cell wall, thereby increasing cell turgor pressure, Yp. This increase in Yp would increase cell water potential Yw, quickly bring-ing ∆Yw to zero. Water uptake would then cease.
In a growing cell, ∆Yw is prevented from reaching zero because the cell wall is “loosened”: It yields irreversibly to the forces generated by turgor and thereby reduces simul-taneously the wall stress and the cell turgor. This process is called stress relaxation, and it is the crucial physical dif-ference between growing and nongrowing cells.
Stress relaxation can be understood as follows. In a turgid cell, the cell contents push against the wall, causing the wall to stretch elastically (i.e., reversibly) and giving rise to a counterforce, a wall stress. In a growing cell, biochem-ical loosening enables the wall to yield inelastically (irre-versibly) to the wall stress. Because water is nearly incom-pressible, only an infinitesimal expansion of the wall is needed to reduce cell turgor pressure and, simultaneously, wall stress. Thus, stress relaxation is a decrease in wall stress with nearly no change in wall dimensions.
As a consequence of wall stress relaxation, the cell water potential is reduced and water flows into the cell, causing a measurable extension of the cell wall and increasing cell surface area and volume. Sustained growth of plant cells entails simultaneous stress relaxation of the wall (which tends to reduce turgor pressure) and water absorption (which tends to increase turgor pressure).
Empirical evidence has shown that wall relaxation and expansion depend on turgor pressure. As turgor is reduced, wall relaxation and growth slow down. Growth usually ceases before turgor reaches zero. The turgor value at which growth ceases is called the yield threshold (usu-ally represented by the symbol Y). This dependence of cell wall expansion on turgor pressure is embodied in the fol-lowing equation: GR = m(Yp – Y) (15.2) where GR is the cell growth rate, and m is the coefficient that relates growth rate to the turgor in excess of the yield thresh-old. The coefficient m is usually called wall extensibility and is the slope of the line relating growth rate to turgor pressure.
Under conditions of steady-state growth, GR in Equa-tion 15.2 is the same as the rate of water uptake in Equation 15.1. That is, the increase in the volume of the cell equals the volume of water taken up. The two equations are plot-ted in Figure 15.24. Note that the two processes of wall expansion and water uptake show opposing reactions to a change in turgor. For example, an increase in turgor increases wall extension but reduces water uptake. Under normal conditions, the turgor is dynamically balanced in a growing cell exactly at the point where the two lines inter-sect. At this point both equations are satisfied, and water uptake is exactly matched by enlargement of the wall chamber.
This intersection point in Figure 15.24 is the steady-state condition, and any deviations from this point will cause transient imbalances between the processes of water uptake and wall expansion. The result of these imbalances is that turgor will return to the point of intersection, the point of dynamic steady state for the growing cell.
The regulation of cell growth—for example, by hor-mones or by light—typically is accomplished by regulation of the biochemical processes that regulate wall loosening and stress relaxation. Such changes can be measured as a change in m or in Y.
The water uptake that is induced by wall stress relax-ation enlarges the cell and tends to restore wall stress and turgor pressure to their equilibrium values, as we have shown. However, if growing cells are physically prevented from taking up water, wall relaxation progressively reduces cell turgor. This situation may be detected, for example, by turgor measurements with a pressure probe or by water potential measurements with a psychrometer or a pressure chamber (see Web Topic 3.6). Figure 15.25 shows the results of such an experiment.
332 Chapter 15 Acid-Induced Growth Is Mediated by Expansins An important characteristic of growing cell walls is that they extend much faster at acidic pH than at neutral pH (Rayle and Cleland 1992). This phenomenon is called acid growth. In living cells, acid growth is evident when grow-ing cells are treated with acid buffers or with the drug fusicoccin, which induces acidification of the cell wall solu-tion by activating an H+-ATPase in the plasma membrane. An example of acid-induced growth can be found in the initiation of the root hair, where the local wall pH drops to a value of 4.5 at the time when the epidermal cell begins to bulge outward (Bibikova et al. 1998). Auxin-induced growth is also associated with wall acidification, but it is probably not sufficient to account for the entire growth induction by this hormone (see Chapter 19), and other wall-loosening processes may be involved. Recent work, for example, implicates the production of hydroxyl radicals in wall loosening during auxin-induced growth (Schopfer 2001). Nevertheless, this pH-dependent mechanism of wall extension appears to be an evolutionarily conserved process common to all land plants (Cosgrove 2000) and involved in a variety of growth processes.
Acid growth may also be observed in isolated cell walls, which lack normal cellular, metabolic, and synthetic processes. Such observation requires the use of an exten-someter to put the walls under tension and to measure the pH-dependent wall creep (Figure 15.26).
The term creep refers to a time-dependent irreversible extension, typically the result of slippage of wall polymers relative to one another. When growing walls are incubated in neutral buffer (pH 7) and clamped in an extensometer, the walls extend briefly when tension is applied, but exten-sion soon ceases. When transferred to an acidic buffer (pH 5 or less), the wall begins to extend rapidly, in some instances continuing for many hours.
This acid-induced creep is characteristic of walls from growing cells, but it is not observed in mature (nongrow-ing) walls. When walls are pretreated with heat, proteases, Cell Walls: Structure, Biogenesis, and Expansion 333 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.8 0.7 Turgor pressure (MPa) Water potential (MPa) Rate of cell expansion (m3 s–1) Rate of water uptake (m3 s–1) –0.7 –0.6 –0.5 –0.4 –0.3 –0.2 –0.1 0 Yield threshold Wall yielding Water uptake dV/dt = A × Lp(∆Yw) Stable point, where both processes are equal Full turgor GR = m(Yp – Y) FIGURE 15.24 Graphic representation of the two equations that relate water uptake and cell expansion to cell turgor pressure and cell water potential. The values for the rates of cell expansion and water uptake are arbi-trary. Steady-state growth is attained only at the point where the two equations intersect.
Any imbalance between water uptake and wall expansion will result in changes in cell turgor and bring the cell back to this stable point of intersection between the two processes.
Yield threshold (Y) 0.7 0.6 0.5 0.4 0.3 0.2 0 2 4 6 Time (hours) Turgor pressure (MPa) Control (P–Y) –Auxin +Auxin FIGURE 15.25 Reduction of cell turgor pressure (water potential) by stress relaxation. In this experiment, the excised stem segments from growing pea seedlings were incubated in solution with or without auxin, then blotted dry and sealed in a humid chamber. Cell turgor pressure (P) was measured at various time points. The segments treated with auxin rapidly reduced their turgor to the yield threshold (Y), as a result of rapid wall relaxation. The seg-ments without auxin showed a slower rate of relaxation.
The control segments were treated the same as the group treated with auxin, except that they remained in contact with a drop of water, which prevented wall relaxation.
(After Cosgrove 1985.) or other agents that denature proteins, they lose their acid growth ability. Such results indicate that acid growth is not due simply to the physical chemistry of the wall (e.g., a weakening of the pectin gel), but is catalyzed by one or more wall proteins.
The idea that proteins are required for acid growth was confirmed in reconstitution experiments, in which heat-inactivated walls were restored to nearly full acid growth responsiveness by addition of proteins extracted from grow-ing walls (Figure 15.27). The active components proved to be a group of proteins that were named expansins (McQueen-Mason et al. 1992; Li et al. 1993). These proteins catalyze the pH-dependent extension and stress relaxation of cell walls. They are effective in catalytic amounts (about 1 part protein per 5000 parts wall, by dry weight).
The molecular basis for expansin action on wall rheol-ogy is still uncertain, but most evidence indicates that expansins cause wall creep by loosening noncovalent adhe-sion between wall polysaccharides (Cosgrove 2000; Li and Cosgrove 2001). Binding studies suggest that expansins may act at the interface between cellulose and one or more hemicelluloses.
With the completion of the Arabidopsis genome, we now know that Arabidopsis has a large collection of expansin genes, divided into two families: α-expansins and β-expansins. The two kinds of expansins act on different polymers of the cell wall (Cosgrove 2000). β-expansins have also been found in grass pollen, where they probably function to aid pollen tube penetration into the stigma and style (Li and Cosgrove 2001).
Glucanases and Other Hydrolytic Enzymes May Modify the Matrix Several types of experiments implicate (1→4)β-D-glucanases in cell wall loosening, especially during auxin-induced cell elongation (see Chapter 19). For example, matrix glucans 334 Chapter 15 0.6 0.4 0.2 0 1 2 Time (hours) Length (mm) Freeze, thaw, abrade Electronic transducer measures extension Solution that can be made acidic Cut pH 4.5 Constant force FIGURE 15.26 Acid-induced extension of isolated cell walls, measured in an extensometer. The wall sample from killed cells is clamped and put under tension in an extensometer that measures the length with an electronic transducer attached to a clamp. When the solution surrounding the wall is replaced with an acidic buffer (e.g., pH 4.5), the wall extends irreversibly in a time-dependent fashion (it creeps).
40 30 20 10 0 Time Length (%) Inactivate with heat Etiolated cucumber seedling Electronic transducer measures extension Wall specimen Excise growing region Control Expansin added pH 4.5 buffer Homogenize.
Collect, and wash walls.
Extract walls to solubilize the protein expansin.
Apply protein to wall Freeze, thaw, abrade Constant force FIGURE 15.27 Scheme for the reconstitution of extensibility of isolated cell walls. (A) Cell walls are prepared as in Figure 15.21, and briefly heated to inactivate the endogenous acid extension response. To restore this response, proteins are extracted from growing walls and added to the solution surrounding the wall. (B) Addition of proteins containing expansins restores the acid extension properties of the wall. (After Cosgrove 1997.) such as xyloglucan show enhanced hydrolysis and turnover in excised segments when growth is stimulated by auxin.
Interference with this hydrolytic activity by antibodies or lectins reduces growth in excised segments. Expression of (1→4)β-D-glucanases is associated with growing tissues, and application of glucanases to cells in vitro may stimulate growth. Such results support the idea that wall stress relaxation and expansion are the direct result of the activity of glucanases that digest xyloglucan in dicotyledons or (1→3,1→4)β-D-glucans in grass cell walls (Hoson 1993).
However, most glucanases and related wall hydrolases do not cause walls to extend in the same way that expansins do. Instead, treatment of walls with glucanases or pectinases may enhance the subsequent extension response to expansins (Cosgrove and Durachko 1994).
These results suggest that wall hydrolytic enzymes such as (1→4)β-D-glucanases are not the principal catalysts of wall expansion, but they may act indirectly by modulating expansin-mediated polymer creep. Xyloglucan endotransglycosylase has also been sug-gested as a potential wall-loosening enzyme. XET helps integrate newly secreted xyloglucan into the existing wall structure, but its function as a wall-loosening agent is still speculative. Many Structural Changes Accompany the Cessation of Wall Expansion The growth cessation that occurs during cell maturation is generally irreversible and is typically accompanied by a reduction in wall extensibility, as measured by various bio-physical methods. These physical changes in the wall might come about by (1) a reduction in wall-loosening processes, (2) an increase in wall cross-linking, or (3) an alteration in the composition of the wall, making for a more rigid struc-ture or one less susceptible to wall loosening. There is some evidence for each of these ideas (Cosgrove 1997).
Several modifications of the maturing wall may con-tribute to wall rigidification: • Newly secreted matrix polysaccharides may be altered in structure so as to form tighter complexes with cellulose or other wall polymers, or they may be resistant to wall-loosening activities.
• Removal of mixed-link β-D-glucans is also coincident with growth cessation in these walls.
• De-esterification of pectins, leading to more rigid pectin gels, is similarly associated with growth cessa-tion in both grasses and dicotyledons.
• Cross-linking of phenolic groups in the wall (such as tyrosine residues in HRGPs, ferulic acid residues attached to pectins, and lignin) generally coincides with wall maturation and is believed to be mediated by peroxidase, a putative wall rigidification enzyme.
Many structural changes occur in the wall during and after cessation of growth, and it has not yet been possible to identify the significance of individual processes for ces-sation of wall expansion.
WALL DEGRADATION AND PLANT DEFENSE The plant cell wall is not simply an inert and static exoskele-ton. In addition to acting as a mechanical restraint, the wall serves as an extracellular matrix that interacts with cell sur-face proteins, providing positional and developmental information. It contains numerous enzymes and smaller molecules that are biologically active and that can modify the physical properties of the wall, sometimes within sec-onds. In some cases, wall-derived molecules can also act as signals to inform the cell of environmental conditions, such as the presence of pathogens. This is an important aspect of the defense response of plants (see Chapter 13).
Walls may also be substantially modified long after growth has ceased. For instance, the cell wall may be mas-sively degraded, such as occurs in ripening fruit or in the endosperm of germinating seeds. In cells that make up the abscission zones of leaves and fruits (see Chapter 22), the middle lamella may be selectively degraded, with the result that the cells become unglued and separate. Cells may also separate selectively during the formation of inter-cellular air spaces, during the emergence of the root from germinating seeds, and during other developmental processes. Plant cells may also modify their walls during pathogen attack as a form of defense.
In the sections that follow we will consider two types of dynamic changes that can occur in mature cell walls: hydrolysis and oxidative cross-linking. We will also discuss how fragments of the cell wall released during pathogen attack, or even during normal cell wall turnover, may act as cellular signals that influence metabolism and development.
Enzymes Mediate Wall Hydrolysis and Degradation Hemicelluloses and pectins may be modified and broken down by a variety of enzymes that are found naturally in the cell wall. This process has been studied in greatest detail in ripening fruit, in which softening is thought to be the result of disassembly of the wall (Rose and Bennett 1999). Glucanases and related enzymes may hydrolyze the backbone of hemicelluloses. Xylosidases and related enzymes may remove the side branches from the backbone of xyloglucan. Transglycosylases may cut and join hemi-celluloses together. Such enzymatic changes may alter the physical properties of the wall, for example, by changing the viscosity of the matrix or by altering the tendency of the hemicelluloses to stick to cellulose.
Messenger RNAs for expansin are expressed in ripen-ing tomato fruit, suggesting that they play a role in wall disassembly (Rose et al. 1997). Similarly, softening fruits Cell Walls: Structure, Biogenesis, and Expansion 335 express high levels of pectin methyl esterase, which hydrolyzes the methyl esters from pectins. This hydrolysis makes the pectin more susceptible to subsequent hydrolysis by pecti-nases and related enzymes. The presence of these and related enzymes in the cell wall indi-cates that walls are capable of significant mod-ification during development.
Oxidative Bursts Accompany Pathogen Attack When plant cells are wounded or treated with certain low-molecular-weight elicitors (see Chapter 13), they activate a defense response that results in the production of high concen-trations of hydrogen peroxide, superoxide radicals, and other active oxygen species in the cell wall. This “oxidative burst” appears to be part of a defense response against invading pathogens (see Chapter 13) (Brisson et al. 1994; Otte and Barz 1996).
Active oxygen species may directly attack the pathogenic organisms, and they may indi-rectly deter subsequent invasion by the path-ogenic organisms by causing a rapid cross-linking of phenolic components of the cell wall. In tobacco stems, for example, proline-rich structural proteins of the wall become rapidly insolu-bilized upon wounding or elicitor treatment, and this cross-linking is associated with an oxidative burst and with a mechanical stiffening of the cell walls.
Wall Fragments Can Act as Signaling Molecules Degradation of cell walls can result in the production of biologically active fragments 10 to 15 residues long, called oligosaccharins, that may be involved in natural devel-opmental responses and in defense responses (see Web Topic 15.5). Some of the reported physiological and devel-opmental effects of oligosaccharins include stimulation of phytoalexin synthesis, oxidative bursts, ethylene synthe-sis, membrane depolarization, changes in cytoplasmic cal-cium, induced synthesis of pathogen-related proteins such as chitinase and glucanase, other systemic and local “wound” signals, and alterations in the growth and mor-phogenesis of isolated tissue samples (John et al. 1997).
The best-studied examples are oligosaccharide elicitors produced during pathogen invasion (see Chapter 13). For example, the fungus Phytophthora secretes an endopoly-galacturonase (a type of pectinase) during its attack on plant tissues. As this enzyme degrades the pectin component of the plant cell wall, it produces pectin fragments—oli-gogalacturonans—that elicit multiple defense responses by the plant cell (Figure 15.28). The oligogalacturonans that are 10 to 13 residues long are most active in these responses. Plant cell walls also contain a β-D-glucanase that attacks the β-D-glucan that is specific to the fungal cell wall. When this enzyme attacks the fungal wall, it releases glucan oligomers with potent elicitor activity. The wall compo-nents serve in this case as part of a sensitive system for the detection of pathogen invasion.
Oligosaccharins may also function during the normal control of cell growth and differentiation. For example, a specific nonasaccharide (an oligosaccharide containing nine sugar residues) derived from xyloglucan has been found to inhibit growth promotion by the auxin 2,4-dichlorophenoxyacetic acid (2,4-D). The nonasaccharide acts at an optimal concentration of 10–9 M. This xyloglu-can oligosaccharin may act as a feedback inhibitor of growth; for example, when auxin-induced breakdown of xyloglucan is maximal, it may prevent excessive weaken-ing of the cell wall. Related xyloglucan oligomers have also been reported to influence organogenesis in tissue cul-tures and may play a wider role in cell differentiation (Creelman and Mullet 1997).
SUMMARY The architecture, mechanics, and function of plants depend crucially on the structure of the cell wall. The wall is secreted and assembled as a complex structure that varies in form and composition as the cell differentiates. Primary cell walls are synthesized in actively growing cells, and sec-ondary cell walls are deposited in certain cells, such as xylem vessel elements and sclerenchyma, after cell expan-sion ceases.
336 Chapter 15 Chitinase Glucanase Pectinase HIGHER-PLANT CELL WALL CYTOPLASM Stimulation of phytoalexin in the plant FUNGAL CELL WALL e e e e e e e e e e FIGURE 15.28 Scheme for the production of oligosaccharins during fungal invasion of plant cells. Enzymes secreted by the plant, such as chitinase and glucanase, attack the fungal wall, releasing oligosaccha-rins that elicit the production of defense compounds (phytoalexins) in the plant. Similarly, fungal pectinase releases biologically active oligosaccharins from the plant cell wall. (After Brett and Waldron 1996.) The basic model of the primary wall is a network of cel-lulose microfibrils embedded in a matrix of hemicelluloses, pectins, and structural proteins. Cellulose microfibrils are highly ordered arrays of glucan chains synthesized on the membrane by protein complexes called particle rosettes.
The genes for cellulose synthase in plants have recently been identified, bringing the realization that a large gene family encodes these and related proteins. The matrix is secreted into the wall via the Golgi apparatus. Hemicellu-loses and proteins cross-link microfibrils, and pectins form hydrophilic gels that can become cross-linked by calcium ions. Wall assembly may be mediated by enzymes. For example, xyloglucan endotransglycosylase has the ability to carry out transglycosylation reactions that integrate newly synthesized xyloglucans into the wall.
Secondary walls differ from primary walls in that they contain a higher percentage of cellulose, they have different hemicelluloses, and lignin replaces pectins in the matrix. Sec-ondary walls can also become highly thickened, sculpted, and embedded with specialized structural proteins.
In diffuse-growing cells, growth directionality is deter-mined by wall structure, in particular the orientation of the cellulose microfibrils, which in turn is determined by the orientation of microtubules in the cytoplasm. Upon leav-ing the meristem, plant cells typically elongate greatly. Cell enlargement is limited by the ability of the cell wall to undergo polymer creep, which in turn is controlled in a complex way by the adhesion of wall polymers to one another and by the influence of pH on wall-loosening pro-teins such as expansins, glucanases, and other enzymes. According to the acid growth hypothesis, proton extru-sion by the plasma membrane H+-ATPase acidifies the wall, activating the protein expansin. Expansins induce stress relaxation of the wall by loosening the bonds hold-ing microfibrils together. The cessation of cell elongation appears to be due to cell wall rigidification caused by an increase in the number of cross-links.
Hydrolytic enzymes may degrade mature cell walls completely or selectively during fruit ripening, seed ger-mination, and the formation of abscission layers. Cell walls can also undergo oxidative cross-linking in response to pathogen attack. In addition, pathogen attack may release cell wall fragments, and certain wall fragments have been shown to be capable of acting as cell signaling agents.
Web Material Web Topics 15.1 Terminology for Polysaccharide Chemistry A brief review of terms used to describe the structures, bonds, and polymers in polysaccha-ride chemistry is provided.
15.2 Molecular Model for the Synthesis of Cellulose and Other Wall Polysaccharides That Consist of a Disaccharide Repeat A model is presented for the polymerization of cellubiose units into glucan chains by the enzyme cellulose synthase.
15.3 Matrix Components of the Cell Wall The secretion of xyloglucan and glycosylated proteins by the Golgi can be demonstrated at the ultrastructural level.
15.4 The Mechanical Properties of Cell Walls: Studies with Nitella Experiments demonstrating that the inner 25% of the cell wall determines the directionality of cell expansion are described.
15.5 Structure of Biologically Active Oligosac-charins Some cell wall fragments have been demon-strated to have biological activity.
Web Essay 15.1 Calcium Gradients and Oscillations in Growing Pollen Tube The role of calcium in regulating pollen tube tip growth is described.
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338 Chapter 15 Growth and Development 16 Chapter THE VEGETATIVE PHASE OF DEVELOPMENT begins with embryo-genesis, but development continues throughout the life of a plant. Plant developmental biologists are concerned with questions such as, How does a zygote give rise to an embryo, an embryo to a seedling? How do new plant structures arise from preexisting structures? Organs are gen-erated by cell division and expansion, but they are also composed of tis-sues in which groups of cells have acquired specialized functions, and these tissues are arranged in specific patterns. How do these tissues form in a particular pattern, and how do cells differentiate? What are the basic principles that govern the size increase (growth) that occurs throughout plant development?
Understanding how growth, cell differentiation, and pattern forma-tion are regulated at the cellular, biochemical, and molecular levels is the ultimate goal of developmental biologists. Such an understanding also must include the genetic basis of development. Ultimately, development is the unfolding of genetically encoded programs. Which genes are involved, what is their hierarchical order, and how do they bring about developmental change?
In this chapter we will explore what is known about these questions, beginning with embryogenesis. Embryogenesis initiates plant develop-ment, but unlike animal development, plant development is an ongoing process. Embryogenesis establishes the basic plant body plan and forms the meristems that generate additional organs in the adult.
After discussing the formation of the embryo, we will examine root and shoot meristems. Most plant development is postembryonic, and it occurs from meristems. Meristems can be considered to be cell factories in which the ongoing processes of cell division, expansion, and differ-entiation generate the plant body. Cells derived from meristems become the tissues and organs that determine the overall size, shape, and struc-ture of the plant.
Vegetative meristems are highly repetitive—they produce the same or similar structures over and over again—and their activity can con-tinue indefinitely, a phenomenon known as indeterminate growth. Some long-lived trees, such as bristlecone pines and the California redwoods, continue to grow for thousands of years. Others, particularly annual plants, may cease veg-etative development with the initiation of flowering after only a few weeks or months of growth. Eventually the adult plant undergoes a transition from vegetative to repro-ductive development, culminating in the production of a zygote, and the process begins again. Reproductive devel-opment will be discussed in Chapter 24.
Cells derived from the apical meristems exhibit specific patterns of cell expansion, and these expansion patterns determine the overall shape and size of the plant. We will ex-amine how plant growth is analyzed after discussing meris-tems, with an emphasis on growth patterns in space (rela-tionship of plant structures) and time (when events occur).
Finally, despite their indeterminate growth habit, plants, like all other multicellular organisms, senesce and die. At the end of the chapter we will consider death as a devel-opmental phenomenon, at both the cellular and organismal levels. Foe an historical overviw of the study of plant development, see Web Essay 16.1.
EMBRYOGENESIS The developmental process known as embryogenesis ini-tiates plant development. Although embryogenesis usually begins with the union of a sperm with an egg, forming a single-celled zygote, somatic cells also may undergo embryogenesis under special circumstances. Fertilization also initiates three other developmental programs: endo-sperm, seed, and fruit development. Here we will focus on embryogenesis because it provides the key to understand-ing plant development.
Embryogenesis transforms a single-celled zygote into a multicellular, microscopic, embryonic plant. A completed embryo has the basic body plan of the mature plant and many of the tissue types of the adult, although these are present in a rudimentary form.
Double fertilization is unique to the flowering plants (see Web Topics 1.1 and 1.2). In plants, as in all other eukaryotes, the union of one sperm with the egg forms a single-celled zygote. In angiosperms, however, this event is accompanied by a second fertilization event, in which another sperm unites with two polar nuclei to form the triploid endosperm nucleus, from which the endosperm (the tissue that supplies food for the growing embryo) will develop.
Embryogenesis occurs within the embryo sac of the ovule while the ovule and associated structures develop into the seed. Embryogenesis and endosperm development typically occur in parallel with seed development, and the embryo is part of the seed. Endosperm may also be part of the mature seed, but in some species the endosperm dis-appears before seed development is completed. Embryo-genesis and seed development are highly ordered, inte-grated processes, both of which are initiated by double fer-tilization. When completed, both the seed and the embryo within it become dormant and are able to survive long periods unfavorable for growth. The ability to form seeds is one of the keys to the evolutionary success of angiosperms as well as gymnosperms.
The fact that a zygote gives rise to an organized embryo with a predictable and species-specific structure tells us that the zygote is genetically programmed to develop in a particular way, and that cell division, cell expansion, and cell differentiation are tightly controlled during embryo-genesis. If these processes were to occur at random in the embryo, the result would be a clump of disorganized cells with no definable form or function.
In this section we will examine these changes in greater detail. We will focus on molecular genetic studies that have been conducted with the model plant Arabidopsis that have provided insights into plant development. It is most likely that most angiosperms probably use similar developmen-tal mechanisms that appeared early in the evolution of the flowering plants and that the diversity of plant form is brought about by relatively subtle changes in the time and place where the molecular regulators of development are expressed, rather than by different mechanisms altogether (Doebley and Lukens 1998).
Arabidopsis thaliana is a member of the Brassicaceae, or mustard family (Figure 16.1). It is a small plant, well suited for laboratory culture and experimentation. It has been called the Drosophila of plant biology because of its wide-spread use in the study of plant genetics and molecular genetic mechanisms, particularly in an effort to understand plant developmental change. It was the first higher plant to have its genome completely sequenced. Furthermore, there is a concerted international effort to understand the function of every gene in the Arabidopsis genome by the year 2010. As a result, we are much closer to an under-standing of the molecular mechanisms governing Ara-bidopsis embryogenesis than of those for any other plant species.
Embryogenesis Establishes the Essential Features of the Mature Plant Plants differ from most animals in that embryogenesis does not directly generate the tissues and organs of the adult.
For example, angiosperm embryogenesis forms a rudi-mentary plant body, typically consisting of an embryonic axis and two cotyledons (if it is a dicot). Nevertheless, embryogenesis establishes the two basic developmental patterns that persist and can easily be seen in the adult plant: 1. The apical–basal axial developmental pattern.
2. The radial pattern of tissues found in stems and roots.
340 Chapter 16 Embryogenesis also establishes the primary meristems.
Most of the structures that make up the adult plant are gen-erated after embryogenesis through the activity of meris-stems. Although these primary meristems are established during embryogenesis, only upon germination will they become active and begin to generate the organs and tissues of the adult.
Axial patterning. Almost all plants exhibit an axial polar-ity in which the tissues and organs are arrayed in a precise order along a linear, or polarized, axis. The shoot apical meristem is at one end of the axis, the root apical meristem at the other. In the embryo and seedling, one or two cotyle-dons are attached just below the shoot apical meristem.
Next in this linear array is the hypocotyl, followed by the root, the root apical meristem, and the root cap. This axial pattern is established during embryogenesis.
What may not be so obvious is the fact that any individ-ual segment of either the root or the shoot also has apical and basal ends with different, distinct physiological and structural properties. For example, whereas adventitious roots develop from the basal ends of stem cuttings, buds develop from the apical ends, even if they are inverted (see Figure 19.12).
Radial patterning. Different tissues are organized in a pre-cise pattern within plant organs. In stems and roots the tis-sues are arranged in a radial pattern extending from the outside of a stem or a root into its center. If we examine a root in cross section, for example, we see three concentric rings of tissues arrayed along a radial axis: An outermost Silique (fruit) Cauline (stem) leaf (A) (B) Rosette leaf Roots Internode Petal Sepal Stamen Carpel (C) (D) FIGURE 16.1 Arabidopsis thaliana. (A) Drawing of a mature Arabidopsis plant showing the various organs. (B) Drawing of a flower showing the floral organs. (C) An immature vegeta-tive plant consisting of basal rosette leaves and a root system (not shown). (D) A mature plant after most of the flowers have matured and the siliques have developed. (A and B after Clark 2001; C and D courtesy of Caren Chang.) Growth and Development 341 layer of epidermal cells (the epidermis) covers a cylinder of cortical tissue (the cortex), which in turn overlies the vascular cylinder (the endodermis, pericycle, phloem, and xylem) (Figure 16.2) (see Chapter 1).
The protoderm is the meristem that gives rise to the epi-dermis, the ground meristem produces the future cortex and endodermis, and the procambium is the meristem that gives rise to the primary vascular tissue and vascular cambium.
Arabidopsis Embryos Pass through Four Distinct Stages of Development The Arabidopsis pattern of embryogenesis has been studied extensively and is the one we will present here, but keep in mind that angiosperms exhibit many different patterns of embryonic development, and this is only one type.
The most important stages of embryogenesis in Ara-bidopsis, and many other angiosperms, are these: 1. The globular stage embryo. After the first zygotic divi-sion, the apical cell undergoes a series of highly ordered divisions, generating an eight-cell (octant) globular embryo by 30 hours after fertilization (Figure 16.3C). Additional precise cell divisions Protoxylem Pericycle Endodermis Cortex Epidermis Casparian strip 1 mm FIGURE 16.2 The radial pattern of tissues found in plant organs can be observed in a crosssection of the root. This crosssection of an Arabidopsis root was taken approximately 1 mm back from the root tip, a region in which the different tissues have formed.
Apical cells Basal cells Cotyledon Axis Protoderm Cotyledon Axis Root apex Shoot apex (A) (B) (D) (E) (F) (G) (H) (C) FIGURE 16.3 Arabidopsis embryogenesis is characterized by a precise pattern of cell division. Successive stages of embryogenesis are depicted here. (A) One-cell embryo after the first division of the zygote, which forms the apical and basal cells; (B) two-cell embryo; (C) eight-cell embryo; (D) early globular stage, which has developed a distinct proto-derm (surface layer); (E) early heart stage; (F) late heart stage; (G) torpedo stage; (H) mature embryo. (From West and Harada 1993 photographs taken by K. Matsudaira Yee; courtesy of John Harada, © American Society of Plant Biologists, reprinted with permission.) 50 µm 25 µm 25 µm 25 µm 25 µm 50 µm 50 µm 50 µm 342 Chapter 16 increase the number of cells in the sphere (Figure 16.3D).
2. The heart stage embryo. This stage forms through rapid cell divisions in two regions on either side of the future shoot apex. These two regions produce outgrowths that later will give rise to the cotyledons and give the embryo bilateral symmetry (Figure 16.3E and F).
3. The torpedo stage embryo. This stage forms as a result of cell elongation throughout the embryo axis and further development of the cotyledons (Figure 16.3G).
4. The maturation stage embryo. Toward the end of embryogenesis, the embryo and seed lose water and become metabolically quiescent as they enter dor-mancy (Figure 16.3H).
Cotyledons are food storage organs for many species, and during the cotyledon growth phase, proteins, starch, and lipids are synthesized and deposited in the cotyledons to be utilized by the seedling during the heterotrophic (nonphotosynthetic) growth that occurs after germination.
Although food reserves are stored in the Arabidopsis cotyle-dons, the growth of the cotyledons is not as extensive in this species as it is in many other dicots. In monocots, the food reserves are stored mainly in the endosperm. In Ara-bidopsis and many other dicots, the endosperm develops rapidly early in embryogenesis but then is reabsorbed, and the mature seed lacks endosperm tissue.
The Axial Pattern of the Embryo Is Established during the First Cell Division of the Zygote Axial polarity is established very early in embryogenesis (see Web Topic 16.1). In fact, the zygote itself becomes polarized and elongates approximately threefold before its first division. The apical end of the zygote is densely cyto-plasmic, but the basal half of the cell contains a large cen-tral vacuole (Figure 16.4).
The first division of the zygote is asymmetric and occurs at right angles to its long axis. This division creates two cells—an apical and a basal cell—that have very different fates (see Figure 16.3A). The smaller, apical daughter cell receives more cytoplasm than the larger, basal cell, which inherits the large zygotic vacuole. Almost all of the struc-tures of the embryo, and ultimately the mature plant, are derived from the smaller apical cell. Two vertical divisions and one horizontal division of the apical cell generate the eight-celled (octant) globular embryo (see Figure 16.3C).
The basal cell also divides, but all of its divisions are hor-izontal, at right angles to the long axis. The result is a fila-ment of six to nine cells known as the suspensor that attaches the embryo to the vascular system of the plant. Only one of the basal cell derivatives contributes to the embryo.
The basal cell derivative nearest the embryo is known as the hypophysis (plural hypophyses), and it forms the columella, or central part of the root cap, and an essential part of the root apical meristem known as the quiescent center, which will be discussed later in the chapter (Figure 16.5).
Even though the embryo is spherical throughout the globular stage of embryogenesis (see Figure 16.3A–D), the cells within the apical and basal halves of the sphere have different identities and functions. As the embryo continues to grow and reaches the heart stage, its axial polarity becomes more distinct (see Figure 16.5), and three axial regions can readily be recognized: 1. The apical region gives rise to the cotyledons and shoot apical meristem.
2. The middle region gives rise to the hypocotyl, root, and most of the root meristem.
3. The hypophysis gives rise to the rest of the root meri-stem (see Figure 16.5).
The cells of the upper and lower tiers of the early globular stage embryo differ, and the embryo is divided into apical and basal halves, reflecting the axial pattern imposed on the embryo in the zygote.
The Radial Pattern of Tissue Differentiation Is First Visible at the Globular Stage The radial pattern of tissue differentiation is first observed in the octant embryo (Figure 16.6). As cell division contin-ues in the globular embryo, transverse divisions divide the Zygote nucleus Endosperm nucleus Embryo sac Nucellus Zygote Ovule integuments Vacuole FIGURE 16.4 Arabidopsis ovule containing the embryo sac at about 4 hours after double fertilization. The zygote exhibits a marked polarization. The terminal half of the zygote has dense cytoplasm and a single large nucleus, while a large central vacuole occupies the basal half of the cell. At this stage, the embryo sac surrounding the zygote also contains 4 endosperm nuclei.
Growth and Development 343 Early seedling Heart stage Octant stage Two-cell stage Hypophysis Suspensor Basal cell of suspensor Central cells Apical cells Basal cell Terminal cell Shoot apical meristem Shoot apical meristem Cotyledons Hypocotyl Embryonic root Root meristem Quiescent center Columella root cap FIGURE 16.5 The apical–basal organization of plant tissues and organs is established very early in embryogenesis. This diagram illustrates how the organs of the early Arabidopsis seedling originate from specific regions of the embryo.
(From Willemsen et al. 1998.) Seedling Cotyledons Shoot apical meristem Root Torpedo stage Heart stage Protoderm Early globular stage Hypophysis Hypocotyl Epidermis Ground meristem/ cortex and epidermis Vascular cambium/ stele Columella of root cap Quiescent center Root cap FIGURE 16.6 The radial tissue patterns are also established during embryogene-sis. This drawing illustrates the origin of the different tissues and organs from embryonic regions in Arabidopsis embryogenesis. The gray lines between the tor-pedo and seedling stages indicate the regions of the embryo that give rise to various regions of the seedling. The expanded regions represent boundaries where developmental fate is somewhat flexible. (After Van Den Berg et al. 1995.) 344 Chapter 16 lower tier of cells radially into three regions.
These regions will become the radially arranged tissues of the root and stem axes. The outermost cells form a one-cell-thick surface layer, known as the protoderm. The protoderm covers both halves of the embryo and will generate the epidermis.
Cells that will become the ground meristem underlie the protoderm. The ground meristem gives rise to the cortex and, in the root and hypocotyl, it will also produce the endodermis.
The procambium is the inner core of elongated cells that will generate the vascular tissues and, in the root, the pericycle (see Figure 16.2).
Embryogenesis Requires Specific Gene Expression Analysis of Arabidopsis mutants that either fail to establish axial polarity or develop abnormally during embryogenesis has led to the identifica-tion of genes whose expression participates in tis-sue patterning during embryogenesis.
The GNOM gene: Axial patterning. Seedlings homozygous for mutations in the GNOM gene lack both roots and cotyledons (Figure 16.7A) (Mayer et al. 1993). Defects in gnom embryos first appear during the initial division of the zygote, and they persist throughout embryogenesis. In the most extreme mutants, gnom embryos are spherical and lack axial polarity entirely. We can conclude that GNOM gene expression is required for the establish-ment of axial polarity.1 The MONOPTEROS gene: Primary root and vascular tissue. Mutations in the MONOPTEROS (MP) gene result in seedlings that lack both a hypocotyl and a root, although they do produce an apical region. The apical structures in the mp mutant embryos are not structurally normal, how-ever, and the tissues of the cotyledons are disorganized (Figure 16.7B) (Berleth and Jürgens 1993). Embryos of mp mutants first show abnormalities at the octant stage, and they do not form a procambium in the lower part of the globular embryo, the part that should give rise to the hypocotyl and root. Later some vascular tissue does form in the cotyledons, but the strands are improperly connected.
Although the mp mutant embryos lack a primary root when they germinate, they will form adventitious roots as the seedlings grow into adult plants. The vascular tissues in all organs of these mutant plants are poorly developed, with frequent discontinuities. Thus the MP gene is required for the formation of the embryonic primary root, but not for root formation in the adult plant. The MP gene is important for the formation of vascular tissue in postem-bryonic development (Przemeck et al. 1996).
The SHORT ROOT and SCARECROW genes: Ground tissue development. Genes have been identified that func-tion in the establishment of the radial tissue pattern in the root and hypocotyl during embryogenesis. These genes also are required for maintenance of the radial pattern dur-ing postembryonic development (Scheres et al. 1995; Di Laurenzio et al. 1996). To identify these genes, investigators isolated Arabidopsis mutants that caused roots to grow slowly (Figure 16.8B). Analysis of these mutants identified several that have defects in the radial tissue pattern. Two of the affected genes, SHORT ROOT (SHR) and SCARE-CROW (SCR), are necessary for tissue differentiation and cell differentiation not only in the embryo, but also in both primary and secondary roots and in the hypocotyl.
Mutants of SHR and SCR both produce roots with a sin-gle-celled layer of ground tissue (Figure 16.8D). Cells mak-ing up the single-celled layer of ground tissue have a mixed identity and show characteristics of both endoder-mal and cortical cells in plants with the scr mutation. These scr mutants also lack the cell layer called the starch sheath, a structure that is involved in the growth response to gravity (see Chapter 19). Roots of plants with the shr mutation also 1 In discussions of plant and yeast genetics, wild-type (nor-mal) genes are capitalized and italicized (in this case GNOM), and mutations are set in lowercase letters (here gnom).
FIGURE 16.7 Genes whose functions are essential for Arabidopsis embryogenesis have been identified by the selection of mutants in which a stage of embryogenesis is blocked, such as gnom and monopteros. The development of mutant seedlings is contrasted here with that of the wild type at the same stage of development. (A) The GNOM gene helps establish apical–basal polarity. A plant homozy-gous for gnom is shown on the right. (B) The MONOPTEROS gene is necessary for basal patterning and formation of the primary root.
Plants homozygous for the monopteros mutation have a hypocotyl, a normal shoot apical meristem, and cotyledons, but they lack the pri-mary root. (A from Willemsen et al. 1998; B from Berleth and Jürgens 1993.) MONOPTEROS genes control formation of the primary root GNOM genes control apical– basal polarity (B) Wild type monopteros mutant (A) Wild type gnom mutant Growth and Development 345 have a single layer of ground tissue, but it has only cortical cell characteristics and lacks endodermal characteristics.
The HOBBIT gene: The root meristem. The primary root and shoot meristems are established during embryogene-sis. Because in most cases they do not become active at this time, the term promeristem may be more appropriate to describe these structures. A promeristem may be defined as an embryonic structure that will become a meristem upon germination.
A molecular marker for the root promeristem has not yet been identified, but it appears to be determined early in embryogenesis. Root cap stem cells (the cells that divide to produce the root cap) are formed from the hypophysis at the heart stage of embryogenesis, indicating that the root promeristem is established at least by this stage of embryo-genesis (Figure 16.9). The expression of the HOBBIT gene may be an early marker of root meristem identity (Willem-sen et al. 1998).
Stem cell Stem cell Anticlinal cell divisions (A) Daughter cell Periclinal cell divisions This step is blocked in scr mutants Endodermal cell Cortical cell FIGURE 16.8 Mutations in the Arabidopsis gene SCARECROW (SCR) alter the pattern of tissues in the root. (A) The cell divisions forming the endodermis and cortex. The endodermal cells and cortical cells are derived from the same initial cells as a result of two asymmetric cell divisions. The cortical–endodermal stem cell (uncommitted cell) expands and then divides anticlinally, reproducing itself and a daughter cell. The daughter cell then divides periclinally to produce a small cell that develops endodermal characteristics and a larger cell that becomes a cortical cell. The second asymmetric division does not occur in scr mutants, and the daughter cell formed as a result of the anticlinal division of the initial has characteristics of both cortical and endodermal cells. (B) The growth of a 12-day-old wild-type seedling (left) is compared with that of two 12-day-old seedlings homozygous for a mutation in the SCARECROW (SCR) gene (middle and right).
(C) Cross section of the primary root of a wild-type seedling. (D) Cross section of the primary root of a seedling homozygous for the scr mutant. (From Di Laurenzio et al. 1996; photos © Cell Press, cour-tesy of P. Benfey.) (B) (D) (C) Epidermis Cortex Pericycle Epidermis Pericycle Mutant layer cell Endodermis 50 µm 50 µm Wild type scr1 scr2 346 Chapter 16 Mutants of the HOBBIT (HBT) gene are defective in the formation of a functional embryonic root, as are plants with mp mutants. However, these two mutations act in very dif-ferent ways. The hbt mutants begin to show abnormalities at the two- or four-cell stage, before the formation of the globular embryo. The primary defect in hbt mutants is in the hypophyseal precursor, which divides vertically instead of horizontally. As a result, the hypophysis does not form, and the root meristem that subsequently forms lacks a quiescent center and the columella (see Figure 16.9F). Embryos of hbt mutants appear to have a root meristem, but it does not function when the seedlings ger-minate. Furthermore, plants grown from hbt mutant embryos are unable to form lateral roots.
The SHOOTMERISTEMLESS gene: The shoot promeri-stem. The shoot promeristem can be recognized morpho-logically by the torpedo stage of embryogenesis in Ara-bidopsis. Oriented cell divisions of some of the cells between the cotyledons result in a layered appearance of this region that is characteristic of the shoot apical meri-stem (as described later in the chapter). However, the pro-genitors of these cells probably acquired the molecular identity of the shoot apical meristem cells much earlier, during the globular stage.
The SHOOTMERISTEMLESS (STM) gene is expressed specifically in the cells that will become the shoot apical meristem, and its expression in these cells is required for the formation of the shoot promeristem. Arabidopsis plants homozygous for a mutated, loss-of-function STM gene do not form a shoot apical meristem, and instead all the cells in this region differentiate (Lincoln et al. 1994). The prod-uct of the wild-type STM gene appears to suppress cell dif-ferentiation, ensuring that the meristem cells remain undif-ferentiated.
STM mRNA can first be detected in one or two cells at the apical end of the midglobular embryo. By the heart stage, STM expression is confined to a few cells between the cotyledons (Long et al. 1996). Because STM acts as a marker for these cells, the shoot apical meristem must be specified long before it can be recognized morphologically.
The STM gene is necessary not only for the formation of the embryonic shoot apical meristem, but also for the maintenance of shoot apical meristem identity in the adult plant. The role of the nucleus in controlling development was first demonstrated in the giant algal unicell, acetabu-laria (see Web Essay 16.2).
LRC QC COL QC (A) Wild type (B) hobbit mutant (C) (D) 25 mm 25 mm (E) (F) FIGURE 16.9 The HOBBIT (HBT) gene is important for the development of a functional root apical meristem. (A) Wild-type Arabidopsis seedling; (B) hobbit mutant seedling; (C) root tip of wild type showing quiescent center (QC), col-umella (COL) and lateral root cap (LRC); (D) root tip of hob-bit mutant; (E) quiescent center and columella of wild-type; (F) absence of quiescent center and columella in hobbit. The seedlings in A and B are both shown 7 days after germina-tion (4× magnification). Staining with iodine reveals starch grains in the columella cells of the root cap in the wild type (E). No starch grains are present in the hbt mutant root tip (F). (From Willemsen et al. 1998.) Growth and Development 347 Embryo Maturation Requires Specific Gene Expression The Arabidopsis embryo enters dormancy after it has gen-erated about 20,000 cells. Dormancy is brought about by the loss of water and a general shutting down of gene tran-scription and protein synthesis, not only in the embryo, but also throughout the seed. To adapt the cell to the special conditions of dormancy, specific gene expression is required. For example, the ABSCISIC ACID INSENSITIVE3 (ABI3) and FUSCA3 genes are necessary for the initiation of dormancy and are sensitive to the hormone abscisic acid, which is the signaling molecule that initiates seed and embryo dormancy. ABI3 also controls the expression of genes encoding the storage proteins that are deposited in the cotyledons during the maturation phase of embryogen-esis (see Chapter 23).
The LEAFY COTYLEDON1 (LEC1) gene also is active in late embryogenesis. Because lec1 mutants cannot survive desiccation and do not enter dormancy, the embryos die unless they are rescued through isolation before desicca-tion occurs. The rescued embryos will germinate in culture and produce fertile plants, which are like wild-type plants except that they lack the 7S storage protein and they have leaflike cotyledons with trichomes on their upper surface. The normal appearance and development of the mature lec1 mutants indicates that the LEC1 gene is required only during embryogenesis. Although the most obvious defects of the lec1 mutants are seen only in the maturation phase embryo, mRNA from LEC1 gene expression can be detected throughout embryogenesis. It has been proposed that LEC1 is a general repressor of vegetative development and its expression is necessary throughout embryogenesis (Lotan et al. 1998).
THE ROLE OF CYTOKINESIS IN PATTERN FORMATION One of the most striking features of tissue organization in many plants, illustrated by Arabidopsis, is the remarkably precise pattern of oriented, often called stereotypic, cell divi-sions. This pattern of divisions generates files of cells extending from the meristem toward the base of the plant.
Although the division pattern is not as precise in all other species, the basic pattern of tissue formation is similar.
How important is the plane of cell division for the estab-lishment of the tissue patterns found in plant organs?
The Stereotypic Cell Division Pattern Is Not Required for the Axial and Radial Patterns of Tissue Differentiation Two Arabidopsis mutants, fass and ton, have dramatic effects on the patterns of cell division in all stages of development Wild-type Arabidopsis (A) (B) (D) (E) (C) (F) Homozygous ton mutant 50 µm FIGURE 16.10 Arabidopsis plants with mutations in the TON gene are unable to form a preprophase band of microtubules in cells at any stage of division. Plants carrying this mutation are highly irregular in their cell division and expansion planes, and as a result they are severely deformed. However, they continue to produce recognizable tissues and organs in their correct positions.
Although the organs and tissues pro-duced by these mutant plants are highly abnormal, the radial tissue pattern is not disturbed. (A–C) Wild-type Arabidopsis: (A) early globular stage embryo; (B) seedling seen from the top; (C) cross section of a root.
(D–F) Comparable stages of Arabidopsis homozygous for the ton mutation: (D) early embryogenesis; (E) mutant seedling seen from the top; (F) cross section of the mutant root showing the random orientation of the cells, but a near wild-type tis-sue order; an outer epidermal layer covers a multicellular cortex, which in turn surrounds the vascular cylin-der. (From Traas et al. 1995.) 60 µm 348 Chapter 16 and eliminate the stereotypic divisions seen in the wild type (Torres-Ruiz and Jürgens 1994; Traas et al. 1995). These mutations probably are in the same gene, and cells in plants homozygous for the ton (fass) mutation lack a cyto-plasmic structure known as the preprophase band of micro-tubules. The preprophase band appears to be essential for the orientation of the phragmoplast during cytokinesis, and thus is required for oriented cell divisions (see Chapter 1 and Web Topic 16.2).
The effects of the ton (fass) mutation are seen from the earliest stages of embryogenesis and persist throughout development. The plants are tiny, never reaching more than 2 to 3 cm in height. They have misshapen leaves, roots, and stems, and they are sterile (Figure 16.10D–F). Nevertheless, the mutant plants not only establish an axial pattern, but they have all the cell types and organs of the wild-type plant, and these occur in their correct positions. The precise numbers of cells found in each tissue layer are radically dif-ferent in the mutants, but each tissue is present and in the proper order.
The fact that these mutations do not prevent the estab-lishment of the radial tissue pattern is strong evidence that the stereotypic cell division pattern found in the Arabidop-sis embryo and in the root is not essential for the radial pat-tern of tissue differentiation.
An Arabidopsis Mutant with Defective Cytokinesis Cannot Establish the Radial Tissue Pattern The Arabidopsis mutant knolle is defective in cytokinesis, the step at the end of mitosis in which a new wall is formed partitioning the daughter nuclei into separate cells. The KNOLLE gene encodes a syntaxin-like protein that is important for vesicle fusion. Syntaxins are proteins that integrate into membranes, permitting the membranes to fuse. Vesicle fusion is essential for cytokinesis (Figure 16.11).
FIGURE 16.11 Encoded by the KNOLLE gene, syntaxin pro-teins play a critical role in the fusion of Golgi-derived mem-branes, which is required for normal cytokinesis in most organisms, including Arabidopsis. (A) Electron micrograph of a region of an Arabidopsis embryo with the knolle mutation. The box outlined is 5 mm wide. (B) Higher-magnification pho-tomicrograph showing an incomplete and abnormal cross-wall attached to the parent cell wall. (C) A model for the fusion of vesicles during cell plate formation. A complex of soluble proteins mediates the interaction of synaptobrevin protein with the syntaxin protein (encoded by the KNOLLE gene) on the target membrane. (A and B from Lukowitz et al.
1996, courtesy of G. Jürgens; C after Assaad et al. 1996.) (C) Syntaxin protein (in Arabidopsis coded by KNOLLE gene) Synaptobrevin (a vesicle membrane protein) C C N N Target membrane Several soluble proteins mediate interactions of membrane proteins Vesicle membrane (A) (B) e o n n Abnormal cross wall Growth and Development 349 Although cell division is not blocked by the knolle muta-tion, cell plate formation is irregular and often incomplete.
As a result, many cells are binucleate, while other cells are only partly separated or are connected by large cytoplas-mic bridges. The division planes also are irregular. These irregularities have severe effects on development.
Plants homozygous for the knolle mutation go through embryogenesis, but the radial tissue pattern is severely dis-rupted and an epidermal layer does not form in early embryogenesis. The knolle mutation does not prevent for-mation of the apical–basal axis, and embryogenesis is com-pleted, although the seedlings are very short-lived and die soon after germination. The plants also lack functional meristems.
The conclusion drawn from studies of the knolle muta-tion appears to contradict what we learned from the ton (fass) mutations. Both the knolle and the ton mutations dis-rupt the normal pattern of cell division in embryonic and postembryonic development. But whereas the knolle muta-tions block the establishment of the radial tissue pattern, in the ton mutants the pattern is established.
One difference between the ton and the knolle mutations is that the latter usually prevents the effective separation of daughter cells during cytokinesis because the cell plate is incomplete. Since cell–cell communication is important for pattern formation, it may be necessary for cells to be iso-lated effectively so that the information exchange can be regulated. Even though the cytosol is continuous between adjacent plant cells through plasmodesmata, complete cel-lularization is required for normal development. Thus the ton mutants are able to perceive positional information cor-rectly, while the knolle mutants cannot. For a review of the mechanisms determining the plane of cell division in plant cells, see Web Essay 16.3.
MERISTEMS IN PLANT DEVELOPMENT Meristems are populations of small, isodiametric (having equal dimensions on all sides) cells with embryonic char-acteristics. Vegetative meristems are self-perpetuating. Not only do they produce the tissues that will form the body of the root or stem, but they also continuously regenerate themselves. A meristem can retain its embryonic character indefinitely, possibly even for thousands of years in the case of trees. The reason for this ability is that some meri-stematic cells do not become committed to a differentiation pathway, and they retain the capacity for cell division, as long as the meristem remains vegetative.
Undifferentiated cells that retain the capacity for cell division indefinitely are said to be stem cells. Although his-torically called initial cells in plants, in function they are very similar, if not identical, to animal stem cells (Weigel and Jürgens 2002). When stem cells divide, on average one of the daughter cells retains the identity of the stem cell, while the other is committed to a particular developmen-tal pathway (Figure 16.12). Stem cells usually divide slowly. Their committed daughters, however, may enter a period of rapid cell divi-sion before they stop dividing and can be recognized as spe-cific cell types. Stem cells represent the ultimate source of all the cells in the meristem and the entire rest of the plant— both roots, leaves, and other organs, as well as stems.
The Shoot Apical Meristem Is a Highly Dynamic Structure The vegetative shoot apical meristem generates the stem, as well as the lateral organs attached to the stem (leaves and lateral buds). The shoot apical meristem typically con-tains a few hundred to a thousand cells, although the Ara-bidopsis shoot apical meristem has only about 60 cells.
The shoot apical meristem is located at the extreme tip of the shoot, but it is surrounded and covered by immature leaves. These are the youngest leaves produced by the activity of the meristem. It is useful to distinguish the shoot apex from the meristem proper. The shoot apex (plural apices) consists of the apical meristem plus the most recently formed leaf primordia. The shoot apical meristem is the undifferentiated cell population only and does not include any of the derivative organs.
The shoot apical meristem is a flat or slightly mounded region, 100 to 300 µm in diameter, composed mostly of small, thin-walled cells, with a dense cytoplasm, and lack-ing large central vacuoles. The shoot apical meristem is a dynamic structure that changes during its cycle of leaf and stem formation. In addition, in many plants it exhibits sea-sonal activity, as does the entire shoot. Shoot apical meri-stems may grow rapidly in the spring, enter a period of slower growth during the summer, and become dormant in the fall, with dormancy lasting through the winter. The size and structure of the shoot apical meristem also change with seasonal activity.
Shoots develop and grow at their tips, as is the case with roots, but the developing regions are not as stratified and precisely ordered as they are in the root. Moreover, growth occurs over a much broader region of the shoot than is the case for roots. At any given time, a region containing sev-eral internodes, typically 10 to 15 cm long, may be under-going primary growth.
Stem cell Committed cells Daughter cells Differentiated cells FIGURE 16.12 Stem cells generate daughter cells, some of which remain uncommitted and retain the property of stem cells, while others become committed to differentiate.
350 Chapter 16 The Shoot Apical Meristem Contains Different Functional Zones and Layers The shoot apical meristem consists of different functional regions that can be distinguished by the orientation of the cell division planes and by cell size and activity. The angiosperm vegetative shoot apical meristem usually has a highly stratified appearance, typically with three distinct layers of cells. These layers are designated L1, L2, and L3, where L1 is the outermost layer (Figure 16.13). Cell divi-sions are anticlinal in the L1 and L2 layers; that is, the new cell wall separating the daughter cells is oriented at right angles to the meristem surface. Cell divisions tend to be less regularly oriented in the L3 layer. Each layer has its own stem cells, and all three layers contribute to the for-mation of the stem and lateral organs.
Active apical meristems also have an organizational pat-tern called cytohistological zonation. Each zone is com-posed of cells that may be distinguished not only on the basis of their division planes, but also by differences in size and by degrees of vacuolation (see Figure 16.13B). These zones exhibit different patterns of gene expression, reflect-ing the different functions of each zone (Nishimura et al.
1999; Fletcher and Meyerowitz 2000).
The center of an active meristem contains a cluster of relatively large, highly vacuolate cells called the central zone. The central zone is somewhat comparable to the qui-escent center of root meristems (which will be discussed later in the chapter). A doughnut-shaped region of smaller cells, called the peripheral zone, flanks the central zone. A rib zone lies underneath the central cell zone and gives rise to the internal tissues of the stem.
These different zones most likely represent different developmental domains. The peripheral zone is the region in which the first cell divisions leading to the formation of leaf primordia will occur. The rib zone contributes cells that become the stem. The central zone contains the pool of stem cells, some fraction of which remains uncommitted, while others replenish the rib and peripheral zone popu-lations (Bowman and Eshed 2000).
Some Meristems Arise during Postembryonic Development The root and shoot apical meristems formed during embryogenesis are called primary meristems. After ger-mination, the activity of these primary meristems gener-ates the primary tissues and organs that constitute the pri-mary plant body.
Most plants also develop a variety of secondary meri-stems during postembryonic development. Secondary meristems can have a structure similar to that of primary meristems, but some secondary meristems have a quite dif-ferent structure. These include axillary meristems, inflo-rescence meristems, floral meristems, intercalary meri-stems, and lateral meristems (the vascular cambium and cork cambium). (Inflorescence and floral meristems will be discussed in Chapter 24.): FIGURE 16.13 The shoot apical meristem generates the aer-ial organs of the plant. (A) This longitudinal section through the center of the shoot apex of Coleus blumei shows the layered appearance of the shoot apical meristem. Most cell divisions are anticlinal in the outer L1 and L2 layers, while the planes of cell divisions are more randomly ori-ented in the L3 layer. The outermost (L1) layer generates the shoot epidermis; the L2 and L3 layers generate internal tissues. (B) The shoot apical meristem also has cytohistolog-ical zones, which represent regions with different identities and functions. The central zone contains the stem cells, which divide slowly but are the ultimate source of the tis-sues that make up the plant body. The peripheral zone, in which cells divide rapidly, surrounds the central zone and produces the leaf primordia. A rib zone lies below the cen-tral zone and generates the central tissues of the stem. (A ©J. N. A. Lott/Biological Photo Service.) (A) Leaf primordia Shoot apical meristem L3, with randomly oriented cell divisions L1 and L2, with anticlinal cell divisions Generate internal tissues Generates epidermis Leaf primordium Shoot apical meristem L1 – L2 L3 Central zone Rib zone Peripheral zone Peripheral zone (B) Growth and Development 351 • Axillary meristems are formed in the axils of leaves and are derived from the shoot apical meristem. The growth and development of axillary meristems pro-duces branches from the main axis of the plant.
• Intercalary meristems are found within organs, often near their bases. The intercalary meristems of grass leaves and stems enables them to continue to grow despite mowing or grazing by cows.
• Branch root meristems have the structure of the pri-mary root meristem, but they form from pericycle cells in mature regions of the root. Adventitious roots also can be produced from lateral root meristems that develop on stems, as when stem cuttings are rooted to propagate a plant.
• The vascular cambium (plural cambia) is a secondary meristem that differentiates along with the primary vascular tissue from the procambium within the vas-cular cylinder. It does not produce lateral organs, but only the woody tissues of stems and roots. The vas-cular cambium contains two types of meristematic cells: fusiform stem cells and ray stem cells. Fusiform stem cells are highly elongated, vacuolate cells that divide longitudinally to regenerate themselves, and whose derivatives differentiate into the conducting cells of the secondary xylem and phloem. Ray stem cells are small cells whose derivatives include the radially oriented files of parenchyma cells within wood known as rays.
• The cork cambium is a meristematic layer that devel-ops within mature cells of the cortex and the sec-ondary phloem. Derivatives of the cork cambium dif-ferentiate as cork cells that make up a protective layer called the periderm, or bark. The periderm forms the protective outer surface of the secondary plant body, replacing the epidermis in woody stems and roots.
Axillary, Floral, and Inflorescence Shoot Meristems Are Variants of the Vegetative Meristem Several different types of shoot meristems can be distin-guished on the basis of their developmental origin, the types of lateral organs they generate, and whether they are determinate (having a genetically programmed limit to their growth) or indeterminate (showing no predeter-mined limit to growth; growth continues so long as resources permit).
The vegetative shoot apical meristem usually is inde-terminate in its development. It repetitively forms phy-tomeres as long as environmental conditions favor growth but do not generate a flowering stimulus. A phytomere is a developmental unit consisting of one or more leaves, the node to which the leaves are attached, the internode below the node, and one or more axillary buds (Figure 16.14).
Axillary buds are secondary meristems; if they are also vegetative meristems, they will have a structure and devel-opmental potential similar to that of the apical meristem.
Vegetative meristems may be converted directly into flo-ral meristems when the plant is induced to flower (see Chapter 24). Floral meristems differ from vegetative meri-stems in that instead of leaves they produce floral organs: sepals, petals, stamens, and carpels. In addition, floral meristems are determinate: All meristematic activity stops after the last floral organs are produced.
In many cases, vegetative meristems are not directly converted to floral meristems. Instead, the vegetative meristem is first transformed into an inflorescence meri-stem. The types of lateral organs produced by an inflores-cence meristem are different from the types produced by a floral meristem. The inflorescence meristem produces bracts and floral meristems in the axils of the bracts, instead of the sepals, petals, stamens, and ovules produced by flo-ral meristems. Inflorescence meristems may be determinate or indeterminate, depending on the species.
LEAF DEVELOPMENT The leaves of most plants are the organs of photosynthesis.
This is where light energy is captured and used to drive the chemical reactions that are vital to the life of the plant.
Although highly variable in size and shape from species to species, in general leaves are thin, flat structures with dor-siventral polarity. This pattern contrasts with that of the Leaf Node Internode Bud Root Phytomere FIGURE 16.14 The shoot apical meristem repetitively forms units known as phytomeres. Each phytomere consists of one or more leaves, the node at which the leaves are attached, the internode immediately below the leaves, and one or more buds in the axils of the leaves.
352 Chapter 16 shoot apical meristem and stem, both of which have radial symmetry. Another important difference is that leaf pri-mordia exhibit determinate growth, while the vegetative shoot apical meristem is indeterminate. As described in the sections that follow, several distinct stages can be recog-nized in leaf development (Sinha 1999).
Stage 1: Organogenesis. A small number of cells in the L1 and L2 layers in the flanks of the apical dome of the shoot apical meristem acquire the leaf founder cell identity.
These cells divide more rapidly than surrounding cells and produce the outgrowth that represents the leaf pri-mordium (plural primordia) (Figure 16.15A). These pri-mordia subsequently grow and develop into leaves.
Stage 2: Development of suborgan domains. Different regions of the primordium acquire identity as specific parts of the leaf. This differentiation occurs along three axes: dor-siventral (abaxial–adaxial), proximodistal (apical–basal), and lateral (margin–blade–midrib) (Figure 16.15B). The upper (adaxial) side of the leaf is specialized for light absorption; the lower (abaxial) surface is specialized for gas exchange. Leaf structure and maturation rates also vary along the proximodistal and lateral axes.
Stage 3: Cell and tissue differentiation. As the develop-ing leaf grows, tissues and cells differentiate. Cells derived from the L1 layer differentiate as epidermis (epidermal cells, trichomes, and guard cells), derivatives of the L2 layer differentiate as the photosynthetic mesophyll cells, and vas-cular elements and bundle sheath cells are derived from the L3 layer. These cells differentiate in a genetically deter-mined pattern that is characteristic of the species but to some degree modified in response to the environment.
The Arrangement of Leaf Primordia Is Genetically Programmed The timing and pattern with which the primordia form is genetically determined and usually is a characteristic of the species. The number and order in which leaf primordia form is reflected in the subsequent arrangement of leaves around the stem, known as phyllotaxy (Figure 16.16).
There are five main types of phyllotaxy: 1. Alternate phyllotaxy. A single leaf is initiated at each node (see Figure 16.16A).
2. Opposite phyllotaxy. Leaves are formed in pairs on opposite side of the stem (see Figure 16.16B).
3. Decussate phyllotaxy. Leaves are initiated in a pat-tern with two opposite leaves per node and with suc-cessive leaf pairs oriented at right angles to each other during vegetative development (see Figure 16.16C).
4. Whorled phyllotaxy. More than two leaves arise at each node (see Figure 16.16D).
5. Spiral phyllotaxy. A type of alternate phyllotaxy in which each leaf is initiated at a defined angle to the previous leaf, resulting in a spiral arrangement of leaves around the stem (see Figure 16.16E).
The positioning of leaf primordia must result from the precise spatial regulation of growth within the apex. We know little about how this positioning is regulated, or about the signals that initiate the formation of a pri-mordium. One idea is that inhibitory fields generated by existing primordia influence the spacing of the next pri-mordium.
Midrib Margin P1 P3 P2 P0 Site of next primordium (A) (B) Most recently formed primordium, which has radial symmetry at this stage Primordium begins to flatten, developing a dorsiventral axis Primordium elongates in the proximodistal axis Dorsal Ventral Distal Proximal Axillary bud Petiole Node Apical meristem FIGURE 16.15 The origin of leaves at the shoot apex and their axes of symmetry on the stem (A) Leaf primordia in the flanks of the shoot apical meristem. (B) Diagram of a shoot showing the various axes along which development occurs. (After Christensen and Weigel 1998.) Growth and Development 353 ROOT DEVELOPMENT Roots are adapted for growing through soil and absorbing the water and mineral nutrients in the capillary spaces between soil particles. These functions have placed con-straints on the evolution of root structure. For example, lat-eral appendages would interfere with their penetration through the soil. As a result, roots have a streamlined axis, and no lateral organs are produced by the apical meristem.
Branch roots arise internally and form only in mature, non-growing regions. Absorption of water and minerals is enhanced by fragile root hairs, which also form behind the growth zone. These long, threadlike cells greatly increase the root’s absorptive surface area.
In this section we will discuss the origin of root form and structure (root morphogenesis), beginning with a description of the four developmental zones of the root tip.
We will then turn to the apical meristem. The absence of leaves or buds makes cell lineages easier to follow in roots than in shoots, thus facilitating molecular genetic studies on the role of patterns of cell division in root development.
The Root Tip Has Four Developmental Zones Roots grow and develop from their distal ends. Although the boundaries are not sharp, four developmental zones can be distinguished in a root tip: the root cap, the meristematic zone, the elongation zone, and the maturation zone (Figure 16.17). These four developmental zones occupy only a little more than a millimeter of the tip of the Arabidopsis root. The developing region is larger in other species, but growth is still confined to the tip. With the exception of the root cap, the boundaries of these zones overlap considerably: (A) Alternate (B) Opposite (D) Whorled (E) Spiral (C) Decussate FIGURE 16.16 Five types of leaf arrangements (phyllotactic pat-terns) along the shoot axis. The same terms also are used for inflorescences and flowers.
Lateral root primordium Pericycle Cortical cells Epidermis Emerging lateral root Root hair Mature vessel elements Endodermal cells differentiate First vessel elements begin to differentiate Maximum rate of cell elongation First sieve tube element begins to differentiate Cell division ceases in most layers Maximum rate of cell division Quiescent center Maturation zone Elongation zone Meristematic zone Root cap FIGURE 16.17 Simplified diagram of a primary root show-ing the root cap, the meristematic zone, the elongation zone, and the maturation zone. Cells in the meristematic zone have small vacuoles and expand and divide rapidly, generating many files of cells.
354 Chapter 16 • The root cap protects the apical meristem from mechanical injury as the root pushes its way through the soil. Root cap cells form by specialized root cap stem cells. As the root cap stem cells produce new cells, older cells are progressively displaced toward the tip, where they are eventually sloughed off. As root cap cells differentiate, they acquire the ability to perceive gravitational stimuli and secrete mucopolysaccharides (slime) that help the root pene-trate the soil.
• The meristematic zone lies just under the root cap, and in Arabidopsis it is about a quarter of a millimeter long. The root meristem generates only one organ, the primary root. It produces no lateral appendages.
• The elongation zone, as its name implies, is the site of rapid and extensive cell elongation. Although some cells may continue to divide while they elon-gate within this zone, the rate of division decreases progressively to zero with increasing distance from the meristem.
• The maturation zone is the region in which cells acquire their differentiated characteristics. Cells enter the maturation zone after division and elongation have ceased. Differentiation may begin much earlier, but cells do not achieve the mature state until they reach this zone. The radial pattern of differentiated tissues becomes obvious in the maturation zone.
Later in the chapter we will examine the differentia-tion and maturation of one of these cell types, the tra-cheary element.
As discussed earlier, lateral or branch roots arise from the pericycle in mature regions of the root. Cell divisions in the pericycle establish secondary meristems that grow out through the cortex and epidermis, establishing a new growth axis (Figure 16.18). The primary and the secondary root meristems behave similarly in that divisions of the cells in the meristem give rise to progenitors of all the cells of the root.
Root Stem Cells Generate Longitudinal Files of Cells Meristems are populations of dividing cells, but not all cells in the meristematic region divide at the same rate or with the same frequency. Typically, the central cells divide much more slowly than the surrounding cells. These rarely divid-ing cells are called the quiescent center of the root meri-stem (see Figure 16.17).
Cells are more sensitive to ionizing radiation when they are dividing. This is the basis of the use of radiation as a treatment for cancer in humans. As a result, the rapidly dividing cells of the meristem can be killed by doses of radiation that nondividing and slowly dividing cells, such as those of the quiescent center, can survive. If the rapidly dividing cells of the root are killed by ionizing radiation, in many cases the root can regenerate from the cells of the quiescent center. This ability suggests that quiescent-cen-ter cells are important for the patterning involved in form-ing a root.
The most striking structural feature of the root tip, when viewed in longitudinal section, is the presence of the long files of clonally related cells. Most cell divisions in the root tip are transverse, or anticlinal, with the plane of cytoki-nesis oriented at right angles to the axis of the root (such divisions tend to increase root length). There are relatively few periclinal divisions, in which the plane of division is parallel to the root axis (such divisions tend to increase root diameter).
Epidermis Cortex Endodermis Pericycle Vasculature Cortical–endodermal stem cell Root cap–epidermal stem cell Quiescent center Root cap Stage 1 Stage 2 Stage 3 Stage 4 Stage 5 Stage 6 FIGURE 16.18 Model for lateral root formation in Arabidopsis. Six major stages are shown in the development of the primordium. The different tissue types are desig-nated by colors. By stage 6, all tissues found in the primary root are present in the typical radial pattern of the branch root. (From Malamy and Benfey 1997.) Growth and Development 355 Periclinal divisions occur mostly near the root tip and establish new files of cells. As a result, the ultimate origin of any particular mature cell can be traced back to one or a few cells in the meristem. These are the stem cells of a par-ticular file. In Arabidopsis, the stem cells surround the quies-cent center, but they are not part of the quiescent center. The stem cells ultimately may be derived from quiescent-center cells, but this origin must occur during embryogenesis, since the quiescent-center cells do not divide after germination in normal development. Analysis of the cell division patterns in the roots of the water fern Azolla have contributed to our detailed understanding of meristem function. (For a discus-sion of this work, see Web Topic 16.3.) Root Apical Meristems Contain Several Types of Stem Cells The patterns of cellular organization found in the root meristems of seed plants are substantially different from those observed in more primitive vascular plants. All seed plants have several stem cells instead of the single stem cell found in plants such as the water fern Azolla. However, they are similar to Azolla in that it is possible to follow files of cells from the region of maturation into the meristem and, in some cases, to identify the stem cell from which the file was produced. The Arabidopsis root apical meristem has the following structure (Figure 16.19): • The quiescent center is composed of a group of four cells, also known as the center cells in the Arabidopsis root meristem. The quiescent-center cells in the Arabidopsis root usually do not divide after embryogen-esis.
• The cortical–endodermal stem cells form a ring of cells that surround the quiescent center. These stem cells generate the cortical and endodermal layers.
They undergo one anticlinal division (i.e., perpendic-ular to the longitudinal axis); then these daughters divide periclinally (i.e., parallel to the longitudinal axis) to establish the files that become the cortex and the endodermis, each of which constitutes only one cell layer in the Arabidopsis root (see also Figures 16.2 and 16.8C).
• The columella stem cells are the cells immediately above (apical to) the central cells. They divide anticli-nally and periclinally to generate a sector of the root cap known as the columella.
• The root cap–epidermal stem cells are in the same tier as the columella stem cells but form a ring sur-rounding them. Anticlinal divisions of the root cap–epidermal stem cells generate the epidermal cell layer. Periclinal divisions of the same stem cells, fol-lowed by subsequent anticlinal divisions of the deriv-atives, produce the lateral root cap.
Columella of root cap Columella stem cell Epidermis Cortex Stele stem cell Pericycle Lateral root cap Root cap– epidermal stem cell Cortical endodermal stem cell Quiescent center cell Endodermis Epidermis (B) FIGURE 16.19 All the tissues in the Arabidopsis root are derived from a small number of stem cells in the root apical meristem. (A) Longitudinal section through the center of a root. The promeristem containing the stem cells that give rise to all the tissues of the root is outlined in green.
(B) Diagram of the promeristem region outlined in A. Only two of the four quiescent-center cells are depicted in this section. The black lines indicate the cell division planes that occur in the stem cells. White lines indicate the secondary cell divisions that occur in the cortical–endoder-mal and lateral root cap–epidermal stem cells. (From Schiefelbein et al.
1997, courtesy of J. Schiefelbein, © the American Society of Plant Biologists, reprinted with permission.) (A) 356 Chapter 16 • The stele stem cells are a tier of cells just behind the quiescent-center cells. These cells generate the pericy-cle and vascular tissues. The stem cells, together with their immediate derivatives in the apical meristem, are called the promeristem.
CELL DIFFERENTIATION Differentiation is the process by which a cell acquires meta-bolic, structural, and functional properties that are distinct from those of its progenitor cell. In plants, unlike animals, cell differentiation is frequently reversible, particularly when dif-ferentiated cells are removed from the plant and placed in tis-sue culture. Under these conditions, cells dedifferentiate (i.e., lose their differentiated characteristics), reinitiate cell division, and in some cases, when provided with the appropriate nutrients and hormones, even regenerate whole plants.
This ability to dedifferentiate demonstrates that differ-entiated plant cells retain all the genetic information required for the development of a complete plant, a prop-erty termed totipotency. The only exceptions to this rule are cells that lose their nuclei, such as sieve tube elements of phloem, and cells that are dead at maturity, such as ves-sel elements and tracheids (collectively referred to as tra-cheary elements) in xylem.
As an example of the process of cell differentiation, we will discuss the formation of tracheary elements. The development of these cells from the meristematic to the fully differentiated state illustrates the types of control that plants exercise over cell specialization and provides an example of the cellular changes that are brought about by differentiation (Fukuda 1996).
A Secondary Cell Wall Forms during Tracheary Element Differentiation As described in Chapter 4, tracheary elements are the con-ducting cells in which water and solutes move through the plant. They are dead at maturity, but before their death they are highly active and construct a secondary wall, often with an elaborate pattern, and they may grow extensively.
Cell death (discussed later in this chapter) is the genetically programmed finale to tracheary element differentiation.
The formation of secondary walls during tracheary ele-ment differentiation involves the deposition of cellulose microfibrils and other noncellulosic polysaccharides at spe-cific sites on the primary or secondary wall, resulting in char-acteristically patterned wall thickenings (see Chapter 15). The secondary walls of tracheary elements have a higher content of cellulose than primary walls, and they are impregnated with lignin, which is not usually present in primary walls.
In rapidly growing regions, the secondary-wall mater-ial is deposited as discrete annular rings, or in a spiral pat-tern, with the thickenings separated by bands of primary wall (Figure 16.20). As the cell grows, the primary wall extends and the rings or spirals are pulled apart. The tra-cheary elements that form after elongation stops usually have walls that are thickened. This thickening can be either uniformly or in a reticulate pattern. These cells cannot be stretched by growth.
Microtubules participate in determining the pattern of secondary-wall deposition. Before any alteration in the pat-tern of wall deposition is evident, cortical microtubules change from being more or less evenly distributed along the longitudinal walls of the cell to being clustered into bands (Figure 16.21A). Secondary wall is then deposited beneath the microtubule clusters (see Figure 16.21B).
The orientation of the cellulose microfibrils within the secondary-wall thickening is reflected in the alignment of microtubules in the cortical cytoplasm (Hepler 1981). If the microtubules are destroyed with an antimicrotubule agent such as colchicine, cell wall deposition can continue, but the cellulose microfibrils are no longer precisely ordered within the thickening, and the pattern of the secondary wall is disrupted (Figure 16.22).
Protoxylem Metaxylem Primary phloem FIGURE 16.20 The formation of primary xylem and pri-mary phloem in a developing strand in a young internode of cucumber (Cucumis sativus). The pattern of secondary-wall deposition during vessel element development varies according to the rate of cell elongation. The two first vessels to differentiate—the protoxylem—are observed on the left with secondary-wall thickening in the pattern of “annular rings.” Because the first formed vessel was strongly stretched by internode growth, the narrow annular rings are pulled apart. The metaxylem vessels differentiate after the protoxylem and are characterized by spiral thickening.
The early formed metaxylem vessel has a stretched helical thickening due to cell elongation, while the later formed vessel shows a dense helical thickening which has not been extended by elongation. The primary phloem sieve tubes are shown on the right, with typical delicate sieve elements.
Their sieve plates are stained light blue, while the cyto-plasm stains dark blue. (Courtesy of R. Aloni).
Plane of section through cell FIGURE 16.21 Development of secondary-wall thickenings in vessel elements in roots of the water fern Azolla. (A) Electron micrograph of a grazing section through a differentiating cell. Groups of microtubules are seen in the cell cortex, forming bands at the site of wall thickening before the secondary wall begins to form. Many small vesicles lie along the microtubules. (B) Annular thickenings develop beneath the bands of microtubules and are hemispheric in profile. (Courtesy of A. Hardham.) 0.2 µm 0.2 µm (A) (B) (C) Recovered cells with normal wall deposition Cells with abnormal wall thickenings FIGURE 16.22 Colchicine treatments that destroy micro-tubules also disrupt the normal formation of secondary-wall thickenings in differentiating vessel elements. (A) During normal root growth in Azolla the wall thickenings are spaced evenly along the side walls. (B) In the presence of colchicine, secondary-wall materials are deposited in irregular patterns. (C) Normal growth resumes when the roots are transferred to fresh medium that lacks colchicine, and the newly differentiated vessel elements form with nor-mal annular thickenings. (A from Hardham and Gunning 1979; B and C from Hardham and Gunning 1980.) 120 µm 120 µm 120 µm (A) (B) Microtubule Secondary-wall thickening 358 Chapter 16 INITIATION AND REGULATION OF DEVELOPMENTAL PATHWAYS Rapid progress has been made in identifying genes that play critical roles in regulating growth, cell differentiation, and pattern formation. This progress is largely a conse-quence of an intensive, international effort focused on Ara-bidopsis—first to sequence its genome, and subsequently to understand the function of all of its genes. However, many important discoveries have been made as a result of stud-ies with other species, including Antirrhinum, maize, petu-nia, tomato, and tobacco. In most cases, genes important for development were revealed by elaborate screens of the offspring of mutage-nized plants to find mutant individuals with altered devel-opment (see the example in Figure 16.8B). These studies often involved heroic efforts to map, clone, and sequence the mutant gene, although now that its genome has been sequenced, the path to identifying any particular mutant gene and what it encodes is now much shorter in Ara-bidopsis.
At this point we have identified some of the players, but the rules of the game and the specific roles of most of the genes are still being worked out. However, many of these developmentally important genes have been found to encode either transcription factors (proteins with the abil-ity to bind to specific DNA sequences and thus control the expression of other genes) or components of signaling pathways. The nature of these genes suggests some pos-sible ways that development might be regulated. Where these molecular genetic studies have been cou-pled with clonal analysis, cell biological, physiological, and/or biochemical studies, it has been possible to identify important principles of plant development. Although we are far from a complete understanding, these insights include the following: • The expression of genes that encode transcription fac-tors determines cell, tissue, and organ identity.
• The fate of a cell is determined by its position and not its clonal history.
• Developmental pathways are controlled by networks of interacting genes.
• Development is regulated by cell-to-cell signaling.
In the following discussion we will first examine the nature of some of the transcription factor and signal trans-duction component genes that have been shown to play key roles in development. Then we will outline in greater detail each of the developmental principles described here.
Transcription Factor Genes Control Development With the completion of the sequencing of the Arabidopsis genome, it became apparent that approximately 1500 of its nearly 26,000 genes encode transcription factors (Riech-mann et al. 2000). Transcription factors are proteins that have an affinity for DNA. They are able to turn the expres-sion of genes on or off by binding to specific DNA sequences (see Chapter 14 on the web site).
These 1500 transcription factor genes belong to numer-ous families. Fewer than half of these families are found only in plants, but the majority are found in all eukaryotes.
It is not known, or can even be estimated at this time, how many of these transcription factor genes regulate develop-mental pathways because only a small percentage of them have been studied. However, many members of two of these families—the MADS box and homeobox genes— have been found to be particularly important in plant development.
MADS box genes are key regulators of important bio-logical functions in plants, animals, and fungi.2 There are about 30 MADS box genes in the Arabidopsis genome, many of which control aspects of development. Specific MADS box genes are important for developmental events in the root, leaf, flower, ovule, and fruit (Riechmann and Meyerowitz 1997). They control the expression of specific sets of target genes, although at this point most of these downstream genes remain to be identified. Any given MADS box gene is expressed in a specific temporally and spatially restricted manner, with its expres-sion determined by other genes or signaling events. This has been established most clearly in the case of the devel-opment of the flower, where interacting sets of MADS box genes have been shown to determine floral organ identity (see Chapter 24).
Homeobox genes encode homeodomain proteins that act as transcription factors. Homeodomain proteins play a major role in regulating developmental pathways in all eukaryotes (see Chapter 14 on the web site). As with the MADS box genes, each homeobox gene participates in reg-ulating a unique developmental event by controlling the expression of a unique set of target genes.
Homeodomain proteins belonging to the KNOTTED1 (KN1) class are involved in maintaining the indeterminacy of the shoot apical meristem. The original knotted (kn1) mutation was found in maize and is a gain-of-function mutation. In gain-of-function, or dominant, mutations, the phenotype results from the abnormal expression of a gene.
In contrast, the phenotypes of loss-of-function mutations result from the loss of gene expression, and the mutations are therefore recessive.
Plants with the kn1 mutation have small, irregular, tumorlike knots along the leaf veins. These knots result from abnormal cell divisions within the vascular tissues that distort the veins to form the knots, which protrude from the leaf surface (Figure 16.23) (Hake et al. 1989).
2 The name MADS comes from the initials of the first four members of a family of transcription factors: MCM1, AGA-MOUS, DEFICIENS, and SRF.
Growth and Development 359 Cell differentiation is relatively normal in the leaves of kn1 mutant plants, except in the vicinity of the knots. The knots are similar to meristems in that they contain undif-ferentiated cells and continue to divide after cells around them have matured and ceased dividing. This behavior suggests that the KN1 gene controls meristem function. The mutant phenotype results from the expression of the gene in the wrong tissues, rather than the loss of the normal developmental expression pattern. KNOTTED1-like home-obox, or KNOX, genes have been found in several other plant species. Arabidopsis has three: KNAT1, KNAT2, and SHOOTMERISTEMLESS (STM) (Lincoln et al. 1994; Long et al. 1996).
Tobacco plants that have been transformed with the maize KN1 gene, driven by a promoter that expresses the gene throughout the plant, develop numerous adventitious shoot meristems along leaf surfaces (Sinha et al. 1993b).
These abnormalities are similar to the original gain-of-func-tion kn1 mutation. We can conclude from this that correct KN1 gene expression is involved in defining meristem function.
Many Plant Signaling Pathways Utilize Protein Kinases Protein kinases are ATP-dependent enzymes that add phos-phate groups to proteins. Protein phosphorylation is a key regulatory mechanism that is utilized extensively to regulate the activity of enzymes and transcription factors. Although widely utilized by all eukaryotes, plant genomes are espe-cially rich in genes that encode these enzymes. The Ara-bidopsis genome contains over 1200 genes that encode protein kinases. Of these, more than 600 encode receptor protein kinases (see Chapter 14 on the web site) (Shiu and Bleecker 2001). The functions of most of these receptor protein kinases are unknown, but recently some have been shown to play important signaling roles in plant development. Arabidop-sis has two such genes: BRI1, which encodes a receptor kinase that functions in brassinosteroid signaling (see Web Topic 19.14) and CLAV ATA1 (CLV1), which encodes a receptor kinase that participates in regulating the size of the uncommitted cell population in shoot apical meristem (we’ll discuss CLV1 a little later in the chapter).
Receptor kinases typically are integral membrane pro-teins. The receptor domain of these kinases resides outside the plasma membrane; the kinase catalytic domain is inside the cell, linked to the receptor domain by a transmembrane domain. The receptor domain has affinity for a signaling molecule, often a small protein or peptide, which is called the receptor ligand.
In the absence of the ligand, the kinase enzyme is inac-tive. The binding of the ligand to the receptor converts the protein to an active kinase (Figure 16.24). In the case of CLV1, ligand binding also triggers the formation of a com-plex consisting of a related protein, CLAVATA, a kinase-associated protein phosphatase (KAPP), and a rho GTPase-related protein. The ligand for CLV1 most likely is a small protein encoded by a third CLAV ATA gene, CLV3 (see Fig-ure 16.24) (Clark et al. 1993; Clark 2001).
The CLAV ATA genes were first identified as mutations that led to an increase in the size of the vegetative shoot apical meristem and floral meristems. One result was an increase in the number of lateral organs produced by the meristems of these mutants, which is particularly evident in the number of floral organs produced by the mutant meristems. Whereas CLV1 encodes a typical receptor-like protein kinase, CLV2 encodes a protein with a receptor domain similar to that of CLV1, but lacking a kinase domain. The protein encoded by the CLV3 gene is unre-lated to either CLV1 or CLV2.
A Cell’s Fate Is Determined by Its Position In both the root and shoot meristem, a small number of stem cells are the ultimate source of any particular tissue, and most of the cells in a given tissue are clonal, having arisen FIGURE 16.23 Inappropriate expression of the KN1 gene during leaf development causes severe abnormalities around the leaf veins. The gain-of-function mutation kn1 causes cell proliferation after normal cell division ceases; in addition, the division planes are abnormal, causing gross distortion of the blade surface. (From Sinha et al. 1993a, courtesy of S. Hake.) 360 Chapter 16 from the same stem cell. However, most evidence supports the view that cell fate does not depend on cell lineage, but instead is determined by positional information (Scheres 2001).
In the vast majority of cases, shoot epidermal cells are derived from a small number of stem cells in the L1 layer.
However, the derivatives of the L1 layer are committed to become epidermal cells because they occupy the outermost layer and lie on top of the cortical cell layer, not because they were clonally derived from the stem cells in the L1 layer.
The plane in which a cell divides will determine the position of its daughter cells within a tissue, and this posi-tioning in turn plays the most significant role in determin-ing the fate of the daughter cells. The strongest evidence for the importance of position in determining a cell’s ulti-mate fate comes from an examination of the fate of cells that are displaced from their usual position, such that they come to occupy a different layer. The vast majority of the divisions in the L1 and L2 lay-ers of the meristem are anticlinal, and anticlinal division is responsible for generating the layers in the first place. Nev-ertheless, occasional periclinal divisions occur, causing one derivative to occupy the adjacent layer. This periclinal divi-sion does not alter the composition of the tissue derived from this layer. Instead, the derivatives assume a function that is appropriate for a cell occupying that layer.
Further support for the importance of position in deter-mining cell fate has been obtained through observations of cell differentiation in leaves of English ivy (Hedera helix), which have a mixture of mutant and wild-type cells. When a mutation occurs in a stem cell in the shoot apical meris-tem, all the cells in the plant derived from that stem cell will carry the mutation. Such a plant is said to be a chimera, a mixture of cells with a different genetic makeup.
The analysis of chimeras is useful for studies on the clonal origin of different tissues.
When the mutation affects the ability of chloroplasts to differentiate, the presence of albino sectors shows that these sectors were derived from the stem cells carrying the muta-tion. In the ivy plant shown in Figure 16.25, the L2 layer car-ried a mutation causing albinism, and the L1 and L3 layers had a wild-type copy of the same gene. The L1 layer gives rise to the leaf and stem epidermis, but it is colorless because chloroplasts do not differentiate in most epidermal cells. Mesophyll tissue typically is derived from the L2 layer, so the leaves should be white because the L2 stem cells car-ried the mutant gene and passed it on to their derivatives. –S—S– –S—S– –S—S– –S—S– P P P P P –S—S– –S—S– P P P P P –S—S– –S—S– P P P P P ATP CLV1 CLV1/CLV2 heterodimer CLV2 CLV2 CLV3 CLV3 X CLV1 CLV3 WUS X CLV2 CLV1 CLV3 X CLV2 CLV1 CLV3 X KAPP ROP MAPKs?
1. WUS gene expression promotes the expression of the CLV3 gene. 4. KAPP is a negative regulator of CLV1.
2. The binding of the CLV3 multimer to the extracellular domain of the CLV1/CLV2 heterodimer induces autophosphorylation of the cytoplasmic domain of CLV1.
3. Phosphorylated CLV1 binds to the downstream effector molecules: kinase-associated protein phosphatase (KAPP) and rho-GTPase (ROP).
5. ROP may act through a mitogen-activated protein kinase (MAPK) cascade to repress WUS gene expression, forming a negative feedback loop.
OUTSIDE OF CELL Plasma membrane CYTOPLASM FIGURE 16.24 Model of the CLAVATA1/CLAVATA2 (CLV1/CLV2) receptor kinase signaling cascade, forming a negative feedback loop with the WUS gene. See Chapter 14 on the web site for further information about receptor kinase signaling pathways. (After Clark 2001.) Growth and Development 361 Although a few of the leaves are white, or nearly so, most of the leaves show green patches. They are varie-gated. The green tissue in these leaves was derived from the cells originally in the L1 or L3 layer; the colorless regions were derived from the L2 layer. The variegation occurs because occasional periclinal divisions in the L1 or L3 layer early in leaf development establish clones of cells that can differentiate as green mesophyll cells. This is fur-ther evidence that cell differentiation is not dependent on cell lineage. The fate of a cell during development is deter-mined by the position it occupies in the plant body.
Developmental Pathways Are Controlled by Networks of Interacting Genes We have a great deal more to learn about the regulatory networks that control developmental pathways. However, several discoveries point to a model in which local and long-distance signaling events control the expression of genes that encode transcription factors. These transcription factors in turn determine the character or activities of a given tissue or cell. Often these mechanisms involve feed-back loops in which two or more genes interact to regulate each other’s expression. These interactions are seen most clearly in the case of the shoot apical meristem.
Expression of the KNOX gene STM (SHOOTMERIS-TEMLESS) is essential for the formation of the shoot apical meristem in the Arabidopsis embryo and for meristem func-tion in the growing plant. STM is expressed throughout the apical dome of the vegetative meristem, except in the developing leaf primordia. Similarly, STM is expressed in the dome of the floral meristem, but it is silenced as floral organs appear. Two additional KNOX genes—KNAT1 and KNAT2—also are expressed in the apical meristem of Ara-bidopsis and participate in maintaining the meristem cells in an undifferentiated state.
Because cells actively divide in the early stages of leaf and floral organ primordia development, STM is not nec-essary for cell division. Rather KN1, STM, and their func-tional homologs maintain meristem identity by suppress-ing differentiation. Another gene, ASYMMETRIC LEAVES1 (AS1) promotes leaf development and is expressed in the primordia and young leaves of Arabidopsis (Figure 16.26) (Byrne et al. 2000). STM represses the expression of AS1, and AS1 in turn represses the expression of KNAT1 in the developing leaf primordia (Ori et al. 2000): FIGURE 16.25 Periclinal chimeras demonstrate that the mesophyll tissue has more than a single clonal origin in English ivy (Hedera helix). These variegated leaves provide clues on the clonal origins of different tissues. A mutation in a gene essential for chloroplast development occurred in some of the initial cells of the meristem, and cells derived from these mutated stem cells lack chloroplasts and are white, while cells derived from other stem cells have nor-mal chloroplasts and appear green. (Courtesy of S.
Poethig.) (B) stm mutant embryos (A) Wild-type embryos 25 mm 25 mm 25 mm 25 mm FIGURE 16.26 The meristem identity gene, STM, inhibits expression of the ASYMMETRIC LEAVES1 (AS1) gene, which promotes leaf development in Arabidopsis. Arrows point to the shoot apical meristem–forming region. (A) Expression of the STM gene is normally confined to the shoot apical meristem in the wild type, and it confers meris-tem identity on the vegetative meristem. In contrast, the AS1 gene is confined to leaf primordia and developing cotyle-dons in the wild type, as shown by in situ hybridization in embryos at two stages of development. (B) In stm mutants, expression of AS1 expands into the region that would nor-mally become the shoot apical meristem. As a result, the api-cal meristem does not form. (From Byrne et al. 2000.) 362 Chapter 16 The WUSCHEL (WUS) gene, which encodes another homeodomain transcription factor, is a key regulator of stem cell indeterminacy (Laux et. al. 1996). In plants with loss-of-function wus mutations, either an apical meristem is lacking entirely, or their stem cells are used up after they have formed a few leaves. The CLAV ATA genes negatively regulate WUS expression. WUS expression is expanded in both clv1 and clv3 mutants (Figure 16.27). Conversely, WUS expression positively regulates CLV3 gene expression; (see Figure 16.24) (Brand et al. 2000).
Development Is Regulated by Cell-to-Cell Signaling How do cells know where they are? If a cell’s fate is deter-mined by its position and not by clonal lineage, then cells must be able to sense their position relative to other cells, tissues, and organs. Neighboring cells and distant tissues and organs provide positional information. Cells in multi-cellular plants usually are in close contact with others around them, and the behavior of each cell is carefully coordinated with that of its neighbors throughout the life of the plant. Furthermore, each cell occupies a specific posi-tion within the tissue and organ to which it belongs.
Coordination of cellular activity requires cell–cell com-munication. That is, some developmentally important genes act nonautonomously. They do not have to be expressed in a given cell to affect the fate of that cell. A given gene or set of genes can exert an effect on development in neighboring cells or even cells in distant tissues through cell–cell com-munication, via at least three different mechanisms: 1. Ligand-induced signaling 2. Hormonal signaling 3. Signaling via trafficking of regulatory proteins and/or mRNAs Ligand-induced signaling. There is evidence that cell wall components, particularly a class of glycoprotein macro-molecules known as arabinogalactan proteins, or AGPs, may communicate positional information that will deter-mine cell fate (see Chapter 15). AGPs would not be involved in signaling over a distance, but rather in telling a given cell who its neighbors were. That information then would program the cell to differentiate, or acquire a fate appropriate to its position.
Because plants have numerous, perhaps hundreds, of receptor kinases, we might expect many signaling events to be initiated by ligand-induced protein phosphorylation.
At present, however, relatively few of the ligands activat-ing protein kinases are known. But there is good evidence that the small protein encoded by the CLV3 gene is the li-gand that activates the CLV1 protein kinase. The CLV3 protein contains fewer than 100 amino acids and contains a leader sequence suggesting that it would be excreted from the cells that produce it (Fletcher et al. 1999).
Because of its small size and water solubility, it could freely diffuse through the extracellular space, or apoplast.
The apoplast consists mostly of the space occupied by the cell walls. Cell wall macromolecules are largely hydrophilic, and the wall contains passages between the macromolecules with an apparent pore size of 3.5 to 5 nm.
This means that molecules with a mass of less than approx-imately 15 kDa can diffuse freely through the apoplast.
With a molecular weight of approximately 11 kDa, the CLV3 protein easily could diffuse through the apoplast.
STM AS1 KNAT1 Promotes leaf development Maintains meristem (A) Wild type (B) clv3 mutant 20 mm 20 mm FIGURE 16.27 WUS gene expression in the shoot apical meristem of the wild type and the clv3 mutant. The localization of WUS mRNA was detected by an in situ hybridization procedure. (A) In the wild type, WUS expression is confined to a small cluster of cells. (B) In the clv3 mutant, WUS expression expands both apically and laterally, and the apical meristem itself is enlarged. (Brand et al.
2000.) Growth and Development 363 The CLV3 gene is expressed in cells of the L1 and L2 lay-ers in the central zone of the shoot apical meristem, but not within the L3 layer or in the peripheral zone. In contrast, CLV1 is expressed in deeper layers within the central zone in the L3 layer, as is the WUS gene. However, CLV1 is expressed within a somewhat larger domain than WUS (Figure 16.28). Although WUS gene expression is required to maintain stem cell identity, WUS is expressed in only a small number of cells in the L3 layer of the meristem. It functions nonautonomously, acting on cells a short distance from the cells that express the gene.
The CLV3 protein controls the size of the stem cell pop-ulation in the shoot apex by negatively regulating the expression of WUS in the L3 layer. The CLV3 gene is expressed in cells in the central zone of the meristem, within the L1 and L2 layers. When CLV1 or CLV3 is knocked out by mutation, WUS gene expression spreads, and the num-ber of undifferentiated stem cells expands (Brand et al.
2000). Because this expansion requires CLV1, it is likely that CLV3 protein diffuses from the L1 cells and binds to the receptor domain of CLV1 to activate its kinase domain to initiate a signal that represses WUS gene transcription.
WUS expression promotes CLV3 expression, which in turn represses WUS expression. Thus the meristem has a sensitive feedback mechanism for controlling the size of the stem cell population.
Hormonal signaling. The plant hormones—auxin, ethyl-ene, gibberellins, abscisic acid, cytokinins, and brassino-steroids—all play roles in regulating development. These roles will be presented in some detail in the chapters and sections devoted to these topics. In this discussion, how-ever, we will focus on auxin signaling as an example of the types of mechanisms these roles might entail. This topic will be discussed in greater detail in Chapter 19.
Auxin signaling is essential for the development of axial polarity and the development of vascular tissue. Auxin has long been known to be the signal for the initiation of vas-cular tissue differentiation (see Chapter 19). This conclusion, however, is based largely on studies of the effects of applied auxins and auxin transport inhibitors. More recently, two Arabidopsis genes—GNOM and MONOPTEROS—known to be essential for the development of axial polarity and tis-sue differentiation during embryogenesis and adult plant development, have been found to be involved in auxin sig-naling. As presented earlier, the Arabidopsis GNOM gene was identified because embryos homozygous for mutations in this gene lack both roots and cotyledons and fail to develop axial polarity (see Figure 16.7A) (Mayer et al. 1993).
The GNOM gene product is required for correct localiza-tion of the auxin efflux carrier protein PIN1 (Figure 16.29).
CLV1 CLV3 WUS STM AS1 AS1 FIGURE 16.28 Patterns of expression of some developmen-tally important genes in the Arabidopsis shoot apical meri-stem. (From Clark 2001.) Wild-type embryos (A) Early globular (B) Midheart gnom mutant embryos (C) Early globular (D) Midheart FIGURE 16.29 Comparison of the distribution patterns of the auxin efflux protein PIN1 in wild-type and gnom mutant Arabidopsis embryos. (A) Wild-type, early globular; PIN1 is localized in the provascular tissue early in the early globular stage, where the protein accumulates at the basal boundary of the four inner cells that will give rise to the provascular tissue. (B) Wild-type, midheart; in the heart stage, the provascular cells have accumulated PIN1 protein at their basal ends (see insert). (C) gnom mutant, early glob-ular; PIN1 does not accumulate in the region where the provascular tissue will form in the early globular stage of the gnom mutant. (From Steinmann et al. 1999). (D) gnom mutant, midheart; formation of provascular tissue is blocked in the gnom mutant, and normal development is disrupted. PIN1 is still inserted in membranes in the mutant, but the localization is disorganized (see insert).
(From Steinmann et al. 1999.) 364 Chapter 16 GNOM encodes a guanine nucleotide exchange factor that is a component of the cellular machinery that establishes cell polarity. This machinery, and the GNOM protein in particular, are required for the correct localization of the auxin efflux carrier protein PIN1 at the basal end of the procambium cells during the globular stage of embryogen-esis and subsequently in vascular cells throughout devel-opment (Steinmann et al. 1999; Grebe et al. 2000).
As we have seen, mutations in the MONOPTEROS (MP) gene result in seedlings that lack both a hypocotyl and root, although they do produce an apical region. The apical structures in the mp mutant embryos are not struc-turally normal, however, and the tissues of the cotyledons are disorganized (see Figure 16.7B) (Berleth and Jürgens 1993). Embryos of mp mutants first show abnormalities at the octant stage, and they do not form a procambium in the lower part of the globular embryo, the part that should give rise to the hypocotyl and root. Later some vascular tis-sue does form in the cotyledons, but the strands are improperly connected.
The MP gene encodes a protein related to the transcrip-tion factor known as ARF (auxin response factor) (Hardtke and Berleth 1998). Both ARF and MONOPTEROS bind to auxin response elements in the promoters of certain genes that are transcribed in the presence of auxin. Apparently the MP gene is required for expression of genes involved in vascular tissue differentiation.
Other evidence in support of auxin signaling during embryogenesis includes the finding that the putative auxin receptor protein, ABP1, is required for organized cell elon-gation and division in embryogenesis. Arabidopsis mutants homozygous for abp1 do not form mature embryos, although they develop normally up to the early globular stage. These mutants cannot make the transition to bilat-eral symmetry, and cells fail to elongate (Chen et al. 2001).
Auxin signaling also participates in organogenesis from the shoot apical meristem and in the formation of lateral roots. Arabidopsis plants with mutations in the auxin efflux carrier gene PIN1 develop a pinlike inflorescence that is devoid of lateral organs (Figure 16.30). In wild-type plants, PIN1 gene expression is up-regulated in the early stages of primordium formation, before the primordia begin to bulge. The shoot apical meristem at the tip of the pinlike inflorescence in the pin1 mutant plants has a normal struc-ture, except that no organs are generated in the peripheral zone and the shoot produced lacks lateral appendages (Vernoux et al. 2000). Thus, auxin is likely to be required for signaling early events necessary for organogenesis from the shoot apical meristem.
This hypothesis is supported by work with tomato.
When tomato apical meristems are cultured on medium containing the auxin transport inhibitor N-1-naphthyl-phthalamic acid (NPA), they continue to grow, but they develop into pinlike shoots lacking lateral appendages.
When these NPA-induced pin meristems were treated with auxin at their tips, leaf initiation was restored (Reinhardt et al. 2000).
Other signaling mechanisms remain to be discovered.
The mechanism by which cells communicate has not been established in other cases, although it is clear that positional information is exchanged between cells in different tissues.
As presented earlier, the SHR and SCR genes are important for the establishment of the radial tissue patterns in roots.
They encode rather similar transcription factors, but these two genes are expressed and function in different tissues. SCR is required for the asymmetric cell division that forms the epidermis and cortex, and it also determines the endodermis cell fate. SCR is expressed in the stem cell that will give rise to the ground tissue before it divides asym-metrically to form the precursors of endodermis and cor-tex (Figure 16.31A). SCR continues to be expressed in the endodermis after the stem cell divides (Figure 16.31B).
SCR gene expression requires SHR expression, but the SHR gene is not expressed in either the cortex or the endo-dermis. Rather, SHR is expressed in the pericycle and the vascular cylinder (Figure 16.31C) (Helariutta et al. 2000).
This implies that SHR gene expression generates a signal (A) (B) (C) Wild-type pin1 mutation FIGURE 16.30 The PIN1 gene is essential for the formation of lateral organs from the inflorescence meristem in Arabidopsis. (A) The inflorescence meristem generates a stem bearing cauline leaves and numerous floral buds in the wild type. (B) Plants with pin1 mutations produce an inflorescence meristem, but it fails to generate lateral organs. (C) The inflorescence meristem produces only axial tissues, similar to the root apical meristem, as shown in this scanning electron micrograph. (From Vernoux et al. 2000.) Growth and Development 365 that is received by the ground tissue stem cells and causes the expression of the SCR gene in these cells. This illus-trates again the potential importance of cell-to-cell signaling in cell fate determi-nation and in plant development. At present it is not known how this com-munication takes place.
Signaling via trafficking of regulatory proteins and/or mRNAs.
Symplastic communication between plant cells occurs via the plasmodesmatal connections through their cell walls (see Chapter 1). Most living cells in a plant are connected symplastically to their neighbors by plasmo-desmata that pass through the adjoining cell walls and pro-vide some degree of cytosolic continuity between them.
There is increasing evidence that the signals exchanged through plasmodesmata include both regulatory proteins and mRNAs (Zambryski and Crawford 2000).
The importance of plasmodesmata for cell–cell commu-nication during development became apparent with the discovery that the mRNA of the maize meristem identity gene KN1 cannot be detected in the L1 layer of the maize vegetative shoot apical meristem. The KN1 gene is expressed only in cells of the L2 layer. The KN1 protein, however, is detected in all regions of the shoot apical meri-stem, including the L1 layer. Since the KN1 protein is not synthesized in the L1 layer, it must be transported into the L1 layer from the L2 layer, through the plasmodesmata joining them (Figure 16.32) (Lucas et al. 1995).
In Antirrhinum, expression of the FLO gene in the L1 layer activates expression of the floral organ identity genes in all cell layers of the meristem (Carpenter and Coen 1995). Although many explanations for this relationship are possible, one is that the FLO protein, by passing through the plasmodesmata, moves into these other layers from the cells in which it is synthesized.
Viruses invade plants and spread from cell to cell by passing through plasmodesmata. Their genomes encode proteins designated movement proteins that can facilitate the movement of the viral RNA genome through plas-modesmata. It is likely that viruses have hijacked a mech-anism that evolved for cell–cell communication. At present it isn’t clear why information exchange would be orga-nized in this manner, but this type of communication may be a fairly general phenomenon in plant development.
Wild-type SHR expression (A) Embryo (B) Root (C) Wild-type root (D) shr mutant root SCR expression st st ep co en CEI QC st ep m ep co en CEI QC st d 25 mm 50 mm 50 mm 50 mm FIGURE 16.31 The SHORTROOT (SHR) and SCARECROW (SCR) genes in Arabidopsis control tissue patterning dur-ing root development. The SHR or SCR proteins have been localized by confocal laser scanning microscopy after being tagged with green fluorescent protein (GFP), which has a greenish-yellow color. (A) During embryogenesis in wild-type Arabidopsis, the SHR protein is localized in the provascular tissues. (B) The SHR protein continues to be local-ized in the vascular cylinder throughout growth of the primary root. (C) In wild-type roots, SCR protein is localized in the quiescent center, endodermis, and cortical–endodermal stem cell (CEI). It is not present in the cortex, vascular cylin-der, or epidermis. (D) The expression of SCR is markedly reduced in the shr mutant root, and now appears only in the mutant cell layer that has characteris-tics of both endodermis and cortex. CEI = cortical–endodermal stem cell; co = cortex; d = daughter cells; en = endo-dermis; ep = epidermis; m = mutant cell layer; QC = quiescent center; st = vascu-lar cylinder. (From Helariutta et al. 2000.) 366 Chapter 16 THE ANALYSIS OF PLANT GROWTH How do plants grow? This deceptively simple question has challenged plant scientists for more than 150 years. New cells form continually in the apical meristems. Cells enlarge slowly in the apical meristem and more rapidly in the sub-apical regions. The resulting increase in cell volume can range from severalfold to 100-fold, depending on the species and environmental conditions. Classically, plant growth has been analyzed in terms of cell number or overall size (or mass). However, these measures tell only part of the story.
Tissue growth is neither uniform nor random. The derivatives of the apical meristems expand in predictable and site-specific ways, and the expansion patterns in these subapical regions largely determine the size and shape of the primary plant body. The total growth of the plant can be thought of as the sum of the local patterns of cell expansion.
The analysis of the motions of cells or “tissue elements” (and the related problem of cell expansion) is called kine-matics. In this section we will discuss both the classical def-initions of growth and the more modern, kinematic approach. As we will see, the advantage of the kinematic approach is that it allows one to describe the growth pat-terns of organs mathematically in terms of the expansion patterns of their component cells.
Plant Growth Can Be Measured in Different Ways Growth in plants is defined as an irreversible increase in volume. The largest component of plant growth is cell expansion driven by turgor pressure. During this process, cells increase in volume manyfold and become highly vac-uolate. However, size is only one criterion that may be used to measure growth.
Growth also can be measured in terms of change in fresh weight—that is, the weight of the living tissue—over a particular period of time. However, the fresh weight of plants growing in soil fluctuates in response to changes in the water status, so this criterion may be a poor indicator of actual growth. In these situations, measurements of dry weight are often more appropriate.
Cell number is a common and convenient parameter by which to measure the growth of unicellular organisms, such as the green alga Chlamydomonas (Figure 16.33). In multicellular plants, however, cell number can be a mis-leading growth measurement because cells can divide without increasing in volume.
For example, during the early stages of embryogenesis, the zygote subdivides into progressively smaller cells with no net increase in the size of the embryo. Only after it 1 2 FIGURE 16.32 The KN1 gene is expressed throughout the maize shoot apical meristem, but it is not expressed in the L1 layer or in leaf primordia. The KN1 mRNA was local-ized here in a longitudinal section through the meristem by a hybridization procedure. The arrow points to the pre-dicted site of the next leaf primordium (P0); the numbers 1 and 2 identify the P1 and P2 leaf primordia, respectively.
(After Jackson et al. 1994.) Logarithmic Stationary 100 120 60 Time (h) 80 20 40 0 1 2 3 4 5 6 Lag Number of cells per mL (× 106) FIGURE 16.33 Growth of the unicellular green alga Chlamydomonas. Growth is assessed by a count of the num-ber of cells per milliliter at increasing times after the cells are placed in fresh growth medium. Temperature, light, and nutrients provided are optimal for growth. An initial lag period during which cells may synthesize enzymes required for rapid growth is followed by a period in which cell number increases exponentially. This period of rapid growth is followed by a period of slowing growth in which the cell number increases linearly. Then comes the station-ary phase, in which the cell number remains constant or even declines as nutrients are exhausted from the medium. Growth and Development 367 reaches the eight-cell stage does the increase in volume begin to mirror the increase in cell number. Because the zygote is an especially large cell, this lack of correspon-dence between an increase in cell number and growth may be unusual, but it points out the potential problem in equating an increase in cell number with growth.
Although cell number may not always be a reliable measure of plant growth, under most circumstances divid-ing cells, particularly in meristems, double in volume dur-ing their cell cycle. Therefore, an increase in cell number, such as the increase brought about by the activity of the apical meristems, does contribute to plant growth. How-ever, the largest component of plant growth is the rapid cell expansion that occurs in the subapical region after cell division ceases.
Because all the cells of the plant axis elongate under normal conditions, the greater the number of cells pro-duced by the apical meristem, the longer the axis will be.
For example, when Arabidopsis plants are transformed with a gene that encodes cyclin, a key component of the cell cycle regulatory machinery (see Chapter 1), the cells of the apical meristem progress through their cell cycles more rapidly, so more cells form per unit time. As a result, the roots of these transgenic plants have more cells and are substantially longer than the roots of wild-type plants grown under similar conditions (Doerner et al. 1996).
New cells form continually in the apical meristems.
With each new round of cell division and associated cell expansion, the older derivatives are displaced a small dis-tance from the apex. As the cells recede farther from the apex, the rate of displacement is greatly accelerated. By viewing plant growth as a process of cell displacement from the apex, we can apply the principles of kinematics.
The Production of Cells by the Meristem Is Comparable to a Fountain Moving fluids such as waterfalls, fountains, and the wakes of boats can generate specific forms. The study of the motion of fluid particles and the shape changes that the flu-ids undergo is called kinematics. The ideas and numerical methods used to study these fluid forms are useful for characterizing meristematic growth. In both cases, an unchanging form is produced, even though it is composed of moving and changing elements.
An example of an unchanging form composed of changing and displaced elements in plants is the hypocotyl hook of a dicot such as the common bean (Fig-ure 16.34). As the bean seedling emerges from the seed coat, the apical end of the hypocotyl bends back on itself to form a hook. The hook is thought to protect the seedling apex from damage during growth through the soil. Dur-ing seedling growth (in soil or dim light) the hook migrates up the stem, from the hypocotyl into the epicotyl and then to the first and second internodes, but the form of the hook remains constant.
If we mark a specific epidermal cell on the seedling stem located close to the seedling apex, we can watch it as it flows into the hook summit, then down into the straight region below the hook (see Figure 16.34). The mark is not crawling over the plant surface, of course; plant cells are cemented together and do not experience much relative motion during development. The change in position of the mark relative to the hook implies that the hook is com-posed of a procession of tissue elements, each of which first curves and then straightens as it is displaced from the plant apex during growth. The steady form is produced by a parade of changing cells.
A root tip is another example of a steady form com-posed of changing tissue elements. Here, too, the form is observed to be steady only when distance is measured from the root tip. A region of cell division occupies perhaps 2 mm of the root tip. The elongation zone extends for about 10 mm behind the root tip. Phloem differentiation is first observed beginning at 3 mm from the tip, and functional xylem elements may be seen at about 12 mm from the tip.
A marked cell near the tip will seem to flow first through the region of cell division, then through the elongation zone and into the region of xylem differentiation, and so on. This shifting implies that developing tissue elements first divide and elongate, and then differentiate.
In an analogous fashion, the shoot bears a succession of leaves of different developmental stages. During a period of 24 hours, a leaf may grow to the same size, shape, and biochemical composition that its neighbor had a day ear-lier. Thus, shoot form is also produced by a parade of changing elements that can be analyzed with kinematics.
Such an analysis is not merely descriptive; it permits cal-culations of the growth and biosynthetic rates of individ-ual tissue elements (cells) within a dynamic structure.
Identifying mark or particle on surface Summit of hook Cotyledons Hook structure is maintained as mark is displaced FIGURE 16.34 The dicot hypocotyl hook is an example of a constant form composed of changing elements. The hooked form is maintained over time, while different tissues first curve and then straighten as they are displaced from the seedling apex during growth. If a mark is placed at a fixed point on the surface, it will be displaced (indicated by the arrow), appearing to flow through the hook over time.
(After Silk 1994.) 368 Chapter 16 Tissue Elements Are Displaced during Expansion As we have seen, growth in shoots and roots is localized in regions at the tips of these organs. Regions with expand-ing tissue are called growth zones. With time, meristems move away from the plant base by the growth of the cells in the growth zone.
If successive marks are placed on the stem or root, the distance between the marks will change, depending on where they are within the growth zone. In addition, all of these marks will move away from the tip of the root or shoot, but their rate of movement will differ depending on their distance from the tip.
From another perspective, if you were to stand at the tip of a root that had marks placed at intervals along the axis, you would see that all marks would move farther away from you with time. The reason is that discrete regions on the plant axis experience displacement as well as expan-sion during growth and development.
As Regions Move Away from the Apex,Their Growth Rate Increases As a given region of the plant axis moves away from the apex, its growth velocity increases (the rate of elongation accelerates) until a constant limiting velocity is reached equal to the overall organ extension rate. The reason for this increase in growth velocity is that with time, progres-sively more tissue is located between the moving particle and the apex, and progressively more cells are expanding, so the particle is displaced more and more rapidly. In a rapidly growing maize root, a tissue element takes about 8 hours to move from 2 mm (the end of the meristematic zone) to 12 mm (the end of the elongation zone).
Beyond the growth zone, elements do not separate; neighboring elements have the same velocity (expressed as the change in distance from the tip per unit of time), and the rate at which particles are displaced from the tip is the same as the rate at which the tip moves through the soil. The root tip of maize is pushed through the soil at 3 mm h–1. This is also the rate at which the nongrowing region recedes from the apex, and it is equal to the final slope of the growth trajectory.
The Growth Velocity Profile Is a Spatial Description of Growth The velocities of different tissue elements are plotted against their distance from the apex to give the spatial pat-tern of growth velocity, or growth velocity profile (Figure 16.35A). Growth velocity increases with position in the growth zone. A constant value is obtained at the base of the growth zone. The final growth velocity is the final, constant slope of the growth trajectory equal to the elongation rate of the organ, as discussed in the previous section. In the rapidly growing maize root, the growth velocity is 1 mm h–1 at 4 mm, and it reaches its final value of nearly 3 mm h–1 at 12 mm.
If the growth velocity is known, the relative elemental growth rate, which represents the fractional change in length per unit time, can be calculated (see Web Topic 16.4). The relative elemental growth rate shows the loca-tion and magnitude of the extension rate and can be used to quantify the effects of environmental variation on the growth pattern (Figure 16.35B).
SENESCENCE AND PROGRAMMED CELL DEATH Every autumn, people who live in temperate regions can enjoy the beautiful color changes that precede the loss of leaves from deciduous trees. The leaves change color (B) Relative elemental growth rate 0.2 0.1 0.4 0.3 0.5 Relative elemental growth rate (h–1) 15 Position (mm from tip) 5 10 0 (A) Growth velocity profile 15 Position (mm from tip) 5 10 1 2 3 Growth velocity (mm h–1) 0 Region of maximum growth velocity FIGURE 16.35 The growth of the primary root of Zea mays (maize) can be represented kinematically by two related growth curves. (A) The growth velocity profile plots the velocity of movement away from the tip of points at differ-ent distances from the tip. This tells us that growth velocity increases with distance from the tip until it reaches a uni-form velocity equal to the rate of elongation of the root. (B) The relative elemental growth rate tells us the rate of expansion of any particular point on the root. It is the most useful measure for the physiologist because it tells us where the most rapidly expanding regions are located.
(From Silk 1994.) Growth and Development 369 because changing day length and cooling temperatures trigger developmental processes that lead to leaf senes-cence and death. Senescence is distinct from necrosis, although both senescence and necrosis lead to death.
Necrosis is death brought about by physical damage, poi-sons, or other external injury. In contrast, senescence is a normal, energy-dependent developmental process that is controlled by the plant’s own genetic program. Leaves are genetically programmed to die, and their senescence can be initiated by environmental cues.
As new leaves are initiated from the shoot apical meri-stem, older leaves often are shaded and lose the ability to function efficiently in photosynthesis. Senescence recovers a portion of the valuable resources that the plant invested in leaf formation. During senescence, hydrolytic enzymes break down many cellular proteins, carbohydrates, and nucleic acids. The component sugars, nucleosides, and amino acids are then transported back into the plant via the phloem, where they will be reused for synthetic processes.
Many minerals also are transported out of senescing organs, back into the main body of the plant.
Senescence of plant organs is frequently associated with abscission, a process whereby specific cells in the petiole dif-ferentiate to form an abscission layer, allowing the senescent organ to separate from the plant. In Chapter 22 we will have more to say about the control of abscission by ethylene.
In this section we will examine the roles that senescence and programmed cell death play in plant development. We will see that there are many types of senescence, each with its own genetic program. Then, in Chapters 21 and 22, we will describe how cytokinins and ethylene can act as sig-naling agents that regulate plant senescence.
Plants Exhibit Various Types of Senescence Senescence occurs in a variety of organs and in response to many different cues. Many annual plants, including major crop plants such as wheat, maize, and soybeans, abruptly yellow and die following fruit production, even under opti-mal growing conditions. Senescence of the entire plant after a single reproductive cycle is called monocarpic senes-cence (Figure 16.36). Other types of senescence include the following: • Senescence of aerial shoots in herbaceous perennials • Seasonal leaf senescence (as in deciduous trees) • Sequential leaf senescence (in which the leaves die when they reach a certain age) • Senescence (ripening) of fleshy fruits; senescence of dry fruits • Senescence of storage cotyledons and floral organs (Figure 16.37) • Senescence of specialized cell types (e.g., trichomes, tracheids, and vessel elements) The triggers for the various types of senescence are dif-ferent and can be internal, as in monocarpic senescence, or external, such as day length and temperature in the autum-nal leaf senescence of deciduous trees. Regardless of the initial stimulus, the different senescence patterns may share common internal programs in which a regulatory senes-cence gene initiates a cascade of secondary gene expression that eventually brings about senescence and death.
Senescence Is an Ordered Series of Cytological and Biochemical Events Because it is genetically encoded, senescence follows a pre-dictable course of cellular events. On the cytological level, some organelles are destroyed while others remain active.
The chloroplast is the first organelle to deteriorate during the onset of leaf senescence, with the destruction of thy-lakoid protein components and stromal enzymes.
In contrast to the rapid deterioration of chloroplasts, nuclei remain structurally and functionally intact until the late stages of senescence. Senescing tissues carry out cata-FIGURE 16.36 Monocarpic senescence in soybeans (Glycine max). The entire plant on the left underwent senescence after flowering and producing fruit (pods). The plant on the right remained remained green and vegetative because its flowers were continually removed. (Courtesy of L.
Noodén.) 370 Chapter 16 bolic processes that require the de novo synthesis of var-ious hydrolytic enzymes, such as proteases, nucleases, lipases, and chlorophyll-degrading enzymes. The synthe-sis of these senescence-specific enzymes involves the acti-vation of specific genes.
Not surprisingly, the levels of most leaf mRNAs decline significantly during the senescence phase, but the abun-dance of certain specific mRNA transcripts increases.
Genes whose expression decreases during senescence are called senescence down-regulated genes (SDGs). SDGs include genes that encode proteins involved in photosyn-thesis. However, senescence involves much more than the simple switching off of photosynthesis genes.
Genes whose expression is induced during senescence are called senescence-associated genes (SAGs). SAGs include genes that encode hydrolytic enzymes, such as pro-teases, ribonucleases, and lipases, as well as enzymes involved in the biosynthesis of ethylene, such as ACC (l-aminocyclopropane-l-carboxylic acid) synthase and ACC oxidase. SAGs of another class have secondary functions in senescence. These genes encode enzymes involved in the conversion or remobilization of breakdown products, such as glutamine synthetase, which catalyzes the conversion of ammonium to glutamine (see Chapter 12) and is responsi-ble for nitrogen recycling from senescing tissues.
Programmed Cell Death Is a Specialized Type of Senescence Senescence can occur at the level of the whole plant, as in monocarpic senescence; at the organ level, as in leaf senes-cence; and at the cellular level, as in tracheary element dif-ferentiation. The process whereby individual cells activate an intrinsic senescence program is called programmed cell death (PCD). PCD plays an important part in animal development, in which the molecular mechanism has been studied extensively. PCD can be initiated by specific sig-nals, such as errors in DNA replication during division, and involves the expression of a characteristic set of genes.
The expression of these genes results in cell death. Much less is known about PCD in plants (Pennell and Lamb 1997).
PCD in animals is usually accompanied by a distinct set of morphological and biochemical changes called apopto-sis (plural apoptoses) (from a Greek word meaning “falling off,” as in autumn leaves). During apoptosis, the cell nucleus condenses and the nuclear DNA fragments in a specific pattern caused by degradation of the DNA between nucleosomes (see Chapter 2 on the web site).
Some plant cells, particularly in senescing tissues, exhibit similar cytological changes. PCD also appears to occur during the differentiation of xylem tracheary ele-ments, during which the nuclei and chromatin degrade and the cytoplasm disappears. These changes result from the activation of genes that encode nucleases and pro-teases.
One of the important functions of PCD in plants is pro-tection against pathogenic organisms. When a pathogenic organism infects a plant, signals from the pathogen cause the plant cells at the site of the infection to quickly accu-mulate high concentrations of toxic phenolic compounds and die. The dead cells form a small circular island of cell death called a necrotic lesion.
The necrotic lesion isolates and prevents the infection from spreading to surrounding healthy tissues by sur-rounding the pathogen with a toxic and nutritionally depleted environment.This rapid, localized cell death due to pathogen attack is called the hypersensitive response (see Chapter 13).
The existence of Arabidopsis mutants that can mimic the effect of infection and trigger the entire cascade of events leading to the formation of necrotic lesions, even in the absence of the pathogen, has demonstrated that the hyper-sensitive response is a genetically programmed process rather than simple necrosis.
FIGURE 16.37 Stages of flower senescence in morning glory (Ipomoea acuminata).
(Courtesy of S. L. Taiz.) Growth and Development 371 SUMMARY The basic body plan of the mature plant is established dur-ing embryogenesis; in this process, tissues are arranged radially: an outer epidermal layer surrounding a cylinder of vascular tissue that is embedded within cortical or ground tissues. The apical–basal axial pattern of the mature plant, with root and shoot polar axes, also is established during embryogenesis, as are the primary meristems that will generate the adult plant.
One common type of angiosperm embryonic develop-ment, exemplified by Arabidopsis thaliana, is characterized by precise patterns of cell divisions, forming successive stages: the globular, heart, torpedo, and maturation stages. The axial body pattern is established during the first division of the zygote, and mutant genes eliminate part of the embryo. The radial tissue pattern is established during the globular stage, apparently as a result of the expression of genes that control cell identity. The SHOOTMERISTEMLESS (STM) gene is expressed in the region that gives rise to the shoot apical meristem during the heart stage of embryogenesis, and its continued expression suppresses differentiation of the cells of the shoot apical meristem. The GNOM gene is required for the establishment of axial polarity, and the MONOPTEROS gene is required for formation of the embryonic primary root as well as vascular development.
A complete explanation of the mechanisms responsible for establishing and maintaining these patterns is not pos-sible at present, but there is evidence that an association of microtubules and microfilaments known as the pre-prophase band is important in determining the plane of cell division. Cell differentiation does not depend on cell lin-eage; however, the division of the stem cell is essential for this process. Expression of the SCR (SCARECROW) gene, which has been cloned and encodes a novel protein, is nec-essary for the division of the stem cell, and the SHR (SHORTROOT) gene must be expressed for the establish-ment of endodermal cell identity.
Meristems are populations of small, isodiametric cells that have “embryonic” characteristics. Vegetative meri-stems generate specific portions of the plant body, and they regenerate themselves. In many plants, the root and shoot apical meristems are capable of indefinite growth.
The vegetative shoot apical meristem repetitively gen-erates lateral organs (leaves and lateral buds), as well as segments of the stem. Shoot apical meristems in angiosperms typically are organized into three distinct lay-ers, designated L1, L2, and L3. The root and shoot apical meristems are primary meri-stems formed during embryogenesis. Secondary meristems are initiated during postembryonic development and include the vascular cambium, cork cambium, axillary meristems, and secondary root meristems.
The repetitive activity of the vegetative shoot apical meristem generates a succession of developmental units, called phytomeres, each consisting of one or more leaves, the node, the internode, and one or more axillary buds. The vegetative shoot apical meristem is indeterminate in its activity in that it may function indefinitely, but it gives rise to leaf primordia that are determinate in their growth.
Leaves form in a characteristic pattern, with three stages: (1) organogenesis, (2) development of suborgan domains, (3) cell and tissue differentiation. The number and order in which leaf primordia form is reflected in the subsequent phyllotaxy (alternate, opposite, decussate, whorled, or spiral). The leaf primordia must be positioned as a result of the precise spatial regulation of cell division within the apex, but the factors controlling this activity are not known.
Roots grow from their distal ends. The root apical meri-stem is subterminal and covered by a root cap. Cell divi-sions in the root apex generate files of cells that subse-quently elongate and differentiate to acquire specialized function. Four developmental zones are recognized in the root: root cap, meristematic zone, elongation zone, and maturation zone. In Arabidopsis, files of mature cells can be traced to stem cells within the meristem cell population.
The Arabidopsis root apical meristem consists of a quiescent center, cortical–endodermal stem cells, columella stem cells, root cap–epidermal stem cells, and stele stem cells.
Differentiation is the process by which cells acquire metabolic, structural, and functional properties distinct from those of their progenitors. Tracheary element differ-entiation is an example of plant cell differentiation. Micro-tubules participate in determining the pattern in which the cellulose microfibrils are deposited in the secondary walls of tracheary elements.
MADS box genes are key regulators of important bio-logical functions in plants, animals, and fungi. Homeobox genes encode homeodomain proteins that act as transcrip-tion factors. These transcription factors control the expres-sion of other genes whose products transform and charac-terize the differentiated cell.
In the determination of a cell’s fate, the cell’s position is more important than its lineage. Plant cell fate is relatively plastic and can be changed when the positional signals nec-essary for its maintenance are altered.
The expression of homeobox genes similar to the maize genes KNOTTED1 and SHOOTMERISTEMLESS is neces-sary for the continued indeterminate character of the shoot apical meristem, but the WUSCHEL gene determines stem cell identity. Loss of expression of KNOX genes in the leaf primordia appears to be important in the shift to determi-nate growth in these structures.
Cell position is communicated via cell–cell signaling, which may involve ligand-induced signaling, hormone sig-naling or trafficking of regulatory proteins and/or mRNAs through plasmodesmata. Molecules ranging in size up to about 1.6 nm (700–1000 Da) can pass from cell to cell through plasmodesmata connecting leaf epidermal cells.
Plasmodesmata are, to some extent, gated so that passage through them can be regulated, and their size exclusion 372 Chapter 16 limit can be modified to permit the passage of much larger molecules, such as viruses.
Growth in plants is defined as an irreversible increase in volume. Plant growth can be quantitatively analyzed with kinematics, the study of particle movement and shape change.
Plant growth can be described in both spatial and mate-rial terms. Spatial descriptions focus on the patterns gener-ated by all the cells located at different positions in the growth zones. Material analyses focus on the fate of the individual cells or tissue elements at various stages of devel-opment. A growth trajectory shows the distance of a tissue element from the apex over time, and is therefore a mater-ial description of growth. The growth velocity is the speed at which the tissue elements are being displaced from the apex. The relative elemental growth rate is a measure of the fractional increase in length of the axis per unit time and represents the magnitude of growth at a particular location.
Senescence and programmed cell death are essential aspects of plant development. Plants exhibit a variety of different senescence phenomena. Leaves are genetically programmed to senesce and die. Senescence is an active developmental process that is controlled by the plant’s genetic program and initiated by specific environmental or developmental cues. Senescence is an ordered series of cytological and bio-chemical events. The expression of most genes is reduced during senescence, but the expression of some genes (senescence-associated genes, or SAGs) is initiated. The newly active genes encode various hydrolytic enzymes, such as proteases, ribonucleases, lipases, and enzymes involved in the biosynthesis of ethylene, which carry out the degradative processes as the tissues die.
Programmed cell death (PCD) is a specialized type of senescence. One important function of PCD in plants is protection against pathogenic organisms in what is called the hypersensitive response, which has been demonstrated to be a genetically programmed process.
Web Material Web Topics 16.1 Polarity of Fucus Zygotes A wide variety of external gradients can polar-ize growth of cells that are initially apolar.
16.2 The Preprophase Band of Microtubules Ultrastructural studies have elucidated the struc-ture of the preprophase band of micro-tubules and its role in orienting the plane of cell division.
16.3 Azolla Root Development Anatomical studies of the root of the aquatic fern,Azolla,have provided insights into cell fate during root development.
16.4 The Relative Elemental Growth Rate The relative elemental growth rate at various points along a root can be evaluated by differ-entiation of the growth velocity with respect to position.
Web Essay 16.1 Plant Meristems: An Historical Overview Scientists have used many approaches to unrav-el the secrets of plant meristems.
16.2 The Mermaids Wineglass The giant marine green alga, Acetabularia acetabulum, holds a classic place in the history of biology.
16.3 Division Plane Determination in Plant Cells Plant cells appear to utilize mechanisms differ-ent from those used by other eukaryotes to control their division planes.
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374 Chapter 16 Phytochrome and Light Control of Plant Development 17 Chapter HAVE YOU EVER LIFTED UP A BOARD that has been lying on a lawn for a few weeks and noticed that the grass growing underneath was much paler and spindlier than the surrounding grass? The reason this happens is that the board is opaque, keeping the underlying grass in darkness. Seedlings grown in the dark have a pale, unusually tall and spindly appearance. This form of growth, known as etiolated growth, is dramatically different from the stockier, green appearance of seedlings grown in the light (Figure 17.1).
Given the key role of photosynthesis in plant metabolism, one might be tempted to attribute much of this contrast to differences in the avail-ability of light-derived metabolic energy. However, it takes very little light or time to initiate the transformation from the etiolated to the green state. So in the change from dark to light growth, light acts as a devel-opmental trigger rather than a direct energy source.
If you were to remove the board and expose the pale patch of grass to light, it would appear almost the same shade of green as the sur-rounding grass within a week or so. Although not visible to the naked eye, these changes actually start almost immediately after exposure to light. For example, within hours of applying a single flash of relatively dim light to a dark-grown bean seedling in the laboratory, one can mea-sure several developmental changes: a decrease in the rate of stem elon-gation, the beginning of apical-hook straightening, and the initiation of the synthesis of pigments that are characteristic of green plants.
Light has acted as a signal to induce a change in the form of the seedling, from one that facilitates growth beneath the soil, to one that is more adaptive to growth above ground. In the absence of light, the seedling uses primarily stored seed reserves for etiolated growth. How-ever, seed plants, including grasses, don’t store enough energy to sus-tain growth indefinitely. They require light energy not only to fuel pho-tosynthesis, but to initiate the developmental switch from dark to light growth. Photosynthesis cannot be the driving force of this transformation because chlorophyll is not present during this time. Full de-etiolation does require some photosynthesis, but the initial rapid changes are induced by a distinctly different light response, called photomorphogenesis (from Latin, meaning literally “light form begins”).
Among the different pigments that can promote photo-morphogenic responses in plants, the most important are those that absorb red and blue light. The blue-light photoreceptors will be discussed in relation to guard cells and phototropism in Chapter 18. The focus of this chapter is phytochrome, a pro-tein pigment that absorbs red and far-red light most strongly, but that also absorbs blue light. As we will see in this chapter and in Chapter 24, phytochrome plays a key role in light-reg-ulated vegetative and reproductive development.
We begin with the discovery of phytochrome and the phenomenon of red/far-red photoreversibility. Next we will discuss the biochemical and photochemical properties of phytochrome, and the conformational changes induced by light. Different types of phytochromes are encoded by dif-ferent members of a multigene family, and different phy-tochromes regulate distinct processes in the plant. These dif-ferent phytochrome responses can be classified according to the amount of light and light quality required to produce the effect. Finally, we will examine what is known about the mechanism of phytochrome action at the cellular and mol-ecular levels, including signal transduction pathways and gene regulation.
THE PHOTOCHEMICAL AND BIOCHEMICAL PROPERTIES OF PHYTOCHROME Phytochrome, a blue protein pigment with a molecular mass of about 125 kDa (kilodaltons), was not identified as a unique chemical species until 1959, mainly because of technical difficulties in isolating and purifying the protein.
However, many of the biological properties of phytochrome had been established earlier in studies of whole plants.
The first clues regarding the role of phytochrome in plant development came from studies that began in the 1930s on red light–induced morphogenic responses, espe-cially seed germination. The list of such responses is now enormous and includes one or more responses at almost every stage in the life history of a wide range of different green plants (Table 17.1).
A key breakthrough in the history of phytochrome was the discovery that the effects of red light (650–680 nm) on morphogenesis could be reversed by a subsequent irradi-ation with light of longer wavelengths (710–740 nm), called far-red light. This phenomenon was first demonstrated in germinating seeds, but was also observed in relation to stem and leaf growth, as well as floral induction (see Chapter 24).
The initial observation was that the germination of lettuce seeds is stimulated by red light and inhibited by far-red light. But the real breakthrough was made many years later when lettuce seeds were exposed to alternating treatments of red and far-red light. Nearly 100% of the seeds that received red light as the final treatment germinated; in seeds that received far-red light as the final treatment, however, germination was strongly inhibited (Figure 17.2) (Flint 1936).
Two interpretations of these results were possible. One is that there are two pigments, a red light–absorbing pig-ment and a far-red light–absorbing pigment, and the two pigments act antagonistically in the regulation of seed ger-mination. Alternatively, there might be a single pigment that can exist in two interconvertible forms: a red 376 Chapter 17 FIGURE 17.1 Corn (Zea mays) (A and B) and bean (Phaseolus vulgaris) (C and D) seedlings grown either in the light (A and C) or the dark (B and D). Symptoms of etiolation in corn, a monocot, include the absence of greening, reduction in leaf size, failure of leaves to unroll, and elongation of the coleoptile and mesocotyl. In bean, a dicot, etiolation symp-toms include absence of greening, reduced leaf size, hypocotyl elongation, and maintenance of the apical hook.
(Photos © M. B. Wilkins.) (C) Light-grown bean (D) Dark-grown bean (A) Light-grown corn (B) Dark-grown corn light–absorbing form and a far-red light–absorbing form (Borthwick et al. 1952). The model chosen—the one-pigment model—was the more radical of the two because there was no precedent for such a photoreversible pigment. Several years later phy-tochrome was demonstrated in plant extracts for the first time, and its unique photoreversible properties were exhib-ited in vitro, confirming the prediction (Butler et al. 1959).
In this section we will consider three broad topics: 1. Photoreversibility and its relationship to phytochrome responses 2. The structure of phytochrome, its synthesis and assembly, and the conformational changes associated with the interconversions of the two main forms of phytochrome: Pr and Pfr 3. The phytochrome gene family, the members of which have different functions in photomorphogenesis Phytochrome Can Interconvert between Pr and Pfr Forms In dark-grown or etiolated plants, phytochrome is present in a red light–absorbing form, referred to as Pr because it Phytochrome and Light Control of Plant Development 377 TABLE 17.1 Typical photoreversible responses induced by phytochrome in a variety of higher and lower plants Group Genus Stage of development Effect of red light Angiosperms Lactuca (lettuce) Seed Promotes germination Avena (oat) Seedling (etiolated) Promotes de-etiolation (e.g., leaf unrolling) Sinapis (mustard) Seedling Promotes formation of leaf primordia, development of primary leaves, and production of anthocyanin Pisum (pea) Adult Inhibits internode elongation Xanthium (cocklebur) Adult Inhibits flowering (photoperiodic response) Gymnosperms Pinus (pine) Seedling Enhances rate of chlorophyll accumulation Pteridophytes Onoclea (sensitive fern) Young gametophyte Promotes growth Bryophytes Polytrichum (moss) Germling Promotes replication of plastids Chlorophytes Mougeotia (alga) Mature gametophyte Promotes orientation of chloroplasts to directional dim light Dark Red Red Far-red Red Far-red Red Red Far-red Far-red Red FIGURE 17.2 Lettuce seed germination is a typical photore-versible response controlled by phytochrome. Red light promotes lettuce seed germination, but this effect is reversed by far-red light. Imbibed (water-moistened) seeds were given alternating treatments of red followed by far-red light. The effect of the light treatment depended on the last treatment given. (Photos © M. B. Wilkins.) is synthesized in this form. Pr, which to the human eye is blue, is converted by red light to a far-red light–absorbing form called Pfr, which is blue-green. Pfr, in turn, can be converted back to Pr by far-red light. Known as photoreversibility, this conversion/recon-version property is the most distinctive property of phy-tochrome, and it may be expressed in abbreviated form as follows: The interconversion of the Pr and Pfr forms can be mea-sured in vivo or in vitro. In fact, most of the spectral prop-erties of carefully purified phytochrome measured in vitro are the same as those observed in vivo.
When Pr molecules are exposed to red light, most of them absorb it and are converted to Pfr, but some of the Pfr also absorbs the red light and is converted back to Pr because both Pr and Pfr absorb red light (Figure 17.3). Thus the proportion of phytochrome in the Pfr form after satu-rating irradiation by red light is only about 85%. Similarly, the very small amount of far-red light absorbed by Pr makes it impossible to convert Pfr entirely to Pr by broad-spectrum far-red light. Instead, an equilibrium of 97% Pr and 3% Pfr is achieved. This equilibrium is termed the pho-tostationary state.
In addition to absorbing red light, both forms of phy-tochrome absorb light in the blue region of the spectrum (see Figure 17.3). Therefore, phytochrome effects can be elicited also by blue light, which can convert Pr to Pfr and vice versa. Blue-light responses can also result from the action of one or more specific blue-light photoreceptors (see Chapter 18). Whether phytochrome is involved in a response to blue light is often determined by a test of the ability of far-red light to reverse the response, since only phytochrome-induced responses are reversed by far-red light. Another way to discriminate between photoreceptors is to study mutants that are deficient in one of the pho-toreceptors.
Short-lived phytochrome intermediates.
The photo-conversions of Pr to Pfr, and of Pfr to Pr, are not one-step processes. By irradiating phytochrome with very brief flashes of light, we can observe absorption changes that occur in less than a millisecond.
Of course, sunlight includes a mixture of all visible wavelengths. Under such white-light conditions, both Pr and Pfr are excited, and phytochrome cycles continuously between the two. In this situation the intermediate forms of phytochrome accumulate and make up a significant frac-tion of the total phytochrome. Such intermediates could even play a role in initiating or amplifying phytochrome responses under natural sunlight, but this question has yet to be resolved.
Pfr Is the Physiologically Active Form of Phytochrome Because phytochrome responses are induced by red light, they could in theory result either from the appearance of Pfr or from the disappearance of Pr. In most cases studied, a quantitative relationship holds between the magnitude of the physiological response and the amount of Pfr gen-erated by light, but no such relationship holds between the physiological response and the loss of Pr. Evidence such as this has led to the conclusion that Pfr is the physiologically active form of phytochrome. In cases in which it has been shown that a phytochrome response is not quantitatively related to the absolute amount of Pfr, it has been proposed that the ratio between Pfr and Pr, or between Pfr and the total amount of phytochrome, deter-mines the magnitude of the response.
The conclusion that Pfr is the physiologically active form of phytochrome is supported by studies with mutants of Arabidopsis that are unable to synthesize phytochrome.
In wild-type seedlings, hypocotyl elongation is strongly inhibited by white light, and phytochrome is one of the photoreceptors involved in this response. When grown under continuous white light, mutant seedlings with long hypocotyls were discovered and were termed hy mutants.
Different hy mutants are designated by numbers: hy1, hy2, and so on. Because white light is a mixture of wavelengths (including red, far red, and blue), some, but not all, of the hy mutants have been shown to be deficient for one or more functional phytochrome(s).
Pr Pfr Red light Far-red light 378 Chapter 17 FIGURE 17.3 Absorption spectra of purified oat phy-tochrome in the Pr (green line) and Pfr (blue line) forms overlap. (After Vierstra and Quail 1983.) The phenotypes of phytochrome-deficient mutants have been useful in identifying the physiologically active form of phytochrome. If the phytochrome-induced response to white light (hypocotyl growth inhibition) is caused by the absence of Pr, such phytochrome-deficient mutants (which have neither Pr nor Pfr) should have short hypocotyls in both darkness and white light. Instead, the opposite occurs; that is, they have long hypocotyls in both darkness and white light. It is the absence of Pfr that prevents the seedlings from responding to white light. In other words, Pfr brings about the physiological response.
Phytochrome Is a Dimer Composed of Two Polypeptides Native phytochrome is a soluble protein with a molecular mass of about 250 kDa. It occurs as a dimer made up of two equivalent subunits. Each subunit consists of two compo-nents: a light-absorbing pigment molecule called the chro-mophore, and a polypeptide chain called the apoprotein.
The apoprotein monomer has a molecular mass of about 125 kDa. Together, the apoprotein and its chromophore make up the holoprotein. In higher plants the chromophore of phytochrome is a linear tetrapyrrole termed phytochro-mobilin. There is only one chromophore per monomer of apoprotein, and it is attached to the protein through a thioether linkage to a cysteine residue (Figure 17.4).
Researchers have visualized the Pr form of phytochrome using electron microscopy and X-ray scattering, and the model shown in Figure 17.5 has been proposed (Nakasako et al. 1990). The polypeptide folds into two major domains separated by a “hinge” region. The larger N-terminal domain is approximately 70 kDa and bears the chro-mophore; the smaller C-terminal domain is approximately 55 kDa and contains the site where the two monomers asso-ciate with each other to form the dimer (see Web Topic 17.1).
Phytochromobilin Is Synthesized in Plastids The phytochrome apoprotein alone cannot absorb red or far-red light. Light can be absorbed only when the polypeptide is covalently linked with phytochromobilin to form the holoprotein. Phytochromobilin is synthesized inside plastids and is derived from 5-aminolevulinic acid via a pathway that branches from the chlorophyll biosyn-thetic pathway (see Web Topic 7.11). It is thought to leak out of the plastid into the cytosol by a passive process.
Assembly of the phytochrome apoprotein with its chro-mophore is autocatalytic; that is, it occurs spontaneously when purified phytochrome polypeptide is mixed with purified chromophore in the test tube, with no additional proteins or cofactors (Li and Lagarias 1992). The resultant holoprotein has spectral properties similar to those observed for the holoprotein purified from plants, and it exhibits red/far-red reversibility (Li and Lagarias 1992).
Mutant plants that lack the ability to synthesize the chromophore are defective in processes that require the action of phytochrome, even though the apoprotein polypeptides are present. For example, several of the hy mutants noted earlier, in which white light fails to suppress hypocotyl elongation, have defects in chromophore biosyn-thesis. In hy1 and hy2 mutant plants, phytochrome apopro-tein levels are normal, but there is little or no spectrally Phytochrome and Light Control of Plant Development 379 N H +N H H 15 15 N H C D O R R N S 5 10 H A B O Pro His Ser Cys His Leu Gln Pro His Ser Cys His Leu Gln N H +N H N H H C D O R R N S 5 H A B O 10 Thioether linkage Chromophore: phytochromobilin Red light converts cis to trans Pr Pfr Polypeptide Cis isomer Trans isomer FIGURE 17.4 Structure of the Pr and Pfr forms of the chro-mophore (phytochromobilin) and the peptide region bound to the chromophore through a thioether linkage. The chro-mophore undergoes a cis–trans isomerization at carbon 15 in response to red and far-red light. (After Andel et al. 1997.) IIB IIA Chromophore-binding domains IB IA FIGURE 17.5 Structure of the phytochrome dimer. The monomers are labeled I and II. Each monomer consists of a chromophore-binding domain (A) and a smaller nonchro-mophore domain (B). The molecule as a whole has an ellip-soidal rather than globular shape. (After Tokutomi et al.
1989.) active holoprotein. When a chromophore precursor is sup-plied to these seedlings, normal growth is restored. The same type of mutation has been observed in other species. For example, the yellow-green mutant of tomato has properties similar to those of hy mutants, suggesting that it is also a chromophore mutant.
Both Chromophore and Protein Undergo Conformational Changes Because the chromophore absorbs the light, conformational changes in the protein are initiated by changes in the chro-mophore. Upon absorption of light, the Pr chromophore undergoes a cis–trans isomerization of the double bond between carbons 15 and 16 and rotation of the C14–C15 single bond (see Figure 17.4) (Andel et al. 1997). During the conversion of Pr to Pfr, the protein moiety of the phy-tochrome holoprotein also undergoes a subtle conforma-tional change.
Several lines of evidence suggest that the light-induced change in the conformation of the polypeptide occurs both in the N-terminal chromophore-binding domain and in the C-terminal region of the protein.
Two Types of Phytochromes Have Been Identified Phytochrome is most abundant in etiolated seedlings; thus most biochemical studies have been carried out on phy-tochrome purified from nongreen tissues. Very little phy-tochrome is extractable from green tissues, and a portion of the phytochrome that can be extracted differs in molec-ular mass from the abundant form of phytochrome found in etiolated plants. Research has shown that there are two different classes of phytochrome with distinct properties. These have been termed Type I and Type II phytochromes (Furuya 1993).
Type I is about nine times more abundant than Type II in dark-grown pea seedlings; in light-grown pea seedlings the amounts of the two types are about equal. More recently, the two types have been shown to be distinct proteins.
The cloning of genes that encode different phytochrome polypeptides has clarified the distinct nature of the phy-tochromes present in etiolated and green seedlings. Even in etiolated seedlings, phytochrome is a mixture of related proteins encoded by different genes.
Phytochrome Is Encoded by a Multigene Family The cloning of phytochrome genes made it possible to carry out a detailed comparison of the amino acid sequences of the related proteins. It also allowed the study of their expression patterns, at both the mRNA and the pro-tein levels.
The first phytochrome sequences cloned were from monocots. These studies and subsequent research indicated that phytochromes are soluble proteins—a finding that is consistent with previous purification studies. A comple-mentary-DNA clone encoding phytochrome from the dicot zucchini (Cucurbita pepo) was used to identify five struc-turally related phytochrome genes in Arabidopsis (Sharrock and Quail 1989). This phytochrome gene family is named PHY, and its five individual members are PHYA, PHYB, PHYC, PHYD, and PHYE.
The apoprotein by itself (without the chromophore) is designated PHY; the holoprotein (with the chromophore) is designated phy. By convention, phytochrome sequences from other higher plants are named according to their homology with the Arabidopsis PHY genes. Monocots appear to have representatives of only the PHYA through PHYC families, while dicots have others derived by gene duplication (Mathews and Sharrock 1997).
Some of the hy mutants have turned out to be selectively deficient in specific phytochromes. For example, hy3 is defi-cient in phyB, and hy1 and hy2 are deficient in chro-mophore. These and other phy mutants have been useful in determining the physiological functions of the different phytochromes (as discussed later in this chapter).
PHY Genes Encode Two Types of Phytochrome On the basis of their expression patterns, the products of members of the PHY gene family can be classified as either Type I or Type II phytochromes. PHYA is the only gene that encodes a Type I phytochrome. This conclusion is based on the expression pattern of the PHYA promoter, as well as on the accumulation of its mRNA and polypeptide in response to light. Additional studies of plants that contain mutated forms of the PHYA gene (termed phyA alleles) have con-firmed this conclusion and have given some clues about the role of this phytochrome in whole plants.
The PHYA gene is transcriptionally active in dark-grown seedlings, but its expression is strongly inhibited in the light in monocots. In dark-grown oat, treatment with red light reduces phytochrome synthesis because the Pfr form of phytochrome inhibits the expression of its own gene. In addition, the PHYA mRNA is unstable, so once etiolated oat seedlings are transferred to the light, PHYA mRNA rapidly disappears. The inhibitory effect of light on PHYA transcription is less dramatic in dicots, and in Arabidopsis red light has no measurable effect on PHYA.
The amount of phyA in the cell is also regulated by pro-tein destruction. The Pfr form of the protein encoded by the PHYA gene, called PfrA, is unstable. There is evidence that PfrA may become marked or tagged for destruction by the ubiquitin system (Vierstra 1994). As discussed in Chapter 14 on the web site, ubiquitin is a small polypeptide that binds covalently to proteins and serves as a recognition site for a large proteolytic complex, the proteasome.
Therefore, oats and other monocots rapidly lose most of their Type I phytochrome (phyA) in the light as a result of a combination of factors: inhibition of transcription, mRNA degradation, and proteolysis: 380 Chapter 17 In dicots, phyA levels also decline in the light as a result of proteolysis, but not as dramatically.
The remaining PHY genes (PHYB through PHYE) encode the Type II phytochromes. Although detected in green plants, these phytochromes are also present in etio-lated plants. The reason is that the expression of their mRNAs is not significantly changed by light, and the encoded phyB through phyE proteins are more stable in the Pfr form than is PfrA.
LOCALIZATION OF PHYTOCHROME IN TISSUES AND CELLS Valuable insights into the function of a protein can be gained from a determination of where it is located. It is not surprising, therefore, that much effort has been devoted to the localization of phytochrome in organs and tissues, and within individual cells.
Phytochrome Can Be Detected in Tissues Spectrophotometrically The unique photoreversible properties of phytochrome can be used to quantify the pigment in whole plants through the use of a spectrophotometer. Because its color is masked by chlorophyll, phytochrome is difficult to detect in green tissue. In dark-grown plants, where there is no chlorophyll, phytochrome has been detected in many angiosperm tis-sues—both monocot and dicot—as well as in gym-nosperms, ferns, mosses, and algae.
In etiolated seedlings the highest phytochrome levels are usually found in meristematic regions or in regions that were recently meristematic, such as the bud and first node of pea (Figure 17.6), or the tip and node regions of the coleoptile in oat. However, differences in expression pat-terns between monocots and dicots and between Type I and Type II phytochromes are apparent when other, more sensitive methods are used.
Phytochrome Is Differentially Expressed In Different Tissues The cloning of individual PHY genes has enabled researchers to determine the patterns of expression of individual phy-tochromes in specific tissues by several methods. The sequences can be used directly to probe mRNAs isolated from different tissues or to analyze transcriptional activity by means of a reporter gene, which visually reveals sites of gene expression. In the latter approach, the promoter of a PHYA or PHYB gene is joined to the coding portion of a reporter gene, such as the gene for the enzyme β-glucuronidase, which is PHYB–E mRNA Pr Pfr Response Red Far red – PHYA mRNA Degradation Pr Pfr Response Red Far red Ubiquitin + Ubiquitin ATP Degradation Phytochrome and Light Control of Plant Development 381 0 2 12 22 20 10 0 20 10 0 Epicotyl First node Cotyledon Root Concentration of phytochrome Distance (mm) FIGURE 17.6 Phytochrome is most heavily concentrated in the regions where dramatic developmental changes are occurring: the apical meristems of the epicotyl and root. Shown here is the distribution of phy-tochrome in an etiolated pea seedling, as measured spec-trophotometrically. (From Kendrick and Frankland 1983.) called GUS (recall that the promoter is the sequence upstream of the gene that is required for transcription).
The advantage of using the GUS sequence is that it encodes an enzyme that, even in very small amounts, con-verts a colorless substrate to a colored precipitate when the substrate is supplied to the plant. Thus, cells in which the PHYA promoter is active will be stained blue, and other cells will be colorless. The hybrid, or fused, gene is then placed back into the plant through use of the Ti plasmid of Agrobacterium tumefaciens as a vector (see Web Topic 21.5).
When this method was used to examine the transcrip-tion of two different PHYA genes in tobacco, dark-grown seedlings were found to contain the highest amount of stain in the apical hook and the root tips, in keeping with earlier immunological studies (Adam et al. 1994). The pat-tern of staining in light-grown seedlings was similar but, as might be expected, was of much lower intensity. Similar studies with Arabidopsis PHYA–GUS and PHYB–GUS fusions placed back in Arabidopsis confirmed the PHYA results for tobacco and indicated that PHYB–GUS is expressed at much lower levels than PHYA–GUS in all tis-sues (Somers and Quail 1995).
A recent study comparing the expression patterns of PHYB–GUS, PHYD–GUS, and PHYE–GUS fusions in Ara-bidopsis has revealed that although these Type II promoters are less active than the Type I promoters, they do show dis-tinct expression patterns (Goosey et al. 1997). Thus the gen-eral picture emerging from these studies is that the phy-tochromes are expressed in distinct but overlapping patterns.
In summary, phytochromes are most abundant in young, undifferentiated tissues, in the cells where the mRNAs are most abundant and the promoters are most active. The strong correlation between phytochrome abun-dance and cells that have the potential for dynamic devel-opmental changes is consistent with the important role of phytochromes in controlling such developmental changes.
However, note that the studies discussed here do not address whether the phytochromes are photoactive as apoproteins or holoproteins.
Because the expression patterns of individual phy-tochromes overlap, it is not surprising that they function cooperatively, although they probably also use distinct sig-nal transduction pathways. Support for this idea also comes from the study of phytochrome mutants, which we will discuss later in this chapter.
CHARACTERISTICS OF PHYTOCHROME-INDUCED WHOLE-PLANT RESPONSES The variety of different phytochrome responses in intact plants is extensive, in terms of both the kinds of responses (see Table 17.1) and the quantity of light needed to induce the responses. A survey of this variety will show how diversely the effects of a single photoevent—the absorption of light by Pr—are manifested throughout the plant. For ease of discussion, phytochrome-induced responses may be logically grouped into two types: 1. Rapid biochemical events 2. Slower morphological changes, including movements and growth Some of the early biochemical reactions affect later developmental responses. The nature of these early bio-chemical events, which comprise signal transduction path-ways, will be treated in detail later in the chapter. Here we will focus on the effects of phytochrome on whole-plant responses. As we will see, such responses can be classified into various types, depending on the amount and duration of light required, and on their action spectra.
Phytochrome Responses Vary in Lag Time and Escape Time Morphological responses to the photoactivation of phy-tochrome may be observed visually after a lag time—the time between a stimulation and an observed response. The lag time may be as brief as a few minutes or as long as sev-eral weeks. The more rapid of these responses are usually reversible movements of organelles (see Web Topic 17.2) or reversible volume changes (swelling, shrinking) in cells, but even some growth responses are remarkably fast. Red-light inhibition of the stem elongation rate of light-grown pigweed (Chenopodium album) is observed within 8 minutes after its relative level of Pfr is increased. Kinetic studies using Arabidopsis have confirmed this observation and further shown that phyA acts within minutes after exposure to red light (Parks and Spalding 1999). In these studies the primary contribution of phyA was found to be over by 3 hours, at which time phyA protein was no longer detectable through the use of antibodies, and the contribu-tion of phyB increased (Morgan and Smith 1978). Longer lag times of several weeks are observed for the induction of flowering (see Chapter 24).
Information about the lag time for a phytochrome response helps researchers evaluate the kinds of biochem-ical events that could precede and cause the induction of that response. The shorter the lag time, the more limited the range of biochemical events that could have been involved.
Variety in phytochrome responses can also be seen in the phenomenon called escape from photoreversibility.
Red light–induced events are reversible by far-red light for only a limited period of time, after which the response is said to have “escaped” from reversal control by light.
A model to explain this phenomenon assumes that phy-tochrome-controlled morphological responses are the result of a step-by-step sequence of linked biochemical reactions in the responding cells. Each of these sequences has a point of no return beyond which it proceeds irrevocably to the response. The escape time for different responses ranges from less than a minute to, remarkably, hours.
382 Chapter 17 Phytochrome Responses Can Be Distinguished by the Amount of Light Required In addition to being distinguished by lag times and escape times, phytochrome responses can be distinguished by the amount of light required to induce them. The amount of light is referred to as the fluence,1 which is defined as the number of photons impinging on a unit surface area (see Chapter 9 and Web Topic 9.1). The most commonly used units for fluence are moles of quanta per square meter (mol m–2). In addition to the fluence, some phytochrome responses are sensitive to the irradiance,2 or fluence rate, of light. The units of irradiance in terms of photons are moles of quanta per square meter per second (mol m–2 s–1).
Each phytochrome response has a characteristic range of light fluences over which the magnitude of the response is proportional to the fluence. As Figure 17.7 shows, these responses fall into three major categories based on the amount of light required: very-low-fluence responses (VLFRs), low-fluence responses (LFRs), and high-irradi-ance responses (HIRs).
Very-Low-Fluence Responses Are Nonphotoreversible Some phytochrome responses can be initiated by fluences as low as 0.0001 µmol m–2 (one-tenth of the amount of light emitted from a firefly in a single flash), and they sat-urate (i.e., reach a maximum) at about 0.05 µmol m–2. For example, in dark-grown oat seedlings, red light can stim-ulate the growth of the coleoptile and inhibit the growth of the mesocotyl (the elongated axis between the coleop-tile and the root) at such low fluences. Arabidopsis seeds can be induced to germinate with red light in the range of 0.001 to 0.1 µmol m–2. These remarkable effects of vanish-ingly low levels of illumination are called very-low-flu-ence responses (VLFRs).
The minute amount of light needed to induce VLFRs converts less than 0.02% of the total phytochrome to Pfr.
Because the far-red light that would normally reverse a red-light effect converts 97% of the Pfr to Pr (as discussed earlier), about 3% of the phytochrome remains as Pfr—sig-nificantly more than is needed to induce VLFRs (Mandoli and Briggs 1984). Thus, far-red light cannot reverse VLFRs.
The VLFR action spectrum matches the absorption spec-trum of Pr, supporting the view that Pfr is the active form for these responses (Shinomura et al. 1996).
Ecological implications of the VLFR in seed germina-tion are discussed in Web Essay 17.1 Low-Fluence Responses Are Photoreversible Another set of phytochrome responses cannot be initiated until the fluence reaches 1.0 µmol m–2, and they are satu-rated at 1000 µmol m–2. These responses are referred to as low-fluence responses (LFRs), and they include most of the red/far-red photoreversible responses, such as the pro-motion of lettuce seed germination and the regulation of leaf movements, that are mentioned in Table 17.1. The LFR action spectrum for Arabidopsis seed germination is shown in Figure 17.8. LFR spectra include a main peak for stim-ulation in the red region (660 nm), and a major peak for inhibition in the far-red region (720 nm).
Both VLFRs and LFRs can be induced by brief pulses of light, provided that the total amount of light energy adds up to the required fluence. The total fluence is a function of two factors: the fluence rate (mol m–2 s–1) and the irradia-tion time. Thus a brief pulse of red light will induce a response, provided that the light is sufficiently bright, and conversely, very dim light will work if the irradiation time is long enough. This reciprocal relationship between fluence rate and time is known as the law of reciprocity, which was first formulated by R. W. Bunsen and H. E. Roscoe in 1850.
VLFRs and LFRs both obey the law of reciprocity.
High-Irradiance Responses Are Proportional to the Irradiance and the Duration Phytochrome responses of the third type are termed high-irradiance responses (HIRs), several of which are listed in Phytochrome and Light Control of Plant Development 383 1 For definitions of fluence, irradiance, and other terms involved in light measurement, see Web Topic 9.1.
2 Irradiance is sometimes loosely equated with light inten-sity. The term intensity, however, refers to light emitted by the source, whereas irradiance refers to light that is incident on the object.
–8 –6 –4 –2 0 2 4 6 8 Log fluence (µmol m–2) Relative response VLFR: Reciprocity applies, not FR-reversible LFR: Reciprocity applies, FR-reversible HIR: Fluence rate dependent, long irradiation required, and not photo-reversible, reciprocity does not apply I1 I2 I3 FIGURE 17.7 Three types of phytochrome responses, based on their sensitivities to fluence. The relative magnitudes of representative responses are plotted against increasing flu-ences of red light. Short light pulses activate VLFRs and LFRs. Because HIRs are also proportional to the irradiance, the effects of three different irradiances given continuously are illustrated (I1 > I2 > I3). (From Briggs et al. 1984.) Table 17.2. HIRs require prolonged or continuous exposure to light of relatively high irradiance, and the response is proportional to the irradiance within a certain range.
The reason that these responses are called high-irradiance responses rather than high-fluence responses is that they are proportional to irradiance (loosely speaking, the brightness of the light) rather than to fluence. HIRs saturate at much higher fluences than LFRs—at least 100 times higher—and are not photoreversible. Because neither continuous expo-sure to dim light nor transient exposure to bright light can induce HIRs, HIRs do not obey the law of reciprocity.
Many of the photoreversible LFRs listed in Table 17.1, particularly those involved in de-etiolation, also qualify as HIRs. For example, at low fluences the action spectrum for anthocyanin production in seedlings of white mustard (Sinapis alba) shows a single peak in the red region of the spectrum, the effect is reversible with far-red light, and the response obeys the law of reciprocity. However, if the dark-grown seedlings are instead exposed to high-irradiance light for several hours, the action spectrum now includes peaks in the far-red and blue regions (see the next section), the effect is no longer photoreversible, and the response becomes proportional to the irradiance. Thus the same effect can be either an LFR or an HIR, depending on its his-tory of exposure to light.
The HIR Action Spectrum of Etiolated Seedlings Has Peaks in the Far-Red, Blue, and UV-A Regions HIRs, such as the inhibition of stem or hypocotyl growth, have usually been studied in dark-grown, etiolated seedlings. The HIR action spectrum for the inhibition of hypocotyl elongation in dark-grown lettuce seedlings is shown in Figure 17.9. For HIRs the main peak of activity is in the far-red region between the absorption maxima of Pr and Pfr, and there are peaks in the blue and UV-A regions as well. Because the absence of a peak in the red region is unusual for a phytochrome-mediated response, at first researchers believed that another pigment might be involved.
A large body of evidence now supports the view that phytochrome is one of the photoreceptors involved in HIRs (see Web Topic 17.3). However, it has long been suspected that the peaks in the UV-A and blue regions are due to a separate photoreceptor that absorbs UV-A and blue light. As a test of this hypothesis, the HIR action spectrum for the inhibition of hypocotyl elongation was determined in dark-grown hy2 mutants of Arabidopsis, which have little or no phytochrome holoprotein. As expected, the wild-type seedlings exhibited peaks in the UV-A, blue, and far-red regions of the spectrum. In contrast, the hy2 mutant failed to respond to either far-red or red light.
Although the phytochrome-deficient hy2 mutant exhibited no peak in the far-red region, it showed a normal response to UV-A and blue light (Goto et al. 1993).
These results demonstrate that phy-tochrome is not involved in the HIR to either UV-A or blue light, and that a sep-arate blue/UV-A photoreceptor is responsible for the response to these 384 Chapter 17 FIGURE 17.8 LFR action spectra for the photoreversible stimula-tion and inhibition of seed ger-mination in Arabidopsis. (After Shropshire et al. 1961.) TABLE 17.2 Some plant photomorphogenic responses induced by high irradiances Synthesis of anthocyanin in various dicot seedings and in apple skin segments Inhibition of hypocotyl elongation in mustard, lettuce, and petunia seedlings Induction of flowering in henbane (Hyoscyamus) Plumular hook opening in lettuce Enlargement of cotyledons in mustard Production of ethylene in sorghum wavelengths. More recent studies indicate that the blue-light photoreceptors CRY1 and CRY2 are involved in blue-light inhibition of hypocotyl elongation.
The HIR Action Spectrum of Green Plants Has a Major Red Peak During studies of the HIR of etiolated seedlings, it was observed that the response to continuous far-red light declines rapidly as the seedlings begin to green. For exam-ple, the action spectrum for the inhibition of hypocotyl growth of light-grown green Sinapis alba (white mustard) seedlings is shown in Figure 17.10. In general, HIR action spectra for light-grown plants exhibit a single major peak in the red, similar to the action spectra of LFRs (see Figure 17.8), except that the effect is nonphotoreversible.
The loss of responsiveness to continuous far-red light is strongly correlated with the depletion of the light-labile pool of Type I phytochrome, which consists mostly of phyA. This finding suggests that the HIR of etiolated seedlings to far-red light is mediated by phyA, whereas the HIR of green seedlings to red light is mediated by the Type II phytochrome phyB and pos-sibly others.
ECOLOGICAL FUNCTIONS: SHADE AVOIDANCE Thus far we have discussed phy-tochrome-regulated responses as studied in the laboratory. However, phytochrome plays important eco-logical roles for plants growing in the environment. In the discussion that follows we will learn how plants sense and respond to shading by other plants, and how phytochrome is involved in regulating various daily rhythms. We will also examine the specialized functions of the dif-ferent phytochrome gene family members in these processes.
Phytochrome Enables Plants to Adapt to Changing Light Conditions The presence of a red/far-red re-versible pigment in all green plants, from algae to dicots, suggests that these wavelengths of light provide information that helps plants adjust to their environment. What environmen-tal conditions change the relative lev-els of these two wavelengths of light in natural radiation?
The ratio of red light (R) to far-red light (FR) varies remarkably in different environments. This ratio can be defined as follows: Phytochrome and Light Control of Plant Development 385 FIGURE 17.9 HIR action spectrum for the inhibition of hypocotyl elongation of dark-grown lettuce seedlings. The peaks of activity for the inhibition of hypocotyl elongation occur in the UV-A, blue, and far-red regions of the spec-trum. (After Hartmann 1967.) FIGURE 17.10 HIR action spectra for the inhibition of hypocotyl elongation of light-grown white mustard (Sinapis alba) seedlings. (After Beggs et al. 1980.) Table 17.3 compares both the total light intensity in photons (400–800 nm) and the R/FR values in eight natural envi-ronments. Both parameters vary greatly in different envi-ronments.
Compared with direct daylight, there is relatively more far-red light during sunset, under 5 mm of soil, or under the canopy of other plants (as on the floor of a forest). The canopy phenomenon results from the fact that green leaves absorb red light because of their high chlorophyll content but are relatively transparent to far-red light.
The R:FR ratio and shading.
An important function of phytochrome is that it enables plants to sense shading by other plants. Plants that increase stem extension in response to shading are said to exhibit a shade avoidance response.
As shading increases, the R:FR ratio decreases. The greater proportion of far-red light converts more Pfr to Pr, and the ratio of Pfr to total phytochrome (Pfr/Ptotal) decreases.
When simulated natural radiation was used to vary the far-red content, it was found that for so-called sun plants (plants that normally grow in an open-field habitat), the higher the far-red content (i.e., the lower the Pfr:Ptotal ratio), the higher the rate of stem extension (Figure 17.11).
In other words, simulated canopy shading (high levels of far-red light) induced these plants to allocate more of their resources to growing taller. This correlation did not hold for “shade plants,” which normally grow in a shaded environment. Shade plants showed little or no reduction in their stem extension rate as they were exposed to higher R/FR values (see Figure 17.11). Thus there appears to be a systematic relationship between phytochrome-controlled growth and species habitat. Such results are taken as an indication of the involvement of phytochrome in shade perception.
For a “sun plant” or “shade-avoiding plant” there is a clear adaptive value in allocating its resources toward more rapid extension growth when it is shaded by another plant.
In this way it can enhance its chances of growing above the canopy and acquiring a greater share of unfiltered, photosyn-thetically active light. The price for favor-ing internode elongation is usually reduced leaf area and reduced branching, but at least in the short run this adapta-tion to canopy shade seems to work.
The R:FR ratio and seed germination.
Light quality also plays a role in regulat-ing the germination of some seeds. As discussed earlier, phytochrome was dis-covered in studies of light-dependent let-tuce seed germination.
In general, large-seeded species, with ample food reserves to sustain prolonged seedling growth in darkness (e.g., under-ground), do not require light for germi-nation. However, a light requirement is R/FR = Photon fluence rate in 10 nm band centered on 660 nm Photon fluence rate in 10 nm band centered on 730 nm 386 Chapter 17 TABLE 17.3 Ecologically important light parameters Photon flux density (µmol m–2 s–1) R/FRa Daylight 1900 1.19 Sunset 26.5 0.96 Moonlight 0.005 0.94 Ivy canopy 17.7 0.13 Lakes, at a depth of 1 m Black Loch 680 17.2 Loch Leven 300 3.1 Loch Borralie 1200 1.2 Soil, at a depth of 5 mm 8.6 0.88 Source: Smith 1982, p. 493.
Note:The light intensity factor (400–800 nm) is given as the photon flux density, and phy-tochrome-active light is given as the R:FR ratio.
aAbsolute values taken from spectroradiometer scans; the values should be taken to indi-cate the relationships between the various natural conditions and not as actual environ-mental means.
0.08 0.10 0.06 0.04 0.02 0.0 0.2 0.4 0.6 0.8 Pfr/Ptotal Logarithm of the stem elongation rate Shade plants Sun plants FIGURE 17.11 Role of phytochrome in shade perception in sun plants (solid line) versus shade plants (dashed line).
(After Morgan and Smith 1979.) often observed in the small seeds of herbaceous and grass-land species, many of which remain dormant, even while hydrated, if they are buried below the depth to which light penetrates. Even when such seeds are on or near the soil surface, their level of shading by the vegetation canopy (i.e., the R:FR ratio they receive) is likely to affect their ger-mination. For example, it is well documented that far-red enrichment imparted by a leaf canopy inhibits germination in a range of small-seeded species.
For the small seeds of the tropical species trumpet tree (Cecropia obtusifolia) and Veracruz pepper (Piper auritum) planted on the floor of a deeply shaded forest, this inhibi-tion can be reversed if a light filter is placed immediately above the seeds that permits the red component of the canopy-shaded light to pass through while blocking the far-red component. Although the canopy transmits very lit-tle red light, the level is enough to stimulate the seeds to germinate, probably because most of the inhibitory far-red light is excluded by the filter and the R:FR ratio is very high. These seeds would also be more likely to germinate in spaces receiving sunlight through gaps in the canopy than in densely shaded spaces. The sunlight would help ensure that the seedlings became photosynthetically self-sustaining before their seed food reserves were exhausted.
As will be discussed later in the chapter, recent studies on light-dependent lettuce seeds have shown that red light–induced germination is the result of an increase in the level of the biologically active form of the hormone gib-berellin. Thus, phytochrome may promote seed germina-tion through its effects on gibberellin biosynthesis (see Chapter 20).
ECOLOGICAL FUNCTIONS: CIRCADIAN RHYTHMS Various metabolic processes in plants, such as oxygen evolution and respiration, cycle alternately through high-activity and low-activity phases with a regular periodicity of about 24 hours. These rhythmic changes are referred to as circadian rhythms (from the Latin circa diem, meaning “approximately a day”). The period of a rhythm is the time that elapses between successive peaks or troughs in the cycle, and because the rhythm persists in the absence of external controlling factors, it is considered to be endogenous.
The endogenous nature of circa-dian rhythms suggests that they are governed by an internal pacemaker, called an oscillator. The endoge-nous oscillator is coupled to a vari-ety of physiological processes. An important feature of the oscillator is that it is unaffected by temperature, which enables the clock to function normally under a wide variety of seasonal and climatic conditions. The clock is said to exhibit temperature compensation.
Light is a strong modulator of rhythms in both plants and animals. Although circadian rhythms that persist under controlled laboratory conditions usually have peri-ods one or more hours longer or shorter than 24 hours, in nature their periods tend to be uniformly closer to 24 hours because of the synchronizing effects of light at daybreak, referred to as entrainment. Both red and blue light are effective in entrainment. The red-light effect is photore-versible by far-red light, indicative of phytochrome; the blue-light effect is mediated by blue-light photoreceptor(s).
Phytochrome Regulates the Sleep Movements of Leaves The sleep movements of leaves, referred to as nyctinasty, are a well-described example of a plant circadian rhythm that is regulated by light. In nyctinasty, leaves and/or leaflets extend horizontally (open) to face the light during the day and fold together vertically (close) at night (Figure 17.12). Nyctinastic leaf movements are exhibited by many legumes, such as Mimosa, Albizia, and Samanea, as well as members of the oxalis family. The change in leaf or leaflet angle is caused by rhythmic turgor changes in the cells of the pulvinus (plural pulvini), a specialized structure at the base of the petiole.
Once initiated, the rhythm of opening and closing per-sists even in constant darkness, both in whole plants and in isolated leaflets (Figure 17.13). The phase of the rhythm (see Chapter 24), however, can be shifted by various exoge-nous signals, including red or blue light.
Phytochrome and Light Control of Plant Development 387 FIGURE 17.12 Thigmotropic (touch-sensitive) leaf movements of Mimosa pudica.
in nyctonasty. (B) (A) (A) Leaflets open. (B) Leaflets closed. Similar leaflet movements occur diurnally (Photos © David Sieren/Visuals Unlimited.) Light also directly affects movement: Blue light stimu-lates closed leaflets to open, and red light followed by dark-ness causes open leaflets to close. The leaflets begin to close within 5 minutes after being transferred to darkness, and closure is complete in 30 minutes. Because the effect of red light can be canceled by far-red light, phytochrome regu-lates leaflet closure.
The physiological mechanism of leaf movement is well understood. It results from turgor changes in cells located on opposite sides of the pulvinus, called ventral motor cells and dorsal motor cells (Figure 17.14). These changes in turgor pressure depend on K+ and Cl– fluxes across the plasma membranes of the dorsal and ventral motor cells. Leaflets open when the ventral motor cells accu-mulate K+ and Cl–, causing them to swell, while the dorsal motor cells release K+ and Cl–, causing them to shrink. Reversal of this process results in leaflet closure. Leaflet closure is therefore an example of a rapid response to phytochrome involving ion fluxes across membranes.
Gene expression and circadian rhy-thms.
Phytochrome can also interact with circadian rhythms at the level of gene expression. The expression of genes in the LHCB family, encoding the light-harvesting chlorophyll a/b–binding pro-teins of photosystem II, is regulated at the transcriptional level by both circa-dian rhythms and phytochrome.
In leaves of pea and wheat, the level of LHCB mRNA has been found to oscillate during daily light–dark cycles, rising in the morning and falling in the evening.
Since the rhythm persists even in contin-uous darkness, it appears to be a circadian rhythm. But phytochrome can perturb this cyclical pattern of expression.
When wheat plants are transferred from a cycle of 12 hours light and 12 hours dark to continuous darkness, the rhythm persists for a while, but it slowly damps out (i.e., reduces in amplitude until no peaks or troughs are discernible). If, however, the plants are given a pulse of red light before they are transferred to continuous darkness, no damping occurs (i.e., the levels of LHCB mRNA continue to oscillate as they do during the light–dark cycles). In contrast, a far-red flash at the end of the day prevents the expression of LHCB in continuous darkness, and the effect of far red is reversed by red light. Note that it is not the oscillator that damps out under constant conditions, but the coupling of the oscillator to the physiological event being monitored. Red light restores the coupling between the oscil-lator and the physiological process.
388 Chapter 17 Up Down Light Dark Dark Dark Light Light 12 24 12 24 24 12 24 12 Time Leaf position Petiole Leaflet Leaf (A) Open (B) Closed Ventral motor cells (turgid) Dorsal motor cells (flaccid) Ventral motor cells (flaccid) Dorsal motor cells (turgid) Epidermis Vascular tissue K+ Cl– K+ Cl– FIGURE 17.13 Circadian rhythm in the diurnal movements of Albizia leaves.
The leaves are elevated in the morning and lowered in the evening. In parallel with the raising and lowering of the leaves, the leaflets open and close. The rhythm persists at a lower amplitude for a limited time in total darkness. FIGURE 17.14 Ion fluxes between the dorsal and ventral motor cells of Albizia pulvini regulate leaflet opening and closing. (After Galston 1994.) Circadian Clock Genes of Arabidopsis Have Been Identified The isolation of clock mutants has been an important tool for the identification of clock genes in other organisms. Iso-lating clock mutants in plants requires a convenient assay that allows monitoring of the circadian rhythms of many thousands of individual plants to detect the rare abnormal phenotype.
To allow screening for clock mutants in Arabidopsis, the promoter region of the LHCB gene was fused to the gene that encodes luciferase, an enzyme that emits light in the presence of its substrate, luciferin. This reporter gene con-struct was then used to transform Arabidopsis with the Ti plasmid of Agrobacterium as a vector. Investigators were then able to monitor the temporal and spatial regulation of bioluminescence in individual seedlings in real time using a video camera (Millar et al. 1995).
A total of 21 independent toc (timing of CAB [LHCB] expression) mutants have been isolated, including both short-period and long-period lines. The toc1 mutant in par-ticular has been implicated in the core oscillator mecha-nism (Strayer et al. 2001). A model for the endogenous oscillator will be discussed later in the chapter.
ECOLOGICAL FUNCTIONS: PHYTOCHROME SPECIALIZATION Phytochrome is encoded by a multigene family: PHYA through PHYE. Despite the great similarity in their structures, each of these phytochromes performs distinct roles in the life of the plant. In this section we will discuss the current state of our knowledge of the ecological functions of the different phytochromes, focusing primarily on phyA and phyB.
Phytochrome B Mediates Responses to Continuous Red or White Light Phytochrome B was first suspected to play a role in responses to continuous light because the hy3 mutant (now called phyB), which has long hypocotyls under continuous white light, was found to have an altered PHYB gene. In these mutants, PHYB mRNA was reduced in amount or was absent, and little or no phyB protein could be detected.
In contrast, the levels of PHYA mRNA and phyA protein were normal.
Phytochrome B mediates shade avoidance by regulating hypocotyl length in response to red light given in low-flu-ence pulses or continuously, and as might be expected, the phyB mutant is unable to respond to shading by increasing hypocotyl extension. In addition, these plants do not extend their hypocotyls in response to far-red light given at the end of each photoperiod (called the end-of-day far-red response). Both of these responses are likely to involve per-ception of the Pfr:Ptotal ratio and occur in the low-fluence region of the spectrum. Although phyB is centrally involved in the shade avoidance response, evidence sug-gests that other phytochromes play important roles as well (Smith and Whitelam 1997).
The phyB mutant is deficient in chlorophyll and in some mRNAs that encode chloroplast proteins, and it is impaired in its ability to respond to plant hormones. Since a muta-tion in PHYB results in impaired perception of continuous red light, the presence of the other phytochromes must not be sufficient to confer responsiveness to continuous red or white light.
Phytochrome B also appears to regulate photoreversible seed germination, the phenomenon that originally led to the discovery of phytochrome. Wild-type Arabidopsis seeds require light for germination, and the response shows red/far-red reversibility in the low-fluence range. Mutants that lack phyA respond normally to red light; mutants defi-cient in phyB are unable to respond to low-fluence red light (Shinomura et al. 1996). This experimental evidence strongly suggests that phyB mediates photoreversible seed germination.
Phytochrome A Is Required for the Response to Continuous Far-Red Light No phytochrome gene mutations other than phyB were found in the original hy collection, so the identification of phyA mutants required the development of more ingenious screens. As discussed previously, because the far-red HIRs were known to require light-labile (Type I) phytochrome, it was suspected that phyA must be the photoreceptor involved in the perception of continuous far-red light. If this is true, then the phyA mutants should fail to respond to continuous far-red light and grow tall and spindly under these light conditions. However, mutants lacking chro-mophore would also look like this because phyA can detect far-red light only when assembled with the chromophore into holophytochrome.
To select for just the phyA mutants, the seedlings that grew tall in continuous far-red light were then grown under continuous red light. The phyA-deficient mutants can grow normally under this regimen, but a chro-mophore-deficient mutant, which also lacks functional phyB, does not respond. The phyA mutant seedlings selected in this screen had no obvious phenotype when grown in normal white light, confirming that phyA has no discernible role in sensing white light. This also explains why phyA mutants were not detected in the original long-hypocotyl screen. Thus, phyA appears to have a limited role in photomorphogenesis, restricted primarily to de-etiolation and far-red responses. For exam-ple, phyA would be important when seeds germinate under a canopy, which filters out much of the red light.
It is also clear from this constant far-red light phenotype that none of the other phytochromes is sufficient for the perception of constant far-red light, and despite the ability of all phytochromes to absorb red and far-red light, at least phyA and phyB have distinct roles in this regard.
Phytochrome and Light Control of Plant Development 389 Phytochrome A also appears to be involved in the ger-mination VLFR of Arabidopsis seeds. Thus, mutants lacking phyA cannot germinate in response to red light in the very-low-fluence range, but they show a normal response to red light in the low-fluence range (Shinomura et al. 1996). This result demonstrates that phyA functions as the primary photoreceptor for this VLFR, although recent evidence sug-gests that phyE is required for this component of seed ger-mination (Hennig et al. 2002).
Table 17.4 summarizes the different roles of phyA, phyB, and other photoreceptors in the various phytochrome-mediated responses.
Developmental Roles for Phytochromes C, D, and E Are Also Emerging Some of the roles of other phytochromes in plant growth and development have recently begun to be elucidated through experiments on mutant plants. Because these phy-tochromes have functions that overlap with those of phyA and phyB, it was necessary to screen for mutants in phyAB null mutant backgrounds to uncover mutations. For exam-ple, both phyD and phyE help mediate the shade avoid-ance response—a response mediated primarily by phyB. The creation of double and triple mutants has made it possible to assess the relative role of each phytochrome in a given response. Thus it was found that, like phyB, phyD plays a role in regulating leaf petiole elongation, as well as in flowering time (see Chapter 24). Similar analyses sup-port the idea that phyE acts redundantly with phyB and phyD in these processes, but also acts redundantly with phyA and phyB in inhibition of internode elongation.
Of the Arabidopsis phytochromes, phyC is the least well characterized. However, although phyAphyBphyDphyE quadruple mutants appear to have normal responses to the red:far red ratio, there are differences in phytochrome-reg-ulated gene expression.
In summary, phyC, phyD, and phyE appear to play roles that are for the most part redundant with those of phyA and phyB. Whereas phyB appears to be involved in regulating all stages of development, the functions of the other phytochromes are restricted to specific developmen-tal steps or responses.
Phytochrome Interactions Are Important Early in Germination Figure 17.15A shows the action of constant red and far-red light absorbed separately by the phyA and phyB systems.
Continuous red light absorbed by phyB stimulates de-eti-390 Chapter 17 TABLE 17.4 Comparison of the very-low-fluence (VLFR), low-fluence (LFR), and high-irradiance responses (HIR) Type of Response Photoreversibility Reciprocity Peaks of action spectraa Photoreceptor VLFR No Yes Red, Blue phyA, phyEa LFR Yes Yes Red, far red phyB, phyD, phyE HIR No No Dark-grown: far red, blue, UV-A Dark-grown: phyA, cryptochrome Light-grown: red Light-grown: phyB a phyE is required for seed germination but not for other VLFR responses mediated by phyA Continuous red light Continuous far-red light PrB PfrB PrA Photo-equilibrium PfrA Red Far red Inhibits de-etiolation Inhibits de-etiolation Stimulates de-etiolation Stimulates de-etiolation Stimulates de-etiolation Stimulates de-etiolation Far red Red (A) (B) Far red Red Far red Red Continuous illumination phyB phyA phyB FIGURE 17.15 Mutually antagonistic roles of phyA and phyB. (After Quail et al. 1995.) olation by maintaining high levels of PfrB. Continuous far-red light absorbed by PfrB prevents this stimulation by reducing the amount of PfrB. The stimulation of de-etiola-tion by phyA depends on the photostationary state of phy-tochrome (indicated in Figure 17.15A by the circular arrows). Continuous far-red light stimulates de-etiolation when absorbed by the phyA system; continuous red light inhibits the response.
The effects of phyA and phyB on seedling development in sunlight versus canopy shade (enriched in far-red light) are shown in Figure 17.15B. In open sunlight, which is enriched in red light compared with canopy shade, de-eti-olation is mediated primarily by the phyB system (on the left in the figure). A seedling emerging under canopy shade, enriched in far-red light, initiates de-etiolation pri-marily through the phyA system (center). Because phyA is labile, however, the response is taken over by phyB (right).
In switching over to phyB, the stem is released from growth inhibition (see Figure 17.15A), allowing for the accelerated rate of stem elongation that is part of the shade avoidance response (see Web Topic 17.4).
For a discussion of how plants sense their neighbors using reflected light, see Web Essay 17.2.
PHYTOCHROME FUNCTIONAL DOMAINS Prior to the identification of the multiple forms of phy-tochrome, it was difficult to understand how a single pho-toreceptor could regulate such diverse processes in the cell. However, the discovery that phytochrome is encoded by members of a multigene family, each with its own pat-tern of expression, provided a more plausible alternative explanation: Each phytochrome-mediated response is reg-ulated by a specific phytochrome, or by interactions between specific phytochromes. As discussed earlier, this hypothesis was supported by the phenotypes of mutants deficient in either phyA or phyB.
As a corollary to this hypothesis, it was further postulated that specific regions of the PHY proteins must be specialized to allow them to perform their distinct functions. Molecular biology provides the tools to answer such difficult questions.
In this section we will describe what is known about the functional domains of the phytochrome holoprotein.
Just as mutations reducing the amount of a particular phytochrome have yielded information about its role, plants genetically engineered to overexpress a specific phy-tochrome are also useful. First, they allow an extension of the range of phytochrome levels testable in relation to func-tion. Second, as we will see, a particular phytochrome sequence can be changed and reintroduced into a normal plant to test its phenotypic effects.
Usually plants overexpressing an introduced PHYA or PHYB gene have a dramatically altered phenotype. Such transgenic plants are often dwarfed, are dark green because of elevated chlorophyll levels, and show reduced apical dominance. This phenotype requires elevated levels of an intact, photoactive holoprotein because overexpression of a mutated form of phytochrome that is unable to combine with its chromophore has a normal phenotype. Similarly, plants expressing only the N-terminal domain of each phy-tochrome have a normal phenotype, even though elevated levels of the photoactive fragment accumulate.
Although protein overexpression greatly perturbs the normal metabolism of a cell and is therefore subject to cer-tain artifacts, such studies of structure and function have helped build a picture of phytochrome as a molecule hav-ing two domains linked by a hinge: an N-terminal light-sensing domain in which the light specificity and stability reside, and a C-terminal domain that contains the signal-transmitting sequences (Figure 17.16).
Phytochrome and Light Control of Plant Development 391 PEST (photodegradation) Dimerization site Phytochrome A/B specificity Signal transmission COOH H2N Chromophore Regulatory region Ubiquitination site 74 kDa N-terminal domain 55 kDa C-terminal domain FIGURE 17.16 Schematic diagram of the phytochrome holoprotein, showing the various functional domains. The chromophore-binding site and PEST sequence are located in the N-terminal domain, which confers photosensory specificity to the molecule—that is, whether it responds to continuous red or far-red light. The C-ter-minal domain contains a dimerization site, a ubiquitination site, and a regulatory region. The C-terminal domain transmits signals to proteins that act downstream of phytochrome.
The C-terminal domain also contains the site for the for-mation of phytochrome dimers and the site for the addition of ubiquitin, a tag for degradation. (For a more detailed description of experiments that helped map the functional domains of phytochrome, see Web Topic 17.5.) CELLULAR AND MOLECULAR MECHANISMS All phytochrome-regulated changes in plants begin with absorption of light by the pigment. After light absorption, the molecular properties of phytochrome are altered, probably causing the signal-transmitting sequences in the C terminus to interact with one or more components of a signal trans-duction pathway that ultimately bring about changes in the growth, development, or position of an organ (see Table 17.1). Some of the signal-transmitting motifs appear to inter-act with multiple signal transduction pathways; others appear to be unique to a specific pathway. Furthermore, it is reasonable to assume that the different phytochrome pro-teins utilize different sets of signal transduction pathways.
Molecular and biochemical techniques are helping to unravel the early steps in phytochrome action and the sig-nal transduction pathways that lead to physiological or developmental responses. These responses fall into two general categories: 1. Relatively rapid turgor responses involving ion fluxes 2. Slower, long-term processes associated with photomor-phogenesis, involving alterations in gene expression In this section we will examine the effects of phy-tochrome on both membrane permeability and gene expression, as well as the possible chain of events consti-tuting the signal transduction pathways that bring about these effects.
Phytochrome Regulates Membrane Potentials and Ion Fluxes Phytochrome can rapidly alter the properties of mem-branes. We have already seen that low-fluence red light is required before the dark period to induce rapid leaflet clo-sure during nyctinasty, and that fluxes of K+ and Cl– into and out of dorsal and ventral motor cells mediate the response. However, the rapidity of leaf closure in the dark (lag time about 5 minutes) would seem to rule out mech-anisms based on gene expression. Instead, rapid phy-tochrome-induced changes in membrane permeability and transport appear to be involved.
During phytochrome-mediated leaflet closure, the apoplastic pH of the dorsal motor cells (the cells that swell during leaflet closure) decreases, while the apoplastic pH of the ventral motor cells (the cells that shrink during leaflet closure) increases. Thus the plasma membrane H+ pump of the dorsal cells appears to be activated by darkness (pro-vided that phytochrome is in the Pfr form), and the H+ pump of the ventral cells appears to be deactivated under the same conditions (see Figure 17.14). The reverse pattern of apoplastic pH change is observed during leaflet opening.
Studies have also been carried out on phytochrome reg-ulation of K+ channels in isolated protoplasts (cells without their cell walls) of both dorsal and ventral motor cells from Samanea leaves (Kim et al. 1993). When the extracellular K+ concentration was raised, K+ entered the protoplasts and depolarized the membrane potential only if the K+ chan-nels were open. When the dorsal and ventral motor cell protoplasts were transferred to constant darkness, the state of the K+ channels exhibited a circadian rhythmicity dur-ing a 21-hour incubation period, and the two cell types var-ied reciprocally, just as they do in vivo. That is, when the dorsal cell K+ channels were open, the ventral cell K+ chan-nels were closed, and vice versa. Thus the circadian rhythm of leaf movements has its origins in the circadian rhythm of K+ channel opening.
On the basis of the evidence thus far, we can conclude that phytochrome brings about leaflet closure by regulating the activities of the primary proton pumps and the K+ chan-nels of the dorsal and ventral motor cells. Although the effect is rapid, it is not instantaneous, and it is therefore unlikely to be due to a direct effect of phytochrome on the membrane.
Instead, phytochrome acts indirectly via one or more signal transduction pathways, as in the case of the regulation of gene expression by phytochrome (see the next section).
However, some effects of red and far-red light on the membrane potential are so rapid that phytochrome may also interact directly with the membrane. Such rapid mod-ulation has been measured in individual cells and has been inferred from the effects of red and far-red light on the sur-face potential of roots and oat (Avena) coleoptiles, where the lag between the production of Pfr and the onset of mea-surable potential changes is 4.5 s for hyperpolarization.
Changes in the bioelectric potential of cells imply changes in the flux of ions across the plasma membrane (see Web Topic 17.6). Membrane isolation studies provide evidence that a small portion of the total phytochrome is tightly bound to various organellar membranes.
These findings led some workers to suggest that mem-brane-bound phytochrome represents the physiologically active fraction, and that all the effects of phytochrome on gene expression are initiated by changes in membrane per-meability. On the basis of sequence analysis, however, it is now clear that phytochrome is a hydrophilic protein with-out membrane-spanning domains. The current view is that it may be associated with microtubules located directly beneath the plasma membrane, at least in the case of the alga, Mougeotia, as described in Web Topic 17.2.
If phytochrome exerts its effects on membranes from some distance, no matter how small, involvement of a sec-ond messenger is implied, and calcium is a good candidate.
Rapid changes in cytosolic free calcium have been impli-cated as second messengers in several signal transduction 392 Chapter 17 pathways, and there is evidence that calcium plays a role in chloroplast movement in Mougeotia.
Phytochrome Regulates Gene Expression As the term photomorphogenesis implies, plant development is profoundly influenced by light. Etiolation symptoms include spindly stems, small leaves (in dicots), and the absence of chlorophyll. Complete reversal of these symp-toms by light involves major long-term alterations in metabolism that can be brought about only by changes in gene expression.
The stimulation and repression of transcription by light can be very rapid, with lag times as short as 5 minutes.
Such early-gene expression is likely to be regulated by the direct activation of transcription factors by one or more phytochrome-initiated signal transduction pathways. The activated transcription factors then enter the nucleus, where they stimulate the transcription of specific genes. Some of these early gene products are transcription fac-tors themselves, which activate the expression of other genes. Expression of the early genes, also called primary response genes, is independent of protein synthesis; expression of the late genes, or secondary response genes, requires the synthesis of new proteins.
The photoregulation of gene expression has focused on the nuclear genes that encode messages for chloroplast pro-teins: the small subunit of ribulose-1,6-bisphosphate car-boxylase/oxygenase (rubisco) and the major light-harvest-ing chlorophyll a/b–binding proteins associated with the light-harvesting complex of photosystem II (LHCIIb pro-teins). These proteins play important roles in chloroplast development and greening; hence their regulation by phy-tochrome has been studied in detail. The genes for both of these proteins—RBCS and LHCB (also called CAB in some studies)—are present in multiple copies in the genome.
We can demonstrate phytochrome regulation of mRNA abundance (e.g., RBCS mRNAs) experimentally by giving etiolated plants a brief pulse of low-fluence red or far-red light, returning them to darkness to allow the signal trans-duction pathway to operate, and then measuring the abun-dance of specific mRNAs in total RNA prepared from each set of plants. If its abundance is regulated by phytochrome, the mRNA is absent or present at low levels in etiolated plants but is increased by red light. The red light–induced increase in expression can be reversed by immediate treat-ment with far-red light, but far-red light alone has little effect on mRNA abundance. The expression of some other genes is down-regulated under these conditions.
Recently red-light stimulation of lettuce seed germina-tion has been correlated with an increase in the biologi-cally active form of the hormone gibberellin. Red light causes a large increase in the expression of the gene cod-ing for a key enzyme in the gibberellin biosynthetic path-way (Toyomasu et al. 1998). The effect of red light is reversed by a treatment with far-red light, indicative of phytochrome. Since gibberellin can substitute for red light in promoting lettuce seed germination, it appears that phytochrome promotes seed germination by increasing the biosynthesis of the hormone. Gibberellins are dis-cussed in detail in Chapter 20.
For an expanded discussion see Web Topic 17.7.
Both Phytochrome and the Circadian Rhythm Regulate LHCB A MYB-related transcription factor whose mRNA level increases rapidly when Arabidopsis is transferred from the dark to the light is involved in phytochrome-mediated expression of LHCB genes (Figure 17.17). (For information on MYB, see Chapter 14 on the web site.) This transcription factor appears to bind to the promoter of certain LHCB genes and regulate their transcription, which, as Figure 17.17 shows, occurs later than the increase in the MYB-related protein (Wang et al. 1997). The gene that encodes the MYB-related protein is therefore probably a primary response gene, and the LHCB gene itself is prob-ably a secondary response gene. Recent work has indicated that this MYB-related pro-tein, now known as circadian clock associated 1 (CCA1), also plays a role in the circadian regulation of LHCB gene expression. A second but distinct MYB-related protein, late elongated hypocotyl (LHY), has also been identified as a potential clock gene. Expression of CCA1 and LHY oscil-lates with a circadian rhythm. Constitutive expression of CCA1 abolishes several circadian rhythms and suppresses both CCA1 and LHY expression. When the CCA1 gene is mutated so that no functional protein is produced, circa-dian and phytochrome regulation of four genes, including LHCB, is affected. These observations suggest that CCA1 and LHY are associated with the circadian clock.
Phytochrome and Light Control of Plant Development 393 0.02 0.01 2 1 0 2 4 6 8 10 12 Time in light (hours) MYB-related protein mRNA LHCB mRNA MYB LHCB FIGURE 17.17 Time course for inducing transcription.
Kinetics of the induction of transcripts for a MYB-related transcription factor (MYB) and the light-harvesting chloro-phyll a/b–binding protein (LHCB) in Arabidopsis after trans-fer of the seedlings from darkness to continuous white light. (After Wang et al. 1997.) A protein kinase (CK2) can interact with and phospho-rylate CCA1. The CK2 kinase is a multisubunit protein with serine/threonine kinase activity. The regulatory sub-unit of CK2 (CKB3) has been shown to interact with, and phosphorylate, CCA1 in vitro. Mutations in CKB3 have also been found to perturb CK2 activity and, in turn, change the period of rhythmic expression of CCA1. These mutations affect many clock outputs, from gene expression to flowering time, suggesting that CK2 is involved in the regulation of the circadian clock via its interactions with CCA1 (Sugano et al. 1999).
The Circadian Oscillator Involves a Transcriptional Negative Feedback Loop The circadian oscillators of cyanobacteria (Synechococcus), fungi (Neurospora crassa), insects (Drosophila melanogaster), and mouse (Mus musculus) have now been elucidated. In these four organisms, the oscillator is composed of several “clock genes” involved in a transcriptional–translational negative feedback loop.
So far, three major clock genes have been identified in Arabidopsis: TOC1, LHY, and CCA1. The protein products of these genes are all regulatory proteins. TOC1 is not related to the clock genes of other organisms, suggesting that the plant oscillator is unique.
According to a recent model (Alabadi et al. 2001), light and the TOC1 regulatory protein activate LHY and CCA1 expression at dawn (Figure 17.18). The increase in LHY and CCA1 represses the expression of the TOC1 gene. Because TOC1 is a positive regulator of the LHY and CCA1 genes, the repression of TOC1 expression causes a progressive reduction in the levels of LHY and CCA1, which reach their minimum levels at the end of the day. As LHY and CCA1 levels decline, TOC1 gene expression is released from inhibition. TOC1 reaches its maximum at the end of the day, when LHY and CCA1 are at their minimum. TOC1 then either directly or indirectly stimulates the expression of LHY and CCA1, and the cycle begins again.
The two MYB regulator proteins—LHY and CCA1— have dual functions. In addition to serving as components of the oscillator, they regulate the expression of other genes, such as LHCB and other “morning genes,” and they repress genes expressed at night. Light acts to reinforce the effect of the TOC1 gene in promoting LHY and CCA1 expression.
This reinforcement represents the underlying mechanism of entrainment. Other proteins, such as the CK2 kinase, affect the activity of CCA1, and thus regulate the clock.
Phytochrome and the blue-light photoreceptor CRY2 (see Chapter 18) mediate the effects of red and blue light, respectively.
Regulatory Sequences Control Light-Regulated Transcription The cis-acting regulatory sequences required to confer light regulation of gene expression have been studied extensively. Most eukaryotic promoters for genes that encode proteins comprise two functionally distinct regions: a short sequence that determines the transcription start site (the TATA box, named for its most abundant nucleotides) and upstream sequences, called cis-acting regulatory elements, that regulate the amount and pattern of transcription (see Chapter 14 on the web site). These regulatory sequences bind specific proteins, called trans-acting factors, that modulate the activity of the general 394 Chapter 17 LHY CCA1 LHY CCA1 TOC1 and other evening genes TOC1 LHCB and other morning genes Light Night Day 1. Light activates LHY and CCA1 expression at dawn.
5. TOC1 augments the expression of LHY and CCA1, which reach maximum levels at dawn, starting the cycle again.
2. LHY and CCA1 activate the expression of LHCB and other morning genes.
3. CCA1 and LHY repress TOC1 and other evening genes.
4. Progressive reduction of LHY and CCA1 expression levels during the day allows TOC1 transcript levels to rise and reach maximum levels toward the end of the day.
FIGURE 17.18 Circadian oscillator model showing the hypothetical interactions between the TOC1 and MYB genes LHY and CCA1. Light acts at dawn to increase LHY and CCA1 expression. LHY and CCA1 act to regulate other daytime and evening genes.
transcription factors that assemble around the transcrip-tion start site with RNA polymerase II.
Overall, the picture emerging for light-regulated plant promoters is similar to that for other eukaryotic genes: a collection of modular elements, the number, position, flanking sequences, and binding activities of which can lead to a wide range of transcriptional patterns. No single DNA sequence or binding protein is common to all phy-tochrome-regulated genes. At first it may appear paradoxical that light-regulated genes have such a range of elements, any combination of which can confer light-regulated expression. However, this array of sequences allows for the differential light- and tis-sue-specific regulation of many genes through the action of multiple photoreceptors. (For an expanded discussion, see Web Topic 17.8.) Regulatory factors. As might be expected, the diverse range of phytochrome regulatory sequences can bind a wide variety of transcription factors. At least 50 of these regulatory factors have been identified recently by the use of genetic and molecular screens (Tepperman et al. 2001). Although some of the early-acting signaling pathways are specific to phyA or phyB, it is clear that late-acting sig-naling pathways common to multiple photoreceptors must be used because different light qualities can trigger the same response (Chory and Wu 2001). For example, SPA1 is a phyA-specific signaling inter-mediate that acts as a light-dependent repressor of photo-morphogenesis in Arabidopsis seedlings (Hoecker and Quail 2001). The SPA1 protein has a coiled-coil protein domain that enables it to interact with another factor, COP1 (con-stitutive photomorphogenesis 1), that acts downstream of both phyA and phyB. The COP1 protein was identified in the screen for constitutive photomorphogenesis mutants that has yielded several other factors that act downstream of photoreceptors (see Web Topic 17.9). COP1 is an E3 ubiquitin ligase that targets other proteins for destruction by the 26S proteasome (see Chapter 14 on the web site).
The functions of many of these factors are probably modulated through the action of HY5, a protein first iden-tified through the long-hypocotyl screen, discussed earlier in the chapter. HY5 is a basic leucine zipper–type tran-scription factor that is always located in the nucleus (see Chapter 14 on the web site). HY5 binds to the G-box motif of multiple light-inducible promoters and is necessary for optimal expression of the corresponding genes. In the dark, HY5 is ubiquitinated by COP1 and degraded by the 26S proteasome complex.
Phytochrome Moves to the Nucleus It has long been a mystery as to how phytochrome could act in the nucleus when it is apparently localized in the cytosol. Recent exciting work has finally opened up the black box between phytochrome and gene expression. The most surprising finding is that in some cases phytochrome itself moves to the nucleus in a light-dependent manner. Detection of this movement relied on the ability to fuse phytochrome to a visible marker, green fluorescent pro-tein (GFP), that can be activated by light of an appropriate wavelength being shone on plant cells. A big advantage of GFP fusions is that they can be visualized in living cells, making it possible to follow dynamic processes within the cell under the microscope. Both phyA–GFP and phyB–GFP show light-activated import into the nucleus (Figure 17.19) (Sakamoto and Nagatani 1996; Sharma 2001). The phyB fusion moves to the nucleus in the Pfr form only, and transport is slow, taking several hours for full mobilization. In contrast, phyA–GFP can move in the Pfr or the Pr form, provided that it has cycled through Pfr first. Movement of phyA–GFP is much more rapid than that of phyB–GFP , taking only about 15 minutes. Phytochrome and Light Control of Plant Development 395 FIGURE 17.19 Nuclear localization of phy–GFP fusion proteins in epi-dermal cells of Arabidopsis hypocotyls. Transgenic Arabidopsis expressing phyA–GFP (left) or phyB–GFP (right) was observed under a fluorescence microscope.
Only nuclei are visible. The plants were placed either under continu-ous far-red light (left) or white light (right) to induce the nuclear accumulation. The smaller bright green dots inside the nucleus are called “speckles.” The significance of speckles is unknown. (From Yamaguchi et al. 1999, courtesy of A. Nagatani).
(A) (B) 10 µm Most satisfying is the observation that phyB–GFP trans-port is promoted by red light and inhibited by far-red light, while transport of phyA–GFP is maximal under continu-ous far-red light. Furthermore, nuclear translocation of phyB is under circadian control, as would be expected, since phyB regulates the expression of clock-regulated genes. These light conditions are the ones known to be responsible for activation of phyA and phyB and would be consistent with their activity in the nucleus.
What happens when Pfr moves to the nucleus? Two nuclear proteins that interact with phytochrome have been identified to date, although there are probably additional targets. The first, phytochrome interacting factor 3 (PIF3), reacts with the C-terminal end of phyA or phyB. However, it reacts preferentially with the full-length phyB protein in a light-dependent manner, and it is thought to be a func-tional primary reaction partner for this phytochrome.
Although its precise function is not yet known, PIF3 resembles transcription factors that bind to a particular ele-ment in plant promoters, the G-box motif, that confers light regulation to genes. It is also known that phyB in the Pfr form can form a complex with PIF3 bound to its target DNA. A picture is therefore emerging in which some phy-tochrome-regulated genes are activated directly by move-ment of phyB to the nucleus in the Pfr form. Once in the nucleus, phyB interacts with transcription factors such as PIF3. A model for the direct activation of gene expression by phyB in the nucleus is shown in Figure 17.20.
Phytochome Acts through Multiple Signal Transduction Pathways Using biochemical approaches, researchers have shown that signaling involves several different mechanisms, including G-proteins, Ca2+, and phosphorylation. We will consider the evidence for each of these in turn.
G-proteins and calcium.
Well-characterized signaling pathways in other systems (e.g., mating in yeasts) often include G-proteins (which are reviewed in Chapter 14 on the web site). These protein complexes are normally mem-brane associated, have three different subunits, and bind GTP or GDP on one subunit. The hydrolysis of GTP to GDP is required for regulation of G-protein function.
Sequences that encode G-protein subunits have been cloned from plants, indicating that this type of system is present. One way that the function of G-proteins can be tested is to treat cells with chemicals that activate or inhibit the ability of the complex to bind or break down GTP.
396 Chapter 17 PrB PfrB PfrB PIC PIC PfrB Red light Far-red light DNA PIF 3 PIF 3 G-BOX TATA MYB PIF 3 PIF 3 G-BOX TATA MYB TATA LHCB MYB MYB Nucleus Cytoplasm 1. PhyB is synthesized in the cytoplasm in the inactive PrB form.
2. When converted to the active PfrB form by red light, it moves into the nucleus.
3. PfrB binds to a dimer of the transcription factor, PIF3, which is bound to the G-BOX elements of MYB gene promoter.
4. Upon addition of the pre-initiation complex (PIC), the transcription of MYB genes, including CCA1 and LHY, is activated.
5. MYB transcription factors in turn activate the transcription of other genes, such as LHCB.
FIGURE 17.20 Direct regulation of gene expression by phyB transport to the nucleus. (After Quail 2000.) Microinjection experiments (see Web Topic 17.10) indi-cate that phytochrome signaling can occur in single cells and does not require light after activation of phytochrome.
At least one G-protein may function downstream of phy-tochrome. After the G-protein step, there are at least two branching pathways. One of these pathways—gene expression and chloroplast development—requires Ca2+ and calmodulin; the other—anthocyanin synthesis—is Ca2+ independent.
The branching pathways can be distinguished further by the cis-acting regulatory elements targeted and the sig-naling intermediate employed. For many years, it has been known that both cyclic AMP (cAMP) and cyclic GMP (cGMP) are important intermediates in hormone- and light-Phytochrome and Light Control of Plant Development 397 ATP P P P P Chromophore Phytochrome Red light Chromophore Chromophore Red light Ser Kinase domain H2N H2N COOH Chromophore Ser Kinase domain X X COOH (A) Bacterial phytochrome (B) Plant phytochrome 1. Phytochrome is autophosphorylated on serine.
ATP Input Transmitter His 2. Phytochrome may phosphorylate other proteins.
Sensor protein Response regulator protein Input Transmitter Receiver His Asp Output Receiver Asp Output Output signal 1. After receiving a signal from the input domain, the transmitter domain of the sensor protein autophosphorylates a histidine. 2. The phosphorylated sensor protein phosphorylates the response regulator protein at an aspartate.
3. The phosphorylated response regulator stimulates the response.
FIGURE 17.21 Phytochrome is an autophospho-rylating protein kinase. (A) Bacterial phy-tochrome is an example of a two-component signaling system, in which phytochrome func-tions as a sensor protein that phosphorylates a response regulator (see Chapter 14 on the web site). (B) Plant phytochrome is an autophospho-rylating serine/threonine kinase that may phos-phorylate other proteins (X).
induced signaling pathways in animals (see Chapter 14 on the web site). Although the presence of cAMP has been dif-ficult to demonstrate in plants, the presence of cGMP in plant tissues is well established. Indeed, recent studies have shown that cGMP may serve as a second messenger in phytochrome action.
However, the role of the G-protein cascade in plants is still controversial. Some key genes (e.g., guanylylate cyclase) have not yet been identified in plant genomes, and cGMP levels are vanishingly small in plants. On the other hand, studies with inhibitors have implicated cGMP as a second messenger for the hormones gibberellin (see Chapter 20) and abscisic acid (see Chapter 23). Thus a role for cGMP in phytochrome signaling, although controver-sial, remains a possibility.
Phosphorylation.
The evidence for a potential role of phosphorylation in phytochrome action first came from red-light regulation of protein phosphorylation and phos-phorylation-dependent binding of transcription factors to the promoters of phytochrome-regulated genes. Some highly purified preparations of phytochrome were also reported to have kinase activity. Kinases are enzymes that have the capacity to transfer phosphate groups from ATP to amino acids such as serine or tyrosine, either on themselves or on other proteins.
Kinases are often found in signal transduction pathways in which the addition or removal of phosphate groups reg-ulates enzyme activity.
Phytochrome is now known to be a protein kinase. The evolutionary origin of phytochrome is very ancient, pre-dating the appearance of eukaryotes. Bacterial phy-tochromes are light-dependent histidine kinases that func-tion as sensor proteins that phosphorylate corresponding response regulator proteins (Figure 17.21A). (See also Chapter 14 on the web site and Web Topic 17.11) However, although higher-plant phytochromes have some homology with the kinase domains, they do not function as histidine kinases. Instead, they are serine/thre-onine kinases. In addition, recombinant versions of higher-plant and algal phytochromes have been shown to be light- and chromophore-modulated kinases that can phos-phorylate themselves, as well as other proteins (Figure 17.21B) (Sharma 2001).
At least one potential target is a cytosolic protein termed phytochrome kinase substrate 1, or PKS1, that can accept a phosphate from phyA. Phosphorylation occurs on serines, and to a lesser extent on threonines.
The PKS1 phosphorylation is regulated by phytochrome both in the test tube and in the plant, with Pfr having a twofold higher level of activity than Pr. Overexpression of PKS1 in transgenic plants suggests that it may function to negatively regulate phyB-mediated events (Fankhauser et al. 1999).
Another protein kinase associated with phytochrome is nucleoside diphosphate kinase 2 (NDPK2). Phytochrome A has been found to interact with this protein, and its kinase activity is increased about twofold when phyA is bound in the Pfr form. Because the NDPK2 protein is found in both the nucleus and the cytosol, the location of its primary site of action is unclear.
A summary of the possible signaling and regulatory pathways of phytochrome is shown in Figure 17.22.
Phytochrome Action Can Be Modulated by the Action of Other Photoreceptors The recent isolation of the genes encoding the cryp-tochrome and phototropin photoreceptors (see Chapter 18) mediating blue light–regulated responses has made it pos-sible to analyze whether these photoreceptors have over-lapping functions (Chory and Wu 2001). This possibility was suspected because mutations in the cryptochrome CRY2 gene led to delayed flowering under continuous white light, and flowering time was also known to be under phytochrome control. In Arabidopsis, continuous blue or far-red light treatment leads to promotion of flowering, and red light inhibits flowering. Far-red light acts through phyA, and the antag-onistic effect of red light is through the action of phyB. One might expect the cry2 mutant to be delayed in flowering, since blue light promotes flowering. However, cry2 mutants flower at the same time as the wild type under either continuous blue or continuous red light. Delay is observed only if both blue and red light are given together.
Therefore, cry2 probably functions to promote flowering in blue light by repressing phyB function. Additional experiments have confirmed that the other cryptochrome, cry1, also interacts with phytochromes. Both cry1 and cry2 interact with phyA in vitro and can be phos-phorylated in a phyA-dependent manner. Phosphorylation of cry1 has also been demonstrated to occur in vivo in a red light–dependent manner. Indeed, the importance of cryp-tochromes as developmental regulators has been under-scored by their subsequent discovery in animal systems, such as mouse and human.
SUMMARY The term photomorphogenesis refers to the dramatic effects of light on plant development and cellular metabolism.
Red light exerts the strongest influence, and the effects of red light are often reversible by far-red light. Phytochrome is the pigment involved in most photo-morphogenic phenomena. Phytochrome exists in two forms: a red light–absorbing form (Pr) and a far-red light–absorbing form (Pfr). Phytochrome is synthesized in the dark in the Pr form. Absorption of red light by Pr con-verts it to Pfr, and absorption of far-red light by Pfr con-398 Chapter 17 Phytochrome and Light Control of Plant Development 399 ATP PfrB PrB Red light Far red light PrA PSK1 Dark Dark Dark Light Light Light Light Light Light PSK1 COP1 SPA1 COP1 PfrA Red light Far red light PIF 3 NUCLEUS CYTOPLASM PfrA P PfrA HY5 P P P G-protein PfrB NDPK2 NDPK2 P PfrB ATP cGMP Ca2+ CAM Y X HY5 degradation COP/DET/FUS proteasome Light-regulated gene expression 1 2 2 1 1 Red light converts PrA and PrB to their Pfr forms.
2 The Pfr forms of phyA and phyB phytochrome can autophosphorylate. 3 Activated PfrA phosphorylates phytochrome kinase substrate 1 (PKS1).
4 Activated PfrA and PfrB may interact with G-proteins.
5 cGMP, calmodulin (CAM), and calcium (Ca2+) may activate transcription factors (X and Y).
6 Activated PfrA and PfrB enter the nucleus.
7 PfrA and PfrB may regulate transcription directly or through interaction with phytochrome interacting factor 3 (PIF3).
8 Nucleoside diphosphate kinase 2 (NDPK2) is activated by PfrB.
9 In the dark, COP1 enters the nucleus and suppresses light-regulated genes.
10 In the dark, COP1, an E3 ligase, ubiquitinates HY5.
11 In the dark, HY5 is degraded with the assistance of the COP/DET/FUS proteasome complex. 12 In the light, COP1 interacts directly with SPA1 and is exported to the cytoplasm.
3 4 4 5 6 12 10 11 8 7 6 9 12 7 FIGURE 17.22 Summary diagram of the known factors involved in phytochrome-regulated gene expression. It is likely that additional shared and phytochrome-spe-cific pathways will be uncovered as more signaling intermediates are identified.
(After Sharma 2001.) verts it to Pr. However, the absorption spectra of the two forms overlap in the red region of the spectrum, leading to an equilibrium between the two forms called a photosta-tionary state. Pfr is considered to be the active form that gives rise to the physiological response; however, Pr, particularly cycled Pr, plays a role in phyA-mediated responses. Other factors in addition to light regulate the steady-state level of Pfr, including the expression level of the protein and its stabil-ity in the Pfr form.
Phytochrome is a large dimeric protein made up of two equivalent subunits. The monomer has a molecular mass of about 125 kDa and is covalently bound to a chro-mophore molecule, an open-chain tetrapyrrole called phy-tochromobilin.
Phytochrome is encoded by a family of divergent genes that give rise to two types of proteins: Type I and Type II.
Type I, which is encoded by the PHYA gene, is abundant in etiolated tissue. However, Type I phytochrome is present at low levels in light-grown plants because of its instability in the Pfr form, the phyA-mediated suppression of tran-scription of its own gene, and the instability of its mRNA.
Type II phytochrome (encoded by the PHYB, PHYC, PHYD, and PHYE genes) is present at low levels in both light-grown and dark-grown plants because its genes are constitutively expressed at low levels and the protein is sta-ble in the Pfr form. Spectrophotometric and immunological studies indicate that the phytochromes are concentrated in meristematic regions. PhyA and phyB move to the nucleus upon con-version to the Pfr forms.
Phytochrome responses have been classified into very-low-fluence, low-fluence, and high-irradiance responses (VLFRs, LFRs, and HIRs). These three types of responses differ not only in their fluence requirements but also in other parameters, such as their escape times, action spec-tra, and photoreversibility. Phytochrome B plays an impor-tant role in the detection of shade in plants adapted to high levels of sunlight; phytochrome A has a more limited role, mediating the far-red HIR during early greening. Phy-tochromes C, D, and E also have specific roles during lim-ited phases of development, and these roles are partially redundant with those of phyA and phyB.
Phytochrome is known to regulate the transcription of numerous genes. Many of the genes involved in greening, such as the nuclear-encoded genes for the small subunit of rubisco and the chlorophyll a/b–binding protein of the light-harvesting complex, are transcriptionally regulated by phytochrome (both phyA and phyB). Phytochrome also represses the transcription of various genes, including PHYA. Activation or repression of these genes is thought to be mediated by general transcription factors that bind to cis-acting regulatory elements within the promoter regions of these genes in a combinatorial fashion. In some cases, phytochrome in the Pfr form inter-acts directly with these factors. These transcription factors, in turn, are linked to phytochrome action by a complex series of signal transduction pathways involving COP and DET proteins, kinases, cyclic GMP, trimeric G-proteins, Ca2+, and calmodulin.
The discovery and characterization of bacterial phy-tochrome suggest that flowering-plant phytochrome evolved from a bacterial histidine kinase that participates in two-component signaling pathways.
In addition to the long-term effects involving changes in gene expression, phytochrome induces a variety of rapid responses, including chloroplast rotation in the alga Mougeotia, leaf closure during nyctinasty, and alterations in membrane potential. These responses involve rapid changes in membrane properties. The current view is that even these rapid effects of phytochrome involve signal transduction pathways.
Web Material Web Topics 17.1 The Structure of Phytochromes The purification and characterization of phy-tochrome as a homodimer are described.
17.2 Mougeotia: A Chloroplast with a Twist Microbeam irradiation experiments have been used to localize phytochrome in this fil-amentous green alga.
17.3 Phytochrome and High-Irradiance Responses Dual-wavelength experiments helped demon-strate the role of phytochrome in HIRs.
17.4 Phytochrome Interactions during Germination The interactions between phyA and phyB dur-ing germination are described.
17.5 Phytochrome Functional Domains Phytochrome overexpression has been used to characterize the functional domains of phytochrome.
17.6 Phytochrome Effects on Ion Fluxes Phytochrome regulates ion fluxes across mem-branes by altering the activities of ion channels and the plasma membrane proton pump.
17.7 Phytochrome Regulation of Gene Expression Evidence shows that phytochrome regulates gene expression at the level of transcription.
17.8 Regulation of Transcription by Cis-Acting Sequences Phytochrome response elements are described briefly.
400 Chapter 17 17.9 Genes That Suppress Photomorphogenesis Further information is provided about genes like COP and DET that negatively regulate photomorphogenesis.
17.10 The Roles of G-Proteins and Calcium in Phytochrome Responses Evidence suggests that G-proteins and cal-cium participate in phytochrome action.
17.11 The Origins of Phytochrome as a Bacterial Two-Component Receptor The discovery of bacterial phytochrome led to the identification of phytochrome as a protein kinase.
Web Essay 17.1 Awakened by a flash of sunlight When placed in the proper soil environment, seeds acquire extraordinary sensitivity to light so that germination can be stimulated by less than a second of exposure to sunlight during soil cultivations.
17.2 Know thy neighbor through phytochrome Plants can detect the proximity of neighbors through phytochrome perception of the R:FR of reflected light and produce adaptive mor-phological changes before being shaded by potential competitors.
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402 Chapter 17 Blue-Light Responses: Stomatal Movements and Morphogenesis 18 Chapter MOST OF US are familiar with the observation that house plants placed near a window have branches that grow toward the incoming light. This response, called phototropism, is an example of how plants alter their growth patterns in response to the direction of incident radiation. This response to light is intrinsically different from light trapping by photo-synthesis. In photosynthesis, plants harness light and convert it into chemical energy (see Chapters 7 and 8). In contrast, phototropism is an example of the use of light as an environmental signal. There are two major families of plant responses to light signals: the phytochrome responses, which were covered in Chapter 17, and the blue-light responses.
Some blue-light responses were introduced in Chapter 9—for exam-ple, chloroplast movement within cells in response to incident photon fluxes, and sun tracking by leaves. As with the family of the phy-tochrome responses, there are numerous plant responses to blue light.
Besides phototropism, they include inhibition of hypocotyl elongation, stimulation of chlorophyll and carotenoid synthesis, activation of gene expression, stomatal movements, phototaxis (the movement of motile unicellular organisms such as algae and bacteria toward or away from light), enhancement of respiration, and anion uptake in algae (Senger 1984). Blue-light responses have been reported in higher plants, algae, ferns, fungi, and prokaryotes.
Some responses, such as electrical events at the plasma membrane, can be detected within seconds of irradiation by blue light. More complex metabolic or morphogenetic responses, such as blue light–stimulated pig-ment biosynthesis in the fungus Neurospora or branching in the alga Vaucheria, might require minutes, hours, or even days (Horwitz 1994).
Readers may be puzzled by the different approaches to naming phy-tochrome and blue-light responses. The former are identified by a spe-cific photoreceptor (phytochrome), the latter by the blue-light region of the visible spectrum. In the case of phytochrome, several of its spectro-scopic and biochemical properties, particularly its red/ far-red reversibil-ity, made possible its early identification, and hundreds of photobiological responses of plants can be clearly attrib-uted to the phytochrome photoreceptor (see Chapter 17).
In contrast, the spectroscopy of blue-light responses is complex. Both chlorophylls and phytochrome absorb blue light (400–500 nm) from the visible spectrum, and other chromophores and some amino acids, such as tryptophan, absorb light in the ultraviolet (250–400 nm) region. How, then, can we then distinguish specific responses to blue light? One important identification criterion is that in spe-cific blue-light responses, blue light cannot be replaced by a red-light treatment, and there is no red/far-red reversibil-ity. Red or far-red light would be effective if photosynthe-sis or phytochrome were involved.
Another key distinction is that many blue-light responses of higher plants share a characteristic action spectrum. You will recall from Chapter 7 that an action spectrum is a graph of the magnitude of the observed light response as a function of wavelength (see Web Topic 7.1 for a detailed discussion of spectroscopy and action spectra). The action spectrum of the response can be compared with the absorption spectra of candidate photoreceptors. A close correspondence between action and absorption spectra provides a strong indication that the pigment under consideration is the pho-toreceptor mediating the light response under study (see Figure 7.8).
Action spectra for blue light–stimulated phototropism, stomatal movements, inhibition of hypocotyl elongation, and other key blue-light responses share a characteristic “three-finger” fine structure in the 400 to 500 nm region (Figure 18.1) that is not observed in spectra for responses to light that are mediated by photosynthesis, phytochrome, or other photoreceptors (Cosgrove 1994).
In this chapter we will describe representative blue-light responses in plants: phototropism, inhibition of stem elon-gation, and stomatal movements. The stomatal responses to blue light are discussed in detail because of the impor-tance of stomata in leaf gas exchange (see Chapter 9) and in plant acclimations and adaptations to their environment.
We will also discuss blue-light photoreceptors and the sig-nal transduction cascade that links light perception with the final expression of blue-light sensing in the organism.
THE PHOTOPHYSIOLOGY OF BLUE-LIGHT RESPONSES Blue-light signals are utilized by the plant in many responses, allowing the plant to sense the presence of light and its direction. This section describes the major mor-phological, physiological, and biochemical changes associ-ated with typical blue-light responses.
Blue Light Stimulates Asymmetric Growth and Bending Directional growth toward (or in special circumstances away from) the light, is called phototropism. It can be observed in fungi, ferns, and higher plants. Phototropism is a photomorphogenetic response that is particularly dra-matic in dark-grown seedlings of both monocots and dicots. Unilateral light is commonly used in experimental studies, but phototropism can also be observed when a seedling is exposed to two unequally bright light sources (Figure 18.2), a condition that can occur in nature.
As it grows through the soil, the shoot of a grass is pro-tected by a modified leaf that covers it, called a coleoptile (Figure 18.3; see also Figure 19.1). As discussed in detail in Chapter 19, unequal light perception in the coleoptile results in unequal concentrations of auxin in the lighted and shaded sides of the coleoptile, unequal growth, and bending.
Keep in mind that phototropic bending occurs only in growing organs, and that coleoptiles and shoots that have stopped elongating will not bend when exposed to unilat-eral light. In grass seedlings growing in soil under sunlight, coleoptiles stop growing as soon as the shoot has emerged from the soil and the first true leaf has pierced the tip of the coleoptile.
On the other hand, dark-grown, etiolated coleoptiles con-tinue to elongate at high rates for several days and, depending on the species, can attain several centimeters in length. The large phototropic response of these etiolated coleoptiles (see Figure 18.3) has made them a classic model for studies of phototropism (Firn 1994).
The action spectrum shown in Figure 18.1 was obtained through measurement of the angles of curvature from oat coleoptiles that were irradiated with light of different 404 Chapter 18 Curvature per photon, relative to 436 nm 0.20 0 0.40 0.60 0.80 1.00 1.20 1.40 300 320 340 360 380 400 420 440 460 480 500 Wavelength (nm) Blue region of spectrum FIGURE 18.1 Action spectrum for blue light–stimulated phototropism in oat coleoptiles. An action spectrum shows the relationship between a biological response and the wavelengths of light absorbed. The “three-finger” pattern in the 400 to 500 nm region is characteristic of specific blue-light responses. (After Thimann and Curry 1960.) wavelengths. The spectrum shows a peak at about 370 nm and the “three-finger” pattern in the 400 to 500 nm region discussed earlier. An action spectrum for phototropism in the dicot alfalfa (Medicago sativa) was found to be very sim-ilar to that of oat coleoptiles, suggesting that a common photoreceptor mediates phototropism in the two species.
Phototropism in sporangiophores of the mold Phy-comyces has been studied to identify genes involved in pho-totropic responses. The sporangiophore consists of a spo-rangium (spore-bearing spherical structure) that develops on a stalk consisting of a long, single cell. Growth in the sporangiophore is restricted to a growing zone just below the sporangium.
When irradiated with unilateral blue light, the sporan-giophore bends toward the light with an action spectrum similar to that of coleoptile phototropism (Cerda-Olmedo and Lipson 1987). These studies of Phycomyces have led to the isolation of many mutants with altered phototropic responses and the identification of several genes that are required for normal phototropism.
In recent years, phototropism of the stem of the small dicot Arabidopsis (Figure 18.4) has attracted much attention because of the ease with which advanced molecular tech-niques can be applied to Arabidopsis mutants. The genetics and the molecular biology of phototropism in Arabidopsis are discussed later in this chapter.
Blue-Light Responses: Stomatal Movements and Morphogenesis 405 Cotyledons Direction of growth Light source Unilateral light Unequal bilateral illumination Two equal lights from the side Two unequal lights from the side FIGURE 18.2 Relationship between direction of growth and unequal incident light. Cotyledons from a young seedling are shown as viewed from the top. The arrows indicate the direction of phototropic curvature. The diagrams illustrate how the direction of growth varies with the location and the intensity of the light source, but growth is always toward light. (After Firn 1994.) FIGURE 18.3 Time-lapse photograph of a corn coleoptile growing toward unilateral blue light given from the right.
The consecutive exposures were made 30 minutes apart.
Note the increasing angle of curvature as the coleoptile bends. (Courtesy of M. A. Quiñones.) FIGURE 18.4 Phototropism in wild-type (A) and mutant (B) Arabidopsis seedlings. Unilateral light was applied from the right. (Courtesy of Dr. Eva Huala.) (A) Wild-type (B) Mutant Blue light Blue light How Do Plants Sense the Direction of the Light Signal?
Light gradients between lighted and shaded sides have been measured in coleoptiles and in hypocotyls from dicot seedlings irradiated with unilateral blue light. When a coleoptile is illuminated with 450 nm blue light, the ratio between the light that is incident to the surface of the illu-minated side and the light that reaches the shaded side is 4:1 at the tip and the midregion of the coleoptile, and 8:1 at the base (Figure 18.5).
On the other hand, there is a lens effect in the sporangio-phore of the mold Phycomyces irradiated with unilateral blue light, and as a result, the light measured at the distal cell surface of the sporangiophore is about twice the amount of light that is incident at the surface of the illumi-nated side. Light gradients and lens effects could play a role in how the bending organ senses the direction of the unilateral light (Vogelmann 1994).
Blue Light Rapidly Inhibits Stem Elongation The stems of seedlings growing in the dark elongate very rapidly, and the inhibition of stem elongation by light is a key morphogenetic response of the seedling emerging from the soil surface (see Chapter 17). The conversion of Pr to Pfr (the red- and far red–absorbing forms of phy-tochrome, respectively) in etiolated seedlings causes a phytochrome-dependent, sharp decrease in elongation rates (see Figure 17.1).
However, action spectra for the decrease in elongation rate show strong activity in the blue region, which cannot be explained by the absorption properties of phytochrome (see Figure 17.9). In fact, the 400 to 500 nm blue region of the action spectrum for the inhibition of stem elongation closely resembles that of phototropism (compare the action spectra in Figures 17.10 and 18.1).
There are several ways to experimentally separate a reduction in elongation rates mediated by phytochrome from a reduction mediated by a specific blue-light response.
If lettuce seedlings are given low fluence rates of blue light under a strong background of yellow light, their hypocotyl elongation rate is reduced by more than 50%. The back-ground yellow light establishes a well-defined Pr:Pfr ratio (see Chapter 17). In such conditions, the low fluence rates of blue light added are too small to significantly change this ratio, ruling out a phytochrome effect on the reduction in elongation rate observed upon the addition of blue light.
Blue light– and phytochrome-mediated hypocotyl responses can also be distinguished by the swiftness of the response. Whereas phytochrome-mediated changes in elongation rates can be detected within 8 to 90 minutes, depending on the species, blue-light responses are rapid, and can be measured within 15 to 30 s (Figure 18.6). Inter-actions between phytochrome and the blue light–depen-dent sensory transduction cascade in the regulation of elon-gation rates will be described later in the chapter.
Another fast response elicited by blue light is a depo-larization of the membrane of hypocotyl cells that precedes the inhibition of growth rate (see Figure 18.6). The membrane depolarization is caused by the activation of anion channels (see Chapter 6), which facilitates the efflux of anions such as chlo-ride. Use of an anion channel blocker prevents the blue light–dependent membrane depolarization and decreases the inhibitory effect of blue light on hypocotyl elongation (Parks et al. 1998).
Blue Light Regulates Gene Expression Blue light also regulates the expression of genes involved in several important morphogenetic processes. Some of these light-activated genes have been studied in detail—for example, the genes that code for the enzyme chalcone synthase, which cat-alyzes the first committed step in flavonoid biosyn-thesis, for the small subunit of rubisco, and for the proteins that bind chlorophylls a and b (see Chap-ters 13, 8, and 7, respectively). Most of the studies on light-activated genes show sensitivity to both blue and red light, as well as red/far-red reversibil-ity, implicating both phytochrome and specific blue-light responses.
A recent study reported that SIG5, one of six SIG nuclear genes in Arabidopsis that play a regulatory role in the transcription of the chloroplast gene 406 Chapter 18 0 0 1.0 1.0 2.0 0 0.4 0.8 1.2 Light (relative units) Distance (mm) Blue light Blue light Probe Probe FIGURE 18.5 Distribution of transmitted, 450 nm blue light in an etiolated corn coleoptile. The diagram in the upper right of each frame shows the area of the coleoptile being measured by a fiber-optic probe. A cross section of the tissue appears at the bottom of each frame. The trace above it shows the amount of light sensed by the probe at each point. A sensing mechanism that depended on light gradients would sense the difference in the amount of light between the lighted and shaded sides of the coleoptile, and this information would be transduced into an unequal auxin concen-tration and bending. (After Vogelmann and Haupt 1985.) psbD, which encodes the D2 subunit of the PSII reaction center (see Chapter 7), is specifically activated by blue light (Tsunoyama et al. 2002). In contrast, the other five SIG genes are activated by both blue and red light.
Another well-documented instance of gene expression that is mediated solely by a blue light–sensing system involves the GSA gene in the photosynthetic unicellular alga Chlamydomonas reinhardtii (Matters and Beale 1995).
This gene encodes the enzyme glutamate-1-semialdehyde aminotransferase (GSA), a key enzyme in the chlorophyll biosynthesis pathway (see Chapter 7). The absence of phy-tochrome in C. reinhardtii simplifies the analysis of blue-light responses in this experimental system.
In synchronized cultures of C. reinhardtii, levels of GSA mRNA are strictly regulated by blue light, and 2 hours after the onset of illumination, GSA mRNA levels are 26-fold higher than they are in the dark (Figure 18.7). These blue light–mediated mRNA increases precede increases in chlorophyll content, indicating that chlorophyll biosyn-thesis is being regulated by activation of the GSA gene.
Blue Light Stimulates Stomatal Opening We now turn our attention to the stomatal response to blue light. Stomata have a major regulatory role in gas exchange in leaves (see Chapter 9), and they can often affect yields of agricultural crops (see Chapter 25). Several characteristics of blue light–dependent stomatal movements make guard cells a valuable experimental system for the study of blue-light responses: • The stomatal response to blue light is rapid and reversible, and it is localized in a single cell type, the guard cell.
• The stomatal response to blue light regulates stom-atal movements throughout the life of the plant. This is unlike phototropism or hypocotyl elongation, which are functionally important at early stages of development.
• The signal transduction cascade that links the percep-tion of blue light with the opening of stomata is understood in considerable detail.
In the following sections we will discuss two central aspects of the stomatal response to light, the osmoregula-tory mechanisms that drive stomatal movements, and the role of a blue light–activated H+-ATPase in ion uptake by guard cells.
Blue-Light Responses: Stomatal Movements and Morphogenesis 407 –160 Membrane potential difference (mV) Growth rate (mm h–1) –140 –120 –100 –80 –60 1.0 1.5 2.0 2.5 0 1 2 3 4 0 1 2 3 4 Blue light on Time (min) (A) (B) FIGURE 18.6 Blue light–induced (A) changes in elongation rates of etiolated cucumber seedlings and (B) transient membrane depolarization of hypocotyl cells. As the mem-brane depolarization (measured with intracellular elec-trodes) reaches its maximum, growth rate (measured with position transducers) declines sharply. Comparison of the two curves shows that the membrane starts to depolarize before the growth rate begins to decline, suggesting a cause–effect relation between the two phenomena. (After Spalding and Cosgrove 1989.) Relative abundance of GSA mRNA 0 –2 2 4 6 8 10 12 Time of blue-light treatment (h) Blue light on FIGURE 18.7 Time course of blue light–dependent gene expression in Chlamydomonas reinhardtii. The GSA gene encodes the enzyme glutamate-1-semialdehyde amino-transferase, which regulates an early step in chlorophyll biosynthesis. (After Matters and Beale 1995.) Light is the dominant environmental signal controlling stomatal movements in leaves of well-watered plants growing in natural environments. Stomata open as light levels reaching the leaf surface increase, and close as they decrease (Figure 18.8). In greenhouse-grown leaves of broad bean (Vicia faba), stomatal movements closely track incident solar radiation at the leaf surface (Figure 18.9).
Early studies of the stomatal response to light showed that DCMU (dichlorophenyl-dimethylurea), an inhibitor of photosynthetic electron transport (see Figure 7.31), causes a partial inhibition of light-stimulated stomatal opening. These results indicated that photo-synthesis in the guard cell chloroplast plays a role in light-dependent stomatal opening, but the observation that the inhibition was only partial pointed to a nonphotosynthetic compo-nent of the stomatal response to light. Detailed studies of the light response of stomata have shown that light activates two distinct responses of guard cells: photosynthesis in the guard cell chloroplast (see Web Essay 18.1), and a specific blue-light response.
The specific stomatal response to blue light cannot be resolved properly under blue-light illumination because blue light simultaneously stimulates both the specific blue-light response and guard cell photosynthesis (for the photo-synthetic response to blue light, see the action spectrum for photosynthesis in Figure 7.8). A clear-cut sep-aration of the responses of the two light responses can be obtained in dual-beam experiments. High fluence rates of red light are used to saturate the photosynthetic response, and low photon fluxes of blue light are added after the response to the saturating red light has been completed (Figure 18.10). The addition of blue light causes substantial further stomatal opening that cannot be explained as a fur-ther stimulation of guard cell photosynthesis because pho-tosynthesis is saturated by the background red light.
An action spectrum for the stomatal response to blue light under background red illumination shows the three-finger pattern discussed earlier (Figure 18.11). This action spectrum, typical of blue-light responses and distinctly dif-ferent from the action spectrum for photosynthesis, further indicates that, in addition to photosynthesis, guard cells respond specifically to blue light.
When guard cells are treated with cellulolytic enzymes that digest the cell walls, guard cell protoplasts are released.
Guard cell protoplasts swell when illuminated with blue light (Figure 18.12), indicating that blue light is sensed within the guard cells proper. The swelling of guard cell 408 Chapter 18 FIGURE 18.8 Light-stimulated stomatal opening in detached epidermis of Vicia faba. Open, light-treated stoma (A), is shown in the dark-treated, closed state in (B). Stomatal opening is quantified by micro-scopic measurement of the width of the stomatal pore. (Courtesy of E. Raveh.) 20 µm Chloroplast Pore Guard cells (A) (B) 2 0 4 6 8 10 12 14 250 0 500 750 1000 1250 (A) (B) 5:00 9:00 13:00 17:00 21:00 Photosynthetically active radiation (400–700 nm) (µmol m–2 s–1) Stomatal aperture (pore width, µm) Time of day FIGURE 18.9 Stomatal opening tracks photosynthetic active radiation at the leaf surface. Stomatal opening in the lower surface of leaves of Vicia faba grown in a greenhouse, measured as the width of the stomatal pore (A), closely follows the levels of photosynthetically active radiation (400–700 nm) incident to the leaf (B), indicating that the response to light was the dominant response regulating stomatal opening. (After Srivastava and Zeiger 1995a.) protoplasts also illustrates how intact guard cells function.
The light-stimulated uptake of ions and the accumulation of organic solutes decrease the cell’s osmotic potential (increase the osmotic pressure). Water flows in as a result, leading to an increase in turgor that in guard cells with intact walls is mechanically transduced into an increase in stomatal apertures (see Chapter 4). In the absence of a cell wall, the blue light–mediated increase in osmotic pressure causes the guard cell protoplast to swell.
Blue Light Activates a Proton Pump at the Guard Cell Plasma Membrane When guard cell protoplasts from broad bean (Vicia faba) are irradiated with blue light under background red-light illumination, the pH of the suspension medium becomes more acidic (Figure 18.13). This blue light–induced acidifi-cation is blocked by inhibitors that dissipate pH gradients, such as CCCP (discussed shortly), and by inhibitors of the proton-pumping H+-ATPase, such as vanadate (see Figure 18.12C; see also Chapter 6). Blue-Light Responses: Stomatal Movements and Morphogenesis 409 1 2 3 4 2 0 4 6 8 10 12 Stomatal aperture (µm) Time (h) Blue light Red light FIGURE 18.10 The response of stomata to blue light under a red-light background. Stomata from detached epidermis of Commelina communis (common dayflower) were treated with saturating photon fluxes of red light (red trace). In a parallel treatment, stomata illuminated with red light were also illuminated with blue light, as indicated by the arrow (blue trace). The increase in stomatal opening above the level reached in the presence of saturating red light indi-cates that a different photoreceptor system, stimulated by blue light, is mediating the additional increases in opening.
(From Schwartz and Zeiger 1984.) 400 350 450 500 Relative effectiveness Wavelength (nm) FIGURE 18.11 The action spectrum for blue light–stimu-lated stomatal opening (under a red-light background).
(After Karlsson 1986.) 20 40 60 30 0 35 40 45 50 55 Guard cell protoplast volume (µm3 × 10–2) Time (min) Control 500 µM Vanadate Blue light on Red light on (B) FIGURE 18.12 Blue light–stimulated swelling of guard cell protoplasts. (A) In the absence of a rigid cell wall, guard cell protoplasts of onion (Allium cepa) swell. (B) Blue light stimulates the swelling of guard cell protoplasts of broad bean (Vicia faba), and vanadate, an inhibitor of the H+-ATPase, inhibits this swelling. Blue light stimulates ion and water uptake in the guard cell protoplasts, which in the intact guard cells provides a mechanical force that drives increases in stomatal apertures. (A from Zeiger and Hepler 1977; B after Amodeo et al. 1992.) (A) Blue light Protoplasts in dark Protoplasts swell in blue light Undigested stomatal pore This indicates that the acidification results from the activa-tion by blue light of a proton-pumping ATPase in the guard cell plasma membrane that extrudes protons into the protoplast suspension medium and lowers its pH. In the intact leaf, this blue-light stimulation of proton pumping lowers the pH of the apoplastic space surrounding the guard cells.
The plasma membrane ATPase from guard cells has been isolated and extensively characterized (Kinoshita et al.
2001).
The activation of electrogenic pumps such as the proton-pumping ATPase can be measured in patch-clamping experiments as an outward electric current at the plasma membrane (see Web Topic 6.2 for a description of patch clamping). A patch clamp recording of a guard cell proto-plast treated with the fungal toxin fusicoccin, a well-char-acterized activator of plasma membrane ATPases, is shown in Figure 18.14A. Exposure to fusicoccin stimulates an out-ward electric current, which is abolished by the proton ionophore carbonyl cyanide m-chlorophenylhydrazone (CCCP). This proton ionophore makes the plasma mem-brane highly permeable to protons, thus precluding the for-mation of a proton gradient across the membrane and abol-ishing net proton efflux.
The relationship between proton pumping at the guard cell plasma membrane and stomatal opening is evident from the observation that fusicoccin stimulates both pro-ton extrusion from guard cell protoplasts and stomatal opening, and that CCCP inhibits the fusiccocin-stimulated opening. The increase in proton-pumping rates as a func-tion of fluence rates of blue light (see Figure 18.13) indicates that the increasing rates of blue photons in the solar radia-tion reaching the leaf cause a larger stomatal opening.
The close relationship among the number of incident blue-light photons, proton pumping at the guard cell plasma membrane, and stomatal opening further suggests that the blue-light response of stomata might function as a sensor of photon fluxes reaching the guard cell.
Pulses of blue light given under a saturating red-light background also stimulate an outward electric current from guard cell protoplasts (see Figure 18.14B). The acidification measurements shown in Figure 18.13 indicate that the out-ward electric current measured in patch clamp experiments is carried by protons.
Blue-Light Responses Have Characteristic Kinetics and Lag Times Some of the characteristics of the responses to blue-light pulses underscore some important properties of blue-light responses: the persistence of the response after the light sig-410 Chapter 18 10 0 20 30 40 50 60 5 10 50 500 Baseline under saturating red light Blue-light pulse Blue photon fluxes (µmol m–2 s–1): Time (min) pH of suspension medium More alkaline More acidic FIGURE 18.13 Acidification of a suspension medium of guard cell protoplasts of Vicia faba stimulated by a 30 s pulse of blue light. The acidification results from the stimu-lation of an H+-ATPase at the plasma membrane by blue light, and it is associated with protoplast swelling (see Figure 18.12). (After Shimazaki et al. 1986.) 2 pA 2 pA Fusicoccin activates H+-ATPase CCCP proton ionophore 30 s Blue-light pulse Electric current Electric current (A) (B) 1 min FIGURE 18.14 Activation of the H+-ATPase at the plasma membrane of guard cell protoplasts by fusiccocin and blue light can be measured as electric current in patch clamp experiments. (A) Outward electric current (measured in picoamps, pA) at the plasma membrane of a guard cell pro-toplast stimulated by the fungal toxin fusicoccin, an activa-tor of the H+-ATPase. The current is abolished by the pro-ton ionophore CCCP (carbonyl cyanide m-chlorophenylhy-drazone). (B) Outward electric current at the plasma mem-brane of a guard cell protoplast stimulated by a blue-light pulse. These results indicate that blue light stimulates the H+-ATPase. (A after Serrano et al. 1988; B after Assmann et al. 1985.) nal has been switched off, and a significant lag time sepa-rating the onset of the light signal and the beginning of the response.
In contrast to typical photosynthetic responses, which are activated very quickly after a “light on” signal, and cease when the light goes off (see, for instance, Figure 7.13), blue-light responses proceed at maximal rates for several minutes after application of the pulse (see Figure 18.14B).
This property can be explained by a physiologically inac-tive form of the blue-light photoreceptor that is converted to an active form by blue light, with the active form revert-ing slowly to the physiologically inactive form in the absence of blue light (Iino et al. 1985). The rate of the response to a blue-light pulse would thus depend on the time course of the reversion of the active form to the inac-tive one.
Another property of the response to blue-light pulses is a lag time, which lasts about 25 s in both the acidification response and the outward electric currents stimulated by blue light (see Figures 18.13 and 18.14). This amount of time is probably required for the signal transduction cas-cade to proceed from the photoreceptor site to the proton-pumping ATPase and for the proton gradient to form. Sim-ilar lag times have been measured for blue light–dependent inhibition of hypocotyl elongation, which was discussed earlier.
Blue Light Regulates Osmotic Relations of Guard Cells Blue light modulates guard cell osmoregulation via its acti-vation of proton pumping (described earlier) and via the stimulation of the synthesis of organic solutes. Before dis-cussing these blue-light responses, let us briefly describe the major osmotically active solutes in guard cells.
The botanist Hugo von Mohl proposed in 1856 that tur-gor changes in guard cells provide the mechanical force for changes in stomatal apertures. The plant physiologist F. E.
Lloyd hypothesized in 1908 that guard cell turgor is regu-lated by osmotic changes resulting from starch–sugar inter-conversions, a concept that led to a starch–sugar hypoth-esis of stomatal movements. The discovery of the changes in potassium concentrations in guard cells in the 1960s led to the modern theory of guard cell osmoregulation by potassium and its counterions.
Potassium concentration in guard cells increases sever-alfold when stomata open, from 100 mM in the closed state to 400 to 800 mM in the open state, depending on the plant species and the experimental conditions. These large con-centration changes in the positively charged potassium ions are electrically balanced by the anions Cl– and malate2– (Figure 18.15A). In species of the genus Allium, such as onion (Allium cepa), K+ ions are balanced solely by Cl–. In most species, however, potassium fluxes are bal-anced by varying amounts of Cl– and the organic anion malate2– (Talbott et al. 1996).
The Cl– ion is taken up into the guard cells during stom-atal opening and extruded during stomatal closing. Malate, on the other hand, is synthesized in the guard cell cytosol, in a metabolic pathway that uses carbon skeletons gener-ated by starch hydrolysis (see Figure 18.15B). The malate content of guard cells decreases during stomatal closing, but it remains to be established whether malate is catabo-lized in mitochondrial respiration or is extruded into the apoplast.
Potassium and chloride are taken up into guard cells via secondary transport mechanisms driven by the gradient of electrochemical potential for H+, ∆mH+, generated by the proton pump (see Chapter 6) discussed earlier in the chap-ter. Proton extrusion makes the electric-potential difference across the guard cell plasma membrane more negative; light-dependent hyperpolarizations as high as 50 mV have been measured. In addition, proton pumping generates a pH gradient of about 0.5 to 1 pH unit.
The electrical component of the proton gradient pro-vides a driving force for the passive uptake of potassium ions via voltage-regulated potassium channels (see Chap-ter 6) (Schroeder et al. 2001). Chloride is thought to be taken up through anion channels. Thus, blue light–depen-dent stimulation of proton pumping plays a key role in guard cell osmoregulation during light-dependent stom-atal movements Guard cell chloroplasts (see Figure 18.8) contain large starch grains, and their starch content decreases during stomatal opening and increases during closing. Starch, an insoluble, high-molecular-weight polymer of glucose, does not contribute to the cell’s osmotic potential, but the hydrolysis of starch into soluble sugars causes a decrease in the osmotic potential (or increase in osmotic pressure) of guard cells. In the reverse process, starch synthesis decreases the sugar concentration, resulting in an increase of the cell’s osmotic potential, which the starch–sugar hypothesis predicted to be associated with stomatal clos-ing.
With the discovery of the major role of potassium and its counterion in guard cell osmoregulation, the sugar– starch hypothesis was no longer considered important (Outlaw 1983). Recent studies, however, described in the next section, have characterized a major osmoregulatory phase of guard cells in which sucrose is the dominant osmotically active solute.
Sucrose Is an Osmotically Active Solute in Guard Cells Studies of daily courses of stomatal movements in intact leaves have shown that the potassium content in guard cells increases in parallel with early-morning opening, but it decreases in the early afternoon under conditions in which apertures continue to increase. The sucrose content of guard cells increases slowly in the morning, but upon potassium efflux, sucrose becomes the dominant osmoti-Blue-Light Responses: Stomatal Movements and Morphogenesis 411 412 Chapter 18 H+ H+ H+ H+ H+ H+ Cl– CYTOPLASM Glucose-1-phosphate Sucrose Sucrose Sucrose Phosphoenol-pyruvate Malate Malate VACUOLE K+ K+ Cl– K+ Cl– CHLOROPLAST Calvin cycle Ribulose-1,5- bisphosphate Fructose-6-phosphate Glucose-6-phosphate Starch Fructose-1,6-bisphosphate Dihydroxyacetone 3-phosphate Dihydroxyacetone 3-phosphate 3 phosphoglycerate CO2 CO2 Maltose Glucose (A) ?
Cl– CYTOPLASM Glucose-1-phosphate Sucrose Sucrose Sucrose Phosphoenol-pyruvate Malate Malate VACUOLE K+ K+ Cl– K+ Cl– CHLOROPLAST Calvin cycle Ribulose-1,5- bisphosphate Fructose-6-phosphate Glucose-6-phosphate Starch Fructose-1,6-bisphosphate Dihydroxyacetone 3-phosphate Dihydroxyacetone 3-phosphate 3 phosphoglycerate CO2 CO2 Maltose Glucose (B) ?
Cl– CYTOPLASM Glucose-1-phosphate Sucrose Sucrose Sucrose Phosphoenol-pyruvate Malate Malate VACUOLE K+ K+ Cl– K+ Cl– CHLOROPLAST Calvin cycle Ribulose-1,5- bisphosphate Fructose-6-phosphate Glucose-6-phosphate Starch Fructose-1,6-bisphosphate Dihydroxyacetone 3-phosphate Dihydroxyacetone 3-phosphate 3 phosphoglycerate CO2 Maltose Glucose (C) ?
CO2 cally active solute, and stomatal closing at the end of the day parallels a decrease in the sucrose content of guard cells (Figure 18.16) (Talbott and Zeiger 1998).
These osmoregulatory features indicate that stomatal opening is associated primarily with K+ uptake, and clos-ing is associated with a decrease in sucrose content (see Figure 18.16). The need for distinct potassium- and sucrose-dominated osmoregulatory phases is unclear, but it might underlie regulatory aspects of stomatal function. Potassium might be the solute of choice for the consistent daily open-ing that occurs at sunrise. The sucrose phase might be asso-ciated with the coordination of stomatal movements in the epidermis with rates of photosynthesis in the mesophyll.
Where do osmotically active solutes originate? Four dis-tinct metabolic pathways that can supply osmotically active solutes to guard cells have been characterized (see Figure 18.15): 1. The uptake of K+ and Cl– coupled to the biosynthesis of malate2– 2. The production of sucrose from starch hydrolysis 3. The production of sucrose by photosynthetic carbon fixation in the guard cell chloroplast 4. The uptake of apoplastic sucrose generated by meso-phyll photosynthesis Depending on environmental conditions, one or several pathways may be activated. For instance, red light–stim-ulated stomatal opening in detached epidermis depends solely on sucrose generated by guard cell photosynthesis, with no detectable K+ uptake. The other osmoregulatory pathways can be selectively activated under different experimental conditions (see Web Topic 18.1). Current studies are beginning to unravel the mysteries of guard cell osmoregulation in the intact leaf (Dietrich et al. 2001).
BLUE-LIGHT PHOTORECEPTORS Experiments carried out by Charles Darwin and his son Francis in the nineteenth century determined that the site of photoreception in blue light–stimulated phototropism is in the coleoptile tip. Early hypotheses about blue-light pho-toreceptors focused on carotenoids and flavins (for a his-torical account of early research on blue-light photorecep-tors, see Web Topic 18.2). Despite active research efforts, no significant advances toward the identification of blue-light photoreceptors were made until the early 1990s. In the case of phototropism and the inhibition of stem elongation, progress resulted from the identification of mutants for key blue-light responses, and the subsequent isolation of the relevant gene.
Cloning of the gene led to the identification and char-acterization of the protein encoded by the gene. In the case of stomatal guard cells, the carotenoid zeaxanthin has been postulated to be the chromophore of a blue-light photore-ceptor, whereas the identity of the apoprotein remains to be established. For a detailed discussion of the basic dif-ferences between carotenoid and flavin photoreceptors, see Web Topic 18.3. In the following section we will describe the three photoreceptors associated with blue-light responses: cryptochromes, phototropins, and zeaxanthin.
Cryptochromes Are Involved in the Inhibition of Stem Elongation The hy4 mutant of Arabidopsis lacks the blue light–stimulated inhibition of hypocotyl elongation described earlier in the chapter. As a result of this genetic defect, hy4 plants show an elongated hypocotyl when irradiated with blue light. Isola-tion of the HY4 gene showed that it encodes a 75 kDa protein with significant sequence homology to microbial DNApho-tolyase, a blue light–activated enzyme that repairs pyrimi-dine dimers in DNA formed as a result of exposure to ultra-violet radiation (Ahmad and Cashmore 1993). In view of this sequence similarity, the hy4 protein, later renamed cryp-tochrome 1 (cry1), was proposed to be a blue-light photore-ceptor mediating the inhibition of stem elongation.
Photolyases are pigment proteins that contain a flavin adenine dinucleotide (FAD; see Figure 11.2B) and a pterin.
Blue-Light Responses: Stomatal Movements and Morphogenesis 413 FIGURE 18.15 Three distinct osmoregulatory pathways in guard cells. The dark arrows identify the major metabolic steps of each pathway that lead to the accumulation of osmotically active solutes in the guard cells. (A) Potassium and its counterions. Potassium and chloride are taken up in secondary transport processes driven by a proton gradient; malate is formed from the hydrolysis of starch. (B) Accumulation of sucrose from starch hydrolysis. (C) Accumulation of sucrose from photosynthetic carbon fixa-tion. The possible uptake of apoplastic sucrose is also indi-cated. (From Talbott and Zeiger 1998.) 10 5 15 20 25 Stomatal aperture (µm) 7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00 Time of day 5 15 25 35 45 55 K+ stain (percent area) Sucrose (pmol/guard cell pair) 0.25 0.75 1.25 1.75 2.25 Stomatal aperture Sucrose K+ FIGURE 18.16 Daily course of changes in stomatal aperture, and in potassium and sucrose content, of guard cells from intact leaves of broad bean (Vicia faba). These results indi-cate that the changes in osmotic potential required for stomatal opening in the morning are mediated by potas-sium and its counterions, whereas the afternoon changes are mediated by sucrose. (After Talbott and Zeiger 1998.) L Pterins are light-absorbing, pteridine derivatives that often function as pigments in insects, fishes, and birds (see Chap-ter 12 for pterin structure). When expressed in Escherichia coli, the cry1 protein binds FAD and a pterin, but it lacks detectable photolyase activity. No information is available on the chromophore(s) bound to cry1 in vivo, or on the nature of the photochemical reactions involving cry1, that would start the postulated sensory transduction cascade mediating the several blue-light responses mediated by cry1.
The most important evidence for a role of cry1 in blue light–mediated inhibition of stem elongation comes from overexpression studies. Overexpression of the CRY1 pro-tein in transgenic tobacco or Arabidopsis plants results in a stronger blue light–stimulated inhibition of hypocotyl elongation than in the wild type, as well as increased production of anthocyanin, another blue-light response (Figure 18.17). Thus, overexpression of CRY1 caused an enhanced sensitivity to blue light in transgenic plants.
Other blue-light responses, such as phototropism and blue light–dependent stomatal movements, appear to be nor-mal in the cry1 mutant phenotype.
A second gene product homologous to CRY1, named CRY2, has been isolated from Arabidopsis (Lin 2000). Both CRY1 and CRY2 appear ubiquitous throughout the plant kingdom. A major difference between them is that CRY2 is rapidly degraded in the light, whereas CRY1 is stable in light-grown seedlings.
Transgenic plants overexpressing the gene that encodes CRY2 show a small enhancement of the inhibition of hypocotyl elongation, indicating that unlike CRY1, CRY2 does not play a primary role in inhibiting stem elongation.
On the other hand, the transgenic plants overexpressing the gene that encodes CRY2 show a large increase in blue light–stimulated cotyledon expansion, yet another blue-light response. In addition, CRY1 has been shown to be involved in the setting of the circadian clock in Arabidopsis (see Chap-ter 17), and both CRY1 and CRY2 have been shown to play a role in the induction of flowering (see Chapter 24). Cryp-tochrome homologs have been found to regulate the circa-dian clock in Drosophila, mouse, and humans.
Phototropins Are Involved in Phototropism and Chloroplast Movements Some recently isolated Arabidopsis mutants impaired in blue light–dependent phototropism of the hypocotyl have provided valuable information about cellular events pre-ceding bending. One of these mutants, the nph1 (nonpho-totropic hypocotyl) mutant has been found to be genetically independent of the hy4 (cry1) mutant discussed earlier: The nph1 mutant lacks a phototropic response in the hypocotyl but has normal blue light–stimulated inhibition of hypocotyl elongation, while hy4 has the converse pheno-type. Recently the nph1 gene was renamed phot1, and the protein it encodes was named phototropin (Briggs and Christie 2002).
The C-terminal half of phototropin is a serine/threonine kinase. The N-terminal half contains two repeated domains, of about 100 amino acids each, that have sequence similarities to other proteins involved in signal-ing in bacteria and mammals. Proteins with sequence sim-ilarity to the N terminus of phototropin bind flavin cofac-tors. These proteins are oxygen sensors in Escherichia coli and Azotobacter, and voltage sensors in potassium channels of Drosophila and vertebrates.
When expressed in insect cells, the N-terminal half of phototropin binds flavin mononucleotide (FMN) (see Fig-ure 11.2B and Web Essay 18.2) and shows a blue light–dependent autophosphorylation reaction. This reac-tion resembles the blue light–dependent phosphorylation of a 120 kDa membrane protein found in growing regions of etiolated seedlings.
The Arabidopsis genome contains a second gene, phot2, which is related to phot1. The phot1 mutant lacks hypocotyl phototropism in response to low-intensity blue light (0.01–1 µmol mol–2 s–1) but retains a phototropic response at higher intensities (1–10 µmol m–2 s–1). The phot2 mutant has a nor-mal phototropic response, but the phot1/phot2 double mutant is severely impaired at both low and high intensi-ties. These data indicate that both phot1 and phot2 are involved in the phototropic response, with phot2 function-ing at high light fluence rates.
Blue light–activated chloroplast movement. Leaves show an adaptive feature that can alter the intracellular dis-tribution of their chloroplasts in order to control light absorption and prevent photodamage (see Figure 9.5). The action spectrum for chloroplast movement shows the “three finger” fine structure typical of blue-light responses.
When incident radiation is weak, chloroplasts gather at the upper and lower surfaces of the mesophyll cells (the “accu-414 Chapter 18 0.6 0.8 Anthocyanin accumulation absorbance change 0.4 0.2 0.0 CRY1 OE WT cry1 1.5 Hypocotyl length (cm) 1.0 0.5 CRY1 OE WT cry1 (A) (B) FIGURE 18.17 Blue light stimulates the accumulation of anthocyanin (A) and the inhibition of stem elongation (B) in transgenic and mutant seedlings of Arabidopsis. These bar graphs show a transgenic phenotype overexpressing the gene that encodes CRY1 (CRY1 OE), the wild type (WT), and cry1 mutants. The enhanced blue-light response of the transgenic plant overexpressing the gene that encodes CRY1 demonstrates the important role of this gene product in stimulating anthocyanin biosynthesis and inhibiting stem elongation. (After Ahmad et al. 1998.) mulation” response; see Figure 9.5B), thus maximizing light absorption.
Under strong light, the chloroplasts move to the cell sur-faces that are parallel to the incident light (the “avoidance” response; see Figure 9.5C), thus minimizing light absorp-tion. Recent studies have shown that mesophyll cells of the phot1 mutant have a normal avoidance response and a rudi-mentary accumulation response. Cells from the phot2 mutant show a normal accumulation response but lack the avoidance response. Cells from the phot1/phot2 double mutant lack both the avoidance and accumulation responses (Sakai et al. 2001). These results indicate that phot2 plays a key role in the avoidance response, and that both phot1 and phot2 contribute to the accumulation response.
The Carotenoid Zeaxanthin Mediates Blue-Light Photoreception in Guard Cells The carotenoid zeaxanthin has been implicated as a pho-toreceptor in blue light–stimulated stomatal opening. Recall from Chapters 7 and 9 that zeaxanthin is one of the three components of the xanthophyll cycle of chloroplasts, which protects photosynthetic pigments from excess excitation energy. In guard cells, however, the changes in zeaxanthin content as a function of incident radiation are distinctly dif-ferent from the changes in mesophyll cells (Figure 18.18).
In sun plants such as Vicia faba, zeaxanthin accumula-tion in the mesophyll begins at about 200 µmol m–2 s–1, and there is no detectable zeaxanthin in the early morning or late afternoon. In contrast, the zeaxanthin content in guard cells closely follows incident solar radiation at the leaf sur-face throughout the day, and it is nearly linearly propor-tional to incident photon fluxes in the early morning and late afternoon. Several key characteristics of the guard cell chloroplast strongly indicate that the primary function of the guard cell chloroplast is sensory transduction and not carbon fixation (Zeiger et al. 2002).
Compelling evidence indicates that zeaxanthin is a blue-light photoreceptor in guard cells: • The absorption spectrum of zeaxanthin (Figure 18.19) closely matches the action spectrum for blue light–stimulated stomatal opening (see Figure 18.11).
• In daily courses of stomatal opening in intact leaves grown in a greenhouse, incident radiation, zeaxan-thin content of guard cells, and stomatal apertures are closely related (see Figure 18.18).
• The blue-light sensitivity of guard cells increases as a function of their zeaxanthin concentration.
Experimentally, zeaxanthin concentration in guard cells can be varied with increasing fluence rates of red light. When guard cells from epidermal peels illuminated with increasing fluence rates of red light are exposed to blue light, the resulting blue light–stimulated stomatal opening is linearly related to the fluence rate of background red-light irradiation (see the wild-type treatment in Figure 18.20) and to Blue-Light Responses: Stomatal Movements and Morphogenesis 415 10 12 14 0 50 100 150 200 250 8 6 4 2 0 6:00 9:00 12:00 15:00 18:00 21:00 6:00 9:00 12:00 15:00 18:00 21:00 Time of day Stomatal aperture (mm) Zeaxanthin (mmol mol–1 Chl a+b) (B) (A) Mesophyll cells Guard cells 250 500 750 1000 1250 Photosynthetically active radiation (µmol m–2 s–1) FIGURE 18.18 The zeaxanthin content of guard cells closely tracks photosynthetic active radiation and stomatal aper-tures. (A) Daily course of photosynthetic active radiation reaching the leaf surface, and of zeaxanthin content of guard cells and mesophyll cells of Vicia faba leaves grown in a greenhouse. The white areas within the graph highlight the contrasting sensitivity of the xanthophyll cycle in meso-phyll and guard cell chloroplasts under the low irradiances prevailing early and late in the day. (B) Stomatal apertures in the same leaves used to measure guard cell zeaxanthin content. (After Srivastava and Zeiger 1995a.) 400 350 0.05 0.1 0.15 0.2 0.25 450 500 Absorbance Wavelength (nm) FIGURE 18.19 The absorption spectrum of zeaxanthin in ethanol.
zeaxanthin content (Srivastava and Zeiger 1995b).
The same relationship among background red light, zeaxanthin content, and blue-light sensitivity has been found in blue light–stimulated phototropism of corn coleoptiles (see Web Topic 18.4).
• Blue light–stimulated stomatal opening is completely inhibited by 3 mM dithiothreitol (DTT), and the inhi-bition is concentration dependent. Zeaxanthin forma-tion is blocked by DTT, a reducing agent that reduces S—S bonds to –SH groups and effectively inhibits the enzyme that converts violaxanthin into zeaxanthin.
The specificity of the inhibition of blue light–stimu-lated stomatal opening by DTT, and its concentration dependence, indicate that guard cell zeaxanthin is required for the stomatal response to blue light.
• In the facultative CAM species Mesembryanthemum crystallinum (see Chapters 8 and 25), salt accumulation 416 Chapter 18 2.8 Stomatal aperture (mm) 2.4 2.0 50 100 Background red light (mmol m–2 s–1) 150 Wild type npq1 (mutant lacking zeaxanthin) FIGURE 18.20 Stomatal responses to blue light in the wild type and npq1, an Arabidopsis mutant that lacks zeaxanthin.
Stomata in detached epidermis were irradiated with red light for 2 hours, and 20 µmol m–2 s–1 of blue light was added for one additional hour. Stomatal opening in the wild type is proportional to the fluence rates of background red light. In contrast, npq1 stomata lacked this response and showed reduced opening under both blue and red light, probably mediated by guard cell photosynthesis. (From Frechilla et al. 1999.) NADPH NADP+ ATP ATP Light energy (PAR) Grana thylakoid Blue-light sensing H+ H+ H+ H+ H+ H+ H+ K+ K+ Cl– H+ Cl– ADP Pi P + ADP Pi + ADP Pi + + ATP synthase Ribulose-1,5 biphosphate Carboxylation Reduction Triose phosphate CO2 CO2 sensing by rubisco ATP + Calvin cycle Violaxanthin Zeaxanthin Serine/threonine protein kinase npq1 C terminus H+-ATPase Inactive 14-3-3 Active phot1 phot2 CHLOROPLAST CYTOPLASM ?
Regeneration FIGURE 18.21 A sensory transduction cascade of blue light–stimulated stomatal opening.
shifts its carbon metabolism from C3 to CAM mode. In the C3 mode, stomata accumulate zeaxanthin and show a blue-light response. CAM induction inhibits the ability of guard cells to accumulate zeaxanthin, and to respond to blue light (Tallman et al. 1997).
The blue-light response of the Arabidopsis mutant npq1.
The Arabidopsis mutant npq1 (nonphotochemical quenching), has a genetic lesion in the enzyme that con-verts violaxanthin into zeaxanthin (see Figure 18.21) (Niyogi et al. 1998). Because of this mutation, neither mes-ophyll nor guard cell chloroplasts of npq1 accumulate zeax-anthin (Frechilla et al. 1999). Availability of this mutant made it possible to test the zeaxanthin hypothesis with guard cells in which zeaxanthin accumulation is genetically blocked.
Because photosynthesis in the guard cell chloroplast is stimulated by blue light (see Figure 18.10), an adequate test for the blue-light response of the zeaxanthin-less npq1 mutant requires an experimental design ensuring that any observed response to blue light is blue light specific and not mediated by photosynthesis. As discussed earlier in the chapter, action spectra provide a stringent test of specificity, but determination of action spectra is time-consuming and labor-intensive.
Another option is to test the enhancement of blue-light sensitivity by background red light, a specific characteris-tic of blue light–stimulated stomatal movements (Assmann 1988), discussed earlier. In experiments testing the enhance-ment of the blue-light response in npq1 by background red light, the zeaxanthin-less stomata showed baseline aper-tures in response to blue or red light, driven by guard cell photosynthesis, and failed to show any increases in the blue-light response.
The close relationship between incident solar radiation and zeaxanthin content in guard cells, and the role of zeax-anthin in blue-light photoreception suggest that the blue-light component of the stomatal response to light functions as a light sensor that couples stomatal apertures to incident photon fluxes at the leaf surface. The photosynthetic component, on the other hand, could function in the coupling of the stomatal responses with photosyn-thetic rates in the mesophyll (see Chapter 9).
The phot1/phot2 mutant lacks blue light–stimu-lated opening.
Stomata from the phot1/phot2 double mutant fail to exhibit a specific blue-light response, whereas in the single phot1 or phot2 mutant the blue-light response is only slightly affected (Kinoshita et al.
2001). These findings implicate phototropin in the blue-light response of stomata (Figure 18.21). It will be of great interest to determine whether phototropin is a second blue-light photoreceptor in guard cells or plays a regulatory role in later steps of the sensory transduction cascade.
SIGNAL TRANSDUCTION Sensory transduction cascades for the blue-light responses encompass the sequence of events linking the initial absorption of blue light by a chromophore and the final expression of a blue-light response, such as stomatal open-ing or phototropism. In this section we will discuss avail-able information on signal transduction cascades for cryp-tochromes, phototropin, and zeaxanthin.
Cryptochromes Accumulate in the Nucleus The sequence similarity of cry1 and cry2 to photolyase sug-gests that like photolyase, cryptochromes initiate their sen-sory transduction cascade by the reduction of a flavin chro-mophore by light, and a subsequent electron transfer reaction to an electron acceptor (see Figure 11.2). However, there is no experimental evidence for an involvement of cry1 or cry2 in redox reactions.
Recent studies have shown that cry2, and to a lesser extent cry1, accumulates in the nucleus. This suggests that both proteins might be involved in the regulation of gene expression. But some of the cryptochrome action in response to blue light seems to occur in the cytoplasm because one of the earliest detected defects in cry1 mutant seedlings is impaired activation of anion channels at the plasma membrane. In addition, cry1 and cry2 have been shown to interact with phytochrome A in vivo, and to be phosphorylated by phytochrome A in vitro (see Chapter 17 and Web Essay 18.3).
Phototropin Binds FMN As discussed earlier, the products of the phot1 and phot2 genes expressed in vitro bind FMN and undergo pho-tophosphorylation in response to blue light. Recent spectro-scopic studies have shown that the blue light–induced spec-tral changes of phototropin-bound FMN resemble those typical of the binding of FMN to a cysteine residue of pho-totropin (Figure 18.22; see also Web Essay 18.2) (Swartz et al. 2001). This reaction is reversed by a dark treatment. Blue-Light Responses: Stomatal Movements and Morphogenesis 417 R N Cys XH NH N O O S– N R N H Cys X– NH N O O S N Light Dark FIGURE 18.22 Proposed adduct formation of FMN and a cys-teine residue of phototropin protein upon blue-light irradiation.
XH and X– represent an unidentified, proton donor acceptor.
(After Briggs and Christie 2002.) These results suggest that blue irradiation of the protein-bound FMN in intact cells causes a conformational change of phototropin that triggers autophosphorylation and starts the sensory transduction cascade. The cellular events that follow the autophosphorylation remain unknown.
High-resolution analysis of the changes in growth rate mediating the inhibition of hypocotyl elongation by blue light has provided valuable information about the interac-tions among phototropin, cry1, cry2, and the phytochrome phyA (Parks et al. 2001). After a lag of 30 s, blue light–treated, wild-type Arabidopsis seedlings show a rapid decrease in elongation rates during the first 30 minutes, and then they grow very slowly for several days (Figure 18.23).
Analysis of the same response in phot1, cry1, cry2, and phyA mutants has shown that suppression of stem elonga-tion by blue light during seedling de-etiolation is initiated by phot1, with cry1, and to a limited extent cry2, modulat-ing the response after 30 minutes. The slow growth rate of stems in blue light–treated seedlings is primarily a result of the persistent action of cry1, and this is the reason that cry1 mutants of Arabidopsis show a long hypocotyl, com-pared to the short hypocotyl of the wild type. There is also a role for phytochrome A in at least the early stages of blue light–regulated growth because growth inhibition does not progress normally in phyA mutants.
Zeaxanthin Isomerization Might Start a Cascade Mediating Blue Light–Stimulated Stomatal Opening Several key steps in the sensory transduction cascade for blue light–stimulated stomatal opening have been charac-terized (see Figure 18.21). The C terminus of the H+-ATPase (see Figure 6.15) has an autoinhibitory domain that regu-lates the activity of the enzyme. If this autoinhibitory domain is experimentally removed by a protease, the H+-ATPase becomes irreversibly activated. The autoinhibitory domain of the C terminus is thought to lower the activity of the enzyme by blocking its catalytic site. Conversely, fus-iccocin appears to activate the enzyme by moving the autoinhibitory domain away from the catalytic site.
Upon blue-light irradiation, the H+-ATPase shows a lower Km for ATP and a higher Vmax (see Chapter 6), indi-cating that blue light activates the H+-ATPase. Activation of the enzyme involves the phosphorylation of serine and threonine residues of the C-terminal domain of the H+-ATPase (Kinoshita and Shimazaki 1999). Blue light–stimu-lated proton pumping and stomatal opening are prevented by inhibitors of protein kinases, which might block phos-phorylation of the H+-ATPase. As with fusiccocin, phos-phorylation of the C-terminal domain appears also to dis-place the autoinhibitory domain of the C-terminal from the catalytic site of the enzyme.
A 14-3-3 protein has been found to bind to the phos-phorylated C terminus of the guard cell H+-ATPase, but not the nonphosphorylated one. The family of 14-3-3 pro-teins was originally discovered in brain tissue, and its members were found to be ubiquitous regulatory proteins in eukaryotic organisms. In plants, 14-3-3 proteins regulate transcription by binding to activators in the nucleus, and they regulate metabolic enzymes such as nitrate reductase.
Only one of the four 14-3-3 isoforms found in guard cells binds to the H+-ATPase, so the binding appears to be specific (Emi et al. 2001). The same 14-3-3 isoform binds to the guard cell H+-ATPase in response to both fusiccocin and blue-light treatments. The 14-3-3 protein seems to dis-sociate from the H+-ATPase upon dephosphorylation of the C-terminal domain.
Proton-pumping rates of guard cells increase with flu-ence rates of blue light (see Figure 18.13), and the electro-chemical gradient generated by the proton pump drives ion uptake into the guard cells, increasing turgor and tur-gor-mediated stomatal apertures. Taken together, these steps define the major sensory transducing steps linking the activation of a serine/threonine protein kinase by blue light and blue light–stimulated stomatal opening (see Fig-ure 18.21).
The zeaxanthin hypothesis postulates that excitation of zeaxanthin in the antenna bed of the guard cell chloroplast by blue light starts the sensory transduction cascade that activates the serine/threonine kinase in the cytosol. Iso-merization is the predominant photochemical reaction of 418 Chapter 18 1 0 2 3 4 5 0.2 0.4 0.6 0.8 1.0 Time (h) phot1 cry1/cry2/phyA (via anion channels) Relative growth rate Blue light on FIGURE 18.23 Sensory transduction cascade of blue light–stimulated inhibition of stem elongation in Arabidopsis. Elongation rates in the dark (0.25 mm h–1) were normalized to 1. Within 30 s of the onset of blue-light irra-diation, growth rates decreased and approached zero within 30 minutes, then continued at very reduced rates for several days. If blue light is applied to a phot1 mutant, dark-growth rates remain unchanged for the first 30 min-utes, indicating that the inhibition of elongation in the first 30 minutes is under phototropin control. Similar experi-ments with cry1, cry2, and phyA mutants indicate that the respective gene products control elongation rates at later times. (After Parks et al. 2001.) carotenoids, so blue light would isomerize zeaxanthin and the conformational change would start the transducing cas-cade.
The reversal of blue light–stimulated opening by green light.
A reversal of blue light–stimulated stomatal open-ing by green light has been recently discovered. Stomata in epidermal strips open in response to a 30 s blue-light pulse (Figure 18.24), but the opening is not observed if the blue-light pulse is followed by a green-light pulse. The opening is restored if the green pulse is followed by a second blue-light pulse, in a response analogous to the red/far-red reversibility of phytochrome responses. (Frechilla et al.
2000.) The blue/green reversibility response has been reported in stomata of several species, and in blue light–stimulated, coleoptile phototropism (see Web Essay 18.4). The role of the blue/green reversal of stomatal movements under nat-ural conditions remains to be established, but it could be related to the sensing of environmental conditions such as sun and shade.
The action spectrum for the green reversal of blue light–stimulated opening shows a maximum at 540 nm, and two minor peaks at 490 and 580 nm. Such an action spectrum rules out the involvement of phytochrome or chlorophylls in the response. Rather, the action spectrum is remarkably similar to the action spectrum for blue light–stimulated stomatal opening (see Figure 18.11), but red-shifted (displaced toward the longer, red wave band of the spectrum) by about 90 nm.
Such spectral red shifts have been observed upon the isomerization of carotenoids in a protein environment (see Web Essay 18.4). In reconstituted vesicles containing chlorophyll a/b–binding protein and the xanthophylls zeax-anthin, violaxanthin, and neoxanthin, blue/green reversible absorption spectrum changes have been associ-ated with zeaxanthin isomerization.
The blue/green reversal of stomatal movements and the absorption spectrum changes elicited by blue and green light suggest that a physiologically inactive, trans isomer of zeaxanthin is converted to a cis isomer by blue light, and that the isomerization starts the sensory transduction cas-cade. Available data suggest that green light converts the cis isomer into the physiologically inactive trans form, and therefore reverses the blue light–stimulated opening signal.
Results from a previous study further indicate that after a blue pulse, the cis form slowly reverts to the trans form in the dark (Iino et al. 1985).
The Xanthophyll Cycle Confers Plasticity to the Stomatal Responses to Light Zeaxanthin concentration in guard cells varies with the activity of the xanthophyll cycle. The enzyme that con-verts violaxanthin to zeaxanthin is an integral thylakoid protein showing a pH optimum at pH 5.2 (Yamamoto 1979). Acidification of lumen pH stimulates zeaxanthin formation, and lumen alkalinization favors violaxanthin formation.
Lumen pH depends on levels of incident photosynthetic active radiation (most effective at blue and red wave-lengths; see Chapter 7), and on the rate of ATP synthesis, that dissipates the pH gradient across the thylakoid. Thus, photosynthetic activity in the guard cell chloroplast, lumen pH, zeaxanthin content, blue-light sensitivity, and stomatal apertures are tightly coupled.
Some unique properties of the guard cell chloroplast appear optimally geared for its sensory transducing func-tion. Compared with their mesophyll counterparts, guard cell chloroplasts are enriched in photosystem II, and they have unusually high rates of photosynthetic electron trans-port and low rates of photosynthetic carbon fixation (Zeiger et al. 2002). These properties favor lumen acidifi-cation at low photon fluxes, and they explain zeaxanthin formation in the guard cell chloroplast early in the day (see Figure 18.18).
The regulation of zeaxanthin content by lumen pH, and the tight coupling between lumen pH and Calvin cycle activity in the guard cell chloroplast (see Figure 18.21) fur-ther suggest that zeaxanthin can also operate as a CO2 sen-sor in guard cells (see Web Essay 18.5).
The remarkable progress achieved by the recent discov-eries in the molecular biology of blue-light responses has Blue-Light Responses: Stomatal Movements and Morphogenesis 419 -10 0 10 20 30 40 Time (min) Stomatal opening Blue Blue-green Blue-green-blue Light pulse: FIGURE 18.24 Blue/green reversibility of stomatal move-ments. Stomata open when given a 30 s blue-light pulse (1800 mmol m–2 s–1) under a background of continuous red light (120 mmol m–2 s–1). A green-light pulse (3600 mmol m–2 s–1) applied after the blue-light pulse blocks the blue-light response, and the opening is restored upon applica-tion of a second blue-light pulse given after the green-light pulse. (After Frechilla et al. 2000.) dramatically increased our understanding of the subject.
The identification of cryptochromes, phototropin, and zeaxanthin as putative blue-light photoreceptors in plant cells has stimulated great interest in this aspect of plant photobiology. Current and future work is addressing important open questions, such as the detailed sequence of the sensory transduction cascades and the precise local-ization and composition of the pigment proteins involved.
Ongoing research on the subject virtually ensures rapid fur-ther progress.
SUMMARY Plants utilize light as a source of energy and as a signal that provides information about their environment. A large family of blue-light responses is used to sense light quan-tity and direction. These blue-light signals are transduced into electrical, metabolic, and genetic processes that allow plants to alter growth, development, and function in order to acclimate to changing environmental conditions. Blue-light responses include phototropism, stomatal move-ments, inhibition of stem elongation, gene activation, pig-ment biosynthesis, tracking of the sun by leaves, and chloroplast movements within cells.
Specific blue-light responses can be distinguished from other responses that have some sensitivity to blue light by a characteristic “three-finger” action spectrum in the 400 to 500 nm region.
The physiology of blue-light responses varies broadly.
In phototropism, stems grow toward unilateral light sources by asymmetric growth on their shaded side. In the inhibition of stem elongation, perception of blue light depolarizes the membrane potential of elongating cells, and the rate of elongation rapidly decreases. In gene acti-vation, blue light stimulates transcription and translation, leading to the accumulation of gene products that are required for the morphogenetic response to light.
Blue light–stimulated stomatal movements are driven by blue light–dependent changes in the osmoregulation of guard cells. Blue light stimulates an H+-ATPase at the guard cell plasma membrane, and the resulting pumping of protons across the membrane generates an electro-chemical-potential gradient that provides a driving force for ion uptake. Blue light also stimulates starch degrada-tion and malate biosynthesis. Solute accumulation within the guard cells leads to stomatal opening. Guard cells also utilize sucrose as a major osmotically active solute, and light quality can change the activity of different osmoreg-ulatory pathways that modulate stomatal movements.
Cry1 and cry2 are two Arabidopsis genes involved in blue light–dependent inhibition of stem elongation, cotyledon expansion, anthocyanin synthesis, the control of flowering, and the setting of circadian rhythms. It has been proposed that CRY1 and CRY2 are apoproteins of flavin-containing pigment proteins that mediate blue-light photoreception.
The cry1 and cry2 gene products have sequence simi-larity to photolyase but no photolyase activity. The cry1 protein, and to a lesser extent cry2, accumulates in the nucleus and might be involved in gene expression. The cry1 protein also regulates anion channel activity at the plasma membrane.
The protein phototropin has a major role in the regulation of phototropism. The C-terminal half of phototropin is a ser-ine/threonine kinase, and the N-terminal half has two flavin-binding domains. In vitro, phototropin binds the flavin FMN and autophosphorylates in response to blue light. Mutants called phot1 and phot2 are defective in phototropism and in chloroplast movements. The phot1/phot2 double mutant lacks blue light–stimulated stomatal opening.
The chloroplastic carotenoid zeaxanthin has been impli-cated in blue-light photoreception in guard cells. Blue light–stimulated stomatal opening is blocked if zeaxanthin accumulation in guard cells is prevented by genetic or bio-chemical means. Manipulation of zeaxanthin content in guard cells makes it possible to regulate their response to blue light. The signal transduction cascade for the blue-light response of guard cells comprises blue-light percep-tion in the guard cell chloroplast, transduction of the blue-light signal across the chloroplast envelope, activation of the H+-ATPase, turgor buildup, and stomatal opening.
Web Material Web Topics 18.1 Guard Cell Osmoregulation and a Blue Light–Activated Metabolic Switch Blue light controls major osmoregulatory path-ways in guard cells and unicellular algae.
18.2 Historical Notes on the Research of Blue-Light Photoreceptors Carotenoids and flavins have been the main candidates for blue-light photoreceptors.
18.3 Comparing Flavins and Carotenoids Flavin and carotenoid photoreceptors have contrasting functional properties.
18.4 The Coleoptile Chloroplast Both the coleoptile and the guard cell chloro-plasts specialize in sensory transduction.
Web Essays 18.1 Guard Cell Photosynthesis Photosynthesis in the guard cell chloroplast shows unique regulatory features.
18.2 Phototropins Phototropins regulate several light responses in plants.
420 Chapter 18 18.3 The Sensory Transduction of the Inhibition of Stem Elongation by Blue Light The regulation of stem elongation rates by blue light has critical importance for plant develop-ment.
18.4 The Blue/Green Reversibility of the Blue-Light Response of Stomata The blue/green reversal of stomatal move-ments is a remarkable photobiological re-sponse.
18.5 Zeaxanthin and CO2 Sensing in Guard Cells The functional relationship between Calvin cycle activity and zeaxanthin content of guard cells couples blue light and CO2 sensing during stomatal movements.
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Auxin:The Growth Hormone 19 Chapter THE FORM AND FUNCTION of multicellular organism would not be possible without efficient communication among cells, tissues, and organs. In higher plants, regulation and coordination of metabolism, growth, and morphogenesis often depend on chemical signals from one part of the plant to another. This idea originated in the nineteenth cen-tury with the German botanist Julius von Sachs (1832–1897).
Sachs proposed that chemical messengers are responsible for the for-mation and growth of different plant organs. He also suggested that external factors such as gravity could affect the distribution of these sub-stances within a plant. Although Sachs did not know the identity of these chemical messengers, his ideas led to their eventual discovery.
Many of our current concepts about intercellular communication in plants have been derived from similar studies in animals. In animals the chemical messengers that mediate intercellular communication are called hormones. Hormones interact with specific cellular proteins called receptors.
Most animal hormones are synthesized and secreted in one part of the body and are transferred to specific target sites in another part of the body via the bloodstream. Animal hormones fall into four general cate-gories: proteins, small peptides, amino acid derivatives, and steroids.
Plants also produce signaling molecules, called hormones, that have profound effects on development at vanishingly low concentrations.
Until quite recently, plant development was thought to be regulated by only five types of hormones: auxins, gibberellins, cytokinins, ethylene, and abscisic acid. However, there is now compelling evidence for the existence of plant steroid hormones, the brassinosteroids, that have a wide range of morphological effects on plant development. (Brassino-steroids as plant hormones are discussed in Web Essay 19.1.) A variety of other signaling molecules that play roles in resistance to pathogens and defense against herbivores have also been identified, including jasmonic acid, salicylic acid, and the polypeptide systemin (see Chapter 13). Thus the number and types of hormones and hormonelike signaling agents in plants keep expanding.
The first plant hormone we will consider is auxin. Auxin deserves pride of place in any discussion of plant hor-mones because it was the first growth hormone to be dis-covered in plants, and much of the early physiological work on the mechanism of plant cell expansion was carried out in relation to auxin action.
Moreover, both auxin and cytokinin differ from the other plant hormones and signaling agents in one impor-tant respect: They are required for viability. Thus far, no mutants lacking either auxin or cytokinin have been found, suggesting that mutations that eliminate them are lethal.
Whereas the other plant hormones seem to act as on/off switches that regulate specific developmental processes, auxin and cytokinin appear to be required at some level more or less continuously.
We begin our discussion of auxins with a brief history of their discovery, followed by a description of their chem-ical structures and the methods used to detect auxins in plant tissues. A look at the pathways of auxin biosynthesis and the polar nature of auxin transport follows. We will then review the various developmental processes con-trolled by auxin, such as stem elongation, apical domi-nance, root initiation, fruit development, and oriented, or tropic, growth. Finally, we will examine what is currently known about the mechanism of auxin-induced growth at the cellular and molecular levels.
THE EMERGENCE OF THE AUXIN CONCEPT During the latter part of the nineteenth century, Charles Darwin and his son Francis studied plant growth phe-nomena involving tropisms. One of their interests was the bending of plants toward light. This phenomenon, which is caused by differential growth, is called phototropism. In some experiments the Darwins used seedlings of canary grass (Phalaris canariensis), in which, as in many other grasses, the youngest leaves are sheathed in a protective organ called the coleoptile (Figure 19.1).
Coleoptiles are very sensitive to light, especially to blue light (see Chapter 18). If illuminated on one side with a short pulse of dim blue light, they will bend (grow) toward the source of the light pulse within an hour. The Darwins found that the tip of the coleoptile perceived the light, for if they covered the tip with foil, the coleoptile would not bend. But the region of the coleoptile that is responsible for the bending toward the light, called the growth zone, is several millimeters below the tip. Thus they concluded that some sort of signal is pro-duced in the tip, travels to the growth zone, and causes the shaded side to grow faster than the illuminated side. The results of their experiments were published in 1881 in a remarkable book entitled The Power of Movement in Plants.
There followed a long period of experimentation by many investigators on the nature of the growth stimulus in coleoptiles. This research culminated in the demonstration in 1926 by Frits Went of the presence of a growth-promot-ing chemical in the tip of oat (Avena sativa) coleoptiles. It was known that if the tip of a coleoptile was removed, coleoptile growth ceased. Previous workers had attempted to isolate and identify the growth-promoting chemical by grinding up coleoptile tips and testing the activity of the extracts. This approach failed because grinding up the tis-sue released into the extract inhibitory substances that nor-mally were compartmentalized in the cell.
Went’s major breakthrough was to avoid grinding by allowing the material to diffuse out of excised coleoptile tips directly into gelatin blocks. If placed asymmetrically on top of a decapitated coleoptile, these blocks could be tested for their ability to cause bending in the absence of a unilateral light source (see Figure 19.1). Because the sub-stance promoted the elongation of the coleoptile sections (Figure 19.2), it was eventually named auxin from the Greek auxein, meaning “to increase” or “to grow.” BIOSYNTHESIS AND METABOLISM OF AUXIN Went’s studies with agar blocks demonstrated unequivo-cally that the growth-promoting “influence” diffusing from the coleoptile tip was a chemical substance. The fact that it was produced at one location and transported in minute amounts to its site of action qualified it as an authentic plant hormone.
In the years that followed, the chemical identity of the “growth substance” was determined, and because of its potential agricultural uses, many related chemical analogs were tested. This testing led to generalizations about the chemical requirements for auxin activity. In parallel with these studies, the agar block diffusion technique was being applied to the problem of auxin transport. Technological advances, especially the use of isotopes as tracers, enabled plant biochemists to unravel the pathways of auxin biosyn-thesis and breakdown.
Our discussion begins with the chemical nature of auxin and continues with a description of its biosynthesis, trans-port, and metabolism. Increasingly powerful analytical methods and the application of molecular biological approaches have recently allowed scientists to identify auxin precursors and to study auxin turnover and distri-bution within the plant.
The Principal Auxin in Higher Plants Is Indole-3-Acetic Acid In the mid-1930s it was determined that auxin is indole-3-acetic acid (IAA). Several other auxins in higher plants were discovered later (Figure 19.3), but IAA is by far the most abundant and physiologically relevant. Because the structure of IAA is relatively simple, academic and indus-trial laboratories were quickly able to synthesize a wide 424 Chapter 19 Auxin: The Growth Hormone 425 FIGURE 19.1 Summary of early experiments in auxin research.
Intact seedling (curvature) Tip of coleoptile excised (no curvature) Opaque cap on tip (no curvature) 45° Darwin (1880) Light 4-day-old oat seedling Coleoptile Seed 1 cm Roots Boysen-Jensen (1913) Went (1926) Mica sheet inserted on dark side (no curvature) Mica sheet inserted on light side (curvature) Tip removed Gelatin between tip and coleoptile stump Normal phototropic curvature remains possible Tip removed Tip replaced on one side of coleoptile stump Growth curvature develops without a unilateral light stimulus Coleoptile tips on gelatin Tips discarded; gelatin cut up into smaller blocks Coleoptile bends in total darkness; angle of curvature can be measured Each gelatin block placed on one side of coleoptile stump IAA in gelatin block (mg/L) Curvature (degrees) 20 15 10 5 0.05 0.10 0.15 0.20 0.25 0.30 Number of coleoptile tips on gelatin Curvature (degrees) 20 15 10 5 0 2 4 6 8 10 Paál (1919) From experiments on coleoptile phototropism, Darwin concluded in 1880 that a growth stimulus is produced in the coleoptile tip and is transmitted to the growth zone.
In 1913, P. Boysen-Jensen discovered that the growth stimulus passes through gelatin but not through water-impermeable barriers such as mica.
In 1926, F. W. Went showed that the active growth-promoting substance can diffuse into a gelatin block. He also devised a coleoptile-bending assay for quantitative auxin analysis.
In 1919, A. Paál provided evidence that the growth-promoting stimulus produced in the tip was chemical in nature.
array of molecules with auxin activity. Some of these are used as herbicides in horticulture and agriculture (Figure 19.4) (for additional synthetic auxins, see Web Topic 19.1).
An early definition of auxins included all natural and synthetic chemical substances that stimulate elongation in coleoptiles and stem sections. However, auxins affect many developmental processes besides cell elongation. Thus aux-ins can be defined as compounds with biological activities similar to those of IAA, including the ability to promote cell elongation in coleoptile and stem sections, cell division in callus cultures in the presence of cytokinins, formation of adventitious roots on detached leaves and stems, and other developmental phenomena associated with IAA action.
Although they are chemically diverse, a common feature of all active auxins is a molecular distance of about 0.5 nm between a fractional positive charge on the aromatic ring and a negatively charged carboxyl group (see Web Topic 19.2).
Auxins in Biological Samples Can Be Quantified Depending on the information that a researcher needs, the amounts and/or identity of auxins in biological samples can be determined by bioassay, mass spectrometry, or enzyme-linked immunosorbent assay, which is abbreviated as ELISA (see Web Topic 19.3).
A bioassay is a measurement of the effect of a known or suspected biologically active substance on living material. In his pioneering work more than 60 years ago, Went used Avena sativa (oat) coleoptiles in a technique called the Avena coleoptile curvature test (see Figure 19.1). The coleoptile curved because the increase in auxin on one side stimulated cell elongation, and the decrease in auxin on the other side (due to the absence of the coleoptile tip) caused a decrease in the growth rate—a phenomenon called differential growth.
Went found that he could estimate the amount of auxin in a sample by measuring the resulting coleoptile curva-(A) (B) FIGURE 19.2 Auxin stimulates the elongation of oat coleoptile sections. These coleoptile sections were incubated for 18 hours in either water (A) or auxin (B). The yellow tissue inside the translucent coleoptile is the primary leaves. (Photos © M. B. Wilkins.) CH2 N H Cl COOH CH2 COOH N H CH2 CH2 CH2 COOH N H Indole-3-acetic acid (IAA) 4-Chloroindole-3-acetic acid (4-CI-IAA) Indole-3-butyric acid (IBA) FIGURE 19.3 Structure of three natural auxins. Indole-3-acetic acid (IAA) occurs in all plants, but other related compounds in plants have auxin activity. Peas, for example, contain 4-chloroindole-3-acetic acid. Mustards and corn contain indole-3-butyric acid (IBA).
426 Chapter 19 ture. Auxin bioassays are still used today to detect the pres-ence of auxin activity in a sample. The Avena coleoptile cur-vature assay is a sensitive measure of auxin activity (it is effective for IAA concentrations of about 0.02 to 0.2 mg L–1). Another bioassay measures auxin-induced changes in the straight growth of Avena coleoptiles floating in solution (see Figure 19.2). Both of these bioassays can establish the presence of an auxin in a sample, but they cannot be used for precise quantification or identification of the specific compound.
Mass spectrometry is the method of choice when infor-mation about both the chemical structure and the amount of IAA is needed. This method is used in conjunction with separation protocols involving gas chromatography. It allows the precise quantification and identification of aux-ins, and can detect as little as 10–12 g (1 picogram, or pg) of IAA, which is well within the range of auxin found in a sin-gle pea stem section or a corn kernel. These sophisticated techniques have enabled researchers to accurately analyze auxin precursors, auxin turnover, and auxin distribution within the plant.
IAA Is Synthesized in Meristems,Young Leaves, and Developing Fruits and Seeds IAA biosynthesis is associated with rapidly dividing and rapidly growing tissues, especially in shoots. Although vir-tually all plant tissues appear to be capable of producing low levels of IAA, shoot apical meristems, young leaves, and developing fruits and seeds are the primary sites of IAA synthesis (Ljung et al. in press).
In very young leaf primordia of Arabidopsis, auxin is synthesized at the tip. During leaf development there is a gradual shift in the site of auxin production basipetally along the margins, and later, in the central region of the lamina. The basipetal shift in auxin production correlates closely with, and is probably causally related to, the basipetal maturation sequence of leaf development and vascular differentiation (Aloni 2001).
By fusing the GUS (β-glucuronidase) reporter gene to a promoter containing an auxin response element, and transforming Arabidopsis leaves with this construct in a Ti plasmid using Agrobacterium, it is possible to visualize the distribution of free auxin in young, developing leaves.
Wherever free auxin is produced, GUS expression occurs— and can be detected histochemically. By use of this tech-nique, it has recently been demonstrated that auxin is produced by a cluster of cells located at sites where hyda-thodes will develop (Figure 19.5).
Hydathodes are glandlike modifications of the ground and vascular tissues, typically at the margins of leaves, that allow the release of liquid water (guttation fluid) through pores in the epidermis in the presence of root pressure (see Chapter 4). As shown in Figure 19.5, during early stages of hydathode differentiation a center of high auxin synthesis is evident as a concentrated dark blue GUS stain (arrow) in the lobes of serrated leaves of Arabidopsis (Aloni et al. 2002).
A diffuse trail of GUS activity leads down to differentiat-ing vessel elements in a developing vascular strand. This remarkable micrograph captures the process of auxin-reg-ulated vascular differentiation in the very act!
We will return to the topic of the control of vascular dif-ferentiation later in the chapter.
Cl O OCH3 Cl Cl COOH Cl CH2 COOH 2-Methoxy-3, 6-dichlorobenzoic acid (dicamba) 2,4-Dichlorophenoxyacetic acid (2,4-D) FIGURE 19.4 Structures of two synthetic auxins. Most syn-thetic auxins are used as herbicides in horticulture and agriculture.
FIGURE 19.5 Detection of sites of auxin synthesis and trans-port in a young leaf primordium of DR5 Arabidopsis by means of a GUS reporter gene with an auxin-sensitive pro-moter. During the early stages of hydathode differentiation, a center of auxin synthesis is evident as a concentrated dark blue GUS stain (arrow) in the lobes of the serrated leaf mar-gin. A gradient of diluted GUS activity extends from the margin toward a differentiating vascular strand (arrow-head), which functions as a sink for the auxin flow originat-ing in the lobe. (Courtesy of R. Aloni and C. I. Ullrich.) Auxin: The Growth Hormone 427 Multiple Pathways Exist for the Biosynthesis of IAA IAA is structurally related to the amino acid tryptophan, and early studies on auxin biosynthesis focused on trypto-phan as the probable precursor. However, the incorpora-tion of exogenous labeled tryptophan (e.g., [3H]trypto-phan) into IAA by plant tissues has proved difficult to demonstrate. Nevertheless, an enormous body of evidence has now accumulated showing that plants convert trypto-phan to IAA by several pathways, which are described in the paragraphs that follow.
The IPA pathway. The indole-3-pyruvic acid (IPA) path-way (see Figure 19.6C), is probably the most common of the tryptophan-dependent pathways. It involves a deam-ination reaction to form IPA, followed by a decarboxylation reaction to form indole-3-acetaldehyde (IAld). Indole-3-acetaldehyde is then oxidized to IAA by a specific dehy-drogenase.
The TAM pathway. The tryptamine (TAM) pathway (see Figure 19.6D) is similar to the IPA pathway, except that the order of the deamination and decarboxylation reactions is reversed, and different enzymes are involved. Species that do not utilize the IPA pathway possess the TAM pathway.
In at least one case (tomato), there is evidence for both the IPA and the TAM pathways (Nonhebel et al. 1993).
The IAN pathway. In the indole-3-acetonitrile (IAN) pathway (see Figure 19.6B), tryptophan is first converted to indole-3-acetaldoxime and then to indole-3-acetonitrile.
The enzyme that converts IAN to IAA is called nitrilase.
The IAN pathway may be important in only three plant families: the Brassicaceae (mustard family), Poaceae (grass NH2 N H COOH N H COOH COOH N H N O N H NOH N H O N H N H NH2 NH2 O N H Tryptophan (Trp) Indole-3-pyruvic acid pathway Indole-3-acetic acid (IAA) Indole-3-acetaldehyde (IAld) Indole-3-pyruvic acid (IPA) Indole-3-acetaldoxime IAN TAM Bacterial pathway Indole-3-acetonitrile (IAN) Tryptamine (TAM) Indole-3-acetamide (IAM) Trp transaminase Trp monooxygenase IAM hydrolase IAld dehydrogenase Nitrilase Trp decarboxylase Amine oxidase IPA decarboxylase (A) (B) (C) (D) FIGURE 19.6 Tryptophan-dependent pathways of IAA biosynthesis in plants and bacteria. The enzymes that are present only in bacteria are marked with an asterisk.
(After Bartel 1997.) 428 Chapter 19 family), and Musaceae (banana family). Nevertheless, nitri-lase-like genes or activities have recently been identified in the Cucurbitaceae (squash family), Solanaceae (tobacco family), Fabaceae (legumes), and Rosaceae (rose family). Four genes (NIT1 through NIT4) that encode nitrilase enzymes have now been cloned from Arabidopsis. When NIT2 was expressed in transgenic tobacco, the resultant plants acquired the ability to respond to IAN as an auxin by hydrolyzing it to IAA (Schmidt et al. 1996).
Another tryptophan-dependent biosynthetic pathway— one that uses indole-3-acetamide (IAM) as an intermedi-ate (see Figure19.6A)—is used by various pathogenic bac-teria, such as Pseudomonas savastanoi and Agrobacterium tumefaciens. This pathway involves the two enzymes tryp-tophan monooxygenase and IAM hydrolase. The auxins produced by these bacteria often elicit morphological changes in their plant hosts.
In addition to the tryptophan-dependent pathways, recent genetic studies have provided evidence that plants can synthesize IAA via one or more tryptophan-indepen-dent pathways. The existence of multiple pathways for IAA biosynthesis makes it nearly impossible for plants to run out of auxin and is probably a reflection of the essen-tial role of this hormone in plant development.
IAA Is Also Synthesized from Indole or from Indole-3-Glycerol Phosphate Although a tryptophan-independent pathway of IAA biosynthesis had long been suspected because of the low levels of conversion of radiolabeled tryptophan to IAA, not until genetic approaches were available could the existence of such pathways be confirmed and defined. Perhaps the most striking of these studies in maize involves the orange pericarp (orp) mutant (Figure 19.7), in which both subunits of the enzyme tryptophan synthase are inactive (Figure 19.8). The orp mutant is a true tryptophan auxotroph, requiring exogenous tryptophan to survive. However, nei-ther the orp seedlings nor the wild-type seedlings can con-vert tryptophan to IAA, even when the mutant seedlings are given enough tryptophan to reverse the lethal effects of the mutation.
Despite the block in tryptophan biosynthesis, the orp mutant contains amounts of IAA 50-fold higher than those of a wild-type plant (Wright et al. 1991). Signficantly, when orp seedlings were fed [15N]anthranilate (see Figure 19.8), the label subsequently appeared in IAA, but not in trypto-phan. These results provided the best experimental evi-dence for a tryptophan-independent pathway of IAA biosynthesis. Further studies established that the branch point for IAA biosynthesis is either indole or its precursor, indole-3-glycerol phosphate (see Figure 19.8). IAN and IPA are pos-sible intermediates, but the immediate precursor of IAA in the tryptophan-independent pathway has not yet been identified.
The discovery of the tryptophan-independent pathway has drastically altered our view of IAA biosynthesis, but the relative importance of the two pathways (tryptophan-dependent versus tryptophan-independent) is poorly understood. In several plants it has been found that the type of IAA biosynthesis pathway varies between different tissues, and between different times of development. For example, during embryogenesis in carrot, the tryptophan-dependent pathway is important very early in develop-ment, whereas the tryptophan-independent pathway takes over soon after the root–shoot axis is established. (For more evidence of the tryptophan-independent biosynthesis of IAA, see Web Topic 19.4.) Most IAA in the Plant Is in a Covalently Bound Form Although free IAA is the biologically active form of the hormone, the vast majority of auxin in plants is found in a covalently bound state. These conjugated, or “bound,” aux-ins have been identified in all higher plants and are con-sidered hormonally inactive.
IAA has been found to be conjugated to both high- and low-molecular-weight compounds.
• Low-molecular-weight conjugated auxins include esters of IAA with glucose or myo-inositol and amide conjugates such as IAA-N-aspartate (Figure 19.9).
• High-molecular-weight IAA conjugates include IAA-glucan (7–50 glucose units per IAA) and IAA-glyco-proteins found in cereal seeds.
The compound to which IAA is conjugated and the extent of the conjugation depend on the specific conjugating enzymes. The best-studied reaction is the conjugation of IAA to glucose in Zea mays.
The highest concentrations of free auxin in the living plant are in the apical meristems of shoots and in young leaves because these are the primary sites of auxin synthe-FIGURE 19.7 The orange pericarp (orp) mutant of maize is missing both subunits of tryptophan synthase. As a result, the pericarps surrounding each kernel accumulate glyco-sides of anthranilic acid and indole. The orange color is due to excess indole. (Courtesy of Jerry D. Cohen.) Auxin: The Growth Hormone 429 sis. However, auxins are widely distributed in the plant.
Metabolism of conjugated auxin may be a major con-tributing factor in the regulation of the levels of free auxin.
For example, during the germination of seeds of Zea mays, IAA-myo-inositol is translocated from the endosperm to the coleoptile via the phloem. At least a portion of the free IAA produced in coleoptile tips of Zea mays is believed to be derived from the hydrolysis of IAA-myo-inositol.
In addition, environmental stimuli such as light and gravity have been shown to influence both the rate of auxin conjugation (removal of free auxin) and the rate of release of free auxin (hydrolysis of conjugated auxin). The forma-tion of conjugated auxins may serve other functions as well, including storage and protection against oxidative degradation.
IAA Is Degraded by Multiple Pathways Like IAA biosynthesis, the enzymatic breakdown (oxida-tion) of IAA may involve more than one pathway. For some time it has been thought that peroxidative enzymes are chiefly responsible for IAA oxidation, primarily because these enzymes are ubiquitous in higher plants and their ability to degrade IAA can be demonstrated in vitro (Figure 19.10A). However, the physiological significance of the peroxidase pathway is unclear. For example, no change in the IAA levels of transgenic plants was observed with either a tenfold increase in peroxidase expression or a ten-fold repression of peroxidase activity (Normanly et al.
1995).
On the basis of isotopic labeling and metabolite identi-fication, two other oxidative pathways are more likely to be involved in the controlled degradation of IAA (see Fig-ure 19.10B). The end product of this pathway is oxindole-3-acetic acid (OxIAA), a naturally occurring compound in the endosperm and shoot tissues of Zea mays. In one path-way, IAA is oxidized without decarboxylation to OxIAA.
N H OH CH2OP OH N H N N H O COOH N H COOH N H NH2 COOH N H Chorismate Anthranilate synthase Anthranilate Anthranilate PR-transferase 5-Phosphoribosylanthranilate Feedback inhibition PR-anthranilate isomerase IGP synthase Trp synthase a (trp3) Trp synthase b (trp2, orp) Trypotophan aminotransferase (hypothetical) Serine + 1-(o-Carboxyphenylamino)-1-deoxyribulose 5-P Indole-3-glycerol phosphate (IGP) Indole Trp ?
Indole-3-acetonitrile (IAN) Indole-3-pyruvic acid (IPA) Nitrilase (nit1) TRYPTOPHAN-INDEPENDENT PATHWAYS OF IAA SYNTHESIS TRYPTOPHAN BIOSYNTHETIC PATHWAY IAA FIGURE 19.8 Tryptophan-independent pathways of IAA biosynthesis in plants. The tryptophan (Trp) biosynthetic pathway is shown on the left.
Mutants discussed in Web Topic 19.4 are indicated in parentheses. The branch-point precursor for tryptophan-independent biosynthesis is uncertain (indole-3-glycerol phosphate or indole), and IAN and IPA are two possible intermediates. PR, phosphoribosyl. (After Bartel 1997.) 430 Chapter 19 In another pathway, the IAA-aspartate conjugate is oxi-dized first to the intermediate dioxindole-3-acetylaspartate, and then to OxIAA.
In vitro, IAA can be oxidized nonenzymatically when exposed to high-intensity light, and its photodestruction in vitro can be promoted by plant pigments such as riboflavin. Although the products of auxin photooxidation have been isolated from plants, the role, if any, of the pho-tooxidation pathway in vivo is presumed to be minor.
Two Subcellular Pools of IAA Exist:The Cytosol and the Chloroplasts The distribution of IAA in the cell appears to be regulated largely by pH. Because IAA−does not cross membranes unaided, whereas IAAH readily diffuses across membranes, O O O CH2COOH CH2 CH2 C CH2 C C H COOH CH2 COOH N H O C O H H H HO OH OH H CH2OH H O H OH H OH H OH H H OH HO H N H N H N H N H Indole-3-acetic acid Indoleacetyl-β-D-glucose Indoleacetyl-2-O-myo-inositol Indoleacetylaspartate Aspartate UDP-glucose myo-Inositol FIGURE 19.9 Structures and proposed metabolic pathways of bound auxins. The diagram shows structures of various IAA conjugates and proposed metabolic pathways involved in their synthesis and break-down. Single arrows indicate irreversible pathways; double arrows, reversible. O B Aspartate O COOH CH2 O O COOH N H N H O Aspartate N H N H N H A Oxindole-3-acetic acid (OxIAA) Indole-3-acetylaspartate Dioxindole-3-acetylaspartate Conjugation (A) Decarboxylation: A minor pathway (B) Nondecarboxylation pathways 3-Methyleneoxindole Indole-3-acetic acid Peroxidase CO2 FIGURE 19.10 Biodegradation of IAA. (A) The peroxidase route (decarboxylation pathway) plays a relatively minor role. (B) The two nondecarboxylation routes of IAA oxida-tive degradation, A and B, are the most common metabolic pathways. Auxin: The Growth Hormone 431 auxin tends to accumulate in the more alka-line compartments of the cell.
The distribution of IAA and its metabo-lites has been studied in tobacco cells. About one-third of the IAA is found in the chloro-plast, and the remainder is located in the cytosol. IAA conjugates are located exclu-sively in the cytosol. IAA in the cytosol is metabolized either by conjugation or by non-decarboxylative catabolism (see Figure 19.10).
The IAA in the chloroplast is protected from these processes, but it is regulated by the amount of IAA in the cytosol, with which it is in equilibrium (Sitbon et al. 1993).
The factors that regulate the steady-state concentration of free auxin in plant cells are diagrammatically summarized in Web Topic 19.5.
AUXIN TRANSPORT The main axes of shoots and roots, along with their branches, exhibit apex–base structural polarity, and this structural polarity has its origin in the polarity of auxin transport. Soon after Went developed the coleoptile curva-ture test for auxin, it was discovered that IAA moves mainly from the apical to the basal end (basipetally) in excised oat coleoptile sections. This type of unidirectional transport is termed polar transport. Auxin is the only plant growth hormone known to be transported polarly.
Because the shoot apex serves as the primary source of auxin for the entire plant, polar transport has long been believed to be the principal cause of an auxin gradient extending from the shoot tip to the root tip. The longitudi-nal gradient of auxin from the shoot to the root affects var-ious developmental processes, including stem elongation, apical dominance, wound healing, and leaf senescence.
Recently it has been recognized that a significant amount of auxin transport also occurs in the phloem, and that the phloem is probably the principal route by which auxin is transported acropetally (i.e., toward the tip) in the root. Thus, more than one pathway is responsible for the distribution of auxin in the plant Polar Transport Requires Energy and Is Gravity Independent To study polar transport, researchers have employed the donor–receiver agar block method (Figure 19.11): An agar block containing radioisotope-labeled auxin (donor block) is placed on one end of a tissue segment, and a receiver block is placed on the other end. The movement of auxin through the tissue into the receiver block can be determined over time by mea-surement of the radioactivity in the receiver block.
From a multitude of such studies, the general properties of polar IAA transport have emerged. Tissues differ in the degree of polarity of IAA transport. In coleoptiles, vegeta-tive stems, and leaf petioles, basipetal transport predomi-nates. Polar transport is not affected by the orientation of the tissue (at least over short periods of time), so it is inde-pendent of gravity.
Polar transport proceeds in a cell-to-cell fashion, rather than via the symplast. That is, auxin exits the cell through the plasma membrane, diffuses across the compound mid-dle lamella, and enters the cell below through its plasma membrane. The loss of auxin from cells is termed auxin efflux; the entry of auxin into cells is called auxin uptake or influx. The overall process requires metabolic energy, as evi-denced by the sensitivity of polar transport to O2 depriva-tion and metabolic inhibitors.
The velocity of polar auxin transport is 5 to 20 cm h–1— faster than the rate of diffusion (see Web Topic 3.2), but slower than phloem translocation rates (see Chapter 10).
Polar transport is also specific for active auxins, both nat-ural and synthetic. Neither inactive auxin analogs nor auxin metabolites are transported polarly, suggesting that polar transport involves specific protein carriers on the plasma membrane that can recognize the hormone and its active analogs.
The major site of basipetal polar auxin transport in stems and leaves is the vascular parenchyma tissue. Coleoptiles appear to be the exception in that basipetal polar transport Shoot apex Seedling Hypocotyl Apical end (A) Excised section Invert A (donor) B (receiver) Transport into receiver takes place Basal end (B) B (donor) A (receiver) Transport into receiver is blocked Agar donor block containing radiolabeled auxin FIGURE 19.11 The standard method for measuring polar auxin transport.
The polarity of transport is independent of orientation with respect to gravity. 432 Chapter 19 A demonstration of the lack of effect of gravity on basipetal auxin transport is shown in Figure 19.12. When stem cuttings, in this case grape hardwood, are placed in a moist chamber, adventitious roots form at the basal ends of the cuttings, and shoots form at the apical ends, even when the cuttings are inverted. Roots form at the base because root differentiation is stimulated by auxin accumulation due to basipetal transport. Shoots tend to form at the apical end where the auxin concentration is lowest.
occurs mainly in the nonvascular tissues. Acropetal polar transport in the root is specifically associated with the xylem parenchyma of the stele (Palme and Gälweiler 1999).
However, as we shall see later in the chapter, most of the auxin that reaches the root tip is translocated via the phloem.
A small amount of basipetal auxin transport from the root tip has also been demonstrated. In maize roots, for example, radiolabeled IAA applied to the root tip is trans-ported basipetally about 2 to 8 mm (Young and Evans 1996). Basipetal auxin transport in the root occurs in the epidermal and cortical tissues, and as we shall see, it plays a central role in gravitropism.
A Chemiosmotic Model Has Been Proposed to Explain Polar Transport The discovery of the chemiosmotic mechanism of solute transport in the late 1960s (see Chapter 6) led to the appli-cation of this model to polar auxin transport. According to the now generally accepted chemiosmotic model for polar auxin transport, auxin uptake is driven by the proton motive force (∆E + ∆pH) across the plasma membrane, while auxin efflux is driven by the membrane potential, ∆E.
(Proton motive force is described in more detail in Web Topic 6.3 and Chapter 7.) A crucial feature of the polar transport model is that the auxin efflux carriers are localized at the basal ends of the conducting cells (Figure 19.13). The evidence for each step in this model is considered separately in the discussion that follows.
Auxin influx. The first step in polar transport is auxin influx. According to the model, auxin can enter plant cells from any direction by either of two mechanisms: 1. Passive diffusion of the protonated (IAAH) form across the phospholipid bilayer 2. Secondary active transport of the dissociated (IAA–) form via a 2H+–IAA– symporter The dual pathway of auxin uptake arises because the pas-sive permeability of the membrane to auxin depends strongly on the apoplastic pH.
The undissociated form of indole-3-acetic acid, in which the carboxyl group is protonated, is lipophilic and readily diffuses across lipid bilayer membranes. In contrast, the dis-sociated form of auxin is negatively charged and therefore does not cross membranes unaided. Because the plasma membrane H+-ATPase normally maintains the cell wall solu-tion at about pH 5, about half of the auxin (pKa = 4.75) in the apoplast will be in the undissociated form and will diffuse passively across the plasma membrane down a concentra-tion gradient. Experimental support for pH-dependent, pas-sive auxin uptake was first provided by the demonstration that IAA uptake by plant cells increases as the extracellular pH is lowered from a neutral to a more acidic value.
A carrier-mediated, secondary active uptake mechanism was shown to be saturable and specific for active auxins (Lomax 1986). In experiments in which the ∆pH and ∆E values of isolated membrane vesicles from zucchini (Cucur-bita pepo) hypocotyls were manipulated artificially, the uptake of radiolabeled auxin was shown to be stimulated in the presence of a pH gradient, as in passive uptake, but also when the inside of the vesicle was negatively charged relative to the outside. These and other experiments suggested that an H+–IAA– symporter cotransports two protons along with the auxin anion. This secondary active transport of auxin allows for greater auxin accumulation than simple diffu-sion does because it is driven across the membrane by the proton motive force.
A permease-type auxin uptake carrier, AUX1, related to bacterial amino acid carriers, has been identified in Ara-bidopsis roots (Bennett et al. 1996). The roots of aux1 mutants are agravitropic, suggesting that auxin influx is a limiting factor for gravitropism in roots. As predicted by the chemiosmotic model, AUX1 appears to be uniformly distributed around cells in the polar transport pathway (Marchant et al. 1999). Thus in general, the polarity of auxin transport is governed by the efflux step rather than the influx step.
Auxin: The Growth Hormone 433 FIGURE 19.12 and shoots grow from the apical ends, of grape hardwood Adventitious roots grow from the basal ends, cuttings, whether they are maintained in the inverted (the two cuttings on the left) or upright orientation (the cuttings (From Hartmann and Kester 1983.) on the right). The roots always form at the basal ends because polar auxin transport is independent of gravity. Auxin efflux. Once IAA enters the cytosol, which has a pH of approximately 7.2, nearly all of it will dissociate to the anionic form. Because the membrane is less per-meable to IAA– than to IAAH, IAA– will tend to accumulate in the cytosol. How-ever, much of the auxin that enters the cell escapes via an auxin anion efflux carrier.
According to the chemiosmotic model, transport of IAA– out of the cell is driven by the inside negative membrane potential.
As noted earlier, the central feature of the chemiosmotic model for polar transport is that IAA– efflux takes place preferentially at the basal end of each cell. The repetition of auxin uptake at the apical end of the cell and preferential release from the base of each cell in the pathway gives rise to the total polar transport effect. A family of putative auxin efflux carriers known as PIN proteins (named after the pin-shaped inflorescences formed by the pin1 mutant of Arabidopsis; Figure 19.14A) are localized precisely as the model would predict—that is, at the basal ends of the conducting cells (see Figure 19.14B).
H+ Plasma membrane Cell wall Apex IAA– pH 5 2H+ IAAH IAA– IAA– IAA– IAAH ATP ATP IAAH pH 7 H+ H+ H+ Vacuole Base Permease H+-cotransport Cytosol ATP H+ IAA– ATP H+ ATP H+ 1. IAA enters the cell either passively in the undissociated form (IAAH) or by secondary active cotransport in the anionic form (IAA–).
2. The cell wall is maintained at an acidic pH by the activity of the plasma membrane H+-ATPase.
3. In the cytosol, which has a neutral pH, the anionic form (IAA–) predominates.
4. The anions exit the cell via auxin anion efflux carriers that are concentrated at the basal ends of each cell in the longitudinal pathway.
FIGURE 19.13 The chemiosmotic model for polar auxin transport. Shown here is one cell in a column of auxin-transporting cells.
(From Jacobs and Gilbert 1983.) FIGURE 19.14 The pin1 mutant of Arabidopsis (A) and localization of the PIN1 protein at the basal ends of con-ducting cells by immunofluorescence microscopy (B). (Courtesy of L.
Gälweiler and K. Palme.) (A) (B) 434 Chapter 19 PIN proteins have 10 to 12 transmembrane regions char-acteristic of a major superfamily of bacterial and eukary-otic transporters, which include drug resistance proteins and sugar transporters (Figure 19.15). Despite topological similarities to other transporters, recent studies suggest that PIN may require other proteins for activity, and may be part of a larger protein complex. Inhibitors of Auxin Transport Block Auxin Efflux Several compounds have been synthesized that can act as auxin transport inhibitors (ATIs), including NPA (1-N-naphthylphthalamic acid) and TIBA (2,3,5-triiodobenzoic acid) (Figure 19.16). These inhibitors block polar transport by preventing auxin efflux. We can demonstrate this phe-nomenon by incorporating NPA or TIBA into either the donor or the receiver block in an auxin transport experi-ment. Both compounds inhibit auxin efflux into the receiver block, but they do not affect auxin uptake from the donor block.
Some ATIs, such as TIBA, that have weak auxin activity and are transported polarly, may inhibit polar transport in part by competing with auxin for its binding site on the efflux carrier. Others, such as NPA, are not transported polarly and are believed to interfere with auxin transport by binding to proteins associated in a complex with the efflux carrier. Such NPA-binding proteins are also found at the basal ends of the conducting cells, consistent with the localization of PIN proteins (Jacobs and Gilbert 1983).
Recently another class of ATIs has been identified that inhibits the AUX1 uptake carrier (Parry et al. 2001). For example, 1-naphthoxyacetic acid (1-NOA) (see Figure 19.16) blocks auxin uptake into cells, and when applied to Arabidopsis plants it causes root agravitropism similar to that of the aux1 mutant. Like the aux1 mutation, neither 1-NOA nor any of the other AUX1-specific inhibitors block polar auxin transport.
PIN Proteins Are Rapidly Cycled to and from the Plasma Membrane The basal localization of the auxin efflux carriers involves targeted vesicle secretion to the basal ends of the conduct-ing cells. Recently it has been demonstrated that PIN pro-teins, although stable, do not remain on the plasma mem-brane permanently, but are rapidly cycled to an unidentified endosomal compartment via endocytotic vesi-cles, and then recycled back to the plasma membrane (Geldner et al. 2001).
CYTOPLASM NH2 COOH OUTSIDE OF CELL I II III IV V VI VII VIII XI X Plasma membrane FIGURE 19.15 The topology of the PIN1 protein with ten transmembrane segments and a large hydrophilic loop in the middle. (After Palme and Gälweiler 1999.) O NH O HO I I I O OH O OH O—CH2—COOH OH HO O O OH OH OH OH HO O NPA (1-N-naphthylphthalamic acid) Auxin transport inhibitors not found in plants Naturally occurring auxin transport inhibitors TIBA (2,3,5-triiodobenzoic acid) Genistein Quercetin (flavonol) 1-NOA (1-naphthoxyacetic acid) FIGURE 19.16 Structures of auxin transport inhibitors. Auxin: The Growth Hormone 435 Prior to treatment, the PIN1 protein is localized at the basal ends (top) of root cortical parenchyma cells (Figure 19.17A). Treatment of Arabidopsis seedlings with brefeldin A (BFA), which causes Golgi vesicles and other endosomal compartments to aggregate near the nucleus, causes PIN to accumulate in these abnormal intracellular compart-ments (see Figure 19.17B). When the BFA is washed out with buffer, the normal localization on the plasma mem-brane at the base of the cell is restored (see Figure 19.17C).
But when cytochalasin D, an inhibitor of actin polymer-ization, is included in the buffer washout solution, normal relocalization of PIN to the plasma membrane is prevented (see Figure 19.17D). These results indicate that PIN is rapidly cycled between the plasma membrane at the base of the cell and an unidentified endosomal compartment by an actin-dependent mechanism.
Although they bind different targets, both TIBAand NPA interfere with vesicle traffic to and from the plasma mem-brane. The best way to demonstrate this phenomenon is to include TIBA in the washout solution after BFA treatment.
Under these conditions, TIBA prevents the normal relocal-ization of PIN on the plasma membrane following the washout treatment (see Figure 19.17E) (Geldner et al. 2001).
The effects of TIBA and NPA on cycling are not specific for PIN proteins, and it has been proposed that ATIs may actually represent general inhibitors of membrane cycling (Geldner et al. 2001). On the other hand, neither TIBA nor NPA alone causes PIN delocalization, even though they block auxin efflux. Therefore, TIBA and NPA must also be able to directly inhibit the transport activity of PIN com-plexes on the plasma membrane—by binding either to PIN (as TIBA does) or to one or more regulatory proteins (as NPA does).
A simplified model of the effects of TIBA and NPA on PIN cycling and auxin efflux is shown in Figure 19.18. A more complete model that incorporates many of the recent findings is presented in Web Essay 19.2.
Flavonoids Serve as Endogenous ATIs There is mounting evidence that flavonoids (see Chapter 13) can function as endogenous regulators of polar auxin transport. Indeed, naturally occurring aglycone flavonoid compounds (flavonoids without attached sugars) are able to compete with NPA for its binding site on membranes (Jacobs and Rubery 1988) and are typically localized on the plasma membrane at the basal ends of cells where the FIGURE 19.17 Auxin transport inhibitors block secretion of the auxin efflux carrier PIN1 to the plasma membrane. (A) Control, showing asymmetric localization of PIN1. (B) After treatment with brefeldin A (BFA).
(C) Following an additional two-hour washout of BFA. (D) Following a BFA washout with cytochalasin D. (E) Following a BFA washout with the auxin transport inhibitor TIBA. (Photos courtesy of Klaus Palme 1999.) (A) (B) (D) (E) (C) 436 Chapter 19 efflux carrier is concentrated (Peer et al. 2001). In addition, recent studies have shown that the cells of flavonoid-defi-cient Arabidopsis mutants are less able to accumulate auxin than wild-type cells, and the mutant seedlings that lack flavonoid have altered auxin distribution profiles (Murphy et al. 1999; Brown et al. 2001).
Many of the flavonoids that displace NPA from its bind-ing site on membranes are also inhibitors of protein kinases and protein phosphatases (Bernasconi 1996). An Arabidop-sis mutant designated rcn1 (roots curl in NPA 1) was iden-tified on the basis of an enhanced sensitivity to NPA. The RCN1 gene is closely related to the regulatory subunit of protein phosphatase 2A, a serine/threonine phosphatase (Garbers et al. 1996). Protein phosphatases are known to play important roles in enzyme regulation, gene expression, and signal trans-duction by removing regulatory phosphate groups from proteins (see Chapter 14 on the web site). This finding sug-gests that a signal transduction pathway involving protein kinases and protein phosphatases may be involved in sig-naling between NPA-binding proteins and the auxin efflux carrier.
Auxin Is Also Transported Nonpolarly in the Phloem Most of the IAA that is synthesized in mature leaves appears to be transported to the rest of the plant nonpo-larly via the phloem. Auxin, along with other components of phloem sap, can move from these leaves up or down the plant at velocities much higher than those of polar trans-port (see Chapter 10). Auxin translocation in the phloem is largely passive, not requiring energy directly.
Although the overall importance of the phloem path-way versus the polar transport system for the long-distance movement of IAA in plants is still unresolved, the evidence suggests that long-distance auxin transport in the phloem is important for controlling such processes as cambial cell divisions, callose accumulation or removal from sieve tube elements, and branch root formation. Indeed, the phloem appears to represent the principal pathway for long-dis-tance auxin translocation to the root (Aloni 1995; Swarup et al. 2001).
Polar transport and phloem transport are not indepen-dent of each other. Recent studies with radiolabeled IAA suggest that in pea, auxin can be transferred from the non-polar phloem pathway to the polar transport pathway. This transfer takes place mainly in the immature tissues of the shoot apex.
A second example of transfer of auxin from the nonpo-lar phloem pathway to a polar transport system has recently been documented in Arabidopsis. It was shown that the AUX1 permease is asymmetrically localized on the plasma membrane at the upper end of root protophloem cells (i.e., the end distal from the tip) (Figure 19.19). It has been proposed that the asymmetrically oriented AUX1 permease promotes the acropetal movement of auxin from the phloem to the root apex (Swarup et al.
2001). This type of polar auxin transport based on the asymmetric localization of AUX1 differs from the polar transport that occurs in the shoot and basal region of the root, which is based on the asymmetric distribution of the PIN complex.
Note in Figure 19.19B that AUX1 is also strongly expressed in a cluster of cells in the columella of the root cap, as well as in lateral root cap cells that overlay the cells of the distal elongation zone of the root. These cells form a minor, but physiologically important, basipetal pathway whereby auxin reaching the columella is redirected back-ward toward the outer tissues of the elongation zone. The importance of this pathway will become apparent when we examine the mechanism of root gravitropism.
Actin-dependent cycling ENDOSOMAL COMPARTMENT Plasma membrane PIN complex Actin microfilament TIBA, NPA Vesicle Vesicle PIN PIN PIN PIN PIN PIN FIGURE 19.18 Actin-dependent PIN cycling between the plasma membrane and an endosomal compartment. Auxin transport inhibitors TIBA and NPA both interfere with relo-calization of PIN1 proteins to basal plasma membranes after BFA washout (see Figure 19.17). This suggests that both of these auxin transport inhibitors interfere with PIN1 cycling.
Auxin: The Growth Hormone 437 PHYSIOLOGICAL EFFECTS OF AUXIN: CELL ELONGATION Auxin was discovered as the hormone involved in the bending of coleoptiles toward light. The coleoptile bends because of the unequal rates of cell elongation on its shaded versus its illuminated side (see Figure 19.1). The ability of auxin to regulate the rate of cell elongation has long fascinated plant scientists. In this section we will review the physiology of auxin-induced cell elongation, some aspects of which were discussed in Chapter 15.
Auxins Promote Growth in Stems and Coleoptiles, While Inhibiting Growth in Roots As we have seen, auxin is synthesized in the shoot apex and transported basipetally to the tissues below. The steady supply of auxin arriving at the subapical region of the stem or coleoptile is required for the continued elongation of these cells. Because the level of endogenous auxin in the elongation region of a normal healthy plant is nearly opti-mal for growth, spraying the plant with exogenous auxin causes only a modest and short-lived stimulation in growth, and may even be inhibitory in the case of dark-grown seedlings, which are more sensitive to supraoptimal auxin concentrations than light-grown plants are.
However, when the endogenous source of auxin is removed by excision of sections containing the elongation zones, the growth rate rapidly decreases to a low basal rate.
Such excised sections will often respond dramatically to exogenous auxin by rapidly increasing their growth rate back to the level in the intact plant.
In long-term experiments, treatment of excised sections of coleoptiles (see Figure 19.2) or dicot stems with auxin stimulates the rate of elongation of the section for up to 20 hours (Figure 19.20). The optimal auxin concentration for elongation growth is typically 10–6 to 10–5 M (Figure 19.21).
Epidermis Cortex Endodermis Pericycle Vasculature Lateral root cap Quiescent center and stem cells Columella of root cap (A) (B) (C) FIGURE 19.19 The auxin permease AUX1 is specifically expressed in a subset of columella, lateral root cap, and stellar tissues. (A) Diagram of tissues in the Arabidopsis root tip. (B) Immunolocalization of AUX1 in protophloem cells of the stele, a central cluster of cells in the columella, and lateral root cap cells. (C) Asymmetric localization of AUX1 in a file of protophloem cells. Scale bar is 2 µm in C. (From Swarup et al. 2001.) 20 mm 438 Chapter 19 The inhibition beyond the optimal concentration is gener-ally attributed to auxin-induced ethylene biosynthesis. As we will see in Chapter 22, the gaseous hormone ethylene inhibits stem elongation in many species.
Auxin control of root elongation growth has been more difficult to demonstrate, perhaps because auxin induces the production of ethylene, a root growth inhibitor. However, even if ethylene biosynthesis is specifically blocked, low concentrations (10–10 to 10–9 M) of auxin promote the growth of intact roots, whereas higher concentrations (10–6 M) inhibit growth. Thus, roots may require a minimum concentration of auxin to grow, but root growth is strongly inhibited by auxin concentrations that promote elongation in stems and coleoptiles.
The Outer Tissues of Dicot Stems Are the Targets of Auxin Action Dicot stems are composed of many types of tissues and cells, only some of which may limit the growth rate. This point is illustrated by a simple experiment. When stem sec-tions from growing regions of an etiolated dicot stem, such as pea, are split lengthwise and incubated in buffer, the two halves bend outward.
This result indicates that, in the absence of auxin the central tissues, including the pith, vascular tissues, and inner cortex, elongate at a faster rate than the outer tissues, consisting of the outer cortex and epidermis. Thus the outer tissues must be limiting the extension rate of the stem in the absence of auxin. However, when the split sections are incubated in buffer plus auxin, the two halves now curve inward, demonstrating that the outer tissues of dicot stems are the primary targets of auxin action during cell elongation.
The observation that the outer cell layers are the targets of auxin seems to conflict with the localization of polar transport in the parenchyma cells of the vascular bundles.
However, auxin can move laterally from the vascular tis-sues of dicot stems to the outer tissues of the elongation zone. In coleoptiles, on the other hand, all of the nonvas-cular tissues (epidermis plus mesophyll) are capable of transporting auxin, as well as responding to it.
The Minimum Lag Time for Auxin-Induced Growth Is Ten Minutes When a stem or coleoptile section is excised and inserted into a sensitive growth-measuring device, the growth response to auxin can be monitored at very high resolution.
Without auxin in the medium, the growth rate declines rapidly. Addition of auxin markedly stimulates the growth rate after a lag period of only 10 to 12 minutes (see the inset in Figure 19.20).
Both Avena (oat) coleoptiles and Glycine max (soybean) hypocotyls (dicot stem) reach a maximum growth rate after 0 1 2 0 Time (hours) Growth (mm) Elongation (% increase in length) 60 30 90 0 30 IAA + Suc IAA Suc 20 10 5 10 Time (min) 15 20 25 IAA Lag phase FIGURE 19.20 Time course for auxin-induced growth of Avena (oat) coleoptile sections. Growth is plotted as the per-cent increase in length. Auxin was added at time zero.
When sucrose (Suc) is included in the medium, the response can continue for as long as 20 hours. Sucrose prolongs the growth response to auxin mainly by providing osmotically active solute that can be taken up for the maintenance of turgor pressure during cell elongation. KCl can substitute for sucrose. The inset shows a short-term time course plot-ted with an electronic position-sensing transducer. In this graph, growth is plotted as the absolute length in millime-ters versus time. The curve shows a lag time of about 15 minutes for auxin-stimulated growth to begin. (From Cleland 1995.) IAA concentration (M) Control growth (no added IAA) +IAA Relative segment elongation growth 0 – + 10–8 10–7 10–6 10–5 10–4 10–3 10–2 FIGURE 19.21 Typical dose–response curve for IAA-induced growth in pea stem or oat coleoptile sections. Elongation growth of excised sections of coleoptiles or young stems is plotted versus increasing concentrations of exogenous IAA. At higher concentrations (above 10–5 M), IAA becomes less and less effective; above about 10–4 M it becomes inhibitory, as shown by the fact that the curve falls below the dashed line, which represents growth in the absence of added IAA. Auxin: The Growth Hormone 439 30 to 60 minutes of auxin treatment (Figure 19.22). This maximum represents a five- to tenfold increase over the basal rate. Oat coleoptile sections can maintain this maxi-mum rate for up to 18 hours in the presence of osmotically active solutes such as sucrose or KCl.
As might be expected, the stimulation of growth by auxin requires energy, and metabolic inhibitors inhibit the response within minutes. Auxin-induced growth is also sen-sitive to inhibitors of protein synthesis such as cyclohex-imide, suggesting that proteins with high turnover rates are involved. Inhibitors of RNA synthesis also inhibit auxin-induced growth, after a slightly longer delay (Cleland 1995).
Although the length of the lag time for auxin-stimulated growth can be increased by lowering of the temperature or by the use of suboptimal auxin concentrations, the lag time cannot be shortened by raising of the temperature, by the use of supraoptimal auxin concentrations, or by abrasion of the waxy cuticle to allow auxin to penetrate the tissue more rapidly. Thus the minimum lag time of 10 minutes is not determined by the time required for auxin to reach its site of action. Rather, the lag time reflects the time needed for the biochemical machinery of the cell to bring about the increase in the growth rate.
Auxin Rapidly Increases the Extensibility of the Cell Wall How does auxin cause a five- to tenfold increase in the growth rate in only 10 minutes? To understand the mech-anism, we must first review the process of cell enlargement in plants (see Chapter 15). Plant cells expand in three steps: 1. Osmotic uptake of water across the plasma membrane is driven by the gradient in water potential (∆Yw).
2. Turgor pressure builds up because of the rigidity of the cell wall.
3. Biochemical wall loosening occurs, allowing the cell to expand in response to turgor pressure.
The effects of these parameters on the growth rate are encapsulated in the growth rate equation: GR = m (Yp – Y) where GR is the growth rate, Yp is the turgor pressure, Y is the yield threshold, and m is the coefficient (wall extensibil-ity) that relates the growth rate to the difference between Yp and Y.
In principle, auxin could increase the growth rate by increasing m, increasing Yp, or decreasing Y. Although extensive experiments have shown that auxin does not increase turgor pressure when it stimulates growth, con-flicting results have been obtained regarding auxin-induced decreases in Y. However, there is general agree-ment that auxin causes an increase in the wall extensibility parameter, m.
Auxin-Induced Proton Extrusion Acidifies the Cell Wall and Increases Cell Extension According to the widely accepted acid growth hypothesis, hydrogen ions act as the intermediate between auxin and cell wall loosening. The source of the hydrogen ions is the plasma membrane H+-ATPase, whose activity is thought to increase in response to auxin. The acid growth hypoth-esis allows five main predictions: 1. Acid buffers alone should promote short-term growth, provided the cuticle has been abraded to allow the protons access to the cell wall.
2. Auxin should increase the rate of proton extrusion (wall acidification), and the kinetics of proton extru-sion should closely match those of auxin-induced growth.
3. Neutral buffers should inhibit auxin-induced growth.
4. Compounds (other than auxin) that promote proton extrusion should stimulate growth.
5. Cell walls should contain a “wall loosening factor” with an acidic pH optimum.
All five of these predictions have been confirmed. Acidic buffers cause a rapid and immediate increase in the growth rate, provided the cuticle has been abraded. Auxin stimu-lates proton extrusion into the cell wall after 10 to 15 min-utes of lag time, consistent with the growth kinetics (Fig-ure 19.23).
Auxin-induced growth has also been shown to be inhib-ited by neutral buffers, as long as the cuticle has been abraided. Fusicoccin, a fungal phytotoxin, stimulates both rapid proton extrusion and transient growth in stem and coleoptile sections (see Web Topic 19.6). And finally, wall-loosening proteins called expansins have been identified in the cell walls of a wide range of plant species (see Chap-ter 15). At acidic pH values, expansins loosen cell walls by weakening the hydrogen bonds between the polysaccha-ride components of the wall.
3 5 2 0 1 Incubation time in 10µM IAA (hours) Elongation rate (% h–1) IAA Soybean Oat FIGURE 19.22 Comparison of the growth kinetics of oat coleoptile and soybean hypocotyl sections, incubated with 10 µM IAA and 2% sucrose. Growth is plotted as the rate at each time point, rather than the rate of the absolute length.
The growth rate of the soybean hypocotyl oscillates after 1 hour, whereas that of the oat coleoptile is constant. (After Cleland 1995.) 440 Chapter 19 Auxin-Induced Proton Extrusion May Involve Both Activation and Synthesis In theory, auxin could increase the rate of proton extrusion by two possible mechanisms: 1. Activation of preexisting plasma membrane H+-ATPases 2. Synthesis of new H+-ATPases on the plasma membrane H+-ATPase activation. When auxin was added directly to isolated plasma membrane vesicles from tobacco cells, a small stimulation (about 20%) of the ATP-driven proton-pumping activity was observed, suggesting that auxin directly activates the H+-ATPase. A greater stimulation (about 40%) was observed if the living cells were treated with IAA just before the membranes were isolated, suggesting that a cellu-lar factor is also required (Peltier and Rossignol 1996).
Although an auxin receptor has not yet been unequivocally identified (as discussed later in the chapter), various auxin-binding proteins (ABPs) have been isolated and appear to be able to activate the plasma membrane H+-ATPase in the presence of auxin (Steffens et al. 2001).
Recently an ABP from rice, ABP57, was shown to bind directly to plasma membrane H+-ATPases and stimulate proton extrusion—but only in the presence of IAA (Kim et al. 2001). When IAA is absent, the activity of the H+-ATPase is repressed by the C-terminal domain of the enzyme, which can block the catalytic site. ABP57 (with bound IAA) interacts with the H+-ATPase, activating the enzyme. A second auxin-binding site interferes with the action of the first, possibly explaining the bell-shaped curve of auxin action. This hypothetical model for the action of ABP57 is shown in Figure 19.24.
H+-ATPase synthesis. The ability of protein synthesis inhibitors, such as cycloheximide, to rapidly inhibit auxin-induced proton extrusion and growth suggests that auxin might also stimulate proton pumping by increasing the synthesis of the H+-ATPase. An increase in the amount of plasma membrane ATPase in corn coleoptiles was detected immunologically after only 5 minutes of auxin treatment, and a doubling of the H+-ATPase was observed after 40 minutes of treatment. A threefold stimulation by auxin of an mRNA for the H+-ATPase was demonstrated specifi-cally in the nonvascular tissues of the coleoptiles.
In summary, the question of activation versus synthe-sis is still unresolved, and it is possible that auxin stimu-lates proton extrusion by both activation and stimulation of synthesis of the H+-ATPase. Figure 19.25 summarizes –10 0 10 20 30 40 50 60 4.5 40 80 120 160 200 240 5.0 5.5 6.0 Time (minutes) pH Elongation (microns) IAA Length pH FIGURE 19.23 Kinetics of auxin-induced elongation and cell wall acidification in maize coleoptiles. The pH of the cell wall was measured with a pH microelectrode. Note the similar lag times (10 to 15 minutes) for both cell wall acidi-fication and the increase in the rate of elongation. (From Jacobs and Ray 1976.) Docking site Inhibitory domain Catalytic site OUTSIDE INSIDE PM H+-ATPase ABP57 IAA H+ H+ ABP57 binds PM H+-ATPase at docking site.
IAA binding causes conformational change in ABP57. ABP57 then interacts with inhibitory domain of PM H+-ATPase activating the enzyme.
Binding of IAA to second site decreases interaction with H+-ATPase inhibitory domain; the enzyme is inhibited.
+ ADP Pi ATP FIGURE 19.24 Model for the activation of the plasma membrane (PM) H+-ATPase by ABP57 and auxin. Auxin: The Growth Hormone 441 the proposed mechanisms of auxin-induced cell wall loos-ening via proton extrusion.
PHYSIOLOGICAL EFFECTS OF AUXIN: PHOTOTROPISM AND GRAVITROPISM Three main guidance systems control the orientation of plant growth: 1. Phototropism, or growth with respect to light, is expressed in all shoots and some roots; it ensures that leaves will receive optimal sunlight for photosynthe-sis.
2. Gravitropism, growth in response to gravity, enables roots to grow downward into the soil and shoots to grow upward away from the soil, which is especially critical during the early stages of germination.
3. Thigmotropism, or growth with respect to touch, enables roots to grow around rocks and is responsi-ble for the ability of the shoots of climbing plants to wrap around other structures for support.
In this section we will examine the evidence that bend-ing in response to light or gravity results from the lateral redistribution of auxin. We will also consider the cellular mechanisms involved in generating lateral auxin gradients during bending growth. Less is known about the mecha-nism of thigmotropism, although it, too, probably involves auxin gradients.
Phototropism Is Mediated by the Lateral Redistribution of Auxin As we saw earlier, Charles and Francis Darwin provided the first clue concerning the mechanism of phototropism by demonstrating that the sites of perception and differen-tial growth (bending) are separate: Light is perceived at the tip, but bending occurs below the tip. The Darwins pro-posed that some “influence” that was transported from the tip to the growing region brought about the observed asymmetric growth response. This influence was later shown to be indole-3-acetic acid—auxin.
When a shoot is growing vertically, auxin is transported polarly from the growing tip to the elongation zone. The ATP H+ ATP H+ ATP H+ ATP ATP H+ H+ H+ H+ ATP H+ ATP H+ Protein processing Rough ER Golgi body ATP ATP Expansin Plasma membrane CELL WALL NUCLEUS Promoter H+-ATPase gene Activation Activation hypothesis: Auxin binds to an auxin-binding protein (ABP1) located either on the cell surface or in the cytosol. ABP1-IAA then interacts directly with plasma membrane H+-ATPase to stimulate proton pumping (step 1). Second messengers, such as calcium or intracellular pH, could also be involved.
ABP1 IAA ABP1 IAA IAA Synthesis hypothesis: IAA-induced second messengers activate the expression of genes (step 2) that encode the plasma membrane H+-ATPase (step 3). The protein is synthesized on the rough endoplasmic reticulum (step 4) and targeted via the secretory pathway to the plasma membrane (steps 5 and 6). The increase in proton extrusion results from an increase in the number of proton pumps on the membrane.
Second messengers 1 3 2 4 5 6 mRNA H+-ATPase in vesicle membrane Activation hypothesis Synthesis hypothesis FIGURE 19.25 Current models for IAA-induced H+ extrusion. In many plants, both of these mechanisms may operate. Regardless of how H+ pumping is increased, acid-induced wall loosening is thought to be mediated by expansins.
442 Chapter 19 polarity of auxin transport from tip to base is developmen-tally determined and is independent of orientation with respect to gravity. However, auxin can also be transported laterally, and this lateral movement of auxin lies at the heart of a model for tropisms originally proposed separately by the Russian plant physiologist, Nicolai Cholodny and Frits Went from the Netherlands in the 1920s.
According to the Cholodny–Went model of phototro-pism, the tips of grass coleoptiles have three specialized functions: 1. The production of auxin 2. The perception of a unilateral light stimulus 3. The lateral transport of IAA in response to the pho-totropic stimulus Thus, in response to a directional light stimulus, the auxin produced at the tip, instead of being transported basipetally, is transported laterally toward the shaded side.
The precise sites of auxin production, light perception, and lateral transport have been difficult to define. In maize coleoptiles, auxin is produced in the upper 1 to 2 mm of the tip. The zones of photosensing and lateral transport extend farther, within the upper 5 mm of the tip. The response is also strongly dependent on the light fluence (see Web Topic 19.7).
Two flavoproteins, phototropins 1 and 2, are the pho-toreceptors for the blue-light signaling pathway (see Web Essay 19.3) that induces phototropic bending in Arabidop-sis hypocotyls and oat coleoptiles under both high- and low-fluence conditions (Briggs et al. 2001). Phototropins are autophosphorylating protein kinases whose activity is stimulated by blue light. The action spec-trum for blue-light activation of the kinase activity closely matches the action spectrum for phototropism, including the multiple peaks in the blue region. Phototropin 1 dis-plays a lateral gradient in phosphorylation during expo-sure to low-fluence unilateral blue light.
According to the current hypothesis, the gradient in phototropin phosphorylation induces the movement of auxin to the shaded side of the coleoptile (see Web Topic 19.7). Once the auxin reaches the shaded side of the tip, it is transported basipetally to the elongation zone, where it stimulates cell elongation. The acceleration of growth on the shaded side and the slowing of growth on the illumi-nated side (differential growth) give rise to the curvature toward light (Figure 19.26).
Direct tests of the Cholodny–Went model using the agar block/coleoptile curvature bioassay have supported the model’s prediction that auxin in coleoptile tips is trans-ported laterally in response to unilateral light (Figure 19.27). The total amount of auxin diffusing out of the tip (here expressed as the angle of curvature) is the same in the presence of unilateral light as in darkness (compare Figure 19.27A and B). This result indicates that light does not cause the photodestruction of auxin on the illuminated side, as had been proposed by some investigators.
Consistent with both the Cholodny–Went hypothesis and the acid growth hypothesis, the apoplastic pH on the shaded side of a phototropically bending stem or coleop-tile is more acidic than the side facing the light (Mulkey et al. 1981).
Gravitropism Also Involves Lateral Redistribution of Auxin When dark-grown Avena seedlings are oriented horizon-tally, the coleoptiles bend upward in response to gravity.
According to the Cholodny–Went model, auxin in a hori-zontally oriented coleoptile tip is transported laterally to the lower side, causing the lower side of the coleoptile to grow faster than the upper side. Early experimental evi-dence indicated that the tip of the coleoptile can perceive gravity and redistribute auxin to the lower side. For exam-ple, if coleoptile tips are oriented horizontally, a greater amount of auxin diffuses from the lower half than the upper half (Figure 19.28).
Tissues below the tip are able to respond to gravity as well. For example, when vertically oriented maize coleop-tiles are decapitated by removal of the upper 2 mm of the tip and oriented horizontally, gravitropic bending occurs at a slow rate for several hours even without the tip. Appli-cation of IAA to the cut surface restores the rate of bending 80 0.6 0 40 20 Time (min) Growth in length (mm) 100 120 60 0.9 1.2 1.5 1.8 Shaded side Control (no light) Irradiated side 0.3 FIGURE 19.26 Time course of growth on the illuminated and shaded sides of a coleoptile responding to a 30-second pulse of unidirectional blue light. Control coleoptiles were not given a light treatment. (After Iino and Briggs 1984.) Auxin: The Growth Hormone 443 to normal levels. This finding indicates that both the per-ception of the gravitational stimulus and the lateral redis-tribution of auxin can occur in the tissues below the tip, although the tip is still required for auxin production.
Lateral redistribution of auxin in shoot apical meristems is more difficult to demonstrate than in coleoptiles because of the presence of leaves. In recent years, molecular mark-ers have been widely used as reporter genes to detect lat-eral auxin gradients in horizontally placed stems and roots.
In soybean hypocotyls, gravitropism leads to a rapid asymmetry in the accumulation of a group of auxin-stim-ulated mRNAs called SAURs (small auxin up-regulated RNAs) (McClure and Guilfoyle 1989). In vertical seedlings, SAUR gene expression is symmetrically distributed. Within 20 minutes after the seedling is oriented horizontally, SAURs begin to accumulate on the lower half of the hypocotyl. Under these conditions, gravitropic bending first becomes evident after 45 minutes, well after the induc-tion of the SAURs (see Web Topic 19.8). The existence of a lateral gradient in SAUR gene expression is indirect evi-dence for the existence of a lateral gradient in auxin detectable within 20 minutes of the gravitropic stimulus.
As will be discussed later in the chapter, the GH3 gene family is also up-regulated within 5 minutes of auxin treat-Coleoptile tip completely divided by thin piece of mica; no redistribution of auxin observed.
Coleoptile tip partly divided by thin piece of mica; lateral redistribution of auxin occurs.
(A) Dark Corn coleoptile tip excised and placed on agar Agar block Curvature angle (degrees) (B) Unilateral light No destruction of auxin Undivided agar block Divided agar block Unilateral light does not cause the photodestruction of auxin on the illuminated side.
Auxin is transported laterally to the shaded side in the tip.
(D) (C) 11.5 11.2 8.1 15.4 25.8 25.6 FIGURE 19.27 Evidence that the lateral redistribution of auxin is stimulated by uni-directional light in corn coleoptiles.
(A) (B) Lower half Upper half FIGURE 19.28 Auxin is transported to the lower side of a horizontally oriented oat coleoptile tip. (A) Auxin from the upper and lower halves of a horizontal tip is allowed to diffuse into two agar blocks. (B) The agar block from the lower half (left) induces greater curvature in a decapitated coleoptile than the agar block from the upper half (right). (Photo © M. B. Wilkins.) 444 Chapter 19 ment and has been used as a molecular marker for the pres-ence of auxin. By fusing an artificial promoter sequence based on the GH3 promoter to the GUS reporter gene, it is possible to visualize the lateral gradient in auxin concentration that occurs during both photo- and gravitropism (Figure 19.29).
Statoliths Serve as Gravity Sensors in Shoots and Roots Unlike unilateral light, gravity does not form a gradient between the upper and lower sides of an organ. All parts of the plant experience the gravitational stimulus equally.
How do plant cells detect gravity? The only way that grav-ity can be sensed is through the motion of a falling or sed-imenting body.
Obvious candidates for intracellular gravity sensors in plants are the large, dense amyloplasts that are present in many plant cells. These specialized amyloplasts are of suf-ficiently high density relative to the cytosol that they read-ily sediment to the bottom of the cell (Figure 19.30). Amy-loplasts that function as gravity sensors are called statoliths, and the specialized gravity-sensing cells in which they occur are called statocytes. Whether the stato-cyte is able to detect the downward motion of the statolith as it passes through the cytoskeleton or whether the stim-ulus is perceived only when the statolith comes to rest at the bottom of the cell has not yet been resolved.
Shoots and Coleoptiles. In shoots and coleoptiles, gravity is perceived in the starch sheath, a layer of cells that sur-rounds the vascular tissues of the shoot. The starch sheath is continuous with the endodermis of the root, but unlike the endodermis it contains amyloplasts. Arabidopsis mutants lacking amyloplasts in the starch sheath display agravitropic shoot growth but normal gravitropic root growth (Fujihira et al. 2000). As noted in Chapter 16, the scarecrow (scr) mutant of Arabidopsis is missing both the endodermis and the starch sheath. As a result, the hypocotyl and inflorescence of the scr mutant are agravitropic, while the root exhibits a nor-mal gravitropic response. On the basis of the phenotypes of these two mutants, we can conclude the following: • The starch sheath is required for gravitropism in shoots.
• The root endodermis, which does not contain sta-toliths, is not required for gravitropism in roots.
Roots. The site of gravity perception in primary roots is the root cap. Large, graviresponsive amyloplasts are located in the statocytes (see Figure 19.30A and B) in the central cylin-der, or columella, of the root cap. Removal of the root cap from otherwise intact roots abolishes root gravitropism without inhibiting growth.
Precisely how the statocytes sense their falling statoliths is still poorly understood. According to one hypothesis, contact or pressure resulting from the amyloplast resting on the endoplasmic reticulum on the lower side of the cell triggers the response (see Figure 19.30C). The endoplasmic reticulum of columella cells is structurally unique, consist-ing of five to seven rough-ER sheets attached to a central nodal rod in a whorl, like petals on a flower. This special-ized “nodal ER” differs from the more tubular cortical ER cisternae and may be involved in the gravity response (Zheng and Staehelin 2001).
The starch–statolith hypothesis of gravity perception in roots is supported by several lines of evidence. Amylo-plasts are the only organelles that consistently sediment in the columella cells of different plant species, and the rate of sedimentation correlates closely with the time required to perceive the gravitational stimulus. The gravitropic responses of starch-deficient mutants are generally much slower than those of wild-type plants. Nevertheless, starch-less mutants exhibit some gravitropism, suggesting that although starch is required for a normal gravitropic response, starch-independent gravity perception mecha-nisms may also exist.
Other organelles, such as nuclei, may be dense enough to act as statoliths. It may not even be necessary for a sta-tolith to come to rest at the bottom of the cell. The cytoskeletal network may be able to detect a partial verti-cal displacement of an organelle.
Auxin: The Growth Hormone 445 (A) (B) FIGURE 19.29 Lateral auxin gradients are formed in Arabidopsis hypocotyls during the differential growth The plants were transformed with the DR5::GUS hypocotyls is indicated by the blue staining shown in the responses to light (A). Treatment with the auxin efflux inhibitor NPA blocks auxin redistribution and bending (B).
reporter gene. Auxin accumulation on the shaded side of the insets (A). A similar redistribution of auxin occurs in gravitropism. (Photos courtesy of Klaus Palme.) Recently Andrew Staehelin and colleagues proposed a new model for gravitropism, called the tensegrity model (Yoder et al. 2001). Tensegrity is an architectural term—a contraction of tensional integrity—coined by the innovative architect R. Buckminster Fuller. In essence, tensegrity refers to structural integrity created by interactive tension between the structural components. In this case the struc-tural components consist of the meshwork of actin micro-filaments that form part of the cytoskeleton of the central columella cells of the root cap. The actin network is assumed to be anchored to stretch-activated receptors on the plasma membrane. Stretch receptors in animal cells are typically mechanosensitive ion channels, and stretch-acti-vated calcium channels have been demonstrated in plants.
According to the tensegrity model, sedimentation of the statoliths through the cytosol locally disrupts the actin meshwork, changing the distribution of tension transmit-ted to calcium channels on the plasma membrane, thus altering their activities. Yoder and colleagues (2001) have further proposed that the nodal ER, which is also con-nected to channels via actin microfilaments, may protect the cytoskeleton from being disrupted by the statoliths in specific regions, thus providing a signal for the direction-ality of the stimulus.
Gravity perception without statoliths? An alternative mechanism of gravity perception that does not involve sta-toliths has been proposed for the giant-celled freshwater alga Chara. See Web Topic 19.8 for details.
Auxin Is Redistribution Laterally in the Root Cap In addition to functioning to protect the sensitive cells of the apical meristem as the tip penetrates the soil, the root cap is the site of gravity perception. Because the cap is some distance away from the elongation zone where bend-ing occurs, a chemical messenger is presumed to be involved in communication between the cap and the elon-gation zone. Microsurgery experiments in which half of the M C P Root tip Amyloplast Root tip Vertical orientation Horizontal orientation Uniform pressure on ER Unequal pressure on ER (C) Amyloplasts tend to sediment in response to reorientation of the cell and to remain resting against the ER. When the root is oriented vertically, the pressure exerted by the amylo-plasts on the ER is equally distributed.
In a horizontal orient-ation the pressure on the ER is unequal on either side of the vertical axis of the root.
FIGURE 19.30 The perception of gravity by statocytes of Arabidopsis. (A) Electron micrograph of root tip, showing apical meristem (M), columella (C), and periph-eral (P) cells. (B) Enlarged view of a columella cell, showing the amyloplasts resting on top of endoplasmic reticulum at the bottom of the cell. (C) Diagram of the changes that occur during reorientation from the vertical to the horizontal position. (A, B courtesy of Dr. John Kiss; C based on Sievers et al. 1996 and Volkmann and Sievers 1979.) (A) (B) Statolith Statolith Endoplasmic reticulum cap was removed showed that the cap produces a root growth inhibitor (Figure 19.31). This finding suggests that the cap supplies an inhibitor to the lower side of the root during gravitropic bending.
Although root caps contain small amounts of IAA and abscisic acid (ABA) (see Chapter 23), IAA is more inhibitory to root growth than ABA when applied directly to the elongation zone, suggesting that IAA is the root cap inhibitor. Consistent with this conclusion, ABA-deficient Arabidopsis mutants have normal root gravitropism, whereas the roots of mutants defective in auxin transport, such as aux1 and agr1, are agravitropic (Palme and Gäl-weiler 1999). The agr mutant lacks an auxin efflux carrier related to the PIN proteins (Chen et al. 1998; Müller et al.
1998; Utsuno et al. 1998). The AGR1 protein is localized at the basal (distal) end of cortical cells near the root tip in Arabidopsis.
How do we reconcile the fact that the shoot apical meristem is the primary source of auxin to the root with the role of the root cap as the source of the inhibitory auxin during gravitropism? As discussed earlier in the chapter, auxin from the shoot is translocated from the stele to the root tip via protophloem cells. Asymmetrically localized AUX1 permeases on the pro-tophloem parenchyma cells direct the acropetal transport of auxin from the phloem to a cluster of cells in the col-umella of the cap. Auxin is then trans-ported radially to the lateral root cap cells, where AUX1 is also strongly expressed (see Figure 19.19).
The lateral root cap cells overlay the distal elongation zone (DEZ) of the root— the first region that responds to gravity.
The auxin from the cap is taken up by the cortical parenchyma of the DEZ and trans-ported basipetally through the elongation zone of the root. This basipetal transport, which is limited to the elongation zone, is facilitated by auxin anion carriers related to the PIN family (called AGR1), which are localized at the basal ends of the cortical parenchyma cells.
The basipetally transported auxin accumulates in the elongation zone and does not pass beyond this region.
Flavonoids capable of inhibiting auxin efflux are synthesized in this region of the root and prob-ably promote auxin retention by these cells (Figure 19.32) (Murphy et al. 2000).
Vertically oriented control root with cap Horizontally oriented control root with cap shows normal gravitropic bending.
Root Root cap Removal of the cap from the vertical root slightly stimulates elongation growth. Removal of half of the cap causes a vertical root to bend toward the side with the remaining half-cap.
Removal of the cap from a horizontal root abolishes the response to gravity, while slightly stimulating elongation growth.
(A) (B) FIGURE 19.31 Microsurgery experiments demonstrating that the root cap produces an inhibitor that regulates root gravitropism. (After Shaw and Wilkins 1973.) Cotyledon and apical region Hypocotyl–root transition zone Root tip FIGURE 19.32 Flavonoid localization in a 6-day-old Arabidopsis seedling. The staining procedure used causes the flavonoids to flu-oresce. Flavonoids are concentrated in three regions: the cotyledon and apical region, the hypocotyl–root transition zone, and the root tip area (inset). In the root tip, flavonoids are localized specifically in the elongation zone and the cap, the tissues involved in basipetal auxin transport. (From Murphy et al. 2000.) Auxin: The Growth Hormone 447 According to the model, basipetal auxin transport in a vertically oriented root is equal on all sides (Figure 19.33A).
When the root is oriented horizontally, however, the cap redirects the bulk of the auxin to the lower side, thus inhibit-ing the growth of that lower side (see Figure 19.33B). Con-sistent with this idea, the transport of [3H]IAA across a hor-izontally oriented root cap is polar, with a preferential downward movement (Young et al. 1990).
PIN3 Is Relocated Laterally to the Lower Side of Root Columella Cells Recently the mechanism of lateral auxin redistribution in the root cap has new been elucidated (Friml et al. 2002).
One of the members of the PIN protein family of auxin efflux carriers, PIN3, is not only required for both photo-and gravitropism in Arabidopsis, but it has been shown to be relocalized to the lower side of the columella cells dur-ing root gravitropism (Figure 19.34). As noted previously, PIN proteins are constantly being cycled between the plasma membrane and intracellular secretory compartments. This cycling allows some PIN pro-teins to be targeted to specific sides of the cell in response to a directional stimulus. In a vertically oriented root, PIN3 is uniformly distributed around the columella cell (see Fig-ure 19.34A). But when the root is placed on its side, PIN3 is preferentially targeted to the lower side of the cell (see Figure 19.34B). As a result, auxin is transported polarly to the lower half of the cap.
Gravity Sensing May Involve Calcium and pH as Second Messengers A variety of experiments have suggested that calcium– calmodulin is required for root gravitropism in maize. Some of these experiments involve EGTA (ethylene glycol-bis(β-aminoethyl ether)-N,N,N′,N′-tetraacetic acid), a compound that can chelate (form a complex with) calcium ions, thus preventing calcium uptake by cells. EGTA inhibits both root gravitropism and the asymmetric distribution of auxin in response to gravity (Young and Evans 1994). Placing a block of agar that contains calcium ions on the side of the cap of a vertically oriented corn root induces the root to grow toward the side with the agar block (Figure 19.35). As in the case of [+H]IAA, 45Ca2+ is polarly trans-ported to the lower half of the cap of a root stimulated by (B) (A) Vertical orientation Horizontal orientation Elongation zone (flavonoid synthesis) IAA IAA IAA IAA IAA IAA IAA Root cap Cortex Root cap cell (enlarged) Statoliths Stele IAA 1. IAA is synthesized in the shoot and transported to the root in the stele.
2. When the root is vertical, the statoliths in the cap settle to the basal ends of the cells. Auxin transported acropetally in the root via the stele is distributed equally on all sides of the root cap. The IAA is then transported basipetally within the cortex to the elongation zone, where it regulates cell elongation.
3. In a horizontal root the statoliths settle to the side of the cap cells, triggering polar transport of IAA to the lower side of the cap.
6. The decreased auxin concentration on the upper side stimulates the upper side to grow. As a result, the root bends down.
4. The majority of the auxin in the cap is then transported basipetally in the cortex on the lower side of the root.
5. The high concentration of auxin on the lower side of the root inhibits growth.
FIGURE 19.33 Proposed model for the redistribution of auxin during gravitro-pism in maize roots. (After Hasenstein and Evans 1988.) 448 Chapter 19 gravity. However, thus far no changes in the distribution of intracellular calcium have been detected in columella cells in response to a gravitational stimulus.
Recent evidence suggests that a change in intracellular pH is the earliest detectable change in columella cells responding to gravity. Fasano et al. (2001) used pH-sensi-tive dyes to monitor both intracellular and extracellular pH in Arabidopsis roots after they were placed in a horizontal position. Within 2 minutes of gravistimulation, the cyto-plasmic pH of the columella cells of the root cap increased from 7.2 to 7.6, and the apoplastic pH declined from 5.5 to 4.5. These changes preceded any detectable tropic curva-ture by about 10 minutes. The alkalinization of the cytosol combined with the acid-ification of the apoplast suggests that an activation of the plasma membrane H+-ATPase is one of the initial events that mediate root gravity perception or signal transduction.
DEVELOPMENTAL EFFECTS OF AUXIN Although originally discovered in relation to growth, auxin influences nearly every stage of a plant’s life cycle from germination to senescence. Because the effect that auxin produces depends on the identity of the target tissue, the response of a tissue to auxin is governed by its develop-mentally determined genetic program and is further influ-enced by the presence or absence of other signaling mole-cules. As we will see in this and subsequent chapters, interaction between two or more hormones is a recurring theme in plant development.
In this section we will examine some additional devel-opmental processes regulated by auxin, including apical dominance, leaf abscission, lateral-root formation, and vas-cular differentiation. Throughout this discussion we assume that the primary mechanism of auxin action is comparable in all cases, involving similar receptors and sig-nal transduction pathways. The current state of our knowl-edge of auxin signaling pathways will be considered at the end of the chapter.
Auxin Regulates Apical Dominance In most higher plants, the growing apical bud inhibits the growth of lateral (axillary) buds—a phenomenon called (A) Vertical orientation (B) Horizontal orientation FIGURE 19.34 Relocalization of the auxin efflux carrier PIN3 during root gravitropism in Arabidopsis. (A) In a vertically oriented root, PIN3 is uniformly distributed around the columella cells. (B) After being ori-ented horizontally for 10 minutes, PIN3 has been relocalized to the lower side of the columella cells. The photo in (B) has been reorientated so that the lower side is on the right. (The direction of gravity is indi-cated by the arrows.) (From Friml et al. 2002, courtesy of Klaus Palme.) FIGURE 19.35 A corn root bending toward an agar block containing calcium placed on the cap. (Courtesy of Michael L. Evans.) 10 mm 10 mm Auxin: The Growth Hormone 449 apical dominance. Removal of the shoot apex (decapitation) usually results in the growth of one or more of the lateral buds. Not long after the discovery of auxin, it was found that IAA could substitute for the apical bud in maintaining the inhibition of lateral buds of bean (Phaseolus vulgaris) plants.
This classic experiment is illustrated in Figure 19.36.
This result was soon confirmed for numerous other plant species, leading to the hypothesis that the outgrowth of the axillary bud is inhibited by auxin that is transported basipetally from the apical bud. In support of this idea, a ring of the auxin transport inhibitor TIBA in lanolin paste (as a carrier) placed below the shoot apex released the axil-lary buds from inhibition.
How does auxin from the shoot apex inhibit the growth of lateral buds? Kenneth V. Thimann and Folke Skoog orig-inally proposed that auxin from the shoot apex inhibits the growth of the axillary bud directly—the so-called direct-inhibition model. According to the model, the optimal auxin concentration for bud growth is low, much lower than the auxin concentration normally found in the stem. The level of auxin normally present in the stem was thought to inhibit the growth of lateral buds.
If the direct-inhibition model of apical dominance is cor-rect, the concentration of auxin in the axillary bud should decrease following decapitation of the shoot apex. How-ever, the reverse appears to be true. This was demonstrated with transgenic plants that contained the reporter genes for bacterial luciferase (LUXA and LUXB) under the control of an auxin-responsive promoter (Langridge et al. 1989).
These reporter genes allowed researchers to study the level of auxin in different tissues by monitoring the amount of light emitted by the luciferase-catalyzed reaction.
When these transgenic plants were decapitated, the expression of the LUX genes increased in and around the axillary buds within 12 hours. This experiment indicated that after decapitation, the auxin content of the axillary buds increased rather than decreased.
Direct physical measurements of auxin levels in buds have also shown an increase in the auxin of the axillary buds after decapitation. The IAA concentration in the axil-lary bud of Phaseolus vulgaris (kidney bean) increased five-fold within 4 hours after decapitation (Gocal et al. 1991).
These and other similar results make it unlikely that auxin from the shoot apex inhibits the axillary bud directly. Other hormones, such as cytokinins and ABA, may be involved. Direct application of cytokinins to axillary buds stimulates bud growth in many species, overriding the inhibitory effect of the shoot apex. Auxin makes the shoot apex a sink for cytokinin synthesized in the root, and this may be one of the factors involved in apical dominance (see Web Topic 19.10).
Finally, ABA has been found in dormant lateral buds in intact plants. When the shoot apex is removed, the ABA levels in the lateral buds decrease. High levels of IAA in the shoot may help keep ABA levels high in the lateral buds.
Removing the apex removes a major source of IAA, which FIGURE 19.36 Auxin sup-presses the growth of axillary buds in bean (Phaseolus vulgaris) plants. (A) The axillary buds are suppressed in the intact plant because of apical dominance. (B) Removal of the terminal bud releases the axil-lary buds from apical domi-nance (arrows). (C) Applying IAA in lanolin paste (contained in the gelatin capsule) to the cut surface prevents the outgrowth of the axillary buds. (Photos ©M. B. Wilkins.) (A) (B) (C) 450 Chapter 19 may allow the levels of bud growth inhibitor to fall (see Web Topic 19.11).
Auxin Promotes the Formation of Lateral and Adventitious Roots Although elongation of the primary root is inhibited by auxin concentrations greater than 10–8 M, initia-tion of lateral (branch) roots and adventitious roots is stimulated by high auxin levels. Lateral roots are commonly found above the elongation and root hair zone and originate from small groups of cells in the pericycle (see Chapter 16). Auxin stimulates these pericycle cells to divide. The dividing cells gradu-ally form into a root apex, and the lateral root grows through the root cortex and epidermis.
Adventitious roots (roots originating from non-root tissue) can arise in a variety of tissue locations from clusters of mature cells that renew their cell division activity. These dividing cells develop into a root apical meristem in a manner somewhat analo-gous to the formation of lateral roots. In horticul-ture, the stimulatory effect of auxin on the formation of adventitious roots has been very useful for the vegetative propagation of plants by cuttings.
A series of Arabidopsis mutants, named alf (aber-rant lateral root formation), have provided some insights into the role of auxin in the initiation of lat-eral roots. The alf1 mutant exhibits extreme prolifer-ation of adventitious and lateral roots, coupled with a 17-fold increase in endogenous auxin (Figure 19.37).
Another mutant, alf4, has the opposite phenotype: It is completely devoid of lateral roots. Microscopic analysis of alf4 roots indicates that lateral-root primordia are absent. The alf4 phenotype cannot be reversed by appli-cation of exogenous IAA.
Yet another mutant, alf3, is defective in the development of lateral-root primordia into mature lateral roots. The pri-mary root is covered with arrested lateral-root primordia that grow until they protrude through the epidermal cell layer and then stop growing. The arrested growth can be alleviated by application of exogenous IAA.
On the basis of the phenotypes of the alf mutants, a model in which IAA is required for at least two steps in the formation of lateral roots has been proposed (Figure 19.38) (Celenza et al. 1995): 1. IAA transported acropetally (toward the tip) in the stele is required to initiate cell division in the pericycle.
2. IAA is required to promote cell division and main-tain cell viability in the developing lateral root.
Auxin Delays the Onset of Leaf Abscission The shedding of leaves, flowers, and fruits from the living plant is known as abscission. These parts abscise in a region called the abscission zone, which is located near the base of the petiole of leaves. In most plants, leaf abscission is preceded by the differentiation of a distinct layer of cells, the abscission layer, within the abscission zone. During leaf senescence, the walls of the cells in the abscission layer are digested, which causes them to become soft and weak.
The leaf eventually breaks off at the abscission layer as a result of stress on the weakened cell walls.
Auxin levels are high in young leaves, progressively decrease in maturing leaves, and are relatively low in senescing leaves when the abscission process begins. The role of auxin in leaf abscission can be readily demonstrated by excision of the blade from a mature leaf, leaving the peti-ole intact on the stem. Whereas removal of the leaf blade accelerates the formation of the abscission layer in the peti-ole, application of IAA in lanolin paste to the cut surface of the petiole prevents the formation of the abscission layer.
(Lanolin paste alone does not prevent abscission.) These results suggest the following: • Auxin transported from the blade normally prevents abscission.
• Abscission is triggered during leaf senescence, when auxin is no longer being produced.
FIGURE 19.37 Root morphology of Arabidopsis (A–C) wild-type and alf1 seedlings (D–F) on hormone-free medium. Note the pro-liferation of root primoridia growing from the pericycle in the alf1 seedlings (D and E). (From Celenza et al. 1995, courtesy of J.
Celenza.) (A) (B) (C) (D) (E) (F) Wild-type alf-1 However, as will be discussed in Chapter 22, ethylene also plays a crucial role as a positive regulator of abscission.
Auxin Transport Regulates Floral Bud Development Treating Arabidopsis plants with the auxin transport inhibitor NPA causes abnormal floral development, sug-gesting that polar auxin transport in the inflorescence meristem is required for normal floral development. In Arabidopsis, the “pin-formed” mutant pin1, which lacks an auxin efflux carrier in shoot tissues, has abnormal flowers similar to those of NPA-treated plants (see Figure 19.14A).
Apparently the developing floral meristem depends on auxin being transported to it from subapical tissues. In the absence of the efflux carriers, the meristem is starved for auxin, and normal phyllotaxis and floral devel-opment are disrupted (Kuhlemeier and Reinhardt 2001).
Auxin Promotes Fruit Development Much evidence suggests that auxin is involved in the regulation of fruit development. Auxin is produced in pollen and in the endosperm and the embryo of developing seeds, and the initial stimulus for fruit growth may result from pollination.
Successful pollination initiates ovule growth, which is known as fruit set. After fertilization, fruit growth may depend on auxin pro-duced in developing seeds. The endosperm may contribute auxin during the initial stage of fruit growth, and the developing embryo may take over as the main auxin source during the later stages.
Figure 19.39 shows the influence of auxin produced by the achenes of strawberry on the growth of the receptacle of strawberry.
Auxin Induces Vascular Differentiation New vascular tissues differentiate directly below developing buds and young growing leaves (see Figure 19.5), and removal of the young leaves prevents vascular differentia-tion (Aloni 1995). The ability of an apical bud to stimulate vascular differentiation can be demonstrated in tissue culture. When the apical bud is grafted onto a clump of undifferentiated cells, or callus, xylem and phloem differentiate beneath the graft. The relative amounts of xylem and phloem formed are regulated by the auxin concentration: High auxin concen-trations induce the differentiation of xylem and phloem, but only phloem differentiates at low auxin concentrations.
Similarly, experiments on stem tissues have shown that low auxin concentrations induce phloem differentiation, whereas higher IAA levels induce xylem (Aloni 1995).
The regeneration of vascular tissue following wounding is also controlled by auxin produced by the young leaf directly above the wound site (Figure 19.40). Removal of the leaf prevents the regeneration of vascular tissue, and applied auxin can substitute for the leaf in stimulating regeneration.
Vascular differentiation is polar and occurs from leaves to roots. In woody perennials, auxin produced by growing buds in the spring stimulates activation of the cambium in ALF4 ALF1 ALF3 Gene and IAA required to maintain lateral-root growth Gene and IAA required to initiate lateral-root formation IAA transported acropetally in the vascular cylinder is required to initiate cell division in the pericycle. IAA normally restricts supply of auxin to root.
IAA IAA FIGURE 19.38 A model for the formation of lateral roots, based on the alf mutants of Arabidopsis. (After Celenza et al. 1995.) (A) Normal fruit (B) Achenes removed (C) Achenes removed; sprayed with auxin Swollen receptacle Achene FIGURE 19.39 (A) The strawberry “fruit” is actually a swollen receptacle whose growth is regulated by auxin produced by the “seeds,” which are actually achenes− the true fruits. (B) When the achenes are removed, the receptacle fails to develop normally. (C) Spraying the achene-less receptacle with IAA restores normal growth and development. (After A. Galston 1994.) 452 Chapter 19 a basipetal direction. The new round of secondary growth begins at the smallest twigs and progresses downward toward the root tip.
Further evidence for the role of auxin in vascular dif-ferentiation comes from studies in which the auxin con-centration is manipulated by the transformation of plants with auxin biosynthesis genes through use of the Ti plas-mid of Agrobacterium. When an auxin biosynthesis gene was overexpressed in petunia plants, the number of xylem tracheary elements increased. In contrast, when the level of free IAA in tobacco plants was decreased by transforma-tion with a gene coding for an enzyme that conjugated IAA to the amino acid lysine, the number of vessel elements decreased and their sizes increased (Romano et al. 1991).
Thus the level of free auxin appears to regulate the number of tracheary elements, as well as their size.
In Zinnia elegans mesophyll cell cultures, auxin is required for tracheary cell differentiation, but cytokinins also participate, perhaps by increasing the sensitivity of the cells to auxin. Whereas auxin is produced in the shoot and transported downward to the root, cytokinins are pro-duced by the root tips and transported upward into the shoot. Both hormones are probably involved in the regula-tion of cambium activation and vascular differentiation (see Chapter 21).
Synthetic Auxins Have a Variety of Commercial Uses Auxins have been used commercially in agriculture and horticulture for more than 50 years. The early commercial uses included prevention of fruit and leaf drop, promotion of flowering in pineapple, induction of parthenocarpic fruit, thinning of fruit, and rooting of cuttings for plant propagation. Rooting is enhanced if the excised leaf or stem cutting is dipped in an auxin solution, which increases the initiation of adventitious roots at the cut end.
This is the basis of commercial rooting compounds, which consist mainly of a synthetic auxin mixed with talcum powder.
In some plant species, seedless fruits may be produced naturally, or they may be induced by treatment of the unpollinated flowers with auxin. The production of such seedless fruits is called parthenocarpy. In stimulating the formation of parthenocarpic fruits, auxin may act primar-ily to induce fruit set, which in turn may trigger the endogenous production of auxin by certain fruit tissues to complete the developmental process. Ethylene is also involved in fruit development, and some of the effects of auxin on fruiting may result from the promotion of ethylene synthesis. The control of ethylene in the commercial handling of fruit is discussed in Chapter 22.
Intact cucumber plant Apical bud (A) Young leaf Mature leaf Cotyledon The stem was decapitated, and the leaves and buds above the wound site were removed to lower the endogenous auxin.
Immediately after the wounding, IAA in lanolin paste was applied to the stem above the wound.
Wound Vascular strands Node IAA in lanolin paste Xylem differentiation occurs around the wound, following the path of auxin diffusion.
FIGURE 19.40 IAA-induced xylem regeneration around the wound in cucumber (Cucumis sativus) stem tissue. (A) Method for carrying out the wound regeneration experiment. (B) Fluorescence micrograph showing regenerating vascular tissue around the wound. (B courtesy of R. Aloni.) Wound (B) Auxin: The Growth Hormone 453 In addition to these applications, today auxins are widely used as herbicides. The chemicals 2,4-D and dicamba (see Figure 19.4) are probably the most widely used synthetic auxins. Synthetic auxins are very effective because they are not metabolized by the plant as quickly as IAA is. Because maize and other monocotyledons can rapidly inactivate synthetic auxins by conjugation, these auxins are used by farmers for the control of dicot weeds, also called broad-leaved weeds, in commercial cereal fields, and by home gardeners for the control of weeds such as dandelions and daisies in lawns.
AUXIN SIGNAL TRANSDUCTION PATHWAYS The ultimate goal of research on the molecular mechanism of hormone action is to reconstruct each step in the signal transduction pathway, from receptor binding to the phys-iological response. In this last section of the chapter, we will examine candidates for the auxin receptor and then discuss the various signaling pathways that have been implicated in auxin action. Finally we will turn our attention to auxin-regulated gene expression.
ABP1 Functions as an Auxin Receptor In addition to its possible direct role in plasma membrane H+-ATPase activation (discussed earlier), the auxin-bind-ing protein ABP1 appears to function as an auxin receptor in other signal transduction pathways. ABP1 homologs have been identified in a variety of monocot and dicot species (Venis and Napier 1997). Knockouts of the ABP1 gene in Arabidopsis are lethal, and less severe mutations result in altered development (Chen et al. 2001). Recent studies indicate that, despite being localized primarily on the endoplasmic reticulum (ER), a small amount of ABP1 is secreted to the plasma membrane outer surface where it interacts with auxin to cause protoplast swelling and H+-pumping (Venis et al. 1996; Steffens et al. 2001).
However, it is unlikely that ABP1 mediates all auxin response pathways because expression of a number of auxin-responsive genes is not affected when protoplasts are incubated with anti-ABP1 antibodies. It is also unclear what role the ABP1 in the ER plays in auxin-responsive sig-nal transduction. Finally, it remains to be determined whether ABP57, the soluble and unrelated ABP from rice that activates the H+-ATPase (see Figure 19.24), is involved in a signal transduction pathway.
Calcium and Intracellular pH Are Possible Signaling Intermediates Calcium plays an important role in signal transduction in animals and is thought to be involved in the action of cer-tain plant hormones as well. The role of calcium in auxin action seems very complex and, at this point in time, very uncertain. Nevertheless, some experimental evidence shows that auxin increases the level of free calcium in the cell.
Changes in cytoplasmic pH can also serve as a second messenger in animals and plants. In plants, auxin induces a decrease in cytosolic pH of about 0.2 units within 4 min-utes of application. The cause of this pH drop is not known. Since the cytosolic pH is normally around 7.4, and the pH optimum of the plasma membrane H+-ATPase is 6.5, a decrease in the cytosolic pH of 0.2 units could cause a marked increase in the activity of the plasma membrane H+-ATPase. The decrease in cytosolic pH might also account for the auxin-induced increase in free intracellular calcium, by promoting the dissociation of bound forms.
MAP kinases (see Chapter 14 on the web site) that play a role in signal transduction by phosphorylating proteins in a cascade that ultimately activates transcription factors have also been implicated in auxin responses. When tobacco cells are deprived of auxin, they arrest at the end of either the G1 or the G2 phase and cease dividing; if auxin is added back into the culture medium, the cell cycle resumes (Koens et al. 1995). (For a description of the cell cycle, see Chapter 1.) Auxin appears to exert its effect on the cell cycle primarily by stimulating the synthesis of the major cyclin-dependent protein kinase (CDK): Cdc2 (cell division cycle 2) (see Chapter 14 on the web site).
Auxin-Induced Genes Fall into Two Classes: Early and Late One of the important functions of the signal transduction pathway(s) initiated when auxin binds to its receptor is the activation of a select group of transcription factors. The activated transcription factors enter the nucleus and pro-mote the expression of specific genes. Genes whose expres-sion is stimulated by the activation of preexisting tran-scription factors are called primary response genes or early genes.
This definition implies that all of the proteins required for auxin-induced expression of the early genes are present in the cell at the time of exposure to the hormone; thus, early-gene expression cannot be blocked by inhibitors of protein synthesis such as cycloheximide. As a consequence, the time required for the expression of the early genes can be quite short, ranging from a few minutes to several hours (Abel and Theologis 1996).
In general, primary response genes have three main functions: (1) Some of the early genes encode proteins that regulate the transcription of secondary response genes, or late genes, that are required for the long-term responses to the hormone. Because late genes require de novo protein synthesis, their expression can be blocked by protein syn-thesis inhibitors. (2) Other early genes are involved in inter-cellular communication, or cell-to-cell signaling. (3) Another group of early genes is involved in adaptation to stress.
454 Chapter 19 Five major classes of early auxin-responsive genes have been identified: • Genes involved in auxin-regulated growth and devel-opment: 1. The AUX/IAA gene family 2. The SAUR gene family 3. The GH3 gene family • Stress response genes: 1. Genes encoding glutathione S-transferases 2. Genes encoding 1-aminocyclopropane-1-car-boxylic acid (ACC) synthase, the key enzyme in the ethylene biosynthetic pathway (see Chapter 22) Early genes for growth and development. Members of the AUX/IAA gene family encode short-lived transcription fac-tors that function as repressors or activators of the expres-sion of late auxin-inducible genes. The expression of most of the AUX/IAA family of genes is stimulated by auxin within 5 to 60 minutes of hormone addition All the genes encode small hydrophilic polypeptides that have putative DNA-binding motifs similar to those of bacterial repres-sors. They also have short half-lives (about 7 minutes), indi-cating that they are turning over rapidly.
The SAUR gene family was mentioned earlier in the chapter in relation to tropisms. Auxin stimulates the expression of SAUR genes within 2 to 5 minutes of treat-ment, and the response is insensitive to cycloheximide. The five SAUR genes of soybean are clustered together, contain no introns, and encode highly similar polypeptides of unknown function. Because of the rapidity of the response, expression of SAUR genes has proven to be a convenient probe for the lateral transport of auxin during photo- and gravitropism.
GH3 early-gene family members, identified in both soy-bean and Arabidopsis, are stimulated by auxin within 5 min-utes. Mutations in Arabidopsis GH3-like genes result in dwarfism (Nakazawa et al. 2001) and appear to function in light-regulated auxin responses (Hsieh et al. 2000). Because GH3 expression is a good reflection of the presence of endogenous auxin, a synthetic GH3-based reporter gene known as DR5 is widely used in auxin bioassays (see Fig-ure 19.5 and Web Topic 19.12) (Ulmasov et al. 1997).
Early genes for stress adaptations. As mentioned earlier in the chapter, auxin is involved in stress responses, such as wounding. Several genes encoding glutathione-S-trans-ferases (GSTs), a class of proteins stimulated by various stress conditions, are induced by elevated auxin concen-trations. Likewise, ACC synthase, which is also induced by stress and is the rate-limiting step in ethylene biosynthesis (see Chapter 22), is induced by high levels of auxin.
To be induced, the promoters of the early auxin genes must contain response elements that bind to the transcrip-tion factors that become activated in the presence of auxin.
A limited number of these response elements appear to be arranged combinatorily within the promoters of a variety of auxin-induced genes.
Auxin-Responsive Domains Are Composite Structures A conserved auxin response element (AuxRE) within the promoters of the early auxin genes, like GH3, is usually combined with other response elements to form auxin response domains (AuxRDs). For example, the GH3 gene promoter of soybean is composed of three independently acting AuxRDs (each containing multiple AuxREs) that contribute incrementally to the strong auxin inducibility of the promoter.
Early Auxin Genes Are Regulated by Auxin Response Factors As noted previously, early auxin genes are by definition insensitive to protein synthesis inhibitors such as cyclo-heximide. Instead of being inhibited, the expression of many of the early auxin genes has been found to be stimu-lated by cycloheximide.
Cycloheximide stimulation of gene expression is accom-plished both by transcriptional activation and by mRNA stabilization. Transcriptional activation of a gene by inhibitors of protein synthesis usually indicates that the gene is being repressed by a short-lived repressor protein or by a regulatory pathway that involves a protein with a high turnover rate.
A family of auxin response factors (ARFs) function as transcriptional activators by binding to the auxin response element TGTCTC, which is present in the promoters of GH3 and other early auxin response genes. Mutations in ARF genes result in severe developmental defects. To bind the AuxRE stably, ARFs must form dimers. It has been proposed that ARF dimers promote transcription by binding to two AuxREs arranged in a palindrome (Ulmasov et al. 1997).
Recent studies also indicate that proteins encoded by the AUX/IAA gene family (itself one of the early auxin response gene families) can inhibit the transcription of early auxin response genes by forming inactive het-erodimers with ARFs. These inactive heterodimers may act to inhibit ARF–AuxRE binding, thereby blocking either gene activation or repression. AUX/IAA proteins may thus function as ARF inhibitors.
It is now believed that auxin induces the transcription of the early response genes by promoting the proteolytic degradation of the inhibitory AUX/IAA proteins so that active ARF dimers can form. The precise mechanism by Auxin: The Growth Hormone 455 which auxin causes AUX/IAA turnover is unknown, although it is known to involve ubiquitination by a ubiq-uitin ligase and proteolysis by the massive 26S proteasome complex (see Chapter 14 on the web site) (Gray et al. 2001; Zenser et al. 2001). Note that a negative feedback loop is introduced into the pathway by virtue of the fact that one of the gene families turned on by auxin is AUX/IAA, which inhibits the response.
A model for auxin regulation of the early response genes based on the findings described here is shown in Figure 19.41.
SUMMARY Auxin was the first hormone to be discovered in plants and is one of an expanding list of chemical signaling agents that regulate plant development. The most common naturally occurring form of auxin is indole-3-acetic acid (IAA). One of the most important roles of auxin in higher plants is the regulation of elongation growth in young stems and coleoptiles. Low levels of auxin are also required for root elongation, although at higher concentrations auxin acts as a root growth inhibitor.
Accurate measurement of the amount of auxin in plant tissues is critical for understanding the role of this hormone in plant physiology. Early coleoptile-based bioassays have been replaced by more accurate techniques, including physicochemical methods and immunoassay.
Regulation of growth in plants may depend in part on the amount of free auxin present in plant cells, tissues, and organs. There are two main pools of auxin in the cell: the cytosol and the chloroplasts. Levels of free auxin can be mod-ulated by several factors, including the synthesis and break-down of conjugated IAA, IAA metabolism, compartmenta-tion, and polar auxin transport. Several pathways have been implicated in IAAbiosynthesis, including tryptophan-depen-dent and tryptophan-independent pathways. Several degradative pathways for IAA have also been identified.
IAA is synthesized primarily in the apical bud and is transported polarly to the root. Polar transport is thought to occur mainly in the parenchyma cells associated with the vascular tissue. Polar auxin transport can be divided into two main processes: IAA influx and IAA efflux. In accord with the chemiosmotic model for polar transport, there are two modes of IAA influx: by a pH-dependent passive transport of the undissociated form, or by an active H+ ATP ARF AUX/IAA AUX/IAA 1. In the absence of IAA, the transcription factor, ARF, forms inactive heterodimers with AUX/IAA proteins.
3. In the presence of auxin, AUX/IAA proteins are targeted for destruction by an activated ubiquitin ligase.
5. IAA-induced degradation of the AUX/IAA proteins allows active ARF homodimers to form.
6. The active ARF homodimers bind to palindromic AuxREs in the promoters of the early genes, activating transcription. 7. Transcription of the early genes initiates the auxin response.
8. The stimulation of AUX/IAA genes introduces a negative feedback loop.
4. The AUX/IAA proteins are tagged with ubiquitin and degraded by the 26S proteasome.
2. Inactive hetero-dimers block the transcription of the early auxin genes. There is no auxin response.
AUX/IAA and other early genes Inactive ARF heterodimer Signal transduction pathway ARF ARF Active ARF homodimer IAA Proteasome Ubiquitin Ubi TGTCTC CTCTGT Palindromic AuxRE AUX/IAA and other early genes Auxin-mediated growth/development DNA Activation of ubiquitin ligase FIGURE 19.41 A model for auxin regulation of transcriptional activation of early response genes by auxin. (After Gray et al. 2001.) 456 Chapter 19 cotransport mechanism driven by the plasma membrane H+-ATPase. Auxin efflux is thought to occur preferentially at the basal ends of the transporting cells via anion efflux carriers and to be driven by the membrane potential generated by the plasma membrane H+-ATPase. Auxin transport inhibitors (ATIs) can interrupt auxin transport directly by competing with auxin for the efflux channel pore or by binding to regulatory or structural proteins associated with the efflux channel. Auxin can be transported nonpolarly in the phloem.
Auxin-induced cell elongation begins after a lag time of about 10 minutes. Auxin promotes elongation growth pri-marily by increasing cell wall extensibility. Auxin-induced wall loosening requires continuous metabolic input and is mimicked in part by treatment with acidic buffers. According to the acid growth hypothesis, one of the important actions of auxin is to induce cells to transport protons into the cell wall by stimulating the plasma mem-brane H+-ATPase. Two mechanisms have been proposed for auxin-induced proton extrusion: direct activation of the proton pump and enhanced synthesis of the plasma mem-brane H+-ATPase. The ability of protons to cause cell wall loosening is mediated by a class of proteins called expansins. Expansins loosen the cell wall by breaking hydrogen bonds between the polysaccharide components of the wall. In addition to proton extrusion, long-term auxin-induced growth involves the uptake of solutes and the synthesis and deposition of polysaccharides and pro-teins needed to maintain the acid-induced wall-loosening capacity.
Promotion of growth in stems and coleoptiles and inhi-bition of growth in roots are the best-studied physiological effects of auxins. Auxin-promoted differential growth in these organs is responsible for the responses to directional stimuli (i.e., light, gravity) called tropisms. According to the Cholodny–Went model, auxin is transported laterally to the shaded side during phototropism and to the lower side during gravitropism. Statoliths (starch-filled amyloplasts) in the statocytes are involved in the normal percepton of gravity, but they are not absolutely required.
In addition to its roles in growth and tropisms, auxin plays central regulatory roles in apical dominance, lateral-root initiation, leaf abscission, vascular differentiation, flo-ral bud formation, and fruit development. Commercial applications of auxins include rooting compounds and her-bicides.
The auxin-binding soluble protein ABP1 is a strong can-didate for the auxin receptor. ABP1 is located primarily in the ER lumen. Studies of the signal transduction pathways involved in auxin action have implicated other signaling intermediates such as Ca2+, intracellular pH, and kinases in auxin-induced cell division.
Auxin-induced genes fall into two categories: early and late. Induction of early genes by auxin does not require protein synthesis and is insensitive to protein synthesis inhibitors. The early genes fall into three functional classes: expression of the late genes (secondary response genes), stress adaptation, and intercellular signaling. The auxin response domains of the promoters of the auxin early genes have a composite structure in which an auxin-inducible response element is combined with a constitutive response element. Auxin-induced genes may be negatively regulated by repressor proteins that are degraded via a ubiquitin acti-vation pathway.
Web Material Web Topics 19.1 Additional Synthetic Auxins Biologically active synthetic auxins have suprisingly diverse structures.
19.2 The Structural Requirements for Auxin Activity Comparisons of a wide variety of compounds that possess auxin activity have revealed common features at the molecular level that are essential for biological activity.
19.3 Auxin Measurement by Radioimmunoassy Radioimmunoassay (RIA) allows the measure-ment of physiological levels (10−9 g = 1 ng) of IAA in plant tissues.
19.4 Evidence for the Tryptophan-Independent Biosynthesis of IAA Additional experimental evidence for the tryptophan-independent biosynthesis of IAA is provided.
19.5 The Multiple Factors That Regulate Steady-State IAA Levels The steady-state level of free IAA in the cytosol is determined by several intercon-nected processes, including synthesis, degra-dation, conjugation, compartmentation and transport.
19.6 The Mechanism of Fusicoccin Activation of the Plasma Membrane H+-ATPase Fusicoccin,a phytotoxin produced by the fun-gus Fusicoccum amygdale, causes membrane hyperpolarization and proton extrusion in nearly all plant tissues, and acts as a “super-auxin“ in elongation assays.
19.7 The Fluence Response of Phototropism The effect of light dose on phototropism is described and a model explaining the phe-nomenon is presented.
Auxin: The Growth Hormone 457 19.8 Differential SAUR Gene Expression during Gravitropism SAUR gene expression is used to detect the lateral auxin gradient during gravitropism.
19.9 Gravity Perception without Statoliths in Chara The giant-celled freshwater alga,Chara,bends in response to gravity without any apparent statoliths.
19.10 The Role of Cytokinins in Apical Dominance In the Douglas fir Pseudotsuga menziesii, there is a correlation between cytokinin levels and axil-lary bud growth.
19.11 The Role of ABA in Apical Dominance In Quackgrass (Elytrigia repens) axillary bud growth is correlated with a reduction in ABA.
19.12 The Facilitation of IAA Measurements by GH3-Based Reporter Constructs Because GH3 expression is a good reflection of the presence of endogenous auxin, a GH3-based reporter gene, known as DR5, is widely used in auxin bioassays.
19.13 The Effect of Auxin on Ubiquitin-Mediated Degradation of AUX/IAA Proteins A model for auxin-regulated degradation of AUX/IAA proteins is discussed.
Web Essays 19.1 Brassinosteroids: A New Class of Plant Steroid Hormones Brassinosteroids have been implicated in a wide range of developmental phenomena in plants, including stem elongation, inhibition of root growth, and ethylene biosynthesis.
19.2 Exploring the Cellular Basis of Polar Auxin Transport.
Experimental evidence indicates that the polar transport of the plant hormone auxin is regulated at the cellular level.This implies that proteins involved in auxin transport must be asymmetrically distributed on the plasma membrane. How those transport proteins get to their destination is the focus of ongoing research.
19.3 Phototropism: From Photoperception to Auxin-Dependent Changes in Gene Ex-pression How photoperception by phototropins is coupled to auxin signaling is the subject of this essay.
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460 Chapter 19 Gibberellins: Regulators of Plant Height 20 Chapter FOR NEARLY 30 YEARS after the discovery of auxin in 1927, and more than 20 years after its structural elucidation as indole-3-acetic acid, West-ern plant scientists tried to ascribe the regulation of all developmental phenomena in plants to auxin. However, as we will see in this and sub-sequent chapters, plant growth and development are regulated by sev-eral different types of hormones acting individually and in concert.
In the 1950s the second group of hormones, the gibberellins (GAs), was characterized. The gibberellins are a large group of related com-pounds (more than 125 are known) that, unlike the auxins, are defined by their chemical structure rather than by their biological activity. Gib-berellins are most often associated with the promotion of stem growth, and the application of gibberellin to intact plants can induce large increases in plant height. As we will see, however, gibberellins play important roles in a variety of physiological phenomena. The biosynthesis of gibberellins is under strict genetic, developmen-tal, and environmental control, and numerous gibberellin-deficient mutants have been isolated. Mendel’s tall/dwarf alleles in peas are a famous example. Such mutants have been useful in elucidating the com-plex pathways of gibberellin biosynthesis.
We begin this chapter by describing the discovery, chemical structure, and role of gibberellins in regulating various physiological processes, including seed germination, mobilization of endosperm storage reserves, shoot growth, flowering, floral development, and fruit set. We then examine biosynthesis of the gibberellins, as well as identification of the active form of the hormone.
In recent years, the application of molecular genetic approaches has led to considerable progress in our understanding of the mechanism of gibberellin action at the molecular level. These advances will be dis-cussed at the end of the chapter.
THE DISCOVERY OF THE GIBBERELLINS Although gibberellins did not become known to American and British scientists until the 1950s, they had been dis-covered much earlier by Japanese scientists. Rice farmers in Asia had long known of a disease that makes the rice plants grow tall but eliminates seed production. In Japan this disease was called the “foolish seedling,” or bakanae, disease.
Plant pathologists investigating the disease found that the tallness of these plants was induced by a chemical secreted by a fungus that had infected the tall plants. This chemical was isolated from filtrates of the cultured fungus and called gibberellin after Gibberella fujikuroi, the name of the fungus.
In the 1930s Japanese scientists succeeded in obtaining impure crystals of two fungal growth-active compounds, which they termed gibberellin A and B, but because of com-munication barriers and World War II, the information did not reach the West. Not until the mid-1950s did two groups—one at the Imperial Chemical Industries (ICI) research station at Welyn in Britain, the other at the U.S.
Department of Agriculture (USDA) in Peoria, Illinois—suc-ceed in elucidating the structure of the material that they had purified from fungal culture filtrates, which they named gibberellic acid: At about the same time scientists at Tokyo University isolated three gibberellins from the original gibberellin A and named them gibberellin A1, gibberellin A2, and gib-berellin A3. Gibberellin A3 and gibberellic acid proved to be identical.
It became evident that an entire family of gibberellins exists and that in each fungal culture different gibberellins predominate, though gibberellic acid is always a principal component. As we will see, the structural feature that all gibberellins have in common, and that defines them as a family of molecules, is that they are derived from the ent-kaurene ring structure: As gibberellic acid became available, physiologists began testing it on a wide variety of plants. Spectacular responses were obtained in the elongation growth of dwarf and rosette plants, particularly in genetically dwarf peas (Pisum sativum), dwarf maize (Zea mays), and many rosette plants.
In contrast, plants that were genetically very tall showed no further response to applied gibberellins. More recently, experiments with dwarf peas and dwarf corn have con-firmed that the natural elongation growth of plants is reg-ulated by gibberellins, as we will describe later.
Because applications of gibberellins could increase the height of dwarf plants, it was natural to ask whether plants contain their own gibberellins. Shortly after the discovery of the growth effects of gibberellic acid, gibberellin-like substances were isolated from several species of plants.1 Gibberellin-like substance refers to a compound or an extract that has gibberellin-like biological activity, but whose chemical structure has not yet been defined. Such a response indicates, but does not prove, that the tested sub-stance is a gibberellin. In 1958 a gibberellin (gibberellin A1) was conclusively identified from a higher plant (runner bean seeds, Phaseo-lus coccineus): Because the concentration of gibberellins in immature seeds far exceeds that in vegetative tissue, immature seeds were the tissue of choice for gibberellin extraction. However, because the concentration of gibberellins in plants is very low (usually 1–10 parts per billion for the active gibberellin in vegetative tissue and up to 1 part per million of total gib-berellins in seeds), chemists had to use truckloads of seeds.
As more and more gibberellins from fungal and plant sources were characterized, they were numbered as gib-berellin AX (or GAX), where X is a number, in the order of their discovery. This scheme was adopted for all gib-berellins in 1968. However, the number of a gibberellin is simply a cataloging convenience, designed to prevent chaos in the naming of the gibberellins. The system implies no close chemical similarity or metabolic relationship between gibberellins with adjacent numbers.
All gibberellins are based on the ent-gibberellane skeleton: 2 3 1 4 18 19 15 13 12 11 16 17 10 20 5 6 7 8 H H A B 9 C 14 D ent-Gibberellane structure COOH O CO CH3 H CH2 HO OH Gibberellin A1 (GA1) CH2 ent-Kaurene COOH O CO CH3 H CH2 HO OH Gibberellic acid (GA3) 1 Phinney (1983) provides a wonderful personal account of the history of gibberellin discoveries.
462 Chapter 20 Some gibberellins have the full complement of 20 carbons (C20-GAs): Others have only 19 (C19-GAs), having lost one carbon to metabolism.
There are other variations in the basic structure, espe-cially the oxidation state of carbon 20 (in C20-GAs) and the number and position of hydroxyl groups on the molecule (see Web Topic 20.1). Despite the plethora of gibberellins present in plants, genetic analyses have demonstrated that only a few are biologically active as hormones. All the oth-ers serve as precursors or represent inactivated forms.
EFFECTS OF GIBBERELLIN ON GROWTH AND DEVELOPMENT Though they were originally discovered as the cause of a disease of rice that stimulated internode elongation, endogenous gibberellins influence a wide variety of devel-opmental processes. In addition to stem elongation, gib-berellins control various aspects of seed germination, including the loss of dormancy and the mobilization of endosperm reserves. In reproductive development, gib-berellin can affect the transition from the juvenile to the mature stage, as well as floral initiation, sex determination, and fruit set. In this section we will review some of these gibberellin-regulated phenomena.
Gibberellins Stimulate Stem Growth in Dwarf and Rosette Plants Applied gibberellin promotes internodal elongation in a wide range of species. However, the most dramatic stimu-lations are seen in dwarf and rosette species, as well as members of the grass family. Exogenous GA3 causes such extreme stem elongation in dwarf plants that they resem-ble the tallest varieties of the same species (Figure 20.1).
Accompanying this effect are a decrease in stem thickness, a decrease in leaf size, and a pale green color of the leaves.
Some plants assume a rosette form in short days and undergo shoot elongation and flowering only in long days (see Chapter 24). Gibberellin application results in bolting (stem growth) in plants kept in short days (Figure 20.2), and normal bolting is regulated by endogenous gibberellin.
In addition, as noted earlier, many long-day rosette plants have a cold requirement for stem elongation and flower-ing, and this requirement is overcome by applied gib-berellin.
GA also promotes internodal elongation in members of the grass family. The target of gibberellin action is the inter-calary meristem—a meristem near the base of the intern-ode that produces derivatives above and below. Deep-water rice is a particularly striking example. We will examine the effects of gibberellin on the growth of deep-water rice in the section on the mechanism of gibberellin-induced stem elongation later in the chapter.
Although stem growth may be dramatically enhanced by GAs, gibberellins have little direct effect on root growth.
However, the root growth of extreme dwarfs is less than that of wild-type plants, and gibberellin application to the shoot enhances both shoot and root growth. Whether the effect of gibberellin on root growth is direct or indirect is currently unresolved.
Gibberellins Regulate the Transition from Juvenile to Adult Phases Many woody perennials do not flower until they reach a certain stage of maturity; up to that stage they are said to H3C COOH COOH H3C 6 20 7 H H CH2 GA12 (a C20-gibberellin) FIGURE 20.1 The effect of exogenous GA1 on normal and dwarf (d1) corn. Gibberellin stimulates dramatic stem elon-gation in the dwarf mutant but has little or no effect on the tall wild-type plant. (Courtesy of B. Phinney.) Gibberellins: Regulators of Plant Height 463 be juvenile (see Chapter 24). The juvenile and mature stages often have different leaf forms, as in English ivy (Hedera helix) (see Figure 24.9). Applied gibberellins can regulate this juvenility in both directions, depending on the species. Thus, in English ivy GA3 can cause a reversion from a mature to a juvenile state, and many juvenile conifers can be induced to enter the reproductive phase by applications of nonpolar gibberellins such as GA4 + GA7.
(The latter example is one instance in which GA3 is not effective.) Gibberellins Influence Floral Initiation and Sex Determination As already noted, gibberellin can substitute for the long-day or cold requirement for flowering in many plants, especially rosette species (see Chapter 24). Gibberellin is thus a component of the flowering stimulus in some plants, but apparently not in others.
In plants where flowers are unisexual rather than her-maphroditic, floral sex determination is genetically regu-lated. However, it is also influenced by environmental fac-tors, such as photoperiod and nutritional status, and these environmental effects may be mediated by gibberellin. In maize, for example, the staminate flowers (male) are restricted to the tassel, and the pistillate flowers (female) are contained in the ear. Exposure to short days and cool nights increases the endogenous gibberellin levels in the tassels 100-fold and simultaneously causes feminization of the tassel flowers. Application of exogenous gibberellic acid to the tassels can also induce pistillate flowers.
For studies on genetic regulation, a large collection of maize mutants that have altered patterns of sex determi-nation have been isolated. Mutations in genes that affect either gibberellin biosynthesis or gibberellin signal trans-duction result in a failure to suppress stamen development in the flowers of the ear (Figure 20.3). Thus the primary role of gibberellin in sex determination in maize seems to be to suppress stamen development (Irish 1996).
In dicots such as cucumber, hemp, and spinach, gib-berellin seems to have the opposite effect. In these species, application of gibberellin promotes the formation of sta-minate flowers, and inhibitors of gibberellin biosynthesis promote the formation of pistillate flowers.
Gibberellins Promote Fruit Set Applications of gibberellins can cause fruit set (the initia-tion of fruit growth following pollination) and growth of some fruits, in cases where auxin may have no effect. For example, stimulation of fruit set by gibberellin has been observed in apple (Malus sylvestris).
Gibberellins Promote Seed Germination Seed germination may require gibberellins for one of sev-eral possible steps: the activation of vegetative growth of FIGURE 20.2 Cabbage, a long-day plant, remains as a rosette in short days, but it can be induced to bolt and flower by applications of gibberellin. In the case illustrated, giant flowering stalks were produced. (© Sylvan Wittwer/Visuals Unlimited.) FIGURE 20.3 Anthers develop in the ears of a gibberellin-deficient dwarf mutant of corn (Zea mays). (Bottom) Unfertilized ear of the dwarf mutant an1, showing conspic-uous anthers. (Top) Ear from a plant that has been treated with gibberellin. (Courtesy of M. G. Neuffer.) 464 Chapter 20 the embryo, the weakening of a growth-constraining endosperm layer surrounding the embryo, and the mobi-lization of stored food reserves of the endosperm. Some seeds, particularly those of wild plants, require light or cold to induce germination. In such seeds this dormancy (see Chapter 23) can often be overcome by application of gib-berellin. Since changes in gibberellin levels are often, but not always, seen in response to chilling of seeds, gib-berellins may represent a natural regulator of one or more of the processes involved in germination.
Gibberellin application also stimulates the production of numerous hydrolases, notably α-amylase, by the aleu-rone layers of germinating cereal grains. This aspect of gib-berellin action has led to its use in the brewing industry in the production of malt (discussed in the next section).
Because this is the principal system in which gibberellin signal transduction pathways have been analyzed, it will be treated in detail later in the chapter.
Gibberellins Have Commercial Applications The major uses of gibberellins (GA3, unless noted other-wise), applied as a spray or dip, are to manage fruit crops, to malt barley, and to increase sugar yield in sugarcane. In some crops a reduction in height is desirable, and this can be accomplished by the use of gibberellin synthesis inhibitors (see Web Topic 20.1).
Fruit production.
Amajor use of gibberellins is to increase the stalk length of seedless grapes. Because of the shortness of the individual fruit stalks, bunches of seedless grapes are too compact and the growth of the berries is restricted. Gib-berellin stimulates the stalks to grow longer, thereby allow-ing the grapes to grow larger by alleviating compaction, and it promotes elongation of the fruit (Figure 20.4).
A mixture of benzyladenine (a cytokinin; see Chapter 21) and GA4 + GA7 can cause apple fruit to elongate and is used to improve the shape of Delicious-type apples under certain conditions. Although this treatment does not affect yield or taste, it is considered commercially desirable.
In citrus fruits, gibberellins delay senescence, allowing the fruits to be left on the tree longer to extend the market period.
Malting of barley.
Malting is the first step in the brew-ing process. During malting, barley seeds (Hordeum vulgare) are allowed to germinate at temperatures that maximize the production of hydrolytic enzymes by the aleurone layer. Gibberellin is sometimes used to speed up the malt-ing process. The germinated seeds are then dried and pul-verized to produce “malt,” consisting mainly of a mixture of amylolytic (starch-degrading) enzymes and partly digested starch.
During the subsequent “mashing” step, water is added and the amylases in the malt convert the residual starch, as well as added starch, to the disaccharide maltose, which is converted to glucose by the enzyme maltase. The resulting “wort” is then boiled to stop the reaction. In the final step, yeast converts the glucose in the wort to ethanol by fer-mentation.
Increasing sugarcane yields.
Sugarcane (Saccharum offic-inarum) is one of relatively few plants that store their car-bohydrate as sugar (sucrose) instead of starch (the other important sugar-storing crop is sugar beet). Originally from New Guinea, sugarcane is a giant perennial grass that can grow from 4 to 6 m tall. The sucrose is stored in the central vacuoles of the internode parenchyma cells. Spraying the crop with gibberellin can increase the yield of raw cane by up to 20 tons per acre, and the sugar yield by 2 tons per acre. This increase is a result of the stimulation of internode elongation during the winter season.
Uses in plant breeding.
The long juvenility period in conifers can be detrimental to a breeding program by pre-venting the reproduction of desirable trees for many years.
Spraying with GA4 + GA7 can considerably reduce the time to seed production by inducing cones to form on very young trees. In addition, the promotion of male flowers in cucurbits, and the stimulation of bolting in biennial rosette crops such as beet (Beta vulgaris) and cabbage (Brassica oler-acea), are beneficial effects of gibberellins that are occa-sionally used commercially in seed production.
Gibberellin biosynthesis inhibitors.
Bigger is not always better. Thus, gibberellin biosynthesis inhibitors are used commercially to prevent elongation growth in some plants.
In floral crops, short, stocky plants such as lilies, chrysan-themums, and poinsettias are desirable, and restrictions on elongation growth can be achieved by applications of gib-berellin synthesis inhibitors such as ancymidol (known commercially as A-Rest) or paclobutrazol (known as Bonzi).
FIGURE 20.4 Gibberellin induces growth in Thompson’s seedless grapes. The bunch on the left is an untreated con-trol. The bunch on the right was sprayed with gibberellin during fruit development. (© Sylvan Wittwer/Visuals Unlimited.) Gibberellins: Regulators of Plant Height 465 Tallness is also a disadvantage for cereal crops grown in cool, damp climates, as occur in Europe, where lodging can be a problem. Lodging—the bending of stems to the ground caused by the weight of water collecting on the ripened heads—makes it difficult to harvest the grain with a com-bine harvester. Shorter internodes reduce the tendency of the plants to lodge, increasing the yield of the crop. Even genetically dwarf wheats grown in Europe are sprayed with gibberellin biosynthesis inhibitors to further reduce stem length and lodging.
Yet another application of gibberellin biosynthesis inhibitors is the restriction of growth in roadside shrub plantings.
BIOSYNTHESIS AND METABOLISM OF GIBBERELLIN Gibberellins constitute a large family of diterpene acids and are synthesized by a branch of the terpenoid pathway, which was described in Chapter 13. The elucidation of the gibberellin biosynthetic pathway would not have been pos-sible without the development of sensitive methods of detection. As noted earlier, plants contain a bewildering array of gibberellins, many of which are biologically inactive.
In this section we will discuss the biosynthesis of GAs, as well as other factors that regulate the steady-state levels of the biologically active form of the hormone in different plant tissues.
Gibberellins Are Measured via Highly Sensitive Physical Techniques Systems of measurement using a biological response, called bioassays, were originally important for detecting gib-berellin-like activity in partly purified extracts and for assessing the biological activity of known gibberellins (Fig-ure 20.5). The use of bioassays, however, has declined with the development of highly sensitive physical techniques that allow precise identification and quantification of spe-cific gibberellins from small amounts of tissue.
High-performance liquid chromatography (HPLC) of plant extracts, followed by the highly sensitive and selec-tive analytical method of gas chromatography combined with mass spectrometry (GC-MS), has now become the method of choice. With the availability of published mass spectra, researchers can now identify gibberellins without possessing pure standards. The availability of heavy-iso-tope-labeled standards of common gibberellins, which can themselves be separately detected on a mass spectrometer, allows the accurate measurement of levels in plant tissues by mass spectrometry with these heavy-isotope-labeled gibberellins as internal standards for quantification (see Web Topic 20.2).
Gibberellins Are Synthesized via the Terpenoid Pathway in Three Stages Gibberellins are tetracyclic diterpenoids made up of four isoprenoid units. Terpenoids are compounds made up of five-carbon (isoprene) building blocks: joined head to tail. Researchers have determined the entire gibberellin biosynthetic pathway in seed and vegetative tis-sues of several species by feeding various radioactive pre-cursors and intermediates and examining the production of the other compounds of the pathway (Kobayashi et al. 1996).
The gibberellin biosynthetic pathway can be divided into three stages, each residing in a different cellular com-partment (Figure 20.6) (Hedden and Phillips 2000).
C CH2 OH CH CH2 FIGURE 20.5 Gibberellin causes elongation of the leaf sheath of rice seedlings, and this response is used in the dwarf rice leaf sheath bioassay. Here 4-day-old seedlings were treated with dif-ferent amounts of GA and allowed to grow for another 5 days. (Courtesy of P. Davies.) 466 Chapter 20 OPP OPP COOH COOH OH COOH COOH R COOH COOH COOH COOH HOCH2 R COOH O HO CO R COOH O CO R COOH O HO CO R COOH O HO HO CO R COOH COOH CHO R ent-Kaurene ent-Kaurene GA12-aldehyde ent-Copalyl diphosphate GGPP COOH CH3 CH3 CHO GA12 GA53 GA12 (R = H) GA53 (R = OH) GA 20-oxidase GA 2-oxidase GA 2-oxidase GA15-OL (R = H) GA44-OL (R = OH) GA 20-oxidase GA 20-oxidase GA 3-oxidase Active GA GA4 (R = H) GA1 (R = OH) GA9 (R = H) GA20 (R = OH) GA34 (R = H) GA8 (R = OH) GA51 (R = H) GA29 (R = OH) GA24 (R = H) GA19 (R = OH) PLASTID ENDOPLASMIC RETICULUM CYTOSOL Stage 1 Stage 2 Stage 3 Inactivation FIGURE 20.6 The three stages of gibberellin biosynthesis. In stage 1, geranylgeranyl diphosphate (GGPP) is converted to ent-kaurene via copalyl diphosphate (CPP) in plastids. In stage 2, which takes place on the endoplasmic reticulum, ent-kaurene is converted to GA12 or GA53, depending on whether the GA is hydroxylated at carbon 13. In most plants the 13-hydroxylation pathway predominates, though in Arabidopsis and some others the non-13-OH pathway is the main pathway. In stage 3 in the cytosol, GA12 or GA53 are converted other GAs. This conversion proceeds with a series of oxidations at carbon 20. In the 13-hydroxylation pathway this leads to the production of GA20. GA20 is then oxidized to the active gibberellin, GA1, by a 3β-hydroxyla-tion reaction (the non-13-OH equivalent is GA4). Finally, hydroxylation at carbon 2 converts GA20 and GA1 to the inactive forms GA29 and GA8, respectively. (OL = Open lactone ring) Stage 1: Production of terpenoid precursors and ent-kau-rene in plastids.
The basic biological isoprene unit is isopentenyl diphosphate (IPP).2 IPP used in gibberellin biosynthesis in green tissues is synthesized in plastids from glyceraldehyde-3-phosphate and pyruvate (Lichtenthaler et al. 1997). However, in the endosperm of pumpkin seeds, which are very rich in gibberellin, IPP is formed in the cytosol from mevalonic acid, which is itself derived from acetyl-CoA.
Thus the IPP used to make gibberellins may arise from dif-ferent cellular compartments in different tissues.
Once synthesized, the IPP isoprene units are added suc-cessively to produce intermediates of 10 carbons (geranyl diphosphate), 15 carbons (farnesyl diphosphate), and 20 carbons (geranylgeranyl diphosphate, GGPP). GGPP is a precursor of many terpenoid compounds, including carotenoids and many essential oils, and it is only after GGPP that the pathway becomes specific for gibberellins.
The cyclization reactions that convert GGPP to ent-kau-rene represent the first step that is specific for the gib-berellins (Figure 20.6). The two enzymes that catalyze the reactions are localized in the proplastids of meristematic shoot tissues, and they are not present in mature chloro-plasts (Aach et al. 1997). Thus, leaves lose their ability to synthesize gibberellins from IPP once their chloroplasts mature.
Compounds such as AMO-1618, Cycocel, and Phosphon D are specific inhibitors of the first stage of gibberellin biosynthesis, and they are used as growth height reducers.
Stage 2: Oxidation reactions on the ER form GA12 and GA53.
In the second stage of gibberellin biosynthesis, a methyl group on ent-kaurene is oxidized to a carboxylic acid, followed by contraction of the B ring from a six- to a five-carbon ring to give GA12-aldehyde. GA12-aldehyde is then oxidized to GA12, the first gibberellin in the pathway in all plants and thus the precursor of all the other gib-berellins (see Figure 20.6).
Many gibberellins in plants are also hydroxylated on carbon 13. The hydroxylation of carbon 13 occurs next, forming GA53 from GA12. All the enzymes involved are monooxygenases that utilize cytochrome P450 in their reac-tions. These P450 monooxygenases are localized on the endoplasmic reticulum. Kaurene is transported from the plastid to the endoplasmic reticulum, and is oxidized en route to kaurenoic acid by kaurene oxidase, which is asso-ciated with the plastid envelope (Helliwell et al. 2001). Further conversions to GA12 take place on the endo-plasmic reticulum. Paclobutrazol and other inhibitors of P450 monooxygenases specifically inhibit this stage of gib-berellin biosynthesis before GA12-aldehyde, and they are also growth retardants.
Stage 3: Formation in the cytosol of all other gib-berellins from GA12 or GA53.
All subsequent steps in the pathway (see Figure 20.6) are carried out by a group of sol-uble dioxygenases in the cytosol. These enzymes require 2-oxoglutarate and molecular oxygen as cosubstrates, and they use Fe2+ and ascorbate as cofactors.
The specific steps in the modification of GA12 vary from species to species, and between organs of the same species.
Two basic chemical changes occur in most plants: 1. Hydroxylation at carbon 13 (on the endoplasmic retic-ulum) or carbon 3, or both.
2. A successive oxidation at carbon 20 (CH2 →CH2OH →CHO). The final step of this oxidation is the loss of carbon 20 as CO2 (see Figure 20.6).
When these reactions involve gibberellins initially hydroxylated at C-13, the resulting gibberellin is GA20.
GA20 is then converted to the biologically active form, Geranylgeranyl diphosphate ls Copalyl diphosphate ent-Kaurene na sln le GA12-aldehyde GA12 GA53 GA 20-oxidase GA44 GA 20-oxidase GA19 GA 20-oxidase GA 2-oxidase GA20 GA 2-oxidase GA 3-oxidase GA29 GA1 GA8 sln FIGURE 20.7 A portion of the gibberellin biosynthetic path-way showing the abbreviations and location of the mutant genes that block the pathway in pea and the enzymes involved in the metabolic steps after GA53.
2 As noted in Chapter 13, IPP is the abbreviation for isopen-tenyl pyrophosphate, an earlier name for this compound.
Similarly, the other pyrophosphorylated intermediates in the pathway are now referred to as diphosphates, but they continue to be abbreviated as if they were called pyrophos-phates.
468 Chapter 20 GA1, by hydroxylation of carbon 3. (Because this is in the beta configuration [drawn as if the bond to the hydroxyl group were toward the viewer], it is referred to as 3β-hydroxylation.) Finally, GA1 is inactivated by its conversion to GA8 by a hydroxylation on carbon 2. This hydroxylation can also remove GA20 from the biosynthetic pathway by converting it to GA29.
Inhibitors of the third stage of the gibberellin biosyn-thetic pathway interfere with enzymes that utilize 2-oxog-lutarate as cosubstrates. Among these, the compound pro-hexadione (BX-112), is especially useful because it specifically inhibits GA 3-oxidase, the enzyme that converts inactive GA20 to growth-active GA1.
The Enzymes and Genes of the Gibberellin Biosynthetic Pathway Have Been Characterized The enzymes of the gibberellin biosynthetic pathway are now known, and the genes for many of these enzymes have been isolated and characterized (see Figure 20.7).
Most notable from a regulatory standpoint are two biosyn-thetic enzymes—GA 20-oxidase (GA20ox)3 and GA 3-oxi-dase (GA3ox)—and an enzyme involved in gibberellin metabolism, GA 2-oxidase (GA2ox): • GA 20-oxidase catalyzes all the reactions involving the successive oxidation steps of carbon 20 between GA53 and GA20, including the removal of C-20 as CO2.
• GA 3-oxidase functions as a 3β-hydroxylase, adding a hydroxyl group to C-3 to form the active gib-berellin, GA1. (The evidence demonstrating that GA1 is the active gibberellin will be discussed shortly.) • GA 2-oxidase inactivates GA1 by catalyzing the addi-tion of a hydroxyl group to C-2.
The transcription of the genes for the two gibberellin biosynthetic enzymes, as well as for GA 2-oxidase, is highly regulated. All three of these genes have sequences in com-mon with each other and with other enzymes utilizing 2-oxoglutarate and Fe2+ as cofactors. The common sequences represent the binding sites for 2-oxoglutarate and Fe2+.
Gibberellins May Be Covalently Linked to Sugars Although active gibberellins are free, a variety of gibberellin glycosides are formed by a covalent linkage between gibberellin and a sugar. These gibberellin conjugates are particularly prevalent in some seeds. The conjugating sugar is usually glucose, and it may be attached to the gibberellin via a car-boxyl group forming a gibberellin glycoside, or via a hydroxyl group forming a gibberellin glycosyl ether.
When gibberellins are applied to a plant, a certain pro-portion usually becomes glycosylated. Glycosylation there-fore represents another form of inactivation. In some cases, applied glucosides are metabolized back to free GAs, so glucosides may also be a storage form of gibberellins (Schneider and Schmidt 1990).
GA1 Is the Biologically Active Gibberellin Controlling Stem Growth Knowledge of biosynthetic pathways for gibberellins reveals The gibberellins of tall pea plants containing the homozygous Le allele (wild type) were compared with dwarf plants having the same genetic makeup, except con-taining the le allele (mutant). Le and le are the two alleles of the gene that regulates tallness in peas, the genetic trait first investigated by Gregor Mendel in his pioneering study in 1866. We now know that tall peas contain much more bioac-tive GA1 than dwarf peas have (Ingram et al. 1983).
As we have seen, the precursor of GA1 in higher plants is GA20 (GA1 is 3β-OH GA20). If GA20 is applied to homozy-gous dwarf (le) pea plants, they fail to respond, although they do respond to applied GA1. The implication is that the Le gene enables the plants to convert GA20 to GA1. Metabolic studies using both stable and radioactive isotopes demon-strated conclusively that the Le gene encodes an enzyme that 3β-hydroxylates GA20 to produce GA1 (Figure 20.8). Mendel’s Le gene was isolated, and the recessive le allele was shown to have a single base change leading to a defec-tive enzyme only one-twentieth as active as the wild-type 3 GA 20-oxidase means an enzyme that oxidizes at carbon 20; it is not the same as GA20, which is gib-berellin 20 in the GA numbering scheme.
HO OH H CH3 CH2 H COOH O CO OH H CH3 CH2 H COOH O CO + OH GA 3b-hydroxylase GA20 GA1 FIGURE 20.8 Conversion of GA20 to GA1 by GA 3β-hydroxylase, which adds a hydroxyl group (OH) to carbon 3 of GA20.
Gibberellins: Regulators of Plant Height 469 growth regulators because gibberellin application caused the genetic control of tallness (Reid and Howell 1995).
where and how dwarf mutations act (Figure 20.7). Although it had long been assumed that gibberellins were natural dwarf plants to grow tall, direct evidence was initially lacking.
In the early 1980s it was demonstrated that tall stems do con- tain more bioactive gibberellin than dwarf stems have, and that the level of the endogenous bioactive gibberellin mediates enzyme, so much less GA1 is produced and the plants are dwarf (Lester et al. 1997).
Endogenous GA1 Levels Are Correlated with Tallness Although the shoots of gibberellin-deficient le dwarf peas are much shorter than those of normal plants (internodes of 3 cm in mature dwarf plants versus 15 cm in mature normal plants), the mutation is “leaky” (i.e., the mutated gene pro-duces a partially active enzyme) and some endogenous GA1 remains to cause growth. Different le alleles give rise to peas differing in their height, and the height of the plant has been correlated with the amount of endogenous GA1 (Figure 20.9).
There is also an extreme dwarf mutant of pea that has even fewer gibberellins. This dwarf has the allele na (the wild-type allele is Na), which completely blocks gibberellin biosynthesis between ent-kaurene and GA12-aldehyde (Reid and Howell 1995). As a result, homozygous (nana) mutants, which are almost completely free of gibberellins, achieve a stature of only about 1 cm at maturity (Figure 20.10).
However, nana plants may still possess an active GA 3β-hydroxylase encoded by Le, and thus can convert GA20 to GA1. If a nana naLe shoot is grafted onto a dwarf le plant, the resulting plant is tall because the nana shoot tip can convert the GA20 from the dwarf into GA1.
Such observations have led to the conclusion that GA1 is the biologically active gibberellin that regulates tallness in peas (Ingram et al. 1986; Davies 1995). The same result has been obtained for maize, a monocot, in parallel studies using genotypes that have blocks in the gibberellin biosyn-thetic pathway. Thus the control of stem elongation by GA1 appears to be universal.
Although GA1 appears to be the primary active gib-berellin in stem growth for most species, a few other gib-16 12 8 4 0.01 0.1 1.0 Length between nodes 4 and 6 (cm) GA1 content of pea plants possessing three different Le le alleles le-2 le-1 Le Endogenous GA1 (ng per plant) FIGURE 20.9 Stem elongation corresponds closely to the level of GA1. Here the GA1 content in peas with three dif-ferent alleles at the Le locus is plotted against the internode elongation in plants with those alleles. The allele le-2 is a more intense dwarfing allele of Le than is the regular le-1 allele. There is a close correlation between the GA level and internode elongation. (After Ross et al. 1989.) FIGURE 20.10 Phenotypes and genotypes of peas that differ in the gibberellin content of their vegetative tissue. (All alleles are homozygous.) (After Davies 1995.) Ultradwarf: no GAs nana Dwarf: contains GA20 Na le Tall: contains GA1 Na Le Ultratall: contains no GAs na la crys 470 Chapter 20 berellins have biological activity in other species or tissues.
For example, GA3, which differs from GA1 only in having one double bond, is relatively rare in higher plants but is able to substitute for GA1 in most bioassays: GA4, which lacks an OH group at C-13, is present in both Arabidopsis and members of the squash family (Cucur-bitaceae). It is as active as GA1, or even more active, in some bioassays, indicating that GA4 is a bioactive gib-berellin in the species where it occurs (Xu et al. 1997). The structure of GA4 looks like this: Gibberellins Are Biosynthesized in Apical Tissues The highest levels of gibberellins are found in immature seeds and developing fruits. However, because the gib-berellin level normally decreases to zero in mature seeds, there is no evidence that seedlings obtain any active gib-berellins from their seeds.
Work with pea seedlings indicates that the gibberellin biosynthetic enzymes and GA3ox are specifically localized in young, actively growing buds, leaves, and upper intern-odes (Elliott et al. 2001). In Arabidopsis, GA20ox is expressed primarily in the apical bud and young leaves, which thus appear to be the principal sites of gibberellin synthesis (Figure 20.11). The gibberellins that are synthesized in the shoot can be transported to the rest of the plant via the phloem. Inter-mediates of gibberellin biosynthesis may also be translo-cated in the phloem. Indeed, the initial steps of gibberellin biosynthesis may occur in one tissue, and metabolism to active gibberellins in another.
Gibberellins also have been identified in root exudates and root extracts, suggesting that roots can also synthesize gibberellins and transport them to the shoot via the xylem.
Gibberellin Regulates Its Own Metabolism Endogenous gibberellin regulates its own metabolism by either switching on or inhibiting the transcription of the genes that encode enzymes of gibberellin biosynthesis and degradation (feedback and feed-forward regulation, respectively). In this way the level of active gibberellins is kept within a narrow range, provided that precursors are available and the enzymes of gibberellin biosynthesis and degradation are functional. For example, the application of gibberellin causes a down-regulation of the biosynthetic genes—GA20ox and GA3ox—and an elevation in transcription of the degrada-tive gene—GA2ox (Hedden and Phillips 2000; Elliott et al.
2001). A mutation in the GA 2-oxidase gene, which prevents GA1 from being degraded, is functionally equivalent to applying exogenous gibberellin to the plant, and produces the same effect on the biosynthetic gene transcription. Conversely, a mutation that lowers the level of active gibberellin, such as GA1, in the plant stimulates the tran-scription of the biosynthetic genes—GA20ox and GA3ox— and down-regulates the degradative enzyme—GA2ox. In peas this is particularly evident in very dwarf plants, such as those with a mutation in the LS gene (CPP synthase) or even more severely dwarf na plants (defective GA12-alde-hyde synthase) (Figure 20.12).
Environmental Conditions Can Alter the Transcription of Gibberellin Biosynthesis Genes Gibberellins play an important role in mediating the effects of environmental stimuli on plant development. Environ-mental factors such as photoperiod and temperature can alter the levels of active gibberellins by affecting gene tran-scription for specific steps in the biosynthetic pathway (Yamaguchi and Kamiya 2000).
H COOH O CO CH3 H CH2 HO Gibberellin A4 (GA4) COOH O CO CH3 H CH2 HO OH Gibberellic acid (GA3) FIGURE 20.11 Gibberellin is synthesized mainly in the shoot apex and in young developing leaves. This false color image shows light emitted by transgenic Arabidopsis plants express-ing the firefly luciferase coding sequence coupled to the GA20ox gene promoter. The emitted light was recorded by a CCD camera after the rosette was sprayed with the substrate luciferin. The image was then color-coded for intensity and superimposed on a photograph of the same plant. The red and yellow regions correspond to the highest light intensity.
(Courtesy of Jeremy P. Coles, Andrew L. Phillips, and Peter Hedden, IACR-Long Ashton Research Station.) Gibberellins: Regulators of Plant Height 471 Light regulation of GA1 biosynthesis.
The presence of light has many profound effects. Some seeds germinate only in the light, and in such cases gibberellin application can stimulate germination in darkness. The promotion of germination by light has been shown to be due to increases in GA1 levels resulting from a light-induced increase in the transcription of the gene for GA3ox, which converts GA20 to GA1 (Toyomasu et al. 1998). This effect shows red/far-red photoreversibility and is mediated by phytochrome (see Chapter 17).
When a seedling becomes exposed to light as it emerges from the soil, it changes its form (see Chapter 17)—a process referred to as de-etiolation. One of the most strik-ing changes is a decrease in the rate of stem elongation such that the stem in the light is shorter than the one in the dark. Initially it was assumed that the light-grown plants would contain less GA1 than dark-grown plants. However, light-grown plants turned out to contain more GA1 than dark-grown plants—indicating that de-etiolation is a com-plex process involving changes in the level of GA1, as well as changes in the responsiveness of the plant to GA1.
In peas, for example, the level of GA1 initially falls within 4 hours of exposure to light because of an increase in transcription of the gene for GA2ox, leading to an increase in GA1 breakdown (Figure 20.13A). The level of GA1 remains low for a day but then increases, so that by PsGA20ox1 PsGA3ox1 PsGA2ox1 ls LS ls LS ls LS ls LS Apical Leaflets Internodes Roots FIGURE 20.12 Northern blots of the mRNA for the enzymes of gibberellin biosynthesis in different tissues of peas. The more intense the band, the more mRNA was present. The plants designated LS are tall wild-type plants. Those designated ls are very dwarf mutants due to a defective copalyl diphosphate synthase that creates a block in the GA biosynthesis pathway. The differences in the spot intensity show that a low level of GA1 in the mutant ls plants causes the upregulation of GA1 biosynthesis by GA20ox and GA3ox, and a repres-sion of GA1 breakdown by GA2ox.
(From Elliott et al. 2001.) Dark Dark to 4 hours light Dark to 24 hours light Dark to 120 hours light Continuous light 1 0 0 2 3 4 5 6 7 GA1 level ng g FW–1 Dark Dark to light 1D after GA1 application Light 5 10 15 20 25 30 Rate of elongation (mm d-1) (B) (A) Rapid decline in GA1 due to degradation FIGURE 20.13 When a plant grows in the light, the rate of extension slows down through regulation by changes in hormone levels and sensitivity. (A) When dark-grown pea seedlings are transferred to light, GA1 level drops rapidly because of metabolism of GA1, but then increases to a higher level, similar to that of light-grown plants, over the next 4 days. (B) To investigate the GA1 response in various light regimes, 10 µg of GA1 was applied to the internode of GA-deficient na plants in darkness, 1 day after the start of the light, or 6 days of continuous light, and growth in the next 24 hours was measured. The results show that the gib-berellin sensitivity of pea seedlings falls rapidly upon trans-fer from darkness to light, so the elongation rate of plants in the light is lower than in the dark, even though their total GA1 content is higher. (After O’Neill et al. 2000.) 472 Chapter 20 5 days there is a fivefold increase in the GA1 content of the stems, even though the stem elongation rate is lower (Fig-ure 20.13B) (O’Neill et al. 2000). The reason that growth slows down despite the increase in GA1 level is that the plants are now severalfold less sensitive to the GA1 present.
As will be discussed later in the chapter, sensitivity to active gibberellin is governed by components of the gib-berellin signal transduction pathway.
Photoperiod regulation of GA1 biosynthesis.
When plants that require long days to flower (see Chapter 24) are shifted from short days to long days, gibberellin metabo-lism is altered. In spinach (Spinacia oleracea), in short days, when the plants maintain a rosette form (Figure 20.14), the level of gibberellins hydroxylated at carbon 13 is relatively low. In response to increasing day length, the shoots of spinach plants begin to elongate after about 14 long days. The levels of all the gibberellins of the carbon 13–hydroxylated gibberellin pathway (GA53 →GA44 → GA19 →GA20 →GA1 →GA8) start to increase after about 4 days (Figure 20.15). Although the level of GA20 increases 16-fold during the first 12 days, it is the fivefold increase in GA1 that induces stem growth (Zeevaart et al. 1993).
The dependence of stem growth on GA1 has been shown through the use of different inhibitors of gibberellin synthesis and metabolism. The inhibitors AMO-1618 and BX-112 both prevent internode elongation (bolting). The effect of AMO-1618, which blocks gibberellin biosynthe-sis prior to GA12-aldehyde, can be overcome by applica-tions of GA20 (Figure 20.16A). However, the effect of another inhibitor, BX-112, which blocks the production of GA1 from GA20, can be overcome only by GA1 (Figure 20.16B). This result demon-strates that the rise in GA1 is the crucial factor in regulating spinach stem growth.
The level of GA20-oxidase mRNA in spinach tissues, which occurs in the highest amount in shoot tips and elongating stems (see Figure 20.11), is increased under long-day conditions (Wu et al. 1996). The fact that GA 20-oxidase is the enzyme that converts GA53 to GA20 (see Figure 20.7) ex-plains why the concentration of GA20 was found to be higher in spinach under long-day conditions (Zeevaart et al. 1993).
Photoperiod control of tuber for-mation.
Potato tuberization is another process regulated by pho-toperiod (Figure 20.17). Tubers form on wild potatoes only in short days (although the requirement for short days has been bred out of many cultivated varieties), and this tuberization can be blocked by applications of gib-berellin. The transcription of GA20ox was found to fluctu-ate during the light–dark cycle, leading to lower levels of GA1 in short days. Potato plants overexpressing the GA20ox gene showed delayed tuberization, whereas trans-FIGURE 20.14 Spinach plants undergo stem and petiole elongation only in long days, remaining in a rosette form in short days. Treatment with the GA biosynthe-sis inhibitor AMO-1618 prevents stem and petiole elongation and maintains the rosette growth habit even under long days. Gibberellic acid can reverse the inhibitory effect of AMO-1618 on stem and petiole elongation. As shown in Figure 20.16, long days cause changes in the gibberellin content of the plant. (Courtesy of J. A. D. Zeevaart.) 1500 1000 500 0 4 8 12 Number of long days Percent change in amount GA20 (inactive GA1 precursor) GA1 (active GA, responsible for growth) GA8 (inactive GA1 metabolite) Level at the start of long days (ng/g fresh weight): GA20: 1.4 GA1: 1.0 GA8: 18.0 FIGURE 20.15 The fivefold increase in GA1 is what causes growth in spinach exposed to an increasing number of long days but before stem elongation starts at about 14 days.
(After Davies 1995; redrawn from data in Zeevaart et al.
1993.) Gibberellins: Regulators of Plant Height 473 formation with the antisense gene for GA20ox promoted tuberization, demonstrating the importance of the tran-scription of this gene in the regulation of potato tuberiza-tion (Carrera et al. 2000).
In general, de-etiolation, light-dependent seed germi-nation, and the photoperiodic control of stem growth in rosette plants and tuberization in potato are all mediated by phytochromes (see Chapter 17). There is mounting evi-dence that many phytochrome effects are in part due to modulation of the levels of gibberellins through changes in the transcription of the genes for gibberellin biosynthesis and degradation.
Temperature effects.
Cold temperatures are required for the germination of certain seeds (stratification) and for flowering in certain species (vernalization) (see Chapter Stem length (cm) 40 20 30 10 0 12 14 16 18 20 22 24 Number of long days (A) AMO-1618 Control AMO-1618 AMO-1618 + GA20 AMO-1618 + GA1 30 10 20 0 12 Stem length (cm) 40 14 16 18 20 22 24 (B) BX-112 Number of long days Control BX-112 BX-112 + GA20 BX-112 + GA1 AMO-1618, which blocks GA biosynthesis at the cyclization step, does not inhibit growth in the presence of either GA20 or GA1.
In contrast, BX-112, which blocks the conversion of GA20 to GA1, inhibits growth even in the presence of GA20.
FIGURE 20.16 The use of specific growth retardants (GA biosynthesis inhibitors) and the reversal of the effects of the growth retardants by different GAs can show which steps in GA biosynthesis are regulated by environmental change, in this case the effect of long days on stem growth in spinach. The control lacks inhibitors or added GA. (After Zeevaart et al. 1993.) FIGURE 20.17 Tuberization of potatoes is promoted by short days. Potato (Solanum tuberosum spp. Andigena) plants were grown under either long days or short days. The formation of tubers in short days is associated with a decline in GA1 levels (see Chapter 24). (Courtesy of S.
Jackson.) 474 Chapter 20 Long days Short days 24). For example, a prolonged cold treatment is required for both the stem elongation and the flowering of Thlaspi arvense (field pennycress), and gibberellins can substitute for the cold treatment.
In the absence of the cold treatment, ent-kaurenoic acid accumulates to high levels in the shoot tip, which is also the site of perception of the cold stimulus. After cold treatment and a return to high temperatures, the ent-kaurenoic acid is converted to GA9, the most active gibberellin for stimulat-ing the flowering response. These results are consistent with a cold-induced increase in the activity of ent-kaurenoic acid hydroxylase in the shoot tip (Hazebroek and Metzger 1990).
Auxin Promotes Gibberellin Biosynthesis Although we often discuss the action of hormones as if they act singly, the net growth and development of the plant are the results of many combined signals. In addition, hormones can influence each other’s biosynthesis so that the effects produced by one hormone may in fact be medi-ated by others. For example, it has long been known that auxin induces ethylene biosynthesis. It is now evident that gibberellin can induce auxin biosynthesis and that auxin can induce gib-berellin biosynthesis. If pea plants are decapitated, leading to a cessation in stem elongation, not only is the level of auxin lowered because its source has been removed, but the level of GA1 in the upper stem drops sharply. This change can be shown to be an auxin effect because replacing the bud with a supply of auxin restores the GA1 level (Figure 20.18). The presence of auxin has been shown to promote the transcription of GA3ox and to repress the transcription of GA2ox (Figure 20.19). In the absence of auxin the reverse occurs. Thus the apical bud promotes growth not only through the direct biosynthesis of auxin, but also through the auxin-induced biosynthesis of GA1 (Figure 20.20) (Ross et al. 2000; Ross and O’Neill 2001).
Figure 20.21 summarizes some of the factors that mod-ulate the active gibberellin level through regulation of the transcription of the genes for gibberellin biosynthesis or metabolism.
Dwarfness Can Now Be Genetically Engineered The characterization of the gibberellin biosynthesis and metabolism genes—GA20ox, GA3ox, and GA2ox—has 0 5 10 15 GA1 level, ng.g–1 Intact Decapitated Decapitated + IAA Intact Decapitated Decapitated + IAA 7 7 7 6 6 6 FIGURE 20.18 Decapitation reduces, and IAA (auxin) restores, endogenous GA1 content in pea plants. Numbers refer to the leaf node. (From Ross et al. 2000.) Intact Decap, Decap. + IAA GA3ox mRNA (GA20 to GA1) GA2ox mRNA (GA20 to GA29, and GA1 to GA8) 0 h 2 h 4 h 6 h 8 h Con. IAA Con. IAA Con.
IAA Con. IAA Con.
IAA Intact GA3ox mRNA (A) (B) FIGURE 20.19 (A) IAA up-regulates the transcription of GA 3β-hydroxy-lase (forming GA1), and down-regu-lates that of GA 2-oxidase, which destroys GA1. (B) The increase in GA 3β-hydroxylase in response to IAA can be seen by 2 hours. Con., control. (From Ross et al. 2000.) Gibberellins: Regulators of Plant Height 475 enabled genetic engineers to modify the transcription of these genes to alter the gibberellin level in plants, and thus affect their height (Hedden and Phillips 2000). The desired effect is usually to increase dwarfness because plants grown in dense crop communities, such as cereals, often grow too tall and thus are prone to lodging. In addition, because gibberellin regulates bolting, one can prevent bolt-ing by inhibiting the rise in gibberellin. An example of the latter is the inhibition of bolting in sugar beet.
Sugar beet is a biennial, forming a swollen storage root in the first season and a flower and seed stalk in the second.
To extend the growing season and obtain bigger beets, farmers sow the beets as early as possible in the spring, but sowing too early leads to bolting in the first year, with the result that no storage roots form. A reduction in the capac-ity to make gibberellin inhibits bolting, allowing earlier sowing of the seeds and thus the growth of larger beets.
Reductions in GA1 levels have recently been achieved in such crops as sugar beet and wheat, either by the transformation of plants with antisense constructs of the GA20ox or GA3ox genes, which encode the enzymes leading to the synthesis of GA1, or by overexpressing the gene responsible for GA1 metabolism: GA2ox.
Either approach results in dwarfing in wheat (Figure 20.22) or an inhibition of bolting in rosette plants such as beet.
The inhibition of seed production in such transgenic plants can be overcome by sprays of gibberellin solution, provided that the reduction in gibberellin has been achieved by blocking the genes for GA20ox or GA3ox, the gibberellin biosynthetic enzymes. A similar strategy has recently been applied to turf grass, keeping the grass short with no seed-heads, so that mowing can be virtually elim-inated—a boon for homeowners!
IAA IAA IAA growth growth GA20 GA1 GA29 GA8 Apical bud FIGURE 20.20 IAA (from the apical bud) promotes and is required for GA1 biosynthesis in subtending internodes.
IAA also inhibits GA1 breakdown. (From Ross and O’Neill 2001.) GA12/53 GA9/20 GA20ox GA4/1 GA response pathway Multiple genes with differential expression GA34/8 GA3ox GA2ox Auxin Photoperiod (stem elongation and tuberization) Red light (germination) = FIGURE 20.21 The pathway of gibberellin biosynthesis showing the iden-tities of the genes for the metabolic enzymes and the way that their tran-scription is regulated by feedback, environment, and other endogenous hormones.
FIGURE 20.22 Genetically engineered dwarf wheat plants.
The untransformed wheat is shown on the extreme left. The three plants on the right were transformed with a gib-berellin 2-oxidase cDNA from bean under the control of a constitutive promoter, so that the endogenous active GA1 was degraded. The varying degrees of dwarfing reflects varying degrees of overexpression of the foreign gene.
(Photo from Hedden and Phillips 2000, courtesy of Andy Phillips.) 476 Chapter 20 PHYSIOLOGICAL MECHANISMS OF GIBBERELLIN-INDUCED GROWTH As we have seen, the growth-promoting effects of gib-berellin are most evident in dwarf and rosette plants. When dwarf plants are treated with gibberellin, they resemble the tallest varieties of the same species (see Figure 20.1). Other examples of gibberellin action include the elongation of hypocotyls and of grass internodes.
A particularly striking example of internode elongation is found in deep-water rice (Oryza sativa). In general, rice plants are adapted to conditions of partial submergence. To enable the upper foliage of the plant to stay above water, the internodes elongate as the water level rises. Deep-water rice has the greatest potential for rapid internode elonga-tion. Under field conditions, growth rates of up to 25 cm per day have been measured. The initial signal is the reduced partial pressure of O2 resulting from submergence, which induces ethylene biosynthesis (see Chapter 22). The ethylene trapped in the submerged tissues, in turn, reduces the level of abscisic acid (see Chapter 23), which acts as an antagonist of gibberellin. The end result is that the tissue becomes more responsive to its endogenous gibberellin (Kende et al.
1998). Because inhibitors of gibberellin biosynthesis block the stimulatory effect of both submergence and eth-ylene on growth, and exogenous gibberellin can stimu-late growth in the absence of submergence, gibberellin appears to be the hormone directly responsible for growth stimulation.
GA-stimulated growth in deep-water rice can be stud-ied in an excised stem system (Figure 20.23). The addition of gibberellin causes a marked increase in the growth rate after a lag period of about 40 minutes. Cell elongation accounts for about 90% of the length increase during the first 2 hours of gibberellin treatment.
Gibberellins Stimulate Cell Elongation and Cell Division The effect of gibberellins applied to intact dwarf plants is so dramatic that it would seem to be a simple task to deter-mine how they act. Unfortunately, this is not the case because, as we have seen with auxin, so much about plant cell growth is not understood. However, we do know some characteristics of gibberellin-induced stem elongation.
Gibberellin increases both cell elongation and cell divi-sion, as evidenced by increases in cell length and cell num-ber in response to applications of gibberellin. For example, internodes of tall peas have more cells than those of dwarf peas, and the cells are longer. Mitosis increases markedly in the subapical region of the meristem of rosette long-day plants after treatment with gibberellin (Figure 20.24). The dramatic stimulation of internode elongation in deep-water rice is due in part to increased cell division activity in the intercalary meristem. Moreover, only the cells of the inter-calary meristem whose division is increased by gibberellin exhibit gibberellin-stimulated cell elongation.
Because gibberellin-induced cell elongation appears to precede gibberellin-induced cell division, we begin our discussion with the role of gibberellin in regulating cell elongation.
Gibberellins Enhance Cell Wall Extensibility without Acidification As discussed in Chapter 15, the elongation rate can be influenced by both cell wall extensibility and the osmoti-cally driven rate of water uptake. Gibberellin has no effect Node 0 1 2 3 4 5 6 7 Time (hours) after internode excised from plant Growth (mm) 3 2 1 GA3 added to internode section Lag period Control internode section (no GA3 added) Excision of internode section Leaf Node Intercalary meristem FIGURE 20.23 Continuous recording of the growth of the upper internode of deep-water rice in the presence or absence of exogenous GA3. The control internode elongates at a constant rate after an initial growth burst during the first 2 hours after excision of the section. Addition of GA after 3 hours induced a sharp increase in the growth rate after a 40-minute lag period (upper curve). The difference in the initial growth rates of the two treatments is not signifi-cant here, but reflects slight variation in experimental mate-rials. The inset shows the internode section of the rice stem used in the experiment. The intercalary meristem just above the node responds to GA. (After Sauter and Kende 1992.) Gibberellins: Regulators of Plant Height 477 on the osmotic parameters but has consistently been observed to cause an increase in both the mechanical exten-sibility of cell walls and the stress relaxation of the walls of living cells. An analysis of pea genotypes differing in gib-berellin content or sensitivity showed that gibberellin decreases the minimum force that will cause wall extension (the wall yield threshold) (Behringer et al. 1990). Thus, both gibberellin and auxin seem to exert their effects by modi-fying cell wall properties.
In the case of auxin, cell wall loosening appears to be mediated in part by cell wall acidification (see Chapter 19).
However, this does not appear to be the mechanism of gib-berellin action. In no case has a gibberellin-stimulated increase in proton extrusion been demonstrated. On the other hand, gibberellin is never present in tissues in the complete absence of auxin, and the effects of gibberellin on growth may depend on auxin-induced wall acidification.
The typical lag time before gibberellin-stimulated growth begins is longer than for auxin; as noted already, in deep-water rice it is about 40 minutes (see Figure 20.23), and in peas it is 2 to 3 hours (Yang et al. 1996). These longer lag times point to a growth-promoting mechanism distinct from that of auxin. Consistent with the existence of a separate gib-berellin-specific wall-loosening mechanism, the growth responses to applied gibberellin and auxin are additive.
Various suggestions have been made regarding the mechanism of gibberellin-stimulated stem elongation, and all have some experimental support, but as yet none pro-vide a clear-cut answer. For example, there is evidence that the enzyme xyloglucan endotransglycosylase (XET) is involved in gibberellin-promoted wall extension. The func-tion of XET may be to facilitate the penetration of expansins into the cell wall. (Recall that expansins are cell wall proteins that cause wall loosening in acidic conditions by weakening hydrogen bonds between wall polysaccha-rides [see Chapter 15].) Both expansins and XET may be required for gibberellin-stimulated cell elongation (see Web Topic 20.3).
Gibberellins Regulate the Transcription of Cell Cycle Kinases in Intercalary Meristems As noted earlier, the growth rate of the internodes of deep-water rice dramatically increases in response to submer-gence, and part of this response is due to increased cell divi-sions in the intercalary meristem. To study the effect of gibberellin on the cell cycle, researchers isolated nuclei from the intercalary meristem and quantified the amount of DNA per nucleus (Figure 20.25) (Sauter and Kende 1992). In submergence-induced plants, gibberellin activates the cell division cycle first at the transition from G1 to S phase, leading to an increase in mitotic activity. To do this, gib-berellin induces the expression of the genes for several cyclin-dependent protein kinases (CDKs), which are involved in regulation of the cell cycle (see Chapter 1). The transcription of these genes—first those regulating the tran-sition from G1 to S phase, followed by those regulating the transition from G2 to M phase—is induced in the inter-calary meristem by gibberellin. The result is a gibberellin-induced increase in the progression from the G1 to the S phase through to mitosis and cell division (see Web Topic 20.4) (Fabian et al. 2000).
Gibberellin Response Mutants Have Defects in Signal Transduction Single-gene mutants impaired in their response to gib-berellin provide valuable tools for identifying genes that encode possible gibberellin receptors or components of sig-nal transduction pathways. In screenings for such mutants, 10 20 30 0 12 24 36 48 Time (hours) following treatment with GA GA applied Control (A) (B) 0 h 24 h 48 h 72 h Distribution of cell division following application of GA Each dot represents a mitotic event Mitotic figures per 64 µm slice FIGURE 20.24 Gibberellin applications to rosette plants induce stem internode elongation in part by increasing cell division. (A) Longitudinal sections through the axis of Samolus parviflorus (brookweed) show an increase in cell division after application of GA. (Each dot represents one mitotic figure in a section 64 µm thick.) (B) The number of such mitotic figures with and without GA in stem apices of Hyoscyamus niger (black henbane). (After Sachs 1965.) 478 Chapter 20 three main classes of mutations affecting plant height have been selected: 1. Gibberellin-insensitive dwarfs 2. Gibberellin-deficient mutants in which the gibberellin deficiency has been overcome by a second “suppres-sor” mutation, so the plants look closer to normal 3. Mutants with a constitutive gibberellin response (“slender” mutants) All three types of gibberellin response mutants have been generated in Arabidopsis, but equivalent mutations have also been found in several other species; in fact, some have been in agricultural use for many years.
The three types of mutant screens have sometimes iden-tified genes encoding the same signal transduction com-ponents, even though the phenotypes being selected are completely different. This is possible because mutations at different sites in the same protein can produce vastly dif-ferent phenotypes, depending on whether the mutation is in a regulatory domain or in an activity, or functional, domain. Some examples of the different phenotypes that can result from changes at different sites in the same pro-tein are described in the sections that follow.
Functional domain (repression).
The principal gib-berellin signal transduction components that have been identified so far are repressors of gibberellin signaling; that is, they repress what we regard as gibberellin-induced tall growth and make the plant dwarf. The repressor proteins are negated or turned off by gibberellin so that the default-type growth—namely, tall—is allowed to proceed. The loss of function resulting from a mutation in the functional domain of such a negative regulator results in the mutant appearing as if it has been treated with gibberellin; that is, it has a tall phenotype. Thus a loss-of-function mutation of a negative regulator is like a double negative in English grammar: It translates into a positive.
Because the effects of these loss-of-function mutations are pleiotropic—that is, they also affect developmental processes other than stem elongation—the steps in the pathway involved in the growth response are probably common to all gibberellin responses.
Regulatory domain.
If a mutation in the gene for the same negative regulator causes a change in the regulatory domain (i.e., that part of the protein that receives a signal from the gibberellin receptor indicating the presence of gib-berellin), the protein is unable to receive the signal, and it retains its growth-repressing activity. The phenotype of such a mutant will be that of a gibberellin-insensitive dwarf. Thus, different mutations in the same gene can give opposite phenotypes (tall versus dwarf), depending on whether the mutation is located in the repression domain or the regulatory domain.
The regulatory domain mutations that confer loss of gib-berellin sensitivity result in the synthesis of a constitutively active form of the repressor than cannot be turned off by gib-berellin. The more of this type of mutant repressor that is present in the cell, the more dwarf the plant will be. Hence, such regulatory domain mutations are semidominant.
In contrast, mutations in the repression domain inacti-vate the negative regulator (i.e., they act as “knockout” alle-les) so that it no longer represses growth; such mutations are recessive because in a heterozygote half the proteins will still be able to repress growth in the absence of gib-berellin. All of the negative regulators have to be nonfunc-tional for the plant to grow tall without gibberellin.
With this as background, we now examine specific examples of mutations in the genes that encode proteins in the gibberellin signal transduction pathway.
Different Genetic Screens Have Identified the Related Repressors GAI and RGA Several gibberellin-insensitive dwarf mutants have been isolated from various species. The first to be isolated in Ara-bidopsis was the gai-1 mutant (Figure 20.26) (Sun 2000). The gai-1 mutants resemble gibberellin-deficient mutants, except that they do not respond to exogenous gibberellin.
Another mutant was obtained by screening for a second mutation in a gibberellin-deficient Arabidopsis mutant that restores, or partially restores, wild-type growth. The origi-0 5 10 15 20 25 GA treatment (hours) Percent nuclei in S and G2 phases 10 30 G2 G1 S 20 Percent nuclei in G1 phase 60 70 80 90 G2 G1 (DNA synthesis) Mitosis S M FIGURE 20.25 Changes in the cell cycle status of nuclei from the intercalary meristems of deep-water rice internodes treated with GA3. Note that the scale for the G1 nuclei is on the right side of the graph. (After Sauter and Kende 1992.) Gibberellins: Regulators of Plant Height 479 nal gibberellin-deficient mutant was ga1-3, and the sec-ond mutation that partially “rescued” the phenotype (i.e., restored normal growth) was called rga (for repres-sor of ga1-3).4 The rga mutation is a recessive mutation that, when present in double copy, gives a plant of intermediate height (see Figure 20.26).
Despite the contrasting phenotypes of the mutants, the wild-type GAI and RGA genes turned out to be closely related, with a very high (82%) sequence iden-tity. The gai-1 mutation is semidominant, as are similar gibberellin-insensitive dwarf mutations in other species.
Genetic analyses have indicated that both the GAI and RGA proteins normally act as repressors of gib-berellin responses. Gibberellin acts indirectly through an unidentified signaling intermediate, which is thought to bind to the regulatory domains of the GAI and RGA proteins (Figure 20.27). The repressor is no longer able to inhibit growth, and the resulting plant is tall.
The reason that gai-1 is dwarf, while rga is tall, is that the mutations are in different parts of the protein. Whereas the gai-1 mutation (which negates sensitivity of the repressor to gibberellin) is in the regulatory domain, the rga mutation (which prevents the action of the repressor in blocking growth) is located in the repression domain, as illustrated in Figure 20.28.
The mutant gai-1 gene has been shown to encode a mutant protein with a deletion of 17 amino acids, which corresponds to the regulatory domain of the repressor (Dill et al. 2001). A similar mutation in the receptor domain of the RGA gene also produces a gibberellin-insensitive dwarf, demonstrating that the two related proteins have overlapping functions. Because of this deletion in the gai-1 mutant, the action of the repressor cannot be alleviated by gibberellin, and growth is consti-tutively inhibited.
Gibberellins Cause the Degradation of RGA Transcriptional Repressors The Arabidopsis wild-type GAI and RGA genes are members of a large gene family encoding tran-+ GA or spy Wild type gai rga ga1 FIGURE 20.26 The effects of gibberellin treatment and mutations in three different genes (gai, ga1, and rga) on the phenotype of Arabidopsis.
4 Be careful not to confuse gai (gibberellin insensitive) and ga1 (gibberellin-deficient #1), which can look alike in print.
Regulatory domain Repression domain Active form GA signaling intermediate Inactive form Degradation NUCLEUS FIGURE 20.27 Two main functional domains of GAI and RGA: the regulatory domain and the repression domain. The repres-sion domain is active in the absence of gibberellin. A gib-berellin-induced signaling intermediate binds to the regulatory domain, targeting it for destruction. Note that the protein forms homodimers.
480 Chapter 20 scriptional repressors that have highly conserved regions with nuclear localization signals. To demonstrate the nuclear localization and repressor nature of the RGA prod-uct, the RGA promoter was fused to the gene for a green fluorescent protein whose product can be visualized under the microscope. The green color could be seen in cell nuclei. When the plants were treated with gibberellin, there was no green color, showing that the RGA protein was not present following gibberellin treatment. However, when the gibberellin content was severely lowered by treatment with the gibberellin biosynthesis inhibitor paclobutrazol, the nuclei acquired a very intense green fluorescence, demonstrating both the presence and nuclear localization of the RGA protein only when gibberellin was absent or low (Figure 20.29) (Silverstone et al. 2001).
Both GAI and RGA also have a conserved region at the amino terminus of the protein referred to as DELLA, after Regulatory domain Repression domain Wild-type repressor in the absence of GA represses elongation growth.
In the presence of GA, the repressor is degraded, allowing elongation to occur.
Active form A mutation in the repression domain disables the regulatory protein, so the plant grows tall even in the absence of GA.
Mutated repression domain A mutation in the regulatory domain turns the repressor into a constitutively active repressor, so the plant is dwarf even in the presence of GA.
Mutated regulatory domain GA signaling intermediate Inactive form Degradation No growth Growth No growth Growth FIGURE 20.28 Different mutations in the repressors GAI and RGA can have different effects on growth.
(A) (B) RGA RGA GFP Promoter DNA construct + GA + Paclobutrazole 2 h 48 h FIGURE 20.29 The RGA pro-tein is found in the cell nucleus, consistent with its identity as a transcription fac-tor, and its level is affected by the level of GA. (A) Plant cells were transformed with the gene for RGA fused to the gene for green fluorescent protein (GFP), allowing detec-tion of RGA in the nucleus by fluorescence microscopy. (B) Effect of GA on RGA. A 2-hour pretreatment with gib-berellin causes the loss of RGA from the cell (top).
When the gibberellin biosyn-thesis is inhibited in the pres-ence of paclobutrazole, the RGA content in the nucleus increases (bottom). (From Silverstone et al. 2001.) Gibberellins: Regulators of Plant Height 481 the code letters for the amino acids in that sequence. This region is involved in the gibberellin response because it is the location of the mutation in gai-1 that renders it nonre-sponsive to gibberellin. It turns out that the RGA protein is synthesized all the time; in the presence of gibberellin this protein is targeted for destruction, and the DELLA region is required for this response (Dill et al. 2001).
It is likely that gibberellin also brings about the turnover of GAI. RGA and GAI have partially redundant functions in maintaining the repressed state of the gibberellin sig-naling pathway. However, RGA appears to play a more dominant role than GAI because in a gibberellin-deficient mutant, a second mutation in the repression domain of gai (gai-t6) does not restore growth, whereas a comparable mutation in rga does. On the other hand, the existence of repression domain mutations in both of these genes allows for complete expression of many characteristics induced by GA, including plant height, in the absence of gibberellin (see Figure 20.26) (Dill and Sun 2001; King et al. 2001).
DELLA Repressors Have Been Identified in Crop Plants Functional DELLA repressors have been found in several crop plants that have dwarfing mutations, analogous to gai-1, in the genes encoding these proteins. Most notable are the rht (reduced height) mutations of wheat that have been in use in agriculture for 30 years. These alleles encode gib-berellin response modulators that lack gibberellin respon-siveness, leading to dwarfness (Peng et al. 1999; Silverstone and Sun 2000). Cereal dwarfs such as these are very important as the foundations of the green revolution that enabled large increases in yield to be obtained. Normal cereals grow too tall when close together in a field, especially with high levels of fertilizer. The result is that plants fall down (lodge), and the yield decreases concomitantly. The use of these stiff-strawed dwarf varieties that resist lodging enables high yields.
The Negative Regulator SPINDLY Is an Enzyme That Alters Protein Activity “Slender mutants” resemble wild-type plants that have been treated with gibberellin repeatedly. They exhibit elon-gated internodes, parthenocarpic (seed-free) fruit growth (in dicots), and poor pollen production. Slender mutants are rare compared to dwarf mutants.
One possible explanation of the slender phenotype could be simply that the mutants have higher-than-normal levels of endogenous gibberellins. For example, in the sln mutation of peas, a gibberellin deactivation step is blocked in the seed. As a result, the mature seed, which in the wild type contains little or no GA, has abnormally high levels of GA20. The GA20 from the seed is then taken up by the ger-minating seedling and converted to the bioactive GA1, giv-ing rise to the slender phenotype. However, once the seedling runs out of GA20 from the seed, its phenotype returns to normal (Reid and Howell 1995).
If, on the other hand, the slender phenotype is not due to an overproduction of endogenous gibberellin, the mutant is considered to be a constitutive response mutant (Sun 2000). The best characterized of such mutants are the ultratall mutants: la crys in pea, (representing mutations at two loci: La and Crys) (see Figure 20.10); procera (pro) in tomato; slender (sln) in barley; and spindly (spy) in Ara-bidopsis (Figure 20.30). All of these mutations are recessive and appear to be loss-of-function mutations in negative regulators of the gibberellin response pathway, as in the case of the DELLA regulators.
SPINDLY (SPY) in Arabidopsis and related genes in other species are similar in sequence to genes that encode glu-cosamine transferases in animals (Thornton et al. 1999). These enzymes modify target proteins by the glycosylation of ser-ine or threonine residues. Glycosylation can modify protein activity either directly or indirectly by interfering with or blocking sites of phosphorylation by protein kinases. The tar-get protein for spindly proteins has not yet been identified.
482 Chapter 20 FIGURE 20.30 The Arabidopsis spy mutation causes the negation of a growth repressor, so the plants look as if they were treated with gibberellin. From left to right: wild type, ga1 (GA-deficient), ga1/spy double mutant, and spy.
(Courtesy of N. Olszewski.) Wild type ga1 ga1/spy spy SPY Acts Upstream of GAI and RGA in the Gibberellin Signal Transduction Chain On the basis of the evidence presented in the preceding sec-tions and other studies on the expression of SPY, GAI, and RGA (Sun 2000; Dill et al. 2001), we can begin to sketch out the following elements of the gibberellin signal transduc-tion chain (Figures 20.31 and 20.32): • Two or more transcriptional regulators encoded by GAI and RGA act as inhibitors of the transcription of genes that directly or indirectly promote growth.
• SPY appears to be a signal transduction intermediate acting upstream of GAI and RGA that, itself, turns on or enhances the transcription or action of GAI and RGA, or another negative regulator.
• In the presence of gibberellin, SPY, GAI, and RGA are all negated or turned off.
Gibberellins: Regulators of Plant Height 483 GA SPY GAI/RGA mRNA transcription leading to growth Growth GAI/RGA: act in the absence of GA to suppress growth – transcription factors – O–GlcNAc transferase: involved in protein modification SPY: also a negative regulator; enhances the effect of GAI and RGA GA acts to block the actions of SPY, GAI, and RGA GA receptor SPY RGA GAI Transcription of GA-induced genes NUCLEUS CYTOPLASM CYTOPLASM Plasma membrane GA-deficient plant cell: No growth GA receptor GA SPY RGA GAI Transcription of GA-induced genes NUCLEUS Plant cell with GA: Growth In a GA-deficient cell in a GA biosynthesis mutant, or a wild-type cell without the GA signal, the transmembrane GA receptor is inactive in the absence of GA signal. In this situation, SPY is an active O-GlcNAc transferase that catalyzes the addition of a signal GlcNAc residue (from UDP-GlcNAc) via an O linkage to specific serine and/or threonine residues of target proteins, possibly RGA and GAI. Active RGA and GAI function as repressors of transcription, and they indirectly or directly inhibit the expression of GA-induced genes.
In the presence of GA the GA receptor is activated by binding of bioactive GA. The GA signal inhibits RGA and GAI repressors both directly and by deactivating SPY. In the absence of repression by RGA and GAI, GA-induced genes are transcribed.
FIGURE 20.32 Proposed roles of the active SPY, GAI, and RGA proteins in the GA signaling pathway within a plant cell.
FIGURE 20.31 Interactions between gibberellin and the genes SPY, GAI, and RGA in the regulation of stem elongation.
• The RGA protein is degraded, and it is likely that GAI is similarly destroyed.
Whether gibberellin negates GAI and RGA through SPY, or independently, or both, is currently under investigation.
However, the basic message in this case and in the cases of other plant hormones, such as ethylene (see Chapter 22) and the photoreceptor phytochrome (see Chapter 17), is that the default developmental program is for the induced type of growth to occur, but the default pathway is pre-vented by the presence of various negative regulators.
Rather than directly promoting an effect, the arrival of the developmental signal—in this case gibberellin—negates the growth repressor, enabling the default condition.
GIBBERELLIN SIGNAL TRANSDUCTION: CEREAL ALEURONE LAYERS Genetic analyses of gibberellin-regulated growth, such as the studies described in the previous section, have identi-fied some of the genes and their gene products, but not the biochemical pathways involved in gibberellin signal trans-duction. The biochemical and molecular mechanisms, which are probably common to all gibberellin responses, have been studied most extensively in relation to the gib-berellin-stimulated synthesis and secretion of α-amylase in cereal aleurone layers (Jacobsen et al. 1995).
In this section we will describe how such studies have shed light on the location of the gibberellin receptor, the transcriptional regulation of the genes for α-amylase and other proteins, and the possible signal transduction path-ways involved in the control of α-amylase synthesis and secretion by gibberellin.
Gibberellin from the Embryo Induces α-Amylase Production by Aleurone Layers Cereal grains (caryopses; singular caryopsis) can be divided into three parts: the diploid embryo, the triploid endosperm, and the fused testa–pericarp (seed coat–fruit wall). The embryo part consists of the plant embryo proper, along with its specialized absorptive organ, the scutellum (plural scutella), which functions in absorbing the solubi-lized food reserves from the endosperm and transmitting them to the growing embryo. The endosperm is composed of two tissues: the centrally located starchy endosperm and the aleurone layer (Figure 20.33A).
The starchy endosperm, typically nonliving at maturity, consists of thin-walled cells filled with starch grains. The aleurone layer surrounds the starchy endosperm and is cytologically and biochemically distinct from it. Aleurone cells are enclosed in thick primary cell walls and contain large numbers of protein-storing vacuoles called protein bodies (Figures 20.33B–D), enclosed by a single membrane.
The protein bodies also contain phytin, a mixed cation salt (mainly Mg2+ and K+) of myo-inositolhexaphosphoric acid (phytic acid).
During germination and early seedling growth, the stored food reserves of the endosperm—chiefly starch and protein—are broken down by a variety of hydrolytic enzymes, and the solubilized sugars, amino acids, and other products are transported to the growing embryo. The two enzymes responsible for starch degradation are α- and β-amylase. α-Amylase hydrolyzes starch chains internally to produce oligosaccharides consisting of α-1,4-linked glu-cose residues. β-Amylase degrades these oligosaccharides from the ends to produce maltose, a disaccharide. Maltase then converts maltose to glucose.
α-Amylase is secreted into the starchy endosperm of cereal seeds by both the scutellum and the aleurone layer (see Figure 20.33A). The sole function of the aleurone layer of the seeds of graminaceous monocots (e.g., barley, wheat, rice, rye, and oats) appears to be the synthesis and release of hydrolytic enzymes. After completing this function, aleurone cells undergo programmed cell death.
Experiments carried out in the 1960s confirmed Gottlieb Haberlandt’s original observation of 1890 that the secretion of starch-degrading enzymes by barley aleurone layers depends on the presence of the embryo. When the embryo was removed (i.e., the seed was de-embryonated), no starch was degraded. However, when the de-embryonated “half-seed” was incubated in close proximity to the excised embryo, starch was digested, demonstrating that the embryo produced a diffusible substance that triggered α-amylase release by the aleurone layer.
It was soon discovered that gibberellic acid (GA3) could substitute for the embryo in stimulating starch degrada-tion. When de-embryonated half-seeds were incubated in buffered solutions containing gibberellic acid, secretion of α-amylase into the medium was greatly stimulated after an 8-hour lag period (relative to the control half-seeds incu-bated in the absence of gibberellic acid).
The significance of the gibberellin effect became clear when it was shown that the embryo synthesizes and releases gibberellins (chiefly GA1) into the endosperm dur-ing germination. Thus the cereal embryo efficiently regu-lates the mobilization of its own food reserves through the secretion of gibberellins, which stimulate the digestive function of the aleurone layer (see Figure 20.33A).
Gibberellin has been found to promote the production and/or secretion of a variety of hydrolytic enzymes that are involved in the solubilization of endosperm reserves; prin-cipal among these is α-amylase. Since the 1960s, investiga-tors have utilized isolated aleurone layers, or even aleurone cell protoplasts (see Figure 20.33C and D), rather than half-seeds (see Figure 20.33B). The isolated aleurone layer, con-sisting of a homogeneous population of target cells, pro-vides a unique opportunity to study the molecular aspects of gibberellin action in the absence of nonresponding cell types.
In the following discussion of gibberellin-induced α-amylase production we focus on three questions: 484 Chapter 20 1. How does gibberellin regulate the increase in a-amy-lase?
2. Where is the gibberellin receptor located in the cell?
3. What signal transduction pathways operate between the gibberellin receptor and a-amylase production?
Gibberellic Acid Enhances the Transcription of α-Amylase mRNA Before molecular biological approaches were developed, there was already physiological and biochemical evidence that gibberellic acid might enhance α-amylase production at the level of gene transcription (Jacobsen et al. 1995). The two main lines of evidence were as follows: 1. GA3-stimulated α-amylase production was shown to be blocked by inhibitors of transcription and transla-tion.
2. Heavy-isotope- and radioactive-isotope-labeling studies demonstrated that the stimulation of α-amy-lase activity by gibberellin involved de novo synthe-sis of the enzyme from amino acids, rather than acti-vation of preexisting enzyme.
Definitive molecular evidence now shows that gib-berellin acts primarily by inducing the expression of the i First foliage leaf Coleoptile Aleurone layer Hydrolytic enzymes Aleurone cells Starchy endosperm Shoot apical meristem GAs GAs Endosperm solutes Scutellum Testa-pericarp Root 1. Gibberellins are synthesized by the embryo and released into the starchy endosperm via the scutellum.
2. Gibberellins diffuse to the aleurone layer.
3. Aleurone layer cells are induced to synthesize and secrete a-amylase and other hydrolases into the endosperm.
4. Starch and other macromolecules are broken down to small molecules.
5. The endosperm solutes are absorbed by the scutellum and transported to the growing embyro.
(A) FIGURE 20.33 Structure of a barley grain and the functions of various tissues during germination (A). Microscope pho-tos of the barley aleurone layer (B) and barley aleurone pro-toplasts at an early (C) and late stage (D) of amylase pro-duction. Protein storage vesicles (PSV) can be seen in each cell. G = phytin globoid; N = nucleus. (Photos from Bethke et al. 1997, courtesy of P. Bethke.) N PSV PSV G PSV (B) (C) (D) Gibberellins: Regulators of Plant Height 485 gene for α-amylase. It has been shown that GA3 enhances the level of translatable mRNA for α-amylase in aleurone layers (Figure 20.34). Furthermore, by using isolated nuclei, investigators also demonstrated that there was an enhanced transcription of the α-amylase gene rather than a decrease in mRNA turnover (see Web Topic 20.5).
The purification of α-amylase mRNA, which is pro-duced in relatively large amounts in aleurone cells, enabled the isolation of genomic clones containing both the struc-tural gene for α-amylase and its upstream promoter sequences. These promoter sequences were then fused to the reporter gene that encodes the enzyme β-glucuronidase (GUS), which yields a blue color in the presence of an arti-ficial substrate when the gene is expressed. The regulation of transcription by gibberellin was proved when such chimeric genes containing α-amylase promoters that were fused to reporter genes were introduced into aleurone pro-toplasts and the production of the blue color was shown to be stimulated by gibberellin (Jacobsen et al. 1995).
The partial deletion of known sequences of bases from α-amylase promoters from several cereals indicates that the sequences conferring gibberellin responsiveness, termed gibberellin response elements, are located 200 to 300 base pairs upstream of the transcription start site (see Web Topic 20.6).
A GA-MYB Transcription Factor Regulates α-Amylase Gene Expression The stimulation of α-amylase gene expression by gibberellin is mediated by a specific transcription factor that binds to the promoter of the α-amylase gene (Lovegrove and Hooley 2000). To demonstrate such DNA-binding proteins in rice, a technique called a mobility shift assay was used (see Web Topic 20.7). This assay detects the increase in size that occurs when the α-amylase promoter binds to a protein isolated from gibberellin-treated aleurone cells (Ou-Lee et al. 1988).
The mobility shift assay also allowed identification of the regulatory DNAsequences (gibberellin response elements) in the promoter that are involved in binding the protein.
Identical gibberellin response elements were found to occur in all cereal α-amylase promoters, and their presence was shown to be essential for the induction of α-amylase gene transcription by gibberellin. These studies demon-strated that gibberellin increases either the level or the activ-ity of a transcription factor protein that switches on the pro-duction of α-amylase mRNA by binding to an upstream regulatory element in the α-amylase gene promoter.
The sequence of the gibberellin response element in the α-amylase gene promoter turned out to be similar to that of the binding sites for MYB transcription factors that are known to regulate growth and development in phy-tochrome responses (see Chapter 14 on the Web site and Chapter 17) (Jacobsen et al. 1995). This knowledge enabled the isolation of mRNA for a MYB transcription factor, named GA-MYB, associated with the gibberellin induction of α-amylase gene expression.
The synthesis of GA-MYB mRNA in aleurone cells increases within 3 hours of gibberellin application, several hours before the increase in α-amylase mRNA (Gubler et al. 1995) (Figure 20.35). The inhibitor of translation, cyclo-heximide, has no effect on the production of MYB mRNA, indicating that GA-MYB is a primary response gene, or early gene. In contrast, the α-amylase gene is a secondary response gene, or late gene, as indicated by the fact that its transcrip-tion is blocked by cycloheximide.
How does gibberellin cause the MYB gene to be expressed? Because protein synthesis is not involved, gib-berellin may bring about the activation of one or more pre-existing transcription factors. The activation of transcription factors is typically mediated by protein phosphorylation events occurring at the end of a signal transduction path-way. We will now examine what is known about the sig-naling pathways involved in gibberellin-induced α-amy-lase production up to the point of GA-MYB production.
a-Amylase translatable mRNA (percent of total in vitro protein synthesis) (B) mRNA synthesis Treated with GA3 No GA treatment 16 12 8 4 0 5 10 15 Duration of exposure to GA3 (h) (A) Enzyme synthesis Rate of α-amylase synthesis (enzyme units per 120 min) No GA treatment 16 12 8 4 0 5 10 15 Treated with GA3 Duration of exposure to GA3 (h) Synthesis of a-amylase by isolated barley aleurone layers is evident after 6–8 hours of treatment with GA3 (10–6 M). A gibberellin-induced increase in translatable a-amylase mRNA precedes the release of the a-amylase from the aleurone cells by several hours.
FIGURE 20.34 Gibberellin effects on enzyme synthesis and mRNA synthesis. The α-amylase mRNA in this case was measured by the in vitro production of α-amylase as a per-centage of the protein produced by the translation of the bulk mRNA. (From Higgins et al. 1976.) 486 Chapter 20 Gibberellin Receptors May Interact with G-Proteins on the Plasma Membrane A cell surface localization of the gibberellin receptor is sug-gested from the fact that gibberellin that has been bound to microbeads that are unable to cross the plasma membrane is still active in inducing α-amylase production in aleurone protoplasts (Hooley et al. 1991). In addition, microinjection of GA3 into aleurone protoplasts had no effect, but when the protoplasts were immersed in GA3 solution, they produced α-amylase (Gilroy and Jones 1994). These results suggest that gibberellin acts on the outer face of the plasma membrane.
Two gibberellin-binding plasma membrane proteins have been isolated through the use of purified plasma membrane and a radioactively labeled gibberellin that was chemically modified to permanently attach to protein to which it was weakly bound. Because the presence of excess gibberellin reduces binding, and these proteins from a semidwarf, gibberellin-insensitive sweet pea bind gib-berellin less strongly, they may represent the gibberellin receptors (Lovegrove et al. 1998).
In animal cells, heterotrimeric GTP-binding proteins (G-proteins) in the cell membrane are often involved as first steps in a pathway between a hormone receptor and sub-sequent cytosolic signals. Evidence has been obtained that G-proteins are also involved in the early gibberellin sig-naling events in aleurone cells (Jones et al. 1998). Treatment of oat aleurone protoplasts with a peptide called Mas7, which stimulates GTP/GDP exchange by G-proteins, was found to induce α-amylase gene expression and to stimulate α-amylase secretion, suggesting that such a GTP/GDP exchange on the cell membrane is a reaction en route to the induction of α-amylase biosynthesis by gib-berellin. In addition, gibberellin-induced α-amylase gene expression and secretion were inhibited by a guanine nucleotide analog that binds to the α subunit of het-erotrimeric G-proteins and inhibits GTP/GDP exchange, further supporting the preceding conclusion.
Recent genetic studies have provided further support for the role of G-proteins as intermediates in the gibberellin signal transduction pathway. The rice dwarf mutant dwarf 1 (d1) has a defective gene encoding the α subunit. Besides being dwarf, the aleurone layers of the d1 mutant synthe-size less α-amylase in response to gibberellin than wild-type aleurone layers do. This reduction in α-amylase pro-duction by the d1 mutant demonstrates that G-proteins are one of the components of the gibberellin signal transduc-tion pathway involved in both the growth response and the production of α-amylase. However, the difference in α-amylase production between the mutant and the wild type goes away with increasing gibberellin concentration, sug-gesting that gibberellin can also stimulate α-amylase pro-duction by a G-protein-independent pathway (Ashikari et al. 1999; Ueguchi-Tanaka et al. 2000).
Cyclic GMP, Ca2+, and Protein Kinases Are Possible Signaling Intermediates In animal cells, G-proteins can activate the enzyme guany-lyl cyclase, the enzyme that synthesizes cGMP from GTP, leading to an increase in cGMP concetration. Cyclic GMP, in turn, can regulate ion channels, Ca2+ levels, protein kinase activity, and gene transcription (see Chapter 14 on the Web site). Gibberellin has been reported to cause a tran-sient rise in cGMP levels in barley aleurone layers, sug-gesting a possible role for cGMP in α-amylase production (Figure 20.36) (see Web Topic 20.8) (Pensen et al. 1996).
Calcium and the calcium-binding protein calmodulin act as second messengers for many hormonal responses in 100 75 50 25 0 6 3 12 18 24 Hours after exposure to GA GA-MYB mRNA a-Amylase mRNA Relative transcript levels FIGURE 20.35 Time course for the induction of GA-MYB and α-amylase mRNA by gibberellic acid. The production of GA-MYB mRNA precedes α-amylase mRNA by about 5 hours. This result is consistent with the role of GA-MYB as an early GA response gene that regulates the transcription of the gene for α-amylase. In the absence of GA, the levels of both GA-MYB and α-amylase mRNAs are negligible.
(After Gubler et al. 1995.) 10 0 100 1000 10,000 0 20 40 60 80 100 Response to GA (percent) Time after GA treatment (min) [Ca2+]i a-Amylase pHi cGMP CaM GA-MYB RNase DNase FIGURE 20.36 Following the addition of GA to barley aleu-rone protoplasts, a multiple signal transduction pathway is initiated. The timing of some of these events is shown.
(From Bethke et al. 1997.) Gibberellins: Regulators of Plant Height 487 animal cells (see Chapter 14 on the Web site), and they have been implicated in various plant responses to environ-mental and hormonal stimuli. The earliest event in aleu-rone protoplasts after the application of gibberellin is a rise in the cytoplasmic calcium concentration that occurs well before the onset of α-amylase synthesis (see Figures 20.36 and 20.37) (Bethke et al. 1997). Without calcium, α-amylase secretion does not occur, though in barley aleurone proto-plasts its synthesis goes ahead normally, so we have to con-clude that, in barley, calcium is not on the signaling path-way to α-amylase gene transcription, though it does play a role in enzyme secretion.
Protein phosphorylation by protein kinases is another component in many signaling pathways, and gibberellin appears to be no exception. The injection of a protein kinase substrate into barley aleurone protoplasts to com-pete with endogenous protein phosphorylation inhibited α-amylase secretion, suggesting the involvement of protein phosphorylation in the α-amylase secretion pathway (Ritchie and Gilroy 1998a). This did not affect the gib-berellin-stimulated increase in calcium, indicating that the protein kinase step is downstream of the calcium signaling event.
In conclusion, gibberellin signal transduction in aleu-rone cells seems to involve G-proteins as well as cyclic GMP, leading to production of the transcription factor GA-MYB, which induces α-amylase gene transcription. α-Amy-lase secretion has similar initial components but also involves an increase in cytoplasmic calcium and protein phosphorylation. The detailed signaling pathways remain to be worked out. A model of the known biochemical com-ponents of the gibberellin signal transduction pathways in aleurone cells is illustrated in Figure 20.38.
The Gibberellin Signal Transduction Pathway Is Similar for Stem Growth and α-Amylase Production It is widely believed that gibberellin initially acts through a common pathway or pathways in all of its effects on devel-opment. As we have seen, the genetic approaches applied to the study of gibberellin-stimulated growth led to the identi-fication of the SPY/GAI/RGA negative regulatory pathway.
The proteins SPY, GAI, and RGA act as repressors of gib-berellin responses. Gibberellin deactivates these repressors. Because the aleurone layers of gibberellin-insensitive dwarf wheat are also insensitive to GA, the same signal transduction pathways that regulate growth appear to reg-ulate gibberellin-induced α-amylase production. Indeed a SPY-type gene associated with α-amylase production has been isolated from barley (HvSPY), and its expression is able to inhibit gibberellin-induced α-amylase synthesis, while GA-MYB-type factors are also implicated in the gib-berellin transduction chain regulating stem growth. Rice with the dwarf 1 mutation also produces little α-amylase in response to gibberellin. As noted earlier, the mutation causing dwarf 1 is known to be in the α subunit of the G-protein complex, providing evidence that the action of gibberellin in both stem elongation and the pro-duction of α-amylase are regulated by plasma membrane heterotrimeric G-proteins. As the entire elongation growth and α-amylase signal-ing pathways are worked out, it will be interesting to see how much they have in common and where they diverge.
SUMMARY Gibberellins are a family of compounds defined by their structure. They now number over 125, some of which are found only in the fungus Gibberella fujikuroi. Gibberellins induce dramatic internode elongation in certain types of plants, such as dwarf and rosette species and grasses.
(A) (B) (C) v v Control GA GA+ ABA Cytoplasmic [Ca2+] (nM) 50 100 300 500 1000 FIGURE 20.37 Increase in the calcium in barley aleurone protoplasts following GA addition can be seen from this false color image. The level of calcium corresponding to the colors is in the lower scale. (A) Untreated protoplast. (B) GA-treated protoplast. (C) Protoplast treated with both abscisic acid (AB) and GA. Abscisic acid opposes the effects of GA in aleurone cells.
(From Ritchie and Gilroy 1998b.) FIGURE 20.38 Composite model for the induction of α-amylase synthesis in barley aleurone layers by gibberellin.
A calcium-independent pathway induces α-amylase gene transcription; a calcium-dependent pathway is involved in α-amylase secretion. (The SPY negative regulator was omit-ted for clarity.) L 488 Chapter 20 GTP GA receptor GA1 Ca2+-dependent signal transduction pathway involving calmodulin and protein kinase Ca2+-independent signal transduction pathway with cGMP GA-MYB gene GA-MYB mRNA Transcription and processing Transcription and processing α-amylase gene α-amylase mRNA Heterotrimeric G-protein ALEURONE LAYER CELL GA-MYB transcription factor Secretory vesicles containing a-amylase DELLA repressor Rough ER Ribosomes Golgi body Activated GA signaling intermediate Plasma membrane Repressor degraded γ β α DNA NUCLEUS Secretion a-amylase Starch degradation in endosperm 1. GA1 from the embryo first binds to a cell surface receptor.
2. The cell surface GA receptor complex interacts with a heterotrimeric G- protein, initiating two separate signal transduction chains.
3. A calcium-independent pathway, involving cGMP, results in the activation of a signaling intermediate.
4. The activated signal-ing intermediate binds to DELLA repressor proteins in the nucleus.
5. The DELLA repressors are degraded when bound to the GA signal.
6. The inactivation of the DELLA repressors allows the expression of the MYB gene, as well as other genes, to proceed through transcription, processing, and translation.
7. The newly synthesized MYB protein then enters the nucleus and binds to the promoter genes for a-amylase and other hydrolytic enzymes.
8. Transcription of a-amylase and other hydrolytic genes is activated.
9. a-Amylase and other hydrolases are synthesized on the rough ER.
10. Proteins are secreted via the Golgi.
11. The secretory pathway requires GA stimulation via a calcium–calmodulin-dependent signal transduction pathway.
2 3 4 5 6 7 8 9 10 11 1 Gibberellins: Regulators of Plant Height 489 Other physiological effects of gibberellin include changes in juvenility and flower sexuality, and the promotion of fruit set, fruit growth, and seed germination. Gibberellins have several commercial applications, mainly in enhance-ment of the size of seedless grapes and in the malting of barley. Gibberellin synthesis inhibitors are used as dwarf-ing agents.
Gibberellins are identified and quantified by gas chro-matography combined with mass spectrometry, following separation by high-performance liquid chromatography.
Bioassays may be used to give an initial idea of the gib-berellins present in a sample. Only certain GAs, notably GA1 and GA4, are responsible for the effects in plants; the others are precursors or metabolites.
Gibberellins are terpenoid compounds, made up of iso-prene units. The first compound in the isoprenoid pathway committed to gibberellin biosynthesis is ent-kaurene. The biosynthesis up to ent-kaurene occurs in plastids. ent-Kau-rene is converted to GA12—the precursor of all the other gibberellins—on the plastid envelope and then on the endoplasmic reticulum via cytochrome P450 monooxyge-nases. Commonly a hydroxylation at C-13 also takes place to give GA53. GA53 or GA12, each of which has 20 carbon atoms, is con-verted to other gibberellins by sequential oxidation of carbon 20, followed by the loss of this carbon to give 19-carbon gib-berellins. This process is followed by hydroxylation at carbon 3 to give the growth-active GA1 or GA4. A subsequent hydroxylation at carbon 2 eliminates biological activity. The steps after GA53 or GA12 occur in the cytoplasm.
The genes for GA 20-oxidase (GA20ox), which catalyzes the steps between GA53 and GA20, GA 3β-hydroxylase (or GA 3-oxidase; GA3ox), which converts GA20 into GA1, and GA 2-oxidase (GA2ox), which converts active GA1 to inac-tive GA8, have been isolated. Dwarf plants have been genetically engineered by the use of antisense GA20ox or GA3ox, or overexpression of GA2ox. Gibberellins may also be glycosylated to give either an inactivated form or a stor-age form.
The endogenous level of active gibberellin regulates its own synthesis by switching on or inhibiting the transcrip-tion of the genes for the enzymes of gibberellin biosynthe-sis and degradation. Environmental factors such as pho-toperiod (e.g., leading to bolting and potato tuberization) and temperature (vernalization), and the presence of auxin from the stem apex, also modulate gibberellin biosynthesis through the transcription of the genes for the gibberellin biosynthetic enzymes. Light regulates both GA1 biosynthe-sis through regulation of the transcription of the gibberellin degradation gene and also causes a decrease in the respon-siveness of stem elongation to the presence of gibberellin.
The most pronounced effect of applied gibberellins is stem elongation in dwarf and rosette plants. Gibberellins stimulate stem growth by promoting both cell elongation and cell division. The activity of some wall enzymes has been correlated with gibberellin-induced growth and cell wall loosening. Gibberellin-stimulated cell divisions in deep-water rice are regulated at the transition between DNA replication and cell division.
Three types of gibberellin response mutants have been useful in the identification of genes involved in the gib-berellin signaling pathway involved in stem growth: (1) gibberellin-insensitive dwarfs (e.g., gai-1), (2) gibberellin deficiency reversion mutants (e.g., rga), and (3) constitutive gibberellin responders (slender mutants) (e.g., spy). GAI and RGA are related nuclear transcription factors that repress growth. In the presence of gibberellin they are degraded. The mutant gai-1, and the related wheat dwarf-ing gene mutant rht, have lost the ability to respond to gib-berellin. SPY encodes a glycosyl transferase that is a mem-ber of a signal transduction chain prior to GAI/RGA.
When a mutation interferes with the repressor function of any of these, the plants grow tall.
Gibberellin induces transcription of the gene for α-amy-lase biosynthesis in cereal grain aleurone cells. This process is mediated by the transcription of a specific transcription factor, GA-MYB, which binds to the upstream region of the α-amylase gene, thus switching it on. The gibberellin recep-tor is located on the surface of aleurone cells. G-proteins and cyclic GMP have been implicated as members of the signal transduction chain on the way to GA-MYB. Calcium is not on the route to α-amylase gene transcription, though it does play a role in α-amylase secretion via protein phos-phorylation.
The gibberellin signal transduction pathway is probably similar for stem elongation and α-amylase production.
Dwarf wheat and rice also have impaired α-amylase gene transcription. Gibberellin acts by deactivating repressors, such as SPY, GAI, and RGA en route to both an increase in cell elongation and the production of α-amylase.
Web Material Web Topics 20.1 Structures of Some Important Gibberellins, Their Precursors and Derivatives, and Inhibitors of Gibberellin Biosynthesis The chemical structures of various gibberellins and inhibitors of gibberellin biosynthesis are presented.
20.2 Gibberellin Detection Gibberellin quantitation is now routine thanks to sensitive modern physical methods of detection.
490 Chapter 20 20.3 Gibberellin-Induced Stem Elongation Various mechanisms of gibberellin-induced cell wall loosening are discussed.
20.4 CDKs and Gibberellin-Induced Cell Division Additional information on the mechanism of gibberellin regulation of the cell cycle is given.
20.5 Gibberellin-Induction of α-amylase mRNA Evidence is provided for gibberellin-induced transcription of α-amylase mRNA.
20.6 Promoter Elements and Gibberellin Responsiveness Gibberellin response elements mediate the effects of gibberellin on α-amylase transcrip-tion.
20.7 Regulation of α-amylase Gene Expression by Transcription Factors Experiments identifying MYB transcription fac-tors as mediators of gibberellin-induced gene transcription are described.
20.8 Gibberellin Signal Transduction Various signaling intermediates have been implicated in gibberellin responsiveness.
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492 Chapter 20 Cytokinins: Regulators of Cell Division 21 Chapter THE CYTOKININS WERE DISCOVERED in the search for factors that stimulate plant cells to divide (i.e., undergo cytokinesis). Since their dis-covery, cytokinins have been shown to have effects on many other phys-iological and developmental processes, including leaf senescence, nutri-ent mobilization, apical dominance, the formation and activity of shoot apical meristems, floral development, the breaking of bud dormancy, and seed germination. Cytokinins also appear to mediate many aspects of light-regulated development, including chloroplast differentiation, the development of autotrophic metabolism, and leaf and cotyledon expansion.
Although cytokinins regulate many cellular processes, the control of cell division is central in plant growth and development and is consid-ered diagnostic for this class of plant growth regulators. For these rea-sons we will preface our discussion of cytokinin function with a brief consideration of the roles of cell division in normal development, wounding, gall formation, and tissue culture. Later in the chapter we will examine the regulation of plant cell pro-liferation by cytokinins. Then we will turn to cytokinin functions not directly related to cell division: chloroplast differentiation, the preven-tion of leaf senescence, and nutrient mobilization. Finally, we will con-sider the molecular mechanisms underlying cytokinin perception and signaling.
CELL DIVISION AND PLANT DEVELOPMENT Plant cells form as the result of cell divisions in a primary or secondary meristem. Newly formed plant cells typically enlarge and differentiate, but once they have assumed their function—whether transport, pho-tosynthesis, support, storage, or protection—usually they do not divide again during the life of the plant. In this respect they appear to be sim-ilar to animal cells, which are considered to be terminally differentiated. However, this similarity to the behavior of animal cells is only super-ficial. Almost every type of plant cell that retains its nucleus at maturity has been shown to be capable of dividing. This property comes into play during such processes as wound healing and leaf abscission.
Differentiated Plant Cells Can Resume Division Under some circumstances, mature, differentiated plant cells may resume cell division in the intact plant. In many species, mature cells of the cortex and/or phloem resume division to form secondary meristems, such as the vascular cambium or the cork cambium. The abscission zone at the base of a leaf petiole is a region where mature parenchyma cells begin to divide again after a period of mitotic inactiv-ity, forming a layer of cells with relatively weak cell walls where abscission can occur (see Chapter 22).
Wounding of plant tissues induces cell divisions at the wound site. Even highly specialized cells, such as phloem fibers and guard cells, may be stimulated by wounding to divide at least once. Wound-induced mitotic activity typi-cally is self-limiting; after a few divisions the derivative cells stop dividing and redifferentiate. However, when the soil-dwelling bacterium Agrobacterium tumefaciens invades a wound, it can cause the neoplastic (tumor-forming) disease known as crown gall. This phenomenon is dramatic natural evidence of the mitotic potential of mature plant cells.
Without Agrobacterium infection, the wound-induced cell division would subside after a few days and some of the new cells would differentiate as a protective layer of cork cells or vascular tissue. However, Agrobacterium changes the character of the cells that divide in response to the wound, making them tumorlike. They do not stop dividing; rather they continue to divide throughout the life of the plant to produce an unorganized mass of tumorlike tissue called a gall (Figure 21.1). We will have more to say about this important disease later in this chapter.
Diffusible Factors May Control Cell Division The considerations addressed in the previous section sug-gest that mature plant cells stop dividing because they no longer receive a particular signal, possibly a hormone, that is necessary for the initiation of cell division. The idea that cell division may be initiated by a diffusible factor origi-nated with the Austrian plant physiologist G. Haberlandt, who, in about 1913, demonstrated that vascular tissue con-tains a water-soluble substance or substances that will stim-ulate the division of wounded potato tuber tissue. The effort to determine the nature of this factor (or factors) led to the discovery of the cytokinins in the 1950s.
Plant Tissues and Organs Can Be Cultured Biologists have long been intrigued by the possibility of growing organs, tissues, and cells in culture on a simple nutrient medium, in the same way that microorganisms can be cultured in test tubes or on petri dishes. In the 1930s, Philip White demonstrated that tomato roots can be grown indefinitely in a simple nutrient medium containing only sucrose, mineral salts, and a few vitamins, with no added hormones (White 1934).
In contrast to roots, isolated stem tissues exhibit very lit-tle growth in culture without added hormones in the medium. Even if auxin is added, only limited growth may occur, and usually this growth is not sustained. Frequently this auxin-induced growth is due to cell enlargement only.
The shoots of most plants cannot grow on a simple medium lacking hormones, even if the cultured stem tis-sue contains apical or lateral meristems, until adventitious roots form. Once the stem tissue has rooted, shoot growth resumes, but now as an integrated, whole plant. These observations indicate that there is a difference in the regulation of cell division in root and shoot meristems.
They also suggest that some root-derived factor(s) may reg-ulate growth in the shoot.
Crown gall stem tissue is an exception to these general-izations. After a gall has formed on a plant, heating the plant to 42°C will kill the bacterium that induced gall for-mation. The plant will survive the heat treatment, and its gall tissue will continue to grow as a bacteria-free tumor (Braun 1958).
Tissues removed from these bacteria-free tumors grow on simple, chemically defined culture media that would not support the proliferation of normal stem tissue of the same species. However, these stem-derived tissues are not organized. Instead they grow as a mass of disorganized, relatively undifferentiated cells called callus tissue.
Callus tissue sometimes forms naturally in response to wounding, or in graft unions where stems of two different plants are joined. Crown gall tumors are a specific type of callus, whether they are growing attached to the plant or in culture. The finding that crown gall callus tissue can be cultured demonstrated that cells derived from stem tissues are capable of proliferating in culture and that contact with 494 Chapter 21 FIGURE 21.1 Tumor that formed on a tomato stem infected with the crown gall bacterium, Agrobacterium tumefaciens. Two months before this photo was taken the stem was wounded and inoculated with a virulent strain of the crown gall bac-terium. (From Aloni et al. 1998, courtesy of R. Aloni.) the bacteria may cause the stem cells to produce cell divi-sion–stimulating factors.
THE DISCOVERY, IDENTIFICATION, AND PROPERTIES OF CYTOKININS A great many substances were tested in an effort to initiate and sustain the proliferation of normal stem tissues in cul-ture. Materials ranging from yeast extract to tomato juice were found to have a positive effect, at least with some tis-sues. However, culture growth was stimulated most dra-matically when the liquid endosperm of coconut, also known as coconut milk, was added to the culture medium. Philip White’s nutrient medium, supplemented with an auxin and 10 to 20% coconut milk, will support the con-tinued cell division of mature, differentiated cells from a wide variety of tissues and species, leading to the forma-tion of callus tissue (Caplin and Steward 1948). This find-ing indicated that coconut milk contains a substance or substances that stimulate mature cells to enter and remain in the cell division cycle. Eventually coconut milk was shown to contain the cytokinin zeatin, but this finding was not obtained until several years after the discovery of the cytokinins (Letham 1974). The first cytokinin to be discovered was the synthetic analog kinetin.
Kinetin Was Discovered as a Breakdown Product of DNA In the 1940s and 1950s, Folke Skoog and coworkers at the University of Wisconsin tested many substances for their ability to initiate and sustain the proliferation of cultured tobacco pith tissue. They had observed that the nucleic acid base adenine had a slight promotive effect, so they tested the possibility that nucleic acids would stimulate division in this tissue. Surprisingly, autoclaved herring sperm DNA had a powerful cell division–promoting effect.
After much work, a small molecule was identified from the autoclaved DNA and named kinetin. It was shown to be an adenine (or aminopurine) derivative, 6-furfury-laminopurine (Miller et al. 1955): In the presence of an auxin, kinetin would stimulate tobacco pith parenchyma tissue to proliferate in culture. No kinetin-induced cell division occurs without auxin in the culture medium. (For more details, see Web Topic 21.1.) Kinetin is not a naturally occurring plant growth regu-lator, and it does not occur as a base in the DNA of any species. It is a by-product of the heat-induced degradation of DNA, in which the deoxyribose sugar of adenosine is converted to a furfuryl ring and shifted from the 9 position to the 6 position on the adenine ring.
The discovery of kinetin was important because it demon-strated that cell division could be induced by a simple chem-ical substance. Of greater importance, the discovery of kinetin suggested that naturally occurring molecules with structures similar to that of kinetin regulate cell division activity within the plant. This hypothesis proved to be correct.
Zeatin Is the Most Abundant Natural Cytokinin Several years after the discovery of kinetin, extracts of the immature endosperm of corn (Zea mays) were found to contain a substance that has the same biological effect as kinetin. This substance stimulates mature plant cells to divide when added to a culture medium along with an auxin. Letham (1973) isolated the molecule responsible for this activity and identified it as trans-6-(4-hydroxy-3-methylbut-2-enylamino)purine, which he called zeatin: The molecular structure of zeatin is similar to that of kinetin. Both molecules are adenine or aminopurine derivatives. Although they have different side chains, in both cases the side chain is attached to the 6 nitrogen of the aminopurine. Because the side chain of zeatin has a double bond, it can exist in either the cis or the trans con-figuration.
In higher plants, zeatin occurs in both the cis and the trans configurations, and these forms can be interconverted by an enzyme known as zeatin isomerase. Although the trans form of zeatin is much more active in biological assays, the cis form may also play important roles, as suggested by the fact that it has been found in high levels in a number of plant species and particular tissues. A gene encoding a glu-cosyl transferase enzyme specific to cis-zeatin has recently been cloned, which further supports a biological role for this isoform of zeatin.
Since its discovery in immature maize endosperm, zeatin has been found in many plants and in some bacte-ria. It is the most prevalent cytokinin in higher plants, but other substituted aminopurines that are active as cytokinins have been isolated from many plant and bac-CH2OH N N H N C C H N HN CH3 CH2OH CH2 N N H N C C H N HN CH3 CH2 trans-Zeatin 6-(4-Hydroxy-3-methylbut-2-enylamino)purine cis-Zeatin N C C O C C C H H H H H C N C C C N N C N H H H 9 1 2 3 4 5 6 7 8 H Kinetin Amino purine Cytokinins: Regulators of Cell Division 495 terial species. These aminopurines differ from zeatin in the nature of the side chain attached to the 6 nitrogen or in the attachment of a side chain to carbon 2: In addition, these cytokinins can be present in the plant as a riboside (in which a ribose sugar is attached to the 9 nitrogen of the purine ring), a ribotide (in which the ribose sugar moiety contains a phosphate group), or a glycoside (in which a sugar molecule is attached to the 3, 7, or 9 nitro-gen of the purine ring, or to the oxygen of the zeatin or dihydrozeatin side chain) (see Web Topic 21.2).
Some Synthetic Compounds Can Mimic or Antagonize Cytokinin Action Cytokinins are defined as compounds that have biological activities similar to those of trans-zeatin. These activities include the ability to do the following: • Induce cell division in callus cells in the presence of an auxin • Promote bud or root formation from callus cultures when in the appropriate molar ratios to auxin • Delay senescence of leaves • Promote expansion of dicot cotyledons Many chemical compounds have been synthesized and tested for cytokinin activity. Analysis of these compounds provides insight into the structural requirements for activ-ity. Nearly all compounds active as cytokinins are N6-sub-stituted aminopurines, such as benzyladenine (BA): and all the naturally occurring cytokinins are aminopurine derivatives. There are also synthetic cytokinin compounds that have not been identified in plants, most notable of which are the diphenylurea-type cytokinins, such as thidi-azuron, which is used commercially as a defoliant and an herbicide: In the course of determining the structural requirements for cytokinin activity, investigators found that some mole-cules act as cytokinin antagonists: These molecules are able to block the action of cytokinins, and their effects may be overcome by the addition of more cytokinin. Naturally occurring molecules with cytokinin activity may be detected and identified by a combination of physical methods and bioassays (see Web Topic 21.3).
Cytokinins Occur in Both Free and Bound Forms Hormonal cytokinins are present as free molecules (not covalently attached to any macromolecule) in plants and certain bacteria. Free cytokinins have been found in a wide spectrum of angiosperms and probably are universal in this group of plants. They have also been found in algae, diatoms, mosses, ferns, and conifers. The regulatory role of cytokinins has been demonstrated only in angiosperms, conifers, and mosses, but they may function to regulate the growth, development, and metab-olism of all plants. Usually zeatin is the most abundant nat-urally occurring free cytokinin, but dihydrozeatin (DZ) and isopentenyl adenine (iP) also are commonly found in higher plants and bacteria. Numerous derivatives of these three cytokinins have been identified in plant extracts (see the structures illustrated in Figure 21.6).
Transfer RNA (tRNA) contains not only the four nucleotides used to construct all other forms of RNA, but also some unusual nucleotides in which the base has been modified. Some of these “hypermodified” bases act as cytokinins when the tRNA is hydrolyzed and tested in one of the cytokinin bioassays. Some plant tRNAs contain cis-N N NH N N CH2 CH3 CH2 CH3 CH3 CH 3-Methyl-7-(3-methylbutylamino)pyrazolo[4,3-D]pyrimidine NH HN C O N H N H S N N N,N′-Diphenylurea (nonamino purine with weak activity) Thidiazuron N N N H N HN CH2 Benzyladenine (benzylaminopurine) (BA) CH2OH N N H N C C H H N HN CH3 CH2 CH3 N 9 N H N C C H N HN CH3 CH2 N6-(∆2-Isopentenyl)-adenine (iP) Dihydrozeatin (DZ) 496 Chapter 21 zeatin as a hypermodified base. However, cytokinins are not confined to plant tRNAs. They are part of certain tRNAs from all organisms, from bacteria to humans. (For details, see Web Topic 21.4.) The Hormonally Active Cytokinin Is the Free Base It has been difficult to determine which species of cytokinin represents the active form of the hormone, but the recent identification of the cytokinin receptor CRE1 has allowed this question to be addressed. The relevant experiments have shown that the free-base form of trans-zeatin, but not its ribo-side or ribotide derivatives, binds directly to CRE1, indicat-ing that the free base is the active form (Yamada et al. 2001).
Although the free-base form of trans-zeatin is thought to be the hormonally active cytokinin, some other compounds have cytokinin activity, either because they are readily con-verted to zeatin, dihydrozeatin, or isopentenyl adenine, or because they release these compounds from other mole-cules, such as cytokinin glucosides. For example, tobacco cells in culture do not grow unless cytokinin ribosides sup-plied in the culture medium are converted to the free base. In another example, excised radish cotyledons grow when they are cultured in a solution containing the cytokinin base benzyladenine (BA, an N6-substituted aminopurine cytokinin). The cultured cotyledons readily take up the hormone and convert it to various BA gluco-sides, BA ribonucleoside, and BA ribonucleotide. When the cotyledons are transferred back to a medium lacking a cytokinin, their growth rate declines, as do the concentra-tions of BA, BA ribonucleoside, and BA ribonucleotide in the tissues. However, the level of the BA glucosides remains constant. This finding suggests that the glucosides cannot be the active form of the hormone.
Some Plant Pathogenic Bacteria, Insects, and Nematodes Secrete Free Cytokinins Some bacteria and fungi are intimately associated with higher plants. Many of these microorganisms produce and secrete substantial amounts of cytokinins and/or cause the plant cells to synthesize plant hormones, including cytokinins (Akiyoshi et al. 1987). The cytokinins produced by microorganisms include trans-zeatin, [9R]iP, cis-zeatin, and their ribosides (Figure 21.2). Infection of plant tissues with these microorganisms can induce the tissues to divide and, in some cases, to form special structures, such as myc-orrhizae, in which the microorganism can reside in a mutu-alistic relationship with the plant.
In addition to the crown gall bacterium, Agrobacterium tumefaciens, other pathogenic bacteria may stimulate plant cells to divide. For example, Corynebacterium fascians is a major cause of the growth abnormality known as witches’-broom (Figure 21.3). The shoots of plants infected by C. fas-cians resemble an old-fashioned straw broom because the lateral buds, which normally remain dormant, are stimu-lated by the bacterial cytokinin to grow (Hamilton and Lowe 1972).
Cytokinins: Regulators of Cell Division 497 CH3 N O 9 N N C C H N HN CH3 CH2OH CH2 HOCH2 O H O H N O 9 N N C C H N HN CH3 CH2 HOCH2 O H O H Ribosylzeatin (zeatin riboside) N6-(D2-Isopentenyl)adenosine ([9R]iP) FIGURE 21.2 Structures of ribosylzeatin and N6-(∆2-isopen-tenyl)adenosine ([9R]iP).
FIGURE 21.3 Witches’ broom on balsam fir (Abies balsamea).
(Photo © Gregory K. Scott/Photo Researchers, Inc.) Infection with a close relative of the crown gall organ-ism, Agrobacterium rhizogenes, causes masses of roots instead of callus tissue to develop from the site of infec-tion. A. rhizogenes is able to modify cytokinin metabolism in infected plant tissues through a mechanism that will be described later in this chapter.
Certain insects secrete cytokinins, which may play a role in the formation of galls utilized by these insects as feeding sites. Root-knot nematodes also produce cytokinins, which may be involved in manipulating host development to produce the giant cells from which the nematode feeds (Elzen 1983).
BIOSYNTHESIS, METABOLISM, AND TRANSPORT OF CYTOKININS The side chains of naturally occurring cytokinins are chemically related to rubber, carotenoid pigments, the plant hormones gibberellin and abscisic acid, and some of the plant defense compounds known as phytoalexins. All of these compounds are constructed, at least in part, from isoprene units (see Chapter 13). Isoprene is similar in structure to the side chains of zeatin and iP (see the structures illustrated in Figure 21.6).
These cytokinin side chains are synthesized from an iso-prene derivative. Large molecules of rubber and the carotenoids are constructed by the polymerization of many isoprene units; cytokinins contain just one of these units. The precursor(s) for the formation of these isoprene structures are either mevalonic acid or pyruvate plus 3-phosphoglycerate, depending on which pathway is involved (see Chapter 13). These precursors are converted to the biological isoprene unit dimethylallyl diphosphate (DMAPP).
Crown Gall Cells Have Acquired a Gene for Cytokinin Synthesis Bacteria-free tissues from crown gall tumors proliferate in culture without the addition of any hormones to the cul-ture medium. Crown gall tissues contain substantial amounts of both auxin and free cytokinins. Furthermore, when radioactively labeled adenine is fed to periwinkle (Vinca rosea) crown gall tissues, it is incorporated into both zeatin and zeatin riboside, demonstrating that gall tissues contain the cytokinin biosynthetic pathway. Control stem tissue, which has not been transformed by Agrobacterium, does not incorporate labeled adenine into cytokinins.
During infection by Agrobacterium tumefaciens, plant cells incorporate bacterial DNA into their chromosomes.
The virulent strains of Agrobacterium contain a large plas-mid known as the Ti plasmid. Plasmids are circular pieces of extrachromosomal DNA that are not essential for the life of the bacterium. However, plasmids frequently con-tain genes that enhance the ability of the bacterium to sur-vive in special environments.
A small portion of the Ti plasmid, known as the T-DNA, is incorporated into the nuclear DNA of the host plant cell (Figure 21.4) (Chilton et al. 1977). T-DNA carries genes necessary for the biosynthesis of trans-zeatin and auxin, as well as a member of a class of unusual nitrogen-containing compounds called opines (Figure 21.5). Opines are not synthesized by plants except after crown gall trans-formation.
The T-DNA gene involved in cytokinin biosynthesis— known as the ipt1 gene—encodes an isopentenyl trans-ferase (IPT) enzyme that transfers the isopentenyl group from DMAPP to AMP (adenosine monophosphate) to form isopentenyl adenine ribotide (Figure 21.6) (Akiyoshi et al.
1984; Barry et al. 1984). The ipt gene has been called the tmr locus because, when inactivated by mutation, it results in “rooty” tumors. Isopentenyl adenine ribotide can be con-verted to the active cytokinins isopentenyl adenine, trans-zeatin, and dihydrozeatin by endogenous enzymes in plant cells. This conversion route is similar to the pathway for cytokinin synthesis that has been postulated for normal tis-sue (see Figure 21.6).
The T-DNA also contains two genes encoding enzymes that convert tryptophan to the auxin indole-3-acetic acid (IAA). This pathway of auxin biosynthesis differs from the one in nontransformed cells and involves indoleacetamide as an intermediate (see Figure 19.6). The ipt gene and the two auxin biosynthetic genes of T-DNA are phyto-onco-genes, since they can induce tumors in plants (see Web Topic 21.5).
Because their promoters are plant eukaryotic promoters, none of the T-DNA genes are expressed in the bacterium; rather they are transcribed after they are inserted into the plant chromosomes. Transcription of the genes leads to synthesis of the enzymes they encode, resulting in the pro-duction of zeatin, auxin, and an opine. The bacterium can utilize the opine as a nitrogen source, but cells of higher plants cannot. Thus, by transforming the plant cells, the bacterium provides itself with an expanding environment (the gall tissue) in which the host cells are directed to pro-duce a substance (the opine) that only the bacterium can utilize for its nutrition (Bomhoff et al. 1976).
An important difference between the control of cytokinin biosynthesis in crown gall tissues and in normal tissues is that the T-DNA genes for cytokinin synthesis are expressed in all infected cells, even those in which the native plant genes for biosynthesis of the hormone are nor-mally repressed.
IPT Catalyzes the First Step in Cytokinin Biosynthesis The first committed step in cytokinin biosynthesis is the transfer of the isopentenyl group of dimethylallyl diphos-498 Chapter 21 1 Bacterial genes, unlike plant genes, are written in lower-case italics.
phate (DMAPP ) to an adenosine moiety. An enzyme that catalyzes such an activity was first identified in the cellu-lar slime mold Dictyostelium discoideum, and subsequently the ipt gene from Agrobacterium was found to encode such an enzyme. In both cases, DMAPP and AMP are converted to isopentenyladenosine-5′-monophosphate (iPMP).
As noted earlier, cytokinins are also present in the tRNAs of most cells, including plant and animal cells. The tRNA cytokinins are synthesized by modification of spe-cific adenine residues within the fully transcribed tRNA.
As with the free cytokinins, isopentenyl groups are trans-ferred to the adenine molecules from DMAPP by an enzyme call tRNA-IPT. The genes for tRNA-IPT have been cloned from many species.
Cytokinins: Regulators of Cell Division 499 Ti plasmid T-DNA Chromosome Chromosomal DNA T-DNA Nucleus Agrobacterium tumefaciens Transformed plant cell Crown gall 2. A virulent bacterium carries a Ti plasmid in addition to its own chromosomal DNA. The plasmid‘s T-DNA enters a cell and integrates into the cell‘s chromosomal DNA.
3. Transformed cells proliferate to form a crown gall tumor.
1. The tumor is initiated when bacteria enter a lesion and attach themselves to cells.
4. Tumor tissue can be cured“ of bacteria by incubation at 42ºC. The bacteria-free tumor can be cultured indefinitely in the absence of hormones.
“ FIGURE 21.4 Tumor induction by Agrobacterium tumefaciens. (After Chilton 1983.) CH COOH NH (CH2)3 C CH NH COOH NH2 NH CH3 CH COOH NH (CH2)3 C CH NH COOH NH2 NH COOH (CH2)2 Octopine Nopaline FIGURE 21.5 The two major opines, octopine and nopaline, are found only in crown gall tumors. The genes required for their synthesis are present in the T-DNA from Agrobacterium tumefaciens. The bacterium, but not the plant, can utilize the opines as a nitrogen source.
The possibility that free cytokinins are derived from tRNA has been explored extensively. Although the tRNA-bound cytokinins can act as hormonal signals for plant cells if the tRNA is degraded and fed back to the cells, it is unlikely that any significant amount of the free hormonal cytokinin in plants is derived from the turnover of tRNA.
An enzyme with IPT activity was identified from crude extracts of various plant tissues, but researchers were unable to purify the protein to homogeneity. Recently, plant IPT genes were cloned after the Arabidopsis genome was analyzed for potential ipt-like sequences (Kakimoto 2001; Takei et al. 2001). Nine different IPT genes were identified N O O N N N NH2 HO OH P P P N O O N N N N HO OH P P P N O O N N N N HO OH OH P P P N O O N N N NH2 HO OH P O P P N O O N N N N HO OH P N O O N N N N HO OH OH P N O HO N N N N HO OH OH N N N N N OH N N H H N N N OH + N N N N N O Glc N N H H N N N O Glc iPTP/iPDP ATP/ADP AtIPT4 ZTP/ZDP iPMP AMP DMAPP First enzyme in biosynthetic pathway for cytokinins iPA iP Bacterial IPT (TMR) ZMP ZR trans-Zeatin cis-Zeatin O-glucosyl-trans-zeatin O-glucosyl-cis-zeatin cis-trans isomerase Plant Bacterial Glucosidase transZOG1 Glucosidase cisZOG1 FIGURE 21.6 Biosynthetic pathway for cytokinin biosynthesis. The first com-mitted step in cytokinin biosynthesis is the addition of the isopentenyl side chain from DMAPP to an adenosine moiety. The plant and bacterial IPT enzymes differ in the adenosine substrate used; the plant enzyme appears to utilize both ADP and ATP, and the bacterial enzyme utilizes AMP. The prod-ucts of these reactions (iPMP, iPDP, or iPTP) are converted to zeatin by an unidentified hydroxylase. The various phosphorylated forms can be intercon-verted and free trans-Zeatin can be formed from the riboside by enzymes of general purine metabolism. trans-Zeatin can be metabolized in various ways as shown, and these reactions are catalyzed by the indicated enzymes.
in Arabidopsis—many more than are present in animal genomes, which generally contain only one or two such genes used in tRNA modification. Phylogenetic analysis revealed that one of the Arabidop-sis IPT genes resembles bacterial tRNA-ipt, another resem-bles eukaryotic tRNA-IPT, and the other seven form a dis-tinct group or clade together with other plant sequences (see Web Topic 21.6). The grouping of the seven Arabidop-sis IPT genes in this unique plant clade provided a clue that these genes may encode the cytokinin biosynthetic enzyme. The proteins encoded by these genes were expressed in E. coli and analyzed. It was found that, with the exception of the gene most closely related to the animal tRNA-IPT genes, these genes encoded proteins capable of synthesiz-ing free cytokinins. Unlike their bacterial counterparts, how-ever, the Arabidopsis enzymes that have been analyzed uti-lize ATP and ADP preferentially over AMP (see Figure 21.6).
Cytokinins from the Root Are Transported to the Shoot via the Xylem Root apical meristems are major sites of synthesis of the free cytokinins in whole plants. The cytokinins synthesized in roots appear to move through the xylem into the shoot, along with the water and minerals taken up by the roots.
This pathway of cytokinin movement has been inferred from the analysis of xylem exudate.
When the shoot is cut from a rooted plant near the soil line, the xylem sap may continue to flow from the cut stump for some time. This xylem exudate contains cyto-kinins. If the soil covering the roots is kept moist, the flow of xylem exudate can continue for several days. Because the cytokinin content of the exudate does not diminish, the cytokinins found in it are likely to be synthesized by the roots. In addition, environmental factors that interfere with root function, such as water stress, reduce the cytokinin content of the xylem exudate (Itai and Vaadia 1971). Con-versely, resupply of nitrate to nitrogen-starved maize roots results in an elevation of the concentration of cytokinins in the xylem sap (Samuelson 1992), which has been correlated to an induction of cytokinin-regulated gene expression in the shoots (Takei et al. 2001).
Although the presence of cytokinin in the xylem is well established, recent grafting experiments have cast doubt on the presumed role of this root-derived cytokinin in shoot development. Tobacco transformed with an inducible ipt gene from Agrobacterium displayed increased lateral bud outgrowth and delayed senescence. To assess the role of cytokinin derived from the root, the tobacco root stock engineered to overproduce cytokinin was grafted to a wild-type shoot. Surprisingly, no pheno-typic consequences were observed in the shoot, even though an increased concentration of cytokinin was mea-sured in the transpiration stream (Faiss et al. 1997). Thus the excess cytokinin in the roots had no effect on the grafted shoot.
Roots are not the only parts of the plant capable of syn-thesizing cytokinins. For example, young maize embryos synthesize cytokinins, as do young developing leaves, young fruits, and possibly many other tissues. Clearly, fur-ther studies will be needed to resolve the roles of cytokinins transported from the root versus cytokinins synthesized in the shoot.
A Signal from the Shoot Regulates the Transport of Zeatin Ribosides from the Root The cytokinins in the xylem exudate are mainly in the form of zeatin ribosides. Once they reach the leaves, some of these nucleosides are converted to the free-base form or to glucosides (Noodén and Letham 1993). Cytokinin glu-cosides may accumulate to high levels in seeds and in leaves, and substantial amounts may be present even in senescing leaves. Although the glucosides are active as cytokinins in bioassays, often they lack hormonal activ-ity after they form within cells, possibly because they are compartmentalized in such a way that they are unavail-able. Compartmentation may explain the conflicting obser-vations that cytokinins are transported readily by the xylem but that radioactive cytokinins applied to leaves in intact plants do not appear to move from the site of appli-cation.
Evidence from grafting experiments with mutants sug-gests that the transport of zeatin riboside from the root to the shoot is regulated by signals from the shoot. The rms4 mutant of pea (Pisum sativum L.) is characterized by a 40-fold decrease in the concentration of zeatin riboside in the xylem sap of the roots. However, grafting a wild-type shoot onto an rms4 mutant root increased the zeatin riboside lev-els in the xylem exudate to wild-type levels. Conversely, grafting an rms4 mutant shoot onto a wild-type root low-ered the concentration of zeatin riboside in the xylem exu-date to mutant levels (Beveridge et al. 1997).
These results suggest that a signal from the shoot can regulate cytokinin transport from the root. The identity of this signal has not yet been determined.
Cytokinins Are Rapidly Metabolized by Plant Tissues Free cytokinins are readily converted to their respective nucleoside and nucleotide forms. Such interconversions likely involve enzymes common to purine metabolism.
Many plant tissues contain the enzyme cytokinin oxi-dase, which cleaves the side chain from zeatin (both cis and trans), zeatin riboside, iP, and their N-glucosides, but not their O-glucoside derivatives (Figure 21.7). However, dihydrozeatin and its conjugates are resistant to cleavage.
Cytokinin oxidase irreversibly inactivates cytokinins, and it could be important in regulating or limiting cytokinin effects. The activity of the enzyme is induced by high cytokinin concentrations, due at least in part to an eleva-tion of the RNA levels for a subset of the genes.
Cytokinins: Regulators of Cell Division 501 A gene encoding cytokinin oxidase was first identified in maize (Houba-Herin et al. 1999; Morris et al. 1999). In Arabidopsis, cytokinin oxidase is encoded by a multigene family whose members show distinct patterns of expres-sion. Interestingly, several of the genes contain putative secretory signals, suggesting that at least some of these enzymes may be extracellular.
Cytokinin levels can also be regulated by conjugation of the hormone at various positions. The nitrogens at the 3, 7, and 9 positions of the adenine ring of cytokinins can be conjugated to glucose residues. Alanine can also be conju-gated to the nitrogen at the 9 positon, forming lupinic acid.
These modifications are generally irreversible, and such conjugated forms of cytokinin are inactive in bioassays, with the exception of the N3-glucosides.
The hydroxyl group of the side chain of cytokinins is also the target for conjugation to glucose residues, or in some cases xylose residues, yielding O-glucoside and O-xyloside cytokinins. O-glucosides are resistant to cleavage by cytokinin oxidases, which may explain why these deriv-atives have higher biological activity in some assays than their corresponding free bases have. Enzymes that catalyze the conjugation of either glucose or xylose to zeatin have been purified, and their respective genes have been cloned (Martin et al. 1999). These enzymes have stringent substrate specificities for the sugar donor and the cytokinin bases. Only free trans-zeatin and dihy-drozeatin bases are efficient substrates; the corresponding nucleosides are not substrates, nor is cis-zeatin. The speci-ficity of these enzymes suggests that the conjugation to the side chain is precisely regulated.
The conjugations at the side chain can be removed by glucosidase enzymes to yield free cytokinins, which, as dis-cussed earlier, are the active forms. Thus, cytokinin gluco-sides may be a storage form, or metabolically inactive state, of these compounds. Agene encoding a glucosidase that can release cytokinins from sugar conjugates has been cloned from maize, and its expression could play an important role in the germination of maize seeds (Brzobohaty et al. 1993). Dormant seeds often have high levels of cytokinin glu-cosides but very low levels of hormonally active free cytokinins. Levels of free cytokinins increase rapidly, how-ever, as germination is initiated, and this increase in free cytokinins is accompanied by a corresponding decrease in cytokinin glucosides.
THE BIOLOGICAL ROLES OF CYTOKININS Although discovered as a cell division factor, cytokinins can stimulate or inhibit a variety of physiological, meta-bolic, biochemical, and developmental processes when they are applied to higher plants, and it is increasingly clear that endogenous cytokinins play an important role in the regulation of these events in the intact plant.
In this section we will survey some of the diverse effects of cytokinin on plant growth and development, including a discussion of its role in regulating cell division. The dis-covery of the tumor-inducing Ti plasmid in the plant-path-ogenic bacterium Agrobacterium tumefaciens provided plant scientists with a powerful new tool for introducing foreign genes into plants, and for studying the role of cytokinin in development. In addition to its role in cell proliferation, cytokinin affects many other processes, including differen-tiation, apical dominance, and senescence.
Cytokinins Regulate Cell Division in Shoots and Roots As discussed earlier, cytokinins are generally required for cell division of plant cells in vitro. Several lines of evidence suggest that cytokinins also play key roles in the regulation of cell division in vivo.
Much of the cell division in an adult plant occurs in the meristems (see Chapter 16). Localized expression of the ipt gene of Agrobacterium in somatic sectors of tobacco leaves causes the formation of ectopic (abnormally located) meris-tems, indicating that elevated levels of cytokinin are suf-ficient to initiate cell divisions in these leaves (Estruch et al.
1991). Elevation of endogenous cytokinin levels in trans-genic Arabidopsis results in overexpression of the KNOT-TED homeobox transcription factor homologs KNAT1 and STM—genes that are important in the regulation of meris-tem function (see Chapter 16) (Rupp et al. 1999). Interest-ingly, overexpression of KNAT1 also appears to elevate cytokinin levels in transgenic tobacco, suggesting an inter-dependent relationship between KNAT and the level of cytokinins.
Overexpression of several of the Arabidopsis cytokinin oxidase genes in tobacco results in a reduction of endoge-nous cytokinin levels and a consequent strong retardation of shoot development due to a reduction in the rate of cell proliferation in the shoot apical meristem (Figures 21.8 and 21.9) (Werner et al. 2001). This finding strongly supports the notion that endogenous cytokinins regulate cell divi-sion in vivo.
Surprisingly, the same overexpression of cytokinin oxi-dase in tobacco led to an enhancement of root growth (Fig-ure 21.10), primarily by increasing the size of the root api-502 Chapter 21 N N H N N HN N N H C CH C N N NH2 CH3 H O CH3 iP Adenine 3-Methyl-2-butenal Cytokinin oxidase O2 + FIGURE 21.7 Cytokinin oxidase irreversibly degrades some cytokinins. cal meristem (Figure 21.11). Since the root is a major source of cytokinin, this result may indicate that cytokinins play opposite roles in regulating cell proliferation in root and shoot meristems.
An additional line of evidence linking cytokinin to the regulation of cell division in vivo came from analyses of mutations in the cytokinin receptor (which will be dis-cussed later in the chapter). Mutations in the cytokinin receptor disrupt the development of the root vasculature.
Known as cre1, these mutants have no phloem in their roots; the root vascular system is composed almost entirely of xylem (see Chapters 4 and 10). Further analysis revealed that this defect was due to an insufficient number of vasculature stem cells. That is, at the time of differentiation of the phloem and xylem, the pool of stem cells is abnormally small in cre1 mutants; all the cells become committed to a xylem fate, and no stem cells remain to specify phloem. These results indicate that cytokinin plays a key role in regulating proliferation of the vasculature stem cells of the root.
Cytokinins Regulate Specific Components of the Cell Cycle Cytokinins regulate cell division by affecting the controls that govern the passage of the cell through the cell division cycle. Zeatin levels were found to peak in synchronized culture tobacco cells at the end of S phase, mitosis, and G1 phase. Cytokinins were discovered in relation to their ability to stimulate cell division in tissues supplied with an optimal level of auxin. Evidence suggests that both auxin and cytokinins participate in regulation of the cell cycle and that they do so by controlling the activity of cyclin-dependent kinases. As discussed in Chapter 1, cyclin-dependent protein kinases (CDKs), in concert with their regulatory subunits, the cyclins, are enzymes that regulate the eukaryotic cell cycle.
The expression of the gene that encodes the major CDK, Cdc2 (cell division cycle 2), is regulated by auxin (see Chap-ter 19). In pea root tissues, CDC2 mRNA was induced within 10 minutes after treatment with auxin, and high lev-els of CDK are induced in tobacco pith when it is cultured on medium containing auxin (John et al. 1993). However, the CDK induced by auxin is enzymatically inactive, and Cytokinins: Regulators of Cell Division 503 FIGURE 21.9 Cytokinin is required for normal growth of the shoot apical meristem. (A) Longitudinal section through the shoot apical meristem of a wild-type tobacco plant.
(B) Longitudinal section through the shoot apical meristem of a transgenic tobacco over-expressing the gene that encodes cytokinin oxidase (AtCKX1). Note the reduction in the size of the apical meristem in the cytokinin-deficient plant. (From Werner et al. 2001.) FIGURE 21.8 Tobacco plants overexpressing the gene for cytokinin oxidase. The plant on the left is wild type. The two plants on the right are overexpressing two different constructs of the Arabidopsis gene for cytokinin oxidase: AtCKX1 and AtCKX2. Shoot growth is strongly inhibited in the transgenic plants. (From Werner et al. 2001.) (A) (B) high levels of CDK alone are not sufficient to permit cells to divide. Cytokinin has been linked to the activation of a Cdc25-like phosphatase, whose role is to remove an inhibitory phosphate group from the Cdc2 kinase (Zhang et al. 1996).
This action of cytokinin provides one potential link between cytokinin and auxin in regulating the cell cycle.
Recently, a second major input for cytokinin in regulating the cell cycle has emerged. Cytokinins elevate the expression of the CYCD3 gene, which encodes a D-type cyclin (Soni et al. 1995; Riou-Khamlichi et al. 1999). In animal cells, D-type cyclins are regulated by a wide variety of growth factors and play a key role in regulating the passage through the restric-tion point of the cell cycle in G1. D-type cyclins are thus key players in the regulation of cell proliferation.
In Arabidopsis, CYCD3 is expressed in proliferating tis-sues such as shoot meristems and young leaf primordia. In a crucial experiment, it was found that overexpression of CYCD3 can bypass the cytokinin requirement for cell pro-liferation in culture (Figure 21.12) (Riou-Khamlichi et al.
1999). These and other results suggest that a major mecha-nism for cytokinin’s ability to stimulate cell division is its increase of CYCD3 function.
The Auxin: Cytokinin Ratio Regulates Morphogenesis in Cultured Tissues Shortly after the discovery of kinetin, it was observed that the differentiation of cultured callus tissue derived from tobacco pith segments into either roots or shoots depends on the ratio of auxin to cytokinin in the culture medium.
Whereas high auxin:cytokinin ratios stimulated the forma-tion of roots, low auxin:cytokinin ratios led to the formation of shoots. At intermediate levels the tissue grew as an undif-ferentiated callus (Figure 21.13) (Skoog and Miller 1965).
The effect of auxin: cytokinin ratios on morpho-genesis can also be seen in crown gall tumors by muta-tion of the T-DNA of the Agrobacterium Ti plasmid (Garfinkel et al. 1981). Mutat-ing the ipt gene (the tmr locus) of the Ti plasmid blocks zeatin biosynthesis in the infected cells. The resulting high auxin:cytokinin ratio in the tumor cells causes the proliferation of roots instead of undifferentiated callus tis-sue. In contrast, mutating either of the genes for auxin biosynthesis (tms locus) low-FIGURE 21.11 Cytokinin suppresses the size and cell divi-sion activity of roots. (A) Wild type. (B) AtCKX1. These roots were stained with the fluorescent dye, 4’, 6-diamidino-2-phenylindole, which stains the nucleus. (From Werner et al. 2001.) (A) (B) FIGURE 21.12 CYCD3-expressing callus cells can divide in the absence of cytokinin. Leaf explants from transgenic Arabidopsis plants expressing CYCD3 under a cauliflower mosaic virus 35S promoter were induced to form calluses through cultur-ing in the presence of auxin plus cytokinin or auxin alone.
The wild-type control calluses required cytokinin to grow.
The CYCD3-expressing cal-luses grew well on medium containing auxin alone. The photographs were taken after 29 days. (From Riou-Khamlichi et al. 1999.) FIGURE 21.10 Cytokinin suppresses the growth of roots.
The cytokinin-deficient AtCKX1 roots (right) are larger than those of the wild-type tobacco plant (left). (From Werner et al. 2001.) Auxin + cytokinin Auxin wild type CYCD3 overexpressor wild type CYCD3 overexpressor ers the auxin:cytokinin ratio and stimulates the pro-liferation of shoots (Figure 21.14) (Akiyoshi et al.
1983). These partially differentiated tumors are known as teratomas.
Cytokinins Modify Apical Dominance and Promote Lateral Bud Growth One of the primary determinants of plant form is the degree of apical dominance (see Chapter 19). Plants with strong apical dominance, such as maize, have a single growing axis with few lateral branches. In contrast, many lateral buds initiate growth in shrubby plants.
Although apical dominance may be determined primarily by auxin, physiological studies indicate that cytokinins play a role in initiating the growth of lat-eral buds. For example, direct applications of cyto-kinins to the axillary buds of many species stimulate cell division activity and growth of the buds.
The phenotypes of cytokinin-overproducing mutants are consistent with this result. Wild-type tobacco shows strong apical dominance during veg-etative development, and the lateral buds of cytokinin overproducers grow vigorously, develop-ing into shoots that compete with the main shoot.
Consequently, cytokinin-overproducing plants tend to be bushy.
Cytokinins: Regulators of Cell Division 505 IAA concentration (mg/ml) 0.0 0.005 0.03 0.18 3.0 1.08 0.0 0.2 1.0 Kinetin concentration (mg/ml) FIGURE 21.13 The regulation of growth and organ formation in cultured tobacco callus at different concentrations of auxin and kinetin. At low auxin and high kinetin concentrations (lower left) buds developed. At high auxin and low kinetin concentrations (upper right) roots developed. At intermediate or high concentra-tions of both hormones (middle and lower right) undifferentiated callus developed. (Courtesy of Donald Armstrong.) T-DNA Genes for auxin biosynthesis Gene for cytokinin biosynthesis Genes for tumor growth Gene for octopine synthase Mutation or deletion of these regions gives Ti plasmids that initiate tumors with specific characteristics: tms tmr tml Shooty tumors produced by tms mutations or deletions Rooty tumors produced by tmr mutations or deletions Large, undifferentiated tumors produced by tml mutations or deletions 3 6b 6a 4 1 2 7 5 FIGURE 21.14 Map of the T-DNA from an Agrobacterium Ti plasmid, showing the effects of T-DNA mutations on crown gall tumor morphology. Genes 1 and 2 encode the two enzymes involved in auxin biosynthesis; gene 4 encodes a cytokinin biosynthesis enzyme. Mutations in these genes produce the phenotypes illustrated. (From Morris 1986, courtesy of R. Morris.) Cytokinins Induce Bud Formation in a Moss Thus far we have restricted our discussion of plant hor-mones to the angiosperms. However, many plant hormones are present and developmentally active in representative species throughout the plant kingdom. The moss Funaria hygrometrica is a well-studied example. The germination of moss spores gives rise to a filament of cells called a pro-tonema (plural protonemata). The protonema elongates and undergoes cell divisions at the tip, and it forms branches some distance back from the tip (see Web Essay 21.1).
The transition from filamentous growth to leafy growth begins with the formation of a swelling or protuberance near the apical ends of specific cells (Figure 21.15). An asymmet-ric cell division follows, creating the initial cell. The initial cell then divides mitotically to produce the bud, the struc-ture that gives rise to the leafy gametophyte. During normal growth, buds and branches are regularly initiated, usually beginning at the third cell from the tip of the filament.
Light, especially red light, is required for bud formation in Funaria. In the dark, buds fail to develop, but cytokinin added to the medium can substitute for the light require-ment. Cytokinin not only stimulates normal bud develop-ment; it also increases the total number of buds (Figure 21.16). Even very low levels of cytokinin (picomolar, or 10–12 M) can stimulate the first step in bud formation: the swelling at the apical end of the specific protonemal cell.
Cytokinin Overproduction Has Been Implicated in Genetic Tumors Many species in the genus Nicotiana can be crossed to gen-erate interspecific hybrids. More than 300 such interspecific hybrids have been produced; 90% of these hybrids are nor-mal, exhibiting phenotypic characteristics intermediate between those of both parents. The plant used for cigarette tobacco, Nicotiana tabacum, for example, is an interspecific hybrid. However, about 10% of these interspecific crosses result in progeny that tend to form spontaneous tumors called genetic tumors (Figure 21.17) (Smith 1988).
Genetic tumors are similar mor-phologically to those induced by Agrobacterium tumefaciens, discussed at the beginning of this chapter, but genetic tumors form spontaneously in the absence of any external induc-ing agent. The tumors are composed of masses of rapidly proliferating cells in regions of the plant that ordi-narily would contain few dividing cells. Furthermore, the cells divide without differentiating into the cell types normally associated with the tissues giving rise to the tumor. Nicotiana hybrids that produce genetic tumors have abnormally high levels of both auxin and cytokinins. Typically, the cytokinin 506 Chapter 21 FIGURE 21.15 Bud formation in the moss Funaria begins with the formation of a protuberance at the apical ends of certain cells in the protonema filament. A–D show various stages of bud development. Once formed, the bud goes on to produce the leafy gametophyte stage of the moss. (Courtesy of K. S. Schumaker.) (A) (B) (C) (D) 25 µm FIGURE 21.16 Cytokinin stimulates bud development in Funaria. (A) Control protonemal filaments. (B) Protonemal filaments treated with benzyladenine. (Courtesy of H.
Kende.) (B) (A) levels in tumor-prone hybrids are five to six times higher than those found in either parent.
Cytokinins Delay Leaf Senescence Leaves detached from the plant slowly lose chlorophyll, RNA, lipids, and protein, even if they are kept moist and provided with minerals. This programmed aging process leading to death is termed senescence (see Chapters 16 and 23). Leaf senescence is more rapid in the dark than in the light. Treating isolated leaves of many species with cytokinins will delay their senescence.
Although applied cytokinins do not prevent senescence completely, their effects can be dramatic, particularly when the cytokinin is sprayed directly on the intact plant. If only one leaf is treated, it remains green after other leaves of similar developmental age have yellowed and dropped off the plant. Even a small spot on a leaf will remain green if treated with a cytokinin, after the surrounding tissues on the same leaf begin to senesce.
Unlike young leaves, mature leaves produce little if any cytokinin. Mature leaves may depend on root-derived cytokinins to postpone their senescence. Senescence is ini-tiated in soybean leaves by seed maturation—a phenom-enon known as monocarpic senescence—and can be delayed by seed removal. Although the seedpods control the onset of senescence, they do so by controlling the delivery of root-derived cytokinins to the leaves.
The cytokinins involved in delaying senescence are pri-marily zeatin riboside and dihydrozeatin riboside, which may be transported into the leaves from the roots through the xylem, along with the transpiration stream (Noodén et al. 1990).
To test the role of cytokinin in regulating the onset of leaf senescence, tobacco plants were transformed with a chimeric gene in which a senescence-specific promoter was used to drive the expression of the ipt gene (Gan and Amasino 1995). The transformed plants had wild-type lev-els of cytokinins and developed normally, up to the onset of leaf senescence.
As the leaves aged, however, the senescence-specific promoter was activated, triggering the expression of the ipt gene within leaf cells just as senescence would have been initiated. The resulting elevated cytokinin levels not only blocked senescence, but also limited further expression of the ipt gene, preventing cytokinin overproduction (Figure 21.18). This result suggests that cytokinins are a natural reg-ulator of leaf senescence.
Cytokinins: Regulators of Cell Division 507 FIGURE 21.17 Expression of genetic tumors in the hybrid Nicotiana langsdorffii × N. glauca. (From Smith 1988.) FIGURE 21.18 Leaf senescence is retarded in a transgenic tobacco plant containing a cytokinin biosynthesis gene, ipt.
The ipt gene is expressed in response to signals that induce senescence. (From Gan and Amasino 1995, courtesy of R.
Amasino.) Age-matched control: advanced senescence, no photosynthesis Plant expressing ipt gene remains green and photosynthetic Cytokinins Promote Movement of Nutrients Cytokinins influence the movement of nutrients into leaves from other parts of the plant, a phenomenon known as cytokinin-induced nutrient mobilization. This process is revealed when nutrients (sugars, amino acids, and so on) radiolabeled with 14C or 3H are fed to plants after one leaf or part of a leaf is treated with a cytokinin. Later the whole plant is subjected to autoradiography to reveal the pattern of movement and the sites at which the labeled nutrients accumulate.
Experiments of this nature have demonstrated that nutrients are preferentially transported to, and accumu-lated in, the cytokinin-treated tissues. It has been postu-lated that the hormone causes nutrient mobilization by cre-ating a new source–sink relationship. As discussed in Chapter 10, nutrients translocated in the phloem move from a site of production or storage (the source) to a site of utilization (the sink). The metabolism of the treated area may be stimulated by the hormone so that nutrients move toward it. However, it is not necessary for the nutrient itself to be metabolized in the sink cells because even nonme-tabolizable substrate analogs are mobilized by cytokinins (Figure 21.19).
Cytokinins Promote Chloroplast Development Although seeds can germinate in the dark, the morphology of dark-grown seedlings is very different from that of light-grown seedlings (see Chapter 17): Dark-grown seedlings are said to be etiolated. The hypocotyl and internodes of etiolated seedlings are more elongated, cotyledons and leaves do not expand, and chloroplasts do not mature.
Instead of maturing as chloroplasts, the proplastids of dark-grown seedlings develop into etioplasts, which do not synthesize chlorophyll or most of the enzymes and structural proteins required for the formation of the chloro-plast thylakoid system and photosynthesis machinery.
When seedlings germinate in the light, chloroplasts mature directly from the proplastids present in the embryo, but etioplasts also can mature into chloroplasts when etiolated seedlings are illuminated.
If the etiolated leaves are treated with cytokinin before being illuminated, they form chloroplasts with more exten-sive grana, and chlorophyll and photosynthetic enzymes are synthesized at a greater rate upon illumination (Figure 21.20). These results suggest that cytokinins—along with other factors, such as light, nutrition, and development— regulate the synthesis of photosynthetic pigments and pro-teins. The ability of exogenous cytokinin to enhance de-eti-olation of dark-grown seedlings is mimicked by certain mutations that lead to cytokinin overproduction. (For more on how cytokinins promote light-mediated development, see Web Topic 21.7.) Cytokinins Promote Cell Expansion in Leaves and Cotyledons The promotion of cell enlargement by cytokinins is most clearly demonstrated in the cotyledons of dicots with leafy cotyledons, such as mustard, cucumber, and sunflower.
The cotyledons of these species expand as a result of cell enlargement during seedling growth. Cytokinin treatment promotes additional cell expansion, with no increase in the dry weight of the treated cotyledons.
Leafy cotyledons expand to a much greater extent when the seedlings are grown in the light than in the dark, and cytokinins promote cotyledon growth in both light- and dark-grown seedlings (Figure 21.21). As with auxin-508 Chapter 21 Sprayed with water only Untreated Site of [14C] aminoisobutyric acid application Sprayed with a kinetin solution Untreated Untreated (no radioactivity) Sprayed with a kinetin solution Seedling A Seedling B Seedling C The dark stippling represents the distribution of the radioactive amino acid as revealed by autoradiography.
The results show that the cytokinin-treated cotyledon has become a nutrient sink. However, radioactivity is retained in the cotyledon to which the amino acid was applied when the labeled cotyledon is treated with kinetin (seedling C).
In seedling A, the left cotyledon was sprayed with water as a control. The left cotyledon of seedling B, and the right cotyledon of seedling C, were each sprayed with a solution containing 50mM kinetin.
FIGURE 21.19 The effect of cytokinin on the movement of an amino acid in cucumber seedlings. A radioactively labeled amino acid that cannot be metabolized, such as aminoisobutyric acid, was applied as a discrete spot on the right cotyledon of each of these seedlings. (Drawn from data obtained by K. Mothes.) induced growth, cytokinin-stimulated expansion of radish cotyledons is associated with an increase in the mechanical extensibility of the cell walls. However, cytokinin-induced wall loosening is not accompanied by proton extrusion.
Neither auxin nor gibberellin promotes cell expansion in cotyledons.
Cytokinins Regulate Growth of Stems and Roots Although endogenous cytokinins are clearly required for normal cell proliferation in the apical meristem, and there-fore normal shoot growth (see Figure 21.9), applied cytokinins typically inhibit the process of cell elongation in both stems and roots. For example, exogenous cytokinin inhibits hypocotyl elongation at concentrations that pro-mote leaf and cotyledon expansion in the dark-grown seedlings.
In related experiments, internode and root elongation are both inhibited in transgenic plants expressing the ipt gene and in cytokinin-overproducing mutants. It is likely that the inhibition of hypocotyl and internode elongation induced by excess cytokinin is due to the production of eth-ylene, and this inhibition thus may represent another example of the interdependence of hormonal regulatory pathways (Cary et al. 1995; Vogel et al. 1998).
On the other hand, other experiments suggest that endogenous cytokinins at normal physiological concentra-tions inhibit root growth. For example, a weak allele of a cytokinin receptor mutant and a loss-of-function allele of a cytokinin signaling element both have longer roots than the wild type (Inoue et al. 2001; Sakai et al. 2001). As previously noted, transgenic tobacco engineered to overexpress cytokinin oxidase (and thus to have lower levels of cytokinin) also has longer roots than its wild-type coun-terpart (see Figure 21.10) (Werner et al. 2001). These results indicate that endogenous cytokinins may negatively regu-late root elongation.
Cytokinin-Regulated Processes Are Revealed in Plants That Overproduce Cytokinin The ipt gene from the Agrobacterium Ti plasmid has been introduced into many species of plants, resulting in Cytokinins: Regulators of Cell Division 509 FIGURE 21.20 Cytokinin influence on the develop-ment of wild-type Arabidopsis seedlings grown in darkness. (A) Plastids develop as etioplasts in the untreated, dark grown con-trol. (B) Cytokinin treatment resulted in thylakoid forma-tion in the plastids of dark-grown seedlings. (From Chory et al. 1994, courtesy of J. Chory, © American Society of Plant Biologists, reprinted with permission.) (A) (B) T0 Light T3 control T3 control T3 + zeatin T3 + zeatin L Dark L FIGURE 21.21 The effect of cytokinin on the expansion of radish cotyledons. The experiment described here shows that the effects of light and cytokinin are additive. T0 rep-resents germinating radish seedlings before the experi-ment began. The detached cotyledons were incubated for 3 days (T3) in either darkness or light with or without 2.5 mM zeatin. In both the light and the dark, zeatin-treated cotyledons expanded more than in the control. (From Huff and Ross 1975.) cytokinin overproduction. These transgenic plants exhibit an array of developmental abnormalities that tell us a great deal about the biological role of cytokinins. As discussed earlier, plant tissues transformed by Agrobacterium carrying a wild-type Ti plasmid proliferate as tumors as a result of the overproduction of both auxin and cytokinin. And as mentioned already, if all of the other genes in the T-DNA are deleted and plant tissues are trans-formed with T-DNA containing only a selective antibiotic resistance marker gene and the ipt gene, shoots proliferate instead of callus. The shoot teratomas formed by ipt-transformed tissues are difficult to root, and when roots are formed, they tend to be stunted in their growth. As a result, it is difficult to obtain plants from shoots expressing the ipt gene under the control of its own promoter because the promoter is a con-stitutive promoter and the gene is continuously expressed.
To circumvent this problem, a variety of promoters whose expression can be regulated have been used to drive the expression of the ipt gene in the transformed tissues.
For example, several studies have employed a heat shock promoter, which is induced in response to elevated tem-perature, to drive inducible expression of the ipt gene in transgenic tobacco and Arabidopsis. In these plants, heat induction substantially increased the level of zeatin, zeatin riboside and ribotide, and N-conjugated zeatin. These cytokinin-overproducing plants exhibit several characteristics that point to roles played by cytokinin in plant physiology and development: • The shoot apical meristems of cytokinin-overproduc-ing plants produce more leaves.
• The leaves have higher chlorophyll levels and are much greener.
• Adventitious shoots may form from unwounded leaf veins and petioles.
• Leaf senescence is retarded.
• Apical dominance is greatly reduced.
• The more extreme cytokinin-overproducing plants are stunted, with greatly shortened internodes.
• Rooting of stem cuttings is reduced, as is the root growth rate.
Some of the consequences of cytokinin overproduction could be highly beneficial for agriculture if synthesis of the hormone can be controlled. Because leaf senescence is delayed in the cytokinin-overproducing plants, it should be possible to extend their photosynthetic productivity (which we’ll discuss shortly). In addition, cytokinin production could be linked to damage caused by predators. For example, tobacco plants transformed with an ipt gene under the control of the pro-moter from a wound-inducible protease inhibitor II gene were more resistant to insect damage. The tobacco horn-worm consumed up to 70% fewer tobacco leaves in plants that expressed the ipt gene driven by the protease inhibitor promoter (Smigocki et al. 1993).
CELLULAR AND MOLECULAR MODES OF CYTOKININ ACTION The diversity of the effects of cytokinin on plant growth and development is consistent with the involvement of sig-nal transduction pathways with branches leading to spe-cific responses. Although our knowledge of how cytokinin works at the cellular and molecular levels is still quite frag-mentary, significant progress has been achieved. In this sec-tion we will discuss the nature of the cytokinin receptor and various cytokinin-regulated genes, as well as a model for cytokinin signaling based on current information.
A Cytokinin Receptor Related to Bacterial Two-Component Receptors Has Been Identified The first clue to the nature of the cytokinin receptor came from the discovery of the CKI1 gene. CKI1 was identified in a screen for genes that, when overexpressed, conferred cytokinin-independent growth on Arabidopsis cells in cul-ture. As discussed already, plant cells generally require cytokinin in order to divide in culture. However, a cell line that overexpresses CKI1 is capable of growing in culture in the absence of added cytokinin.
CKI1 encodes a protein similar in sequence to bacterial two-component sensor histidine kinases, which are ubiq-uitous receptors in prokaryotes (see Chapter 14 on the web site and Chapter 17). Bacterial two-component regulatory systems mediate a range of responses to environmental stimuli, such as osmoregulation and chemotaxis. Typically these systems are composed of two functional elements: a sensor histidine kinase, to which a signal binds, and a down-stream response regulator, whose activity is regulated via phosphorylation by the sensor histidine kinase. The sensor histidine kinase is usually a membrane-bound protein that contains two distinct domains, called the input and histi-dine kinase, or “transmitter,” domains (Figure 21.22). Detection of a signal by the input domain alters the activity of the histidine kinase domain. Active sensor kinases are dimers that transphosphorylate a conserved histidine residue. This phosphate is then transferred to a conserved aspartate residue in the receiver domain of a cognate response regulator (see Figure 21.22), and this phosphorylation alters the activity of the kinases. Most response regulators also contain output domains that act as transcription factors.
The phenotype resulting from CKI1 overexpression, combined with its similarity to bacterial receptors, sug-gested that the CKI1 and/or similar histidine kinases are cytokinin receptors. Support for this model came from identification of the CRE1 gene (Inoue et al. 2001). 510 Chapter 21 Like CKI1, CRE1 encodes a protein similar to bacterial histidine kinases. Loss-of-function cre1 mutations were identified in a genetic screen for mutants that failed to develop shoots from undifferentiated tissue culture cells in response to cytokinin. This is essentially the opposite screen from the one just described, from which the CKI1 gene was identified by a gain-of-function (ability to divide in the absence of cytokinin) mutation. The cre1 mutants are also resistant to the inhibition of root elongation observed in response to cytokinin.
Convincing evidence that CRE1 encodes a cytokinin receptor came from analysis of the expression of the pro-tein in yeast. Yeast cells also contain a sensor histidine kinase, and deletion of the gene that encodes this kinase— SLN1—is lethal. Expression of CRE1 in SLN1-deficient yeast can restore viability, but only if cytokinins are present in the medium. Thus the activity of CRE1 (i.e., its ability to replace SLN1) is dependent on cytokinin, which, coupled with the cytokinin-insensitive phenotype of the cre1 mutants in Arabidopsis, unequivocally demonstrates that CRE1 is a cytokinin receptor. It remains to be determined if CKI1 is also a cytokinin receptor.
Two other genes in the Arabidopsis genome (AHK2 and AHK3) are closely related to CRE1, suggesting that, like the ethylene receptors (see Chapter 22), the cytokinin receptors are encoded by a multigene family. Indeed, it has been demonstrated that cytokinins bind to the predicted extra-cellular domains of CRE1, AHK2, and AHK3 with high affinity, confirming that they are indeed cytokinin recep-tors (Yamada et al. 2001). This raises the possibility that these genes are at least partially genetically redundant (as are the ethylene receptors), which may explain the rela-tively mild phenotypes that result from loss-of-function cre1 mutations.
Cytokinins Cause a Rapid Increase in the Expression of Response Regulator Genes One of the primary effects of cytokinin is to alter the expression of various genes. The first set of genes to be up-regulated in response to cytokinin are the ARR (Arabidop-sis response regulator) genes. These genes are homologous to the receiver domain of bacterial two-component response regulators, the downstream target of sensor his-tidine kinases (see the previous section). In Arabidopsis, response regulators are encoded by a multigene family. They fall into two basic classes: the type-A ARR genes, which are made up solely of a receiver domain, and the type-B ARR genes, which contain a tran-scription factor domain in addition to the receiver domain (Figure 21.23). The rate of transcription of the type-A gene is increased within 10 minutes in response to applied cytokinin (Figure 21.24) (D’Agostino et al. 2000). This rapid induction is specific for cytokinin and does not require new protein synthesis. Both of these features are hallmarks of primary response genes (discussed in Chapters 17 and 19).
The rapid induction of the type-A genes, coupled with their similarity to signaling elements predicted to act downstream of sensor histidine kinases, suggests that these elements act downstream of the CRE1 cytokinin receptor family to mediate the primary cytokinin response. Inter-estingly, one of these type-A genes, ARR5, is expressed pri-marily in the apical meristems of both shoots and roots (Figure 21.25), consistent with a role in regulating cell pro-liferation, a key aspect of cytokinin action.
Cytokinins: Regulators of Cell Division 511 P P P P P P H D Input Transmitter Receiver Output Sensor histidine kinase Response regulator Simple two-component signaing system Activation of transcription H H D D Hybrid sensor histidine kinase Hpt (AHP) Response regulator (ARR) Phosphorelay two-component signaling system Activation of transcription FIGURE 21.22 Simple versus phosphorelay types of two-component signaling systems. (A) In simple two-compo-nent systems, the input domain is the site where the signal is sensed. This regulates the activity of the histidine kinase domain, which when activated autophosphorylates on a conserved His residue. The phosphate is then transferred to an Asp residue that resides within the receiver domain of a response regulator. Phosphorylation of this Asp regulates the activity of the output domain of the response regulator, which in many cases is a transcription factor. (B) In the phosphorelay-type two-component signaling system, an extra set of phosphotransfers is mediated by a histidine phosphotransfer protein (Hpt), called AHP in Arabidopsis.
The Arabidopsis response regulators are called ARRs. H = histidine, D = aspartate.
The expression of a wide variety of other genes is altered in response to cytokinin, but generally with slower kinetics than the type-A genes. These include the gene that encodes nitrate reductase, light-regulated genes such as LHCB and SSU, and defense-related genes such as PR1, as well as genes that encode an extensin (cell wall protein rich in hydroxyproline), rRNAs, cytochrome P450s, and perox-idase. Cytokinin elevates the expression of these genes both by increasing the rate of transcription (as in the case of the type-A ARRs) and/or by a stabilization of the RNA tran-script (e.g., the ß -extensin gene).
Histidine Phosphotransferases May Mediate the Cytokinin Signaling Cascade From the preceding discussions we have seen that cytokinin binds to the CRE1 receptors to initiate a response that culminates in the elevation of transcription of the type-A ARRs. The type-A ARR proteins, in turn, may regulate the expression of numerous other genes, as well as the activities of various target proteins that ultimately alter cel-lular function. How is the signal propagated from CRE1 (which is at the plasma membrane) to the nucleus to alter type-A ARR transcription?
One set of genes that are likely to be involved in this signaling cascade encode the AHP (Arabidopsis histidine phosphotransfer) proteins. In two-component systems that involve a sensor kinase fused to a receiver domain (the structure of most eukaryotic sensor histidine kinases, including those of the CRE1 family), there is an additional set of phosphotransfers that are mediated by a his-tidine phosphotransfer protein (Hpt). Phosphate is first transferred from ATP to a histidine within the histidine kinase domain, and then transferred to an aspar-tate residue on the fused receiver. From the aspartate residue the phosphate group is then transferred to a histidine on the Hpt protein and then finally to an aspartate on the receiver domain of the response regula-tor (see Figure 21.22). This phosphorylation of the receiver domain of the response reg-ulator alters its activity. Thus, Hpt proteins are predicted to mediate the phosphotrans-fer between sensor kinases and response regulators.
In Arabidopsis there are 5 Hpt genes, called AHPs. The AHP proteins have been shown to physically associate with receiver 512 Chapter 21 Receiver domain D COOH Receiver domain D COOH Output domain (transcription factor) Type A ARRs Type B ARRs ARR6 ARR5 ARR7 ARR4 ARR15 ARR3 ARR16 ARR17 ARR19 ARR8 ARR14 ARR13 ARR11 ARR1 ARR2 ARR10 ARR12 FIGURE 21.23 Phylogenetic tree of Arabidopsis response regulators. The top part of the figure shows a phylogenetic tree that represents the degree of relatedness of the receiver domains present in the Arabidopsis genome. The closer two proteins are on the tree, the more similar are their amino acid sequences. Note that these proteins fall into two dis-tinct groups, or clades, called the type-A ARRs (blue) and the type-B ARRs (red). These differences in sequence are also reflected in a distinct domain structure, as depicted below the tree. The type-A ARRs consist solely of a receiver domain, but the type-A proteins also contain a fused output domain at the carboxy-terminus.
Time following cytokinin treatment (min) 0 2 5 10 15 25 30 40 60 120 180 ARR4 ARR5 ARR6 ARR7 ARR16 Tubulin Probe FIGURE 21.24 Induction of type-A ARR genes in response to cytokinin.
RNA from Arabidopsis seedlings treated for the indicated time with cytokinin was isolated and analyzed by Northern blotting. Each row shows the result of probing the Northern blot with an individual type-A gene, and each lane contains RNA derived from Arabidopsis seedlings treated for the indicated time with cytokinin. The darker the band, the higher the level of ARR mRNA in that sample. (From D’Agostino et al. 2000.) domains from several Arabidopsis histidine kinases, includ-ing CRE1, and a subset of the AHPs have been demon-strated to transiently translocate from the cytoplasm to the nucleus in response to cytokinin (Figure 21.26) (Hwang and Sheen 2001). This finding suggests that the AHPs are the immediate downstream targets of the acti-vated CRE receptors, and that these proteins transduce the cytokinin signal into the nucleus.
Cytokinin-Induced Phosphorylation Activates Transcription Factors The question now becomes, How do the acti-vated AHPs, once in the nucleus, act to regulate gene transcription? Genetic studies in intact Ara-bidopsis plants and overexpression studies in iso-lated Arabidopsis protoplasts using a cytokinin responsive reporter have provided a likely answer (Hwang and Sheen 2001; Sakai et al. 2001). Disruption of ARR1, one of the type-B ARR genes, reduces the induction of the type-A ARR genes in response Cytokinins: Regulators of Cell Division 513 FIGURE 21.25 Expression of ARR5. The pattern of ARR5 expression was examined by fusion of the promoter to a GUS reporter gene (A) or by whole-mount in situ hybridization (B and C). For the latter, the tissue is hybridized with labeled single-stranded ARR5 RNA in either the sense orientation (B) or the antisense (C). The sense RNA is a negative control and reveals background, nonspecific staining. The antisense probe specifically hybridizes with the ARR5 mRNA present in the tissue, thereby revealing its spatial distribution. With both methods, ARR5 expression is observed primarily in the apical meristems. (From D’Agostino et al. 2000.) (A) (B) (C) –Zeatin +Zeatin, 0.5 h +Zeatin, 1.5 h AHP1-GFP AHP2-GFP AHP5-GFP FIGURE 21.26 Cytokinin induces the transient movement of some AHP proteins into the nucleus. Arabidopsis protoplasts expressing vari-ous AHP genes fused to green fluorescent pro-tein (GFP) as a reporter were treated with zeatin and monitored for 1.5 hours. AHP1-GFP and AHP2-GFP show nuclear localization after 30 minutes, but this localization is transient in the case of AHP1-GFP. Zeatin did not seem to affect the distribution of AHP5-GFP. (From Hwang and Sheen 2001.) to cytokinin. Conversely, an increase in ARR1 function increases the response of the type-A genes to cytokinin. This suggests that ARR1, which is a transcription factor, directly regulates transcription of the type-A ARRs, and that by analogy other members of the type-B ARR family (see Fig-ure 21.23) also mediate cytokinin-regulated gene expression. This conclusion is supported by the findings that type-B ARRs operate as transcriptional activators and that there are multiple binding sites for ARR1, a type-B ARR, in the 5′ DNA regulatory sequences of the type-A ARR genes.
A model of cytokinin signaling is presented in Figure 21.27. Cytokinin binds to the CRE1 receptor and initiates a phosphorylation cascade that results in the phosphoryla-tion and activation of a subset of the type-B ARR proteins.
Activation of the type-B proteins (transcription factors) leads to the transcriptional activation of the type-A genes.
The type-AARR proteins are likely also phosphorylated in response to cytokinin, and perhaps together with the type-B proteins, they interact with various targets to mediate the changes in cellular function, such as an activation of the cell 514 Chapter 21 P P P P P P H H H D D H Output domain Receiver domain Phy B Other effectors?
Cytokinin responses Type-B ARR Type-A ARR AHP AHP Phosphorylation Phosphorylation?
Other effectors?
Cytokinin responses DNA mRNA Type A ARR transcription D COOH Receiver domain CHASE domain Plasma membrane D COOH NH4 NH4 His kinase domain Cytokinin CRE1, AHK2, AHK3 CYTOPLASM NUCLEUS 1. Cytokinin binds to CRE1, which is likely to occur as a dimer. Cytokinin binds to an extracellular portion of CRE1 called the CHASE domain.Two other hybrid sensor kinases (AHK2 and AHK3) containing a CHASE domain are also likely to act as cytokinin receptors in Arabidopsis.
2. Cytokinin binding to these receptors activates their histidine kinase activity. The phosphate is transferred to an asparate residue (D) on the fused receiver domains. 3. The phosphate is then transferred to a conserved histidine present in an AHP protein.
4. Phosphorylation causes the AHP protein to move into the nucleus, where it transfers the phosphate to an asparate residue located within the receiver domain of a type-B ARR.
5. The phosphorylation of the type-B ARR activates the output domain to induce transcription of genes encoding type-A ARRs.
6. The type-A ARRs are likely also to be phosphorylated by the AHP proteins.
7. The phosphorylated type-A ARRs interact with various effectors to mediate the changes in cell function appropriate to cytokinin (indicated in the model as "cytokinin responses").
ATP ADP 2 1 3 4 6 7 5 FIGURE 21.27 Model of cytokinin signaling. The near future should see significant refinement of this model, the tools are now in hand to analyze the interactions among these elements.
cycle. Type-A ARRs are also able to inhibit their own expression by an unknown mechanism, providing a nega-tive feedback loop (see Figure 21.27). Much work needs to be done to confirm and refine this model, but we are beginning to glimpse for the first time the molecular basis for cytokinin action in plants.
SUMMARY Mature plant cells generally do not divide in the intact plant, but they can be stimulated to divide by wounding, by infection with certain bacteria, and by plant hormones, including cytokinins. Cytokinins are N6-substituted aminopurines that will initiate cell proliferation in many plant cells when they are cultured on a medium that also contains an auxin. The principal cytokinin of higher plants—zeatin, or trans-6-(4-hydroxy-3-methylbut-2-eny-lamino)purine—is also present in plants as a riboside or ribotide and as glycosides. These forms are generally also active as cytokinins in bioassays through their enzymatic conversion to the free zeatin base by plant tissue.
The first committed step in cytokinin biosynthesis—the transfer of the isopentenyl group from DMAPP to the 6 nitrogen of adenosine tri- and diphosphate—is catalyzed by isopentenyl transferase (IPT). The product of this reac-tion is readily converted to zeatin and other cytokinins.
Cytokinins are synthesized in roots, in developing embryos, young leaves, fruits, and crown gall tissues.
Cytokinins are also synthesized by plant-associated bacte-ria, insects, and nematodes.
Cytokinin oxidases degrade cytokinin irreversibly and may play a role in regulation of the levels of this hormone.
Conjugation of both the side chain and the adenosine moi-ety to sugars (mostly glucose) also may play a role in the regulation of cytokinin levels and may target subpools of the hormone for distinct roles, such as transport.
Cytokinins are also interconverted among the free base and the nucleoside and nucleotide forms.
Crown galls originate from plant tissues that have been infected with Agrobacterium tumefaciens. The bacterium injects a specific region of its Ti plasmid called T-DNA into wounded plant cells, and the T-DNA is incorporated into the host nuclear genome. The T-DNA contains a gene for cytokinin biosynthesis, as well as genes for auxin biosyn-thesis. These phyto-oncogenes are expressed in the plant cells, leading to hormone synthesis and unregulated pro-liferation of the cells to form the gall.
Cytokinins are most abundant in the young, rapidly dividing cells of the shoot and root apical meristems. They do not appear to be actively transported through living plant tissues. Instead, they are transported passively into the shoot from the root through the xylem, along with water and minerals. At least in pea, however, the shoot can regulate the flow of cytokinin from the root.
Cytokinins participate in the regulation of many plant processes, including cell division, morphogenesis of shoots and roots, chloroplast maturation, cell enlargement, and senescence. Both cytokinin and auxin regulate the plant cell cycle and are needed for cell division. The roles of cytokinins have been elucidated from application of exoge-nous cytokinins, the phenotype of transgenic plants designed to overexpress cytokinins as a result of introduc-tion of the bacterial ipt gene, and recently from transgenic plants that have a reduced endogenous cytokinin content as a result of overexpression of cytokinin oxidase.
In addition to cell division, the ratio of auxin to cytokinin determines the differentiation of cultured plant tissues into either roots or buds: High ratios promote roots; low ratios, buds. Cytokinins also have been implicated in the release of axillary buds from apical dominance. In the moss Funaria, cytokinins greatly increase the number of “buds,” the structures that give rise to the leafy gameto-phyte stage of development.
The mechanism of action of cytokinin is just beginning to emerge. A cytokinin receptor has been identified in Ara-bidopsis. This transmembrane protein is related to the bac-terial two-component sensor histidine kinases. Cytokinins increase the abundance of several specific mRNAs. Some of these are primary response genes that are similar to bac-terial two-component response regulators. The signal trans-duction mechanism from CRE1 to transcriptional activa-tion of the type-A ARRs involves other homologs of two-component elements.
Web Material Web Topics 21.1 Cultured Cells Can Acquire the Ability to Synthesize Cytokinins The phenomenon of habituation is described, whereby callus tissues become cytokinin inde-pendent.
21.2 Structures of Some Naturally Occurring Cytokinins The structures of various naturally occurring cytokinins are presented.
21.3 Various Methods Are Used to Detect and Identify Cytokinins Cytokinins can be qualified using immunologi-cal and sensitive physical methods.
21.4 Cytokinins Are Also Present in Some tRNAs in Animal and Plant Cells Modified adenosines near the 3′ end of the anti-codons of some tRNAs have cytokinin activity.
Cytokinins: Regulators of Cell Division 515 21.5 The Ti Plasmid and Plant Genetic Engineering Applications of the Ti plasmid of Agrobacterium in bioengineering are described.
21.6 Phylogenetic Tree of IPT Genes Arabidopsis contains nine different IPT genes, several of which form a distinct clade with other plant sequences.
21.7 Cytokinin Can Promote Light-Mediated Development Cytokinins can mimic the effect of the det mutation on chloroplast development and de-etiolation.
Web Essay 21.1 Cytokinin-Induced Form and Structure in Moss The effects of cytokinins on the development of moss protonema are described.
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Cytokinins: Regulators of Cell Division 517 Samuelson, M. E., Eliasson, L., and Larsson, C. M. (1992) Nitrate-regulated growth and cytokinin responses in seminal roots of Ethylene: The Gaseous Hormone 22 Chapter DURING THE NINETEENTH CENTURY, when coal gas was used for street illumination, it was observed that trees in the vicinity of street-lamps defoliated more extensively than other trees. Eventually it became apparent that coal gas and air pollutants affect plant growth and devel-opment, and ethylene was identified as the active component of coal gas.
In 1901, Dimitry Neljubov, a graduate student at the Botanical Insti-tute of St. Petersburg in Russia, observed that dark-grown pea seedlings growing in the laboratory exhibited symptoms that were later termed the triple response: reduced stem elongation, increased lateral growth (swelling), and abnormal, horizontal growth. When the plants were allowed to grow in fresh air, they regained their normal morphology and rate of growth. Neljubov identified ethylene, which was present in the laboratory air from coal gas, as the molecule causing the response.
The first indication that ethylene is a natural product of plant tissues was published by H. H. Cousins in 1910. Cousins reported that “ema-nations” from oranges stored in a chamber caused the premature ripen-ing of bananas when these gases were passed through a chamber con-taining the fruit. However, given that oranges synthesize relatively little ethylene compared to other fruits, such as apples, it is likely that the oranges used by Cousins were infected with the fungus Penicillium, which produces copious amounts of ethylene. In 1934, R. Gane and oth-ers identified ethylene chemically as a natural product of plant metabo-lism, and because of its dramatic effects on the plant it was classified as a hormone.
For 25 years ethylene was not recognized as an important plant hor-mone, mainly because many physiologists believed that the effects of ethylene were due to auxin, the first plant hormone to be discovered (see Chapter 19). Auxin was thought to be the main plant hormone, and eth-ylene was considered to play only an insignificant and indirect physi-ological role. Work on ethylene was also hampered by the lack of chem-ical techniques for its quantification. However, after gas chromatography was introduced in ethylene research in 1959, the importance of ethylene was rediscovered and its physiological significance as a plant growth regulator was recognized (Burg and Thi-mann 1959).
In this chapter we will describe the discovery of the eth-ylene biosynthetic pathway and outline some of the impor-tant effects of ethylene on plant growth and development.
At the end of the chapter we will consider how ethylene acts at the cellular and molecular levels.
STRUCTURE, BIOSYNTHESIS, AND MEASUREMENT OF ETHYLENE Ethylene can be produced by almost all parts of higher plants, although the rate of production depends on the type of tissue and the stage of development. In general, meristematic regions and nodal regions are the most active in ethylene biosynthesis. However, ethylene production also increases during leaf abscission and flower senescence, as well as during fruit ripening. Any type of wounding can induce ethylene biosynthesis, as can physiological stresses such as flooding, chilling, disease, and temperature or drought stress.
The amino acid methionine is the precursor of ethylene, and ACC (1-aminocyclopropane-1-carboxylic acid) serves as an intermediate in the conversion of methionine to eth-ylene. As we will see, the complete pathway is a cycle, tak-ing its place among the many metabolic cycles that operate in plant cells.
The Properties of Ethylene Are Deceptively Simple Ethylene is the simplest known olefin (its molecular weight is 28), and it is lighter than air under physiological conditions: It is flammable and readily undergoes oxidation. Ethylene can be oxidized to ethylene oxide: and ethylene oxide can be hydrolyzed to ethylene glycol: In most plant tissues, ethylene can be completely oxidized to CO2, in the following reaction: Ethylene is released easily from the tissue and diffuses in the gas phase through the intercellular spaces and out-side the tissue. At an ethylene concentration of 1 µL L–1 in the gas phase at 25°C, the concentration of ethylene in water is 4.4 × 10–9 M. Because they are easier to measure, gas phase concentrations are normally given for ethylene.
Because ethylene gas is easily lost from the tissue and may affect other tissues or organs, ethylene-trapping sys-tems are used during the storage of fruits, vegetables, and flowers. Potassium permanganate (KMnO4) is an effective absorbent of ethylene and can reduce the concentration of ethylene in apple storage areas from 250 to 10 µL L–1, markedly extending the storage life of the fruit.
Bacteria, Fungi, and Plant Organs Produce Ethylene Even away from cities and industrial air pollutants, the environment is seldom free of ethylene because of its pro-duction by plants and microorganisms. The production of ethylene in plants is highest in senescing tissues and ripening fruits (>1.0 nL g-fresh-weight–1 h–1), but all organs of higher plants can synthesize ethylene. Ethylene is biologically active at very low concentrations—less than 1 part per million (1 µL L–1). The internal ethylene con-centration in a ripe apple has been reported to be as high as 2500 µL L–1.
Young developing leaves produce more ethylene than do fully expanded leaves. In bean (Phaseolus vulgaris), young leaves produce 0.4 nL g–1 h–1, compared with 0.04 nL g–1 h–1 for older leaves. With few exceptions, nonse-nescent tissues that are wounded or mechanically per-turbed will temporarily increase their ethylene production severalfold within 30 minutes. Ethylene levels later return to normal.
Gymnosperms and lower plants, including ferns, mosses, liverworts, and certain cyanobacteria, all have shown the ability to produce ethylene. Ethylene produc-tion by fungi and bacteria contributes significantly to the ethylene content of soil. Certain strains of the common enteric bacterium Escherichia coli and of yeast (a fungus) produce large amounts of ethylene from methionine. There is no evidence that healthy mammalian tissues produce ethylene, nor does ethylene appear to be a meta-bolic product of invertebrates. However, recently it was found that both a marine sponge and cultured mammalian 520 Chapter 22 C H H C H H Ethylene C H H C H H O Ethylene oxide C H H C H H HO OH Ethylene glycol C H H C H H C H H C H H O [O] O2 HOOC COOH CO2 Oxalic acid Carbon dioxide Ethylene Ethylene oxide Complete oxidation of ethylene cells can respond to ethylene, raising the possibility that this gaseous molecule acts as a signaling molecule in ani-mal cells (Perovic et al. 2001).
Regulated Biosynthesis Determines the Physiological Activity of Ethylene In vivo experiments showed that plant tissues convert l-[14C]methionine to [14C]ethylene, and that the ethylene is derived from carbons 3 and 4 of methionine (Figure 22.1).
The CH3—S group of methionine is recycled via the Yang cycle. Without this recycling, the amount of reduced sulfur present would limit the available methionine and the syn-thesis of ethylene. S-adenosylmethionine (AdoMet), which is synthesized from methionine and ATP, is an intermedi-ate in the ethylene biosynthetic pathway, and the immedi-ate precursor of ethylene is 1-aminocyclopropane-1-car-boxylic acid (ACC) (see Figure 22.1).
The role of ACC became evident in experiments in which plants were treated with [14C]methionine. Under anaerobic conditions, ethylene was not produced from the [14C]methionine, and labeled ACC accumulated in the tis-sue. On exposure to oxygen, however, ethylene production surged. The labeled ACC was rapidly converted to ethylene in the presence of oxygen by various plant tissues, suggest-ing that ACC is the immediate precursor of ethylene in higher plants and that oxygen is required for the conversion.
In general, when ACC is supplied exogenously to plant tissues, ethylene production increases substantially. This Ethylene: The Gaseous Hormone 521 CH3 CH2 S CH2 CO COO– R C H NH3 + COO– R CO COO– CH3 CH2 S CH2 CH COO– NH3 + O OPO3H– O H O H CH3 CH2 S O OH O H O H CH3 CH2 S O O H O H CH3 CH2 S Adenine O O H O H CH3 CH2 CH2 S + Adenine CH2 COO– HC NH3 + H2C H2C C NH3 + COO– H2C CH2 H2C H2C C NH3 + COO– CO CH2 COO– YANG CYCLE ATP ATP ADP Methionine (Met) HCOO– O2 2-HPO4 – Adenine AdoMet synthetase S-Adenosyl-methionine (AdoMet) ACC synthase ACC oxidase Inhibits ethylene synthesis: AOA AVG Inhibits ethylene synthesis: Co2+ Anaerobiosis Temp. >35°C Promotes ethylene synthesis: Fruit ripening Flower senescence IAA Wounding Chilling injury Drought stress Flooding 1-Aminocyclopropane-1-carboxylic acid (ACC) Ethylene Promotes ethylene synthesis: Ripening Malonyl-CoA N-Malonyl ACC 1/2 O2 CO2 + HCN α-Keto-γ-methylthiobutyric acid 5′-Methylthioribose 5′-Methylthioadenosine 5′-Methylthio-ribose-1-P PPi Pi + FIGURE 22.1 Ethylene biosynthetic pathway and the Yang cycle. The amino acid methionine is the precursor of ethylene. The rate-limiting step in the pathway is the conversion of AdoMet to ACC, which is catalyzed by the enzyme ACC synthase. The last step in the pathway, the conversion of ACC to ethylene, requires oxygen and is catalyzed by the enzyme ACC oxidase. The CH3—S group of methionine is recycled via the Yang cycle and thus con-served for continued synthesis. Besides being converted to ethylene, ACC can be conjugated to N-malonyl ACC. AOA = aminooxyacetic acid; AVG = aminoethoxy-vinylglycine. (After McKeon et al. 1995.) observation indicates that the synthesis of ACC is usually the biosynthetic step that limits ethylene production in plant tissues.
ACC synthase, the enzyme that catalyzes the conver-sion of AdoMet to ACC (see Figure 22.1), has been charac-terized in many types of tissues of various plants. ACC synthase is an unstable, cytosolic enzyme. Its level is regu-lated by environmental and internal factors, such as wounding, drought stress, flooding, and auxin. Because ACC synthase is present in such low amounts in plant tis-sues (0.0001% of the total protein of ripe tomato) and is very unstable, it is difficult to purify the enzyme for bio-chemical analysis (see Web Topic 22.1).
ACC synthase is encoded by members of a divergent multigene family that are differentially regulated by vari-ous inducers of ethylene biosynthesis. In tomato, for exam-ple, there are at least nine ACC synthase genes, different subsets of which are induced by auxin, wounding, and/or fruit ripening.
ACC oxidase catalyzes the last step in ethylene biosyn-thesis: the conversion of ACC to ethylene (see Figure 22.1).
In tissues that show high rates of ethylene production, such as ripening fruit, ACC oxidase activity can be the rate-lim-iting step in ethylene biosynthesis. The gene that encodes ACC oxidase has been cloned (see Web Topic 22.2). Like ACC synthase, ACC oxidase is encoded by a multigene family that is differentially regulated. For example, in ripen-ing tomato fruits and senescing petunia flowers, the mRNA levels of a subset of ACC oxidase genes are highly elevated.
The deduced amino acid sequences of ACC oxidases revealed that these enzymes belong to the Fe2+/ascorbate oxidase superfamily. This similarity suggested that ACC oxidase might require Fe2+ and ascorbate for activity—a requirement that has been confirmed by biochemical analysis of the protein. The low abundance of ACC oxi-dase and its requirement for cofactors presumably explain why the purification of this enzyme eluded researchers for so many years.
Catabolism.
Researchers have studied the catabolism of ethylene by supplying 14C2H4 to plant tissues and tracing the radioactive compounds produced. Carbon dioxide, eth-ylene oxide, ethylene glycol, and the glucose conjugate of ethylene glycol have been identified as metabolic break-down products. However, because certain cyclic olefin compounds, such as 1,4-cyclohexadiene, have been shown to block ethylene breakdown without inhibiting ethylene action, ethylene catabolism does not appear to play a sig-nificant role in regulating the level of the hormone (Raskin and Beyer 1989).
Conjugation.
Not all the ACC found in the tissue is con-verted to ethylene. ACC can also be converted to a conju-gated form, N-malonyl ACC (see Figure 22.1), which does not appear to break down and accumulates in the tissue. A second conjugated form of ACC, 1-(γ-L-glutamylamino) cyclopropane-1-carboxylic acid (GACC), has also been iden-tified. The conjugation of ACC may play an important role in the control of ethylene biosynthesis, in a manner analo-gous to the conjugation of auxin and cytokinin.
Environmental Stresses and Auxins Promote Ethylene Biosynthesis Ethylene biosynthesis is stimulated by several factors, including developmental state, environmental conditions, other plant hormones, and physical and chemical injury.
Ethylene biosynthesis also varies in a circadian manner, peaking during the day and reaching a minimum at night.
Fruit ripening.
As fruits mature, the rate of ACC and eth-ylene biosynthesis increases. Enzyme activities for both ACC oxidase (Figure 22.2) and ACC synthase increase, as do the mRNA levels for subsets of the genes encoding each enzyme. However, application of ACC to unripe fruits only slightly enhances ethylene production, indicating that an increase in the activity of ACC oxidase is the rate-limiting step in ripening (McKeon et al. 1995).
522 Chapter 22 ACC (nmol g–1) 0 0 10 100 Ethylene (nL g–1) or ACC oxidase (nL g–1 h–1) 2 4 6 8 14 Days after harvest 5 Ethylene 10 12 1 0.1 4 3 2 1 ACC oxidase ACC FIGURE 22.2 Changes in ethylene and ACC content and ACC oxidase activity during fruit ripening. Changes in the ACC oxidase activity and ethylene and ACC concentrations of Golden Delicious apples. The data are plotted as a func-tion of days after harvest. Increases in ethylene and ACC concentrations and in ACC oxidase activity are closely cor-related with ripening. (From Yang 1987.) Stress-induced ethylene production.
Ethylene biosyn-thesis is increased by stress conditions such as drought, flooding, chilling, exposure to ozone, or mechanical wounding. In all these cases ethylene is produced by the usual biosynthetic pathway, and the increased ethylene production has been shown to result at least in part from an increase in transcription of ACC synthase mRNA. This “stress ethylene” is involved in the onset of stress responses such as abscission, senescence, wound healing, and increased disease resistance (see Chapter 25).
Auxin-induced ethylene production.
In some instances, auxins and ethylene can cause similar plant responses, such as induction of flowering in pineapple and inhibition of stem elongation. These responses might be due to the ability of auxins to promote ethylene synthesis by enhanc-ing ACC synthase activity. These observations suggest that some responses previously attributed to auxin (indole-3-acetic acid, or IAA) are in fact mediated by the ethylene produced in response to auxin.
Inhibitors of protein synthesis block both ACC and IAA-induced ethylene synthesis, indicating that the syn-thesis of new ACC synthase protein caused by auxins brings about the marked increase in ethylene production.
Several ACC synthase genes have been identified whose transcription is elevated following application of exoge-nous IAA, suggesting that increased transcription is at least partly responsible for the increased ethylene pro-duction observed in response to auxin (Nakagawa et al.
1991; Liang et al. 1992).
Posttranscriptional regulation of ethylene produc-tion.
Ethylene production can also be regulated post-transcriptionally. Cytokinins also promote ethylene biosyn-thesis in some plant tissues. For example, in etiolated Arabidopsis seedlings, application of exogenous cytokinins causes a rise in ethylene production, resulting in the triple-response phenotype (see Figure 22.5A). Molecular genetic studies in Arabidopsis have shown that cytokinins elevate ethylene biosynthesis by increasing the stability and/or activity of one isoform of ACC syn-thase (Vogel et al. 1998). The carboxy-terminal domain of this ACC synthase isoform appears to be the target for this posttranscriptional regulation. Consistent with this, the car-boxy-terminal domain of an ACC synthase isoform from tomato has been shown to be the target for a calcium-dependent phosphorylation (Tatsuki and Mori 2001).
Ethylene Production and Action Can Be Inhibited Inhibitors of hormone synthesis or action are valuable for the study of the biosynthetic pathways and physiological roles of hormones. Inhibitors are particularly helpful when it is difficult to distinguish between different hormones that have identical effects in plant tissue or when a hormone affects the synthesis or the action of another hormone. For example, ethylene mimics high concentrations of auxins by inhibiting stem growth and causing epinasty (a downward curvature of leaves). Use of specific inhibitors of ethylene biosynthesis and action made it possible to dis-criminate between the actions of auxin and ethylene. Stud-ies using inhibitors showed that ethylene is the primary effector of epinasty and that auxin acts indirectly by caus-ing a substantial increase in ethylene production.
Inhibitors of ethylene synthesis.
Aminoethoxy-vinyl-glycine (AVG) and aminooxyacetic acid (AOA) block the conversion of AdoMet to ACC (see Figure 22.1). AVG and AOA are known to inhibit enzymes that use the cofactor pyridoxal phosphate. The cobalt ion (Co2+) is also an inhibitor of the ethylene biosynthetic pathway, blocking the conversion of ACC to ethylene by ACC oxidase, the last step in ethylene biosynthesis.
Inhibitors of ethylene action.
Most of the effects of eth-ylene can be antagonized by specific ethylene inhibitors.
Silver ions (Ag+) applied as silver nitrate (AgNO3) or as sil-ver thiosulfate (Ag(S2O3)2 3–) are potent inhibitors of ethyl-ene action. Silver is very specific; the inhibition it causes cannot be induced by any other metal ion.
Carbon dioxide at high concentrations (in the range of 5 to 10%) also inhibits many effects of ethylene, such as the induction of fruit ripening, although CO2 is less efficient than Ag+. This effect of CO2 has often been exploited in the storage of fruits, whose ripening is delayed at elevated CO2 concentrations. The high concentrations of CO2 required for inhibition make it unlikely that CO2 acts as an ethylene antagonist under natural conditions.
The volatile compound trans-cyclooctene, but not its isomer cis-cyclooctene, is a strong competitive inhibitor of ethylene binding (Sisler et al. 1990); trans-cyclooctene is thought to act by competing with ethylene for binding to the receptor. A novel inhibitor, 1-methylcyclopropene (MCP), was recently found that binds almost irreversibly to the ethylene receptor (Figure 22.3) (Sisler and Serek 1997). MCP shows tremendous promise in commercial applications.
Ethylene: The Gaseous Hormone 523 H3C 1-Methylcyclopropene (MCP) trans-Cyclooctene cis-Cyclooctene FIGURE 22.3 Inhibitors that block ethylene binding to its receptor. Only the trans form of cyclooctene is active. Ethylene Can Be Measured by Gas Chromatography Historically, bioassays based on the seedling triple response were used to measure ethylene levels, but they have been replaced by gas chromatography. As little as 5 parts per billion (ppb) (5 pL per liter)1 of ethylene can be detected, and the analysis time is only 1 to 5 minutes. Usually the ethylene produced by a plant tissue is allowed to accumulate in a sealed vial, and a sample is withdrawn with a syringe. The sample is injected into a gas chromatograph column in which the different gases are separated and detected by a flame ionization detector.
Quantification of ethylene by this method is very accurate.
Recently a novel method to measure ethylene was devel-oped that uses a laser-driven photoacoustic detector that can detect as little as 50 parts per trillion (50 ppt = 0.05 pL L–1) ethylene (Voesenek et al. 1997).
DEVELOPMENTAL AND PHYSIOLOGICAL EFFECTS OF ETHYLENE As we have seen, ethylene was discovered in connection with its effects on seedling growth and fruit ripening. It has since been shown to regulate a wide range of responses in plants, including seed germination, cell expansion, cell dif-ferentiation, flowering, senescence, and abscission. In this section we will consider the phenotypic effects of ethylene in more detail.
Ethylene Promotes the Ripening of Some Fruits In everyday usage, the term fruit ripening refers to the changes in fruit that make it ready to eat. Such changes typ-ically include softening due to the enzymatic breakdown of the cell walls, starch hydrolysis, sugar accumulation, and the disappearance of organic acids and phenolic com-pounds, including tannins. From the perspective of the plant, fruit ripening means that the seeds are ready for dis-persal.
For seeds whose dispersal depends on animal ingestion, ripeness and edibility are synonymous. Brightly colored anthocyanins and carotenoids often accumulate in the epi-dermis of such fruits, enhancing their visibility. However, for seeds that rely on mechanical or other means for dis-persal, fruit ripening may mean drying followed by splitting.
Because of their importance in agriculture, the vast major-ity of studies on fruit ripening have focused on edible fruits.
Ethylene has long been recognized as the hormone that accelerates the ripening of edible fruits. Exposure of such fruits to ethylene hastens the processes associated with ripening, and a dramatic increase in ethylene production accompanies the initiation of ripening. However, surveys of a wide range of fruits have shown that not all of them respond to ethylene.
All fruits that ripen in response to ethylene exhibit a characteristic respiratory rise before the ripening phase called a climacteric.2 Such fruits also show a spike of eth-ylene production immediately before the respiratory rise (Figure 22.4). Inasmuch as treatment with ethylene induces the fruit to produce additional ethylene, its action can be described as autocatalytic. Apples, bananas, avocados, and tomatoes are examples of climacteric fruits.
In contrast, fruits such as citrus fruits and grapes do not exhibit the respiration and ethylene production rise and are called nonclimacteric fruits. Other examples of climacteric and nonclimacteric fruits are given in Table 22.1.
When unripe climacteric fruits are treated with ethylene, the onset of the climacteric rise is hastened. When noncli-macteric fruits are treated in the same way, the magnitude of the respiratory rise increases as a function of the ethylene concentration, but the treatment does not trigger produc-tion of endogenous ethylene and does not accelerate ripen-ing. Elucidation of the role of ethylene in the ripening of cli-macteric fruits has resulted in many practical applications aimed at either uniform ripening or the delay of ripening.
Although the effects of exogenous ethylene on fruit ripen-ing are straightforward and clear, establishing a causal rela-tion between the level of endogenous ethylene and fruit ripening is more difficult. Inhibitors of ethylene biosynthe-524 Chapter 22 Ethylene CO2 0 50 100 CO2 production (µL g–1 h–1) 2 3 4 5 9 Days after harvest 25 Ethylene content (µL L–1) 6 7 8 20 15 10 5 30 FIGURE 22.4 Ethylene production and respiration. In banana, ripening is characterized by a climacteric rise in respiration rate, as evidenced by the increased CO2 produc-tion. A climacteric rise in ethylene production precedes the increase in CO2 production, suggesting that ethylene is the hormone that triggers the ripening process. (From Burg and Burg 1965.) 1 pL = picoliter = 10–12 L.
2 The term climacteric can be used either as a noun, as in “most fruits exhibit a climacteric during ripening” or as an adjective, as in “a climacteric rise in respiration.” The term nonclimacteric, however, is used only as an adjective.
sis (such as AVG) or of ethylene action (such as CO2, MCP, or Ag+) have been shown to delay or even prevent ripening.
However, the definitive demonstration that ethylene is required for fruit ripening was provided by experiments in which ethylene biosynthesis was blocked by expression of an antisense version of either ACC synthase or ACC oxidase in transgenic tomatoes (see Web Topic 22.3). Elimination of ethylene biosynthesis in these transgenic tomatoes com-pletely blocked fruit ripening, and ripening was restored by application of exogenous ethylene (Oeller et al. 1991).
Further demonstration of the requirement for ethylene in fruit ripening came from the analysis of the never-ripe mutation in tomato. As the name implies, this mutation completely blocks the ripening of tomato fruit. Molecular analysis revealed that never-ripe was due to a mutation in an ethylene receptor that rendered it unable to bind eth-ylene (Lanahan et al. 1994). These experiments provided unequivocal proof of the role of ethylene in fruit ripening, and they opened the door to the manipulation of fruit ripening through biotechnology.
In tomatoes several genes have been identified that are highly regulated during ripening (Gray et al. 1994). During tomato fruit ripening, the fruit softens as the result of cell wall hydrolysis and changes from green to red as a conse-quence of chlorophyll loss and the synthesis of the carotenoid pigment lycopene. At the same time, aroma and flavor components are produced.
Analysis of mRNA from tomato fruits from wild-type and transgenic tomato plants genetically engineered to lack ethylene has revealed that gene expression during ripen-ing is regulated by at least two independent pathways: 1.
An ethylene-dependent pathway includes genes involved in lycopene and aroma biosynthesis, respi-ratory metabolism, and ACC synthase.
2.
A developmental, ethylene-independent pathway includes genes encoding ACC oxidase and chlorophyllase.
Thus, not all of the processes associated with ripening in tomato are ethylene dependent.
Leaf Epinasty Results When ACC from the Root Is Transported to the Shoot The downward curvature of leaves that occurs when the upper (adaxial) side of the petiole grows faster than the lower (abaxial) side is termed epinasty (Figure 22.5B). Eth-ylene and high concentrations of auxin induce epinasty, and it has now been established that auxin acts indirectly by inducing ethylene production. As will be discussed later in the chapter, a variety of stress conditions, such as salt stress or pathogen infection, increase ethylene production and also induce epinasty. There is no known physiological function for the response.
In tomato and other dicots, flooding (waterlogging) or anaerobic conditions around the roots enhances the syn-thesis of ethylene in the shoot, leading to the epinastic response. Because these environmental stresses are sensed by the roots and the response is displayed by the shoots, a signal from the roots must be transported to the shoots.
This signal is ACC, the immediate precursor of ethylene.
ACC levels were found to be significantly higher in the xylem sap after flooding of tomato roots for 1 to 2 days (Figure 22.6) (Bradford and Yang 1980).
Because water fills the air spaces in waterlogged soil and O2 diffuses slowly through water, the concentration of oxygen around flooded roots decreases dramatically. The elevated production of ethylene appears to be caused by the accumulation of ACC in the roots under anaerobic con-ditions, since the conversion of ACC to ethylene requires oxygen (see Figure 22.1). The ACC accumulated in the anaerobic roots is then transported to shoots via the tran-spiration stream, where it is readily converted to ethylene.
Ethylene Induces Lateral Cell Expansion At concentrations above 0.1 µL L–1, ethylene changes the growth pattern of seedlings by reducing the rate of elon-gation and increasing lateral expansion, leading to swelling of the region below the hook. These effects of ethylene are common to growing shoots of most dicots, forming part of the triple response. In Arabidopsis, the triple response con-sists of inhibition and swelling of the hypocotyl, inhibition of root elongation, and exaggeration of the apical hook (Figure 22.7).
As discussed in Chapter 15, the directionality of plant cell expansion is determined by the orientation of the cel-lulose microfibrils in the cell wall. Transverse microfibrils reinforce the cell wall in the lateral direction, so that turgor pressure is channeled into cell elongation. The orientation of the microfibrils in turn is determined by the orientation of the cortical array of microtubules in the cortical (periph-eral) cytoplasm. In typical elongating plant cells, the corti-cal microtubules are arranged transversely, giving rise to transversely arranged cellulose microfibrils.
Ethylene: The Gaseous Hormone 525 TABLE 22.1 Climacteric and nonclimacteric fruits Climacteric Nonclimacteric Apple Bell pepper Avocado Cherry Banana Citrus Cantaloupe Grape Cherimoya Pineapple Fig Snap bean Mango Strawberry Olive Watermelon Peach Pear Persimmon Plum Tomato During the seedling triple response to ethylene, the transverse pattern of microtubule alignment is disrupted, and the microtubules switch over to a longitudinal orien-tation. This 90° shift in microtubule orientation leads to a parallel shift in cellulose microfibril deposition. The newly deposited wall is reinforced in the longitudinal direction rather than the transverse direction, which promotes lat-eral expansion instead of elongation.
How do microtubules shift from one orientation to another? To study this phenomenon, pea (Pisum sativum) epidermal cells were injected with the microtubule protein tubulin, to which a fluorescent dye was covalently attached. The fluorescent “tag” did not interfere with the assembly of microtubules. This procedure allowed researchers to monitor the assembly of microtubules in liv-ing cells using a confocal laser scanning microscope, which can focus in many planes throughout the cell.
It was found that microtubules do not reorient from the transverse to the longitudinal direction by complete depolymerization of the transverse microtubules followed by repolymerization of a new longitudinal array of micro-tubules. Instead, increasing numbers of nontransversely 526 Chapter 22 (A) (B) (C) (D) FIGURE 22.5 Some physiological effects of ethylene on plant tissue in various developmental stages. (A) Triple response of etiolated pea seedlings. Six-day-old pea seedlings were treated with 10 ppm (parts per million) ethylene (right) or left untreated (left). The treated seedlings show a radial swelling, inhibition of elongation of the epicotyl, and hori-zontal growth of the epicotyl (diagravitropism). (B) Epinasty, or downward bending of the tomato leaves (right), is caused by ethylene treatment. Epinasty results when the cells on the upper side of the petiole grow faster than those on the bottom. (C) Inhibition of flower senescence by inhibi-tion of ethylene action. Carnation flowers were held in deionized water for 14 days with (left) or without (right) silver thiosulfate (STS), a potent inhibitor of ethylene action.
Blocking of ethylene results in a marked inhibition of floral senescence. (D) Promotion of root hair formation by ethyl-ene in lettuce seedlings. Two-day-old seedlings were treated with air (left) or 10 ppm ethylene (right) for 24 hours before the photo was taken. Note the profusion of root hairs on the ethylene-treated seedling. (A and B courtesy of S. Gepstein; C from Reid 1995, courtesy of M. Reid; D from Abeles et al.
1992, courtesy of F. Abeles.) Air Ethylene aligned microtubules appear in particular locations (Fig-ure 22.8). Neighboring microtubules then adopt the new alignment, so at one stage different alignments coexist before they adopt a uniformly longitudinal orientation (Yuan et al., 1994). Although the reorientations observed in this study were spontaneous rather than induced by ethylene, it is presumed that ethylene-induced micro-tubule reorientation operates by a similar mechanism.
The Hooks of Dark-Grown Seedlings Are Maintained by Ethylene Production Etiolated dicot seedlings are usually characterized by a pronounced hook located just behind the shoot apex (see Figure 22.7). This hook shape facilitates penetration of the seedling through the soil, protecting the tender apical meristem.
Like epinasty, hook formation and maintenance result from ethylene-induced asymmetric growth. The closed shape of the hook is a consequence of the more rapid elongation of the outer side of the stem compared with the inner side. When the hook is exposed to white light, it opens because the elongation rate of the inner side Ethylene: The Gaseous Hormone 527 FIGURE 22.7 The triple response in Arabidopsis. Three-day-old etiolated seedlings grown in the presence (right) or absence (left) of 10 ppm ethylene. Note the shortened hypocotyl, reduced root elongation and exaggeration of the curvature of the apical hook that results from the presence of ethylene.
0 1.2 Ethylene (nL g–1 h–1) 24 48 72 Hours flooded 3.0 ACC (nmol h–1) ACC (flooded) Ethylene (flooded) Ethylene (control) 1.0 0.8 0.6 0.4 0.2 2.5 2.0 1.5 1.0 0.5 ACC (control) FIGURE 22.6 Changes in the amounts of ACC in the xylem sap and ethylene production in the petiole following flood-ing of tomato plants. ACC is synthesized in roots, but it is converted to ethylene very slowly under anaerobic condi-tions of flooding. ACC is transported via the xylem to the shoot, where it is converted to ethylene. The gaseous ethyl-ene cannot be transported, so it usually affects the tissue near the site of its production. The ethylene precursor ACC is transportable and can produce ethylene far from the site of ACC synthesis. (From Bradford and Yang 1980.) FIGURE 22.8 Reorientation of microtubules from transverse to vertical in pea stem epidermis cells in response to wounding. A living epidermal cell was microinjected with rhodamine-conju-gated tubulin, which incorporates into the plant microtubules.
A time series of approximately 6-minute intervals shows the cortical microtubules undergoing reorientation from net trans-verse to oblique/longitudinal. The reorientation seems to involve the appearance of patches of new “discordant” micro-tubules in the new direction, concomitant with the disappear-ance of microtubules from the previous alignment. (From Yuan et al. 1994, photo courtesy of C. Lloyd.) Transverse microtubules increases, equalizing the growth rates on both sides. The kinematic aspects of hook growth (i.e., maintenance of the hook shape over time) were discussed in Chapter 16.
Red light induces hook opening, and far-red light reverses the effect of red, indicating that phytochrome is the photoreceptor involved in this process (see Chapter 17).
A close interaction between phytochrome and ethylene controls hook opening. As long as ethylene is produced by the hook tissue in the dark, elongation of the cells on the inner side is inhibited. Red light inhibits ethylene forma-tion, promoting growth on the inner side, thereby causing the hook to open.
The auxin-insensitive mutation axr1 and treatment of wild-type seedlings with NPA (1-N-naphthylphthalamic acid), an inhibitor of polar auxin transport, both block the formation of the apical hook in Arabidopsis. These and other results indicate a role for auxin in maintaining hook struc-ture. The more rapid growth rate of the outer tissues rela-tive to the inner tissues could reflect an ethylene-dependent auxin gradient, analogous to the lateral auxin gradient that develops during phototropic curvature (see Chapter 19).
A gene required for formation of the apical hook, HOOKLESS1 (so called because mutations in this gene result in seedlings lacking an apical hook), was identified in Arabidopsis (Lehman et al. 1996). Disruption of this gene severely alters the pattern of expression of auxin-respon-sive genes. When the gene is overexpressed in Arabidopsis, it causes constitutive hook formation even in the light.
HOOKLESS1 encodes a putative N-acetyltransferase that is hypothesized to regulate—by an unknown mechanism— differential auxin distribution in the apical hook induced by ethylene.
Ethylene Breaks Seed and Bud Dormancy in Some Species Seeds that fail to germinate under normal conditions (water, oxygen, temperature suitable for growth) are said to be dor-mant (see Chapter 23). Ethylene has the ability to break dor-mancy and initiate germination in certain seeds, such as cereals. In addition to its effect on dormancy, ethylene increases the rate of seed germination of several species. In peanuts (Arachis hypogaea), ethylene production and seed germination are closely correlated. Ethylene can also break bud dormancy, and ethylene treatment is sometimes used to promote bud sprouting in potato and other tubers.
Ethylene Promotes the Elongation Growth of Submerged Aquatic Species Although usually thought of as an inhibitor of stem elon-gation, ethylene is able to promote stem and petiole elon-gation in various submerged or partially submerged aquatic plants. These include the dicots Ranunculus sceler-atus, Nymphoides peltata, and Callitriche platycarpa, and the fern Regnellidium diphyllum. Another agriculturally impor-tant example is the cereal deepwater rice (see Chapter 20).
In these species, submergence induces rapid internode or petiole elongation, which allows the leaves or upper parts of the shoot to remain above water. Treatment with ethylene mimics the effects of submergence.
Growth is stimulated in the submerged plants because ethylene builds up in the tissues. In the absence of O2, eth-ylene synthesis is diminished, but the loss of ethylene by diffusion is retarded under water. Sufficient oxygen for growth and ethylene synthesis in the underwater parts is usually provided by aerenchyma tissue.
As we saw in Chapter 20, in deepwater rice it has been shown that ethylene stimulates internode elongation by increasing the amount of, and the sensitivity to, gibberellin in the cells of the intercalary meristem. The increased sen-sitivity to GA (gibberellic acid) in these cells in response to ethylene is brought about by a decrease in the level of abscisic acid (ABA), a potent antagonist of GA.
Ethylene Induces the Formation of Roots and Root Hairs Ethylene is capable of inducing adventitious root forma-tion in leaves, stems, flower stems, and even other roots.
Ethylene has also been shown to act as a positive regulator of root hair formation in several species (see Figure 22.5D).
This relationship has been best studied in Arabidopsis, in which root hairs normally are located in the epidermal cells that overlie a junction between the underlying cortical cells (Dolan et al. 1994).
In ethylene-treated roots, extra hairs form in abnormal locations in the epidermis; that is, cells not overlying a cor-tical cell junction differentiate into hair cells (Tanimoto et al.
1995). Seedlings grown in the presence of ethylene inhibitors (such as Ag+), as well as ethylene-insensitive mutants, dis-play a reduction in root hair formation in response to ethyl-ene. These observations suggest that ethylene acts as a pos-itive regulator in the differentiation of root hairs.
Ethylene Induces Flowering in the Pineapple Family Although ethylene inhibits flowering in many species, it induces flowering in pineapple and its relatives, and it is used commercially in pineapple for synchronization of fruit set. Flowering of other species, such as mango, is also ini-tiated by ethylene. On plants that have separate male and female flowers (monoecious species), ethylene may change the sex of developing flowers (see Chapter 24). The pro-motion of female flower formation in cucumber is one example of this effect.
Ethylene Enhances the Rate of Leaf Senescence As described in Chapter 16, senescence is a genetically pro-grammed developmental process that affects all tissues of the plant. Several lines of physiological evidence support roles for ethylene and cytokinins in the control of leaf senescence: 528 Chapter 22 • Exogenous applications of ethylene or ACC (the pre-cursor of ethylene) accelerate leaf senescence, and treatment with exogenous cytokinins delays leaf senescence (see Chapter 21).
• Enhanced ethylene production is associated with chlorophyll loss and color fading, which are charac-teristic features of leaf and flower senescence (see Figure 22.5C); an inverse correlation has been found between cytokinin levels in leaves and the onset of senescence.
• Inhibitors of ethylene synthesis (e.g., AVG or Co2+) and action (e.g., Ag+ or CO2) retard leaf senescence.
Taken together, the physiological studies suggest that senescence is regulated by the balance of ethylene and cytokinin. In addition, abscisic acid (ABA) has been impli-cated in the control of leaf senescence. The role of ABA in senescence will be discussed in Chapter 23.
Senescence in ethylene mutants.
Direct evidence for the involvement of ethylene in the regulation of leaf senescence has come from molecular genetic studies on Arabidopsis. As will be discussed later in the chapter, sev-eral mutants affecting the response to ethylene have been identified. The specific bioassay employed was the triple-response assay in which ethylene significantly inhibits seedling hypocotyl elongation and promotes lateral expansion.
Ethylene-insensitive mutants, such as etr1 (ethylene-resistant 1) and ein2 (ethylene-insensitive 2), were identi-fied by their failure to respond to ethylene (as will be described later in the chapter). The etr1 mutant is unable to perceive the ethylene signal because of a mutation in the gene that codes for the ethylene receptor protein; the ein2 mutant is blocked at a later step in the signal transduction pathway.
Consistent with a role for ethylene in leaf senescence, both etr1 and ein2 were found to be affected not only dur-ing the early stages of germination, but throughout the life cycle, including senescence (Zacarias and Reid 1990; Hensel et al. 1993; Grbiˇ c and Bleecker 1995). The ethylene mutants retained their chlorophyll and other chloroplast components for a longer period of time compared to the wild type. However, because the total life spans of these mutants were increased by only 30% over that of the wild type, ethylene appears to increase the rate of senescence, rather than acting as a developmental switch that initiates the senescence process.
Use of genetic engineering to probe senescence.
Another very useful genetic approach that offers direct evidence for the function of specific gene(s) is based on transgenic plants. Through genetic engineering technology, the roles of both ethylene and cytokinins in the regulation of leaf senescence have been confirmed. One way to suppress the expression of a gene is to trans-form the plant with antisense DNA, which consists of the gene of interest in the reverse orientation with respect to the promoter. When the antisense gene is transcribed, the resulting antisense mRNA is complementary to the sense mRNA and will hybridize to it. Because double-stranded RNA is rapidly degraded in the cell, the effect of the anti-sense gene is to deplete the cell of the sense mRNA.
Transgenic plants expressing antisense versions of genes that encode enzymes involved in the ethylene biosynthetic pathway, such as ACC synthase and ACC oxidase, can syn-thesize ethylene only at very low levels. Consistent with a role for ethylene in senescence, such antisense mutants have been shown to exhibit delayed leaf senescence, as well as fruit ripening, in tomato (see Web Topic 22.1).
The Role of Ethylene in Defense Responses Is Complex Pathogen infection and disease will occur only if the inter-actions between host and pathogen are genetically com-patible. However, ethylene production generally increases in response to pathogen attack in both compatible (i.e., pathogenic) and noncompatible (nonpathogenic) interac-tions.
The discovery of ethylene-insensitive mutants has allowed the role of ethylene in the response to various pathogens to be assessed. The emerging picture is that the involvement of ethylene in pathogenesis is complex and depends on the particular host–pathogen interaction. For example, blocking the ethylene response does not affect the resistance response to Pseudomonas bacteria in Arabidopsis or to tobacco mosaic virus in tobacco. In compatible inter-actions of these pathogens and hosts, however, elimination of ethylene responsiveness prevents the development of disease symptoms, even though the growth of the pathogen appears to be unaffected.
On the other hand, ethylene, in combination with jas-monic acid (see Chapter 13), is required for the activation of several plant defense genes. In addition, ethylene-insen-sitive tobacco and Arabidopsis mutants become susceptible to several necrotrophic (cell-killing) soil fungal pathogens that are normally not plant pathogens. Thus, ethylene appears to be involved in the resistance response to some pathogens, but not others.
Ethylene Biosynthesis in the Abscission Zone Is Regulated by Auxin The shedding of leaves, fruits, flowers, and other plant organs is termed abscission (see Web Topic 22.4). Abscis-sion takes place in specific layers of cells, called abscission layers, which become morphologically and biochemically differentiated during organ development. Weakening of the cell walls at the abscission layer depends on cell wall–degrading enzymes such as cellulase and polygalac-turonase (Figure 22.9).
Ethylene: The Gaseous Hormone 529 The ability of ethylene gas to cause defoliation in birch trees is shown in Fig-ure 22.10. The wild-type tree on the left has lost all its leaves. The tree on the right has been transformed with a gene for the Arabidopsis ethylene receptor ETR1-1 car-rying a dominant mutation (discussed in the next section). This tree is unable to respond to ethylene and does not shed its leaves after ethylene treatment.
Ethylene appears to be the primary regulator of the abscission process, with auxin acting as a suppressor of the ethyl-ene effect (see Chapter 19). However, supraoptimal auxin concentrations stimu-late ethylene production, which has led to the use of auxin analogs as defoliants. For example, 2,4,5-T, the active ingredient in Agent Orange, was widely used as a defo-liant during the Vietnam War. Its action is based on its ability to increase ethylene biosynthesis, thereby stimulating leaf abscission.
A model of the hormonal control of leaf abscission describes the process in three distinct sequential phases (Figure 22.11) (Reid 1995): 1. Leaf maintenance phase. Prior to the perception of any signal (internal or external) that initiates the abscission process, the leaf remains healthy and fully functional in the plant. A gradi-ent of auxin from the blade to the stem maintains the abscission zone in a nonsensitive state.
2. Shedding induction phase. A reduction or reversal in the auxin gradient from the leaf, normally associated with leaf senescence, causes the abscission zone to become sensitive to ethylene. Treatments that enhance leaf senescence may promote abscis-sion by interfering with auxin syn-thesis and/or transport in the leaf.
3. Shedding phase. The sensitized cells of the abscission zone respond to low concentrations of endogenous ethylene by synthesizing and secret-ing cellulase and other cell wall–degrading enzymes, resulting in shedding.
During the early phase of leaf mainte-nance, auxin from the leaf prevents abscis-sion by maintaining the cells of the abscis-530 Chapter 22 (A) (B) FIGURE 22.9 During the formation of the abscission layer, in this case that of jewelweed (Impatiens), two or three rows of cells in the abscission zone (A) undergo cell wall breakdown because of an increase in cell wall–hydrolyzing enzymes (B). The resulting protoplasts round up and increase in volume, pushing apart the xylem tracheary cells, and facilitating the separation of the leaf from the stem. (From Sexton et al. 1984.) FIGURE 22.10 Effect of ethylene on abscis-sion in birch (Betula pendula). The plant on the left is the wild type; the plant on the right was transformed with a mutated version of the Arabidopsis ethylene recep-tor, ETR1-1. The expression of this gene was under the transcriptional control of its own promoter. One of the characteris-tics of these mutant trees is that they do not drop their leaves when fumigated 3 days with 50 ppm of ethylene.
sion zone in an ethylene-insensitive state. It has long been known that removal of the leaf blade (the site of auxin pro-duction) promotes petiole abscission. Application of exoge-nous auxin to petioles from which the leaf blade has been removed delays the abscission process. However, applica-tion of auxin to the proximal side of the abscission zone (i.e., the side closest to the stem) actually accelerates the abscission process. These results indicate that it is not the absolute amount of auxin at the abscission zone, but rather the auxin gradient, that controls the ethylene sensitivity of these cells.
In the shedding induction phase, the amount of auxin from the leaf decreases and the ethylene level rises. Ethyl-ene appears to decrease the activity of auxin both by reduc-ing its synthesis and transport and by increasing its destruction. The reduction in the concentration of free auxin increases the response of specific target cells to eth-ylene. The shedding phase is characterized by the induc-tion of genes encoding specific hydrolytic enzymes of cell wall polysaccharides and proteins.
The target cells, located in the abscission zone, synthesize cellulase and other polysaccharide-degrading enzymes, and secrete them into the cell wall via secretory vesicles derived from the Golgi. The action of these enzymes leads to cell wall loosening, cell separation, and abscission.
Ethylene Has Important Commercial Uses Because ethylene regulates so many physiological processes in plant development, it is one of the most widely used plant hormones in agriculture. Auxins and ACC can trigger the natural biosynthesis of ethylene and in several cases are used in agricultural practice. Because of its high diffusion rate, ethylene is very difficult to apply in the field as a gas, but this limitation can be overcome if an ethylene-releasing compound is used. The most widely used such compound is ethephon, or 2-chloroethylphosphonic acid, which was discovered in the 1960s and is known by various trade names, such as Ethrel.
Ethephon is sprayed in aqueous solution and is readily absorbed and transported within the plant. It releases eth-ylene slowly by a chemical reaction, allowing the hormone to exert its effects: Ethephon hastens fruit ripening of apple and tomato and degreening of citrus, synchronizes flowering and fruit set in pineapple, and accelerates abscission of flowers and fruits. It can be used to induce fruit thinning or fruit drop in cotton, cherry, and walnut. It is also used to promote female sex expression in cucumber, to prevent self-polli-nation and increase yield, and to inhibit terminal growth of some plants in order to promote lateral growth and compact flowering stems.
Storage facilities developed to inhibit ethylene produc-tion and promote preservation of fruits have a controlled atmosphere of low O2 concentration and low temperature that inhibits ethylene biosynthesis. A relatively high con-centration of CO2 (3 to 5%) prevents ethylene’s action as a ripening promoter. Low pressure (vacuum) is used to remove ethylene and oxygen from the storage chambers, reducing the rate of ripening and preventing overripening.
Specific inhibitors of ethylene biosynthesis and action are also useful in postharvest preservation. Silver (Ag+) is Ethylene: The Gaseous Hormone 531 Leaf maintenance phase High auxin from leaf reduces ethylene sensitivity of abscission zone and prevents leaf shedding.
Shedding induction phase A reduction in auxin from the leaf increases ethylene production and ethylene sensitivity in the abscission zone, which triggers the shedding phase.
Shedding phase Synthesis of enzymes that hydrolyze the cell wall polysaccharides, resulting in cell separation and leaf abscission.
Auxin Auxin Ethylene Separation layer digested Yellowing FIGURE 22.11 Schematic view of the roles of auxin and eth-ylene during leaf abscission. In the shedding induction phase, the level of auxin decreases, and the level of ethyl-ene increases. These changes in the hormonal balance increase the sensitivity of the target cells to ethylene. (After Morgan 1984.) used extensively to increase the longevity of cut carnations and several other flowers. The potent inhibitor AVG retards fruit ripening and flower fading, but its commercial use has not yet been approved by regulatory agencies. The strong, offensive odor of trans-cyclooctene precludes its use in agri-culture. Currently, 1-methylcyclopropene (MCP) is being developed for use in a variety of postharvest applications. The near future may see a variety of agriculturally important species that have been genetically modified to manipulate the biosynthesis of ethylene or its perception.
The inhibition of ripening in tomato by expression of an antisense version of ACC synthase and ACC oxidase has already been mentioned. Another example of this technol-ogy is in petunia, in which ethylene biosynthesis has been blocked by transformation of an antisense version of ACC oxidase. Senescence and petal wilting of cut flowers are delayed for weeks in these transgenic plants.
CELLULAR AND MOLECULAR MODES OF ETHYLENE ACTION Despite the broad range of ethylene’s effects on develop-ment, the primary steps in ethylene action are assumed to be similar in all cases: They all involve binding to a recep-tor, followed by activation of one or more signal transduc-tion pathways (see Chapter 14 on the web site) leading to the cellular response. Ultimately, ethylene exerts its effects primarily by altering the pattern of gene expression. In recent years, remarkable progress has been made in our understanding of ethylene perception, as the result of mol-ecular genetic studies of Arabidopsis thaliana.
One key to the elucidation of ethylene signaling com-ponents has been the use of the triple-response morphol-ogy of etiolated Arabidopsis seedlings to isolate mutants affected in their response to ethylene (see Figure 22.7) (Guzman and Ecker 1990). Two classes of mutants have been identified by experiments in which mutagenized Ara-bidopsis seeds were grown on an agar medium in the pres-ence or absence of ethylene for 3 days in the dark: 1.
Mutants that fail to respond to exogenous ethylene (ethylene-resistant or ethylene-insensitive mutants) 2.
Mutants that display the response even in the absence of ethylene (constitutive mutants) Ethylene-insensitive mutants are identified as tall seedlings extending above the lawn of short, triple-responding seedlings when grown in the presence of eth-ylene. Conversely, constitutive ethylene response mutants are identified as seedlings displaying the triple response in the absence of exogenous ethylene.
Ethylene Receptors Are Related to Bacterial Two-Component System Histidine Kinases The first ethylene-insensitive mutant isolated was etr1 (ethylene-resistant 1) (Figure 22.12). The etr1 mutant was identified in a screen for mutations that block the response of Arabidopsis seedlings to ethylene. The amino acid sequence of the carboxy-terminal half of ETR1 is sim-ilar to bacterial two-component histidine kinases—recep-tors used by bacteria to perceive various environmental cues, such as chemo-sensory stimuli, phosphate avail-ability, and osmolarity.
Bacterial two-component systems consist of a sensor his-tidine kinase and a response regulator, which often acts as a transcription factor (see Chapter 14 on the web site).
ETR1 was the first example of a eukaryotic histidine kinase, 532 Chapter 22 2-Chloroethylphosphonic acid (ethephon) CH2 O Cl CH2 P OH OH– O + CH2 Cl– + CH2 +H2PO4– Ethylene FIGURE 22.12 Screen for the etr1 mutant of Arabidopsis.
Seedlings were grown for 3 days in the dark in ethylene.
Note that all but one of the seedlings are exhibiting the triple response: exaggeration in curvature of the apical hook, inhibition and radial swelling of the hypocotyl, and horizontal growth. The etr1 mutant is completely insensi-tive to the hormone and grows like an untreated seedling.
(Photograph by K. Stepnitz of the MSU/DOE Plant Research Laboratory.) but others have since been found in yeast, mammals, and plants. Both phytochrome (see Chapter 17) and the cytokinin receptor (see Chapter 21) also share sequence similarity to bacterial two-component histidine kinases.
The similarity to bacterial receptors and the ethylene insensitivity of the etr1 mutants suggested that ETR1 might be an ethylene receptor. Consistent with this hypothesis, ETR1 expression in yeast conferred the ability to bind radi-olabeled ethylene with an affinity that closely parallels the dose-response curve of Arabidopsis seedlings to ethylene (see Web Topic 22.5).
The Arabidopsis genome encodes four additional pro-teins similar to ETR1 that also function as ethylene recep-tors: ETR2, ERS1 (ETR1-related sequence 1), ERS2, and EIN4 (Figure 22.13). Like ETR1, these receptors have been shown to bind ethylene, and missense mutations in the genes that encode these proteins, analogous to the original etr1 mutation, prevent ethylene binding to the receptor while allowing the receptor to function normally as a reg-ulator of the ethylene response pathway in the absence of ethylene.
All of these proteins share at least two domains: 1.
The amino-terminal domain spans the membrane at least three times and contains the ethylene-binding site. Ethylene can readily access this site because of its hydrophobicity.
2.
The middle portion of the ethylene receptors con-tains a histidine kinase catalytic domain.
A subset of the ethylene receptors also have a carboxy-terminal domain that is similar to bacterial two-component receiver domains. In other two-component systems, binding of ligand regulates the activity of the histidine kinase domain, which autophosphorylates a conserved histidine residue. The phosphate is then transferred to an aspartic acid residue located within the fused receiver domain.Although histidine kinase activity has been demonstrated for one of the ethylene receptors—ETR1—several others are missing critical amino acids, making it unlikely that they possess his-tidine kinase activity. Thus the biochemical mechanism of these ethylene receptors is not known.
Recent studies indicate that ETR1 is located on the endo-plasmic reticulum, rather than on the plasma membrane as originally assumed. Such an intracellular location for the ethylene receptor is consistent with the hydrophobic nature of ethylene, which enables it to pass freely through the plasma membrane into the cell. In this respect ethylene is similar to the hydrophobic signaling molecules of animals, such as steroids and the gas nitric oxide, which also bind to intracellular receptors.
High-Affinity Binding of Ethylene to Its Receptor Requires a Copper Cofactor Even prior to the identification of its receptor, scientists had predicted that ethylene would bind to its receptor via a transition metal cofactor, most likely copper or zinc. This prediction was based on the high affinity of olefins, such as ethylene, for these transition metals. Recent genetic and biochemical studies have borne out these predictions. Analysis of the ETR1 ethylene receptor expressed in yeast demonstrated that a copper ion was coordinated to the protein and that this copper was necessary for high-affinity ethylene binding (Rodriguez et al. 1999). Silver ion could substitute for copper to yield high-affinity binding, which indicates that silver blocks the action of ethylene not by interfering with ethylene binding, but by preventing the changes in the protein that normally occur when ethylene binds to the receptor.
Evidence that copper binding is required for ethylene receptor function in vivo came from identification of the RAN1 gene in Arabidopsis (Hirayama et al. 1999). Strong ran1 mutations block the formation of functional ethylene receptors (Woeste and Kieber 2000). Cloning of RAN1 revealed that it encodes a protein similar to a yeast protein required for the transfer of a copper ion cofactor to an iron transport protein. In an analogous manner, RAN1 is likely to be involved in the addition of a copper ion cofactor nec-essary for the function of the ethylene receptors.
Ethylene: The Gaseous Hormone 533 D COOH Histidine kinase Degenerate histidine kinase domains Receiver GAF Ethylene binding ETR1 ERS1 D EIN4 D ETR2 ERS2 Subfamily 1 Subfamily 2 H H H FIGURE 22.13 Schematic diagram of five eth-ylene receptor proteins and their functional domains. The GAF domain is a conserved cGMP-binding domain found in a diverse group of proteins. Note that EIN4, ETR2, and ERS2 have degenerate histidine kinase domains.
Unbound Ethylene Receptors Are Negative Regulators of the Response Pathway In Arabidopsis, tomato, and probably most other plant species, the ethylene receptors are encoded by multigene families. Targeted disruption (complete inactivation) of the five Arabidopsis ethylene receptors (ETR1, ETR2, ERS1, ERS2, and EIN4) has revealed that they are functionally redundant (Hua and Meyerowitz 1998). That is, disruption of any single gene encoding one of these proteins has no effect, but a plant with disruptions in all five receptor genes exhibits a constitutive ethylene response phenotype (Figure 22.14D).
The observation that ethylene responses, such as the triple response, become constitutive when the receptors are disrupted indicates that the receptors are normally “on” (i.e., in the active state) in the absence of ethylene, and that the function of the receptor minus its ligand (ethylene), is to shut off the signaling pathway that leads to the response (Figure 22.14B). Binding of ethylene turns off the receptors, thus allowing the response pathway to proceed (Figure 22.14A).
This somewhat counterintuitive model for ethylene receptors as negative regulators of a signaling pathway is unlike the mechanism of most animal receptors, which, after binding their ligands, serve as positive regulators of their respective signal transduction pathways.
In contrast to the disrupted receptors, receptors with missense mutations at the ethylene binding site (as occurs in the original etr1 mutant) are unable to bind ethylene, but are still active as negative regulators of the ethylene 534 Chapter 22 EIN4 Plasma membrane (D) Disruptions in the regulatory domains of multiple ethylene receptors (at least three) Disrupted receptors are inactive in the presence or absence of ethylene. Ethylene response pathway ETR1 ETR2 ERS1 ERS2 EIN4 (B) Ethylene response pathway In the absence of ethylene, the receptors are active and suppress the ethylene response. ETR1 ETR2 ERS1 ERS2 EIN4 (C) Ethylene response pathway Ethylene (C2H4) Missense mutation at binding site makes receptor insensitive to ethylene.
The active receptor inhibits the response.
Ethylene binding inactivates receptors ETR1 ETR2 ERS1 ERS2 The response does not occur; the mutant exhibits a dominant negative phenotype.
ETR1 ETR2 ERS1 ERS2 EIN4 (A) Ethylene response pathway Ethylene (C2H4) Ethylene binding inactivates receptors The ethylene response occurs.
The ethylene response occurs.
FIGURE 22.14 Model for ethylene receptor action based on the phenotype of receptor mutants. (A) In the wild type, ethylene binding inactivates the receptors, allowing the response to occur. (B) In the absence of ethylene the recep-tors act as negative regulators of the response pathway. (C) A missense mutation that interferes with ethylene binding to its receptor, but leaves the regulatory site active, results in a dominant negative phenotype. (D) Disruption muta-tions in the regulatory sites result in a constitutive ethylene response.
response pathway. Such missense mutations result in a plant that expresses a subset of receptors that can no longer be turned off by ethylene, and thus confer a domi-nant ethylene-insensitive phenotype (Figure 22.14C). Even though the normal receptors can all be turned off by eth-ylene, the mutant receptors continue to signal the cell to suppress ethylene responses whether ethylene is present or not.
A Serine/Threonine Protein Kinase Is Also Involved in Ethylene Signaling The recessive ctr1 (constitutive triple response 1 = triple response in the absence of ethylene) mutation was identi-fied in screens for mutations that constitutively activated ethylene responses (Figure 22.15). The fact that the muta-tion caused an activation of the ethylene response suggests that the wild-type protein also acts as a negative regulator of the response pathway (Kieber et al. 1993), similar to the ethylene receptors. CTR1 appears to be related to RAF-1, a MAPKKK ser-ine/threonine protein kinase (mitogen-activated protein kinase kinase kinase) that is involved in the transduction of various external regulatory signals and developmental sig-naling pathways in organisms ranging from yeast to humans (see Chapter 14 on the web site). In animal cells, the final product in the MAP kinase cascade is a phospho-rylated transcription factor that regulates gene expression in the nucleus.
EIN2 Encodes a Transmembrane Protein The ein2 (ethylene-insensitive 2) mutation blocks all ethyl-ene responses in both seedling and adult Arabidopsis plants.
The EIN2 gene encodes a protein containing 12 membrane-spanning domains that is most similar to the N-RAMP (natural resistance–associated macrophage protein) family of cation transporters in animals (Alonso et al. 1999), sug-gesting that it may act as a channel or pore. To date, how-ever, researchers have failed to demonstrate a transport activity for this protein, and the intracellular location of the protein is not known. Interestingly, mutations in the EIN2 gene have also been identified in genetic screens for resistance to other hor-mones, such as jasmonic acid and ABA, suggesting that EIN2 may be a common intermediate in the signal trans-duction pathways of various hormones and other chemi-cal signals.
Ethylene Regulates Gene Expression One of the primary effects of ethylene signaling is an alter-ation in the expression of various target genes. Ethylene affects the mRNA transcript levels of numerous genes, including the genes that encode cellulase, as well as ripen-ing-related genes and ethylene biosynthesis genes. Regula-tory sequences called ethylene response elements, or EREs, have been identified from the ethylene-regulated genes.
Key components mediating ethylene’s effects on gene expression are the EIN3 family of transcription factors (Chao et al. 1997). There are at least four EIN3-like genes in Arabidopsis, and homologs have been identified in both tomato and tobacco. In response to an ethylene signal, homodimers of EIN3 or its paralogs (closely related pro-teins), bind to the promoter of a gene called ERF1 (ethylene response factor 1) and activate its transcription (Solano et al. 1998). ERF1 encodes a protein that belongs to the ERE-binding protein (EREBP) family of transcription factors, which were first identified in tobacco as proteins that bind to ERE sequences (Ohme-Takagi and Shinshi 1995). Several EREBPs are rapidly up-regulated in response to ethylene. The EREBP genes exist in Arabidopsis as a very large gene family, but only a few of the genes are inducible by ethylene.
Genetic Epistasis Reveals the Order of the Ethylene Signaling Components The order of action of the genes ETR1, EIN2, EIN3, and CTR1 has been determined by the analysis of how the mutations interact with each other (i.e., their epistatic order). Two mutants with opposite phenotypes are crossed, and a line harboring both mutations (the double mutant) is identified in the F2 generation. In the case of the ethylene response mutants, researchers constructed a line doubly mutant for ctr1, a constitutive ethylene response mutant, and one of the ethylene-insensitive mutations. The phenotype that the double mutant displays reveals which of the mutations is epistatic to the other. For exam-ple, if an etr1/ctr1 double mutant displays a ctr1 mutant phenotype, the ctr1 mutation is said to be epistatic to etr1.
From this it can be inferred that CTR1 acts downstream of Ethylene: The Gaseous Hormone 535 FIGURE 22.15 Screen for Arabidopsis mutants that constitu-tively display the triple response. Seedlings were grown for 3 days in the dark in air. A single ctr1 mutant seedling is evident among the taller, wild-type seedlings. (Courtesy of J. Kieber.) ETR1 (Avery and Wasserman 1992). In this way, the order of action of ETR1, EIN2, and EIN3 were determined rel-ative to CTR1.
The ETR1 protein has been shown to interact physically with the predicted downstream protein, CTR1, suggesting that the ethylene receptors may directly regulate the kinase activity of CTR1 (Clark et al. 1998). The model in Figure 22.16 summarizes these and other data. Genes that are similar to several of these Arabidopsis signaling genes have been found in other species (see Web Topic 22.6). This model is still incomplete because other ethylene response mutations have been identified that act in this pathway. In addition, we are only beginning to under-stand the biochemical properties of these proteins and how they interact. However, we are beginning to glimpse the outline of the molecular basis for the perception and transduction of this hormonal signal.
SUMMARY Ethylene is formed in most organs of higher plants. Senesc-ing tissues and ripening fruits produce more ethylene than do young or mature tissues. The precursor of ethylene in vivo is the amino acid methionine, which is converted to AdoMet (S-adenosylmethionine), ACC (1-aminocyclo-propane-1-carboxylic acid), and ethylene. The rate-limiting step of this pathway is the conversion of AdoMet to ACC, which is catalyzed by ACC synthase. ACC synthase is encoded by members of a multigene family that are differ-entially regulated in various plant tissues and in response to various inducers of ethylene biosynthesis.
Ethylene biosynthesis is triggered by various develop-mental processes, by auxins, and by environmental stresses.
In all these cases the level of activity and of mRNA of ACC synthase increases. The physiological effects of ethylene can 536 Chapter 22 P P ATP ADP –S–S– ER membrane His kinase domain ETR1 histidine kinase EIN2 N-RAMP homolog EIN3 ERF1 Ethylene response genes CTR1 RAF-like kinase Receiver domain C2H4 NUCLEUS In the absence of ethylene, ETR1 and the other ethylene receptors activate the kinase activity of CTR1. This leads to a repression of the ethylene response pathway, possibly through a MAP kinase cascade. The binding of ethylene to the ETR1 dimer results in its inactivation, which causes CTR1 to become inactive.
The inactivation of CTR1 allows the transmembrane protein EIN2 to become active. The RAN1 protein is required to assemble the copper cofactor into the ethylene receptor.
Activation of EIN2 turns on the EIN3 family of transcription factors, which in turn induce the expression of ERF1. The activation of this transcriptional cascade leads to large-scale changes in gene expression, which ultimately bring about alterations in cell functions.
Transcription factors Cu Cu RAN1 C N MAPKK?
MAPK?
Activation H D COOH HOOC FIGURE 22.16 Model of ethylene signaling in Arabidopsis. Ethylene binds to the ETR1 recep-tor, which is an integral membrane protein of the ER membrane. Multiple isoforms of ethyl-ene receptors may be present in a cell; only ETR1 is shown for simplicity. The receptor is a dimer, held together by disulfide bonds.
Ethylene binds within the trans-membrane domain, through a copper co-factor, which is assembled into the ethylene receptors through the RAN1 protein.
be blocked by biosynthesis inhibitors or by antagonists.
AVG (aminoethoxy-vinylglycine) and AOA (aminooxy-acetic acid) inhibit the synthesis of ethylene; carbon diox-ide, silver ions, trans-cyclooctene, and MCP inhibit ethyl-ene action. Ethylene can be detected and measured by gas chromatography.
Ethylene regulates fruit ripening and other processes associated with leaf and flower senescence, leaf and fruit abscission, root hair development, seedling growth, and hook opening. Ethylene also regulates the expression of various genes, including ripening-related genes and patho-genesis-related genes.
The ethylene receptor is encoded by a family of genes that encode proteins similar to bacterial two-component histidine kinases. Ethylene binds to these receptors in a transmembrane domain through a copper cofactor. Down-stream signal transduction components include CTR1, a member of the RAF family of protein kinases; and EIN2, a channel-like transmembrane protein. The pathway acti-vates a cascade of transcription factors, including the EIN3 and EREBP families, which then modulate gene expression.
Web Material Web Topics 22.1 Cloning of ACC Synthase A brief description of the cloning of the gene for ACC synthase using antibodies raised against the partially purified protein.
22.2 Cloning of the ACC Oxidase Gene The ACC oxidase gene was cloned by a cir-cuitous route using antisense DNA.
22.3 ACC Synthase Gene Expression and Biotechnology A discussion of the use of the ACC synthase gene in biotechnology.
22.4 Abscission and the Dawn of Agriculture A short essay on the domestication of modern cereals based on artificial selection for non-shattering rachises.
22.5 Ethylene Binding to ETR1 and Seedling Response to Ethylene Ethylene-binding to its receptor ETR1 was first demonstrated by expressing the gene in yeast.
22.6 Conservation of Ethylene Signaling Components in Other Plant Species The evidence suggests that ethylene signaling is similar in all plant species.
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538 Chapter 22 Abscisic Acid: A Seed Maturation and Antistress Signal 23 Chapter THE EXTENT AND TIMING OF PLANT GROWTH are controlled by the coordinated actions of positive and negative regulators. Some of the most obvious examples of regulated nongrowth are seed and bud dor-mancy, adaptive features that delay growth until environmental con-ditions are favorable. For many years, plant physiologists suspected that the phenomena of seed and bud dormancy were caused by inhibitory compounds, and they attempted to extract and isolate such compounds from a variety of plant tissues, especially dormant buds. Early experiments used paper chromatography for the separation of plant extracts, as well as bioassays based on oat coleoptile growth. These early experiments led to the identification of a group of growth-inhibit-ing compounds, including a substance known as dormin purified from sycamore leaves collected in early autumn, when the trees were enter-ing dormancy. Upon discovery that dormin was chemically identical to a substance that promotes the abscission of cotton fruits, abscisin II, the compound was renamed abscisic acid (ABA) (see Figure 23.1), to reflect its supposed involvement in the abscission process.
It is now known that ethylene is the hormone that triggers abscission and that ABA-induced abscission of cotton fruits is due to ABA’s ability to stimulate ethylene production. As will be discussed in this chapter, ABA is now recognized as an important plant hormone in its own right.
It inhibits growth and stomatal opening, particularly when the plant is under environmental stress. Another important function is its regulation of seed maturation and dormancy. In retrospect, dormin would have been a more appropriate name for this hormone, but the name abscisic acid is firmly entrenched in the literature.
OCCURRENCE, CHEMICAL STRUCTURE, AND MEASUREMENT OF ABA Abscisic acid has been found to be a ubiquitous plant hormone in vas-cular plants. It has been detected in mosses but appears to be absent in liverworts (see Web Topic 23.1). Several genera of fungi make ABA as a secondary metabolite (Milborrow 2001).
Within the plant, ABA has been detected in every major organ or living tissue from the root cap to the apical bud.
ABA is synthesized in almost all cells that contain chloro-plasts or amyloplasts.
The Chemical Structure of ABA Determines Its Physiological Activity ABA is a 15-carbon compound that resembles the terminal portion of some carotenoid molecules (Figure 23.1). The orientation of the carboxyl group at carbon 2 determines the cis and trans isomers of ABA. Nearly all the naturally occurring ABA is in the cis form, and by convention the name abscisic acid refers to that isomer.
ABA also has an asymmetric carbon atom at position 1′ in the ring, resulting in the S and R (or + and –, respec-tively) enantiomers. The S enantiomer is the natural form; commercially available synthetic ABA is a mixture of approximately equal amounts of the S and R forms. The S enantiomer is the only one that is active in fast responses to ABA, such as stomatal closure. In long-term responses, such as seed maturation, both enantiomers are active. In contrast to the cis and trans isomers, the S and R forms can-not be interconverted in the plant tissue.
Studies of the structural requirements for biological activity of ABA have shown that almost any change in the molecule results in loss of activity (see Web Topic 23.2).
ABA Is Assayed by Biological, Physical, and Chemical Methods A variety of bioassays have been used for ABA, including inhibition of coleoptile growth, germination, or GA-induced α-amylase synthesis. Alternatively, promotion of stomatal closure and gene expression are examples of rapid inductive responses (see Web Topic 23.3).
Physical methods of detection are much more reliable than bioassays because of their specificity and suitability for quantitative analysis. The most widely used techniques are those based on gas chromatography or high-perfor-mance liquid chromatography (HPLC). Gas chromatogra-phy allows detection of as little as 10–13 g ABA, but it requires several preliminary purification steps, including thin-layer chromatography. Immunoassays are also highly sensitive and specific.
BIOSYNTHESIS, METABOLISM, AND TRANSPORT OF ABA As with the other hormones, the response to ABA depends on its concentration within the tissue and on the sensitiv-ity of the tissue to the hormone. The processes of biosyn-thesis, catabolism, compartmentation, and transport all contribute to the concentration of active hormone in the tis-sue at any given stage of development. The complete biosynthetic pathway of ABA was elucidated with the aid of ABA-deficient mutants blocked at specific steps in the pathway.
ABA Is Synthesized from a Carotenoid Intermediate ABA biosynthesis takes place in chloroplasts and other plastids via the pathway depicted in Figure 23.2. Several ABA-deficient mutants have been identified with lesions at specific steps of the pathway. These mutants exhibit abnormal phenotypes that can be corrected by the appli-cation of exogenous ABA. For example, flacca (flc) and sitiens (sit) are “wilty mutants” of tomato in which the ten-dency of the leaves to wilt (due to an inability to close their stomata) can be prevented by the application of exogenous ABA. The aba mutants of Arabidopsis also exhibit a wilty phenotype. These and other mutants have been useful in elucidating the details of the pathway (Milborrow 2001).
The pathway begins with isopentenyl diphosphate (IPP), the biological isoprene unit, and leads to the synthesis of the C40 xanthophyll (i.e., oxygenated carotenoid) violaxanthin (see Figure 23.2). Synthesis of violaxanthin is catalyzed by zeaxanthin epoxidase (ZEP), the enzyme encoded by the ABA1 locus of Arabidopsis. This discovery provided conclu-sive evidence that ABA synthesis occurs via the “indirect” or carotenoid pathway, rather than as a small molecule.
Maize mutants (vp) that are blocked at other steps in the carotenoid pathway also have reduced levels of ABA and exhibit vivipary—the precocious germination of seeds in the fruit while still attached to the plant (Figure 23.3). Vivip-ary is a feature of many ABA-deficient seeds.
Violaxanthin is converted to the C40 compound 9′-cis-neoxanthin, which is then cleaved to form the C15 com-540 Chapter 23 O OH H3C CH3 CH3 COOH CH3 5‘ 5 4 3 2 1 4‘ 3‘ 6‘ 2‘ 1‘ O OH H3C CH3 COOH CH3 CH3 O OH H3C CH3 COOH CH3 (S)-cis-ABA (naturally occurring active form) (R)-cis-ABA (inactive in stomatal closure) (S)-2-trans-ABA (inactive, but interconvertible with active [cis] form) FIGURE 23.1 The chemical structures of the S (counterclock-wise array) and R (clockwise array) forms of cis-ABA, and the (S)-2-trans form of ABA. The numbers in the diagram of (S)-cis-ABA identify the carbon atoms. OH OH HO O CHO O OH CHO O COOH O O O COOH OH COOH OH H Oxidation O C O O O OH OH CH2OH OH HO O OH HO OH 9‘-cis-Neoxanthin (C40) Xanthoxal (C15) ABA-aldehyde (C15) Vp14: Corn mutant Cleavage site flacca, sitiens: Tomato mutants droopy: Potato mutants aba3: Arabidopsis mutant nar2a: Barley mutant Abscisic acid (C15) (ABA) ABA-β-D-glucose ester Phaseic acid (PA) 4‘-Dihydrophaseic acid (DPA) Conju-gation ABA inactivation by conjugation with monosaccharides ABA inactivation by oxidation Growth inhibitor OPP HO OH OPP Bonding of farnesyl component to specific proteins attaches them to membrane.
Isopentenyl diphosphate (IPP) Farnesyl diphosphate (C15) Zeaxanthin (C40) vp2, vp5, vp7, vp9: Corn mutants aba1: Arabidopsis mutant ZEP NCED O2 HO OH O O all trans-Violaxanthin (C40) FIGURE 23.2 ABA biosynthesis and metabolism. In higher plants, ABA is synthesized via the terpenoid pathway (see Chapter 13). Some ABA-deficient mutants that have been helpful in elucidating the pathway are shown at the steps at which they are blocked. The pathways for ABA catabo-lism include conjugation to form ABA-β-D-glucosyl ester or oxidation to form phaseic acid and then dihydrophaseic acid. ZEP = zeaxanthin epoxidase; NCED = 9-cis-epoxy-carotenoids dioxygenase.
pound xanthoxal, previously called xanthoxin, a neutral growth inhibitor that has physiological properties similar to those of ABA. The cleavage is catalyzed by 9-cis-epoxy-carotenoid dioxygenase (NCED), so named because it can cleave both 9-cis-violaxanthin and 9′-cis-neoxanthin. Synthesis of NCED is rapidly induced by water stress, suggesting that the reaction it catalyzes is a key regulatory step for ABA synthesis. The enzyme is localized on the thy-lakoids, where the carotenoid substrate is located. Finally, xanthoxal is converted to ABA via oxidative steps involv-ing the intermediate(s) ABA-aldehyde and/or possibly xanthoxic acid. This final step is catalyzed by a family of aldehyde oxidases that all require a molybdenum cofactor; the aba3 mutants of Arabidopsis lack a functional molybde-num cofactor and are therefore unable to synthesize ABA.
ABA Concentrations in Tissues Are Highly Variable ABA biosynthesis and concentrations can fluctuate dra-matically in specific tissues during development or in response to changing environmental conditions. In devel-oping seeds, for example, ABA levels can increase 100-fold within a few days and then decline to vanishingly low lev-els as maturation proceeds. Under conditions of water stress, ABA in the leaves can increase 50-fold within 4 to 8 hours. Upon rewatering, the ABA level declines to normal in the same amount of time.
Biosynthesis is not the only factor that regulates ABA concentrations in the tissue. As with other plant hormones, the concentration of free ABA in the cytosol is also regulated by degradation, compartmentation, conjugation, and trans-port. For example, cytosolic ABA increases during water stress as a result of synthesis in the leaf, redistribution within the mesophyll cell, import from the roots, and recir-culation from other leaves. The concentration of ABA declines after rewatering because of degradation and export from the leaf, as well as a decrease in the rate of synthesis.
ABA Can Be Inactivated by Oxidation or Conjugation A major cause of the inactivation of free ABA is oxidation, yielding the unstable intermediate 6-hydroxymethyl ABA, which is rapidly converted to phaseic acid (PA) and dihy-drophaseic acid (DPA) (see Figure 23.2). PA is usually inac-tive, or it exhibits greatly reduced activity, in bioassays.
However, PA can induce stomatal closure in some species, and it is as active as ABA in inhibiting gibberellic acid–induced α-amylase production in barley aleurone lay-ers. These effects suggest that PA may be able to bind to ABA receptors. In contrast to PA, DPA has no detectable activity in any of the bioassays tested.
Free ABA is also inactivated by covalent conjugation to another molecule, such as a monosaccharide. A common example of an ABA conjugate is ABA-b-D-glucosyl ester (ABA-GE). Conjugation not only renders ABA inactive as a hormone; it also alters its polarity and cellular distribu-tion. Whereas free ABA is localized in the cytosol, ABA-GE accumulates in vacuoles and thus could theoretically serve as a storage form of the hormone.
Esterase enzymes in plant cells could release free ABA from the conjugated form. However, there is no evidence that ABA-GE hydrolysis contributes to the rapid increase in ABA in the leaf during water stress. When plants were sub-jected to a series of stress and rewatering cycles, the ABA-GE concentration increased steadily, suggesting that the conjugated form is not broken down during water stress.
ABA Is Translocated in Vascular Tissue ABA is transported by both the xylem and the phloem, but it is normally much more abundant in the phloem sap.
When radioactive ABA is applied to a leaf, it is transported both up the stem and down toward the roots. Most of the radioactive ABA is found in the roots within 24 hours.
Destruction of the phloem by a stem girdle prevents ABA accumulation in the roots, indicating that the hormone is transported in the phloem sap.
ABA synthesized in the roots can also be transported to the shoot via the xylem. Whereas the concentration of ABA in the xylem sap of well-watered sunflower plants is between 1.0 and 15.0 nM, the ABA concentration in water-stressed sunflower plants increases to as much as 3000 nM (3.0 µM ) (Schurr et al. 1992). The magnitude of the stress-induced change in xylem ABA content varies widely among species, and it has been suggested that ABA also is transported in a conjugated form, then released by hydrol-ysis in leaves. However, the postulated hydrolases have yet to be identified.
542 Chapter 23 FIGURE 23.3 Precocious germination in the ABA-deficient vp14 mutant of maize. The VP14 protein catalyzes the cleavage of 9-cis-epoxycarotenoids to form xanthoxal, a precursor of ABA. (Courtesy of Bao Cai Tan and Don McCarty.) As water stress begins, some of the ABA carried by the xylem stream is synthesized in roots that are in direct contact with the drying soil. Because this transport can occur before the low water potential of the soil causes any measurable change in the water status of the leaves, ABA is believed to be a root signal that helps reduce the transpiration rate by closing stomata in leaves (Davies and Zhang 1991).
Although a concentration of 3.0 µM ABA in the apoplast is sufficient to close stomata, not all of the ABA in the xylem stream reaches the guard cells. Much of the ABA in the transpiration stream is taken up and metabolized by the mesophyll cells. During the early stages of water stress, however, the pH of the xylem sap becomes more alkaline, increasing from about pH 6.3 to about pH 7.2 (Wilkinson and Davies 1997).
The major control of ABA distribution among plant cell compartments follows the “anion trap” concept: The disso-ciated (anion) form of this weak acid accumulates in alkaline compartments and may be redistributed according to the steepness of the pH gradients across membranes. In addi-tion to partitioning according to the relative pH of compart-ments, specific uptake carriers contribute to maintaining a low apoplastic ABA concentration in unstressed plants.
Stress-induced alkalinization of the apoplast favors for-mation of the dissociated form of abscisic acid, ABA–, which does not readily cross membranes. Hence, less ABA enters the mesophyll cells, and more reaches the guard cells via the transpiration stream (Figure 23.4). Note that ABA is redis-tributed in the leaf in this way without any increase in the total ABAlevel. This increase in xylem sap pH may function as a root signal that promotes early closure of the stomata.
DEVELOPMENTAL AND PHYSIOLOGICAL EFFECTS OF ABA Abscisic acid plays primary regulatory roles in the initiation and maintenance of seed and bud dormancy and in the plant’s response to stress, particularly water stress. In addi-tion, ABA influences many other aspects of plant develop-ment by interacting, usually as an antagonist, with auxin, cytokinin, gibberellin, ethylene, and brassinosteroids. In this section we will explore the diverse physiological effects of ABA, beginning with its role in seed development.
ABA Levels in Seeds Peak during Embryogenesis Seed development can be divided into three phases of approximately equal duration: 1. During the first phase, which is characterized by cell divisions and tissue differentiation, the zygote under-goes embryogenesis and the endosperm tissue prolif-erates.
2. During the second phase, cell divisions cease and storage compounds accumulate.
3. In the final phase, the embryo becomes tolerant to desiccation, and the seed dehydrates, losing up to 90% of its water. As a consequence of dehydration, metabolism comes to a halt and the seed enters a qui-escent (“resting”) state. In contrast to dormant seeds, quiescent seeds will germinate upon rehydration.
The latter two phases result in the production of viable seeds with adequate resources to support germination and Abscisic Acid: A Seed Maturation and Antistress Signal 543 ABA– ABA ABAH Well-watered conditions pH 6.3 Water stress pH 7.2 Mesophyll cells Palisade parenchyma Upper epidermis Lower epidermis Xylem Guard cell During water stress, the slightly alkaline xylem sap favors the dissociation of ABAH to ABA–. Because ABA– does not easily pass through membranes, under conditions of water stress, more ABA reaches guard cells. Acidic xylem sap favors uptake of the undis-sociated form of ABA (ABAH) by the mesophyll cells.
FIGURE 23.4 Redistribution of ABA in the leaf result-ing from alkalinization of the xylem sap during water stress.
the capacity to wait weeks to years before resuming growth. Typically, the ABA content of seeds is very low early in embryogenesis, reaches a maximum at about the halfway point, and then gradually falls to low levels as the seed reaches maturity. Thus there is a broad peak of ABA accumulation in the seed corresponding to mid- to late embryogenesis.
The hormonal balance of seeds is complicated by the fact that not all the tissues have the same genotype. The seed coat is derived from maternal tissues (see Web Topic 1.2); the zygote and endosperm are derived from both par-ents. Genetic studies with ABA-deficient mutants of Ara-bidopsis have shown that the zygotic genotype controls ABA synthesis in the embryo and endosperm and is essen-tial to dormancy induction, whereas the maternal geno-type controls the major, early peak of ABA accumulation and helps suppress vivipary in midembryogenesis (Raz et al. 2001).
ABA Promotes Desiccation Tolerance in the Embryo An important function of ABA in the developing seed is to promote the acquisition of desiccation tolerance. As will be described in Chapter 25 (on stress physiology), desic-cation can severely damage membranes and other cellular constituents. During the mid- to late stages of seed devel-opment, specific mRNAs accumulate in embryos at the time of high levels of endogenous ABA. These mRNAs encode so-called late-embryogenesis-abundant (LEA) proteins thought to be involved in desiccation tolerance.
Synthesis of many LEA proteins, or related family mem-bers, can be induced by ABA treatment of either young embryos or vegetative tissues. Thus the synthesis of most LEA proteins is under ABA control (see Web Topic 23.4).
ABA Promotes the Accumulation of Seed Storage Protein during Embryogenesis Storage compounds accumulate during mid- to late embryogenesis. Because ABA levels are still high, ABA could be affecting the translocation of sugars and amino acids, the synthesis of the reserve materials, or both.
Studies in mutants impaired in both ABA synthesis and response showed no effect of ABA on sugar translocation.
In contrast, ABA has been shown to affect the amounts and composition of storage proteins. For example, exoge-nous ABA promotes accumulation of storage proteins in cultured embryos of many species, and some ABA-defi-cient or -insensitive mutants have reduced storage protein accumulation. However, storage protein synthesis is also reduced in other seed developmental mutants with nor-mal ABA levels and responses, indicating that ABA is only one of several signals controlling the expression of storage protein genes during embryogenesis.
ABA not only regulates the accumulation of storage proteins during embryogenesis; it can also maintain the mature embryo in a dormant state until the environmen-tal conditions are optimal for growth. Seed dormancy is an important factor in the adaptation of plants to unfavorable environments. As we will discuss in the next few sections, plants have evolved a variety of mechanisms, some of them involving ABA, that enable them to maintain their seeds in a dormant state.
Seed Dormancy May Be Imposed by the Coat or the Embryo During seed maturation, the embryo enters a quiescent phase in response to desiccation. Seed germination can be defined as the resumption of growth of the embryo of the mature seed; it depends on the same environmental con-ditions as vegetative growth does. Water and oxygen must be available, the temperature must be suitable, and there must be no inhibitory substances present.
In many cases a viable (living) seed will not germinate even if all the necessary environmental conditions for growth are satisfied. This phenomenon is termed seed dormancy. Seed dormancy introduces a temporal delay in the germination process that provides additional time for seed dispersal over greater geographic distances. It also maximizes seedling survival by preventing germination under unfavorable conditions. Two types of seed dor-mancy have been recognized: coat-imposed dormancy and embryo dormancy.
Coat-imposed dormancy. Dormancy imposed on the embryo by the seed coat and other enclosing tissues, such as endosperm, pericarp, or extrafloral organs, is known as coat-imposed dormancy. The embryos of such seeds will germinate readily in the presence of water and oxygen once the seed coat and other surrounding tissues have been either removed or damaged. There are five basic mechanisms of coat-imposed dormancy (Bewley and Black 1994): 1. Prevention of water uptake.
2. Mechanical constraint. The first visible sign of germi-nation is typically the radicle breaking through the seed coat. In some cases, however, the seed coat may be too rigid for the radicle to penetrate. For the seeds to germinate, the endosperm cell walls must be weakened by the production of cell wall–degrading enzymes.
3. Interference with gas exchange. Lowered permeability of seed coats to oxygen suggests that the seed coat inhibits germination by limiting the oxygen supply to the embryo.
4. Retention of inhibitors. The seed coat may prevent the escape of inhibitors from the seed.
5. Inhibitor production. Seed coats and pericarps may contain relatively high concentrations of growth inhibitors, including ABA, that can suppress germi-nation of the embryo.
544 Chapter 23 Embryo dormancy. The second type of seed dormancy is embryo dormancy, a dormancy that is intrinsic to the embryo and is not due to any influence of the seed coat or other surrounding tissues. In some cases, embryo dor-mancy can be relieved by amputation of the cotyledons.
Species in which the cotyledons exert an inhibitory effect include European hazel (Corylus avellana) and European ash (Fraxinus excelsior). A fascinating demonstration of the cotyledon’s ability to inhibit growth is found in species (e.g., peach) in which the isolated dormant embryos germinate but grow extremely slowly to form a dwarf plant. If the cotyledons are removed at an early stage of development, however, the plant abruptly shifts to normal growth.
Embryo dormancy is thought to be due to the presence of inhibitors, especially ABA, as well as the absence of growth promoters, such as GA (gibberellic acid). The loss of embryo dormancy is often associated with a sharp drop in the ratio of ABA to GA.
Primary versus secondary seed dormancy. Different types of seed dormancy also can be distinguished on the basis of the timing of dormancy onset rather than the cause of dormancy: • Seeds that are released from the plant in a dormant state are said to exhibit primary dormancy.
• Seeds that are released from the plant in a nondor-mant state, but that become dormant if the conditions for germination are unfavorable, exhibit secondary dormancy. For example, seeds of Avena sativa (oat) can become dormant in the presence of temperatures higher than the maximum for germination, whereas seeds of Phacelia dubia (small-flower scorpionweed) become dormant at temperatures below the mini-mum for germination. The mechanisms of secondary dormancy are poorly understood.
Environmental Factors Control the Release from Seed Dormancy Various external factors release the seed from embryo dor-mancy, and dormant seeds typically respond to more than one of three factors: 1. Afterripening. Many seeds lose their dormancy when their moisture content is reduced to a certain level by drying—a phenomenon known as afterripening.
2. Chilling. Low temperature, or chilling, can release seeds from dormancy. Many seeds require a period of cold (0–10°C) while in a fully hydrated (imbibed) state in order to germinate.
3. Light. Many seeds have a light requirement for ger-mination, which may involve only a brief exposure, as in the case of lettuce, an intermittent treatment (e.g., succulents of the genus Kalanchoe), or even a specific photoperiod involving short or long days.
For further information on environmental factors affecting seed dormancy, see Web Topic 23.5. For a discussion of seed longevity, see Web Topic 23.6.
Seed Dormancy Is Controlled by the Ratio of ABA to GA Mature seeds may be either dormant or nondormant, depending on the species. Nondormant seeds, such as pea, will germinate readily if provided with water only. Dor-mant seeds, on the other hand, fail to germinate in the pres-ence of water, and instead require some additional treat-ment or condition. As we have seen, dormancy may arise from the rigidity or impermeability of the seed coat (coat-imposed dormancy) or from the persistence of the state of arrested development of the embryo. Examples of the lat-ter include seeds that require afterripening, chilling, or light to germinate.
ABA mutants have been extremely useful in demon-strating the role of ABA in seed dormancy. Dormancy of Arabidopsis seeds can be overcome with a period of after-ripening and/or cold treatment. ABA-deficient (aba) mutants of Arabidopsis have been shown to be nondormant at maturity. When reciprocal crosses between aba and wild-type plants were carried out, the seeds exhibited dormancy only when the embryo itself produced the ABA. Neither maternal nor exogenously applied ABA was effective in inducing dormancy in an aba embryo.
On the other hand, maternally derived ABA constitutes the major peak present in seeds and is required for other aspects of seed development—for example, helping sup-press vivipary in midembryogenesis. Thus the two sources of ABA function in different developmental pathways. Dor-mancy is also greatly reduced in seeds from the ABA-insensitive mutants abi1 (ABA-insensitive1), abi2, and abi3, even though these seeds contain higher ABA concentra-tions than those of the wild type throughout development, possibly reflecting feedback regulation of ABA metabolism.
ABA-deficient tomato mutants seem to function in the same way, indicating that the phenomenon is probably a general one. However, other mutants with reduced dor-mancy, but normal ABA levels and sensitivity, point to additional regulators of dormancy.
Although the role of ABA in initiating and maintaining seed dormancy is well established, other hormones con-tribute to the overall effect. For example, in most plants the peak of ABA production in the seed coincides with a decline in the levels of IAA and GA.
An elegant demonstration of the importance of the ratio of ABA to GA in seeds was provided by the genetic screen that led to isolation of the first ABA-deficient mutants of Arabidopsis (Koornneef et al. 1982). Seeds of a GA-deficient mutant that could not germinate in the absence of exoge-nous GA were mutagenized and then grown in the green-house. The seeds produced by these mutagenized plants were then screened for revertants—that is, seeds that had regained their ability to germinate. Abscisic Acid: A Seed Maturation and Antistress Signal 545 Revertants were isolated, and they turned out to be mutants of abscisic acid synthesis. The revertants germi-nated because dormancy had not been induced, so subse-quent synthesis of GA was no longer required to overcome it. This study elegantly illustrates the general principle that the balance of plant hormones is often more critical than are their absolute concentrations in regulating develop-ment. However, ABA and GA exert their effects on seed dormancy at different times, so their antagonistic effects on dormancy do not necessarily reflect a direct interaction.
Recent genetic screens for suppressors of ABA insensi-tivity have identified additional antagonistic interactions between ABA and ethylene or brassinosteroid effects on germination. In addition, many new alleles of ABA-defi-cient or ABA-insensitive4 (abi4) mutants have been identi-fied in screens for altered sensitivity to sugar. These stud-ies show that a complex regulatory web integrates hormonal and nutrient signaling.
ABA Inhibits Precocious Germination and Vivipary When immature embryos are removed from their seeds and placed in culture midway through development before the onset of dormancy, they germinate precociously—that is, without passing through the normal quiescent and/or dormant stage of development. ABA added to the culture medium inhibits precocious germination. This result, in combination with the fact that the level of endogenous ABA is high during mid- to late seed development, sug-gests that ABA is the natural constraint that keeps devel-oping embryos in their embryogenic state.
Further evidence for the role of ABA in preventing pre-cocious germination has been provided by genetic studies of vivipary. The tendency toward vivipary, also known as preharvest sprouting, is a varietal characteristic in grain crops that is favored by wet weather. In maize, several viviparous (vp) mutants have been selected in which the embryos ger-minate directly on the cob while still attached to the plant.
Several of these mutants are ABA deficient (vp2, vp5, vp7, and vp14) (see Figure 23.3); one is ABA insensitive (vp1).
Vivipary in the ABA-deficient mutants can be partially pre-vented by treatment with exogenous ABA. Vivipary in maize also requires synthesis of GA early in embryogene-sis as a positive signal; double mutants deficient in both GA and ABA do not exhibit vivipary (White et al. 2000).
In contrast to the maize mutants, single-gene mutants of Arabidopsis (aba1, aba3, abi1, and abi3) fail to exhibit vivip-ary, although they are nondormant. The lack of vivipary might reflect a lack of moisture because such seeds will ger-minate within the fruits under conditions of high relative humidity. However, other Arabidopsis mutants with a nor-mal ABA response and only moderately reduced ABA lev-els (e.g., fusca3, which belongs to a class of mutants1 defec-tive in regulating the transition from embryogenesis to ger-mination) exhibit some vivipary even at low humidities.
Furthermore, double mutants combining either defects in ABA biosynthesis or ABA response with the fusca3 muta-tion have a high frequency of vivipary (Nambara et al.
2000), suggesting that redundant control mechanisms sup-press vivipary in Arabidopsis.
ABA Accumulates in Dormant Buds In woody species, dormancy is an important adaptive fea-ture in cold climates. When a tree is exposed to very low temperatures in winter, it protects its meristems with bud scales and temporarily stops bud growth. This response to low temperatures requires a sensory mechanism that detects the environmental changes (sensory signals), and a control system that transduces the sensory signals and triggers the developmental processes leading to bud dormancy.
ABA was originally suggested as the dormancy-induc-ing hormone because it accumulates in dormant buds and decreases after the tissue is exposed to low temperatures.
However, later studies showed that the ABA content of buds does not always correlate with the degree of dor-mancy. As we saw in the case of seed dormancy, this appar-ent discrepancy could reflect interactions between ABA and other hormones as part of a process in which bud dor-mancy and growth are regulated by the balance between bud growth inhibitors, such as ABA, and growth-inducing substances, such as cytokinins and gibberellins.
Although much progress has been achieved in eluci-dating the role of ABA in seed dormancy by the use of ABA-deficient mutants, progress on the role of ABA in bud dormancy, which applies mainly to woody perennials, has lagged because of the lack of a convenient genetic system.
This discrepancy illustrates the tremendous contribution that genetics and molecular biology have made to plant physiology, and it underscores the need for extending such approaches to woody species. Analyses of traits such as dormancy are complicated by the fact that they are often controlled by the combined action of several genes, resulting in a gradation of pheno-types referred to as quantitative traits. Recent genetic map-ping studies suggest that homologs of ABI1 may regulate bud dormancy in poplar trees. For a description of such studies, see Web Topic 23.7.
ABA Inhibits GA-Induced Enzyme Production ABA inhibits the synthesis of hydrolytic enzymes that are essential for the breakdown of storage reserves in seeds.
For example, GA stimulates the aleurone layer of cereal grains to produce α-amylase and other hydrolytic enzymes that break down stored resources in the endosperm during germination (see Chapter 20). ABA inhibits this GA-depen-dent enzyme synthesis by inhibiting the transcription of α-amylase mRNA. ABA exerts this inhibitory effect via at least two mechanisms: 546 Chapter 23 1 Named after the Latin term for the reddish brown color of the embryos.
1. VP1, a protein originally identified as an activator of ABA-induced gene expression, acts as a transcrip-tional repressor of some GA-regulated genes (Hoecker et al. 1995).
2. ABA represses the GA-induced expression of GA-MYB, a transcription factor that mediates the GA induction of α-amylase expression (Gomez-Cadenas et al. 2001).
ABA Closes Stomata in Response to Water Stress Elucidation of the roles of ABA in freezing, salt, and water stress (see Chapter 25) led to the characterization of ABA as a stress hormone. As noted earlier, ABA concentrations in leaves can increase up to 50 times under drought con-ditions—the most dramatic change in concentration reported for any hormone in response to an environmen-tal signal. Redistribution or biosynthesis of ABA is very effective in causing stomatal closure, and its accumulation in stressed leaves plays an important role in the reduction of water loss by transpiration under water stress condi-tions (Figure 23.5).
Stomatal closing can also be caused by ABA synthesized in the roots and exported to the shoot. Mutants that lack the ability to produce ABA exhibit permanent wilting and are called wilty mutants because of their inability to close their stomata. Application of exogenous ABA to such mutants causes stomatal closure and a restoration of turgor pressure.
ABA Promotes Root Growth and Inhibits Shoot Growth at Low Water Potentials ABA has different effects on the growth of roots and shoots, and the effects are strongly dependent on the water status of the plant. Figure 23.6 compares the growth of shoots and roots of maize seedlings grown under either abundant water conditions (high water potential) or dehydrating conditions (low water potential). Two types of seedlings were used: (1) wild-type seedlings with normal ABA lev-els and (2) an ABA-deficient, viviparous mutant.
When the water supply is ample (high water potential), shoot growth is greater in the wild-type plant (normal endogenous ABA levels) than in the ABA-deficient mutant.
The reduced shoot growth in the ABA-deficient mutant could be due in part to excessive water loss from the leaves.
In maize and tomato, however, the stunted shoot growth of ABA-deficient plants at high water potentials seems to be due to the overproduction of ethylene, which is normally inhibited by endogenous ABA (Sharp et al. 2000). This find-ing suggests that endogenous ABA promotes shoot growth in well-watered plants by suppressing ethylene production.
When water is limiting (i.e., at low water potentials), the opposite occurs: Shoot growth is greater in the ABA-defi-cient mutant than in the wild type. Thus, endogenous ABA acts as a signal to reduce shoot growth only under water stress conditions.
Now let’s examine how ABA affects roots. When water is abundant, root growth is slightly greater in the wild type (normal endogenous ABA) than in the ABA-deficient mutant, similar to growth in shoots. Therefore, at high water potentials (when the total ABA levels are low), endogenous ABA exerts a slight positive effect on the growth of both roots and shoots.
Under dehydrating conditions, however, the growth of the roots is much higher in the wild type than in the ABA-deficient mutant, although growth is still inhibited relative to root growth of either genotype when water is abundant.
In this case, endogenous ABA promotes root growth, appar-ently by inhibiting ethylene production during water stress (Spollen et al. 2000).
To summarize, under dehydrating conditons, when ABA levels are high, the endogenous hormone exerts a strong positive effect on root growth by suppressing ethylene pro-duction, and a slight negative effect on shoot growth. The overall effect is a dramatic increase in the root:shoot ratio at low water potentials (see Figure 23.6C), which, along with the effect of ABA on stomatal closure, helps the plant cope with water stress. For another example of the role of ABA in the response to dehydration, see Web Essay 1.
ABA Promotes Leaf Senescence Independently of Ethylene Abscisic acid was originally isolated as an abscission-caus-ing factor. However, it has since become evident that ABA stimulates abscission of organs in only a few species and Abscisic Acid: A Seed Maturation and Antistress Signal 547 0 70 35 20 –0.8 –1.6 Stomatal resistance (s cm–1) Leaf water potential (MPa) 2 0 4 6 8 0 0 Time (days) 4 8 ABA (ng cm–2) Water potential decreases as soil dries out Water provided Water withheld Stomatal resistance decreases (stomata open as soil rehydrates) ABA content FIGURE 23.5 Changes in water potential, stomatal resis-tance (the inverse of stomatal conductance), and ABA con-tent in maize in response to water stress. As the soil dried out, the water potential of the leaf decreased, and the ABA content and stomatal resistance increased. The process was reversed by rewatering. (After Beardsell and Cohen 1975.) that the primary hormone causing abscission is ethylene.
On the other hand, ABA is clearly involved in leaf senes-cence, and through its promotion of senescence it might indirectly increase ethylene formation and stimulate abscis-sion. (For more discussion on the relationship between ABA and ethylene, see Web Topic 23.8.) Leaf senescence has been studied extensively, and the anatomical, physiological, and biochemical changes that take place during this process were described in Chapter 16. Leaf segments senesce faster in darkness than in light, and they turn yellow as a result of chlorophyll breakdown. In addition, the breakdown of proteins and nucleic acids is increased by the stimulation of several hydrolases. ABAgreatly accelerates the senescence of both leaf segments and attached leaves.
CELLULAR AND MOLECULAR MODES OF ABA ACTION ABA is involved in short-term physiological effects (e.g., stomatal closure), as well as long-term developmental processes (e.g., seed maturation). Rapid physiological responses frequently involve alterations in the fluxes of ions across membranes and may involve some gene regu-lation as well, and long-term processes inevitably involve major changes in the pattern of gene expression.
Signal transduction pathways, which amplify the pri-mary signal generated when the hormone binds to its receptor, are required for both the short-term and the long-term effects of ABA. Genetic studies have shown that many conserved signaling components regulate both short- and long-term responses, indicating that they share common signaling mechanisms. In this section we will describe what is known about the mechanism of ABA action at the cellular and molecular levels.
ABA Is Perceived Both Extracellularly and Intracellularly Although ABA has been shown to interact directly with phospholipids, it is widely assumed that the ABA receptor is a protein. To date, however, the protein receptor for ABA has not been identified. Experiments have been performed to determine whether the hormone must enter the cell to be effective, or whether it can act externally by binding to a receptor located on the outer surface of the plasma mem-brane. The results so far suggest multiple sites of perception.
Some experiments point to a receptor on the outer sur-face of the cell. For example, microinjected ABA fails to alter stomatal opening in the spiderwort Commelina, or to inhibit GA-induced α-amylase synthesis in barley aleurone protoplasts (Anderson et al. 1994; Gilroy and Jones 1994).
Furthermore, impermeant ABA–protein conjugates have been shown to activate both ion channel activity and gene expression (Schultz and Quatrano 1997; Jeannette et al.
1999).
Other experiments, however, support an intracellular location for the ABA receptor: 548 Chapter 23 10 60 50 40 30 20 10 0 20 30 40 50 Hours after transplanting Shoot length increase (mm) (A) Shoot 30 0 30 60 90 120 150 60 90 120 Hours after transplanting Root length increase (mm) (B) Root High Yw wild type High Yw wild type High Yw mutant High Yw mutant Low Yw mutant Low Yw wild type Low Yw wild type Low Yw mutant 15 0 1.0 2.0 3.0 4.0 5.0 30 45 60 Hours after transplanting Root:shoot ratio (C) Root:shoot ratio Water stress conditions (Low Yw) Wild type (+ ABA) ABA-deficient mutant FIGURE 23.6 Comparison of the growth of the shoots (A) and roots (B) of normal versus ABA-deficient (viviparous) maize plants growing in vermiculite maintained either at high water potential (–0.03 MPa) or at low water potential (–0.3 Mpa in A and –1.6 MPa in B). Water stress (low water potential) depresses the growth of both shoots and roots compared to the controls. (C) Note that under water stress conditions (low Yw), the ratio of root growth to shoot growth is much higher when ABA is present (i.e., in the wild type) than when it is absent (in the mutant). (From Saab et al. 1990.) • Extracellular application of ABA was nearly twice as effective at inhibiting stomatal opening at pH 6.15, when it is fully protonated and readily taken up by guard cells, versus at pH 8, when it is largely dissoci-ated to the anionic form that does not readily cross membranes (Anderson et al. 1994).
• ABA supplied directly and continuously to the cytosol via a patch pipette inhibited K+ in channels, which are required for stomatal opening (Schwartz et al. 1994).
• Microinjection of an inactive “caged” form of ABA into guard cells of Commelina resulted in stomatal clo-sure after the stomata were treated briefly with UV irradiation to activate the hormone—that is, release it from its molecular cage (Figure 23.7) (Allan et al.
1994). Control guard cells injected with a nonpho-tolyzable form of the caged ABA did not close after UV irradiation.
Taken together, these results indicate that extracellular perception of ABA can prevent stomatal opening and reg-ulate gene expression, and intracellular ABA can both induce stomatal closure and inhibit the K+ in current required for opening. Thus there appear to be both extra-cellular and intracellular ABA receptors. However, they have yet to be identified or localized.
ABA Increases Cytosolic Ca2+, Raises Cytosolic pH, and Depolarizes the Membrane As discussed in Chapter 18, stomatal closure is driven by a reduction in guard cell turgor pressure caused by a mas-sive long-term efflux of K+ and anions from the cell. Dur-ing the subsequent shrinkage of the cell due to water loss, the surface area of the plasma membrane may contract by as much as 50%. Where does the extra membrane go? The answer seems to be that it is taken up as small vesicles by endocytosis—a process that also involves reorganization of the actin cytoskeleton. However, the first changes detected after exposure of guard cells to ABA are transient mem-brane depolarization caused by the net influx of positive charge, and transient increases in the cytosolic calcium con-centration (Figure 23.8).
ABAstimulates elevations in the concentration of cytoso-lic Ca2+ by inducing both influx through plasma membrane channels and release of calcium into the cytosol from inter-nal compartments, such as the central vacuole (Schroeder et al. 2001). Stimulation of influx occurs via a pathway that uses reactive oxygen species (ROS), such as hydrogen peroxide (H2O2) or superoxide (O2 •–), as secondary messengers lead-ing to plasma membrane channel activation (Pei et al. 2000).
Calcium release from intracellular stores can be induced by a variety of second messengers, including inositol 1,4,5-trisphosphate (IP3), cyclic ADP-ribose (cADPR), and self-Abscisic Acid: A Seed Maturation and Antistress Signal 549 O OH CO2CH CH3 O2N O OH H3C CH3 CH3 CH3 COOH CH HO + CH3 O2N UV CH3 CH3 CH3 H3C Photolyzable caged ABA (S)-cis-ABA (A) (B) 10 Time (min) Aperture (µm) 20 30 40 1 0 2 3 4 5 6 7 30 s UV flash Photolyzable caged ABA Nonphotolyzable caged ABA Uninjected FIGURE 23.7 Stomatal closure induced by UV photolysis of caged ABA in the guard cell cytoplasm. Single guard cells in stomatal complexes of Commelina were microinjected with caged ABA. (A) Photolysis reaction induced by UV irradia-tion. (B) The stomatal apertures recorded before and after a 30-second exposure of the cells to UV. (C, D) Light micro-graphs of the same stomatal complex in which the right-hand guard cell was loaded with the photolyzable cages ABA 10 minutes before UV photolysis (C) and 30 minutes after pho-tolysis (D). (A and B from Allan et al. 1994; C and D courtesy of A. Allan, from Allan et al. 1994; © American Society of Plant Biologists, reprinted with permission.) (C) (D) amplifying (calcium-induced) Ca2+ release. Recent studies have shown that ABA stimulates nitric oxide (NO) synthesis in guard cells, which induces stomatal closure in a cADPR-dependent manner, indicating that NO is an even earlier secondary messenger in this response pathway (Neill et al. 2002) (for background on NO, see Chapter 14 on the Web site). The combination of calcium influx and the release of cal-cium from internal stores raises the cytosolic calcium con-centration from 50 to 350 nM to as high as 1100 nM (1.1 mM) (Figure 23.9) (Mansfield and McAinsh, in Davies 1995). This increase is sufficient to cause stomatal closure, as demonstrated by the following experiment.
As in the experiment described earlier, cal-cium was microinjected into guard cells in a caged form that could be hydrolyzed by a pulse of UV light. This method allowed the investi-gators to control both the concentration of free calcium and the time of release to the cytosol. At cytosolic concentrations of 600 nM or more, release of calcium from its cage triggered sto-matal closure (Gilroy et al. 1990). This level of intracellular calcium is well within the concen-tration range observed after ABA treatment.
In the preceding studies, intracellular free calcium was measured by the use of microin-jected calcium-sensitive ratiometric fluorescent dyes2, such as fura-2 or indo-1. However, microinjections of fluorescent dyes into single plant cells are difficult and often result in cell death. Success rates of viable injections into Arabidopsis guard cells can be less than 3%. In contrast, transgenic plants expressing the gene for the calcium indicator protein yellow cameleon make it possible to monitor several fluo-rescing cells in parallel, without the need for invasive injec-tions (Allen et al. 1999b) (see Web Topic 23.9). Such studies have demonstrated that the cytosolic Ca2+ concentration oscillates with distinct periodicities, depending on the sig-nals received (Figure 23.10).
550 Chapter 23 Size of stomatal opening 8 9 10 11 12 13 10–5 10–4 10–3 Stomatal aperture (µm) Cytosolic [Ca 2+] (mol m–3) ABA ABA 0 5 10 15 20 Time (min) Cytostolic Ca2+ concentration after addition of ABA Control FIGURE 23.9 Time course of the ABA-induced increase in guard cell cytosolic Ca2+ concentration (upper panel) and ABA-induced stomatal aperture (lower panel). (From Mansfield and McAinsh 1995.) 5 minutes The increases in cytoplasmic Ca2+ roughly coincide with the membrane depolarization events.
Inward positive currents (membrane depolarization events) Increases in cytosolic Ca2+ 2 µM –20 Picoamps +20 0 Calcium concentration Current [Ca2+] ABA ABA FIGURE 23.8 Simultaneous measurements of ABA-induced inward positive currents and ABA-induced increases in cytosolic Ca2+ concentrations in a guard cell of Vicia faba (broad bean). The current was measured by the patch clamp technique; calcium was measured by use of a fluo-rescent indicator dye. ABA was added to the system at the arrow in each case. (From Schroeder and Hagiwara 1990.) 2 Ratiometric fluorescent dyes undergo a shift in their excitation and emission spectra when they bind calcium. On the basis of property, one can determine the intracellular concentra-tions of both forms of the dye (with and with-out bound calcium) by exciting them with the appropriate two wavelengths. The ratio of the two emissions provides a measure of the cal-cium concentration that is independent of dye concentration.
These results support the hypothesis that an increase in cytosolic calcium, partly derived from intracellular stores, is responsible for ABA-induced stomatal closure. However, the growth hormone auxin can induce stomatal opening, and this auxin-induced stomatal opening, like ABA-induced stomatal closure, is accompanied by increases in cytosolic cal-cium. This finding suggests that the detailed characteristics of the location and periodicity of Ca2+ oscillations (the “Ca2+ signature”), rather than the overall concentration of cytoso-lic calcium, determine the cellular response.
In addition to increasing the cytosolic calcium concen-tration, ABA causes an alkalinization of the cytosol from about pH 7.67 to pH 7.94. The increase in cytosolic pH has been shown to activate the K+ efflux channels on the plasma membrane apparently by increasing the number of channels available for activation (see Chapter 6).
ABA Activation of Slow Anion Channels Causes Long-Term Membrane Depolarization The rapid, transient depolarizations induced by ABA are insufficient to open the K+ efflux channels, which require long-term membrane depolarization in order to open.
However, long-term depolarizations in response to ABA have been demonstrated. According to a widely accepted model, long-term membrane depolarization is triggered by two factors: (1) an ABA-induced transient depolariza-tion of the plasma membrane, coupled with (2) an increase in cytosolic calcium. Both of these conditions are required to open calcium-activated slow (S-type) anion channels on the plasma membrane (Schroeder and Hagiwara 1990) (see Chapter 6). ABA has been shown to activate slow anion channels in guard cells (Grabov et al. 1997; Pei et al. 1997).
The prolonged opening of these slow anion channels permits large quantities of Cl– and malate2– ions to escape from the cell, moving down their electrochemical gradients.
(The inside of the cell is negatively charged, thus pushing Cl– and malate2– out of the cell, and the outside has lower Cl– and malate2– concentrations than the interior.) The out-ward flow of negatively charged Cl– and malate2– ions gen-erated in this way strongly depolarizes the membrane, trig-gering the voltage-gated K+ efflux channels to open.
In support of this model, inhibitors that block slow anion channels, such as 5-nitro-2,3-phenylpropy-laminobenzoic acid (NPPB), also block ABA-induced stom-atal closing. Inhibitors of the rapid (R-type) anion channels, such as 4,4′-diisothiocyanatostilbene-2,2′-disulfonic acid (DIDS), have no effect on ABA-induced stomatal closing (Schwartz et al. 1995).
Another factor that can contribute to membrane depo-larization is inhibition of the plasma membrane H+-ATPase. ABA inhibits blue light–stimulated proton pump-ing by guard cell protoplasts (Figure 23.11), consistent with the model that the depolarization of the plasma membrane by ABA is partially caused by a decrease in the activity of the plasma membrane H+-ATPase. However, ABA does not inhibit the proton pump directly.
In Vicia faba (broad bean), at least, the plasma membrane H+-ATPase of the leaves is strongly inhibited by calcium.
A calcium concentration of 0.3 µM blocks 50% of the activ-ity of H+-ATPase, and 1 µM calcium blocks the enzyme completely (Kinoshita et al. 1995). It appears that two fac-Abscisic Acid: A Seed Maturation and Antistress Signal 551 1.1 1.2 1.3 1.4 1.0 535:480 nm ratio 5 min (A) ABA Time (minutes) FIGURE 23.10 ABA-induced calcium oscillations in Arabidopsis guard cells express-ing yellow cameleon, a calcium indicator protein dye. (A) Oscillations elicited by ABA are indicated by increases in the ratio of flourescence emission at 535 and 480 nm. (B) Pseudo colored images of fluorescence in Arabidopsis guard cells, where blue, green, yellow and red represent increasing cytosolic calcium concentration.
(From Schroeder et al. 2001.) (B) tors contribute to ABA inhibition of the plasma membrane proton pump: an increase in the cytosolic Ca2+ concentra-tion, and alkalinization of the cytosol.
In addition to causing stomatal closure, ABA prevents light-induced stomatal opening. In this case ABA acts by inhibiting the inward K+ channels, which are open when the membrane is hyperpolarized by the proton pump (see Chapters 6 and 18). Inhibition of the inward K+ channels is mediated by the ABA-induced increase in cytosolic calcium concentration. Thus calcium and pH affect guard cell plasma membrane channels in two ways: 1. They prevent stomatal opening by inhibiting inward K+ channels and plasma membrane proton pumps.
2. They promote stomatal closing by activating outward anion channels, thus leading to activation of K+ efflux channels.
ABA Stimulates Phospholipid Metabolism As discussed previously, much evidence supports a role for calcium both in the promotion of stomatal closing and in the inhibition of stomatal opening. According to the classic calcium-dependent signal transduction pathway of animal cells, IP3 is released, along with diacylglycerol (DAG), when phospholipase C is activated by a G-protein in the plasma membrane (see Chapter 14 on the web site). Does ABA use the same pathway when it induces stomatal closure?
In agreement with this model, ABA has been shown to stimulate phosphoinositide metabolism in Vicia faba (broad bean) guard cells. To detect the effect of ABA on IP3 release, it was necessary to include Li+ in the incubation medium as an inhibitor of inositol phosphatase, which rapidly removes phosphate groups from IP3. Under these conditions, a 90% ABA-induced increase in the level of IP3 was measured within 10 seconds of hor-mone treatment (Lee et al. 1996). Recent studies in Arabidopsis using antisense DNA to block expression of an ABA-induced phospholipase C have shown that this enzyme is required for ABA effects on germination, growth, and gene expression (Sanchez and Chua 2001).
Heterotrimeric G-proteins may medi-ate the effects of ABA on stomatal move-ments. For example, in Vicia faba most studies have shown that G-protein acti-vators, such as GTPγS, can inhibit the activity of the inward K+ channels. Con-sistent with the inhibitor results, ABA failed to inhibit inward K+ channels or light-induced stomatal opening in an Ara-bidopsis mutant with a defective Gα sub-unit (Wang et al. 2001). However, ABA still promoted stomatal closure in this mutant, indicating that inhibition of opening and promo-tion of closing take two distinct paths to the same end point—that is, closed stomata.
Other potential second messengers mediating the ABA response, such as phosphatidic acid and myo-inositol-hexa-phosphate (IP6) have been identified, but the relationship of these compounds to IP3 and Ca2+ signaling is not yet known.
All of these experiments indicate that stomatal guard cells respond to multiple signals, possibly involving multiple receptors and overlapping signal transduction pathways.
Protein Kinases and Phosphatases Participate in ABA Action Nearly all biological signaling systems involve protein phosphorylation and dephosphorylation reactions at some step in the pathway. Thus we can expect that signal trans-duction in guard cells, with their multiple sensory inputs, involves protein kinases and phosphatases. Artificially rais-ing the ATP concentration inside guard cells by allowing the cytoplasm to equilibrate with the solution inside a patch pipette (see Chapter 6) strongly activates the slow anion channels.
This activation of the slow anion channels by ATP is abolished by the inclusion of protein kinase inhibitors in the patch pipette solution (Schmidt et al. 1995). Protein kinase inhibitors also block ABA-induced stomatal closing.
In contrast, lowering the concentration of ATP in the cytosol inactivates the slow anion channels. Additional experiments confirm that this inactivation is due to the presence of protein phosphatases, which remove phos-phate groups that are covalently attached to proteins. In 552 Chapter 23 7.5 Time (minutes) 15 30 0 Increasing pH 5 µM ABA 50 µM ABA Control Blue light 1. A pulse of blue light activates the plasma membrane H+-ATPase, which pumps protons into the external medium and lowers the pH.
2. Addition of ABA to the medium inhibits the acidification by 40%.
3. These results demonstrate that ABA induces changes in the cell that inhibit the plasma membrane H+-ATPase. FIGURE 23.11 ABA inhibition of blue light–stimulated proton pumping by guard cell protoplasts. A suspension of guard cell protoplasts was incubated under red-light irradiation, and the pH of the suspension medium was mon-itored with a pH electrode. The starting pH was the same in all cases (the curves are displaced for ease of viewing). (After Shimazaki et al. 1986.) view of these results, it appears that protein phosphoryla-tion and dephosphorylation play important roles in the ABA signal transduction pathway in guard cells.
There is now direct evidence for an ABA-activated pro-tein kinase (AAPK) in Vicia faba guard cells (Li and Ass-mann 1996; Mori and Muto 1997). AAPK activity appears to be required for ABA activation of S-type anion currents and stomatal closing. This enzyme is an autophosphory-lating protein kinase that either forms part of a Ca2+-inde-pendent signal transduction pathway for ABA, or acts far-ther downstream of calcium-induced signaling events. (The presence of both Ca2+-dependent and Ca2+-independent pathways for ABA action will be discussed shortly.) In addition, two Ca2+-dependent protein kinases, as well as MAP kinases, have been implicated in the ABA regulation of stomatal aperture.
The analysis of ABA-insensitive mutants has begun to help in the identification of genes coding for components of the signal transduction pathway. The Arabidopsis abi1-1 and abi2-1 mutations result in insensitivity to ABA in both seeds and adult plants. These abi mutants display pheno-types consistent with a defect in ABA signaling, including reduced seed dormancy, a tendency to wilt (due to improper regulation of stomatal aperture), and decreased expression of various ABA-inducible genes. The defects in stomatal response include the ABA insen-sitivity of S-type anion channels—both inward and out-ward K+ channels—and actin reorganization. Although nonresponsive to ABA, the mutant stomata will close when exposed to high external concentrations of Ca2+, suggest-ing that they are defective in their ability to initiate Ca2+ signaling. Consistent with this finding, ABA does not induce Ca2+ oscillations in these mutants (Allen et al.
1999a).
ABI Protein Phosphatases Are Negative Regulators of the ABA Response The Arabidopsis ABI1 and ABI2 genes have been cloned and identified as encoding two closely related serine/threonine protein phosphatases. This finding suggests that ABI1 and ABI2 regulate the activity of target proteins by dephos-phorylating specific serine or threonine residues, but none of their substrates have been definitively identified.
Because the abi1-1 and abi2-1 mutations result in decreased response to ABA, it was initially assumed that the wild-type genes promote the ABA response. However, the original mutations turned out to be dominant rather than recessive, and recent studies have shown that they act as “dominant negatives”; that is, one defective copy of the gene is sufficient to disrupt the ABA response by poison-ing the activity of the functional gene products from the remaining wild-type allele.
Subsequently, recessive mutants of ABI1 were obtained that exhibited a simple loss of ABI1 activity. These recessive mutants of ABI1 actually showed increased ABA sensitiv-ity (Gosti et al. 1999). Furthermore, overproducing the wild-type gene products or their homologs (closely related proteins) by reintroducing the gene into plants, under con-trol of a highly expressed promoter, confers reduced ABA sensitivity (Sheen 1998). Thus the wild-type function of these protein phosphatases is to inhibit the ABA response.
ABA Signaling Also Involves Ca2+-Independent Pathways Although an ABA-induced increase in cytosolic calcium concentration is a key feature of the current model for ABA-induced guard cell closure, ABA is able to induce stomatal closure even in guard cells that show no increase in cytosolic calcium (Allan et al. 1994). In other words, ABA seems to be able to act via one or more calcium-indepen-dent pathways.
In addition to calcium, ABA can utilize cytosolic pH as a signaling intermediate. As previously discussed, a rise in cytosolic pH can lead to the activation of outward K+ chan-nels, and one effect of the abi1 mutation is to render these K+ channels insensitive to pH.
Such redundancy in the signal transduction pathways explains how guard cells are able to integrate a wide range of hormonal and environmental stimuli that affect stomatal aperture, and such redundancy is probably not unique to guard cells.
A simplified general model for ABA action in stomatal guard cells is shown in Figure 23.12. For clarity, only the cell surface receptors are shown.
ABA Regulation of Gene Expression Is Mediated by Transcription Factors Downstream of the early ABA signal transduction processes already discussed, ABA causes changes in gene expression. ABA has been shown to regulate the expression of numerous genes during seed maturation and under cer-tain stress conditions, such as heat shock, adaptation to low temperatures, and salt tolerance (Rock 2000). The ABA-and stress-induced genes are presumed to contribute to adaptive aspects of induced tolerance (see Chapter 25).
They include genes encoding proteases, chaperonins, pro-teins similar to LEA proteins, enzymes of sugar or other compatible solute3 metabolism, ion and water channel pro-teins, enzymes that detoxify active oxygen species, and reg-ulatory proteins such as transcription factors and protein kinases.
In a few cases, stimulation of transcription by ABA has been demonstrated directly. Gene activation by ABA is mediated by transcription factors. Four main classes of reg-ulatory sequences conferring ABA inducibility have been identified, and proteins that bind to these sequences have Abscisic Acid: A Seed Maturation and Antistress Signal 553 3 An organic compound that can serve as a nontoxic, osmot-ically active solute in the cytosol; such compounds usually accumulate during water or salt stress (see Chapter 25).
been characterized (see Web Topic 23.10). Under stress conditions, induction of gene expression may be ABA dependent or ABA independent, and additional transcrip-tion factors have been identified that specifically mediate responses to cold, drought, or salt (see Chapter 25).
A few DNA elements have been identified that are involved in transcriptional repression by ABA. The best-characterized of these are the gibberellin response elements (GAREs) that mediate the gibberellin-inducible, ABA-repressible expression of the barley α-amylase gene (see Chapter 20).
Four transcription factors involved in ABA gene acti-vation in maturing seeds have been identified by genetic means; mutations in the genes encoding any of these pro-teins reduce seed ABA responsiveness. The maize VP1 (VIVIPAROUS-1) and Arabidopsis ABI3 (ABA-INSENSI-TIVE3) genes encode highly similar proteins, and the ABI4 and ABI5 genes encode members of two other transcrip-tion factor families. VP1/ABI3, and ABI4 are members of gene families found only in plants. In contrast, ABI5 is a member of the basic leucine zipper (bZIP) family, whose members are present in all eukaryotes (Finkelstein and Lynch 2000). Additional members of the ABI5 subfamily have been identified by nongenetic means and are also correlated with ABA-, embryonic-, drought-, or salt stress–induced gene expression. Characterization of vp1, abi4, and abi5 mutants has shown that each of these genes can either activate or repress transcription, depending on the target gene. Because the promoter of any given gene contains binding sites for a variety of regulators, it is likely that these transcription fac-tors act in complexes made up of varying combinations of regulators, whose composition is determined by the com-bination of available regulators and binding sites.
To date, the protein ABI3/VP1 has been shown to inter-act physically with a variety of proteins, including ABI5 and its rice homolog (TRAB1). ABI5 also forms homodimers and heterodimers with other bZIP family members. There is additional evidence for indirect interactions that may be mediated by 14-3-3 proteins, a class of acidic proteins that dimerize and facilitate protein–protein interactions in a vari-ety of signaling, transport, and enzymatic functions (see 554 Chapter 23 ATP cADPR, IP3 ADP + Pi ABA 2 4 6 8 9 5 7 1 ABA ABA 1 3 ABA PLC ROS (H2O2, O2•–) Ca2+ Ca2+ Ca2+ Ca2+ Ca2+ Ca2+ Ca2+ Ca2+ K+ H+ H+ K+ K+ K+ K+ Cl– Cl– Cl– Cl– Vacuole Vacuole pH increase 1. ABA binds to its receptors.
2. ABA-binding induces the formation of reactive oxygen species, which activate plasma membrane Ca2+ channels.
3. ABA increases the levels of cyclic ADP-ribose and IP3, which activate additional calcium channels on the tonoplast.
4. The influx of calcium initiates intracellular calcium oscillations and promotes the further release of calcium from vacuoles.
5. The rise in intracellular calcium blocks K+ in channels.
6. The rise in intracellular calcium promotes the opening if Cl– out (anion) channels on the plasma membrane, causing membrane depolarization.
7. The plasma membrane proton pump is inhibited by the ABA-induced increase in cytostolic calcium and a rise in intracellular pH, further depolarizing the membrane.
8. Membrane depolarization activates K+ out channels.
9. K+ and anions to be released across the plasma membrane are first released from vacuoles into the cytosol.
ROS pathway IP3, cADPR pathways FIGURE 23.12 Simplified model for ABA signaling in stomatal guard cells. The net effect is the loss of potassium and its anion (Cl– or malate2–) from the cell. (R = receptor; ROS = reactive oxygen species; cADPR = cyclic ADP-ribose; G-protein = GTP-binding protein; PLC = phospholipiase C.) Web Topic 23.11). These studies demonstrate the capacity for specific binding among a variety of transcription factors predicted to interact as components of regulatory com-plexes involved in ABA-induced gene expression.
Other Negative Regulators of the ABA Response Have Been Identified As described already, negative regulators of the ABA response (protein phosphatases) have been identified by isolation of dominant negative mutants such as abi1 and abi2 that result in ABA-insensitive phenotypes (analogous to the dominant negative effects of the ethylene receptor mutant etr1; see Chapter 22).
Other negative regulators have been identified through isolation of mutants exhibiting enhanced responses to ABA. Mutants showing increased sensitivity to ABA dur-ing germination include era (enhanced response to ABA) and abh (ABA hypersensitive) (Cutler et al. 1996; Hugou-vieux et al. in press). The era and abh mutants both confer ABA hypersensitivity in both stomatal closing and germi-nation, making these mutants resistant to wilting and mildly drought tolerant.
Farnesyl transferase. The ERA1 gene was cloned, and its protein product was identified as a subunit of the enzyme farnesyl transferase. Farnesyl transferases catalyze attach-ment of the isoprenoid intermediate farnesyl diphosphate (see Chapter 13) to proteins that contain a specific signal sequence of amino acids. Many proteins that have been shown to participate in signal transduction are farnesylated.
Farnesylated proteins are anchored to the membrane via hydrophobic interactions between the farnesyl group and the membrane lipids (see Figure 1.6). The identification of ERA1 as part of farnesyl transferase suggests that a protein that normally suppresses the ABA response requires farne-sylation and is possibly anchored to the membrane.
mRNA processing. ABH1 encodes an mRNA 5′ cap–bind-ing protein that may be involved in mRNA processing of negative regulators of ABA signaling. (Recall that eukary-otic messenger RNAs have a “cap” consisting of methy-lated guanosine at the 5′ end.) Comparison of transcript accumulation in wild-type and abh1 plants showed a small number of misexpressed genes in the mutant, including some encoding possible signaling molecules.
Ethylene insensitivity. ERA3 was found to be allelic to a previously identified ethylene signaling locus, ETHYLENE-INSENSITIVE 2 (EIN2) (Ghassemian et al. 2000) (see Chap-ter 22). In addition to displaying defects in ABA and ethyl-ene responses, mutations in this gene result in defects in the responses to auxin, jasmonic acid, and stress. This gene encodes a membrane-bound protein that appears to repre-sent a point of “cross-talk”—i.e., a common signaling inter-mediate—mediating the responses to many different signals.
IP3 catabolism. Other screens have identified ABA sig-naling mutants on the basis of incorrect expression of reporter genes controlled by ABA-responsive promoters.
Although the defects in some of these mutants are limited to gene expression, others affect plant growth responses.
One such mutant, termed fiery (fry) to reflect the intensity of light emission by its ABA/stress-responsive luciferase reporter, is also hypersensitive to ABA and stress inhibition of germination and growth. The FIERY gene encodes an enzyme required for IP3 catabolism (Xiong et al. 2001). The mutant phenotype demonstrates that the ability to attenu-ate, as well as induce, stress signaling is important for suc-cessful induction of stress tolerance.
Similar to the signaling mechanisms documented for other plant hormones, ABA signaling involves the coordi-nated action of positive and negative regulators affecting processes as diverse as transcription, RNA processing, pro-tein phosphorylation or farnesylation, and metabolism of secondary messengers. As the signaling components are identified, and often are found to function in responses to multiple signals, the next challenge is to determine how they can lead to ABA-specific responses.
SUMMARY Abscisic acid plays major roles in seed and bud dormancy, as well as responses to water stress. ABA is a 15-carbon terpenoid compound derived from the terminal portion of carotenoids. ABA in tissues can be measured by bioassays based on growth, germination, or stomatal closure. Gas chromatography, HPLC, and immunoassays are the most reliable and accurate methods available for measuring ABA levels.
ABA is produced by cleavage of a 40-carbon carotenoid precursor that is synthesized from isopentenyl diphosphate via the plastid terpenoid pathway. ABA is inactivated by both oxidative degradation and conjugation.
ABA is synthesized in almost all cells that contain plas-tids and is transported via both the xylem and the phloem.
The level of ABA fluctuates dramatically in response to developmental and environmental changes. During seed maturation, ABA levels peak in mid- to late embryogenesis. ABA is required for the development of desiccation tol-erance in the developing embryo, the synthesis of storage proteins, and the acquisition of dormancy. Seed dormancy and germination are controlled by the ratio of ABA to GA, and ABA-deficient embryos may exhibit precocious ger-mination and vivipary. ABA is also antagonized by ethyl-ene and brassinosteroid promotion of germination.
Although less is known about the role of ABA in buds, ABA is one of the inhibitors that accumulates in dormant buds.
During water stress, the ABA level of the leaf can increase 50-fold. In addition to closing stomata, ABA increases the hydraulic conductivity of the root and Abscisic Acid: A Seed Maturation and Antistress Signal 555 increases the root:shoot ratio at low water potentials. ABA and an alkalinization of the xylem sap are thought to be two chemical signals that the root sends to the shoot as the soil dries. The increased pH of the xylem sap may allow more of the ABA of the leaf to be translocated to the stom-ata via the transpiration stream.
ABA exerts both short-term and long-term control over plant development. The long-term effects are mediated by ABA-induced gene expression. ABA stimulates the syn-thesis of many classes of proteins during seed development and during water stress, including the LEA family, pro-teases and chaperonins, ion and water channels, and enzymes catalyzing compatible solute metabolism or detoxification of active oxygen species. These proteins may protect membranes and other proteins from desiccation damage, or they may aid in recovery from the deleterious effects of stress. ABA response elements and several tran-scription factors that bind to them have been identified.
ABA also suppresses GA-induced gene expression—for example, the synthesis of GA-MYB and α-amylase by bar-ley aleurone layers.
There is evidence for both extracellular and intracellu-lar ABA receptors in guard cells. ABA closes stomata by causing long-term depolarization of the guard cell plasma membrane. Depolarization is believed to be caused by an increase in cytosolic Ca2+, as well as alkalinization of the cytosol. The increase in cytosolic calcium is due to a com-bination of calcium uptake and release of calcium from internal stores. This calcium increase leads to the opening of slow anion channels, which results in membrane depo-larization. IP3, IP6, cADPR, PA, and reactive oxygen species all function as secondary messengers in ABA-treated guard cells, and G-proteins participate in the response. Outward K+ channels open in response to mem-brane depolarization and to the rise in pH, bringing about massive K+ efflux.
In general, the ABA response appears to be regulated by more than one signal transduction pathway, even within a single cell type. This redundancy is consistent with the abil-ity of plant cells to respond to multiple sensory inputs.
There is genetic evidence for cross-talk between ABA sig-naling and the signaling of all other major classes of phy-tohormones, as well as sugars.
Web Material Web Topics 23.1 The Structure of Lunularic Acid from Liverworts Although inactive in higher plants, lunularic acid appears to have a function similar to ABA in liverworts.
23.2 Structural Requirements for Biological Activity of Abscisic Acid To be active as a hormone, ABA requires cer-tain functional groups 23.3 The Bioassay of ABA Several ABA-responding tissues have been used to detect and measure ABA.
23.4 Proteins Required for Desiccation Tolerance ABA induces the synthesis of proteins that protect cells from damage due to dessica-tion.
23.5 Types of Seed Dormancy and the Roles of Environmental Factors This discussion expands on the various types of seed dormancy and describes how envi-ronmental factors affect seed dormancy.
23.6 The Longevity of Seeds Under certain conditions, seeds can remain dormant for hundreds of years.
23.7 Genetic Mapping of Dormancy: Quantitative Trait Locus (QTL) Scoring of Vegetative Dormancy Combined with a Candidate Gene Approach A genetic method for determining the num-ber and chromosomal locations of genes affecting a quantitative trait affected by many unlinked genes is described.
23.8 ABA-Induced Senescence and Ethylene Hormone-insensitive mutants have made it possible to distinguish the effects of ethylene from those of ABA on senescence.
23.9 Yellow Cameleon: A Noninvasive Tool for Measuring Intracellular Calcium The features of the yellow cameleon protein that enable it to act as a reporter for calcium concentration are described.
23.10 Promoter Elements That Regulate ABA Induction of Gene Expression A table of the different ABA response ele-ments is presented.
23.11 The Two-Hybrid System The GAL4 transcription factor can be used to detect protein-protein interactions in yeast.
Web Essay 23.1 Heterophylly in Aquatic Plants Abscisic acid induces aerial-type leaf mor-phology in many aquatic plants.
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558 Chapter 23 The Control of Flowering 24 Chapter MOST PEOPLE LOOK FORWARD to the spring season and the profu-sion of flowers it brings. Many vacationers carefully time their travels to coincide with specific blooming seasons: Citrus along Blossom Trail in southern California, tulips in Holland. In Washington, D.C., and throughout Japan, the cherry blossoms are received with spirited cere-monies. As spring progresses into summer, summer into fall, and fall into winter, wildflowers bloom at their appointed times.
Although the strong correlation between flowering and seasons is common knowledge, the phenomenon poses fundamental questions that will be addressed in this chapter: • How do plants keep track of the seasons of the year and the time of day?
• Which environmental signals control flowering, and how are those signals perceived?
• How are environmental signals transduced to bring about the developmental changes associated with flowering?
In Chapter 16 we discussed the role of the root and shoot apical meristems in vegetative growth and development. The transition to flowering involves major changes in the pattern of morphogenesis and cell differentiation at the shoot apical meristem. Ultimately this process leads to the production of the floral organs—sepals, petals, stamens, and carpels (see Figure 1.2.A in Web Topic 1.2).
Specialized cells in the anther undergo meiosis to produce four hap-loid microspores that develop into pollen grains. Similarly, a cell within the ovule divides meiotically to produce four haploid megaspores, one of which survives and undergoes three mitotic divisions to produce the cells of the embryo sac (see Figure 1.2.B in Web Topic 1.2). The embryo sac represents the mature female gametophyte. The pollen grain, with its germinating pollen tube, is the mature male gametophyte generation.
The two gametophytic structures produce the gametes (egg and sperm cells), which fuse to form the diploid zygote, the first stage of the new sporophyte generation.
Clearly, flowers represent a complex array of function-ally specialized structures that differ substantially from the vegetative plant body in form and cell types. The transition to flowering therefore entails radical changes in cell fate within the shoot apical meristem. In the first part of this chapter we will discuss these changes, which are mani-fested as floral development. Recently genes have been iden-tified that play crucial roles in the formation of the floral organs. Such studies have shed new light on the genetic control of plant reproductive development.
The events occurring in the shoot apex that specifically commit the apical meristem to produce flowers are collec-tively referred to as floral evocation. In the second part of this chapter we will discuss the events leading to floral evo-cation. The developmental signals that bring about floral evocation include endogenous factors, such as circadian rhythms, phase change, and hormones, and external factors, such as day length (photoperiod) and temperature (vernal-ization). In the case of photoperiodism, transmissible sig-nals from the leaves, collectively referred to as the floral stimulus, are translocated to the shoot apical meristem.
The interactions of these endogenous and external factors enable plants to synchronize their reproductive develop-ment with the environment.
FLORAL MERISTEMS AND FLORAL ORGAN DEVELOPMENT Floral meristems usually can be distinguished from vege-tative meristems, even in the early stages of reproductive development, by their larger size. The transition from veg-etative to reproductive development is marked by an increase in the frequency of cell divisions within the cen-tral zone of the shoot apical meristem. In the vegetative meristem, the cells of the central zone complete their divi-sion cycles slowly. As reproductive development com-mences, the increase in the size of the meristem is largely a result of the increased division rate of these central cells.
Recently, genetic and molecular studies have identified a network of genes that control floral morphogenesis in Ara-bidopsis, snapdragon (Antirrhinum), and other species.
In this section we will focus on floral development in Arabidopsis, which has been studied extensively (Figure 24.1). First we will outline the basic morphological changes that occur during the transition from the vegetative to the reproductive phase. Next we will consider the arrangement of the floral organs in four whorls on the meristem, and the types of genes that govern the normal pattern of floral development. According to the widely accepted ABC model (which is described in Figure 24.6), the specific loca-tions of floral organs in the flower are regulated by the overlapping expression of three types of floral organ iden-tity genes.
The Characteristics of Shoot Meristems in Arabidopsis Change with Development During the vegetative phase of growth, the Arabidopsis veg-etative apical meristem produces phytomeres with very short internodes, resulting in a basal rosette of leaves (see Figure 24.1A). (Recall from Chapter 16 that a phytomere consists of a leaf, the node to which the leaf is attached, the axillary bud, and the internode below the node.) As plants initiate reproductive development, the vege-tative meristem is transformed into an indeterminate pri-mary inflorescence meristem that produces floral meri-stems on its flanks (Figure 24.2). The lateral buds of the 560 Chapter 24 Cauline leaf Rosette leaf Secondary inflorescence (A) Primary inflorescence Flower (B) FIGURE 24.1 (A) The shoot apical meristem in Arabidopsis thaliana generates different organs at dif-ferent stages of development.
Early in development the shoot apical meristem forms a rosette of basal leaves. When the plant makes the transition to flowering, the shoot apical meristem is transformed into a primary inflo-rescence meristem that ultimately produces an elongated stem bear-ing flowers. Leaf primordia initi-ated prior to the floral transition become cauline leaves, and sec-ondary inflorescences develop in the axils of the cauline leaves. (B) Photograph of an Arabidopsis plant. (Photo courtesy of Richard Amasino.) cauline leaves (inflorescence leaves) develop into sec-ondary inflorescence meristems, and their activity repeats the pattern of development of the primary inflorescence meristem, as shown in Figure 24.1A.
The Four Different Types of Floral Organs Are Initiated as Separate Whorls Floral meristems initiate four different types of floral organs: sepals, petals, stamens, and carpels (Coen and Car-penter 1993). These sets of organs are initiated in concen-tric rings, called whorls, around the flanks of the meristem (Figure 24.3). The initiation of the innermost organs, the carpels, consumes all of the meristematic cells in the apical dome, and only the floral organ primordia are present as the floral bud develops. In the wild-type Arabidopsis flower, the whorls are arranged as follows: • The first (outermost) whorl consists of four sepals, which are green at maturity.
The second whorl is composed of four petals, which are white at maturity.
• The third whorl contains six stamens, two of which are shorter than the other four.
• The fourth whorl is a single complex organ, the gynoecium or pistil, which is composed of an ovary with two fused carpels, each containing numerous ovules, and a short style capped with a stigma (Figure 24.4).
The Control of Flowering 561 FIGURE 24.2 Longitudinal sections through a vegetative (A) and a reproductive (B) shoot apical region of Arabidopsis. (Photos courtesy of V. Grbic´ and M. Nelson, and assembled and labeled by E. Himelblau.) (A) (B) Stamen Carpel Petal Sepal Vascular tissue Whorl 1: sepals Whorl 2: petals Whorl 3: stamens Whorl 4: carpels (A) Longitudinal section through developing flower (B) Cross- section of developing flower showing floral whorls (C) Schematic diagram of developmental fields Field 1 Field 2 Field 3 FIGURE 24.3 The floral organs are initiated sequentially by the floral meristem of Arabidopsis. (A and B) The floral organs are produced as successive whorls (concentric cir-cles), starting with the sepals and progressing inward. (C) According to the combinatorial model, the functions of each whorl are determined by overlapping developmental fields. These fields correspond to the expression patterns of specific floral organ identity genes. (From Bewley et al.
2000.) Three Types of Genes Regulate Floral Development Mutations have identified three classes of genes that regu-late floral development: floral organ identity genes, cadas-tral genes, and meristem identity genes.
1. Floral organ identity genes directly control floral identity. The proteins encoded by these genes are transcription factors that likely control the expression of other genes whose products are involved in the for-mation and/or function of floral organs.
2. Cadastral genes act as spatial regulators of the floral organ identity genes by setting boundaries for their expression. (The word cadastre refers to a map or sur-vey showing property boundaries for taxation pur-poses.) 3. Meristem identity genes are necessary for the initial induction of the organ identity genes. These genes are the positive regulators of floral organ identity.
Meristem Identity Genes Regulate Meristem Function Meristem identity genes must be active for the primordia formed at the flanks of the apical meristem to become flo-ral meristems. (Recall that an apical meristem that is form-ing floral meristems on its flanks is known as an inflores-cence meristem.) For example, mutants of Antirrhinum (snapdragon) that have a defect in the meristem identity gene FLORICAULA develop an inflorescence that does not produce flowers. Instead of causing floral meristems to form in the axils of the bracts, the mutant floricaula gene results in the development of additional inflorescence meristems at the bract axils. The wild-type floricaula (FLO) gene controls the determination step in which floral meris-tem identity is established.
In Arabidopsis, AGAMOUS-LIKE 201 (AGL20), APETALA1 (AP1), and LEAFY (LFY) are all critical genes in the genetic pathway that must be activated to establish floral meristem identity. LFY is the Arabidopsis version of the snapdragon FLO gene. AGL20 plays a central role in floral evocation by integrating signals from several different pathways involv-ing both environmental and internal cues (Borner et al.
2000). AGL20 thus appears to serve as a master switch ini-tiating floral development.
Once activated, AGL20 triggers the expression of LFY, and LFY turns on the expression of AP1 (Simon et al. 1996).
In Arabidopsis, LFY and AP1 are involved in a positive feed-back loop; that is, AP1 expression also stimulates the expression of LFY.
Homeotic Mutations Led to the Identification of Floral Organ Identity Genes The genes that determine floral organ identity were dis-covered as floral homeotic mutants (see Chapter 14 on the 562 Chapter 24 Stigma Style Ovary Transmitting tissue Ovules (A) (B) FIGURE 24.4 The Arabidopsis pistil consists of two fused carpels, each containing many ovules. (A) Scanning electron micrograph of a pistil, showing the stigma, a short style, and the ovary. (B) Longitudinal section through the pistil, showing the many ovules. (From Gasser and Robinson-Beers 1993, courtesy of C. S. Gasser, © American Society of Plant Biologists, reprinted with permission.) 1 Also known as SUPPRESSOR OF OVEREXPRESSION OF CONSTANS 1 (SOC1).
web site). As discussed in Chapter 14, mutations in the fruit fly, Drosophila, led to the identification of a set of homeotic genes encoding transcription factors that determine the locations at which specific structures develop. Such genes act as major developmental switches that activate the entire genetic program for a particular structure. The expression of homeotic genes thus gives organs their identity.
As we have seen already in this chapter, dicot flowers consist of successive whorls of organs that form as a result of the activity of floral meristems: sepals, petals, stamens, and carpels. These organs are produced when and where they are because of the orderly, patterned expression and interactions of a small group of homeotic genes that spec-ify floral organ identity.
The floral organ identity genes were identified through homeotic mutations that altered floral organ identity so that some of the floral organs appeared in the wrong place. For example, Arabidopsis plants with mutations in the APETALA2 (AP2) gene produce flowers with carpels where sepals should be, and stamens where petals normally appear.
The homeotic genes that have been cloned so far encode transcription factors—proteins that control the expression of other genes. Most plant homeotic genes belong to a class of related sequences known as MADS box genes, whereas animal homeotic genes contain sequences called home-oboxes (see Chapter 14 on the web site).
Many of the genes that determine floral organ identity are MADS box genes, including the DEFICIENS gene of snapdragon and the AGAMOUS, PISTILLATA1, and APETALA3 genes of Arabidopsis. The MADS box genes share a characteristic, conserved nucleotide sequence known as a MADS box, which encodes a protein structure known as the MADS domain. The MADS domain enables these transcription factors to bind to DNA that has a spe-cific nucleotide sequence.
Not all genes containing the MADS box domain are homeotic genes. For example, AGL20 is a MADS box gene, but it functions as a meristem identity gene.
Three Types of Homeotic Genes Control Floral Organ Identity Five different genes are known to specify floral organ identity in Arabidopsis: APETALA1 (AP1), APETALA2 (AP2), APETALA3 (AP3), PISTILLATA (PI), and AGA-MOUS (AG) (Bowman et al. 1989; Weigel and Meyerowitz 1994). The organ identity genes initially were identified through mutations that dramatically alter the structure and thus the identity of the floral organs pro-duced in two adjacent whorls (Figure 24.5). For example, plants with the ap2 mutation lack sepals and petals (see Figure 24.5B). Plants bearing ap3 or pi mutations produce sepals instead of petals in the second whorl, and carpels instead of stamens in the third whorl (see Figure 24.5C).
And plants homozygous for the ag mutation lack both sta-mens and carpels (see Figure 24.5D).
Because mutations in these genes change floral organ identity without affecting the initiation of flowers, they are homeotic genes. These homeotic genes fall into three classes—types A, B, and C—defining three different kinds of activities (Figure 24.6): The Control of Flowering 563 Stamen Carpel Petal Sepal Wild type apetala2-2 pistillata2 agamous1 (A) (B) (C) (D) FIGURE 24.5 Mutations in the floral organ identity genes dramatically alter the structure of the flower. (A) Wild type; (B) apetala2-2 mutants lack sepals and petals; (C) pistillata2 mutants lack petals and stamens; (D) agamous1 mutants lack both stamens and carpels. (From Bewley et al. 2000.) 1. Type A activity, encoded by AP1 and AP2, controls organ identity in the first and second whorls. Loss of type A activity results in the formation of carpels instead of sepals in the first whorl, and of stamens instead of petals in the second whorl.
2. Type B activity, encoded by AP3 and PI, controls organ determination in the second and third whorls.
Loss of type B activity results in the formation of sepals instead of petals in the second whorl, and of carpels instead of stamens in the third whorl.
3. Type C activity, encoded by AG, controls events in the third and fourth whorls. Loss of type C activity results in the formation of petals instead of stamens in the third whorl, and replacement of the fourth whorl by a new flower such that the fourth whorl of the ag mutant flower is occupied by sepals.
The control of organ identity by type A, B, and C homeotic genes (the ABC model) is described in more detail in the next section.
The role of the organ identity genes in floral development is dramatically illustrated by experiments in which two or three activities are eliminated by loss-of-function mutations (Figure 24.7). Quadruple-mutant plants (ap1, ap2, ap3/pi, and ag) produce floral meristems that develop as pseudoflowers; all the floral organs are replaced with green leaflike struc-tures, although these organs are produced with a whorled phyllotaxy. Evolutionary biologists, beginning with the eigh-teenth-century German poet, philosopher, and natural sci-entist Johann Wolfgang von Goethe (1749–1832), have spec-ulated that floral organs are highly modified leaves, and this experiment gives direct support to these ideas.
The ABC Model Explains the Determination of Floral Organ Identity In 1991 the ABC model was proposed to explain how homeotic genes control organ identity. The ABC model postulates that organ identity in each whorl is determined by a unique combination of the three organ identity gene activities (see Figure 24.6): • Activity of type A alone specifies sepals.
• Activities of both A and B are required for the forma-tion of petals.
• Activities of B and C form stamens.
• Activity of C alone specifies carpels.
The model further proposes that activities A and C mutu-ally repress each other (see Figure 24.6); that is, both A- and C-type genes have cadastral function in addition to their function in determining organ identity.
The patterns of organ formation in the wild type and most of the mutant phenotypes are predicted and explained by this model (Figure 24.8). The challenge now is to understand how the expression pattern of these organ identity genes is controlled by cadastral genes; how organ identity genes, which encode transcription factors, alter the pattern of other genes expressed in the developing organ; and finally how this altered pattern of gene expression results in the development of a specific floral organ.
564 Chapter 24 Sepal Structure Petal Stamen Carpel Activity type A B C Sepal Structure Petal Stamen Carpel Genes APETALA2 APETALA3/PISTILLATA AGAMOUS 1 2 3 4 Whorl FIGURE 24.6 The ABC model for the acquisition of floral organ identity is based on the interactions of three different types of activities of floral homeotic genes: A, B, and C. In the first whorl, expression of type A (AP2) alone results in the formation of sepals. In the second whorl, expression of both type A (AP2) and type B (AP3/PI) results in the forma-tion of petals. In the third whorl, the expression of B (AP3/PI) and C (AG) causes the formation of stamens. In the fourth whorl, activity C (AG) alone specifies carpels. In addition, activity A (AP2) represses activity C (AG) in whorls 1 and 2, while C represses A in whorls 3 and 4.
FIGURE 24.7 A quadruple mutant (ap1, ap2, ap3/pi, ag ) results in the production of leaf-like structures in place of floral organs. (Courtesy of John Bowman.) FLORAL EVOCATION: INTERNAL AND EXTERNAL CUES A plant may flower within a few weeks after germinating, as in annual plants such as groundsel (Senecio vulgaris).
Alternatively, some perennial plants, such as many forest trees, may grow for 20 or more years before they begin to produce flowers. Different species flower at widely differ-ent ages, indicating that the age, or perhaps the size, of the plant is an internal factor controlling the switch to repro-ductive development. The case in which flowering occurs strictly in response to internal developmental factors and does not depend on any particular environmental condi-tions is referred to as autonomous regulation.
In contrast to plants that flower entirely through an autonomous pathway, some plants exhibit an absolute requirement for the proper environmental cues in order to flower. This condition is termed an obligate or qualitative response to an environmental cue. In other plant species, flowering is promoted by certain environmental cues but will eventually occur in the absence of such cues. This is called a facultative or quantitative response to an environ-mental cue. The flowering of this latter group of plants, which includes Arabidopsis, thus relies on both environ-mental and autonomous flowering systems.
Photoperiodism and vernalization are two of the most important mechanisms underlying seasonal responses.
Photoperiodism is a response to the length of day; vernaliza-The Control of Flowering 565 1 2 3 4 Sepal Structure Petal Stamen Carpel Genes Whorl A B C 1 2 3 4 Sepal Structure Petal Petal Sepal Genes Whorl A B 1 2 3 4 Carpel Structure Stamen Stamen Carpel Genes Whorl B C 1 2 3 4 Sepal Structure Sepal Carpel Carpel Genes Whorl A C (A) Wild type (B) Loss of C function (C) Loss of A function (D) Loss of B function FIGURE 24.8 Interpretation of the phe-notypes of floral homeotic mutants based on the ABC model. (A) Wild type. (B) Loss of C function results in expansion of the A function throughout the floral meristem. (C) Loss of A func-tion results in the spread of C function throughout the meristem. (D) Loss of B function results in the expression of only A and C functions.
tion is the promotion of flowering—at subsequent higher temperatures—brought about by exposure to cold. Other signals, such as total light radiation and water availability, can also be important external cues.
The evolution of both internal (autonomous) and exter-nal (environment-sensing) control systems enables plants to carefully regulate flowering at the optimal time for reproductive success. For example, in many populations of a particular species, flowering is synchronized. This syn-chrony favors crossbreeding and allows seeds to be pro-duced in favorable environments, particularly with respect to water and temperature.
THE SHOOT APEX AND PHASE CHANGES All multicellular organisms pass through a series of more or less defined developmental stages, each with its charac-teristic features. In humans, infancy, childhood, adoles-cence, and adulthood represent four general stages of development, and puberty is the dividing line between the nonreproductive and the reproductive phases. Higher plants likewise pass through developmental stages, but whereas in animals these changes take place throughout the entire organism, in higher plants they occur in a single, dynamic region, the shoot apical meristem.
Shoot Apical Meristems Have Three Developmental Phases During postembryonic development, the shoot apical meristem passes through three more or less well-defined developmental stages in sequence: 1. The juvenile phase 2. The adult vegetative phase 3. The adult reproductive phase The transition from one phase to another is called phase change. The primary distinction between the juvenile and the adult vegetative phases is that the latter has the ability to form reproductive structures: flowers in angiosperms, cones in gymnosperms. However, actual expression of the reproductive competence of the adult phase (i.e., flower-ing) often depends on specific environmental and devel-opmental signals. Thus the absence of flowering itself is not a reliable indicator of juvenility.
The transition from juvenile to adult is frequently accom-panied by changes in vegetative characteristics, such as leaf morphology, phyllotaxy (the arrangement of leaves on the stem), thorniness, rooting capacity, and leaf retention in deciduous plants (Figure 24.9; see also Web Topic 24.1). Such changes are most evident in woody perennials, but they are apparent in many herbaceous species as well. Unlike the abrupt transition from the adult vegetative phase to the reproductive phase, the transition from juvenile to vegeta-tive adult is usually gradual, involving intermediate forms. Sometimes the transition can be observed in a single leaf. A dramatic example of this is the progressive trans-formation of juvenile leaves of the leguminous tree Acacia heterophylla into phyllodes, a phenomenon noted by Goethe. Whereas the juvenile pinnately compound leaves consist of rachis (stalk) and leaflets, adult phyllodes are specialized structures representing flattened petioles (Fig-ure 24.10).
Intermediate structures also form during the transition from aquatic to aerial leaf types of aquatic plants such as Hippuris vulgaris (common marestail). As in the case of A.
heterophylla, these intermediate forms possess distinct regions with different developmental patterns. To account for intermediate forms during the transition from juvenile to adult in maize (see Web Topic 24.2), a combinatorial model has been proposed (Figure 24.11). According to this model, shoot development can be described as a series of independently regulated, overlapping programs (juvenile, adult, and reproductive) that modulate the expression of a common set of developmental processes.
566 Chapter 24 FIGURE 24.9 Juvenile and adult forms of ivy (Hedera helix).
The juvenile form has lobed palmate leaves arranged alter-nately, a climbing growth habit, and no flowers. The adult form (projecting out to the right) has entire ovate leaves arranged in spirals, an upright growth habit, and flowers.
(Photo by L. Taiz.) In the transition from juvenile to adult leaves, the inter-mediate forms indicate that different regions of the same leaf can express different developmental programs. Thus the cells at the tip of the leaf remain committed to the juve-nile program, while the cells at the base of the leaf become committed to the adult program. The developmental fates of the two sets of cells in the same leaf are quite different.
Juvenile Tissues Are Produced First and Are Located at the Base of the Shoot The sequence in time of the three developmental phases results in a spatial gradient of juvenility along the shoot axis. Because growth in height is restricted to the apical meristem, the juvenile tissues and organs, which form first, are located at the base of the shoot. In rapidly flowering herbaceous species, the juvenile phase may last only a few days, and few juvenile structures are produced. In contrast, woody species have a more prolonged juvenile phase, in some cases lasting 30 to 40 years (Table 24.1). In these cases the juvenile structures can account for a significant portion of the mature plant.
Once the meristem has switched over to the adult phase, only adult vegetative structures are produced, culminating in floral evocation. The adult and reproductive phases are therefore located in the upper and peripheral regions of the shoot.
Attainment of a sufficiently large size appears to be more important than the plant’s chronological age in determin-ing the transition to the adult phase. Conditions that retard growth, such as mineral deficiencies, low light, water stress, defoliation, and low temperature tend to prolong the juve-nile phase or even cause rejuvenation (reversion to juve-nility) of adult shoots. In contrast, conditions that promote vigorous growth accelerate the transition to the adult phase.
When growth is accelerated, exposure to the correct flower-inducing treatment can result in flowering.
Although plant size seems to be the most important fac-tor, it is not always clear which specific component associ-ated with size is critical. In some Nicotiana species, it appears that plants must produce a certain number of leaves to transmit a sufficient amount of the floral stimu-lus to the apex.
The Control of Flowering 567 Adult phase Juvenile phase Petiole Intermediate stages Flattened petiole FIGURE 24.10 Leaves of Acacia heterophylla, showing transitions from pinnately compound leaves (juvenile phase) to phyllodes (adult phase). Note that the previ-ous phase is retained at the top of the leaf in the intermediate forms. (A) Vegetative young adult plant (B) Flowering plant Processes required at all phases Phases Juvenile Vegetative adult Reproductive Flower FIGURE 24.11 Schematic representation of the combinatorial model of shoot development in maize. Overlapping gradients of expression of the juvenile, vegetative adult, and reproductive phases are indicated along the length of the main axis and branches. The continuous black line represents processes that are required during all phases of devel-opment. Each of the three phases may be regulated by separated developmental programs, with intermediate phases arising when the programs overlap. (A) Vegetative young adult plant. (B) Flowering plant. (After Poethig 1990.) Once the adult phase has been attained, it is relatively stable, and it is maintained during vegetative propagation or grafting. For example, in mature plants of English ivy (Hedera helix), cuttings taken from the basal region develop into juvenile plants, while those from the tip develop into adult plants. When scions were taken from the base of the flowering tree silver birch (Betula verrucosa) and grafted onto seedling rootstocks, there were no flowers on the grafts within the first 2 years. In contrast, the grafts flow-ered freely when scions were taken from the top of the flowering tree. In some species, the juvenile meristem appears to be capable of flowering but does not receive sufficient floral stimulus until the plant becomes large enough. In mango (Mangifera indica), for example, juvenile seedlings can be induced to flower when grafted to a mature tree. In many other woody species, however, grafting to an adult flow-ering plant does not induce flowering.
Phase Changes Can Be Influenced by Nutrients, Gibberellins, and Other Chemical Signals The transition at the shoot apex from the juvenile to the adult phase can be affected by transmissible factors from the rest of the plant. In many plants, exposure to low-light con-ditions prolongs juvenility or causes reversion to juvenility.
A major consequence of the low-light regime is a reduction in the supply of carbohydrates to the apex; thus carbohy-drate supply, especially sucrose, may play a role in the tran-sition between juvenility and maturity. Carbohydrate sup-ply as a source of energy and raw material can affect the size of the apex. For example, in the florist’s chrysanthe-mum (Chrysanthemum morifolium), flower primordia are not initiated until a minimum apex size has been reached.
The apex receives a variety of hormonal and other fac-tors from the rest of the plant in addition to carbohydrates and other nutrients. Experimental evidence shows that the application of gibberellins causes reproductive structures to form in young, juvenile plants of several conifer fami-lies. The involvement of endogenous GAs in the control of reproduction is also indicated by the fact that other treat-ments that accelerate cone production in pines (e.g., root removal, water stress, and nitrogen starvation) often also result in a buildup of GAs in the plant.
On the other hand, although gibberellins promote the attainment of reproductive maturity in conifers and many herbaceous angiosperms as well, GA3 causes rejuvenation in Hedera and in several other woody angiosperms. The role of gibberellins in the control of phase change is thus complex, varies among species, and probably involves interactions with other factors.
Competence and Determination Are Two Stages in Floral Evocation The term juvenility has different meanings for herbaceous and woody species. Whereas juvenile herbaceous meris-tems flower readily when grafted onto flowering adult plants (see Web Topic 24.3), juvenile woody meristems generally do not. What is the difference between the two?
Extensive studies in tobacco have demonstrated that flo-ral evocation requires the apical bud to pass through two developmental stages (Figure 24.12) (McDaniel et al. 1992).
One stage is the acquisition of competence. A bud is said to be competent if it is able to flower when given the appro-priate developmental signal. For example, if a vegetative shoot (scion) is grafted onto a flowering stock and the scion flowers immediately, it is demonstrably capable of responding to the level of floral stimulus present in the stock and is therefore competent.
Failure of the scion to flower would indicate that the shoot apical meristem has not yet attained competence. Thus the juvenile meristems of herbaceous plants are competent to flower, but those of woody species are not.
The next stage that a competent vegetative bud goes through is determination. A bud is said to be determined if it progresses to the next developmental stage (flowering) even after being removed from its normal context. Thus a florally determined bud will produce flowers even if it is grafted onto a vegetative plant that is not producing any floral stimulus.
In a day-neutral tobacco, for example, plants typically flower after producing about 41 leaves or nodes. In an experiment to measure the floral determination of the axil-lary buds, flowering tobacco plants were decapitated just above the thirty-fourth leaf (from the bottom). Released from apical dominance, the axillary bud of the thirty-fourth leaf grew out, and after producing 7 more leaves (for a total of 41), it flowered (Figure 24.13A) (McDaniel 1996). How-ever, if the thirty-fourth bud was excised from the plant and either rooted or grafted onto a stock without leaves near the base, it produced a complete set of leaves (41) before flowering. This result shows that the thirty-fourth bud was not yet florally determined.
568 Chapter 24 TABLE 24.1 Length of juvenile period in some woody plant species Length of juvenile Species period Rose (Rosa [hybrid tea]) 20–30 days Grape (Vitis spp.) 1 year Apple (Malus spp.) 4–8 years Citrus spp.
5–8 years English ivy (Hedera helix) 5–10 years Redwood (Sequoia sempervirens) 5–15 years Sycamore maple (Acer pseudoplatanus) 15–20 years English oak (Quercus robur) 25–30 years European beech (Fagus sylvatica) 30–40 years Source: Clark 1983.
In another experiment, the donor plant was decapitated above the thirty-seventh leaf. This time the thirty-seventh axillary bud flowered after producing four leaves in all three situations (see Figure 24.13B). This result demonstrates that the terminal bud became florally determined after initiat-ing 37 leaves.
Extensive grafting of shoot tips among tobacco varieties has established that the number of nodes a meristem pro-duces before flowering is a function of two factors: (1) the strength of the floral stimulus from the leaves and (2) the competence of the meristem to respond to the signal (McDaniel et al. 1996).
In some cases the expression of flowering may be delayed or arrested even after the apex becomes deter-mined, unless it receives a second developmental signal that stimulates expression (see Figure 24.12). For example, intact Lolium temulentum (darnel ryegrass) plants become committed to flowering after a single exposure to a long day. If the Lolium shoot apical meristem is excised 28 hours after the beginning of the long day and cultured in vitro, it will produce normal inflorescences in culture, but only if the hormone gibberellic acid (GA) is present in the medium. Because apices cultured from plants grown exclu-sively in short days never flower, even in the presence of The Control of Flowering 569 Induction Expressed: The apical meristem undergoes morphogenesis. Signal Photoperiod Vegetative growth Flowers Hormones ?
Determined: Able to follow same developmental program even after removal from its normal position in plant.
Competent: Able to respond in expected manner when given the appropriate developmental signals.
FIGURE 24.12 A simplified model for floral evocation at the shoot apex in which the cells of the vegetative meristem acquire new developmental fates. To initiate floral develop-ment, the cells of the meristem must first become compe-tent. A competent vegetative meristem is one that can respond to a floral stimulus (induction) by becoming flo-rally determined (committed to producing a flower). The determined state is usually expressed, but this may require an additional signal. (After McDaniel et al. 1992.) Rooted Grafted Decapitation here Donor Donor In situ In situ Rooted Grafted Decapitation here (A) Bud not determined (B) Bud florally determined FIGURE 24.13 Demonstration of the deter-mined state of axillary buds in tobacco. A specific axillary bud of a flowering donor plant is forced to grow, either directly on the plant (in situ) by decapitation, or by rooting or grafting to the base of the plant. The new leaves and flowers produced by the axillary bud are indicated by shading. (A) Result when the bud is not determined. (B) Result when the bud is florally determined. (After McDaniel 1996.) GA, we can conclude that long days are required for deter-mination in Lolium, whereas GA is required for expression of the determined state.
In general, once a meristem has become competent, it exhibits an increasing tendency to flower with age (leaf number). For example, in plants controlled by day length, the number of short-day or long-day cycles necessary to achieve flowering is often fewer in older plants (Figure 24.14). As will be discussed later in the chapter, this increas-ing tendency to flower with age has its physiological basis in the greater capacity of the leaves to produce a floral stimulus.
Before discussing how plants perceive day length, how-ever, we will lay the foundation by examining how organ-isms measure time in general. This topic is known as chronobiology, or the study of biological clocks. The best-understood biological clock is the circadian rhythm.
CIRCADIAN RHYTHMS: THE CLOCK WITHIN Organisms are normally subjected to daily cycles of light and darkness, and both plants and animals often exhibit rhythmic behavior in association with these changes.
Examples of such rhythms include leaf and petal move-ments (day and night positions), stomatal opening and closing, growth and sporulation patterns in fungi (e.g., Pilobolus and Neurospora), time of day of pupal emergence (the fruit fly Drosophila), and activity cycles in rodents, as well as metabolic processes such as photosynthetic capac-ity and respiration rate.
When organisms are transferred from daily light–dark cycles to continuous darkness (or continuous dim light), many of these rhythms continue to be expressed, at least for several days. Under such uniform conditions the period of the rhythm is then close to 24 hours, and consequently the term circadian rhythm is applied (see Chapter 17).
Because they continue in a constant light or dark environ-ment, these circadian rhythms cannot be direct responses to the presence or absence of light but must be based on an internal pacemaker, often called an endogenous oscillator.
A molecular model for a plant endogenous oscillator was described in Chapter 17.
The endogenous oscillator is coupled to a variety of physiological processes, such as leaf movement or photo-synthesis, and it maintains the rhythm. For this reason the endogenous oscillator can be considered the clock mecha-nism, and the physiological functions that are being regu-lated, such as leaf movements or photosynthesis, are some-times referred to as the hands of the clock.
Circadian Rhythms Exhibit Characteristic Features Circadian rhythms arise from cyclic phenomena that are defined by three parameters: 1. Period, the time between comparable points in the repeating cycle. Typically the period is measured as the time between consecutive maxima (peaks) or minima (troughs) (Figure 24.15A).
2. Phase2, any point in the cycle that is recognizable by its relationship to the rest of the cycle. The most obvi-ous phase points are the peak and trough positions.
3. Amplitude, usually considered to be the distance between peak and trough. The amplitude of a biolog-ical rhythm can often vary while the period remains unchanged (as, for example, in Figure 24.15C).
In constant light or darkness, rhythms depart from an exact 24-hour period. The rhythms then drift in relation to solar time, either gaining or losing time depending on whether the period is shorter or longer than 24 hours.
Under natural conditions, the endogenous oscillator is 570 Chapter 24 6 5 4 3 2 1 Oldest plant (6–7 leaves), flowering after 1 LD cycle Flowering stage: Vegetative stage: 1 0 2 3 4 Number of LD cycles Spike length (mm) Younger plant (4–5 leaves), flowering after 2 LD cycles Youngest plant (2–3 leaves), flowering after 4 LD cycles FIGURE 24.14 Effect of plant age on the number of long-day (LD) inductive cycles required for flowering in the long-day plant Lolium temulentum (darnel ryegrass). An inductive long-day cycle consisted of 8 hours of sunlight followed by 16 hours of low-intensity incandescent light.
The older the plant is, the fewer photoinductive cycles are needed to produce flowering.
2 The term phase should not be confused with the term phase change in meristem development, discussed earlier.
entrained (synchronized) to a true 24-hour period by envi-ronmental signals, the most important of which are the light-to-dark transition at dusk and the dark-to-light tran-sition at dawn (see Figure 24.15B). Such environmental signals are termed zeitgebers (Ger-man for “time givers”). When such signals are removed— for example, by transfer to continuous darkness—the rhythm is said to be free-running, and it reverts to the cir-cadian period that is characteristic of the particular organ-ism (see Figure 24.15B).
Although the rhythms are generated internally, they normally require an environmental signal, such as expo-sure to light or a change in temperature, to initiate their expression. In addition, many rhythms damp out (i.e., the The Control of Flowering 571 Phase points A typical circadian rhythm. The period is the time between comparable points in the repeating cycle; the phase is any point in the repeating cycle recognizable by its relationship with the rest of the cycle; the amplitude is the distance between peak and trough.
A circadian rhythm entrained to a 24 h light–dark (L–D) cycle and its reversion to the free-running period (26 h in this example) following transfer to continuous darkness.
Suspension of a circadian rhythm in continuous bright light and the release or restarting of the rhythm following transfer to darkness.
Typical phase-shifting response to a light pulse given shortly after transfer to darkness. The rhythm is rephased (delayed) without its period being changed.
(A) (B) (D) (C) Amplitude Period 12D 12L 26 h 24 h 12D 12L 12D 12L (h) (h) 12D 12L 12D 12L 12D 12L (h) Light pulse Rephased rhythm Light FIGURE 24.15 Some characteristics of circadian rhythms.
amplitude decreases) when the organism is in a constant environment for some time and then require an environ-mental zeitgeber, such as a transfer from light to dark or a change in temperature, to be restarted (see Figure 24.15C).
Note that the clock itself does not damp out; only the cou-pling between the molecular clock (endogenous oscillator) and the physiological function is affected.
The circadian clock would be of no value to the organ-ism if it could not keep accurate time under the fluctuating temperatures experienced in natural conditions. Indeed, temperature has little or no effect on the period of the free-running rhythm. The feature that enables the clock to keep time at different temperatures is called temperature com-pensation. Although all of the biochemical steps in the pathway are temperature-sensitive, their temperature responses probably cancel each other. For example, changes in the rates of synthesis of intermediates could be compensated for by parallel changes in their rates of degra-dation. In this way, the steady-state levels of clock regula-tors would remain constant at different temperatures.
Phase Shifting Adjusts Circadian Rhythms to Different Day–Night Cycles In circadian rhythms, the operation of the endogenous oscillator sets a response to occur at a particular time of day. A single oscillator can be coupled to multiple circadian rhythms, which may even be out of phase with each other.
How do such responses remain on time when the daily durations of light and darkness change with the seasons?
The answer to this question lies in the fact that the phase of the rhythm can be changed if the whole cycle is moved for-ward or backward in time without its period being altered.
Investigators test the response of the endogenous oscil-lator usually by placing the organism in continuous dark-ness and examining the response to a short pulse of light (usually less than 1 hour) given at different phase points in the free-running rhythm. When an organism is entrained to a cycle of 12 hours light and 12 hours dark and then allowed to free-run in darkness, the phase of the rhythm that coincides with the light period of the previous entrain-ing cycle is called the subjective day, and the phase that coincides with the dark period is called the subjective night.
If a light pulse is given during the first few hours of the subjective night, the rhythm is delayed; the organism inter-prets the light pulse as the end of the previous day (see Fig-ure 24.15D). In contrast, a light pulse given toward the end of the subjective night advances the phase of the rhythm; now the organism interprets the light pulse as the begin-ning of the following day. As already pointed out, this is precisely the pattern of response that would be expected if the rhythm is to stay on local time. Therefore, these phase-shifting responses enable the rhythm to be entrained to approximately 24-hour cycles with different durations of light and darkness, and they demonstrate that the rhythm will run differently under dif-ferent natural conditions of day length.
Phytochromes and Cryptochromes Entrain the Clock The molecular mechanism whereby a light signal causes phase shifting is not yet known, but studies in Arabidopsis have identified some of the key elements of the circadian oscillator and its inputs and outputs (see Chapter 17). The low levels and specific wavelengths of light that can induce phase shifting indicate that the light response must be mediated by specific photoreceptors rather than rates of photosynthesis. For example, the red-light entrainment of rhythmic nyctonastic leaf movements in Samanea, a semi-tropical leguminous tree, is a low-fluence response medi-ated by phytochrome (see Chapter 17).
Arabidopsis has five phytochromes, and all but one of them (phytochrome C) have been implicated in clock entrainment.
Each phytochrome acts as a specific photoreceptor for red, far-red, or blue light. In addition, the CRY1 and CRY2 pro-teins participate in blue-light entrainment of the clock, as they do in insects and mammals (Devlin and Kay 2000). Surpris-ingly, CRY proteins also appear to be required for normal entrainment by red light. Since these proteins do not absorb red light, this requirement suggests that CRY1 and CRY2 may act as intermediates in phytochrome signaling during entrainment of the clock (Yanovsky and Kay 2001). In Drosophila, CRY proteins interact physically with clock components and thus constitute part of the oscillator mechanism (Devlin and Kay 2000). However, this does not appear to be the case in Arabidopsis, in which cry1/cry2 dou-ble mutants have normal circadian rhythms. Precisely how Arabidopsis CRY proteins interact with the endogenous oscillator mechanism to induce phase shifting remains to be elucidated (Yanovsky et al. 2001).
PHOTOPERIODISM: MONITORING DAY LENGTH As we have seen, the circadian clock enables organisms to determine the time of day at which a particular molecular or biochemical event occurs. Photoperiodism, or the abil-ity of an organism to detect day length, makes it possible for an event to occur at a particular time of year, thus allow-ing for a seasonal response. Circadian rhythms and pho-toperiodism have the common property of responding to cycles of light and darkness.
Precisely at the equator, day length and night length are equal and constant throughout the year. As one moves away from the equator toward the poles, the days become longer in summer and shorter in winter (Figure 24.16). Not surprisingly, plant species have evolved to detect these sea-sonal changes in day length, and their specific photoperi-odic responses are strongly influenced by the latitude from which they originated.
572 Chapter 24 Photoperiodic phenomena are found in both animals and plants. In the animal kingdom, day length controls such seasonal activities as hibernation, development of summer or winter coats, and reproductive activity. Plant responses controlled by day length are numerous, includ-ing the initiation of flowering, asexual reproduction, the formation of storage organs, and the onset of dormancy.
Perhaps all plant photoperiodic responses utilize the same photoreceptors, with subsequent specific signal trans-duction pathways regulating different responses. Because it is clear that monitoring the passage of time is essential to all photoperiodic responses, a timekeeping mechanism must underlie both the time-of-year and the time-of-day responses. The circadian oscillator is thought to provide an endogenous time-measuring mechanism that serves as a reference point for the response to incoming light (or dark) signals from the environment. How changing photoperi-ods are evaluated against the circadian oscillator reference will be discussed shortly.
Plants Can Be Classified by Their Photoperiodic Responses Numerous plant species flower during the long days of summer, and for many years plant physiologists believed that the correlation between long days and flowering was a consequence of the accumulation of photosynthetic prod-ucts synthesized during long days.
This hypothesis was shown to be incorrect by the work of Wightman Garner and Henry Allard, conducted in the 1920s at the U.S. Department of Agriculture laboratories in Beltsville, Maryland. They found that a mutant variety of tobacco, Maryland Mammoth, grew profusely to about 5 m in height but failed to flower in the prevailing con-ditions of summer (Figure 24.17). However, the plants flowered in the greenhouse during the winter under natural light conditions.
These results ultimately led Garner and Allard to test the effect of artifi-cially providing short days by cover-ing plants grown during the long days of summer with a light-tight tent from late in the afternoon until the follow-ing morning. These artificial short days also caused the plants to flower. This requirement for short days was difficult to reconcile with the idea that longer peri-ods of radiation and the resulting increase in photosynthesis promote flowering in gen-eral. Garner and Allard concluded that the length of the day was the determining factor in flowering and were able to confirm this hypothesis in many different species and conditions. This work laid the foundations for the extensive subsequent research on photoperiodic responses.
The classification of plants according to their photoperi-odic responses is usually based on flowering, even though many other aspects of plants’ development may also be affected by day length. The two main photoperiodic response categories are short-day plants and long-day plants: 1. Short-day plants (SDPs) flower only in short days (qualitative SDPs), or their flowering is accelerated by short days (quantitative SDPs).
The Control of Flowering 573 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Hours of daylight J F M A M J J A S O N D Month of year 60˚ 50˚ 40˚ 30˚ 30˚ 30˚ 60˚ 60˚ 20˚ 10˚ 0˚ 0˚ (A) (B) FIGURE 24.16 (A) The effect of latitude on day length at different times of the year. Day length was measured on the twentieth of each month. (B) Global map showing longi-tudes and latitudes.
2. Long-day plants (LDPs) flower only in long days (qualitative LDPs), or their flowering is accelerated by long days (quantitative LDPs).
The essential distinction between long-day and short-day plants is that flowering in LDPs is promoted only when the day length exceeds a certain duration, called the critical day length, in every 24-hour cycle, whereas promotion of flowering in SDPs requires a day length that is less than the critical day length. The absolute value of the critical day length varies widely among species, and only when flow-ering is examined for a range of day lengths can the correct photoperiodic classification be established (Figure 24.18).
Long-day plants can effectively measure the lengthen-ing days of spring or early summer and delay flowering until the critical day length is reached. Many varieties of wheat (Triticum aestivum) behave in this way. SDPs often flower in fall, when the days shorten below the critical day length, as in many varieties of Chrysanthemum morifolium.
However, day length alone is an ambiguous signal because it cannot distinguish between spring and fall.
Plants exhibit several adaptations for avoiding the ambi-guity of day length signal. One is the coupling of a tem-perature requirement to a photoperiodic response. Certain plant species, such as winter wheat, do not respond to pho-toperiod until after a cold period (vernalization or over-wintering) has occurred. (We will discuss vernalization a little later in the chapter.) Other plants avoid seasonal ambiguity by distinguish-ing between shortening and lengthening days. Such “dual–day length plants” fall into two categories: 1. Long-short-day plants (LSDPs) flower only after a sequence of long days followed by short days. LSDPs, such as Bryophyllum, Kalanchoe, and Cestrum noctur-num (night-blooming jasmine), flower in the late sum-mer and fall, when the days are shortening.
2. Short-long-day plants (SLDPs) flower only after a sequence of short days followed by long days.
SLDPs, such as Trifolium repens (white clover), Campanula medium (Canterbury bells), and Echeveria harmsii (echeveria), flower in the early spring in response to lengthening days.
Finally, species that flower under any photoperiodic con-dition are referred to as day-neutral plants. Day-neutral plants (DNPs) are insensitive to day length. Flowering in DNPs is typically under autonomous regulation—that is, internal developmental control. Some day-neutral species, 574 Chapter 24 FIGURE 24.17 Maryland Mammoth mutant of tobacco (right) compared to wild-type tobacco (left). Both plants were grown during summer in the greenhouse. (University of Wisconsin graduate students used for scale.) (Photo courtesy of R. Amasino.) 6 18 Long-day plants (LDPs) Short-day plants (SDPs) 8 16 10 14 12 12 14 10 16 8 18 6 20 4 22 2 24 (h) 0 (h) 100 50 0 Percent flowering Day length Night length Long-day plants flower when the day length exceeds (or the night length is less than) a certain critical duration in a 24-hour cycle.
Short-day plants flower when the day length is less than (or the night length exceeds) a certain critical duration in a 24-hour cycle.
FIGURE 24.18 The photoperi-odic response in long- and short-day plants. The critical duration varies between species: In this example, both the SDPs and the LDPs would flower in photoperiods between 12 and 14 h long. such as Phaseolus vulgaris (kidney bean) evolved near the equator where the daylength is constant throughout the year. Many desert annuals, such as Castilleja chromosa (desert paintbrush) and Abronia villosa (desert sand verbena), evolved to germinate, grow, and flower quickly whenever sufficient water is available. These are also DNPs.
Plants Monitor Day Length by Measuring the Length of the Night Under natural conditions, day and night lengths config-ure a 24-hour cycle of light and darkness. In principle, a plant could perceive a critical day length by measuring the duration of either light or darkness. Much experimental work in the early studies of photoperiodism was devoted to establishing which part of the light–dark cycle is the controlling factor in flowering. Results showed that flow-ering of SDPs is determined primarily by the duration of darkness (Figure 24.19A). It was possible to induce flow-ering in SDPs with light periods longer than the critical value, provided that these were followed by sufficiently long nights (Figure 24.19B). Similarly, SDPs did not flower when short days were followed by short nights.
More detailed experiments demonstrated that photope-riodic timekeeping in SDPs is a matter of measuring the duration of darkness. For example, flowering occurred only when the dark period exceeded 8.5 hours in cocklebur LDP Short-day plants Lighting treatment Flowering response Darkness SDP Light Vegetative Flowering Vegetative Vegetative Vegetative Flowering Vegetative Vegetative Flowering Flowering Flowering Flowering Long-day plants (A) (B) 24 h Light Critical duration of darkness Flash of light Darkness 24 h 24 h Short-day (long-night) plants flower when night length exceeds a critical dark period. Interruption of the dark period by a brief light treatment (a night break) prevents flowering.
Long-day (short-night) plants flower if the night length is shorter than a critical period. In some long-day plants, shortening the night with a night break induces flowering.
Night break FIGURE 24.19 The photoperiodic regulation of flowering.
(A) Effects on SDPs and LDPs. (B) Effects of the duration of the dark period on flowering. Treating short- and long-day plants with different photoperiods clearly shows that the critical variable is the length of the dark period.
The Control of Flowering 575 (Xanthium strumarium) or 10 hours in soybean (Glycine max). The duration of darkness was also shown to be important in LDPs (see Figure 24.19). These plants were found to flower in short days, provided that the accompa-nying night length was also short; however, a regime of long days followed by long nights was ineffective.
Night Breaks Can Cancel the Effect of the Dark Period A feature that underscores the importance of the dark period is that it can be made ineffective by interruption with a short exposure to light, called a night break (see Figure 24.19A). In contrast, interrupting a long day with a brief dark period does not cancel the effect of the long day (see Figure 24.19B). Night-break treatments of only a few minutes are effective in preventing flowering in many SDPs, including Xanthium and Pharbitis, but much longer exposures are often required to promote flowering in LDPs.
In addition, the effect of a night break varies greatly according to the time when it is given. For both LDPs and SDPs, a night break was found to be most effective when given near the middle of a dark period of 16 hours (Fig-ure 24.20).
The discovery of the night-break effect, and its time dependence, had several important consequences. It estab-lished the central role of the dark period and provided a valuable probe for studying photoperiodic timekeeping.
Because only small amounts of light are needed, it became possible to study the action and identity of the photore-ceptor without the interfering effects of photosynthesis and other nonphotoperiodic phenomena. This discovery has also led to the development of commercial methods for regulating the time of flowering in horticultural species, such as Kalanchoe, chrysanthemum, and poinsettia (Euphor-bia pulcherrima).
The Circadian Clock Is Involved in Photoperiodic Timekeeping The decisive effect of night length on flowering indicates that measuring the passage of time in darkness is central to photoperiodic timekeeping. Most of the available evi-dence favors a mechanism based on a circadian rhythm (Bünning 1960). According to the clock hypothesis, pho-toperiodic timekeeping depends on an endogenous circa-dian oscillator of the type involved in the daily rhythms described in Chapter 17 in relation to phytochrome. The central oscillator is coupled to various physiological processes that involve gene expression, including flower-ing in photoperiodic species.
Measurements of the effect of a night break on flower-ing can be used to investigate the role of circadian rhythms in photoperiodic timekeeping. For example, when soybean 576 Chapter 24 2 4 6 8 10 12 14 16 100 50 0 Percentage of maximum flowering Time of night break from beginning of dark period (h) 8-h light period Xanthium (SDP) 16 h dark period Night break: 1 min red light Fuchsia (LDP) 16 h dark period Night break: 1 h of red light FIGURE 24.20 The time when a night break is given deter-mines the flowering response. When given during a long dark period, a night break promotes flowering in LDPs and inhibits flowering in SDPs. In both cases, the greatest effect on flowering occurs when the night break is given near the middle of the 16-hour dark period. The LDP Fuchsia was given a 1-hour exposure to red light in a 16-hour dark period. Xanthium was exposed to red light for 1 minute in a 16-hour dark period. (Data for Fuchsia from Vince-Prue 1975; data for Xanthium from Salisbury 1963 and Papenfuss and Salisbury 1967.) plants, which are SDPs, are transferred from an 8-hour light period to an extended 64-hour dark period, the flow-ering response to night breaks shows a circadian rhythm (Figure 24.21). This type of experiment provides strong support for the clock hypothesis. If this SDP were simply measuring the length of night by the accumulation of a particular inter-mediate in the dark, any dark period greater than the crit-ical night length should cause flowering. Yet long dark periods are not inductive for flowering if the light break is given at a time that does not properly coincide with a cer-tain phase of the endogenous circadian oscillator. This find-ing demonstrates that flowering in SDPs requires both a dark period of sufficient duration and a dawn signal at an appropriate time in the circadian cycle (see Figure 24.15).
Further evidence for the role of a circadian oscillator in photoperiod measurement is the observation that the pho-toperiodic response can be phase-shifted by light treat-ments (see Web Topic 24.4).
The Coincidence Model Is Based on Oscillating Phases of Light Sensitivity The involvement of a circadian oscillator in photoperi-odism poses an important question: How does an oscilla-tion with a 24-hour period measure a critical duration of darkness of, say, 8 to 9 hours, as in the SDP Xanthium?
Erwin Bünning proposed in 1936 that the control of flow-ering by photoperiodism is achieved by an oscillation of phases with different sensitivities to light. This proposal has evolved into a coincidence model (Bünning 1960), in which the circadian oscillator controls the timing of light-sensitive and light-insensitive phases.
The ability of light either to promote or to inhibit flow-ering depends on the phase in which the light is given.
When a light signal is administered during the light-sensi-tive phase of the rhythm, the effect is either to promote flow-ering in LDPs or to prevent flowering in SDPs. As shown in Figure 24.21, the phases of sensitivity and insensitivity to light continue to oscillate in darkness in SDPs. Flowering in SDPs is induced only when exposure to light from a night break or from dawn occurs after completion of the light-sensitive phase of the rhythm. In other words, flower-ing is induced when the light exposure is coincident with the appropriate phase of the rhythm. This continued oscillation of sensitive and insensitive phases in the absence of dawn and dusk light signals is characteristic of a variety of processes controlled by the circadian oscillator.
The Leaf Is the Site of Perception of the Photoperiodic Stimulus The photoperiodic stimulus in both LDPs and SDPs is per-ceived by the leaves. For example, treatment of a single leaf of the SDP Xanthium with short photoperiods is sufficient to cause the formation of flowers, even when the rest of the plant is exposed to long days. Thus, in response to pho-toperiod the leaf transmits a signal that regulates the tran-sition to flowering at the shoot apex. The photoperiod-reg-ulated processes that occur in the leaves resulting in the transmission of a floral stimulus to the shoot apex are referred to collectively as photoperiodic induction.
Photoperiodic induction can take place in a leaf that has been separated from the plant. For example, in the SDP Per-illa crispa, an excised leaf exposed to short days can cause flowering when subsequently grafted to a noninduced plant maintained in long days (Zeevaart and Boyer 1987).
This result indicates that photoperiodic induction depends on events that take place exclusively in the leaf.
Grafting experiments, which have contributed greatly to our understanding of the floral stimulus, will be dis-cussed in more detail later in the chapter.
The Floral Stimulus Is Transported via the Phloem Once produced, the flowering stimulus appears to be trans-ported to the meristem via the phloem, and it appears to be The Control of Flowering 577 8 16 24 32 40 48 56 64 72 100 50 0 Percentage of maximum flowering Time at which night break was given (h) Light period Flowering Light sensitivity Sensitivity to light FIGURE 24.21 Rhythmic flowering in response to night breaks. In this experiment, the SDP soybean (Glycine max) received cycles of an 8-hour light period followed by a 64-hour dark period. A 4-hour night break was given at vari-ous times during the long inductive dark period. The flow-ering response, plotted as the percentage of the maximum, was then plotted for each night break given. Note that a night break given at 26 hours induced maximum flowering, while no flowering was obtained when the night break was given at 40 hours. Moreover, this experiment demonstrates that the sensitivity to the effect of the night break shows a circadian rhythm. These data support a model in which flowering in SDPs is induced only when dawn (or a night break) occurs after the completion of the light-sensitive phase. In LDPs the light break must coincide with the light-sensitive phase for flowering to occur. (Data from Coulter and Hamner 1964.) 578 Chapter 24 chemical rather than physical in nature. Treatments that block phloem transport, such as girdling or localized heat-killing (see Chapter 10), prevent movement of the floral signal.
It is possible to measure rates of movement of the flow-ering stimulus by removing a leaf at different times after induction, and comparing the time it takes for the signal to reach two buds located at different distances from the induced leaf. The rationale for this type of measurement is that a threshold amount of the signaling compound has reached the bud when flowering takes place, despite the removal of the leaf. Studies using this method have shown that the rate of transport of the flowering signal is comparable to, or somewhat slower than, the rate of translocation of sugars in the phloem (see Chapter 10). For example, export of the floral stimulus from adult leaves of the SDP Chenopodium is complete within 22.5 hours from the beginning of the long night period. In the LDP Sinapis, movement of the flo-ral stimulus out of the leaf is complete by as early as 16 hours after the start of the long-day treatment. These rates are consistent with a floral stimulus that moves in the phloem (Zeevaart 1976).
Because the floral stimulus is translocated along with sugars in the phloem, it is subject to source–sink relations.
An induced leaf positioned close to the shoot apex is more likely to cause flowering than an induced leaf at the base of a stem, which normally feeds the roots. Similarly, non-induced leaves positioned between the induced leaf and the apical bud will tend to inhibit flowering by serving as the preferred source leaves for the bud, thus preventing the floral stimulus from the more distal induced leaf from reaching its target. This inhibition also explains why a minimum amount of photosynthesis is required by the induced leaf to drive translocation.
Phytochrome Is the Primary Photoreceptor in Photoperiodism Night-break experiments are well suited for studying the nature of the photoreceptors involved in the reception of light signals during the photoperiodic response. The inhi-bition of flowering in SDPs by night breaks was one of the first physiological processes shown to be under the con-trol of phytochrome (Figure 24.22).
In many SDPs, a night break becomes effective only when the supplied dose of light is sufficient to saturate the photoconversion of Pr (phytochrome that absorbs red light) to Pfr (phytochrome that absorbs far-red light) (see Chapter 17). A subsequent exposure to far-red light, which photoconverts the pigment back to the physiologically inactive Pr form, restores the flowering response.
In some LDPs, red and far-red reversibility has also been demonstrated. In these plants, a night break of red light promoted flowering, and a subsequent exposure to far-red light prevented this response.
Action spectra for the inhibition and restoration of the flowering response in SDPs are shown in Figure 24.23. A peak at 660 nm, the absorption maximum of Pr (see Chap-ter 17), is obtained when dark-grown Pharbitis seedlings are 24 20 16 12 8 4 0 Hours Critical night length R R FR FR R R R FR FR R Long-day (short-night) plant Short-day (long-night) plant FIGURE 24.22 Phytochrome control of flowering by red (R) and far-red (FR) light. A flash of red light dur-ing the dark period induces flow-ering in an LDP, and the effect is reversed by a flash of far-red light.
This response indicates the involve-ment of phytochrome. In SDPs, a flash of red light prevents flower-ing, and the effect is reversed by a flash of far-red light. used to avoid interference from chlorophyll. In contrast, the spectra for Xanthium provide an example of the response in green plants, in which the presence of chlorophyll can cause some discrepancy between the action spectrum and the absorption spectrum of Pr. These action spectra and the reversibility between red light and far-red light confirm the role of phytochrome as the photoreceptor that is involved in photoperiod measurement in SDPs.
In LDPs the role of phytochrome is more complex, and a blue-light photoreceptor (which will be discussed shortly) also plays a role in controlling flowering.
Far-Red Light Modifies Flowering in Some LDPs Circadian rhythms have also been found in LDPs. A circa-dian rhythm in the promotion of flowering by far-red light has been observed in barley (Hordeum vulgare) and Ara-bidopsis (Deitzer 1984), as well as in darnel ryegrass (Lolium temulentum) (Figure 24.24). The response is proportional to the irradiance and duration of far-red light and is therefore a high-irradiance response (HIR). Like other HIRs, PHYA is the phytochrome that mediates the response to far-red light (see Chapter 17). In both cases, when the plant is exposed to far-red light for 4 to 6 hours, flowering is pro-moted compared with plants maintained under continu-ous white or red light—a response mediated by PHYB. The rhythm continues to run in the light.
In SDPs, on the other hand, a characteristic feature of the timing mechanism is that the rhythm of the response to far-red light damps out after a few hours in continuous light and is restarted upon transfer to darkness.
The response to far-red light is not the only rhythmic feature in LDPs. Although relatively insensitive to a night break of only a few minutes, many LDPs can be induced to flower with a longer night break, usually of at least 1 hour. A circadian oscillation in the flowering response to such a long night break has been observed in LDPs, show-ing that a rhythm of responsiveness to light continues to run in darkness.
Thus, circadian rhythms that modify the flowering response in LDPs have been shown to run both in the light (promotion by far-red light) and in the dark (promotion by red or white light). However, we do not yet know how the circadian rhythm is coupled to the photoperiodic response.
The Control of Flowering 579 500 600 700 800 100 50 0 Relative effectiveness of light Wavelength (nm) Inhibition of flowering by a night break Reversal of the night break inhibition Xanthium Xanthium Pharbitis FIGURE 24.23 Action spectra for the control of flowering by night breaks implicates phytochrome. Flowering in SDPs is inhibited by a short light treatment (night break) given in an otherwise inductive period. In the SDP Xanthium stru-marium, red-light night breaks of 620 to 640 nm are the most effective. Reversal of the red-light effect is maximal at 725 nm. In the dark-grown SDP Pharbitis nil, which is devoid of chlorophyll and its interference with light absorption, night breaks of 660 nm are the most effective.
This 660 nm maximum coincides with the absorption maxi-mum of phytochrome. (Data for Xanthium from Hendricks and Siegelman 1967; data for Pharbitis from Saji et al. 1983.) Sensitivity to light 12 24 36 48 60 72 20 40 60 80 100 Time (h) at which far-red light was given Relative increase in number of floral buds (% of control) Light sensitivity FIGURE 24.24 Effect of far-red light on floral induction in Arabidopsis. Four hours of far-red light was added at the indicated times during a continuous 72-hour daylight period. Data points in the graph are plotted at the centers of the 6-hour treatments. The data show a circadian rhythm of sensitivity to the far-red promotion of flowering (red line). This supports a model in which flowering in LDPs is promoted when the light treatment (in this case far-red light) coincides with the peak of light sensitivity.
(After Deitzer 1984.) A Blue-Light Photoreceptor Also Regulates Flowering In some LDPs, such as Arabidopsis, blue light can promote flowering, suggesting the possible participation of a blue-light photoreceptor in the control of flowering. The role of blue light in flowering and its relationship to circadian rhythms have been investigated by use of the luciferase reporter gene construct mentioned in Web Topic 24.6. In continuous white light, the cyclic luminescence has a period of 24.7 hours, but in constant darkness the period lengthens to 30 to 36 hours. Either red or blue light, given individually, shortens the period to 25 hours.
To distinguish between the effects of phytochrome and a blue-light photoreceptor, researchers transformed phy-tochrome-deficient hy1 mutants, which are defective in chromophore synthesis and are therefore deficient in all phytochromes (see Chapter 17), with the luciferase con-struct to determine the effect of the mutation on the period length (Millar et al. 1995).
Under continuous white light, the hy1 plants had a period similar to that of the wild type, indicating that little or no phytochrome is required for white light to affect the period. Furthermore, under continuous red light, which would be perceived only by PHYB (see Chapter 17), the period of hy1 was significantly lengthened (i.e., it became more like constant darkness), whereas the period was not lengthened by continuous blue light. These results indicate that both phytochrome and a blue-light photoreceptor are involved in period control.
The role of blue light in regulating both circadian rhyth-micity and flowering is also supported by studies with an Arabidopsis flowering-time mutant: elf3 (early flowering 3) (see Web Topics 24.5 and 24.6). Confirmation that a blue-light photoreceptor is involved in sensing inductive pho-toperiods in Arabidopsis was recently provided by experi-ments demonstrating that mutations in one of the cryptochrome genes, CRY2 (see Chapter 18), caused a delay in flowering and an inability to perceive inductive pho-toperiods (Guo et al. 1998). As discussed in Chapter 18, CRY1 encodes a blue-light photoreceptor controlling seedling growth in Arabidopsis. Thus, various CRY family members have, through evolution, become specialized for different functions in the plant. As noted earlier, the CRY protein has also been implicated in the entrainment of the circadian oscillator (see Chapter 17).
VERNALIZATION: PROMOTING FLOWERING WITH COLD Vernalization is the process whereby flowering is promoted by a cold treatment given to a fully hydrated seed (i.e., a seed that has imbibed water) or to a growing plant. Dry seeds do not respond to the cold treatment. Without the cold treat-ment, plants that require vernalization show delayed flow-ering or remain vegetative. In many cases these plants grow as rosettes with no elongation of the stem (Figure 24.25).
In this section we will examine some of the character-istics of the cold requirement for flowering, including the 580 Chapter 24 FIGURE 24.25 Vernalization induces flowering in the win-ter-annual types of Arabidopsis thaliana. The plant on the left is a winter-annual type that has not been exposed to cold.
The plant on the right is a genetically identical winter-annual type that was exposed to 40 days of temperatures slightly above freezing (4 °C) as a seedling. It flowered 3 weeks after the end of the cold treatment with about 9 leaves on the primary stem. (Courtesy of Colleen Bizzell.) Winter-annual Arabidopsis without vernalization Winter-annual Arabidopsis with vernalization range and duration of the inductive temperatures, the sites of perception, the relationship to photoperiodism, and a possible molecular mechanism.
Vernalization Results in Competence to Flower at the Shoot Apical Meristem Plants differ considerably in the age at which they become sensitive to vernalization. Winter annuals, such as the win-ter forms of cereals (which are sown in the fall and flower in the following summer), respond to low temperature very early in their life cycle. They can be vernalized before germination if the seeds have imbibed water and become metabolically active. Other plants, including most bienni-als (which grow as rosettes during the first season after sowing and flower in the following summer), must reach a minimal size before they become sensitive to low tem-perature for vernalization.
The effective temperature range for vernalization is from just below freezing to about 10°C, with a broad optimum usually between about 1 and 7°C (Lang 1965). The effect of cold increases with the duration of the cold treatment until the response is saturated. The response usually requires several weeks of exposure to low temperature, but the pre-cise duration varies widely with species and variety.
Vernalization can be lost as a result of exposure to dev-ernalizing conditions, such as high temperature (Figure 24.26), but the longer the exposure to low temperature, the more permanent the vernalization effect.
Vernalization appears to take place primarily in the shoot apical meristem. Localized cooling causes flowering when only the stem apex is chilled, and this effect appears to be largely independent of the temperature experienced by the rest of the plant. Excised shoot tips have been suc-cessfully vernalized, and where seed vernalization is pos-sible, fragments of embryos consisting essentially of the shoot tip are sensitive to low temperature.
In developmental terms, vernalization results in the acquisition of competence of the meristem to undergo the floral transition. Yet, as discussed earlier in the chapter, com-petence to flower does not guarantee that flowering will occur. A vernalization requirement is often linked with a requirement for a particular photoperiod (Lang 1965). The most common combination is a requirement for cold treat-ment followed by a requirement for long days—a combina-tion that leads to flowering in early summer at high latitudes (see Web Topic 24.7). Unless devernalized, the vernalized meristem can remain competent to flower for as long as 300 days in the absence of the inductive photoperiod.
Vernalization May Involve Epigenetic Changes in Gene Expression It is important to note that for vernalization to occur, active metabolism is required during the cold treatment. Sources of energy (sugars) and oxygen are required, and tempera-tures below freezing at which metabolic activity is sup-pressed are not effective for vernalization. Furthermore, cell division and DNA replication also appear to be required.
One model for how vernalization affects competence is that there are stable changes in the pattern of gene expression in the meristem after cold treatment. Changes in gene expres-sion that are stable even after the signal that induced the change (in this case cold) is removed are known as epige-netic regulation. Epigenetic changes of gene expression in many organisms, from yeast to mammals, often require cell division and DNAreplication, as is the case for vernalization.
The involvement of epigenetic regulation in the vernal-ization process has been confirmed in the LDP Arabidopsis.
In winter-annual ecotypes of Arabidopsis that require both vernalization and long days to flower, a gene that acts as a repressor of flowering has been identified: FLOWERING LOCUS C (FLC). FLC is highly expressed in nonvernalized shoot apical meristems (Michaels and Amasino 2000). After vernalization, this gene is epigenetically switched off by an unknown mechanism for the remainder of the plant’s life cycle, permitting flowering in response to long days to occur (Figure 24.27). In the next generation, however, the gene is switched on again, restoring the requirement for The Control of Flowering 581 8 6 4 2 100 80 60 40 20 0 Percent of seeds remaining vernalized after devernalizing treatment Duration of cold treatment (weeks) FIGURE 24.26 The duration of exposure to low temperature increases the stability of the vernalization effect. The longer that winter rye (Secale cereale) is exposed to a cold treatment, the greater the number of plants that remain vernalized when the cold treatment is followed by a devernalizing treatment. In this experiment, seeds of rye that had imbibed water were exposed to 5°C for different lengths of time, then immediately given a dever-nalizing treatment of 3 days at 35°C. (Data from Purvis and Gregory 1952.) cold. Thus in Arabidopsis, the state of expression of the FLC gene represents a major determinant of meristem compe-tence (Michaels and Amasino 2000).
BIOCHEMICAL SIGNALING INVOLVED IN FLOWERING In the preceding sections we examined the influence of environmental conditions (such as temperature and day length) versus that of autonomous factors (such as age) on flowering. Although floral evocation occurs at the apical meristems of the shoots, some of the events that result in floral evocation are triggered by biochemical signals arriv-ing at the apex from other parts of the plant, especially from the leaves. Mutants have been isolated that are defi-cient in the floral stimulus (see Web Topic 24.6).
In this section we will consider the nature of the bio-chemical signals arriving from the leaves and other parts of the plant in response to photoperiodic stimuli. Such sig-nals may serve either as activators or as inhibitors of flow-ering. After years of investigation, no single substance has been identified as the universal floral stimulus, although certain hormones, such as gibberellins and ethylene, can induce flowering in some species. Hence, most current models of the floral stimulus are based on multiple factors.
Grafting Studies Have Provided Evidence for a Transmissible Floral Stimulus The production in photoperiodically induced leaves of a biochemical signal that is transported to a distant target tis-sue (the shoot apex) where it stimulates a response (flow-ering) satisfies an important criterion for a hormonal effect.
In the 1930s, Mikhail Chailakhyan, working in Russia, pos-tulated the existence of a universal flowering hormone, which he named florigen.
The evidence in support of florigen comes mainly from early grafting experiments in which noninduced receptor plants were stimulated to flower by being grafted onto a leaf or shoot from photoperiodically induced donor plants.
For example, in the SDP Perilla crispa, a member of the mint family, grafting a leaf from a plant grown under inductive short days onto a plant grown under noninductive long days causes the latter to flower (Figure 24.28). Moreover, the floral stimulus seems to be the same in plants with different photoperiodic requirements. Thus, grafting an induced leaf from the LDP Nicotiana sylvestris, grown under long days, onto the SDP Maryland Mammoth tobacco caused the lat-ter to flower under noninductive (long day) conditions.
The leaves of DNPs have also been shown to produce a graft-transmissible floral stimulus (Table 24.2). For exam-ple, grafting a single leaf of a day-neutral variety of soy-582 Chapter 24 Winter annual without cold Winter annual after 40 days cold Winter annual without cold, but with an FLC mutation FLC mRNA FIGURE 24.27 (Left) Vernalization blocks the expression of the gene FLOWERING LOCUS C (FLC) in cold-requiring winter annual ecotypes of Arabidopsis. (Right) A winter annual with an FLC mutation exhibits early flowering with-out cold treatment. (Photo courtesy of R. Amasino.) bean, Agate, onto the short-day variety, Biloxi, caused flow-ering in Biloxi even when the latter was maintained in non-inductive long days. Similarly, a leaf from a day-neutral variety of tobacco (Nicotiana tabacum, cv. Trapezond) grafted onto the LDP Nicotiana sylvestris induced the latter to flower under noninductive short days.
In a few cases, flowering has been induced by grafts between different genera. The SDP Xanthium strumarium flowered under long-day conditions when shoots of flow-ering Calendula officinalis were grafted onto a vegetative Xan-thium stock. Similarly, grafting a shoot from the LDP Petunia hybrida onto a stock of the cold-requiring biennial Hyoscya-mus niger (henbane) caused the latter to flower under long days, even though it was nonvernalized (Figure 24.29).
In Perilla (see Figure 24.28), the movement of the floral stimulus from a donor leaf to the stock across the graft union FIGURE 24.28 Demonstration by grafting of a leaf-generated floral stimulus in the SDP Perilla. (Left) Grafting an induced leaf from a plant grown under short days onto a noninduced shoot causes the axillary shoots to produce flowers. The donor leaf has been trimmed to facilitate grafting, and the upper leaves have been removed from the stock to promote phloem translocation from the scion to the receptor shoots. (Right) Grafting a noninduced leaf from a plant grown under LDs results in the formation of vegetative branches only. (Photo courtesy of J. A. D.
Zeevaart.) TABLE 24.2 Transmissible factors regulate flowering.
Donor plants maintained under flower-Photoperiod Vegetative receptor plant Photoperiod inducing conditions typea,b induced to flower typea,b Helianthus annus DNP in LD H.tuberosus SDP in LD Nicotiana tabacum Delcrest DNP in SD N.sylvestris LDP in SD Nicotiana sylvestris LDP in LD N.tabacum SDP in LD Maryland Mammoth Nicotiana tabacum SDP in SD N.sylvestris LDP in SD Maryland Mammoth Note:The successful transfer of a flowering induction signal by grafting between plants of different pho-toperiodic response groups shows the existence of a transmissible floral hormone that is effective.
aLDPs = Long-day plants; SDPs = Short- day plants; DNPs = Day-neutral plants.
bLD, long days; SD, short days.
FIGURE 24.29 Successful transfer of the floral stimulus between different genera: The scion (right branch) is the LDP Petunia hybrida, and the stock is nonvernalized Hyoscyamus niger (henbane). The graft combination was maintained under LDs. (Photo courtesy of J. A. D.
Zeevaart.) Induced graft donor Uninduced graft donor correlated closely with the translocation of 14C-labeled assimilates from the donor, and this movement was depen-dent on the establishment of vascular continuity across the graft union (Zeevaart 1976). These results confirmed earlier girdling studies showing that the floral stimulus is translo-cated along with photoassimilates in the phloem.
Indirect Induction Implies That the Floral Stimulus Is Self-Propagating In at least three cases—Xanthium (SDP), Bryophyllum (SLDP), and Silene (LDP)—the induced state appears to be self-propagating (Zeevaart 1976). That is, young leaves that develop on the receptor plant after it has been induced to flower by a donor leaf can themselves be used as donor leaves in subsequent grafting experiments, even though these leaves have never been subjected to an inductive pho-toperiod. This phenomenon is called indirect induction.
It is characteristic of indirect induction that the strength of the floral stimulus from the donor leaf remains constant even after serial grafting of new donors to several plants has taken place (Figure 24.30A). This suggests that the induced state is in some way propagated throughout the 584 Chapter 24 Induced Xanthium plant First noninduced stock Male inflorescence First graft First graft Second noninduced stock Second graft Third noninduced stock Third graft Fourth noninduced stock Fourth graft Induced plant Uninduced stock Uninduced stock Uninduced stock Uninduced leaves removed from stock to promote source sink movement to axillary bud from induced leaf (B) Grafting of induced leaf to uninduced shoot causes flowering in multiple grafts in Perilla.
(A) Indirect induction can be demonstrated in serial grafting experiments in Xanthium.
Second graft Third graft FIGURE 24.30 Different types of leaf induction in Xanthium and Perilla. (A) Xanthium exhibits indirect induction. Noninduced leaves from a plant induced to flower are capable of inducing other plants to flower even though they have never received an inductive photope-riod. This suggests that the flo-ral stimulus is self-propagating.
(B) In Perilla, only the leaf given the inductive photoperiod is capable of serving as a donor for the floral stimulus. In Perilla as well as Xanthium, one leaf can continue to induce flower-ing in successive grafting exper-iments (Lang 1965).
plant. Although this feature of the floral stimulus has some-times been described as viruslike, it is unlikely that the flo-ral stimulus can replicate itself like a virus. Rather, the flo-ral stimulus is likely to be a molecule that induces its own production in a positive feedback loop. In Xanthium (cock-lebur), removal of all buds from the shoot blocks indirect induction, indicating that meristematic tissue, or perhaps auxin, is required for propagation of the induced state.
On the other hand, indirect induction does not occur in the SDP Perilla. In Perilla, only the leaf actually given an inductive photoperiod is capable of transmitting the floral stimulus in a grafting experiment (see Figure 24.30B). Thus the floral stimulus of Perilla is not self-propagating as it is in Xanthium, Bryophyllum, and Silene. Either the mechanism for a positive feedback loop is absent in Perilla leaves, or translocation of the floral stimulus is restricted to the meris-tem so that it never enters the leaves.
Unlike Xanthium, which requires the presence of a bud for stable induction, Perilla leaves can be stably induced even when detached from the plant. Once induced, Perilla leaves cannot be uninduced, and the same leaf can con-tinue to serve as a donor of the floral stimulus in successive grafting experiments without any reduction in potency (Zeevaart 1976).
Evidence for Antiflorigen Has Been Found in Some LDPs Grafting studies have implicated transmissible inhibitors in flowering regulation as well. Such inhibitors have been called antiflorigen, but (like florigen) antiflorigen may con-sist of multiple compounds. For example, grafting an unin-duced leafy shoot from the LDP Nicotiana sylvestris onto the day-neutral tobacco cultivar Trapezond suppressed flower-ing in the day-neutral plant under short days but not long-day conditions (Figure 24.31). On the other hand, when an uninduced donor from the SDP Maryland Mammoth was grafted onto Trapezond, it had no effect on flowering in either short-day or long-day conditions. This and similar results suggest that the leaves of LDPs, but not SDPs, pro-duce flowering inhibitors under noninductive conditions.
Similar studies in peas have led to the identification of several genetic loci that regulate steps in the biosynthetic pathways of both floral activators and floral inhibitors (see Web Topic 24.5).
Attempts to Isolate Transmissible Floral Regulators Have Been Unsuccessful The many attempts to isolate and characterize the floral stimulus have been largely unsuccessful. The most com-mon approach has been to make extracts from induced leaf tissue and test for their ability to elicit flowering in nonin-duced plants. In other experiments, investigators have extracted and analyzed phloem sap from induced plants.
In some studies, extracts from one of these sources have induced flowering in test plants, but these results have not been consistently reproduced. Most of these extractions have focused on small molecules.
Recent studies using fluorescent tracers have shown that in Arabidopsis there is actually a decrease in the movement of small molecules from the leaf-to-shoot apex via the sym-plast at the time of floral induction (Gisel et al. 2002). The lack of tracer movement from the leaf to the shoot apex may indicate either a reduction in overall symplastic trans-port to the shoot apex, or a change in the selectivity of the plasmodesmata during floral induction. There is increas-ing evidence that macromolecular traffic between cells via plasmodesmata plays essential roles in normal meristem development and function (see Chapter 16). Particles as large as viruses can move from cell to cell via plasmodes-mata, and throughout the plant via the phloem. Phloem translocation of small RNAs has recently been implicated in the spread of a viral resistance mechanism throughout plants (Hamilton and Baulcombe 1999). It is therefore pos-sible that the floral stimulus is a macromolecule, such as RNA or protein, that is translocated via the phloem from the leaf to the apical meristem, where it functions as a reg-ulator of gene expression (Crawford and Zambryski 1999).
FIGURE 24.31 Graft transmission of an inhibitor of flower-ing. Non-induced rosettes from the LDP Nicotiana sylvestris were grafted onto the day-neutral tobacco (Nicotiana tabacum, cv. Trapezond). Flowering of the day-neutral plant was suppressed under short days (left branch of plant on right), but not under long days (left branch of plant on left).
Arrowheads indicate graft unions. (From Lang et al. 1977.) The Control of Flowering 585 Long days Short days However, thus far attempts to identify such a signal have been unsuccessful.
Efforts to isolate a specific, graft-transmissible inhibitor of flowering have also been unsuccessful. Thus, despite unequivocal data from grafting experiments showing that transmissible factors regulate flowering (see Table 24.2) (Zeevaart 1976), the substances involved remain elusive.
Gibberellins and Ethylene Can Induce Flowering in Some Plants Among the naturally occurring growth hormones, gib-berellins (GAs) (see Chapter 20) can have a strong influence on flowering (see Web Topic 24.8). Recent studies suggest that gibberellin promotes flowering in Arabidopsis by acti-vating expression of the LFY gene (Blazquez and Weigel 2000). Exogenous gibberellin can evoke flowering when applied either to rosette LDPs like Arabidopsis, or to dual–day length plants such as Bryophyllum, when grown under short days (Lang 1965; Zeevaart 1985). In addition, application of GAs can evoke flowering in a few SDPs in noninductive conditions, and in cold-requir-ing plants that have not been vernalized. As previously dis-cussed, cone formation can also be promoted in juvenile plants of several gymnosperm families by addition of GAs.
Thus, in some plants exogenous GAs can bypass the endogenous trigger of age in autonomous flowering, as well as the primary environmental signals of day length and temperature.
As discussed in Chapter 20, plants contain many GA-like compounds. Most of these compounds are either pre-cursors to, or inactive metabolites of, the active forms of GA. In some situations different GAs have markedly dif-ferent effects on flowering and stem elongation, such as in the long-day plant Lolium temulentum (darnel ryegrass) (see Web Topic 24.9). These observations suggest that the regulation of flow-ering may be associated with specific GAs, but they do not prove that GA is the hypothetical flowering hormone. In fact, a certain level of GA is likely to be required for flow-ering in many species, but other pathways to flowering are necessary as well. For example, a mutation in GA biosyn-thesis renders the quantitative LDP Arabidopsis thaliana unable to flower in noninductive short days but has little effect on flowering in long days, demonstrating that endogenous GA is required for flowering in specific situa-tions (Wilson et al. 1992).
Considerable attention has been given to the effects of day length on GA metabolism in the plant (see Chapter 20).
For example, in the long-day plant spinach (Spinacia oler-acea), the levels of gibberellins are relatively low in short days, and the plants maintain a rosette form. After the plants are transferred to long days, the levels of all the gib-berellins of the 13-hydroxylated pathway (GA53 →GA44 → GA19 →GA20 →GA1; see Chapter 20) increase. However, the fivefold increase in the physiologically active gib-berellin, GA1, is what causes the marked stem elongation that accompanies flowering.
In addition to GAs, other growth hormones can either inhibit or promote flowering. One commercially important example is the striking promotion of flowering in pineap-ple (Ananas comosus) by ethylene and ethylene-releasing compounds—a response that appears to be restricted to members of the pineapple family (Bromeliaceae). Thus, as discussed next, the floral stimulus may be composed of many components, and these components may differ in different groups of plants.
The Transition to Flowering Involves Multiple Factors and Pathways It is clear that the transition to flowering involves a com-plex system of interacting factors that include, among oth-ers, carbohydrates, gibberellins, cytokinins, and, in the bromeliads, ethylene (see Web Topic 24.10). Leaf-generated transmissible signals are required for determination of the shoot apex in both autonomously regulated and photope-riodic species. Determining whether these transmissible signals consist of single or multiple components is a major challenge for the future.
Recent genetic studies have established that there are four genetically distinct developmental pathways that con-trol flowering in the LDP Arabidopsis (Blazquez 2000). Fig-ure 24.32 shows a simplified version of the four pathways: 1. The photoperiodic pathway involves phytochromes and cryptochromes. (Note that PHYA and PHYB have contrasting effects on flowering; see Web Topic 24.11.) The interaction of these photoreceptors with a circadian clock initiates a pathway that eventually results in the expression of the gene CONSTANS (CO), which encodes a zinc-finger transcription factor that promotes flowering. CO acts through other genes to increase the expression of the floral meristem iden-tity gene LEAFY (LFY).
2. In the dual autonomous/vernalization pathway, flower-ing occurs either in response to internal signals—the production of a fixed number of leaves—or to low temperatures. In the autonomous pathway of Arabidopsis, all of the genes associated with the path-way are expressed in the meristem. The autonomous pathway acts by reducing the expression of the flow-ering repressor gene FLOWERING LOCUS C (FLC), an inhibitor of LFY (Michaels and Amasino 2000).
Vernalization also represses FLC, but perhaps by a different mechanism (an epigenetic switch). Because the FLC gene is a common target, the autonomous and vernalization pathways are grouped together.
3. The carbohydrate, or sucrose, pathway reflects the meta-bolic state of the plant. Sucrose stimulates flowering in Arabidopsis by increasing LFY expression, although the genetic pathway is unknown.
586 Chapter 24 4. The gibberellin pathway is required for early flowering and for flowering under noninductive short days.
All four pathways converge by increasing the expres-sion of the key floral meristem identity gene AGAMOUS-LIKE 20 (AGL20). The role of AGL20, a MADS box–con-taining transcription factor, is to integrate the signals coming from all four pathways into a unitary output. Obvi-ously the strongest output signal occurs when all four path-ways are activated.
Figure 24.33 shows the level of AGL20 gene expression in the shoot apical meristem of an Arabidopsis plant after shifting from noninductive short days (8-hour day length) to inductive long days (16-hour day length). Note that an increase in AGL20 expression can be detected as early as 18 hours after the beginning of the long-day treatment (Borner et al. 2000). Thus it takes only 10 hours beyond an 8-hour short day for the meristem to begin responding to the floral stimulus from the leaves. This timing is consistent with pre-vious measurements of the rates of export of the floral stim-ulus from induced leaves (discussed earlier in the chapter).
Although many pathways feed into AGL20, there must be some redundancy in the system because flowering is only delayed, but not completely blocked, in agl20 mutants.
Thus, one or two other genes must be able to take over the role of AGL20 when it is mutated.
Once turned on by AGL20, LFY activates the floral homeotic genes—APETALA1 (AP1), APETALA3 (AP3), PISTILLATA (PI), and AGAMOUS (AG)—that are required for floral organ development. APETALA2 (AP2) is expressed in both vegetative and floral meristems and is therefore not affected by LFY. However, as discussed ear-lier in the chapter, AP2 exerts a negative effect on AG expression (see Figure 24.6).
Besides serving as a floral homeotic gene, AP1 functions as a meristem identity gene in Arabidopsis because it is involved in a positive feedback loop with LFY. Conse-The Control of Flowering 587 Light CLOCK GENES "Florigen" (phloem) CONSTANS FLOWERING LOCUS C AGAMOUS-LIKE 20 LEAFY Photoperiodism Sucrose Energy pathway Gibberellin pathway GA receptor Red PHYB PHYA CRY1 CRY2 Far red Blue Autonomous pathway Vernalization Leaf number Low temperature Gibberellins ?
?
Meristem identity genes Floral homeotic genes Floral organs AP1 AP3, PI AP2 AG Sepals Stamens Petals Carpels Inhibits flowering FIGURE 24.32 Four developmental path-ways for flowering in Arabidopsis: the photoperiodism, autonomous/vernaliza-tion, sucrose, and gibberellin pathways.
A transmissible floral stimulus (“flori-gen”) from leaves is only involved in the photoperiodic pathway. (After Blazquez 2000.) quently, once the transition to flowering has reached this stage, flowering is irreversible.
The existence of multiple flowering pathways provides angiosperms with maximum reproductive flexibility, enabling them to produce seeds under a wide variety of conditions. Redundancy within the pathways ensures that reproduction, the most crucial of all physiological func-tions, will be relatively insensitive to mutations and evo-lutionarily robust. The details of the pathways undoubtedly vary among different species. In maize, for example, at least one of the genes involved in the autonomous pathway is expressed in leaves (see Web Topic 24.12). Nevertheless, the presence of multiple flowering pathways is probably universal among angiosperms.
SUMMARY Flower formation occurs at the shoot apical meristem and is a complex morphological event. The rosette plant Ara-bidopsis has been an important model for studies on floral development. The four floral organs (sepals, petals, sta-mens, and carpels) are initiated as successive whorls. Three classes of genes regulate floral development. The first class contains positive regulators of the floral meristem identity.
APETALA1 (AP1) and LEAFY (LFY) are the most important Arabidopsis floral meristem identity genes. Meristem identity genes are positive regulators of another class of genes that determine floral organ identity.
There are five known floral organ identity genes in Ara-bidopsis: APETALA1 (AP1), APETALA2 (AP2), APETALA3 (AP3), PISTILLATA (PI), and AGAMOUS (AG). Cadastral genes make up the third group. Cadastral genes act as spa-tial regulators of the floral organ identity genes by setting boundaries for their expression.
The genes that control floral organ identity are homeotic. Most homeotic genes in plants contain the MADS box. Mutations in these genes alter the identity of the floral organs produced in two adjacent whorls. The ABC model seeks to explain how the floral homeotic genes control organ identity through the unique combinations of their products. Type A genes control organ identity in the first and second whorls. Type B activity controls organ determination in the second and third whorls. The third and fourth whorls are controlled by type C activity.
The ability to flower (i.e., to make the transition from juvenility to maturity) is attained when the plant has reached a certain age or size. In some plants, the transition to flowering then occurs independently of the environment (autonomously). Other plants require exposure to appro-priate environmental conditions. The most common envi-ronmental inputs for flowering are day length and tem-perature.
The response to day length—photoperiodism—pro-motes flowering at a particular time of year, and several different categories of responses are known. The photope-riodic signal is perceived by the leaf. Exposure to low tem-perature—vernalization—is required for flowering in some plants, and this requirement is often coupled with a day length requirement. Vernalization occurs at the shoot api-cal meristem. Photoperiodism and vernalization interact in several ways.
Daily rhythms—circadian rhythms—can locate an event at a particular time of day. Timekeeping in these rhythms is based on an endogenous circadian oscillator. Keeping the rhythm on local time depends on the phase response of the rhythm to environmental signals. The most important sig-nals are dawn and dusk. Short-day plants flower when a critical duration of dark-ness is exceeded. Long-day plants flower when the length 588 Chapter 24 Short days to long days at time 0 0 h 18 h 42 h 5 d FIGURE 24.33 Increase in expression of the gene AGAMOUS-LIKE 20 (AGL20) dur-ing floral evocation in the shoot apical meristem of Arabidopsis. The times after shifting the plants from SDs to LDs are indicated. (From Borner et al. 2000.) of the dark period is less than a critical value. Light given at certain times in a dark period that is longer than the crit-ical value—a night break—prevents the effect of the dark period. Light also acts on the circadian oscillator to entrain the photoperiodic rhythm, an effect that is important for timekeeping in the dark. The photoperiodic mechanism shows some variation in short-day and long-day responses, but both appear to involve phytochrome and a circadian oscillator.
When photoperiod-responsive plants are induced to flower by exposure to appropriate day lengths, leaves send a chemical signal to the apex to bring about flowering. This transmissible signal is able to cause flowering in plants of different photoperiodic response groups. In noninductive day lengths, a transmissible inhibitor of flowering may be produced by the leaves of LDPs. Although physiological experiments, especially graft-ing, indicate the existence of a transmissible floral stimulus and, in some cases, flowering inhibitors, the chemical iden-tity of these factors is not known. Plant growth hormones, especially the gibberellins, can modify flowering in many plants. The transition to flowering is regulated by multiple sig-nals and multiple pathways. In Arabidopsis, flowering is controlled by four pathways: the photoperiodic, autonomous/vernalization, sucrose, and GA pathways. All of these pathways converge to regulate the meristem iden-tity genes AGAMOUS-LIKE 20 (AGL20) and LEAFY (LFY).
AGL20 and LFY, in turn, regulate the floral homeotic genes to produce the floral organs. The existence of multiple pathways for flowering provides angiosperms with the flexibility to reproduce under a variety of environmental conditions, thus increasing their evolutionary fitness.
Web Material Web Topics 24.1 Contrasting the Characteristics of Juvenile and Adult Phases of English Ivy (Hedera helix) and Maize (Zea mays) A table of juvenile vs. adult morphological characteristics is presented.
24.2 Regulation of Juvenility by the TEOPOD (TP) Genes in Maize The genetic control of juvenility in maize is discussed.
24.3 Flowering of Juvenile Meristems Grafted to Adult Plants The competence of juvenile meristems to flower can be tested in grafting experiments.
24.4 Characteristics of the Phase-Shifting Response in Circadian Rhythms Petal movements in Kalenchoe have been used to study circadian rhythms.
24.5 Genes That Control Flowering Time A discussion of genes that control different apects of flowering time is presented.
24.6 Support for the Role of Blue-Light Regulation of Circadian Rhythms The role of ELF3 in mediating the effects of blue light on flowering time is discussed.
24.7 Regulation of Flowering in Canterbury Bell by Both Photoperiod and Vernalization Short days acting on the leaf can substitute for vernalization at the shoot apex in Canterbury Bell.
24.8 Examples of Floral Induction by Gibberellins in Plants with Different Environmental Requirements for Flowering A table of the effects of gibberellins on plants with different photoperiodic requirements.
24.9 The Different Effects of Two Different Gibberellins on Flowering (Spike Length) and Elongation (Stem Length) GA1 and GA32 have different effects on flower-ing in Lolium.
24.10 The Influence of Cytokinins and Polyamines on Flowering Other growth regulators beside gibberellins may participate in the flowering response.
24.11 The Contrasting Effects of Phytochromes A and B on Flowering A brief discussion of the effects of phyA and phyB on flowering in Arabidopsis and other species.
24.12 A Gene That Regulates the Floral Stimulus in Maize The INDETERMINATE 1 gene of maize regu-lates the transition to flowering and is expressed in young leaves.
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590 Chapter 24 Stress Physiology 25 Chapter IN BOTH NATURALAND AGRICULTURAL CONDITIONS, plants are frequently exposed to environmental stresses. Some environmental fac-tors, such as air temperature, can become stressful in just a few minutes; others, such as soil water content, may take days to weeks, and factors such as soil mineral deficiencies can take months to become stressful. It has been estimated that because of stress resulting from climatic and soil conditions (abiotic factors) that are suboptimal, the yield of field-grown crops in the United States is only 22% of the genetic potential yield (Boyer 1982).
In addition, stress plays a major role in determining how soil and cli-mate limit the distribution of plant species. Thus, understanding the physiological processes that underlie stress injury and the adaptation and acclimation mechanisms of plants to environmental stress is of immense importance to both agriculture and the environment.
The concept of plant stress is often used imprecisely, and stress ter-minology can be confusing, so it is useful to start our discussion with some definitions. Stress is usually defined as an external factor that exerts a disadvantageous influence on the plant. This chapter will con-cern itself with environmental or abiotic factors that produce stress in plants, although biotic factors such as weeds, pathogens, and insect pre-dation can also produce stress. In most cases, stress is measured in rela-tion to plant survival, crop yield, growth (biomass accumulation), or the primary assimilation processes (CO2 and mineral uptake), which are related to overall growth.
The concept of stress is intimately associated with that of stress tol-erance, which is the plant’s fitness to cope with an unfavorable envi-ronment. In the literature the term stress resistance is often used inter-changeably with stress tolerance, although the latter term is preferred.
Note that an environment that is stressful for one plant may not be stressful for another. For example, pea (Pisum sativum) and soybean (Glycine max) grow best at about 20°C and 30°C, respectively. As tem-perature increases, the pea shows signs of heat stress much sooner than the soybean. Thus the soybean has greater heat stress tolerance.
If tolerance increases as a result of exposure to prior stress, the plant is said to be acclimated (or hardened).
Acclimation can be distinguished from adaptation, which usually refers to a genetically determined level of resistance acquired by a process of selection over many generations.
Unfortunately, the term adaptation is sometimes used in the literature to indicate acclimation. And to add to the com-plexity, we will see later that gene expression plays an important role in acclimation.
Adaptation and acclimation to environmental stresses result from integrated events occurring at all levels of orga-nization, from the anatomical and morphological level to the cellular, biochemical, and molecular level. For example, the wilting of leaves in response to water deficit reduces both water loss from the leaf and exposure to incident light, thereby reducing heat stress on leaves.
Cellular responses to stress include changes in the cell cycle and cell division, changes in the endomembrane sys-tem and vacuolization of cells, and changes in cell wall architecture, all leading to enhanced stress tolerance of cells. At the biochemical level, plants alter metabolism in various ways to accommodate environmental stresses, including producing osmoregulatory compounds such as proline and glycine betaine. The molecular events linking the perception of a stress signal with the genomic responses leading to tolerance have been intensively investigated in recent years.
In this chapter we will examine these principles, and the ways in which plants adapt and acclimate to water deficit, salinity, chilling and freezing, heat, and oxygen deficiency in the root biosphere. Air pollution, an important source of plant stress, is discussed in Web Essay 25.1. Although it is convenient to examine each of these stress factors sepa-rately, most are interrelated, and a common set of cellular, biochemical, and molecular responses accompanies many of the individual acclimation and adaptation processes.
For example, water deficit is often associated with salin-ity in the root biosphere and with heat stress in the leaves (resulting from decreased evaporative cooling due to low transpiration), and chilling and freezing lead to reductions in water activity and osmotic stress. We will also see that plants often display cross-tolerance—that is, tolerance to one stress induced by acclimation to another. This behav-ior implies that mechanisms of resistance to several stresses share many common features.
WATER DEFICIT AND DROUGHT RESISTANCE In this section we will examine some drought resistance mechanisms, which are divided into several types. First we can distinguish between desiccation postponement (the ability to maintain tissue hydration) and desiccation tol-erance (the ability to function while dehydrated), which are sometimes referred to as drought tolerance at high and low water potentials, respectively. The older literature often uses the term drought avoidance (instead of drought tolerance), but this term is a misnomer because drought is a meteoro-logical condition that is tolerated by all plants that survive it and avoided by none. A third category, drought escape, comprises plants that complete their life cycles during the wet season, before the onset of drought. These are the only true “drought avoiders.” Among the desiccation postponers are water savers and water spenders. Water savers use water conservatively, pre-serving some in the soil for use late in their life cycle; water spenders aggressively consume water, often using prodigious quantities. The mesquite tree (Prosopis sp.) is an example of a water spender. This deeply rooted species has ravaged semiarid rangelands in the southwestern United States, and because of its prodigious water use, it has prevented the reestablishment of grasses that have agronomic value.
Drought Resistance Strategies Vary with Climatic or Soil Conditions The water-limited productivity of plants (Table 25.1) depends on the total amount of water available and on the water-use efficiency of the plant (see Chapters 4 and 9). A plant that is capable of acquiring more water or that has higher water-use efficiency will resist drought better. Some plants possess adaptations, such as the C4 and CAM modes of photosynthesis that allow them to exploit more arid environments. In addition, plants possess acclimation mechanisms that are activated in response to water stress.
Water deficit can be defined as any water content of a tissue or cell that is below the highest water content exhib-ited at the most hydrated state. When water deficit devel-ops slowly enough to allow changes in developmental processes, water stress has several effects on growth, one of which is a limitation in leaf expansion. Leaf area is important because photosynthesis is usually proportional to it. However, rapid leaf expansion can adversely affect water availability.
592 Chapter 25 TABLE 25.1 Yields of corn and soybean crops in the United States Crop yield (percentage of 10-year average) Year Corn Soybean 1979 104 106 1980 87 88 Severe drought 1981 104 100 1982 108 104 1983 77 87 Severe drought 1984 101 93 1985 112 113 1986 113 110 1987 114 111 1988 80 89 Severe drought Source: U.S. Department of Agriculture 1989.
If precipitation occurs only during winter and spring, and summers are dry, accelerated early growth can lead to large leaf areas, rapid water depletion, and too little resid-ual soil moisture for the plant to complete its life cycle. In this situation, only plants that have some water available for reproduction late in the season or that complete the life cycle quickly, before the onset of drought (exhibiting drought escape), will produce seeds for the next genera-tion. Either strategy will allow some reproductive success.
The situation is different if summer rainfall is significant but erratic. In this case, a plant with large leaf area, or one capable of developing large leaf area very quickly, is better suited to take advantage of occasional wet summers. One acclimation strategy in these conditions is a capacity for both vegetative growth and flowering over an extended period. Such plants are said to be indeterminate in their growth habit, in contrast to determinate plants, which develop preset numbers of leaves and flower over only very short periods.
In the discussions that follow, we will examine several acclimation strategies, including inhibited leaf expan-sion, leaf abscission, enhanced root growth, and stomatal closure.
Decreased Leaf Area Is an Early Adaptive Response to Water Deficit Typically, as the water content of the plant decreases, its cells shrink and the cell walls relax (see Chapter 3). This decrease in cell volume results in lower turgor pressure and the subsequent concentration of solutes in the cells.
The plasma membrane becomes thicker and more com-pressed because it covers a smaller area than before.
Because turgor reduction is the earliest significant bio-physical effect of water stress, turgor-dependent activities such as leaf expansion and root elongation are the most sensitive to water deficits (Figure 25.1).
Cell expansion is a turgor-driven process and is extremely sensitive to water deficit. Cell expansion is described by the relationship GR = m(Yp – Y) (25.1) where GR is growth rate, Yp is turgor, Y is the yield thresh-old (the pressure below which the cell wall resists plastic, or nonreversible, deformation), and m is the wall extensi-bility (the responsiveness of the wall to pressure).
This equation shows that a decrease in turgor causes a decrease in growth rate. Note also that besides showing that growth slows down when stress reduces Yp, Equation 25.1 shows that Yp need decrease only to the value of Y, not to zero, to eliminate expansion. In normal conditions, Y is usually only 0.1 to 0.2 MPa less than Yp, so small decreases in water content and turgor can slow down or fully stop growth.
Water stress not only decreases turgor, but also decreases m and increases Y. Wall extensibility (m) is nor-mally greatest when the cell wall solution is slightly acidic.
In part, stress decreases m because cell wall pH typically rises during stress. The effects of stress on Y are not well understood, but presumably they involve complex struc-tural changes of the cell wall (see Chapter 15) that may not be readily reversed after relief of stress. Water-deficient plants tend to become rehydrated at night, and as a result substantial leaf growth occurs at that time. Nonetheless, because of changes in m and Y, the growth rate is still lower than that of unstressed plants having the same turgor (see Figure 25.1).
Because leaf expansion depends mostly on cell expan-sion, the principles that underlie the two processes are sim-ilar. Inhibition of cell expansion results in a slowing of leaf expansion early in the development of water deficits. The smaller leaf area transpires less water, effectively conserv-ing a limited water supply in the soil over a longer period.
Reduction in leaf area can thus be considered a first line of defense against drought.
In indeterminate plants, water stress limits not only leaf size, but also leaf number, because it decreases both the number and the growth rate of branches. Stem growth has been studied less than leaf expansion, but stem growth is probably affected by the same forces that limit leaf growth during stress.
Keep in mind, too, that cell and leaf expansion also depend on biochemical and molecular factors beyond those that control water flux. Much evidence supports the view that plants change their growth rates in response to Stress Physiology 593 1.6 1.2 0.8 0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 Turgor (MPa), YP Leaf growth rate (mm h–1), GR Plants never exposed to water stress Plants grown under continuous water stress GR = m(YP–Y) Y FIGURE 25.1 Dependence of leaf expansion on leaf turgor.
Sunflower (Helianthus annuus) plants were grown either with ample water or with limited soil water to produce mild water stress. After rewatering, plants of both treat-ment groups were stressed by the withholding of water, and leaf growth rates (GR) and turgor (Ψp) were periodi-cally measured. Both decreased extensibility (m) and increased threshold turgor for growth (Y) limit the leaf’s capacity to grow after exposure to stress. (After Matthews et al. 1984.) stress by coordinately controlling many other important processes such as cell wall and membrane biosynthesis, cell division, and protein synthesis (Burssens et al. 2000).
Water Deficit Stimulates Leaf Abscission The total leaf area of a plant (number of leaves × surface area of each leaf) does not remain constant after all the leaves have matured. If plants become water stressed after a substantial leaf area has developed, leaves will senesce and eventually fall off (Figure 25.2). Such a leaf area adjust-ment is an important long-term change that improves the plant’s fitness in a water-limited environment. Indeed, many drought-deciduous, desert plants drop all their leaves during a drought and sprout new ones after a rain.
This cycle can occur two or more times in a single season.
Abscission during water stress results largely from enhanced synthesis of and responsiveness to the endoge-nous plant hormone ethylene (see Chapter 22).
Water Deficit Enhances Root Extension into Deeper, Moist Soil Mild water deficits also affect the development of the root system. Root-to-shoot biomass ratio appears to be gov-erned by a functional balance between water uptake by the root and photosynthesis by the shoot (see Figure 23.6). Sim-ply stated, a shoot will grow until it is so large that water uptake by the roots becomes limiting to further growth; conversely, roots will grow until their demand for photosynthate from the shoot equals the supply. This functional balance is shifted if the water supply decreases.
As discussed already, leaf expansion is affected very early when water uptake is curtailed, but photosynthetic activity is much less affected. Inhibition of leaf expansion reduces the consumption of carbon and energy, and a greater proportion of the plant’s assimilates can be distrib-uted to the root system, where they can support further root growth. At the same time, the root apices in dry soil lose turgor. All these factors lead to a preferential root growth into the soil zones that remain moist. As water deficits progress, the upper layers of the soil usually dry first. Thus, plants commonly show a mainly shallow root system when all soil layers are wetted, and a loss of shallow roots and pro-liferation of deep roots as water in top layers of the soil is depleted. Deeper root growth into wet soil can be consid-ered a second line of defense against drought.
Enhanced root growth into moist soil zones during stress requires allocation of assimilates to the growing root tips.
During water deficit, assimilates are directed to the fruits and away from the roots (see Chapter 10). For this reason the enhanced water uptake resulting from root growth is less pronounced in reproductive plants than in vegetative plants. Competition for assimilates between roots and fruits is one explanation for the fact that plants are generally more sensitive to water stress during reproduction.
Stomata Close during Water Deficit in Response to Abscisic Acid The preceding sections focused on changes in plant devel-opment during slow, long-term dehydration. When the onset of stress is more rapid or the plant has reached its full leaf area before initiation of stress, other responses protect the plant against immediate desiccation. Under these con-ditions, stomata closure reduces evaporation from the exist-ing leaf area. Thus, stomatal closure can be considered a third line of defense against drought.
Uptake and loss of water in guard cells changes their turgor and modulates stomatal opening and closing (see Chapters 4 and 18). Because guard cells are located in the leaf epidermis, they can lose turgor as a result of a direct loss of water by evaporation to the atmosphere. The decrease in turgor causes stomatal closure by hydropassive closure. This closing mechanism is likely to operate in air of low humidity, when direct water loss from the guard cells is too rapid to be balanced by water movement into the guard cells from adjacent epidermal cells.
A second mechanism, called hydroactive closure, closes the stomata when the whole leaf or the roots are dehy-drated and depends on metabolic processes in the guard cells. A reduction in the solute content of the guard cells results in water loss and decreased turgor, causing the stomata to close; thus the hydraulic mechanism of hydroac-tive closure is a reversal of the mechanism of stomatal opening. However, the control of hydroactive closure dif-fers in subtle but important ways from stomatal opening.
Solute loss from guard cells can be triggered by a decrease in the water content of the leaf, and abscisic acid (ABA) (see Chapter 23) plays an important role in this 594 Chapter 25 FIGURE 25.2 The leaves of young cotton (Gossypium hirsu-tum) plants abscise in response to water stress. The plants at left were watered throughout the experiment; those in the middle and at right were subjected to moderate stress and severe stress, respectively, before being watered again.
Only a tuft of leaves at the top of the stem is left on the severely stressed plants. (Courtesy of B. L. McMichael.) process. Abscisic acid is synthesized continuously at a low rate in mesophyll cells and tends to accumulate in the chloroplasts. When the mesophyll becomes mildly dehy-drated, two things happen: 1. Some of the ABA stored in the chloroplasts is released to the apoplast (the cell wall space) of the mesophyll cell (Hartung et al. 1998). The redistribution of ABA depends on pH gradients within the leaf, on the weak-acid properties of the ABA molecule, and on the permeability properties of cell membranes (Figure 25.3). The redistribution of ABA makes it possible for the transpiration stream to carry some of the ABA to the guard cells.
2. ABA is synthesized at a higher rate, and more ABA accumulates in the leaf apoplast. The higher ABA concentrations resulting from the higher rates of ABA synthesis appear to enhance or prolong the initial closing effect of the stored ABA. The mechanism of ABA-induced stomatal closure is discussed in Chapter 23.
Stomatal responses to leaf dehydration can vary widely both within and across species. The stomata of some dehy-dration-postponing species, such as cowpea (Vigna unguic-ulata) and cassava (Manihot esculenta), are unusually responsive to decreasing water availability, and stomatal conductance and transpiration decrease so much that leaf water potential (Yw; see Chapters 3 and 4) may remain nearly constant during drought.
Chemical signals from the root system may affect the stomatal responses to water stress (Davies et al. 2002). Stomatal conductance is often much more closely related to soil water status than to leaf water status, and the only plant part that can be directly affected by soil water status is the root system. In fact, dehydrating only part of the root system may cause stomatal closure even if the well-watered portion of the root system still delivers ample water to the shoots. When corn (Zea mays) plants were grown with roots trained into two separate pots and water was withheld from only one of the pots, the stomata closed partially, and the leaf water potential increased, just as in the dehydration postponers already described. These results show that stomata can respond to conditions sensed in the roots.
Besides ABA (Sauter et al. 2001), other signals, such as pH and inorganic ion redistribution, appear to play a role in long-distance signaling between the roots and the shoots (Davies et al. 2002).
Water Deficit Limits Photosynthesis within the Chloroplast The photosynthetic rate of the leaf (expressed per unit leaf area) is seldom as responsive to mild water stress as leaf expansion is (Figure 25.4) because photosynthesis is much less sensitive to turgor than is leaf expansion. However, mild water stress does usually affect both leaf photosyn-thesis and stomatal conductance. As stomata close during early stages of water stress, water-use efficiency (see Chap-ters 4 and 9) may increase (i.e., more CO2 may be taken up per unit of water transpired) because stomatal closure inhibits transpiration more than it decreases intercellular CO2 concentrations.
As stress becomes severe, however, the dehydration of mesophyll cells inhibits photosynthesis, mesophyll metab-olism is impaired, and water-use efficiency usually decreases. Results from many studies have shown that the relative effect of water stress on stomatal conductance is significantly larger than that on photosynthesis. The response of photosynthesis and stomatal conductance to water stress can be partitioned by exposure of stressed Stress Physiology 595 Sunlight Stroma Grana CHLOROPLAST H+ ABA– + H+ H+ + ABA– ABA•H 2. In alkaline stroma, ABA•H dissociates.
3. ABA•H diffuses passively from cytosol into stroma. 4. Since chloroplast membrane is nearly impermeable to ABA–, the charged ABA– is largely impermeable.
1. Light stimulates photosynthesis and active transport of H+ into the grana, increases stroma pH. ABA•H FIGURE 25.3 Accumulation of ABA by chloroplasts in the light. Light stimulates proton uptake into the grana, making the stroma more alkaline. The increased alka-linity causes the weak acid ABA•H to dissociate into H+ and the ABA– anion. The concentration of ABA•H in the stroma is lowered below the concentration in the cytosol, and the concentration difference drives the passive diffusion of ABA•H across the chloroplast membrane. At the same time, the concentration of ABA– in the stroma increases, but the chloroplast membrane is almost impermeable to the anion (red arrows), which thus remains trapped. This process continues until the ABA•H concentrations in the stroma and the cytosol are equal. But as long as the stroma remains more alkaline, the total ABA concentration (ABA•H + ABA–) in the stroma greatly exceeds the concentration in the cytosol.
leaves to air containing high concentrations of CO2. Any effect of the stress on stomatal conductance is eliminated by the high CO2 supply, and differences between photo-synthetic rates of stressed and unstressed plants can be directly attributed to damage from the water stress to pho-tosynthesis.
Does water stress directly affect translocation? Water stress decreases both photosynthesis and the consumption of assimilates in the expanding leaves. As a consequence, water stress indirectly decreases the amount of photosyn-thate exported from leaves. Because phloem transport depends on turgor (see Chapter 10), decreased water potential in the phloem during stress may inhibit the movement of assimilates. However, experiments have shown that translocation is unaffected until late in the stress period, when other processes, such as photosynthe-sis, have already been strongly inhibited (Figure 25.5).
This relative insensitivity of translocation to stress allows plants to mobilize and use reserves where they are needed (e.g., in seed growth), even when stress is extremely severe. The ability to continue translocating assimilates is a key factor in almost all aspects of plant resistance to drought.
Osmotic Adjustment of Cells Helps Maintain Plant Water Balance As the soil dries, its matric potential (see Web Topic 3.3) becomes more negative. Plants can continue to absorb water only as long as their water potential (Yw) is lower (more negative) than that of the soil water. Osmotic adjust-ment, or accumulation of solutes by cells, is a process by which water potential can be decreased without an accom-panying decrease in turgor or decrease in cell volume.
Recall Equation 3.6 from Chapter 3: Yw = Ys + Yp. The change in cell water potential results simply from changes in solute potential (Ys), the osmotic component of Yw.
Osmotic adjustment is a net increase in solute content per cell that is independent of the volume changes that result from loss of water. The decrease in Ys is typically limited to about 0.2 to 0.8 MPa, except in plants adapted to extremely dry conditions. Most of the adjustment can usu-ally be accounted for by increases in concentration of a variety of common solutes, including sugars, organic acids, amino acids, and inorganic ions (especially K+).
Cytosolic enzymes of plant cells can be severely inhib-ited by high concentrations of ions. The accumulation of ions during osmotic adjustment appears to be restricted to the vacuoles, where the ions are kept out of contact with enzymes in the cytosol or subcellular organelles. Because of this compartmentation of ions, other solutes must accu-mulate in the cytoplasm to maintain water potential equi-librium within the cell.
These other solutes, called compatible solutes (or com-patible osmolytes), are organic compounds that do not interfere with enzyme functions. Commonly accumulated compatible solutes include the amino acid proline, sugar alcohols (e.g., sorbitol and mannitol), and a quaternary amine called glycine betaine. Synthesis of compatible solutes helps plants adjust to increased salinity in the root-ing zone, as discussed later in this chapter.
Osmotic adjustment develops slowly in response to tis-sue dehydration. Over a time course of several days, other changes (such as growth or photosynthesis) are also taking place. Thus it can be argued that osmotic adjustment is not an independent and direct response to water deficit, but a result of another factor, such as decreased growth rate.
596 Chapter 25 Photosynthesis rate (µmol CO2 m–2 s–1) 15 10 20 0 10 5 0 –0.4 –0.8 –1.2 –1.6 Leaf water potential (MPa) Leaf expansion rate (percent increase in leaf area per 24 h) Leaf expansion Photosynthesis FIGURE 25.4 Effects of water stress on photosynthesis and leaf expansion of sunflower (Helianthus annuus). This species is typical of many plants in which leaf expansion is very sensitive to water stress, and it is completely inhibited under mild stress levels that hardly affect photosynthetic rates. (After Boyer 1970.) 50 40 30 35 30 20 25 –1.5 –2.0 –2.5 Leaf water potential (MPa) Photosynthesis rate (µmol 14CO2 m–2 s–1) Translocation rate (percent 14C removed per hour) Translocation is maintained until stress is severe.
Photosynthesis starts to decline at mild stress.
FIGURE 25.5 Relative effects of water stress on photosyn-thesis and translocation in sorghum (Sorghum bicolor).
Plants were exposed to 14CO2 for a short time interval. The radioactivity fixed in the leaf was taken as a measure of photosynthesis, and the loss of radioactivity after removal of the 14CO2 source was taken as a measure of the rate of assimilate translocation. Photosynthesis was affected by mild stress, whereas, translocation was unaffected until stress was severe. (After Sung and Krieg 1979.) Nonetheless, leaves that are capable of osmotic adjustment clearly can maintain turgor at lower water potentials than nonadjusted leaves. Maintaining turgor enables the con-tinuation of cell elongation and facilitates higher stomatal conductances at lower water potentials. This suggests that osmotic adjustment is an acclimation that enhances dehy-dration tolerance.
How much extra water can be acquired by the plant because of osmotic adjustment in the leaf cells? Most of the extractable soil water is held in spaces (filled with water and air) from which it is readily removed by roots (see Chapter 4). As the soil dries, this water is used first, leav-ing behind the small amount of water that is held more tightly in small pores. Osmotic adjustment enables the plant to extract more of this tightly held water, but the increase in total available water is small. Thus the cost of osmotic adjustment in the leaf is offset by rapidly diminishing returns in terms of water availability to the plant, as can be seen by a comparison of the water relations of adjusting and nonadjusting species (Figure 25.6). These results show that osmotic adjustment promotes dehydration tolerance but does not have a major effect on productivity (McCree and Richardson 1987).
Osmotic adjustment also occurs in roots, although the process in roots has not been studied so extensively as in leaves. The absolute magnitude of the adjustment is less in roots than in leaves, but as a percentage of the original tis-sue solute potential (Ys), it can be larger in roots than in leaves. As with leaves, these changes may in many cases increase water extraction from the previously explored soil only slightly. However, osmotic adjustment can occur in the root meristems, enhancing turgor and maintaining root growth. This is an important component of the changes in root growth patterns as water is depleted from the soil.
Does osmotic adjustment increase plant productivity?
Researchers have engineered the accumulation of osmo-protective solutes by conventional plant breeding, by phys-iological methods (inducing adjustment with controlled water deficits), and through the use of transgenic plants expressing genes for solute synthesis and accumulation.
However, the engineered plants grow more slowly, and they are only slightly more tolerant to osmotic stresses.
Thus the use of osmotic adjustment to improve agricultural performance is yet to be perfected.
Water Deficit Increases Resistance to Liquid-Phase Water Flow When a soil dries, its resistance to the flow of water increases very sharply, particularly near the permanent wilt-ing point. Recall from Chapter 4 that at the permanent wilt-ing point (usually about –1.5 MPa), plants cannot regain turgor pressure even if all transpiration stops (for more details on the relationship between soil hydraulic conduc-tivity and soil water potential, see Figure 4.2.A in Web Topic 4.2). Because of the very large soil resistance to water flow, water delivery to the roots at the permanent wilting point is too slow to allow the overnight rehydration of plants that have wilted during the day.
Rehydration is further hindered by the resistance within the plant, which has been found to be larger than the resis-tance within the soil over a wide range of water deficits (Blizzard and Boyer 1980). Several factors may contribute to the increased plant resistance to water flow during dry-ing. As plant cells lose water, they shrink. When roots shrink, the root surface can move away from the soil par-ticles that hold the water, and the delicate root hairs may be damaged. In addition, as root extension slows during soil drying, the outer layer of the root cortex (the hypoder-mis) often becomes more extensively covered with suberin, Stress Physiology 597 0 –1 –2 6 4 2 0 3 2 1 0 5 10 15 20 Time after last watering (days) Water lost (kg per plant) Carbon gained (g per plant) Leaf water potential (MPa) Cowpea (osmotic nonadjuster) Sugar beet (osmotic adjuster) Cowpea Cowpea Sugar beet Sugar beet FIGURE 25.6 Water loss and carbon gain by sugar beet (Beta vulgaris), an osmotically adjusting species, and cowpea (Vigna unguiculata), a nonadjusting species that conserves water during stress by stomatal closure. Plants were grown in pots and subjected to water stress. On any given day after the last watering, the sugar beet leaves maintained a lower water potential than the cowpea leaves, but photo-synthesis and transpiration during stress were only slightly greater in the sugar beet. The major difference between the two plants was the leaf water potential. These results show that osmotic adjustment promotes dehydration tolerance but does not have a major effect on productivity. (After McCree and Richardson 1987.) a water-impermeable lipid (see Figure 4.4), increasing the resistance to water flow.
Another important factor that increases resistance to water flow is cavitation, or the breakage of water columns under tension within the xylem. As we saw in Chapter 4, transpiration from leaves “pulls” water through the plant by creating a tension on the water column. The cohesive forces that are required to support large tensions are pre-sent only in very narrow columns in which the water adheres to the walls.
Cavitation begins in most plants at moderate water potentials (–1 to –2 MPa), and the largest vessels cavitate first. For example, in trees such as oak (Quercus), the large-diameter vessels that are laid down in the spring function as a low-resistance pathway early in the growing season, when ample water is available. As the soil dries out during the summer, these large vessels cease functioning, leaving the small-diameter vessels produced during the stress period to carry the transpiration stream. This shift has long-lasting consequences: Even if water becomes available, the original low-resistance pathway remains nonfunctional, reducing the efficiency of water flow.
Water Deficit Increases Wax Deposition on the Leaf Surface A common developmental response to water stress is the production of a thicker cuticle that reduces water loss from the epidermis (cuticular transpiration). Although waxes are deposited in response to water deficit both on the surface and within the cuticle inner layer, the inner layer may be more important in controlling the rate of water loss in ways that are more complex than by just increasing the amount of wax present (Jenks et al. in press).
A thicker cuticle also decreases CO2 permeability, but leaf photosynthesis remains unaffected because the epi-dermal cells underneath the cuticle are nonphotosynthetic.
Cuticular transpiration, however, accounts for only 5 to 10% of the total leaf transpiration, so it becomes significant only if stress is extremely severe or if the cuticle has been damaged (e.g., by wind-driven sand).
Water Deficit Alters Energy Dissipation from Leaves Recall from Chapter 9 that evaporative heat loss lowers leaf temperature. This cooling effect can be remarkable: In Death Valley, California—one of the hottest places in the world—leaf temperatures of plants with access to ample water were measured to be 8°C below air temperatures. In warm, dry climates, an experienced farmer can decide whether plants need water simply by touching the leaves because a rapidly transpiring leaf is distinctly cool to the touch. When water stress limits transpiration, the leaf heats up unless another process offsets the lack of cooling.
Because of these effects of transpiration on leaf tempera-ture, water stress and heat stress are closely interrelated (see the discussion of heat stress later in this chapter).
Maintaining a leaf temperature that is much lower than the air temperature requires evaporation of vast quantities of water. This is why adaptations that cool leaves by means other than evaporation (e.g., changes in leaf size and leaf orientation) are very effective in conserving water. When transpiration decreases and leaf temperature becomes warmer than the air temperature, some of the extra energy in the leaf is dissipated as sensible heat loss (see Chapter 9). Many arid-zone plants have very small leaves, which minimize the resistance of the boundary layer to the trans-fer of heat from the leaf to the air (see Figure 9.14).
Because of their low boundary layer resistance, small leaves tend to remain close to air temperature even when transpiration is greatly slowed. In contrast, large leaves have higher boundary layer resistance and dissipate less thermal energy (per unit leaf area) by direct transfer of heat to the air.
In larger leaves, leaf movement can provide additional protection against heating during water stress. Leaves that orient themselves away from the sun are called parahe-liotropic; leaves that gain energy by orienting themselves nor-mal (perpendicular) to the sunlight are referred to as diahe-liotropic (see Chapter 9). Figure 25.7 shows the strong effect of water stress on leaf position in soybean. Other factors that can alter the interception of radiation include wilting, which changes the angle of the leaf, and leaf rolling in grasses, which minimizes the profile of tissue exposed to the sun.
Absorption of energy can also be decreased by hairs on the leaf surface or by layers of reflective wax outside the cuticle. Leaves of some plants have a gray-white appear-ance because densely packed hairs reflect a large amount of light. This hairiness, or pubescence, keeps leaves cooler by reflecting radiation, but it also reflects the visible wave-lengths that are active in photosynthesis and thus it decreases carbon assimilation. Because of this problem, attempts to breed pubescence into crops to improve their water-use efficiency have been generally unsuccessful.
Osmotic Stress Induces Crassulacean Acid Metabolism in Some Plants Crassulacean acid metabolism (CAM) is a plant adaptation in which stomata open at night and close during the day (see Chapters 8 and 9). The leaf-to-air vapor pressure dif-ference that drives transpiration is much reduced at night, when both leaf and air are cool. As a result, the water-use efficiencies of CAM plants are among the highest mea-sured. A CAM plant may gain 1 g of dry matter for only 125 g of water used—a ratio that is three to five times greater than the ratio for a typical C3 plant (see Chapter 4).
CAM is very prevalent in succulent plants such as cacti.
Some succulent species display facultative CAM, switch-ing to CAM when subjected to water deficits or saline con-ditions (see Chapter 8). This switch in metabolism is a remarkable adaptation to stress, involving accumulation of the enzymes phosphoenolpyruvate (PEP) carboxylase (Fig-ure 25.8), pyruvate–orthophosphate dikinase, and NADP malic enzyme, among others.
598 Chapter 25 As discussed in Chapters 8 and 9, CAM metabolism involves many structural, physiological, and biochemical features, including changes in carboxylation and decar-boxylation patterns, transport of large quantities of malate into and out of the vacuoles, and reversal of the periodic-ity of stomatal movements. Thus, CAM induction is a remarkable adaptation to water deficit that occurs at many levels of organization.
Osmotic Stress Changes Gene Expression As noted earlier, the accumulation of compatible solutes in response to osmotic stress requires the activation of the metabolic pathways that biosynthesize these solutes. Sev-eral genes coding for enzymes associated with osmotic adjustment are turned on (up-regulated) by osmotic stress and/or salinity, and cold stress. These genes encode enzymes such as the following (Buchanan et al. 2000): • ∆′1-Pyrroline-5-carboxylate synthase, a key enzyme in the proline biosynthetic pathway • Betaine aldehyde dehydrogenase, an enzyme involved in glycine betaine accumulation • myo-Inositol 6-O-methyltransferase, a rate-limiting enzyme in the accumulation of the cyclic sugar alco-hol called pinitol Several other genes that encode well-known enzymes are induced by osmotic stress. The expression of glycer-aldehyde-3-phosphate dehydrogenase increases during osmotic stress, perhaps to allow an increase of carbon flow into organic solutes for osmotic adjustment. Enzymes involved in lignin biosynthesis are also controlled by osmotic stress.
Reduction in the activities of key enzymes also takes place. The accumulation of the sugar alcohol mannitol in response to osmotic stress appears not to be brought about by the up-regulation of genes producing enzymes involved in mannitol biosynthesis, but rather by the down-regula-tion of genes associated with sucrose production and man-nitol degradation. In this way mannitol accumulation is enhanced during episodes of osmotic stress.
Other genes regulated by osmotic stress encode proteins associated with membrane transport, including ATPases Stress Physiology 599 (A) Well-watered (B) Mild water stress (C) Severe water stress FIGURE 25.7 Orientation of leaflets of field-grown soybean (Glycine max) plants in the normal, unstressed, position (A); during mild water stress (B); and during severe water stress (C). The large leaf movements induced by mild stress are quite different from wilting, which occurs during severe stress. Note that during mild stress (B), the terminal leaflet has been raised, whereas the two lateral leaflets have been lowered; each is almost vertical. (Courtesy of D. M.
Oosterhuis.) 1 2 3 4 5 6 Days after salt stress Increasing PEP carboxylase protein FIGURE 25.8 Increases in the content of phosphoenolpyru-vate (PEP) carboxylase in ice plant, Mesembryanthemum crystallinum, during the salt-induced shift from C3 metabo-lism to CAM. Salt stress was induced by the addition of 500 mM NaCl to the irrigation water. The PEP carboxylase pro-tein was revealed in the gels by the use of antibodies and a stain. (After Bohnert et al. 1989.) (Niu et al. 1995) and the water channel proteins, aquaporins (see Chapter 3) (Maggio and Joly 1995). Several protease genes are also induced by stress, and these enzymes may degrade (remove and recycle) other proteins that are dena-tured by stress episodes. The protein ubiquitin tags proteins that are targeted for proteolytic degradation. Synthesis of the mRNA for ubiquitin increases in Arabidopsis upon des-iccation stress. In addition, some heat shock proteins are 600 Chapter 25 Table 25.2 The five groups of late embryogenesis abundant (LEA) proteins found in plants Group Structural characteristics Functional information/ (family name)a Protein(s) in the group and motifs proposed function Group 1 Cotton D-19 Conformation is predominantly Contains more water of hydration (D-19 family) Wheat Em random coil with some than typical globular proteins (early methionine-predicted short α helices Overexpression confers labeled protein) Charged amino acids and glycine water deficit tolerance on Sunflower Ha ds10 are abundant yeast cells Barley B19 Group 2 Maize DHN1, M3, RAB17 Variable structure includes α Often localized to the cytoplasm (D-11 family) Cotton D-11 helix–forming lysine-rich regions or nucleus (also referred to Arabidopsis pRABAT1, The consensus sequence for group More acidic members of the family as dehydrins) ERD10, ERD14 2 dehydrins is EKKGIMDKIKELPG are associated with the plasma Craterostigma pcC 27-04, The number of times this consensus membrane pcC 6-19 repeats per protein varies May act to stabilize macromole-Tomato pLE4,TAS14 Often contains a poly(serine) region cules at low water potential Barley B8, B9, B17 Often contains regions of variable Rice pRAB16A length rich in polar residues Carrot pcEP40 and either Gly or Ala., and Pro Group 3 Barley HVA1 Eleven amino-acid consensus Transgenic plants expressing HVA1 (D-7 family) (ABA-induced) sequence motif TAQAAKEKAXE is demonstrate enhanced water Cotton D-7 repeated in the protein deficit stress tolerance Wheat pMA2005, Contains apparent amphipathic D-7 is an abundant protein in pMA1949 α helices cotton embryos (estimated Craterostigma Dimeric protein concentration 0.25 mM) pcC3-06 Each putative dimer of D-7 may bind as many as ten inorganic phosphates and their counterions Group 4 Soybean D-95 Slightly hydrophobic In tomato, a gene encoding a (D-95 family) Craterostigma pcC27-45 N-terminal region is predicted similar protein is expressed to form amphipathic α helices in response to nematode feeding Group 5 Tomato LE25 Family members share sequence Binds to membranes and/or (D-113 family) Sunflower Hads11 homology at the conserved proteins to maintain structure Cotton D-113 N terminus during stress N-terminal region is predicted Possibly functions in ion to form α helices sequestration to protect C-terminal domain is predicted cytosolic metabolism to be a random coil of variable When LE25 is expressed in length and sequence yeast, it confers salt and Ala, Gly, and Thr are abundant freezing tolerance in the sequence D-113 is abundant in cottonseeds (up to 0.3 mM) aThe protein family names are derived from the cotton seed proteins that are most similar to the family.
Source: After Bray et al. 2000.
osmotically induced and may protect or renature proteins inactivated by desiccation.
The sensitivity of cell expansion to osmotic stress (see Figure 25.1) has stimulated studies of various genes that encode proteins involved in the structural composition and integrity of cell walls. Genes coding for enzymes such as S-adenosylmethionine synthase and peroxidases, which may be involved in lignin biosynthesis, have been shown to be controlled by stress.
A large group of genes that are regulated by osmotic stress was discovered by examination of naturally desic-cating embryos during seed maturation. These genes code for so-called LEA proteins (named for late embryogenesis abundant), and they are suspected to play a role in cellular membrane protection. Although the function of LEA pro-teins is not well understood (Table 25.2), they accumulate in vegetative tissues during episodes of osmotic stress. The proteins encoded by these genes are typically hydrophilic and strongly bind water. Their protective role might be associated with an ability to retain water and to prevent crystallization of important cellular proteins and other mol-ecules during desiccation. They might also contribute to membrane stabilization.
More recently, microarray techniques have been used to examine the expression of whole genomes of some plants in response to stress. Such studies have revealed that large numbers of genes display changes in expression after plants are exposed to stress. Stress-controlled genes reflect up to 10% of the total number of rice genes examined (Kawasaki et al. 2001) Osmotic stress typically leads to the accumulation of ABA (see Chapter 23), so it is not surprising that products of ABA-responsive genes accumulate during osmotic stresses. Studies of ABA-insensitive and ABA-deficient mutants have shown that numerous genes that are induced by osmotic stress are in fact induced by the ABA accumu-lated during the stress episode. However, not all genes that are up-regulated by osmotic stresses are ABA regulated. As discussed in the next section, other mechanisms for regu-lating gene expression of osmotic stress–regulated genes have been uncovered.
Stress-Responsive Genes Are Regulated by ABA-Dependent and ABA-Independent Processes Gene transcription is controlled through the interaction of regulatory proteins (transcription factors) with specific reg-ulatory sequences in the promoters of the genes they reg-ulate (Chapter 14 on the web site discusses these processes in detail). Different genes that are induced by the same sig-nal (desiccation or salinity, for example) are controlled by a signaling pathway leading to the activation of these spe-cific transcription factors.
Studies of the promoters of several stress-induced genes have led to the identification of specific regulatory sequences for genes involved in different stresses. For example, the RD29 gene contains DNAsequences that can be activated by osmotic stress, by cold, and by ABA (Yamaguchi-Shinozaki and Shinozaki 1994; Stockinger et al. 1997).
The promoters of ABA-regulated genes contain a six-nucleotide sequence element referred to as the ABA response element (ABRE), which probably binds tran-scriptional factors involved in ABA-regulated gene activa-tion (see Chapter 23). The promoters of these genes, which are regulated by osmotic stress in an ABA-dependent man-ner, contain an alternative nine-nucleotide regulatory sequence element, the dehydration response element (DRE) which is recognized by an alternative set of proteins regulating transcription. Thus the genes that are regulated by osmotic stresses appear to be regulated either by signal transduction pathways mediated by the action of ABA (ABA-dependent genes), or by an ABA-independent, osmotic stress–responsive signal transduction pathway.
At least two signaling pathways have been implicated in the regulation of gene expression in an ABA-indepen-dent manner (Figure 25.9). Transacting transcription factors (called DREB1 and DREB2) that bind to the DRE elements in the promoters of osmotic stress–responsive genes are apparently activated by an ABA-independent signaling cascade. Other ABA-independent, osmotic stress–respon-Stress Physiology 601 Osmotic stress Osmotic stress signal receptor bZIP transcription factor Protein synthesis (MYC/MYB) MAP kinase cascade DREB/CBF Altered gene expression Altered gene expression Osmotic stress tolerance ABA ABA independent FIGURE 25.9 Signal transduction pathways for osmotic stress in plant cells. Osmotic stress is perceived by an as yet unknown receptor in the plasma membrane activating ABA-independent and an ABA-dependent signal transduc-tion pathways. Protein synthesis participates in one of the ABA-dependent pathways involving MYC/MYB. The bZIP ABA-dependent pathway involves recognition of ABA-responsive elements in gene promoters. Two ABA-independent pathways, one involving the MAP kinase sig-naling cascade and the other involving DREBP/CBF-related transcription factors have also been demonstrated.
(After Shinozaki and Yamaguchi-Shinozaki, 2000.) sive genes appear to be directly controlled by the so-called MAP kinase signaling cascade of protein kinases (discussed in detail in Chapter 14 on the web site). Other changes in gene expression appear to be mediated via other mecha-nisms not involving DREBs.
This complexity and “cross-talk” found in signaling cas-cades, exemplified here by both ABA-dependent and ABA-independent pathways, is typical of eukaryotic signaling.
Such complexity reflects the wealth of interaction between gene expression and the physiological processes mediating adaptation to osmotic stress.
HEAT STRESS AND HEAT SHOCK Most tissues of higher plants are unable to survive extended exposure to temperatures above 45°C. Non-growing cells or dehydrated tissues (e.g., seeds and pollen) can survive much higher temperatures than hydrated, veg-etative, growing cells (Table 25.3). Actively growing tissues rarely survive temperatures above 45°C, but dry seeds can endure 120°C, and pollen grains of some species can endure 70°C. In general, only single-celled eukaryotes can complete their life cycle at temperatures above 50°C, and only prokaryotes can divide and grow above 60°C.
Periodic brief exposure to sublethal heat stresses often induces tolerance to otherwise lethal temperatures, a phe-nomenon referred to as induced thermotolerance. The mechanisms mediating induced thermotolerance will be discussed later in the chapter. As mentioned earlier, water and temperature stress are interrelated; shoots of most C3 and C4 plants with access to abundant water supply are maintained below 45°C by evaporative cooling; if water becomes limiting, evaporative cooling decreases and tissue temperatures increase. Emerging seedlings in moist soil may constitute an exception to this general rule. These seedlings may be exposed to greater heat stress than those in drier soils because wet, bare soil is typically darker and absorbs more solar radiation than drier soil.
High Leaf Temperature and Water Deficit Lead to Heat Stress Many CAM, succulent higher plants, such as Opuntia and Sempervivum, are adapted to high temperatures and can tol-erate tissue temperatures of 60 to 65°C under conditions of intense solar radiation in summer (see Table 25.3). Because CAM plants keep their stomata closed during the day, they cannot cool by transpiration. Instead, they dissipate the heat from incident solar radiation by re-emission of long-wave (infrared) radiation and loss of heat by conduction and convection (see Chapter 9).
On the other hand, typical, nonirrigated C3 and C4 plants rely on transpirational cooling to lower leaf tem-perature. In these plants, leaf temperature can readily rise 4 to 5°C above ambient air temperature in bright sunlight near midday, when soil water deficit causes partial stom-atal closure or when high relative humidity reduces the potential for evaporative cooling. The physiological con-sequences of these increases in tissue temperature are dis-cussed in the next section.
Increases in leaf temperature during the day can be pro-nounced in plants from arid and semiarid regions experi-encing drought and high irradiance from sunshine. Heat stress is also a potential danger in greenhouses, where low air speed and high humidity decrease the rate of leaf cool-ing. A moderate degree of heat stress slows growth of the whole plant. Some irrigated crops, such as cotton, use tran-spirational cooling to dissipate heat. In irrigated cotton, enhanced transpirational cooling is associated with higher agronomic yields (see Web Topic 25.1).
At High Temperatures, Photosynthesis Is Inhibited before Respiration Both photosynthesis and respiration are inhibited at high temperatures, but as temperature increases, photosynthetic rates drop before respiratory rates (Figure 25.10A and B).
The temperature at which the amount of CO2 fixed by pho-tosynthesis, equals the amount of CO2 released by respira-tion, in a given time interval is called the temperature com-pensation point.
At temperatures above the temperature compensation point, photosynthesis cannot replace the carbon used as a substrate for respiration. As a result, carbohydrate reserves decline, and fruits and vegetables lose sweetness. This imbal-ance between photosynthesis and respiration is one of the main reasons for the deleterious effects of high temperatures.
602 Chapter 25 TABLE 25.3 Heat-killing temperatures for plants Heat-killing temperature Time of Plant (C°) exposure Nicotiana rustica (wild tobacco) 49–51 10 min Cucurbita pepo (squash) 49–51 10 min Zea mays (corn) 49–51 10 min Brassica napus (rape) 49–51 10 min Citrus aurantium (sour orange) 50.5 15–30 min Opuntia (cactus) >65 — Sempervivum arachnoideum 57–61 — (succulent) Potato leaves 42.5 1 hour Pine and spruce seedlings 54–55 5 min Medicago seeds (alfalfa) 120 30 min Grape (ripe fruit) 63 — Tomato fruit 45 — Red pine pollen 70 1 hour Various mosses Hydrated 42–51 — Dehydrated 85–110 — Source: After Table 11.2 in Levitt 1980.
In the same plant the temperature compensation point is usually lower for shade leaves than for sun leaves that are exposed to light (and heat). Enhanced respiration rates rela-tive to photosynthesis at high temperatures are more detri-mental in C3 plants than in C4 or CAM plants because the rates of both dark respiration and photorespiration are increased in C3 plants at higher temperatures (see Chapter 8).
Plants Adapted to Cool Temperatures Acclimate Poorly to High Temperatures The extent to which plants that are genetically adapted to a given temperature range can acclimate to a contrasting temperature range is illustrated by a comparison of the responses of two C4 species: Atriplex sabulosa (frosted orache, family Chenopodiaceae) and Tidestromia oblongifo-lia (Arizona honeysweet, family Amaranthaceae).
A. sabulosa is native to the cool climate of coastal north-ern California, and T. oblongifolia is native to the very hot climate of Death Valley, California, where it grows in a tem-perature regime that is lethal for most plant species. When these species were grown in a controlled environment and their growth rates were recorded as a function of tempera-ture, T. oblongifolia barely grew at 16°C, while A. sabulosa was at 75% of its maximum growth rate. By contrast, the growth rate of A. sabulosa began to decline between 25 and 30°C, and growth ceased at 45°C, the temperature at which T. oblongifolia growth showed a maximum (see Figure 25.10A) (Björkman et al. 1980). Clearly, neither species could acclimate to the temperature range of the other.
High Temperature Reduces Membrane Stability The stability of various cellular membranes is important during high-temperature stress, just as it is during chilling and freezing. Excessive fluidity of membrane lipids at high temperatures is correlated with loss of physiological func-tion. In oleander (Nerium oleander), acclimation to high tem-peratures is associated with a greater degree of saturation of fatty acids in membrane lipids, which makes the mem-branes less fluid (Raison et al. 1982).
At high temperatures there is a decrease in the strength of hydrogen bonds and electrostatic interactions between polar groups of proteins within the aqueous phase of the membrane. High temperatures thus modify membrane composition and structure and can cause leakage of ions (see Figure 25.10C). Membrane disruption also causes the inhibition of processes such as photosynthesis and respi-ration that depend on the activity of membrane-associated electron carriers and enzymes.
Photosynthesis is especially sensitive to high tempera-ture (see Chapter 9). In their study of Atriplex and Tidestro-mia, O. Björkman and colleagues (1980) found that electron transport in photosystem II was more sensitive to high temperature in the cold-adapted A. sabulosa than in the heat-adapted T. oblongifolia. In these plants the enzymes ribulose-1,5-bisphosphate carboxylase, NADP:glyceralde-hyde-3-phosphate dehydrogenase, and phosphoenolpyru-vate carboxylase were less stable at high temperatures in A. sabulosa than in T. oblongifolia.
However, the temperatures at which these enzymes began to denature and lose activity were distinctly higher than the temperatures at which photosynthesis began to decline. These results suggest that early stages of heat injury to photosynthesis are more directly related to changes in membrane properties and to uncoupling of the energy transfer mechanisms in chloroplasts than to a gen-eral denaturation of proteins.
Several Adaptations Protect Leaves against Excessive Heating In environments with intense solar radiation and high tem-peratures, plants avoid excessive heating of their leaves by decreasing their absorption of solar radiation. This adap-Stress Physiology 603 0.1 0.2 0.3 0 35 40 45 50 60 65 55 Pretreatment leaf temperature (ºC) Conductivity change (percent/min) CO2 evolution CO2 uptake (percent of unheated control) 50 100 0 0 50 100 (C) (B) (A) Photo-synthesis Respiration Ion leakage T. oblongifolia A. sabulosa FIGURE 25.10 Response of frosted orache (Atriplex sabulosa) and Arizona honeysweet (Tidestromia oblongifolia) to heat stress.
Photosynthesis (A) and respiration (B) were measured on attached leaves, and ion leakage (C) was measured in leaf slices submerged in water. At the beginning of the experiment, control rates were measured at a noninjurious 30°C. Attached leaves were then exposed to the indicated temperatures for 15 minutes and returned to the initial control conditions before the rates were recorded. Arrows indicate the temperature thresholds for inhibi-tion of photosynthesis in each of the two species. Photosynthesis, respiration, and membrane permeability were all more sensitive to heat damage in A. sabulosa than in T. oblongifolia. In both species, however, photosynthesis was more sensitive to heat stress than either of the other two processes, and photosynthesis was completely inhibited at temperatures that were noninjurious to respiration. (From Björkman et al. 1980.) tation is important in warm, sunny environments in which a transpiring leaf is near its upper limit of temperature tol-erance. In these conditions, any further warming arising from decreased evaporation of water or increased energy absorption can damage the leaf.
Both drought resistance and heat resistance depend on the same adaptations: reflective leaf hairs and leaf waxes; leaf rolling and vertical leaf orientation; and growth of small, highly dissected leaves to minimize the boundary layer thickness and thus maximize convective and con-ductive heat loss (see Chapters 4 and 9). Some desert shrubs—for example, white brittlebush (Encelia farinosa, family Compositae)—have dimorphic leaves to avoid excessive heating: Green, nearly hairless leaves found in the winter are replaced by white, pubescent leaves in the summer.
At Higher Temperatures, Plants Produce Heat Shock Proteins In response to sudden, 5 to 10°C rises in temperature, plants produce a unique set of proteins referred to as heat shock proteins (HSPs). Most HSPs function to help cells withstand heat stress by acting as molecular chaperones.
Heat stress causes many cell proteins that function as enzymes or structural components to become unfolded or misfolded, thereby leading to loss of proper enzyme struc-ture and activity. Such misfolded proteins often aggregate and precipitate, creating serious problems within the cell. HSPs act as mol-ecular chaperones and serve to attain a proper folding of misfolded, aggregated proteins and to prevent misfolding of proteins. This facilitates proper cell functioning at ele-vated, stressful temperatures.
Heat shock proteins were discovered in the fruit fly (Drosophila melanogaster) and have since been identified in other animals, and in humans, as well as in plants, fungi, and microorganisms. For example, when soybean seedlings are suddenly shifted from 25 to 40°C (just below the lethal temperature), synthesis of the set of mRNAs and proteins commonly found in the cell is suppressed, while transcription and translation of a set of 30 to 50 other pro-teins (HSPs) is enhanced. New mRNA transcripts for HSPs can be detected 3 to 5 minutes after heat shock (Sachs and Ho 1986).
Although plant HSPs were first identified in response to sudden changes in temperature (25 to 40°C) that rarely occur in nature, HSPs are also induced by more gradual rises in temperature that are representative of the natural environment, and they occur in plants under field condi-tions. Some HSPs are found in normal, unstressed cells, and some essential cellular proteins are homologous to HSPs but do not increase in response to thermal stress (Vierling 1991).
Plants and most other organisms make HSPs of differ-ent sizes in response to temperature increases (Table 25.4).
The molecular masses of the HSPs range from 15 to 104 kDa (kilodaltons), and they can be grouped into five classes based on size. Different HSPs are localized to the nucleus, mitochondria, chloroplasts, endoplasmic reticulum, and cytosol. Members of the HSP60, HSP70, HSP90, and HSP100 groups act as molecular chaperones, involving ATP-dependent stabilization and folding of proteins, and the assembly of oligomeric proteins. Some HSPs assist in polypeptide transport across membranes into cellular com-partments. HSP90s are associated with hormone receptors in animal cells and may be required for their activation, but there is no comparable information for plants.
Low-molecular-weight (15–30 kDa) HSPs are more abundant in higher plants than in other organisms.
Whereas plants contain five to six classes of low-molecu-lar-weight HSPs, other eukaryotes show only one class (Buchanan et al. 2000). The different classes of 15–30 kDa molecular-weight HSPs (smHSPs) in plants are distributed in the cytosol, chloroplasts, ER and mitochondria. The function of these small HSPs is not understood.
Cells that have been induced to synthesize HSPs show improved thermal tolerance and can tolerate exposure to temperatures that are otherwise lethal. Some of the HSPs are not unique to high-temperature stress. They are also induced by widely different environmental stresses or con-ditions, including water deficit, ABA treatment, wounding, low temperature, and salinity. Thus, cells previously 604 Chapter 25 TABLE 25.4 The five classes of heat shock proteins found in plants HSP class Size (kDa) Examples (Arabidopsis / prokaryotic) Cellular location HSP100 100–114 AtHSP101 / ClpB, ClpA/C Cytosol, mitochondria, chloroplasts HSP90 80–94 AtHSP90 / HtpG Cytosol, endoplasmic reticulum HSP70 69–71 AtHSP70 / DnaK Cytosol/nucleus, mitochondria, chloroplasts HSP60 57–60 AtTCP-1 / GroEL, GroES Mitochondria, chloroplasts smHSP 15–30 Various AtHSP22, AtHSP20, AtHSP18.2, Cytosol, mitochondria, chloroplasts, AtHSP17.6 / IBPA/B endoplasmic reticulum Source: After Boston et al. 1996.
exposed to one stress may gain cross-protection against another stress. Such is the case with tomato fruits, in which heat shock (48 hours at 38°C) has been observed to pro-mote HSP accumulation and to protect cells for 21 days from chilling at 2°C.
A Transcription Factor Mediates HSP Accumulation in Response to Heat Shock All cells seem to contain molecular chaperones that are constitutively expressed and function like HSPs. These chaperones are called heat shock cognate proteins. How-ever, when cells are subjected to a stressful, but nonlethal heat episode, the synthesis of HSPs dramatically increases while the continuing translation of other proteins is dra-matically lowered or ceases. This heat shock response appears to be mediated by a specific transcription factor (HSF) that acts on the transcription of HSP mRNAs.
In the absence of heat stress, HSF exists as monomers that are incapable of binding to DNA and directing tran-scription (Figure 25.11). Stress causes HSF monomers to associate into trimers that are then able to bind to specific sequence elements in DNA referred to as heat shock ele-ments (HSEs). Once bound to the HSE, the trimeric HSF is phosphorylated and promotes the transcription of HSP mRNAs. HSP70 subsequently binds to HSF, leading to the dissociation of the HSF/HSE complex, and the HSF is sub-sequently recycled to the monomeric HSF form. Thus, by the action of HSF, HSPs accumulate until they become abundant enough to bind to HSF, leading to the cessation of HSP mRNA production.
HSPs Mediate Thermotolerance Conditions that induce thermal tolerance in plants closely match those that induce the accumulation of HSPs, but that correlation alone does not prove that HSPs play an essential role in acclimation to heat stress. More conclusive experi-ments show that expression of an activated HSF induces constitutive synthesis of HSPs and increases the thermotol-erance of Arabidopsis. Studies with Arabidopsis plants con-taining an antisense DNAsequence that reduces HSP70 syn-thesis showed that the high-temperature extreme at which the plants could survive was reduced by 2°C compared with controls, although the mutant plants grew normally at opti-mum temperatures (Lee and Schoeffl 1996).
Stress Physiology 605 FIGURE 25.11 The heat shock factor (HSF) cycle activates the synthesis of heat shock protein mRNAs. In nonstressed cells, HSF normally exists in a monomeric state (1) associ-ated with HSP70 proteins. Upon the onset of an episode of heat stress, HSP70 dissociates from HSF which subse-quently trimerizes (2). Active trimers bind to heat shock elements (HSE) in the promoter of heat shock protein (HSP) genes (3), and activate the transcription of HSP mRNAs leading to the translation of HSPs among which are HSP70 (4). The HSF trimers associated with the HSE are phospho-rylated (5) facilitating the binding of HSP70 to the phos-phorylated trimers (6). The HSP70 trimer complex (7) disso-ciates from the HSE and disassembles and dephosphory-lates into HSF monomers (8), which subsequently bind HSP reforming the resting HSP70/HSF complex. (After Bray et al. 2000.) P P P P P Heat stress nGaannTTCnnGAAn DNA Heat shock element Heat shock protein mRNA Heat shock proteins (HSP) Heat shock factor (HSF) HSP70 1 2 3 4 6 7 8 5 Presumably failure to synthesize the entire range of HSPs that are usually induced in the plant would lead to a much more dramatic loss of thermotolerance. Other stud-ies with both Arabidopsis mutants (Hong and Vierling 2000) and transgenic plants (Queitsch et al. 2000) demonstrate that at least HSP101 is a critical component of both induced and constitutive thermotolerance in plants.
Adaptation to Heat Stress Is Mediated by Cytosolic Calcium Enzymes participating in metabolic pathways can have dif-ferent temperature responses, and such differential ther-mostability may affect specific steps in metabolism before HSPs can restore activity by their molecular chaperone capacity. Heat stress can therefore cause changes in metab-olism leading to the accumulation of some metabolites and the reduction of others. Such changes can dramatically alter the function of metabolic pathways and lead to imbalances that can be difficult to correct.
In addition, heat stress can alter the rate of metabolic reactions that consume or produce protons, and it can affect the activity of proton-pumping ATPases that pump protons from the cytosol into the apoplast or vacuoles (see Chapter 6). This might lead to an acidification of the cytosol, which could cause additional metabolic perturba-tions during stress. Cells can have metabolic acclimation mechanisms that ameliorate these effects of heat stress on metabolism.
One of the metabolic acclimations to heat stress is the accumulation of the nonprotein amino acid γ-aminobutyric acid (GABA). During episodes of heat stress, GABA accu-mulates to levels six- to tenfold higher than in unstressed plants. GABA is synthesized from the amino acid L-gluta-mate, in a single reaction catalyzed by the enzyme gluta-mate decarboxylase (GAD). GAD is one of several enzymes whose activity is modulated by the calcium-activated, reg-ulatory protein calmodulin (for details on the mode of action of calmodulin, see Chapter 14 on the web site).
Calcium-activated calmodulin activates GAD (Figure 25.12) and increases the biosynthesis rate of GABA (Sned-den et al. 1995). In transgenic plants expressing the cal-cium-sensing protein aequorin, it has been shown that 606 Chapter 25 ADP ADP ATP H+ H+ H+ + Pi ATP ATP H+ H+ + Pi H+ H+ Pi PPi + Pi ADP Ca+ Ca2+ Ca2+ Ca+ Ca+ Ca+ Ca+ CaM CaM Ca2+ Ca2+ CaM GAD (inactive) GAD (active) Glutamate + H+ GABA + CO2 CAX1 CAX2 ACA ATP + Pi ADP ACA Ca+ Ca+ Ca+ Ca+ Apoplast pH ˜5.5 Cytosol acidification Vacuole pH ˜5.5 2 FIGURE 25.12 Heat stress causes a reduction in cytosolic pH from the normal slightly alkaline value, probably by inhibiting proton-pumping ATPases and pyrophosphatases that pump protons across the plasma membrane or into the vacuole. Additionally, heat stress effects a change in cal-cium homeostasis inside the cell by affecting the influx of calcium into the cytosol through either plasma membrane or vacuolar calcium channels, or by action on efflux ATPases or proton cotransporters. This increase in cytosolic calcium leads to the activation of calmodulin (CaM), which binds to glutamate decarboxylase (GAD) converting it from the inactive to the active form. Glutamate conversion to γ− aminobutyric acid (GABA) is then accomplished consum-ing protons in the process and mediating an increase in cytosolic pH. CAX1 and CAX2 are transport proteins, ACA: Ca2+ ATPase. high-temperature stress increases cytosolic levels of cal-cium, and that these increases lead to the calmodulin-medi-ated activation of GAD and the high-temperature induced accumulation of GABA.
Although GABA is an important signaling molecule in mammalian brain tissue, there is no evidence that it func-tions as a signaling molecule in plants. Possible functions of GABA in heat stress resistance are under investigation.
CHILLING AND FREEZING Chilling temperatures are too low for normal growth but not low enough for ice to form. Typically, tropical and sub-tropical species are susceptible to chilling injury. Among crops, maize, Phaseolus bean, rice, tomato, cucumber, sweet potato, and cotton are chilling sensitive. Passiflora, Coleus, and Gloxinia are examples of susceptible ornamentals.
When plants growing at relatively warm temperatures (25 to 35°C) are cooled to 10 to 15°C, chilling injury occurs: Growth is slowed, discoloration or lesions appear on leaves, and the foliage looks soggy, as if soaked in water for a long time. If roots are chilled, the plants may wilt.
Species that are generally sensitive to chilling can show appreciable variation in their response to chilling temper-atures. Genetic adaptation to the colder temperatures asso-ciated with high altitude improves chilling resistance (Fig-ure 25.13). In addition, resistance often increases if plants are first hardened (acclimated) by exposure to cool, but noninjurious, temperatures. Chilling damage thus can be minimized if exposure is slow and gradual. Sudden expo-sure to temperatures near 0°C, called cold shock, greatly increases the chances of injury.
Freezing injury, on the other hand, occurs at tempera-tures below the freezing point of water. Full induction of tolerance to freezing, as with chilling, requires a period of acclimation at cold temperatures.
In the discussion that follows we will examine how chilling injury alters membrane properties, how ice crys-tals damage cells and tissues, and how ABA, gene expres-sion, and protein synthesis mediate acclimation to freezing.
Membrane Properties Change in Response to Chilling Injury Leaves from plants injured by chilling show inhibition of photosynthesis, slower carbohydrate translocation, lower respiration rates, inhibition of protein synthesis, and increased degradation of existing proteins. All of these responses appear to depend on a common primary mecha-nism involving loss of membrane function during chilling. For instance, solutes leak from the leaves of chilling-sensitive Passiflora maliformis (conch apple) floated on water at 0°C, but not from those of chilling-resistant Pas-siflora caerulea (passionflower). Loss of solutes to the water reflects damage to the plasma membrane and possibly also to the tonoplast. In turn, inhibition of photosynthesis and of respiration reflects injury to chloroplast and mitochon-drial membranes.
Why are membranes affected by chilling? Plant mem-branes consist of a lipid bilayer interspersed with proteins and sterols (see Chapters 1 and 11). The physical properties of the lipids greatly influence the activities of the integral membrane proteins, including H+-ATPases, carriers, and channel-forming proteins that regulate the transport of ions and other solutes (see Chapter 6), as well as the transport of enzymes on which metabolism depends.
In chilling-sensitive plants, the lipids in the bilayer have a high percentage of saturated fatty acid chains, and mem-branes with this composition tend to solidify into a semi-crystalline state at a temperature well above 0°C. Keep in mind that saturated fatty acids that have no double bonds and lipids containing trans-monounsaturated fatty acids solidify at higher temperatures than do membranes com-posed of lipids that contain unsaturated fatty acids.
As the membranes become less fluid, their protein com-ponents can no longer function normally. The result is inhi-bition of H+-ATPase activity, of solute transport into and out of cells, of energy transduction (see Chapters 7 and 11), and of enzyme-dependent metabolism. In addition, chill-ing-sensitive leaves exposed to high photon fluxes and chilling temperatures are photoinhibited (see Chapter 7), causing acute damage to the photosynthetic machinery.
Membrane lipids from chilling-resistant plants often have a greater proportion of unsaturated fatty acids than those from chilling-sensitive plants (Table 25.5), and dur-ing acclimation to cool temperatures the activity of desat-urase enzymes increases and the proportion of unsaturated lipids rises (Williams et al. 1988; Palta et al. 1993). This modification lowers the temperature at which the mem-Stress Physiology 607 60 40 0 20 1 2 3 Altitude of origin (km) Chilling resistance (percent surviving seedlings) 80 Seeds from high altitudes FIGURE 25.13 Survival at low temperature of seedlings of different populations of tomato collected from different alti-tudes in South America. Seed was collected from wild tomato (Lycopersicon hirsutum) and grown in the same greenhouse at 18 to 25°C. All seedlings were then chilled for 7 days at 0°C and then kept for 7 days in a warm growth room, after which the number of survivors was counted. Seedlings from seed collected from high altitudes showed greater resistance to chilling (cold shock) than those from seed collected from lower altitudes. (From Patterson et al. 1978.) brane lipids begin a gradual phase change from fluid to semicrystalline and allows membranes to remain fluid at lower temperatures. Thus, desaturation of fatty acids pro-vides some protection against damage from chilling.
The importance of membrane lipids to tolerance of low temperatures has been demonstrated by work with mutant and transgenic plants in which the activity of particular enzymes led to a specific change in membrane lipid com-position independent of acclimation to low temperature.
For example, Arabidopsis was transformed with a gene from Escherichia coli that raised the proportion of high-melting-point (saturated) membrane lipids. This gene greatly increased the chilling sensitivity of the transformed plants.
Similarly, the fab1 mutants of Arabidopsis have increased levels of saturated fatty acids, particularly 16:0 (see Table 25.5, and Tables 11.3 and 11.4). During a period of 3 to 4 weeks at chilling temperatures, photosynthesis and growth were gradually inhibited, and exposure to chilling tem-perature eventually destroyed the chloroplasts of this mutant. At nonchilling temperatures, the mutant grew as well as wild-type controls did (Wu et al. 1997). (For addi-tional transformation examples, see Web Topic 25.2.) Ice Crystal Formation and Protoplast Dehydration Kill Cells The ability to tolerate freezing temperatures under natural conditions varies greatly among tissues. Seeds, other partly dehydrated tissues, and fungal spores can be kept indefi-nitely at temperatures near absolute zero (0 K, or –273°C), indicating that these very low temperatures are not intrin-sically harmful.
Fully hydrated, vegetative cells can also retain viability if they are cooled very quickly to avoid the formation of large, slow-growing ice crystals that would puncture and destroy subcellular structures. Ice crystals that form dur-ing very rapid freezing are too small to cause mechanical damage. Conversely, rapid warming of frozen tissue is required to prevent the growth of small ice crystals into crystals of a damaging size, or to prevent loss of water vapor by sublimation, both of which take place at inter-mediate temperatures (–100 to –10°C).
Under natural conditions, cooling of intact, multicellu-lar plant organs is never fast enough to limit crystal for-mation in fully hydrated cells to only small, harmless ice crystals. Ice usually forms first within the intercellular spaces, and in the xylem vessels, along which the ice can quickly propagate. This ice formation is not lethal to hardy plants, and the tissue recovers fully if warmed. However, when plants are exposed to freezing temperatures for an extended period, the growth of extracellular ice crystals results in the movement of liquid water from the protoplast to the extracellular ice, causing excessive dehydration (for a detailed description of this process, see Web Topic 25.3).
During rapid freezing, the protoplast, including the vac-uole, supercools; that is, the cellular water remains liquid even at temperatures several degrees below its theoretical freezing point. Several hundred molecules are needed for an ice crystal to begin forming. The process whereby these hundreds of water molecules start to form a stable ice crys-tal is called ice nucleation, and it strongly depends on the properties of the involved surfaces. Some large polysac-charides and proteins facilitate ice crystal formation and are called ice nucleators.
Some ice nucleation proteins made by bacteria appear to facilitate ice nucleation by aligning water molecules along repeated amino acid domains within the protein. In plant cells, ice crystals begin to grow from endogenous ice nucleators, and the resulting, relatively large intracellular ice crystals cause extensive damage to the cell and are usu-ally lethal.
Limitation of Ice Formation Contributes to Freezing Tolerance Several specialized plant proteins may help limit the growth of ice crystals by a noncolligative mechanism—that is, an effect that does not depend on the lowering of the 608 Chapter 25 TABLE 25.5 Fatty acid composition of mitochondria isolated from chilling-resistant and chilling-sensitive species Percent weight of total fatty acid content Chilling-resistant species Chilling-sensitive species Major fatty acidsa Cauliflower bud Turnip root Pea shoot Bean shoot Sweet potato Maize shoot Palmitic (16:0) 21.3 19.0 12.8 24.0 24.9 28.3 Stearic (18:0) 1.9 1.1 2.9 2.2 2.6 1.6 Oleic (18:0) 7.0 12.2 3.1 3.8 0.6 4.6 Linoleic (18:2) 16.4 20.6 61.9 43.6 50.8 54.6 Linolenic (18:3) 49.4 44.9 13.2 24.3 10.6 6.8 Ratio of unsaturated to saturated fatty acids 3.2 3.9 3.8 2.8 1.7 2.1 a Shown in parentheses are the number of carbon atoms in the fatty acid chain and the number of double bonds.
Source: After Lyons et al. 1964.
freezing point of water by the presence of solutes. These antifreeze proteins are induced by cold temperatures, and they bind to the surfaces of ice crystals to prevent or slow further crystal growth.
In rye leaves, antifreeze proteins are localized in the epi-dermal cells and cells surrounding the intercellular spaces, where they can inhibit the growth of extracellular ice.
Plants and animals may use similar mechanisms to limit ice crystals: A cold-inducible gene identified in Arabidopsis has DNA homology to a gene that encodes the antifreeze protein in fishes such as winter flounder. Antifreeze pro-teins are discussed in more detail later in the chapter.
Sugars and some of the cold-induced proteins are sus-pected to have cryoprotective (cryo- = “cold”) effects; they stabilize proteins and membranes during dehydration induced by low temperature. In winter wheat, the greater the sucrose concentration, the greater the freezing toler-ance. Sucrose predominates among the soluble sugars asso-ciated with freezing tolerance that function in a colligative fashion, but in some species raffinose, fructans, sorbitol, or mannitol serves the same function.
During cold acclimation of winter cereals, soluble sug-ars accumulate in the cell walls, where they may help restrict the growth of ice. A cryoprotective glycoprotein has been isolated from leaves of cold-acclimated cabbage (Bras-sica oleracea). In vitro, the protein protects thylakoids iso-lated from nonacclimated spinach (Spinacia oleracea) against damage from freezing and thawing.
Some Woody Plants Can Acclimate to Very Low Temperatures When in a dormant state, some woody plants are extremely resistant to low temperatures. Resistance is determined in part by previous acclimation to cold, but genetics plays an important role in determining the degree of tolerance to low temperatures. Native species of Prunus (cherry, plum, and other pit fruits) from northern cooler cli-mates in North America are hardier after acclimation than those from milder climates. When the species were tested together in the laboratory, those with a northern geo-graphic distribution showed greater ability to avoid intra-cellular ice formation, underscoring distinct genetic differ-ences (Burke and Stushnoff 1979).
Under natural conditions, woody species acclimate to cold in two distinct stages (Weiser 1970): 1. In the first stage, hardening is induced in the early autumn by exposure to short days and nonfreezing chilling temperatures, both of which combine to stop growth. A diffusible factor that promotes acclimation (probably ABA) moves in the phloem from leaves to overwintering stems and may be responsible for the changes. During this period, woody species also with-draw water from the xylem vessels, thereby prevent-ing the stem from splitting in response to the expan-sion of water during later freezing. Cells in this first stage of acclimation can survive temperatures well below 0°C, but they are not fully hardened.
2. In the second stage, direct exposure to freezing is the stimulus; no known translocatable factor can confer the hardening resulting from exposure to freezing.
When fully hardened, the cells can tolerate exposure to temperatures of –50 to –100°C.
Resistance to Freezing Temperatures Involves Supercooling and Slow Dehydration In many species of the hardwood forests of southeastern Canada and the eastern United States, acclimation to freez-ing involves the suppression of ice crystal formation at tem-peratures far below the theoretical freezing point (see Web Topic 25.3 for details). This deep supercooling is seen in species such as oak, elm, maple, beech, ash, walnut, hickory, rose, rhododendron, apple, pear, peach, and plum (Burke and Stushnoff 1979). Deep supercooling also takes place in the stem and leaf tissue of tree species such as Engelmann spruce (Picea engelmannii) and subalpine fir (Abies lasiocarpa) growing in the Rocky Mountains of Colorado.
Resistance to freezing is quickly weakened once growth has resumed in the spring (Becwar et al. 1981). Stem tissues of subalpine fir, which undergo deep supercooling and remain viable to below –35°C in May, lose their ability to suppress ice formation in June and can be killed at –10°C.
Cells can supercool only to about –40°C, at which tem-perature ice forms spontaneously. Spontaneous ice forma-tion sets the low-temperature limit at which many alpine and subarctic species that undergo deep supercooling can sur-vive. It also explains why the altitude of the timberline in mountain ranges is at or near the –40°C minimum isotherm.
The cell protoplast suppresses ice nucleation when undergoing deep supercooling. In addition, the cell wall acts as a barrier both to the growth of ice from the intercellular spaces into the wall, and to the loss of liquid water from the protoplast to the extracellular ice, which is driven by a steep vapor pressure gradient (Wisniewski and Arora 1993). Many flower buds (e.g., grape, blueberry, peach, azalea, and flowering dogwood) survive the winter by deep supercooling, and serious economic losses, particularly of peach, can result from the decline in freezing tolerance of the flower buds in the spring. The cells then no longer supercool, and ice crystals that form extracellularly in the bud scales draw water from the apical meristem, killing the floral apex by dehydration.
The floral buds of apple and pear, the vegetative buds of all temperate fruit trees, and the living cells in their bark do not supercool, but they resist dehydration during extra-cellular ice formation. Resistance to cellular dehydration is highly developed in woody species that are subject to aver-age annual temperature minima below –40°C, particularly species found in northern Canada, Alaska, northern Europe, and Asia.
Stress Physiology 609 Ice formation starts at –3 to –5°C in the intercellular spaces, where the crystals continue to grow, fed by the gradual withdrawal of water from the protoplast, which remains unfrozen. Resistance to freezing temperatures depends on the capacity of the extracellular spaces to accommodate the volume of growing ice crystals and on the ability of the protoplast to withstand dehydration.
This restriction of ice crystal formation to extracellular spaces, accompanied by gradual protoplast dehydration, may explain why some woody species that are resistant to freezing are also resistant to water deficit during the grow-ing season. For example, species of willow (Salix), white birch (Betula papyrifera), quaking aspen (Populus tremu-loides), pin cherry (Prunus pensylvanica), chokecherry (Prunus virginiana), and lodgepole pine (Pinus contorta) tol-erate very low temperatures by limiting the formation of ice crystals to the extracellular spaces. However, acquisi-tion of resistance depends on slow cooling and gradual extracellular ice formation and protoplast dehydration.
Sudden exposure to very cold temperatures before full acclimation causes intracellular freezing and cell death.
Some Bacteria That Live on Leaf Surfaces Increase Frost Damage When leaves are cooled to temperatures in the –3 to –5°C range, the formation of ice crystals on the surface (frost) is accelerated by certain bacteria that naturally inhabit the leaf surface, such as Pseudomonas syringae and Erwinia her-bicola, which act as ice nucleators. When artificially inocu-lated with cultures of these bacteria, leaves of frost-sensi-tive species freeze at warmer temperatures than leaves that are bacteria free (Lindow et al. 1982). The surface ice quickly spreads to the intercellular spaces within the leaf, leading to cellular dehydration.
Bacterial strains can be genetically modified so that they lose their ice-nucleating characteristics. Such strains have been used commercially in foliar sprays of valuable frost-sensitive crops like strawberry to compete with native bac-terial strains and thus minimize the number of potential ice nucleation points.
ABA and Protein Synthesis Are Involved in Acclimation to Freezing In seedlings of alfalfa (Medicago sativa L.), tolerance to freez-ing at –10°C is greatly improved by previous exposure to cold (4°C) or by treatment with exogenous ABA without exposure to cold. These treatments cause changes in the pattern of newly synthesized proteins that can be resolved on two-dimensional gels. Some of the changes are unique to the particular treatment (cold or ABA), but some of the newly synthesized proteins induced by cold appear to be the same as those induced by ABA (see Chapter 23) or by mild water deficit.
Protein synthesis is necessary for the development of freezing tolerance, and several distinct proteins accumulate during acclimation to cold, as a result of changes in gene expression (Guy 1999). Isolation of the genes for these pro-teins reveals that several of the proteins that are induced by low temperature share homology with the RAB/LEA/DHN (responsive to ABA, late embryo abundant, and dehydrin, respectively) protein family. As described earlier in the sec-tion on gene regulation by osmotic stress, these proteins accumulate in tissues exposed to different stresses, such as osmotic stress. Their functions are under investigation.
ABAappears to have a role in inducing freezing tolerance.
Winter wheat, rye, spinach, and Arabidopsis thaliana are all cold-tolerant species, and when they are hardened by water shortages, their freezing tolerance also increases. This toler-ance to freezing is increased at nonacclimating temperatures by mild water deficit, or at low temperatures, either of which increases endogenous ABA concentrations in leaves. Plants develop freezing tolerance at nonacclimating temperatures when treated with exogenous ABA. Many of the genes or proteins expressed at low temperatures or under water deficit are also inducible by ABA under nonac-climating conditions. All these findings support a role of ABA in tolerance to freezing.
Mutants of Arabidopsis that are insensitive to ABA (abi1) or are ABA deficient (aba1) are unable to undergo low-tem-perature acclimation to freezing. Only in aba1, however, does exposure to ABA restore the ability to develop freez-ing tolerance (Mantyla et al. 1995). On the other hand, not all the genes induced by low temperature are ABA depen-dent, and it is not yet clear whether expression of ABA-induced genes is critical for the full development of freez-ing tolerance. For instance, research on the tolerance of rye crowns to freezing has found that the lethal temperature for 50% of the crowns (LT50) is –2 to –5°C for controls grown at 25°C, –8°C for ABA-treated crowns, and –28°C after acclimation at 2°C.
Clearly exogenous ABA cannot confer the same freezing acclimation that exposure to low temperatures does. Cell cultures of bromegrass (Bromus inermis) show a more dra-matic induction of freezing tolerance when treated with ABA: Whereas controls grown at 25°C could survive to –9°C, 7 days of exposure to ABA improved the freezing tol-erance to –40°C (Gusta et al. 1996).
Typically, a minimum of several days of exposure to cool temperatures is required for freezing resistance to be induced fully. Potato requires 15 days of exposure to cold.
On the other hand, when rewarmed, plants lose their freez-ing tolerance rapidly, and they can become susceptible to freezing once again in 24 hours. The need for cool temperatures to induce acclimation to chilling or freezing, and the rapid loss of acclimation upon warming, explain the susceptibility of plants in the south-ern United States (and similar climatic zones with highly variable winters) to extremes of temperature in the winter months, when air temperature can drop from 20 to 25°C to below 0°C in a few hours.
610 Chapter 25 Numerous Genes Are Induced during Cold Acclimation Expression of certain genes and synthesis of specific pro-teins are common to both heat and cold stress, but some aspects of cold-inducible gene expression differ from that produced by heat stress (Thomashow 2001). Whereas dur-ing cold episodes the synthesis of “housekeeping” proteins (proteins made in the absence of stress) is not substantially down-regulated, during heat stress housekeeping-protein synthesis is essentially shut down.
On the other hand, the synthesis of several heat shock proteins that can act as molecular chaperones is up-regu-lated under cold stress in the same way that it is during heat stress. This suggests that protein destabilization accompanies both heat and cold stress and that mecha-nisms for stabilizing protein structure during both heat and cold episodes are important for survival.
Another important class of proteins whose expression is up-regulated by cold stress is the antifreeze proteins.
Antifreeze proteins were first discovered in fishes that live in water under the polar ice caps. As discussed earlier, these proteins have the ability to inhibit ice crystal growth in a noncolligative manner, thus preventing freeze damage at intermediate freezing temperatures. Antifreeze proteins confer to aqueous solutions the property of thermal hys-teresis (transition from liquid to solid is promoted at a lower temperature than is transition from solid to liquid), and thus they are sometimes referred to as thermal hysteresis proteins (THPs).
Several types of cold-induced, antifreeze proteins have been discovered in cold-acclimated winter-hardy mono-cots. When the specific genes coding for these proteins were cloned and sequenced, it was found that all antifreeze proteins belong to a class of proteins such as endochitinases and endoglucanases, which are induced upon infection of different pathogens. These proteins, called pathogenesis-related (PR) proteins are thought to protect plants against pathogens. It thus appears that at least in monocots, the dual role of these proteins as antifreeze and pathogenesis-related proteins might protect plant cells against both cold stress and pathogen attack.
Another group of proteins found to be associated with osmotic stress (see the discussion earlier in this chapter) are also up-regulated during cold stress. This group includes proteins involved in the synthesis of osmolytes, proteins for membrane stabilization, and the LEA proteins. Because the formation of extracellular ice crystals generates significant osmotic stresses inside cells, coping with freezing stress also requires the means to cope with osmotic stress.
A Transcription Factor Regulates Cold-Induced Gene Expression More than 100 genes are up-regulated by cold stress. Because cold stress is clearly related to ABAresponses and to osmotic stress, not all the genes up-regulated by cold stress neces-sarily need to be associated with cold tolerance, but most likely many of them are. Many cold stress–induced genes are activated by transcriptional activators called C-repeat bind-ing factors (CBF1, CBF2, CBF3; also called DREB1b, DREB1c, and DREB1a, respectively) (Shinozaki and Yam-aguchi-Shinozaki 2000).
CBF/DREB1-type transcription factors bind to CRT/DRE elements (C-repeat/dehydration-responsive, ABA-independent sequence elements) in gene promoter sequences, which were discussed earlier in the chapter.
CBF/DREB1 is involved in the coordinate transcriptional response of numerous cold and osmotic stress–regulated genes, all of which contain the CRT/DRE elements in their promoters. CBF1/DREB1b is unique in that it is specifically induced by cold stress and not by osmotic or salinity stress, whereas the DRE-binding elements of the DREB2 type (dis-cussed earlier in the section on osmotic stresses) are induced only by osmotic and salinity stresses and not by cold.
The expression of CBF1/DREB1b is controlled by a sep-arate transcription factor, called ICE (inducer of CBF expression). ICE transcription factors do not appear to be induced by cold, and it is presumed that ICE or an associ-ated protein is posttranscriptionally activated, permitting activation of CBF1/DRE1b, but the precise signaling path-way(s) of cold perception, calcium signaling, and the acti-vation of ICE are presently under investigation.
Transgenic plants constitutively expressing CBF1 have more cold–up-regulated gene transcripts than wild-type plants have, suggesting that numerous cold–up-regulated proteins that may be involved in cold acclimation are being produced in the absence of cold in these CBF1 transgenic plants. In addition, CBF1 tansgenic plants are more cold tolerant than control plants.
SALINITY STRESS Under natural conditions, terrestrial higher plants encounter high concentrations of salts close to the seashore and in estuaries where seawater and freshwater mix or replace each other with the tides. Far inland, natural salt seepage from geologic marine deposits can wash into adjoining areas, rendering them unusable for agriculture.
However, a much more extensive problem in agriculture is the accumulation of salts from irrigation water.
Evaporation and transpiration remove pure water (as vapor) from the soil, and this water loss concentrates solutes in the soil. When irrigation water contains a high concentration of solutes and when there is no opportunity to flush out accumulated salts to a drainage system, salts can quickly reach levels that are injurious to salt-sensitive species. It is estimated that about one-third of the irrigated land on Earth is affected by salt.
In this section we discuss how plant function is affected by water and soil salinity, and we examine the processes that assist plants in avoiding salinity stress.
Stress Physiology 611 Salt Accumulation in Soils Impairs Plant Function and Soil Structure In discussing the effects of salts in the soil, we distinguish between high concentrations of Na+, referred to as sodic-ity, and high concentrations of total salts, referred to as salinity. The two concepts are often related, but in some areas Ca2+, Mg2+, and SO2 4 –, as well as NaCl, can con-tribute substantially to salinity. The high Na+ concentration of a sodic soil can not only injure plants directly but also degrade the soil structure, decreasing porosity and water permeability. A sodic clay soil known as caliche is so hard and impermeable that dynamite is sometimes required to dig through it!
In the field, the salinity of soil water or irrigation water is measured in terms of its electrical conductivity or in terms of osmotic potential. Pure water is a very poor con-ductor of electric current; the conductivity of a water sam-ple is due to the ions dissolved in it. The higher the salt concentration in water, the greater its electrical conductiv-ity and the lower its osmotic potential (higher osmotic pres-sure) (Table 25.6).
The quality of irrigation water in semiarid and arid regions is often poor. In the United States the salt content of the headwaters of the Colorado River is only 50 mg L–1, but about 2000 km downstream, in southern California, the salt content of the same river reaches about 900 mg L–1, enough to preclude growth of some salt-sensitive crops, such as maize. Water from some wells used for irrigation in Texas may contain as much as 2000 to 3000 mg salt L–1.
An annual application of irrigation water totaling 1 m from such wells would add 20 to 30 tons of salts per hectare (8–12 tons per acre) to the soil. These levels of salts are damaging to all but the most resistant crops.
Salinity Depresses Growth and Photosynthesis in Sensitive Species Plants can be divided into two broad groups on the basis of their response to high concentrations of salts. Halo-phytes are native to saline soils and complete their life cycles in that environment. Glycophytes (literally “sweet plants”), or nonhalophytes, are not able to resist salts to the same degree as halophytes. Usually there is a threshold concentration of salt above which glycophytes begin to show signs of growth inhibition, leaf discoloration, and loss of dry weight.
Among crops, maize, onion, citrus, pecan, lettuce, and bean are highly sensitive to salt; cotton and barley are mod-erately tolerant; and sugar beet and date palms are highly tolerant (Greenway and Munns 1980). Some species that are highly tolerant of salt, such as Suaeda maritima (a salt marsh plant) and Atriplex nummularia (a saltbush), show growth stimulation at Cl– concentrations many times greater than the lethal level for sensitive species (Figure 25.14).
Salt Injury Involves Both Osmotic Effects and Specific Ion Effects Dissolved solutes in the rooting zone generate a low (more negative) osmotic potential that lowers the soil water potential. The general water balance of plants is thus affected because leaves need to develop an even lower water potential to maintain a “downhill” gradient of water potential between the soil and the leaves (see Chapter 4).
This effect of dissolved solutes is similar to that of a soil water deficit (as discussed earlier in this chapter), and most plants respond to excessive levels of soil salinity in the same way as described earlier for water deficit.
A major difference between the low-water-potential environments caused by salinity versus soil desiccation is the total amount of water available. During soil desicca-tion a finite amount of water can be obtained from the soil profile by the plant, causing ever decreasing water poten-tials. In most saline environments a large (essentially unlimited) amount of water at a constant, low water potential is available. Of particular importance here is the fact that most plants can adjust osmotically when growing in saline soils. Such adjustment prevents loss of turgor (which would slow cell growth; see Figure 25.1) while generating a lower water potential, but these plants often continue to grow more slowly after this adjustment for an unknown reason that curi-ously is not related to insufficient turgor (Bressan et al. 1990) In addition to the plant responses to low water poten-tial, specific ion toxicity effects also occur when injurious concentrations of ions—particularly Na+, Cl–, or SO4 2–— accumulate in cells. Under nonsaline conditions, the cytosol of higher-plant cells contains 100 to 200 mM K+ and 1 to 10 mM Na+, an ionic environment in which many enzymes function optimally. An abnormally high ratio of Na+ to K+ and high concentrations of total salts inactivate enzymes and inhibit protein synthesis. At a high concen-tration, Na+ can displace Ca2+ from the plasma membrane of cotton root hairs, resulting in a change in plasma mem-brane permeability that can be detected as leakage of K+ from the cells (Cramer et al. 1985).
612 Chapter 25 TABLE 25.6 Properties of seawater and of good quality irrigation water Irrigation Property Seawater water Concentration of ions (mM) Na+ 457 <2.0 K+ 9.7 <1.0 Ca2+ 10 0.5–2.5 Mg2+ 56 0.25–1.0 Cl– 536 <2.0 SO4 2– 28 0.25–2.5 HCO3 – 2.3 <1.5 Osmotic potential (MPa) –2.4 –0.039 Total dissolved salts 32,000 500 (mg L–1 or ppm) Photosynthesis is inhibited when high concentrations of Na+ and/or Cl– accumulate in chloroplasts. Since photosyn-thetic electron transport appears relatively insensitive to salts, either carbon metabolism or photophosphorylation may be affected. Enzymes extracted from salt-tolerant species are just as sensitive to the presence of NaCl as enzymes from salt-sen-sitive glycophytes are. Hence the resistance of halophytes to salts is not a consequence of salt-resistant metabolism.
Instead, other mechanisms come into play to avoid salt injury, as discussed in the following section.
Plants Use Different Strategies to Avoid Salt Injury Plants minimize salt injury by excluding salt from meris-tems, particularly in the shoot, and from leaves that are actively expanding and photosynthesizing. In plants that are salt sensitive, resistance to moderate levels of salinity in the soil depends in part on the ability of the roots to pre-vent potentially harmful ions from reaching the shoots.
Recall from Chapter 4 that the Casparian strip imposes a restriction to the movements of ions into the xylem. To bypass the Casparian strips, ions need to move from the apoplast to the symplastic pathway across cell membranes.
This transition offers salt-resistant plants a mechanism to partially exclude harmful ions.
Sodium ions enter roots passively (by moving down an electrochemical-potential gradient; see Chapter 6), so root cells must use energy to extrude Na+ actively back to the outside solution. By contrast, Cl– is excluded by negative electric potential across the cell membrane, and the low permeability of root plasma membranes to this ion. Move-ment of Na+ into leaves is further minimized by absorption of Na+ from the transpiration stream (xylem sap) during its movement from roots to shoots and leaves.
Some salt-resistant plants, such as salt cedar (Tamarix sp.) and salt bush (Atriplex sp.), do not exclude ions at the root, but instead have salt glands at the surface of the leaves. The ions are transported to these glands, where the salt crystallizes and is no longer harmful. In general, halo-phytes have a greater capacity than glycophytes for ion accumulation in shoot cells.
Although some plants, such as mangroves, grow in saline environments with abundant water supplies, the abil-ity to acquire that water requires that they make osmotic adjustments to obtain water from the low-water-potential external environment. As discussed earlier in relation to water deficit, plant cells can adjust their water potential (Yw) in response to osmotic stress by lowering their solute potential (Ys). Two intracellular processes contribute to the decrease in Ys: the accumulation of ions in the vacuole and the synthesis of compatible solutes in the cytosol.
As mentioned earlier in the chapter, compatible solutes include glycine betaine, proline, sorbitol, mannitol, pinitol, and sucrose. Specific plant families tend to use one or two of these compounds in preference to others. The amount of car-bon used for the synthesis of these organic solutes can be rather large (about 10% of the plant weight). In natural veg-etation this diversion of carbon to adjust water potential does not affect survival, but in agricultural crops it can reduce growth and therefore total biomass and harvestable yields.
Many halophytes exhibit a growth optimum at moder-ate levels of salinity, and this optimum is correlated with the capacity to accumulate ions in the vacuole, where they can contribute to the cell osmotic potential without dam-aging the salt-sensitive enzymes. To a lesser extent, this process also occurs in more salt-sensitive glycophytes, but the adjustment may be slower.
Stress Physiology 613 40 60 80 20 0 100 200 300 500 400 CI– (mM) in the external medium Growth (percent of control at low CI– external) 100 120 140 600 700 IA IB II III Group IA (halophytes) includes sea blite (Suaeda maritima) and salt bush (Atriplex nummularia). These species show growth stimulation with Cl– levels below 400 nM.
Group II (halophytes and nonhalophytes) includes salt-tolerant halophytic grasses that lack salt glands, such as Festuca rubra subsp. red fescue (littoralis) and Puccinellia peisonis, and nonhalophytes, such as cotton (Gossypium spp.) and barley (Hordeum vulgare). All are inhibited by high salt concentra-tions. Within this group, tomato (Lycopersicon esculentum) is intermediate, and common bean (Phaseolus vulgaris) and soybean (Glycine max) are sensitive.
The species in Group III (very salt-sensitive nonhalophytes) are severely inhibited or killed by low salt concentrations. Included are many fruit trees, such as citrus, avocado, and stone fruit.
Group IB (halophytes) includes Townsend's cordgrass (Spartina x townsendii ) and sugar beet (Beta vulgaris).These plants tolerate salt, but their growth is retarded.
FIGURE 25.14 The growth of different species subjected to salinity relative to that of unsalinized controls. The curves dividing the regions are based on data for different species. Plants were grown for 1 to 6 months. (From Greenway and Munns 1980.) Besides making adjustments in water potential, plants adjusting to salinity stress undergo the other osmotic stress–related acclimations described earlier for water deficit. For example, plants subjected to salt stress can reduce leaf area and or drop leaves via leaf abscission just as during episodes of osmotic stress. In addition, changes in gene expression associated with osmotic stress are sim-ilarly associated with salinity stress. Keep in mind, how-ever, that in addition to acclimation to a low-water-poten-tial environment, plants experiencing salinity stress must cope with the toxicity of high ion concentrations associated with salinity stress.
Ion Exclusion Is Critical for Acclimation and Adaptation to Salinity Stress In terms of metabolic energy, use of ions to balance tissue water potential in a saline environment clearly has a lower energy cost for the plant than use of carbohydrates or amino acids, the production of which has a significantly higher energy cost. On the other hand, high ion concentra-tions are toxic to many cytosolic enzymes, so ions must be accumulated in the vacuole to minimize toxic concentra-tions in the cytosol.
Because NaCl is the most abundant salt encountered by plants under salinity stress, transport systems that facilitate compartmentation of Na+ into the vacuole are critical (Binzel et al. 1988). Both Ca2+ and K+ affect intracellular Na+ concentrations (Zhong and Läuchli 1994). At high con-centrations of Na+, K+ uptake through a high-affinity K+–Na+ transporter, HKT1, is inhibited, and the transporter operates as an Na+ uptake system (Figure 25.15). Calcium, on the other hand, enhances K+/Na+ selectivity and in so doing increases salt tolerance (Liu and Zhu 1997).
Sodium Is Transported across the Plasma Membrane and the Tonoplast As discussed in Chapter 6, H+ pumps in the plasma mem-brane and tonoplast provide the driving force (H+ electro-614 Chapter 25 ADP H+ ATP H+ H+ H+ H+ Na+ H+ H+ H+ H+ Na+ Na+ Na+ SOS1 AtHKT1 Na+ Na+ Na+ Na+ NSCC AKT1 ATP ADP ACA Ca+ Ca+ Apoplast pH ˜5.5 Cytosol pH ˜7.5 Vacuole pH ˜5.5 K+ K+ K+ K+ Ca2+ Ca2+ ADP KUP1 TRH1 ATP ADP ACA CAX1 CAX2 Ca2+ Ca2+ Ca2+ Ca2+ Ca2+ Ca2+ AtNHX 1,2,5 ATP H+ H+ H+ H+ Pi PPi 2 FIGURE 25.15 Membrane transport proteins mediating sodium, potassium, and calcium transport during salinity stress. SOS1, plasma membrane Na+/H+ antiporter; ACA, plasma/tonoplast membrane Ca2+-ATPase; KUP1/TRH1, high-affinity K+-H+ co-transporter; atHKT1, sodium influx transporter; AKT1, K+ in channel; NSCC, non selective cation channel; CAX1 or 2, Ca2+/H+ antiporter; atNHX1, 2 or 5, endomembrane Na+/H+ antiporter. Also indicated in the figure are proteins that have been implicated in ion homeostasis, but whose molecular identity is either not presently known or cofirmed in plants. These include plasma membrane and tonoplast calcium channel proteins, and vacuolar proton-pumping ATPases and pyrophos-phatases. The membrane potential difference across the plasma membrane is typically 120 to 200 mV, negative inside; across the tonoplast 0 to 20 mV; positive inside.
chemical potential) for secondary transport of ions (see Figure 25.15). An ATPase is primarily responsible for the large ∆pH and membrane potential gradient found across the plasma membrane. A vacuolar H +-ATPase generates a ∆pH and membrane potential across the tonoplast (Hasegawa et al. 2000).
Activity of these pumps is required for the secondary transport of excess ions associated with plant responses to salinity stress. This is indicated by findings showing that the activity of these H+ pumps is increased by salinity, and induced gene expression may account for some of this up-regulation.
Energy-dependent transport (efflux) of Na+ from the cytosol of plant cells across the plasma membrane is medi-ated by the gene product of the SOS1 (salt overly sensitive 1) gene that function as a Na+–H+ antiporter (Figure 25.16).
The SOS1 antiporter is regulated by the gene products of at least two other genes, referred to as SOS2 and SOS3 (Shi et al. 2000). SOS2 is a serine/threonine kinase that is appar-ently activated by calcium through the function of SOS3, a calcium-regulated protein phosphatase (see Web Topic 25.4 for details on Ca2+ signaling and the SOS gene family).
Vacuolar compartmentation of Na+ results in part from the activity of a family of Na+–H+ antiporters such as Ara-bidopsis AtNHX1 (see Figure 25.15). Transgenic Arabidopsis and tomato plants overexpressing the gene that encodes AtNHX1 exhibit enhanced salt tolerance (Apse et al. 1999; Quintero et al. 2000). (See Web Topic 25.5 for details on molecular studies of Na+ compartmentation.) These mole-cular findings are another example of the wealth of new information emerging from studies on transgenic plants, gene sequencing, and protein characterization (see Web Topic 25.6 for details on work with transgenic plants for stress studies).
Stress Physiology 615 H+ H+ Na+ H+ H+ Na+ Na+ Na+ SOS1 AtHKT1 Na+ Na+ Na+ Na+ NSCC AKT1 Apoplast pH ˜5.5 Cytosol pH ˜7.5 Vacuole pH ˜5.5 K+ K+ Ca2+ Ca2+ AtNHX 1,2,5 SOS2 SOS3 Ca2+ Transcription factor FIGURE 25.16 The regulation of ion homeostasis by the SOS signal transduction pathway, salinity stress, and calcium levels. Red arrows indicate positive regulation of the effected transport protein while blue arrows indicate nega-tive regulation. Proteins shown in yellow are activated by salinity stress. SOS1, plasma membrane Na+/H+ antiporter; SOS2, serine/threonine kinase; SOS3, Ca2+ bind-ing protein; HKT1, sodium influx transporter; AKT1, K+ in channel; NSCC, non selective cation channel; NHX1, 2 or 5, endomembrane Na+/H+ antiporter; shown in orange is an undertermined calcium channel protein. Salinity stress acti-vates a calcium channel leading to an increase in cytosolic calcium that activates the SOS cascade through SOS3. The SOS cascade must negatively regulate HKT1 which in turn secondarily regulates AKT1. At the same time, the SOS cas-cade increases the activity of SOS1 and AKT1. Working through an as yet undefined transcription factor the SOS cascade increases transcription of SOS1 while decreasing transcription of NHX gene(s). At low calcium NSCC can also function as an alternative sodium influx system, but this transporter is inhibited at high calcium levels. The membrane potential difference across the plasma mem-brane is typically 120 to 200 mV, negative inside, that of the tonoplast is 0 to 20 mV, positive inside.
OXYGEN DEFICIENCY Roots usually obtain sufficient oxygen (O2) for aerobic res-piration (see Chapter 11) directly from the gaseous space in the soil. Gas-filled pores in well-drained, well-structured soil readily permit the diffusion of gaseous O2 to depths of sev-eral meters. Consequently, the O2 concentration deep in the soil is similar to that in humid air. However, soil can become flooded or waterlogged when it is poorly drained or when rain or irrigation is excessive. Water then fills the pores and blocks the diffusion of O2 in the gaseous phase. Dissolved oxygen diffuses so slowly in stagnant water that only a few centimeters of soil near the surface remain oxygenated.
When temperatures are low and plants are dormant, oxygen depletion is very slow and the consequences are relatively harmless. However, when temperatures are higher (greater than 20°C), oxygen consumption by plant roots, and soil fauna and microorganisms, can totally deplete the oxygen from the bulk of the soil water in as lit-tle as 24 hours.
Flooding-sensitive plants are severely damaged by 24 hours of anoxia. The growth and survival of many plant species are greatly depressed under such conditions, and crop yields can be severely reduced. For example, garden pea (Pisum sativum) yields can be halved by 24 hours of flooding, making garden pea an example of a flooding-sen-sitive plant. Other plants, particularly species not adapted to grow in continually wet conditions and many crop plants, are affected by flooding in a milder way and are considered flooding-tolerant plants. Flooding-tolerant plants can withstand anoxia (lack of oxygen) temporarily, but not for prolonged periods of more than a few days.
On the other hand, specialized natural vegetation found in wetlands such as marshes and swamps, and crops such as rice, are well adapted to resist oxygen deficiency in the root environment. Wetland plants can resist anoxia, and they grow and survive for extended periods of up to months with their root systems in anoxic conditions. Most of these plants have special adaptations, which we will discuss here, that permit oxygen available in nearby environments to reach the tissues held in anoxic conditions. Practically all plants require oxygen when they are engaging in rapid metabolic activity, and plants can be classified according to the time they can withstand anoxic conditions in their root environ-ment without demonstrating substantial damage.
In the following sections we discuss the damage caused by anaerobiosis to roots and shoots, how wetland vegeta-tion copes with low oxygen tensions, and different accli-mations to anoxic stress that distinguish between flooding-tolerant and flooding-susceptible species.
Anaerobic Microorganisms Are Active in Water-Saturated Soils When soil is completely depleted of molecular O2, the func-tion of soil microbes becomes significant for plant life and growth. Anaerobic soil microorganisms (anaerobes) derive their energy from the reduction of nitrate (NO3 –) to nitrite (NO2 –) or to nitrous oxide (N2O) and molecular nitrogen (N2). These gases (N2O and N2) are lost to the atmosphere in a process called denitrification. As conditions become more reducing, anaerobes reduce Fe3+ to Fe2+, and because of its greater solubility, Fe2+ can rise to toxic concentrations when some soils are anaerobic for many weeks. Other anaerobes may reduce sulfate (SO4 2–) to hydrogen sulfide (H2S), which is a respiratory poison.
When anaerobes have an abundant supply of organic substrate, bacterial metabolites such as acetic acid and butyric acid are released into the soil water, and these acids along with reduced sulfur compounds account for the unpleasant odor of waterlogged soil. All of these sub-stances made by microorganisms under anaerobic condi-tions are toxic to plants at high concentrations.
Roots Are Damaged in Anoxic Environments Root respiration rate and metabolism are affected even before O2 is completely depleted from the root environ-ment. The critical oxygen pressure (COP) is the oxygen pressure at which the respiration rate is first slowed by O2 deficiency. The COP for a maize root tip growing in a well-stirred nutrient solution at 25°C, is about 0.20 atmosphere (20 kPa, or 20% O2 by volume), almost the concentration in ambient air. At this oxygen partial pressure (for a discus-sion of partial pressures, see Web Topic 9.3), the rate of dif-fusion of dissolved O2 from the solution into the tissue and from cell to cell barely keeps pace with the rate of O2 uti-lization. However, a root tip is metabolically very active, with respiration rates and ATP turnover comparable to those of mammalian tissue.
In older zones of the root, where cells are mature and fully vacuolated and the respiration rate is lower, the COP is often in the range of 0.1 to 0.05 atmosphere. When O2 concentrations are below the COP, the center of the root becomes anoxic (completely lacking oxygen) or hypoxic (partly deficient in oxygen).
The COP is lower when respiration slows down at cooler temperatures; it also depends on how bulky the organ is and how tightly the cells are packed. Large, bulky fruits are able to remain fully aerobic because of the large intercellular spaces that readily allow gaseous diffusion.
For single cells, an O2 partial pressure as low as 0.01 atmos-phere (1% O2 in the gaseous phase) can be adequate because diffusion over short distances ensures an adequate O2 supply to mitochondria. A very low partial pressure of O2 at the mitochondrion is sufficient to maintain oxidative phosphorylation.
The Km value (Michaelis–Menten constant; see Chapter 2 on the web site) for cytochrome oxidase is 0.1 to 1.0 µM dis-solved O2, a tiny fraction of the concentration of dissolved O2 in equilibrium with air (277 µM at 20°C). The large dif-ference between the COP values for an organ or tissue and 616 Chapter 25 the O2 requirements of mitochondria is explained by the slow diffusion of dissolved O2 in aqueous media.
In the absence of O2, electron transport and oxidative phosphorylation in mitochondria cease, the tricarboxylic acid cycle cannot operate, and ATP can be produced only by fer-mentation. Thus when the supply of O2 is insufficient for aer-obic respiration, roots first begin to ferment pyruvate (formed in glycolysis; see Chapter 11) to lactate, through the action of lactate dehydrogenase (LDH) (Figure 25.17). In the root tips of maize, lactate fermentation is transient because lowered intracellular pH quickly leads to a switch from lactate fer-mentation to ethanol fermentation. The shift occurs because of the different pH optima of the cytosolic enzymes involved.
At acidic pH, LDH is inhibited and pyruvate decar-boxylase is activated. The net yield of ATP in fermentation is only 2 moles of ATP per mole of hexose sugar respired (compared with 36 moles of ATP per mole of hexose respired in aerobic respiration). Thus, injury to root metab-olism by O2 deficiency originates in part from a lack of ATP to drive essential metabolic processes (Drew 1997).
Nuclear magnetic resonance (NMR) spectroscopy was used to measure the intracellular pH of living maize root tips under nondestructive conditions (Roberts et al. 1992).
In healthy cells, the vacuolar contents are more acidic (pH 5.8) than the cytoplasm (pH 7.4). But under conditions of extreme O2 deficiency, protons gradually leak from the vac-uole into the cytoplasm, adding to the acidity generated in the initial burst of lactic acid fermentation. These changes in pH (cytosolic acidosis) are associated with the onset of cell death.
Apparently, active transport of H+ into the vacuole by tonoplast ATPases is slowed by lack of ATP, and without ATPase activity the normal pH gradient between cytosol and vacuole cannot be maintained. Cytosolic acidosis irre-versibly disrupts metabolism in the cytoplasm of higher-plant cells, as it does in anoxic cells of animals. It is essen-tially this cytosolic acidosis that causes damage, and the timing and degree to which it is limited are the primary factors distinguishing flooding-sensitive from flooding-tol-erant species.
Stress Physiology 617 PPi ADP ATP ATP ADP NADH Sucrose UDP-glucose Glucose-1-P Glucose-6-P Anoxia Pyruvate Lactate Ethanol Acetaldehyde Lactate dehydrogenase Alcohol dehydrogenase TCA cycle Fructose-6-P Glucose + Fructose Glucose H2O Fructose UDP UTP Glycolysis + 2H+ NADH NAD NAD + H+ NADH + H+ H+ CO2 Pyruvate decarboxylase Reduced pH (–) (+) (–) FIGURE 25.17 During episodes of anoxia, pyruvate pro-duced by glycolysis is initially fermented to lactate. Proton production by glycolysis, and other metabolic pathways, and decreased proton translocation across the plasma mem-brane and tonoplast lead to a lowering of cytosolic pH. At lower pHs, lactate dehydrogenase activity is inhibited, and pyruvate decarboxylase is activated. This leads to an increase in the fermentation of ethanol and a decrease in the fermentation of lactate at lower pHs. The pathway of ethanol fermentation consumes more protons than does the pathway of lactate fermentation. This increases the cytosol-ic pH and enhances the ability of the plant to survive the episode of anoxia.
Damaged O2-Deficient Roots Injure Shoots Anoxic or hypoxic roots lack sufficient energy to support physiological processes on which the shoots depend.
Experiments have shown that the failure of the roots of wheat or barley to absorb nutrient ions and transport them to the xylem (and from there to the shoot) quickly leads to a shortage of ions within developing and expanding tis-sues. Older leaves senesce prematurely because of reallo-cation of phloem-mobile elements (N, P, K) to younger leaves. The lower permeability of roots to water often leads to a decrease in leaf water potential and wilting, although this decrease is temporary if stomata close, preventing fur-ther water loss by transpiration.
Hypoxia also accelerates production of the ethylene pre-cursor ACC (1-aminocyclopropane-1-carboxylic acid) in roots (see Chapter 22). In tomato, ACC travels via the xylem sap to the shoot, where, in contact with oxygen, it is converted by ACC oxidase to ethylene. The upper (adax-ial) surfaces of the leaf petioles of tomato and sunflower have ethylene-responsive cells that expand more rapidly when ethylene concentrations are high. This expansion results in epinasty, the downward growth of the leaves such that they appear to droop. Unlike wilting, epinasty does not involve loss of turgor.
In some species (e.g., pea and tomato), flooding induces stomatal closure apparently without detectable changes in leaf water potential. Oxygen shortage in roots, like water deficit or high concentrations of salts, can stimulate abscisic acid (ABA) production and movement of ABA to leaves.
However, stomatal closure under these conditions can be attributed mostly to the additional production of ABA by the older, lower leaves. These leaves do wilt, and they export their ABA to the younger turgid leaves, leading to stomatal closure (Zhang and Zhang 1994).
Submerged Organs Can Acquire O2 through Specialized Structures In contrast to flooding-sensitive and flooding-tolerant species, wetland vegetation is well adapted to grow for extended periods in water-saturated soil. Even when shoots are partly submerged, they grow vigorously and show no signs of stress.
In some wetland species, such as the water lily (Nymphoides peltata), submergence traps endogenous eth-ylene, and the hormone stimulates cell elongation of the petiole, extending it quickly to the water surface so that the leaf is able to reach the air. Internodes of deep-water (float-ing) rice respond similarly to trapped ethylene, so the leaves extend above the water surface despite increases in water depth. In the case of pondweed (Potamogeton pecti-natus), an aquatic monocot, stem elongation is insensitive to ethylene; instead elongation is promoted even under anaerobic conditions by acidification of the surrounding water caused by the accumulation of respiratory CO2.
In most wetland plants, and in many plants that accli-mate well to wet conditions, the stem and roots develop longitudinally interconnected, gas-filled channels that pro-vide a low-resistance pathway for movement of oxygen and other gases. The gases (air) enter through stomata, or through lenticels on woody stems and roots, and travel by molecular diffusion, or by convection driven by small pres-sure gradients.
In many wetland plants, exemplified by rice, cells are separated by prominent, gas-filled spaces, which form a tis-sue called aerenchyma, that develop in the roots indepen-dently of environmental stimuli. In a few nonwetland plants, however, including both monocots and dicots, oxy-gen deficiency induces the formation of aerenchyma in the stem base and newly developing roots (Figure 25.18). In the root tip of maize, hypoxia stimulates the activity of ACC synthase and ACC oxidase, thus causing ACC and ethylene to be produced faster. The ethylene leads to the death and disintegration of cells in the root cortex. The spaces these cells formerly occupied provide the gas-filled voids that facilitate movement of O2.
Ethylene-signaled cell death is highly selective; cells not destined to die in the root are unaffected. A rise in cytoso-lic Ca2+ concentration is thought to be part of the ethylene signal transduction pathway leading to cell death. Chemi-cals that elevate cytosolic Ca2+ concentration promote cell death under noninducing conditions; conversely, chemicals that lower cytosolic Ca2+ concentration block cell death in hypoxic roots that would normally form aerenchyma. Eth-ylene-dependent cell death in response to hypoxia is an example of programmed cell death, which was discussed in Chapter 16 (Drew et al. 2000).
Some plants (or parts of them) can tolerate exposure to strictly anaerobic conditions for an extended period (weeks or months) before developing aerenchyma. These include the embryo and coleoptile of rice and of Echinochloa crus-galli var. oryzicola (rice grass), and rhizomes (underground horizontal stems) of Schoenoplectus lacustris (giant bulrush), Scirpus maritimus (salt marsh bulrush), and Typha angusti-folia (narrow-leafed cattail). These rhizomes can survive for several months and expand their leaves in an anaerobic atmosphere.
In nature, rhizomes overwinter in anaerobic mud at the edges of lakes. In spring, once the leaves have expanded above the mud or water surface, O2 diffuses down through the aerenchyma into the rhizome. Metabolism then switches from an anaerobic (fermentative) to an aerobic mode, and roots begin to grow using the available oxygen.
Likewise, during germination of paddy (wetland) rice and of rice grass, the coleoptile breaks the water surface and becomes a diffusion pathway (a “snorkel”) for O2 to the rest of the plant. (Even though rice is a wetland species, its roots are as intolerant of anoxia as maize roots are.) As the root extends into oxygen-deficient soil, the con-tinuous formation of aerenchyma just behind the tip allows oxygen movement within the root to supply the apical zone. In roots of rice and other typical wetland plants, structural barriers composed of suberized and lignified 618 Chapter 25 cells prevent O2 diffusion outward to the soil. The O2 thus retained supplies the apical meristem and allows growth to proceed 50 cm or more into anaerobic soil.
In contrast, roots of nonwetland species, such as maize, leak O2, failing to conserve it to the same extent. Thus, in the root apex of these plants, internal O2 becomes insuffi-cient for aerobic respiration, and this lack of O2 severely limits the depth to which such roots can extend into anaer-obic soil.
Most Plant Tissues Cannot Tolerate Anaerobic Conditions Most tissues of higher plants cannot survive prolonged anaerobic conditions. Root tips of maize, for example, remain viable for only 20 to 24 hours if they are suddenly deprived of O2. Under anoxia, some ATP is generated slowly by fermentation, but the energy status of cells grad-ually declines during cytosolic acidosis. The precise com-bination of biochemical characteristics that allow some cells to tolerate anoxia for long periods is not fully understood.
Root tips of maize and other cereals show a modest degree of acclimation if they first are made hypoxic, whereupon they can survive up to 4 days of anoxia.
Acclimation to an anaerobic condition is associated with expression of the genes that encode many of the anaerobic stress proteins (see the next section). After accli-mation, the ability to carry out ethanolic fermentation under anoxia (thereby producing ATP to keep some metabolism going) is improved, and this improvement is accompanied by an ability to transport lactate out of the cytosol to the external medium, thus minimizing cytoso-lic acidosis (Drew 1997).
The ability of organs of wetland plants to tolerate chronic anoxia may depend on strategies similar to those just described, but they are clearly employed to greater effect: Critical features appear to be control of cytosolic pH, continued generation of ATP by glycolysis and fermenta-tion, and sufficient storage of fuel for anaerobic respiration over extended periods. It has been suggested that synthe-sis of alanine, succinate, and γ-aminobutyric acid under anoxia consumes protons and minimizes cytosolic acido-sis. Evidence to this effect has been found in anoxia-toler-ant shoots of rice and rice grass, but not in anoxia-sensitive shoots of wheat and barley.
Organs of species that alternate between anaerobic and aerobic metabolism need to deal with the consequences of the entry of O2 following anoxia. Highly reactive oxygen species are generated during aerobic metabolism, and they are normally detoxified by cellular defense mechanisms that involve superoxide dismutase (SOD). This enzyme converts superoxide radicals to hydrogen peroxide, which is then converted to water by peroxidase. In anoxia-tolerant rhizomes of Iris pseudacorus (yellow flag), SOD activity increases 13-fold during 28 days of Stress Physiology 619 FIGURE 25.18 Scanning electron micrographs of transverse sections through roots of maize, showing changes in struc-ture with oxygen supply. (150×) (A) Control root, supplied with air, with intact cortical cells. (B) Oxygen-deficient root growing in a nonaerated nutrient solution. Note the promi-nent gas-filled spaces (gs) in the cortex (cx), formed by degeneration of cells. The stele (all cells interior to the endodermis, En) and the epidermis (Ep) remain intact. X, xylem. (Courtesy of J. L. Basq and M. C. Drew.) (A) X cx Ep (B) X gs Ep En En anoxia. This increase is not observed in rhizomes of other Iris species that are not anoxia tolerant. In the tolerant species, SOD may be available to cope with the influx of O2 that occurs when the leaves emerge into the air from water or mud, so it may assist in resisting postanoxic stress.
Acclimation to O2 Deficit Involves Synthesis of Anaerobic Stress Proteins When maize roots are made anoxic, protein synthesis ceases except for the continued production of about 20 polypeptides (Sachs and Ho 1986). Most of these anaerobic stress proteins have been identified as enzymes of the gly-colytic and fermentation pathways.
The mechanism for sensing reduced oxygen levels under hypoxic or anoxic conditions is not completely clear.
However, one of the earliest events to occur following low-ering of O2 levels is an elevation of the intracellular Ca2+.
Evidence suggests that this calcium signal is involved in the signal transduction of anoxia. Within minutes of the onset of anoxia, a rise in cytosolic Ca2+ concentration acts as a signal leading to increases in mRNA levels of alcohol dehydrogenase (ADH) and sucrose synthase in maize cells in culture.
Chemicals that block a rise in intracellular Ca2+ concen-tration also prevent the expression of the genes for ADH and sucrose synthase from being induced by anoxia, and they greatly enhance the sensitivity of maize seedlings to anoxia (Sachs et al. 1996). Further research is needed to resolve these mechanisms and to explain how intracellular Ca2+ concentration signals both the early survival of cells under anoxia and the induction of cell death and aerenchyma formation during prolonged hypoxia.
The accumulation of mRNAs of the anaerobic stress genes results from changes in the rate of transcription of these genes. Analysis of common sequence elements in the promoters of the ADH genes of maize and Arabidopsis and of the other anaerobic stress genes has led to the identifi-cation of an anaerobic stress element and a G-box element that bind cis-acting transcription factors leading to the tran-scriptional activation of these genes. However, the exact details of how oxygen deficiency is sensed, how the signal is transduced through elevations in cytosolic Ca2+ leading to alterations in the transcription of specific genes, remains to be determined.
Note also that there is strong evidence that some type of translational control of anaerobic stress genes is also occur-ring. The efficiency with which mRNAs for non-anaerobic stress–regulated genes are translated following hypoxic stress is dramatically lower than that of stress-regulated genes such as ADH.
SUMMARY Stress is usually defined as an external factor that exerts a disadvantageous influence on the plant. Under both nat-ural and agricultural conditions, plants are exposed to unfavorable environments that result in some degree of stress. Water deficit, heat stress and heat shock, chilling and freezing, salinity, and oxygen deficiency are major stress factors restricting plant growth such that biomass or agro-nomic yields at the end of the season express only a frac-tion of the plant’s genetic potential.
The capacity of plants to cope with unfavorable envi-ronments is known as stress resistance. Plant adaptations that confer stress resistance, such as CAM metabolism, are genetically determined. Acclimation improves resistance as a result of prior exposure of a plant to stress.
Drought resistance mechanisms vary with climate and soil conditions. Indeterminate growth patterns such as that of sorghum and soybean allow these species to take advan-tage of late-occurring rains; plants with a determinate growth pattern, such as that of corn, lack that form of resis-tance to water stress. Inhibition of leaf expansion is one of the earliest responses to water stress, occurring when decreases in turgor ensuing from water deficit reduce or eliminate the driving force for cell and leaf expansion.
Additional stress resistance mechanisms in response to water stress include leaf abscission, root extension into deeper, wetter soil, and stomatal closure.
Stress caused by water deficit leads to the expression of sets of genes involved in acclimation and adaptation to the stress. These genes mediate the cellular and whole-plant responses described here. The sensing and activation of sig-nal transduction cascades mediating these changes in gene expression involve both an ABA-dependent pathway and an ABA-independent pathway.
Heat stress and heat shock are caused by high tempera-tures. Some CAM species can tolerate temperatures of 60 to 65°C, but most leaves are damaged above 45°C. The temperature of actively transpiring leaves is usually lower than air temperature, but water deficit curtails transpira-tion and causes overheating and heat stress. Heat stress inhibits photosynthesis and impairs membrane function and protein stability. Adaptations that confer heat resistance include responses that decrease light absorption by the leaves, such as leaf rolling, and a decrease in leaf size that minimizes boundary layer resistance and increases conductive heat loss. Heat shock proteins synthesized at high temperatures act as molecular chaperones that promote stabilization and correct folding of cell proteins, and biochemical responses leading to pH and metabolic homeostasis are also associ-ated with acclimation and adaptation to rapid rises in tem-perature.
Chilling and freezing stress ensue from low tempera-tures. Chilling injury occurs at temperatures that are too low for normal growth but are above freezing, and it is typ-ical of species of tropical or subtropical origin exposed to temperate climates. Chilling injuries include slow growth, leaf lesions, and wilting. The primary cause of most chill-ing injuries is the loss of membrane properties ensuing from changes in membrane fluidity. Membrane lipids of 620 Chapter 25 chilling-resistant plants often have a greater proportion of unsaturated fatty acids than those of chilling-sensitive plants. Freezing injury is associated primarily with damage caused by ice crystals formed within cells and organs.
Freezing-resistant species have mechanisms that limit the growth of ice crystals to extracellular spaces. Mechanisms that confer the resistance to freezing that is typical of woody plants include dehydration and supercooling.
Cold stress reduces water activity and leads to osmotic stress within the cells. This osmotic stress effect leads to the activation of osmotic stress–related signaling pathways, and the accumulation of proteins involved in cold accli-mation. Other cold specific, non-osmotic stress–related genes are also activated. Transgenic plants overexpressing cold stress–activated signaling components demonstrate increased cold tolerance.
Salinity stress results from salt accumulation in the soil.
Some halophyte species are highly tolerant to salt, but salinity depresses growth and photosynthesis in sensitive species. Salt injury ensues from a decrease in the water potential of the soil that makes soil water less available and from toxicity of specific ions accumulated at injurious con-centrations. Plants avoid salt injury by exclusion of excess ions from leaves or by compartmentation of ions in vac-uoles. Some of the molecular determinants of Na+ exclu-sion and vacuolar partitioning have been determined, and a signaling pathway, the SOS pathway, regulating the expression of these genes involved in ion homeostasis has been established.
Oxygen deficiency is typical of flooded or waterlogged soils. Oxygen deficiency depresses growth and survival of many species. On the other hand, plants of marshes and swamps, and crops such as rice, are well adapted to resist oxygen deficiency in the root environment. Most tissues of higher plants cannot survive anaerobically, but some tis-sues, such as the embryo and coleoptiles from rice, can sur-vive for weeks under anoxic conditions. The metabolic pathways for resisting anoxic damage and their regulation have been uncovered.
Web Material Web Topics 25.1 Stomatal Conductance and Yields of Irrigated Crops Stomatal conductance predicts yields of irrigat-ed crops grown in hot environments.
25.2 Membrane Lipids and Low Temperatures Lipid enzymes from mutant and transgenic plants mimic the effects of low-temperature acclimation.
25.3 Ice Formation in Higher-Plant Cells Heat is released when ice forms in intercellular spaces.
25.4 Ca2+ Signaling and Activation of the Salt Overly Sensitive (SOS) Signal Pathway Three genetically linked loci control ion homeo-stasis and salt tolerance.
25.5 Na+ Transport across the Plasma Membrane and Vacuolar Compartmentation SOS1 is an Na+–H+ antiporter that controls Na+ fluxes across the plasma membrane.
25.6 Gene Transfer and Stress Tolerance Transgenic plants are valuable tools for study-ing stress tolerance.
Web Essay 25.1 The Effect of Air Pollution on Plants Polluting gases inhibit stomatal conductance, photosynthesis,and growth.
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| | | | Written by Robert Dunlop Microsoft DirectX MVP | Introduction The dot product is a value expressing the angular relationship between two vectors. In this article we will learn how this value is calculated, its mathematical significance, and several ways in which this function is useful in 3D applications. Calculating the Dot Product A dot product is a scalar value that is the result of an operation of two vectors with the same number of components. Given two vectors A and B each with n components, the dot product is calculated as: A · B = A1B1 + ... + AnBn The dot product is thus the sum of the products of each component of the two vectors. For example if A and B were 3D vectors: A · B = A.x B.x + A.y B.y + A.z B.z A generic C++ function to implement a dot product on two floating point vectors of any dimensions might look something like this: float dot_product(float a,float b,int size) { float dp = 0.0f; for (int i=0;i This sample code is provided solely for the purpose of showing a generic function to clarify how the dot product is calculated; DirectX provides several implementations of this function for you, as you will see further on, though if you did need to write your own function (for example if using C++ without the D3DX libraries) you would likely just write separate functions to handle the vector types commonly used (2D,3D,4D) as inline code. So what does it mean? Earlier we said that the dot product represents an angular relationship between two vectors, and left it at that. Now we'll take a closer look at what this value represents. Let's say we have two vectors, A and B, as shown to the left. The values |A| and |B| represent the lengths of vectors A and B, respectively, and Θ is the angle between the two vectors. The dot product of vectors A and B will have the following relationship to these values: A · B = |A| |B| cos(Θ) That is to say, the dot product of two vectors will be equal to the cosine of the angle between the vectors, times the lengths of each of the vectors. Angular Domain of Dot Product: Given the characteristics of the cosine function, we can deduce three possible conditions: 1. If A and B are perpendicular (at 90 degrees to each other), the result of the dot product will be zero, because cos(Θ) will be zero. 2. If the angle between A and B are less than 90 degrees, the dot product will be positive (greater than zero), as cos(Θ) will be positive, and the vector lengths are always positive values. 3. If the angle between A and B are greater than 90 degrees, the dot product will be negative (less than zero), as cos(Θ) will be negative, and the vector lengths are always positive values. Angle from Dot Product of Unit Vectors The above characteristics are true for any vectors with non-zero length. In addition, there is a special case when both vectors are unit vectors, that is, vectors with a length of one (1.0). In this case, the lengths of the vectors does not contribute to the equation, simplifying to: A · B = |A| |B| cos(Θ) A · B = 1 1 cos(Θ) A · B = cos(Θ) In this case, the dot product is equal to the cosine of the angle between the vectors. Thus the angle between unit vectors can be calculated as: Θ = acos(A · B) Angle from Dot Product of Non-Unit Vectors Angles between non-unit vectors (vectors with lengths not equal to 1.0) can be calculated either by first normalizing the vectors, or by dividing the dot product of the non-unit vectors by the length of each vector. Dot Product of Vector with Itself Taking the dot product of a vector against itself (i.e. A · A) results in a value equal to the square of the vector's length. This is a familiar portion of the distance equation, d=sqrt(xx+yy+zz). Projection of Vector onto another Vector If one were to take the dot product of a unit vector A and a second vector B of any non-zero length, the result is the length of vector B projected in the direction of vector A (see illustration to left). This is used in a number of ways, such as collision response and conversion of vectors from one coordinate system to another (this forms the basis of matrix transformations). DirectX Implementations DirectX Graphics provides several implementations of the dot product function: | | | --- | | Programming in... | Functions Provided | | C++ | FLOAT D3DXVec2Dot(const D3DXVECTOR2 ,const D3DXVECTOR2 ) FLOAT D3DXVec3Dot(const D3DXVECTOR3 ,const D3DXVECTOR3 ) FLOAT D3DXVec4Dot(const D3DXVECTOR4 ,const D3DXVECTOR4 ) | | Managed DX | Microsoft.DirectX.Vector2.Dot(Vector2,Vector2) Microsoft.DirectX.Vector3.Dot(Vector3,Vector3) Microsoft.DirectX.Vector4.Dot(Vector4,Vector4) | | HLSL Shader Language | dot(vector,vector) mul(vector,vector) | | Vertex Shader (Assembly) | dp3 dest,src0,src1 dp4 dest,src0,src1 | | Pixel Shader (Assembly) | dp2add dest,src0,src1,src2.{x|y|z|w} dp3 dest,src0,src1 dp4 dest,src0,src1 | |
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13442 | https://www.saskoer.ca/intro-organic-chemistry/chapter/4-3/ | 4.3. Unusual Cases of Chirality and Stereogenicity – Introduction to Organic Chemistry
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Contents
Introduction
CHAPTER 1: Refresher and Basics of Organic Chemistry
1.1. (Very) Brief Refresher of the Basics
1.2. The Octet Rule
1.3. Basics of Bonding
1.4. VSEPR Theory
1.5. Hybrid Orbitals
1.6. Lewis Structures
1.7. Hashed and Wedged Notation
1.8. Other Representations of Molecules
Chapter 1 Learning Outcomes
Chapter 1 Practice Problems
Chapter 1 Practice Problems - Answers
Chapter 1 References
CHAPTER 2: Functional Groups and Nomenclature
2.1. Why Do We Care?
2.2. Functional Groups
2.3. Types of Intermolecular Forces
2.4. Effects of Intermolecular Forces
2.5. Nomenclature
Chapter 2 Learning Outcomes
Chapter 2 Practice Problems
Chapter 2 Practice Problems - Answers
CHAPTER 3: Conformations
3.1. Rotations Around Single (σ) Bonds
3.2. Newman Projections
3.3. Dihedral/Torsion Angles
3.4. Types of Strain in Molecules
3.5. Naming Conformations from Rotations Around a σ Bond
3.6. Strain and Conformation in Cyclic Molecules
Chapter 3 Learning Outcomes
Chapter 3 Practice Problems
Chapter 3 Practice Problems - Answers
CHAPTER 4: Stereochemistry
4.1. Preamble – Stereochemistry and Other Textbooks
4.2. Classification of Isomers
4.3. Unusual Cases of Chirality and Stereogenicity
4.4. Stereoisomerism From Pi (π) Bonds
4.5. Adding Stereochemical Information to IUPAC Names
4.6. Physical Properties of Enantiomers vs. Diastereomers
4.7. Optical Rotation
Chapter 4 Learning Outcomes
Chapter 4 Practice Problems
Chapter 4 Practice Problems - Answers
Chapter 4 References
CHAPTER 5: Reactions, Electron Flow, and Resonance
5.1. Reaction Equations vs. Reaction Mechanisms
5.2. Over-the-Arrow Notation in Chemical Reactions
5.3. Drawing Reaction Mechanisms
5.4. Reaction Coordinates
5.5. Resonance
Chapter 5 Learning Outcomes
Chapter 5 Practice Problems
Chapter 5 Practice Problems - Answers
Chapter 5 References
CHAPTER 6: Acid-Base Reactions
6.1. (Very) Brief Refresher of the Basics
6.2. Reaction Coordinates of Acid-Base Reactions
6.3. Qualitative Estimates of Acidity
6.4. Quantitative Acidity
Chapter 6 Learning Outcomes
Chapter 6 Practice Problems
Chapter 6 Practice Problems - Answers
CHAPTER 7: Pi (π) Bonds as Electrophiles
7.1. (Very) Brief Refresher of the Basics
7.2. Terminology: Nucleophiles and Electrophiles
7.3. Simple Nucleophilic Attacks on Carbonyls
7.4. Oxidation States
7.5. Catalysis of Addition Reactions
7.6. Additions of Organometallics to Pi (π) Bonds
7.7. Leaving Groups
7.8. Stereochemistry of Addition Reactions
Chapter 7 Learning Outcomes
Chapter 7 Practice Problems
Chapter 7 Practice Problems - Answers
CHAPTER 8: Pi (π) Bonds as Nucleophiles
8.1. (Very) Brief Refresher of the Basics
8.2. General Form of the Reaction
8.3. Regioselectivity
8.4. Stereoselectivity
8.5. Reaction: Addition of H-X
8.6. Reaction: Addition of H-OH
8.7. Reaction: Addition of X-X
8.8. Reaction: Addition of X-OH or X-OR
8.9. Reaction: Epoxidation
8.10. Reaction: Addition of HO-OH or HO-OR
8.11. Reaction: Addition of H-H
Chapter 8 Learning Outcomes
Chapter 8 Practice Problems
Chapter 8 Practice Problems - Answers
CHAPTER 9: Conjugation and Aromaticity
9.1. (Very) Brief Discussion on the Uses of Molecular Orbital Theory with Aromaticity
9.2. Aromaticity
9.3. Practical Considerations – Achieving Aromaticity and Avoiding Anti-Aromaticity
9.4. How to Classify Compounds as Aromatic, Anti-Aromatic, and Non-Aromatic
9.5. Nomenclature
Chapter 9 Learning Outcomes
Chapter 9 Practice Problems
Chapter 9 Practice Problems - Answers
CHAPTER 10: Electrophilic Aromatic Substitution
10.1. (Very) Brief Refresher of the Basics
10.2. Terminology: Electrophilic Aromatic Substitution (EAS) // SEAr
10.3. General Form and Mechanism
10.4. Reaction Coordinate and Rate-Determining Step
10.5. Reaction: Halogenation
10.6. Reaction: Nitration
10.7. Reaction: Sulfonation
10.8. Reaction: Alkylation via Friedel-Crafts
10.9. Reaction: Acylation via Friedel-Crafts
10.10. Regioselectivity and Substituent Effects
Chapter 10 Learning Outcomes
Chapter 10 Practice Problems
Chapter 10 Practice Problems - Answers
CHAPTER 11: Nucleophilic Substitution Reactions
11.1. (Very) Brief Refresher of the Basics
11.2. Substitution Reactions: SN2 Reactions
11.3. Substitution Reactions: SN1 Reactions
11.4. How to Determine if a Reaction Follows an SN2 or SN1 Mechanism
11.5. Solving Problems Using Special Nucleophiles
Chapter 11 Learning Outcomes
Chapter 11 Practice Problems
Chapter 11 Practice Problems - Answers
CHAPTER 12: Elimination Reactions
12.1. Addition vs. Elimination, SN2 and SN1 vs. E2 and E1
12.2. Elimination Reactions: E2 Reactions
12.3. Elimination Reactions: E1 Reactions
12.4. Determining if a Reaction Follows an E2 or E1 Mechanism
12.5. Reaction: Elimination of H-OH (Dehydration)
12.6. Reaction: Elimination of H-X (Dehydrohalogenation)
12.7. Oxidation of Alcohols via Elimination
Chapter 12 Learning Outcomes
Chapter 12 Practice Problems
Chapter 12 Practice Problems - Answers
CHAPTER 13: Addition-Elimination Reactions
13.1. (Very) Brief Refresher of the Basics
13.2. Concept and General Form
13.3. Mechanism, Reaction Coordinate, and Rate-Determining Step
13.4. Reaction Rates and Relative Reactivity
13.5. Reactions with Acid Halide Electrophiles
13.6. Reactions with Anhydride Electrophiles
13.7. Reactions with Carboxylic Acid/Ester Electrophiles
13.8. Reductions of Acyl Compounds Using Hydrides
13.9. Multiple Additions of Organometallic Reagents to Acyl Compounds
Chapter 13 Learning Outcomes
Chapter 13 Practice Problems
Chapter 13 Practice Problems - Answers
Acknowledgements
Introduction to Organic Chemistry
4.3. Unusual Cases of Chirality and Stereogenicity
Some special instances of chirality and stereogenicity are less common, but still important for an understanding of stereochemistry.
4.3.1. Stereocentres of Heteroatoms
Under the definition of stereogenic centre (see Section 4.2.2.3.) elements other than carbon can be stereogenic(Figure 4.24). This is slightly uncommon in nature but still plays important roles in some systems.
Figure 4.24 – Examples of Stereogenic Nitrogen, Sulfur, and Silicon.
Note that nitrogen atoms with a lone pair on them are not (usually) stereogenic. This is because the lone pair on the nitrogen is able to ‘move’ from one side to the other, causing the two isomers to interconvert (Figure 4.25). This process is sometimes referred to as (pyramidal) inversion. Why lone pairs on nitrogen are able to do this is beyond the scope of this text.
Figure 4.25 – Interconversion of Stereoisomers Due to Inversion at Nitrogen Atoms with Lone Pairs.
Nitrogen atoms with lone pairs can be stereogenic if they are part of highly rigid systems and thus cannot undergo inversion. Usually this requires a geometric constraint such as a ring system (Figure 4.26). These types of stereogenic centres are rare.
Figure 4.26 – Example of Stereogenic Nitrogen Atoms.
4.3.2. Advanced Stereocentres – Beyond Four Groups
Some older sources provide definitions of stereogenic centres that rely on “four different groups”. No part of the definition of stereogenic centres (see Section 4.2.2.3.) requires “four different groups”. Many commonly encountered stereogenic centres have this trait, but that is coincidental. For example, stereogenic centres with five or six groups are common in inorganic and organometallic chemistry (Figure 4.27).
Figure 4.27 – Examples of Pentacoordinate and Hexacoordinate Stereocentres.
These are not classified using the R/S descriptors and have special rules for assigning their absolute configurations. As these are not common in organic chemistry these lie outside the scope of this text. However, it is important to understand that stereogenicity is possible in more advanced geometries and does not require “four different groups”.
4.3.3. Unusual Chirality by Hindered/Impossible Rotations
Stereogenicity and chirality are distinct concepts. As such, some molecules are chiral without any stereogenic centres. These typically have some feature that prohibits interconverting three-dimensional geometries by making some “normal” aspect of the molecule impossible.
Molecules may be chiral due to hindered/impossible rotations around σ bonds. These are sometimes referred to as atropisomers. For example, the compound BINOL exists as a pair of enantiomers (Figure 4.28). Full rotation around the central C-C bond is impossible because two hydrogens on the aromatic rings would have to physically pass through each other for rotation to occur.
Figure 4.28 – Example of Chirality Through Hindered/Impossible Rotations.
Although interconverting the two stereoisomers of BINOL would require an impossible rotation, other examples only have (VERY) large energy barriers; the actual rotation is theoretically possible to achieve, just not realistic (hindered). Atropisomers may be classified as R or S, but use modified rules to do so. This lies outside the scope of this text.
4.3.4. Unusual Chirality by Hindered/Impossible Geometries
Molecules may be chiral due to hindered/impossible geometries. These are not atropisomers because there is no single σ bond about which rotation is hindered. For example, the compound helicene exists as a pair of enantiomers (Figure 4.29). Planarity of the entire molecule is impossible because two hydrogens on the aromatic rings would have to physically occupy the same space. As a result, the ring spirals into a chiral helix shape.
Figure 4.29 – Example of Chirality Through Hindered/Impossible Geometries.
Although interconverting the two stereoisomers of helicene would require an impossible geometry, other examples only have (VERY) large energy barriers; the actual geometry is theoretically possible to achieve, just not realistic (hindered). Helicenes may be classified as M or P, but this nomenclature system lies outside the scope of this text.
4.3.5.MesoCompounds
Stereogenicity and chirality are distinct concepts. As such, some molecules are achiral despite having multiple stereogenic centres (Figure 4.30). Compounds that fit this description are referred to as being meso. It is important to recognize that meso is a description of a molecule, not a relationship between two stereoisomers.
Figure 4.30 – Examples ContrastingMesoCompounds with Related Stereoisomers.
The easiest way to determine if a molecule is meso is to first identify if there is more than one stereocentre and then check if the molecule is achiral; if it has one or fewer stereocentres it cannot be meso.
Previous/next navigation
Previous: 4.2. Classification of Isomers
Next: 4.4. Stereoisomerism From Pi (π) Bonds
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13443 | https://www.youtube.com/watch?v=ML6r7BEZo7M | Calculating Elapsed Time Using a Timeline | EasyTeaching
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Learn how to calculate elapsed time using the timeline method.
Calculate elapsed time using the T Chart method:
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Transcript:
Intro elapsed time is the amount of time that passes from a start point to an end point calculating elapsed time is an important everyday skill it's useful when cooking taking a drive catching a bus or even watching a movie in this video we're going to use the timeline method for calculating elapsed time if you'd like to also learn the t-chart method see the link in the description below we'll use the timeline method to solve three problems Example 1 Cooking number one jess puts some food in the oven at 5 50 pm it needs to cook for 1 hour and 15 minutes what time will it be ready we start by drawing a timeline we know the start time 5 50 pm we don't know the finish time but we do know the amount of time that has elapsed 1 hour and 15 minutes to work out the end time we have to jump a total of 1 hour and 15 minutes along this timeline doing this in one jump is a bit tricky so instead we'll break it down into chunks of time that suit us let's start by jumping 10 minutes that will bring us to exactly six o'clock for each jump we make we must record the elapsed time here it is ten minutes and what time we land at after the jump in this case six o'clock we've already jumped ten minutes but we still need to jump one hour and five minutes jumping an hour from six o'clock will be easy we'll land at seven o'clock [Music] we still have five minutes to add seven pm plus five minutes is 705 pm the food will be ready at five past seven [Music] Example 2 Bus number two chris is taking a bus from london to paris it leaves london at 8 17 a.m and arrives in paris at 3 40 p.m how long does the trip take we have the start time 8 17 am and we have the end time 3 40 pm we need to calculate how much time has elapsed in the previous problem we had a set total time we had to jump this time we have to keep jumping along the timeline until we reach our end time [Music] to make things easier let's start by adding 3 minutes eight seventeen plus three minutes is eight twenty eight twenty is an easier time for us to work with again we must record each jump and the time we land to make it easier still let's jump 40 minutes this lands us at nine o'clock now we can jump easily in multiples of an hour three hours will take us to 12 p.m three more hours takes us to 3 p.m a final jump of 40 minutes lands us right on the end time 3 40 p.m now to calculate how much time has elapsed from the start to the end we just have to add up our jumps 3 minutes plus 40 minutes plus 3 hours plus 3 hours plus 40 minutes equals 7 hours and 23 minutes the trip takes 7 hours and 23 minutes Example 3 Movie number 3 brad wants to watch a movie it goes for 1 hour and 32 minutes he doesn't want to stay up too late and so wants to finish the movie by 8 45 pm what time should he start the movie by we know the elapsed time one hour and 32 minutes and the end time 8 45 pm we must work out the start time [Music] notice in this problem we'll be starting at the end of our timeline we're going to be working backwards that means we'll be subtracting time instead of adding again jumping all of this in one go might be a bit tricky so let's break our elapsed time into chunks we'll start by subtracting one hour 8 45 take away one hour is 7 45 as always we must record the jump and the time at which we land now we're left with 32 minutes to subtract we could do this in one jump but i'm going to start with a jump of 30 minutes this lands us at 7 15. [Music] now a final jump of two minutes lands us at 7 13. brad needs to start watching his movie by at least 7 13 pm to be finished by 8 45 pm this is how we can use the timeline strategy to solve problems involving elapsed time if you'd like to learn or practice the t-chart strategy check out the link to the video in the description below easyteaching.net |
13444 | https://www.scribd.com/document/425090428/MIT18-01SCF10-Ses31c | Related Rates, A Conical Tank | PDF | Volume | Geometry
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Related Rates, A Conical Tank
The document describes a related rates problem involving a conical water tank. It is being filled at a rate of 2 cubic feet per minute. The tank has a radius of 4 feet at the top and is 10 f…
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Related
Rates,
A
Conical
Tank
Example:
Consider
a
conical
tank
whose
radius
at
the
top
is
4
feet
and
whose
depth
is
10
feet.
It’s
being
filled
with
water
at
the
rate
of
2
cubic
feet
per
minute.
How
fast
is
the
water
level
rising
when
it
is
at
depth
5
feet?
As
always,
our
first
step
is
to
set
up
a
diagram
and
variables.
h r
Figure
1:
Illustration
of
example
2:
inverted
cone
water
tank.
This
diagram
just
helps
us
to
start
thinking
about
the
problem.
F or
instance,
we
see
that
because
the
cone
is
narrower
at
the
bottom
the
rate
of
change
of
the
depth
will
vary;
we
need
to
depict
the
water
level.
W e
also
realize
that
it’s
difficult
to
draw
useful
and
accurate
diagrams
of
three
dimensional
figures
—
a
simple
schematic
may
be
more
helpful.
The
key
here
is
to
draw
a
two-dimensional
cross-section.
In
the
figure
we’re
looking
at
one
half
of
a
vertical
slice
of
the
tank.
The
height
of
the
slice
equals
10
feet,
which
is
the
height
of
the
tank.
The
widest
part
of
the
slice
is
4
feet,
which
is
the
distance
from
center
to
edge
of
the
top
of
the
tank.
We’ll
use
the
variable
r
will
represent
the
distance
from
center
to
edge
of
the
top
of
the
water,
and
h
will
represent
the
height
of
the
top
of
the
water
(which
is
also
the
depth
of
the
water).
W e
can
find
the
relationship
between
r
and
h
from
Fig.
2)
using
similar
triangles:
r
4
=
.
h
10
1
adDownload to read ad-free
10 4 r h
Figure
2:
Relating
r
and
h
.
Our
goal
is
to
find
out
how
fast
the
water
is
rising
when
the
tank
is
half
full.
What
we
know
is
that
the
volume
of
water
in
the
tank
is
changing
at
a
rate
of
2
cubic
feet
per
minute.
W e
need
equations
relating
the
volume
of
water
in
the
tank
to
its
depth,
h
.
The
volume
of
a
cone
is
3 1
base
height.
From
Fig.
1),
the
volume
of
this
· ·
tank
is
given
by:
V
=1
πr
2
h
3
·
·
base
height
This
relates
the
volume
to
the
height
and
radius,
and
we
know
the
relation
between
the
hight
and
the
radius.
W e
have
one
more
piece
of
information
that
we
can
use:
dV
=
2.
dt
The
question
is:
“What
is
dh
when
h
=
5?”
dt
We’ve
now
translated
all
of
the
words
in
the
original
problem
into
formulas.
Our
word
problem
is
now
simply
a
calculus
problem.
W e
could
do
this
by
implicit
differentiation,
but
it’s
easy
enough
to
solve
for
r
in
terms
of
h
that
there’s
no
need
to.
2
r
=
h.
5
W e
plug
this
expression
for
r
back
into
V
to
get:
�
2
V
=1
π
2
h h
=4
πh
3
3
5
3(25)
2
adDownload to read ad-free
At
this
point
we
could
solve
for
h
,
but
that
turns
out
to
be
a
bad
idea.
Implicit
differentiation
is
much
easier.
dV
dV dh
=
dt
dh dt
�
2
=
π
2
3
h
2
dh
3
5
dt
4
πh
2
h
�
=
25
Now
that
we’ve
calculated
the
rates
of
change
we
can
plug
in
the
numbers
dV
=
2
and
h
=
5:
dt
�
2 =
4
π
(5)
2
h
�
25
2 = 4
πh
�
1
h
�
=
ft/min 2
π
W e
were
given
the
rate
at
which
the
volume
of
water
in
the
tank
was
changing
and
we
used
that
to
compute
the
rate
at
which
the
water
in
the
tank
was
rising.
At
the
heart
of
this
calculation
was
the
chain
rule:
dV
dV dh
=
.
dt
dh dt
Related
rates
problems
are
all
about
applying
the
chain
rule
to
solve
word
problems.
3
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M
IT OpenCourseWare
18.01SC Single Variable Calculus�
Fall 2010 �
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When Not To Use Mean , Median in Statistical Analysis
M Dhanunjaya
6 min readDec 30, 2022
We can’t use the mean value for the analysis when we have the outliers in the data.
What is a variable?
A variable is any characteristics, number, or quantity that can be measured or counted. A variable may also be called a data point. Examples of variables are Age, sex, business income and expenses, country of birth.
What are the types of variables?
Variables can be described by the way they are studied and measured. Basically variables can be broadly classified into two categories
Quantitative / Numeric variables
Qualitative / Categorical variables
Quantitative / Numeric variables :
These variables can be described as the numerical data which can be measured numerically, like ‘how many’ or ‘how much’. Therefore, numeric variables are quantitative variables.
These numeric variables may be further described as either continuous or discrete:
A continuous variable is a numeric variable. It includes elements with decimal points and numerical values.
Examples of continuous variables include height, time, age, and temperature.
A discrete variable is a numeric variable. Only whole numbers are allowed.
Examples of discrete variables include the number of registered cars, number of business locations, and number of children in a family.
Qualitative / Categorical variables :
Categorical variables have values that describe a ‘quality’ or ‘characteristic’ of a data unit, like ‘what type’ or ‘which category’. These represent non numerical elements.
Categorical variables may be further described as ordinal or nominal:
An ordinal variable is a categorical variable and the observations take values that can be logically ordered or ranked. The categories associated with ordinal variables can be ranked higher or lower than another, but do not necessarily establish a numeric difference between each category.
Examples of ordinal categorical variables include academic grades (i.e. A, B, C), clothing size (i.e. small, medium, large, extra large) and attitudes (i.e. strongly agree, agree, disagree, strongly disagree).
A nominal variable is a categorical variable and the observations can take values that are not possible to be organized in a logical sequence.
Examples of nominal categorical variables include sex, business type, eye color, religion, and brand.
Measures of Central Tendency
Introduction
A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data. The mean, median and mode are all valid measures of central tendency, but under different conditions, some measures of central tendency become more appropriate to use than others.
Mean (Arithmetic)
The mean is equal to the sum of all the values in the data set divided by the number of values in the data set(Average).
So the values in a data set and they have values x1,x2,x3,x4 …………..xn.
Types of Mean with the data:
Population Mean(µ)
Sample Mean(x̄)
The Population mean is referred to as mu.
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µ=(∑x)/N
The Sample mean is referred to as x-bar.
x̄=(∑x)/n
Here N is the size of the total dataset, n is the sample data from the population dataset. An important property of the mean is that it includes every value in your data set as part of the calculation. In addition, the mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.
When not to use the mean value in analysis
We can’t use the mean value for the analysis when we have the outliers in the data. For example, consider the wages of staff at a factory below:
The mean salary for these ten staff is $30.7k. However, inspecting the raw data suggests that this mean value might not be the best way to accurately reflect the typical salary of a worker, as most workers have salaries in the $12k to 18k range. The mean is being skewed by the two large salaries.
Median
The median is the middle value for a set of data that has been arranged in ascending order. The median is less affected by outliers and skewed data.
Our median mark is the middle mark — in this case, 56 . It is the middle mark because there are 5 scores before it and 5 scores after it. This works fine when you have an odd number of scores, but what happens when you have an even number of scores? What if you had only 10 scores? Well, you simply have to take the middle two scores and average the result.
Mode
The mode is the most frequent score in our data set. On a histogram it represents the highest bar in a bar chart or histogram. You can, therefore, sometimes consider the mode as being the most popular option. An example of a mode is presented below:
Normally, the mode is used for categorical data where we wish to know which is the most common category, as illustrated below:
We can see above that the most common form of transport, in this particular data set, is the bus.
However, one of the problems with the mode is that it is not unique, so it leaves us with problems when we have two or more values that share the highest frequency, such as below:
We are now stuck as to which mode best describes the central tendency of the data. To use the mode to describe the central tendency of this data set would be misleading.
Skewed Distributions and the Mean and Median
We often test whether our data is normally distributed or not because this is a common assumption underlying many statistical tests.
An example of a normally distributed set of data is presented below:
When you have a normally distributed sample,we can use both the mean or the median as your measure of central tendency.
In fact, in any symmetrical distribution, the mean, and mode are equal.
Mostly mean is widely preferred as the best measure of central tendency because it is the measure that includes all the values in the data set for its calculation, and any change in any of the scores will affect the value of the mean, but this is not the case with the median or mode.
However, when our data is skewed, for example, as with the right-skewed data set below:
Summary of when to use the mean, median and mode
Reference :
Mean
Statistics
Statistical Analysis
Data Science
Median
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13446 | https://mnemonicdictionary.com/word/chimerical | chimerical meaning - definition of chimerical by Mnemonic Dictionary
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chimerical - Dictionary definition and meaning for word chimerical
Definition
(adj) being or relating to or like a chimera Synonyms : chimeral , chimeric
Example Sentence
his Utopia is not as chimeric commonwealth but a practical improvement on what already exists
Definition
(adj) produced by a wildly fanciful imagination
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Mnemonics (Memory Aids) for chimerical
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chimerical has root word chimera which is a mythical creature and also means fantasy..
1 0
1st one is awesome mnemonic bt still for those who hate chemistry... it sounds like chemical so chemical reactions are highly unrealistic, only imaginative.. :P lol
1 0
Think America which sounds like chimerical...to go America is dream for many people..some make it real but most of them cannot go which is unrealistic for them
0 0
It has "miracle" in it-> Miracle is imaginative.
73 3
chi(she)-meri(marry)-cal
5 6
chimerical resembles camera...and camera is about photographs...photos are clicked with imagination
3 8
looks like COMMERCIAL which is always imaginative and unrealistic
3 0
Powered by Mnemonic Dictionary
CHIna + AMERICAl -> its imaginative to believe that china and america can come to a concensus
2 0
Rleate it with Cindrella which is in fantasy
1 4
CHIC+MARRY+KAL= i'll marry the hot chic in this movie tomorrow (Doesn't it sound IMAGINATIVE,UNREALISTIC)
1 0
chimerical has root word chimera which is a mythical creature and also means fantasy..
1 0
1st one is awesome mnemonic bt still for those who hate chemistry... it sounds like chemical so chemical reactions are highly unrealistic, only imaginative.. :P lol
1 0
Think America which sounds like chimerical...to go America is dream for many people..some make it real but most of them cannot go which is unrealistic for them
0 0
It has "miracle" in it-> Miracle is imaginative.
73 3
chi(she)-meri(marry)-cal
5 6
chimerical resembles camera...and camera is about photographs...photos are clicked with imagination
3 8
looks like COMMERCIAL which is always imaginative and unrealistic
3 0
Powered by Mnemonic Dictionary
CHIna + AMERICAl -> its imaginative to believe that china and america can come to a concensus
2 0
Rleate it with Cindrella which is in fantasy
1 4
CHIC+MARRY+KAL= i'll marry the hot chic in this movie tomorrow (Doesn't it sound IMAGINATIVE,UNREALISTIC)
1 0
chimerical has root word chimera which is a mythical creature and also means fantasy..
1 0
1st one is awesome mnemonic bt still for those who hate chemistry... it sounds like chemical so chemical reactions are highly unrealistic, only imaginative.. :P lol
1 0
Think America which sounds like chimerical...to go America is dream for many people..some make it real but most of them cannot go which is unrealistic for them
0 0
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13447 | https://stackoverflow.com/questions/37450302/send-more-money-puzzle-in-python | Stack Overflow
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Send More Money Puzzle in Python
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Asked
Modified 1 year, 10 months ago
Viewed 12k times
0
A famous puzzle follows. SEND + MORE = MONEY
Substitute each letter in the equation with a single integer 0-9 (no duplicates) such that the addition is correct. Write a program to solve this puzzle. Hint: Brute force works well {try all possibilities}.
Here's my code so far:
def solution(): letters = ('s', 'e', 'n', 'd', 'm', 'o', 'r', 'y') for s in range(9, 0, -1): for e in range(9, -1, -1): for n in range(9, -1, -1): for d in range(9, -1, -1): for m in range(9, 0, -1): for o in range(9, -1, -1): for r in range(9, -1, -1): for y in range(9, -1, -1): if len(set((letters))) != len(letters): send = 1000 s + 100 e + 10 n + d more = 1000 m + 100 o + 10 r + e money = 10000 m + 1000 o + 100 n + 10 e + y if send + more == money: return send, more, money print(solution())
But it isn't working. It gives no output. How can I fix this?
python
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edited May 26, 2016 at 2:24
kevmo314
4,33766 gold badges3434 silver badges5252 bronze badges
asked May 26, 2016 at 1:52
anonanon
2511 gold badge11 silver badge33 bronze badges
6
1
len(set((letters))) != len(letters) is invariant and never true. What is it for?
kevmo314
– kevmo314
2016-05-26 02:00:46 +00:00
Commented May 26, 2016 at 2:00
@Shankar That's not happening, though.
Veedrac
– Veedrac
2016-05-26 02:07:15 +00:00
Commented May 26, 2016 at 2:07
@Shankar - No such string multiplication is taking place.
TigerhawkT3
– TigerhawkT3
2016-05-26 02:07:18 +00:00
Commented May 26, 2016 at 2:07
I'm not sure what to use to meet the uniqueness requirement.
anon
– anon
2016-05-26 02:23:49 +00:00
Commented May 26, 2016 at 2:23
1
In keeping with the brute-force nature of your code, consider adding if e == s: continue at the top of the e loop, and something like if n in (s, e): continue in the n loop, and ... and if y in (s,e,n,d,m,o,r): continue at the top of the y loop.
aghast
– aghast
2016-05-26 02:33:30 +00:00
Commented May 26, 2016 at 2:33
| Show 1 more comment
7 Answers 7
Reset to default
5
with uniqueness requirement and search for all solutions:
def solutions(): # letters = ('s', 'e', 'n', 'd', 'm', 'o', 'r', 'y') all_solutions = list() for s in range(9, -1, -1): for e in range(9, -1, -1): for n in range(9, -1, -1): for d in range(9, -1, -1): for m in range(9, 0, -1): for o in range(9, -1, -1): for r in range(9, -1, -1): for y in range(9, -1, -1): if len(set([s, e, n, d, m, o, r, y])) == 8: send = 1000 s + 100 e + 10 n + d more = 1000 m + 100 o + 10 r + e money = 10000 m + 1000 o + 100 n + 10 e + y if send + more == money: all_solutions.append((send, more, money)) return all_solutions print(solutions())
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edited Nov 17, 2018 at 15:00
Muhammad Haseeb Khan
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answered May 26, 2016 at 2:36
Olivier Pellier-CuitOlivier Pellier-Cuit
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1 Comment
anon
anon
This works great! How can I add a for loop at the end to return all the possible solutions for the problem?
2
I could not resist to write a little more concise brute-force solution since I never heard of the puzzle before.
from itertools import combinations, permutations a, b, c = 'SEND', 'MORE', 'MONEY' for comb in combinations(range(10), 8): for perm in permutations(comb): d = dict(zip('SENDMORY', perm)) f = lambda x: sum(d[e] 10i for i, e in enumerate(x[::-1])) if f(a) + f(b) == f(c): print "{} + {} = {}".format(f(a), f(b), f(c))
Note that I did not exclude the possibility of S -> 0 or M -> 0 here.
EDIT: Similar, but using a generator and neglecting replacements that would lead to leading zeros.
from itertools import combinations, permutations def replacements(): for comb in combinations(range(10), 8): for perm in permutations(comb): if perm perm != 0: yield dict(zip('SMENDORY', perm)) a, b, c = 'SEND', 'MORE', 'MONEY' for replacement in replacements(): f = lambda x: sum(replacement[e] 10i for i, e in enumerate(x[::-1])) if f(a) + f(b) == f(c): print('{} + {} = {}'.format(f(a), f(b), f(c)))
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edited Jul 14, 2017 at 15:59
phd
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answered May 26, 2016 at 3:31
S FS F
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Comments
0
Casting lists to sets will only change their length if they have non-unique elements. Check how sets work:
From community guidelines:
Explain how you encountered the problem you're trying to solve, and any difficulties that have prevented you from solving it yourself. The first paragraph in your question is the second thing most readers will see, so make it as engaging and informative as possible.
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edited May 23, 2017 at 11:52
CommunityBot
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answered May 26, 2016 at 2:09
cdilgacdilga
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@ siwica: your 'fast' solution provides a list of multiple results, so I propose a change in your second last line:
if (f(a) + f(b) == f(c)) & (len(a) == len(str(f(a)))) & (len(b) == len(str(f(b)))):
so, I have no rights to comment, which is why I write this 'answer'
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answered May 26, 2016 at 14:43
user1739581user1739581
8522 silver badges1414 bronze badges
1 Comment
S F
S F
It has multiple solutions since I assumed M -> 0 would be a valid replacement. The problem did not clearly exclude this option. If no leading zeros are allowed you would check for this case right at the beginning of the loop though and not at the point that you suggested. Also, I did not say my code was fast but only that it is concise. Those terms aren't always related.
0
first we can get m = 1, use permutations to avoid same number appear
from itertools import permutations perm = permutations([0,2,3,4,5,6,7,8,9], 7) for i in perm: if((i1000 + i100 + i10 + i + 1000 + 100i + 10 i + i) == (10000+1000i+i100+i10+i)): print(i1000 + i100 + i10 + i) print(1000 + 100i + 10 i + i)
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edited Sep 11, 2018 at 15:04
answered Sep 11, 2018 at 14:59
Eric JiEric Ji
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Solution with list comprehension (constraint programming):
[(send, more, money) for send in range(1023,9877) for more in range(1023,9877) for money in [send+more] if send + more > 9999 and str(send) == str(more) and str(money)[:4] == str(more)[:2] + str(send)[2:0:-1] and len("".join(set(str(money) + str(send) + str(more)))) == 8]
send and more are both 4 digit numbers
money is a 5 digit number
send and more have e as common digit
the first 4 digits in money must match the respective ones in send and more
there must be 8 different digits in total
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answered Nov 4, 2018 at 11:44
kinnlakinnla
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from itertools import permutations def solve_cryptarithmetic(): # Define the letters and possible digits letters = ('S', 'E', 'N', 'D', 'M', 'O', 'R', 'Y') digits = range(10) # Generate all possible permutations of digits for the letters for perm in permutations(digits, len(letters)): sol = dict(zip(letters, perm)) # Check for leading zeros if sol['S'] == 0 or sol['M'] == 0: continue # Calculate the values for SEND, MORE, and MONEY send = 1000 sol['S'] + 100 sol['E'] + 10 sol['N'] + sol['D'] more = 1000 sol['M'] + 100 sol['O'] + 10 sol['R'] + sol['E'] money = 10000 sol['M'] + 1000 sol['O'] + 100 sol['N'] + 10 sol['E'] + sol['Y'] # Check if the equation holds true if send + more == money: print(f" SEND: {send}") print(f" MORE: {more}") print(f" MONEY: {money}") return sol # Call the function solution = solve_cryptarithmetic()
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answered Nov 16, 2023 at 5:48
user22925243user22925243
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Picture of negative pion at the end of their range (upper, right) : Short lengths of the tracks of π– and μ– cannot be distinguished by inspection, but the effects at the end of the range are commonly decisive. Negative pion produce characteristic nuclear disintegrations at the end of their range. Very rarely μ– produce ‘two-prong’ star following nuclear capture. Positive pion, which can’t approach a nucleus due to the electrostatic repulsion and make nuclear disintegration, decay into a muon with a range of 600 μm in emulsion (4,12 MeV kinetic energy). Positive muon decays into an electron when it reaches the end of its range.Sometimes, however, no secondary tracks appear from the ends of the range of π– and μ– due to lack of well-developed electron sensitive emulsion.
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a) There is the rare possibility that the interaction was due to a K– particle or a negative hyperon. It may be possible to show that the total visible energy of the disintegration, made manifest in the tracks of the charged particles, is greater than the value corresponding to the rest-mass of the pion (>140 MeV).
b) Negative muon sometimes but very rarely, produce ‘two prong stars’ following nuclear capture. In such events, however, the energy of the two charged particles is generally very small and their ranges less than that commonly observed in the ‘two prong’ stars produced by pion (this is because in the muon captureprocess, the neutron receive a dozen of MeV, the neutrino and the nucleons the rest of the rest-mass energy of the muon. On the other hand, when a negative pion is captured by a nucleus, it interacts with two or more nucleons, and a large fraction of the energy corresponding to the rest-mass of the pion can appear in the resulting disintegration.)
The π+ particles produce at the end of their range a muon with a range of 600 microns in emulsions.
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13450 | https://math1089.in/2021/03/22/telescoping-sums-in-mathematics/ | Skip to content
Telescoping Sums in Mathematics
by Math10894 Comments
First, it is necessary to study the facts, to multiply the number of observations, and then later to search for formulas that connect them so as thus to discern the particular laws governing a certain class of phenomena. In general, it is not until after these particular laws have been established that one can expect to discover and articulate the more general laws that complete theories by bringing a multitude of apparently very diverse phenomena together under a single governing principle.
Augustin Louis Cauchy
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Telescoping sums are finite sums in which pairs of consecutive terms cancel each other, leaving only few terms (in most of the cases the initial and final terms). This is a challenging portion of algebra that requires the solver to look for patterns. These patterns will more than often cause mass cancellation, making the problem solvable easily. Often, partial fractions are used to solve the problems. Let tn be a sequence of numbers. Then
Mathematically speaking, a telescoping series is a series whose partial sums eventually only have a finite number of terms after cancellation. The cancellation technique, with part of each term cancelling with part of the next term, is known as the method of differences. Consider the following example, which is easy and good to start.
Example 1
Solution. Since it is evident that this is an example of telescoping series, we need to look for patterns. The terms in the denominators of the series are 2, 6, 12, 20, . . . and we can write them as 1 × 2, 2 × 3, 3 × 4, 4 × 5, . . . , 200 × 201. In view of these, we can rewrite the series as
As mentioned earlier, it’s time for partial fractions. The difference between the terms in the denominators is 1 and 1 is there in the numerator. Therefore, a general term looks like
In view of this result, we can easily write
Finally, it follows that
We now consider the following example, slightly different from the previous one. Analyse the terms given in the series and then proceed.
Example 2
Solution. Since it is evident that this is an example of telescoping series, we need to look for patterns. The terms in the denominators of the series are 4, 28, 70, 130, . . . and we can write them as 1 × 4, 4 × 7, 7 × 10, 10 × 13, . . . , 97 × 100. Satisfy yourself that, this is the correct pattern because 4 is there in the first and second term; 7 is there in the second and third term; and so on. In view of these, we can rewrite the series as
Now, the difference between the terms in the denominators is 3. Therefore, a general term looks like
In view of this result, we can easily write
Finally, it follows that
Example 3
Solution. Recall the formula (√a + √b) (√a – √b) = a – b. Moreover, the numbers inside the square root in each term differ by 1. Again, we need to transform the given sum into a telescoping type sum. To do this, we need to multiply both numerator and denominator by the rationalising factor. Combining all these facts, a general term looks like
In view of this result, we can easily write
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Really interesting and insightful. Though we use these often in high school math, I wasn’t aware of the term telescopic sums. Thank you.
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13451 | https://www.wikidoc.org/index.php/Supraorbital_ridge | Supraorbital ridge - wikidoc
Supraorbital ridge
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File:Austrolopithecus africanus.jpg
Supraorbital ridges seen in Australopithecus africanus
The supraorbital ridge, supraorbital torus, superciliary ridge, arcus superciliaris, or brow ridge, refer to a bony ridge located above the eye sockets of all primates. In Homo sapiens sapiens (modern man) the eyebrows are located on their lower margin.
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Contents
1 Anthropological concept
2 Purpose
3 Myths
4 In modern humans
5 See also
6 External links
Anthropological concept
The size of these ridges varies also between different species of Primate, either living or fossil. The closest living relatives of man, the Great Apes, have relatively pronounced supraorbital ridges, while in modern humans it is relatively reduced. The fossil record indicates that the supraorbital ridge in early homo was reduced as the cranial vault grew and became positioned vertically, above the face.
Some palaeanthropologists distinguish between "torus" and "ridge." In anatomy a torus is a projecting shelf of bone. Fossil hominids, in this theory, have the torus, but modern humans only have the ridge.
Gorilla face. Gorilla face.
Chimpanzee face. Chimpanzee face.
Purpose
The brow ridge is a thick piece of bone on top of the eyes. Its purpose is to reinforce the weaker bones of the face in much the same way that the chin of modern humans was developed to reinforce their comparatively thin mandibles. This was necessary in pongids and early hominids because of the tremendous strain put on the cranium by their tremendous chewing apparatuses, which is best demonstrated by any of the members of the genus Paranthropus. The brow ridge was one of the last traits to be lost in the path to modern humans, and only disappeared with the development of the modern pronounced frontal lobe. This is one of the most salient differences between Homo sapiens sapiens and Homo sapiens neanderthalensis The name for this theory is the Bio-mechanical model for brow ridge formation.
Myths
The folk-myth that the size of the ridges is a mark of the degree of development of rationality has no basis in fact. There is no link between the size of the ridges and any other anatomical trait, including intelligence, in modern humans.
In modern humans
Some varieties of modern man have slightly more pronounced ridges than others; for example, indigenous Australians, conventionally termed "aborigines." However, there is no basic genetic difference between these people and any other type of modern humans, and again, the presence of a brow ridge is not in any way indicative of intelligence or development.
File:NSRW Australian Types.png
Some faces of non-European Australians ca. 1914. The slightly more pronounced ridges can best be seen in profile.
↑For some basic English definitions refer to the American Heritage Dictionary online under supraorbital and torus. Webster's Third New International Dictionary also does not make the distinction.
See also
Supraorbital
External links
The Frontal Bone, California State University at Chico site.
Template:Dorlands.
ARCUS SUPERCILIARIS, Webster's Online Dictionary.
Retrieved from "
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13452 | https://math.stackexchange.com/questions/822215/prove-that-if-2p-1-is-prime-then-n-2p-12p-1-is-a-perfect-number | discrete mathematics - Prove that if $2^{p}-1$ is prime then $n=2^{p-1}(2^p-1)$ is a perfect number - Mathematics Stack Exchange
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Prove that if 2^{p}-1 is prime then n=2^{p-1}(2^p-1) is a perfect number
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\begingroup
Prove that if 2^{p}-1 is prime then n=2^{p-1}(2^p-1) is a perfect number here is what i did: We need to prove the \sigma(n)=n
so \sigma(n)=\sigma(2^{p-1})\sigma(2^p-1)
since 2^{p}-1 is a prime thus \sigma(2^p-1)=2^p
since 2 is prime we have \sigma(2^{p-1})=\frac{2^p-1}{2-1}=2^p-1
so we have \sigma(n)= 2^p(2^p-1)\neq n
someone please help where did i go wrong?
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edited Mar 22, 2021 at 21:20
RobPratt
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asked Jun 5, 2014 at 21:01
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2
6 \begingroup We need to prove that \sigma(n)=2n. And you have.\endgroup André Nicolas –André Nicolas 2014-06-05 21:03:37 +00:00 Commented Jun 5, 2014 at 21:03
\begingroup oh right forgot about that\endgroup H_Hassan –H_Hassan 2014-06-05 21:05:10 +00:00 Commented Jun 5, 2014 at 21:05
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\begingroup
Let p \geq 2 and that d=2^p-1 is a prime.
Then,the divisors of 2^{p-1} d are these: 1,2, \dots, 2^{p-1},d,2d, \dots , 2^{p-1} d
Therefore,
\sigma(n)=1+2+ \dots+ 2^{p-1}+d+2d+ \dots+ 2^{p-1} d=(1+2+ \dots+ 2^{p-1})(1+d) \ =(2^p-1)2^p=2n
So,we conclude that n is a perfect number.
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answered Jun 6, 2014 at 10:59
evindaevinda
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\begingroup
A perfect number is one whose sum of divisors is twice the number. For the given n, the sum of the factors is \sum_{r=0}^{p-1}\: ^nC_r \cdot 2^r \cdot (2^p - 1) = 2^p \cdot (2^p -1) = 2n. Thus, proved that n is a perfect number.
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answered Jun 6, 2014 at 10:49
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13453 | https://www.oxfordreference.com/display/10.1093/oi/authority.20110803100231994 | Treaty of Newport - Oxford Reference
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1648.
The end of the second civil war found Charles I still at Carisbrooke in the Isle of Wight. In September, Parliament resumed negotiations with the king in the town hall at Newport. Charles made substantial concessions over episcopacy and control of the militia, but admitted privately that he negotiated ‘merely in order for my escape’. When the negotiations foundered, the king was moved to Hurst castle on the mainland, before being brought to trial.
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13454 | https://byjus.com/hypochlorous-acid-formula/ | Hypochlorous acid is a weak acid formed when chlorine dissolves in water. It goes by several names such as chloranol, chloric acid and chlorine hydroxide. The chemical formula of hypochlorous acid is given by HOCl but its molecular formula is given by HClO. It is a simple molecule that consists central oxygen atom connected to hydrogen and chlorine through single bonds. In the human body, hypochlorous acid is produced by the immune cells to fight infections. In the article, let us learn more about the hypochlorous acid formula, its properties and uses.
Hypochlorous Acid Properties
| | |
--- |
| Hypochlorous Acid Properties | |
| Name | Hypochlorous Acid |
| Alias | Chloric acid, chloranol, chlorine hydroxide and hypochlorite |
| Appearance | Colourless aqueous solution |
| Molecular Formula | HClO |
| Solubility in Water | Soluble |
| Molar Mass | 52.460 g/mol |
Hypochlorous Acid Chemical Structure
Hypochlorous Acid Uses
Used as a sanitising agent.
Used as a skin cleansing agent in cosmetics.
Used in the making of disinfectants, bleaching powder and deodorant.
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数列的通项公式
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数列的通项公式
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第一次编辑文章(๑•̀ㅂ•́) ✧，
如有不周之处，请多多指教 鞠躬m( )m
ps：不动点和特征根，数学考试130以上建议食用。
数列是高考中重要考察的内容，而数列的递推关系是研究数列性质的基础。因此，求数列的通项公式是频频出现在历次高考中。对于广大同学来说，这一块的知识是必须要掌握的，高考中这一块的考题也要尽可能的拿满分。
在分享几类【数列求通项】的方法前，请允许笔者赘述数列的通项公式以及递推公式的概念。
1.通项公式：数列的第 N N项 a n a_{n}与项的序数 n n之间的关系可以用一个公式 a n=f(n)a_{n}=f\left( n\right)来表示，这个公式就叫做这个数列的通项公式
特点：
(1）有些数列的通项公式可以有不同形式，即不唯一；
(2）有些数列没有通项公式（如：素数由小到大排成一列2，3，5，7，11，...）。
2.递推公式：如果数列{ a n a_{n}}的第 n n项与它前一项或几项的关系可以用一个式子来表示，那么这个公式叫做这个数列的递推公式。
特点：
(1）有些数列的递推公式可以有不同形式，即不唯一。
(2）有些数列没有递推公式，即有递推公式不一定有通项公式。
求数列通项的方法主要有：公式法、迭代法、构造法、不动点法、特征根法等。
下面我们来介绍一下五种常用的方法：
一、公式法求数列通项
1.若 \left{ a_{n}\right}是等差数列，首项为 a_{1}，公差为 d，则其通项公式为 a_{n}=a_{1}+\left( n-1\right) d.
2.若 \left{ a_{n}\right}是等比数列，首项为 a_{1}，公比为 q，则其通项公式为 a_{n}=a_{1}q^{n-1}.
3.若数列的前 n项和为 S_{n}，则 a_{n}=\begin{cases}S_{1},n=1\ S_{n}-S_{n-1},n\geq 2\end{cases}.
特别地：当出现 a_{n+1}-a_{n-1}=d或 \dfrac{a_{n+1}}{a_{n-1}}=q( n\geq 2) 时，数列通项需要分奇数项和偶数项讨论，结果可能是分段形式。
例一：
例二
二、迭代法求数列通项
迭代思想源于等差和等比数列求通项问题，其本质是差分（商分）思想。
1.已知 a_{1}=b， a_{n+1}=a_{n}+f\left( n\right) ，求通项 a_n.
累加法： a_{n}=\left( a_{n-}a_{n-1}\right) +\left( a_{n-1}-a_{n-2}\right) +\ldots +\left( a_{2}-a_{1}\right) +a_{1}；
2.已知 a_{1}=b， a_{n+1}=f\left( n\right) a_{n}，求通项 a_n.
累乘法：a_{n}=\dfrac{a_{n}}{a_{n-1}}\cdot \dfrac{a_{n-1}}{a_{n-2}}·…·\dfrac{a_{2}}{a_{1}}·a_1(a_n\neq 0).
例一（累加法）：
例二（累乘法）：
总结：已知 a_1=a，a_{n+1}-a_n=f(n),其中 f（n）可以是关于 n的一次函数、二次函数、指数函数、分数函数，求通项 a_n。
若 f（n）是关于 n的一次函数，累加后可转化为等差数列求和。
若 f（n）是关于 n的二次函数，累加后可分组求和。
若 f（n）是关于 n的指数函数，累加后可转化为等比数列求和。
若 f（n）是关于 n的分数函数，累加后可裂项求和
三、构造法求数列通项
1.求形如 a_{n+1}=pa_{n}+q的递推公式的通项，基本思路是转化为等差数列或等比数列。
（1）若 p=1，数列为等差数列；
（2）若 q=0，数列为等比数列；
（3）若 p\ne 1，数列为线性递推数列，可采用如下两种方法求数列的通项公式：
①待定系数法：设a_{n} +x =p(a_{n-1} +x)，用待定系数法可求出 x=\dfrac{q}{1-p}，进而构造新的等比数列{ { {a_{n} -x} }}，求出通项。其中 x为方程 x=px+q的解，被称为数列的不动点。
②逐步相减法：也可由 a_{n+1}=pa_{n}+q及 a_{n}=pa_{n-1}+q，两式相减得 a_{n+1}-a_{n}=p（a_{n}-a_{n-1}），所以 \left{ a_{n+1}-a_{n}\right} 是首项 a_{2} -a_1公比为 p的等比数列，先求出 a_{n+1}-a_{n}，再求出 a_{n}。
例一：
2018湖北八校联考理17
例二
2016 浙江理 13
2形如 a_{n+1}=pa_{n}+kn+b（其中 k，b是常数，且 k\ne0 ）
方法1：逐项相减法（阶差法）
方法2：待定系数法
通过凑配可转化为 a_n+xn+y=p[a_{n-1}+x(n-1)+y]；
解题基本步骤：
（1）确定 f（n）=kn+b；
（2）设等比数列 b_n=a_n+xn+y，公比为 p；
（3）列出关系式a_n+xn+y=p[a_{n-1}+x(n-1)+y]，即 b_n=pb_{n-1};
（4）比较系数求 x，y；
（5）解得数列 \left{ a_n+xn+y\right} 的通项公式；
（6）解得数列 \left{ a_n\right} 的通项公式。
例题一
例题二
3.形如 a_{n+1}=pa_{n}+q^{n}（p\ne0,1，且q\ne0,1）的递归式，有以下两种方法：
（1）等号两边同除以 p^{n+1}，再累加求通项。
（2）等号两边同加上xp^{n+1}，再构造等比数列 \left{ a_{n}+xq^{n}\right} 。
若 p=q，则只能采用（1），而用（2）无法求解。
例一：
例二：
例三：
4.形如 a_{n+1}=pa^{q}n(p>0,a_n>0)的递归式，等号两边取对数有 \lg a{n+1}=q\lg a_{n}+\lg p，令 b_n=\lg a_{n}，则 b_{n+1}=qb_n+\lg p,仿方法2.得 b_n，再求 a_n。
例1：
例2：
四、不动点法求数列通项
不动点法求数列通项，这篇文章会写的无比详实，看官可移步前往。
上文待定系数法已经用到了不动点法，下文主要补充求分式递推数列的方法。
先补充关于不动点的概念：
一般地，数列 {x_n}的递推式可以由公式 x_{n+1}=f(x_n)给出，因此可以定义递推数列的不动点：对于递推数列 {x_n}，若其递推式为 x_{n+1}=f(x_n)，且存在实数 x_0，使得 f(x_0)=x_0，则称 x_0是数列 {x_n}的不动点。
再来看看求分式递推数列的方法：
1.已知 a_{n+1}=\frac{aa_n+b}{ca_n+d}（其中 c\ne0，ad-bc\ne0 ），求通项 a_n 。
形如a_{n+1}=\frac{aa_n+b}{ca_n+d}（其中 c\ne0，ad-bc\ne0）的递推式，求其通项可采用不动点法，方程 x=\frac{ax+b}{cx+d}的根称为上述数列的不定点。
考虑方程x=\frac{ax+b}{cx+d}\Leftrightarrow cx^2+(d-a)x-b=0，得到了一个二次方程。
①若该数列只有一个不定点 \lambda，则可令 \frac{1}{a_{n+1}-\lambda}=\frac{1}{a_n-\lambda}+A（其中 A是待定常数），代入 a_1，a_2的值可求得 A的值。这样数列 {\frac{1}{a_n-\lambda}}是首项为 \frac{1}{a_1-\lambda}，公差为 A的等差数列，于是可求得 a_n。
②若该数列有两个不定点 \lambda和 \mu，则可令 \frac{a_{n+1}-\lambda}{a_{n+1}-\mu}=A·\frac{a_n-\lambda}{a_n-\mu}（其中 A是待定常数），代入 a_1，a_2的值可求得 A的值。这样数列 {\frac{{a_n-\lambda}}{a_n-\mu}}是首项为 \frac{a_1-\lambda}{a_1-\mu}，公比为 A的等比数列，于是可求得 a_n。
例题1：
例题2：
例题3（担心有小童鞋看不清楚又补了一道）：
简记：形如a_{n+1}=\frac{aa_n+b}{ca_n+d}（其中 c\ne0，ad-bc\ne0）的递推式对应特征方程为 x=\frac{ax+b}{cx+d}，该方程的解称为上述数列的不定点。
（1）若若该数列有两个不定点 \lambda和 \mu，数列 {\frac{{a_n-\lambda}}{a_n-\mu}}是首项为 \frac{a_1-\lambda}{a_1-\mu}，公比为 A的等比数列。
(2)若该数列只有一个不定点 \lambda，数列 {\frac{1}{a_n-\lambda}}是首项为 \frac{1}{a_1-\lambda}，公差为 A的等差数列。
（3）若该数列只有没有不定点 ，则数列为周期数列。
a_{n+1}=\frac{a_{n}^{2}+P}{2\cdot a_{n}+Q}，其中 n\in\mathbb{N}^{} ， P,Q 为常数
显然这个数列的极限是方程 \lambda=\frac{\lambda^{2}+P}{2\cdot \lambda+Q}的一个根
方程 \lambda=\frac{\lambda^{2}+P}{2\cdot \lambda+Q}有两个不等的根 \alpha,\beta时
a_{n+1}-\alpha=\frac{a_{n}^{2}+P}{2\cdot a_{n}+Q}-\alpha=\frac{\left( a_{n}-\alpha \right)^{2}}{2\cdot a_{n}+Q}
a_{n+1}-\beta=\frac{a_{n}^{2}+P}{2\cdot a_{n}+Q}-\beta=\frac{\left( a_{n}-\beta \right)^{2}}{2\cdot a_{n}+Q}
显然有 \frac{a_{n+1}-\alpha}{a_{n+1}-\beta}=\frac{\left( a_{n}-\alpha \right)^{2}}{\left( a_{n}-\beta \right)^{2}}
这样易得 \frac{a_{n}-\alpha}{a_{n}-\beta}=\left( \frac{a_{1}-\alpha}{a_{1}-\beta} \right)^{2^{n-1}}
最后结果为：
a_{n}=\frac{\beta\left( a_{1}-\alpha \right)^{n-1}-\alpha\left( a_{1}-\beta \right)^{n-1}}{\left( a_{1}-\alpha \right)^{n-1}-\left( a_{1}-\beta \right)^{n-1}}
五、特征根法求数列通项
设二阶常系数线性齐次递推式为 x_{n+2}=px_{n+1}+qx_n（ n\geq1， p，q为常数， q\ne0），其特征方程为 x^{2}=px+q，其根为特征根。
1.若特征方程有两个不相等的实数根 \alpha，\beta，则其通项公式为 x_n=A\alpha^{n}+B\beta^{n}(n\geq1),其中 A, B 由初始值确定。
2.若特征方程有两个相等的实数根 \alpha，则其通项公式为 x_n=[A\alpha+B(n-1)]a^{n-1}(n\geq1),其中 A, B 由初始值确定。
证明：
设特征根为 \alpha，\beta ，则 \alpha+\beta=p，\alpha\beta=-q .
所以 x_{n+2}-\alpha x_{n+1}= px_{n+1}+qx_n-\alpha x_{n+1}=(p-\alpha)x_{n+1}+qx_n=\beta x_{n+1}-\alpha\beta x_n=\beta( x_{n+1}-\alpha x_n）.
故 \left{ x_{n+1}-\alpha x_{n}\right} 是以 \beta 为公比， x_{2}-\alpha x_{1}(\ne0) 为首项的等比数列.
从而 x_{n+1}-\alpha x_n=(x_{2}-\alpha x_{1})\beta^{n-1} .
所以 x_{n}=\alpha x_{n-1}+（x_{2}-\alpha x_{1}）\beta^{n-2} .
（1）当 \alpha\ne\beta ，其通项公式为 x_n=A\alpha^{n}+B\beta^{n} ，其中 A=\dfrac{x_{2}-\beta x_{1}}{\left( \alpha -\beta \right) \alpha } ， B=\dfrac{x_{2}-\alpha x_{1}}{\left( \alpha -\beta \right) \beta } ;
(2)当 \alpha=\beta ，其通项公式为 x_n=[A\alpha+B(n-1)]a^{n-1} ,其中 A=\dfrac{x_{1}}{\alpha } ， B=\dfrac{x_{2}-\alpha x_{1}}{\alpha } .
例题1：
例题2：
补充：一般数列的处理方法（递推数列）
（1）形如 A S _ { n } + B a _ { n } + C = 0 (Sn是数列前n项和)的递推数列通常利用公式 S _ { n } = a _ { n } - a _ { n - 1 } ( n \geq 2 ) 消和Sn或消项an, 从而化成型如前面的递推数列。
（2）求形如a_{n+1}=\frac{aa_n}{ba_n+c}，abc\ne0，一般用倒数法求通项。
取倒数 \frac{1}{a_{n+1}}=\frac{ba_n+c}{aa_n}=\frac{c}{a}·\frac{1}{a_n}+\frac{b}{a}。
（1）当 a=c时，\frac{1}{a_{n+1}}=\frac{1}{a_n}+\frac{c}{a}，则{\frac{1}{a_n}}为等差数列。
（2）当 a\ne c时，\frac{1}{a_{n+1}}=\frac{c}{a}·\frac{1}{a_n}+\frac{b}{a}，则{\frac{1}{a_n}+x}为等比数列， x=\frac{b}{c-a}。
例一：
（3）奇偶型数列处理方式：
若 a _ { n } = \left{ \begin{array} { l l } { f ( n ) , } & { n=2k-1 } \ { g ( n ) , } & { n=2k } \end{array} \right.,k\in N^ 则 a _ { n } = \frac { f ( n ) + \mathrm { g } ( n ) } { 2 } + ( - 1 ) ^ { n - 1 } \frac { f ( n ) - \mathrm { g } ( n ) } { 2 } (合二为一)
（4）其它类型的递推数列可根据不同的题采取不同的方法处理,比如归纳,猜想,再用数学归纳法证明等等。
例一：
数学归纳法详情请见
，
参考
^苏卫军《数列的秘密》
^高中数学：求数列通项公式的十一种方法（方法全，例子全，归纳细）
^【数列】浅谈“不动点”求数列通项的方法
^张杨文 兰师勇主编《新高考数学你真的掌握了吗？》
^怎么用特征根法和不动点法求数列的通项公式？ - 淳于建的回答 - 知乎
编辑于 2022-03-08 01:02
数列
数列的通项与递推公式
数列通项公式
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17 条评论
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Selvori
钻个牛角尖，素数有通项公式
2023-08-15
回复1
雾言
累乘法的例题a1是2
2023-07-20
回复1
Depaser
zyzdsb（暗号）
2021-09-24
回复1
择梦舟
作者
xymdsb（暗号）
2021-09-25
回复喜欢
sillyPig
其实素数是有通项公式的
06-12
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xmsusu
太好了，弄回去给小孩看，用得上
01-14
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雾言
特征根的公式是不是不对，B应该是负的吧？
2023-07-20
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山芋
请问一下，高中生用不动点和特征根解大题会被扣分吗
2023-01-07
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择梦舟
作者
应该是不能直接书写
2023-01-07
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欣欣子
后面的公式是高中学的吗？？？
2022-11-04
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择梦舟
作者
是的
2022-11-04
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林海
嗐，太难搞，还没有数学书上面讲的清楚
2021-09-26
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择梦舟
作者
能具体说说吗，好让我修改修改
2021-09-26
回复3
sillyPig
美其名曰
您可以去了解一下生成函数，我个人感觉特征根法是生成函数的一种特化，特征根的做法太 trick 了，生成函数就比较有普适性
06-12
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展开其他 2 条回复
lll
补充中应该是an=Sn-Sn-1
2022-05-01
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Operator Equipment – 5 Differences Between Ice Hockey and Street Hockey
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Street hockey is an incredibly inclusive sport and opens the doors to many players, including female athletes.
For some families, it’s the perfect introduction to the game—a chance to develop fundamental skills without the full commitment (and higher price tag) of joining an ice hockey program. On the other hand, many seasoned players use street hockey as an opportunity to work on their technical ability in the offseason.
To give you a better idea of what street hockey is all about, we’ve outlined the five biggest differences between street hockey and ice hockey—besides the ice, of course.
Street hockey is played with a ball, not a puck
Street hockey is played on foot with a ball (instead of a puck). But like ice hockey, it’s a fast-paced, competitive game with the same objective: to get the ball in the opposing team’s net.
Less equipment is required in street hockey
Because players are on foot, they don’t have as much equipment as ice hockey. NHL STREET leagues, for example, provide every player with a hockey stick and uniform as a part of their registration—and that’s all they need. That being said, some players choose to wear optional equipment, such as helmets, gloves, shin-pads, glasses, mouthguards, and sweatbands, but they’re not required.
Game structure and positions
NHL STREET teams play four on four, with goalies, so you won’t find a center in street hockey. Instead, most teams play with two forwards and two defenders. Additionally, street hockey leagues consist of two 15-minute halves, unlike three periods in ice hockey.
Strategy
Since street hockey rules slightly differ from ice hockey, you’ll find that game strategy changes, too. For example, in ice hockey, one way to penetrate the zone is to sacrifice possession. While NHL STREET leagues enforce offsides, there isn’t any icing. This means that one of the best street hockey strategies is to never sacrifice possession.
Skills
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13457 | https://pmc.ncbi.nlm.nih.gov/articles/PMC2993775/ | Vitamin D Effects on Pregnancy and the Placenta - PMC
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Placenta
. Author manuscript; available in PMC: 2011 Dec 1.
Published in final edited form as: Placenta. 2010 Sep 22;31(12):1027–1034. doi: 10.1016/j.placenta.2010.08.015
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Vitamin D Effects on Pregnancy and the Placenta
Joong Sik Shin
Joong Sik Shin, M.D., Ph.D.
a Department of Obstetrics and Gynecology, CHA University School of Medicine, Seoul, Korea
b Department of Obstetrics and Gynecology, Washington University School of Medicine, St. Louis, MO, USA
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a,b, Mee Yun Choi
Mee Yun Choi, M.D.
b Department of Obstetrics and Gynecology, Washington University School of Medicine, St. Louis, MO, USA
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b, Mark S Longtine
Mark S Longtine, Ph.D.
b Department of Obstetrics and Gynecology, Washington University School of Medicine, St. Louis, MO, USA
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b, D Michael Nelson
D Michael Nelson, M.D., Ph.D.
b Department of Obstetrics and Gynecology, Washington University School of Medicine, St. Louis, MO, USA
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a Department of Obstetrics and Gynecology, CHA University School of Medicine, Seoul, Korea
b Department of Obstetrics and Gynecology, Washington University School of Medicine, St. Louis, MO, USA
✉
CORRESPONDING AUTHOR: D. Michael Nelson, M.D., Ph.D., Department of Obstetrics and Gynecology, Washington University School of Medicine, 4566 Scott Ave, St. Louis, MO 63110, USA, TEL (314) 747-0738, FAX (314) 362-8580, nelsondm@wudosis.wustl.edu
Issue date 2010 Dec.
PMC Copyright notice
PMCID: PMC2993775 NIHMSID: NIHMS240523 PMID: 20863562
The publisher's version of this article is available at Placenta
Abstract
Vitamin D is a pleiotropic secosteroid hormone important for health and disease prevention. The actions of vitamin D are mediated by the vitamin D receptor that binds the active form of vitamin D [1,25(OH)2 D] to induce both transcriptional and non-genomic responses. Vitamin D has well known classical functions in calcium uptake and bone metabolism, but more recent work highlights the importance of the nonclassical actions of vitamin D in a variety of cell types. These actions include modulation of the innate and adaptive immune systems and regulation of cell proliferation. Adequate vitamin D intake is essential for maternal and fetal health during pregnancy, and epidemiological data indicate that many pregnant women have sub-optimal vitamin D levels. Notably, vitamin D deficiency correlates with preeclampsia, gestational diabetes mellitus, and bacterial vaginosis, and an increased risk for C-section delivery. Recent work emphasizes the importance of nonclassical roles of vitamin D in pregnancy and the placenta. The placenta produces and responds to vitamin D where vitamin D functions as a modulator of implantation, cytokine production and the immune response to infection. We describe vitamin D metabolism and the cellular responses to vitamin D, and then summarize the role of vitamin D in placental trophoblast, pregnancy and the fetus.
Keywords: Vitamin D, Vitamin D receptor, Placenta, Pregnancy, Trophoblast
1. Introduction
The vitamin D endocrine system is pivotal for calcium homeostasis, bone mineralization, immune function, cell proliferation, and disease prevention . Vitamin D is not a true vitamin because there are sources other than diet. Instead, this key nutrient is a pro-hormone, which can be synthesized from a steroid precursor if not obtained from diet. Vitamin D was discovered as a preventive treatment for rickets, a disease of children that yields bone softening, fractures, and deformity . The classical actions of this hormone were first described in kidney and bone. We now know that vitamin D is also involved in many nonclassical processes . Vitamin D itself is devoid of biological activity, but enzymatic conversion to 1α,25-dihydroxyvitamin D [1,25(OH)2 D] generates the hormonal form with diverse biological activities . The actions of 1,25(OH)2 D are mediated through specific, high affinity binding to the vitamin D receptor (VDR), which is present in multiple tissues [5,6]. Target organs for the nonclassical actions of the vitamin D endocrine system include the adaptive and innate immune systems, pancreatic β-cells, the heart and cardiovascular system, and the brain . Tissue responses include effects on hormone secretion, modulation of immune responses, and control of cellular proliferation and differentiation . Vitamin D analogs may prove useful to prevent some human diseases and to treat autoimmune diseases and cancer [7,8].
Recent work suggests important roles for the VDR and VDR signaling pathways in the placenta. Human placental trophoblasts express the VDR, and the P450 cytochromes encoded by the CYP27B1 and CYP24A1 genes. Trophoblasts both produce and respond to 1,25(OH)2 D. 1,25(OH)2 D regulates synthesis of hormones involved in pregnancy and influences the trophoblast anti-inflammatory and anti-microbial responses [9–13]. In early pregnancy, 1,25(OH)2 D induces decidualization, which is key to implantation [14, 15]. Moreover, CYP27B1 modulates immune function during early gestation and vitamin D deficiency associates with bacterial vaginosis, impaired calcium metabolism and fetal growth, preeclampsia, insulin resistance, gestational diabetes mellitus and primary cesarean section [17–21]. This review summarizes vitamin D metabolism and action, with a focus on the function of vitamin D during human pregnancy and on human placental villi and cultures of placental trophoblasts.
2. Biochemistry of vitamin D and the vitamin D receptor
2.1. Metabolism and transport of vitamin D
Vitamin D is a general term for a chemically related family of secosteroid hormones. Vitamin D 2 is produced in plants and vitamin D 3 is produced in mammals (Fig. 1). In humans, vitamin D 2, also called ergocholecalciferol, is one-third as potent as vitamin D 3, which is also called cholecalciferol . Vitamin D can be obtained from dietary sources but can also be synthesized. Ultraviolet B light induces cleavage of the B-ring of 7-dehydrocholesterol in skin to yield the secosteroid vitamin D 3 [1, 23] (Fig. 2). Hereafter, “vitamin D” is used to represent either vitamin D 2 or vitamin D 3.
Figure 1.
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Chemical structures of vitamins D 2 and D 3.
Figure 2. Synthesis and metabolism of vitamin D.
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Vitamin D 2 and D 3 can be obtained by diet. Vitamin D 2 is metabolized similarly to vitamin D 3, but with only one third of the biological activity (see text). Vitamin D 3 is synthesized photochemically in the skin from 7-dehydrocholesterol by ultraviolet B exposure and converted to 25OHD 3 by a 25-hydroxylase in the liver. The major circulating form of vitamin D, 25OHD 3, is hydroxylated in the kidney, placenta, and other tissues by the enzyme, 1α– hydroxylase (encoded by the CYP27B1 gene), to the bioactive form, 1,25-dihydroxyvitamin D 3 [1,25(OH)2 D 3]. The enzyme, 24-hydroxylase (encoded by the CYP24A1 gene), catabolizes both 25OHD 3 and 1,25(OH)2 D 3 to inactive metabolites 24,25(OH)2 D 3 and 1,24,25(OH)3 D 3, respectively, which are then excreted.
Vitamin D and metabolites are hydrophobic, and >99% are transported in the blood bound to vitamin D binding protein (DBP, also known as Gc-globulin) which binds with high affinity in the order 25OHD=24,25(OH)2 D>1,25(OH)2 D>vitamin D 2 or D 3. A small fraction (<1%) of these metabolites are also carried by albumin and lipoprotein [2,24]. DBP-bound vitamin D 2 and D 3 are internalized in the liver and hydroxylation by a mitochondrial P450 enzyme generates 25OHD, which is the predominant vitamin D compound in the circulation. In the renal proximal tubules of the kidney, DBP-25OHD binds to and is internalized by megalin/cubilin, a heterodimeric endocytic receptor pair [25,26]. The 25OHD is released and is hydroxylated by 25-hydroxyvitamin D 3 1α-hydroxylase, the product of the CYP27B1 gene, to yield 1,25(OH)2 D. This kidney generated 1,25(OH)2 D is key in mediating the classical functions of vitamin D in calcium homeostasis and bone mineralization [4,27,28]. The production of 1,25(OH)2 D in the kidney is stimulated by parathyroid hormone and inhibited by fibroblast growth factor 23 and by elevated calcium and phosphate concentrations . Extra-renal expression of CYP27B1 and 1,25(OH)2 D production from 25OHD occurs in immune cells, the skin, the placenta and other tissues [1,13,30] and may contribute to health in both non-pregnant and pregnant women [13,31,32].
Importantly, both 1,25(OH)2 D and 25OHD are inactivated by CYP24A1, a 24-hydroxylase mitochondrial cytochrome p450 enzyme. This hydroxylase converts both substrates into inactive end products, including 1,24,25-trihydroxyvitamin D and 24,25-dihydroxyvitamin D [27,33]. As CYP24A1 transcription is induced by 1,25(OH)2 D , 1,25(OH)2 D provides a negative feedback control on 1,25(OH)2 D levels.
The mechanisms of 25OHD and 1,25(OH)2 D import into most non-kidney tissues are poorly understood. DBP-bound vitamin D compounds have limited effect on most target cells and biological activity often correlates with the free hormone concentration [2,36,37]. This is in agreement with the “free hormone hypothesis” which postulates the active form for most target cells is unbound 1,25(OH)2 D that diffuses across the plasma membrane and binds the VDR to effect either non-genomic, transcriptional, or both, responses . However, megalin/cubilin mediates the import of DBP-bound 25OHD into mammary cells, which express CYP27B1 and can therefore produce 1,25(OH)2 D intracellularly . Megalin/cubilin-mediated endocytosis may be involved in import of DBP-25OHD into other CYP27B1-expressing target cells . One such candidate is the placenta, which expresses megalin and cubilin [40–45]. What has not been studies is whether or not vitamin D compounds enter placental cells by endocytosis of DBP-25OHD, by diffusion of free hormone, or by both mechanisms. Polymorphisms and allelic variants of the vitamin D system have been correlated with disease. Notably, polymorphisms in the VDR and DBP genes associate with several forms of cancer, multiple sclerosis and chronic obstructive pulmonary disease and polymorphisms in the VDR, CYP27B1 and cubilin genes are associated with type I diabetes [46–50]. Some of these polymorphisms yield altered levels of circulating 25OHD, while others may affect the vitamin D pathway at other levels .
2.2. Vitamin D receptor and response pathways
The biological activity of vitamin D occurs via two pathways, a slow genomic response and a rapid, non-genomic response (Fig. 3). Both involve binding of 1,25(OH)2 D with the VDR, a member of the super family of nuclear receptors for steroid hormones [51–53]. In the genomic response pathway, ligand-bound VDR then binds a partner receptor, typically the retinoid X receptor (RXR), and the heterodimer regulates the transcription of vitamin D target genes by binding with high affinity to vitamin D response elements (VDREs) in the promoter region of the gene [2,52]. The VDR contains two globular domains, a DNA-binding domain (DBD) and a ligand-binding domain (LBD) [52,53]. The DBD has two zinc-finger motifs responsible for recognition and binding to the VDREs. The LBD binds to 1,25(OH)2 D with high affinity and is involved in dimerization and transcriptional activation. Coactivators and corepressors also affect VDR molecular action [3,54,55]. The steroid receptor coactivator complex (SRC) 1–3 and vitamin D receptor interacting complex (DRIP) act as coactivators to enhance gene transcription. Corepressors, such as those encoded by the hairless gene, bind to VDR in the absence of ligand and block VDR-mediated transcription but the corepressors rapidly detach from the VDR in the presence of 1,25(OH)2 D. In the non-genomic response pathway, 1,25(OH)2 D binds to VDR associated with caveolae of the plasma membrane and the ligand-bound VDR then activates one or more signaling cascades, including protein kinase C, mitogen-activated protein kinases, phospholipase A 2, and phospholipase C [6,56].
Figure 3.
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Genomic and non-genomic responses of vitamin D receptor binding to 1,25(OH)2 D.
In the genomic response, 1,25(OH)2 D binds to the nuclear vitamin D receptor (VDR). Heterodimerization of the VDR with the retinoid X receptor (RXR) and binding to vitamin D response elements (VDREs) in the promoters of target genes affects transcription, usually by increasing transcription, and generating downstream biological responses. In the non-genomic response pathway, binding of 1,25(OH)2 D to VDR associated with caveolae of the plasma membrane activates one or more second messenger systems to elicit rapid responses. PI3K, phosphatidylinositol-3-kinase; PKC, protein kinase C
3. Nonclassical actions of vitamin D
The classical functions of vitamin D are in the kidney, liver and intestine to regulate calcium and phosphate absorption and bone synthesis and metabolism. Recent data indicate vitamin D functions in nonclassical ways as well. Over 30 human tissues express the vitamin D receptor and are thus equipped to respond to 1,25(OH)2 D . Vitamin D and the VDR play a role in immune function, cell proliferation, cellular differentiation and hormone secretion.
3.1. Regulation of immune function
Vitamin D affects the function of both the adaptive and innate immune systems. In general, 1,25(OH)2 D reduces the activity of the adaptive immune system and enhances the activity of the innate immune system [3,57,58].
In the adaptive immune system, 1,25(OH)2 D inhibits IgG production, proliferation and differentiation of B lymphocytes and inhibits proliferation of T lymphocytes [58–61]. 1,25(OH)2 D also inhibits proliferation of T helper 1 (Th1) cells and thus limits the cytokines produced by these cells. Conversely, 1,25(OH)2 D induces the cytokines of T helper 2 (Th2) and regulatory T cells (Treg) [58,62]. Th1 cells produce interferon gamma (IFN-γ), interleukin-2 (IL-2), and tumor necrosis factor-alpha (TNF-α) and Th2 cells produce IL-4, IL-5, IL-6, IL-9, IL-10, and IL-13 . Perhaps because of its ability to inhibit the adaptive immune response and inflammation, vitamin D and vitamin D agonists are effective in suppression of autoimmune disorders in several animal models. Among these disorders are rheumatoid arthritis, type I diabetes, experimental allergic encephalitis, inflammatory bowel disease, and systemic lupus erythematosus . Vitamin D analogs are currently being investigated for treatment of autoimmune diseases in humans [64,65]. Recommendations for treatment however must await clinical studies of safety as suppression of the adaptive immune system may compromise resistance to infection.
The innate immune system acts immediately when confronted with microbial infection. This process involves vitamin D and myeloid and epithelial cells that express Toll-like receptors (TLRs), CYP27B1, and the VDR [66–68]. There are ten TLRs in humans and they are activated by binding ligands of microbial origin. Antimicrobial peptides, including α- and β-defensins and cathelicidins, kill organisms in the macrophage and are secreted by epithelial cells . A typical antimicrobial secreted by epithelium is cathelicidin antimicrobial peptide (CAMP), which is also called LL-37/FALL-39 in the cleaved, active form [67,70,71]. TLR activation induces LL-37 secretion in multiple epithelial lined tissues exposed to microbial agents, from salivary glands to reproductive tissues . TLR activation also increases CYP27B1 transcription, 1,25(OH)2 D levels, and CAMP transcription [66,67,70,71]. CAMP activation and the response capability is limited if VDR is blocked, CYP24A1 is inhibited, or 25OHD is deficient. These data show that vitamin D clearly affects multiple arms of the body’s immune response.
3.2. Regulation of cell proliferation and differentiation
1,25(OH)2 D can regulate cell cycle progression, cell differentiation and induce apoptosis [8,72–76]. Over the last several decades, 1,25(OH)2 D has been shown to have anti-proliferative and pro-differentiation activity in a variety of cell types, including keratinocytes, osteoblasts, mesenchymal, neural, vascular endothelial, chondrocytes and immune cells. The proliferation effects are mediated, at least in part, by the induction of cell-cycle inhibitors that prevent the transition from the G1 to the S phase of the cell cycle, and the differentiation effects by changes in the expression of growth factors and cytokines. 1,25(OH)2 D does not always inhibit proliferation and promote differentiation: in dendritic cells 1,25(OH)2 D promotes a persistent state of immaturity . Thus, the effects of vitamin D on cell proliferation and differentiation are complex and vary between cell types.
Vitamin D and its analogs have clinical importance in the treatment of psoriasis, a skin condition characterized by keratinocyte hyperproliferation, abnormal differentiation, and immune-cell infiltration into the epidermis and dermis . Topical administration of calcipotriene, a vitamin D analog, and corticosteroids are an effective treatment . The anti-psoriatic activity of calcipotriene and other vitamin D analogs likely involves increased differentiation and decreased proliferation of keratinocytes, and reduced expression of pro-inflammatory cytokines and of several genes, including keratin 16 which is abnormally expressed in psoriatic epidermal cells [74,78]. The anti-proliferative and pro-differentiation effects of vitamin D has recently suggested a role for this hormone in cancer evolution and in the suppression of tumor growth. Vdr−/− mutant mice display hyperproliferation of cells in the kidney and mammary gland and develop cancer at elevated rates when challenged with carcinogens . Parathyroid hyperplasia is a serious secondary complication in patients with kidney failure, and recent studies indicate vitamin D or its analogs may have clinical relevance. In a uremic rat model of kidney disease, parathyroid hyperplasia is associated with an increase in expression of transforming growth factor-alpha (TGF-α) and its receptor (epidermal growth factor receptor, EGFR), are increased . Treatment with 1,25(OH)2 D diminished TGF-α expression and increased expression of p21 WAF with a concomitant reduction in parathyroid cell proliferation . In a recent clinical trial with dialysis patients, intravenous treatment with 1,25(OH)2 D reduced the progression of parathyroid enlargement .
Breast, colon, prostate and other cancers are associated with vitamin D deficiency [29,53,83]. Importantly, postmenopausal women who received four years of 1,100 IU vitamin D per day and 1500 mg calcium per day had substantially lower risks of many forms of cancer compared to control . Vitamin D and its analogs show promise in the treatment of breast, colon and prostate cancers in animal and cell culture models [8,53,85], likely because of the anti-proliferative, pro-differentiation and pro-apoptotic activities of this hormone. Because the hypercalcemic effects of vitamin D limit its therapeutic application, non-hypercalcemic analogs are more likely to have clinical value. Collectively, these studies show that vitamin D has wide ranging effects on normal and dysregulated cellular growth.
4. Vitamin D effects during pregnancy
4.1. Effects of vitamin D on the placenta and trophoblast cells
The human placenta expresses all components for vitamin D signaling, including the VDR, RXR, CYP27B1 and CYP24A1. Weisman et al. found that human decidual and placental tissues synthesize 1,25(OH)2 D and 24,25(OH)2 D. In agreement with these findings, cultured primary human syncytiotrophoblasts and decidual cells produce 1,25(OH)2 D and secrete the active form into the culture medium [86–89]. Increased levels of 1,25(OH)2 D reduces transcription of CYP27B1 in primary human cytotrophoblasts and syncytiotrophoblasts [13,34] but transcription of CYP24A1 increases . Antagonists of VDR can block the 1,25(OH)2 D induced increase in CYP24A1 levels, suggesting the effect is mediated by ligand-bound VDR . Insulin-like growth factor I (IGF-I), a key regulator of fetal growth, stimulates hydroxylation of 25OHD in a dose-dependent manner in cultured placental cells . In the 3A human trophoblast cell line, unlike in macrophages, CYP27A1 expression is not increased by TLR2 binding ligand [13,91]. 1,25(OH)2 D inhibits expression of cytokines, such as granulocyte macrophage colony stimulating factor 2 (GMCSF-2), TNF-α, IL-6, and increases expression of CAMP in primary cultured human decidual cells and cytotrophoblasts [12,13,89]. Importantly, when the 3A trophoblast cell line was exposed to E. coli, vitamin D treatment resulted in a lower rate of infection and reduced cell death, likely because of the increased CAMP levels . This finding suggests vitamin D supplementation may reduce infection during pregnancy.
4.2. Vitamin D functions during pregnancy
Important changes occur in the maternal concentration of vitamin D and in calcium metabolism during pregnancy. Calcium is transported from the mother to the fetus through the placenta. In rats, the placenta transports 25(OH)2 D and 24,25(OH)2 D but not 1,25(OH)2 D . Although transplacental transport has not been studied in humans, vitamin D passage from the mother to the fetus would be facilitated by serum concentrations of 1,25(OH)2 D being higher in the maternal compared to the fetal cirulations . Synthesis in the kidney of 1,25(OH)2 D increases during pregnancy. In addition, the decidua and placenta generate a large amount of 1,25(OH)2 D by CYP27B1 enzyme activity . Moreover, specific methylation of the placental CYP24A1 represses transcription of this gene . Production thus exceeds clearance and 1,25(OH)2 D levels increase, being two-fold higher in serum of women in the third trimester of pregnancy than in non-pregnant or post-partum women [93,95].
The synthesis, metabolism and function of vitamin D compounds during pregnancy are complex. The human endometrial decidua makes 1,25(OH)2 D and 24,25(OH)2 D and the placenta synthesizes 24,25OH 2 D . Notably, the 24,25(OH)2 D synthesized by the placenta accumulates in bone and may be involved in ossification of the fetal skeleton . Although the sheep fetus can synthesize 24,25(OH)D from 25OH and the 24 hydroxylase enzyme is expressed in the fetal kidney the sheep fetus cannot produce 1,25(OH)2 D, as renal 1 hydroxylase activity is suppressed in this relatively hypercalcemic and hyperphosphatemic environment. 24,25(OH)2 D is the major form of vitamin D in the fetal lamb and this metabolite, instead of 1,25(OH)2 D, may promote calcium absorption by the placenta and enhance skeletal ossification, without increasing fetal blood calcium concentrations or urinary excretion of calcium. If the sheep placenta produces 1,25(OH)2D, as does the human placenta, increased calcium absorption by the maternal gut may be enhanced to meet the increasing demands of the fetus for calcium through gestation.
1,25(OH)2 D and CYP27B1 play a role in the autocrine and paracrine immunomodulatory networks prominent during gestation . 1,25(OH)2 D affects decidual dendritic cells and macrophages, which in turn interact in the maternal-fetal interface to stimulate T-regulatory cells [97,98]. 1,25(OH)2 D also inhibits the release of Th1 cytokines and increases release of Th2 cytokines, as discussed in section 3.1, and Th2 cytokines thus dominate at implantation [16,63]. This modulation of the immune system may prevent rejection of the implanted embryo. 1,25(OH)2 D also aids in the transformation of endometrial cells into decidual cells [14,97] and increases expression of HOXA10 a gene important for embryo implantation and myeloid differentiation in early pregnancy [14,15,97].
Established as the chorioallantoic placenta at the end of the first trimester, villous tissues secrete multiple hormones that maintain pregnancy and regulate placental physiology. In human syncytiotrophoblasts, the VDR, CYP27B1, CYP24A1 and 1,25(OH)2 D, in an autocrine manner, combine to regulate the expression of human chorionic gonadotropin (hCG), human placental lactogen (hPL), estradiol and progesterone [9–11]. Collectively, the data suggest that 1,25(OH)2 D aids implantation and maintains normal pregnancy, supports fetal growth through delivery of calcium, controls secretion of multiple placental hormones, and limits production of proinflammatory cytokines.
4.3. Vitamin D effects on the mother and child
Vitamin D intake is essential for maternal health and prevention of adverse outcomes. Circulating 25OHD concentrations reflect vitamin D status, and the normal range is between ~32ng/mL and ~80ng/mL, with values below ~32 ng/mL defined as deficient [29,99] (Table 1). Pregnancy does not exacerbate hypocalcaemia and secondary hyperparathyroidism in people with pre-existing vitamin D deficiency . However, vitamin D deficiency during pregnancy is associated with the nonclassical actions of this hormone, being linked with preeclampsia insulin resistance, and gestational diabetes mellitus [18,32,98,101,102]. Notably, vitamin D deficiency during pregnancy is of epidemic proportions, present in ~20–85% of women, depending on country of residence and other factors [99,103].
Table 1.
Risks of vitamin D deficiency (serum 25OHD <32ng/mL) during pregancy mothers and offspring
| Mother | Fetus and newborn | Child |
:---
| Preeclampsia | Low birth weight | Bone weakening [120,121] |
| Gestational diabetes | Craniotabes | Type I diabetes |
| Cesarean section | Acute lower respiratory tract infection | Schizophrenia |
| Bacterial vaginosis | Hypocalcemic seizure Reduced femur growth in utero Infant heart failure | Asthma [122,123] |
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Preeclampsia, as identified by new onset hypertension and proteinuria during pregnancy, is a serious disorder affecting 5–8% of pregnancies, and is alleviated only by delivery of the placenta. Preeclampsia rates are elevated during winter months, when sunlight-dependent 25OHD production is reduced , and vitamin D deficiency increases the risk of preeclampsia [18, 102]. Vitamin D supplementation reduces preeclampsia risk, compared to unsupplemented controls . Preeclampsia is associated with low circulating levels of IGF-I and 1,25(OH)2 D and, in vitro, IGF-1 increases 1,25(OH)2 D production by primary human syncytiotrophoblasts from placentas from normal pregnancies but not from preeclamptic pregnancies . Furthermore, trophoblasts isolated from the placentas of preeclamptic women have only one-tenth the CYP27B1 enzyme activity of trophoblasts from uncomplicated pregnancies . Although the role of vitamin D in preeclampsia is unclear [32,102,106], one hypothesis is that low vitamin D levels impair the normal Th1 to Th2 cytokine balance, with higher Th1 cytokine expression adversely affecting the immunological tolerance of embryo implantation .
Insulin resistance, glucose intolerance, and diabetes are correlated with deficits in vitamin D. 1,25(OH)2 D regulates insulin secretion by pancreatic β-cells and thereby affects circulating glucose levels [32,108,109]. As expected, low concentration of 25OHD is a risk factor for glucose intolerance while higher serum concentrations of 25OHD correlate with improved insulin sensitivity . Vitamin D deficiency during early pregnancy significantly increases the risk for gestational diabetes in later pregnancy .
Vitamin D may influence the course of infectious diseases during pregnancy. In limited studies, low vitamin D levels in HIV-positive pregnant women were correlated with increased mortality and mother-to-child HIV transmission [110,111] and a polymorphism in the VDR gene is correlated with the frequency of HIV-to-AIDS progression . Low 25OHD levels are correlated with increased bacterial vaginosis in the first trimester and bacterial vaginosis is more prevalent in black women. Indeed, black women typically have lower serum 25OHD concentrations and have a six-fold higher chance of vitamin D deficiency, compared with white women [17,103]. Vitamin D effects on the immune system, cytokines, and antibacterial peptides likely regulate the bacterial flora.
Serum 25OHD levels are inversely related to primary cesarean section in nulliparous women, an unexpected and unexplained maternal outcome recently identified . The risk was four-fold higher in women with serum 25OHD level below 37.5 nM/L (15ng/mL) controlling for multiple confounding factors. VDR and 1,25(OH)2 D normally increase skeletal muscle function. Conversely, vitamin D deficiency results in proximal muscle weakness and decreased lower extremity muscle function , perhaps contributing to the risk for cesarean section .
Adequate maternal vitamin D levels are also important for fetal and child health (Table 1). Inadequate vitamin D intake during pregnancy is associated with low infant birth weight in populations at risk for adverse outcomes . Maternal vitamin D deficiency also has been associated with craniotabes , a softening of skull bones that is one of the earliest signs of vitamin D deficiency, in a case study with neonatal seizures of a hypocalcemic infant and with impaired skeletal development in utero . Recent retrospective studies found a significant and previously undetected association of maternal vitamin D deficiency with rickets-associated infant heart failure and with acute lower respiratory tract infection , a serious complication often associated with sepsis without clinical signs of rickets. Interestingly, vitamin D deficiency during pregnancy is also associated with risks of health problems later in childhood, including improper bone development at 9 yrs of age [120,121], asthma [122,123], schizophrenia , and type I diabetes .
5. Conclusions
We have described the multiple effects of vitamin D in human health. The classical and nonclassical pathways of this hormone affect calcium metabolism, the immune system, cell proliferation and differentiation, infection, and cancer. The enzymes encoded by the CYP27B1 and CYP24A1 genes are local regulators of levels of 1,25(OH)2 D, which binds the VDR to induce both the genomic and non-genomic responses. Importantly, vitamin D analogs offer new potentials for treatments of a variety of diseases and disorders. What is clear is that adequate vitamin D intake in pregnancy is optimal for maternal, fetal and child health. However, vitamin D deficiency is prevalent and this potentially has negative consequences for both mother and child. Clearly, further investigation into the effects of vitamin D, of vitamin D supplementation, and of vitamin D analogs will contribute to an improvement in human health generally and mothers and children specifically.
Acknowledgments
This work was supported by National Institutes of Health grant RO1-HD29190 to D.M.N. CHA University provided financial support for J.S. We thank Baosheng Chen for helpful discussions.
Abbreviations
1,25(OH)2 D
1α,25-dihydroxyvitamin D
25OHD
25-hydroxyvitamin D
CYP24A1
24-hydroxylase
CYP27B1
1α-hydroxylase
CAMP
cathelicidin antimicrobial peptide
DBD
DNA-binding domain
EGFR
epidermal growth factor receptor
hCG
human chorionic gonadotropin
hPL
human placental lactogen
IFN-γ
interferon-gamma
IGF
insulin-like growth factor
IL
interleukin
LBD
ligand-binding domain
RXR
retinoid X receptor
Th1
T helper 1
Th2
T helper 2
TLR
toll-like receptor
TGF-α
tumor growth factor-alpha
TNF-α
tumor necrosis factor-alpha
Treg
regulatory T cell
DBP
vitamin D binding protein (Gc-globulin)
VDR
vitamin D receptor
VDRE
vitamin D response element
Footnotes
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Arithmetic Progression: Definitions and Examples
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Home / Educational Resources / Math Resources / Arithmetic Progression: Definitions and Examples
An arithmetic progression is a sequence of numbers in which each term is obtained by adding a fixed number, called the common difference, to the preceding term. The common difference is usually represented by the letter “d” and the first term in the sequence is usually represented by “a1”.
The nth term of an arithmetic progression is given by the formula: an = a1 + (n – 1)d
For example, consider the following arithmetic progression: 3, 7, 11, 15, 19, …
In this arithmetic progression, the common difference is 4, since each term is obtained by adding 4 to the preceding term. The first term is 3. Using the formula above, we can find the 10th term: a10 = 3 + (10 – 1)4 = 3 + 36 = 39
Arithmetic progressions are useful in solving problems in which a series of quantities is increasing or decreasing by a fixed amount.
Here are 5 examples of arithmetic progressions:
Example 1: Consider the following arithmetic progression: 2, 4, 6, 8, 10, … In this arithmetic progression, the common difference is 2 and the first term is 2. Using the formula above, we can find the 8th term: a8 = 2 + (8 – 1)2 = 2 + 14 = 16
Example 2: Consider the following arithmetic progression: -3, 1, 5, 9, 13, … In this arithmetic progression, the common difference is 4 and the first term is -3. Using the formula above, we can find the 6th term: a6 = -3 + (6 – 1)4 = -3 + 20 = 17
Example 3: Consider the following arithmetic progression: 10, 6, 2, -2, -6, … In this arithmetic progression, the common difference is -4 and the first term is 10. Using the formula above, we can find the 4th term: a4 = 10 + (4 – 1)(-4) = 10 – 12 = -2
Example 4: Consider the following arithmetic progression: 1, -1, -3, -5, -7, … In this arithmetic progression, the common difference is -2 and the first term is 1. Using the formula above, we can find the 6th term: a6 = 1 + (6 – 1)(-2) = 1 – 10 = -9
Example 5: Consider the following arithmetic progression: 8, 12, 16, 20, 24, … In this arithmetic progression, the common difference is 4 and the first term is 8. Using the formula above, we can find the 3rd term: a3 = 8 + (3 – 1)4 = 8 + 8 = 16
Quiz:
What is an arithmetic progression?
What is the common difference in an arithmetic progression?
What is the formula for finding the nth term in an arithmetic progression?
How do you find the 10th term in the arithmetic progression 3, 7, 11, 15, 19, …?
What is the common difference in the arithmetic progression 10, 6, 2, -2, -6, …?
What is the 3rd term in the arithmetic progression 1, -1, -3, -5, -7, …?
How do you find the 8th term in the arithmetic progression 2, 4, 6, 8, 10, …?
What is the common difference in the arithmetic progression 8, 12, 16, 20, 24,…?
Arithmetic Progression:
Alternate name
arithmetic sequence
Definition
An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0 + k d}_(k = 0)^(n - 1) such that the differences between successive terms is a constant d. An arithmetic progression can be generated in the Wolfram Language using the command Range[a_1, a_n, d].
Related terms
arithmetic series | Baudet's conjecture | Dirichlet's theorem | Erdős-Turán conjecture | geometric sequence | nonarithmetic progression sequence | prime arithmetic progression | sequence | Szemerédi's theorem
Related Wolfram Language symbol
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13459 | https://words2025.loria.fr/files/2025/07/webpage-Kabore_Final-2-7-2025.pdf | On the abelian complexity of infinite words Idrissae KABORE Universit´ e Nazi BONI, Bobo Dioulasso (Burkina Faso) WORDS 2025-Nancy, July, 2, 2025 WORDS 2025-Nancy-Juillet 2025 Outline Introduction Definitions, notations Classical complexity Abelian complexity Abelian complexity of Thue-Morse words, Tribonacci Abelian comlexity and uniform recurrence Link between abelian complexity and uniform frequency of letters Abelian comlexity and equi-frequency of letters in binary words Two questions Definitions, notations Ad = {a1, a2, · · · , ad}, d-ary alphabet.
A∗ d: set of finite words on Ad Aω d : set of infinite words on Ad Let u be a finite word on Ad χ(u) = (|u|a1, |u|a2, · · · , |u|ad) is the Parikh vector of u.
Definitions, notations Let u ∈Aω Fn(u): set of factors of u of length n.
F(u): set of all factors of u.
u is aperiodic if u is not ultimately periodic.
u is recurrent if any factor of u appears infinitely often.
u is uniformly recurrent if for all n ∈N, there exists N such that any factor of u of length N contains any factor of u of length n.
Definitions, notations A morphism is a map f : A∗→A∗such that f (uv) = f (u)f (v), for all u, v ∈A∗.
If, for a letter a ∈A, f (a) = au with u ̸= ε, the morphism has a unique fixed point beginning with a, which is the infinite word limn→∞f n(a).
Classical complexity Definition Given an infinite word u, the factor complexity of u is the map defined by ρu(n) = #Fn(u) for all n ∈N.
Classical complexity Definition Given an infinite word u, the factor complexity of u is the map defined by ρu(n) = #Fn(u) for all n ∈N.
It counts the number of distinct factors of u of given length.
Morse and Hedlund used factor complexity function to characterize aperiodic infinite words and define Sturmian words as follows: Theorem (Morse Hedlund, 1938) Let u be an infinite word. The following statements are equivalent: 1 u is aperiodic.
2 There exists n such that ρu(n) ≤n.
3 (ρu(n))n is bounded.
Classical complexity Sturmians Definition An infinite word u is called Sturmian if its complexity satisfies ρu(n) = n + 1 for all n ∈N.
Sturmian words constitute the class of non-ultimately periodic infinite words whose complexity is minimal.
Inspired by the notion of factor complexity, other notions of complexity have been developed. One such notion is the Abelian complexity of infinite words, the topic of this talk.
Abelian complexity Two words u and v in A∗are said to be abelian equivalent, and we note u ∼ab v, if |u|a = |v|a for all a ∈A, ∼ab define an equivalence relation on A∗.
Definition The abelian complexity of an infinite word u is the function defined by ρab u (n) = #Fn(u)/ ∼ab= # {χ (v) : v ∈Fn (u)} .
Abelian complexity Let u be an infinite word, n be an integer and a be a letter.
Define, ma(n) = min {|w|a : w ∈Fn(u)} and Ma(n) = max {|w|a : w ∈Fn(u)}.
Lemma (Intermidiate Vectors Lemma) Let u be an infinite word and n be an integer. Then, for any letter a, we have ∀m ∈[ma(n), Ma(n)] , ∃v ∈Fn (u) , |v|a = m.
Abelian complexity Lemma (first difference of ma and Ma) Let u be an infinite word. Then, for any letter a and every n ∈N, we have: ma(n + 1) −ma(n) ∈{0, 1} Ma(n + 1) −Ma(n) ∈{0, 1} .
Abelian complexity Lemma (Max-min formula of ρab u ) Let u be an infinite binary word. Then, for all n ∈N: ma(n) + Mb(n) = Ma(n) + mb(n) = n; ρab u (n) = Ma(n) −ma(n) + 1 = Mb(n) −mb(n) + 1.
Proof.
For any w ∈Fn(u), χ(w) is in the set {(ma(n), n −ma(n)) ; (ma(n) + 1, n −ma(n) −1) ; · · · ; · · · ; (Ma(n), n −Ma(n))} .
By Intermidiate Vectors Lemma, all these vectors are attained.
Therefore, Mb(n) = n −ma(n) and mb(n) = n −Ma(n). The results follow.
Abelian complexity Lemma (first difference of ρab u ) Let u be an infinite binary word. Then ∀n ∈N : ρab u (n + 1) −ρab u (n) ∈{−1, 0, +1} .
Proof.
We have ρab u (n) = Ma(n) −ma(n) + 1. Since, by Lemma of first difference of ma and Ma, ma(n + 1) −ma(n) ∈{0, 1} and Ma(n + 1) −Ma(n) ∈{0, 1} , it follows that ρab u (n+1)−ρab u (n) = (Ma(n + 1) −Ma(n))−(ma(n + 1) −ma(n)) ∈{−1, 0, +1} .
Abelian complexity It is known that Theorem (Richomme, Saari, Zamboni, 2009) For all infinite word u over Ad, and for all n ≥0, 1 ≤ρab u (n) ≤ n + d −1 d −1 In particular, the abelian complexity is bounded by O(nd).
Abelian complexity: periodic words and Sturmian words Like the classical complexity, the abelian complexity intervenes in characterization of some classes of infinite words: infinite periodic words and Sturmian words.
Theorem (Coven, Hedlund, 1973) An infinite word u is periodic if and only if ρab u (n) = 1 for some n ≥1.
Abelian complexity: periodic words and Sturmian words Like the classical complexity, the abelian complexity intervenes in characterization of some classes of infinite words: infinite periodic words and Sturmian words.
Theorem (Coven, Hedlund, 1973) An infinite word u is periodic if and only if ρab u (n) = 1 for some n ≥1.
Theorem (Coven, Hedlund, 1973) An infinite word u is Sturmian if and only if, ρab u (n) = 2, for all n ≥1.
Inspired by this characterization of Sturmian words, Rauzy asked whatether there exist aperiodic words on a ternary alphabet such that ρab u (n) = 3 for all n ≥1.
Due to Richomme et al. the two folowing results provide positive answers: Abelian complexity: Sturmian words and following Theorem (Richomme, Saari, Zamboni, 2009) For all aperiodic balanced word u on a ternary alphabet, ρab u (n) = 3, for all n ≥1.
Theorem (Richomme, Saari, Zamboni, 2009) Let u be an aperiodic binary word on {a, b}. then ρab σ(u)(n) = 3, for all n ≥1 where σ denotes the substitution defined by σ(a) = abc and σ(b) = acb.
So, Richomme et al. posed the question: ”Does there exist a recurrent word over a 4-ary alphabet with exactly 4 Abelian factors of each length?” Currie and Rampersad provide a negative answer: Theorem (Currie, Rampersad, 2011) Let d ≥4 be an integer. There is no recurrent word over an d-ary alphabet with exactly d Abelian factors of each length ≥1.
Abelian complexity: binary Thue-Morse word The binary Thue-Morse word t2 is the fixed point from a of the Thue-Morse substition µ2 : a 7→ab, b 7→ba.
Theorem (Cassaigne, Richomme, Saari, Zamboni, 2011) The abelian complexity of t2 is given by: ρab t2 (n) = 3 if n is even, n ≥2 2 if n is odd .
Abelian complexity: Thue-Morse words The binary Thue-Morse word t3 is the fixed point from a of the substition µ3 : a 7→abc, b 7→bca, c 7→cab.
Theorem (Kabor´ e, Kient´ ega, 2017) The abelian complexity of t3 is given by: ρab t3 (n) = 1 if n = 0 3 if n = 1 7 if n = 3k, k ≥1 6 otherwise Chen and Wen (2019) determine completely the abelian complexity of generalized Thue-Morse word td (d ≥2) and find that the sequence ρab td (n) n is ultimately periodic with period d.
Abelian complexity: Tribonacci word The Tribonacci word T is the fixed point from a of the substitution τ : a 7→ab, b 7→ac, c 7→a.
Theorem (Richomme, Saari, Zamboni (2009), Turek (2013), Shallit (2021)) ∀n ≥1, ρab t3 (n) ∈{3, 4, 5, 6, 7} where eah element appears infinitely many times.
And more generally, Shallit get the following result: Abelian complexity and automaticity Theorem (Shallit, 2021) Let u be a sequence that is automatic in some regular numeration system. Suppose that (a) the Parikh vectors of length-n prefixes of u form a synchronized sequence; and (b) the abelian complexity ρab u is bounded above by a constant.
Then ρab u (n) n≥0 is an automatic sequence and the DFAO computing it is effectively computable.
Furthermore, if condition (a) holds, then condition (b) can be tested algorithmically.
Abelian complexity: general results Joint work with Julien Cassaigne (2016).
Abelian complexity and uniform recurrence Theorem Let u be a uniformly recurrent binary word. Then, there exists a positive real number α < 1 and a non-negative integer n0 such that: ∀n ≥n0, ρab u (n) ≤αn.
Abelian complexity and uniform recurrence Proof.
Let u be a uniformly recurrent word on {0, 1}.
u is constant. Then, ρab u (n) = 1 and the result holds, u is not constant. Then ∃N ∈N, ∀w ∈FN(u), 0, 1 ∈F(w) So, 1 ≤|w|1 ≤| ≤N −1and thus ρab u (N) ≤N −1.
Let n ∈N such that n N ≥3 and take w ∈Fn(u). We can write: w = w1w2 · · · wkw′ where k = n N , |wi| = N and |w′| < N. So, k ≤|w|1 ≤n −k That is letter 1 appears in w at least k times and at most n −k times.
Therefore ρab u (n) ≤n −2k + 1 ≤n −2 · n N + 3 ≤n −n N = n(1 −1 N ) .
To obtain the result it suffices to put α = 1 −1 N and n0 = 3N .
Abelian complexity and uniform recurrence Theorem (Control formula of uniform recurrence by ρab u ) Let u be a uniformly recurrent d-ary word. Then, there exist a positive real number α < 1 and a non-negative integer n0 such that: ∀n ≥n0, ρab u (n) ≤αnd−1 (d −1)!.
Link between abelian complexity and uniform frequency of letters Definition We say that u admits frequencies of letters if for any letter a, and any sequence (wn) of prefixes of u such that limn→∞|wn| = ∞, then limn→∞ |wn|a |wn| exists.
uniform frequencies of letters if for any letter a, and any sequence (wn) of factors of u such that limn→∞|wn| = ∞, then limn→∞ |wn|a |wn| exists.
Link between abelian complexity and uniform frequency of letters Lemma Let u be an infinite word, (wi) be a sequence of factors of u and f be a real number in (0, 1) such that limi→∞|wi| = ∞and limi→∞ |wi|a |wi| = f . Then ∀δ > 0, ∃n0 ∈N, ∀n ≥n0, ∃v ∈Fn (u) , |v|a |v| −f ≤δ.
Lemma Let u be an infinite word with a letter a that does not admit frequency. Then, ma(n) n and Ma(n) n converge and further lim ma(n) n < lim Ma(n) n .
Link between abelian complexity and uniform frequency of letters Theorem Let u be an infinite binary word. Then ρab u (n) = o(n) if and only if u admits uniform frequencies of letters.
The above theorem provides a characterization of binary words with uniform frequencies of letters. On a larger alphabet, we have a weaker result.
Link between abelian complexity and uniform frequency of letters Proof.
Let u be an infinite binary word which does not admit uniform frequencies of letters and suppose by contradiction that ρab u (n) = o(n). Then ∀δ > 0, ∃n0 ∈N, ∀n ≥n0, ρab u (n) ≤δn.
For every integer n ≥n0, we have Ma(n) −ma(n) + 1 = ρab u (n) ≤δn.
Let v be a factor of length N sufficiently large. It follows ma(n) N n ≤|v|a ≤Ma(n) N n + 1 hence Link between abelian complexity and uniform frequency of letters Proof.
ma(n) 1 n −1 N ≤|v|a N ≤Ma (n) 1 n + 1 N .
Since u does not admit uniform frequencies of letters, there exists two distinct reals f1 and f2 and two sequences of factors (vk) and (v′ k) satisfying |vk| = |v′ k| = k and limk→∞ |vk|a k = f1; limk→∞ |v′ k|a k = f2.
It follows ma(n) n ≤fi ≤Ma(n) n , i = 1, 2. So, |f1 −f2| ≤Ma(n)−ma(n) n ≤δ. As δ is arbitrarily small, f1 = f2.
Contradiction!
Conversely, if u admits uniform frequencies of letters, then both ma(n) n and Ma(n) n converge to the same limit fa. It follows that ρab u ( n)n = Ma(n)−ma(n)+1 n = o(1).
Link between abelian complexity and uniform frequency of letters Theorem Let u be an infinite d-ary word. We have the following statements: 1 If ρab u (n) = o(n) then u admits uniform frequencies of letters.
2 If u admits uniform frequencies of letters then ρab u (n) = o nd−1 .
Abelian complexity and equi-frequency of letters in infinite binary words It is well known that the Thue-Morse word possesses uniform frequencies of letters and its abelian complexity satisfies ρab t2 (2n) = 3 and ρab t2 (2n + 1) = 2 for all n ≥1.
Theorem Let u be an infinite binary word such that for all n ≥1, ρab u (n) = 3 if n is even 2 if n is odd Then, u admits uniform frequencies of letters and the letters have the same frequencies i.e., f0(u) = f1(u) = 1 2.
Abelian complexity and equi-frequency of letters in infinite binary words Proof.
Suppose ∀n ≥1, ρab u (n) = 3 if n is even 2 if n is odd By induction, we check that ∀n ≥1, ∀w ∈F2n(u), |w|0 ∈{n −1, n, n + 1} .
Through the examples below we observe that the converse of the a bove Theorem does not hold.
• The image of any infinite binary aperiodic word u by substitution Φ : 0 7→0101, 1 7→1100 satisfies: ρab Φ(u) (n) ≥3 and f0(Φ(u)) = f1(Φ(u)) = 1 2.
• The word u = (000111)ω satisfies: ρab u (3) = 4 and f0 (u) = f1 (u) = 1 2.
Abelian complexity and equi-frequency of letters in infinite binary words Theorem Let u be an infinite binary word satisfying: 1 ρab u (n) = o(n), 2 ∃n0, ∀n ≥n0, ρab u (n + 1) ̸= ρab u (n) Then, u admits uniform frequencies of letters and the frequencies are: f0(u) = f1(u) = 1 2.
Two questions The Theorem on the equi-frequency of letters for any binary word having the same abelian complexity as the binary Thue-Morse word can be extended to the d-ary alphabet (d ≥3)?
As in the last Theorem, any d-ary word having the same abelian complexity of the d-ary Thue-Morse word td does admit equi-frequency of letters: fa(u) = 1 d ?
Thank you for your attention! |
13460 | https://apcentral.collegeboard.org/media/pdf/cm-hum-geo-urban-geography.pdf | AP ® Human Geography Urban Geography Curriculum Module Professional Development The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the College Board is composed of more than 5,700 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,800 colleges through major programs and services in college readiness, college admission, guidance, assessment, financial aid and enrollment. Among its widely recognized programs are the SAT®, the PSAT/NMSQT®, the Advanced Placement Program® (AP®), SpringBoard® and ACCUPLACER®. The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities and concerns. For further information, visit www.collegeboard.com.
Page 25: James M. Rubenstein, The Cultural Landscape: An Introduction to Human Geography, Eighth Edition. Copyright © 2005. Printed and electronically reproduced by permission of Pearson Education Inc., Upper Saddle River, New Jersey.
© 2010 The College Board. College Board, ACCUPLACER, Advanced Placement Program, AP, AP Central, Pre-AP, SAT, SpringBoard and the acorn logo are registered trademarks of the College Board. inspiring minds is a trademark owned by the College Board. PSAT/ NMSQT is a registered trademark of the College Board and National Merit Scholarship Coporation. All other products and services may be trademarks of their respective owners. Contents Introduction.
.........................................................................................1 Christopher Hall Lesson 1: Urban Models..................................................................................3 Christopher Hall Lesson 2: Case Study of Pittsburgh.
............................................................9 Carol Ann Gillespie Lesson 3: Ghettoization and Gentrification.
...........................................15 Carol Ann Gillespie Lesson 4: Megacities in Less-Developed Countries.............................19 Christopher Hall Appendixes.......................................................................................................23 About the Contributors.
................................................................................. 41 1 Introduction Christopher Hall.
Davis School District.
Davis County, Utah The Industrial Revolution ushered in a new age of great urbanization in the world’s history. The urban population is growing at a much faster rate than that of the rural population. Nearly half of the world’s people now live in cities, and this proportion is higher in the developed regions of the world. Seventy-five percent of Americans now live in urban areas, and more than two-thirds of the people of Europe, Russia, Japan, and Australia do as well. Cities, it would seem, are our future. Although many students live in or near cities, and believe they know a great deal about them, the AP® Human Geography course and curriculum will present them with information that will challenge their current understanding of cities. Questions such as how to define and categorize cities, how to dissect and understand their functional regions, and the impact of changing population and land use matrixes in cities will likely be new to most students. This curriculum module presents AP Human Geography teachers with resources and ideas for addressing the final content area of the AP course outline — Cities and Urban Land Use. Four lessons are presented here, but it might be helpful for teachers to think of what follows more as “activities” that have been organized according to the curriculum framework of the AP Human Geography course. These lessons do not cover the entirety of the curricular requirements of the urbanization portion of the AP Human Geography course outline. It is not necessary to teach these lessons in any particular order, nor is it necessary to present them in their entirety. It is not even necessary to teach these lessons at the same point in your academic year. Some teachers may choose to introduce cities and the models that describe them (Lesson 1) very early in the year, and they may use the rest of the lessons at a much later date. Other teachers may feel that introducing the idea of a specific location as a case study is important at a point earlier in their year than when they will be discussing cities; they may choose to use Lesson 2, which presents urban changes in Pittsburgh as a case study, separate from the rest of the lessons. 3 Lesson 1: Urban Models Christopher Hall.
Davis School District.
Davis County, Utah Plan the Lesson Connections to the Course Outline The content of this lesson addresses the following areas of the AP Human Geography course outline: • I.B. The evolution of key geographical concepts and models associated with notable geographers is addressed through the examination of the three classic North American models and their evolution and reinterpretation into the new ideas informing our view.
• VII. A.4 Suburbanization and edge cities are explored by students as they investigate changes and current developments in urban forms.
• VII. C Models of internal city structure are studied as students will analyze three classic models of urban structure for North American cities and then compare and contrast them with a model of a Latin American city and the recent interpretations of North American cities.
• VII. D.4 Urban planning and design is explored by students as they investigate changes and current developments in urban forms.
Objectives This lesson helps students come to an understanding of the basic elements of urban models outside of North America and more recent interpretations of urban structure. The students may also gain an increased understanding of urban structure models describing North American cities by comparing them to a model describing a Latin American city. The students will understand how the classic North American models are being reinterpreted as new forces act upon and change cities today. 4 A Curriculum Module for AP Human Geography Background Information The internal organization of cities may be taught by comparing different models that attempt to describe cities. The major textbooks all discuss three classic models describing North American cities: concentric zone, sector, and multiple nuclei. Understanding these models provides a foundation from which students examine more recent interpretations of cities. This lesson asks the students to compare the North American models to a model of the typical Latin American city and to more recent interpretations of urban forms in North America.
Through a classroom discussion, check for understanding of student reading of the text regarding the classic North American models. The following notes could be written on the whiteboard as the students make contributions, and/or students can amend their own notes as the discussion progresses.
All Three Models • Developed during the first half of the twentieth century, a period of rapid urbanization in North America • Based on studies in Chicago (Burgess and Hoyt) • Focus of the models is different types of land use Concentric Zone Model • Developed by E. W. Burgess.
• Argues that urban land use is best represented by a series of concentric circles.
• Recognizes five distinct zones: — The central business district/nonresidential — Zone in transition/poorest quality housing/immigrants/apartments — Zone of workingmen’s homes/second-generation immigrant settlement — Zone of “better residences”/middle class — Commuters’ zone/high-class residential • The concentric pattern arises as land uses compete and are sorted according to ability to pay for land. As one moves toward the central city, land becomes scarcer but accessibility improves, the rent therefore increases, and land uses that cannot exact sufficient rent are sorted out. Similar activities are likely to be found at similar distances from the central business district (CBD). 5 Urban Geography Sector Model • Developed by H. Hoyt.
• This model assumes the land use is conditioned by transportation routes radiating outward from a city center.
• Industrial, retailing, and residential districts extend out from the CBD like wedges.
• Hoyt saw the best housing extending north from Chicago along Lake Michigan.
Multiple Nuclei Model • Developed by C. D. Harris and E. L. Ullman.
• This model assumes that urban areas have more than one focal point influencing land use.
• Land-use patterns are formed around several discrete nuclei that attract certain uses and repel others. These nuclei most often develop in response to the evolving transportation network. They form, for example, around major highway intersections and surrounding airports.
• These multiple nuclei may have arisen in one of two ways: — They were once separate settlements but were absorbed by growth of the urban area.
— They appeared as urban growth stimulated specialization and specialized centers outside the CBD, around which complementary uses then located.
• Residential land use develops in response to the influence of the various nuclei.
Tell the students that they will make comparisons between these three models and two others. The first is a parallel model of a typical Latin American city. The second is a look at newer interpretations of the North American city.
Teach the Lesson 1. Students read a description of the model of a typical Latin American city and complete a table in which they list similarities and differences between the classic models of North American cities and that of a typical Latin American city (see Appendixes A to C). Many textbooks contain selections describing the Latin American model. The source of this model was published as “A Model of Latin American City Structure” (Ford and Griffin 1980). Basic information regarding the model is also readily available from online sources.
6 A Curriculum Module for AP Human Geography 2. Ask the students to think about the three basic geometric forms used to describe urban structure in the models: concentric circles, sectors, and polygons. They should use these forms as they compare the models and describe their similarities and differences.
3. Review the charts together as a class. Be sure the students understand the following main points: Similarities and differences between the Latin American model and the concentric zone model • Concentric zones of housing of different quality exist, radiating from the city center.
• The housing in the zones, however, is reversed from that which exists in North America. The highest-quality homes are in the innermost rings and the poorest quality are in the outermost.
• The market is centrally located, as opposed to North American cities where retailing is becoming increasingly suburbanized. Similarities and differences between the Latin American model and the sector model • In both models spines of land use radiate from the city center. • The “Grand Boulevard” of elite shops is in the Latin American model only.
• North American–style suburbanization may occur associated with the spine of development.
• An industrial spine may develop along a transportation route such as a railroad or highway in both models. Similarities and differences between the Latin American model and the multiple nuclei model • Both may contain government housing projects.
• Both may contain industrial parks.
• Disamenity zones exist in association with less-desirable land only in the Latin American model.
4. By conducting brief research on a list of suggested topics, the students will examine important changes and developments in land uses and land use patterns in North American cities. You can introduce the research activity by informing the students of two of the most important changes: a. Inner cities that were once reserved for business and a ring of the poorest-quality housing are being “revived.” A resource that may be of help is the scoring guideline for Question 3 from the 2005 AP Human Geography Exam. See
collegeboard.com/apc/public/repository/_ap05_sg_human geogra_46637.pdf.
7 Urban Geography b. Suburbs have begun to take on the roles more typically associated with the central business districts. The students will research elements that contribute to the two trends described above. Some possible topics for student research include: • Edge cities • Decentralized cities • Gentrification • High-tech corridors • Master-planned communities • New urbanism • Office parks • Postindustrial cities • Suburbanization of business • Technoburbs • The “galactic city”/peripheral model • Urban realms The students should be instructed to find and report on three things in regard to their topics: a definition of the term, specific examples, and a description of how this represents a change in land use from earlier models. Differentiate the lesson by allowing the students to present their information in a variety of ways. PowerPoint presentations, poster-board discussions, skits, Web pages, or illustrated handouts could all be used effectively according to the students’ desires and abilities.
5. The students can practice the information covered in the lesson, and the teacher can check for understanding, by using a free-response question similar to those used on the AP Exam. Appendix B contains a suggested question and rubric. Having the students work in groups allows the teacher to circulate around the room and use the scoring rubric and student conversations and responses to determine which areas of the lesson need clarification and reteaching.
Reflect on the Lesson The students should come away from the lesson with a clear understanding of several important points regarding the urban models that geographers use. These include: 8 A Curriculum Module for AP Human Geography • Human geographers have developed tools for describing cities. • These models focus on different types of urban land use and their locations relative to the central business district. • There are different models, but they contain many of the same or similar elements. • Urban land use has changed since the models were developed and continues to change today. • The models may need to be adjusted in order to reflect current land use in urban areas. Resources Brockerhoff, Martin. “ An Urbanizing World.” Population Bulletin 55, No. 3 (Sept. 2000): 3–44.
Ford, Larry. “Cities and Urban Land Use in Advanced Placement Human Geography.” Journal of Geography 99 (May–August 2000): 153–168.
Ford, Larry, and Ernest Griffin. “ A Model of Latin American City Structure.” Geographical Review 70, No. 4 (Oct. 1980): 397–442.
Goodall, Brian, ed. The Penguin Dictionary of Human Geography. Bungay, Suffolk, Great Britain: Richard Clay (The Chaucer Press) Ltd., 1987.
Jordan-Bychkov, Terry, Mona Domosh, Roderick P. Neuman, and Patricia L. Price. The Human Mosaic: A Thematic Introduction to Cultural Geography. New York: W. H. Freeman and Company, 2006.
Rubenstein, James M. The Cultural Landscape: An Introduction to Human Geography. Upper Saddle River, N.J.: Pearson Prentice Hall, 2005. 9 Lesson 2: Case Study of Pittsburgh Carol Ann Gillespie.
Pennsylvania Homeschoolers.
Kittaning, Pennsylvania Plan the Lesson Connection to the Course Outline The content of this lesson addresses the following areas of the AP Human Geography course outline: • VII. D Built environment and social space is explored as students look carefully at urban land use and consider problems and possible solutions. Transportation and urban infrastructure, public spaces and their use by different types of people, housing, and other relevant issues — as determined by students — could all be examined.
Objectives In this lesson, the students will research an actual urban problem on several scales by collecting and analyzing spatial data using maps and other graphic media. They will practice decision-making skills as they work through community planning to solve urban problems presented by vacant lots.
Background Information This lesson examines some of the ways modern cities cope with the increasing pressures of crowding, pollution, and wasted space. These processes are examined through a case study of Pittsburgh, Pennsylvania — a postindustrial city that is successfully turning urban challenges and problems into productive opportunities. The lesson examines how Pittsburgh faced the challenges of reclaiming unproductive vacant lots as part of the city’s strategy to fight urban decay. After the steel mills began to close, Pittsburgh underwent an urban renaissance that created one of the leading “green” urban areas in the country. Through the combination of work by the community, the city government, nongovernmental organizations (NGOs), and industries, vacant lots were reclaimed and turned into productive gardens that generated revenue, fed residents, and beautified neighborhoods.
10 A Curriculum Module for AP Human Geography Teach the Lesson You should have a video clip or slide of an urban area on the screen as the students come into class. In lieu of using this technology, hold up or pass around large photos from magazines that depict a central urban issue. The video clip or slide should show an obvious problem occurring in the city. Have the students identify the problem, and begin a discussion of why the problem exists. (Example: a slide showing urban crowding and congestion. The reason it is happening: Migration from rural areas is occurring faster than the city has the resources or the time to cope.) The students may have the following common misconceptions about urban crowding and congestion: • Urbanization is inherently bad.
• Most urban growth is occurring in megacities. • Rural–urban migration should be controlled.
• The poor are a drain on the economy.
• City growth inevitably hurts the environment.
Begin a brainstorming session by asking the students to list some of the major problems currently facing world cities, starting with the local urban area and expanding to the region, the country, and the world. This demonstrates the application of human geography at various scales.
Learning Activity #1 The teacher assigns the students to research the actual case study performed by graduate students at the Carnegie Mellon Heinz School of Public Policy and Management in 2006. This case study, “Greening Vacant Lots for Pittsburgh’s Sustainable Neighborhood Revitalization, ” can be found at Students can either access this study online in a school computer lab, or the teacher can reproduce the referenced pages for the students. Differentiate the instruction by allowing students who are especially computer literate to use the computer in this activity and proceed at their own pace. Students who require more guidance can be provided with hard copies of the maps while you provide additional support through the use of an overhead or digital projector.
1. Ask the students to interpret the map of Pittsburgh neighborhoods on page 2 of the “Policy Recommendations” by doing the following three activities in class together; provide immediate instructional feedback to the students’ responses: a. Locate and identify the three rivers on the map.
b. Locate and identify the Hill District, one of Pittsburgh’s most economically distressed neighborhoods. (Middle Hill and Upper Hill are two of the neighborhoods included in this district.) 11 Urban Geography c. Ask the students what relationship between the map key and the toponyms clues them in on the location of the Hill District. (Orange vacant lot densities are high in this area. Also, topographic maps of the Pittsburgh urban area can be used to cross-reference topography for additional clues.) d. Ask the students to identify and list other urban neighborhoods that have high densities of vacant lots. Have them list some of the other urban problems that are also likely to be found in these neighborhoods.
e. Ask the students to locate and list the neighborhoods with a low density of vacant lots. Who lives there? (Squirrel Hill North and South — 76 and 77 — are affluent suburbs adjacent to Carnegie Mellon University, the University of Pittsburgh– Oakland campus, and several private colleges and prestigious research hospitals.) Help the students come to the conclusion that the density of urban lots is directly related to the economic level of the neighborhood’s inhabitants. Ask the students what a possible connection could be between these neighborhoods and the major neighborhoods just named.
2. Ask the students to examine the choropleth map on page 5 and answer the following questions: a. Using the map key, ask the students what conclusions they can draw about the density of vacant lots in relation to the fair market values in the three Pittsburgh neighborhoods shown. (Fair market values are markedly lower in areas that have the highest density of vacant lots. The areas with the greatest amount of “blue” are embedded in areas with housing in the “less than $50,000” market value range.) b. Ask the students to refer to the map of Pittsburgh neighborhoods on page 2 and label the map on page 5, “The Negative Effects of Vacant Lots in Urban Neighborhoods,” with the number and name of the following three neighborhoods: East Liberty, Point Breeze, and Homewood. Ask the students what some of the problems might be for residents who live in these neighborhoods, which are afflicted with high densities of vacant lots (e.g., higher crime rates, more drug-related activity, trash dumping areas, lower real estate values, etc.).
3. Ask the students to examine the map on page 7 showing Pittsburgh’s neighborhood greenways and parks and respond to the following: a. Using the map on page 7, name the Pittsburgh neighborhoods in which the four largest parks are located. (Perry North, Marshall, Highland Park, and Squirrel Hill South.) b. Develop a neighborhood profile for the areas surrounding the four parks. What kinds of people live in the neighborhoods surrounding the parks? Hint: Refer to the map on page 2 to determine the vacant lot density. (The neighborhoods with the four largest parks are affluent areas with historically Caucasian populations.) 12 A Curriculum Module for AP Human Geography 4. Divide the students into four groups, based on your knowledge of the individual students’ strengths and abilities. Assign each of the four student groups to one of the four vacant lot reclamation projects in Pittsburgh listed below: a. South Side Slopes Neighborhood Association (www.southsideslopes.org) b. Nine Mile Run Watershed Association (www.ninemilerun.org) c. Rosedale Block Cluster (www.rosedaleblock.org) d. The Brassica Project (Sponsor: Steel City Biofuels, www.omnibydesign.com/steelcity/home.html) Have each group develop a summary report of the project. The report should describe the best practices and strategies for managing vacant lots that the sponsor group (one of the four listed above) is following. Each report should include a map of the project area, what neighborhood is involved, who is involved in the project, what “green” strategies are being implemented, and the results of the project so far. Each group should present their project to the class.
Based on the students’ reports to the class, the teacher should assess student learning at this point in the lesson. If the teacher observes that some students do not grasp a concept, she or he can design a review activity or use a different instructional strategy. Learning Activity #2 Have the students research and investigate an urban problem in the nearest large urban area. This topic should be chosen by each student to reflect his or her area of interest. As a formative assessment, have the students complete the two tables in Appendix C. Provide feedback for each student as they are completing the two tables in Appendix C to ensure they understand the concepts. For example, for Table 2, using the Pittsburgh plight of underutilized vacant lots, neighborhoods could create urban gardens with the motivation and benefit of neighborhood safety and unity. Homeowners could buy adjacent vacant lots with the incentive to have larger yards and a safer neighborhood. Entrepreneurs could grow cash crops on vacant lots for an economic incentive, and the city government could expedite the regulations releasing these vacant lots for neighborhood garden plots with the incentive of decreasing crime and property devaluation. NGOs could use grant money to “seed” these neighborhood garden projects and provide volunteers to lend leadership and labor with the incentive or motivation that they are furthering their cause of “greening” the city. You could use the Pittsburgh example to explain how each party can make a meaningful contribution by working together and solving a urban problem if you feel the students need further clarification of this activity before undertaking it, or if you want to generate a discussion on how the different parties can work together to contribute to a positive outcome.
13 Urban Geography Learning Activity #3 Using Activity #2 as a model, have the students research and complete Appendix C on a global scale by examining an urban problem in a world city. The topic each student selects should be based on a region and topic of the student’s particular interest. (For example, the street monkeys in New Delhi, India, are an urban problem. A contributing factor could be the Hindu religion and their reverence for a monkey god, thus bringing in cultural factors. A possible creative solution could be devising monkey “lures” to attract the monkeys into certain areas of the city where they can be distracted by food or play and, therefore, they will not steal from vendors or harass people.) This activity should also serve as a formative assessment to check for understanding of the concepts on different scales. Provide immediate written or oral feedback for each student as they complete Appendix C.
Reflect on the Lesson Consider with students how they would respond to the following questions, having completed the lesson: • What are some of the pressures on the built environment of a city as more of the world’s population moves to urban centers?
• How are modern cities coping with these pressures?
• What are some of the ways Pittsburgh has solved these problems, and how can these solutions be used by other urban centers of the world?
This lesson may be modified in the following ways: • Limited resources: If the teacher does not have computers for all students to access the Web site, the case study can be printed and enough copies made for all the students. If the teacher is unable to show a video clip due to necessary classroom technology, magazine photos or posters of scenes depicting urban problems can be displayed or passed around the classroom.
• Limited time: If the teacher’s time for this lesson is restricted, Activity #1 or Activity #2 could be used as stand-alone instruction on this topic. Activity #3 could also be used as an individual instruction with slight modification to include additional research time on other countries. This extra time could consist of a class period in the school library or in the school computer lab.
• Block scheduling: This lesson lends itself well to block scheduling. The activities provide the teacher with many opportunities for spending time with the students on an individual basis. Videos on urban topics can be shown for part of each extended period. The group summary reports give the teacher an opportunity to diversify the instructional period with a good small-group activity. 14 A Curriculum Module for AP Human Geography Resources “Greening Vacant Lots for Pittsburgh’s Sustainable Neighborhood Revitalization.” Carnegie Mellon Heinz School of Public Policy and Management’s graduate students in 2006.
15 Lesson 3: Ghettoization and Gentrification Carol Ann Gillespie.
Pennsylvania Homeschoolers.
Kittaning, Pennsylvania Plan the Lesson Connections to the Course Outline The content of this lesson addresses the following areas of the AP Human Geography course outline: • VII.C.5; 6 Changing demographic and social structures: Uneven development, ghettoization, and gentrification are addressed when students discuss and define relevant terms related to these concepts. • VII.D.1; 4; 5 Housing, urban planning, and design: Patterns of race, ethnicity, gender, and socioeconomic status are investigated through a discussion of the merits and problems of changes in the neighborhoods in inner-city zones. Objectives The students will be able to use various resources to investigate the causes and outcomes of ghettoization and gentrification. Working in pairs, the students will develop skills in researching, working collaboratively, and defending viewpoints as they analyze the pros and cons of both gentrification and ghettoization of an urban neighborhood. Background Information Some additional materials will be required for the lesson: • Excerpt from Unafraid of the Dark by Rosemary Bray • Video trailer from Flag Wars 16 A Curriculum Module for AP Human Geography Teach the Lesson The teacher will read a passage aloud from Rosemary Bray’s autobiography, Unafraid of the Dark. This is the author’s account of her childhood growing up in a Chicago ghetto in the 1960s. An excerpt for reading aloud or for copying and distributing to the students can be found at www.readinggroupguides.com/guides_U/unafraid_of_the_dark3.asp#excerpt.
Discuss the origins of the term “ghetto” and discuss how ghettos result from involuntary segregation of a group of people based on their race or ethnicity, among other factors. Ask the students to define “gentrification” (the revitalization and renovation that takes place in an older urban neighborhood as a result of new residents’ efforts). Show the class the video trailer from Flag Wars (available at www.pbs.org/pov/pov2003/flagwars/update.html).
Discuss how gentrification sets in motion forces that disperse the lower-income residents of the gentrified neighborhood. Ask the students how both ghettoization and gentrification often lead to a similar outcome.
Learning Activity #1 Group the students into pairs. One student in each pair will defend gentrification as a positive contribution to the urban community (reduced crime, new investment in buildings and infrastructure, and increased economic activity). The second student will take the opposing side and discuss the negative effects of gentrification (large increases in rents and home prices, increases in the number of evictions, crowding out of lower-income residents, racial unrest, etc.). After 10 minutes of discussion in pairs, list the pros and cons of gentrification on the board by letting each pair of students contribute their arguments to the lists. The students may have the following misconceptions regarding gentrification: • Racial diversity always leads to social conflict.
• Neighborhoods cannot retain ethnic and racial diversity while gentrifying.
• Gentrification is always disruptive to a neighborhood. In fact, research has shown that several U.S. cities have been able to provide public policies enabling peaceful and successful gentrification in their urban neighborhoods while maintaining ethnic and racial diversity (Nyden et al. 1997). Provide ongoing verbal feedback to the students as they give their arguments. To differentiate this activity, arrange the students in groups of four and allow each student to choose whether to defend or protest gentrification in a mock neighborhood setting. 17 Urban Geography To differentiate the instruction, you can also ask each student to demonstrate the concepts of ghettoization and gentrification in one of the following ways: • Create a graphic organizer using either the word “ghetto” or the word “gentrification” as the central concept. • Design a project that could solve a major neighborhood problem in either a ghettoized or gentrified neighborhood (e.g., safety of residents or trash accumulation).
• Write a newspaper article. • Create and label diagrams of a gentrified neighborhood and a ghettoized neighborhood to compare them spatially.
• Build models of a gentrified or ghettoized neighborhood.
If this approach is chosen, rubrics that explain the requirements of the assignment and how the activity will be evaluated should be created. The students will present and explain their projects to the class. Provide the students with immediate verbal feedback on their projects. Reflect on the Lesson Use the following questions to promote discussion and check for understanding: • What is the difference between ghettoization and gentrification?
• How are the outcomes of ghettoization and gentrification similar? • What are the conflicts associated with both practices?
This lesson may be modified in the following ways if there are time or resource constraints: 1. Limited time: The teacher can use Activity #1 as a stand-alone lesson in teaching the concepts of ghettoization and gentrification. 2. Block scheduling: The teacher can expand the background information to include a longer portion of Bray’s autobiography or include additional literature excerpts that reference life in a ghetto. An expanded discussion can be used to engage students in exploration of life in the ghetto. In addition, an age-appropriate video that depicts life in a ghetto may be shown. 18 A Curriculum Module for AP Human Geography Resources Beauregard, Robert A. “Federal Policy and Postwar Urban Decline: A Case of Government Complicity?” www.mi.vt.edu/data/files/hpd%2012(1)/hpd%2012(1)_beauregard.pdf.
Birch, Eugenie. “Housing and Urban Communities” In Planning for a New Century: The Regional Agenda, edited by Jonathan Barnett. Washington, D.C.: Island Press, 2000.
Bray, Rosemary. Unafraid of the Dark.
Flag Wars. www.pbs.org/pov/pov2003/flagwars/update.html. This website gives useful information about the film Flag Wars and provides additional resources and links on housing, zoning, and gentrification issues. Nyden, Philip, John Lukehart, and Mike Maly. ”The Emergence of Stable Racially and Ethnically Diverse Urban Communities: A Case Study of Nine U.S. Cities.” Housing Policy Debate 8, No. 2 (1997): 491–534.
“ A Tale of Three Cities” interactive map case studies of gentrification of Columbus, Ohio; San Francisco, California; and New York, New York. Click on these three maps to access interviews with residents, pictures of landmarks, U.S. Census data, and historical information about each neighborhood. Ten years of change (1990–2000) are represented in each map in addition to a brief history of the neighborhood.
U.S. Department of Housing and Urban Development. This is the official site of the U.S. Department of Housing and Urban Development and includes a wide range of information on housing issues.
19 Lesson 4: Megacities in Less-Developed Countries Christopher Hall.
Davis School District.
Davis County, Utah Plan the Lesson Connections to the Course Outline The content of this lesson addresses the following areas of the AP Human Geography course outline: • VII. A.2 Rural-urban migration and urban growth are presented as one of the main causes of megacities and their growth in LDCs.
• VII. A.3 Global cities and megacities are studied as students work with maps and graphs to identify and analyze the largest cities in the world.
• VII. D.1: 5 Housing: Patterns of race, ethnicity, gender, and socioeconomic status are explored as students investigate and learn about squatter settlements, their inhabitants and characteristics.
Objectives In this lesson the students will examine various aspects of the world’s megacities. At the conclusion of the lesson, they should be able to define megacities, describe their historic and current distributions, and understand some of the problems associated with them in LDCs.
Background Information Discuss the following information with students: According to the United Nations, 60 percent of the world’s population will be living in urban areas by 2030. Although the more developed countries (MDCs) are more urbanized than the LDCs, urbanization is increasing at a higher rate in the LDCs. One of the results 20 A Curriculum Module for AP Human Geography of urbanization has been the creation of megacities, defined as urban agglomerations of more than 10 million inhabitants. Two aspects of these megacities become important. First, the distribution of the urban centers has been changing. In the past, most of the world’s largest cities were in MDCs, but currently (and increasingly) a greater number is found in the LDCs. Second, the impact of the spectacular growth in the cities of LDCs has had an enormous impact on both the environment and the quality of life of the millions of new immigrants who live in settlements on the edges of these centers.
Teach the Lesson Learning Activity #1 Assess the students’ prior knowledge about urbanization around the world by asking the following questions and discussing answers: • What is a city?
• What does it mean to be “urbanized”?
• Which regions of the world are the most “urbanized” and which are the least “urbanized”?
• Is urbanization increasing or decreasing worldwide? Or it is increasing in some regions and decreasing in others?
The students may respond by characterizing urban areas and cities as places with tall buildings, crowded places, places with more inhabitants than towns, or places with lots of businesses. Provide a more formal definition of a city for them, such as a large settlement, whose population is engaged in secondary and tertiary economic activities, and which has a greater diversity of retail and service functions than smaller settlements (Goodall 1987). See Appendix G for an instructional activity with a formative assessment designed to help the students clarify their definitions of a city.
Learning Activity #2 Have the students use colored pencils to construct a graph showing world urbanization trends. This graph can be found in Appendix D. Use the line graphs they create to discuss the following questions: • Which region showed the largest, most consistent increase in urbanization during the period?
• Which region had the largest percentage change in urban population during the period?
• Which region is likely to experience the fastest growth in urbanization in the next decade? Why do you think so?
21 Urban Geography • Which region is likely to experience the slowest growth in urbanization in the next decade? Why do you think so?
Learning Activity #3 Show the students the information in Appendix E: Ten Largest Cities Over Time. You can make an overhead transparency or project the image from a computer. Ask the students to make generalizations about what they see. Prompt them to consider questions such as the following: • Which cities appear multiple times?
• Which cities appear only in later lists? Which cities drop out?
• What regions of the world are the most/the least represented in the lists?
Help the students understand that the largest cities in the world are increasingly found in the less-developed countries. Learning Activity #4 Have the students create maps of the distribution of the world’s megacities by using Appendix F. The students will likely need access to a world map in order to locate some of the cities. This activity could be used as a homework assignment or could be completed by small groups of students working together to find the listed cities. You may wish to extend this activity by having the students focus more specifically on the number of cities in MDCs versus LDCs. Do this by helping the students do the following: • Draw a line separating the MDCs from the LDCs. Most textbooks contain maps that show this division. This is often in a chapter or section on development. Otherwise, an example can be found online at www.geographyalltheway.com/ ib_geography/ib_development/patterns_in_development.htm. • Count the number of megacities located on each side of the line.
Learning Activity #5 It is important for students to understand the impact of rapid urbanization on the lives of the inhabitants of the world’s megacities. Given that most of these cities are now located in LDCs and that most AP Human Geography students live in MDCs, they may not have much of an understanding of this. It is appropriate to introduce the concept of “squatter settlements” at this point. Allow the students to define this term from their textbook. Alternatively, use the information found at www.gdrc.org/uem/define-squatter.html. Be sure that the students understand that there are a variety of terms, used regionally, that refer to these areas; these terms include the following: • Favelas = Brazil 22 A Curriculum Module for AP Human Geography • Barong-Barong = Philippines • Gecekondu = Turkey • Bastee = India Have the students consider the following statement: Many residents in LDCs lead rural-like lifestyles even though they live in massive urban areas. Ask the students to explain what these rural-like lifestyles might include. They should suggest things such as the following: • Lack of access to electricity, plumbing, and public transportation • The practice of subsistence agriculture and “barnyard” animals living in close proximity to humans • Long distances to schools and services Emphasize that growth is generally not controlled by municipal governments and is often not welcomed. Reflect on the Lesson Political cartoons dealing with the presence of megacities in LDCs and/or the squatter settlements associated with them are not difficult to find from online, international newspaper sources. Use one of these to finalize your discussion of megacities in LDCs. The students can be asked to answer basic questions about the cartoon. One idea for an analysis worksheet is available from the National Archives website at www.archives.gov/education/lessons/worksheets/cartoon_analysis_worksheet.pdf.
Resources www.archives.gov/education/lessons/worksheets/cartoon_analysis_worksheet.pdf Brockerhoff, Martin. “ An Urbanizing World.” Population Bulletin 55, No. 3 (Sept. 2000): 10.
“Cities: Challenges for Humanity.” In Human Geography: Landscapes of Human Activities, Jerome Fellman, Arthur Getis, and Judith Getis. New York: McGraw-Hill, 2007. Retrieved from http:www.nationalgeographic.com.
www.geographyalltheway.com/ib_geography/ib_development/patterns_in_development.htm. Goodall, Brian. The Penguin Dictionary of Human Geography. Bungay, Suffolk, Great Britain: Richard Clay (The Chaucer Press) Ltd., 1987.
23 Appendix A Model Comparison Table Comparison to Latin American City Model Concentric zone model Sector model Multiple nuclei model Similarities Differences 25 Appendix B Latin American Model 1. Shown here is the urban land use model of a typical Latin American city. a. Identify and describe TWO ways in which the model is similar to models of North American cities.
b. Identify and describe ONE feature that differentiates land use in a typical Latin American city from one of the North American models.
Source: The Cultural Landscape, 8th edition by James M. Rubenstein (Pearson Prentice Hall, 2005) 26 A Curriculum Module for AP Human Geography Suggested Rubric A. Two ways the model is similar to North American models: Identification Description Concentric rings The concentric zone model and the Latin American model include rings of different land use that surround the central city.
Sectors Both the sector model and the Latin American model have areas of land use that radiate outward from the city. The highest quality of housing, in both cases, extends in an elite sector from the central city.
Separate nucleus Both the multiple nuclei model and the Latin American model propose nuclei of land use separate from the central city. The Latin American model indicates a mall and an industrial park.
2 Points 2 Points B. One feature that differentiates the model from the North American models: Identification Description Location of lowest quality of housing Whereas the highest-quality housing areas are indicated in the outermost ring of North American cities, in the Latin American city the lowest quality of housing is found in squatter settlement there.
The lowest-quality housing is expected to be found in the inner city (concentric zone model) or near transportation routes (in the sector model), but in the Latin American model this type of housing is found in a ring around the periphery.
Presence of disamenity zones None of the North American models show the existence of disamenity zones. Although there are sectors of poor housing in those models, they are associated with nearness to the central city in the concentric zone model, or to a transport route or an industrial area in the sector model and the multiple nuclei model. In neither North American case is a physical feature such as steep or unstable terrain a consideration.
1 Point 1 Point TOTAL POSSIBLE: 6 points 27 Appendix C Urban Problem Table 1. Name a major problem in your city. Complete the two tables below. Be ready to share in class.
Name of City and State Major Urban Problem Factors Contributing to Problem My Creative Solutions 2. List the possible tasks each group below could assume to alleviate the problem listed above. Be realistic. City government budgets are financially strapped already.
Responsible Party Solution Incentive or Motivation City government Entrepreneurs Homeowners Nonprofit organizations Neighborhood 29 Appendix D Urban Percentages Worksheet Transfer the data presented in the chart into the blank graph to create a line graph. Use a different color for each region and, in the lower chart, shade the name of the region with the color to create a key.
Percent Urban Source: Population Reference Bureau 1950 2007 2030 Africa 15 37 51 Asia 17 41 54 Europe 51 72 76 Latin America – Caribbean 42 76 84 North America 64 79 87 100 Africa Asia Europe Latin America – Caribbean North America 90 80 70 60 50 40 30 20 10 0 1950 2007 2030 Source: 31 Appendix E Ten Largest Cities Over Time Top ten largest urban agglomerations in 1950, 2000, and 2015 1950 2000 2015 1. New York, USA .
12.3 million 1. Tokyo, Japan .
26.4 million 1. Tokyo, Japan .
26.4 million 2. London, England .
8.7 million 2. Mexico City, Mexico .
18.4 million 2. Bombay, India .
26.1 million 3. Tokyo, Japan .
6.9 million 3. Bombay, India .
18.0 million 3. Lagos, Nigeria .
23.2 million 4. Paris, France .
5.4 million 4. Sao Paulo, Brazil .
17.8 million 4. Dhaka, Bangladesh .
21.1 million 5. Moscow, Russia .
5.4 million 5. New York, USA .
16.6 million 5. Sao Paulo, Brazil.
20.4 million 6. Shanghai, China .
5.3 million 6. Lagos, Nigeria.
13.4 million 6. Karachi, Pakistan .
19.2 million 7. Essen, Germany .
5.3 million 7. Los Angeles, USA .
13.1 million 7. Mexico City, Mexico .
19.2 million 8. Buenos Aires, Argentina.
5.0 million 8. Calcutta, India .
12.9 million 8. New York, USA.
17.4 million 9. Chicago, USA .
4.9 million 9. Shanghai, China .
12.9 million 9. Jakarta, Indonesia .
17.3 million 10. Calcutta, India .
4.4 million 10. Buenos Aires, Argentina.
12.6 million 10. Calcutta, India .
17.3 million Source: Population Reference Bureau 33 Appendix F The World’s Megacities Using a colored dot, locate each of the following cities to create a map of the 20 largest cities in the world. Megacities, 2005 34 A Curriculum Module for AP Human Geography Rank City Population in millions 1 Tokyo, Japan 35,197 2 Mexico City, Mexico 19,411 3 New York–Newark, USA 18,718 4 Sao Paulo, Brazil 18,333 5 Mumbai (Bombay), India 18,196 6 Delhi, India 15,048 7 Shanghai, China 14,503 8 Kolkata (Calcutta), India 14,277 9 Jakarta, Indonesia 13,215 10 Buenos Aires, Argentina 12,550 11 Dhaka, Bangladesh 12,430 12 Los Angeles–Long Beach–Santa Ana, USA 12.298 13 Karachi, Pakistan 11,608 14 Rio de Janeiro, Brazil 11,469 15 Osaka–Kobe, Japan 11,268 16 Al-Qahirah (Cairo), Egypt 11,128 17 Lagos, Nigeria 10,886 18 Beijing, China 10,717 19 Manila, Philippines 10,686 20 Moskva (Moscow), Russia 10,654 Source: Population Reference Bureau 35 Appendix G Formative Assessment: Defining a City Part 1: Background Defining a city is a more complicated task than it might at first seem. The term “city” is used to mean different things to different people. Perhaps the greatest problem with the term is that when the average person refers to a city, he or she generally uses the term without providing any qualification. Do they mean the legally defined city, or are they referencing an entire metropolitan area? Is the term used to refer to a way of life, as it is when employed as an adjective (“city life”) or to a landscape description meant to evoke tall buildings?
The students will have diverse preconceptions of what a city is and is not. Two possible definitions are: (1) an agglomerated settlement whose inhabitants are primarily engaged in nonagricultural activities; and (2) a population cluster having a continuous built-up area with a population of at least 5,000 people. Students in an AP Human Geography class should be exposed to simple definitions such as these, but they also should have an understanding of the complexity of the term. There are at least two basic ways to define a city. The first is structurally or administratively. Definitions of this type will consider things such as the total number of people or the population density. In both cases, a minimum threshold is usually offered. However, these standards are applied in different ways in different states. In some countries, settlements with as few as 100 inhabitants are classified as urban. Most North American students would find this standard far too low, and because of this it is almost impossible to make international comparisons of cities without first adopting a single definition to be applied to all, regardless of their defined legal status in the country where they are found. Additionally, the standards themselves are changeable and often do change. For example, in the 1980s the Chinese government reclassified hundreds of places that would be considered rural in the United States as urban. In the history of the United States, the minimum size of a “city” has changed several times.
Legally defined boundaries of municipal areas are also part of this type of definition. Only the area located within these boundaries forms part of the legal city. A city may also be considered to include the continuously built-up areas surrounding the legal city. “Urban” areas, which may extend far beyond the city, may also include the suburban fringes and even engulf neighboring towns. Another way to define cities is functionally or behaviorally. The most important functional definition of a city for the AP Human Geography student is the metropolitan 36 A Curriculum Module for AP Human Geography statistical area (MSA). Defined in this way, the entire county in which a major city lies is classified as part of the “city,” and it may include a number of adjacent counties if a number of people from those counties commute to the major city. Another functional consideration for defining cities is the type of activities that take place there. Urban areas distinguish themselves from rural areas because it is in settlements, in cities both large and small, that populations find that most of their goods and services are provided. In this sense, a city is a commercial center, a place for businesses, shops, and manufacturing. These distinctly urban activities are nonagricultural and their presence distinguishes the places where they are found as cities.
Cities were famously defined by Louis Wirth as a “way of life.” This is a behavioral definition of a city. Wirth considered that cities differentiated themselves from rural areas by their heterogeneous populations and the distinctive social interactions between them. For example, he described interpersonal contacts in cities as more superficial and anonymous than in rural settings. He further characterized urbanites as having “segmental roles” and being “dependent upon more people for the satisfactions of their life-needs than…rural people” (Wirth 1938).
In summary, cities do not defy definition, but an AP Human Geography student must be aware of the many possibilities and difficulties that exist in defining them. Teachers should present students with multiple ways of defining cities, but they should also realize that we must be able to talk about cities rather generically. The activity that follows asks students to focus on the most basic definition of a city and asks them to think critically about what complications and extensions may be part of this definition. Part 2: For the Students 1. Compare the following definitions of a city: • Definition 1: an agglomerated settlement whose inhabitants are primarily engaged in nonagricultural activities • Definition 2: a population cluster having a continuous built-up area with a population of at least 5,000 people What elements do these definitions share? What elements are present in one definition but not in the other?
2. Define or describe a “metropolitan statistical area.” 37 Urban Geography Part 3: Interpretive Framework Compare the Definitions There is not a single word that is used in both definitions. Some students may be looking for this. Remind them that the assignment asks for them to find “elements” of the definitions that are shared. In this case, they should think about “parts” of a city, or “characteristics” of an urban area that are used by both definitions.
Some of the elements that students may identify include: (a) people and size, (b) contiguousness, and (c) goods and services. A. People and Size The first definition talks about “inhabitants” and the second refers twice to the “population.” The first definition uses the term “agglomerated,” which implies a certain number of people, and the second definition specifically identifies a minimum size of 5,000 people. Review with students the idea of a city as defined “legally”: a government may decide that unless a settlement has a population of a certain number, it will not be considered a city. Because there are many different governments (as a general rule there is one for every country in the world, although some countries have more than one and others do not arguably have one at all), there are many different ideas about the minimum size of a city. The size of a city changes over time as well. In the United States this number has changed from 8,000 (in 1874) to 4,000 (in 1880), and then lowered to 2,500 in 1906. Additionally, a legal definition requires that a line be drawn around an area — a legal boundary of the city. If people live within the line, they are residents, inhabitants of the city. If they live beyond the line, then they are legally not a part of the city. When first asked for elements that define a city, students will typically mention large buildings and populations. These are quickly followed by a description of elements of city life, that is, the amenities that have come to be identified with urban life (e.g., electricity, running water, transportation, and service industries). Size cannot be the only part of a definition of a city: A large population size will not necessarily have all the characteristics that one associates with urbanization and the concept of a city. For example, in Asia, Africa, and South America there are enormous settlements in which residents lack one or more of the above-referenced amenities. Conversely, there are small towns and even isolated settlements in the more developed world where residents have ready access to these amenities. It should not be difficult for students to see that size alone is therefore not enough for defining a city.
B. The Idea of Contiguousness The first definition uses the term “agglomerated” and the second definition uses the term “continuous.” Each of these terms should help students to think of a city as compact and relatively unbroken. It may be useful to show students an image of a region as seen from space at night. Bright white areas of light are evidence of larger urban areas, of 38 A Curriculum Module for AP Human Geography cities. It is easy to see — rather intuitively — where the cities begin and end based on the “agglomerated” and “continuous” lights. Areas of darkness separate the various cities, or urban areas, on the map. Students often struggle with the concept of multiple continuous municipalities that are so compact and connected as to defy separation visually. This generally occurs because they may speak about something being in a city — or someone living in a city — when in reality they live in a smaller municipality adjacent to the city. The best way to make this clear to students is to show them a map of a city that is familiar to them and that makes clear the various municipalities that surround the city. Remind the students that each of these municipalities constitutes a separate, legally defined city. The definition of a municipality is “a town, city or district having local powers of self-government” (The New Lexicon Webster’s Dictionary of the English Language: Encyclopedia Edition 1990). These municipalities often have their own police force. The various names on the sides of the vehicles serve as a visual reminder that what one thinks of as a single city may in fact be a conglomeration of several self-governing entities. C. Goods and Services The first definition, “nonagricultural activities,” and the second definition indicate that the area of the city is “built up.” In each case, the idea of “buildings” is conjured up. The students will be familiar with the image of a city as an area covered with buildings. The terms “nonagricultural” and “built up,” however, will be less familiar.
“Nonagricultural” is a term whose definition is fairly intuitive: It refers to economic activities that do not deal with the production of food. Help the students realize that by excluding food production we are left with manufacturing and service industries. Cities are zones of manufacturing and the exchange of goods and services as opposed to areas where crops or animals are raised. In fact, cities are often divided into specific zones wherein these various activities will take place. The legal authorities who administer cities usually create laws that keep the economic activities of cities separated from each other and from the homes of the inhabitants discussed above. Sometimes agricultural activities are forbidden by law (as in the case of keeping livestock) or sometimes it is simply not economically feasible to conduct agricultural activities, such as raising wheat, on land that is very valuable due to its proximity to other land uses (such as central business districts, train stations, or office parks). Metropolitan Statistical Area: The City as a Region In reviewing their text for information about defining cities, the students will come across the concept of the metropolitan statistical area. Definitions and descriptions MSAs are often confusing to students. They will likely be able to list the required characteristics without fully conceptualizing the definition.
39 Urban Geography Remind them of the definition of a “functional” (sometimes called nodal) region. It is fairly simple for students to visualize people flowing to a node, and therefore creating a functional region. The concept of an MSA is, in effect, defining a city as a functional region. In this case, a legal city is the node and people from surrounding counties flow to it for work and to access its services. This region is clearly “part” of the city in that it serves as the node to which they go for their needs. It “functions” as a part of it.
It may also be helpful to show students the definition of the term “metropolitan”: the chief city of a region (The New Lexicon Webster’s Dictionary of the English Language: Encyclopedia Edition 1990). The very use of this term in defining a city implies two things — first that there are multiple “cities” (one of which is “chief”) and that they operate together in a region. Resources Brockerhoff, Martin. “ An Urbanizing World.” Population Bulletin 55, No. 3 (Sept. 2000): 3–44.
Fik, T. J. The Geography of Economic Development. New York: McGraw-Hill, 1997.
Johnston, R.J., Derek Gregory, Geraldine Pratt, and Michael Watts. The Dictionary of Human Geography. Malden, Mass.: Blackwell Publishers Ltd, 2000.
The New Lexicon Webster’s Dictionary of the English Language: Encyclopedia Edition. New York: Lexicon Publications, Inc., 1990.
Rubenstein, James M. The Cultural Landscape: An Introduction to Human Geography. Upper Saddle River, N.J.: Pearson Prentice Hall, 2005.
Wirth, Louis. “Urbanism as a Way of Life.” The American Journal of Sociology 44, No. 1 (July 1938): 1–24.
41 About the Contributors Carol Ann Gillespie developed and teaches AP® Human Geography online for Pennsylvania Homeschoolers. She is affiliated with the Pennsylvania Alliance for Geographic Education and has served as a Reader for the AP Human Geography Exam.
Christopher Hall is the social studies curriculum supervisor in the Davis School District in Davis County, Utah. He also serves as the College Board Advisor on the AP Human Geography Development Committee, and he has served as a Reader for the AP Human Geography Exam.
CM10HUMHB01800 |
13461 | https://physics.stackexchange.com/questions/12841/coherence-length | waves - coherence length - Physics Stack Exchange
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coherence length
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Suppose i have two waves emanating from a point source. The waves start out completely in phase. Is the coherence length consistently defined as the length at which these two waves achieve a phase difference of 1 radian? That seems arbitrary to me, you could easily choose a phase difference of π 10 π 10
I'm kind of lost on this whole topic of wave coherence to be honest... I'd appreciate someone giving an overview for the example of two standard plane waves (with full mathematical description).
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edited Jul 27, 2011 at 12:56
TimtamTimtam
asked Jul 27, 2011 at 12:50
TimtamTimtam
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also... if the only thing that matters is constant relative phase... then they needn't be initially in phase... it's a question of when does the relative phase stop being constant by 1 radian... is that where the critical length is?Timtam –Timtam 2011-07-27 12:59:15 +00:00 Commented Jul 27, 2011 at 12:59
does it matter if they are monochromatic or not? yikes...Timtam –Timtam 2011-07-27 13:03:37 +00:00 Commented Jul 27, 2011 at 13:03
Note the Wiener–Khinchin theorem. It states how the spectrum of the light source is related to the temporal coherence function. There is an analogue realtion for the spatial coherence function. It blew my mind when I learned that you can estimate the diameter of stars by measuring there spatial coherence in a Young interferometer.whoplisp –whoplisp 2011-07-27 15:19:38 +00:00 Commented Jul 27, 2011 at 15:19
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The coherence length is just the coherence time multiplied by the propagation speed.
To understand the coherence time, say you have a wave described, in complex notation, by
E(t)=A(t)e i ω t E(t)=A(t)e i ω t
where A(t)A(t) is a slowly varying complex amplitude. You make this wave interfere with a delayed version of itself and collect the intensity
|E(t)+E(t−τ)|2=|E(t)|2+|E(t−τ)|2+2 R(E(t)E∗(t−τ)).|E(t)+E(t−τ)|2=|E(t)|2+|E(t−τ)|2+2 ℜ(E(t)E∗(t−τ)).
where R ℜ means real part and ∗∗ means complex conjugate. The interference term is
2 R(E(t)E∗(t−τ))=2 R(A(t)A∗(t−τ)e i ω τ)2 ℜ(E(t)E∗(t−τ))=2 ℜ(A(t)A∗(t−τ)e i ω τ)
If A(t)A(t) is constant, or roughly constant within a time interval τ τ, then this becomes
2|A(t)|2 cos(ω τ)2|A(t)|2 cos(ω τ)
which is the interference pattern. On the other hand, if A(t)A(t) fluctuates sufficiently fast, and τ τ is larger than its correlation time, then A(t)A∗(t−τ)A(t)A∗(t−τ) averages to zero and there is no interference. Thus, the coherence time can be simply seen as the correlation time of the complex amplitude A(t)A(t).
Now, I'm not sure there is a very quantitative definition of the correlation time. You could define it as the delay where the autocorrelation function drops below some arbitrary threshold. This is equivalent to setting a threshold on the visibility of the interference pattern. The relationship with the shape of the spectral line should also be apparent: the squared modulus of the Fourier transform of A(t)A(t) is the shape of the line (the spectrum of the wave shifted by −ω−ω). It is also the Fourier transform of the autocorrelation function of A(t)A(t). Thus, when the line is wide, the autocorrelation function is narrow,and the coherence time is short.
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answered Jul 27, 2011 at 14:17
Edgar BonetEdgar Bonet
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Mandel has defined (a good definition) the coherence time as : τ c=∫∞−∞γ(τ)γ∗(τ)d τ τ c=∫−∞∞γ(τ)γ∗(τ)d τ where γ(τ)γ(τ) is the complex degree of coherence.daaxix –daaxix 2012-12-31 07:29:30 +00:00 Commented Dec 31, 2012 at 7:29
What is autocorrelation function? I lost you when you started talking about correlation time.Nanashi No Gombe –Nanashi No Gombe 2019-01-25 12:33:35 +00:00 Commented Jan 25, 2019 at 12:33
@NanashiNoGombe: en.wikipedia.org/wiki/AutocorrelationEdgar Bonet –Edgar Bonet 2019-01-25 14:17:11 +00:00 Commented Jan 25, 2019 at 14:17
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Is the coherence length consistently defined as the length at which these two waves achieve a phase difference of 1 radian?
No
Coherence length is the maximal difference in way traveled by the to rays without losing the phase relation which allows interference. This lenghts can be some µmeters (eg for white light from a glowing body) or several meters (eg for very narrow lines from discharge lamps) or even more for mode selected/stabilized lasers.
To first order approximation coherence length is inversly to the bandwidth of the light, but divergence of the bundle plays a role too. Coherence length is important in interference, eg why Newtons rings are only a few around the center of that lens for white sunlight, but hundreds when illuminated with a He/Ne laser.
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answered Jul 27, 2011 at 13:07
GeorgGeorg
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"Coherence length is the maximal difference in way traveled by the to rays without losing the phase relation which allows interference." i'm sorry but I really need an example w/ full mathematical detail... you seem to know what your talking about... but it's not helping me Timtam –Timtam 2011-07-27 13:08:55 +00:00 Commented Jul 27, 2011 at 13:08
what happens when the they can no longer interfere?Timtam –Timtam 2011-07-27 13:13:42 +00:00 Commented Jul 27, 2011 at 13:13
4 @Timtam: I'm not sure how you can "tell he is a chemist." I'm an optical engineer and this is absolutely a correct answer. He didn't include equations, but everything he said is completely accurate and expressed in the same way that you would hear it from an optical engineer.Colin K –Colin K 2011-07-27 15:47:45 +00:00 Commented Jul 27, 2011 at 15:47
1 Several comments deleted after multiple flags.dmckee --- ex-moderator kitten –dmckee --- ex-moderator kitten 2011-07-28 12:32:24 +00:00 Commented Jul 28, 2011 at 12:32
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13462 | https://www.quora.com/What-is-the-pressure-at-10m-depth | What is the pressure at 10m depth? - Quora
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What is the pressure at 10m depth?
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1y
To calculate the pressure at a depth of 10 meters in a fluid (like water), you can use the formula:
P=P 0+ρ g h P=P 0+ρ g h
where:
P P is the total pressure at depth,
P 0 P 0 is the atmospheric pressure at the surface (approximately 101,325 Pa or 101.3 kPa at sea level),
ρ ρ is the density of the fluid (for water, it's about 1000 kg/m³),
g g is the acceleration due to gravity (approximately 9.81 m/s²),
h h is the depth in meters.
Plugging in the values for 10 meters depth:
P=101325 Pa+(1000 kg/m 3×9.81 m/s 2×10 m)P=101325 Pa+(1000 kg/m 3×9.81 m/s 2×10 m)
Calculating the second term:
P=P=
Continue Reading
To calculate the pressure at a depth of 10 meters in a fluid (like water), you can use the formula:
P=P 0+ρ g h P=P 0+ρ g h
where:
P P is the total pressure at depth,
P 0 P 0 is the atmospheric pressure at the surface (approximately 101,325 Pa or 101.3 kPa at sea level),
ρ ρ is the density of the fluid (for water, it's about 1000 kg/m³),
g g is the acceleration due to gravity (approximately 9.81 m/s²),
h h is the depth in meters.
Plugging in the values for 10 meters depth:
P=101325 Pa+(1000 kg/m 3×9.81 m/s 2×10 m)P=101325 Pa+(1000 kg/m 3×9.81 m/s 2×10 m)
Calculating the second term:
P=101325 Pa+98100 Pa P=101325 Pa+98100 Pa
P=199425 Pa P=199425 Pa
So, the pressure at a depth of 10 meters in water is approximately 199.4 kPa.
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Sableagle
Former Soldier at British Army · Author has 4.1K answers and 4.3M answer views
·2y
Originally Answered: There is 1 ATM of pressure exerted on the diver at sea level. How much pressure is exerted on the diver at a depth of 10 m? ·
10 m in what? The sea? Presumably the sea.
1 atmosphere is 101325 Pascal or 14.6959 lb / in².
The sea has a density of one point zero something g / cm³, kg / l or t / m³:
That “minus ten” in the top left would be a density of 0.990 g / cm³. Also it would be dangerously hot. You’d have a hard time diving in that. Way out in the bottom right is ice-cold water at 40 ppt salinity, unpleasantly cold and unusually salty.
A more normal salinity and a more pleasant temperature give us a density of about 1.024 t / m³.
At a depth of 10 m, that’s 10.24 t of water per m², and gravity gives that water weight.
Th
Continue Reading
10 m in what? The sea? Presumably the sea.
1 atmosphere is 101325 Pascal or 14.6959 lb / in².
The sea has a density of one point zero something g / cm³, kg / l or t / m³:
That “minus ten” in the top left would be a density of 0.990 g / cm³. Also it would be dangerously hot. You’d have a hard time diving in that. Way out in the bottom right is ice-cold water at 40 ppt salinity, unpleasantly cold and unusually salty.
A more normal salinity and a more pleasant temperature give us a density of about 1.024 t / m³.
At a depth of 10 m, that’s 10.24 t of water per m², and gravity gives that water weight.
That’s 9.8643 N / kg to 9.7644 N / kg, depending on latitude. It’s generalised to 9.81 N / kg on Earth.
That gives us a general answer of 9.81 10 1.024 1000 N / m² of water weight at that depth. That’s 100454.4 N / m², which is 0.9914 atmospheres. To that, we add the air pressure that’s acting on the water, and we get: 2.0 atmospheres (to two sig figs). That’s probably the answer you need.
It could be as low as 9.7644 10 0.990 1000 N / m² = 96667.56 Pa or 0.9540 atmospheres of water weight, which is still 2.0 atmospheres (to two sig figs) of pressure at 10 m.
It could be as high as 9.8643 10 1.032 1000 N / m² = 101799.576 Pa or 1.0047 atmospheres of water weight, which is still 2.0 atmospheres (to two sig figs) of pressure at 10 m.
If your diver is diving in wine, that density could be as high as 1.090 g / cm³, for an extra 0.064453125 times the weight you’d get from seawater, or 1.0553 atmospheres, so the answer could be as high as 2.1 atmospheres (to two sig figs).
If you want that in pounds and inches, 1 t / m³ is 0.0361273 lb / in³ and 10 m is 393.701 in, and the answers at the end are the same, because the question stated pressure in atmospheres and we’re answering in atmospheres.
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Gene
M.S. in Physics, University of Minnesota - Twin Cities (Graduated 1971) · Author has 9K answers and 2.7M answer views
·2y
Originally Answered: There is 1 ATM of pressure exerted on the diver at sea level. How much pressure is exerted on the diver at a depth of 10 m? ·
play a game with me.
You win the drawing to go to the SuperBowl and only your ticket is selected and awards you a million dollars … but you are required to participate in the halftime stuff.
YOU must lie down at center field.
all those in losing seats have agreed to come out of the stands and lie in the playing field (losers not about to make this easy on you).
60+ thousand more than cover the field so there are several layers
you don’t feel the crush of tens of thousands; you just support two or four bodies as does most of the field.
simple concept; just feel the weight of what’s above you. So,
Air
Continue Reading
play a game with me.
You win the drawing to go to the SuperBowl and only your ticket is selected and awards you a million dollars … but you are required to participate in the halftime stuff.
YOU must lie down at center field.
all those in losing seats have agreed to come out of the stands and lie in the playing field (losers not about to make this easy on you).
60+ thousand more than cover the field so there are several layers
you don’t feel the crush of tens of thousands; you just support two or four bodies as does most of the field.
simple concept; just feel the weight of what’s above you. So,
Air pressure, 1 atm, ~15 lb/square inch is your/mine/a playing field/an ocean's share of the atmosphere above. Since the crust has been spread out by gravity so has the air to be a roughly even layer above us. Air is light and fluffy; so it needs to be piled high to amount to those 15 pounds or ~65 newtons per square inch.
Water is not so fluffy as air. You only need about 32 feet or 10 meters of water over you to match miles of air. So every 10 m of water adds another atm of pressure. Just remember you’re not supporting the whole lake just what’s above you.
Upvote ·
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James Strube
Feb 13
Assuming a water density of 1000 kg/m3 at 4 degrees Celsius and an acting gravity of 9.80665 m/s2, the conversion from metres of water head to kilopascals can be calculated as follows:
1 kPa = 1000 Pascals (Pa)
1 mH2O = 9806.65 Pascals (Pa)
Since the density of a liquid is affected by changes in temperature, metres of water column should be accompanied by the temperature of the liquid that the units were derived. A pure water density of 1000 kg/m3 at 4 deg C and standard gravity of 9.80665 m/s2 is used in the calculation of this pressure unit. The significance of 4 degrees Celsius (39.2 degrees F
Continue Reading
Assuming a water density of 1000 kg/m3 at 4 degrees Celsius and an acting gravity of 9.80665 m/s2, the conversion from metres of water head to kilopascals can be calculated as follows:
1 kPa = 1000 Pascals (Pa)
1 mH2O = 9806.65 Pascals (Pa)
Since the density of a liquid is affected by changes in temperature, metres of water column should be accompanied by the temperature of the liquid that the units were derived. A pure water density of 1000 kg/m3 at 4 deg C and standard gravity of 9.80665 m/s2 is used in the calculation of this pressure unit. The significance of 4 degrees Celsius (39.2 degrees Fahrenheit) is that it is very close to the temperature that water reaches its maximum density.
It is conventional practice to use 1000 kg/m3 as the density of pure water at 4 deg C which is very close to the precise density and for most measurements this does not introduce any significant error. In fact since the temperature can vary significantly, measuring pressure in metres of water is never going to be a precise representation of the true liquid height. Local gravity also varies at different geological locations, which also adds some minor uncertainties to the use of metres of water gauge as an indication of exact water level in different parts of the world.
Derivation
The calculation below shows how the pressure unit Metres of Water Column (mH2O) is derived from SI Units.
Formula
Pressure = Force / Area
Force = Mass x Acceleration
Mass = Density x Volume
Volume = Area x Height
Acceleration = Distance / (Time x Time)
SI Units
Mass: kilogram (kg)
Length: metre (m)
Time: second (s)
Force: newton (N)
Pressure: pascal (Pa)
Input Values
Density = Water Density at 4degC = 1000 kg/m³
Area = 1 m²
Height = 1 m
Acceleration = Standard Gravity = 9.80665 m/s²
Calculation
1 mH2O Mass = 1000 kg/m³ x 1 m² x 1 m = 1000 kg
1 mH2O Force = 1000 kg x 9.80665 m/s² = 9806.65 N
1 mH2O Pressure = 9806.65 N / 1 m² = 9806.65 Pa
Upvote ·
9 1
Related questions
More answers below
At what depth of water would the pressure kill you?
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Why does pressure increase as we go downwards in depth of the ocean?
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What is the pressure at the bottom of a 10m tank of water?
Brian Alan Whatcott
Worked most European and N. American countries. · Author has 6.7K answers and 8.7M answer views
·7y
Originally Answered: What is the pressure of water 10 foot deep? ·
Long ago, in the Birmingham (UK) suburbs, a man named Priestley fixed up a barometer outside his house. Unlike the later barometers which used a column of mercury which usually stayed about 776 millimeters or 29.94 inches tall, he used what he had on hand: water. Water is much less dense than mercury; 1/13.6 as dense fact. So the column of water that the atmospheric pressure could usually hold up was 13.6 X 29.94 inches or 34 feet tall. He was a non-conformist too, and discovered and named the gas: Oxygen. The locals thought him peculiar, and a mob finally drove him out of town, so he sailed t
Continue Reading
Long ago, in the Birmingham (UK) suburbs, a man named Priestley fixed up a barometer outside his house. Unlike the later barometers which used a column of mercury which usually stayed about 776 millimeters or 29.94 inches tall, he used what he had on hand: water. Water is much less dense than mercury; 1/13.6 as dense fact. So the column of water that the atmospheric pressure could usually hold up was 13.6 X 29.94 inches or 34 feet tall. He was a non-conformist too, and discovered and named the gas: Oxygen. The locals thought him peculiar, and a mob finally drove him out of town, so he sailed to America, where he lived until he died.
One more piece of data you need to work out your question: the normal pressure of atmospheric air at sea level (and Birmingham is not a high elevation which would see a lower pressure) - That pressure is given as 14.7 psi.
So: if 14.7 psi is 34 feet of water, a 10 ft water column needs a smaller pressure to hold it up. 10/34 X 14.7 psi, in fact. And that is 4.3 psi.
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Kush Varshney
Mechanical Design Engineer at Rolls-Royce Power Systems AG
·8y
Originally Answered: The atmospheric pressure is 10⁵ Pa and the density of water is 1000 kg/m³. What is the pressure underwater at a depth of 10 m? ·
Pressure at any point within the homogeneous fluid can be found out using the formula:
Pressure at point x (Px) = Po + ρgh
where Po is the atmospheric pressure, ρ is the density of fluid, g is the acceleration due to gravity which is 9.8m/s^2 and h is the depth at which point x is located within the fluid.
Every fluid exerts pressure on its surroundings. Since air is in the surrounding of water in your scenario, you have to consider the pressure exerted by air on the water surface, which is Po in above equation.
If you plug in all the values in above equation, you will find your answer. Hence, p
Continue Reading
Pressure at any point within the homogeneous fluid can be found out using the formula:
Pressure at point x (Px) = Po + ρgh
where Po is the atmospheric pressure, ρ is the density of fluid, g is the acceleration due to gravity which is 9.8m/s^2 and h is the depth at which point x is located within the fluid.
Every fluid exerts pressure on its surroundings. Since air is in the surrounding of water in your scenario, you have to consider the pressure exerted by air on the water surface, which is Po in above equation.
If you plug in all the values in above equation, you will find your answer. Hence, pressure underwater at the depth of 10m would be:
P = 10^5 + (10009.810) = 198,000 Pa or 198kPa, which is greater than atmospheric pressure and makes sense as pressure increases as you go deep inside the water.
Upvote ·
9 3
Brett Schmidt
Author has 2K answers and 3.2M answer views
·5y
Originally Answered: What is the pressure of water at the bottom of a well if the depth of water is 10 m (g=9.8m/s^2)? ·
QUESTION:
What is the pressure of water at the bottom of a well if the depth of water is 10 m (g = 9.8 m/s²)?
ANSWER:
The precise answer depends on the density and therefore the temperature of the water, but we can obtain a reasonable approximation by assuming that the density of the water is 1000 kilograms per cubic metre (kg/m³).
Since the depth of the water in the well is 10 m, the volume of water directly above an area A of a square metres (m²) at the bottom of the well is 10×a m³.
Since the density of the water is 1,000 kg/m³, the mass of water directly above area A is (1,000 kg/m³) × (10×a m³
Continue Reading
QUESTION:
What is the pressure of water at the bottom of a well if the depth of water is 10 m (g = 9.8 m/s²)?
ANSWER:
The precise answer depends on the density and therefore the temperature of the water, but we can obtain a reasonable approximation by assuming that the density of the water is 1000 kilograms per cubic metre (kg/m³).
Since the depth of the water in the well is 10 m, the volume of water directly above an area A of a square metres (m²) at the bottom of the well is 10×a m³.
Since the density of the water is 1,000 kg/m³, the mass of water directly above area A is (1,000 kg/m³) × (10×a m³) = (1000×10×a kg) = 10,000×a kg.
Since g = 9.8 m/s², the force of gravity acting on the water directly above area A is (9.8 m/s²) ×(10,000×a kg) = 9.8×10,000×a N (newtons) = 98,000×a N.
So the pressure of water acting on area A is (98,000×a N)/(a m²) = (98,000×a)/a N/m² = 98,000 pascals (pa). And since A could be any given area at the bottom of the well, this is the pressure at any point at the bottom of the well.
So the pressure at the bottom of the well is 98,000 pascals (or 98,000/101,325 standard atmospheres = 560/579 atmospheres ~ 0.967 standard atmospheres).
Upvote ·
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Harshal Thakar
B.Tech in Chemical Engineering, Bharat Jambucha (Graduated 2011)
·6y
Originally Answered: What is the pressure experienced at a point on the bottom of a swimming pool 10 meters in depth? ·
See below calculations step by step and understand.
On that point, 10 m bottom, total pressure will be summation of atmospheric pressure and fluid pressure.
P (total) = P (atmosphere) + P (fluid)
Here, P (atmosphere) will be pressure on the water surface, i.e. pressure on each and everything i.e. 101325 Pascal.
P (fluid) will be multiplication of density acceleration gravity factor height below water surface.
P (fluid) = 1000 kg/m3 9.8 m/s2 10 m = 0.98 10^5 N/m2
So, total pressure will be,
P (total) = 1.01 10^5 + 0.98 10^5 = 1.99 10^5 Pascal
Here, density of swimming pool water conside
Continue Reading
See below calculations step by step and understand.
On that point, 10 m bottom, total pressure will be summation of atmospheric pressure and fluid pressure.
P (total) = P (atmosphere) + P (fluid)
Here, P (atmosphere) will be pressure on the water surface, i.e. pressure on each and everything i.e. 101325 Pascal.
P (fluid) will be multiplication of density acceleration gravity factor height below water surface.
P (fluid) = 1000 kg/m3 9.8 m/s2 10 m = 0.98 10^5 N/m2
So, total pressure will be,
P (total) = 1.01 10^5 + 0.98 10^5 = 1.99 10^5 Pascal
Here, density of swimming pool water considered as 1000 kg/m3.
Upvote ·
9 1
Chuck Britton
Author has 6.7K answers and 5.1M answer views
·5y
This question clearly illustrates why ‘pressure’ questions can have two very different but correct answers. The answer depends on what method is used to measure the pressure and how the pressure is reported. When you measure the pressure in your car’s tire, you are measuring the ‘gauge pressure’. This is the pressure difference between the interior of the tire and the surrounding atmosphere. Scientist who are doing calculations (like those involving gas laws), must know the ‘absolute pressure’ which is measured with respect to a vacuum.
‘One Atmosphere’ is a convenient unit for measuring pressu
Continue Reading
This question clearly illustrates why ‘pressure’ questions can have two very different but correct answers. The answer depends on what method is used to measure the pressure and how the pressure is reported. When you measure the pressure in your car’s tire, you are measuring the ‘gauge pressure’. This is the pressure difference between the interior of the tire and the surrounding atmosphere. Scientist who are doing calculations (like those involving gas laws), must know the ‘absolute pressure’ which is measured with respect to a vacuum.
‘One Atmosphere’ is a convenient unit for measuring pressure. In the metric world 1 atm is ~100kPa. In the US it is ~15 psi.
10m of depth in fresh water adds ~1 atm of pressure. So the Gauge Pressure is ~1 atm while the Absolute Pressure is ~2 atm.
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Ryan Saridar
BEng in Electronic Engineering (Course), King's College London (KCL) (Graduated 2021) · Author has 92 answers and 274.5K answer views
·8y
Originally Answered: The atmospheric pressure is 10⁵ Pa and the density of water is 1000 kg/m³. What is the pressure underwater at a depth of 10 m? ·
Pressure can be written as follows:
P=F A P=F A
Where P P is pressure, F F is force, and A A is area.
The force in question is the total weight pushing down at the given depth. The weight can be calculated through F=m g F=m g.
Density can be written as:
ρ=m V ρ=m V
Where ρ ρ is density, m m is mass, and V V is volume.
Re-arranging this:
m=V ρ m=V ρ
Thus, we can write:
P=g V ρ A P=g V ρ A
Now, volume is length (depth) times the area in question, so:
V=A d V=A d
Where d d is depth.
Putting this back in:
P=g A d ρ A P=g A d ρ A
Cancelling the
Continue Reading
Pressure can be written as follows:
P=F A P=F A
Where P P is pressure, F F is force, and A A is area.
The force in question is the total weight pushing down at the given depth. The weight can be calculated through F=m g F=m g.
Density can be written as:
ρ=m V ρ=m V
Where ρ ρ is density, m m is mass, and V V is volume.
Re-arranging this:
m=V ρ m=V ρ
Thus, we can write:
P=g V ρ A P=g V ρ A
Now, volume is length (depth) times the area in question, so:
V=A d V=A d
Where d d is depth.
Putting this back in:
P=g A d ρ A P=g A d ρ A
Cancelling the area:
P=g d ρ P=g d ρ
Putting in values of g≈9.81 m s−2 g≈9.81 m s−2, d=10 m d=10 m, and ρ=1000 kg m−3 ρ=1000 kg m−3 gives us:
P≈9.81⋅10⋅1000=98,100 Pa P≈9.81⋅10⋅1000=98,100 Pa
We also need to account for atmospheric pressure, so we add that on to our calculated value:
P≈100,000+98,100=198,100 Pa P≈100,000+98,100=198,100 Pa
So, the conclusion, with the given data:
P≈198,100 Pa P≈198,100 Pa
Upvote ·
9 2
Varshini Lolla
student and a scratcher. · Author has 148 answers and 118.6K answer views
·3y
Originally Answered: What is the water pressure at a depth of 10 feet? ·
Formula for pressure is “ Height density gravity” in this case.
Given,
Height= 10 feet=120inches=2.5120cm=300cm=3m.
Now, gravity= 10m/s^2. (consider)
Density of water=1000kg/m^3.
All quantities are in SI system.
Now, multiply them:
3101000=310^4 N/m^2. (or)30,000 Pa.
Upvote ·
9 4
Nishant Padnavis
Expert in helping people buy a water purifier/filter.
·8y
Originally Answered: What is the pressure of water 10 foot deep? ·
Fresh water: 0.43 psi per foot ; Sea water: 0.44 psi per foot.
Therefore, 4.3 to 4.4 psi at 10 feet depth.
So, for each additional 10 feet of depth, it should be about 4.3 to 4.4 psi increase in pressure.
Upvote ·
99 13
9 3
Kim Aaron
Has PhD in fluid dynamics from Caltech · Author has 8.4K answers and 27.4M answer views
·8y
Originally Answered: The atmospheric pressure is 10⁵ Pa and the density of water is 1000 kg/m³. What is the pressure underwater at a depth of 10 m? ·
The pressure increases approximately 1 atm for every 10 m depth in water. The pressure at the surface of the water is 1 atm (absolute) so it would be approximately 2 atm (absolute) at 10 m depth. That is, it would be about 2 bar or 200,000 Pa.
Upvote ·
9 4
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13463 | https://courses.lumenlearning.com/suny-mcc-introductorychemistry/chapter/9-3-solution-stoichiometry/ | 9.3 Solution Stoichiometry
earning Objectives
By the end of this section, you will be able to:
Perform stoichiometric calculations involving solution molarity
As we have seen in lab, many reactions such as single or double displacement reactions are carried out in aqueous medium (i.e. in water). Because these reactions occur in aqueous solution, we can use the concept of molarity to directly calculate the number of moles of reactants or products that will be formed, and hence their amounts (i.e. volume of solutions or mass of precipitates).
More complex stoichiometry problems using balanced chemical reactions can also use concentrations as conversion factors.
For example, suppose the following equation represents a chemical reaction:
2 AgNO3(aq) + CaCl2(aq)→2 AgCl(s) + Cu(NO3)2(aq)
If we wanted to know what volume of 0.555 M CaCl2 would react with 1.25 mol of AgNO3, we first use the balanced chemical equation to determine the number of moles of CaCl2 that would react and then use molarity to convert to liters of solution:
1.25 mol AgNO3×1 mol CaCl22 mol AgNO3×1 L solution0.555 mol CaCl2=1.13 L CaCl2 solution
This can be extended by starting with the mass (grams) of one reactant, instead of moles of a reactant.
Example 1: Solution Stoichiometry–Mass to Volume Conversion
What volume of 0.0995 M Al(NO3)3 will react with 3.66 g of Ag according to the following chemical equation?
3 Ag(s) + Al(NO3)3(aq)→3 AgNO3(aq) + Al(s)
Show Answer
Here, we first must convert the mass of Ag to moles before using a mole to mole ratio from the balanced chemical equation and then the definition of molarity as a conversion factor:
3.66 g Ag×1 mol Ag107.97 g Ag×1 mol Al(NO3)33 mol Ag×1 L solution0.0995 mol Al(NO3)3=0.114 L Al(NO3)3 solution
Check Your Learning
What volume of 0.512 M NaOH will react with 17.9 g of H2C2O4(s) according to the following chemical equation?
H2C2O4(s) + 2 NaOH(aq)→Na2C2O4(aq) + 2 H2O(l)
Show Answer
0.777 L of NaOH solution
We can extend our skills even further by recognizing that we can relate quantities of one solution to quantities of another solution. Knowing the volume and concentration of a solution containing one reactant, we can determine how much of another solution of another reactant will be needed using the balanced chemical equation.
Example 2: Solution Stoichiometry–Volume to Volume Conversion
A student takes a precisely measured sample, called an aliquot, of 10.00 mL of a solution of FeCl3. The student carefully adds 0.1074 M Na2C2O4 until all the Fe3+(aq) has precipitated as Fe2(C2O4)3(s). Using a precisely measured tube called a burette, the student finds that 9.04 mL of the Na2C2O4 solution was added to completely precipitate the Fe3+(aq). What was the concentration of the FeCl3 in the original solution? (A precisely measured experiment like this, which is meant to determine the amount of a substance in a sample, is called a titration.) The balanced chemical equation is as follows:
2 FeCl3(aq) + 3 Na2C2O4(aq)→ Fe2(C2O4)3(s) + 6 NaCl(aq)
Show Answer
9.04 mL Na2C2O4×1 L1000 mL×0.1074 mol Na2C2O41 L Na2C2O4×2 mol FeCl33 mol Na2C2O4×10.01000 L soln=0.0647 M FeCl3
Check Your Learning
A student titrates 25.00 mL of H3PO4 with 0.0987 M KOH. She uses 54.06 mL to complete the chemical reaction. What is the concentration of H3PO4?
H3PO4(aq) + 3 KOH(aq)→K3PO4(aq) + 3 H2O(l)
Show Answer
0.0711 M
When a student performs a titration, a measured amount of one solution is added to another reactant. “Chemistry titration lab” by Kentucky Country Day is licensed under the Creative Commons Attribution-NonCommercial 2.0 Generic.
Example 3: Solution Stoichiometry & the IDeal GAs law
How many liters of carbon dioxide gas can form at STP when 125 mL of a 2.25 M HCl solution reacts with excess lithium carbonate?
2 HCl(aq) + Li2CO3(aq)→CO2(g) + 2 LiCl(aq) + H2O(l)
Show Answer
First determine the moles of carbon dioxide:
125 mL HCl×1 L1000 mL×2.25 mol HCl1 L HCl×1 mol CO22 mol HCl=0.140625 mol CO2
Next, use the ideal gas law to calculate the volume of carbon dioxide:
V=nRTP=(0.140625 mol CO2)(0.0821L⋅atmK⋅mol)(273.15 K)(1.00 atm)=3.15 L CO2
Alternatively, since the reaction is at STP, we know 1 mol of gas equals 22.41 L of gas (known as molar volume).
125 mL HCl×1 L1000 mL×2.25 mol HCl1 L HCl×1 mol CO22 mol HCl×22.41 L CO21 mol CO2=3.15 L CO2
Check Your Learning
If 355 mL of hydrogen gas is collected at 25 oC at a total pressure of 740 mmHg from the reaction of excess zinc and a 3.0 M HCl solution, how many mL of the HCl solution was required?
Zn(s) + 2 HCl(aq)→ZnCl2(aq) + H2(g)
Show Answer
9.4 mL HCl
Key Concepts and Summary
Molarity can be used as a conversion factor in combination with reaction stoichiometry.
End of Module Problems
1. Magnesium reacts with hydrochloric acid to produce hydrogen gas and magnesium chloride. How many liters of a 0.750 M HCl solution will react with 12.25 g of Mg?
Mg(s) + 2 HCl(aq)→H2(g) + MgCl2(aq)
2. Consider the following reaction:
Pb(NO3)2(aq) + 2 NaI(aq)→PbI2(s) + 2 NaNO3(aq)
a. How many grams of lead(II) iodide will be formed from 25.0 mL of a 2.00 M sodium iodide solution?
b. How many milliliters of a 1.25 M lead(II) nitrate solution will react with 25.0 mL of a 1.50 M sodium iodide solution?
c. What is the molarity of a 20.0 mL solution of sodium iodide that reacts completely with 60.0 mL of a 0.750 M lead(II) nitrate solution?
3. Consider the following reaction:
Al2(SO4)3(aq) + 6 KOH(aq)→2 Al(OH)3(s) + 3 K2SO3(aq)
a. How many grams of aluminum hydroxide will be formed from 55.0 mL of a 1.50 M potassium hydroxide solution?
b. How many milliliters of a 0.250 M aluminum sulfate solution will react with 10.0 mL of a 3.00 M potassium hydroxide solution?
c. What is the molarity of a 40.0 mL solution of potassium hydroxide that reacts completely with 20.0 mL of a 0.500 M aluminum sulfate solution?
Copper(II) oxide reacts with hydrochloric acid to produce copper(II) chloride and water. How many liters of a 4.50 M HCl solution will react with 33.0 g of copper(II) oxide?
CuO(s) + 2 HCl(aq)→CuCl2(aq) + H2O(l)
What volume, in liters, of NO2 gas at 750 mmHg and 25 oC will be required to produce 0.150 L of a 0.500 M HNO3 solution given the reaction below?
3 NO2(g) + H2O(l)→2 HNO3(aq) + NO(g)
The reaction of 34.4 mL of a HCl solution reacts with excess zinc to produce 0.720 L of hydrogen gas at 740 torr and 24 oC. What will be the molarity of the original HCl solution?
Zn(s) + 2 HCl(aq)→ZnCl2(aq) + H2(g)
Show Selected Answers
1.34 L HCl solution
12.25 g Mg×1 mol Mg24.31 g Mg×2 mol HCl1 mol Mg×1 L solution0.750 mol HCl=1.34 L HCl solution
2.
(a). 11.5 g PbI2
25.0 mL NaI×1 L1000 mL×2.00 mol NaI1 L NaI×1 mol PbI22 mol NaI×461.01 g PbI21 mol PbI2=11.5 g PbI2
(b). 15.0 mL Pb(NO3)2
25.0 mL NaI×1.50 mol NaI1000 mL NaI×1 mol Pb(NO3)32 mol NaI×1000 mL Pb(NO3)31.25 mol Pb(NO3)3=15.0 mL Pb(NO3)3
(c). 4.5 M NaI
60.0 mL Pb(NO3)3×0.750 mol Pb(NO3)31000 mL Pb(NO3)3×2 mol NaI1 mol Pb(NO3)3×10.0200 L NaI=4.5 M NaI
3.
(a). 2.15 g Al(OH)3
55.0 mL KOH×1.50 mol KOH1000 mL KOH×2 mol Al(OH)36 mol KOH×78.00 g Al(OH)31 mol Al(OH)3=2.15 g Al(OH)3
(b). 20.0 mL Al2(SO4)3
10.0 mL KOH×3.00 mol KOH1000 mL KOH×1 mol Al2(SO4)36 mol KOH×1000 mL Al2(SO4)30.250 mol Al2(SO4)3=20.0 mL Al2(SO4)3
(c). 1.50 M KOH
20.0 mL Al2(SO4)3×0.500 mol Al2(SO4)31000 mL Al2(SO4)3×6 mol KOH1 mol Al2(SO4)3×1 0.0400 L Al2(SO4)3=1.50 M KOH
0.184 L HCl solution
33.0 g CuO×1 mol CuO79.55 g CuO×2 mol HCl1 mol CuO×1 L solution4.50 mol HCl=0.184 L HCl solution
2.80 L NO2
0.150 L HNO3×0.500 mol HNO31 L HNO3×3 mol NO22 mol HCl=0.113 mol NO2
V=nRTP=(0.113 mol NO2)(0.0821L⋅atmK⋅mol)(298 K)(750 mmHg×1 atm760 mmHg)=2.80 L NO2
1.67 M HCl
n=PVRT=(740 torr×1 atm760 torr)(0.720 L H2)(0.0821L⋅atmK⋅mol)(297 K)=0.0288 mol H2
0.0288 mol H2×2 mol HCl1 mol H2×10.0344 L solution=1.67 M HCl
Candela Citations
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Solution Stoichiometry . Authored by: Paul R. Young, Professor of Chemistry, University of Illinois at Chicago, Wiki: AskTheNerd; PRYufe6baskthenerd.com - pyoungufe6buic.edu; ChemistryOnline.com, Marisa Alviar-Agnew (Sacramento City College), Henry Agnew (UC Davis). Provided by: Libre Text. Located at: License: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
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CC licensed content, Shared previously
Solution Stoichiometry . Authored by: Paul R. Young, Professor of Chemistry, University of Illinois at Chicago, Wiki: AskTheNerd; PRYufe6baskthenerd.com - pyoungufe6buic.edu; ChemistryOnline.com, Marisa Alviar-Agnew (Sacramento City College), Henry Agnew (UC Davis). Provided by: Libre Text. Located at: License: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike |
13464 | https://realhistoryww.com/world_history/ancient/Misc/Crests/Black_as_status_symbol.htm | The Black Page Boy as Status Symbol
This is a specific subject page, dealing exclusively with, or primarily with, the subject in the title. Because of need, there are many such pages at RHWW: usually, but not always, linked to primary pages. For those in a hurry, they enable a quick summary of many important subjects. The menu for these pages is here:Click>>>
The Black Page Boy as Status Symbol
BACKGROUND:
THE MEDIEVAL HOUSEHOLD.
The classical model of the medieval household, particularly as it evolved in Carolingian France and from there spread over great parts of Europe.
As a result of the military nature of the medieval noble household, its composition was predominately male. The higher level positions – in particular those attending on the lord – were often filled by men of rank: sons of the lord's relatives, or his retainers.
The presence of servants of noble birth imposed a social hierarchy on the household that went parallel to the hierarchy dictated by function.
THE KNIGHTS, SQUIRES AND PAGES.
The main occupants of the Medieval Castle could be divided into two basic groups - the knights and the servants. The life of the Medieval Knights and their retinues centered around enhancing their Knightly skills in the use of weapons, horsemanship and medieval warfare.
The sons of the Nobility, except those who were destined to take Holy Orders, were placed in the service of the great Lords of the land.
These children were sent to live in the castle of their liege lord and commence their education as a Knight. The castle served as a 'Knight School!' A knight would start their life in a castle as a Page and then move up to the role of a Squire.
LIFE OF THE PAGE
The life of a castle Page would start at a very young age - seven years old. A Page was junior to a Squire. It was the duty of a Page to wait at table, care for the Lord's clothes and assist them in dressing. The Page was provided with a uniform of the colors and livery of the Lord.
LIFE OF THE SQUIRE
The life of a Squire (also called Esquire) would start as a teenager, usually fourteen years of age. A Squire was junior to a Knight. It was the duty of a Squire to learn about the Code of Chivalry, the rules of Heraldry, horsemanship and practice the use of weapons. It was also their duty to enter into the social life of the castle and learn courtly etiquette, music and dancing. The Squire served in this role for seven years and became a Knight at the age of twenty-one. Sometimes knighthood was conferred earlier as the reward for bravery on the battlefield
LIFE OF THE KNIGHT
It was the duty of a Knight to learn how to fight and so serve their Lord according to the Code of Chivalry.
STATUS SYMBOL:
A status symbol is a perceived visible, external denotation of one's social position and perceived indicator of economic or social status. Many luxury goods are often considered status symbols. Mercedes-Benz luxury vehicles are status symbols in many cultures.
Blacks were the Nobility in Medieval Europe:
Their children served as Pages and Squires...
So, including a little Black Boy in you portrait is akin to saying that you are ROYALTY,
whether you are or aren't..
Thus that little Black Boy is:
A STATUS SYMBOL!
They convey high status on the pretender, and legitimacy for
the newly noble, as it implies connection with the old guard.
It was Thomas Cromwell who destroyed all evidences of Black Rule in Britain.
Article from the Daily Telegraph Media Group Limited Jan. 2015
Main Quote: No one can be sure of the exact figure, but it is estimated that the destruction started and legalised by Cromwell amounted to 97% of the English art then in existence. Statues were hacked down. Frescoes were smashed to bits. Mosaics were pulverized. Illuminated manuscripts were shredded. Wooden carvings were burned. Precious metalwork was melted down. Shrines were reduced to rubble. This vandalism went way beyond a religious reform. It was a frenzy, obliterating the artistic patrimony of centuries of indigenous craftsmanship with an intensity of hatred for imagery and depicting the divine that has strong and resonant parallels today.
Note the figure quoted below by Albinos themselves: "97%"
That means that almost ALL of the portraits that Albinos show you of their "WHITE"
Kings, Queens, Nobility, and other Important People... ARE FAKES!!!
Click here for a link to the full article
The nonsense of the African Slave/Servant in Medieval Europe.
Europe was already awash in Slaves! THEY WERE CALLED SERFS!
Serfdom is the status of peasants under feudalism, specifically relating to manorialism. It was a condition of bondage which developed primarily during the High Middle Ages in Europe and lasted in some countries until the mid-19th century.
Serfs who occupied a plot of land were required to work for the Lord of the Manor who owned that land, and in return were entitled to protection, justice and the right to exploit certain fields within the manor to maintain their own subsistence. Serfs were often required not only to work on the lord's fields, but also his mines, forests and roads. The manor formed the basic unit of feudal society and the Lord of the Manor and his serfs were bound legally, economically, and socially. Serfs formed the lowest social class of feudal society. Germany between 1336 and 1525 witnessed no fewer than sixty instances Peasant revolt.
FAKE PORTRAITS
The Albino people have prepared bogus explanations for every possible situation, even to explain these portraits. But they can provide only words, they cannot provide physical proof. It has been established that the personal household servants of nobility were themselves the CHILDREN OF NOBILITY! Thus the ABSENCE of Albino pages and Squires AND KNIGHTS: INDICATES THAT THERE WERE "NO" ALBINO NOBILITY BEFORE THE TAKEOVER! Thus no Albino children as Pages, Squires: and no grown children as Knights. And further, those portraits showing Albino Nobility are modern FAKES! So if one sees a picture with a White Knight, inspect it closely, it is likely a fake!
Since the albinos can only produce modern portraits lyingly identified as Medieval or Renaissance portraits, we need a way to help us in identifying these Fake portraits. To do that, we need only compare the suspect portrait to the best known and best maintained medieval portrait in the world. If it looks brighter, clearer, cleaner, newer, than the Mona Lisa - then you KNOW it's a FAKE!
COMPARE!
Note: No doubt some or all of these paintings are modern fakes, judging by their condition. But the duplicity is in replacing Black nobles with White nobles in the time period indicated, this in support of bogus Albino history. The relationships depicted in the portraits were true following the overthrow of Black rule.
Naturally lying Albinos don't make fake paintings of Black nobility.
Therefore if you find a portrait of Black nobility, it is of course real and authentic.
Click here for link to page on the Black nobility of medieval Europe.
Click for Realhistoryww Home Page |
13465 | https://www.youtube.com/watch?v=Mvx4GIEmJ_U | Solve Logarithmic Equation: Log(Base 3) of (4x+15)= 2. One Log Term and a Constant
Wendy
1630 subscribers
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Description
264 views
Posted: 10 Apr 2021
The equation to be solved is log(base 3) of (4x+15)=2. The steps for solving an equation containing one logarithm are: (1) Isolate the logarithmic term (2) Write the equation in exponential form (3) Solve for the variable and (4) MUST check for extraneous solutions. In this case the solution is a negative number but it is still a good solution as it makes the argument of the logarithm a positive number.
Timestamps
0:00 Explanation
0:30 Isolate Logarithmic Term
0:51 Convert from Logarithmic to Exponential Form
1:20 Solve Resulting Linear Equation
2:36 Check for Extraneous Solutions
Transcript:
Explanation in this example we need to solve the equation log to the base 3 of the quantity 4x plus 15 equals 2. well what type of equation do we have here notice it has a log in it so this is a logarithmic equation but how many logs do i have in this problem just one so let's quickly review the steps to solve equations containing one logarithm step one Isolate Logarithmic Term isolate the logarithmic term is that already done in this case yes it looks good but double check you need to make sure the coefficient of the logarithmic term is a 1 which it is in this case and when that is true we can go on to Convert from Logarithmic to Exponential Form step 2 that says write the equation in exponential form so the base of the log is 3 so the base of the exponent is going to be 3 3 raised to the second power equals the argument of the log which is 4 x plus fifteen so step two is complete now step three says solve for the variable Solve Resulting Linear Equation notice i originally had a logarithmic equation but now what type of equation do i have don't let the squared term on the three confuse you the highest exponent on an x is a one so this is a linear equation and those are easy to solve 3 squared 3 times 3 is 9 equals 4 x plus 15. now let's isolate the x term first thing i'm going to do is subtract 15 from both sides so i get 9 minus 15 is negative 6 equals 4 x lastly divide both sides by four so on the right hand side the fours reduce and i just get left with x how about the left hand side i'm going to have a negative number i think six and four both reduce by two so i'm going to get left with negative three halves so i think my solution is negative three halves but don't Check for Extraneous Solutions forget you must check for extraneous solutions the way to check for extraneous solutions in logarithmic equations is you have to make sure that the argument of every single logarithm is a positive number i only have one logarithm in my problem so i just need to make sure that the quantity 4x plus fifteen is a positive number so i get four times x is negative three halves plus fifteen so i'm going to turn 4 into 4 divided by 1 so 2 reduces with the 4 twice and i get 2 times negative 3 is negative 6 plus 15 which is positive nine is nine a positive number yes so x equals negative three halves is not extraneous so it is the solution to this equation one last thing i want to point out x can land up being a negative number but the argument of a log cannot be negative or zero so don't automatically assume negative solutions for the variable are extraneous |
13466 | https://blog.computationalcomplexity.org/2011/03/update-on-17x17-problem.html | Computational Complexity: Update on 17x17 problem
Computational Complexity
Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch
Thursday, March 17, 2011
Update on 17x17 problem
UPDATE: Problem HAS been solved. See Feb 8, 2012 post. There IS a 4-coloring of 17x17 and also of 18x18. Can also see my arXiv paper on grid coloring.
Long time readers may recall that 17x17 problem that I posted on Nov 30, 2009 here. I am sometimes asked if the problem is still open. Alas it is. Is the bounty on it still available. Alas it is. Some thoughts and experiences
See this for a different take on it.
When I wrote the post not that many people tried it seriously. Because of the post and because Brian Hayes picked up on it (see here) many people have worked on it seriously. This is good in that I now know that its hard, but bad in that its still unsolved.
A High School Student wanted a formal contract before showing me his alleged solution. I told him that if he posted a comment with the coloring ON MY BLOG I would have to pay up and would do so gladly. His solution didn't work anyway.
Do I still think that 17x17 is 4-colorable? The problem is that this is a finite problem. The fact that nobody has found a 4-coloring MIGHT mean there isn't one. But it might just mean there are very few of them.
As a pessimist I think that 17x17 IS 4-colorable. Why is that? The following three problems are open: is 17x17 4-colorable? is 17x18 4-colorable? is 18x18 4-colorable? If 17x17 was NOT 4-colorable then the rest would NOT be 4-colorable with no additional work. We will not be that lucky. By the same reasoning I think 18x18 is NOT 4-colorable. (There are a few other grids where we do not know if they are 4-colorable but not many.)
Will future faster computers help? Maybe, but there needs to be a math breakthrough, even a small one, as well.
Will future Quantum Computers help? I doubt anyone will go to the expense of building a quantum computer for the 17x17 grid problem. And I doubt there will be general-purpose quantum computers.
The following problem is inspired by my problem but has not gotten that much attention: How hard is the following: Given (n,m,c) and a partial rectangle-free c-coloring of nxm, can it be completed to a total rectangle-free c-coloring of nxm. Should be NP-complete but I have not been able to prove this I also haven't tried that hard- Maybe I'll get a bright High School Student to do it and get some free lunches out of it (see here).
JohnPaul Adamovsky claimed that they had a proof that 17x17 was NOT 4-colorable and had comments on it on my blog here. I could not make sense of his proof. I suspect he no longer believes this since recent email from him describes an approach to finding a 4-coloring. He also made an offer that if I bought him some type of computer (he says which type) he will solve the problem. I have declined it; however, I offered to do a post on updated status of the 17x17 problem so he could make a comment on it offering it to others (I am doing that NOW). Note that if he posted on my older posts very few people would see it. He did not respond kindly to my offer; however, we'll see if he comments.
I gave a talk on grid colorings at an Algorithms and Theory of Computation Day that Zachos invited me to in New York. A the end I had the following exchange with Lane Hemaspaandra who had also given a talk.
LANE: What does this have to do with Algorithms or Theory of Computation?
BILL: I could make something up but I respect you and the audience too much for that. The answer is NOTHING.
LANE: Then why are you giving a talk on it at Algorithms and Theory of Computation day?
BILL: Because Zachos invited me. You could ask why he invited me, but I think it is because he knows my parents live in the area so I would be a cheap date- no housing costs.
OTHER AUDIENCE MEMBER: Actually this material does have applications. This is part of Ramsey Theory and there is an entire website of applications of Ramsey Theory to Computer Science.
BILL (Thinking- there's ANOTHER one aside from mine? I should take a look at it) OH- that's good to know- what is the pointer to it?
OTHER AUDIENCE MEMBER: Its Oh- that's you! (READERS- see here.)
BILL: YES, Ramsey Theory has had applications to computer science and that's great! However, I am not going to make the following incorrect claim: (1) Ramsey theory has had apps to CS, (2) The Grid problem was inspired by Ramsey Theory. Hence (3) The Gird problem has apps to CS. That would be bad logic.
Posted by GASARCH at 1:47 PM
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49 comments:
Emmel3:48 PM, March 17, 2011
Being a fellow "g17" enthusiast, I'm glad to see an update.
For those interested in joining the hunt: good luck, have fun. It's a really tough problem, but a really fun one at the same time. I had many "amazing" ideas in the course of working on a solution, but all of them found eventual dead ends. I ended up with a stack of proofs that "Graph with property X is not 4-colorable". Many of these are obvious after a little thought, others can also be seen in Beth Kupin's thorough work .
Unfortunately, visible attention to the problem waned and real life caught up with me as well. I still have one of those "amazing" ideas on a back burner somewhere. It'd be fun to prove that one wrong as well. =P
Anyway, many thanks to Bill for occupying many hours my advisor would have happily dedicated elsewhere. Casual problem solving has always kept me sane during busy times and g17 definitely hit the spot.
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Lev Reyzin8:22 PM, March 17, 2011
This discussion on TCS-SE might be of interest:
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Unknown4:50 AM, March 18, 2011
Hi, I've been working on this for a while, and would like someone to help me verify an observation:
The two 74s that Beth Kupin has identified are indeed permutations of each other. By inserting rows GHIJ before the row C and inserting column 2 before column 1, we end up where we started, but the special symbols are inverted.
If this is the case, and Beth's proof otherwise holds up, the 74 is unique, which means we have the first 74 (or 73) cells of a solution, if one exists.
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Unknown4:52 AM, March 18, 2011
@Emmel: If you could share with us which classes you have ruled out, that would be great!
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John Sidles8:10 AM, March 18, 2011
GASARCH Remarks: "And I doubt there will be general-purpose quantum computers."
Hmmm. It seems to me that the doubts that GASARCH's remark expresses might easily be over-interpreted.
First, from a systems engineering point-of-view, there's no such thing as a "general-purpose computer" because every physical computer (classical or otherwise) ends up being optimized for some-purpose-or-other.
Modern informatic environments have therefore evolved into adaptive "clouds" of linked computing devices, sensors, and actuators ... and this adaptive cloud aspect is strikingly evident even in single, isolated laptop computers.
So its best to keep in mind that there are STEM roadmaps under which many job-creating enterprises, and essentially every campus, will (reasonably soon) deploy many thousands of desktop devices whose state-space is quantum-coherent and strongly entangled.
So yes, under some STEM roadmaps, the global informatic state-space is destined to include very substantial quantum-coherent elements ... perhaps mighty soon.
The broader point about STEM roadmaps is that every robust academic discipline has more than one of them. Evaluated by a multi-roadmap robustness criterion, it's becoming clear that quantum information theory is among the most robust, and has the broadest informatic span, of all STEM disciplines.
In summary, we shouldn't underestimate the capacity of quantum information theory to surprise us ... that's what systems engineers think, anyway.
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Jim Blair8:26 AM, March 18, 2011
With respect to the 17X17 problem, it might be useful to take a look at Minkowski's "Taxicab Geometry".
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Jim Blair9:06 AM, March 18, 2011
To carry things a step further:
Arrange the coordinates of the corners of rectangles in an ordered square: x,y+b,z - x+a,y+b,z
x,y,z - x+a,y,z
Where x and y are normal Cartesian coordinates and z is the color coordinate.
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Tom Hayden11:57 AM, March 18, 2011
I found a great application of this problem: teaching intractability to non-CS kids. I've been using the semi-game found on this site:
I modified it a bit and added a 17x17 grid. I let the kids start solving the smaller grids - they usually do it greedily. Then, by the time they get to the 17x17 grid, they find that the greedy method totally breaks. Then, we can talk about intractability, hardness, and algorithms. It's a really great tool and the students are motivated by the $289.
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JohnPaul Adamovsky8:11 AM, March 19, 2011
I've successfully enumerated every possible perfect 10x10 3-Coloring, using a novel and dazzling algorithm, as a Proof-Of-Concept for solving the 17x17 problem. In response to my proposal, requiring a 24 thread machine, William Gasarch said it was long, so he wasn't interested in reading it.
When my work is long, it can be more accurately described as:
RIGOROUS, EXACT, DETAILED, CONSISTENT, THOROUGH, CONSCIENTIOUS,
METICULOUS, COMPREHENSIVE, PAINSTAKING, RELENTLESS, PROVEN, UNCOMPROMISING, DILIGENT, SYSTEMATIC, DEDICATED, CONVICTION, VIGILANT, METHODICAL, TESTED, DISCIPLINED, ALL THE VERY BEST, PERFECT.
In one word: SCIENTIFIC.
I will now give you a link to the entire email I send to William Gasarch with my proposal, so you can judge for yourself, if the program, I took it upon myself to write for him, is the most powerful algorithm ever coded to solve this class of problem.
My program finds the first perfect coloring is seconds, and enumerates all of them, over night.
Proposal-Email.zip
Explain this:
A Perfect 10x10 3-Coloring -
0|000|111|222|
-?---?---?---?-
0|211|221|020|
0|212|012|101|
0|221|100|211|
-?---?---?---?-
1|012|120|002|
1|022|201|110|
1|101|212|200|
-?---?---?---?-
2|102|001|021|
2|120|102|102|
2|110|020|210|
-?---?---?---?-
Each row-col has a (3, 3, 4) color distribution, but the square as a whole, has the following color spread:
34 0's
34 1's
32 2's
Pick up on this pattern: Of the 2 colors with a 34 count, each (4-count) row intersects with a (4-count) col of the same color.
From the top-left to bottom right, there are 9 enumerated sets, which must be internally rectangle free, and must not rectangle with the static row and column. Further, set 0, 4, and 8 are limited to an in-order "Permutation 0" configuration.
Bottom line, 864 configurations are found using the above template, and 864 = 3^3x2^5, there are many less unique configurations.
You got valid color-swaps, valid column shuffles, valid (4-4 Intersect) flips, and row-col exchange. Testing for uniqueness is not a trivial exercise, so I am leaving for each, his own.
I consider myself something of an Oracle-Machine-Automaton, so I need Gasarch for NOTHING.
I will use the Proof-Of-Concept template to solve the 17x17 problem in my own time, and share the solution with Gasarch, NEVER.
All the very best,
JohnPaul Adamovsky
PS - Gasarch, you have been weighed, you have been measured, and you have been found wanting.
PPS - If you want to know who I am, look me up on Google, you genius. Then READ.
PPPS - You are now playing "THE MANS GAME". Investigate and produce something of value, or finish crumbling.
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Unknown11:34 AM, March 19, 2011
@JohnPaul, will you first admit that your previous proofs of 'impossibility' were wrong? Without that, your self-aggrandisement rings hollow, as you were equally certain of your previous proofs. The SCIENTIFIC way to go about this with dignity is to first retract your previous claims.
Now, the 3-colour 10x10 has approx. 5.1510^47 raw alternatives, and that goes down to 6.510^33 if you remove the obvious symmetries. How is that even indicative of anything when we're talking about a problem of the magnitude of 10^143?
If going through the 3-colour 10x10 takes your algorithm 8 hours on your computer, it will take it 3.9910^110 HOURS to go through the 4-colour 17x17. No amount of extra processing power with current technology will be enough for your algorithm to solve this problem while we're still around to see the result.
You know what, your result on the 3-colour 10x10 is indeed indicative. It indicates that your algorithm is way too slow for this problem. You need to speed it up about 10^100 times to get anywhere. A 24-core machine will get you only 1 or 2 of those orders of magnitude. What do you intend to do for the other 98?
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Anonymous2:00 PM, March 19, 2011
Was the above a misquote of a Bible passage or a correct quote of a 2001 Romance/Drama?
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Anonymous2:16 PM, March 19, 2011
Kamouna might have a new kindred spirit.
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JohnPaul Adamovsky7:49 PM, March 19, 2011
Alexandros Marinos,
It seems like you have a mild case of Down Syndrome. Your Nike's won't help you when you bring them to a "Nuclear Arms Race". You are so completely out of your league in this arena, and the fact that you are ignorant of it, is going to make this no-contest-victory quite unremarkable for me.
When I've just reduced a search space by 10^49, it will make my algorithm that much more powerful than all others before it. When your numbers are based on worthless anecdotes, keep them in your head.
Simulated-Annealing completely ignores a computer's ability to keep records. It is the fat-lazy-slob's algorithm. The Intelligent-Locus-Swarm algorithm, which I published documentation on, will mutilate any kind of record-free approach.
As for my initial impossibility proof: why didn't you bless us with your mediocrity as a form of PEER-REVIEW when it was fresh. Without peer review, there is no SCIENTIFIC-COMMUNITY. A turd stating the obvious about old-work is still very much, a turd.
Now, you will read the entirety of my Proof-Of-Concept documentation, and realize that it finds the first perfect coloring in seconds, running on a single thread. You will also read the text-book-stock documentation of DeepSearch.c, which isolates the 10 best 5x5 Boggle boards for TWL06 over night on a quad-core.
That's who I am, and you're nothing. The instant you decided not to READ my work, is the instant that you showed up DEAD-ON-ARRIVAL.
READ, READ, READ, THINK, THINK, and then write your own program, and we'll compare the performance. I will HUMBLE you, and if that doesn't work, I will PUBLICLY-HUMILIATE you.
You think you're CLEVER, think again, pal.
All the very best,
JohnPaul Adamovsky
PS - I need you for NOTHING.
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JohnPaul Adamovsky12:50 AM, March 20, 2011
When I write a comment, it should really be posted, without having to coerce Gasarch into posting it.
All the very best,
JohnPaul Adamovsky
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Anonymous11:11 AM, March 20, 2011
To speak in the language of JohnPaul, "put up or shut up". "Solving" an already-solved problem and talking big is worthless without something to back up your bravado. If your technique works, prove it. Provide the 17x17. Anything else from you is meaningless posturing.
If you reply to this with insults or bluster or rant-like comments about nuclear arms races, I will simply take that as an acknowledgment that you admit that you have nothing more than hot air to contribute at the moment.
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Unknown12:59 PM, March 20, 2011
Oh boy, this is fun. I didn't need to peer review your previous claims, as our host on this blog did when he told you 10x10 3-colourings exist. What did he get for his kindness? Abuse from you. Same as you did from me when I showed you why your algorithm is too slow. And now you spin on a dime and manage to write a program to produce 10x10 3-colourings. Congratulations. Since you're so good, why don't you send us some real results so we can put on the leaderboard here? ( Oh, I forgot, you have no real results, but you can write walls of text.
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Daniel Apon2:58 PM, March 21, 2011
Alexandros Marinos said:
"Hi, I've been working on this for a while, and would like someone to help me verify an observation:
"The two 74s that Beth Kupin has identified are indeed permutations of each other. By inserting rows GHIJ before the row C and inserting column 2 before column 1, we end up where we started, but the special symbols are inverted.
"If this is the case, and Beth's proof otherwise holds up, the 74 is unique, which means we have the first 74 (or 73) cells of a solution, if one exists."
Alexandros, you are correct! Beth's two 74s are identical under the permutation you describe.
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Bill Broadley3:07 AM, March 22, 2011
This comment has been removed by the author.
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Bill Broadley4:47 AM, March 22, 2011
Seems like one thing hindering the efforts to solve this problem is a way to identify unique family of grids. Where a family is a set of grid that through any rotation, color rotation, or row/column translation that doesn't change the number of (or lack of) single color rectangles. So:
Sorry, not sure how to get a fixed font.
======(swap = (swap =(rot == (rot
======rows) = cols) =colors)= 90 deg)
0 0 1 = 1 3 1 = 3 1 1 = 0 2 2 = 1 1 0
1 3 1 = 0 0 1 = 0 0 1 = 1 1 2 = 2 1 2
1 0 2 = 1 0 2 = 0 1 2 = 1 2 0 = 0 2 2
I propose sort by row, then by column. Hrm, that still leaves mirrors, rotations, and color rotations.
Can anyone think of a way to reduce any grid to a unique grid that represents the family so we can compare equivalent grids?
That way we can avoid burning CPU cycles on grids that have already been used as seeds.
Once we have that people could share databases of the grids they find.
For those who have written solvers. Any estimate on CPU time for 16x16? What language did you use?
From my reading it seems like 16x16 grids are at (barely) feasible to generate. Seems like a few 1000 16x16 would be a particularly nice seeds for the various search algorithms to attempt a 17x17 from. If that's impractical maybe a distributed client could help generate the 16x16s or if necessary 15x15s.
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Dave Bacon6:06 PM, March 22, 2011
"And I doubt there will be general-purpose quantum computers."
Hey man I thought computer scientists were supposed to talk about stuff they could prove. You're starting to sound like a physicist ;)
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Daniel Apon8:29 PM, March 27, 2011
Dave, you're on a complexity blog! -- When you can't prove it, conjecture it and count it good! ;)
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Martin Thoma7:32 AM, April 05, 2011
Does anyone know how many rectangle free sets with more than 72 positions exist? Does a generator for these exist? If you don't know how many of these sets exist, can you give me a upper bound?
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Jim Blair10:01 AM, May 15, 2011
Finally started to make some progress on this one.
This intersection rule has proven useful:
If m is the number of same colored spots on a row on a nXn grid, then the maximum number of spots on the m columns crossing at those spots is m+n-1.
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Jim Blair7:45 AM, May 19, 2011
Back of the envelope calculation for 20X20 Grid:
20X20 Grid = 400 points
400 points divided into 4 color sets = 100 pts./set
100 pts. = 5pts./row
5 pts./row = (5 times 4) divided by 2 = number of ordered intervals/row = 10 intervals/row
10 intervals/row times 20 rows = 200 required intervals
On the other hand:
20 pt. line = (20 times 19) divided by 2 ordered intervals = 190 available intervals
Not enough available intervals.
Changing the distribution doesn’t seem to help:
Changing a 5 pt. row to a 4 pt. row saves 4 intervals – but we then have to create a six pt row which adds 5 intervals.
Same calculation for 18X18 Grid indicates there should be a surplus of 9 available intervals.
But:
The feeling is we may be using up the excess intervals to avoid conflicts and maintain an even distribution between rows and columns of the same color and/or the cumulative effect of adding additional colors.
A curiously difficult problem.
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Jim Blair10:20 AM, June 23, 2011
The intersection rule should have read:
If m is the number of spots colored A on a row on a nXn grid, then the maximum number of spots colored A on the m columns crossing at those spots is m+n-1.
Here is a "potential" choke point for 18X18 grids where the number of spots of each of the four colors is evenly distributed by row:
Color A uses 144 of a possible 153 intervals.
Color B uses 135 intervals used by A and the nine intervals not used by A.
Color C uses 126 intervals used by A and B, 9 intervals not used by A and 9 intervals not used by B.
Color D has to use 126 intervals already used by A, B, and C?
It takes 6X18 or 108 intervals to correctly place 4 spots of one color on each of the 18 rows.
For an even distribution by row, we
need to color an additional 9 spots for each color repeating at least 18 intervals.
It only takes one set of 10 intervals used by all four colors to lock out 14 spots from being correctly colored.
We may have some wiggle room by going to an uneven distribution.
The general idea is that there may be unavoidable sets which are also mutually exclusive.
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Marzio De Biasi6:00 AM, September 09, 2011
Hi,
In your 17x17advice.pdf document ("Some brief thoughts on 17x17") you say:
"... Is there a rectangle free subset of 5x17
which has 5 elements in each column? There is. However, there is only one (up to perms of columns and rows). Here it is:
44444------------
4----4444--------
4--------4444----
-4---4---4---44--
--4---4---4----44
..."
But I found another one that seems not to be "isomorphic":
44444------------
4----4444--------
4--------4444----
-4---4---4---44--
-4----4---4----44
The coloring with four 1,2,3 cells in each row is:
44444312213213231
41111444422333223
43232123344442111
24333411141324422
34223343224111144
And another one with an "empty" column :
44444------------
4----4444--------
4--------4444----
-4---4---4---44--
--4---4---4---44-
44444123313212213
41111444423323322
41233332244442111
34322411141234432
33432243224111441
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GASARCH9:26 AM, September 09, 2011
Great, Thanks.
can you get ALL non-isom proper 4-colorings of 17x5
that have 5 R's in each column? If so this might help
FIND a coloring of 17x17 OR show that NONE exist.
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Marzio De Biasi10:09 AM, September 09, 2011
I think there are too many of them ...
... but I'll start with the easier task of enumerating the non-isom 1-colored rectangle free 17x5 "skeleton" grids containing 5 R's in each column, then eliminate those who don't allow a valid 4-coloring with 4G, 4B, 4Y in each column.
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Marzio De Biasi4:36 AM, September 10, 2011
... there are 66, 17x5 non isom rectangle free "skeleton-grids" having 5 Rs in each row.
All of them allow a valid 4-coloring with 5R,4G,4B,4Y in each row.
Any idea on how to use them ???
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Marzio De Biasi4:58 AM, September 10, 2011
... and there are 84 17x5 rectangle free "skeleton" grids with 5Rs in each row.
All of them allow a valid 4-coloring with 5R, 4G, 4B, 4Y in each row.
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GASARCH9:14 AM, September 10, 2011
1) Are you saying there are 66 NON-ISOM rect free
subsets of 17x5, and 84 TOTAL (including ISOM ones?)
(All of which can be extended to full colorings.)
2) If so then the next thing to do would be to see which of the 84^2 ways to form a rect free
set of 17x10 that have the property are really rect free.
3) Then see which 17x15 are...
4) the remaining 2 rows are easy- try all possibilities.
5) When DONE then you have ALL Rect Free sets of
17x17 that have the property.
6) (This may be the hard step) See which of those
can be extended to a full coloring.
SEE NEXT ITEM for another approach
7) Rather than get all possible RECT FREE SETS
you can try to get all possible COLORINGS-
you say that each of your rect free sets of
17x5 can be extended to a full coloring of
17x5. Can you get ALL colorings?
8) The UPSHOT of all this would HOPEFULLY be
to FIND A COLORING. However, if everything you say is correct and you show that NONE of the
rect free sets of 17x17 that you obtain can be
extended then you will get that 17x17 is
NOT 4-colorable, also worth knowing.
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Marzio De Biasi10:38 AM, September 10, 2011
... some fixes:
A) "66" are the 17x5 rectangle free non-isom "skeletons" i.e. 17x5 rectangle free grids filled only with one color (BUT I found an ERROR in the enumeration routine, so the correct value is greater than 66, but less than 124 ... still working on it)
B) "84" are the 17x4 rectangle free non-isom "skeletons" (but the value is not correct due to the same problem on the enumeration routine ... still working on it)
About your answer:
1) I think that there are much more ISOM variants of the 17x5 "skeletons" (every valid permutation of the columns give one) ... however I'm still interested in checking how many full non-isom coloring can be obtained from a single non isom 17x5 (or 17x4) skeleton.
2) I think that checking what pairs of skeletons (both 17x5 and 17x4) are compatible up to columns swap can be useful, but I think unfeasible (see point 1).
3) there are no valid 17x8 "skeleton" grids with 5Rs in each row.
6) ... I agree with you ... (I tried to solve the 17x17 rectangle free grid filled with 74 REDS without success)
7) ... still working on it (at least I'll try to get all non-isom full coloring extensions) ...
If I make some progress and get the exact count of the non-isom 17x5 skeletons, I'll post a new comment.
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Anonymous2:39 PM, September 12, 2011
That there are NO 17x8 RFS with 5 R per row is VERY INTERESTING- might help to cut down the number of possible
large RFS's of 17x17 there are and hence cut down what to look at.
(OH- This is BILL GASARCH even though it will show up a
anonymous- sorry about that).
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Marzio De Biasi12:03 PM, September 14, 2011
A question regarding the colors count in a 17x17 valid 4-coloring (perhaps I missed the information in the linked papers).
Which of these configurations (if any) have been proved to be impossible?
74 74 71 70
74 73 72 70
74 73 71 71
74 72 72 71
73 73 73 70
73 73 72 71
73 72 72 72
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GASARCH12:16 PM, September 14, 2011
I do not understand your notation, however, no
configs have been ruled out. I am sure that some
could be easily- with the help of a program.
It might be more efficient to email me directly and
have me email you directly if you have more thoughts-
my email is gasarch@cs.umd.edu but I don't know yours.
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Unknown5:26 AM, October 02, 2011
Marzio - We know from Beth Kupin's work that all 73's can be extended to 74's, so you can reduce your scope.
eg:
a 73-72-72-72 can always be turned to a 74-72-72-71.
a 73-73-73-70 can become either a 74-73-72-70 or a 74-73-73-69.
This may or may not help depending what you want to do with the configurations
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Marzio De Biasi4:54 AM, October 12, 2011
@Alexandros: thanks.
Using a SAT solver I noticed an odd property.
1) find a 2-coloring of a 16x16 grid that has no 3x3 monochromatic rectangle;
2) pick this grid as the high-bits of the 4-coloring of a 16x16 grid, and run the solver;
If an entry in the 2-colored grid is 0 then the corresponding entry in the 4-coloring must be 0 or 1; if an entry in the 2-colored grid is 1 then the corresponding entry in the 4-coloring must be 2 or 3.
3) the SAT solver quickly (2 secs) finds a valid 4-coloring of the 16x16 grid ... and a 4-coloring of a 17x16 grid (the added row is without constraint on the high bits)
... obviously the solver hangs if I add another colunm (17x17).
We know from Ramsey theory that there is no 17x17 2-colored grid without monochromatic 3x3 rectangles.
So a possible way to prove that no 17x17 4-colored and rectangle free grid exists, is by contraddiction: find a constructive method to build a 17x17 2-colored grid without 3x3 monochromatic rectangles starting from the 4-colored one (without 2x2 monochromatic rectangle).
Alas I'm not an expert of Ramsey theory ... hoping that someone else solves this nightmare!
(P.S. obviously I think that there is no valid 4-coloring :-))))
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Marzio De Biasi4:21 PM, October 19, 2011
... waiting (in vain) for the SAT solver I made an "artistic" grid with 74 zeroes: ... it belongs to a new artistic movement called "the 17x17 art" :-)
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Marzio De Biasi9:19 AM, October 20, 2011
... and another highly symmetric 74s ....
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Anonymous4:04 AM, November 14, 2011
I've been counting the total number of unique solutions for arbitrary nxm grids here:
Unfortunately 5x5 has eluded me so far, due to lack of RAM. :)
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Marzio De Biasi5:36 AM, December 04, 2011
Ongda: suppose you have an enumeration of non isom 17x5 skeleton grids containing 5 Rs in each column + an unique 74 skeleton grid that - as proved by Beth - can be used as valid starting grid. Have you any idea on how to merge the 17x5 skeleton grids in the 74 one?
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Anonymous10:48 AM, December 04, 2011
Ongda appears to be a spambot, as the text is copied from an earlier comment by Marzio. :)
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Lance Fortnow10:51 AM, December 04, 2011
Thanks for the catch Esaj, I removed Ongda's post. These spambots are getting clever.
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Unknown12:39 AM, December 21, 2011
Here are some more 4-colourings of 17×17 with 3 rectangles. These are different from Alexandros’ grid (see I fixed the first 3 rows from Rohan Puttagunta’s solution and used a version of simulated annealing for the remaining rows.
11111222233334444
12222233334444111
13333244431114222
41234313223141243
42143342321321421
21234142342413312
24321124143143421
32134424112312234
14344211132224333
23414231424132413
31442324131423142
34321441324211142
22143113244233134
31243431413242321
43412412343214231
13412143212341324
44321312411432314
11111222233334444
12222233334444111
13333244431114222
43241321323241431
24123124312341342
31432112442342134
34123342124123124
33241143141422342
21432443113213421
44123413241232231
42314313422311243
22314134244123431
14444211132224333
41432334221431312
23241412414133213
24113231423412413
32314421311432124
Just for fun, here is a solution with 4 rectangles that is composed from 16 4×4 Latin squares. It turns out that solutions of this form are quite easy to find. Looks like JohnPaul Adamovsky was right after all, maybe he is a genius. See his 10th of July 2010 post:
4312|1342|2143|2413|1
2134|2134|3421|1324|1
3421|4213|4312|3241|1
1243|3421|1234|4132|1
———————
1243|1342|4312|1324|2
3421|2134|1234|2413|2
4312|3421|3421|3241|2
2134|4213|2143|4132|2
———————
1243|2134|2143|3241|3
4312|4213|1234|1324|3
2134|3421|4312|2413|3
3421|1342|3421|4132|3
———————
1243|4213|3421|2413|4
4312|2134|4312|4132|4
3421|3421|2143|1324|4
2134|1342|1234|3241|4
———————
4444|2222|1111|3333|1
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Marzio De Biasi11:08 AM, December 23, 2011
I never saw a 74R+74G rectangle free skeleton, so I post one just for curiosity.
I found many of them, but all cannot be expanded to a valid 4-coloring (rejected by SAT solver).
12-2-21111--2--2-
21-2--1--211-2-12
-21---12---2111-2
2--12--1--12-1-21
2---1-221--12-1-1
222--1---12-1--11
11122-2---2-----1
1--1-22--2-2--11-
12--1-2-2-1-12---
1---21--2--121--2
-12122-21---12---
-12-1-2--1---1222
-21-21--121---2--
2-11-2--21-1--2--
--1-1--1--222221-
-122-1-12--2--1--
---11112222----2-
Merry Christmas Everybody!
ReplyDelete Replies
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Anonymous5:31 AM, January 02, 2012
The above Unknown poster (December 21st, 2011) is Dmitry Kamenetsky.
Marzio, I have found some 74R+74G rectangle-free skeletons earlier in
Cheers,
Dmitry
ReplyDelete Replies
Reply
Marzio De Biasi2:23 AM, January 09, 2012
@Dmitry: Ok, I didn't see them! (I checked them but none can be expanded to a valid 4-coloring) :-(
ReplyDelete Replies
Reply
GASARCH7:19 AM, February 08, 2012
THE PROBLEM HAS BEEN SOLVED! There is a 4-coloring of 17x17 and
even if 18x18. See my Feb 8, 2012 post.
ReplyDelete Replies
Reply
GASARCH7:20 AM, February 08, 2012
THE PROBLEM HAS BEEN SOLVED! There is a 4-coloring of 17x17 and
even of 18x18. See my Feb 8, 2012 post.
ReplyDelete Replies
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13469 | https://pubmed.ncbi.nlm.nih.gov/39111847/ | Levonorgestrel intrauterine system versus dienogest effect on quality of life of women with deep endometriosis: a randomized open-label clinical trial - PubMed
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. 2024 Aug;64(7):551-558.
doi: 10.1080/03630242.2024.2382418. Epub 2024 Aug 7.
Levonorgestrel intrauterine system versus dienogest effect on quality of life of women with deep endometriosis: a randomized open-label clinical trial
Beatriz Taliberti da Costa Porto1,Paulo Ayroza Ribeiro1,Fábio Kuteken1,Fábio Ohara1,Helizabet Salomão Abdalla Ribeiro1
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1 Gynecological Endoscopy and Endometriosis Division Clinic, Santa Casa de Misericórdia do Brasil, São Paulo, Brasil.
PMID: 39111847
DOI: 10.1080/03630242.2024.2382418
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Randomized Controlled Trial
Levonorgestrel intrauterine system versus dienogest effect on quality of life of women with deep endometriosis: a randomized open-label clinical trial
Beatriz Taliberti da Costa Porto et al. Women Health.2024 Aug.
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. 2024 Aug;64(7):551-558.
doi: 10.1080/03630242.2024.2382418. Epub 2024 Aug 7.
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Beatriz Taliberti da Costa Porto1,Paulo Ayroza Ribeiro1,Fábio Kuteken1,Fábio Ohara1,Helizabet Salomão Abdalla Ribeiro1
Affiliation
1 Gynecological Endoscopy and Endometriosis Division Clinic, Santa Casa de Misericórdia do Brasil, São Paulo, Brasil.
PMID: 39111847
DOI: 10.1080/03630242.2024.2382418
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Women with deep infiltrating endometriosis (DIE) can benefit from the use of progestins. Our aim is to explore if levonorgestrel-releasing intrauterine system (LNG-IUS) non inferior to dienogest (DNG) in improving deep endometriosis women's quality of life (QoL). This randomized open-label clinical trial included forty women with DIE assessed using clinical history and physical examination, transvaginal ultrasonography and magnetic resonance of the pelvis without any previous surgical treatment, with two treatments arms. The two groups underwent a 3-month washout of hormonal treatments, and then received either DNG or LNG-IUS for 6 months. QoL was assessed prior to and 6 months after the intervention, using the SF36 and the EHP30. DNG and LNG-IUS showed an increase on all domains of the SF36 (p< .001). There was no difference between treatments on the improvement observed (p> .05 for all domains). DNG and LNG-IUS, also, showed improvement on all domains of EHP30 (p< .001), except "relationship with children" and "feelings about pregnancy." However, there was no statistical difference between treatments for all sections scores (p> .05). The treatment of deep endometriosis symptoms using either DNG or LNG-IUS in women with no prior surgical treatment is associated with improvement in QoL.Trial Registration Number: This trial is registered on "The Brazilian Registry of Clinical Trials (ReBECID: RBR-8fjx2jp)," that is part of Primary Registries in the WHO Registry Network, under the title: "Dienogest versus Levonorgestrel IUS on deep endometriosis patient´s QoL without surgery" on June 14, 2021;
Keywords: Chronic pain; disease impact profile; menstrual diseases; pharmacological treatment.
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January 2015 - Volume 94 - Issue 1
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Outline
INTRODUCTION
MATERIAL AND METHODS
Specimens and Study Groups
Instrumentation and Testing
Data Acquisition and Analysis
RESULTS
DISCUSSION
CONCLUSION
ACKNOWLEDGMENTS
REFERENCES
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Article: Clinical Trial/Experimental Study
Biomechanical Evaluation of Interfragmentary Compression At Tibia Plateau Fractures In Vitro Using Different Fixation Techniques
A CONSORT-compliant article
Kojima, K. MD; Gueorguiev, B. PhD; Seva, G. MD; Stoffel, K. MD, PhD; de Oliveira, R. Garcia MD; Eberli, U. MSc; Nicolino, T. MD; Lenz, M. MD
Editor(s): Gaines., Robert
Author Information
From the Department of Orthopaedics and Traumatology, Faculty of Medicine, University of Sao Paulo, Brazil (KK, GS, GdO); AO Research Institute, Davos, Switzerland (BG, GS, UE, TN, ML); University of Basel, Cantonal Hospital Baselland, Liestal, Switzerland (KS); Department of Orthopaedics and Traumatology, Italian Hospital of Buenos Aires, Argentina (TN); and Department of Trauma, Hand and Reconstructive Surgery, University Hospital Jena, Germany (ML).
Correspondence: Mark Lenz, AO Research Institute Davos, Clavadelerstrasse 8, 7270 Davos Platz, Switzerland (e-mail: mark.lenz@med.uni-jena.de).
K. Kojima and B. Gueorguiev contributed equally to this article.
Abbreviations: ANOVA = One-way Analysis of Variance, LCP = Locking Compression Plate, MPa = MegaPascal, TAN = Titanium Aluminum Niobium.
This is an open access article distributed under the Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0, where it is permissible to download, share and reproduce the work in any medium, provided it is properly cited. The work cannot be changed in any way or used commercially.
Received September 17, 2014
Received in revised form October 13, 2014
Accepted October 26, 2014
Medicine 94(1):p e282, January 2015. | DOI: 10.1097/MD.0000000000000282
Open
Abstract
Reliable osteosynthesis of intraarticular fractures depends on lasting interfragmentary compression. Its amount differs in the applied fixation method. The interfragmentary compression of cancellous and cortical lag screws and angle stable locking plates was quantified in an osteoporotic and non-osteoporotic synthetic human bone model.
A split fracture of the lateral tibia plateau (AO/OTA type 41-B1.1) was mimicked by an osteotomy in right adult synthetic human tibiae with hard or soft cancellous bone. Specimens were fixed with either two 6.5 mm cancellous, four 3.5 mm cortical lag screws, or 3.5 mm LCP proximal lateral tibia plate preliminary compresed by a reduction clamp (n = 5 per group). A pressure sensor film was used to register the interfragmentary compression. One-way analysis of variance (ANOVA) with Bonferroni post hoc correction was performed for statistical analysis (p < 0.05).
Interfragmentary compression under reduction clamp was 0.59 ± 0.12 MPa in the non-osteoporotic and 0.55 ± 0.14 MPa in the osteoporotic group. The locking plate itself maintained the compression in non-osteoporotic (0.53 ± 0.11 MPa) and osteoporotic bone (0.50 ± 0.14 MPa). Four 3.5 mm cortical lag screws provided a compression of 1.69 ± 0.65 MPa in non-osteoporotic bone, being not significantly different to the osteoporotic bone group (1.43 ± 0.47 MPa, P = 1.0). Two 6.5 mm cancellous lag screws showed a significantly higher compression in non-osteoporotic (2.1 ± 0.59 MPa) compared to osteoporotic (0.77 ± 0.21 MPa, P< 0.01) bone.
Angle stable locking plates maintained the compression preliminarily applied by a reduction clamp. Two 6.5 mm cancellous lag screws are especially suited for non-osteoporotic bone, whereas four 3.5 mm cortical screws exhibited comparable compression in both bone qualities.
INTRODUCTION
Proximal tibia fractures comprise about 1.2% of all fractures.1 One of the most common fracture pattern is a simple lateral split (AO/OTA type 41-B1.1, Schatzker type I).2,3This type of fracture usually occurs in two different groups: Young patients after high-energy trauma or elderly osteopenic patients after low-energy injuries. In the latter, a depression component is often associated.4 The main trauma mechanism in this fracture type is pure abduction force or valgus combined with axial load.5 Soft tissue injury, bone quality, patient's age, redisplacement, and posttraumatic arthritis are important factors influencing the outcome of proximal tibia fractures.2,4,6–11 During the last decades, the treatment shifted from predominantly conservative with unsatisfactory results to a more operative one. Most authors advocate reduction and internal fixation in case of an articular step of 2 to 3 mm and above, an instability of more than 5 to 10° in full extension2,12,13 and to prevent tibia plateau widening during fracture consolidation.
In these injuries, a functional aftercare including early joint motion13–15 is well established. Internal fixation techniques are required to endure rehabilitation. Koval et al16 and Parker et al17 published biomechanical studies supporting the use of solely two 6.5 mm cancellous screws in lateral split fractures. Current fixation techniques of lateral tibia plateau fractures include 6.5 mm cancellous lag screws, 3.5 or 4.5 mm cortical lag screws, both with optional antiglide plate or L and T-shaped angle stable locking compression plates (LCP). Some of these methods can be performed either in an open or percutaneous fashion.18,19 To achieve interfragmentary compression with the use of a locking plate, an additional lag screw has to be applied before plate fixation or the plate has to be fixed and compressed to the reduced fracture by a reduction clamp prior to locking screw insertion.
The aim of this study was to investigate the interfragmentary compression of 3 different fixation techniques for lateral tibia plateau split fracture fixation, using 3.5 mm cortical lag screws, 6.5 mm cancellous lag screws, and 3.5 mm LCP proximal lateral tibia plate preliminary compressed by a reduction clamp. The interfragmentary compression was measured in 2 surrogate bone models, simulating osteoporotic and non-osteoporotic bone quality.
MATERIAL AND METHODS
Specimens and Study Groups
Thirty right adult synthetic human tibiae with cortical and cancellous bone structure (Synbone, Malans, Switzerland) were used in this study. Each specimen provided hard or soft cancellous bone to mimic non-osteoporotic and osteoporotic bone quality, respectively. It has been shown in previous studies, that synthetic human tibiae are a valid substitute for human bones.20,21 The surrogate tibiae were randomly assigned into 6 groups in total, consisting of 3 groups with non-osteoporotic bone quality and 3 groups with osteoporotic bone quality. Each group comprised 5 specimens (n = 5). Three different fixation techniques were investigated using implants made of TiAl6N7 (TAN) alloy (Synthes GmbH, Solothurn Switzerland): Two 6.5 mm cancellous screws (length 60 mm, thread length 16 mm); four 3.5 mm cortex screws (length 65 mm) and right lateral 3.5 mm LCP proximal tibia plate (4 holes, length 81 mm, Synthes, Solothurn Switzerland), fixed proximally with four 3.5 mm self-tapping locking screws (length 56 mm) (Figure 1). All 3 fixation techniques were investigated in surrogate non-osteoporotic and osteoporotic bone.
FIGURE 1:
Instrumented specimens: Two 6.5 mm cancellous lag screws with washers (left), four 3.5 mm cortical lag screws (middle) and 3.5 mm LCP proximal lateral tibia plate (right).
Instrumentation and Testing
An-osteotomy on the lateral tibia plateau was set, representing a simple split fracture of the lateral tibia plateau (AO/OTA type 41-B1.1, Schatzker type I). The osteotomy was oriented in the sagittal plane orthogonal to the tibia plateau plane, 17 mm medial from the lateral edge of the tibia plateau, created by a 1 mm saw blade.
The drill holes were set according to the distance of the plate head locking holes of the 3.5 mm LCP proximal tibia plate to provide a standardized and comparable orientation of the holes between the groups. The LCP proximal tibia plate was placed on the lateral aspect of the tibia head with the locking-head screw holes located in the subcortical area of the tibia plateau. The proximal edge of the plate was oriented in parallel to the joint line so that the locking holes were located 7.5 mm below the tibia plateau surface. The four holes for 3.5 mm cortical lag screw instrumentation were drilled in the same position as the locking holes in the plate head with a Ø2.5 mm drill bit, oriented in parallel to the dorsal edge of the tibia plateau. The lateral fragment was overdrilled with a Ø3.5 mm drill bit to set a gliding hole for lag screw application. Due to a limited space between the screw heads, application of washers was not possible for this fixation technique. The two 6.5 mm cancellous screws were set at the position of the most anterior and posterior hole of the locking plate head and oriented in parallel to the dorsal edge of the tibia plateau. The holes were predrilled with a Ø3.5 mm drill bit. Each screw was equipped with a washer (Synthes GmbH, Solothurn, Switzerland). Prior to screw tightening, a pressure sensor film (Model 5033, TekScan Inc., South Boston, MA), protected by two rubber pads of 1 mm thickness on each side, was introduced in the osteotomy gap from the articular side to determine the amount of interfragmentary compression at the osteotomy gap at the level of the tibia plateau (Figure 2).
FIGURE 2:
Test setup. Specimen instrumented with a pressure sensor film in the osteotomy gap and four 3.5 mm cortical lag screws. Two rubber pads of 1 mm thickness were applied at each side of the sensor for a better transmission of the pressure to the sensor film and smoothening of the pressure peaks due to minimal local mismatch at the osteotomy.
For instrumentation of the LCP, two Kirschner wires were used to preliminarily fix the plate in the position mentioned above and Ø2.8 mm drill holes were set via a Ø2.8 mm drill guide in the 4 plate head locking holes according to the manufacturer's guidelines. After removal of the Kirschner wires, the sensor film and the rubber pads were installed as mentioned above. The plate was fixed to the reduced fracture by a clamp with the sensor film in place and the interfragmentary compression effected by the clamp was registered. After instrumentation of the 4 locking screws at the plate head, the clamp was removed and the compression force at the fracture site was measured again.
Data Acquisition and Analysis
Pressure was recorded along the articular osteotomy gap and mean pressure of each sample was calculated. Statistical analysis was performed using SPSS software package (SPSS 20.0.0; SPSS, Chicago, IL). Normal distribution of the data within each study group was indicated by the Shapiro–Wilk Test. Significant differences between the study groups regarding mean pressure at the fracture site were tested statistically with one-way Analysis of Variance (ANOVA) and Bonferroni post hoc test. Significance level was set at P = 0.05.
Since no human material and no patient-related data were used, ethical approval was not necessary.
RESULTS
Mean pressure values in each study group are shown in Figure 3. Both lag screw techniques, 2 cancellous screws (2.12 MPa SD ±0.59) and 4 cortical screws (1.69 MPa SD ± 0.65) exhibited a comparable interfragmentary compression in non-osteoporotic bone (P = 1.00). Interfragmentary compression in osteoporotic bone was not significantly different using 4 cortical lag screws 1.42 MPa (SD ± 0.46) or 2 cancellous screws 0.77 MPa (SD ± 0.21) (P = 0.32). Comparing the 4 cortical lag screw fixation in non-osteoporotic and osteoporotic bone, the amount of interfragmentary compression was similar in both groups (P = 1.00). Two cancellous screws exhibited a significantly higher compression in non-osteoporotic bone compared to osteoporotic bone (P< 0.01). A significantly lower interfragmentary compression was achieved when the plate was fixed by a reduction clamp in comparison to both lag screw techniques in non-osteoporotic bone (P< 0.01) and in comparison to 4 cortical lag screws in osteoporotic bone (P = 0.03). The locking plate, instrumented under compression was able to maintain the interfragmentary compression, applied during preliminary fixation by the reduction clamp in both, non-osteoporotic and osteoporotic bone. The mean pressure was 0.60 MPa (SD ± 0.11) under preliminary clamp fixation and 0.53 MPa (SD ± 0.10) after plate fixation (P = 0.4) in non-osteoporotic bone. In osteoporotic bone the mean pressure under preliminary clamp fixation was 0.55MPa (SD ± 0.14) and 0.50MPa (SD ± 0.14) after plate fixation (P = 0.6).
FIGURE 3:
Mean interfragmentary compression of two 6.5 mm cancellous lag screws (2sc), four 3.5 mm cortical lag screws (4sc), and 3.5 mm LCP lateral proximal tibia locking plate (pl) investigated in non-osteoporotic (no) and osteoporotic (o) surrogate bone. The interfragmentary compression in the plate group was determined after preliminary fixation of the plate to the reduced fracture by a reduction clamp (clamp) and subsequent definite plate fixation and clamp removal (fixed). The columns and error bars indicate mean pressure (MPa) with standard deviation in each study group, consisting of 5 specimens (n = 5). Mean pressure values between the study groups fixed with two 6.5 mm cancellous screws in osteoporotic and non-osteoporotic bone were significantly different. Mean pressure values in all plate groups under clamping and after definite plate instrumentation and clamp removal were not significantly different. The mean pressure values between the groups with 4 cortical screw fixation in osteoporotic and non-osteoporotic bone were not significantly different.
DISCUSSION
Lasting interfragmentary compression can be achieved by lag screw techniques and locking plates, preliminarily compressed by a reduction clamp. Interfragmentary compression with two 6.5 mm cancellous screws was in a comparable range to four 3.5 mm cortical screws. The choice between these 2 options would depend on the fracture pattern: For osteosynthesis of a simple split fracture of the lateral tibia plateau, two 6.5 mm cancellous screws would be sufficient. In split fractures with additional central depression fragment, four 3.5 mm cortical screws would be more appropriate as demonstrated by Karunakar et al,22 who observed a significantly lower local depression stiffness in this fracture type, fixed with two 6.5 mm cancellous screws compared to four 3.5 mm cortical screws. An antiglide plate placed at the inferior edge of the fracture secures the fracture fragment from inferior dislocation.22 The same effect can be achieved using a buttress plate.22 Using an osteoporotic bone foam model with a split depression fracture, Patil et al23 observed a significantly higher force required to produce a depression in the four 3.5 mm cortical screw construct than in the two 6.5 mm cancellous screw construct. In the non-osteoporotic bone foam model, difference in force required to produce a depression was not significant in-between the two constructs, indicating that the two cancellous screw technique would be better suited for non-osteoporotic bones. Comparing the two 6.5 mm cancellous screw fixation placed orthogonally to the fracture in a posterolateral coronal shear fracture model of the tibia plateau to a laterally placed 3.5 mm LCP proximal tibia plate, a smaller displacement under axial load was observed in the plate group, although the plate was not ideally placed for this fracture type.21 Best stability was obtained by a posteriorly placed buttress plate in this study.21 Mueller et al24 reported no significant difference between two dual plating constructs and a lateral fixed angle plate construct in terms of stiffness, maximum load to failure, and medial condylar displacement. Consistent with our results, pullout force of subchondrally placed screws of 6.5 and 3.5 mm diameter, did not differ significantly in a human tibia model.25
Although locking plates function via the principle of angular stability, holding the tibia plateau comparable to a ceiling beam, preliminarily applied compression after proper reduction is advisable for sufficient fracture fixation. The lateral 3.5 mm proximal tibia locking plate construct maintained the compression preliminarily applied by the Weber clamp in non-osteoporotic and osteoporotic bone. Even though a lesser amount of compression was achieved by the Weber clamp compared to both screw constructs, persisting compression combined with good interdigitation of the fracture fragments would prevent loss of reduction.
This study has some limitations: It is a bench study. The ability of each construct to maintain the fracture reduction under physiologic motion of the knee joint was not evaluated. Construct stability after postoperative knee joint motion could not be judged on.
CONCLUSION
Two 6.5 mm cancellous screws should only be used in non-osteoporotic bone, since interfragmentary compression was significantly lower for these screws in osteoporotic bone. Four 3.5 mm cortical screws could be applied in both bone qualities, because interfragmentary compression was comparable in osteoporotic and non-osteoporotic bone.
The success of any internal fixation depends on the ability to maintain interfragmentary compression. Locked implants like the locking compression plate maintain the interfragmentary compression preliminarily applied by a reduction clamp.
ACKNOWLEDGMENTS
The authors are not compensated and there are no other institutional subsidies, corporate affiliations, or funding sources supporting this work unless clearly documented and disclosed. This investigation was performed with the assistance of the AO Foundation via the AOTRAUMA Network (Grant no. AR 2012_11).
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Parker PJ, Tepper KB, Brumback RJ, et al. Biomechanical comparison of fixation of type-I fractures of the lateral tibial plateau. Is the antiglide screw effective? J Bone Joint Surg Br 1999; 81:478–480.
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Keogh P, Kelly C, Cashman WF, et al. Percutaneous screw fixation of tibial plateau fractures. Injury 1992; 23:387–389.
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Sirkin MS, Bono CM, Reilly MC, et al. Percutaneous methods of tibial plateau fixation. Clin Orthop Relat Res 2000; 60–68.
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Ali AM, Saleh M, Bolongaro S, et al. Experimental model of tibial plateau fracture for biomechanical testing. J Biomech 2006; 39:1355–1360.
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Zhang W, Luo CF, Putnis S, et al. Biomechanical analysis of four different fixations for the posterolateral shearing tibial plateau fracture. Knee 2012; 19:94–98.
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Karunakar MA, Egol KA, Peindl R, et al. Split depression tibial plateau fractures: a biomechanical study. J Orthop Trauma 2002; 16:172–177.
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Patil S, Mahon A, Green S, et al. A biomechanical study comparing a raft of 3.5 mm cortical screws with 6.5 mm cancellous screws in depressed tibial plateau fractures. Knee 2006; 13:231–235.
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Mueller KL, Karunakar MA, Frankenburg EP, et al. Bicondylar tibial plateau fractures: a biomechanical study. Clin Orthop Relat Res 2003; 189–195.
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Westmoreland GL, McLaurin TM, Hutton WC. Screw pullout strength: a biomechanical comparison of large-fragment and small-fragment fixation in the tibial plateau. J Orthop Trauma 2002; 16:178–181.
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Biomechanical Evaluation of Interfragmentary Compression At Tibia Plateau Fractures In Vitro Using Different Fixation Techniques: A CONSORT-compliant article
Medicine94(1):e282, January 2015.
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13471 | https://ericrowland.github.io/investigations/modulararithmetic.html | Modular arithmetic is quite a useful tool in number theory. In particular, it can be used to obtain information about the solutions (or lack thereof) of a specific equation. This page gives a fairly detailed introduction. Another good introduction, in the form of an interactive tutorial, can be found in Part 2 of Math Alive: Cryptography.
Contents
I. An Introductory Example
II. Definition and Further Examples
III. Properties of Congruence
IV. Exercises
I. An Introductory Example
Everyone knows that set of integers can be broken up into the following two classes:
the even numbers (..., –6, –4, –2, 0, 2, 4, 6,...); and
the odd numbers (..., –5, –3, –1, 1, 3, 5,...).
There are certain generalizations we can make about the arithmetic of numbers based on which of these two classes they come from. For example, we know that the sum of two even numbers is even. The sum of an even number and an odd number is odd. The sum of two odd numbers is even. The product of two even numbers is even, etc.
Modular arithmetic lets us state these results quite precisely, and it also provides a convenient language for similar but slightly more complex statements. In the above example, our _modulus_ is the number 2. The modulus can be thought of as the number of classes that we have broken the integers up into. It is also the difference between any two "consecutive" numbers in a given class.
Now we represent each of our two classes by a single symbol. We let the symbol "0" mean "the class of all even numbers" and the symbol "1" mean "the class of all odd numbers". There is no great reason why we have chosen the symbols 0 and 1; we could have chosen 2 and 1, or –32 and 177, but 0 and 1 are the conventional choices.
The statement "the sum of two even numbers is even" can be expressed by the following:
0 + 0 ≡ 0 mod 2.
Here, the "≡" symbol is not equality but _congruence_, and the "mod 2" just signifies that our modulus is 2. The above statement is read "Zero plus zero is congruent to zero, modulo two." The statement "the sum of an even number and an odd number is odd" is represented by
0 + 1 ≡ 1 mod 2.
Those examples are natural enough. But how do we write "the sum of two odd numbers is even"? It is the (at first strange looking) expression
1 + 1 ≡ 0 mod 2.
Here the symbols "≡" and "mod 2" are suddenly very important! We have analogous statements for multiplication:
0 × 0 ≡ 0 mod 2,
0 × 1 ≡ 0 mod 2,
1 × 1 ≡ 1 mod 2.
In a sense, we have created a number system with addition and multiplication but in which the only numbers that exist are 0 and 1. You may ask what use this has. Well, our number system is the system of _integers modulo 2_, and because of the previous six properties, any arithmetic done in the integers translates to arithmetic done in the integers modulo 2. This means that if we take any equality involving addition and multiplication of integers, say
12 × 43 + 65 × 78 = 5586,
then reducing each integer _modulo 2_ (i.e. replacing each integer by its class "representative" 0 or 1), then we will obtain a valid congruence. The above example reduces to
0 × 1 + 1 × 0 ≡ 0 mod 2,
or 0 + 0 ≡ 0 mod 2.
More useful applications of reduction modulo 2 are found in solving equations. Suppose we want to know which integers might solve the equation
3 _a_ – 3 = 12.
Of course, we could solve for _a_, but if we didn't need to know what _a_ is exactly and only cared about, say, whether it was even or odd, we could do the following. Reducing modulo 2 gives the congruence
1 _a_ + 1 ≡ 0 mod 2,
or
_a_ ≡ –1 ≡ 1 mod 2,
so any integer _a_ satisfying the equation 3 _a_ – 3 = 12 must be odd.
Since any integer solution of an equation reduces to a solution modulo 2, it follows that if there is no solution modulo 2, then there is no solution in integers. For example, assume that _a_ is an integer solution to
2 _a_ – 3 = 12,
which reduces to
0 · _a_ + 1 ≡ 0 mod 2,
or 1 ≡ 0 mod 2. This is a contradiction because 0 and 1 are different numbers modulo 2 (no even number is an odd number, and vice versa). Therefore the above congruence has no solution, so _a_ couldn't have been an integer. This proves that the equation 2 _a_ – 3 = 12 has no integer solution.
Less trivially, consider the system of equations
6 _a_ – 5 _b_ = 4,
2 _a_ + 3 _b_ = 3.
Modulo 2, these equations reduce to
0 + 1 _b_ ≡ 0 mod 2,
0 + 1 _b_ ≡ 1 mod 2.
This says that _b_ is both even and odd, which is a contradiction. Therefore we know that the original system of equations has no integer solutions, and to prove this we didn't even need to know anything about _a_.
As shown by the preceding examples, one of the powers of modular arithmetic is the ability to show, often very simply, that certain equations and systems of equations have no integer solutions. Without modular arithmetic, we would have to find all of the solutions and then see if any turned out to be integers.
II. Definition and Further Examples
Of course, there is nothing special about the number 2. Any integer (except 0) will work for the modulus _m_. We now give the mathematical definition of congruence.
Definition. Let _m_ ≠ 0 be an integer. We say that two integers _a_ and _b_ are _congruent modulo m_ if there is an integer _k_ such that _a_ – _b_ = _km_, and in this case we write
_a_ ≡ _b_ mod _m_.
Notice that the condition "_a_ – _b_ = _km_ for some integer _k_" is equivalent to the condition "_m_ divides _a_ – _b_".
In the previous section we used the modulus _m_ = 2. Although we wrote congruences using only 0 and 1, really any integers are valid. Modulo 2, all of the even numbers are congruent to each other since the difference of any two even numbers is divisible by 2:
... ≡ –6 ≡ –4 ≡ –2 ≡ 0 ≡ 2 ≡ 4 ≡ 6 ≡ ... mod 2.
Also, every odd number is congruent to every other odd number modulo 2 since the difference of any two odd numbers is even:
... ≡ –5 ≡ –3 ≡ –1 ≡ 1 ≡ 3 ≡ 5 ≡ ... mod 2.
Therefore, anywhere we wrote "0" we could have written any other even number, and similarly "1" could have been replaced by any odd number. For example, instead of writing 0 × 1 + 1 × 0 ≡ 0 mod 2, an equally valid statement would have been
10 × (–13) + 27 × 6 ≡ –122 mod 2.
Let's now look at other values for the modulus _m_. For example, let _m_ = 3. All multiples of 3 are congruent to each other modulo 3 since the difference of any two is divisible by 3. Similarly, all numbers of the form 3 _n_ + 1 are congruent to each other, and all numbers of the form 3 _n_ + 2 are congruent to each other.
... ≡ –9 ≡ –6 ≡ –3 ≡ 0 ≡ 3 ≡ 6 ≡ 9 ≡ ... mod 3.
... ≡ –8 ≡ –5 ≡ –2 ≡ 1 ≡ 4 ≡ 7 ≡ ... mod 3.
... ≡ –7 ≡ –4 ≡ –1 ≡ 2 ≡ 5 ≡ 8 ≡ ... mod 3.
How about when _m_ = 1? The difference of _any_ two integers is divisible by 1, so all integers are congruent to each other modulo 1:
... ≡ –3 ≡ –2 ≡ –1 ≡ 0 ≡ 1 ≡ 2 ≡ 3 ≡ ... mod 1.
For this reason, _m_ = 1 is not very interesting, and reducing an equation modulo 1 doesn't give any information about its solutions.
The modulus _m_ = 12 comes up quite frequently in everyday life, and its application illustrates a good way to think about modular arithmetic — the "clock arithmetic" analogy. If it's 7:00, what time will it be in 25 hours? Since 25 ≡ 1 mod 12, we simply add 1 to 7:
7 + 25 ≡ 7 + 1 ≡ 8 mod 12.
So the clock will read 8:00. Of course, we don't need the formality of modular arithmetic in order to compute this, but when we do this kind of computation in our heads, this is really what we are doing.
With _m_ = 12, there are only 12 numbers ("hours") we ever need to think about. We count them 1, 2, 3, ..., 10, 11, 12, 1, 2, ... , starting over after 12. The numbers 1, 2, ..., 12 represent the twelve equivalence classes modulo 12: Every integer is congruent to exactly one of the numbers 1, 2, ..., 12, just as the hour on the clock always reads exactly one of 1, 2, ..., 12. These classes are given by
12 _n_ + 1, 12 _n_ + 2, 12 _n_ + 3, ..., 12 _n_ + 11, 12 _n_
as _n_ ranges over the integers.
Of course, the minutes and seconds on a clock are also modular. In these cases the modulus is _m_ = 60. If we think of the days of the week as labeled by the numbers 0, 1, 2, 3, 4, 5, 6, then the modulus is _m_ = 7. The point is that we measure many things, both in mathematics and in real life, in periodicity, and this can usually be thought of as an application of modular arithmetic.
III. Properties of Congruence
It is fairly easy to show that for any integers _a_, _b_, _c_, and _m_ ≠ 0, the following properties hold:
reflexivity: _a_ ≡ _a_ mod _m_.
symmetry: If _a_ ≡ _b_ mod _m_, then _b_ ≡ _a_ mod _m_.
transitivity: If _a_ ≡ _b_ mod _m_ and _b_ ≡ _c_ mod _m_, then _a_ ≡ _c_ mod _m_.
Therefore congruence modulo _m_ is an equivalence relation, and this relation partitions the integers into _m_ equivalence classes:
_mn_ + 0, _mn_ + 1, _mn_ + 2, ..., _mn_ + (_m_ – 1).
(Since 0 ≡ _m_ mod _m_, we can either choose 0 or _m_ as a representative for the first class. It is conventional to choose 0.) To be a little more formal than we were above, we can write the equivalence class of an integer _a_ as [_a_]. The brackets signify that this is an equivalence _class_ and not simply a number. In this way we can write
... = [–3 _m_] = [–2 _m_] = [–_m_] = = [_m_] = [2 _m_] = [3 _m_] = ...,
... = [–3 _m_ + 1] = [–2 _m_ + 1] = [–_m_ + 1] = = [_m_ + 1] = [2 _m_ + 1] = [3 _m_ + 1] = ...,
... = [–3 _m_ + 2] = [–2 _m_ + 2] = [–_m_ + 2] = = [_m_ + 2] = [2 _m_ + 2] = [3 _m_ + 2] = ...,
... = [–3 _m_ + 3] = [–2 _m_ + 3] = [–_m_ + 3] = = [_m_ + 3] = [2 _m_ + 3] = [3 _m_ + 3] = ...,
:
... = [–2 _m_ – 1] = [–_m_ – 1] = [–1] = [_m_ – 1] = [2 _m_ – 1] = [3 _m_ – 1] = [4 _m_ – 1] = ... .
(Notice that each congruence symbol "≡" has been replaced by equality "=".) With this notation, we have the following property for any integers _a_ and _b_, which justifies "reduction under addition":
[_a_ + _b_] = [_a_] + [_b_].
Similarly, for any integers _a_ and _b_ we have
[_a_ · _b_] = [_a_] · [_b_],
justifying "reduction under multiplication". (In the fancy language of abstract algebra, these two properties can be summarized by saying that reduction modulo _m_ is a homomorphism of rings. In this case the two rings are the ring of integers and the ring of integers modulo _m_.)
IV. Exercises
1. Show that there is no integer _x_ satisfying
2 _x_ + 1 = 5 _x_ – 4.
2. Show that there is no integer _x_ satisfying
18 _x_ 2 + 39 _x_ – 7 = 0.
3. Show that the system of equations
11 _x_ – 5 _y_ = 7,
+9 _x_ + 10 _y_ = –3. has no integer solutions.
4. Show that the system of equations
24 _x_ – 5 _y_ = 10,
11 _x_ – 9 _y_ = 13. has no integer solutions.
5. Show that if _x_, _y_, _z_ are integers such that _x_ 2 + _y_ 2 = _z_ 2, then at least one of them is divisible by 2, at least one is divisible by 3, and at least one is divisible by 5.
6. Show that if _x_, _y_, _z_ are integers such that _x_ 3 + _y_ 3 = _z_ 3, then at least one of them is divisible by 7.
Hints (for after you've tried lots of things — no cheating!): 123456
Solutions (for when you're completely dehydrated from sweating over one of the problems with no success): 123456 |
13472 | https://www.youtube.com/watch?v=m45vbkpc8pA | Calculus 1 (Stewart) Ep 23, First Derivative Test (Nov 2, 2021)
Chris Staecker
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Posted: 3 Nov 2021
This is a recording of a live class for Math 1171, Calculus 1, an undergraduate course for math majors (and others) at Fairfield University, Fall 2021. The textbook is Stewart.
PDF of the written notes, and a list of all episodes is at the class website.
Class website:
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Transcript:
hope everybody got some twizzlers if you wanted some i brought twizzlers they're over there anybody wants them help yourself i don't like them um so we are gonna talk some more today about um the first derivative and what it means about the graph that's what we started talking about last time the derivative and what it means when you look at the graph um so last time we discussed increasing versus decreasing and this uh is related to the derivative the sign of the derivative so f is increasing when the derivative is positive and it's decreasing when the derivative is negative when f x is less than zero right confusing i'll just write the word and uh you know a typical function will be increasing sometimes and decreasing some other times this one that i drew there you could tell me intervals of x values where it's increasing versus where it's decreasing in this case i would say this you know for this one right here i would say it's increasing for x in the interval um actually there's two places where it's increasing right i'm just looking at where it's going up as we go left to right that would be here and also here right so in terms of intervals of x values that would be minus infinity to 2 that's that's this part over here x values from negative infinity to x equals 2. and then also this part over here is one two three four five five to infinity right everything greater than five five to infinity and then it's decreasing in the middle there so that's where it's increasing and i will say decreasing i'll write it over here decreasing for x in the interval from two to five right and when we say these we always are going to say them as open intervals because right for instance um this is uh from minus infinity up to 2 as an open interval right at 2 it's this point right here specifically at x equals 2 the function is not increasing or decreasing there so technically where it's increasing is only up to but not including two and so on it's always going to be open intervals for this increasing versus decreasing all right any questions about that it's pretty simple in my opinion if you know what you're looking for to look at the picture and say where is it increasing or decreasing give me intervals like that all right um i would like to talk what's more interesting is how do we do the same thing answer the same question but without looking at a picture so just from i will say just uh algebraically we can do the same thing algebraically that is using the equation not looking at the the graph how can you do this well sorry about that i'm gonna turn the volume down this is my new my life hack i may be ruining it for people who want to use these later and don't try that to turn the volume back on um how do we do this without looking at the graph well those uh you can still identify these two points without looking at the graph right those two points can be identified by finding when the derivative is zero and you can do that just with the equation you take the derivative you set it equal to zero and then solve for x so first to do this just algebraically i'm going to say first find the critical numbers remember the critical numbers are where the derivative equals 0 and also where the derivative does not exist for for really nice functions you don't even have to care about the does not exist part that does come up if you have like that denominator or something you'll have to check when the derivative does not exist but anyway first we're going to find the critical numbers these are the places where the derivative is 0 or does not exist for all values in between the derivative either has to be positive or negative and you can just check those i'm going to say first find the critical numbers this will become much clearer when we actually do an example in a moment but i'll i'm going to try and describe first first find the critical numbers and then plug in values in between to see where um f prime is positive versus negative all right the critical numbers are the specific points when the derivative is zero or does not exist that means everywhere else it's got to be either positive or negative and we can check if it's positive or negative in this or that region by just plugging in specific numbers and see if they're positive or negative right let's do an example i'm going to do a few examples actually first is a you know more or less easy example and then we'll do a slightly harder one um how about f of x equals 3x to the 4 minus 4x cubed minus 12x squared plus five and i would like to say where it's increasing and decreasing that is intervals of x values increasing on this interval decreasing on this interval that's what i want to do all right like i said before we begin by finding the critical numbers that's where the derivative actually is zero or does not exist although this being a polynomial there's no opportunity for the derivative to not exist so we should start by finding the derivative somebody want to shout it out for me what's the derivative here yeah great that's the derivative this is a simple derivative and then uh like i said i'm going to set this equal to zero to find the critical numbers i think actually before i do that i'm going to try and simplify as much as possible you know you know me i'm usually not really into simplifying things unless there's a good reason to there is a good reason to in this problem we're going to be using the derivative over and over again as we go on the problem so i'm going to simplify as much as i can in this case that would involve factoring ordinarily a cubic is hard to factor but this one is not so hard because uh there's no constant like everything has an x in it so i'm going to take out x of everything and actually you can also factor 12 out of everything so i'm going to factor 12x out of everything and what remains is x squared from the first part and then minus another x and then minus 2 right and then you can factor that all the way one of these right anyone say what are the what are the factors going to be somebody else want to shout out the factors yes thank you x minus two x plus one by the way thank you for desegregating the middle section here the first time a female student has sat in the middle thank you for that i don't know if anyone noticed i notice these sorts of things um all right i forgot the x 12x in the front right like that this is as simple as it's going to get right this is fully factored so this is my f prime of x i'm going to like put this on a little box or something we're gonna be referring back to this formula several times anyway let's find the critical numbers those are the places when the derivative does not exist or uh equals zero so the critical numbers there's like you know two categories one is f prime equals zero so that would look like 12x times x minus two times x plus one equals zero and this we can solve by you know factoring we already factored so it's a it's nicely set up you just sort of break this out and set each part equals zero right and so the first guy is x equals zero and then i also get x equal two and i also get x equals negative one so these are three critical numbers remember critical number means when the derivative is zero or when the derivative does not exist so we also should check f prime does not exist but this just never happens in this case the derivative is right here there is no uh value of x when this does not exist what i'm looking for is like zero in the denominator or something like that but that that can't happen in this formula so uh f prime does not exist i will just say not applicable right there there are no values where the f prime does not exist in this example what you're looking for in that step is something like 0 in the denominator but that doesn't happen in this case so we don't have to worry about that anyway these are my only critical numbers then i have three critical numbers right zero minus one and two so my critical numbers are 0 negative 1 and 2. and remember what i said my my strategy was going to be i find the critical numbers and then that means all the other values are where the derivative is either positive or negative all the all the other numbers that are like in between these ones um and i'm just going to make a little chart here in which i mark off the critical numbers and i'm putting them in order if you mess up the order then it'll confuse you these are my special x values and then i'm trying to determine f prime of x it is zero at those three points that's that's why i care about those points because those are the three points where the derivative is zero and then at all other points i want to know is it positive or negative and so what i'm going to do eventually is fill in this chart with with like signs in between those zeros either positives or negatives i want to know is it positive negative in between all you got to do is just choose your favorite number say between 0 and 2 choose your favorite number between zero and two plug it into the derivative and see what you get is it positive or negative all right um whatever it is is going to be that same sign all the way throughout this interval because it can't be zero any other place so if it's positive somewhere in between it has to be zero it has to be positive between all points uh in this you know little range from zero to two anyway um what do you think what's your favorite number between zero and two one yeah you should choose a nice uh friendly number as the kids call them these days um so in this interval here i'm going to choose one so i'm gonna do f prime of one all right this is called a test point so you um our strategy here is choose test points in each little interval on this line right so i'm going to choose one between zero and two one between the minus one and zero and then also ones on the ends all right um let's see what we got f prime of one okay i've uh look back on your paper to the formula for f prime you should use the the simplest one you can although you could use any formula like any of any of these here would would be okay because they're all equal to one another but because uh i'm about to plug a value in i'm gonna use this one especially say on the test when you don't have a calculator i would just bring this on down here put it there maybe all right i'm going to plug in 1 to that i get 12 times 1 1 minus 2 1 plus 1 right and then whatever that is remember i don't actually care if this is uh i don't actually care what the number is i care only if it's positive versus negative so here's a little a little hack for doing this without using your calculator this one's not so bad but all i care about is positive versus negative right what i have here is four things multiplied together this is positive times a positive times one minus two is negative and then one plus one here is positive right i'm just going to think about positives versus negatives because i don't actually care what the answer is i only care if it's positive or negative and what is that 3 positive times a negative is a negative yeah the rule is like if there's an even number of negatives then they all cancel out and you get a positive there's an odd number of negatives you get a negative anyway this is a negative so i'm going to put a big ol that's a minus sign right there between in this little range here because the value that i chose was in between 0 and 2 and apparently the derivative is negative in that range all right i'm just going to do that three more times it's not so hard how about uh what's your favorite number bigger than two how about three there's no reason to choose any anything else again plugging into the formula in the box up there it's going to be this time 12 times 3 times 3 minus 2 times 3 plus 1. and these uh you could try to compute that number but it's easier to just think in terms of positives or negatives that's a positive that's positive that's positive and that's positive these are all positive and so the product is positive and so over here the derivative is positive all right and we're just gonna continue this how about all the way on the far left i'm gonna choose uh minus two i guess to the left of negative one so i do f prime of minus two that's twelve times minus two times minus two minus two times minus two plus one this is positive negative negative negative those are three negatives makes a negative so i get a negative over here and then finally this is the worst step i have to plug in like a negative a half in between minus one and zero so let's plug in negative a half f prime of minus a half 12 minus a half minus a half minus two and minus a half ah plus one this is positive negative negative positive right minus a half plus 1 is positive and so that's positive overall so these are my signs come on minus plus minus plus all right you'll find in many cases that the signs alternate this is true generally of a of a polynomial which will fully factor like this with no um with no double roots that's always going to be the case the signs will alternate although in every other case you should not expect them to alternate so the signs do not always alternate but they do in the in the nicest examples all right we're pretty much done at this point i said you know the question i was trying to ask is on which intervals is it increasing and on which intervals is it decreasing so the answer is according to this chart the pluses are increasing the minuses are decreasing so in conclusion i say i'm gonna have to scroll back and forth so f the original function is increasing on the intervals minus one to zero and two to infinity minus 1 to 0 and 2 to infinity and the f is decreasing on the other intervals minus infinity to minus 1 and 0 to two all right that's how we do on this will take you uh you know take you ten minutes or so to do one of these problems the individual steps are not all that difficult anybody got questions about that this is how you say where the function is increasing versus decreasing all right i'm going to try another one that's a little more interesting that was sort of an easy one it still took us a long time to do but um not not so difficult really uh how about same question where is it increasing slash decreasing uh this time my function is f of x equals x squared minus seven over x minus four about that we're going to try to do all the same steps remember we began by finding the critical numbers those are the numbers you put on the chart then you plug values in between and see the pluses and the minuses so to find the critical numbers that's how we begin we take the derivative here and then say when the derivative is zero or derivative does not exist we think about the derivative here what's my strategy going to be anybody feeling like using one of the rules i feel like using one of the rules what do you think the quotient rule yeah this is a fraction the way to handle that is with the quotient rule i hope you remember the quotient rule it is uh the bottom times derivative of the top which is 2x minus the top x squared minus 7 times derivative of the bottom which is 1 all of this over the bottom squared all right that's my derivative as before i want to simplify this as much as possible like if this whole question was just find the derivative and then i would leave it like that that is the derivative but for the sake of doing the rest of this problem you're going to want this to be as simple as possible um what can we do to simplify well one thing is i would say don't multiply out on the bottom that's already good usually when in this type of problem you want to factor things as much as you can now the top here i hope you're not tempted to do this kind of thing that is a bogus cancellation right there because the x minus 4 up top is not factored out of everything it's only on like the first half right here if you want to cancel something has to be factored out of everything anybody have a suggestion about what we could do here i would like to somehow my goal at this point is to combine the top into like one thing it what i have is this piece minus this piece i want to like actually subtract them uh any any suggestions i want to actually combine everything up there i see some people writing things but they're not saying things to me somebody want to shout it out yeah what do you think yeah right i'm going to distribute this 2x maybe distribute the minus sign too and then we can just sort of add everything up in the numerator right this i hope you agree this times one doesn't really make any difference um so yeah let's do all of that distributing like he said uh up top i'm gonna get 2x squared minus eight x and then minus x squared plus seven that's distributing the minus sign there unfortunately if you screw this part up you're gonna be screwed for the whole rest of the problem um so the moral of the story is do it right not very uh helpful comment but yeah uh it's it's true i think it's like this x squared minus 8x minus 7 over x minus 4 squared and let's factor the top i like to see everything factored out in this type of problem that's the way you want to do it so i factor the top oh it's going to be x minus 7 x minus 1 right over x minus 4 squared okay this is the simplest form that this is gonna get the derivative i want it all to be factored just so that it makes the plugging in at the end easier when i go to plug those numbers in i go like this is positive this is negative that stuff that is best to do when it's factored otherwise you're gonna have to use a calculator which it's fine in your own personal life but on a test or whatever i would expect you to do all of these without using calculator all right that's my derivative now i need to say when the derivative equals zero and also when the derivative does not exist and in this case you actually do need to consider both parts let's try the derivative equaling zero first i set that whole thing equal to zero right how would you solve this equaling zero well when i have a fraction on the left side i would do like a cross cross multiply the denominator of the fraction so this denominator here multiplies over to the right side and it will just say this stuff x minus 7 x minus 1 equals 0 times x minus four squared but that is just zero on the right side zero times something is always zero so it's just x minus seven x minus one equals zero and lucky for us this is already factored so you can just say immediately x equals seven and x equal one are my critical numbers where the derivative is zero all right so those two numbers are going to go on my chart we also have uh we also have to check when the derivative does not exist which that actually is relevant in this problem you look at the derivative formula which is in the box there and you ask um is it possible that this thing could fail to exist for any values of x that would be what you're looking for is zero in the denominator what value of x makes a zero in the denominator here show me the fingers if you want yeah four right east coast it's too many to do it the wrong way let's do this um four is the answer yeah so if you wanted to write out some steps really it's what you're looking for is the denominator equaling zero which would be x minus four squared equals zero and this when you you know i guess you could square root on both sides x equal four however you want to come up with that but this is in a harder problem you might have to actually do some work here although it was all factored already for us so no problem all right these are my three critical numbers i get this this and this right one four and seven so i'm going to make my little chart here with my critical numbers 1 4 and 7. and then we're going to choose values in between just like we did before and plug them into the derivative formula which i'll copy down there so we can still see it right that's the derivative formula so let's uh choose your favorite values in between these plug them into the formula in the box uh far on the left all the way on the left let's choose zero i always choose zero when that's a when that's an option so um left most value to choose oh anyway sorry i'm going to write down f prime down here we have 0 there i'm going to write this dne in the middle and a 0 there right these are the values of the derivative 1 and 7 were places where the derivative was and four is the place where the derivative does not exist okay anyway plug in values in between when i plug in uh all on the left side i'm going to use x equals zero so i go f prime of zero this is going to be zero minus seven zero minus one over zero minus four squared here's a here's a little tip um no matter what the denominator in this example the denominator is always going to be positive right because it's a thing squared so you can just remember that i guess what is this this is a sorry that's negative times a negative divided by positive all right and so overall that one is positive positive again you're looking for sort of are there is there an even or an odd number of negatives when you multiply it all together all right how about between one and four what should we choose two yeah what your favorite number between one and four you don't have to choose like the number exactly in the middle which is inconvenient in this case um it'll be two and a half which i i don't want to get get into that two f prime of two is two minus seven two minus one over let me just say something squared is always going to be positive down there this is negative times positive over a positive which is negative so that region is negative this is pretty you know routine it's a little tedious you just got to plug all these numbers in how about between 4 and 7 i'm going to use 5 f prime of 5 is 5 minus 7 5 minus 1 over something squared this is negative positive over positive so that is also negative all right here's an example where the signs do not alternate as you go across they you should not always expect them to alternate sometimes they just don't and then to the right of seven seven is our rightmost value there on the right of seven let's choose 8 i guess f prime of 8 is 8 minus 7 8 minus 1 over something squared this is positive positive over positive all positive positive like so right i hope i did it right any any thoughts about that just a lot of uh it takes you awhile to do this but every step is pretty simple on its own all right and then what's my final answer i said the question remember was tell me where it's increasing and decreasing so i'm going to say it's increasing on wherever you see pluses the interval minus infinity to one and the interval seven to infinity and it's decreasing otherwise that would be one to four and four to seven uh you might be tempted to say can i just say like from one to seven it's decreasing that's um that's not technically correct because it is technically it is not decreasing right at the number four it's decreasing between one and four but not at one and also not at four and it's decreasing between four and seven but not four all right that's how we do it i don't know if you're uh if you wonder like what does this even look like how could it how could it be that it decreases and then does not exist and then decrease again this is because this function the original function has an asymptote at four so it looks like this is for this function looks something like um like this so it has this it increases up to this point and then decreases until four it just there's nothing at four but then after four it's still decreasing and then it starts to increase again this so that's what this function looks something like that all right any thoughts about that one these are the kinds of examples that you're going to do on the next homework assignment not the one for this week for next week all right uh this picture actually you know looking at the picture that i just drew you may um you may gather that this increasing decreasing business also has a lot to do with the relative extrema remember the relative minimum and maximum points like in this picture they would be here and here in fact they would be oops they would be uh these numbers one and seven right that's where these points are um basically the same procedure procedure that we've just been following is sufficient to find where those kinds of points are the minimum and the maximum points and not only that but you like you can tell those points in this example they're at one and seven and also by looking at the chart you can tell the difference between a minimum and a maximum point the the local minimum and the local maximum so all of this uh is sort of summarized in a theorem so i can say we can use that same chart with the pluses and the minuses to identify local minimum and maximum points local min and max's and there's sort of a big sounding name for this concept and it um it's called i'll go to the next page here i'll write this as a theorem it's called the first derivative test it's called the first derivative test plus you use the first derivative to do it there's that there's also a second derivative test which uses the second derivative the derivative of the derivative but um this is the first derivative test um you should the sort of picture you should have in your mind is you know you have some kind of function like this and it has some local minimum and maximum points now that function it just drew it increases over here it decreases in the middle and then it increases again right that's uh increasing decreasing just means is it going up or down as you go to the right the first derivative test it says let c be a critical number of f of x and assume that f is continuous at c this means for example this rules out the asymptote case the function actually has to be continuous at the point for this to be true but this is usually going to be the case in our examples then it says i'm going to write a lot of words here that are very the meaning is very intuitive although there's not a very short way to say it um if f goes from [Music] increasing to decreasing at uh i'll say near c then c is a local i'm going to fill in the blank here local minimum or local maximum you can see on the picture here like this point right here near this point it goes from increasing to decreasing that means that point must be a maximum right it increases it goes up until it gets that point and then it goes back down again that means this point must be like the top of the hill it has to be a local maximum so if f goes from increasing to decreasing near c then c is a local maximum all right why we why this is good is you can tell this just by looking at the chart where those pluses and minuses go if it goes from a minus then to a plus it means that point is a maximum and all the way around if f goes from decreasing to increasing near c then c is a local minimum right on this picture that's what happens right here it's decreasing and then you hit that point and then it increases again that means that point must be like the bottom of the hill so it's a local minimum and there's one other case it could go increasing and then increasing again or could go decreasing and then decreasing again and in that case the point is not a local minimum or maximum so if f goes increasing [Music] to increasing or decreasing to decreasing that is it doesn't switch it just keeps doing the same thing then that means your point is just like in the middle like it increases up to your point and then continues to increase some more that means that point is not at the top or the bottom of the hill it's just it's nothing it's not a local maximum or minimum so if f goes increasing increasing or decreasing to decreasing then c is not a local max or middle right this is called all of these words together are called the first derivative test it is how you can find where the local maximum and minimum values are you make that big chart and then you just look how the signs are changing if it goes plus to minus that's a maximum if it goes minus the plus that's the minimum and if it's plus the plus or minus or minus that's that's neither all right so for example the previous example we just did remember eventually we got down to this chart here one four seven and the signs went there was a dna in the middle for the derivative the signs went plus minus minus plus right so according to the first derivative test you can just look at the chart here and say which of these points is a maximum a local maximum or a minimum so x equal one is a local maximum that's because when you look on the chart near x equal one it goes from plus to minus that's the rule if it goes increasing and then decreasing that means it's a local maximum so the reason it's a local max is because it went goes from plus to minus near one on the chart all right four on the chart goes minus to minus so that means four is not a maximum or a minimum furthermore the function doesn't even exist at 4 so the the 4 is not is not anything really but 7 is x equals 7 is a local uh minimum this time because it goes minus the plus and this those uh you know this rule the first derivative test i guess you just have to memorize although it's i think it's pretty easy to remember if it goes my plus to minus that means it goes up and then back down again which means your point is uh is the maximum all right and i will just say parenthetically x equal four is not a minimum or a maximum right in fact in this particular example x equal 4 is not even part of the domain of the function right it was an asymptote all right this is called the first derivative test to identify where the local extremum extrema are all right any thoughts about that i got one for you all to try see if you can for this function f of x equals three x to the four plus four x to the third plus one um i would like you to find intervals where it's positive or negative sorry where it's increasing or decreasing and also find x values for the local i will say i'll use a fancy word the local extrema that means minimum and maximum points all right these are two different questions but they they both can be answered directly from that chart so basically the bulk of this is making the chart and then you just read these two answers straight off the chart at the end all right see what you think so so so foreign so um i got more twizzlers you guys are into red vines i guess right um i don't like i don't like either let's try this out it looks like most people are doing great with this um we should start by doing the derivative i get 12x squared plus 12x what no 12x cubed plus 12x squared right and then i'm going to factor 12x squared out and what remains is x plus 1. and so my critical numbers when the derivative equals 0 is x equals 0 and x equal minus one right here the zero is kind of a repeated root because of this uh you know x squared thing here uh f prime does not exist we don't really need to worry about because there are no denominators to check or anything like that so um 0 and negative 1 are the only points that need to go on your chart i'll put them on here these are my x values this is my f prime of x will be zero at those two points and then i choose values in between to plug in on the left side let's choose so this is my derivative on the left side let's pick f prime of minus two that would be 12 times -2 squared times minus 2 plus 1. this is positive positive and negative so it's negative over there i hope that's what you got in between minus 1 and 0 i guess i have to use negative a half so i go f prime of minus a half 12 times minus a half squared minus a half plus one this is positive positive because it's a square and then minus half plus one is positive right that's positive half so positive here and then finally to the right of 0 i will use 1. so this will be f prime of 1 12 times 1 squared times 1 plus 1. these are all positive so it's positive over there all right remember i said when you have a polynomial with no repeated roots you should expect the signs to alternate but uh this one had a this repeated root here x squared which is why this doesn't it doesn't alternate okay that's the chart i hope you got something like that anyway to answer the specific questions the first question was give me intervals where it's increasing or decreasing so i say increasing is where the positives are so it's increasing on the interval minus one to zero and also zero to infinity and it's decreasing on the other one minus infinity to minus one right those are the intervals of x values and then how about uh extrema you look on the chart and you see where does it go from minus to plus or plus to minus actually it never goes from plus to minus as you look across the chart from left to right it goes minus the plus right here so this one i'm going to say x equal minus 1 is a local minus the plus means down and then back up so it must be a minimum x equal minus 1 is a local minimum all right if you want you could say x equals 0 is not is not anything but i mean if i ask you tell me where the local minimum and maximum points are that's that's my answer x equal minus one it's a local minimum there is no other local experiment all right any questions about that i hope you got it excellent great um everything that i've said so far has been about the first derivative right we are only using the derivative f prime um remember there is such a thing as the second derivative f double prime that is the derivative of the derivative it turns out the derivative of the derivative f double prime is also meaningful or i'll say visible graphically right when your friends ask you at the at dinner time what is the derivative mean on the graph it means is like going up or going down that's what the derivative means increasing versus decreasing but the second derivative also has meaning when you're looking on a graph this is a little more complicated but we can handle it remember uh f if f prime is positive means the original function f is increasing right that's just what the first derivative means but i put that in in brackets that's just like a review everybody already knows that what i'm trying to talk about now though is the second derivative f double prime but if you believe this line here just write this again but using the derivative of the derivative instead what this means is that f double prime is positive means f prime is increasing f prime is increasing what that means is as you go left to right on the picture the slope is increasing that is it's getting steeper as you go from left to right the slope is becoming bigger and bigger all right f prime is increasing what that means in more ordinary language the slope is becoming bigger and bigger as you move left to right on the picture right what does that look like on a graph it looks something like this this is an example where as you move to the right the slope is becoming bigger and bigger steeper and steeper right now this is slightly confusing because it might look like on this side as i move to the right it starts off quite steep and then gets less steep as i move to the right but that actually also counts as increasing in slope because here the slope is uh is super negative and it becomes less negative which counts as the slope getting bigger and bigger all right this is a technicality but both sides of this picture have you have the property that the slope is increasing as you move from the left to the right either the slope is super negative and becoming less so less negative or on the right side the slope is already positive but it's getting more more and more positive as you go to the right all right so this is the classic picture of a function so in when you see that kind of shape this uh has f double prime greater than zero this is what it looks like when the second derivative is positive and there's a name for that kind of shape it's called concave up and it means you have well i'll draw i'll draw the other alternative uh let me just say other other situations which can look like concave up would be have two other um maybe it's just kind of flat on the left side but still doing that sort of increasing slope on one side or maybe it just has like the other half any of these pictures here they are all called concave up this general shape it is a shape in which the slopes are increasing as you move from the left to the right by increasing i mean either really getting bigger or getting less negative that's what that's the case in this one that counts as increasing getting less negative or getting more positive all right all of those shapes count as concave up the opposite is that the slope is getting smaller it could be uh super positive and becoming less positive or it could be negative and becoming more negative that picture would look like it would look like this right as you move from the left to the right here the slopes are positive but they are becoming less so positive and over here the slopes are already negative and becoming even more negative this shape is called concave down it could also look like so other other kinds of shapes that are also concave down would be maybe just like half of that picture something like that or maybe something like that these are all concave down so for these f double prime is less than zero and it's called concave down all right that's the terminology and concave up versus down is fairly simple i mean i i always think of it in terms of like my the fingers right this is off this is down this is concave up this straight this is concave down um concave up is the um concave up is like like the smiley right and the concave down is the frowny is this way a frowny right and you just have to remember that concave up this one means that the f pro f double prime is positive positive means smiley right and the uh this one is the one where the f double prime is negative meaning the frowny shape okay this is how you identify concave up versus down on a picture and this is the graphical meaning of the second derivative so the first derivative is is the curve actually going up or down that's the first derivative the second derivative is this sort of smiley versus frowny shape all right does it have the smiley shape or the frowny shape that's the this is called the concavity of the of the graph all right let's just look at a picture and see if we can identify you know as usual a typical function is like sometimes concave up and sometimes concave down it's like sometimes the smiley sometimes the frowny um a simple example would be like a typical cubic equation looks something like that come on now something like this right you can see part of it is the frowny and part of it is the is the smiley right and there's there's some point i suppose right in the middle somewhere maybe around here where it switches from being the frowning to the smiley all right but i would say this region right there maybe till around there somewhere versus this region over here right this part is concave down because that's the frowny shape and this part over here is concave up because that's the uh smiling shape all right and that point right in the middle is is neither at that specific point in the middle it is not concave up or concave down there's a name for that this is called an inflection point this is a point at which the concavity changes from being up to down so right at that point it is neither in fact in this case the second derivative will equal zero remember the concavity is determined by the second derivative is it positive versus negative on this picture to the left of that dot it's negative because the concave is it's concave down to the right of that dot it's positive and right at the dot the concavity or the second derivative must be zero all right well let's do a more more complicated more interesting picture here how about i'm going to try to make these points the way i want them like that all right i would like to give me intervals where it's concave up versus concave down that's what i want intervals for concavity you want to look at that picture and identify where is it a smiley shape versus where is it a frowny shape sometimes you don't get the full smile you only get like half of the smiley shape or the frowny shake anyway for the concave up i'm looking for the smilies right uh i would say there's definitely a smiley region over here right i see that smiley face there you'll have to kind of judge exactly how far over does the smiley shape go um does anybody see another smiley region like i said sometimes you only you don't get the full smile sometimes you only get half of the smile yeah after yeah like between two and three it has this kind of at least half of the smiley shape right and i think those are the only places on this graph where you get the smiley shape i think everywhere else is going to be the frowny shape um the frowny shape you know maybe i'll put those in green here i see the frowny sort of a half frowny right there and then a full frowny over there right these are the concave up versus concave down region so writing those as intervals i would say it's concave up uh over here that is everything to the left of x equals one so from minus x equals minus infinity up to one it's concave up and also this bit right here and it looks like right there i tried to draw the picture so that right there is is where it switches from being up to down so the other concave operation is here two to three those are the upsies and the downsies are the other parts um i guess from one to two this one and then over here everything greater than three so concave down will be one to two and three to infinity all right this is the concavity i would like to contrast this with increasing versus decreasing these are really two completely different concepts you can also i mean we can also do looking at this uh same example i will say note what are the increasing decreasing intervals it's increasing um that is everywhere it's going up i guess from here all the way to there it's increasing right and that's it so the increasing um and maybe this point is where i tried to draw this so that the slope is zero there so technically it's increasing here from zero zero to two and two to four right that's this region and this region it's increasing that is going up from left to right and then it's decreasing over here minus infinity to zero and also four to infinity these intervals are really completely different from the concavity intervals right there there's no simple relationship between the two so they are really two completely different uh concepts they mean different things right increasing decreasing is just is it going up or is it going down the concavity is about the the shape the courageousness of the shape is it the smiley shape or the frowny shape all right all right and i was going to say what um are there any inflection points here i think there are remember inflection point means it's one of the uh points where the derivative switches from being positive to negative or negative positive or the concavity switches and that would happen like every time these these fine frownies and smileys bump up against each other so the inflection points if i were to mark them with dots would be here here and here right those are where the concavity switches so i'll just write that in here inflection points at x equals one two and three on this picture that's where it switches from being smiley to frowny or frowning to smiley inflection point they are similar to the critical numbers but critical numbers are about the first derivative the inflection points are about the second derivative all right inflection points you know you can always eyeball them on a picture they are just like the points in between sort of in between the bumpity bumps if i have something like that where are the inflection points there's one here because i see smiley followed by frowny there's one around here there's one somewhere like that and one in there somewhere right those are the inflection points on this picture everywhere it switches from being a smiley to a frowny or vice versa all right the inflection points some people uh sometimes you hear people use the word inflection point in like the real world to just mean like when something changes mathematically i mean it is about when the concavity changes but it's it's a specific kind of change in the function all right any uh any questions about that pictures let's try and do the same thing but algebraically that is looking at an equation not looking at the picture can we identify intervals of the concavity of concavity using the formula not by looking at the picture all right the process is almost exactly like the increasing decreasing thing only you use the second derivative instead of the first derivative right the increasing decreasing is about the sign of the first derivative so i'm going to say we do the same procedure as increasing slash decreasing but we use f double prime instead of f prime because f prime tells you the increase in decreasing f double prime tells you to concave up versus concave down so do the whole the whole same thing make set the thing equal to zero make the chart plug in points in between let's try it i got um i thought we'd just revisit the first example we talked about today it seems so long ago doesn't it 3x to the four minus four x to the three minus twelve x squared plus five all right and my uh your job is find intervals where it's um concave up versus down all right like i said we're going to do the same procedure but use the second derivative instead of the first derivative so my first step will be immediately find the second derivative now you can't find the second derivative all at once the only way to do it is take the derivative first and then take the derivative again so f prime of x is 12x cubed minus 12x squared minus 24x remember that guy and then take the derivative again right i don't care about the first derivative at all in this problem i care about the second derivative so this will be 36x squared minus 24x minus 24 right is all right somebody has a puzzled look on their face that's okay what should we do from here maybe try and factor this i mean i always try and simplify as much as we can here you could factor 12 out of all of that what remains will be 3x squared minus 2x minus 2 right and then try to factor that part that's left over um unfortunately that part there doesn't factor in in ordinary numbers well what do we do in that case um if it doesn't factor i still want to find the uh i mean i expect to get two values for x right um if it doesn't factor the best you can do is use the quadratic formula which usually we don't like to do but um in this case it's the only way we're going to do this so first anyway this is this is the most simple form of the derivative it doesn't factor anymore sorry the second derivative is what i'm talking about anyway i'm going to set the second derivative equal to zero it'll say twelve three x squared minus two x minus two equals zero i can get rid of the twelve is not relevant it's just three x squared minus two x minus two equals zero and here i need to use the quadratic formula because like i said this doesn't factor nicely um i hope you remember your quadratic formula anybody remember i like asking rooms full of people to say the quadratic formula they just sort of mumble a lot and then everybody says all over 2a everybody knows that part that's the end uh it's minus i'm just i'll just write the formula for now minus b plus or minus the square root of b squared minus 4ac all over 2a right i hope that you know the quadratic formula um my uh one of my teachers in middle school sang the quadratic formula song to the tune of the yellow submarine i'm not going to get into that there are songs for that if you if you require songs anyway this is going to be 2 plus or minus square root negative 2 squared is 4 minus four times a which is three times c which is negative two all over two times three that would be two plus or minus square root four minus uh i guess that's going to be a plus 4 plus 4 times 3 times 2 is 24 right over 6. so this is 2 plus or minus the square root of 28 over 6. and now it's clear why this wasn't why you can't factor because that root 28 is not a nice number um i plug this into my calculator you know you plug it if you're going to plug this into your calculator you do it once with the plus again with the minus you get two different answers they were negative with the minus you get negative 0.548 and with the plus you get 1.215 right anyway remember what we were doing here we're trying to find where the second derivative is positive and negative we found these numbers with the intention of putting them on the chart right these are kind of like the critical numbers although they're not critical numbers in this context they are coming from the second derivative so really they are inflection points anyway i make my chart of the second derivative this time and i mark those two values negative 0.548 and positive 1.215 those are two numbers where the second derivative is zero it is important that you know what those numbers are like you actually do have to put that into your calculator because you need to uh my next step will be to choose values that are smaller and greater and you have to know what those numbers are in order to make sure you're picking values in the right regions anyway let's do it what do you want to use uh what's your favorite number on the left side negative one yeah and i'm plugging into the second derivative which is here's scroll up here that thing in the uh in the box here right this is what i'm plugging into all the way down here so i get 12 3 times minus 1 squared minus two times minus one minus two unfortunately i can't do my normal trick about negative times a negative times a negative whatever because inside the parentheses there those are actually added up they're not they're not multiplied together so you really do have to compute the number although it's not not terribly difficult negative one squared is is plus one so this is going to be a three and then a plus two and then a minus two this is 12 times three which is a positive times a positive so that's positive on the left side all right it's still you don't actually care what the number is you just care if it's positive negative okay in the middle region i'm gonna choose zero right that's my favorite number to plug in in all situations in the middle region i use zero again plug into the formula in the box twelve three times zero squared minus two times zero minus two this is twelve times negative two which is negative right and then on the right side i suppose we should use 2. it's bigger than 1.215 so f double prime of 2 is in the box 12 three times two squared minus two times two minus two this is twelve times three times two squared is twelve again minus four minus two that's positive times a positive so this is positive also signs alternate which is not a surprise because this was a uh a polynomial with no repeated roots okay we're pretty much done at this point my final answer is should be intervals where is it concave up versus concave down you just look at the signs here so my final answer is it's concave up on the interval minus infinity to that number negative 0.548 and also concave up on the interval 1.215 to infinity and it's concave down oh come on buddy concave down on the uh one in the middle right minus point five four eight to one point two one hit my page up button there you go this is my final answer based on the chart there all right that's how we find concavity intervals without looking at the graph unfortunately you have to use the quadratic formula you don't always have to use a quadratic formula if you're lucky the second derivative will factor and then you don't you won't need it all right i think that'll do it for today see y'all next time take it take a twizzler on your way out i got enough you |
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Playing card suit
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From Wikipedia, the free encyclopedia
Categories into which the cards of a deck are divided
This article contains suit card Unicode characters. Without proper rendering support, you may see question marks, boxes, or other symbols.
In playing cards, a suit is one of the categories into which the cards of a deck are divided. Most often, each card bears one of several pips (symbols) showing to which suit it belongs; the suit may alternatively or additionally be indicated by the color printed on the card. The rank for each card is determined by the number of pips on it, except on face cards. Ranking indicates which cards within a suit are better, higher or more valuable than others, whereas there is no order between the suits unless defined in the rules of a specific card game. In most decks, there is exactly one card of any given rank in any given suit. A deck may include special cards that belong to no suit, often called jokers.
While English-speaking countries traditionally use cards with the French suits of Clubs, Spades, Hearts and Diamonds, many other countries have their own traditional suits. Much of central Europe uses the Germanic suits of Acorns, Leaves, Hearts and Bells; Spain and parts of Italy and South America use the Latin suits of Swords, Batons, Cups and Coins; German Switzerland uses the Swiss suits of Acorns, Shields, yellow Roses and Bells. Asian countries such as China and Japan also have their own traditional suits. Tarot card packs have a set of distinct picture cards alongside the traditional four suits.
History
[edit]
Modern Western playing cards are generally divided into two or three general suit-systems. The older Latin suits are subdivided into the Italian and Spanish suit-systems. The younger Germanic suits are subdivided into the German and Swiss suit-systems. The French suits are a derivative of the German suits but are generally considered a separate system.
Origin and development of the Latin suits
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Main articles: Italian playing cards, Spanish-suited playing cards, and Portuguese-suited playing cards
The earliest card games were trick-taking games and the invention of suits increased the level of strategy and depth in these games. A card of one suit cannot beat a card from another regardless of its rank. The concept of suits predates playing cards and can be found in Chinese dice and domino games such as Tien Gow.
Chinese money-suited cards are believed to be the oldest ancestor to the Latin suit system. The money-suit system is based on denominations of currency: Coins, Strings of Coins, Myriads of Strings (or of coins), and Tens of Myriads. Old Chinese coins had holes in the middle to allow them to be strung together. A string of coins could easily be misinterpreted as a stick to those unfamiliar with them.
By then the Islamic world had spread into Central Asia and had contacted China, and had adopted playing cards. The Muslims renamed the suit of myriads as cups; this may have been due to seeing a Chinese character for "myriad" (万) upside-down. The Chinese numeral character for Ten (十) on the Tens of Myriads suit may have inspired the Muslim suit of swords. Another clue linking these Chinese, Muslim, and European cards are the ranking of certain suits. In many early Chinese games like Madiao, the suit of coins was in reverse order so that the lower ones beat the higher ones. In the Indo-Persian game of Ganjifa, half the suits were also inverted, including a suit of coins. This was also true for the European games of Tarot and Ombre. The inverting of suits had no purpose in terms of play but was an artifact from the earliest games.
These Turko-Arabic cards, called Kanjifa, used the suits coins, clubs, cups, and swords, but the clubs represented polo sticks; Europeans changed that suit, as polo was an obscure sport to them.
The Latin suits are coins, clubs, cups, and swords. They are the earliest suit-system in Europe, and were adopted from the cards imported from Mamluk Egypt and Moorish Granada in the 1370s.
There are four types of Latin suits: Italian, Spanish, Portuguese,[a] and an extinct archaic type. The systems can be distinguished by the pips of their long suits: swords and clubs.
Northern Italian swords are curved outward and the clubs appear to be batons. They intersect one another.
Southern Italian and Spanish swords are straight, and the clubs appear to be knobbly cudgels. They do not cross each other (except in the three of clubs).
Portuguese pips are like the Spanish, but they intersect like Northern Italian ones. They sometimes have dragons on the aces. This system lingers on only in the Tarocco Siciliano and the Unsun Karuta and Komatsufuda of Japan. Unsun Karuta additionally has a fifth Guru suit (circular whirls).
The archaic system[b] is like the Northern Italian one, but the swords are curved inward so they touch each other without intersecting.
Minchiate (a game that used a 97-card deck) used a mixed system of Italian clubs and Portuguese swords.
Despite a long history of trade with China, Japan was not introduced to playing cards until the arrival of the Portuguese in the 1540s.[c] Early locally made cards, Karuta, were very similar to Portuguese decks. Increasing restrictions by the Tokugawa shogunate on gambling, card playing, and general foreign influence, resulted in the Hanafuda deck that today is used most often for fishing-type games and the Komatsufuda and Kabufuda decks that are used for gambling. In hanafuda, the role of rank and suit in organizing cards became switched, so the deck has 12 suits, each representing a month of the year, and each suit has 4 cards, most often two normal, one Ribbon and one Special (though August, November and December each differ uniquely from this convention). In komatsufuda and kabufuda, the designs of the suits became much more abstract. The latter much moreso to the point where the suit does not matter (only rank) and the face cards indistinguishable; thus becoming a single-suited deck with ranks 1-10 and the designs quadruplicated. Unsun karuta did not face the same restrictions and instead developed an additional suit and additional ranks.
Invention of German and French suits
[edit]
Main articles: French-suited playing cards, German-suited playing cards, and Swiss playing cards
During the 15th-century, manufacturers in German speaking lands experimented with various new suit systems to replace the Latin suits. One early deck had five suits, the Latin ones with an extra suit of shields. The Swiss-Germans developed their own suits of shields, roses, acorns, and bells around 1450. Instead of roses and shields, the Germans settled with hearts and leaves around 1460. The French derived their suits of trèfles (clovers or clubs ♣), carreaux (tiles or diamonds ♦), cœurs (hearts ♥), and piques (pikes or spades ♠) from the German suits around 1480. French suits correspond closely with German suits with the exception of the tiles with the bells but there is one early French deck that had crescents instead of tiles. The English names for the French suits of clubs and spades may simply have been carried over from the older Latin suits.
Tarot cards
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Beginning around 1440 in northern Italy, some decks started to include an extra suit of (usually) 21 numbered cards known as trionfi or trumps, to play tarot card games. Always included in tarot decks is one card, the Fool or Excuse, which may be part of the trump suit depending on the game or region. These cards do not have pips or face cards like the other suits. Most tarot decks used for games come with French suits but Italian suits are still used in Piedmont, Bologna, and pockets of Switzerland. A few Sicilian towns use the Portuguese-suited Tarocco Siciliano, the only deck of its kind left in Europe.
The esoteric use of Tarot packs emerged in France in the late 18th century, since when special packs intended for divination have been produced. These typically have the suits cups, pentacles (based on the suit of coins), wands (based on the suit of batons), and swords. The trump cards and Fool of traditional card playing packs were named the Major Arcana; the remaining cards, often embellished with occult images, were the Minor Arcana. Neither term is recognised by card players.
Suits
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Symbolic origin
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In divinatory, esoteric and occult tarot, the Minor Arcana, and the suits by extension, are believed to represent relatively mundane features of life. The court cards may represent the people whom one meets.
Each suit also has distinctive characteristics and connotations commonly held to be as follows:
| Latin suit | Element | Class | Faculty |
--- --- |
| Wands, batons, clubs, staves | Fire | Artisans | Will and creativity |
| Swords, blades | Air | Nobility and military | Reason or logic, wisdom, and intellect |
| Cups, chalices, goblets, vessels | Water | Clergy | Spiritual matters, or emotions and love |
| Pentacles, coins, disks, rings | Earth | Merchants | Material matters, or possessions and career |
Comparisons between suits
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| Origin | Suits | | | | | | | | | | | |
--- --- --- --- --- ---
| Latin card suits | | | | | | | | | | | | |
| Italian[d] | Clubs (Bastoni) | Cups (Coppe) | Swords (Spade) | Coins (Denari) |
| Spanish[e] | Clubs (Bastos) | Cups (Copas) | Swords (Espadas) | Coins (Oros) |
| Portuguese | Clubs (Paus) | Cups (Copas) | Swords (Espadas) | Coins (Ouros) |
| Comparison of German, French and Swiss suits[f] | | | | | | | | | | | | |
| Swiss-German[g] | Acorns[h] | Shields[i] | Roses[j] | Bells[k] |
| German | Acorns[l] | Hearts[m] | Leaves[n] | Bells[o] |
| French | Clover (Clubs)[p] | Hearts | Pikes (Spades)[q] | Tiles (Diamonds) |
| Karuta suits | | | | | | | | | | | | |
| Komatsufuda | Clubs | Cups | Swords | Coins |
| Unsun Karuta | Clubs (パオ) | Cups (コツ) | Swords (イス) | Coins (オウル) | Guru (クル) |
| Kabufuda | Clubs |
| Hanafuda[r] | Pine[s] | Plum[t] | Cherry[u] | Wisteria[v] | Iris[w] | Peony[x] | Bush Clover[y] | Susuki Grass[z] | Chrysanthemum[aa] | Maple[ab] | Willow[ac] | Paulownia[ad] |
Suits in games with traditional decks
[edit]
Trumps
[edit]
In a large and popular category of trick-taking games, one suit may be designated in each deal to be trump and all cards of the trump suit rank above all non-trump cards, and automatically prevail over them, losing only to a higher trump if one is played to the same trick. Non-trump suits are called plain suits.
Special suits
[edit]
Some games treat one or more suits as being special or different from the others. A simple example is Spades, which uses spades as a permanent trump suit. A less simple example is Hearts, which is a kind of point trick game in which the object is to avoid taking tricks containing hearts. With typical rules for Hearts (rules vary slightly) the queen of spades and the two of clubs (sometimes also the jack of diamonds) have special effects, with the result that all four suits have different strategic value. Tarot decks have a dedicated trump suit.
Chosen suits
[edit]
Games of the Karnöffel Group have between one and four chosen suits, sometimes called selected suits or, misleadingly, trump suits. The chosen suits are typified by having a disrupted ranking and cards with varying privileges which may range from full to none and which may depend on the order they are played to the trick. For example, chosen Sevens may be unbeatable when led, but otherwise worthless. In Swedish Bräus some cards are even unplayable. In games where the number of chosen suits is less than four, the others are called unchosen suits and usually rank in their natural order.
Ranking of suits
[edit]
Whist-style rules generally preclude the necessity of determining which of two cards of different suits has higher rank, because a card played on a card of a different suit either automatically wins or automatically loses depending on whether the new card is a trump. However, some card games also need to define relative suit rank. An example of this is in auction games such as bridge, where if one player wishes to bid to make some number of heart tricks and another to make the same number of diamond tricks, there must be a mechanism to determine which takes precedence in the bidding order.
There is no standard order for the four suits and so there are differing conventions among games that need a suit hierarchy. Examples of suit order are (from highest to lowest):
| High → low | | | | Games | Mnemonic |
--- --- --- |
| ♠ | ♥ | ♦ | ♣ | Bridge for bidding and scoring Poker occasionally Taiwanese version of Big Two | Alphabetical order reversed: S, H, D, C |
| ♠ | ♥ | ♣ | ♦ | Big Two outside Taiwan | 1 tip, 2 halves, 3 leaves, 4 corners |
| ♥ | ♦ | ♣ | ♠ | Preferans only used for bidding Five Hundred for bidding and scoring Thirteen | |
| ♥ | ♦ | ♠ | ♣ | Préférence only used for bidding | |
| ♣ | ♠ | ♥ | ♦ | Skat for bidding (valued 12, 11, 10, 9) and to determine which Jack beats which in play Other European games such as Bruus | |
| ♣ | ♠ | ♥ | ♦ | Cego for determining highest card in certain situations |
| ♣ | ♥ | ♠ | ♦ | Ninety-nine for scoring | 3, 2, 1, 0 lobes |
Pairing or ignoring suits
[edit]
The pairing of suits is a vestigial remnant of Ganjifa, a game where half the suits were in reverse order, the lower cards beating the higher. In Ganjifa, progressive suits were called "strong" while inverted suits were called "weak". In Latin decks, the traditional division is between the long suits of swords and clubs and the round suits of cups and coins. This pairing can be seen in Ombre and Tarot card games. German and Swiss suits lack pairing but French suits maintained them and this can be seen in the game of Spoil Five.
In some games, such as blackjack, suits are ignored. In other games, such as Canasta, only the color (red or black) is relevant. In yet others, such as bridge, each of the suit pairings are distinguished.
In contract bridge, there are three ways to divide four suits into pairs: by color, by rank and by shape resulting in six possible suit combinations.
Color is used to denote the red suits (hearts and diamonds) and the black suits (spades and clubs).
Rank is used to indicate the major (spades and hearts) versus minor (diamonds and clubs) suits.
Shape is used to denote the pointed (diamonds and spades, which visually have a sharp point uppermost) versus rounded (hearts and clubs) suits. This is used in bridge as a mnemonic.
Four-color suits
[edit]
See also: Four-color deck
Some decks, while using the French suits, give each suit a different color to make the suits more distinct from each other. In bridge, such decks are known as no-revoke decks, and the most common colors are black spades, red hearts, blue diamonds and green clubs, although in the past the diamond suit usually appeared in a golden yellow-orange. A pack occasionally used in Germany uses green spades (comparable to leaves), red hearts, yellow diamonds (comparable to bells) and black clubs (comparable to acorns). This is a compromise deck devised to allow players from East Germany (who used German suits) and West Germany (who adopted the French suits) to be comfortable with the same deck when playing tournament Skat after the German reunification.
Other suited decks
[edit]
Swiss-German Experimental Suit Systems
[edit]
This is a list of suit systems devised by early Swiss-German cardmakers mentioned by Michael Dummett:
15th-16th Century Swiss-German suit systems
| Name | Time | Suit 1 | Suit 2 | Suit 3 | Suit 4 | Other Suits |
| Incomplete sheet from Basel | c. 1531 | Purses | Keys |
| Several incomplete packs from Basel | c. 1470 to 1529 | Feathers | Hats | Shields | Bells |
| Cards from Shields suit (presumed Swiss suit system) | c. 1433-1451 | Shields | Acorns (presumed) | Roses (presumed) | Bells (presumed) |
| Stuttgart pack | c. 1427-1431 | Stags | Hounds | Ducks | Falcons |
| Ambraser Hofjagdspiel | c. 1440-1445 | Falcons | Lures | Hounds | Herons |
| Pack by Virgil Solis | c. 1540-1545 | Lions | Apes | Parrots | Peacocks |
| 2 fragmentary sheets from the Upper Rhine | 16th century | Carnations | Beans | Birds |
| Pack by Thomas Murner for teaching logic | 1509 | Bells | Acorns | Hearts | Shields | Crowns, et al. (total 16 suits) |
| Pack by Thomas Murner for teaching law | 1515 | Bells | Acorns | Hearts | Shields | Crowns, et al. (total 12 suits) |
| Liechtenstein pack | c. 1440-1450, c. 1494-1500 (disputed) | Coins | Batons (or polosticks) | Cups | Swords | Shields |
| Pack by Hopfer of Nuremburg[verification needed] | c. 1536-1539 | Coins | Batons (arranged as spokes of a wheel) | Cups | Swords (arranged as spokes of a wheel) |
| 2 packs by Heinrich Hauk of Frankfurt | 1585 and 1588 | Roses | Acorns | Birds | Bells |
| Pack perhaps by Heinrich Hauk | | Lions | Apes | Parrots | Eagles |
| Pack by Hans Sebald Beham | c. 1523 | Leaves | Acorns | Roses | Pomegranates |
| Pack attributed to Hans Sebald Beham | | Acorns | Bells | Roses | Parrots |
| Listed by Dominican Meister Ingold | 1450 | Roses | Crowns | Pennies | Rings |
| Set of mutilated cards from Alsace | c. 1480 | Shields | Crowns | Bells | Acorns |
| Fragmentary sheet of Maihinger pack | c. 1450 | Lions | Bears | Dogs |
Other suit systems:
15th-16th Century Swiss-German suit system
| Name | Time | Suit 1 | Suit 2 | Suit 3 | Suit 4 | Other Suits |
| Pack by Master of the Playing Cards | c. 1455 | Flowers | Wild men | Beasts of prey | Stags | Herons |
| Hofämterspiel | c. 1460 | Shields (France) | Shields (Germany) | Shields (Bohemia) | Shields (Hungary) |
| Flemish Hunting Deck | c. 1475-1480 | Dog collars | Dog tethers | Gaming nooses | Hunting horns |
| Pack by south German engraver | c. 1496 | Pomegranates[ae] | Batons | Cups | Swords |
| Pack by Master P. W. | c. 1500 | Hares | Parrots | Carnations | Columbines | Roses |
| Pack by Jost Amman | 1588 | Books | Ink pads | Pots | Cups |
Suited-and-ranked decks
[edit]
A large number of games are based around a deck in which each card has a rank and a suit (usually represented by a color), and for each suit there is exactly one card having each rank, though in many cases the deck has various special cards as well.
Color suits used by some modern card games
| Games | Suits | red | orange brown gold | yellow | green | cyan teal | blue | purple | magenta pink | black grey white |
| DUO | 4 | | | | | | | | | |
| UNO, Phase 10 | 4 | | | | | | | | | |
| UNO Flip | 8 | | | | | | | | | |
| 4-Colour Suits | 4 | | | | | | | | | |
| 4-Colour Suits (Old) | 4 | | | | | | | | | |
| Rook, 4-Colour Suits (German) | 4 | | | | | | | | | |
| Sticheln | 5 | | | | | | | | | |
| Mü | 5 | | | | | | | | | |
| Rage, Level 8 | 6 | | | | | | | | | |
| Schotten Totten | 6 | | | | | | | | | |
Other modern decks
[edit]
Decks for some games are divided into suits, but otherwise bear little relation to traditional games. An example would be the board game Taj Mahal, in which each card has one of four background colors, the rule being that all the cards played by a single player in a single round must be the same color. The selection of cards in the deck of each color is approximately the same and the player's choice of which color to use is guided by the contents of their particular hand.
In the trick-taking card game Flaschenteufel ("The Bottle Imp"), all cards are part of a single sequence ranked from 1 to 37 but split into three suits depending on its rank. players must follow the suit led, but if they are void in that suit they may play a card of another suit and this can still win the trick if its rank is high enough. For this reason every card in the deck has a different number to prevent ties. A further strategic element is introduced since one suit contains mostly low-ranking cards and another, mostly high-ranking cards.
Whereas cards in a traditional deck have two classifications—suit and rank—and each combination is represented by one card, giving for example 4 suits × 13 ranks = 52 cards, each card in a Set deck has four classifications each into one of three categories, giving a total of 3 × 3 × 3 × 3 = 81 cards. Any one of these four classifications could be considered a suit, but this is not really enlightening in terms of the structure of the game.
Uses of playing card suit symbols
[edit]
Card suit symbols occur in places outside card playing:
The four suits were famously employed by the United States' 101st Airborne Division during World War II to distinguish its four constituent regiments:
Clubs (♣) identified the 327th Glider Infantry Regiment; currently worn by the 1st Brigade Combat Team.
Diamonds (♦) identified the 501st PIR. 1st Battalion, 501st Infantry Regiment is now part of the 4th Brigade (ABN), 25th Infantry Division in Alaska; the Diamond is currently used by the 101st Combat Aviation Brigade.
Hearts (♥) identified the 502nd PIR; currently worn by the 2nd Brigade Combat Team.
Spades (♠) identified the 506th PIR; currently worn by the 4th Brigade Combat Team.
Character encodings
[edit]
Main article: Playing cards in Unicode
In computer and other digital media, suit symbols can be represented with character encoding, notably in the ISO and Unicode standards, or with Web standard (SGML's named entity syntax):
Playing card characters in Unicode
| UTF code: | U+2660 (9824dec) | U+2665 (9829dec) | U+2666 (9830dec) | U+2663 (9827dec) |
| Symbol: | ♠ | ♥ | ♦ | ♣ |
| Name: | Black Spade Suit | Red Heart Suit | Red Diamond Suit | Black Club Suit |
| Entity: | ♠ | ♥ | ♦ | ♣ |
| UTF code: | U+2664 (9828dec) | U+2661 (9825dec) | U+2662 (9826dec) | U+2667 (9831dec) |
| Symbol: | ♤ | ♡ | ♢ | ♧ |
| Name: | White Spade Suit | White Heart Suit | White Diamond Suit | White Club Suit |
| UTF codes are expressed by the Unicode code point "U+hexadecimal number" syntax, and as subscript the respective decimal number. Symbols are expressed here as they are in the web browser's HTML renderization. Name is the formal name adopted in the standard specifications. | | | | |
Unicode is the most frequently used encoding standard, and suits are in the Miscellaneous Symbols Block (2600–26FF) of the Unicode.
It is recommended to use stylistic fonts for regional variations of the French suits. Though fleurons (e.g. ✿/❀) can be used for the flower suit, and stars (e.g. ★/☆) can be used for a fifth suit such as for Five Crowns.
Metaphorical uses
[edit]
In some card games the card suits have a dominance order, for example: club (lowest) - diamond - heart - spade (highest). That led to in spades being used to mean more than expected, in abundance, very much.
Other expressions drawn from bridge and similar games include strong suit (any area of personal strength) and to follow suit (to imitate another's actions).
See also
[edit]
Hearts (card game)
Spades (card game)
Stripped deck
Five-suit bridge
Russian playing cards
Notes
[edit]
^ "Portuguese" is slightly misleading nomenclature. The suit system may have originated in Catalonia and spread out through the western Mediterranean before being replaced by the "Spanish" system. The association with Portugal comes from the fact that they continued to use it until completely going over to French suits at the beginning of the 20th century.
^ Probably associated with the Duchy of Ferrara and likely abandoned after the 15th century.
^ The only users of Chinese cards during the Edo period were the expat community in Nagasaki.
^ Sample pips come from the Venetian pattern
^ Sample pips come from the Castilian pattern
^ The French suit system is generally considered to be separate from the German and Swiss due to its different set of face cards. However, when comparing only the pips, it is German in origin.
^ There does not appear to be a single universal system of correspondences between Swiss-German and French suits. Cards combining the two suit systems are manufactured in different versions with different combinations of suits.
^ Swiss-German: Eichel
^ Swiss-German: Schilten
^ Swiss-German: Rosen
^ Swiss-German: Schellen
^ German: Eichel (acorn), Ecker (beechnut), Hungarian: Makk (acorn), Czech: Žaludy (acorns)
^ German: Herz (heart), Rot (red), Hungarian: Piros (red), Czech: Srdce (heart), Červené (red)
^ German: Laub (leaves), Grün (green), Gras (grass), Blatt (leaf) Hungarian: Zöld (green), Czech: Listy (leaves), Zelené (green)
^ German: Schellen (bells), Hungarian: Tök (pumpkin), Czech: Kule (balls)
^ The shape of the clubs symbol is believed to be an adaptation of the German suit of acorns. Clubs are also known as clovers, flowers and crosses. The French name for the suit is trèfles meaning clovers, the Italian name for the suit is fiori meaning flowers and the German name for the suit is Kreuz meaning cross.
^ In German-speaking countries the spade was the symbol associated with the blade of a spade. The English term spade originally did not refer to the tool but was derived from the Spanish word espada meaning sword from the Spanish suit. Those symbols were later changed to resemble the digging tool instead to avoid confusion. In German and Dutch the suit is alternatively named Schippen and schoppen respectively, meaning shovels.
^ In Hanafuda, each of the 12 suits is associated with a month of the year. The traditional month associations differ from region to region. Most notable in modern usage, is that in Korea the suits for November and December are switched compared to the standard Japanese order.
^ Japanese: matsu (松, pine), Korean: 송학; 松鶴; songhak; lit. pine crane. Associated with the month January.
^ Japanese: ume (梅, plum blossom), Korean: 매조; 梅鳥; maejo; lit. plum bird. Associated with the month February.
^ Japanese: sakura (桜, cherry blossom), Korean: 벚꽃; beotkkot; lit. cherry blossom or 사쿠라; sakura. Associated with the month March.
^ Japanese: fuji (藤, wisteria), Korean: 흑싸리; heugssali; lit. black bush clover. Associated with the month April.
^ Japanese: ayame (菖蒲, iris) or kakitsubata (杜若, Iris laevigata), Korean: 난초; 蘭草; nancho; lit. orchid. Associated with the month May.
^ Japanese: botan (牡丹, peony), Korean: 모란; 牡丹; moran; lit. peony. Associated with the month June.
^ Japanese: hagi (萩, bush clover), Korean: 홍싸리; hongssari; lit. red bush clover. Associated with the month July.
^ Japanese: susuki (芒, Japanese silver grass) or bōzu (坊主, Buddhist monk, shorn head), Korean: 공산; 空山; gongsan; lit. empty mountain. Associated with the month August.
^ Japanese: kiku (菊, chrysanthemum), Korean: 국진; gukjin. Associated with the month September.
^ Japanese: momiji (紅葉, maple, red leaves), Korean: 단풍; 丹楓; danpung; lit. maple, autumn leaves. Associated with the month October.
^ Japanese: yanagi (柳, willow) or ame (雨, rain), Korean: 비; bi; lit. rain. Associated with the month November in Japan and December in Korea.
^ Japanese: kiri (桐, paulownia), Korean: 오동; odong; lit. paulownia. Associated with the month December in Japan and November in Korea.
^ Possibly alludes to the kingdom of Granada.
References
[edit]
^ Parlett, David (1990). The Oxford Guide to Card Games. Oxford: Oxford University Press. pp. 27–34.
^ McLeod, John. Games classified by type of cards or tiles used at pagat.com. Retrieved 24 March 2017.
^ Pollett, Andrea (2002). "Tuman, or the Ten Thousand Cups of the Mamluk Cards". The Playing-Card. 31 (1): 34–41.
^ Mann, Sylvia (1974). "A Suit-System Subdivided". The Playing-Card. 3 (1): 51.
^ McLeod, John. Games played with Latin suited cards at pagat.com. Retrieved 10 November 2015.
^ Wintle, Adam. Portuguese Playing Cards at the World of Playing Cards. Retrieved 26 March 2017.
^ Dummett, Michael (1990–1991). "A Survey of 'Archaic' Italian Cards". The Playing-Card. 19 (2, 4): 43–51, 128–131.
^ Gjerde, Tor. Italian renaissance woodcut playing cards at old.no. Retrieved 26 March 2017.
^ "（六）鎖国時代の中国の紙牌 - 日本かるた文化館". Japan Playing Card Museum (in Japanese). Retrieved 2 September 2023.
^ Meyer, Huck. Liechtenstein'sches Spiel at trionfi.com. Retrieved 24 March 2017.
^ Jump up to: a b Dummett, Michael (1980). The Game of Tarot. London: Duckworth. pp. 14–16.
^ Berry, John (1999). "French suits and English names". The Playing-Card. 28 (2): 84–89.
^ McLeod, John. Card Games: Tarot Games at pagat.com. Retrieved 10 November 2015.
^ Renée, Janina (2001). Tarot for a New Generation (First ed.). St. Paul, Minnesota: Llewellyn Publications. p. 5. ISBN 0738701602. In the system that is most commonly used, these suits are designated as Wands, Swords, Cups, and Pentacles.
^ Smith, Caroline; Astrop, John (1999). The Elemental Tarot. New York: St. Martin's Griffin. p. 7. ISBN 0312241399. The Minor Arcana comprises fifty-six cards divided into four suits, which in most decks are swords, wands, cups, and coins or pentacles.
^ Dee, Jonathan (2002). "Introduction to the Minor Arcana". In Liz Dean (ed.). Tarot, An illustrated guide. Silverdale Books. ISBN 1-85605-685-6.
^ McLeod, John. Mechanics of Card Games at pagat.com. Retrieved 24 March 2017.
^ Parlett, David. The Language of Cards at David Parlett Gourmet Games. Retrieved 24 March 2017.
^ Leyden, Rudolf von; Dummett, Michael (1982). Ganjifa, The Playing Cards of India. London: Victoria and Albert Museum. pp. 52–53.
^ "Kartenbilder" (in German). deutscherskatverband.de. 17 January 2012. Retrieved 12 December 2012.
^ Meyer, Huck. Liechtenstein'sches Spiel at trionfi.com. Retrieved 24 March 2017.
^ Wintle, Simon (February 7, 2017). "Master of the Playing Cards". www.wopc.co.uk. The World of Playing Cards. Retrieved August 31, 2024.
^ "Master of the Playing Cards - The Queen of Flowers". MetMuseum.org. Metropolitan Museum of Art. Retrieved September 4, 2024.
^ Wintle, Simon (July 3, 1996). "Hofamterspiel, c.1460". www.wopc.co.uk. The World of Playing Cards. Retrieved August 31, 2024.
^ Wintle, Simon (May 6, 2015). "Flemish Hunting Deck". www.wopc.co.uk. The World of Playing Cards. Retrieved August 31, 2024.
^ Wintle, Simon (July 3, 1996). "South German Engraver". www.wopc.co.uk. The World of Playing Cards. Retrieved August 31, 2024.
^ Wintle, Simon (July 17, 2011). "Master PW Circular Cards". www.wopc.co.uk. The World of Playing Cards. Retrieved August 31, 2024.
^ Wintle, Simon (July 3, 1996). "The Book of Trades by Jost Amman, 1588". www.wopc.co.uk. The World of Playing Cards. Retrieved August 31, 2024.
^ Zaloga, Steven J (2007). US Airborne Divisions in the ETO 1944-45. Osprey Publishing. p. 58.
^ Stötzner, Andreas (December 7, 2010). "Swiss/German/Latin playing card symbols". unicode.org. Retrieved August 27, 2024.
^ Martin, Gary. "'In spades' - the meaning and origin of this phrase". Retrieved 24 March 2017.
| v t e Playing cards | |
--- |
| Standard 52-card deck | | | | --- | | Playing card suits (French) | Spades Hearts Diamonds Clubs | | Ranks | Ace + Ace of spades + Ace of hearts King Queen + Queen of spades Jack Curse of Scotland Beer card | | Specific decks | Ambraser Hofjagdspiel Archaeology awareness Charruan Flemish Hunting Deck Hamas most wanted Hofämterspiel Jerry's Nugget Most-wanted Iraqi Politicards Stuttgart pack Transformation | |
| Other packs and decks | As-Nas Chinese Four-colour pack Ganjifa + Ganjapa Karuta + Hanafuda + Hyakunin Isshu + Kabufuda + Uta-garuta Kvitlech Polish Russian Tarot pack Tujeon Zi pai |
| Cards | Banner Blank Court card + Knight + Ober + Unter Pip card + Deuce + Weli Joker Nicknames Stripped deck Talon Unicode |
| Other suits | | | | --- | | German | | | Swiss | Shields Roses | | German and Swiss | Acorns Bells | | Latin (Italian/Spanish/Portuguese) | Cups Coins Batons Swords | | Chinese (Money) | Cash Strings of Cash Myriads of Strings Tens of Myriads | |
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| Notable people | Lee Asher Hubert Auer Bryan Berg David Blaine Derren Brown Lewis Cohen Dan and Dave Thierry Depaulis S. W. Erdnase Lennart Green Richard Harding Johann Kaspar Hechtel Ricky Jay Sekiryo Kaneda René Lavand Ed Marlo Master of the Playing Cards John McLeod Anton Moser Samuel J. Murray David Parlett Ferdinand Piatnik Richard Valentine Pitchford Franco Pratesi Johann Georg Rauch Juan Tamariz Howard Thurston Charles Troedel Dai Vernon Fusajiro Yamauchi |
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| Art and media | | | | --- | | Paintings | - The Acrobats - The Bezique Game - The Card Players - The Card Players II - Card Players in a Rich Interior - The Card Sharp with the Ace of Diamonds - Cardplayers in a Sunlit Room - The Cardsharps - Dogs Playing Poker - Still Life with a Poem - Violin and Playing Cards on a Table | | Film and television | Card Sharks Playing Cards (1896) Play Your Cards Right | | Video games | | | Literature | Alice's Adventures In Wonderland (1865) | |
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CBSE Class 11 » CBSE Class 11 Study Materials » Mathematics » Equation of Family of Lines
Equation of Family of Lines
The family of straight lines is a collection of continuous lines that share a similar feature, in which the inclination of a straight line indicates how steeply it climbs or falls.
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What is a family of lines?
Just think about your family members. You most likely have a lot in common, yet you are not entirely the same. The same may be true for the line family. What characteristics does a line family share? What may be different? Many mathematicians and experts have evidenced that a straight line has two essential properties: slope and y-intercept. The inclination indicates how steeply the straight line climbs or falls, while the y-intercept indicates where the line crosses the y-axis. We can demonstrate this concept with two families of straight lines to illustrate this notion. A “family of straight lines” is a collection of unbroken lines that share a similar feature.
We can classify straight lines into two groups: those with the same slope and y-intercept location and those without it.
We can say that we have two types of family lines.
Keep the slope constant while varying the y-intercept; parallel lines
Change the slope while keeping the y-intercept constant.
What is the general equation of the family of lines?
The universal equation of the family of lines via the point of intersection of two provided lines is L + λ L ‘= 0, where L = 0 and L’ = 0 are the two assigned lines, and λ works as a parameter.
An explanation and understanding of the general equation of the family of lines are as mentioned below.
It forms a line of the form L = L1 + λ L2 = 0. On the other hand, it goes through the point formed by the junction of the lines L1 = 0 and L2 = 0. (where λ is a parameter) .
A linear equation with an indeterminate coefficient can depict a family of straight lines. It is necessary to note that the straight line L = 0 cannot be a fixed line in this scenario.
We understand that L1 and L2 meet at infinity if they are parallel.
If ax + by + c = 0, the perpendicular line is bx-ay + k = 0, where k is a parameter.
If we have a line ax + by + c = 0, then ax + by + k = 0, where k is a parameter, is the line parallel to it.
We can define the equation of a line as having a slope and an intercept form.
The equation y = mx + b may describe a straight line in the coordinate plane, where m is the slope and b is the intercept.
How will you find the equation of the family of lines with an x-intercept -6?
Solution
The family’s x-intercept is set to -6, with each member passing through the point (-6, 0).
The equation of such a family of lines in point-slope form is y-0 = m (x-(-6)), i.e., y = m (x + 6), where m is a parameter.
The above equation of the family does not give the vertical line through the point (-6, 0).
However, the equation of this line is x = -6, i.e., x + 6 = 0.
The equation of a straight line is sometimes given to us in a different form.
How can we show that this represents a straight line and find its gradient and intercept value on the y-axis?
Suppose we have the equation 5y – 5x = 25.
We can use algebraic rearrangement to obtain an equation in the form of y = mx + c:
5y-5x = 25 ⇨ 5y = 25+5x ⇨ y =5x+255 or y = x+5
So now the equation is in its standard form, and we can see that the gradient is 1, and the intercept value on the y-axis is +5.
We can also work in a reverse way. Suppose we know that a line has a gradient of 1/5 and has a vertical intercept at y = 3.
What would its equation be?
To find the equation, we substitute the correct values into the general formula y = mx + c. Here, m is 1/5, and c is 3, so the equation is y = x5 + 3. If we want to remove the fraction, we can also give the equation y = x+155
How do you solve the equation for a straight line with a 3 unit x-intercept parallel to 4x-7 y = 11?
Solution
According to the equation, the presented line is 4x – 7y – 11 = 0…. …..(1)
As per the above equation of the family of lines parallel to
(1) 4 x -7 y+k = 0…… …. …………(equation number 2 will be)….(2)
(2), where k denotes the parameter
By putting y = 0, you can find the x-intercept.
We get 4 x + k = 0 => x = – k4
For the required members of the family who make x-intercept 3 units,
– k4 = 3, which equals k = -12.
We can replace this value of k in (2), the equation of the required line is
4 x – 7 y – 12 = 0
How will you write an equation of the family of lines satisfying the following conditions?
parallel to the x-axis
through the point (0, -1)
1) All lines with a zero gradient are parallel to the x-axis, and the y-intercept can be anything. In conclusion, the straight line family is y = 0x+b, abbreviated as y = b.
2) All lines travelling through the point (0,-1) have the same y-intercept and b = -1 according to the given criteria.
As a result, a line family becomes y = mx -1.
How do you investigate families of lines?
Family 1: Keep the slope unchanged and vary the y−intercept.
The family of lines of the equations is of the form y=−2x+z.Although all the lines have a slope of –2, the value of z varies between them. We may note here that all the lines in this family are parallel. All lines are identical except that they shift up and down the y-axis. The line rises on the y-axis as b increases, and as b decreases, the line falls on the y-axis. We describe it as a “vertical shift” type of behaviour.
Family 2: We can change the slope while keeping the y-intercept constant. The family of lines with equations of the form y=mx+2 is considered. The slope varies, even though all the lines have a y-intercept of two. The higher the value of “m,” the sharper the line.
Conclusion
With this, we have gained a good amount of knowledge and got an insight into the topic ‘ Family of straight lines ’. Here we have discussed the representation of a family of lines and have solved several examples on the same. Family of straight lines is a very important topic, it helps in understanding some more advanced topics in coordinate geometry to follow.
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13475 | https://www.aapm.org/meetings/05SS/program/Radionuclides.pdf | Sources and Delivery Systems I: Radionuclides Ravinder Nath, Ph.D.
Yale University 2005 AAPM Summer School Outline • Photon-Emitting Radionuclides Used in Brachytherapy • Beta-Emitting Radionuclides Used in Brachytherapy • Neutron-Emitting Radionuclides Used in Brachytherapy Photon-Emitting Radionuclides Used in Brachytherapy –Cesium-137 –Iridium-192 –Radium-226 –Gold-192 –Iodine-125 –Pd-103 Radium-226 1600 year Alpha decay to radon-222 Table of Isotopes 1996 Radium-226 Uranium Series Sixth member Alpha decay to Radon-222 49 photons 0.184 to 2.45 MeV Average 0.83 MeV HVL 14 mm Pb 0.5 mm Pt encapsulation Radiological Health Handbook 1970 Cesium-137 30 year Beta decay to Ba-137m 662 keV photons Table of Isotopes 1996 Cesium-137 • Bye-product of nuclear fission • Half life 30 years • 662 keV photons • HVL 5.5 mm Pb • Stainless steel encapsulation • Less shielding compared to radium-226 • Need to adjust activity due to decay • Typically needs replacement after 7 years Iridium-192 74 days Beta decay to Excited states of Pt-192 and electron capture to Os-192 Complex energy spectrum Average 0.38 MeV Table of Isotopes 1996 Iridium-192 • Produced neutron activation in a reactor • Small tubes or wires • High specific activity • High activity small sources for HDR • Temporary brachytherapy applications • HVL 2.5 mm Pb • Widely used in multiple applications Gold-198 2.7 days Beta decays to Hg-198 0.412 MeV photons Nearly monoenergetic Table of Isotopes 1996 Gold-198 • Produced by neutron activation in a reactor • Typically 0.1 mm Pt encapsulation • Small seeds or gold “grains” • Suitable for permanent implants • Not commonly used in US • HVL 2.5 mm Pb Iodine-125 59.4 days Electron capture to excited state of Te-125 followed by characteristic x-ray emission Average 0.028 MeV Table of Isotopes 1996 Iodine-125 • Produced in a nuclear reactor • Widely used for permanent implants • HVL 0.025 mm Pb • Wide range of activities available • Numerous models available Palladium-103 17 days Decays by electron capture to excited states of Rh-103 followed by characteristic x-ray emission 20-23 keV photons Average 21 keV Table of Isotopes 1996 Palladium-103 • Can be produced in a nuclear reactor or in a cyclotron by proton bombardment • Widely used for permanent implants • Wide range of activities available • Various models available • HVL 0.004 Pb Cesium-131 10 days Decays by electron capture to Xe-131 followed by characteristic x-ray emission 4-34 keV photons Average 30 keV Table of Isotopes 1996 Dose Rate Constant of a Cesium-131 Interstitial Brachytherapy Seed Measured by Thermoluminescent Dosimetry and Gamma-ray Spectroscopy Zhe Chen, Ph.D., Paul Bongiorni, M.S., and Ravinder Nath, Ph.D. Yale University School of Medicine Introduction • A new low-energy interstitial brachytherapy seeds containing 131Cs (model CS-1) has been introduced by IsoRay Medical Inc. Gold X-Ray Marker (0.25 mm diameter) 4.5 mm Titanium Case (0.05 mm wall) Inorganic Substrate w/Cs-131 Attached Laser Welded Ends (0.1 mm wall) 4.1 mm 0.8 mm • Physical characteristics Results – Spectrum 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 0 5 10 15 20 25 30 35 40 Energy (keV) Counts Ti-Kα & Kβ Fe-Kα Cu-Kα & Kβ Kβ2 Kβ(Kβ) Kβ(Kα) CS131 - 251 Kβ1,β3 Kα1,α2 Kα(Kβ) Kα(Kα) Fluorescent x-rays Peaks X-rays Escape P k Principal Peaks Nb-Kα&Kβ A. Typical measured photon energy spectrum for a Cs-131 seed Results – Relative Spectrum B. Measured average relative photon energy spectrum for the Cs-131 seeds Relative Intensity Energy (keV) Radiation Source Bare 131Cs 131Cs seed 4.1 131Cs – L 0.143 0.0 16.6 Fluorescent (Nb - Kα) - 0.007 ± 0.0003 18.7 Fluorescent (Nb - Kβ) - 0.001 ± 0.00006 29.7 131Cs – Kα 1.000 1.000 33.6 131Cs – Kβ1, β3 0.178 0.201 ± 0.0007 34.4 131Cs – Kβ2 0.035 0.050 ± 0.0003 (Standard deviation represents deviations among the eight seeds) Monte Carlo Simulations and experimental determinations complement each other, neither alone is sufficient for characterization of a new brachytherapy source Results – Dose Rate Constant 1.058 ± 0.099 cGyh-1U-1 ⇒Approximately 15% greater than a previously measured value of 0.915 ± 0.020 cGyh-1U-1 C. Dose rate constant determined by TLD dosimetry: 1.066 ± 0.064 cGyh-1U-1 D. Dose rate constant determined by the gamma-ray spectroscopy technique: Beta-Emitting Radionuclides Used in Brachytherapy –Strontium-90 –Phosphorus-32 –Ytrium-90 Strontium-90 29 year Beta decay to Y-90 and Y-90m with a maximum energy of about 0.5 MeV Table of Isotopes 1996 Ytrium-90 64 hours Beta decay with a maximum energy of 2.27 MeV Table of Isotopes 1996 Ytrium-90m 3 hours Beta decay with a maximum energy of 2.28 MeV Table of Isotopes 1996 Strontium-90 • Bye product of nuclear fission • Therapeutic radiation is primarily from 2.27 MeV betas from Y-90 • Suitable for treatment of superficial lesions, ocular lesions and coronary vessels • Limited depth of penetration Phosphorus-32 14 days Beta decay to S-32 with a maximum energy of 1.7 MeV Table of Isotopes 1996 Phosphorus-32 • Pure beta emitter • Often used as a liquid in a balloon • Used as wire in an intravascular brachytherapy delivery system • Even more limited depth of penetration compared to Sr-90 Neutron-Emitting Radionuclides Used in Brachytherapy Californium-252 Californium-252 2.6 years Alpha decay (97%) Fission (3%) Fission neutrons Average neutron energy 2.15 MeV Average photon energy 0.8 MeV Table of Isotopes 1996 Californium-252 • Pt-Ir encapsulation • Small tube sources available • Limited use only • Temporary intracavitary brachytherapy • Difficult to shield the OR • Risk of neutron-induced carcinogenesis Some of the Possible Radionuclides For Intravascular Brachytherapy Radionuclide 32P 90Y 90Sr 192Ir 103Pd 125I 106Rh 188Re 48V Average Energy (keV) 695 934 196 370 21 28 307 756 144 Half-Life 14.28 days 2.671 days 28.5 years 73.831 days 16.97 days 60.14 days 2.17 hours 16.98 hours 15.976 days Delivery System C,S,L C,S,L C C S S L L S Emission Beta Bet a Beta Gamma X-ray X-ray Beta Beta Positron Maximum Energy (keV) 1710 2282 546 612 23 35 923 2120 696 Principal or mean energies from encapsulated sources, MeV Radionuclide Half-life Photon Beta Neutron Radium-226 1622 y 0.830 Cesium-137 30 y 0.662 Iridium-192 74 d 0.380 Gold-190 2.7 d 0.412 Iodine-125 60 d 0.028 Palladium-103 17 d 0.021 Strontium-90 29 y 0.50 Ytterbium-90 64 h 2.27 Phosphorus-32 14 d 1.71 Californium-252 2.65 y 2.15 These are nominal values assuming typical encapsulation for sources.
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13476 | https://www.youtube.com/watch?v=K88iqV0RFm4 | How To Estimate Rope Lengths (even if you SUCK at math!)
Nomadic Homesteaders - Tom Wylie
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Posted: 28 Mar 2018
In this video I'll show you how to quickly estimate the length of ANY coiled object: rope, wire, cable, hose—anything that can be coiled into a circular shape.
Not many people use the mathematical relationship of Pi in their everyday life. Well I'd bet you've never used it like THIS before!
I also give an update on my new video posting schedule (you're going to love it :) and how we're coping with a great deal of MUD on our homestead.
11 comments
Transcript:
Intro I got within three inches of the exact length of this rope by quickly doing math in my head so that's pretty good hey friends Tom Whalley here my goal with this channel is to help you gain confidence and grow your self sufficiency by sharing with you my family's story of homesteading a raw piece of land from scratch and also sharing with you how to and handyman tips showing you that you can actually accomplish for yourself a lot of things that you may not even believe to be possible at this point and showing you how to do it with things you can get your hands on well today's video is actually a segment out of a class that I taught a while back where I showed dads and kids how to lift and move huge heavy objects without power equipment or hurting their backs and it was a great time at that class I'm actually in the process of rebuilding that class into an online course that will be available sometime in the future but for now I wanted to share this piece of it where I show you how you can quickly and easily estimate using nothing but mental math the length of a rope a cable a wire anything that can be coiled up and wrapped in a circle this is applicable in all kinds of realms I've used it anywhere from if I'm wiring a room putting in an electrical outlet and I have a scrap of wire I can use this to quickly estimate if that wire is long enough to do to to power that circuit or to run to that outlet over there or whatever you can also be used if you are winching a vehicle and you need to know do I have enough cable to reach from my vehicle bumper to the that tree stump over there do I have enough rope to repel down this rock face there's all kinds of applications for this it's quick to learn and even faster to apply I've also used this when I'm buying used materials or buying materials by the pound I've bought a lot of wire by the pound and it's a lot cheaper that way but sometimes you have to double check to make sure that the price you're paying is actually a deal especially if you're getting something used so I hope you enjoy it I'll just let you dive right in and stay tuned to the end because I will be sharing an announcement and some updates on what's going on around our homestead so I'll see it after the video but for now enjoy how would you like to be able to quickly estimate the length of this item in your head even if you're terrible at math well that's what I'm How to estimate length going to show you today how do I know how long this rope is without unspooling it and measuring it and without doing super complicated math to do that I'll show you a principle called pi and it's no nothing fancy you have learned about it in school or you will soon if you're younger but but it's very very simple here's a circle and here is a piece of wire that I cut to be exactly the length of the what's called the diameter of the circle just the distance across the circle that wire is the same length so that wire equals one diameter of this circle there's a relationship between the diameter and the circumference the distance around the circle and we can demonstrate that by just bending the wire to roughly the shape of the perimeter or the circumference of this circle and I'm just going to draw starting up here at the top I'm going to draw there's where the wire starts here that where's here's where the wire ends so that's one length of wire I'm going to start it and end it again there's one a second length of wire and then here's one more length of it so you can see if I know the distance across then I can calculate the distance around by just multiplying by 3 plus a little bit the technically pie is 3.14 etc the number keeps going with a longer decimal but we aren't going to be worried about that in fact I usually don't even worry about the 0.14 we might even address 3.1 but basically we're estimating we are just wanting to see if we're in the ballpark of having enough rope for our project or if the wire that we're buying by the pound is a comparable price to buying it by the foot okay so here's the formula to remember to estimate the length of a coiled item the formula is the number of wraps times how close is it to one foot across in diameter is that one foot or is it one and a half feet or one and a quarter feet or two feet what is that relationship for one it normally it's going to be times one because it would be one foot across ideally but that number can change and then times three if you get fancy times three point one three point one four but just do it times three and usually we'll add a little bit to cover that point one four that equals your length so let's put that to work this coiled rope is one foot across because I happened to make this coiled rope but I'll show you you know put it in a rough circle shape and yep it's about twelve inches across there's there's a foot right there so this thing is one foot across so because of that relationship that pi relationship I know that for each each time I have a full loop of a rope around here that represents a little over three feet going around one time so all I do all I have to do is count okay how many times did it go around times three feet and really if you're if you look at it if you just go three point one what does that mean that means that it's three feet for every wrap that's a foot across it's three feet plus a tenth of a foot so that means if I have ten wraps then I would have an extra foot by the time I get through those ten wraps that tenth will add up and be one foot it's a way to get close we're not after your super accuracy we're just after is this thing closed or do I need to do something else so how many wraps because I see that here's one end of the rope here's the other end of the rope the there's going to be one more half loop on this side because both the tails are are here so I'm going to count do my counting on the opposite end where I know there's not that extra half wrap so just count the wraps 1 2 3 4 5 6 7 8 9 10 11 12 12 wraps plus a half wrap so very quickly in my head 12 wraps 12 times 3 is 36 plus a half wrap what's half of 3 one and a half so 36 37 and a half so 32 seven and a half and then for every 10 wraps we have 12 wraps so that would be another 1.2 feet they're about a foot and a quarter so in total we're looking at 37 and a half plus so 30 38 basically 38 and 3/4 39 feet right around there about 39 feet of rope right there well guess what if I were to measure this it's 39 and 1/4 feet long so hey I got within a quarter of a foot that's only 3 inches I got within 3 inches of the exact length of this rope by quickly doing math in my head so More examples that's pretty good ok let's try another example but with with a greater number of wraps to see how our accuracy does this one it's it's wire that I bought by the pound at a recycler and so say I'm wanting to see okay is this comparable to buying the wire new by the foot or or should I just not buy it here this one is also one foot across thankfully so we are our factor here is still one both ends of the wire are right here so there's so there's you know there's tiny bit of overlap so basically I can count anywhere on this side and I know I don't have a an extra partial wrap so count the number of wraps 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 that's handy 20 wraps so 20 times 3 would be 60 so I know I have more than 60 feet here sometimes that's enough like you can get that far and go Oh 60 feet okay great I only needed 50 good to go let's let's get out of here but sometimes you need a little more than that so okay I know I have at least 60 feet because I had 20 wraps how about the tenth here for every 10 wraps it's an extra foot so 20 wraps that'd be 2 feet extra so 62 feet maybe you had a smidge more 62 and a half 63 feet something like that if I measured this exactly it's 62.8 feet so right between my 62 and a half 63 it's dead-on like that is the length of this wire so that's pretty accurate what if your your wrap your your wrapped wire this is a chopped-off extension cord just wire stock basically what is the motive it's not a foot across now what well that's where this part comes in let's measure it kind of hard when it's in the air like this but we'll do our best so you go like this and suspend it and then I'll just bring this up until it's about a round shape a circle yeah somewhere close close to there that looks pretty round if I can get my tape measure to cooperate it's about a foot and a half 18 inches I'll call that good a foot and a half all right so all we have to do now is change this number to 1.5 so its wraps times one and a half because this is one and a half feet across the circle one and a half times three and then to get that extra tenth in this case every 10 wraps you have is going to be one and a half feet not just one feet or one foot so wraps times one and a half times three plus the extra one and a half feet per 10 wraps you have so let's count the wraps both ends of the wire are here here's one end here's the other end so our overlap area is here so any anywhere over here is going to be good for County so count wraps one two three four five six seven eight nine ten wraps exactly so ten wraps ten times one and a half that's 15 times 3 is 15 times 3 is 45 plus the extra one and a half feet per 10 wraps well we have 10 wraps here so an extra foot and a half so 45 46 and a half 46 and a half feet is our estimate well if I were to measure this which and I did it was exactly forty seven point one feet long so we were at 46 and a half so we were only smidge over six inches off in our estimate so pretty accurate so that's how you do it that's how you can estimate quickly in your head with no calculator no fancy anything and believe me I'm not good at math but I'm able to quickly and pretty accurately estimate lengths when when you use this method I hope you learned Outro something from this video that you can apply to your homesteading efforts I wanted to just give you an update on this channel my posting schedule as of late has been kind of sporadic but I want to change that because my goal is to help you gain confidence in fulfilling your homesteading dreams and to do that I need to post regularly so starting last week actually I am now posting every Friday so it won't necessarily be the same time of day at this point I'm still dialing things in but every Friday you can expect to see a new video from me at this point it'll be between vlog video updates on our homestead we've there's a lot of things that I've filmed over the last year that I haven't had time to edit or upload yet so those are still coming as well as the how-to tips like today to actually teaching you how to do something so it'll all kind of alternate between a vlog and a tip based on what's appropriate for that day so expect that to be coming as far as updates on our homestead we are nearing the end of winter it feels like it's getting warmer the snow is melting away we have we're having less and less snow nowadays and seeing more and more mud coming back so we're dealing with a lot of mud right now I just built a sort of third world country esque log bridge over some really muddy area of our driveway actually need to do more of that so I'll put that up in a video here coming soon how we are getting through this muddy season with our front wheel drive minivan that has really low clearance and our two-wheel drive 1972 pickup neither of which cars are all that great in heavy mud but we're making it through with a little bit of creativity and some frugal use of resources available to us so stay tuned for that and if you like this video give me a thumbs up share it with a friend you think might appreciate it comment below with any questions or suggestions on things you'd like to learn and as always if you like what you see here subscribe if you haven't already and you'll get more well thanks a lot for watching and I'll catch you later [Music] let's go kind of fast on this burke's it's so soft still Oh yep we need to fix that and then aim hit the bridge all right we did it [Music] on our way [Music] |
13477 | https://www.scribd.com/document/382233667/OpenStax-Calculus-Volume-3 | OpenStax - Calculus Volume 3 | PDF | Orbit | Equations
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OpenStax - Calculus Volume 3
Volume 3 of the OpenStax Calculus series covers Multivariable calculus in chapters 1-6, and provides an introduction to more advanced differential equations in chapter 7.
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13478 | https://www.imsc.res.in/~vikram/DiscreteMaths/2011/pp.pdf | Pigeonhole Principle and Ramsey Theory The Pigeonhole Principle (PP) has often been termed as one of the most fundamental principles in combinatorics. The familiar statement is that if we have n pigeonholes and more than n pigeons, then there must be a pigeonhole with more than one pigeon.1. More formally, a function f that maps a set X, |X| = m, to a set Y , |Y | = n, where m > n, cannot be injective, i.e., there is a y ∈Y such that |f −1(y)| > 1. But this is not the complete picture. The stronger implication is that there are two elements y, z such that |f −1(y)| ≥m/n ≥|f −1(z)|.
Though the principle is very simple to state, proofs involving the principle are usually considered in-genious, since finding the “pigeonholes” and the “pigeons” is non-trivial.
In this lecture, we give some interesting applications of the principle.
The principle is a special case of the more general theory is that was developed by Ramsey, namely a large structure should satisfy some property. For instance, for any given n, if we pick sufficiently many points in the plane (no three collinear) then there will be a subset amongst them that form a convex polygon with n vertices (5 points for a quadrilateral, 9 for a pentagon). Or, given two numbers a, b there is a number n such that a two-coloring of Kn either contains a monochromatic Ka or a monochromatic Kb. We will subsequently study some results from the general theory, where the existence of such numbers and bounds on them are derived.2 ¶1. Initiating Examples: Given the numbers 1, . . . , 2n, let f(n) be the number such that any subset of [2n] of size f(n) contains two numbers that are relatively prime. Formulated in this way the solution is not evident. But if we find two numbers that are consecutive, then we know that they are relatively prime.
Clearly, f(n) > n, since we can pick the n even numbers. So we guess f(n) = n + 1, and indeed that is the case, since in any subset of n + 1 numbers two must be consecutive. To formulate in terms of pigeonhole principle, let x1, . . . , xn+1 be the numbers; x0 := 1. Let gi, i = 1, . . . , n, be the number of elements remaining between xi and xi+1. Then Pn i=1 gi = n −1. Thus there must be a gi that is zero, i.e., two elements xi and xi+1 must be consecutive.
Now let’s consider the complement property: let f(n) be the number such that any subset of [2n] of size f(n) contains two numbers such that one divides the other. Again f(n) > n, since in the set {n + 1, . . . , 2n} no number divides another. What is surprising is f(n) = n + 1 again, i.e., any subset of size n + 1 has two numbers that are relatively prime and two numbers such that one divides the other. The proof via pigeonhole principle is tricky and is based upon the observation that any number in [2n] can be expressed in the form 2km, where m is an odd number. Since there are only n odd numbers in [2n], in any subset of size n + 1 there must be two numbers that have the same odd part, and hence one divides the other. This result already shows the ingenuity needed to apply pigeonhole principle.
1 Dirichlet’s Application One of the earliest non-trivial applications of pigeonhole principle was by Dirichlet in Diophantine Approxi-mation, and basically says that every irrational real number can be approximated quite well with rationals.
1Dijkstra’s remarks: The Strange Case of the Pigeonhole Principle 2The complement problem is, How large can a structure be such that it avoids a certain property. For instance, how many edges can a graph on n vertices have have such that we do not have a cycle of length 4? Such problems are called extremal problems.
1 More precisely, let α be an irrational number, then for all N ∈N, there exists p, q, 1 ≤q ≤N, such that α −p q ≤1 q2 .
(1) This implies that there are infinitely many rationals p/q for which the above holds. Also, there is at most one rational with a fixed denominator q that satisfies this inequality (any two rationals with the same denominator q differ by 1/q).
We will show the stronger claim: α −p q < 1 q(N + 1), or equivalently |qα −p| < 1 (N + 1).
(2) The above inequality suggests that p must be the integer nearest to qα, and since 1 ≤q ≤N, it makes sense to define αi := iα −⌊iα⌋, i = 1, . . . , N. Then αi ∈(0, 1), and αi are irrationals (otherwise α will be a rational).
Consider the partition of (0, 1) into N + 1 open intervals of the form Ij := (j/(N + 1), (j + 1)/(N + 1)), j = 0, . . . , N. There are three cases to consider. In all the cases, we will show that there exists p, q s.t.
q ≤N and they satisfy (2).
1. If there is an i s.t. αi ∈I0. Then 0 < iα −⌊iα⌋< 1 N + 1, and so we can choose p := ⌊iα⌋and q := i.
2. If there is an i s.t. αi ∈IN+1. Then N N + 1 < iα −⌊iα⌋< 1.
Subtracting one from the inequality we get −1 N + 1 < iα −⌊iα⌋−1 < 0, which implies |iα −⌊iα⌋−1| < 1 N + 1.
Thus in this case we choose p := ⌊iα⌋+ 1 and q := i.
3. If there is no i falling in the first two cases, then the N numbers αi must be contained in N −1 intervals I1, . . . , IN−1. Thus by pigeonhole principle there are two indices i, j (say i < j) s.t. αi and αj are in the same interval Ik, k = 1, . . . , N −1, i.e., k N + 1 < iα −⌊iα⌋< (k + 1) N + 1 and k N + 1 < jα −⌊jα⌋< (k + 1) N + 1 .
Therefore, |jα −⌊jα⌋−(iα −⌊iα⌋)| < 1 N + 1, which implies |(j −i)α −⌊jα⌋+ ⌊iα⌋)| < 1 N + 1.
So we can choose q := (j −i) and p := ⌊jα⌋−⌊iα⌋.
Thue-Siegel-Roth theorem states that there are numbers for which (1) is in some sense the best, namely irrational algebraic numbers cannot be approximated by infinitely many rationals better than what (1) suggests, i.e., with 2 replaced by 2+ϵ, for some ϵ > 0. This property is very useful in numerical computations with algebraic numbers.
2 2 Erd¨ os-Szekeres: Monotone Sequences Given N numbers a1, . . . , aN, an increasing subsequence of length k is a set of k indices, i1 < · · · < ik , such that ai1 < · · · < aik; similarly define a decreasing subsequence.
Theorem 1. Any set of mn + 1 distinct real numbers a0, . . . , amn either contains an increasing subsequence of length m + 1 or a decreasing subsequence of length n + 1.
Proof 1 (PTB): Let ti, i = 0, . . . , mn + 1, be the length of a longest increasing subsequence starting from ai, and let f be this map, i.e., f(ai) = ti. If there is a ti ≥m + 1 then we are done. So assume all ti ≤m. Since there are only m possible values of ti and mn + 1 numbers are mapped to these values, there must be a value, say t ≤m, and n+1 numbers ai0, . . . , ain such that f(ai0) = f(ai1) = · · · = f(ain) = t. We claim that these n + 1 numbers form a decreasing subsequece; if aij < aij+1, for some j ∈[0, . . . , n −1], then we have an increasing subsequence of length t + 1 starting from aij, namely the one obtained by prefixing aij to the increasing subsequence starting from aij+1, which is a contradiction.
Proof 2 (Seiderling): The fact that there are mn + 1 numbers suggests us that we should try to map then into a matrix of size mn. Instead of assigning a single number, we assign a pair with each number: Let si be the length of a longest decreasing subsequence starting from ai, and ti be the length of a longest increasing subsequence starting from ai. Let f be this map. If there exists an i, for which either ti > m or si > n then we are done. So suppose for all i, 1 ≤ti, si ≤m. Thus f maps mn + 1 numbers into mn pairs, thus by pigeonhole principle two numbers must have the same pair associated with them. But this cannot be, since if ai < aj then ti > tj, and if ai ≥aj then si > sj, giving us a contradiction.
Proof 3 (Hammersley): This is a constructive proof, and instead of assigning a pair with each number we try to fit them in a matrix of size mn; clearly, there will either be a row of length n + 1 or a column of length m + 1; the construction additionally ensures that the rows and columns are ordered subsequences.
Arrange the mn + 1 numbers in a column/stack as follows: place x1 in the first column; if at any given stage we have place x1, . . . , xi−1 into som columns, then place xi at the top of the first column that has the topmost entry smaller than xi; if no such column exists then place xi at the starting of a new column. Let k be the number of columns obtained. The crucial observation is that entries in a column form an increasing subsequence, and the topmost entries from the first to the kth column form a decreasing subsequence. If k > n then we have a decreasing subsequence of length n + 1. So suppose k ≤n. By pigeonhole principle we know that there is a column that has length at least mn/k + 1. Since k ≤n, the length of this column is at least m + 1, and so we have an increasing subsequence of the desired length.
Proof 4 (Erd¨ os-Szekeres): By induction.
The theorem is tight as shown by the following sequence of mn numbers: m, m −1, . . . , 1, 2m, 2m −1, . . . , m + 1, 3m, 3m −1, . . . , 2m + 1, . . . , nm, nm −1, . . . , (n −1)m + 1.
Note that in proving Theorem 1 we have not used the fact that the numbers are real numbers. A more general statement is the following.
Corollary 2. Given an ordered set S containing mn + 1 elements, and a linear order π on these elements, there is an ordered subset T of S that is monotone wrt π. Note that T preserves the ordering of S as well as the ordering imposed by π.
We now given an application of this generalization.
A set of linear orders π1, . . . , πm on [n] is said to realize Kn if for all i, j ∈[n] and k ∈[n] −{i, j} there exists a order πi such that i, j precede k; express this as i, j ≺k. The order dimension of Kn is the size of the smallest set of linear orders that realize Kn. So dim(K3) = 3. It is also clear that dim(Kn+1) ≥dim(Kn), since in any set of linear orders realizing Kn+1 if we delete n + 1 we get a linear order realizing Kn. Thus dim(K4) ≥3, and it is 3 as the following set shows: (1, 2, 3, 4), (2, 4, 3, 1), (1, 4, 3, 2).
We claim that dim(Kn) ≥log log n, and it suffices to verify it for n = 22m + 1, i.e., in this special case dim(Kn) ≥m + 1. Suppose not, and let π1, . . . , πm be a set of linear orders over [n] realizing Kn. From Corollary 2, we know that π1 contains a monotone subset A1 of length 22m−1. Consider the set A1 in π2, 3 then it contains a monotone subset A2 of length 22m−2 + 1 (the indices of the elements of A2 are ordered wrt the indices in A, therefore, A2 is monotone in π1). Continuing in this manner, we will eventually get that πn contains an ordered monotone subset Am ⊆Am−1 of length 22m−m + 1 = 3. Let Am = (xi, xj, xk), where i < j < k are the indices of the elements in A1. Then what we’ve shown is that xi, xj, xk form a monotone subsequence in all the linear orders π1, . . . , πm. That is, either xi < xj < xk or xi > xj > xk in all the linear orders, which implies that there is no linear order in which xi, xk are dominated by xj, which is a contradiction since π1, . . . , πn realize Kn. J. Spencer showed that this bound is tight, namely dim(Kn) = log log n + o(log log log n).
4 3 Ramsey Theory In this section we study a generalization of pigeonhole principle. One way to state pigeonhole principle is that given n objects and m < n colors, in any coloring of the n objects there will be two objects that have the same color. Instead of coloring objects, what if we color pairs of objects, i.e., subsets of [n]2? What will be the analogue of the pigeonhole principle? Let’s start with a standard puzzle: How many people do we need in a room such that we are sure that either there is a triplet that are mutual friends, or mutual strangers? We assume that friendship is mutual (or symmetric), but not transitive. If we had asked for a pair of friends or strangers, then the answer is trivially two. As Figure 1 shows, even five is not sufficient.
However, we next show that six is sufficient. This is the first non-trivial illustration of Ramsey theory.
• • • • • Figure 1: Five people do not necessarily have 3 friends or strangers; bold edges represent friendship and dashes represent strangers.
Let A, B, C, D, E, F be the six people. Now A either is friends with three people or stranger to three people; if neither of this is true, then A is friends with at most two people and stranger to at most two people, which only accounts for four out of the remaining five, which can’t be. Suppose A is friends with B, C, D (the argument is similar when A is stranger to them). There are two cases to consider: 1. if amongst B, C, D there are two friends, say B, C, then A, B, C are mutual friends; 2. B, C, D are mutual strangers, in which case we are done.
How many people do we need to ensure that there are four mutual friends or strangers? Perhaps it’s easier to ask the following question: How many people do we need to ensure that there are either four mutual friends or three mutual strangers? That is, we can ask mixed questions as well. It can be verified that ten is sufficient, but this is not tight. The argument is similar to above. A either knows at least 6 or doesn’t know at least 4 people (WHY?). If he knows 6, then within the six there are either three friends or three strangers; in the former case, the three friends along with A give us four mutual friends, and in the latter we have three strangers. If A doesn’t know four people, then there are two cases: if all the four know each other then we are done, otherwise there is a pair that don’t know each other, and along with A we get three people that are mutual strangers. The inductive approach in the first case will be useful later on.
In general, we can ask given some ℓhow many people do we need to ensure that there are ℓmutual friends or strangers. The existence of such a number is not even clear a priori. A special case of Ramsey’s theory shows that such a number indeed exists for every ℓ. Before we proceed we formalize the setting using graph theoretic terms. What we have shown is that given a coloring of K6 using two colors there always exists a monochromatic triangle, or K3. The question on ten people shows that any two-coloring of K10 contains either a monochromatic K4 or K3.
Given (ℓ1, . . . , ℓr) ∈Nr, define the Ramsey function R(ℓ1, . . . , ℓr) as the smallest number n such that in all colorings of Kn using at most r colors there will always be a monochromatic Kℓi, for some color i.
This is usually represented as n →(ℓ1, . . . , ℓr).
(3) If ℓ1 = ℓ2 = · · · = ℓr = ℓ, then we succinctly write n →(ℓ)r and the Ramsey function as R(ℓ; r). Thus the puzzles above show that 6 →(3), and 10 →(4, 3). The key result of Ramsey was to show that such a function is well-defined. Before we proceed further, we show some properties of the function.
5 P1. If ℓ′ i ≤ℓi, i = 1, . . . , r, then n →(ℓ1, . . . , ℓr) implies n →(ℓ′ 1, . . . , ℓ′ r). Clearly, if there is a monochromatic Kℓi, then all induced subgraphs of it of size ℓ′ i are monochromatic as well.
P2. If m ≥n and n →(ℓ1, . . . , ℓr) then m →(ℓ1, . . . , ℓr). This is obvious, since any r-coloring of Km contains an r-coloring of Kn, which contains a monochromatic Kℓi.
P3. For any permutation π : [r] →[r], n →(ℓ1, . . . , ℓr) iffn →(ℓπ(1), . . . , ℓπ(r)). Intuitively, this statement says that permuting the colors doesn’t matter. More precisely, there is a monochromatic Kℓi iffthere is a monochromatic Kℓπ(j), where j := π−1(i).
P4. n →(ℓ1, . . . , ℓr) iffn →(ℓ1, . . . , ℓr, 2). The necessary part follows, since if we use r colors then there is a monochromatic Kℓi in Kn still holds when we increase the number of colors, since the additional color may not be used in the coloring. For the sufficient part, if n →(ℓ1, . . . , ℓr, 2) then we know that in any (r + 1)-coloring, where we only use the first r colors, we must have a monochromatic Kℓi, for some i, therefore n →(ℓ1, . . . , ℓr). Note that the following is trivially true n →(2)r, for n ≥2, and n →(n, 2), for any n; thus R(n, 2) = R(2, n) = n.
Ramsey’s theorem, in its most simplified form, states the following: Theorem 3 (Ramsey Theorem Weak Form). The Ramsey function is well defined, i.e., given (ℓ1, . . . , ℓr) there exists an n satisfying (3).
We start with r = 2 and give two proofs: one an inductive argument, and another an explicit upper bound on R(ℓ; 2). We want to show that given (ℓ1, ℓ2), R(ℓ1, ℓ2) exists.
Proof 1. From P4 we know that R(ℓ, 2) = R(2, ℓ) = ℓ. Inductively, assume that R(ℓ1−1, ℓ2) and R(ℓ1, ℓ2−1) are well-defined. We claim that n := R(ℓ1, ℓ2 −1) + R(ℓ1 −1, ℓ2) →(ℓ1, ℓ2).
Pick a vertex x ∈[n], and consider the edges from x to the remaining n −1 vertices. In any two-coloring of Kn, say by red and green, one of the following must hold true: either the number of red edges from x are greater than R(ℓ1 −1, ℓ2), or the number of green edges are greater than R(ℓ1, ℓ2 −1); if either condition does not hold, then we have only accounted for < n −1 neighbors of x. In the first case, either there is a green Kℓ2 or a red Kℓ1−1, which along with x gives us a red Kℓ1. In the second case, we similarly get either a red Kℓ1 or a green Kℓ2 containing x. Note that the formula above explains (3, 3) + (4, 2) = 10 →(4, 3). In general for r colors we should choose n := 2 + Pr i=1 R(ℓ1, . . . , ℓi −1, . . . , ℓr) −1.
Proof 2. The second proof derives shows that R(ℓ, ℓ) ≤n := 22l−1 −1. Pick an x1 ∈S1 := [n]. Consider a two-coloring χ of Kn; let the colors be R and G. Consider the edges from x to the remaining n −1 vertices. The set of n −1 vertices that are connected to x are partitioned into two classes depending on the color of the connecting edge; let S2 be the larger of these two sets; clearly |S2| ≥(|S1| −1)/2 = 22l−2 −1. Pick an x2 ∈S2 arbitrarily, and again look at the edges from x2 to the remaining elements in S2; let S3 be the larger set in the partitioning of S2 induced by the color of edges emanating from x2; then |S3| ≥22l−3 −1. Continue in this manner defining Si+1 from Si always satisfying |Si+1| ≥(|Si| −1)/2. In this way we can construct S1, S2, , . . . , S2ℓ−1, since in general |Si| ≥22ℓ−i −1, and elements x1, . . . , x2ℓ−1, where xi ∈Si. Note that xi is connected to xi+1, . . . , x2ℓ−1, i = 1, . . . , 2ℓ−2, with the same color. Let the dominating color of xi be the color connecting it to all the vertices in Si+1. Let TR be the set of those xi that have dominating color R; similarly, define TG. One of TR or TG is of size ≥ℓ. We claim that this is the monochromatic set Kℓthat we are looking for. In general for r colors we should choose n := r(ℓ−1)r+1 −1.
The stronger form of Ramsey’s theorem applies to the k-uniform hypergraph on n vertices, i.e., hyper-graphs where all edges are sets of size k, i.e., in [n] k . Given (ℓ1, . . . , ℓr), the Ramsey function Rk(ℓ1, . . . , ℓr) is defined as the smallest number n such that in any r-coloring of the k-uniform hypergraph on [n] there 6 exists a subset T of vertices of size ℓi such that all edges in T k are monochromatic in color i. This is usually represented as n →(ℓ1, . . . , ℓr)k.
The weak form states that R2(ℓ1, . . . , ℓr) is well-defined, but how about R1(ℓ1, . . . , ℓr)? Now we are looking at r-coloring of vertices. How large n should be to ensure than in any r-coloring of [n] some ℓi vertices have the same color. We claim that n := Pr i=1(ℓi −1) + 1 suffices. This is the pigeonhole principle, and this is the reason why Ramsey theory is considered a generalization of pigeonhole principle. The stronger form of Ramsey’s theorem states that Theorem 4 (Ramsey Theorem Strong Form). Given k, ℓ1, . . . , ℓr the function Rk(ℓ1, . . . , ℓr) is well-defined.
3.1 Applications ¶2.
Monotone Subsequences: Given m, n, we claim that there exists a function f(m, n) such that any sequence x0, . . . , xf(mn) of real numbers contains a either an increasing subsequence of length m + 1 or decreasing subsequence of length n + 1. We claim that N := f(m, n) := R2(m + 1, n + 1) −1 does the job.
The key question is how do we 2-color the edges of the complete graph on KN? Let’s say the edge between xi and xj is colored R if xi < xj and B if xi > xj. We know that any 2-coloring of KN+1 contains either a R Km+1 or a B Kn+1; in particular, this holds for the coloring we introduced; say we have an R Km+1.
What does it mean? Let the vertices be xi0, . . . , xim, where i0 < · · · < im. Then a red edge between xij and xij+1, j = 0, . . . , m, implies that xi0 < xi1 < · · · < xim as desired; a similar argument shows that a B Kn+1 implies a decreasing subsequence of length n + 1. The above argument does not give us an explicit value of the function, as was the case earlier.
¶3. Convex Polygons: 3 Given a k > 2, how many points n(k) do we need in the plane such that we are sure they contain a convex polygon on k vertices, where points are in general position, i.e., no three points are collinear? If k = 3 then it is clear that three points suffice, since the three points are not collinear, they must form a triangle. How about k = 4? Do four points suffice? Claim n(4) = 5.
We start with a characterization of convex k polygons. Given k vertices of a convex polygon, it is clear that any four must form a quadrilateral; for if a point is contained inside a triangle formed by the remaining three, then that point cannot occur as a vertex of the k-gon. Is the converse also true, i.e., if k points in the plane in general position are such that all sets of four points form a convex quadrilateral then the k points form a k-gon? We show that if a set of k points in general position do not form a k-gon then there must be a point that is contained in a triangle formed by some other three points. Consider a triangulation of the convex hull of the k-points. Clearly, one of the k points must be inside some triangle in this triangulation; moreover, it cannot be on the boundary of the triangle since points are in general position. How do we use this result to show the existence of n(k)?
We claim that n(k) := R4(k, 5) points in general position must contain a k convex gon. Consider the following coloring of [n] 4 , i.e., the set of sets of size four of [n]: if a T ∈ [n] 4 forms a convex quadrilateral then color T red, otherwise color it blue. By definition of n(k) there is either a subset of size k such that all sets in [k] 4 are colored red, which by our earlier assumption implies that these k points form a convex polygon; the other case is if all sets in 4 are colored blue, i.e., there are five points such that any subset of four points do not form a convex quadrilateral, but this cannot be the case since n(4) = 5. Therefore, R4(k, 5) points in general position in the plane must contain k points that form a convex k polygon.
¶4. Schur’s Result: Given r, there exists n(r) ∈N such that for any r-coloring of 1, . . . , n, there exists three monochromatic 1 ≤x, y, z ≤n such that x + y = z.
Claim is n := R2(3; r) −1. Given a coloring of 1, . . . , n, we color the edge between the vertices i, j in Kn+1 with the color of 1 ≤|i−j| ≤n. Thus we know that in this coloring of Kn+1 there must be a monochromatic 3The Happy Ending problem, since it led to the marriage of Esther Klein and George Szekeres.
7 triangle K3, say between the vertices i, j, k. Suppose i < j < k, then x := j −i, y := k −j, and z := k −i.
Since the edges of the triangle have the same color, it follows that x, y, z have the same color and clearly, x + y = z.
8 |
13479 | https://planspace.org/20230316-solving_a_matching_problem_with_ortools_cpsat/ | Solving a matching problem with OR-Tools CP-SAT
Thursday March 16, 2023
Optimizing matching for preference satisfaction often focuses on stability, which prioritizes individual interests. When maximizing resource utilization is more important, Constraint Programming (CP) can be used to find good matches. Google's OR-Tools package includes the CP-SAT solver, which is one way to implement this.
For example, we may be assigning a pool of interns to specific roles. Managers for each role have ranked some of the candidates, and a candidate can only be matched to a role for which they have been ranked. Roles often have one spot to be filled, but some have more. Candidates have been ranked for multiple roles, but can only be assigned one.
This problem is similar to the medical residency matching problem, which famously applies the Nobel-prize-winning Gale–Shapley algorithm. One difference is that the present example only has preferences from one side. Sometimes random preferences are created in order to still allow the application of algorithms like Gale–Shapley, but this will not be necessary here because there is a bigger issue.
The salient difference between what Gale–Shapley does and the goal of the example here is that we really want to fill every available role, even if it means the match isn't perfectly stable. Gale–Shapley will create a match that leaves some roles unfilled if this is necessary to ensure that no trade would better satisfy the preferences of the individuals involved. In general, Gale–Shapley will leave some roles unfilled.
To begin a solution with the OR-Tools (OR for Operations Research) package, we start by converting the rankings to scores, where 1 is the best and 0 is the worst: rankings.csv (There are different ways of doing this, like percentiles; here we assume we have scores.)
role,person,score Role 23,Person 11,0.5238095238095238 Role 23,Person 109,0.7619047619047619 Role 23,Person 111,0.6190476190476191 ...
Each role has some maximum number of spots to fill: spots.csv
Role 23,4 Role 31,1 Role 8,1 ...
We can start reading in data using Python.
import csv spots = {role: int(n) for role, n in csv.reader(open('spots.csv'))} all_rankings = [ranking for ranking in csv.DictReader(open('rankings.csv'))]
It will be convenient to have quick access to all the people ranked for a role, and all the roles a person is ranked for.
by_role, by_person = {}, {} for ranking in all_rankings: by_role.setdefault(ranking['role'], []).append(ranking) by_person.setdefault(ranking['person'], []).append(ranking)
Now we can start using OR-Tools.
from ortools.sat.python import cp_model model = cp_model.CpModel() solver = cp_model.CpSolver()
The matching will be represented via a Boolean variable for each ranking that is true to select that match and false otherwise.
for ranking in all_rankings: ranking['selected'] = model.NewBoolVar('')
OR-Tools lets us use natural Python expressions to express constraints. First, we dictate that each role should have no more than the allowed number of people.
for role, rankings in by_role.items(): total = sum(ranking['selected'] for ranking in rankings) model.Add(total <= spots[role])
Similarly, we require that each person is matched with at most one role.
for person, rankings in by_person.items(): total = sum(ranking['selected'] for ranking in rankings) model.Add(total <= 1)
The objective will be to maximize the total score of selected matches.
total_score = 0 for ranking in all_rankings: score = float(ranking['score']) ranking['selected'] total_score += score
At this point, we need only ask for the solution.
model.Maximize(total_score) status = solver.Solve(model) print(solver.Value(total_score), solver.StatusName(status)) # 82.87644300144302 OPTIMAL
You can check that every role has its maximal number of people, and every person has one role (or zero; this example has more people than spots). The CP-SAT solver has done the heavy lifting of finding a solution and even guaranteeing that it is optimal.
with open('results.csv', 'w') as f: writer = csv.DictWriter(f, all_rankings.keys()) writer.writeheader() for ranking in all_rankings: ranking['selected'] = solver.Value(ranking['selected']) writer.writerow(ranking)
Code is also available in a notebook. Writing out results produces: results.csv
role,person,score,selected Role 23,Person 11,0.5238095238095238,0 ... Role 23,Person 41,0.5714285714285714,1 ...
The approach here is general enough that with modifications it can be applied to a wide range of more or less related problems. There is always a question of whether the chosen metric is the right one to optimize, but making some choice can get you pretty far toward a good solution, with a solver that makes optimization easy. Indeed, what other problems might be formulated in a manner amenable to solving in this way? OR-Tools are handy!
Thanks to Maxime Labonne, whose Linear Programming course was very helpful as I started to use OR-Tools. |
13480 | https://pmc.ncbi.nlm.nih.gov/articles/PMC11411811/ | Protocol for a systematic review and meta-analysis investigating the impact of continuous versus intermittent enteral feeding in critically ill patients - PMC
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Syst Rev
. 2024 Sep 19;13:239. doi: 10.1186/s13643-024-02652-8
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Protocol for a systematic review and meta-analysis investigating the impact of continuous versus intermittent enteral feeding in critically ill patients
Lydia S Acharya
Lydia S Acharya
1 Faculty of Health Sciences, University of Ottawa, Ottawa, ON Canada
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1,✉, Anne M Clayton
Anne M Clayton
2 Department of Health Research Methods, Evidence and Impact, McMaster University, Hamilton, ON Canada
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2, Lawrence Mbuagbaw
Lawrence Mbuagbaw
2 Department of Health Research Methods, Evidence and Impact, McMaster University, Hamilton, ON Canada
3 St. Joseph’s Healthcare Hamilton, Hamilton, ON Canada
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2,3, Simon Oczkowski
Simon Oczkowski
2 Department of Health Research Methods, Evidence and Impact, McMaster University, Hamilton, ON Canada
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2, Bram Rochwerg
Bram Rochwerg
2 Department of Health Research Methods, Evidence and Impact, McMaster University, Hamilton, ON Canada
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2, Jennifer Tsang
Jennifer Tsang
2 Department of Health Research Methods, Evidence and Impact, McMaster University, Hamilton, ON Canada
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2, Kaitryn Campbell
Kaitryn Campbell
3 St. Joseph’s Healthcare Hamilton, Hamilton, ON Canada
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3, Karin Dearness
Karin Dearness
3 St. Joseph’s Healthcare Hamilton, Hamilton, ON Canada
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3, Joanna C Dionne
Joanna C Dionne
2 Department of Health Research Methods, Evidence and Impact, McMaster University, Hamilton, ON Canada
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1 Faculty of Health Sciences, University of Ottawa, Ottawa, ON Canada
2 Department of Health Research Methods, Evidence and Impact, McMaster University, Hamilton, ON Canada
3 St. Joseph’s Healthcare Hamilton, Hamilton, ON Canada
✉
Corresponding author.
Received 2023 Mar 10; Accepted 2024 Sep 2; Collection date 2024.
© The Author(s) 2024
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PMCID: PMC11411811 PMID: 39300571
Abstract
Introduction
Enteral nutrition (EN) is the recommended nutritional support in most critically ill populations. When given by feeding tube, EN may be administered either continuously or intermittently. It is unclear which approach is superior in reducing gastrointestinal complications—such as diarrhea—and meeting nutritional targets. The main objectives of this systematic review and meta-analysis are to (1) determine whether continuous or intermittent enteral nutrition is associated with higher incidence of adverse gastrointestinal outcomes, including diarrhea, and (2) determine which feeding modality is associated with reaching nutritional goals.
Methods and analysis
This systematic review protocol is reported in accordance with guidelines from the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Protocols (PRISMA-P) statement. We will search MEDLINE, Embase, the Cochrane Library, and the World Health Organization (WHO) International Clinical Trials Registry (ICTRP) search portal for studies comparing continuous EN and intermittent EN in critically ill patients with no date or language restrictions. Studies will be screened, selected, and extracted independently and in duplicate. We will assess the risk-of-bias assessment using the Cochrane Collaboration’s Risk of Bias (RoB) 2 tool. The primary outcome will include the incidence of diarrhea; secondary outcomes include other adverse GI outcomes (nausea, vomiting, abdominal pain, and constipation), as well as reaching nutritional goals, and length of ICU and hospital stay and mortality. We will pool data using a random-effects model and assess the certainty of the evidence for each outcome using Grading of Recommendations, Assessment, Development and Evaluations (GRADE) methodology.
Ethics and dissemination
Ethics approval is not required for this study as no original data will be collected. We will disseminate results through peer-reviewed publication and conference presentations.
Systematic review registration
PROSPERO CRD42022330118.
Supplementary Information
The online version contains supplementary material available at 10.1186/s13643-024-02652-8.
Keywords: Diarrhea, Intermittent feeding, Continuous feeding, Bolus feeding, Intensive care unit, Enteral nutrition, Gastrointestinal system
Strengths and limitations of this study
This systematic review protocol adheres to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Protocol (PRISMA) guidelines.
This paper addresses a current gap in the literature, and the results from this work may inform future nutritional protocols in critical care.
We developed the search strategy for this systematic review along with two experienced medical librarians.
This review is limited to evidence from randomized controlled trials.
This review may be limited by the restricted number of studies conducted on this topic, as well as potential high risk of bias.
Introduction
Rationale
The current European Society for Clinical Nutrition and Metabolism (ESPEN) guidelines for nutrition in the ICU recommend enteral nutrition (EN) as the most effective form of feeding in critically ill patients who cannot receive at least 70% of their nutritional needs through oral feeding . EN is a safer alternative to parenteral nutrition and is associated with a decreased risk of infectious complications , maintains GI tract integrity, and is less costly . Enteral nutrition may be administered to a patient continuously (EN received continuously over 24 h) or through intermittently (EN received in scheduled doses with rest periods in between).
Recently, the diarrhea: interventions, consequences and epidemiology in the intensive care unit (DICE-ICU) study identified multiple risk factors for diarrhea, including the use of EN . Diarrhea is described by the World Health Organization (WHO) as the passage of three or more loose or liquid stools a day . Diarrhea is further subcategorized into three categories: acute watery diarrhea, acute bloody diarrhea, and persistent diarrhea. It may also be classified according to its etiology as inflammatory, secretory, or due to altered motility . Diarrhea may result in fluid loss with consequent dehydration with the potential to progress to vascular collapse and hypovolemic shock and is associated with a myriad of electrolyte abnormalities, including but not limited to bicarbonate loss leading to metabolic acidosis, hypokalemia, and hypomagnesemia .
Reports of incidence of diarrhea in the ICU differ depending on the definition used; the DICE-ICU study found an incidence of 73.8% (95% CI 71.1–76.6) employing the WHO definition, 53.5% (95% CI 50.4–56.7) using the Bristol stool chart, and 37.7% (95% CI 34.9–40.4) using the Bliss Stool Classification System . Diarrhea was found to be associated with an increase in intensive care unit (ICU) length of stay and hospital length of stay, as well as with a decrease in quality of life and complications including skin breakdown . Although diarrhea is linked to both to enteral nutrition and worse clinical outcomes, it remains unclear whether continuous versus intermittent approaches to EN mitigate the risk of these outcomes or improve nutrition delivery. Previous studies on this topic have had conflicting or unclear results .
Objectives
In this review, we seek to investigate the effects of continuous versus intermittent enteral feeding on outcomes important to ICU patients, including GI outcomes (diarrhea, constipation, abdominal pain, nausea, and vomiting) and nutritional deficiencies. This has the potential to provide information that may reduce the incidence of diarrhea and other adverse outcomes in patients and inform ICU feeding protocols and clinical practice guidelines globally.
Methods
This protocol has been registered within the International Prospective Register of Systematic Reviews (PROSPERO) database (registration ID: CRD42022330118). This protocol is reported in accordance with guidance from the Preferred Reporting Items for Systematic Reviews and Meta-Analyses Protocols (PRISMA-P) statement .
Eligibility criteria
Types of studies
This systematic review will include randomized controlled trials (RCTs). We will exclude animal trials and conference abstracts.
Types of participants
The participants of studies included in this review will be restricted to adult patients (age 18 or older) who are receiving enteral nutrition and who are admitted to an ICU at the time of study enrolment. We will exclude pediatric studies due to this population’s unique needs while receiving EN . We will exclude studies that include subjects with preexisting conditions that independently contribute to adverse GI outcomes. These may include, but are not limited to, patients with active Clostridioides difficile infection and patients with existing GI disorders such as irritable bowel syndrome, inflammatory bowel disease, ostomy, and celiac disease.
Type of intervention
The studied intervention is intermittent EN, defined as administration of 200–400 mL of feed over 15–60 min at regular intervals or as defined by the author. We will not include studies that include administration of parenteral nutrition as part of the nutrition regimen.
Type of comparator
The comparator is continuous EN, defined as feed administered at a steady rate over the course of 12–24 h or as defined by the author.
Outcome measures
Primary outcome
The primary outcome of interest in this review is the incidence of diarrhea in ICU patients. Diarrhea will be defined in this study according to the most recent definition of diarrhea created by WHO. Diarrhea is defined as the passing of three or more loose or liquid stools in a day . We will consult the definition of diarrhea each selected study uses, and if necessary, we will adopt the author’s definition of diarrhea if it differs from the WHO definition.
Secondary outcomes
Secondary outcomes of interest in this review include incidence of other GI intolerances including vomiting, nausea, abdominal pain and discomfort, and constipation. These will be defined according to the authors’ definitions. We will also capture hospital length of stay, ICU length of stay, and mortality using the time frame selected by the author.
Information sources
Electronic sources
The literature search will be performed by an information specialist (KC) following PRISMA-S guidance , using a search strategy peer-reviewed by KD (Supplementary 1). The search strategy will be reviewed according to the methods described in McGowan, 2016 . Published literature will be identified by searching the following bibliographic databases: MEDLINE (1946–) with in-process records and daily updates via Ovid, Embase (1974–) via Ovid, and the Cochrane Library via Wiley. The search strategy will consist of both controlled vocabulary, such as the National Library of Medicine’s MeSH (Medical Subject Headings), and keywords. The ICTRP search portal and ClinicalTrials.gov will be searched for reports of additional trials. The main search concepts will be intensive care and bolus or continuous feeding.
Methodological filters will be applied to limit the retrieval to reports of randomized controlled trials or systematic reviews/meta-analyses/health technology assessments. Trial report retrieval will be limited to the human population where possible but was not limited by publication date or language. Duplicate records will be removed between MEDLINE and Embase using Ovid default duplicate detection, with any additional duplicates identified and removed in Covidence.
Searching other relevant sources
The reference list of all studies selected for inclusion will be reviewed for any additional publications that may meet the inclusion criteria for this study. If any potentially relevant studies are identified, they will be screened using the same process as the other included studies to determine if they meet the inclusion criteria.
Data collection and analysis
Selection of studies
Two reviewers (L. S. A., A. M. C.) will independently review the title and abstract of each publication retrieved to determine which should be assessed further as a full-text review. For any citation selected as potentially relevant, the same reviewers will assess the full text for eligibility. At this stage, we will capture reasons for exclusion, and any discrepancies will be resolved by either consensus or review by a third independent reviewer (J. C. D.).
Data extraction and management
We will extract the frequency and details of the outcome data from each study. We will collect the year of publication, duration of intervention, location of study, and number of participants randomized of each study. We will also collect medical comorbidities, age, sex, and ethnicity of the participants. We will collect all data using a pre-piloted data extraction sheet created using Covidence .
Assessment of risk of bias in included studies
Two reviewers (L. S. A., A. M. C.) will independently assess risk of bias for each study. In cases of disagreement, resolution will be reached by consensus after discussion or by assessment completed by a third reviewer (J. C. D.). Risk of bias (RoB) in randomized trials will be assessed by using V.2 of the Cochrane RoB tool for RCTs (RoB 2) .
We will assess certainty of evidence for each outcome effect estimate using the Grading of Recommendations, Assessment, Development and Evaluations (GRADE) classification, which considers risk of bias, imprecision, indirectness, inconsistency, and publication bias in determining the certainty of the evidence .
Dealing with missing data
We will contact research authors for clarification when data is missing from publications selected for inclusion. In the case that this data is not obtainable, we will incorporate this into the risk-of-bias assessment and GRADE certainty rating.
Assessment of reporting biases
We will use funnel plots to assess the risk and presence of publication bias. These plots will be used if there are 10 or more studies investigating the same outcome to assess for asymmetry. If asymmetry is found present in the studies, we will consider rating down the overall certainty of evidence for the outcome.
Data synthesis
We will pool extracted data for meta-analysis using RevMan . For dichotomous variables, we will report pooled risk ratio (RR) along with a 95% confidence interval (CI). For continuous variables, we will report mean differences along with a 95% confidence interval (CI). Meta-analysis will be performed using a random-effects model, unless there is a very small number of studies or significant statistical heterogeneity, in which case we will consider both fixed-effects and random-effects models. We will evaluate statistical heterogeneity using the I-squared statistic, the chi-squared test, and visual inspection of the forest plots. For the purpose of this study, and based on Cochrane Collaboration recommendations, we will consider a I 2 over 80% to indicate substantial heterogeneity; 60 to 80% will indicate moderate heterogeneity and percentages lower than 60% to indicate little to no important heterogeneity . Although categorizing I 2 heterogeneity may not be appropriate and thresholds may be misleading as heterogeneity depends on several factors , we will focus on exploring sources of heterogeneity as described in the following section.
Subgroup analysis and investigation of heterogeneity
We will consider a number of subgroup analyses in order to address clinical heterogeneity. These will include surgical ICU patients (including neurosurgery, cardiac surgery, and trauma) versus medical ICU patients, patients receiving early EN versus those receiving late EN, and continuous feeds equal to or lasting more than 18 h compared to those lasting less than 18 h. To address methodological heterogeneity, we will conduct subgroup analyses to compare high risk-of-bias studies versus lower risk-of-bias studies. We plan to use the restricted maximum likelihood (REML) to estimate heterogeneity variance; however, we may consider using an alternative method depending on the size of studies included in the analysis and the frequency of heterogeneity events . In alignment with recent guidelines, early enteral nutrition will be defined as EN started within 48 h of ICU admission, whereas late EN will be defined as EN started greater than 48 h after ICU admission . Surgical patients will be identified per the author’s classification. The results of the subgroup analyses will be compared in the summary of findings table. Any subgroups that have a p-value of < 0.05 will be evaluated using ICEMAN for subgroup credibility . We hypothesize that (1) the surgical ICU patients will experience more negative outcomes compared to medical ICU patients, including GI intolerances, potentially due to the effects of anesthesia or surgical procedures; (2) the late EN subgroups will experience more negative outcomes, including GI intolerances, than the early EN subgroup; (3) participants with continuous feeds lasting 18 or more hours will experience more negative outcomes compared to participants with continuous feeds lasting less than 18 h; and (4) there will be more negative outcomes in studies with a lower risk of bias than those with a high risk of bias.
Ethics and dissemination
Ethics board approval is not required as this review is using published data on anonymous participants. We will employ our search criteria and begin selecting studies in the fall of 2022. Data extraction will follow. Once completed, results will be presented at conference proceedings. The final manuscript will be submitted to a peer-reviewed journal for publication.
Discussion
This proposed systematic review aims to determine whether continuous or intermittent enteral feeding is associated with higher rates of diarrhea and other adverse GI outcomes, as well as to determine which feeding modality is associated with better meeting patients’ nutritional goals. This review also seeks to determine whether differences exist between relevant subgroups such as early versus late EN and surgical vs. medical ICU patients receiving EN. Strengths of this review include adherence to the PRISMA-P statement, publishing of this protocol a priori, determining the certainty of evidence using GRADE, and use of a trial sequential analysis.
Diarrhea remains a costly and prevalent complication in patients admitted to the ICU and contributes to numerous adverse outcomes including dehydration, hypovolemia, electrolyte imbalances, loss of dignity, and decreased quality of life. In the absence of contraindications, enteral nutrition remains preferred over parenteral nutrition in critically ill patients due to its contribution to maintaining integrity of the GI tract, lower rates of infectious complications, and lower cost. Evidence obtained through completion of this review will be helpful in informing future guidelines regarding choice of feeding modality in ICU patients, as well as to guide selection of feeding modality individual patients. This review will also serve to identify areas of research opportunity, potentially guiding new studies in this field.
This systematic review and meta-analysis will help inform future trial development regarding the effect of continuous versus intermittent enteral nutrition on incidence of diarrhea in patients admitted to the ICU.
Supplementary Information
13643_2024_2652_MOESM1_ESM.docx (47.3KB, docx)
Supplementary Material 1:Supplementary 1. Supplementary data: Search strategy.
Authors’ contributions
The protocol was designed by LSA, AMC, and JCD. The first draft was written by LSA and AMC, was subsequently reviewed by JCD, and revised appropriately. The search strategy was developed by KC and reviewed by KD. The manuscript was reviewed and revised for important intellectual content by LM, SO, BR, and JT. All authors approved the final manuscript prior to publication.
Funding
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
Declarations
Consent for publication
Not required.
Competing interests
The authors declare that they have no competing interests.
Footnotes
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
References
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
13643_2024_2652_MOESM1_ESM.docx (47.3KB, docx)
Supplementary Material 1:Supplementary 1. Supplementary data: Search strategy.
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13481 | https://readingfeynman.org/tag/time-dilation/ | time dilation – Reading Feynman
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Tag: time dilation
The nature of time: an easy explanation of relativity
My manuscript offers a somewhat sacrilegious but intuitive explanation of (special) relativity theory (The Emperor Has No Clothes: the force law and relativity, p. 24-27). It is one of my lighter and more easily accessible pieces of writing. The argument is based on the idea that we may define infinity or infinite velocities as some kind of limit (or some kind of limiting idea), but that we cannot really imagine it: it leads to all kinds of logical inconsistencies.
Let me give you a very simple example here to illustrate these inconsistencies: if something is traveling at an infinite velocity, then it is everywhere and nowhere at the same time, and no theory of physics can deal with that.
Now, if I would have to rewrite that brief introduction to relativity theory, I would probably add another logical argument. One that is based on our definition or notion of time itself. What is the definition of time, indeed? When you think long and hard about this, you will have to agree we can only measure time with reference to some fundamental cycle in Nature, right? It used to be the seasons, or the days or nights. Later, we subdivided a day into hours, and now we have atomic clocks. Whatever you can count and meaningfully communicate to some other intelligent being who happens to observe the same cyclical phenomenon works just fine, right?
Hence, if we would be able to communicate to some other intelligent being in outer space, whose position we may or may not know but both he/she/it (let us think of a male Martian for ease of reference) and we/me/us are broadcasting our frequency- or amplitude-modulated signals wide enough so as to ensure ongoing communication, then we would probably be able to converge on a definition of time in terms of the fundamental frequency of an elementary particle – let us say an electron to keep things simple. We could, therefore, agree on an experiment where he – after receiving a pre-agreed start signal from us – would starting counting and send us a stop signal back after, say, three billion electron cycles (not approximately, of course, but three billion exactly). In the meanwhile, we would be capable, of course, to verify that, inbetween sending and receiving the start and stop signal respectively (and taking into account the time that start and stop signal needs to travel between him and us), his clock seems to run somewhat differently than ours.
So that is the amazing thing, really. Our Martian uses the same electron clock, but our/his motion relative to his/ours leads us to the conclusion his clock works somewhat differently, and Einstein’s (special) relativity theory tells us how, exactly: time dilation, as given by the Lorentz factor.
Does this explanation make it any easier to truly understand relativity theory? Maybe. Maybe not. For me, it does, because what I am describing here is nothing but the results of the Michelson-Morley experiment in a slightly more amusing context which, for some reason I do not quite understand, seems to make them more comprehensible. At the very least, it shows Galilean relativity is as incomprehensible – or as illogical or non-intuitive, I should say – as the modern-day concept of relativity as pioneered by Albert Einstein.
You may now think (or not): OK, but what about relativistic mass? That concept is, and will probably forever remain, non-intuitive. Right? Time dilation and length contraction are fine, because we can now somehow imagine the what and why of this, but how do you explain relativistic mass, really?
The only answer I can give you here it to think some more about Newton’s law: mass is a measure of inertia, so that is a resistance to a change in the state of motion of an object. Motion and, therefore, your measurement of any acceleration or deceleration (i.e. a change in the state of motion) will depend on how you measure time and distance too. Therefore, mass has to be relativistic too.
QED: quod erat demonstrandum. In fact, it is not a proof, so I should not say it’s QED. It’s SE: a s atisfactory e xplanation. Why is an explanation and not a proof? Because I take the constant speed of light for granted, and so I kinda derive the relativity of time, distance and mass from my point of departure (both figuratively and literally speaking, I’d say).
Post scriptum: For the mentioned calculation, we do need to know the (relative) position of the Martian, of course. Any event in physics is defined by both its position as well as its timing. That is what (also) makes it all very consistent, in fact. I should also note this short story here (I mean my post) is very well aligned with Einstein’s original 1905 article, so you can (also) go there to check the math. The main difference between his article and my explanation here is that I take the constant speed of light for granted, and then all that’s relative derives its relativity from that. Einstein looked at it the other way around, because things were not so obvious then. 🙂
Jean Louis Van BellePhilosophy of science, PhysicsLeave a commentSeptember 15, 2020 September 15, 20203 Minutes
Wavefunctions and the twin paradox
My previous post was awfully long, so I must assume many of my readers may have started to read it, but… Well… Gave up halfway or even sooner. 🙂 I added a footnote, though, which is interesting to reflect upon. Also, I know many of my readers aren’t interested in the math—even if they understand one cannot really appreciate quantum theory without the math. But… Yes. I may have left some readers behind. Let me, therefore, pick up the most interesting bit of all of the stories in my last posts in as easy a language as I can find.
We have that weird 360/720° symmetry in quantum physics or—to be precise—we have it for elementary matter-particles (think of electrons, for example). In order to, hopefully, help you understand what it’s all about, I had to explain the often-confused but substantially different concepts of a reference frame and a representational base(or representation tout court). I won’t repeat that explanation, but think of the following.
If we just rotate the reference frame over 360°, we’re just using the same reference frame and so we see the same thing: some object which we, vaguely, describe by some e i·θ function. Think of some spinning object. In its own reference frame, it will just spin around some center or, in ours, it will spin while moving along some axis in its own reference frame or, seen from ours, as moving in some direction while it’s spinning—as illustrated below.
To be precise, I should say that we describe it by some Fourier sum of such functions. Now, if its spin direction is… Well… In the other direction, then we’ll describe it by by some e−i·θ function (again, you should read: a Fourier sum of such functions). Now, the weird thing is is the following: if we rotate the object itself, over the same 360°, we get a different object: our e i·θ and e−i·θ function (again: think of a Fourier sum, so that’s a wave packet, really) becomes a−e±i·θ thing. We get a minus sign in front of it.So what happened here? What’s the difference, really?
Well… I don’t know. It’s very deep. Think of you and me as two electrons who are watching each other. If I do nothing, and you keep watching me while turning around me, for a full 360° (so that’s a rotation of your reference frame over 360°), then you’ll end up where you were when you started and, importantly, you’ll see the same thing: me. 🙂 I mean… You’ll see exactly the same thing: if I was an e+i·θ wave packet, I am still an an e+i·θ wave packet now. Or if I was an e−i·θ wave packet, then I am still an an e−i·θ wave packet now. Easy. Logical. Obvious, right?
But so now we try something different:I turn around, over a full 360° turn, and you stay where you are and watch me while I am turning around. What happens? Classically, nothing should happen but… Well… This is the weird world of quantum mechanics: when I am back where I was—looking at you again, so to speak—then… Well… I am not quite the same any more. Or… Well… Perhaps I am but you see me differently. If I was e+i·θ wave packet, then I’ve become a−e+i·θ wave packet now.
Not hugely different but… Well… That minus sign matters, right? Or If I was wave packet built up from elementary a·e−i·θ waves, then I’ve become a−e−i·θ wave packet now. What happened?
It makes me think of the twin paradox in special relativity. We know it’s a paradox—so that’s an apparent contradiction only: we know which twin stayed on Earth and which one traveled because of the gravitational forces on the traveling twin. The one who stays on Earth does not experience any acceleration or deceleration. Is it the same here? I mean… The one who’s turning around must experience some force.
Can we relate this to the twin paradox? Maybe. Note that a minus sign in front of the e−±i·θ functions amounts a minus sign in front of both the sine and cosine components. So… Well… The negative of a sine and cosine is the sine and cosine but with a phase shift of 180°: −cos θ =cos(θ ± π) and−sin θ =sin(θ ± π). Now, adding or subtracting a common phase factor to/from the argument of the wavefunction amounts to changing the origin of time. So… Well… I do think the twin paradox and this rather weird business of 360° and 720° symmetries are, effectively, related. 🙂
Post scriptum:Google honors Max Born’s 135th birthday today. 🙂 I think that’s a great coincidence in light of the stuff I’ve been writing about lately (possible interpretations of the wavefunction). 🙂
Jean Louis Van BelleMathematics, Philosophy of science, Physics, quantum mechanicsLeave a commentDecember 11, 2017 December 17, 20173 Minutes
Another post for my kids: introducing (special)relativity
Pre-scriptum (dated 26 June 2020): These posts on elementary math and physics have not suffered much the attack by the dark force—which is good because I still like them. While my views on the true nature of light, matter and the force or forces that act on them have evolved significantly as part of my explorations of a more realist (classical) explanation of quantum mechanics, I think most (if not all) of the analysis in this post remains valid and fun to read. In fact, I find the simplest stuff is often the best. 🙂
Original post:
In my previous post, I talked about energy, and I tried to keep it simple– but also accurate. However, to be completely accurate, one must, of course, introduce relativity at some point. So how does that work? What’s ‘relativistic’ energy? Well… Let me try to convey a few ideas here.
The first thing to note is that the energy conservation law still holds: special theory or not, the sum of the kinetic and potential energies in a (closed) system is always equal to some constant C.What constant? That doesn’t matter: Nature does not care about our zero point and, hence, we can add or subtract any(other) constant to the equation K.E. + P.E. = T + U = C.
That being said, in my previous post, I pointed out that the constant depends on the reference point for the potential energy term U: we will usually take infinity as the reference point (for a force that attracts) and associate it with zero potential (U = 0). We then get a function U(x) like the one below: for gravitational energy we have U(x) =–GMm/x, and for electrical charges, we have U(x) = q 1 q 2/4πε 0 x. The mathematical shape is exactly the same but, in the case of the electromagnetic forces, you have to remember that likes repel, and opposites attract,so we don’t need the minus sign: the sign of the charges takes care of it.
Minus sign? In case you wonder why we need that minus sign for the potential energy function, well… I explained that in my previous post and so I’ll be brief on that here: potential energy is measured by doing work against the force. That’s why. So we have an infinite sum (i.e. an integral) over some trajectory or path looking like this: U =– ∫F·ds.
For kinetic energy, we don’t need any minus sign: as an object picks up speed, it’s the force itself that is doing the work as its potential energy is converted into kinetic energy, so the change in kinetic energy will equal the change in potential energy, but with opposite sign: as the object loses potential energy, it gains kinetic energy. Hence, we write ΔT =–ΔU = ∫F·ds..
That’s all kids stuff obviously. Let’s go beyond this and ask some questions. First, why can we add or subtract any constant to the potential energy but not to the kinetic energy? The answer is… Well… We actually can add or subtract a ‘constant’ to the kinetic energy as well. Now you will shake your head: Huh? Didn’t we have that T = m v 2/2 formula for kinetic energy? So how and why could one add or subtract some number to that?
Well… That’s where relativity comes into play. The velocity v depends on your reference frame. If another observer would move with and/or alongside the object, at the same speed, that observer would observe a velocity equal to zero and, hence, its kinetic energy – as that observer would measure it – would also be zero. You will object to that, saying that a change of reference frame does not change the force, and you’re right: the force will cause the object to accelerate or decelerate indeed, and if the observer is not subject to the same force, then he’ll see the object accelerate or decelerate indeed, regardless of his reference frame is a moving or inertial frame. Hence, both the inertial as well as the moving observer will see an increase(or decrease) in its kinetic energy and, therefore, both will conclude that its potential energy decreases(or increases)accordingly. In short, it’s the change in energy that matters, both for the potential as well as for the kinetic energy. The reference point itself, i.e. the point from where we start counting so to say, does not: that’s relative. [This also shows in the derivation for kinetic energy which I’ll do below.]
That brings us to the second question. We all learned in high school that mass and energy are related through Einstein’s mass-energy relation, E = m c 2, which establishes an equivalence between the two: the mass of an object that’s picking up speed increases, and so we need to look at both speed and mass as a function of time. Indeed, remember Newton’s Law: force is the time rate of change of momentum: F = d(mv)/dt. When the speed is low (i.e. non-relativistic), then we can just treat m as a constant and write thatF= mdv/dt = ma(the mass times the acceleration). Treating m as a constant also allows us to derive the classical (Newtonian) formula for kinetic energy:
So if we assume that the velocity of the object at point O is equal to zero (so v o= 0), then ΔT will be equal to T and we get what we were looking for: the kinetic energy at point P will be equal to T = m v 2/2.
Now, y ou may wonder why we can’t do that same derivation for a non-constant mass? The answer to that question is simple: taking the m factor out of the integral can only be done if we assume it is a constant. If not, then we should leave it inside. It’s similar to taking a derivative. If m would not be constant, then we would have to apply the product rule to calculate d(mv)/dt, so we’d write d(m v)/dt = (dm/dt)v + m(dv/dt). So we have two terms here and it’s only when m is constant that we can reduce it to d(m v)/dt = m(dv/dt).
So we have our classical kinetic energy function. However, when the velocity gets really high – i.e. if it’s like the same order of magnitude as the velocity of light – then we cannot assume that mass is constant. Indeed, the same high-school course in physics that taught you that E = m c 2 equation will probably also have taught you that an object can never go faster than light, regardless of the reference frame. Hence, as the object goes faster and faster, it will pick up more momentum, but its rate of acceleration should (and will) go down in such way that the object can never actually reach the speed of light. Indeed, if Newton’s Law is to remain valid, we need to correct it such a way that m is no longer constant: m itself will increase as a function of its velocity and, hence, as a function of time. You’ll remember the formula for that:
This is often written as m =γm 0, with m 0 denoting the mass of the object at rest (in your reference frame that is) and γ = (1 –v 2/c 2)–1/2 the so-called Lorentz factor. The Lorentz factor is named after a Dutch physicist who introduced it near the end of the 19th century in order to explain why the speed of light is always c, regardless of the frame of reference (moving or not), or – in other words – why the speed of light is not relative. Indeed, while you’ll remember that there is no such thing as an absolute velocity according to the (special) theory of relativity, the velocity of light actually is absolute ! That means you will always see light traveling at speed c regardless of your reference frame. To put it simply, you can never catch up with light and, if you would be traveling away from some star in a spaceship with a velocity of 200,000 km per second, and a light beam from that star would pass you, you’d measure the speed of that light beam to be equal to 300,000 km/s, not 100,000 km/s. So c is an absolute speed that acts as an absolute speed limit regardless of your reference frame. [Note that we’re talking only about reference frames moving at a uniform speed: when acceleration comes into play, then we need to refer to the general theory of relativity and that’s a somewhat different ball game.]
The graph below shows how γ varies as a function of v. As you can see, the mass increase only becomes significant at speeds of like 100,000 km per second indeed.Indeed, for v = 0.3 c, the Lorentz factor is 1.048, so the increase is about 5% only. For v= 0.5 c, it’s still limited to an increase of some 15%. But then it goes up rapidly: for v= 0.9 c, the mass is more than twice the rest mass: m≈ 2.3m 0; for v= 0.99 c, the mass increase is 600%: m ≈ 7m 0; and so on. For v= 0.999 c – so when the speed of the object differs from c only by 1 part in 1,000 – the mass of the object will be more than twenty-two times the rest mass (m ≈ 22.4m 0).
You probably know that we can actually reach such speeds and, hence, verify Einstein’s correction of Newton’s Law in particle accelerators: the electrons in an electron beam in a particle accelerator get usually pretty close to c and have a mass that’s like 2000 times their rest mass. How do we know that? Because the magnetic field needed to deflect them is like 2000 times as great as their (theoretical) rest mass. So how fast do they go? For their mass to be 2000 times m 0, 1 –v 2/c 2 must be equal to 1/4,000,000. Hence, their velocity v differs from c only by one part in 8,000,000. You’ll have to admit that’s very close.
Other effects of relativistic speeds
So we mentioned the thing that’s best known about Einstein’s (special) theory of relativity: the mass of an object, as measured by the inertial observer, increases with its speed. Now, you may or may not be familiar with two other things that come out of relativity theory as well:
The first is length contraction: objects are measured to be shortened in the direction of motion with respect to the (inertial) observer. The formula to be used incorporates the reciprocal of the Lorentz factor: L = (1/γ)L 0. For example, a meter stick in a space ship moving at a velocity v = 0.6 c will appear to be only 80 cm to the external/inertial observer seeing it whizz past… That is if he can see anything at all of course: he’d have to take like a photo-finish picture as it zooms past ! 🙂
The second is time dilation, which is also rather well known – just like the mass increase effect – because of the so-called twin paradox: time will appear to be slower in that space ship and, hence, if you send one of two twins away on a space journey, traveling at such relativistic speed, he will come back younger than his brother. The formula here is a bit more complicated, but that’s only because we’re used to measure time in seconds. If we would take a more natural unit, i.e. the time it takes light to travel a distance of 1 m, then the formula will look the same as our mass formula: t= γt 0 and, hence, one ‘second’ in the space ship will be measured as 1.25 ‘seconds’ by the external observer. Hence, the moving clock will appear to run slower – to the external (inertial) observer that is.
Again, the reality of this can be demonstrated. You’ll remember that we introduced the muon in previous posts: muons resemble electrons in the sense that they have the same charge, but their mass is more than 200 times the mass of an electron. As compared to other unstable particles, their average lifetime is quite long: 2.2 micro seconds. Still, that would not be enough to travel more than 600 meters or so– even at the speed of light (2.2 μs × 300,000 km/s = 660 m). But so we do detect muons in detectors down here that come all the way down from the stratosphere, where they are created when cosmic rays hit the Earth’s atmosphere some 10 kilometers up. So how do they get here if they decay so fast? Well, those that actually end up in those detectors, do indeed travel very close to the speed of light and, hence, while from their own point of view they live only like two millionths of a second, they live considerably longer from our point of view.
Relativistic energy: E = m c 2
Let’s go back to our main story line: relativistic energy. We wrote above that it’s the change of energy that matters really. So let’s look at that.
You may or may not remember that the concept of work in physics is closely related to the concept of power. In fact, you may actually remember that power, in physics at least, is defined as the work done per second.Indeed, we defined work as the (dot) product of the force and the distance. Now, when we’re talking a differential distance only (i.e. an infinitesimally small change only), then we can write dT = F·ds, but when we’re talking something larger, then we have to do that integral: ΔT = ∫F·ds. However, we’re interested in the time rate of change of T here, and so that’s the time derivative dT/dt which, as you easily verify, will be equal to dT/dt = (F·ds)/dt = F·(ds/dt) = F·vand so we can use that differential formula and we don’t need the integral. Now, that (dot) product of the force and the velocity vectors is what’s referred to as the power. [Note that only the component of the force in the direction of motion contributes to the work done and, hence, to the power.]
OK. What am I getting at? Well… I just want to show an interesting derivation: if we assume, with Einstein, that mass and energy are equivalent and, hence, that the total energy of a body always equals E = m c 2, then we can actually derive Einstein’s mass formula from that. How? Well… If the time rate of change of the energy of an object is equal to the power expended by the forces acting on it, then we can write:
dE/dt = d(m c 2)/dt = F·v
Now, we can not take the mass out of those brackets after the differential operator (d) because the mass is not a constant in this case (relativistic speeds) and, hence, dm/dt≠ 0. However, we can take out c 2(that’s an absolute constant, remember?) and we can also substitute F using Newton’s Law (F = d(m v)/dt), again taking care to leave m between the brackets, not outside. So then we get:
d(m c 2)/dt = c 2 dm/dt = [d(m v)/dt]·v = v· d(m v)/dt
In case you wonder why we can replace the vectors (bold face) v and d(mv) by their magnitudes (or lengths) v and d(m v):v and mvhave the same direction and, hence, the angle θ between them is zero, and so v·v =│v││v│cosθ =v 2. Likewise, d(mv) and v also have the same direction and so we can just replace the dot product by the product of the magnitudes of those two vectors.
Now, let’s not forget the objective: we need to solve this equation for m and, hopefully, we’ll find Einstein’s mass formula, which we need to correct Newton’s Law. How do we do that? We’ll first multiply both sides by 2m. Why? Because we can then apply another mathematical trick, as shown below:
c 2(2m)·dm/dt = 2m v· d(m v)/dt⇔d(m 2 c 2)/dt = d(m 2 v 2)/dt
However, if the derivatives of two quantities are equal, then the quantities themselves can only differ by a constant, say C. So we integrate both sides and get:
m 2 c 2=m 2 v 2+ C
Be patient: we’re almost there. The above equation must be true for all velocities v and, hence, we can choose the special case where v = 0 and call this mass m 0, and then substitute, so we get m 0 c 2=m 0 0 2+ C = C. Now we put this particular value for C back in the more general equation above and we get:
m c 2=m v 2+ m 0 c 2⇔m=m v 2/c 2+m 0⇔m(1–v 2/c 2) = m 0⇔m = m 0/(1–v 2/c 2)–1/2
So there we are: we have just shown that we get the relativistic mass formula (it’s on the right-hand side above) if we assume that Einstein’s mass-energy equivalence relation holds.
Now, you may wonder why that’s significant. Well… If you’re disappointed, then, at the very least, you’ll have to admit that it’s nice to show how everything is related to everything in this theory: from E =m c 2, we get m 0/(1–v 2/c 2)–1/2. I think that’s kinda neat!
In addition, let us analyze that mass-energy relation in another way. It actually allows us to re-definekinetic energy as the excess of a particle over its rest mass energy, or – it’s the same expression really – or the difference between its total energy and its rest energy.
How does that work? Well… When we’re looking at high-speed or high-energy particles, we will write the kinetic energy as:
K.E. = m c 2– m 0 c 2= (m–m 0)c 2= γm 0 c 2– m 0 c 2= m 0 c 2(γ– 1).
Now, we can expand that Lorentz factor γ = (1 –v 2/c 2)–1/2 into a binomial series (the binomial series is an infinite Taylor series, so it’s not to be confused with the (finite) binomial expansion: just check it online if you’re in doubt). If we do that, we we can write γ as an infinite sum of the following terms:
γ = 1 + (1/2)v 2/c 2+ (3/8)v 4/c 4+ (5/16)v 6/c 6+ …
Now, when we plug this back into our (relativistic) kinetic energy equation, we can scrap a few things (just do it) to get where I wanted to get:
K.E. = (1/2)m 0 v 2+ (3/8)m 0 v 4/c 2+ (5/16)m 0 v 6/c 4+ …
Again, you’ll wonder: so what? Well… See how the non-relativistic formula for kinetic energy (K.E. = m 0 v 2/2) appears here as the first term of this series and, hence, how the formula above shows that our ‘Newtonian’ formula is just an approximation. Of course,at low speeds, the second, third etcetera terms represent close to nothing and, hence, then our Newtonian ‘approximation is obviously pretty good of course !
OK… But… Now you’ll say: that’s fine, but how did Einstein get inspired to write E = m c 2 in the first place? Well, truth be told, the relativistic mass formula was derived first (i.e. before Einstein wrote his E = m c 2 equation),out of a derivation involving the momentum conservation law and the formulas we must use to convert the space-time coordinates from one reference frame to another when looking at phenomena (i.e. the so-called Lorentz transformations). And it was only afterwards that Einstein noted that, when expanding the relativistic mass formula, that the increase in mass of a body appeared to be equal to the increase in kinetic energy divided by c 2(Δm = Δ(K.E.)/c 2). Now, that, in turn, inspired him to also assign an equivalent energy to the rest mass of that body: E 0= m 0 c 2. […] At least that’s how Feynman tells the story in his 1965 Lectures… But so we’ve actually been doing it the other way around here!
Hmm… You will probably find all of this rather strange, and you may also wonder what happened to our potential energy. Indeed, that concept sort of ‘disappeared’ in this story: from the story above, it’s clear that kinetic energy has an equivalent mass, but what about potential energy?
That’s a very interesting question but, unfortunately, I can only give a rather rudimentary answer to that. Let’s suppose that we have two masses M and m. According to the potential energy formula above, the potential energy U between these two masses will then be equal to U =–GMm/r. Now, that energy is not interpreted as energy of either M or m, but as energy that is part of the (M, m)system, which includes the system’s gravitational field. So that energy is considered to be stored in that gravitational field. If the two masses would sit right on top of each other, then there would be no potential energy in the (M, m) system and, hence, the system as a whole would have less energy. In contrast, when we separate them further apart, then we increase the energy of the system as a whole, and so the system’s gravitational field then increases. So, yes, the potential energy does impact the (equivalent) mass of the system, but not the individual masses M and m. Does that make sense?
For me , it does, but I guess you’re a bit tired by now and, hence, I think I should wrap up here. In my next (and probably last) post on relativity, I’ll present those Lorentz transformations that allow us to ‘translate’ the space and time coordinates from one reference frame to another, and in that post I’ll also present the other derivation of Einstein’s relativistic mass formula, which is actually based on those transformations.In fact, I realize I should have probably started with that (as mentioned above, that’s how Feynman does it in his Lectures) but, then, for some reason, I find the presentation above more interesting, and so that’s why I am telling the story starting from another angle. I hope you don’t mind. In any case, it should be the same, because everything is related to everything in physics – just like in math. That’s why it’s important to have a good teacher. 🙂
Jean Louis Van BellePhysicsLeave a commentMay 24, 2014 June 26, 202015 Minutes
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13482 | https://courses.lumenlearning.com/ccbcmd-math/chapter/converting-between-degrees-and-radians/ | Dividing a circle into 360 parts is an arbitrary choice, although it creates the familiar degree measurement. We may choose other ways to divide a circle. To find another unit, think of the process of drawing a circle. Imagine that you stop before the circle is completed. The portion that you drew is referred to as an arc. An arc may be a portion of a full circle, a full circle, or more than a full circle, represented by more than one full rotation. The length of the arc around an entire circle is called the circumference of that circle.
The circumference of a circle is C=2 π r.If we divide both sides of this equation by r, we create the ratio of the circumference to the radius, which is always 2 π regardless of the length of the radius. So the circumference of any circle is 2 π≈6.28 times the length of the radius. That means that if we took a string as long as the radius and used it to measure consecutive lengths around the circumference, there would be room for six full string-lengths and a little more than a quarter of a seventh, as shown in Figure 10.
Figure 10
This brings us to our new angle measure. One radian is the measure of a central angle of a circle that intercepts an arc equal in length to the radius of that circle. A central angle is an angle formed at the center of a circle by two radii. Because the total circumference equals 2 π times the radius, a full circular rotation is 2 π radians. So
2 π radians=360∘π radians=360∘2=180∘1 radian=180∘π≈57.3∘
Note that when an angle is described without a specific unit, it refers to radian measure. For example, an angle measure of 3 indicates 3 radians. In fact, radian measure is dimensionless, since it is the quotient of a length (circumference) divided by a length (radius) and the length units cancel out.
Figure 11. The angle _t_ sweeps out a measure of one radian. Note that the length of the intercepted arc is the same as the length of the radius of the circle.
Relating Arc Lengths to Radius
An arc lengths is the length of the curve along the arc. Just as the full circumference of a circle always has a constant ratio to the radius, the arc length produced by any given angle also has a constant relation to the radius, regardless of the length of the radius.
This ratio, called the radian measure, is the same regardless of the radius of the circle—it depends only on the angle. This property allows us to define a measure of any angle as the ratio of the arc length s to the radius r.
s=r θ θ=s r
If s=r, then θ=r r=1 radian.
Figure 12.(a) In an angle of 1 radian, the arc length s equals the radius r. (b) An angle of 2 radians has an arc length s=2 r. (c) A full revolution is 2 π or about 6.28 radians.
To elaborate on this idea, consider two circles, one with radius 2 and the other with radius 3. Recall the circumference of a circle is C=2 π r, where r is the radius. The smaller circle then has circumference 2 π(2)=4 π and the larger has circumference 2 π(3)=6 π.Now we draw a 45° angle on the two circles, as in Figure 13.
Figure 13. A 45° angle contains one-eighth of the circumference of a circle, regardless of the radius.
Notice what happens if we find the ratio of the arc length divided by the radius of the circle.
Smaller circle:1 2 π 2=1 4 π Larger circle:3 4 π 3=1 4 π
Since both ratios are 1 4 π, the angle measures of both circles are the same, even though the arc length and radius differ.
A General Note: Radians
One radian is the measure of the central angle of a circle such that the length of the arc between the initial side and the terminal side is equal to the radius of the circle. A full revolution (360°) equals 2 π radians. A half revolution (180°) is equivalent to π radians.
The radian measure of an angle is the ratio of the length of the arc subtended by the angle to the radius of the circle. In other words, if s is the length of an arc of a circle, and r is the radius of the circle, then the central angle containing that arc measures s r radians. In a circle of radius 1, the radian measure corresponds to the length of the arc.
Q & A
A measure of 1 radian looks to be about 60°. Is that correct?
_Yes. It is approximately 57.3°. Because 2 π radians equals 360°, 1 radian equals 360∘2 π≈57.3∘._
Using Radians
Because radian measure is the ratio of two lengths, it is a unitless measure. For example, in Figure 12, suppose the radius were 2 inches and the distance along the arc were also 2 inches. When we calculate the radian measure of the angle, the “inches” cancel, and we have a result without units. Therefore, it is not necessary to write the label “radians” after a radian measure, and if we see an angle that is not labeled with “degrees” or the degree symbol, we can assume that it is a radian measure.
Considering the most basic case, the unit circle (a circle with radius 1), we know that 1 rotation equals 360 degrees, 360°. We can also track one rotation around a circle by finding the circumference, C=2 π r, and for the unit circle C=2 π. These two different ways to rotate around a circle give us a way to convert from degrees to radians.
1 rotation=360∘=2 π radians 1 2 rotation=180∘=π radians 1 4 rotation=90∘=π 2 radians
Identifying Special Angles Measured in Radians
In addition to knowing the measurements in degrees and radians of a quarter revolution, a half revolution, and a full revolution, there are other frequently encountered angles in one revolution of a circle with which we should be familiar. It is common to encounter multiples of 30, 45, 60, and 90 degrees. These values are shown in Figure 14. Memorizing these angles will be very useful as we study the properties associated with angles.
Figure 14. Commonly encountered angles measured in degrees
Now, we can list the corresponding radian values for the common measures of a circle corresponding to those listed in Figure 14, which are shown in Figure 15. Be sure you can verify each of these measures.
Figure 15. Commonly encountered angles measured in radians
Example 2: Finding a Radian Measure
Find the radian measure of one-third of a full rotation.
Solution
For any circle, the arc length along such a rotation would be one-third of the circumference. We know that
1 rotation=2 π r
So,
s=1 3(2 π r)=2 π r 3
The radian measure would be the arc length divided by the radius.
radian measure=2 π r 3 r=2 π r 3 r=2 π 3
Try It 2
Find the radian measure of three-fourths of a full rotation.
Solution
Converting between Radians and Degrees
Because degrees and radians both measure angles, we need to be able to convert between them. We can easily do so using a proportion.
θ 180=θ R π
This proportion shows that the measure of angle θ in degrees divided by 180 equals the measure of angle θ in radians divided by π. Or, phrased another way, degrees is to 180 as radians is to π.
Degrees 180=Radians π
Converting between Radians and Degrees
To convert between degrees and radians, use the proportion
θ 180=θ R π
Example 3: Converting Radians to Degrees
Convert each radian measure to degrees.
a. π 6
b. 3
Solution
Because we are given radians and we want degrees, we should set up a proportion and solve it.
a. We use the proportion, substituting the given information.
θ 180=θ R π θ 180=π 6 π θ=180 6 θ=30∘
b. We use the proportion, substituting the given information.
θ 180=θ R π θ 180=3 π θ=3(180)π θ≈172∘
Try It 3
Convert −3 π 4 radians to degrees.
Solution
Example 4: Converting Degrees to Radians
Convert 15 degrees to radians.
Solution
In this example, we start with degrees and want radians, so we again set up a proportion and solve it, but we substitute the given information into a different part of the proportion.
θ 180=θ R π 15 180=θ R π 15 π 180=θ R π 12=θ R
Analysis of the Solution
Another way to think about this problem is by remembering that 30∘=π 6.
Because 15∘=1 2(30∘), we can find that 1 2(π 6) is π 12.
Try It 4
Convert 126° to radians.
Solution
Watch the following video for an explanation of radian measure and examples of converting between radians and degrees.
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13483 | https://www.statisticshowto.com/how-to-calculate-odds-of-winning/ | Published Time: 2022-02-19T15:58:26+00:00
How To Calculate Odds of Winning - Statistics How To
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How To Calculate Odds of Winning
Probability in Real Life> How To Calculate Odds of Winning
A billboard for the Powerball and Mega Millions lottery game prizes in Missouri.
Difference Between Probability and Odds
Probability and odds are very closely related; the terms are often used interchangeably, but there is an important difference.
Probability: divide chances of winning by the total number of chances available . For example, if you buy one ticket for a raffle with 100 tickets sold, you have one possible chance at a win, with 100 possible chances overall. Your probability of winning is 1/100. Probabilities can also be expressed as:
Decimals; 1/100 = 0.01 (a fraction is just a division problem: plug 1/100 into any calculator to get the decimal equivalent)
Percentages: to convert to a percent, multiply your decimal by 100 and add a % sign: 0.01 100 = 1%.
Oddsare a ratio of your chances of losing to your chances of winning. Using the above raffle example, your chances of losing are 99 (the “other” tickets) and your chances of winning are 1 (the ticket you purchased). Your odds are 99 to 1.
To convert odds to probability:
Place your chance of winning (1 in this example) in the numerator (top) of a fraction.
1/?
2. Add both values in the odds (99 and 1 in this example) and place that value in the fraction’s denominator (bottom): 1 + 99 = 100.
1/100
How To Calculate Odds of Winning: Example
You’ll often find sweepstakes listing odds in their official rules, but they are normally quite high. Sometimes, the odds will be explicitly stated. For example, Quilted Northern Bathroom Tissue’s 2005 sweepstakes published odds of 1:11,000,000 . But in the vast majority of cases, you’ll find this statement in the official rules, like this one from Ellen’s 2021 sweepstakes :
“Odds of winning depend upon the number of eligible entries received during the Entry Period.”
In order to calculate odds of winning (or probability of winning), you have to know how many total entries. Thanks to the advent of the internet, these contests gather millions of entries, which means your odds are extremely small of winning a particular sweepstakes. Let’s take a look at an example.
HGTV’s 2021 Smart Home sweepstakes, which offered the winner $100,000, a 2021 Mercedes-Benz, and a brand-new smart home in Naples, Florida, had 106 million entries . You can use that information to calculate your odds of winning. The contest, which runs every year, allows each person two entries a day for around six weeks (42 days).
Maximum entries = 2 42 = 84.
Probability of winning = 84 / 106 million = .00000079245283, or 0.000079%.
To put that into perspective, if you take all of the people visiting Walt Disney World over a period of two years (that’s around 58 million people a year), and gave each of them one entry, 84 people would be winners. This analogy might sound like good odds, but if you’ve ever visited Disney World on one day, you’ll know how slim this probability is!
To calculate the odds, you would take your potential winning entries (84) and your potential losses (106,000,000 – 84 = 105,999,916). That’s odds of 84 to 105,999,916. Reducing this by simplifying (I used an online calculator), we get odds of 21 to 26,499,979.
This example shows that when you have a small number of “events” (in this example a sweepstakes is an “event”), odds are probabilities are almost identical.
Some Notable Exceptions
In gambling, like poker or blackjack, the odds is usually a subjective estimate of winning, not a mathematical computation. You also can’t calculate the odds of winning the lotteryusing the above technique. That’s because the odds are based on combinations(how many different ways the numbers can be chosen), not how many people enter. In other words, the odds never change whether fifty people enter or fifty million. See: How Lottery Odds are Calculated.
How to Calculate Odds of Winning: References
Consumer Value-Maximizing Sweepstakes and Contests.
Ellen 12 Days 2021 Sweepstakes.
Seattle education worker wins luxury home from HGTV
Odds of Winning Sweepstakes
Equally Likely Outcomes
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13485 | https://documents.cap.org/protocols/cp-femalereproductive-endometrium-20-4102.pdf | © 2020 College of American Pathologists (CAP). All rights reserved. For Terms of Use please visit www.cap.org/cancerprotocols. Protocol for the Examination of Specimens From Patients With Carcinoma and Carcinosarcoma of the Endometrium Version: Endometrium 4.1.0.2 Protocol Posting Date: February 2020 CAP Laboratory Accreditation Program Protocol Required Use Date: November 2020 Includes pTNM requirements from the 8th Edition, AJCC Staging Manual and 2018 FIGO Cancer Report For accreditation purposes, this protocol should be used for the following procedures AND tumor types: Procedure Description Hysterectomy Tumor Type Description Carcinoma Includes carcinomas, carcinosarcomas (malignant mixed Müllerian tumor) and neuroendocrine carcinomas arising in the endometrium This protocol is NOT required for accreditation purposes for the following: Procedure Endometrial biopsy Endometrial curettage Primary resection specimen with no residual cancer (eg, following previous biopsy or curettage) Cytologic specimens The following tumor types should NOT be reported using this protocol Tumor Type Carcinomas arising in the uterine cervix (consider the Uterine Cervix protocol) Uterine sarcoma, including adenosarcoma (consider the Uterine Sarcoma protocol) Lymphoma (consider the Hodgkin or non-Hodgkin Lymphoma protocols) Authors Uma Krishnamurti, MD, PhD; Saeid Movahedi-Lankarani, MD; George G. Birdsong, MD; Christopher N. Chapman Jr, MD; Bojana Djordjevic, MD; Veronica Klepeis, MD, PhD; Teri A. Longacre, MD; Marisa R. Nucci, MD; Christopher N. Otis, MD With guidance from the CAP Cancer and CAP Pathology Electronic Reporting Committees. Denotes primary author. All other contributing authors are listed alphabetically. Female Reproductive • Endometrium 4.1.0.2 2 Accreditation Requirements This protocol can be utilized for a variety of procedures and tumor types for clinical care purposes. For accreditation purposes, only the definitive primary cancer resection specimen is required to have the core and conditional data elements reported in a synoptic format. • Core data elements are required in reports to adequately describe appropriate malignancies. For accreditation purposes, essential data elements must be reported in all instances, even if the response is “not applicable” or “cannot be determined.” • Conditional data elements are only required to be reported if applicable as delineated in the protocol. For instance, the total number of lymph nodes examined must be reported, but only if nodes are present in the specimen. • Optional data elements are identified with “+” and although not required for CAP accreditation purposes, may be considered for reporting as determined by local practice standards. The use of this protocol is not required for recurrent tumors or for metastatic tumors that are resected at a different time than the primary tumor. Use of this protocol is also not required for pathology reviews performed at a second institution (ie, secondary consultation, second opinion, or review of outside case at second institution). Synoptic Reporting All core and conditionally required data elements outlined on the surgical case summary from this cancer protocol must be displayed in synoptic report format. Synoptic format is defined as: • Data element: followed by its answer (response), outline format without the paired "Data element: Response" format is NOT considered synoptic. • The data element should be represented in the report as it is listed in the case summary. The response for any data element may be modified from those listed in the case summary, including “Cannot be determined” if appropriate. • Each diagnostic parameter pair (Data element: Response) is listed on a separate line or in a tabular format to achieve visual separation. The following exceptions are allowed to be listed on one line: o Anatomic site or specimen, laterality, and procedure o Pathologic Stage Classification (pTNM) elements o Negative margins, as long as all negative margins are specifically enumerated where applicable • The synoptic portion of the report can appear in the diagnosis section of the pathology report, at the end of the report or in a separate section, but all Data element: Responses must be listed together in one location Organizations and pathologists may choose to list the required elements in any order, use additional methods in order to enhance or achieve visual separation, or add optional items within the synoptic report. The report may have required elements in a summary format elsewhere in the report IN ADDITION TO but not as replacement for the synoptic report ie, all required elements must be in the synoptic portion of the report in the format defined above. Summary of Changes Version 4.1.0.2 The following data elements were modified: Updated the Background Documentation (Notes) CAP Approved Female Reproductive • Endometrium • 4.1.0.2 + Data elements preceded by this symbol are not required for accreditation purposes. These optional elements may be clinically important but are not yet validated or regularly used in patient management. 3 Surgical Pathology Cancer Case Summary Protocol posting date: February 2020 ENDOMETRIUM: Select a single response unless otherwise indicated. Procedure (select all that apply) (Note A) ___ Total hysterectomy and bilateral salpingo-oophorectomy ___ Radical hysterectomy ___ Simple hysterectomy ___ Supracervical hysterectomy ___ Bilateral salpingo-oophorectomy ___ Right salpingo-oophorectomy ___ Left salpingo-oophorectomy ___ Salpingo-oophorectomy, side not specified ___ Right oophorectomy ___ Left oophorectomy ___ Oophorectomy, side not specified ___ Bilateral salpingectomy ___ Right salpingectomy ___ Left salpingectomy ___ Salpingectomy, side not specified ___ Vaginal cuff resection ___ Omentectomy ___ Peritoneal biopsies ___ Peritoneal washing ___ Other (specify): ____ Note: For information about lymph node sampling, please refer to the Regional Lymph Node section. + Hysterectomy Type + ___ Abdominal + ___ Vaginal + ___ Vaginal, laparoscopic-assisted + ___ Laparoscopic + ___ Laparoscopic, robotic-assisted + ___ Other (specify): ____ + ___ Not specified +Specimen Integrity (Note A) + Intact + Opened + Morcellated + Other (specify): ____ + Tumor Site (select all that apply) + ___ Endometrium + ___ Lower uterine segment + ___ Endometrial polyp + ___ Other (specify): ____ + ___ Cannot be determined CAP Approved Female Reproductive • Endometrium • 4.1.0.2 + Data elements preceded by this symbol are not required for accreditation purposes. These optional elements may be clinically important but are not yet validated or regularly used in patient management. 4 + Tumor Size + Greatest dimension: ___ cm + Additional dimensions: ___ x ___ cm + ___ Cannot be determined (explain): ____ Histologic Type (Note B) ___ Endometrioid carcinoma, NOS ___ Endometrioid carcinoma with squamous differentiation ___ Endometrioid carcinoma, villoglandular variant ___ Endometrioid carcinoma with secretory differentiation ___ Endometrioid carcinoma, other variant (specify): __ ___ Serous endometrial intraepithelial carcinoma ___ Serous carcinoma ___ Carcinosarcoma (malignant mixed Müllerian tumor) ___ Mucinous carcinoma ___ Clear cell carcinoma ___ Small cell neuroendocrine carcinoma ___ Large cell neuroendocrine carcinoma ___ Mixed cell carcinoma (specify types and percentages): ____ ___ Undifferentiated carcinoma ___ Dedifferentiated carcinoma ___ Other histologic type not listed (specify): ____ Histologic Grade (required only if applicable) (Note C)# ___ FIGO grade 1 ___ FIGO grade 2 ___ FIGO grade 3 ___ Other (specify): __ ___ Cannot be assessed (explain): ___ # International Federation of Gynecology and Obstetrics (FIGO) Grading System applies to endometrioid and mucinous carcinomas only. Serous, clear cell, transitional, small cell and large cell neuroendocrine carcinomas, undifferentiated/ dedifferentiated carcinomas, and carcinosarcomas are generally considered to be high grade and it is not recommended to assign a histologic grade to these tumor types. Myometrial Invasion (Note D) ___ Not identified ___ Present Depth of Myometrial Invasion (millimeters): ___ mm Myometrial Thickness (millimeters): ___ mm Percentage of Myometrial Invasion: % OR, if exact percentage of invasion cannot be determined, state: ___ Depth of myometrial invasion cannot be determined (explain): ___ ___ Myometrial thickness cannot be determined (explain): ___ Estimated Percentage of Myometrial Invasion ___ Less than 50% ___ 50% or greater ___ Cannot be determined (explain): ____ + Adenomyosis + ___ Not identified + ___ Present, uninvolved by carcinoma + ___ Present, involved by carcinoma + ___ Cannot be determined CAP Approved Female Reproductive • Endometrium • 4.1.0.2 + Data elements preceded by this symbol are not required for accreditation purposes. These optional elements may be clinically important but are not yet validated or regularly used in patient management. 5 Uterine Serosa Involvement ___ Not identified ___ Present ___ Cannot be determined (explain): ____ + Lower Uterine Segment Involvement (Note E) + ___ Not identified + ___ Present, superficial (non-myoinvasive) + ___ Present, myoinvasive + ___ Present __ + ___ Cannot be determined (explain): ___ Cervical Stromal Involvement (Note F) ___ Not identified ___ Present ___ Cannot be determined (explain): ____ Other Tissue/Organ Involvement (select all that apply) Note: Any organ not selected is either not involved or was not submitted. ___ Not applicable ___ Not identified ___ Right ovary ___ Left ovary ___ Ovary (side not specified) ___ Right fallopian tube ___ Left fallopian tube ___ Fallopian tube (side not specified) ___ Vagina ___ Right parametrium ___ Left parametrium ___ Parametrium (side not specified) ___ Pelvic wall ___ Bladder wall ___ Bladder mucosa# ___ Rectal wall ___ Bowel mucosa# ___ Omentum ___ Other organs/tissue (specify): ___ ___ Cannot be determined (explain): ___ #Note: Tumor should involve the mucosal surface + Peritoneal/ Ascitic Fluid (Note G) + ___ Not submitted/unknown + ___ Negative for malignancy (normal/benign) + ___ Atypical and/or suspicious (explain): ____ + ___ Malignant (positive for malignancy) + ___ Unsatisfactory/nondiagnostic (explain): ____ + ___ Results pending Margins (required only if cervix and/or parametrium/paracervix is involved by carcinoma) (Note H) Ectocervical/Vaginal Cuff Margin __ Cannot be assessed (explain): ___ _ Involved by carcinoma Uninvolved by carcinoma + Distance of invasive carcinoma from margin (millimeters): ___ mm CAP Approved Female Reproductive • Endometrium • 4.1.0.2 + Data elements preceded by this symbol are not required for accreditation purposes. These optional elements may be clinically important but are not yet validated or regularly used in patient management. 6 Parametrial/Paracervical Margin _ Cannot be assessed (explain): ___ __ Involved by carcinoma _ Uninvolved by carcinoma + Distance of invasive carcinoma from margin (millimeters): ___ mm Lymphovascular Invasion (Note I) ___ Not identified ___ Present ___ Cannot be determined Regional Lymph Nodes Note: Lymph nodes designated as pelvic (parametrial, obturator, internal iliac (hypogastric), external iliac, common iliac, sacral, presacral) and para-aortic are considered regional lymph nodes. Any other involved nodes should be categorized as metastases (pM1) and commented on in the distant metastasis section. Presence of isolated tumor cells no greater than 0.2 mm in regional lymph node(s) is considered N0 (i+). ___ No lymph nodes submitted or found Lymph Node Examination (required only if lymph nodes are present in the specimen) ___ All lymph nodes negative for tumor cells ___ Positive for tumor cells (select all that apply) Number of Pelvic Nodes with Macrometastases: Number of Pelvic Nodes with Micrometastases: _ Number of Pelvic Nodes with Isolated Tumor Cells (if applicable): and/or Number of Para-aortic Nodes with Macrometastases: _ Number of Para-aortic Nodes with Micrometastases: Number of Para-aortic Nodes with Isolated Tumor Cells (if applicable): _ Number cannot be determined (explain): ____ Note: Macrometastases (>2 mm), Micrometastases (>0.2 mm to 2 mm and/or >200 cells), Isolated Tumor Cells (≤0.2 mm and ≤200 cells). Reporting the number of nodes with or without macrometastases and micrometastases is required If pelvic and/or para-aortic lymph nodes are submitted and either are positive for tumor cell. Reporting isolated tumor cells is required only in the absence of macrometastasis or micrometastasis Laterality of Nodes with Tumor Cells (select all that apply) ___ Right pelvic ___ Left pelvic ___ Right para-aortic ___ Left para-aortic ___ Cannot be determined (explain): __ Number of Lymph Nodes Examined (select all that apply) Total Number of Pelvic Nodes Examined: Number of Pelvic Sentinel Nodes Examined: _ Total Number of Para-aortic Nodes Examined: Number of Para-aortic Sentinel Nodes Examined: _ CAP Approved Female Reproductive • Endometrium • 4.1.0.2 + Data elements preceded by this symbol are not required for accreditation purposes. These optional elements may be clinically important but are not yet validated or regularly used in patient management. 7 Pathologic Stage Classification (pTNM, AJCC 8th Edition) (Note J) Note: Reporting of pT, pN, and (when applicable) pM categories is based on information available to the pathologist at the time the report is issued. Only the applicable T, N, or M category is required for reporting; their definitions need not be included in the report. The categories (with modifiers when applicable) can be listed on 1 line or more than 1 line. TNM Descriptors (required only if applicable) (select all that apply) ___ r (recurrent) ___ y (posttreatment) Primary Tumor (pT) ___ pTX: Primary tumor cannot be assessed ___ pT0: No evidence of primary tumor ___ pT1: Tumor confined to the corpus uteri, including endocervical glandular involvement ___ pT1a: Tumor limited to endometrium or invading less than half of the myometrium ___ pT1b: Tumor invading one-half or more of the myometrium ___ pT2: Tumor invading the stromal connective tissue of the cervix but not extending beyond the uterus. This does NOT include endocervical glandular involvement ___ pT3: Tumor involving serosa, adnexa, vagina, or parametrium ___ pT3a: Tumor involves serosa and/or adnexa (direct extension or metastasis) ___ pT3b: Vaginal involvement (direct extension or metastasis) or parametrial involvement ___ pT4: Tumor invading the bladder mucosa and/or bowel mucosa (bullous edema is not sufficient to classify a tumor as T4)# # Note: Tumor has to involve the mucosal surface Regional Lymph Nodes Modifier (required only if applicable) ___ (sn)# # Note: Suffix (sn) is required if applicable and added to the N category when only sentinel lymph node biopsy is performed. If after a sentinel node biopsy, the patient then undergoes a complete lymph node dissection, the (sn) suffix is not used. Regional Lymph Nodes (pN) ___ pNX: Regional lymph nodes cannot be assessed ___ pN0: No regional lymph node metastasis ___ pN0(i+): Isolated tumor cells in regional lymph node(s) no greater than 0.2 mm ___ pN1: Regional lymph node metastasis to pelvic lymph nodes ___ pN1mi: Regional lymph node metastasis (greater than 0.2 mm but not greater than 2 mm in diameter) to pelvic lymph nodes# ___ pN1a Regional lymph node metastasis (greater than 2 mm in diameter) to pelvic lymph nodes ___ pN2: Regional lymph node metastasis to para-aortic lymph nodes, with or without positive pelvic lymph nodes ___ pN2mi: Regional lymph node metastasis (greater than 0.2 mm but not greater than 2 mm in diameter) to para-aortic lymph nodes, with or without positive pelvic lymph nodes# ___ pN2a: Regional lymph node metastasis (greater than 2 mm in diameter) to para-aortic lymph nodes, with or without positive pelvic lymph nodes # Note: Even one metastasis >2.0 mm would qualify the classification as pN1a and pN2a. Distant Metastasis (pM) (required only if confirmed pathologically in this case) ___ pM1: Distant metastasis (includes metastasis to inguinal lymph nodes, intraperitoneal disease, lung, liver, or bone. It excludes metastasis to pelvic or para-aortic lymph nodes, vagina, uterine serosa, or adnexa) Specify Site(s), if known: ______ + FIGO Stage (2018 FIGO Cancer Report) + ___ I: Tumor confined to the corpus uteri + ___ IA: No or less than half myometrial invasion + ___ IB: Invasion equal to or more than half of the myometrium CAP Approved Female Reproductive • Endometrium • 4.1.0.2 + Data elements preceded by this symbol are not required for accreditation purposes. These optional elements may be clinically important but are not yet validated or regularly used in patient management. 8 + ___ II: Tumor invades cervical stroma, but does not extend beyond the uterus + ___ III: Local and/or regional spread of the tumor + ___ IIIA: Tumor invades the serosa of the corpus uteri and/or adnexae + ___ IIIB: Vaginal involvement and/ or parametrial involvement + ___ IIIC: Metastases to pelvic and/or para-aortic lymph nodes + ___ IIIC1: Positive pelvic nodes + ___ IIIC2: Positive para-aortic nodes with or without positive pelvic lymph nodes + ___ IV: Tumor invades bladder and/or bowel mucosa, and/or distant metastases + ___ IVA: Tumor invasion of bladder and/or bowel mucosa + ___ IVB: Distant metastasis, including intraabdominal metastases and/or inguinal nodes + Additional Pathologic Findings (select all that apply) (Note K) + ___ None identified + ___ Atypical hyperplasia/endometrial intraepithelial neoplasia (EIN) + ___ Other (specify): _____ + Ancillary Studies Note: For reporting molecular testing, immunohistochemistry, and other cancer biomarker testing results, the CAP endometrium biomarker template should be used. Pending biomarker studies should be listed in the Comments section of this report. + Clinical History (select all that apply) (Note L) + ___ Lynch syndrome + ___ Other (specify): ______ + Comment(s) Background Documentation Female Reproductive • Endometrium • 4.1.0.2 9 Explanatory Notes A. Specimen Type In rare occasions when an endometrial carcinoma is not suspected, the pathologist may receive a supracervical hysterectomy specimen removed by laparoscopy. It has been reported that hysterectomies performed using certain laparoscopic techniques result in the finding of venous tumor emboli that are likely to be iatrogenic.1 The FDA discourages morcellation for removal of uterus in women with suspected or known uterine cancer because there is risk of spreading tumor cells to the pelvis and peritoneal cavity. Therefore, if applicable reporting of such a procedure is recommended (and listed under Specimen Integrity in the case summary). References 1. Logani S, Herdman AV, Little JV, Moller KA. Vascular "pseudo invasion" in laparoscopic hysterectomy specimens: a diagnostic pitfall. Am J Surg Pathol. 2008;32:560-565. B. Histologic Type For consistency in reporting, the histologic classification of endometrial carcinoma and hyperplasia proposed by the World Health Organization (WHO) is recommended.1 Mucinous carcinomas defined as an endometrial carcinoma in which > 50% of the neoplasm is mucinous are very rare. Most tumors that are mucinous are endometrioid adenocarcinoma with mucinous differentiation. The term mixed carcinoma should only be used when two or more distinctive subtypes of endometrial carcinoma are identified, each representing at least 5% of the tumor. Optimally, the diagnosis is made on examination of a hysterectomy specimen, but if only a smaller specimen is available, any amount of a second tumor category suffices for the diagnosis. When a carcinoma is classified as “mixed,” the major and minor types and their relative proportions should be specified. High-grade tumors with ambiguous features should be classified as “carcinoma, subtype cannot be determined”; however, this is a very infrequent situation and every effort should be made to subclassify such tumors. It should be noted that for mixed endometrioid and serous carcinomas, studies have found variable results regarding tumor behavior based on percentage of the serous component. Some studies have found that tumors with >25% serous component behave like pure serous carcinomas, whereas other studies have shown that tumors with <10% serous component also behave like pure serous carcinomas.2,3 It is important to be aware that some serous carcinomas may display a glandular architecture.4 Thus, when a gland-forming endometrial carcinoma shows high-grade nuclear features, the diagnosis of serous carcinoma should be considered. Finally, the term endometrial intraepithelial carcinoma is discouraged because it is not uncommon for these lesions to be associated with extrauterine spread.5-7 Instead, the term serous endometrial intraepithelial carcinoma should be used. In addition, carcinosarcoma (also referred to as malignant Müllerian mixed tumor [MMMT]) has been added to the above list of tumors in the case summary. Carcinosarcoma is a high-grade endometrial neoplasm that is staged like endometrial carcinomas because it is thought to represent a high-grade metaplastic carcinoma. The diagnosis of carcinosarcoma requires presence of both a high grade malignant epithelial component and a high grade malignant mesenchymal (sarcomatous) component in the neoplasm, which should not merge. Proposed criteria distinguishing Well-Differentiated Endometrioid Endometrial Adenocarcinoma from EIN or Atypical Endometrial Hyperplasia (1) Irregular infiltration of myometrium associated with an altered fibroblastic stroma (desmoplastic response), or (2) Confluent glandular pattern (cribriform growth, or complex folded mazelike epithelium), or (3) Solid nonsquamous epithelial growth Some investigators have offered specific measurements to assess confluent glandular growth more objectively. Kurman and Norris proposed 1.9 mm as a cutoff,8 whereas Longacre and colleagues proposed 30% of total architecturally atypical proliferation as a cutoff.9 However, it is important to note that different investigators did not find these parameters to have the same predictive value. References Background Documentation Female Reproductive • Endometrium • 4.1.0.2 10 1. Kurman RJ, Carcangiu ML, Harrington CS, Young RH, eds. WHO Classification of Tumors of the Female Reproductive Organs. Geneva, Switzerland: WHO Press; 2014. World Health Organization Classification of Tumors. 4th ed. 2. Williams KE, Waters ED, Woolas RP, Hammond IG, McCartney AJ. Mixed serous-endometrioid carcinoma of the uterus: pathologic and cytopathologic analysis of a high-risk endometrial carcinoma. Int J Gynecol Cancer. 1994;4:7-18. 3. Lim P, Al Kushi A, Gilks B, Wong F, Aquino-Parsons C. Early stage papillary serous carcinoma of the endometrium: effect of adjuvant whole abdominal radiotherapy and pathologic parameters on outcome. Cancer. 2001;91:752-757. 4. Darvishian F, Hummer A, Thaler H, et al. Serous endometrial cancers that mimic endometrioid adenocarcinomas: a clinicopathologic and immunohistochemical study of a group of problematic cases. Am J Surg Pathol. 2004;28:1568-1578. 5. Soslow RA, Pirog E, Isacson C. Endometrial intraepithelial carcinoma with peritoneal dissemination. Am J Surg Pathol. 2000;24:726-732. 6. Ambros RA, Sherman ME, Zahn CM, Bitterman P, Kurman RJ. Endometrial intraepithelial carcinoma: a distinctive lesion specifically associated with tumors displaying serous differentiation. Hum Pathol. 1995;26:1260-1267. 7. Hui P, Kelly M, O'Malley DM, Tavassoli F, Schwartz PE. Minimal uterine serous carcinoma: a clinicopathological study of 40 cases. Mod Pathol. 2005;18:75-82. 8. Kurman RJ, Norris HJ. Evaluation of criteria for distinguishing atypical endometrial hyperplasia from well-differentiated carcinoma. Cancer. 1982;2547-2559. 9. Longacre TA, Chumg MH, Jensen DN, Hendrickson MR. Proposed criteria for the diagnosis of well-differentiated endometrial carcinoma: a diagnostic test for myoinvasion. Am J Surg Pathol. 1995;19:371-406. C. Histologic Grading The International Federation of Gynecology and Obstetrics (FIGO) grading system for carcinomas of the uterine corpus is only officially designated for endometrioid carcinomas and is based on architectural features as follows:1 Grade 1 5% or less nonsquamous solid growth pattern Grade 2 6% to 50% nonsquamous solid growth pattern Grade 3 >50% nonsquamous solid growth pattern Notable nuclear atypia, which exceeds that which is routinely expected for the architectural grade, increases the tumor grade by 1. In addition, the following guidelines should be used in grading: (1) The squamous component of endometrioid adenocarcinoma should not be graded because the degree of differentiation typically parallels that of the glandular component.2 (2) Because mucinous carcinomas are closely related to endometrioid carcinomas, they can be graded by the same criteria. (3) Serous, clear cell, transitional, small cell and large cell neuroendocrine carcinomas, undifferentiated/ dedifferentiated carcinomas, and carcinosarcomas are generally considered to be high grade and it is not recommended to assign a FIGO grade to these tumor types.1,3 When the case summary is being completed, these should be designated as “not applicable” for histologic grade. (4) In mixed carcinomas, the highest grade should be assigned. References 1. Bhatla N, Denny L. FIGO Cancer Report 2018. Int J Gynecol Obstet. 2018;142(Suppl 2):i-iv, 1-158.. 2. Zaino RJ, Kurman RJ. Squamous differentiation in carcinoma of the endometrium: a critical appraisal of adenoacanthoma and adenosquamous carcinoma. Sem Diagn Pathol. 1988;5:154-171. 3. Kurman RJ, Carcangiu ML, Harrington CS, Young RH, eds. WHO Classification of Tumors of the Female Reproductive Organs. Geneva, Switzerland: WHO Press; 2014. World Health Organization Classification of Tumors. 4th ed. D. Myometrial Invasion Assessing myometrial invasion may be difficult. Depth of invasion should be measured from the endomyometrial junction to the deepest point of invasion, which may not be easy because the endomyometrial junction in normal Background Documentation Female Reproductive • Endometrium • 4.1.0.2 11 conditions is often irregular. In these cases, it is always helpful to look for compressed, non-neoplastic endometrial glands at the nearby endomyometrial junction or even at the base of the tumor. Carcinoma involving adenomyotic foci should not be interpreted as invasive carcinoma. However, the distinction between invasive carcinoma and carcinoma involving adenomyosis may be difficult, because in some cases invasive carcinoma may not elicit stromal response. In the absence of adenomyosis uninvolved by tumor in other sections of the specimen, a diagnosis of adenomyosis involved by adenocarcinoma should be made with caution. CD10 staining is not helpful in this differential diagnosis because stromal cells surrounding foci of invasive carcinoma are also frequently CD10 positive. There are no rules for determining how to measure the depth of invasion in the rare cases where myoinvasive carcinoma is only encountered in foci of adenomyosis involved by carcinoma. In such cases, it is advised that the distance from the adenomyotic focus to the deepest area of invasion be measured (Figure 1).1 Therefore, if there is a tumor with a 2-mm focus of myoinvasion from a focus of adenomyosis in the deep myometrium, it is still considered as having <50% myometrial invasion (FIGO stage IA). Figure 1. Schematic of measurement of depth of invasion in (A) tumor with a regular interface; (B) tumor with an irregular endomyometrial interface; (C) and (D) tumor with an exophytic growth; (E) tumor arising from adenomyosis. From Ali A, Black D, Soslow RA. Difficulties in assessing the depth of myometrial invasion in endometrial carcinoma. Int J Gynecol Pathol. 2007;26:115-123. Copyright © 2007, Wolters Kluwer Health. Reproduced with permission. References 1. Ali A, Black D, Soslow RA. Difficulties in assessing the depth of myometrial invasion in endometrial carcinoma. Int J Gynecol Pathol. 2007;26:115-123. E. Lower Uterine Segment Involvement The prevalence of Lynch syndrome in patients with LUS endometrial carcinoma (29%) has been reported to be much greater than that of the general endometrial cancer patient population (1.8%) or in endometrial cancer patients younger than age 50 years (8% to 9%).1 References 1. Westin SN, Lacour RA, Urbauer DL, et al. Carcinoma of the lower uterine segment: a newly described association with Lynch syndrome. J Clin Oncol. 2008;26:5965-5971 F. Cervical Involvement The American Joint Committee on Cancer (AJCC)/FIGO staging system considers stage II disease only when cervical stromal involvement is seen. Involvement of the surface endocervical epithelium and/or endocervical glands (either by direct extension or drop metastases) does not have any prognostic significance and is not T2/Stage II. Background Documentation Female Reproductive • Endometrium • 4.1.0.2 12 G. Peritoneal Washings or Ascites Fluid The prognostic significance of presence of tumor cells in peritoneal washings or ascites fluid is controversial. There are studies that indicate either a worse prognosis or no alteration of prognosis on the basis of positive cytology. Consequently, staging systems no longer utilize positive cytology to alter stage. When collected, however, cytology results should be recorded. H. Margins The parametrial/paracervical soft tissue and the vaginal cuff are the only true margins in total hysterectomy specimens. These margins should be reported if the cervix and/or parametrium/paracervix is involved by carcinoma. If not, reporting the status of the vaginal and parametrial margins in a hysterectomy specimen is optional. I. Lymphovascular Invasion Lymphovascular invasion (LVI) indicates whether microscopic lymphovascular invasion is identified. LVI includes lymphatic invasion, vascular invasion, or lymphovascular invasion. According to AJCC/International Union Against Cancer (UICC) convention, LVI does not affect the T category indicating local extent of tumor unless specifically included in the definition of a T category. J. Pathologic Stage Classification The TNM staging system for endometrial cancer endorsed by the AJCC and the UICC,1,2 and the parallel system formulated by FIGO3 are recommended. According to AJCC/UICC convention, the designation “T” refers to a primary tumor that has not been previously treated. The symbol “p” refers to the pathologic classification of the TNM, as opposed to the clinical classification, and is based on gross and microscopic examination. pT entails a resection of the primary tumor or biopsy adequate to evaluate the highest pT category, pN entails removal of nodes adequate to validate lymph node metastasis, and pM implies microscopic examination of distant lesions. Clinical classification (cTNM) is usually carried out by the referring physician before treatment during initial evaluation of the patient or when pathologic classification is not possible. Pathologic staging is usually performed after surgical resection of the primary tumor. Pathologic staging depends on pathologic documentation of the anatomic extent of disease, whether or not the primary tumor has been completely removed. If a biopsied tumor is not resected for any reason (eg, when technically infeasible) and if the highest T and N categories or the M1 category of the tumor can be confirmed microscopically, the criteria for pathologic classification and staging have been satisfied without total removal of the primary cancer. TNM Descriptors For identification of special cases of TNM or pTNM classifications, the “m” suffix and “y,” “r,” and “a” prefixes are used. Although they do not affect the stage grouping, they indicate cases needing separate analysis. The “y” prefix indicates those cases in which classification is performed during or after initial multimodality therapy (ie, neoadjuvant chemotherapy, radiation therapy, or both chemotherapy and radiation therapy). The cTNM or pTNM category is identified by a “y” prefix. The ycTNM or ypTNM categorizes the extent of tumor actually present at the time of that examination. The “y” categorization is not an estimate of tumor before multimodality therapy (ie, before initiation of neoadjuvant therapy). The “r” prefix indicates a recurrent tumor when staged after a documented disease-free interval and is identified by the “r” prefix: rTNM. The “a” prefix designates the stage determined at autopsy: aTNM. T Category Considerations It is important to note that in endometrial cancer, as in cancer of other organs, the validity of T stage depends upon the adequacy and completeness of the surgical staging. N Category Considerations Background Documentation Female Reproductive • Endometrium • 4.1.0.2 13 Isolated tumor cells (ITCs) are single cells or small clusters of cells not more than 0.2 mm in greatest dimension. Lymph nodes or distant sites with ITCs found by either histologic examination (eg, immunohistochemical evaluation for cytokeratin) or nonmorphological techniques (eg, flow cytometry, DNA analysis, polymerase chain reaction [PCR] amplification of a specific tumor marker) should be so identified. There is currently no guidance in the literature as to how these patients should be coded; until more data are available, they should be coded as “N0(i+)” with a comment noting how the cells were identified. Sentinel nodes should be sliced at 2.0 mm intervals. The sentinel nodes should undergo ultrastaging, Currently, there is no universal ultrastaging protocol. However, all institutions undertaking sentinel lymph node examination should have a standard procedure in place for sentinel lymph nodes. Protocols used at the 2 largest cancer centers in the United Stated are as follows: 1) Memorial Sloan Kettering Cancer Center Protocol:4 If the initial H&E-stained slide is negative for carcinoma and the endometrial cancer is myo-invasive or associated with vascular/lymphatic invasion, 2 additional levels at 50 µm apart are examined, at each level 2 slides are obtained, one for H&E and the second for keratin cocktail IHC if the H&E-stained slide is negative. 2) The University of Texas M.D. Anderson Cancer Center Protocol:5 If the H&E-stained slide is negative for tumor, 3 consecutive sections at 250 µm into the paraffin block are obtained (one for H&E and one of the remaining 2 is to be used for keratin cocktail IHC if the additional H&E-stained slide is negative. There is little data to assign risk for nonsentinel lymph node metastasis based on the size of the metastasis in the sentinel lymph node. However, the size criteria for micrometastasis and macrometastasis is adopted from the experience in breast carcinoma. Micrometastasis is defined as a metastasis measuring greater than 0.2 mm but less than 2 mm. Primary Tumor (T) FIGO T Category Stage Definition T1 I Tumor confined to corpus uteri T1a IA Tumor limited to endometrium or invades less than one-half of the myometrium T1b IB Tumor invades one-half or more of the myometrium T2 II Tumor invades stromal connective tissue of the cervix T3 III Tumor involving serosa, adnexa, vagina, or parametrium, ie, local and/or regional spread as specified in T3a and T3b, and in FIGO IIIA and IIIB T3a IIIA Tumor involving the serosa and/or adnexa (direct extension or metastasis) T3b IIIB Vaginal involvement (direct extension or metastasis) or parametrial involvement T4# IVA Tumor invading bladder mucosa# and/or bowel mucosa# # Tumor should involve the mucosal surface; Presence of bullous edema is not sufficient evidence to classify a tumor as T4. Regional Lymph Nodes (N):# TNM Staging System FIGO N Category Stage Definition NX Regional lymph nodes cannot be assessed N0 No regional lymph node metastasis N0(i+) Isolated tumor cells in regional lymph node(s) no greater than 0.2 mm N1 IIIC1 Regional lymph node metastasis to pelvic lymph nodes N1mi# IIIC1 Regional lymph node metastasis (greater than 0.2 mm but not greater than 2 mm in diameter) to pelvic lymph nodes N1a IIIC1 Regional lymph node metastasis (greater than 2 mm in diameter) to pelvic lymph nodes N2 IIIC2 Regional lymph node metastasis to para-aortic lymph nodes with or without positive pelvic lymph nodes Background Documentation Female Reproductive • Endometrium • 4.1.0.2 14 N2mi# IIIC2 Regional lymph node metastasis (greater than 0.2 mm but not greater than 2 mm in diameter) to para-aortic lymph nodes, with or without positive pelvic lymph nodes N2a IIIC2 Regional lymph node metastasis (greater than 2 mm in diameter)) to para-aortic lymph nodes, with or without positive pelvic lymph nodes # Regional lymph nodes include the pelvic, obturator, internal iliac (hypogastric), external iliac, common iliac, para-aortic, presacral, and parametrial lymph nodes. Even one metastasis >2.0 mm would qualify the classification as pN1a and pN2a. Distant Metastasis (M): TNM Staging System FIGO M Category Stage Definition M0 No distant metastasis M1 IVB Distant metastasis (includes metastasis to abdominal lymph nodes [other than para-aortic], and/or inguinal lymph nodes, intraperitoneal disease, lung, liver, or bone; excludes metastasis to vagina, pelvic serosa, or adnexa) References 1. Amin MB, Edge SB, Greene FL, et al, eds. AJCC Cancer Staging Manual. 8th ed. New York, NY: Springer; 2017. 2. Brierley JD, Gospodarowicz MK, Wittekind C, et al, eds. TNM Classification of Malignant Tumours. 8th ed. Oxford, UK: Wiley; 2016. 3. FIGO Cancer Report. Cancer of the corpus uteri. Int J Gynecol Obstet. 2018; 143 (Suppl 2);37-50 . 4. Abu-Rustum NR. Sentinel lymph node mapping for endometrial cancer: a modern approach to surgical staging. J Natl Compr Canc Netw 2014;12:288–97. 5. Euscher E, Sui D, Soliman P, et al. Ultrastaging of sentinel lymph nodes in endometrial carcinoma according to use of 2 different methods. Int J Gynecol Pathol 2018;37:242–251. 97. K. Additional Findings Atypical Hyperplasia/Endometrioid Intraepithelial Neoplasia This is composed of crowded aggregates of cytologically altered tubular or branching glands. The volume of crowded glands exceeds that of the stroma. In addition, there is nuclear atypia in the form of nuclear enlargement, pleomorphism, rounding, loss of polarity, and nucleoli.1 The diagnosis of atypia is aided by the comparison with adjacent normal glands when present. References 1. Kurman RJ, Carcangiu ML, Harrington CS, Young RH, eds. WHO Classification of Tumors of the Female Reproductive Organs. Geneva, Switzerland: WHO Press; 2014. World Health Organization Classification of Tumors. 4th ed. L. Clinical History and Biomarker Testing Colon carcinoma is the most common malignancy in hereditary nonpolyposis colon cancer (HNPCC; Lynch syndrome (LS)). However, endometrial carcinoma develops before colon carcinoma in >50% of women with HNPCC.1-4 Still, the reported series of HNPCC/LS-related endometrial carcinomas are much smaller in number than those reported for HNPCC/LS colonic carcinoma. Histopathologic features suggestive of HNPCC/LS-related carcinoma are well characterized in the colon, but not as well in the uterus. While lower uterine segment tumors and high grade tumors in the endometrium seem to have a higher rate of being LS-associated tumors, tumor morphology and anatomic location of tumor cannot be used to select patients for screening for LS. Many LS-associated endometrial carcinomas are seen in probands that do not meet Bethesda or Amsterdam personal/family history criteria for Lynch Syndrome. However, when examining an endometrial carcinoma in a patient under 50 years of age or with a personal or family history of colon carcinoma, it is important to consider the possibility of an HNPCC/LS-related endometrial carcinoma. According to the NCCN guidelines there should be universal testing of endometrial carcinomas for mismatch repair (MMR) proteins/microsatellite instability (MSI). This can be tested on the hysterectomy specimen or the pre-surgical biopsy. Testing for defective DNA mismatch repair proteins by immunohistochemistry is the most cost-effective method (MLH1, MSH2, MSH6, and PMS2 antibodies are commercially available).5 Loss of MSH2 or MSH6 expression essentially always indicates Lynch syndrome. HNPCC/LS-related endometrial carcinoma is predominantly associated with MSH2 mutations, and Background Documentation Female Reproductive • Endometrium • 4.1.0.2 15 MSH6 mutations.1-4 PMS2 loss is often associated with loss of MLH1 and is only independently meaningful if MLH1 is intact. MLH1 hypermethylation analysis should be completed on tumors that show loss of MLH1 on IHC to help triage appropriate cases for germline testing. There should be genetic counseling and testing for all other MMR abnormalities. PCR assays can be used to detect high levels of microsatellite alterations (MSI), a condition that is definitional for defective DNA mismatch repair. This testing is performed on paraffin-embedded tissue and compares the results of tumor DNA to those of non-neoplastic tissues from the same patient. In addition, Estrogen receptor (ER) testing is recommended for stage III, IV, and recurrent disease and may be requested by the treating clinician in order to predict response to endocrine therapy. HER2 immunohistochemistry (with reflex test to HER2 FISH for equivocal IHC) should be considered for serous endometrial cancer. Please refer to the CAP endometrial cancer biomarker reporting template on www.cap.org/cancerprotocols for further details. References 1. Aarnio M, Sankila R, Pukkala E, Salovaara R, Aaltonen LA, de la Chapelle A, Peltomäki P, Mecklin JP, Järvinen HJ. Cancer risk in mutation carriers of DNA-mismatch-repair genes. Int J Cancer. 1999;81:214-218. 2. Watson P, Vasen HF, Mecklin JP, Järvinen H, Lynch HT. The risk of endometrial cancer in hereditary nonpolyposis colorectal cancer. Am J Med. 1994;96:516-520. 3. Wijnen J, de Leeuw W, Vasen H, et al. Familial endometrial cancer in female carriers of MSH6 germline mutations. Nat Genet. 1999;23:142-144. 4. Charames GS, Millar AL, Pal T, Narod S, Bapat B. Do MSH6 mutations contribute to double primary cancers of the colorectum and endometrium? Hum Genet. 2000;107:623-629. 5. Mills AM, Liou S, Ford JM, Berek JS, Pai RK, Longacre TA. Lynch syndrome screening should be considered for all patients with newly diagnosed endometrial cancer. Am J Surg Pathol. 2014;38:1501-1509. |
13486 | https://tasks.illustrativemathematics.org/content-standards/tasks/1488 | Illustrative Mathematics
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Origami Silver Rectangle
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Alignments to Content Standards:8.G.A.1G-CO.D.12
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Task
This task examines the mathematics behind an origami construction of a rectangle whose sides have the ratio (2√:1). Such a rectangle is called a silver rectangle.
Beginning with a square piece of paper, first fold and unfold it leaving the diagonal crease as shown here:
Next fold the bottom right corner up to the diagonal:
After unfolding then fold the left hand side of the rectangle over to the crease from the previous fold:
Here is a picture, after the last step has been unfolded, with all folds shown and some important points marked. In the picture T is the reflection of S about ℓ.
Suppose s is the side length of our square. Show that |P T|=s.
Show that △P Q T is a 45-45-90 isosceles triangle.
Calculate |P Q| and conclude that P Q R S is a silver rectangle.
IM Commentary
The purpose of this task is to apply geometry in order analyze the shape of a rectangle obtained by folding paper. The central geometric ideas involved are reflections (used to model the paper folds), analysis of angles in triangles, and the Pythagorean Theorem. The task is appropriate either at the 8th grade level or in high school: the only difference would be the level of rigor expected in the explanation. The solution given is appropriate for either level.
The silver rectangle is one of three rectangles identified in ancient times as having important properties: the bronze rectangle has a side ratio of (3√,1) and the golden rectangle has a side ratio of (1+5√:2). Each of these three rectangles can be constructed by folding paper. Further properties of silver rectangles are examined in www.illustrativemathematics.org/illustrations/1489. Much more interesting information about the silver rectangle can be found here:
This task could be given in a much more open ended form, particularly if done in high school. Teachers could go through the different steps of the construction and then prompt students to examine the ratio of side lengths in the final rectangle. There are many possible solution paths revolving around the different triangles in the picture that are similar: half of the original square, △T Q P, and the small triangle in the lower left of the last picture. These are all 45-45-90 triangles and the dimensions of the rectangle can be found by calculating the scale factor between any pair of these triangles.
The Standards for Mathematical Practice focus on the nature of the learning experiences by attending to the thinking processes and habits of mind that students need to develop in order to attain a deep and flexible understanding of mathematics. Certain tasks lend themselves to the demonstration of specific practices by students. The practices that are observable during exploration of a task depend on how instruction unfolds in the classroom. While it is possible that tasks may be connected to several practices, the commentary will spotlight one practice connection in depth. Possible secondary practice connections may be discussed but not in the same degree of detail.
Students engage in Mathematical Practice Standard 5, Use appropriate tools strategically,†by considering a tool’s usefulness, its strengths and limitations, as well as knowing how to use it appropriately. This task examines the mathematics of the paper folding of a square piece of paper resulting in the creation of a silver rectangle. The tools, including paper, directions, straight edges, etc. allow students to analyze the shape of the paper as it is folded and unfolded revealing different triangular and rectangular shapes. This experimentation with paper folding allows students to explore and discuss observations before forming conclusions about the final rectangle. Students will also ''Reason abstractly and quantitatively'' (MP.2) as they need to represent the paper folding geometrically in order to calculate angles and side lengths.
Solution
Since reflection about ℓ maps P to itself and maps S to T this means that segments P S¯¯¯¯¯¯¯ and P T¯¯¯¯¯¯¯ are interchanged by reflection about ℓ. Hence
|P S|=|P T| because reflections preserve lengths of segments. We are given that |P S|=s since it is one side of the square so |P T|=s.
2. We know that m(∠Q P T)=45 because the diagonal of a square bisects the 90 degree angles. Alternatively, reflection over the diagonal P T←→ is a symmetry of the square: this reflection interchanges angles Q P T and S P T and so these must each measure 45 degrees. Angle T Q P is a right angle because Q R¯¯¯¯¯¯¯¯ is a crease resulting from a horizontal fold of the paper. Since
m(∠Q T P)+m(∠Q P T)+m(∠T Q P)=180 this means that m(∠Q T P)=45. Thus △P Q T is a 45-45-90 triangle: it is isosceles because m(∠Q T P)=m(∠Q P T).
3. To find |P Q| we use the fact that △P Q T is a right isosceles triangle. Thus we know that |T Q|=|P Q| and, from the Pythagorean Theorem,
|P Q|2+|T Q|2=|P T|2. Substituting |P Q| for |T Q| this is equivalent to 2|P Q|2=|P T|2. From part (a) this means that |P Q|2=s 2 2. So |P Q|=s 2√.
We can now check that P Q R S is a silver rectangle. Our calculations show that |P SP Q| is s:s 2√. But the ratio s:s 2√ is equivalent to the ratio 2√:1 as we can see using a scaling factor of 2√s.
Origami Silver Rectangle
This task examines the mathematics behind an origami construction of a rectangle whose sides have the ratio (2√:1). Such a rectangle is called a silver rectangle.
Beginning with a square piece of paper, first fold and unfold it leaving the diagonal crease as shown here:
Next fold the bottom right corner up to the diagonal:
After unfolding then fold the left hand side of the rectangle over to the crease from the previous fold:
Here is a picture, after the last step has been unfolded, with all folds shown and some important points marked. In the picture T is the reflection of S about ℓ.
Suppose s is the side length of our square. Show that |P T|=s.
Show that △P Q T is a 45-45-90 isosceles triangle.
Calculate |P Q| and conclude that P Q R S is a silver rectangle.
Print Task
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13487 | https://www.nrla.org.uk/resources/looking-after-your-property/smoke-and-carbon-monoxide-requirements | This website uses cookies to ensure you get the best experience on our website, read about our cookie policy.
Landlord Carbon Monoxide Detector & Smoke Alarm Requirements
By law, landlords in England must ensure smoke alarms are installed in all of their rented properties and carbon monoxide alarms are fitted in every room with a solid fuel heating appliance.
In this guide, we cover everything you need to know about landlord carbon monoxide detector and smoke alarm requirements, including:
These regulations only apply in England at the moment. However, similar carbon monoxide alarm regulations for landlords have been introduced in Wales under the Renting Homes (Wales) Act 2016.
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What are the requirements for smoke and carbon monoxide alarms in rental properties?
From 1 October 2022, both private and social landlords must ensure that a smoke alarm is equipped on each story where there is a room used wholly or partially as living accommodation. This has been a legal requirement for private landlords since 2015, but now applies to social housing landlords as well.
All properties are expected to have a carbon monoxide detector fitted in any room that is used as living accommodation and contains a fuel burning appliance. This is any appliance that uses fuel to generate heat, including gas boilers, wooden stoves, and open fires. However, gas cookers are excluded.
What type of alarm is required to meet smoke and carbon monoxide regulations?
The regulations do not stipulate what kind of smoke or carbon monoxide alarm for landlords is required, just that it works.
However, for smoke alarms, ideally, it should be a mains-wired, interconnected alarm system as this is the modern standard required in the building regulations. If you use a standalone battery-powered smoke alarm, local authorities are likely to consider this a hazard if they inspect, likely requiring you to improve it using their powers under the Housing Health and Safety Rating System.
Where should smoke and carbon monoxide alarms be placed?
You’ll need at least one smoke alarm on every storey which is used as living accommodation and one carbon monoxide alarm in every room which is used as living accommodation containing a fuel burning appliance.
However, the regulations do not stipulate exactly where the alarms should be fitted or placed. You should follow the alarm manufacturer’s instructions to find out where to place them. This will typically be at head height between 1-3 meters away from the fuel-burning source for carbon monoxide alarms and in a circulation point for smoke detectors.
What are my obligations as a landlord?
Landlord carbon monoxide detector and smoke alarm obligations include making sure that all alarms are in proper working order on the day a new tenancy begins as part of your pre-tenancy landlord duties.
Additionally, if you’re notified by a tenant that a smoke or carbon monoxide alarm is not working properly, the latest regulations stipulate that you must investigate and repair or replace the alarm as soon as reasonably possible.
What obligations do my tenants have?
It is the tenant’s responsibility to check the alarm during the tenancy. As the landlord, it’s advised that you provide them with the instruction manual or demonstrate how to perform these checks to ensure they’re done correctly.
If tenants find that their alarms are not in working order during the tenancy, they should replace the batteries themselves. If the alarm still does not work after replacing the batteries or the tenant is unable to replace the batteries themselves, they should report this to the landlord.
What tenancies do the regulations apply to?
These regulations apply to almost all residential premises in the private rented sector. This includes tenancies where the building is in mixed use, such as a flat above a shop.
There are various excluded tenancies found in the Act, such as:
How are alarm regulations enforced?
Smoke and carbon monoxide alarm regulations are enforced by the local authority.
A local authority must serve a remedial notice within 21 days where they have reason to believe that the landlord is in breach of any of these duties relating to smoke alarms or carbon monoxide alarms. A remedial notice must specify the action to be taken within 28 days of the date of service of the notice.
Should the landlord wish to make representations to the local authority they have 28 days in which to respond to the remedial notice. Once this has been done, the notice is suspended until the local authority reviews their decision and notifies the landlords of the outcome.
The outcome of the review must be provided to the landlord in writing no later than 35 days after the original notice is served. If the local authority does not do this, then the notice is considered to be withdrawn.
If the notice is confirmed after review, landlords will have 21 days to address the contents of the notice and fix the issues.
If the landlord is in breach the local authority may require the landlord to pay a penalty charge up to a maximum of £5,000. It has discretion whether or not to impose this charge and if intends to impose a charge, must serve a penalty charge notice within six weeks from when first satisfied that a breach has occurred. A right to make representations against the penalty notice is given and the local authority may reduce the charge for prompt payment.
For licensed properties, failure to comply with this regulation is a breach of a mandatory condition. This carries a potential civil penalty of up to £30,000.
I have tried to fit the carbon monoxide alarms but my tenant refuses access - what should I do?
The existing smoke and carbon monoxide alarm law for landlords makes clear that you must take all reasonable steps to comply with a remedial notice but are not expected to go to court to gain access in order to be compliant. Landlords should be able to demonstrate that they have taken all reasonable steps to comply with local authorities.
If your tenant refuses access, you should write to them to explain that it is a legal requirement to install the alarms and that it is for their own safety. You should try to arrange a time to visit that is convenient for the tenant, and keep a written record of access attempts to provide to the local housing authority if required.
You should attempt to understand why tenants cannot or will not provide access and work with them to find a solution.
What other safety responsibilities do I have as a landlord?
Complying with landlord carbon monoxide detector and smoke alarm requirements is just one of many safety responsibilities you have as a landlord. Other obligations include:
For a full list of your safety responsibilities, please see our guide on what safety certificates landlords need to provide.
Stay compliant with the NRLA
Keeping on top of your landlord obligations can be a difficult task. That’s why the NRLA are on hand to provide you with the expert support you need, when you need it.
Join the NRLA for unlimited support and advice on everything from staying compliant to dealing with difficult tenants, as well as access to exclusive landlord discounts on essential services, furnishings, and more. |
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find the horizontal asymptote for f(x) = (3x^2-x-2) / (5x^2+4x+1)
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Question: find the horizontal asymptote for f(x) = (3x^2-x-2) / (5x^2+4x+1)
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13489 | https://www.sciencedirect.com/science/article/pii/S0167299108609301 | Chapter 7 Oxygen on Oxides - ScienceDirect
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Abstract
References (40)
Cited by (5)
Studies in Surface Science and Catalysis
Volume 45, 1989, Pages 110-120
Chapter 7 Oxygen on Oxides
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This chapter discusses oxygen on oxides. The nature of adsorbed oxygen is described. Adsorbed oxygen on a stoichiometric surface of a fully oxidized oxide is readily identifiable. It is usually desorbed at temperatures lower than the sublimation temperature of surface lattice oxygen. On a partially reduced surface, adsorbed oxygen may result in reoxidation of the surface cations to different degrees, depending on the extent of charge transfer between the reduced center and the adsorbed oxygen. If the charge transfer is such that an adsorbed oxygen atom acquires the same electron density, as a surface lattice oxygen ion and it occupies a lattice site, the surface is reoxidized and the adsorbed oxygen becomes lattice oxygen. If the charge transfer is less extensive and/or the oxygen species occupies a site different from a surface lattice site, it is adsorbed oxygen. Adsorbed oxygen may be present as atomic or molecular species with various charges. One method to detect the presence of adsorbed oxygen is by temperature programmed desorption after exposing the oxide to O 2. Adsorbed oxygen species vary greatly in their reactivities, depending on their nature and the nature of the oxide.
Recommended articles
References (40)
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B. Yang et al.### J. Catal. (1982)
A. Tench et al.### Chem. Phys. Lett. (1971)
H.-C. Liu et al.### J. Catal. (1980)
N.K. Nag### J. Catal. (1985)
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B. Yang et al.### J. Catal. (1982)
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V.A. Shvets et al.### J. Catal. (1972)
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M. Anpo et al.### J. Catal. (1982)
A.A. Davydov et al.### J. Catal. (1979)
F. Blunt et al.### Chem. Commun. (1969)
J. Lunsford### Adv. Catal. (1973)
A. Bielanski et al.### Adv. Catal. (1979)
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View more references
Cited by (5)
Nanoferrites gas sensors: A critical review
2024, Sensors and Actuators A Physical Show abstract Gas sensing characteristics of nanoferrites have been critically and comprehensively reviewed along with a discussion on their unique spinel structural and defect characteristics. A special focus on pure as well as doped CoFe 2 O 4, NiFe 2 O 4, ZnFe 2 O 4, CuFe 2 O 4, MnFe 2 O 4. has been given due to their technological potential The dependence of gas sensing properties on the gas sensing parameters such as gas concentration, operating temperature, relaxation, and recovery time as well as sensitivity, limit of detection and response etc. The influence of crystallite size, adsorption, chemical surface state, and area of sensor on sensitivity has also been analyzed. A critical review of various reported results on nanoferrites gas sensors towards variety of gases has also been included. Finally, a discussion on future developments in designing integrated nanoferrites gas sensors has been presented.
### Adsorption of methylene blue and metachromasy over analcime zeolites synthesized by using different Al precursors
2023, Materials Today Chemistry Show abstract Pure crystalline Analcime (ANA) zeolite samples were successfully synthesized using various aluminum precursors such as aluminum nitrate (ANA-nit), aluminum sulfate (ANA-sul), aluminum isopropoxide (ANA-isop), sodium aluminate (ANA-sodalu) and aluminum chloride (ANA-chl) to study the influence of various anions on the physicochemical properties of ANA zeolite structure. The physicochemical properties of the samples have been studied using elemental analysis, X-ray diffraction, Fourier-transformed infrared spectroscopy, scanning electron microscope, N 2-physisorption, X-ray photon spectroscopy, and diffuse reflectance UV–vis measurements. The synthesized analcime samples exhibited highly crystalline ANA structure; however, the anions present in the Al precursor influenced the crystallite and particle sizes. All the samples possessed a band gap energy of around 3.8 eV. The metachromasy phenomenon of methylene blue (MB) over synthesized Analcime samples was investigated under UV irradiation. The UV–vis absorption spectra of MB solution show a transformation from mono-MB to H-aggregated MB species due to the metachromasy phenomenon occurring over the surface of synthesized analcime samples. The formation of H-aggregated MB species differs for the synthesized ANA samples, which depends on the presence of active species on the ANA surface. The ANA-nit sample exhibited a fast metachromatic phenomenon due to more surface basic sites (e.g., O 2−, O−) distributed over different (micro-, meso- and macro-) pores.
### Highly sensitive NO2 sensor based on ZnO nanostructured thin film prepared by SILAR technique
2021, Sensors and Actuators B Chemical Citation Excerpt :
As the operating temperature is increased above 150 °C, O− becomes the dominant species till 400 °C and thereafter (>400 °C), O2- dominates . The reactivity of these adsorbed oxygen species differ significantly and among them, O− has been shown to be very reactive using EPR . Hence with increase in temperature, the response of the ZnO sensor increases, and maximum is attained at temperature of ∼200 °C due to presence of adsorbed O− ions. Show abstract Present study reports highly sensitive, selective and rapid sub-ppm level detection of nitrogen di-oxide (NO 2) using pristine zinc oxide (ZnO) thin films prepared by a simple and efficient technique - Successive Ion Layer Adsorption and Reaction (SILAR). Synthesized ZnO thin films were characterized for their physical and chemical properties. Gas sensing studies revealed that these films are highly sensitive to NO 2 with a sensor response of 249 for 20 ppm at an optimum temperature of 200 °C, with a lowest detection limit of 500 ppb. These sensors are found to be highly selective to NO 2 with fast response and recovery times (11 and 44 s for 20 ppm). XPS studies of these films have been carried out after NO 2 exposure in order to understand the sensing mechanism. Presence of nitride (N - 395.9 eV) species in N-1s spectra, decrease in binding energy position (∼ 1 eV) of Zn-2p peaks along with reduction of the concentration of total oxygen species on the surface of the film (from 73 % to 54 %), indicates that NO 2 does not only interact with adsorbed oxygen but also with lattice oxygen. Optical studies (Raman and Photoluminescence) as well as observance of a higher work function value ∼ 5.24 eV in pure ZnO samples established the existence of defects in these ZnO thin films, which forms the basis for their superior sensor response and faster response kinetics.
### Remarkable N2-selectivity enhancement of practical NH3-SCR over Co0.5Mn1Fe0.25Al0.75Ox-LDO: The role of Co investigated by transient kinetic and DFT mechanistic studies
2020, Applied Catalysis B Environmental Citation Excerpt :
According to the steady-state formation rates of N2 and N2O, about 50-56% of the ammonia present in the feed gas stream (500 ppm) reacted in the presence of 5 vol% O2 to give N2 and N2O. By comparing the transient response curves in Fig. 12C with those in Fig. 8C (He → 500 ppm NH3/1% Kr/Ar/He (45 min)), it can be stated that ammonia oxidation to N2O must proceed via labile lattice oxygen present in the LDO materials, which is replaced by gaseous oxygen upon dissociation onto oxygen vacant sites but also onto cationic metal sites [90,91]. At the same time, by comparing the transient response curves of N2 in Fig. 8B (500 ppm NH3/He) with those in Fig. 12B (500 ppm NH3/5 % O2/He), it appears that the selective oxidation of ammonia to N2 is facilitated on the Co0.5Mn1Fe0.25Al0.75Ox-LDO surface, likely also due to the presence of other kinds of adsorbed oxygen species, in harmony with the XPS results (Section 3.4, Table 2, Oα chemisorbed species). Show abstract A Co 0.5 Mn 1 Fe 0.25 Al 0.75 O x-LDO catalyst was developed which showed excellent performance for the low-temperature NH 3-SCR. NO x conversions ∼100% were achieved in the whole 100-250 °C range, while after 10-h operation at 150 °C with 100 ppm SO 2/5 vol% H 2 O in the feed, the NO x conversion was maintained at 80%. This catalyst provided a much better N 2-selectivity than the Mn 1 Fe 0.25 Al 0.75 O x-LDO and Mn 1 Al 1 O x-LDO, especially at 150-300 °C. It was found that Co 0.5 Mn 1 Fe 0.25 Al 0.75 O x possessed higher surface acidity and reducibility, while XPS analyses indicated an electron transfer between Co 3+/Co 2+ and Mn 4+/Mn 3+ redox cycles, leading to a much lower N 2 O formation, supported by Density Functional Theory (DFT) calculations. Detailed analysis of gas responses obtained upon various step-gas switches was performed, which allowed to measure the surface concentration and reactivity of preadsorbed NO x-s and NH x-s leading to N 2 and N 2 O. Transient kinetic and DFT studies strongly suggested likely mechanisms of NH 3-SCR and the critical role of Co for N 2-selectivity enhancement.
### Gas sensing properties of YMnO3 based materials for the detection of NOx and CO
2017, Sensors and Actuators B Chemical Citation Excerpt :
In particular, for resistive gas sensing it is necessary that, due to the interaction with gas, a negative (or positive) charge is trapped at the surface, on the other hand this is not needed for catalysis. For instance, it can be thought that low temperature catalysis involves non-ionized adsorbed oxygen, chemisorbed but with a negligible charge transfer [40–43]. As expected the presence of Pd is found to be extremely relevant for CO conversion, and the half-conversion temperatures, T50%, for Pd added materials, are ∼70 °C lower than the one of the base material. Show abstract This paper deals with chemoresistive behavior of hexagonal YMnO 3 produced by gel combustion. Stoichiometric, defective and doped compositions were studied and both reducing (CO) and oxidizing test gases (NO x) were used. The materials were characterized by means of X-ray diffraction, CO conversion tests, and oxygen temperature programmable desorption (TPD) and temperature programmable reduction (TPR) with H 2. Experiments indicate that, besides the oxygen chemisorption, the direct adsorption of the target gases at the material surface plays an important role in resistive gas sensing. A model based on these assumptions was developed and excellently fits the transient response of the sensors under test to NO 2 in the absence of oxygen. All the tested materials behave as p-type semiconductors and have a fast reversible response to NO 2 which is optimum at temperatures close to 180°C (30% @10 ppm NO 2, after about 1 min). In particular, it was found that the best sensor performance in NO 2 detection is obtained with defective materials in terms of response, while an interesting trade-off between temperature response and gas response is obtained with Pd doped materials. Regarding CO detection, materials impregnated with Pd showed the best performance both in terms of speed and of response, with an optimum temperature of 300°C.
View full text
Copyright © 1989 Published by Elsevier B.V. All rights reserved.
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13490 | https://hinative.com/questions/25084528 | Quality Point(s): 822
Answer: 178
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What is the difference between practical and convenient ?Feel free to just provide example sentences.
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"Practical" and "convenient" are related concepts but have slightly different nuances: 1. Practical: - Relates to things that are sensible, efficient, and suitable for a particular purpose, often focusing on utility and functionality. Example sentence: "Buying a fuel-efficient car is a practical choice for commuting long distances." 2. Convenient: - Refers to things that are easy to use, accessible, or save time, emphasizing comfort and ease of use. Example sentence: "Living near public transportation is convenient for daily commuting." In summary, "practical" tends to emphasize usefulness and suitability, while "convenient" focuses more on ease and comfort in terms of use or access.
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13491 | https://www.osmosis.org/blog/usmle-step-1-question-of-the-day-quadruple-test | Skip to content
USMLE® Step 1 Question of the Day: Quadruple test
Allopathic Medicine (MD), Exam Prep, Osteopathic Medicine (DO), Questions of the Day, USMLE Step 1, USMLE® Step 1
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This USMLE Step 1 Question of the Day addresses abnormal lab results in a 17-week pregnant patient. Learn about the interpretation of quadruple test results and their implications.
A 39-year-old woman, gravida 1, para 0, comes to the office for the evaluation of abnormal laboratory results. The patient is at 17 weeks gestation according to her last menstrual period. She used to drink 1 glass of wine on weekends during the first trimester, as she was unaware of the pregnancy. Past medical history is unremarkable. She regularly takes prenatal vitamins, and her immunizations are up to date. Results of the quadruple test are shown:
| | |
--- |
| Laboratory value | Result |
| Maternal serum alpha fetoprotein | Low |
| Unconjugated estriol | Low |
| β-HCG | High |
| Inhibin A | High |
The fetus is at greatest risk of developing which of the following?
A. Myelomeningocele
B. Omphalocele
C. Fetal alcohol syndrome
D. Duodenal atresiaE. Gastroschisis
Scroll down for the correct answer!
The correct answer to today’s USMLE® Step 1 Question is…
D. Duodenal atresia
Before we get to the Main Explanation, let’s look at the incorrect answer explanations. Skip to the bottom if you want to see the correct answer right away!
Incorrect Answer Explanations
A. Myelomeningocele
Incorrect: Myelomeningocele results from a neural tube defect and causes increased maternal serum AFP, whereas unconjugated estriol, β-HCG and inhibin A is within normal limits.
B. Omphalocele
Incorrect: Omphalocele can be seen in association with Trisomy 18. The quadruple test shows reduced levels of maternal serum AFP, unconjugated estriol, β-HCG and inhibin A. Neonates with Down syndrome are at slightly elevated risk of developing omphalocele; however, their risk for another gastrointestinal anomaly is greater.
C. Fetal alcohol syndrome
Incorrect: Pregnant women should be advised to avoid alcohol intake during pregnancy. However, 1 glass of wine a week does not significantly increase the risk of fetal alcohol syndrome, and the results of this quadruple test suggest a different diagnosis.
E. Gastroschisis
Incorrect: Gastroschisis results from an abdominal wall defect and causes increased maternal serum and amniotic fluid AFP, whereas unconjugated estriol, β-HCG and inhibin A are within normal limits.
Main Explanation
This pregnant patient’s results from the quadruple test demonstrate an elevated hCG and inhibin A with low AFP and estriol; these findings are most indicative of Down syndrome (trisomy 21). Down syndrome is the most common autosomal trisomy and the most frequent form of intellectual disability caused by a chromosomal aberration. It is characterized by the presence of an extra copy of genetic material on chromosome 21, either in whole (trisomy 21) or in part (such as due to translocations).
A fetus with Down syndrome is at greatest risk of duodenal atresia, which results from the failure of canalization of the duodenum in early gestation. Affected infants present with bilious emesis during the first few days of life and “double bubble” sign (dilated stomach and proximal duodenum) on an abdominal x-ray. Other gastrointestinal abnormalities associated with Down syndrome include Hirschsprung disease, imperforate anus, tracheoesophageal fistula, and celiac disease.
Major Takeaway
Duodenal atresia is the most common gastrointestinal anomaly associated with Down syndrome. Affected infants present with bilious emesis during the first few days of life and “double bubble” sign (dilated stomach and proximal duodenum) on an abdominal x-ray. Hirschsprung disease, imperforate anus, tracheoesophageal fistula, and celiac disease are other common associations of Trisomy 21.
References
Stoll, C., Dott, B., Alembik, Y., & Roth, M. P. (2015). Associated congenital anomalies among cases with Down syndrome. European journal of medical genetics, 58(12), 674-680.
Epstein CJ. Down syndrome (Trisomy 21). In: The metabolic and molecular bases of inherited disease, 8th ed, Scriver CR, Beaudet AL, Sly WS, Valle D (Eds), McGraw-Hill, New York 2001. p.1223.
Want more USMLE® Step 1 practice questions? Try Osmosis by Elsevier today! Access yourfree trialand find out why millions of current and future clinicians and caregivers love learning with us.
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13492 | https://www.cut-the-knot.org/triangle/ABisector.shtml | Site...
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Elementary geometry
The Angle Bisectors
For every angle, there exists a line that divides the angle into two equal parts. This line is known as the angle bisector. In a triangle, there are three such lines. Three angle bisectors of a triangle meet at a point called the incenter of the triangle. There are several ways to see why this is so.
Angle Bisectors as Cevians
This is Corollary 2 of Ceva's theorem.
Let's here prove the required proportion. Let AD be the angle bisector of angle A. The area of a triangle can be computed in many ways. I'll use two of them to compute the areas of triangles ABD and ACD. Let a denote half the angle BAC. Then
Area(ABD) / Area(ACD) = [AB·AD·sin(a)/2] / [AC·AD·sin(a)/2] = AB / AC.
On the other hand, if AHa is the altitude from A to BC, then
Area(ABD) / Area(ACD) = [AHa·BD/2] / [AHa·CD/2] = BD / CD.
Combining the two gives the required identity: AB / AC = BD / CD.
(A dynamic illustration of a different proof can be found elsewhere. And there is another one.)
2. Via Transitivity of Equality
An angle bisector of an angle is known to be the locus of points equidistant from the two rays (half-lines) forming the angle. Existence of the incenter is then a consequence of the transitivity property of equality.
3. Angle Bisectors as Axes of a 2-line
If we adopt Frank Morley's outlook, transitivity of equality will still be present but only implicitly.
An angle bisector can be looked at as the locus of centers of circles that touch two rays emanating from the same point. In a triangle, there are three such pairs of rays. Pick any angle and consider its bisector. Circles that touch two sides of the angle have their centers on the bisector. Conversely, any point on the bisector serves as the center of a circle that touches both sides of the angle. Consider two bisectors of angles formed by the pair a and b and by the pair b and c. The circle with the center at the point of intersection of the two bisectors touches all three sides. In particular, it touches the sides a and c and, therefore, has its center on the bisector of the angle formed by these two sides.
4. Angle Bisectors as Altitudes
Altitudes of a triangle serve as angle bisectors of the associated orthic triangle. This association can be used in reverse.
Consider ΔABC. Through each vertex draw a line perpendicular to the corresponding angle bisector. These three lines will form a triangle - say ΔA'B'C'. Note that, since A'B' is perpendicular to CLc, ∠BCA' = ∠ACB'. The same is true of the pairs of angles at vertices A and B. Let's call this a mirror property. As we know, the orthic triangle of ΔA'B'C' has the mirror property. We'll make use of this observation shortly.
What we have to show now is that the bisectors ALa, BLb, and CLc pass through the vertices A', B', and C', respectively. Assume to the contrary, that at least one of them does not pass through the corresponding vertex. Then the orthic triangle of ΔA'B'C' could not possibly coincide with ΔABC. But, assuming they are different, in the ΔA'B'C' there would be two distinct inscribed triangles (ABC and the orthic) that possess the mirror property. However, it can be shown that this is impossible. There is only one triangle with that property. (For other properties of the orthic triangle see the discussion on Fagnano's problem.)
The proof is pretty simple.
It appears that angles in a triangle with the mirror property are not arbitrary. Count the angles in the diagram. (Two cases - of obtuse and acute-angle triangles - should be considered separately. In the former case, instead of talking of inscribed triangles, we should consider triangles with vertices on the sides, or the extensions thereof, of a given triangle.) Any triangle with the mirror property must have the same angles as the orthic triangle and have its sides parallel to the latter. As the third diagram suggests, this is clearly impossible for a triangle different from orthic. (Similar considerations worked in one of the proofs of Morley's Theorem.)
5. Complex numbers
As in the study of altitudes, let vertices of a given triangle be located on the unit circle. For convenience sake, lets take them to be squares of complex numbers: x12, x22, and x32. The midpoint of the arc x1x2 opposite the vertex x3 is then equal ±x1x2. And similarly for midpoints of arcs x2x3 and x1x3. Let's choose x1, x2, x3 such that all the signs are taken to be "+". The clinant of the line through x1x2 and x3 (the angle bisector at the vertex x3) is given by
| | |
--- |
| M | = (y32 - y1y2)/(x32 - x1x2) |
| | = - 1/(x1x2x32) |
which readily gives an equation of the angle bisector
y = - (x - x1x2)/(x1x2x32) + y1y2
Write down a similar equation for a second angle bisector, for instance,
y = - (x - x1x3)/(x1x3x22) + y1y3
and solve the two equations for y. As x is the conjugate of y, with a little effort the result reduces to
x = - (x1x2 + x2x3 + x3x1)
a symmetric expression of all three indices. Therefore, this point also belongs to the third angle bisector.
References
Liang-shin Hahn, Complex Numbers & Geometry, MAA, 1994
| | |
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| Related material Read more... | |
| | Angle Bisector |
| | |
| | |
| | - Angle Bisector |
| | - Angle Bisector Theorem |
| | - Angle Bisectors in Ellipse |
| | - Angle Bisectors in Ellipse II |
| | - Angle Bisector in Equilateral Trapezoid |
| | - Angle Bisector in Rectangle |
| | - Property of Angle Bisectors |
| | - Property of Angle Bisectors II |
| | - A Property of Angle Bisectors III |
| | - External Angle Bisectors |
| | - Projections on Internal and External Angle Bisectors |
| | - Angle Bisectors On Circumcircle |
| | - Angle Bisectors in a Quadrilateral - Cyclic and Otherwise |
| | - Problem: Angle Bisectors in a Quadrilateral |
| | - Triangle From Angle Bisectors |
| | - Property of Internal Angle Bisector - Hubert Shutrick's PWW |
| | - Angle Bisectors Cross Circumcircle |
| | - For Equality Choose Angle Bisector |
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13493 | http://www.math.emory.edu/~vicki/preprint/PsdSosSurvey.pdf | Positive Polynomials and Sums of Squares: Theory and Practice Victoria Powers ∗ November 12, 2015 Abstract If a real polynomial f can be written as a sum of squares of real polynomials, then clearly f is nonnegative on Rn, and an explicit expression of f as a sum of squares is a certificate of positivity for f.
This idea, and generalizations of it, underlie a large body of theoretical and computational results concerning positive polynomials and sums of squares. In this survey article, we review the history of the subject and give an overview of recent results, both theoretical results concerning the existence of certificates of positivity and work on computational and algorithmic issues.
Keywords: sums of squares, positive polynomials, certificates of positivity, Hilbert’s 17th Problem, positivstellens¨ atze.
In theory, theory and practice are the same. In practice, they are different. - A. Einstein If a real polynomial f in n variables can be written as a sum of squares of real polynomials, then clearly f must take only nonnegative values in Rn. This simple, but powerful, fact and generalizations of it underlie a large body of theoretical and computational results concerning positive polynomials and sums of squares.
An explicit expression of f as a sum of squares is a certificate of positiv-ity for f, i.e., a polynomial identity which gives an immediate proof of the positivity of of f on Rn. In recent years, much work has been devoted to the study of certificates of positivity for polynomials. In this paper we will give an overview of some recent results in the theory and practice of positivity and sums of squares, with detailed references to the literature. By “the-ory”, we mean theoretical results concerning the existence of certificates of positivity. By “practice”, we mean work on computational and algorithmic issues, such as finding certificates of positivity for a given polynomial.
For the most part, we restrict results to those in a real polynomial ring. This is somewhat misleading, since it is impossible to prove most ∗Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322. Email: vicki@mathcs.emory.edu.
1 of the results for polynomials without using a more abstract approach.
For example, in order to obtain a solution to Hilbert’s 17th problem, it was necessary for Artin (along with Schreier) to first develop the theory of ordered fields!
The reader should keep in mind that underneath the theorems in this paper lie the elegant and beautiful subjects of Real Algebra and Real Algebraic Geometry, among others.
The subject of positivity and sums of squares has been well-served by its expositors. There are a number of books and survey articles devoted to various aspects of the subject. Here we mention a few of these that the interested reader could consult for more details and background on the topics covered in this paper, as well as related topics that are not included: There are the books by Prestel and Delzell and Marshall on positive polynomials, a survey article by Reznick about psd and sos polynomials with a wealth of historical information, and a recent survey article by Scheiderer on positivity and sums of squares which discusses results up to about 2007. Finally, there is a survey article by Laurent which discusses positivity and sums of squares in the context of applications to polynomial optimization.
1 Preliminaries and background In this section, we introduce the basic concepts and review some of the fundamental results in the subject, starting with results in the late 19th century. For a fuller account of the historical background, see the survey . For a more detailed survey of the subject up to about 2007, readers should consult the survey article .
1.1 Notation Throughout, we fix n ∈N and let R[X] denote the real polynomial ring R[X1, . . . , Xn]. We denote by R[X]+ the set of polynomials in R[X] with nonnegative coefficients. The following monomial notation is convenient: For α = (α1, . . . , αn) ∈Nn, let Xα denote Xα1 1 · · · Xαn n . For a commutative ring A, we denote the set of sums of squares of elements of A by P A2.
We define the basic objects studied in real algebraic geometry. Given a set G of polynomials in R[X], the closed semialgebraic set defined by G is S(G) := {x ∈Rn | g(x) ≥0 for all g ∈G}.
If G is finite, S(G) is the basic closed semialgebraic set generated by G.
The basic algebraic objects of interest are defined as follows. For a finite 2 subset G = {g1, . . . , gr} of R[X], the preordering generated by G is PO(G) := { X e=(e1,...,er)∈{0,1}r sege1 1 . . . ger r | each se ∈ X R[X]2}.
The quadratic module generated by G is M(G) := {s0 + s1g1 + · · · + srgr | each si ∈ X R[X]2}.
Notice that if f ∈PO(G) or f ∈M(G), then f is clearly positive on S(G) and an identity f = P e∈{0,1}r sege1 1 . . . ger r or f = s0 + s1g1 + · · · + srgr is a certificate of positivity for f on S(G).
Traditionally, a result implying the existence of certificates of positivity for polynomials on semialgebraic sets is called a Positivstellensatz or a Nichtnegativstellensatz, depending on whether the polynomial is required to be strictly positive or non-strictly positive on the set. We will use the term “representation theorem” for any theorem of this type and refer to a “representation of f” (as a sum of squares, in the preordering, etc.), meaning an explicit identity for f.
1.2 Classic results A polynomial f ∈R[X] is positive semidefinite, psd for short, if f(x) ≥0 for all x ∈Rn. We say f is sos if f ∈P R[X]2. Of course, f sos implies that f is psd, and for n = 1, the converse follows from the Fundamental Theorem of Algebra.
We begin our story in 1888, when the 26-year-old Hilbert published his seminal paper on sums of squares in which he showed that for n ≥3, there exist psd forms (homogenous polynomials) in n variables which are not sums of squares. In the same paper, he proved that every psd ternary quartic – homogenous polynomial of degree 4 in 3 variables – is a sum of squares.
1 Hilbert was able to prove that for n = 3, every psd form is a sum of squares of rational functions, but he was not able to prove this for n > 2.
This became the seventeenth on his famous list of twenty-three mathematical problems that he announced at the 1900 International Congress of Mathematicians in Berlin. In 1927, E. Artin settled the question: Theorem 1 (Artin’s Theorem). Suppose f ∈R[X] is psd, then there exists nonzero g ∈R[X] such that g2f is sos.
1Hilbert worked with forms, however for the purposes of this paper we prefer to work in a non-homogenous setting.
A form can be dehomogenized into a polynomial in one less variable and the properties of being psd and sos are inherited under dehomogenization. When discussing work related to Hilbert’s work, we will use the language of forms, otherwise, we state results in terms of polynomials.
3 The following Positivstellensatz has until recently been attributed to Stengle , who proved it in 1974. It is now known that the main ideas were in a paper of Krivine’s from the 1960’s.
Theorem 2 (Classical Positivstellensatz). Suppose S = S(G) for finite G ⊆R[X] and f ∈R[X] with f > 0 on S. Then there exist p, q ∈PO(G) such that pf = 1 + q.
1.3 Bernstein’s and P´ olya’s theorems Certificates of positivity for a univariate p ∈R[x] such that p ≥0 or p > 0 on an interval [a, b] have been studied since the late 19th century.
Questions about polynomials positive on an interval come in part from the relationship with the classic Moment Problem, in particular, Hausdorf’s solution to the Moment Problem on [0, 1] .
In 1915, Bernstein proved that if p ∈R[x] and p > 0 on (−1, 1), then p can be written as a positive linear combination of polynomials (1 − x)i(1 + x)j for suitable integers i and j; however, it might be necessary for i + j to exceed the degree of p. Notice that writing p as such a positive linear combination is a certificate of positivity for p on [−1, 1].
P´ olya’s Theorem, which he proved in 1928 , concerned forms positive on the standard n−1-simplex ∆n−1 := {(x1, . . . , xn) ∈Rn | xi ≥0, P i xi = 1}.
Theorem 3 (P´ olya’s Theorem). Suppose f ∈R[X] is homogeneous and is strictly positive on ∆n−1, then for sufficiently large N, all of the coefficients of (X1 + · · · + Xn)Nf are positive.
Here “all coefficients are positive” means that every monomial of degree deg f + N appears with a strictly positive coefficient.
Bernstein’s result is equivalent to the one-variable dehomogenized ver-sion of P´ olya’s Theorem: If p ∈R[x] is positive on (0, ∞), then there exists N ∈N such that (1 + x)Np has only positive coefficients. The equivalence is immediate by applying the “Goursat transform” which sends p to (x + 1)dp 1 −x 1 + x , where d = deg p.
1.4 Schm¨ udgen’s Theorem and beyond In 1991, Schm¨ udgen proved his celebrated theorem on representations of polynomials strictly positive on compact basic closed semialgebraic sets.
This result began a period of much activity in Real Algebraic Geometry, which continues today, and stimulated new directions of research.
4 Theorem 4 (Schm¨ udgen’s Positivstellensatz). Suppose G is a finite subset of R[X] and S(G) is compact. If f ∈R[X] is such that f > 0 on S(G), then f ∈PO(G).
Schm¨ udgen’s theorem yields “denominator-free” certificates of positiv-ity, in contrast to Artin’s theorem and the Classic Positivstellensatz. The underlying reason that such certificates exist is that the preordering PO(G) in this case is archimedean: Given any h ∈R[X], there exists N ∈N such that N ± h ∈PO(G).
Equivalently, there is some N ∈N such that N −P X2 i ∈PO(G). It is a fact that if S(G) is compact, then PO(G) is archimedean. This follows from Schm¨ udgen’s proof of his theorem; there is a direct proof due to W¨ ormann .
The definition of archimedean for a quadratic module M is the same as for a preordering. If M(G) if archimedean, then it is immediate that S(G) is compact; the converse is not true in general. In 1993, Putinar gave a denominator-free representation theorem for archimedean quadratic modules.
Theorem 5 (Putinar’s Positivstellensatz). Suppose G is a finite subset of R[X] and M(G) is archimedean. If f ∈R[X] is such that f > 0 on S(G), then f ∈M(G).
In 1999, Scheiderer began a systematic study of questions concerning the existence of certificates of positivity in a broader setting. Let A be a commutative ring, then a ∈A is called psd if its image is nonnegative in every element of the real spectrum of A. One then asks when does psd = sos in A? In a series of fundamental papers, Scheiderer settles this question in many cases for coordinate rings of real affine varieties, and more general rings , , , , . This work led to many new representation theorems for polynomial rings. See for a detailed account.
2 Theory: Certificates of Positivity In this section we look at very recent theoretical results concerning sums of squares, psd polynomials, and certificates of positivity. We start with some modern riffs on Hilbert’s 1888 paper. We then look at the sums of squares on algebraic curves.
We discuss stability in quadratic modules, a topic which is important in computational questions and applications.
Finally, we look at recent work concerning sums of squares in cases where the polynomials have some special structure.
5 2.1 Psd ternary quartics Hilbert’s 1888 proof that a psd ternary quartic is a sum of three squares of quadratic forms is short, but difficult; arguably a high point of 19th century algebraic geometry. Even today the proof is not easy to understand and Hilbert’s exposition lacks details in a number of key points. Several authors have given modern expositions of Hilbert’s proof, with details filled in.
There is an approach due to Cassels, published in Rajwade’s book Squares [72, Chapter 7], and articles by Rudin and Swan .
In 1977, Choi and Lam gave a short elementary proof that a psd ternary quartic must be a sum of five squares of quadratic forms. In 2004, Pfister gave an elementary proof that a psd ternary quartic is a sum of four squares of quadratic forms and he gave an elementary and constructive argument in the case that the ternary quartic has a non-trivial real zero.
Very recently, Pfister and Scheiderer gave a complete proof of Hilbert’s Theorem, different from Hilbert’s proof. Although the proof is not easy, it uses only elementary techniques such as the theorems on implicit functions and symmetric functions.
In the “Practice” section of this paper, we will discuss computational issues around Hilbert’s theorem on ternary quartics.
2.2 Hilbert’s construction of psd, not sos, polynomials In Hilbert’s 1888 paper, he described how to find psd forms which are not sums of squares. However, his construction did not yield an explicit example of a psd, not sos, polynomial. It took nearly 80 years for an explicit example of a psd, not sos, polynomial to appear in the literature; the first published example was due to Motzkin. Since then, other examples and families of examples have been produced (see the survey for a detailed account), however only recently has there been attempts to exploit the constructive side of Hilbert’s proof.
Reznick has isolated the underlying mechanism of Hilbert’s con-struction and shown that it applies to more general situations than those considered by Hilbert. He is then able to produce many new examples of psd, not sos, polynomials.
Hilbert’s proof, and Reznick’s modern exposition and generalization, use the fact that forms of degree d satisfy certain linear relations, known as the Cayley-Bacharach relations, which are not satisfied by forms of full degree 2d. Very recently, Blekherman shows that the Cayley-Bacharach rela-tions are, in fact, the fundamental reason that there are psd polynomials that are not sos. In small cases, he is able to give a complete characteriza-tion of the difference between psd and sos forms. For example, the result for forms of degree 6 in 3 variables is the following: 6 Theorem 6 (,Theorem 1.1). Let H3,6 be the vector space of degree 6 forms in 3 variables. Suppose p ∈H3,6 is psd and not sos. Then there exist two real cubics q1, q2 intersecting in 9 (possible complex) projective points γ1, . . . , γ9 such that the values of p on γi certify that p is not a sum of squares in the following sense: There is a linear functional l on H3,6, defined in terms of the γi’s, such that l(q) ≥0 for all sos q and l(p) < 0.
2.3 The gap between psd and sos polynomials It is often useful to view the sets of psd and sos polynomials as cones in the vector space of all polynomials. One might ask how big is the “gap” between the sos and psd polynomials, i.e., what is the quantitative relationship between the cones of psd and sos polynomials.
Blekherman showed that for fixed degree, there are significantly more psd polynomials than sos polynomials, in a precise quantitative sense. He gives asymptotic bounds for the sizes of these sets as the number of variables grows.
On the other hand, there are results which show that if the degree is variable, then in some sense sos polynomials are plentiful among psd poly-nomials. Berg, Christensen, and Ressel showed that sos polynomials are dense among polynomials which are non-negative on the unit cube [−1, 1]n with respect to the l1-norm of coefficients. An explicit version of this result is given by Lasserre and Netzer . Lasserre , showed that psd polynomials can be approximated coefficient-wise by sos polynomials. Of course, the degrees of the approximating polynomials go to infinity in these results.
Finally, we mention recent work of Chesi , who gives a matrix char-acterization of psd, not sos, polynomials. This characterization is based on eigenvector and eigenvalue decompositions.
2.4 Denominators in Artin’s Theorem Artin’s Theorem says that if f ∈R[X] is psd, then there exists nonzero p ∈R[X] such that p2f is a sos. We can think of p2 as a denominator in a representation of f as a sum of squares of rational functions. Artin’s proof was not constructive, which leads to a natural question: Given psd f, what type and degree of denominators can occur? In this section, we discuss both classical and more recent work related to denominators in Artin’s Theorem.
In 1893, Hilbert showed that if f ∈R[x, y] is psd of degree m, then there exists psd p ̸= 0 of degree m −4 so that pf is a sum of three squares. This implies that there is a representation of p as a quotient of sums of squares with denominator of degree ≤(m −4)(m −8) . . . . In , de Klerk and 7 Pasechnik use Hilbert’s result to give an an algorithm for finding p and writing pf as a sum of squares.
P´ olya’s Theorem implies that if f is both positive definite and even, then for sufficiently large r, f is a sum of squares of rational functions with common denominator (1 + P Xi)r. Habicht used P´ olya’s Theorem to show that a positive definite form is a quotient of two sums of squares of monomials. It follows that if f is positive definite, then f can be written as a sum of squares of rational functions with positive denominators. In 1995, in , Reznick showed that for a positive definite form f, there is N so that (P Xi)nf is sos. He gave a bound on N, in terms of the degree, number of variables, and a measure of how close f is to having a zero.
In the above examples for positive definite forms f, a “uniform” denom-inator is obtained in the sense that for every such f, (P Xi)r will serve as a denominator. The restriction to positive definite forms in necessary, due to the fact that there exist psd forms f in n ≥4 variables so that if p2f is sos, the p must have a specified zero. The existence of these so-called “bad points” means that (P Xi)rf can never be sos. Bad points were first noticed by Straus and were extensively studied by Delzell in his PhD thesis .
Scheiderer has shown that in the case of forms of three variables (dehomogenizing, polynomials of two variables), there is a uniform denom-inator and in fact, any positive de nite quadratic form will serve. This shows that ternary forms do not have bad points. On the other hand, Reznick showed that for any given n, m, there does not exist a single form p which serves as a denominator for every psd form f in n variables of degree m.
Very recently, Guo, Kaltofen, and Zhi developed an algorithmic method for proving lower bounds for the degree of the denominator in any representation in P R[X]2 of a specified psd polynomial. As an example, they look at some symmetric forms of degree 6 in four and five variables and prove that any representation as a quotient of sums of squares must have denominator degree at least 4 and 6, respecitively. This will be discussed further in §3.3.
2.5 Polynomials positive on noncompact semialgebraic sets We now turn to representation theorems for polynomials positive on non-compact basic closed semialgebraic sets. Given finite G ⊆R[X], let S = S(G) and suppose that S is not compact. Let P = PO(G) and M = M(G).
We would like to know if Schm¨ udgen’s Theorem or Putinar’s Theorem ex-tends to this case: Given f > 0 on S, is f ∈P or f ∈M? More generally, we can ask whether this holds for f ≥0 on S, in which case we say that P 8 or M is saturated. We have the following negative results due to Scheiderer: Theorem 7 ().
1. Suppose dim S ≥3. Then there exists p ∈R[X] such that p ≥0 on Rn and p ̸∈P.
2. If n = 2 and S contains an open 2-dimensional cone, then there is p ∈R[X] with p ≥0 on R2 and p ̸∈P.
In contrast to these, the n = 1 case has been completely settled, by Kuhlmann and Marshall , extending work of Berg and Maserick . In this case, the preordering P is saturated, provided one chooses the right set of generators.
Definition 1 (, 2.3). Suppose S is a closed semialgebraic set in R, then S is a union of finitely many closed intervals and points. Define a set of polynomials F in R[x] as follows: • If a ∈S and (−∞, a] ∩S = ∅, then x −a ∈F.
• If a ∈S and (a, ∞) ∩S = ∅, then ax ∈F.
• If a, b ∈S and (a, b) ∩S = ∅, then (x −a)(x −b) ∈F.
It is easy to see that S(F) = S; F is called the natural choice of generators for S.
Theorem 8 (,Thm. 2.2, Thm. 2.5). Let S be as above and suppose G is any finite subset in R[X] such that S(G) = S. Let P = PO(G) and let F be the natural choice of generators.
1. Every p ∈R[x] such that p ≥0 on S is in P iffthe set of generators G of S contains F.
2. Let M = M(F), then every p ∈R[x] such that p ≥0 on S is in M iff |F| ≤1, or |F| = 2 and S has an isolated point.
One case not covered by the above results is that of noncompact semial-gebraic subsets of R2 which do not contain a 2-dimensional cone. We write R[x] for the polynomial ring in one variable and R[x, y] for the polynomial ring in two variables. The first example given of a noncompact basic closed semialgebraic set in R2 for which the corresponding preordering is saturated is due to Scheiderer . His example is the preordering in R[x, y] gener-ated by {x, 1 −x, y, 1 −xy}. Powers and Reznick studied polynomials positive on noncompact rectangles in R2 and obtained some partial results.
They showed that if F = {f1, . . . , fr, y} with f1, . . . , fr ∈R[x] and S(F) is the half-strip [0, 1] × R+, then there always exists g > 0 on [0, 1] × R+ with g ̸∈M(F). On the other hand, it is shown that under a certain condition, 9 g ≥0 on [0, 1]×R implies g = s+t(x−x2) with s, t ∈P R[x, y]2. Recently, Marshall proved this without the condition on g, settling a long-standing open problem.
Theorem 9 (). Suppose p ∈R[x, y] is non-negative on the strip [0, 1]× R. Then there exist s, t ∈P R[x, y]2 such that p = s + t(x −x2).
In other words, any p which is nonnegative on the strip [0, 1] × R is in the quadratic module M(x −x2). This result has been extended by H.
Nguyen in her PhD thesis and by Nguyen and Powers.
Theorem 10 (, Thm. 2). Suppose U ⊆R is compact and F is the natural choice of generators for U. Let S = U × R ⊆R2 and let M be the quadratic module in R[x, y] generated by F. Then every p ∈R[x, y] with p ≥0 on S is in M.
By the result from , we know that this does not generalize to the half-strip case, however we do obtain a representation theorem if the quadratic module is replaced by a preordering and we use the natural choice of gen-erators.
Theorem 11 (, Thm. 3). Given compact U ⊆R with natural choice of generators {s1, . . . , sk} and q(x) ∈R[x] with q(x) ≥0 on U, let F = {s1, . . . , sk, y −q(x)}, so that S(F) is the upper half of the strip U × R cut by {q(x) = 0}. If P is the preordering in R[x, y] generated by F, then P is saturated.
There are also examples for which no corresponding finitely generated preorder is saturated.
The following from is a generalization of an example from due to Netzer.
Example 1. Suppose F = {x −x2, y2 −x, y}, so that S = S(F) is the half-strip [0, 1] × R+ cut by the parabola y2 = x. Then for any ˜ F ⊆R[x, y] such that S( ˜ F) = S, there is some p ∈R[x, y] such that p ≥0 on S and p ̸∈PO( ˜ F).
For all of the positive examples above, the fibers S ∩{y = a} are con-nected. It is not known if there are positive examples for which this doesn’t hold, e.g., we have the following open problem: Question: Let S = S({x −x2, y2 −1}) in R2, so that S = [0, 1] × ((−∞, −1] ∪[1, ∞)).
Given g ∈R[x, y] such that g ≥0 on S, is g ∈ PO({x −x2, y2 −1})?
2.6 Sums of squares on real algebraic varieties We now look at a more general setting than polynomial rings. Let V be an affine variety defined over R, R[V ] the coordinate ring of V , and V (R) 10 the set of real points of V .
Then f ∈R[V ] is psd if f(x) ≥0 for all x ∈V (R), and f is sos if f is a finite sum of squares of elements of R[V ].
It is interesting to ask whether psd = sos in this more general setting.
If dim(V ) ≥3, then Hilbert’s result that psd ̸= sos has been extended extended to R[V ] by Scheiderer . In the dimension 2 case, Scheiderer proves the surprising theorem that if V is a nonsingular affine surface and V (R) is compact, then psd = sos holds on V , see . There is a nice application of this to Hilbert’s 17th problem: If f ∈R[x, y, z] is a psd ternary forms and g is any positive definite ternary form, then there exists N ∈N such that gNf is sos.
The case where dim(V ) = 1 (real algebraic curves) is completely un-derstood in the case where V is irreducible, again due to Scheiderer .
In 2010, Plaumann showed that in the reducible case, the answer de-pends on the irreducible components of the curve, and also on how these irreducible components are configured with respect to each other. He gives necessary and sufficient conditions for psd = sos in this case. He shows, for example, that for the family of curves Ca = {(y −x2)(y −a) = 0} for a ∈R (the union of a parabola and a line), psd ̸= sos always.
2.7 Stability A quadratic module M = M(g1, . . . , gk) in R[X] is stable if there exists a function φ : N →N such that the following holds: For every d ∈N and every f ∈M with deg f ≤d, there is a representation of f in M, f = s0 + s1g1 + · · · + skgk such that for all i, deg si ≤φ(d). A similar definition can be made for preorders, although stability has been studied mostly in the quadratic module case. The notion of stability was introduced in , where it was used to study the multivariable Moment Problem for noncompact semialgebraic sets.
The easiest example of a stable quadratic module in R[X] is P R[X]2: If f is sos and f = h2 1 + · · · + h2 r, then for all i, deg h2 i ≤deg f, since the leading forms of the h2 i ’s cannot cancel. A generalization of this simple argument yields families of stable preorderings in . (The arguments apply immediately to quadratic modules as well.) On the other hand, if S(G) has dimension ≥2 and M(G) is archimedean, then M(G) is never stable; this follows from [82, Thm. 5.4].
The notion of stability is important for computational problems as well as applications to the Moment Problem. It is this key property of stability that allows for effective algorithms for the problem of deciding whether f ∈R[X] is sos, and finding an explicit representation if so. See §3.1 for further discussion of these algorithims. In the case of compact semialgebraic sets, the non-stability of the underlying preordering or quadratic module 11 means the problem of finding representations of polynomials positive on the set must be difficult.
Netzer generalizes the idea of stability of a quadratic module to the notion of stable with respect to a given grading on a polynomial ring.
The usual notion of stability is then stability with respect to the standard grading. Considering stability with respect to other gradings allows the development of tools to prove stability with respect to the standard grading by proving it first for finitely many non-standard ones.
The paper contains interesting new examples of stable quadratic modules.
2.8 Certificates of positivity for polynomials with special struc-ture If a polynomial f for which there is a certificate of positivity has some special structure, it can happen that there exists a certificate of positivity with nice properties related to the structure. This can have implications for applications, since it can imply the existence of smaller certificates for f than the general theory implies.
2.8.1 Invariant sums of squares In practical applications of sums of squares, there is often some inherent symmetry in the problem. This symmetry can be exploited to yield finer representation theorems which in turn can lead to a reduction in problem size for applications.
Consider the following general situation: Suppose K is a closed subset of Rn which is invariant under some subgroup G of the general linear group.
Can we characterize G-invariant polynomials which are positive on K? For example, can they be described in terms of invariant sums of squares, or even sums of squares of invariant polynomials?
Gatermann and Parrilo considered these questions in the context of finding effective sum of squares decompositions of invariant polynomials.
They look at finding a decomposition of an sos polynomial f which is invariant under the action of a finite group.
Cimpric, Kuhlmann, and Scheiderer consider a more general set-up: G is a reductive group over R acting on an affine R-variety V with an induced dual action on the coordinate ring R[V ] and on the linear dual space of R[V ]. In this setting, given an invariant closed semialgebraic set K in Rn, they study the problem of representations of invariant polynomials that are positive on K using invariant sums of squares. Most of their results apply in the case where the group G(R) is compact. They obtain a generalization of the main theorem of and apply their results to an investigation of the equivariant version of the K-moment problem.
12 2.8.2 Polynomials with structured sparsity We discuss a “sparse” version of Putinar’s theorem, where the variables consist of finitely many blocks that are allowed to overlap in certain ways, and we seek a certificate of positivity for a polynomial f that is sparse in the sense that each monomial in f involves only variables in one block.
Then there is a representation of f in the quadratic module in which the sums of squares respect the block structure.
For I ⊆{1, . . . , n}, let XI denote the set of variables {Xi | i ∈I} and R[XI] the polynomial ring in the variables XI. Suppose that I1, . . . Ir are subsets of {1, . . . , n} satisfying the running intersection property: For all i = 2, . . . , r, there is some k < i such that Ii ∩S j 0.
For every z ∈F and every y ∈K \ F, assume Dy−zf(z) > 0. Then f ∈S.
Here Dvf(z) denotes the directional derivative of f at z in the direction of v. Roughly speaking, the last assumption in the theorem says that every directional derivative of f at a point of F pointing into K and not tangential to F should be strictly positive.
Previous to this work, examples of Nichtnegativstellens¨ atze required that the nonnegative polynomial f on a compact basic closed semialge-braic set S have discrete zeros in S. Results in are the first that allow f to have arbitrary zeros in S.
Example 2 (, Example 7.13). Suppose M is an archimedean quadratic module in R[x, y, z], K = {x ∈R3 | g(x) = 0 for all g ∈M} and let Z = {(0, 0, t) | t ∈R}, the z-axis in R3. Assume p, q, r ∈R[x, y, z] are such that f = x2p + y2q + 2xyr, f > 0 on S \ Z, and f = 0 on Z. Then if p and pq −r2 are strictly positive on Z ∩S, f ∈M.
3 Practice: Computational and algorithmic issues Recently, there has been much interest in developing algorithms for decid-ing positivity of a polynomial and finding certificates of positivity, in part because of the many applications of these algorithms. In this section, we discuss computational problems and issues related to postivity and sums of squares. We will discuss algorithms for finding explicit certificates of positivity for f ∈R[X], both in the global case (sums of squares) and for f positive on a compact basic closed semialgebraic set (algorithmic Schm¨ udgen and Putinar theorems). We also discuss computational issues around Bernstein’s Theorem and P´ olya’s Theorem as well as quantitative questions on psd ternary quartics (Hilbert’s Theorem).
3.1 Finding sum of squares representations For f ∈R[X], suppose we would like to decide if f is sos and if so, find an explicit representation of f as a sum of squares. The method we describe, sometimes called the Gram matrix method reduces the problem to linear algebra. For more details and examples, see e.g. , , [42, §3.3].
Suppose f ∈R[X] has degree 2d, let N = n−1+d d and let V be the N × 1 vector of all monomials in R[X] of degree at most d. Then f is sos 14 iffthere exists an N × N symmetric psd matrix A such that f(X) = V · A · V T, (1) The set of matrices A such that (1) holds is an affine subset L of the space of N × N symmetric matrices; a matrix in L is often called a Gram matrix for f. Then f is sos iffL ∩PN ̸= ∅, where PN is the convex cone of psd symmetric N × N matrices over R. Finding this intersection is a semidefinite program (SDP). There are good numerical algorithms – and software – for solving semidefinite programs. For details on using SDPs to find sum of squares representations , see e.g. , .
Since there is an a priori bound on the size of the SDP corresponding to writing a particular f as a sum of squares, this gives an exact algorithm.
However, since we are using numerical software, there are issues of exact versus numerical answers.
Consider the following example, due to C. Hillar: Suppose f = 3 −12y −6x3 + 18y2 + 3x6 + 12x3y −6xy3 + 6x2y4, is f sos? If we try to decide this with software we might get the answer “yes” and a decomposition similar to this: f = (x3 + 3.53y + .347xy2 −1)2 + (x3 + .12y + 1.53xy2 −1)2+ (x3 + 2.35y −1.88xy2 −1)2.
(2) The coefficients of the right-hand side of (2) are not exactly the same as the coefficients of f, so we might wonder if f is really sos. It turns out that f is sos, and (2) is an approximation of a decomposition for f of the form (x3 + a2y + bxy2 −1)2 + (x3 + b2y + cxy2 −1)2 + (x3 + c2y + axy2 −1)2, where a, b, c are real roots of x3 −3x + 1.
In theory, a SDP problem can be solved purely algebraically, for ex-ample, using quantifier elimination. In practice, this is impossible for all but trivial problems. Work by Nie, Ranestand, and Sturmfels shows that optimal solutions of relatively small SDP’s can have minimum defining polynomials of huge degree, and hence we could encounter sos polynomials of relatively small size which have decompositions using algebraic numbers of large degree.
Since solving the underlying SDP exactly is impossible in most cases, we are led to the following question: Suppose f ∈P Q[X]2 and we find a numerical (approximate) certificate f = P g2 i (via SDP software, say), can we find an exact decomposition of f in P Q[X]2? Recent approaches using hybrid symbolic-numeric approaches are very promising.
15 Peyrl and Parrilo give an algorithm for converting a numerical sos decomposition into an exact certificate, in some cases. The idea: Given f ∈P Q[X]2, we want to find a symmetric psd matrix A with rational entries so that f = V · A · V T (3) The SDP software will produce a psd matrix A which only approximately satisfies (3). The idea is to project A onto the affine space of solutions to (3) in such a way that the projection remains in the cone of psd symmetric matrices. The Peyrl-Parrilo method is (theoretically!) guaranteed to work if there exists a rational solution and the underlying SDP is strictly feasible, i.e., there is a solution with full rank. Kaltofen, Li, Yang, and Zhi have generalized the technique of Peyrl and Parrilo and used these ideas to find sos certificates certifying rational lower bounds for several well-known problems.
3.2 Certificates of positivity via Artin’s Theorem Recall Artin’s solution to Hilbert’s 17th Problem which says that if f ∈ R[X] is psd, then f is a sum of squares in the rational function field R(X), i.e., f can be written as a quotient of sos polynomials. Recent work of Kaltofen, Li, Yang, and Zhi turns Artin’s theorem into a symbolic-numeric algorithm for finding certificates of positivity for any psd f ∈ Q[X]. They extend the hybrid symbolic-numeric approaches to finding an exact sos representation of a polynomial discussed above. The algorithm finds a numerical representation of f as a quotient g/h, where g and h are sos, and then converts this to an exact rational identity using techniques described above. The algorithm has been implemented as software called ArtinProver. Kaltofen, Yang, and Zhi have used this technique and the software to settle the dimension 4 case of the Monotone Column Permanent Conjecture, see .
3.3 Cerificates of impossibility of sos representability The proof that the Motzkin form M(x, y) is not sos involves a term-by-term inspection of the equation M(x, y) = P hi(x, y)2. Proofs for examples of Choi and Lam were done using a similar term-inspection method. This term-inspection method was generalized by Choi, Lam, and Reznick using the Newton polytope of a polynomial. Proofs for other known exam-ples, e.g. the Robinson example, involve the zeros of the polynomial.
Recently, another method for proving that a given polynomial is not sos, and producing a certificate of impossibility, was given by Ahmadi and Parrilo , using a generalization of Farkas Lemma to semidefinite pro-gramming. As discussed in §3.1, determining if a given polynomial is sos is 16 equivalent to deciding if a certain semidefinite program has a solution. This method produces a certificate of infeasibility for the semidefinite program via a separating hyperplane.
This method has been generalized by Guo, Kaltofen, and Zhi , who developed an algorithm, using semidefinite programming and Farkas Lemma, for certifying a lower bound on the degree of the denominator in any representation in P R(X)2 of a specified psd polynomial.
3.4 Schm¨ udgen’s and Putinar’s theorems Let G ⊆R[X] be a finite and suppose S := S(G) is compact. Set P = PO(G).
Recall Schm¨ udgen’s Theorem says that every polynomial that is strictly positive on S is in P, regardless of the choice of generating polynomials G. Schm¨ udgen’s proof uses functional analytic methods and is not constructive in the sense that no information is given concerning how to find an explicit certificate of positivity in P for a given f which is strictly positive on S.
3.4.1 Algorithmic Sch¨ umdgen Theorem In 2002, Schweighofer gave a proof of Schm¨ udgen’s Theorem which is algorithmic, apart from an application of the Classical Positivstellensatz.
The idea of the proof is to reduce to P´ olya’s Theorem (in a larger number of variables). The Classical Positivstellensatz is used to imply the existence of a “certificate of compactness” for S, i.e., the existence of s, t ∈P and r ∈R such that s(r2 − X X2 i ) = 1 + t (4) 3.4.2 Degree bounds for Schm¨ udgen Theorem Unlike the global (sum of squares) case, in general, there is no bound on the degree of the sums of squares in a representation of f in P in terms of the degree of f only. This has obvious implications for applications of Schm¨ udgen’s Theorem, for example in recent work on the approximation of polynomial optimization problems via semidefinite programming. Using model and valuation theoretic methods, Prestel [69, Theorem 8.3.4] showed that there exists a bound on the degree of the sums of squares which de-pends on three parameters, namely, the polynomials G used to define S, the degree of f, and a measure of how close f is to having a zero on S.
Schweighofer used his algorithmic proof of the result to give a bound on the degree of the sums of squares in a representation of f in P. Roughly speaking, the bound makes explicit the dependence on the second and third parameter in Prestel’s theorem. The first parameter appears in the bound 17 as a constant, which depends only on the polynomials G, and which comes from the compactness certificate (4). The exact result is as follows: Theorem 14 (,Theorem 3). Let G = {g1, . . . , gk}, S, and P be as above and suppose S ⊆(−1, 1)n. Then there exists c ∈N so that for every f ∈R[X] of degree d with f > 0 on S and f ∗= min{g(x) | x ∈S}, f = X e∈{0,1}k sege1 1 . . . gek k , where se ∈P R[X]2 and se = 0 or deg(sege1 1 . . . gek k ) ≤cd2 1 + d2nd||f|| f ∗ c .
Here ||f|| is a measure of the size of the coefficients of f. The constant c depends on the polynomials G in an unspecified way, however in concrete cases one could (in theory!) obtain an explicit c from the proof of the theorem.
3.4.3 Putinar’s Theorem Let G and S be as above and set M = M(G). Recall Putinar’s Theorem says that if M is archimedean, then every f > 0 on S is in M. Again, Putinar’s proof is functional analytic and does not show how to find an explicit certificate of positivity for f in M. In , Schweighofer extends the algorithmic proof of Schm¨ udgen’s Theorem to give an algorithmic proof of Putinar’s Theorem. Nie and Schweighofer then use this proof to give a bound for the degree of the sums of squares in a representation, similar to Theorem 14. Recently, Putinar’s Theorem has been used by Lasserre to give an algorithm for approximating the minimum of a polynomial on a compact basic closed semialgebraic set, see . The results in yields information about the convergence rate of the Lasserre method.
3.5 Rational certificates of positivity In §3.1, an algorithm for finding sum of squares certificates of positivity for sos polynomials f is described, using semidefinite programming. This technique can also be used to find certificates of positivity for a polynomial f which is positive on a compact semialgebraic set.
However, there is another question which arises when we are using numerical software: All polynomials found in a certificate of positivity, for example in the sums of squares, will have rational coefficients. But do we know that such a certificate exists, even if we start with f ∈Q[X]?
18 3.5.1 Sums of squares of rational polynomials Sturmfels asked the following question: Suppose f ∈Q[X] is in P R[X]2, is f ∈P Q[X]2? Here is a trivial, but illustrative example: The rational polynomial 2x2 is a square, since 2x2 = ( √ 2x)2. But 2x2 is also in P Q[x]2 since 2x2 = x2 + x2. Less trivially, recall the Hillar example: f = 3 −12y −6x3 + 18y2 + 3x6 + 12x3y −6xy3 + 6x2y4, as noted above, f is a sum of three squares in R[x, y]. It turns out that f is a sum of five squares in Q[x, y]: f = (x3+xy2+3 2y−1)2+(x3+2y−1)2+(x3−xy2+5 2y−1)2+(2y−xy2)2+3 2y2+3x2y4.
Partial results on Sturmfels question have been given: In the univari-ate case, the answer is “yes”; proofs have been given by Landau and Schweighofer .
Pourchet showed that at most five squares are needed. Hillar showed that the answer to Sturmfel’s question is “yes” if f ∈P K2, where K is a totally real extension of Q, and he gave bounds for the number of squares needed. There is a simple proof of a slightly more general result with a better bound given (independently) by Scheiderer and Quarez .
Recently, Scheiderer answered Sturmfels question in the negative.
He constructed families of polynomials with rational coefficients that are sums of squares over R but not over Q. He showed that these counterex-amples are the only ones in the case of ternary quartics.
Remark 1. The proof of Artin’s Theorem shows immediately that if f ∈ Q[X] is psd, then there always exist g, h ∈P Q[X]2 such that f = g/h.
The rationality question is not an issue in this case.
3.5.2 Rational certificates of positivity on compact sets There is an obvious analog of Sturmfels’ question for the case of polynomials positive on compact semialgebraic sets. Let P = PO(G) for finite G ⊆ Q[X]. If f ∈Q[X] is in P, does there exist a representation of f in P such that the sums of squares that occur are in P Q[X]2? We can ask a similar question for the quadratic module M(G). In , it is shown that the answer is “yes” for P in the compact case and “yes” for M with an additional assumption.
Theorem 15. Let G = {g1, . . . , gr} ⊆Q[X] and suppose S = S(G) is compact. Let P = PO(F) and M = M(F). Given f ∈Q[X] such that f > 0 on S, then 19 1. There is a representation of f in the preordering P, f = X e∈{0,1}r σege1 1 . . . ger r , with all σe ∈P Q[X]2.
2. There is a rational representation of f in M provided one of the gener-ators is N −P X2 i . More precisely, there exist σ0 . . . σs, σ ∈P Q[X]2 and N ∈N so that f = σ0 + σ1g1 + · · · + σsgs + σ(N − X X2 i ).
The proof of the first part follows from an algebraic proof of Schm¨ udgen’s Theorem, due to T. W¨ ormann, which uses the Abstract Positivstellensatz.
W¨ ormann’s proof can be found in or [69, Thm. 5.1.17]. The second part follows from Schweighofer’s algorithmic proof of Putinar’s Theorem.
3.6 Certificates of positivity using Bernstein’s and P´ olya’s the-orems Using Bernstein’s Theorem and P´ olya’s Theorem, certificates of positiv-ity for polynomials positive on simplices can be obtained. Furthermore, this approach yields degree bounds for the certificates and, in some cases, practical algorithms for finding certificates.
3.6.1 The univariate case For k ∈N, define in R[x]: Bk := X i+j≤k cij(1 −x)i(1 + x)j | cij ≥0 .
Suppose a univariate p ∈R[x] is strictly positive on [−1, 1], then Bernstein’s Theorem says that there is some r = r(p) such that p ∈Br.
Suppose p ∈R[x] has degree d, then let ˜ p denote the Goursat transform applied to p, i.e., ˜ p(x) = (1 + x)dp 1 −x 1 + x .
Powers and Reznick gave a bound on r(p) in terms of the minimum of p on [−1, 1] and size of the coefficients of ˜ p, which in turn yields a bound for the size of a certificate of positivity for p.
More recently, F. Boudaoud, F. Caruso, and M.-F. Roy obtain a local version of Bernstein’s Theorem which yields a better bound. They 20 show that if deg p = d and p > 0 on [−1, 1], then there exists a subdivision −1 = y1 < · · · < yt = 1 of [−1, 1] such that Bernstein-like certificates of positivity for p can be obtained on each interval [yi, yi+1]. This yields a certificate of positivity for p on [−1, 1] of bit-size O((d4(τ + log2 d)), where d = deg p and the coefficients of p have bit-size ≤τ.
Moreover, their result holds with R replaced by any real-closed field, which is not true for Bernstein’s Theorem.
3.6.2 Polynomials positive on a simplex Recall that P´ olya’s Theorem says that if a form (homogeneous polynomial) f is strictly positive on the standard simplex ∆n−1 := {x ∈Rn | xi ≥0 for all i and P xi = 1}, then for sufficiently large N ∈N, all coefficients of (P Xi)Nf are strictly positive. Powers and Reznick gave a bound on N, in terms of the degree of f, the minimum of f on ∆n−1, and the size of the coefficients. This result has been used in several applications, for exam-ple the algorithmic proof of Schm¨ udgen’s theorem given by Schweighofer discussed in §3.4.1. Also, de Klerk and Pasechnik used it to give results on approximating the stability number of a graph.
In theory, the bound for P´ olya’s Theorem could be used to obtain certifi-cates of positivity on the simplex, however in practice the bounds require finding minimums of forms on closed subsets of the simplex and so are not of much practical use. Another, more feasible, approach to certificates of positivity for polynomials positive on a simplex, due to R. Leroy , uses the multivariable Bernstein polynomials and a generalization of the ideas in . The Bernstein polynomials are more suitable that the stan-dard monomial basis in this case since this approach gives results for an arbitrary non-degenerate simplex and yields an algorithm for deciding pos-itivity of a polynomial on a simplex. The idea is to subdivide the simplex and obtain local certificates so that the sizes of the local certificates are smaller than those of a global certificate.
Let V be a non-degenerate simplex in Rn, i.e., the convex hull of n + 1 affinely independent points v0, v1, . . . , vn in Rn. The barycentric coordi-nates of V , λ1, . . . , λk, are linear polynomials in R[X] such that n X i=0 λi = 1, (X1, . . . , Xn) = n X i=1 λi(X)vi.
Then for d ∈N, the Bernstein polynomials of degree d with respect to V are {Bd α | α ∈Nn+1, |α| = d}, where Bd α = d!
α0!α1! · · · αn!
n Y i=0 λαi i .
21 They form a basis for the vector space of polynomials in R[X] of degree ≤d, hence any f ∈R[X] of degree ≤d can be written uniquely as a linear combination of the Bd α’s. The coefficients are called the Bernstein coefficients of f. If f > 0 on V , then for sufficiently large D, the Bernstein coefficients using the BD α ’s are nonnegative, which yields a certificate of positivity for f on V .
This can be made computationally feasible, as well as lead to an algo-rithm for deciding if f is positive on V . The idea is to triangulate V into smaller simplices and look for certificates of positivity on the sub-simplices.
A stopping criterion is obtained using a lower bound on the minimum of a positive polynomial on V , in terms of the degree, the number of variables, and the bitsize of the coefficients. This was proven by S. Basu, Leroy, and Roy and later improved by G. Jeronimo and D. Perrucci .
3.6.3 P´ olya’s Theorem with zeros What can we say if the condition “strictly positive on ∆n−1” in P´ olya’s Theorem is replaced by “nonnegative on ∆n−1”?
It is easy to see that in this case we must use a slightly relaxed version of P´ olya’s Theorem, replacing the condition of “strictly positive coefficients” by “nonnegative coefficients”. Let Po(n, d) be the set of forms of degree d in n variables for which there exists an N ∈N such that (X1+· · ·+Xn)Np ∈R+[X]. In other words, Po(n, d) are the forms which satisfy the conclusion of P´ olya’s The-orem, with “positive coefficients” replaced by “nonnegative coefficients.” It is easy to see that p ∈Po(n, d) implies p ≥0 on ∆n−1 and that p > 0 on the interior of ∆n−1. Further, Z(p), the zero set of p, must be a union of faces of ∆n−1. P´ olya’s Theorem and the bound are generalized to forms that are positive on the simplex apart from zeros on the corners (zero dimensional faces) of ∆n−1, in papers by Powers and Reznick and M.
Castle, Powers, and Reznick . See also work by H.-N. Mok and W.-K.
To , who give a sufficient condition for a form to satisfy the relaxed version of P´ olya’s Theorem, along with a bound in this case.
Very recently, Castle, Powers, and Reznick give a complete char-acterization of forms that are in Po(n, d) along with a a recursive bound for the N needed. Before stating the main theorem of , we need a few definitions.
Definition 2. Let α = (α1, . . . , αn), β = (β1, . . . , βn) be in Nn.
1. We write α ⪯β if αi ≤βi for all i, and α ≺β if α ⪯β and α ̸= β.
2. Suppose F is a face of ∆n−1, say F = {(x1, . . . , xn) ∈∆n−1 | xi = 0 for i ∈I} for some I ⊆{1, 2, . . . , n}. Then we denote by αF the vector (˜ α1, . . . , ˜ αn) ∈Nn, where ˜ αi = αi for i ∈I and ˜ αj = 0 for j / ∈I.
22 3. For a form p ∈R[X], let Λ+(p) denote the exponents of p with positive coefficients and Λ−(p) the exponents of p with negative coefficients.
4. For a face F of ∆n−1 and a subset S ⊆N, we say that α ∈N is minimal in S with respect to F if there is no γ ∈S such that γF ≺αF.
Theorem 16. Given p = P aβXβ, a nonzero form of degree d, such that p ≥0 on ∆n−1 and Z(p) ∩∆n−1 is a union of faces. Let Λ+(p) denote the exponents of p with positive coefficients and Λ−(p) the exponents of p with negative coefficients. Then p ∈Po(n, d) if and only if for every face F ⊆Z(p) the following two conditions hold: 1. For every β ∈Λ−(p), there is α ∈Λ+(p) so that αF ⪯βF.
2. For every α ∈Λ+(p) which is minimal on Λ+(p) with respect to F, the form P is strictly positive on the relative interior of F.
3.6.4 Certificates of positivity on the hypercube Finally, we mention briefly some recent work by de Klerk and Laurent concerning polynomials positive on a hypercube Q = [0, 1]n. Using Bernstein approximations, they obtain bounds for certificates of positivity for a polynomial f which is strictly positive on Q, in terms of the degree of f, the size of the coefficients, and the minimum of f on Q. They also give lower bounds, and sharper bounds in the case where f is quadratic.
3.7 Psd ternary quartics Recall Hilbert’s 1888 theorem that says every psd ternary quartic (homo-geneous polynomial of degree 4 in 3 variables) is a sum of three squares of quadratic forms. Hilbert’s proof in non-constructive in the sense that it gives no information about the following questions: Given a psd ternary quartic, how can one find three such quadratic forms? How many “funda-mentally different” ways can this be done?
Several recent works have addressed these issues. In , Powers and Reznick describe methods for finding and counting representations of a psd ternary quartic and answer these questions completely for some special cases. In several examples, it was found that there are exactly 63 inequiv-alent representations as a sum of three squares of complex quadratic forms and, of these, 8 correspond to representations as a sum of squares of real quadratic forms. By “inequivalent representations” we mean up to orthog-onal equivalence; two representations are equivalent iffthey have the same Gram matrix (see §3.1).
The fact that a psd ternary quartic f has 63 inequivalent representations as a sum of squares of complex quadratic forms is a result due to Coble .
23 In 2004, Powers, Reznick, Scheiderer, and Sottile showed that for every real psd ternary quartic f such that the complex plane curve Q defined by f = 0 is smooth, exactly 8 of the 63 inequivalent representations correspond to a sum of three squares of real quadratic forms. More recently, in , Scheiderer extends this analysis to the singular case and computes the number of representations, depending on the configuration of the singular points. For example, if f is a psd singular ternary quartic and Q has a real double point, then there are exactly four inequivalent representations of f as a sum of three squares of quadratic forms.
Information about the number of representations also follows from the elementary proof of Hilbert’s Theorem on ternary quartics given by Pfister and Scheiderer in .
The quantitative analysis in and uses tools of modern algebraic geometry and is not in any sense elementary.
The work in yields a new, elementary proof of the fact that for a generically chosen psd ternary quartic f, there are exactly 8 inequivalent representations and when f is generically chosen with a real zero, there are 4 inequivalent representations.
Finally, we mention very recent work on quartic curves due to Plaumann, Sturmfels, and Vinzant . They give a new proof of the Coble result which yields an algorithm for computing all representations of a smooth ternary quartic as a sum of squares of three complex quadratic forms.
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13494 | https://hinative.com/questions/24772811 | 🆚What is the difference between "credulous" and "gullible" and "naïve" ? "credulous" vs "gullible" vs "naïve" ? | HiNative
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4 Oct 2023
Question about English (UK)
What is the difference between credulous and gullible and naïve ?Feel free to just provide example sentences.
What is the difference between credulous, gullible, and naïve?
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AI_monga
4 Oct 2023
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The words "credulous," "gullible," and "naïve" have similar meanings, but there are subtle differences between them.
"Credulous" means that someone is easily fooled or ready to believe things without having enough evidence or consideration. It refers to people who tend to trust others without being skeptical or questioning the truthfulness of the information. It can also mean that someone can be easily convinced by lies or deceptions.
Example: He is so credulous that he believes everything he's told.
"Gullible" means something similar to "credulous," but it has a stronger connotation of naivety and gullibility. It refers to people who can be easily deceived or manipulated because they are too trusting and can't recognize others' intentions.
Example: She is so gullible that she keeps falling for scams.
"Naïve" means that someone is innocent or inexperienced and has little knowledge of the world. It refers to people who can be easily exploited by others due to their lack of experience or poor judgment.
Example: He is so naïve that he thinks everyone is honest and good.
In summary, "credulous" and "gullible" refer to the tendency to easily believe others, while "naïve" refers to lack of experience and innocence. It is important to note that these words are often used in a negative context to describe people who can be easily deceived.
Wörter "credulous", "gullible" und "naïve" haben ähnliche Bedeutungen, aber es gibt subtile Unterschiede zwischen ihnen.
"Credulous" bedeutet, dass jemand leichtgläubig oder bereit ist, Dinge zu glauben, ohne genügend Beweise oder Überlegungen zu haben. Es bezieht sich auf Menschen, die dazu neigen, anderen zu vertrauen, ohne skeptisch zu sein oder die Wahrhaftigkeit der Informationen zu hinterfragen. Es kann auch bedeuten, dass jemand leicht von Lügen oder Täuschungen überzeugt werden kann.
Beispiel: Er ist so credulous, dass er alles glaubt, was ihm erzählt wird.
"Gullible" bedeutet ähnliches wie "credulous", aber es hat eine stärkere Konnotation von Naivität und Leichtgläubigkeit. Es bezieht sich auf Menschen, die leicht getäuscht oder manipuliert werden können, weil sie zu gutgläubig sind und nicht in der Lage sind, die Absichten anderer zu erkennen.
Beispiel: Sie ist so gullible, dass sie immer wieder auf Betrügereien hereinfällt.
"Naïve" bedeutet, dass jemand unschuldig oder unerfahren ist und wenig Wissen über die Welt hat. Es bezieht sich auf Menschen, die aufgrund ihrer mangelnden Erfahrung oder ihres Mangels an Urteilsvermögen leicht von anderen ausgenutzt werden können.
Beispiel: Er ist so naïve, dass er denkt, jeder ist ehrlich und gut.
Zusammenfassend kann man sagen, dass "credulous" und "gullible" sich auf die Tendenz beziehen, anderen leicht zu glauben, während "naïve" sich auf mangelnde Erfahrung und Unschuld bezieht. Es ist wichtig zu beachten, dass diese Wörter oft in einem negativen Kontext verwendet werden, um Menschen zu beschreiben, die leicht getäuscht werden können.
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Oldgeezer
4 Oct 2023
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"Credulous" means someone easily believes something. It is usually used in the negative "incredulous", which can mean astounded or disbelieving. "Gullible" means that a person is easily fooled. The believe almost anything. They believe things that sensible people do not believe. "Naïve" means the person is inexperienced and simple. It is hard for them to know what is true and what is not true.
"Credulous" means someone easily believes something.
It is usually used in the negative "incredulous", which can mean astounded or disbelieving.
"Gullible" means that a person is easily fooled. The believe almost anything. They believe things that sensible people do not believe.
"Naïve" means the person is inexperienced and simple. It is hard for them to know what is true and what is not true.
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@OldGeezer Thank you so much for your good explanation!
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13495 | https://alecb.me/permutation-parity | Permutation Pairity
Permutation Pairity
A quick proof that if two sequences of swaps lead to the same overall permutation, the number of swaps must both be even or both be odd (i.e., the number of swaps has the same parity).
First note that any permutation can be broken up into cycles, where a cycle is just N positions all swapping places with each other in a circle.
To see this for any given permutation, just start at the first position, note where it goes, then note where that position goes, and keep going, until you get back to 1. If there are any positions you haven’t touched yet, start the process again starting there.
For example:
The permutation of 4 elements where everything stays the same is made up of four cycles: 1 swapping with itself, 2 swapping with itself, 3 swapping with itself, and 4 swapping with itself
Here, 1 maps to 2, 2 maps to 3, 3 maps to 4, and 4 maps to 1. So this is the single cycle 1 → 2 → 3 → 4
In this permutation:
1 maps to 2, 2 maps to 5, 5 maps 1; this is the cycle (1 → 2 → 5)
4 maps to 3 and 3 maps to 4, which is the cycle (3 → 4)
Importantly, there is just one, unique way to break up any given permutation into cycles.
Now, note that if we take a permutation and swap any two elements, a and b, one of two things happens:
either a and b were already part of the same cycle, in which case their cycle will split into two
or, a and b were part of two different cycles, in which case their cycles will join together
Importantly, the number of cycles always changes (up or down) by exactly one.
And that’s all we need! If we can build up a permutation with N swaps, adding an (N+1)st swap will change the number of cycles by 1, resulting in a different permutation. We need at least an (N+2)nd swap to get us back to the original permutation.
An (N+2)nd swap will either get us back to the correct cycle count, or, put us 2 away from the correct cycle count, which means we need at least an (N+3)rd and an (N+4)th swap to get back to the correct count.
No matter what happens, you always need to add an even number of swaps to get back to the right count, which means the total number of swaps will remain at whatever pairity it was to begin with.
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13496 | https://www.khanacademy.org/standards/GA.Math/LACS.PARc | Standards Mapping - Georgia Math | Khan Academy
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Numerical Reasoning – Fraction Equivalence, Comparison Of Fractions, and Addition and Subtraction Of Fractions With Like Denominators
Measurement & Data Reasoning – Time, Metric Measurements, Distance, Elapsed Time, Liquid Volume, Mass, and Length
Geometric & Spatial Reasoning – Polygons, Points, Lines, Line Segments, Rays, Angles, Perpendicular Lines, Area, Perimeter
Grade 5
Numerical Reasoning – Place Value, Multiplying By Powers Of 10, Multiplication and Division Of Multi-Digit Numbers, Fractions, Decimal Numbers, Numerical Expressions
Patterning & Algebraic Reasoning – Generating Patterns, Plotting Ordered Pairs In The First Quadrant
Measurement & Data Reasoning – Measurements Within The Metric System, Measurement Conversions and Time As A Unit Of Measurement
Geometric & Spatial Reasoning – Properties Of Polygons and Rectangular Prisms, Classify Polygons
Grade 6
Numerical Reasoning – Multiplication and Division Of Whole Numbers and Fractions, and All Four Operations With Decimal Numbers
Geometric & Spatial Reasoning – Area Of Polygons, Volume Of Right Rectangular Prisms, Surface Area Of 3-D Figures
Patterning & Algebraic Reasoning – Numerical and Algebraic Expressions, Factors, Multiples, Algebraic Expressions, Plotting Points In All Four Quadrants, Rational Numbers On A Number Line, Polygons In The Coordinate Plane
Grade 7
Numerical Reasoning – Integers, Percentages, Fractions, Decimal Numbers
Patterning & Algebraic Reasoning – Linear Expressions With Rational Coefficients, Complex Unit Rates, Proportional Relationships
Geometric & Spatial Reasoning – Vertical, Adjacent, Complementary, and Supplementary Angles, Circumference and Area Of Circles, Area and Surface Area, Volume Of Cubes, Right Prisms, and Cylinders
Probability Reasoning – Likelihood, Theoretical and Experimental Probability
Grade 8
Numerical Reasoning – Rational and Irrational Numbers, Decimal Expansion, Integer Exponents, Square and Cube Roots, Scientific Notation
Patterning & Algebraic Reasoning – Expressions, Linear Equations, and Inequalities
Functional & Graphical Reasoning – Relate Domain To Linear Functions, Rate Of Change, Linear Vs. Nonlinear Relationships, Graphing Linear Functions, Systems Of Linear Equations, Parallel and Perpendicular Lines
Geometric & Spatial Reasoning – Pythagorean Theorem and Volume Of Triangles, Rectangles, Cones, Cylinders, and Spheres
Algebra: Concepts & Connections
Mathematical Modeling
Functional & Graphical Reasoning – Function Notation, Modeling Linear Functions, Linear Vs. Nonlinear Comparisons
Geometric & Spatial Reasoning – Distance, Midpoint, Slope, Area, and Perimeter
Patterning & Algebraic Reasoning – Linear Inequalities and Systems Of Linear Inequalities
Numerical Reasoning - Rational and Irrational Numbers, Square Roots and Cube Roots
Patterning & Algebraic Reasoning – Quadratic Expressions & Equations
Functional & Graphical Reasoning – Quadratic Functions
Patterning & Algebraic Reasoning – Exponential Expressions and Equations
Functional & Graphical Reasoning – Exponential Functions
Data & Statistical Reasoning – Univariate Data and Single Quantitative Variables; Bivariate Data
Advanced Algebra (Algebra II): Concepts and Connections
Mathematical Modeling
Data & Statistical Reasoning – Descriptive and Inferential Statistics
Functional & Graphical Reasoning – Exponential and Logarithmic Functions
Functional & Graphical Reasoning – Radical Functions
Functional & Graphical Reasoning – Polynomial Functions
Patterning & Algebraic Reasoning – Linear Algebra and Matrices
Geometric & Spatial Reasoning – Trigonometry and The Unit Circle
Functional & Graphical Reasoning – Rational Functions
Advanced Financial Algebra
Mathematical Modeling
Numerical (Quantitative) Reasoning – Fractions, Decimals, Percents, and Ratios
Functional & Graphical Reasoning – Linear, Exponential, Quadratic, Cubic, Rational, Square Root, Greatest Integer, and Piecewise Functions
Patterning & Algebraic Reasoning – Formulas
Patterning & Algebraic Reasoning – Systems Of Equations and Inequalities
Geometric & Spatial Reasoning – Polygons, Circles, and Trigonometry
Data & Statistical Reasoning – Data Displays
Data & Statistical Reasoning – Investigative Research
Linear Algebra With Computer Science Applications
Mathematical Modeling
Abstract & Digital Reasoning – Programming
Geometric & Spatial Reasoning – Vectors
Patterning & Algebraic Reasoning – Matrices
Geometric & Spatial Reasoning – Matrices
Probabilistic Reasoning – Markov Chains
Patterning & Algebraic Reasoning – Vector Spaces
Patterning & Algebraic Reasoning – Eigenvalues and Eigenvectors
Geometry: Concepts & Connections
Mathematical Modeling
Patterning & Algebraic Reasoning – Polynomial Expressions
Geometric & Spatial Reasoning – Congruence
Geometric & Spatial Reasoning – Geometric Foundations, Constructions, and Proof
Geometric & Spatial Reasoning – Similarity
Geometric & Spatial Reasoning – Right Triangle Trigonometry
Geometric & Spatial Reasoning – Trigonometry and The Unit Circle
Geometric & Spatial Reasoning – Circles
Geometric & Spatial Reasoning – Equations and Measurement
Probabilistic Reasoning – Compound Events and Expected Values
Data & Statistical Reasoning; Probablistic Reasoning – Categorical Data In Two-Way Frequency Tables; Conditional Probability
Advanced Finite Mathematics
Mathematical Modeling
Logical Reasoning – Methods Of Proof
Logical Reasoning – Logical Symbolism and Binary
Numerical Reasoning – Number Theory
Abstract & Quantitative Reasoning – Set Theory
Abstract & Quantitative Reasoning – Probabilities and Combinatorics
Abstract & Quantitative Reasoning – Graph Theory
Advanced Mathematical Decision Making
Mathematical Modeling
Quantitative & Proportional Reasoning – Ratios, Rates, & Percents
Quantitative & Proportional Reasoning – Averages & Indices
Patterning & Algebraic Reasoning – Identification Numbers, Voting, & Algorithms
Probabilistic Reasoning – Conditional Probabilities & Compound Events
Probabilistic Reasoning – Mathematical Assumptions & Expected Value
Data & Statistical Reasoning – Investigative Research
Patterning & Algebraic Reasoning – Financial Models
Functional & Graphical Reasoning – Modeling With Functions
Geometric & Spatial Reasoning – Deterministic Models
Patterning & Algebraic Reasoning – Vectors & Matrices
Patterning & Algebraic Reasoning – Networks
Precalculus
Mathematical Modeling
Functional & Graphical Reasoning – Functions and Their Characteristics
Functional & Graphical Reasoning – Trigonometric Relationships and Functions
Algebraic & Geometric Reasoning – Trigonometric Identities and Equations
Geometric & Spatial Reasoning – Conic Sections and Polar Equations
Algebraic & Graphical Reasoning – Vectors and Parametric Equations
Patterning & Algebraic Reasoning – Sequences and Series
Multivariable Calculus
Mathematical Modeling
Patterning & Algebraic Reasoning – Vectors, Functions, and Analytic Geometry In Three Dimensions
Abstract & Quantitative Reasoning – Partial Differentiation
Abstract & Quantitative Reasoning – Integration
Differential Equations
Mathematical Modeling
Abstract Reasoning – First Order Differential Equations
Abstract Reasoning – Higher Order Differential Equations
Abstract Reasoning – Systems Of Differential Of Equations
Abstract Reasoning – Laplace Transforms
Engineering Calculus
Mathematical Modeling
Abstract Reasoning – Impact Of Engineering In Mathematics
Abstract Reasoning – Algebra In Engineering
Abstract Reasoning – Partial Differentiation In Engineering
Abstract Reasoning – Integration In Engineering
College Readiness Mathematics
Mathematical Modeling
Numerical & Quantitative Reasoning – Real Number System
Patterning & Algebraic Reasoning – Expressions, Equations, & Inequalities
Functional & Graphical Reasoning – Building & Interpreting Functions
Geometric & Spatial Reasoning – Measurement, Surface Area, Volume, & Right Triangle Trigonometry
Data & Statistical Reasoning – Interpreting Data & Calculating Probabilities Of Compound Events
Mathematics Of Industry and Government
Mathematical Modeling
Abstract Reasoning & Deterministic Decision-Making – Linear Programming
Abstract Reasoning & Deterministic Decision-Making – Optimal Locations
Abstract Reasoning & Deterministic Decision-Making – Optimal Paths
Abstract Reasoning & Probabilistic Decision-Making – Normal Distributions
Abstract Reasoning & Probabilistic Decision-Making – Binomial, Geometric, and Poisson Distributions
Probabilistic Reasoning – Probabilistic Models
Abstract Reasoning & Probabilistic Decision-Making – Simulations
Abstract Reasoning & Probabilistic Decision-Making – Fair Representation
Statistical Reasoning
Mathematical Modeling
Data & Statistical Reasoning – Formulate Statistical Investigative Questions
Data & Statistical Reasoning – Collect Data
Data & Statistical Reasoning – Analyze Data
Data & Statistical Reasoning – Interpret Results
History Of Mathematics
Mathematical Modeling
Numerical Reasoning – Origins Of Mathematics
Logical, Mathematical & Investigative Reasoning – Ancient Greek Mathematics
Logical, Mathematical & Investigative Reasoning – Mathematics In The Middles Ages
Logical, Mathematical & Investigative Reasoning – Mathematics Of The Classical Era
Logical, Mathematical & Investigative Reasoning – Modern Mathematics
Logical, Mathematical & Investigative Reasoning – 20Th Century Mathematics
Georgia Math
Linear Algebra With Computer Science Applications: Patterning & Algebraic Reasoning – Eigenvalues and Eigenvectors
LACS.PARc.8 ----------- Solve contextual, mathematical problems using eigenvalues and eigenvectors to explain real-life phenomena. ----------------------------------------------------------------------------------------------------------
LACS.PAR.8.1
Not covered
Evaluate the determinant of a matrix along any row or column and use a recursive procedure for evaluating a determinant for matrices larger than 3-by-3.
(Content unavailable)
LACS.PAR.8.2
Not covered
Justify properties of the determinant.
(Content unavailable)
LACS.PAR.8.3
Not covered
Calculate the determinant of the product of two matrices; calculate the determinant of the transpose of a matrix.
(Content unavailable)
LACS.PAR.8.4
Not covered
Determine if a matrix has a nonzero determinant and extend the nonzero determinant property to problems involving linear dependency, rank, and matrix inverses.
(Content unavailable)
LACS.PAR.8.5
Fully covered
Extend the definition and geometric interpretation of the cross product to n – 1 vectors in n dimensions.
Add vectors
Add vectors: magnitude & direction
Direction of vectors
Subtract vectors
Use matrices to transform 3D and 4D vectors
Use matrices to transform the plane
Vector components from magnitude & direction
LACS.PAR.8.6
Mostly covered
Use Cramer’s Rule to solve a system of linear equations.
Age word problem: Arman & Diya
Age word problem: Ben & William
Age word problem: Imran
Age word problems
Combining equations
Creating systems in context
Elimination method review (systems of linear equations)
Elimination strategies
Elimination strategies
Interpret points relative to a system
Interpreting points in context of graphs of systems
Reasoning with systems of equations
Solutions of systems of equations
Substitution method review (systems of equations)
System of equations word problem: infinite solutions
System of equations word problem: no solution
System of equations word problem: walk & ride
Systems of equations with elimination
Systems of equations with elimination (and manipulation)
Systems of equations with elimination challenge
Systems of equations with elimination: apples and oranges
Systems of equations with elimination: coffee and croissants
Systems of equations with elimination: King's cupcakes
Systems of equations with elimination: potato chips
Systems of equations with elimination: TV & DVD
Systems of equations with elimination: x-4y=-18 & -x+3y=11
Systems of equations with graphing
Systems of equations with graphing: exact & approximate solutions
Systems of equations with graphing: y=7/5x-5 & y=3/5x-1
Systems of equations with substitution
Systems of equations with substitution: -3x-4y=-2 & y=2x-5
Systems of equations with substitution: coins
Systems of equations with substitution: potato chips
Systems of equations word problems
Systems of equations word problems (with zero and infinite solutions)
Systems of equations: trolls, tolls (1 of 2)
Systems of equations: trolls, tolls (2 of 2)
Testing a solution to a system of equations
LACS.PAR.8.7
Find the characteristic polynomial of a matrix and interpret the characteristic polynomial geometrically.
(Content unavailable)
LACS.PAR.8.8
Fully covered
Find the eigenvalues and eigenvectors of a matrix and interpret them geometrically.
Add & subtract matrices
Multiply matrices
Multiply matrices by scalars
Use matrices to transform 3D and 4D vectors
Use matrices to transform the plane
LACS.PAR.8.9
Fully covered
Use a basis of eigenvectors to create a change of basis matrix.
Add & subtract matrices
Multiply matrices
Multiply matrices by scalars
Use matrices to transform 3D and 4D vectors
Use matrices to transform the plane
LACS.PAR.8.10
Fully covered
Find the dimension of the eigenspace corresponding to the eigenvalues of a symmetric matrix.
Add & subtract matrices
Multiply matrices
Multiply matrices by scalars
Use matrices to transform 3D and 4D vectors
Use matrices to transform the plane
LACS.PAR.8.11
Determine an orthogonal matrix that diagonalizes a given matrix.
(Content unavailable)
LACS.PAR.8.12
Fully covered
Apply eigenvalues and eigenvectors to problems in context.
Add & subtract matrices
Multiply matrices
Multiply matrices by scalars
Use matrices to transform 3D and 4D vectors
Use matrices to transform the plane
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13497 | https://support.oracle.com/knowledge/Oracle%20E-Business%20Suite/466715_1.html | 11i:AP:Invoice GL Date Defaults at System Date Even when it is Already Changed
11i:AP:Invoice GL Date Defaults at System Date Even when it is Already Changed (Doc ID 466715.1)
Last updated on MAY 05, 2025
Applies to:
Oracle Payables - Version 11.5.10.2 to 11.5.10.2 [Release 11.5]
Information in this document applies to any platform.
APXINWKB
Symptoms
When the Invoice date is filled in the Invoice Workbench, the GL date is automatically defaulted to the system date even if the date filled is different from the system date.
Assuming that the System Date is the 24/06 and the Payables Options set the GL Date default based on the System Date :
1)Invoice Entry
Navigate to: Invoices/ Entry / Invoices
Enter a Standard Invoice (the Invoice Date is 20/06)
The GL date automatically defaults to the System Date: 24/06
Action: Modify the GL date to 23/06
2) Adjustment
Adjust the Invoice Date to 21/06
Observe that the GL Date has been automatically changed from the 23/06 to the 24/06!!!
Cause
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In this Document
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Cause
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13498 | https://askfilo.com/user-question-answers-smart-solutions/ix-higher-order-thinking-skills-1-how-high-does-the-mercury-3337333232323136 | Question asked by Filo student
IX. Higher Order Thinking Skills.
Views: 5,519 students
Updated on: Aug 29, 2025
Text SolutionText solutionverified iconVerified
Below are the solutions to the Higher Order Thinking Skills questions:
Question 1: How high does the mercury barometer stand on a day when atmospheric pressure is 98.6 kPa?
Solution:
The height h of mercury in a barometer is given by:
P=hρg
Where:
Solving for h:
h=ρgP
Substituting values:
h=13,600×9.898,600
=133,28098,600
≈0.74 m
=74 cm
So, the mercury barometer would stand at approximately 74 cm.
Question 2: How does a fish manage to rise up and move down in water?
Solution:
A fish controls its vertical movement in water by adjusting the volume of its swim bladder (an internal gas-filled organ):
Question 3: If you put one ice cube in a glass of water and another in a glass of alcohol, what would you observe? Explain your observations.
Solution:
Explanation: An object floats when its density is less than the liquid. Ice's density is about 0.92 g/cm³, water's is 1.0 g/cm³, but alcohol (ethanol) has a density of about 0.79 g/cm³. Therefore:
Question 4: Why does a boat with a hole in the bottom would eventually sink?
Solution:
A boat floats by displacing water whose weight is equal to the boat's own weight (Archimedes' principle). If there is a hole in the bottom, water starts filling the boat, increasing its overall weight.
In summary: The boat will eventually sink because the incoming water adds to its weight, overcoming the upward buoyant force.
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| Question Text | IX. Higher Order Thinking Skills. 1. How high does the mercury barometer stand on a day when atmospheric pressure is 98.6 kPa? 2. How does a fish manage to rise up and move down in water? 3. If you put one ice cube in a glass of water and another in a glass of alcohol, what would you observe? Explain your observations. 4. Why does a boat with a hole in the bottom would eventually sink? |
| Updated On | Aug 29, 2025 |
| Topic | All topics |
| Subject | Smart Solutions |
| Class | Government Job |
| Answer Type | Text solution:1 |
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13499 | http://www.boyleschool.com/scoring.pdf | Understanding Championship Scoring by Jim Montague The preliminary and championship events are the highest dance levels at a feis. As the dancer's skills have sharpened and competition becomes keener, it becomes necessary for the performances to be evaluated independently by three judges. As in the lower competition levels (Beginner, Novice, and Prizewinner), each judge scores the dancer from 0 to 100 points (although you'll normally see a score somewhere between 70 and 95). These are known as the "raw" scores. The three "raw" scores earned by any one dancer mean nothing by themselves ‐‐ these scores must be restated so that they are in relation to the other competitors. Take for example a set piece in which Katie competes with five other dancers in front of three judges ‐ Alex, Beth, and Cora. After all six competitors have danced, we see that the judges have given Katie scores of 82, 88, and 79 respectively. These "raw" scores are meaningless by themselves ‐ now each judge must rank the performances ‐ from best (1st) to worst (6th). Here's what the scoresheets might look like both before and after the judges have ranked the competitors. Judge's Scoresheets (before ranking) Judge Alex's Scores Judge Beth's Scores Judge Cora's Scores Dancer #1 Katie 82 Katie 88 Katie 79 Dancer #2 Kevin 84 Kevin 79 Kevin 70 Dancer #3 Mary 83 Mary 92 Mary 80 Dancer #4 Carri 79 Carri 83 Carri 79.5 Dancer #5 Julie 78 Julie 80 Julie 74 Dancer #6 Kelly 81 Kelly 85 Kelly 73 Judge's Scoresheets (after ranking) Judge Alex's Scores Judge Beth's Scores Judge Cora's Scores Dancer #1 Katie 82 ‐ 3 Katie 88 ‐ 2 Katie 79 ‐ 3 Dancer #2 Kevin 84 ‐ 1 Kevin 79 ‐ 6 Kevin 70 ‐ 6 Dancer #3 Mary 83 ‐ 2 Mary 92 ‐ 1 Mary 80 ‐ 1 Dancer #4 Carri 79 ‐ 5 Carri 83 ‐ 4 Carri 79.5 ‐ 2 Dancer #5 Julie 78 ‐ 6 Julie 80 ‐ 5 Julie 74 ‐ 4 Dancer #6 Kelly 81 ‐ 4 Kelly 85 ‐ 3 Kelly 73 ‐ 5 Off the subject a bit ‐ we see Judge Cora gave Carri a raw score of 79.5. Indeed, when she initially scored, she gave Carri only a 79, but upon review, discovered that it would result in a tie with Katie... but she liked Carri's dancing better (for whatever reason). So she a 1/2 after her 79 (instead of making it an 80 where she'd then have "tie" problems with Mary, whom she liked the best). People shouldn't have a problem when they see half points added to the "raw" scores. Judges are just doing their job ‐ a feis doesn't pay a judge simply to tie everyone. The next step in championship tabulation is to convert these rankings to "Irish points". Understand that the rankings are converted, not the "raw" scores. A table of the Irish point conversions is shown at the end of this article... you may want to clip it out to keep in your purse or wallet. Each 1st place ranking receives 100 points, 2nd place gets 75, 3rd gets 65 and so on. Kindly note that in larger competitions like the Oireachtas, only the top 50 dancers are ranked ‐ the 51st dancer and beyond receive no Irish points. After this conversion, the Irish points from each judge are added for each dancer. The dancer with the most (Irish) points is the winner, the second most Irish points is awarded second place and so on. In Katie's reel example above, the final results are as follows: When reviewing Katie's "marks", we see that she took overall third place with 205 overall points. A 2nd and two 3rds gave her a third overall in this case. She was very close to Kevin... only one point away from second place. When we review the overall field, we find pretty consistent rankings except with Kevin/Judge Alex. All the judges ranked the dancers within a place or two of each other and there should be no doubt that Mary "won"... that's what we like to see. But we have to wonder what Alex saw in Kevin's performance (scoring him the best) that the other two judges didn't see (both giving him last place). I included Kevin's scores in this example to show the strength of one judge's 1st place ranking... the 25 point difference between a judge's first and second place is a lot to make up. But for both consistent and inconsistent judges is the reason a feis will hire three judges... to smooth things out; to make things more fair when it comes to somewhat subjective scoring. In the above example, I used only one dance being scored. Local feisanna have each competitor perform two dances in front of the same panel of judges. As this is normally the case, I should mention how the judges score the results. Then, each judge adds their two dances together to arrive at the dancer's "raw" score. The judge now ranks from the combined scores and converts to Irish points as discussed above. Of course, at the Oireachtas, Nationals, etc. when there is a separate panel of judges each time, each dance will be scored separately and then Irish points added together to determine recalls and/or final results. If you're not thoroughly confused by now, perhaps when I mention how ties are handled, I'll put you over the edge. When ties occur after ranking the field, Irish points are determined by computing the average score for the places involved. For instance, in a two‐way tie for 2nd, take the average Irish points awarded for 2nd and 3rd place and award both dancers 70 points [(75+65)/2 = 70]. If there were a three‐way tie for 3rd place, 60.33 Irish points would be awarded to each involved dancer [(65+60+56)/3 = 60.33]. Not really a problem so far, but here's what makes it confusing... the Irish points are properly distributed but the rankings which follow the tie are not! Take this three‐way tie for 3rd, for example, in a field of seven competitors. The rankings that appear are 1st, 2nd, 3rd, 3rd, 3rd, 4th, and 5th! (rather than 1st, 2nd, 3rd, 3rd, 3rd, 6th, and 7th). The Irish points awarded are 100, 75, 60.33, 60.33, 60.33, 53, 50 respectively. The 5th place dancer receives only 7th place points! When you have a whole bunch of ties in a large event like an Oireachtas, the dancer's "place" becomes meaningless, especially when the dancer receives 1st, 2nd, and 3rd places and "Your Marks" with the results that are purchased. However unfair it is on the surface, the reader of the results has to understand the disclaimer noted "Due to ties, you may not have placed as high as this report suggests!" I understand that this method of determining "places" came from the North American teachers in order to qualify more kids for the Worlds. Think about it. Say An Coimisiún allowed the to 25% places from the Eastern Regional to qualify for the world competition. If an event had 100 entrants and there were 15 ties spread among the top 25 places, we could send 40 dancers to the worlds! Of course, this rule was changed three years ago when an exact number of qualifiers per certain number of entrants was spelled out. Regardless, here's how to interpret those "disclaimed" results... simply go from the Irish points earned back to the conversion chart to determine approximately how many dancers placed ahead of you. For example, say a judge awards you 17th place but only 13.336 Irish points. When you look up 13 points, you'll see that some 37 dancers placed ahead of you (some 17th place, huh?). I helped a first time Oireachtas mother face reality last fall. She approached me saying "Something's really wrong! They "recalled" 28 dancers in (her daughter's) competition and she placed between 22nd and 27th from five of the six judges and was 30 place from the sixth judge. How come she didn't recall?" I merely explained to her that she had to review the points, not the place, for a more accurate analysis. Needless to say, daughter didn't want to accept reality. Irish 100 Point Conversions Rank Pts Rank Pts Rank Pts Rank Pts Rank Pts 1st 100 11th 41 21st 30 31st 20 41st 10 2nd 75 12th 39 22nd 29 32nd 19 42nd 9 3rd 65 13th 38 23rd 28 33rd 18 43rd 8 4th 60 14th 37 24th 27 34th 17 44th 7 5th 56 15th 36 25th 26 35th 16 45th 6 6th 53 16th 35 26th 25 36th 15 46th 5 7th 50 17th 34 27th 24 37th 14 47th 4 8th 47 18th 33 28th 23 38th 13 48th 3 9th 45 19th 32 29th 22 39th 12 49th 2 10th 43 20th 31 30th 21 40th 11 50th 1 51st + 0 |
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