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Nitrogen ( $N_2$ ) constitutes 79% of the atmosphere, but only few living organisms can utilize this nitrogen directly [16, 60]. Plants and animals can only take advantage of "fixed" nitrogen in form of nitrate ( $NO_3$ ) or ammonia ( $NH_3$ ). A few species of prokaryotes (characterized by not having a cell nucleus) c... | {
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"Header 2": "3.3 NITROGEN CYCLE",
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| Reaction | Energy yield (kJ) |
|---------------------------------------------------------------------------------------------------------------------------------------------|------... | {
"Header 1": "3.2.1 INCREASED GREENHOUSE EFFECT",
"Header 2": "3.3 NITROGEN CYCLE",
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All living organisms contain sulphur (about 1.2% on dry weight basis). The most common form of sulphur (S) is sulphydryl (-SH) groups in organic molecules. The heterotrophic organisms cover their individual requirements by consuming sulphur-containing amino acids (cysteine and methionine) which the plants have build by... | {
"Header 1": "3.4 SULPHUR CYCLE",
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Most biologically important elements β apart from the already mentioned (C, N, S) β have only a small or no reservoir in the atmosphere. An example is phosphorus (P) present in the environment as a phosphate (PO4 ---) or one of its analogues (HPO4 --, H2 PO4 - ). The importance of phosphorus for living organisms appear... | {
"Header 1": "3.5 PHOSPHORUS CYCLE",
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Solar energy drives the water cycle [1, 7]. The sun heats the ocean surface, and large amounts of water evapourates and rise into the air. The lower temperature at higher altitudes makes the water vapour condense into clouds, which consists of very small water droplets. Winds, which are also driven by solar energy, blo... | {
"Header 1": "3.6 WATER CYCLE",
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A population is defined as all individuals of the same species in a given area. A population has a number of features that are characteristic of this organization level, and not found on the organizational level below (individual) or above (community). A population has, for example, an age structure, a distribution, an... | {
"Header 1": "4 POPULATION ECOLOGY",
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A population's size, density, age structure and growth is regulated by a complex interplay of impacts from: 1) the abiotic surroundings, 2) populations of other species (interspecific factors), and 3) impacts from the population itself (intraspecific factors), see Fig. 23.
Fig. 23. Facto... | {
"Header 1": "4.1 REGULATION OF POPULATION DENSITY",
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It has been proposed to define the ecological niche of a species that the niche can only contain one species in a given ecosystem. But this definition is not entirely satisfactory. A more precise definition of an organism's niche can be derived as follows: Plot linearly on an x-axis an environmental factor (e.g. temper... | {
"Header 1": "4.1.1 NICHE CONCEPT AND IMPORTANCE OF ABIOTIC FACTORS FOR REGULATION OF POPULATIONS",
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When the fundamental niches of two species completely or partly overlap one another, there will be competition for food and/or space (see Figs. 25 & 26). This kind of competition is called *interspecific competition*. The following sections describe four types of observations that illustrate or demonstrate interspecifi... | {
"Header 1": "**4.1.2.1 Competition**",
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In the 1930s, the Russian biologist Georgy Gause conducted a large number of laboratory experiments on competition between different species of single-celled ciliates of the genus *Paramecium* fed with bacteria or yeast cells. In some of the experiments, two species were cultivated separately with the amount of feed of... | {
"Header 1": "1) Displacement of a species from another species",
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If two species are not equally well adapted to all the habitats in "the fundamental niche", but otherwise exploit the same food resources, they can often co-exist by sharing the niche between them. The part of "the fundamental niche" which is utilized when there is an interaction (interspecific competition) with other ... | {
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"Header 2": "2) Fundamental and realized niche is not identical",
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By niche diversification it is meant that related species living in the same area exhibits a specialization so as to avoid competing for the same limited resources β i.e. they avoid niche overlap. Only two examples are cited from the abundant literature on the subject.
A study of the food choices of the great black c... | {
"Header 1": "3) Niche diversification",
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When two related species geographically overlap each other, they tend to deviate from each other in their form and construction (morphological) and there is less variation within the species than in those cases where the species live apart from each other. This phenomenon is called character displacement and can be con... | {
"Header 1": "4) Character displacement",
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There is a gradual transition of possibilities for interaction between a predator and its prey: 1) the predator limits the prey so much that the population of prey becomes extinct or nearly eradicated, 2) the predator regulates the stock so that the prey population does not become so large that the food resources are d... | {
"Header 1": "**4.1.2.2 Predation**",
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**PDF** components for **PHP** developers
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A predator has often a positive regulatory influence on a prey population by maintaining it at a level that does not exceed the area's carrying capacity. A c... | {
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Keystone species are in contrast to the dominant species not necessarily abundant in a community. They exert strong control over the community structure, not by number but by their key ecological niches. One way to identify a keystone species is to experimentally remove or eliminate the species so that its importance b... | {
"Header 1": "**4.1.2.3 Keystone species**",
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An invasive species is a plant or an animal that has been spread by human action over large geographical distances to a new area. This new species reproduce unrestrained and out of control due to not having any natural enemies, thereby out-competing the native species. In recent years, problems with invasive species ha... | {
"Header 1": "**4.1.2.4 Invasive species**",
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Two species' populations can be linked together in a cohabitation called symbiosis. Symbiosis may be beneficial for one or both species. Therefore it is common practice to distinguish between two main types of symbiosis, namely commensalism and mutualism. Commensalism is a form of partnership where one species ("the gu... | {
"Header 1": "**4.1.2.5 Symbiosis**",
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Many biotic factors that help to regulate the densities of populations are intraspecific. These factors are never completely separated from interspecific- and abiotic factors, but together these intraspecific factors may ensure the stability of a population. Intraspecific factors can be passive (e.g. competition betwee... | {
"Header 1": "4.1.3 IMPORTANCE OF INTRASPECIFIC FACTORS FOR THE REGULATION OF POPULATIONS",
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If the number of births per individual and per unit time (birth rate = natality) is called x, and the number of deaths per individual and per unit time (mortality) is called y, the specific growth rate is defined as: r = x β y. If a population has N individuals, the population specific growth rate can be described by t... | {
"Header 1": "4.2 POPULATION GROWTH AND MATHEMATICAL MODELS",
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Thus, the model does not taken into account: 1) the age structure of the population, 2) the minimum size of the population for survival, 3) social animals have a minimal density, 4) changes in the environment are not immediately reflected in a changed population growth rate, 5) competition with other species' populatio... | {
"Header 1": "4.2 POPULATION GROWTH AND MATHEMATICAL MODELS",
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In words the model can be described as follows:
{ *The change in the number of prey per unit of time* } *=* { *Unlimited growth of prey per unit of time* } β { *Extermination of prey per unit of time caused by the predator* }
and
{ *The change in the number of predators per unit of time* } *=* { *The increase in ... | {
"Header 1": "4.2 POPULATION GROWTH AND MATHEMATICAL MODELS",
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A population of algae is growing exponentially. It is observed that after 2 days there are 400 algal cells are present, while after 6 days there are 800 algal cells.
- a. What is the size of the initial population?
- b. If the specific growth rate is constant, what is then the population size after 10 days?
Answer:... | {
"Header 1": "4.2 POPULATION GROWTH AND MATHEMATICAL MODELS",
"Header 2": "*Example 3*",
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A population of yeast cells grows 48.2% per hour. At time t = 0 the population size is N0 = 8.34 g biomass (DM = dry matter). During this growth period, the consumption of glucose is f = 0.345 g per g of biomass (DM) per hour (h). What is the consumption of glucose, Ft=4-5 from t = 4 to t = 5 h?
Answer:
$$r = ln(1 + ... | {
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"Header 2": "*Example 5*",
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Species diversity is the multiplicity of species. If an area has high species diversity with regards to butterflies, it is a good locality for a butterfly collector. As a measure of diversity the number of species per individual can be used. If you collect 100 individuals in a community and find 50 species, one can say... | {
"Header 1": "5 SPECIES DIVERSITY",
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| Flowering plants | | Land snails | |
|------------------|------|----------------|------|
| Labrador | 390 | Labrador | 25 |
| Massachusetts | 1650 | Massachusetts | 100 |
| Florida | 2500 | Florida | 250 |
| Marine mussels | | Ants | |
| Newf... | {
"Header 1": "5 SPECIES DIVERSITY",
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It is often difficult or impossible to determine where plant and animal communities end and new ones start. The reason is that they are usually interconnected with an environmental gradient (temperature, rainfall, water depth, etc.) that causes smooth transitions. If the environmental gradient between two communities i... | {
"Header 1": "5.1 TRANSITION ZONES AND EDGE EFFECTS",
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In 1917, the bird fauna was registered on nine islands off southern California. In 1968, the study was repeated. A comparison of the two studies demonstrated several notable features, see Table 5. Most notable was that the total number of species on the islands were almost unchanged over the past 51 years, but from 18%... | {
"Header 1": "5.2 ISLAND BIOGEOGRAPHY",
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An ecological succession is a characteristic temporal order in which plant and animal species replace each other in an ecosystem. A succession can for example be initiated by burning a forest area or by adding nutrients to a biotope. One can distinguish between two different models that describe ecological successions:... | {
"Header 1": "6 ECOLOGICAL SUCCESSION",
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All ecosystems have a tendency to develop along certain predictable trajectories when under stable external conditions. An ecological succession is called *autogenous* if it is allowed to proceed to climax without any external physical disturbances. A succession where the primary production is dominating in the beginni... | {
"Header 1": "6 ECOLOGICAL SUCCESSION",
"Header 2": "6.1 AUTOGENOUS SUCCESSION",
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The natural autogenous succession that an ecosystem will go through in time, if the external physical conditions were stable, can often be studied in "space". The natural succession a sand dune close to the sea would undergo, if it was not constantly under strong influence of physical forces (coastal erosion, sand drif... | {
"Header 1": "6.5 SUCCESSION IN \"SPACE\"",
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The development (evolution) of the biosphere, which is the layer of the planet Earth where life exists, is an interesting example of how there can be an interaction between allogeneic succession processes caused by climatic/geological changes and autogenous succession processes which run on due to the activity of the l... | {
"Header 1": "6.6 THE BIOSPHERE AS AN ECOSYSTEM",
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The food resources in nature are often found in a "continuum of qualities" (e.g. as a sizegradient of food particles) [60]. Various animals' use of a resource-continuum is depicted in Fig. 53.
Fig. 53. Three species' (I, II, III) exploitation of a resource with a gradient of qualities (... | {
"Header 1": "6.7 ECOSYSTEM COMPLEXITY AND STABILITY",
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In principle β and sometimes in practice β the energy flow through the various components of an ecosystem can be quantified by means of mathematical models (using computers). These models can analytically examine the characteristics of the system based on different assumptions. One can assess the consequences of interv... | {
"Header 1": "6.8 ECOSYSTEM MODELS AND LIMITS TO GROWTH",
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Oceans cover about 70% of the Earth's surface, and this is where you find the biggest and the "thickest" ecosystems in the world. Fig. 54 shows a diagrammatic cross-sectional view of an ocean adjacent to a continent. It is seen that the continent continues beneath the ocean as a continental shelf which at a depth of 12... | {
"Header 1": "7 MARINE ECOSYSTEMS",
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The food chains in the open sea begins with the microscopic plankton algae, collectively called phytoplankton. It is phytoplankton's primary production that forms the basis of all higher and lower marine life. It is the smallest known autotrophic organisms (diatoms, dinoflagellates, coccolithophores and others) which f... | {
"Header 1": "7.1 OPEN SEAS",
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Fig. 56. The "microbial loop". A significant proportion (30β50%) of the primary production is lost from the classical grazing food chain, as dissolved organic matter (DOM). DOM is utilized almost exclusively by free-living heterotrophic bacteria and therefore gives rise to a significant bacterial secondary production. ... | {
"Header 1": "Zooplankton Micro agellates Bacteria Cyanobacteria DOM GRAZING FOOD CHAIN \"MICROBIAL LOOP\" Plankton algae (Primary production) Carbon dioxide Ammonia Phosphate (Herbivores) (Carnivores) Zooplankton Fish Ciliates",
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The photic zone reaches down to approximately 100 m in the open ocean areas, but closer to land it does not penetrate that far down, due to suspended particles. The photic zone is typically 30β40 m in the more coastal waters. Nevertheless, the primary production is significantly higher in coastal areas than in the open... | {
"Header 1": "Zooplankton Micro agellates Bacteria Cyanobacteria DOM GRAZING FOOD CHAIN \"MICROBIAL LOOP\" Plankton algae (Primary production) Carbon dioxide Ammonia Phosphate (Herbivores) (Carnivores) Zooplankton Fish Ciliates",
"Header 2": "7.1.1 PRIMARY PRODUCTION AND HYDROGRAPHY",
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"sou... |
The main primary producers in protected marine shallow water areas are macroalgae, higher plants (eelgrass, seagrass) and microscopic diatoms (living on the surface of the sea floor). In the summer months, these areas are very productive. Macroalgae and eelgrass are negligibly being eaten, but they enter indirectly int... | {
"Header 1": "7.2 MARINE SHALLOW WATER AREAS",
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Figure 60 shows a diagrammatic cross section of a lake with its various life zones.
Fig. 60. The three main zones in a lake ecosystem. The boundary between the limnetic zone and the profundal zone is marked by the light-compensation depth. The littoral zone extends from the lake shore ... | {
"Header 1": "8 LAKE ECOSYSTEMS",
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There are few examples of a physical factor that exerts a more direct control over an ecosystem than the temperature of a lake. In the following sections, this shall be explained in more detail. The density of freshwater is greatest at 4 Β°C, see Fig. 62.
GENERAL ECOLOGY LAKE ECOSYSTEMS
 ... | {
"Header 1": "8.1 TEMPERATURE STRATIFICATION IN LAKES",
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The seasonal thermal stratification and total circulation of the water masses in spring and autumn are critical to the energy and nutrient cycling in deeper lakes. This fact can be illustrated with an example from one of the world's most studied lakes, namely Lake Esrum in Denmark, see Fig. 66.
GENERAL ECOLOGY LAKE E... | {
"Header 1": "8.2 SEASONAL VARIATIONS IN LAKES",
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A deciduous forest can be divided into several layers, with the highest peaks of trees forming a canopy, and below, where there is an undergrowth of smaller trees, can be found low shrubs and shrubbery. Finally on the forest floor, there may be found a layer of herbaceous plants. This stratification is caused by the li... | {
"Header 1": "9 FOREST ECOSYSTEMS",
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Only a few larger animals directly eat the vegetation in a forest, but some insects graze on, suck the fluids or eat their way inside the leaves (tunnelling). Fig. 70 shows an example of a grazing food chain in a forest. It is only a small part of a forest ecosystem's primary production that passes through the "grazing... | {
"Header 1": "9.1 FOOD CHAINS IN FORESTS",
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In young forest ecosystems, it is characteristic that the organisms in the detritus food chain are not able to totally break down the dead organic material that is added to the soil in the form of leaves, twigs, branches, herbs, animal waste etc. The end products of the organic matter decomposition are typically a vari... | {
"Header 1": "9.2 HUMUS AND NUTRIENT BALANCE",
"token_count": 389,
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- [1] Odum, E.P. 1971. Fundamentals of ecology. Saunders Co., Philadelphia, 574 pp.
- [2] Solomon et al. 2016. Emergence of healing in the Antarctic ozone layer. Science, doi: 10.1126/science.aae0061
- [3] Clapham, W.B. 1983. Natural ecosystems. Macmillan Publishing Co., Inc., New York, 282 pp.
- [4] Ingersoll, A.P. 19... | {
"Header 1": "**REFERENCES**",
"token_count": 2035,
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Natur., 102: 243β282.
- [41] MacArthur, R.H. 1972. Geographical ecology. Harper & Row, New York, 269 pp.
- [42] Lassen, H.H. 1975. The diversity of freshwater snails in view of the equilibrium theory of island biogeography. Oceologia, 19, 1β8.
- [43] Estes, J.E., N.S. Smith & J.F. Palmisano. 1978. Sea otter predation a... | {
"Header 1": "**REFERENCES**",
"token_count": 1499,
"source_pdf": "datasets/websources/biochem/General_Ecology.pdf"
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| A | barnacle 55 |
|-----------------------------------------------------|--------------------------------------------------|
| abiotic 7, 27, 44, 47, 65, 130, 131, 132, 137 | bathyal zone 109 |... | {
"Header 1": "INDEX",
"token_count": 2672,
"source_pdf": "datasets/websources/biochem/General_Ecology.pdf"
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facilitation model [95](#page-94-0) facilitation-successions [95](#page-94-0) faecal material [110](#page-109-0) faecal pellets [110](#page-109-0) Fe+++ [43,](#page-42-0) [44](#page-43-0) Fe(OH)3 [43](#page-42-0) FeS2 [43](#page-42-0) filter-feeders [26,](#page-25-0) [110](#page-109-0), [112](#page-111-0) finches [59](... | {
"Header 1": "INDEX",
"Header 2": "**F**",
"token_count": 732,
"source_pdf": "datasets/websources/biochem/General_Ecology.pdf"
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Galapagos Islands [59](#page-58-0) gaseous types of cycles [28](#page-27-0) Gause [52](#page-51-0), [54](#page-53-0), [56](#page-55-0) generation time [69](#page-68-0), [80](#page-79-0) global energy balance [13](#page-12-0) global temperature [32](#page-31-0), [34](#page-33-0) glucose [14](#page-13-0), [37](#page-36-0... | {
"Header 1": "INDEX",
"Header 2": "**G**",
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| respiration 14, 17, 18, 22, 23, 24, 25, 28, 31, 96, 97, | stratification 116, 124, 125, 129 |
|---------------------------------------------------------|-----------------------------------------------------|
| 98, 99, 100, 101, 105, 109, 129, 130, 135, 136 | S... | {
"Header 1": "R R<sub>0</sub> 69 rainforests 32, 107, 132 realised niche 52 resource-continuum 105, 106",
"token_count": 1998,
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**Rodney M. J. Cotterill**
*Danish Technical University, Denmark*
Copyright Β© 2002 by Rodney M. J. Cotterill
Published by John Wiley & Sons Ltd,
Baffins Lane, Chichester,
West Sussex PO19 1UD, England
*N ational* 01243 779777
*International* (+44) 1243 779777
e-mail (for or... | {
"Header 1": "An Introduction",
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"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
| Preface | | |
|---------|-----------------------------------------------------------------|----|
| 1 | Introduction | 1 |
| | Exercises ... | {
"Header 1": "**Contents**",
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This book is based on the course in biophysics that I have taught for the past two decades at the Danish Technical University, and it should be suitable for similar courses at other places of higher education.
I originally delivered the lectures in Danish and Henrik JΓΈrgensen, one of my first students, recorded my wo... | {
"Header 1": "**Preface**",
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It is probably no exaggeration to say that many regard biophysics as a discipline still waiting to be adequately defined. This conclusion appears to be endorsed by the considerable differences between several of the publications on the subject cited at the end of this chapter. Indeed, in terms of the items they discuss... | {
"Header 1": "**1 Introduction**",
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Although this is a notable achievement in its own right, it still falls far short of the desired ability to predict any protein's structure from the primary sequence, and this is an obvious obstacle to full realization of the potential inherent in genetic manipulation. If one were able to overcome that hurdle, this wou... | {
"Header 1": "**1 Introduction**",
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Through his own experimental work on the atomic nucleus, Ernest Rutherford put forward a picture of the atom in which the heavy nucleus is located at the centre, while the electrons, discovered by Joseph (J. J.) Thomson, move in the surrounding space, their characteristic distances from the nucleus being of the order o... | {
"Header 1": "**2.1 Quantum Mechanics**",
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Although we do not need to go into all the details here, there are certain rules which are useful when considering situations in which there is more than one electron present in an atom. For a start, no two electrons can be associated with the same atomic nucleus and have precisely the same values for all four of the q... | {
"Header 1": "2.2 Pauli Exclusion Principle",
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It is interesting to note that these considerations were well appreciated even before it had been unequivocally demonstrated that atoms actually exist. It is not surprising, therefore, that the arguments do not take into account possible redistribution of the subatomic particles when two atoms approach one another suff... | {
"Header 1": "2.3 Ionization Energy, Electron Affinity and Chemical Binding",
"token_count": 403,
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When the fluorine
Atomic Number Element Orbital electronic configuration *E*I(aJ ) *E*A(aJ ) 1H 1*s* 2.178 0.120 2 He 1*s*<sup>2</sup> 3.938 3 Li [He]2*s* 0.863 0.087 4 Be [He]2*s*<sup>2</sup> 1.493 -0.096 5B [He]2*s*22*p* 1.329 0.032 6C [He]2*s*22*p*<sup>2</sup> 1.804 0.200 7N [He]2*s*22*p*<sup>3</sup> 2.329 - 0.016... | {
"Header 1": "2.3 Ionization Energy, Electron Affinity and Chemical Binding",
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"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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Because *E*<sup>I</sup> is usually larger than *E*A, this electron transfer process might seem to require a net input of energy (see Table 2.2). However, we must remember that the situation does not involve two atoms that are well separated. On the contrary, they remain in the vicinity of each other, and so there are o... | {
"Header 1": "2.3 Ionization Energy, Electron Affinity and Chemical Binding",
"token_count": 788,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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Although the propensity that a given atomic species displays for losing or gaining electrons is determined by the dual factors of ionization potential and electron affinity, an adequate qualitative measure of the same thing is provided by a single parameter known as the electronegativity, $e_N$ . Atoms with large elec... | {
"Header 1": "2.3 Ionization Energy, Electron Affinity and Chemical Binding",
"Header 2": "2.4 Electronegativity and Strong Bonds",
"token_count": 1851,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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Because there exist forms of condensed matter comprising assemblies of molecules that retain their individual identity, there must be types of intermolecular force that we have not yet considered. These are known as secondary bonds and they are quite weak compared with those that we have considered until now. In those ... | {
"Header 1": "2.3 Ionization Energy, Electron Affinity and Chemical Binding",
"Header 2": "**2.5 Secondary Bonds**",
"token_count": 1031,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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The arguments given in the preceding chapter regarding the repulsive, attractive and equilibrium aspects of the interatomic potential were actually put forward by Ludwig Seeber in 1824. His conjectures showed remarkable insight, given that they were being made about 50 years before there was any real evidence for the e... | {
"Header 1": "**3.1 Interatomic Potentials for Strong Bonds**",
"token_count": 2037,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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There is a second distance parameter, namely *r*0, which does not have a counterpart in those other potential functions. It appears because the Morse potential has both repulsive and attractive terms, and the *r*<sup>0</sup> is the distance at which the potential function has its minimum value. Finally, *E* Morse is <s... | {
"Header 1": "**3.1 Interatomic Potentials for Strong Bonds**",
"token_count": 290,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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Having covered the various forms of strong interaction, we turn now to the weaker bonds, and begin with the attraction that can occur between filled orbitals. That there should be repulsion when filled orbitals approach sufficiently closely is not surprising, because the Pauli Exclusion Principle will ultimately prohib... | {
"Header 1": "**3.1 Interatomic Potentials for Strong Bonds**",
"Header 2": "**3.2 Interatomic Potentials for Weak Bonds**",
"token_count": 1632,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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It has the following form
$$\mathcal{E}_{\text{total}} = \sum_{b} \left[ k_{2}(b - b_{0})^{2} + k_{3}(b - b_{0})^{3} + k_{4}(b - b_{0})^{4} \right]$$
$$+ \sum_{\theta} \left[ k_{2}(\theta - \theta_{0})^{2} + k_{3}(\theta - \theta_{0})^{3} + k_{4}(\theta - \theta_{0})^{4} \right]$$
$$+ \sum_{\phi} \left[ k_{1}(1 -... | {
"Header 1": "**3.1 Interatomic Potentials for Strong Bonds**",
"Header 2": "**3.2 Interatomic Potentials for Weak Bonds**",
"token_count": 755,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
Before putting interatomic potentials to use, it will be helpful to get an idea of the energies of the bonds commonly encountered in molecules of biological relevance. This will give us a better view of the types of reactions and processes that can occur in the biological domain. We will be considering many cases in wh... | {
"Header 1": "**3.1 Interatomic Potentials for Strong Bonds**",
"Header 2": "**3.4 Bond Energies**",
"token_count": 2042,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
It is for this reason
**Figure 3.8** The naturally kinked molecular configuration of *cis*-polyisoprene gives it a high degree of elasticity
**Figure 3.9** Molecules of *trans*-polyisoprene do not have the kinked structure of their *cis* counterparts and... | {
"Header 1": "**3.1 Interatomic Potentials for Strong Bonds**",
"Header 2": "**3.4 Bond Energies**",
"token_count": 1197,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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Until now in this chapter, we have been considering the forces that act at the atomic and molecular level. In many biophysical problems, however, we need to know something about the forces that act on a more macroscopic level. These forces are ultimately due to those atomic and molecular level forces, of course, but we... | {
"Header 1": "**3.1 Interatomic Potentials for Strong Bonds**",
"Header 2": "**3.5 Spring Constants**",
"token_count": 2036,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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and Kestner, N. R., (1969). *T heory of Intermolecular Forces*. Pergamon, Oxford.
Mason, E. A. and Rice, W. E., (1954). The intermolecular potentials for some simple nonpolar molecules. *Journal of Chemical Physics* **22**, 843β851.
Morse, P. M., (1929). Diatomic molecules according to the wave mechanics II Vibrati... | {
"Header 1": "**3.1 Interatomic Potentials for Strong Bonds**",
"Header 2": "**3.5 Spring Constants**",
"token_count": 431,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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The discussion in the two preceding chapters was strictly applicable to a state that is not actually attainable, namely the absolute zero of temperature, for it ignored the thermal motions that all atoms and molecules must have when they are at a finite temperature. And when considering the motions of atoms and molecul... | {
"Header 1": "4 Rates of Reaction",
"token_count": 1911,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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In our initial example of just two atoms, the kinetic energy and the potential energy showed wild (and counter-phase) fluctuations between their maximum and zero values. As mentioned earlier, with increasing numbers of atoms in the system, these fluctuations would become less and less pronounced, because the individual... | {
"Header 1": "4.3 Thermodynamics and Statistical Mechanics",
"token_count": 1840,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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The number of ways, Ξ© , in which the
**Figure 4.1** These two different situations correspond to different degrees of filling the available phase space
N items can be distributed in two groups comprising, respectively, $n_1$ and $n_2$ states is given by the simple combinatorial exp... | {
"Header 1": "4.3 Thermodynamics and Statistical Mechanics",
"token_count": 2021,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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As was noted earlier, in our
discussion of interatomic bonds, normal rubber is the name given to the polymer *cis*-polyisoprene, in which the individual chains are kinked and interwoven in the relaxed form of the substance. There are numerous different ways in which the disorder can be achieved, and they have associa... | {
"Header 1": "4.3 Thermodynamics and Statistical Mechanics",
"token_count": 1743,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
The rates at which chemical reactions proceed are governed by the principles discussed above. However, in order to establish contact with what can be observed experimentally, we need to discuss a number of formal definitions. The reaction
$$A + B \to C \tag{4.27}$$
is said to be mono-molecular, while the reverse re... | {
"Header 1": "4.3 Thermodynamics and Statistical Mechanics",
"Header 2": "**4.4 Reaction Kinetics**",
"token_count": 1723,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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Water is the most common substance on earth, and it is one of only two liquids which occur naturally in appreciable quantities, the other being petroleum. About 60% of the weight of the human body is water, it being present in the interior of every cell. It also accounts for the bulk of such specialized media as blood ... | {
"Header 1": "4.3 Thermodynamics and Statistical Mechanics",
"Header 2": "**4.5 Water, Acids, Bases and Aqueous Reactions**",
"token_count": 2016,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
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According to a suggestion by Svante Arrhenius in 1887, an acid is a chemical compound that dissociates in solution to produce hydrogen ions, while an alkali, formally referred to as a base, is a compound that yields hydroxyl ions. As we saw above, the pH of neutral water is 7, and the presence of an acid increases the ... | {
"Header 1": "4.3 Thermodynamics and Statistical Mechanics",
"Header 2": "**4.5 Water, Acids, Bases and Aqueous Reactions**",
"token_count": 2037,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
#### 4.6 Radiation Energy
The molecules of our bodies are constantly being subjected to radiation. This comes in a variety of wavelengths, some of which correspond to radiation that is quite harmless, for example the radiation we call cosmic rays. Radiation at X-ray wavelengths is useful as a diagnostic tool, as lo... | {
"Header 1": "4.3 Thermodynamics and Statistical Mechanics",
"Header 2": "**4.5 Water, Acids, Bases and Aqueous Reactions**",
"token_count": 2035,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
Use these data to calculate the minimum wavelength of electromagnetic radiation which would produce such ionization of a hydrogen atom.
#### *Further reading*
Atkins, P. W., (1990). *Physical Chemistry*. Oxford University Press, Oxford.
Eisenberg, D. and Kauzmann, W., (1969). *T he Structure and Properties of W a... | {
"Header 1": "4.3 Thermodynamics and Statistical Mechanics",
"Header 2": "**4.5 Water, Acids, Bases and Aqueous Reactions**",
"token_count": 398,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
Movement is one of the defining characteristics of the biological world. It is seen in one form or another in all living things. The movements associated with animals are of various types, and they range from the relatively subtle movements of their various internal organs to the more obvious locomotion of entire organ... | {
"Header 1": "**5 Transport Processes**",
"token_count": 334,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
Although diffusion is clearly caused by the motion of particles through space, for our biological purposes here it can be regarded as the mixing of particles amongst one another. The phenomenon was investigated first by the English
botanist Robert Brown, who in 1828 observed pollen particles in a glass of water, with... | {
"Header 1": "**5 Transport Processes**",
"Header 2": "**5.1 Diffusion**",
"token_count": 2008,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
The flux of particles leaving the first slab in the direction of the second slab will be
$$J = -D(\delta C / \delta x) \tag{5.5}$$
The flux of particles leaving the second slab in the *same* direction, that is to say in the direction away from the first slab, will be
$$J + l\left(\frac{dJ}{dx}\right) = -D \left(\... | {
"Header 1": "**5 Transport Processes**",
"Header 2": "**5.1 Diffusion**",
"token_count": 2032,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
The situation was analysed by Paul Langevin in 1908, and he arrived at the relationship
$$m\frac{d^2x(t)}{dt^2} + \gamma_{\text{Drag}}\frac{dx(t)}{dt} + \kappa x(t) = \mathcal{F}_{\text{Stochastic}}(t)$$
(5.19)
In this Langevin equation, m is the particle's mass, $\gamma_{\rm Drag}$ is the drag coefficient and $... | {
"Header 1": "**5 Transport Processes**",
"Header 2": "**5.1 Diffusion**",
"token_count": 2004,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
#### *Exercises*
- 5.1 After they have influenced the receptors in the post-synaptic membrane, those neurotransmitter molecules which are not broken down by enzymes diffuse back to the pre-synaptic membrane, which lies 2 Γ 10 β<sup>8</sup> m away, with a diffusion coefficient which has been determined to be 5 Γ 10 ... | {
"Header 1": "**5 Transport Processes**",
"Header 2": "**5.1 Diffusion**",
"token_count": 638,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
An individual biological molecule typically comprises hundreds or even thousands of atoms, and it is naturally important to know how these are arranged with respect to one another, for it is this arrangement that dictates the molecule's physical behaviour under a given set of conditions. The most straightforward techni... | {
"Header 1": "**6.1 X-Ray Diffraction and Molecular Structure**",
"token_count": 2046,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
The question then remains as to how the relative electron densities can be described. This is most conveniently accomplished by imagining the density $\rho$ at a given point as being composed of Fourier components. We recall that the most general form of Fourier series (named for Joseph Fourier) involves a sum of w... | {
"Header 1": "**6.1 X-Ray Diffraction and Molecular Structure**",
"token_count": 2039,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
Figures 6.2(a) and 6.2(b) show the various lines and planes in a two-dimensional and a three-dimensional crystal, respectively, corresponding to various Miller indices. If one of these lines or planes lies parallel to a particular axis, the intercept can be imagined as lying at infinity, and the corresponding Miller in... | {
"Header 1": "**6.1 X-Ray Diffraction and Molecular Structure**",
"token_count": 1566,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
Although X-ray diffraction is a highly useful technique for studying the structure of biological molecules, it does suffer from the disadvantage that the molecules have to be investigated in an environment that contrasts with the one in
which they normally operate; the diffraction method requires crystals whereas the... | {
"Header 1": "**6.1 X-Ray Diffraction and Molecular Structure**",
"Header 2": "**6.2 Nuclear Magnetic Resonance**",
"token_count": 2001,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
The solution of Equation (6.25) is
$$M_z = M_0(1 - e^{t/\tau_1}) (6.26)$$
In practice, the molecular system under investigation is subjected simultaneously to a fixed field, $H_0$ , and a sinusoidally varying field whose peak value is $H_1$ , and there is then a second relaxation time constant, $\tau_2$ , which ... | {
"Header 1": "**6.1 X-Ray Diffraction and Molecular Structure**",
"Header 2": "**6.2 Nuclear Magnetic Resonance**",
"token_count": 974,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
As was discussed in Appendix A, a quantum mechanical wave has a finite probability of tunnelling through an energy barrier even though this obstacle has a height that exceeds that of the wave's energy. In practice, however, the barrier width must be of near-atomic dimensions if the tunnelling current is to be measurabl... | {
"Header 1": "**6.1 X-Ray Diffraction and Molecular Structure**",
"Header 2": "**6.3 Scanning Tunnelling Microscopy**",
"token_count": 2034,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
The technique known as optical tweezers has its roots in the early 1970s, when Arthur Ashkin used light scattering to trap small glass beads. The basic mechanism relies on exploitation of the force associated with the change of momentum when a light beam is scattered. Together with Steven Chu, Ashkin subsequently exten... | {
"Header 1": "**6.5 Optical Tweezers**",
"token_count": 2025,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
As will be discussed in a number of the later chapters in this book, the membranes of several different types of cell are dotted with myriad channels and receptors. These are all protein molecules, and they are embedded within the membranes, spanning its roughly 5 nm thickness. It had become apparent by the middle of t... | {
"Header 1": "**6.5 Optical Tweezers**",
"Header 2": "**6.6 Patch Clamping**",
"token_count": 1794,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
Having reviewed a number of experimental techniques for investigating bioapproach, namely computer simulation. Some have referred to this as the third basic scientific activity, because it is neither experimental nor theoretical; it has been called theoretical experimentation. There is hardly a branch of the scientific... | {
"Header 1": "**6.5 Optical Tweezers**",
"Header 2": "**6.7 Molecular Dynamics**",
"token_count": 1993,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
The angular velocity components are
$$\omega_{\alpha,i} = \overset{\bullet}{\mathbf{\pi}}_{i} \sin(\beta_{i}) \sin(\gamma_{i}) + \overset{\bullet}{\beta}_{i} \cos(\gamma_{i}) \tag{6.61}$$
$$\omega_{\beta,i} = \overset{\bullet}{\alpha_i} \sin(\beta_i) \cos(\gamma_i) - \overset{\bullet}{\beta_i} \sin(\gamma_i)$$
(6.6... | {
"Header 1": "**6.5 Optical Tweezers**",
"Header 2": "**6.7 Molecular Dynamics**",
"token_count": 2047,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
#### Exercises
6.1 Prove that the relationship
$$d_{hkl} = \left(\frac{h^2}{a^2} + \frac{k^2}{b^2} + \frac{l^2}{c^2}\right)^{-1/2}$$
is true, $d_{hkl}$ being the inter-planar spacing between a set of planes with Miller indices h, k and l, while a, b and c are the side lengths of the unit cell. In the simple c... | {
"Header 1": "**6.5 Optical Tweezers**",
"Header 2": "**6.7 Molecular Dynamics**",
"token_count": 2032,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
and Block, S. M., (1994). Biological applications of optical forces. *A nn. Rev. Biophys. Biomol. Struct.* **23**, 247β285.
#### *Patch clamp*
- Neher, E. and Sakmann, B., (1976). Single-channel currents recorded from membrane of denervated frog muscle fibres. *Nature* **260**, 779β802.
- Hamill, O. P. *et al.*, (1... | {
"Header 1": "**6.5 Optical Tweezers**",
"Header 2": "**6.7 Molecular Dynamics**",
"token_count": 741,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
The word polymer is, appropriately, a composite of the Greek word *poly*, which means many, and another Greek word *meros*, which means parts. The choice of this name stems from what has been found to be the defining characteristic of a polymer: it is a composite structure based on consolidation of many smaller units (... | {
"Header 1": "**7 Biological Polymers**",
"token_count": 526,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
The importance of nucleic acids to heredity emerged only gradually. Gregor Mendel's discoveries in 1865, based on his observations on the breeding of peas, were followed 20 years later by August Weismann's hypothesis that the number of chromosomes must be constant. There is not a simple relationship between the number ... | {
"Header 1": "**7 Biological Polymers**",
"Header 2": "**7.1 Nucleic Acids**",
"token_count": 2033,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
The upper left-hand diagram shows the molecule unwound and with the bases rotated into plan view. Thymine pairs only with adenine, and cytosine only with guanine, such base pairings producing rungs of equal length. The backbones are twisted into a double helix, as indicated in the original Watson-Crick diagram (upper r... | {
"Header 1": "**7 Biological Polymers**",
"Header 2": "**7.1 Nucleic Acids**",
"token_count": 527,
"source_pdf": "datasets/websources/biochem/Introduction_of_Biophysics.pdf"
} |
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