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Isobutyronitrile is a complex organic molecule that has recently been found in several meteorites arrived from space. The singularity of this chemical is due to the fact that it is the only one among the molecules arriving from the universe that has a branched, rather than straight, carbon backbone. The backbone is also larger than usual, in comparison with others.
Both isobutyronitrile and its straight-chain isomer, Butyronitrile , were detected by astronomers from Cornell University , the Max Planck Institute for Radio Astronomy and the University of Cologne by means of using the Atacama Large Millimeter/submillimeter Array (ALMA) [ 3 ] — a set of radiotelescopes in Chile. The chemical was found within an immense gas cloud in the star-forming region called Sagittarius B2 . This interstellar space is located at about 300 light years away from the Galactic Center Sgr A* . [ 4 ] and about 27,000 light years from Earth . [ 5 ]
About 50 individual features for isobutyronitrile and 120 for normal propyl cyanide (n-propyl cyanide) were identified in the ALMA spectrum of the Sagittarius B2 region. The published astrochemical model indicates that both isomers are produced within or upon dust grain ice mantles through the addition of molecular radicals , albeit via differing reaction pathways.
Scientists have come to the conclusion that isobutyronitrile could have been essential for the creation of primary life. The discovery of this particular cyanide suggests that the complex molecules needed for life may have their origins in interstellar space . Those molecules would have been rising during the process of early star formation and been transferred to our planet later. [ 6 ]
According to Rob Garrod, this detection opens a new frontier in the field regarding the complexity of molecules that can be formed in interstellar space and that might ultimately find their way to the surfaces of planets. How widespread these complex organic molecules really are in our Galaxy is one of the questions raised by this new discovery.
Isobutyronitrile (C 3 H 7 CN) contains a carbon atom bounded by a simple link to two methyl (-CH 3 ) structures and to a cyano group (–CN). The cyano group is constituted by a triple link bond between one carbon and one nitrogen atom.
The greatest contribution to the production of i-PrCN comes from the reaction of CN radicals (which are accreted from the gas) with the CH3CHCH3 radical, whereas the dominant formation mechanism for n-PrCN is the addition of C2H5 and CH2CN, a process that has no equivalent for the production of i-PrCN.
i-PrCN production dominates all reaction mechanisms for which parallel processes are available to both isomers.It is also the most complex shaped molecule in the history. [ 7 ]
The rotational spectrum of the branched isomer iso- or i-PrCN, which had only been previously studied to a limited extent in the microwave region , has recently been extensively recorded in the laboratory from the microwave to the submillimeter wave region along with a redetermination of the dipole moment , which appears to be 4.29 D.
The latter uncertainty assumes the same source size and rotation temperature for both isomers.
Scientists were able to observe transitions in both types of cyanides. Thus, the microwave spectrum of the isobutyronitrile has been recorded from 26.5 to 40.0 GHz. Three different excited states were found in the R-branch of i-PrCN. In the experiments carried out by the scientists, different parameters were studied: The bond distance between the different atoms and the angles between them. The results indicated that the bond distance between de carbon atom and the cyano group is 1.501 Å; the angle between the three carbon atoms is 113º while the angle between the CCC and the CN bond is 53.8º. Two different torsional modes were observed, according to the relative intensities of the excited state lines, the frequencies of which were, respectively, 200±20 and 249±10 cm −1 . This could give an idea of the internal rotation energy of this molecule, which has been found to be of 3.3 Kcal/mole. [ 8 ]
The branched carbon structure of isobutyronitrile is a common feature in those molecules that are considered to be necessary for life – such as amino acids , which are the building blocks of proteins . This new discovery lends weight to the idea that biologically crucial molecules, like the mentioned amino acids which are also commonly found in meteorites , were produced even before the process of star formation or before planets such as the Earth were formed.
The importance of the cyanides found in comets remains in their C-N bond . This bond has been proved to participate in the abiotic amino acid synthesis.
The two cyanide molecules – isobutyronitrile and n-butyronitrile – are the largest molecules yet detected in any star-forming region.
Some more specific properties are:
Chemically speaking, the simple inorganic cyanides behave as chlorides in many ways. Organic nitriles act as solvents and are reacted further for various applications such as: [ 10 ] Working as an extraction solvent for fatty acids, oils and unsaturated hydrocarbons . They are also good solvents for spinning and casting and extractive distillation based on its selective miscibility with organic compounds and can act as removing agents of colouring matters and aromatic alcohols. Inorganic cyanides are also able to perform a recrystallization of steroids or to be compounds for organic synthesis. Therefore, they basically act as solvents or chemical intermediates in biochemistry (pesticide sequencing and DNA synthesis, for example).
Some other useful applications of these organic nitriles are the performance of high-pressure liquid chromatographic analysis . Also, the action they have as catalysts and components of transition-metal complex catalysts, stabilizers for chlorinated solvents. Furthermore, they may work as chemical intermediates and solvents for perfumes and pharmaceutical products.
[ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/Isobutyronitrile |
Isobutyryl chloride ( 2-methylpropanoyl chloride ) is the organic compound with the formula (CH 3 ) 2 CHCOCl . A colorless liquid, it the simplest branched-chain acyl chloride . It is prepared by chlorination of isobutyric acid. [ 2 ]
As an ordinary acid chloride, isobutyryl chloride is the subject of many reported transformations. Dehydrohalogenation of isobutyryl chloride with triethylamine gives 2,2,4,4-tetramethylcyclobutanedione . [ 3 ] Treatment of isobutyryl chloride with hydrogen fluoride gives the acid fluoride. [ 4 ]
This article about an organic compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isobutyryl_chloride |
In genetics, an isochore is a large region of genomic DNA (greater than 300 kilobases ) with a high degree of uniformity in GC content ; that is, guanine (G) and cytosine (C) bases. The distribution of bases within a genome is non-random: different regions of the genome have different amounts of G-C base pairs, such that regions can be classified and identified by the proportion of G-C base pairs they contain.
Bernardi and colleagues first noticed the compositional non-uniformity of vertebrate genomes using thermal melting and density gradient centrifugation . [ 1 ] [ 2 ] [ 3 ] The DNA fragments extracted by the gradient centrifugation were later termed "isochores", [ 4 ] which was subsequently defined as "very long (much greater than 200 KB) DNA segments" that "are fairly homogeneous in base composition and belong to a small number of major classes distinguished by differences in guanine-cytosine (GC) content". [ 3 ] Subsequently, the isochores "grew" and were claimed to be ">300 kb in size." [ 5 ] [ 6 ] The theory proposed that the isochore composition of genomes varies markedly between "warm-blooded" ( homeotherm ) vertebrates and "cold-blooded" ( poikilotherm ) vertebrates [ 3 ] and later became known as the isochore theory.
The isochore theory purported that the genome of "warm-blooded" vertebrates (mammals and birds) are mosaics of long isochoric regions of alternating GC-poor and GC-rich composition, as opposed to the genome of "cold-blooded" vertebrates (fishes and amphibians) that were supposed to lack GC-rich isochores. [ 3 ] [ 7 ] [ 8 ] [ 9 ] [ 10 ] [ 11 ] These findings were explained by the thermodynamic stability hypothesis, attributing genomic structure to body temperature. GC-rich isochores were purported to be a form of adaptation to environmental pressures, as an increase in genomic GC-content could protect DNA, RNA, and proteins from degradation by heat. [ 3 ] [ 4 ] Despite its attractive simplicity, the thermodynamic stability hypothesis has been repeatedly shown to be in error [ 12 ] [ 13 ] [ 14 ] . [ 15 ] [ 16 ] [ 17 ] [ 18 ] [ 19 ] Many authors showed the absence of a relationship between temperature and GC-content in vertebrates, [ 17 ] [ 18 ] while others showed the existence of GC-rich domains in "cold-blooded" vertebrates such as crocodiles, amphibians, and fish. [ 14 ] [ 20 ] [ 21 ] [ 22 ]
The isochore theory was the first to identify the nonuniformity of nucleotide composition within vertebrate genomes and predict that the genome of "warm-blooded" vertebrates such as mammals and birds are mosaic of isochores (Bernardi et al. 1985). The human genome, for example, was described as a mosaic of alternating low and high GC content isochores belonging to five compositional families, L1, L2, H1, H2, and H3, whose corresponding ranges of GC contents were said to be <38%, 38%-42%, 42%-47%, 47%-52%, and >52%, respectively. [ 23 ]
The main predictions of the isochore theory are that:
Two opposite explanations that endeavored to explain the formations of isochores were vigorously debated as part of the neutralist-selectionist controversy. The first view was that isochores reflect variable mutation processes among genomic regions consistent with the neutral model. [ 26 ] [ 27 ] Alternatively, isochores were posited as a result of natural selection for certain compositional environment required by certain genes. [ 28 ] Several hypotheses derive from the selectionist view, such as the thermodynamic stability hypothesis [ 6 ] [ 29 ] and the biased gene conversion hypothesis. [ 27 ] Thus far, none of the theories provides a comprehensive explanation to the genome structure, and the topic is still under debate.
The isochore theory became one of the most useful theories in molecular evolution for many years. It was the first and most comprehensive attempt to explain the long-range compositional heterogeneity of vertebrate genomes within an evolutionary framework. Despite the interest in the early years in the isochore model, in recent years, the theory’s methodology, terminology, and predictions have been challenged.
Because this theory was proposed in the 20th century before complete genomes were sequenced, it could not be fully tested for nearly 30 years. In the beginning of the 21st century, when the first genomes were made available it was clear that isochores do not exist in the human genome [ 30 ] nor in other mammalian genomes. [ 31 ] When failed to find isochores, many attacked the very existence of isochores. [ 30 ] [ 32 ] [ 33 ] [ 34 ] [ 35 ] The most important predictor of isochores, GC3 was shown to have no predictable power [ 36 ] [ 37 ] to the GC content of nearby genomic regions, refuting findings from over 30 years of research, which were the basis for many isochore studies. Isochore-originators replied that the term was misinterpreted [ 23 ] [ 38 ] [ 39 ] as isochores are not "homogeneous" but rather fairly homogeneous regions with a heterogeneous nature (especially) of GC-rich regions at the 5 kb scale , [ 40 ] which only added to the already growing confusion. The reason for this ongoing frustration was the ambiguous definition of isochores as long and homogeneous , allowed some researchers to discover "isochores" and others to dismiss them, although both camps used the same data.
The unfortunate side effect of this controversy was an "arms race" in which isochores are frequently redefined and relabeled following conflicting findings that failed to reveal "mosaic of isochores." [ 23 ] [ 32 ] [ 34 ] The unfortunate outcomes of this controversy and the following terminological-methodological mud were the loss of interest in isochores by the scientific community. When the most important core-concept in isochoric literature, the thermodynamic stability hypothesis, was rejected, the theory lost its appeal. Even today, there is no clear definition to isochores nor is there an algorithm that detects isochores. [ 41 ] Isochores are detected manually by visual inspection of GC content curves , [ 42 ] however because this approach lacks scientific merit and is difficult to replicate by independent groups, the findings remain disputed.
As the study of isochores was de facto abandoned by most scientists, an alternative theory was proposed to describe the compositional organization of genomes in accordance with the most recent genomic studies. The Compositional Domain Model depicts genomes as a medley of short and long homogeneous and nonhomogeneous domains. [ 35 ] The theory defines "compositional domains" as genomic regions with distinct GC-contents as determined by a computational segmentation algorithm. [ 35 ] The homogeneity of compositional domains is compared to that of the chromosome on which they reside using the F-test, which separated them into compositionally homogeneous domains and compositionally nonhomogeneous domains based on the outcome of test. Compositionally homogeneous domains that are sufficiently long (≥ 300 kb) are termed isochores or isochoric domains. These terms are in accordance with the literature as they provide clear distinction between isochoric- and nonisochoric-domains.
A comprehensive study of the human genome unraveled a genomic organization where two-thirds of the genome is a mixture of many short compositionally homogeneous domains and relatively few long ones. The remaining portion of the genome is composed of nonhomogeneous domains. In terms of coverage, only 1% of the total number of compositionally homogeneous domains could be considered "isochores" which covered less than 20% of the genome. [ 35 ]
Since its inception the theory received wide attention and was extensively used to explain findings emerging from over dozen new genome sequencing studies. [ 31 ] [ 43 ] [ 44 ] [ 45 ] [ 46 ] [ 47 ] [ 48 ] [ 49 ] [ 50 ] However, many important questions remain open, such as which evolutionary forces shaped the structure of compositional domains and the ways they differ between different species. | https://en.wikipedia.org/wiki/Isochore_(genetics) |
In the mathematical theory of dynamical systems , an isochron is a set of initial conditions for the system that all lead to the same long-term behaviour. [ 1 ] [ 2 ]
Consider the ordinary differential equation for a solution y ( t ) {\displaystyle y(t)} evolving in time:
This ordinary differential equation (ODE) needs two initial conditions at, say, time t = 0 {\displaystyle t=0} . Denote the initial conditions by y ( 0 ) = y 0 {\displaystyle y(0)=y_{0}} and d y / d t ( 0 ) = y 0 ′ {\displaystyle dy/dt(0)=y'_{0}} where y 0 {\displaystyle y_{0}} and y 0 ′ {\displaystyle y'_{0}} are some parameters. The following argument shows that the isochrons for this system are here the straight lines y 0 + y 0 ′ = constant {\displaystyle y_{0}+y'_{0}={\mbox{constant}}} .
The general solution of the above ODE is
Now, as time increases, t → ∞ {\displaystyle t\to \infty } , the exponential terms decays very quickly to zero ( exponential decay ). Thus all solutions of the ODE quickly approach y → t + A {\displaystyle y\to t+A} . That is, all solutions with the same A {\displaystyle A} have the same long term evolution. The exponential decay of the B exp ( − t ) {\displaystyle B\exp(-t)} term brings together a host of solutions to share the same long term evolution. Find the isochrons by answering which initial conditions have the same A {\displaystyle A} .
At the initial time t = 0 {\displaystyle t=0} we have y 0 = A + B {\displaystyle y_{0}=A+B} and y 0 ′ = 1 − B {\displaystyle y'_{0}=1-B} . Algebraically eliminate the immaterial constant B {\displaystyle B} from these two equations to deduce that all initial conditions y 0 + y 0 ′ = 1 + A {\displaystyle y_{0}+y'_{0}=1+A} have the same A {\displaystyle A} , hence the same long term evolution, and hence form an isochron.
Let's turn to a more interesting application of the notion of isochrons. Isochrons arise when trying to forecast predictions from models of dynamical systems. Consider the toy system of two coupled ordinary differential equations
A marvellous mathematical trick is the normal form (mathematics) transformation. [ 3 ] Here the coordinate transformation near the origin
to new variables ( X , Y ) {\displaystyle (X,Y)} transforms the dynamics to the separated form
Hence, near the origin, Y {\displaystyle Y} decays to zero exponentially quickly as its equation is d Y / d t = ( negative ) Y {\displaystyle dY/dt=({\text{negative}})Y} . So the long term evolution is determined solely by X {\displaystyle X} : the X {\displaystyle X} equation is the model.
Let us use the X {\displaystyle X} equation to predict the future. Given some initial values ( x 0 , y 0 ) {\displaystyle (x_{0},y_{0})} of the original variables: what initial value should we use for X ( 0 ) {\displaystyle X(0)} ? Answer: the X 0 {\displaystyle X_{0}} that has the same long term evolution. In the normal form above, X {\displaystyle X} evolves independently of Y {\displaystyle Y} . So all initial conditions with the same X {\displaystyle X} , but different Y {\displaystyle Y} , have the same long term evolution. Fix X {\displaystyle X} and vary Y {\displaystyle Y} gives the curving isochrons in the ( x , y ) {\displaystyle (x,y)} plane. For example, very near the origin the isochrons of the above system are approximately the lines x − X y = X − X 3 {\displaystyle x-Xy=X-X^{3}} . Find which isochron the initial values ( x 0 , y 0 ) {\displaystyle (x_{0},y_{0})} lie on: that isochron is characterised by some X 0 {\displaystyle X_{0}} ; the initial condition that gives the correct forecast from the model for all time is then X ( 0 ) = X 0 {\displaystyle X(0)=X_{0}} .
You may find such normal form transformations for relatively simple systems of ordinary differential equations, both deterministic and stochastic, via an interactive web site. [1] | https://en.wikipedia.org/wiki/Isochron |
In telecommunications , an isochronous signal is a signal in which the time interval separating any two significant instants is equal to the unit interval or a multiple of the unit interval. Variations in the time intervals are constrained within specified limits.
" Isochronous " is a characteristic of one signal, while " synchronous " indicates a relationship between two or more signals.
This article incorporates public domain material from Federal Standard 1037C . General Services Administration . Archived from the original on 2022-01-22. (in support of MIL-STD-188 ).
This article related to telecommunications is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isochronous_signal |
In organic chemistry , isocyanate is the functional group with the formula R−N=C=O . Organic compounds that contain an isocyanate group are referred to as isocyanates . An organic compound with two isocyanate groups is known as a diisocyanate. Diisocyanates are manufactured for the production of polyurethanes , a class of polymers . [ 1 ] [ 2 ] [ page needed ] [ 3 ] [ page needed ]
Isocyanates should not be confused with cyanate esters and isocyanides , very different families of compounds. The cyanate (cyanate ester) functional group ( R−O−C≡N ) is arranged differently from the isocyanate group ( R−N=C=O ). Isocyanides have the connectivity R−N≡C , lacking the oxygen of the cyanate groups.
In terms of bonding, isocyanates are closely related to carbon dioxide (CO 2 ) and carbodiimides (C(NR) 2 ). The C−N=C=O unit that defines isocyanates is planar, and the N=C=O linkage is nearly linear. In phenyl isocyanate , the C=N and C=O distances are respectively 1.195 and 1.173 Å . The C−N=C angle is 134.9° and the N=C=O angle is 173.1°. [ 4 ]
Isocyanates are usually produced from amines by phosgenation , i.e. treating with phosgene :
These reactions proceed via the intermediacy of a carbamoyl chloride ( RNHC(O)Cl ). Owing to the hazardous nature of phosgene, the production of isocyanates requires special precautions. [ 1 ] A laboratory-safe variation masks the phosgene as oxalyl chloride . [ 5 ] Also, oxalyl chloride can be used to form acyl isocyanates from primary amides , which phosgene typically dehydrates to nitriles instead. [ 6 ]
Another route to isocyanates entails addition of isocyanic acid to alkenes. Complementarily, alkyl isocyanates form by displacement reactions involving alkyl halides and alkali metal cyanates. [ 7 ]
Aryl isocyanates can be synthesized from reductive carbonylation of nitro- and nitrosoarenes ; a palladium catalyst is necessary to avoid side-reactions of the nitrene intermediate. [ 8 ] [ 9 ]
Three rearrangement reactions involving nitrenes give isocyanates:
An isocyanate is also the immediate product of the Hofmann rearrangement , but typically hydrolyzes under reaction conditions. [ 10 ]
Isocyanates are electrophiles , and as such they are reactive toward a variety of nucleophiles including alcohols , amines , and even water having a higher reactivity compared to structurally analogous isothiocyanates . [ 11 ]
Upon treatment with an alcohol, an isocyanate forms a urethane linkage:
where R and R' are alkyl or aryl groups.
If a diisocyanate is treated with a compound containing two or more hydroxyl groups, such as a diol or a polyol , polymer chains are formed, which are known as polyurethanes .
Isocyanates react with water to form carbon dioxide :
This reaction is exploited in tandem with the production of polyurethane to give polyurethane foams. The carbon dioxide functions as a blowing agent . [ 12 ]
Isocyanates also react with amines to give ureas :
The addition of an isocyanate to a urea gives a biuret :
Reaction between a di-isocyanate and a compound containing two or more amine groups produces long polymer chains known as polyureas .
Carbodiimides are produced by the decarboxylation of alkyl and aryl isocyanate using phosphine oxides as a catalyst: [ 13 ]
Isocyanates also can react with themselves. Aliphatic diisocyanates can trimerise to from substituted isocyanuric acid groups. This can be seen in the formation of polyisocyanurate resins (PIR) which are commonly used as rigid thermal insulation . Isocyanates participate in Diels–Alder reactions , functioning as dienophiles .
Isocyanates are common intermediates in the synthesis of primary amines via hydrolysis :
The global market for diisocyanates in the year 2000 was 4.4 million tonnes, of which 61.3% was methylene diphenyl diisocyanate (MDI), 34.1% was toluene diisocyanate (TDI), 3.4% was the total for hexamethylene diisocyanate (HDI) and isophorone diisocyanate (IPDI), and 1.2% was the total for various others. [ 18 ] A monofunctional isocyanate of industrial significance is methyl isocyanate (MIC), which is used in the manufacture of pesticides.
MDI is commonly used in the manufacture of rigid foams and surface coating. [ 1 ] Polyurethane foam boards are used in construction for insulation. TDI is commonly used in applications where flexible foams are used, such as furniture and bedding. Both MDI and TDI are used in the making of adhesives and sealants due to weather-resistant properties. Isocyanates, both MDI and TDI are widely used in as spraying applications of insulation due to the speed and flexibility of applications. Foams can be sprayed into structures and harden in place or retain some flexibility as required by the application. [ 19 ] HDI is commonly utilized in high-performance surface-coating applications, including automotive paints.
The risks of isocyanates was brought to the world's attention with the 1984 Bhopal disaster , which caused the death of nearly 4000 people from the accidental release of methyl isocyanate . In 2008, the same chemical was involved in an explosion at a pesticide manufacturing plant in West Virginia. [ 20 ]
LD50s for isocyanates are typically several hundred milligrams per kilogram. [ 21 ] Despite this low acute toxicity, an extremely low short-term exposure limit (STEL) of 0.07 mg/m 3 is the legal limit for all isocyanates (except methyl isocyanate: 0.02 mg/m 3 ) in the United Kingdom. [ 22 ] These limits are set to protect workers from chronic health effects such as occupational asthma , contact dermatitis , or irritation of the respiratory tract. [ 23 ]
Since they are used in spraying applications, the properties of their aerosols have attracted attention. [ 24 ] [ 25 ] In the U.S., OSHA conducted a National Emphasis Program on isocyanates starting in 2013 to make employers and workers more aware of the health risks. [ 26 ] Polyurethanes have variable curing times, and the presence of free isocyanates in foams vary accordingly. [ 27 ]
Both the US National Toxicology Program (NTP) and International Agency for Research on Cancer (IARC) have evaluated TDI as a potential human carcinogen and Group 2B "possibly carcinogenic to humans". [ 28 ] [ 29 ] MDI appears to be relatively safer and is unlikely a human carcinogen. [ 29 ] The IARC evaluates MDI as Group 3 "not classifiable as to its carcinogenicity in humans". [ 30 ]
All major producers of MDI and TDI are members of the International Isocyanate Institute, which promotes the safe handling of MDI and TDI.
Isocyanates can present respiratory hazards as particulates, vapors or aerosols. Autobody shop workers are a very commonly examined population for isocyanate exposure as they are repeatedly exposed when spray painting automobiles [ 31 ] and can be exposed when installing truck bed liners. [ 32 ] [ 33 ] Hypersensitivity pneumonitis has slower onset and features chronic inflammation that can be seen on imaging of the lungs. Occupational asthma is a worrisome outcome of respiratory sensitization to isocyanates as it can be acutely fatal. [ 34 ] Diagnosis of occupational asthma is generally performed using pulmonary function testing (PFT) and performed by pulmonology or occupational medicine physicians. [ 35 ] Occupational asthma is much like asthma in that it causes episodic shortness of breath and wheezing. Both the dose and duration of exposure to isocyanates can lead to respiratory sensitization. [ 36 ] Dermal exposures to isocyanates can sensitize an exposed person to respiratory disease.
Dermal exposures can occur via mixing, spraying coatings or applying and spreading coatings manually. Dermal exposures to isocyanates is known to lead to respiratory sensitization. [ 37 ] Even when the right personal protective equipment (PPE) is used, exposures can occur to body areas not completely covered. [ 38 ] Isocyanates can also permeate improper PPE, necessitating frequent changes of both disposable gloves and suits if they become over exposed.
Methyl isocyanate (MIC) is highly flammable. [ 39 ] MDI and TDI are much less flammable. [ 40 ] Flammability of materials is a consideration in furniture design. [ 41 ] The specific flammability hazard is noted on the safety data sheet (SDS) for specific isocyanates.
Industrial science attempts to minimize the hazards of isocyanates through multiple techniques. The EPA has sponsored ongoing research on polyurethane production without isocyanates. [ 42 ] [ 43 ] Where isocyanates are unavoidable but interchangeable, substituting a less hazardous isocyanate may control hazards. Ventilation and automation can also minimizes worker exposure to the isocyanates used. [ 24 ] [ 44 ]
If human workers must enter isocyanate-contaminated regions, personal protective equipment (PPE) can reduce their intake. In general, workers wear eye protection [ 44 ] and gloves and coveralls to reduce dermal exposure [ 45 ] [ 46 ] [ 25 ] [ 47 ] For some autobody paint and clear-coat spraying applications, a full-face mask is required. [ 31 ] [ 32 ]
The US Occupational Safety and Health Administration (OSHA) requires frequent training to ensure isocyanate hazards are appropriately minimized. [ 48 ] Moreover, OSHA requires standardized isocyanate concentration measurements to avoid violating occupational exposure limits . In the case of MDI, OSHA expects sampling with glass-fiber filters at standard air flow rates, and then liquid chromatography. [ 49 ]
Combined industrial hygiene and medical surveillance can significantly reduce occupational asthma incidence. [ 50 ] Biological tests exist to identify isocyanate exposure; [ 51 ] the US Navy uses regular pulmonary function testing and screening questionnaires. [ 52 ]
Emergency management is a complex process of preparation and should be considered in a setting where a release of bulk chemicals may threaten the well-being of the public. In the Bhopal disaster , an uncontrolled MIC release killed thousands, affected hundreds of thousands more, and spurred the development of modern disaster preparation. [ 53 ]
Exposure limits can be expressed as ceiling limits, a maximal value, short-term exposure limits (STEL), a 15-minute exposure limit or an 8-hour time-weighted average limit (TWA). Below is a sampling, not exhaustive, as less common isocyanates also have specific limits within the United States, and in some regions there are limits on total isocyanate, which recognizes some of the uncertainty regarding the safety of mixtures of chemicals as compared to pure chemical exposures. For example, while there is no OEL for HDI, NIOSH has a REL of 5 ppb for an 8-hour TWA and a ceiling limit of 20 ppb, consistent with the recommendations for MDI. [ 54 ]
The Occupational Safety and Health Administration (OSHA) is the regulatory body covering worker safety. OSHA puts forth permissible exposure limit (PEL) 20 ppb for MDI and detailed technical guidance on exposure assessment. [ 52 ]
The National Institutes of Health ( NIOSH ) is the agency responsible for providing the research and recommendations regarding workplace safety, while OSHA is more of an enforcement body. NIOSH is responsible for producing the science that can result in recommended exposure limits (REL), which can be lower than the PEL. OSHA is tasked with enforcement and defending the enforceable limits (PELs). In 1992, when OSHA reduced the PEL for TDI to the NIOSH REL, the PEL reduction was challenged in court, and the reduction was reversed. [ 61 ]
The Environmental Protection Agency ( EPA ) is also involved in the regulation of isocyanates with regard to the environment and also non-worker persons that might be exposed. [ 62 ]
The American Conference of Governmental Industrial Hygienists (ACGIH) is a non-government organization that publishes guidance known as threshold limit values (TLV) [ 61 ] for chemicals based research as constant work exposure level without ill-effect [ clarify ] . The TLV is not an OSHA-enforceable value, unless the PEL is the same.
The European Chemicals Agency (ECHA) provides regulatory oversight of chemicals used within the European Union. [ 63 ] ECHA has been implementing policy aimed at limiting worker exposure through elimination by lower allowable concentrations in products and mandatory worker training, an administrative control. [ 64 ] Within the European Union, many nations set their own occupational exposure limits for isocyanates.
The United Nations , through the World Health Organization (WHO) together with the International Labour Organization (ILO) and United Nations Environment Programme (UNEP), collaborate on the International Programme on Chemical Safety (IPCS) to publish summary documents on chemicals. The IPCS published one such document in 2000 summarizing the status of scientific knowledge on MDI. [ 65 ]
The IARC evaluates the hazard data on chemicals and assigns a rating on the risk of carcinogenesis. In the case of TDI, the final evaluation is possibly carcinogenic to humans (Group 2B). [ 66 ] For MDI, the final evaluation is not classifiable as to its carcinogenicity to humans (Group 3). [ 67 ]
The International Isocyanate Institute is an international industry consortium that seeks promote the safe utilization of isocyanates by promulgating best practices. [ 68 ] | https://en.wikipedia.org/wiki/Isocyanate |
An isocyanide (also called isonitrile or carbylamine ) is an organic compound with the functional group – N + ≡C − . It is the isomer of the related nitrile (–C≡N), hence the prefix is isocyano . [ 1 ] The organic fragment is connected to the isocyanide group through the nitrogen atom, not via the carbon . They are used as building blocks for the synthesis of other compounds. [ 2 ]
The C-N distance in isocyanides is 115.8 pm in methyl isocyanide . The C-N-C angles are near 180°. [ 3 ]
Akin to carbon monoxide , isocyanides are described by two resonance structures , one with a triple bond between the nitrogen and the carbon and one with a double bond between. The π lone pair of the nitrogen stabilizes the structure and is responsible of the linearity of isocyanides, although the reactivity of isocyanides reflects some carbene character, at least in a formal sense. Thus, both resonance structures are useful representations. [ 4 ] They are susceptible to polymerization . [ 4 ]
Isocyanides exhibit a strong absorption in their IR spectra in the range of 2165–2110 cm −1 . [ 5 ]
The electronic symmetry about the isocyanide 14 N nucleus results in a slow quadrupolar relaxation so that 13 C- 14 N nuclear spin coupling can be observed, with coupling constants of ca. 5 Hz for the isocyanide 13 C nucleus and 5–14 Hz for the 13 C nucleus which the isocyanide group is attached to. [ 5 ]
Isocyanides have a very disagreeable odour. Lieke remarked that " Es besitzt einen penetranten, höchst unangenehmen Geruch; das Oeffnen eines Gefässes mit Cyanallyl [ sic ] reicht hin, die Luft eines Zimmers mehrere Tage lang zu verpesten [It has a penetrating, extremely unpleasant odour; the opening of a flask of allyl cyanide [ sic ] is enough to foul up the air in a room for several days]...." [ 6 ] : 319 Note that in Lieke's day, the difference between isocyanide and nitrile was not fully appreciated.
Ivar Karl Ugi states that "The development of the chemistry of isocyanides has probably suffered only little delay through the characteristic odor of volatile isonitriles, which has been described by Hofmann and Gautier as 'highly specific, almost overpowering', 'horrible', and 'extremely distressing'. It is true that many potential workers in this field have been turned away by the odour, but this is heavily outweighed by the fact that isonitriles can be detected even in traces, and that most of the routes leading to the formation of isonitriles were discovered through the odor of these compounds." [ 7 ] Isocyanides have been investigated as potential non-lethal weapons . [ 8 ]
Some isocyanides convey less offensive odours such as malt, natural rubber, creosote, cherry or old wood. [ 9 ] Non-volatile derivatives such as tosylmethyl isocyanide do not have an odor. [ 10 ]
While some isocyanides ( e.g., cyclohexyl isocyanide) are toxic, others "exhibit no appreciable toxicity for mammals". Referring to ethyl isocyanide, toxicological studies in the 1960s at Bayer showed that "oral and subcutaneous doses of 500-5000 mg/kg can be tolerated by mice". [ 7 ]
Many routes to isocyanides have been developed. [ 2 ]
Commonly, isocyanides are synthesized by dehydration of formamides . The formamide can be dehydrated with toluenesulfonyl chloride , phosphorus oxychloride , phosgene , diphosgene , or the Burgess reagent in the presence of a base such as pyridine or triethylamine. [ 11 ] [ 12 ] [ 13 ] [ 14 ]
The formamide precursors are, in turn, prepared from amines by formylation with formic acid or formyl acetyl anhydride, [ 15 ] or from the Ritter reaction of alkenes (and other sources of carbocations) and hydrogen cyanide . [ 16 ]
In the carbylamine reaction (also known as the Hofmann isocyanide synthesis) alkali base reacts with chloroform to produce dichlorocarbene . The carbene then converts primary amines to isocyanides. Illustrative is the synthesis of tert -butyl isocyanide from tert -butylamine in the presence of catalytic amount of the phase transfer catalyst benzyltriethylammonium chloride. [ 17 ]
As it is only effective for primary amines, this reaction can be used as a chemical test for their presence.
Of historical interest but not often of practical value, the first isocyanide, allyl isocyanide, was prepared by the reaction of allyl iodide and silver cyanide . [ 6 ]
Another route to isocyanides entails deprotonation of oxazoles and benzoxazoles in the 2-position. [ 9 ] The resulting organolithium compound exists in chemical equilibrium with the 2-isocyanophenolate , which can be captured by an electrophile such as an acid chloride .
In some cases, a phosphonite ester-amide can desulfurize thiocyanates to isocyanides. [ 18 ]
Isocyanides have diverse reactivity. [ 2 ]
Isocyanides are stable to strong base (they are often made under strongly basic conditions), but they are sensitive to acid. In the presence of aqueous acid, isocyanides hydrolyse to the corresponding formamides :
This reaction is used to destroy odorous isocyanide mixtures. Some isocyanides can polymerize in the presence of Lewis and Bronsted acids. [ 19 ]
Isocyanides participate in many multicomponent reactions of interest in organic synthesis , two of which are: the Ugi reaction and the Passerini reaction .
Isocyanides also participate in cycloaddition reactions, such as the [4+1] cycloaddition with tetrazines. [ 20 ] Depending on the degree of substitution of the isocyanide, this reaction converts isocyanides into carbonyls or gives stable cycloadducts. [ 21 ] They also undergo insertion into the C–Cl bonds of acyl chlorides in the Nef isocyanide reaction , a process that is believed to be concerted and illustrates their carbene character.
Isocyanides have also been shown to be a useful reagent in palladium catalysed reactions with a wide variety of compounds being formed using this method. [ 22 ]
Much like nitriles , isocyanides are electron-withdrawing and easily deprotonate at the α position. For example, benzyl isocyanide has a p K a of 27.4 and benzyl cyanide has a p K a of 21.9, but toluene has a p K a in the 40s. [ 23 ] In the gas phase, CH 3 NC is 1.8 kcal/mol less acidic than CH 3 CN . [ 24 ]
Chlorination of isocyanides gives isocyanide dichlorides .
Isocyanides form coordination complexes with most transition metals. [ 25 ] They behave as electron-rich analogues of carbon monoxide. For example tert-butyl isocyanide forms Fe 2 (tBuNC) 9 , which is analogous to Fe 2 (CO) 9 . [ 26 ] Although structurally similar, the analogous carbonyls differ in several ways, mainly because t -BuNC is a better donor ligand than CO. Thus, Fe(tBuNC) 5 is easily protonated, whereas its counterpart Fe(CO) 5 is not. [ 27 ]
Only few naturally occurring compounds exhibit the isocyanide functionality. The first was discovered in 1957 in an extract of the mold Penicillium notatum . The compound xanthocillin later was used as an antibiotic . Since then numerous other isocyanides have been isolated. Most of the marine isocyanides are terpenoid, while some of the terrestrial isocyanides originate from α-aminoacids. [ 28 ]
IUPAC uses the prefix "isocyano" for the systematic nomenclature of isocyanides: isocyanomethane , isocyanoethane, isocyanopropane, etc.
The sometimes used old term "carbylamine" conflicts with systematic nomenclature. An amine always has three single bonds, [ 29 ] whereas an isocyanide has only one single and one multiple bond.
The isocyanamide functional group consists of an amino group attached to an isocyano moiety. The isonitrile suffix or isocyano- prefix is used depending upon priority table. | https://en.wikipedia.org/wiki/Isocyanide |
Isocyanide dichlorides are organic compounds containing the RN=CCl 2 functional group . Classically they are obtained by chlorination of isocyanides . Phenylcarbylamine chloride is a well-characterized example.
Chlorination of organic isothiocyanates is also well established: [ 1 ]
Alkylisocyanates are chlorinated by phosphorus pentachloride :
Cyanogen chloride also chlorinates to give the isocyanide dichloride: [ 1 ]
Isocyanide dichlorides participate in Friedel-Crafts-like reactions , leading, after hydrolysis, to benzamides : | https://en.wikipedia.org/wiki/Isocyanide_dichloride |
An isodesmic reaction is a chemical reaction in which the type of chemical bonds broken in the reactant are the same as the type of bonds formed in the reaction product. This type of reaction is often used as a hypothetical reaction in thermochemistry .
An example of an isodesmic reaction is
Equation 1 describes the deprotonation of a methyl halide by a methyl anion . The energy change associated with this exothermic reaction which can be calculated in silico increases going from fluorine to chlorine to bromine and iodine making the CH 2 I − anion the most stable and least basic of all the halides. Although this reaction is isodesmic the energy change in this example also depends on the difference in bond energy of the C-X bond in the base and conjugate acid . In other cases, the difference may be due to steric strain . This difference is small in fluorine but large in iodine (in favor of the anion) and therefore the energy trend is as described despite the fact that C-F bonds are stronger than C-I bonds. [ 1 ]
The related term homodesmotic reaction also takes into account orbital hybridization and in addition there is no change in the number of carbon to hydrogen bonds. | https://en.wikipedia.org/wiki/Isodesmic_reaction |
Isodesmosine is a lysine derivative found in elastin . Isodesmosine is an isomeric pyridinium-based amino acid resulting from the condensation of four lysine residues between elastin proteins by lysyl-oxidase . These represent ideal biomarkers for monitoring elastin turnover because these special cross-links are only found in mature elastin in mammals. [ 1 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isodesmosine |
Nuclides (or nucleides , from nucleus , also known as nuclear species) are a class of atoms characterized by their number of protons , Z , their number of neutrons , N , and their nuclear energy state . [ 1 ]
The word nuclide was coined by the American nuclear physicist Truman P. Kohman in 1947. [ 2 ] [ 3 ] Kohman defined nuclide as a "species of atom characterized by the constitution of its nucleus" containing a certain number of neutrons and protons. The term thus originally focused on the nucleus.
A nuclide is a species of an atom with a specific number of protons and neutrons in the nucleus, for example carbon-13 with 6 protons and 7 neutrons. The nuclide concept (referring to individual nuclear species) emphasizes nuclear properties over chemical properties, while the isotope concept (grouping all atoms of each element) emphasizes chemical over nuclear. The neutron number has large effects on nuclear properties, but its effect on chemical reactions is negligible for most elements. Even in the case of the very lightest elements, where the ratio of neutron number to atomic number varies the most between isotopes, it usually has only a small effect, but it matters in some circumstances. For hydrogen, the lightest element, the isotope effect is large enough to affect biological systems strongly. In the case of helium, helium-4 obeys Bose–Einstein statistics , while helium-3 obeys Fermi–Dirac statistics . Since isotope is the older term, it is better known than nuclide , and is still occasionally used in contexts in which nuclide might be more appropriate, such as nuclear technology and nuclear medicine.
Although the words nuclide and isotope are often used interchangeably, being isotopes is actually only one relation between nuclides. The following table names some other relations.
A nuclide and its alpha decay product are isodiaphers. [ 4 ]
(Z 1 = N 2 and Z 2 = N 1 )
but with different energy states
A set of nuclides with equal proton number ( atomic number ), i.e., of the same chemical element but different neutron numbers , are called isotopes of the element. Particular nuclides are still often loosely called "isotopes", but the term "nuclide" is the correct one in general (i.e., when Z is not fixed). In similar manner, a set of nuclides with equal mass number A , but different atomic number , are called isobars (isobar = equal in weight), and isotones are nuclides of equal neutron number but different proton numbers. Likewise, nuclides with the same neutron excess ( N − Z ) are called isodiaphers. [ 4 ] The name isoto n e was derived from the name isoto p e to emphasize that in the first group of nuclides it is the number of neutrons (n) that is constant, whereas in the second the number of protons (p). [ 5 ]
See Isotope#Notation for an explanation of the notation used for different nuclide or isotope types.
Nuclear isomers are members of a set of nuclides with equal proton number and equal mass number (thus making them by definition the same isotope), but different states of excitation. An example is the two states of the single isotope 99 43 Tc shown among the decay schemes . Each of these two states (technetium-99m and technetium-99) qualifies as a different nuclide, illustrating one way that nuclides may differ from isotopes (an isotope may consist of several different nuclides of different excitation states).
The longest-lived non- ground state nuclear isomer is the nuclide tantalum-180m ( 180m 73 Ta ), which has a half-life in excess of 1,000 trillion years. This nuclide occurs primordially, and has never been observed to decay to the ground state. (In contrast, the ground state nuclide tantalum-180 does not occur primordially, since it decays with a half life of only 8 hours to 180 Hf (86%) or 180 W (14%).)
There are 251 nuclides in nature that have never been observed to decay. They occur among the 80 different elements that have one or more stable isotopes. See stable nuclide and primordial nuclide . Unstable nuclides are radioactive and are called radionuclides . Their decay products ('daughter' products) are called radiogenic nuclides .
Natural radionuclides may be conveniently subdivided into three types. [ 6 ] First, those whose half-lives t 1/2 are at least 2% as long as the age of the Earth (for practical purposes, these are difficult to detect with half-lives less than 10% of the age of the Earth) ( 4.6 × 10 9 years ). These are remnants of nucleosynthesis that occurred in stars before the formation of the Solar System . For example, the isotope 238 U (t 1/2 = 4.5 × 10 9 years ) of uranium is still fairly abundant in nature, but the shorter-lived isotope 235 U (t 1/2 = 0.7 × 10 9 years ) is 138 times rarer. About 34 of these nuclides have been discovered (see List of nuclides and Primordial nuclide for details).
The second group of radionuclides that exist naturally consists of radiogenic nuclides such as 226 Ra (t 1/2 = 1602 years ), an isotope of radium , which are formed by radioactive decay . They occur in the decay chains of primordial isotopes of uranium or thorium. Some of these nuclides are very short-lived, such as isotopes of francium . There exist about 51 of these daughter nuclides that have half-lives too short to be primordial, and which exist in nature solely due to decay from longer lived radioactive primordial nuclides.
The third group consists of nuclides that are continuously being made in another fashion that is not simple spontaneous radioactive decay (i.e., only one atom involved with no incoming particle) but instead involves a natural nuclear reaction . These occur when atoms react with natural neutrons (from cosmic rays, spontaneous fission , or other sources), or are bombarded directly with cosmic rays . The latter, if non-primordial, are called cosmogenic nuclides . Other types of natural nuclear reactions produce nuclides that are said to be nucleogenic nuclides.
An example of nuclides made by nuclear reactions, are cosmogenic 14 C ( radiocarbon ) that is made by cosmic ray bombardment of other elements, and nucleogenic 239 Pu which is still being created by neutron bombardment of natural 238 U as a result of natural fission in uranium ores. Cosmogenic nuclides may be either stable or radioactive. If they are stable, their existence must be deduced against a background of stable nuclides, since every known stable nuclide is present on Earth primordially.
Beyond the naturally occurring nuclides, more than 3000 radionuclides of varying half-lives have been artificially produced and characterized.
The known nuclides are shown in Table of nuclides . A list of primordial nuclides is given sorted by element, at List of elements by stability of isotopes . List of nuclides is sorted by half-life, for the 905 nuclides with half-lives longer than one hour.
This is a summary table [ 7 ] for the 905 nuclides with half-lives longer than one hour, given in list of nuclides . Note that numbers are not exact, and may change slightly in the future, if some "stable" nuclides are observed to be radioactive with very long half-lives.
Atomic nuclei other than hydrogen 1 1 H have protons and neutrons bound together by the residual strong force . Because protons are positively charged, they repel each other. Neutrons, which are electrically neutral, stabilize the nucleus in two ways. Their copresence pushes protons slightly apart, reducing the electrostatic repulsion between the protons, and they exert the attractive nuclear force on each other and on protons. For this reason, one or more neutrons are necessary for two or more protons to be bound into a nucleus. As the number of protons increases, so does the ratio of neutrons to protons necessary to ensure a stable nucleus (see graph). For example, although the neutron–proton ratio of 3 2 He is 1:2, the neutron–proton ratio of 238 92 U is greater than 3:2. A number of lighter elements have stable nuclides with the ratio 1:1 ( Z = N ). The nuclide 40 20 Ca (calcium-40) is observationally the heaviest stable nuclide with the same number of neutrons and protons. All stable nuclides heavier than calcium-40 contain more neutrons than protons.
The proton–neutron ratio is not the only factor affecting nuclear stability. It depends also on even or odd parity of its atomic number Z , neutron number N and, consequently, of their sum, the mass number A . Oddness of both Z and N tends to lower the nuclear binding energy , making odd nuclei, generally, less stable. This remarkable difference of nuclear binding energy between neighbouring nuclei, especially of odd- A isobars , has important consequences: unstable isotopes with a nonoptimal number of neutrons or protons decay by beta decay (including positron decay), electron capture or more exotic means, such as spontaneous fission and cluster decay .
The majority of stable nuclides are even-proton–even-neutron, where all numbers Z , N , and A are even. The odd- A stable nuclides are divided (roughly evenly) into odd-proton–even-neutron, and even-proton–odd-neutron nuclides. Odd-proton–odd-neutron nuclides (and nuclei) are the least common. | https://en.wikipedia.org/wiki/Isodiapher |
In organic chemistry , an isodiazene , also known by the incorrectly constructed (but commonly used) name 1,1-diazene or systematic name diazanylidene , [ 1 ] is an organic derivative of the parent isodiazene (H 2 N + =N – , also called 1,1-diimide) with general formula R 1 R 2 N + =N – . The functional group has two major resonance forms, a diazen-2-ium-1-ide form, and an aminonitrene form:
Although isodiazenes are formally isoelectronic with ketones and aldehydes , the reactivity of this exotic functional group is very different. They are generally prepared by oxidation of the hydrazine (R 2 N–NH 2 ), reduction of the 1,1-diazene oxide (R 2 N–N=O), 1,1-elimination of MX from R 2 N–NMX (M = Na, K; X = SO 2 Ar), or treatment of secondary amines with Angeli's salt , Na 2 N 2 O 3 , in the presence of acid. Isodiazenes participate in cycloaddition reactions with alkenes to generate N -aminoaziridines. In the absence of other reactants, they undergo reactions in which N 2 is eliminated to give an organic residue or residues through both concerted and nonconcerted pathways. Cyclic isodizenes in particular readily undergo cycloelimination and chelotropic elimination reactions. [ 2 ] Some of these reactions are believed to be concerted pericyclic processes , as evidenced by stereospecificity that is consistent with the conservation of orbital symmetry .
The absence of cyclobutane from the decomposition of the isodiazene derived from the saturated 5-membered azacycle is evidence against radical intermediates, and the process is also believed to be concerted and pericyclic.
Due to the facile elimination of N 2 , most isodiazenes can only be isolated in a matrix at cryogenic temperatures. [ 3 ] A small number of highly hindered derivatives with tertiary R groups (e.g., R 1 = R 2 = t- Bu, stable at –127 °C, decomposes at –90 °C; R 1 —R 2 = C(CH 3 ) 2 CH 2 CH 2 CH 2 (CH 3 ) 2 C, stable up to –78 °C) are isolable by preparation and chromatography or filtration at low temperature as red solutions. [ 4 ]
Isodiazenes have been observed to serve as ligands in transition metals complexes, including those of molybdenum and vanadium. [ 5 ] | https://en.wikipedia.org/wiki/Isodiazene |
In organic chemistry, isodiazomethane , also known as isocyanamide , aminoisonitrile , or systematically as isocyanoamine , [ 1 ] is the parent compound of a class of derivatives of general formula R 2 N–NC. It has the condensed formula H 2 N–N + ≡C – , making it an isomer of diazomethane . It is prepared by protonating an ethereal solution of lithiodiazomethane, LiCHN 2 , with aqueous NaH 2 PO 4 or NH 4 Cl. [ 2 ] The parent compound is only marginally stable at room temperature and is isolated by removal of solvent at –50 °C. [ 3 ] Derivatives are generally prepared by dehydration of the corresponding substituted formylhydrazine with COCl 2 and Et 3 N. [ 4 ]
Earlier, the compound was misidentified as the isomeric nitrilimine , HN – –N + ≡CH. However, this structure was disproven by 1 H NMR studies, which show a compound with a single signal at δ 6.40 ppm in (CD 3 CD 2 ) 2 O instead of two signals expected for nitrilimine. Moreover, an infrared band at 2140 cm −1 was assigned to the isocyano group. Transition metal complexes of isodiazomethane have been prepared. [ 5 ] In bulk form isodiazomethane is a liquid which decomposes when the temperature exceeds 15 °C. If it is heated to 40 °C, the substance explodes. [ 6 ] A solution of isodiazomethane in diethyl ether at –30 °C gradually isomerizes to diazomethane upon exposure to sodium hydroxide for 20 min. [ 4 ]
Microwave spectroscopy indicates that unlike diazomethane, isodiazomethane is not completely planar, with the amino nitrogen undergoing inversion. [ 7 ] An ab initio study indicated that there is some N–N double bond character in H 2 N–N≡C, although less so than in the N–C bond of H 2 N–C≡N. [ 8 ] Like other isocyanide derivatives and carbon monoxide , its primary resonance form carries a negative charge and lone pair on carbon, a comparatively rare situation for neutral molecules. A resonance form with zero formal charge on all atoms also has some importance; however, the carbon atom only has a sextet of electrons and is formally a carbene . | https://en.wikipedia.org/wiki/Isodiazomethane |
Isoelectric focusing ( IEF ), also known as electrofocusing , is a technique for separating different charged molecules by differences in their isoelectric point (pI). [ 1 ] [ 2 ] It is a type of zone electrophoresis usually performed on proteins in a gel that takes advantage of the fact that overall charge on the molecule of interest, i.e. the net charge density , is a function of the pH of its surroundings. [ 3 ]
IEF involves adding an ampholyte solution into immobilized pH gradient (IPG) gels. IPGs are the acrylamide gel matrix co-polymerized with the pH gradient, which result in completely stable gradients except the most alkaline (>12) pH values. The immobilized pH gradient is obtained by the continuous change in the ratio of immobilines . An immobiline is a weak acid or base defined by its pK value.
A protein that is in a pH region below its isoelectric point (pI) will be positively charged and so will migrate toward the cathode (negatively charged electrode). As it migrates through a gradient of increasing pH, however, the protein's overall charge will decrease until the protein reaches the pH region that corresponds to its pI. At this point it has no net charge and so migration ceases (as there is no electrical attraction toward either electrode). As a result, the proteins become focused into sharp stationary bands with each protein positioned at a point in the pH gradient corresponding to its pI. The technique is capable of extremely high resolution with proteins differing by a single charge being fractionated into separate bands.
Molecules to be focused are distributed over a medium that has a pH gradient (usually created by aliphatic ampholytes ). An electric current is passed through the medium, creating a "positive" anode and "negative" cathode end. Negatively charged molecules migrate through the pH gradient in the medium toward the "positive" end while positively charged molecules move toward the "negative" end. As a particle moves toward the pole opposite of its charge it moves through the changing pH gradient until it reaches a point in which the pH of that molecule's isoelectric point is reached. At this point the molecule no longer has a net electric charge (due to the protonation or deprotonation of the associated functional groups) and as such will not proceed any further within the gel. The gradient is established before adding the particles of interest by first subjecting a solution of small molecules such as polyampholytes with varying pI values to electrophoresis.
The method is applied particularly often in the study of proteins , which separate based on their relative content of acidic and basic residues , whose value is represented by the pI. Proteins are introduced into an immobilized pH gradient gel composed of polyacrylamide , starch , or agarose where a pH gradient has been established. Gels with large pores are usually used in this process to eliminate any "sieving" effects, or artifacts in the pI caused by differing migration rates for proteins of differing sizes. Isoelectric focusing can resolve proteins that differ in pI value by as little as 0.01. [ 4 ] Isoelectric focusing is the first step in two-dimensional gel electrophoresis , in which proteins are first separated by their pI value and then further separated by molecular weight through SDS-PAGE . Isoelectric focusing, on the other hand, is the only step in preparative native PAGE at constant pH. [ 5 ]
According to some opinions, [ 6 ] [ 7 ] living eukaryotic cells perform isoelectric focusing of proteins in their interior to overcome a limitation of the rate of metabolic reaction by diffusion of enzymes and their reactants, and to regulate the rate of particular biochemical processes. By concentrating the enzymes of particular metabolic pathways into distinct and small regions of its interior, the cell can increase the rate of particular biochemical pathways by several orders of magnitude. By modification of the isoelectric point (pI) of molecules of an enzyme by, e.g., phosphorylation or dephosphorylation, the cell can transfer molecules of the enzyme between different parts of its interior, to switch on or switch off particular biochemical processes.
Microchip based electrophoresis is a promising alternative to capillary electrophoresis since it has the potential to provide rapid protein analysis, straightforward integration with other microfluidic unit operations, whole channel detection, nitrocellulose films, smaller sample sizes and lower fabrication costs.
The increased demand for faster and easy-to-use protein separation tools has accelerated the evolution of IEF towards in-solution separations. In this context, a multi-junction IEF system was developed to perform fast and gel-free IEF separations. The multi-junction IEF system utilizes a series of vessels with a capillary passing through each vessel. [ 8 ] Part of the capillary in each vessel is replaced by a semipermeable membrane. The vessels contain buffer solutions with different pH values, so that a pH gradient is effectively established inside the capillary. The buffer solution in each vessel has an electrical contact with a voltage divider connected to a high-voltage power supply, which establishes an electrical field along the capillary. When a sample (a mixture of peptides or proteins) is injected in the capillary, the presence of the electrical field and the pH gradient separates these molecules according to their isoelectric points. The multi-junction IEF system has been used to separate tryptic peptide mixtures for two-dimensional proteomics [ 9 ] and blood plasma proteins from Alzheimer's disease patients for biomarker discovery. [ 8 ] | https://en.wikipedia.org/wiki/Isoelectric_focusing |
The isoelectric point ( pI , pH(I) , IEP ), is the pH at which a molecule carries no net electrical charge or is electrically neutral in the statistical mean . The standard nomenclature to represent the isoelectric point is pH(I). [ 1 ] However, pI is also used. [ 2 ] For brevity , this article uses pI. The net charge on the molecule is affected by pH of its surrounding environment and can become more positively or negatively charged due to the gain or loss, respectively, of protons (H + ).
Surfaces naturally charge to form a double layer . In the common case when the surface charge-determining ions are H + /HO − , the net surface charge is affected by the pH of the liquid in which the solid is submerged.
The pI value can affect the solubility of a molecule at a given pH. Such molecules have minimum solubility in water or salt solutions at the pH that corresponds to their pI and often precipitate out of solution . Biological amphoteric molecules such as proteins contain both acidic and basic functional groups . Amino acids that make up proteins may be positive, negative, neutral, or polar in nature, and together give a protein its overall charge. At a pH below their pI, proteins carry a net positive charge; above their pI they carry a net negative charge. Proteins can, thus, be separated by net charge in a polyacrylamide gel using either preparative native PAGE , which uses a constant pH to separate proteins, or isoelectric focusing , which uses a pH gradient to separate proteins. Isoelectric focusing is the first step in 2-D polyacrylamide gel electrophoresis . [ 3 ]
In biomolecules, proteins can be separated by ion exchange chromatography . Biological proteins are made up of zwitterionic amino acid compounds; the net charge of these proteins can be positive or negative depending on the pH of the environment. The specific pI of the target protein can be used to model the process around and the compound can then be purified from the rest of the mixture. Buffers of various pH can be used for this purification process to change the pH of the environment. When a mixture containing a target protein is loaded into an ion exchanger, the stationary matrix can be either positively-charged (for mobile anions) or negatively-charged (for mobile cations). At low pH values, the net charge of most proteins in the mixture is positive – in cation exchangers, these positively-charged proteins bind to the negatively-charged matrix. At high pH values, the net charge of most proteins is negative, where they bind to the positively-charged matrix in anion exchangers. When the environment is at a pH value equal to the protein's pI, the net charge is zero, and the protein is not bound to any exchanger, and therefore, can be eluted out. [ 4 ]
For an amino acid with only one amine and one carboxyl group, the pI can be calculated from the mean of the pKas of this molecule. [ 5 ]
The pH of an electrophoretic gel is determined by the buffer used for that gel. If the pH of the buffer is above the pI of the protein being run, the protein will migrate to the positive pole (negative charge is attracted to a positive pole). If the pH of the buffer is below the pI of the protein being run, the protein will migrate to the negative pole of the gel (positive charge is attracted to the negative pole). If the protein is run with a buffer pH that is equal to the pI, it will not migrate at all. This is also true for individual amino acids.
In the two examples (on the right) the isoelectric point is shown by the green vertical line. In glycine the pK values are separated by nearly 7 units. Thus in the gas phase, the concentration of the neutral species, glycine (GlyH), is effectively 100% of the analytical glycine concentration. [ 6 ] Glycine may exist as a zwitterion at the isoelectric point, but the equilibrium constant for the isomerization reaction in solution
is not known.
The other example, adenosine monophosphate is shown to illustrate the fact that a third species may, in principle, be involved. In fact the concentration of (AMP)H 2+ 3 is negligible at the isoelectric point in this case.
If the pI is greater than the pH, the molecule will have a positive charge.
A number of algorithms for estimating isoelectric points of peptides and proteins have been developed. Most of them use Henderson–Hasselbalch equation with different pK values. For instance, within the model proposed by Bjellqvist and co-workers, the pKs were determined between closely related immobilines by focusing the same sample in overlapping pH gradients. [ 7 ] Some improvements in the methodology (especially in the determination of the pK values for modified amino acids) have been also proposed. [ 8 ] [ 9 ] More advanced methods take into account the effect of adjacent amino acids ±3 residues away from a charged aspartic or glutamic acid , the effects on free C terminus, as well as they apply a correction term to the corresponding pK values using genetic algorithm . [ 10 ] Other recent approaches are based on a support vector machine algorithm [ 11 ] and pKa optimization against experimentally known protein/peptide isoelectric points. [ 12 ]
Moreover, experimentally measured isoelectric point of proteins were aggregated into the databases. [ 13 ] [ 14 ] Recently, a database of isoelectric points for all proteins predicted using most of the available methods had been also developed. [ 15 ]
In practice, a protein with an excess of basic aminoacids (arginine, lysine and/or histidine) will bear an isoelectric point roughly greater than 7 (basic), while a protein with an excess of acidic aminoacids (aspartic acid and/or glutamic acid) will often have an isoelectric point lower than 7 (acidic).
The electrophoretic linear (horizontal) separation of proteins by Ip along a pH gradient in a polyacrylamide gel (also known as isoelectric focusing ), followed by a standard molecular weight linear (vertical) separation in a second polyacrylamide gel ( SDS-PAGE ), constitutes the so called two-dimensional gel electrophoresis or PAGE 2D. This technique allows a thorough separation of proteins as distinct "spots", with proteins of high molecular weight and low Ip migrating to the upper-left part of the bidimensional gel, while proteins with low molecular weight and high Ip locate to the bottom-right region of the same gel.
The isoelectric points (IEP) of metal oxide ceramics are used extensively in material science in various aqueous processing steps (synthesis, modification, etc.). In the absence of chemisorbed or physisorbed species particle surfaces in aqueous suspension are generally assumed to be covered with surface hydroxyl species, M-OH (where M is a metal such as Al, Si, etc.). [ 16 ] At pH values above the IEP, the predominant surface species is M-O − , while at pH values below the IEP, M-OH 2 + species predominate. Some approximate values of common ceramics are listed below: [ 17 ] [ 18 ]
Note: The following list gives the isoelectric point at 25 °C for selected materials in water. The exact value can vary widely, depending on material factors such as purity and phase as well as physical parameters such as temperature. Moreover, the precise measurement of isoelectric points can be difficult, thus many sources often cite differing values for isoelectric points of these materials.
Mixed oxides may exhibit isoelectric point values that are intermediate to those of the corresponding pure oxides. For example, a synthetically prepared amorphous aluminosilicate (Al 2 O 3 -SiO 2 ) was initially measured as having IEP of 4.5 (the electrokinetic behavior of the surface was dominated by surface Si-OH species, thus explaining the relatively low IEP value). [ 26 ] Significantly higher IEP values (pH 6 to 8) have been reported for 3Al 2 O 3 -2SiO 2 by others. [ 23 ] Similarly, also IEP of barium titanate , BaTiO 3 was reported in the range 5–6 [ 23 ] while others got a value of 3. [ 27 ] Mixtures of titania (TiO 2 ) and zirconia (ZrO 2 ) were studied and found to have an isoelectric point between 5.3–6.9, varying non-linearly with %(ZrO 2 ). [ 28 ] The surface charge of the mixed oxides was correlated with acidity. Greater titania content led to increased Lewis acidity, whereas zirconia-rich oxides displayed Br::onsted acidity. The different types of acidities produced differences in ion adsorption rates and capacities.
The terms isoelectric point (IEP) and point of zero charge (PZC) are often used interchangeably, although under certain circumstances, it may be productive to make the distinction.
In systems in which H + /OH − are the interface potential-determining ions, the point of zero charge is given in terms of pH. The pH at which the surface exhibits a neutral net electrical charge is the point of zero charge at the surface. Electrokinetic phenomena generally measure zeta potential , and a zero zeta potential is interpreted as the point of zero net charge at the shear plane . This is termed the isoelectric point. [ 29 ] Thus, the isoelectric point is the value of pH at which the colloidal particle remains stationary in an electrical field. The isoelectric point is expected to be somewhat different from the point of zero charge at the particle surface, but this difference is often ignored in practice for so-called pristine surfaces, i.e., surfaces with no specifically adsorbed positive or negative charges. [ 16 ] In this context, specific adsorption is understood as adsorption occurring in a Stern layer or chemisorption . Thus, point of zero charge at the surface is taken as equal to isoelectric point in the absence of specific adsorption on that surface.
According to Jolivet, [ 20 ] in the absence of positive or negative charges, the surface is best described by the point of zero charge. If positive and negative charges are both present in equal amounts, then this is the isoelectric point. Thus, the PZC refers to the absence of any type of surface charge, while the IEP refers to a state of neutral net surface charge. The difference between the two, therefore, is the quantity of charged sites at the point of net zero charge. Jolivet uses the intrinsic surface equilibrium constants, p K − and p K + to define the two conditions in terms of the relative number of charged sites:
For large Δp K (>4 according to Jolivet), the predominant species is MOH while there are relatively few charged species – so the PZC is relevant. For small values of Δp K , there are many charged species in approximately equal numbers, so one speaks of the IEP. | https://en.wikipedia.org/wiki/Isoelectric_point |
Isoelectronicity is a phenomenon observed when two or more molecules have the same structure (positions and connectivities among atoms ) and the same electronic configurations , but differ by what specific elements are at certain locations in the structure. For example, CO , NO + , and N 2 are isoelectronic, while CH 3 COCH 3 and CH 3 N = NCH 3 are not. [ 1 ]
This definition is sometimes termed valence isoelectronicity . Definitions can sometimes be not as strict, sometimes requiring identity of the total electron count and with it the entire electronic configuration . [ 2 ] More usually, definitions are broader, and may extend to allowing different numbers of atoms in the species being compared. [ 3 ]
The importance of the concept lies in identifying significantly related species, as pairs or series. Isoelectronic species can be expected to show useful consistency and predictability in their properties, so identifying a compound as isoelectronic with one already characterised offers clues to possible properties and reactions. Differences in properties such as electronegativity of the atoms in isolelectronic species can affect reactivity.
In quantum mechanics , hydrogen-like atoms are ions with only one electron such as Li 2+ . These ions would be described as being isoelectronic with hydrogen .
The N atom and the O + ion are isoelectronic because each has five valence electrons , or more accurately an electronic configuration of [He] 2s 2 2p 3 .
Similarly, the cations K + , Ca 2+ , and Sc 3+ and the anions Cl − , S 2− , and P 3− are all isoelectronic with the Ar atom.
CO , CN − , N 2 , and NO + are isoelectronic because each has two atoms triple bonded together, and due to the charge have analogous electronic configurations ( N − is identical in electronic configuration to O so CO is identical electronically to CN − ).
Molecular orbital diagrams best illustrate isoelectronicity in diatomic molecules, showing how atomic orbital mixing in isoelectronic species results in identical orbital combination, and thus also bonding.
More complex molecules can be polyatomic also. For example, the amino acids serine , cysteine , and selenocysteine are all isoelectronic to each other. They differ by which specific chalcogen is present at one location in the side-chain.
CH 3 COCH 3 ( acetone ) and CH 3 N 2 CH 3 ( azomethane ) are not isoelectronic. They do have the same number of electrons but they do not have the same structure. | https://en.wikipedia.org/wiki/Isoelectronicity |
Isofalcarintriol (IUPAC name (3 S ,8 R ,9 R , E )-heptadeca-10-en-4,6-diyne-3,8,9-triol ) is a polyacetylene contained in the root of carrots ( Daucus carota ). [ 1 ] [ better source needed ] | https://en.wikipedia.org/wiki/Isofalcarintriol |
The biosynthesis of isoflavonoids involves several enzymes; These are:
Liquiritigenin,NADPH:oxygen oxidoreductase (hydroxylating, aryl migration) , also known as Isoflavonoid synthase, is an enzyme that uses liquiritigenin (a flavanone), O 2 , NADPH and H + to produce 2,7,4'-trihydroxyisoflavanone (an isoflavonoid), H 2 O and NADP + .
This article about an aromatic compound is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isoflavonoid_biosynthesis |
Isofurans are a family of organic compounds termed nonclassic eicosanoids . [ 1 ] They arise nonenzymatically by free radical peroxidation of arachidonic acid . The isofurans are similar to the isoprostanes and are formed under similar conditions, but contain a substituted tetrahydrofuran ring. The concentration of oxygen affects this process; at elevated oxygen concentrations, the formation of isofurans is favored whereas the formation of isoprostanes is disfavored. [ 2 ] [ 3 ]
Isofurans have also be found to have pro-angiogenic potential. Studies analyzing the affects of isofurans on rat brain endothelial cells (RBECs) show that they induce the growth of new blood vessels through promotion of endothelial cell proliferation , migration and cellular protection. Additionally, they have been found to play a role in the regulation of other pro-angiogenic signaling factors in RBECs. [ 4 ]
Isofurans, alongside F2-isoprostanes, accumulate in stored red blood cells (RBCs) as products of lipid peroxidation. These bioactive lipids impair platelet (PLT) function in vitro and may contribute to adverse transfusion outcomes. Elevated levels of these compounds, along with cell-free hemoglobin—which inhibits platelet spreading and may interfere with wound healing and angiogenic processes—have been proposed as biomarkers for evaluating the quality of blood components. Post-storage washing of RBCs reduces the concentration of these mediators and may help lower the risk of transfusion-related complications. [ 5 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isofuran |
Isogamy is a form of sexual reproduction that involves gametes of the same morphology (indistinguishable in shape and size), and is found in most unicellular eukaryotes . [ 1 ] Because both gametes look alike, they generally cannot be classified as male or female . [ 2 ] Instead, organisms that reproduce through isogamy are said to have different mating types , most commonly noted as "+" and "−" strains. [ 3 ]
The etymology of isogamy derives from the Greek adjective isos (meaning equal) and the Greek verb gameo (meaning to have sex/to reproduce), eventually meaning "equal reproduction" which refers to a hypothetical initial model of equal contribution of resources by both gametes to a zygote in contrast to a later evolutional stage of anisogamy . [ 4 ] The term isogamy was first used in the year 1891. [ 5 ] [ 6 ]
Isogamous species often have two mating types ( heterothallism ), but sometimes can occur between two haploid individuals that are mitotic descendents ( homothallism ). [ 1 ] [ Note 1 ] Some isogamous species have more than two mating types, but the number is usually lower than ten. In some extremely rare cases, such as in some basidiomycete species, a species can have thousands of mating types. [ 7 ]
Under the strict definition of isogamy, fertilization occurs when two gametes fuse to form a zygote . [ 8 ] Sexual reproduction between two cells that does not involve gametes (e.g. conjugation between two mycelia in basidiomycete fungi), is often called isogamy, although it is not technically isogametic reproduction in the strict sense. [ 1 ]
As the first stage in the evolution of sexual reproduction in all known lifeforms , isogamy is thought to have evolved just once, in a single unicellular eukaryote species, the common ancestor of all eukaryotes . It is generally accepted that isogamy is an ancestral state for anisogamy . [ 1 ] [ 9 ] Isogamous reproduction evolved independently in several lineages of plants and animals into anisogamy (species with gametes of male and female types) and subsequently into oogamy (species in which the female gamete is much larger than the male and has no ability to move). This pattern may have been driven by the physical constraints on the mechanisms by which two gametes get together as required for sexual reproduction . [ 10 ]
Since it appeared, isogamy has remained the norm in unicellular eukaryote species , and it is possible that isogamy is also evolutionarily stable in multicellular species. [ 1 ]
Almost all unicellular eukaryotes are isogamous. [ 11 ] Among multicellular organisms, isogamy is restricted to fungi and eukaryotic algae . [ 12 ] Many species of green algae are isogamous. It is typical in the genera Ulva , Hydrodictyon , Tetraspora , Zygnema , Spirogyra , Ulothrix , and Chlamydomonas . [ 1 ] [ 13 ] Many fungi are also isogamous, including single-celled species such as Saccharomyces cerevisiae and Schizosaccharomyces pombe . [ 1 ] [ 14 ]
In some multicellular fungi, such as basidiomycetes , sexual reproduction takes place between two mycelia , but there is no exchange of gametes. [ 1 ]
There are no known examples of isogamous metazoans , red algae or land plants . [ 1 ] | https://en.wikipedia.org/wiki/Isogamy |
Isogenic human disease models are a family of cells that are selected or engineered to accurately model the genetics of a specific patient population, in vitro . They are provided with a genetically matched 'normal cell' to provide an isogenic system to research disease biology and novel therapeutic agents. [ 1 ] They can be used to model any disease with a genetic foundation. Cancer is one such disease for which isogenic human disease models have been widely used.
Human isogenic disease models have been likened to 'patients in a test-tube', since they incorporate the latest research into human genetic diseases and do so without the difficulties and limitations involved in using non-human models. [ 2 ]
Historically, cells obtained from animals, typically mice, have been used to model cancer-related pathways. However, there are obvious limitations inherent in using animals for modelling genetically determined diseases in humans. Despite a large proportion of genetic conservation between humans and mice, there are significant differences between the biology of mice and humans that are important to cancer research. For example, major differences in telomere regulation enable murine cells to bypass the requirement for telomerase upregulation, which is a rate-limiting step in human cancer formation. As another example, certain ligand-receptor interactions are incompatible between mice and humans. Additionally, experiments have demonstrated important and significant differences in the ability to transform cells, compared with cells of murine origin. For these reasons, it remains essential to develop models of cancer that employ human cells. [ 3 ]
Isogenic cell lines are created via a process called homologous gene-targeting. Targeting vectors that utilize homologous recombination are the tools or techniques that are used to knock-in or knock-out the desired disease-causing mutation or SNP ( single nucleotide polymorphism ) to be studied. Although disease mutations can be harvested directly from cancer patients, these cells usually contain many background mutations in addition to the specific mutation of interest, and a matched normal cell line is typically not obtained. Subsequently, targeting vectors are used to ' knock-in ' or ' knock out ' gene mutations enabling a switch in both directions; from a normal to cancer genotype; or vice versa; in characterized human cancer cell lines such as HCT116 or Nalm6. [ 4 ]
There are several gene targeting technologies used to engineer the desired mutation, the most prevalent of which are briefly described, including key advantages and limitations, in the summary table below.
rAAV can introduce subtle point mutations, SNPs as well as small insertions with high efficiency. Moreover, many peer reviewed studies have shown that rAAV does not introduce any confounding off target genomic events. [ citation needed ]
Appears to be the preferred method being adopted in academia, Biotech and Pharma on a precision versus time versus cost basis. [ citation needed ] |
This process can therefore generate 3 genotypes (+/+; -/+ and -/-); enabling therefore the analysis of haplo-insufficient gene function.
Current limitation is the need to sequentially target single alleles making generation of knock-out cell lines a two-step process.|
Homologous recombination (HR) is a kind of genetic recombination in which genetic sequences are exchanged between two similar segments of DNA. HR plays a major role in eukaryotic cell division, promoting genetic diversity through the exchange between corresponding segments of DNA to create new, and potentially beneficial combinations of genes. [ citation needed ]
HR performs a second vital role in DNA repair, enabling the repair of double-strand breaks in DNA which is a common occurrence during a cell's lifecycle. It is this process which is artificially triggered by the above technologies and bootstrapped in order to engender 'knock-ins' or 'knockouts' in specific genes 5, 7.
A recent key advance was discovered using AAV-homologous recombination vectors, which increases the low natural rates of HR in differentiated human cells when combined with gene-targeting vectors-sequences. [ citation needed ]
Factors leading to the recent commercialization of isogenic human cancer cell disease models for the pharmaceutical industry and research laboratories are twofold. [ citation needed ]
Firstly, successful patenting of enhanced targeting vector technology has provided a basis for commercialization of the cell-models which eventuate from the application of these technologies. [ citation needed ]
Secondly, the trend of relatively low success rates in pharmaceutical RnD and the enormous costs have created a real need for new research tools that illicit how patient sub-groups will respond positively or be resistant to targeted cancer therapeutics based upon their individual genetic profile. [ citation needed ] | https://en.wikipedia.org/wiki/Isogenic_human_disease_models |
Isogonal , a mathematical term meaning "having similar angles", may refer to: | https://en.wikipedia.org/wiki/Isogonal |
An Isograft is a graft of tissue between two individuals who are genetically identical (i.e. monozygotic twins ). Transplant rejection between two such individuals virtually never occurs, making isografts particularly relevant to organ transplantations; patients with organs from their identical twins are incredibly likely to receive the organs favorably and survive. Monozygotic twins have the same major histocompatibility complex , leading to the low instances of tissue rejection by the adaptive immune system . Furthermore, there is virtually no incidence of graft-versus-host disease .
In 1993 a research article demonstrated that islet isografts were being transplanted into young diabetic mice [STZ induced diabetic NOD mice] and the mice survived at least about 22 days post transplantation. [ 1 ]
This immunology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isograft |
Isogrid is a type of partially hollowed-out structure formed usually from a single metal plate with integral triangular stiffening stringers . It was patented by McDonnell Douglas (now part of Boeing ) in 1975. [ 1 ] [ 2 ] Isogrids are extremely light and stiff. [ 3 ] Compared to other materials, it is expensive to manufacture, and so it is restricted to spaceflight applications and some aerospace use. [ citation needed ]
Isogrid structures are related to sandwich-structured composite panels; both can be modeled using sandwich theory , which describes structures with separated, stiff face sheets and a lighter interconnecting layer. Isogrids are manufactured from single sheets of material and with large-scale triangular openings, and an open pattern to the flanges , compared to closed sheets and foam or honeycomb structures for the sandwich-composite structures.
Isogrid structures are constituted by a thin skin reinforced with a lattice structure. Such structures are adopted in the aeronautical industry since they present both structural resistance and lightness. [ 5 ]
The term isogrid is used because the structure acts like an isotropic material, having the same properties along any axis.
Traditionally, the equilateral triangle pattern was used because it was amenable to simplified analysis. [ 6 ] [ 7 ] A variant is the orthogrid (sometimes called a waffle grid), which uses rectangular rather than triangular openings. It is not isotropic (has different properties in different orientations), but matches many use cases well and is easier to manufacture.
The stiffeners of an isogrid are generally machined from one face of a single sheet of material such as aluminium with a CNC milling machine . A thickness less than 0.04 inches (1.0 mm) might require chemical milling processes. [ 8 ]
A major push has been made toward additive manufacturing techniques due to a decrease in overall material and production costs and high efficiency and accuracy while providing control over parameters like porosity. Also, the ease of prototype manufacturing for testing purposes has made a huge contribution. [ 9 ]
Composite isogrids are rib-skin configurations, where at least a part of the rib is a different material from the skin, the composite assembled by various manual or automated processes. [ 10 ] This can give extremely high strength-to-weight ratios. [ 11 ]
Isogrid panels form self-stiffened structures where low weight, stiffness, strength and damage tolerance are important, such as in aircraft or space vehicles.
Aerospace isogrid structures include payload shrouds and boosters, which must support the full weight of upper stages and payloads under high G loads. Their open configuration with a single, sealed sheet facing the outside makes them especially useful for propellant tanks for rockets, where sealing the propellant in, but allowing it to drain in use or maintenance are necessary features. [ citation needed ]
Some spacecraft and launch vehicles which use isogrid structures include:
Orthogrid (also known as waffle grid) is similar to isogrid, but with a square pattern; examples include: | https://en.wikipedia.org/wiki/Isogrid |
The isohydric principle is the phenomenon whereby multiple acid/base pairs in solution will be in equilibrium with one another, tied together by their common reagent: the hydrogen ion and hence, the pH of solution. That is, when several buffers are present together in the same solution, they are all exposed to the same hydrogen ion activity. Hence, the pK of each buffer will dictate the ratio of the concentrations of its base and weak acid forms at the given pH, in accordance with the Henderson-Hasselbalch equation .
Any condition that changes the balance of one of the buffer systems, also changes the balance of all the others because the buffer systems actually buffer one another by shifting hydrogen ions back and forth from one to the other.
The isohydric principle has special relevance to in vivo biochemistry where multiple acid/ base pairs are in solution. The simplifying isohydric principle gives two important concepts. First, all of the buffers in a multiple-buffered system contribute to pH of the system. Secondly, the pH (at equilibrium) can be calculated from an individual buffer system regardless of other buffers present. That is, in vivo, knowing the concentration of pCO 2 (weak acid) and bicarbonate (conjugate base) and the pKa of that buffer system, the pH can be calculated regardless of the presence of other contributing buffers. The clinical relevance is that arterial blood gas often directly measures the CO 2 levels and the pH, but the bicarbonate levels are then calculated from that information—without regard to other buffers present [ 1 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isohydric_principle |
Isolated organ perfusion technique is employed to precipitate an organ's perfusion and circulation that are independent/isolated from the body's systemic circulation for various purposes such as organ-localized chemotherapy , organ-targeted delivery of drug, gene or anything else, organ transplantation , and organ injury recovery. The technique has been widely studied in animal and human for decades. [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 6 ] [ 7 ] Before the implementation, the perfusion system will be selected and the process can be similar to organ bath . [ 8 ] Isolated organ perfusion technique, nevertheless, is averagely conducted in vivo without leaving the organ alone as a whole out of the body. [ 9 ] | https://en.wikipedia.org/wiki/Isolated_organ_perfusion_technique |
In physical science , an isolated system is either of the following:
Though subject internally to its own gravity, an isolated system is usually taken to be outside the reach of external gravitational and other long-range forces.
This can be contrasted with what (in the more common terminology used in thermodynamics) is called a closed system , being enclosed by selective walls through which energy can pass as heat or work, but not matter; and with an open system , which both matter and energy can enter or exit, though it may have variously impermeable walls in parts of its boundaries.
An isolated system obeys the conservation law that its total energy–mass stays constant. Most often, in thermodynamics, mass and energy are treated as separately conserved.
Because of the requirement of enclosure, and the near ubiquity of gravity, strictly and ideally isolated systems do not actually occur in experiments or in nature. Though very useful, they are strictly hypothetical. [ 1 ] [ 2 ] [ 3 ]
Classical thermodynamics is usually presented as postulating the existence of isolated systems. It is also usually presented as the fruit of experience. Obviously, no experience has been reported of an ideally isolated system.
It is, however, the fruit of experience that some physical systems, including isolated ones, do seem to reach their own states of internal thermodynamic equilibrium. Classical thermodynamics postulates the existence of systems in their own states of internal thermodynamic equilibrium. This postulate is a very useful idealization.
In the attempt to explain the idea of a gradual approach to thermodynamic equilibrium after a thermodynamic operation , with entropy increasing according to the second law of thermodynamics , Boltzmann’s H-theorem used equations , which assumed a system (for example, a gas ) was isolated. That is, all the mechanical degrees of freedom could be specified, treating the enclosing walls simply as mirror boundary conditions . This led to Loschmidt's paradox . If, however, the stochastic behavior of the molecules and thermal radiation in real enclosing walls is considered, then the system is in effect in a heat bath. Then Boltzmann’s assumption of molecular chaos can be justified.
The concept of an isolated system can serve as a useful model approximating many real-world situations. It is an acceptable idealization used in constructing mathematical models of certain natural phenomena ; e.g., the planets in the Solar System , and the proton and electron in a hydrogen atom are often treated as isolated systems. But, from time to time, a hydrogen atom will interact with electromagnetic radiation and go to an excited state .
For radiative isolation, the walls should be perfectly conductive, so as to perfectly reflect the radiation within the cavity, as for example imagined by Planck .
He was considering the internal thermal radiative equilibrium of a thermodynamic system in a cavity initially devoid of substance. He did not mention what he imagined to surround his perfectly reflective and thus perfectly conductive walls. Presumably, since they are perfectly reflective, they isolate the cavity from any external electromagnetic effect. Planck held that for radiative equilibrium within the isolated cavity, it needed to have added to its interior a speck of carbon. [ 4 ] [ 5 ] [ 6 ]
If the cavity with perfectly reflective walls contains enough radiative energy to sustain a temperature of cosmological magnitude, then the speck of carbon is not needed because the radiation generates particles of substance, such as for example electron-positron pairs, and thereby reaches thermodynamic equilibrium.
A different approach is taken by Roger Balian . For quantizing the radiation in the cavity, he imagines his radiatively isolating walls to be perfectly conductive. Though he does not mention mass outside, and it seems from his context that he intends the reader to suppose the interior of the cavity to be devoid of mass, he does imagine that some factor causes currents in the walls. If that factor is internal to the cavity, it can be only the radiation, which would thereby be perfectly reflected. For the thermal equilibrium problem, however, he considers walls that contain charged particles that interact with the radiation inside the cavity; such cavities are of course not isolated, but may be regarded as in a heat bath. [ 7 ] | https://en.wikipedia.org/wiki/Isolated_system |
In microbiology, the term isolation refers to the separation of a strain from a natural, mixed population of living microbes , as present in the environment, for example in water or soil , or from living beings with skin flora , oral flora or gut flora , in order to identify the microbe(s) of interest. [ 1 ] Historically, the laboratory techniques of isolation first developed in the field of bacteriology and parasitology (during the 19th century), before those in virology during the 20th century.
The laboratory techniques of isolating microbes first developed during the 19th century in the field of bacteriology and parasitology using light microscopy . 1860 marked the successful introduction of liquid medium by Louis Pasteur . The liquid culture pasteur developed allowed for the visulization of promoting or inhibiting growth of specific bacteria. This same technique is utilized today through various mediums like Mannitol salt agar , a solid medium. Solid cultures were developed in 1881 when Robert Koch solidified the liquid media through the addition of agar [ 2 ]
Proper isolation techniques of virology did not exist prior to the 20th century. The methods of microbial isolation have drastically changed over the past 50 years, from a labor perspective with increasing mechanization, and in regard to the technologies involved, and with it speed and accuracy.
In order to isolate a microbe from a natural, mixed population of living microbes , as present in the environment, for example in water or soil flora , or from living beings with skin flora , oral flora or gut flora , one has to separate it from the mix.
Traditionally microbes have been cultured in order to identify the microbe(s) of interest based on its growth characteristics.
Depending on the expected density and viability of microbes present in a liquid sample, physical methods to increase the gradient as for example serial dilution or centrifugation may be chosen.
In order to isolate organisms in materials with high microbial content, such as sewage, soil or stool, serial dilutions will increase the chance of separating a mixture.
In a liquid medium with few or no expected organisms, from an area that is normally sterile (such as CSF , blood inside the circulatory system) centrifugation, decanting the supernatant and using only the sediment will increase the chance to grow and isolate bacteria or the usually cell-associated viruses.
If one expects or looks for a particularly fastidious organism, the microbiological culture and isolation techniques will have to be geared towards that microbe. For example, a bacterium that dies when exposed to air, can only be isolated if the sample is carried and processed under airless or anaerobic conditions. A bacterium that dies when exposed to room temperature (thermophilic) requires a pre-warmed transport container, and a microbe that dries and dies when carried on a cotton swab will need a viral transport medium before it can be cultured successfully.
Laboratory technicians inoculate the sample onto certain solid agar plates with the streak plate method or into liquid culture medium , depending what the objective of the isolation is:
After the sample is inoculated into or onto the choice media, they are incubated under the appropriate atmospheric settings, such as aerobic, anaerobic or microaerophilic conditions or with added carbon dioxide (5%), at different temperature settings, for example 37 °C in an incubator or in a refrigerator for cold enrichment, under appropriate light, for example strictly without light wrapped in paper or in a dark bottle for scotochromogen mycobacteria, and for different lengths of time, because different bacteria grow at a different speed, varying from hours ( Escherichia coli ) to weeks (e.g. mycobacteria ).
At regular, serial intervals laboratory technicians and microbiologists inspect the media for signs of visible growth and record it. The inspection again has to occur under conditions favoring the isolate's survival, i.e. in an 'anaerobic chamber' for anaerobe bacteria for example, and under conditions that do not threaten the person looking at the plates from being infected by a particularly infectious microbe, i.e. under a biological safety cabinet for Yersinia pestis (plague) or Bacillus anthracis (anthrax) for example.
When bacteria have visibly grown, they are often still mixed. The identification of a microbe depends upon the isolation of an individual colony , as biochemical testing of a microbe to determine its different physiological features depends on a pure culture .
To make a subculture , one again works in aseptic technique in microbiology , lifting a single colony off the agar surface with a loop and streaks the material into the 4 quadrants of an agar plate or all over if the colony was singular and did not look mixed.
Gram staining allows for visualization of the bacteria's cell wall composition based on the color the bacteria stains after a series of staining and decolorization steps. [ 4 ] This staining process allows for the identification of gram-negative and gram positive bacteria. Gram-negative bacteria will stain a pink color due to the thin layer of peptidoglycan. If a bacteria stains purple, due to the thick layer of peptidoglycan, the bacteria is a gram-positive bacteria. [ 4 ]
In clinical microbiology numerous other staining techniques for particular organisms are used (acid fast bacterial stain for mycobacteria). Immunological staining techniques, such as direct immunofluorescence have been developed for medically important pathogens that are slow growing ( Auramine-rhodamine stain for mycobacteria ) or difficult to grow (such as Legionella pneumophila species) and where the test result would alter standard management and empirical therapy .
Biochemical testing of bacteria involves a set of agars in vials to separate motile from non-motile bacteria .
In 1970 a miniaturized version was developed, called the analytical profile index .
Successful identification via e.g. genome sequencing and genomics depends on pure cultures.
While the most rapid method to identify bacteria is by sequencing their 16S rRNA gene, which has been PCR-amplified beforehand, this method does not require isolation. Since most bacteria cannot be grown with conventional methods (particularly environmental or soil bacteria) metagenomics or metatranscriptomics are used, shotgun sequencing or PCR directed sequencing of the genome . Sequencing with mass spectrometry as in Matrix-assisted laser desorption/ionization (MALDI-TOF MS) is used in the analysis of clinical specimens to look for pathogens. Whole genome sequencing is an option for a singular organism that cannot be sufficiently characterized for identification. Small DNA microarrays can also be used for identification. | https://en.wikipedia.org/wiki/Isolation_(microbiology) |
The Isolation chip (or ichip ) is a method of culturing bacteria. Using regular methods, 99% of bacterial species are not able to be cultured as they do not grow in conditions made in a laboratory, a problem called the "Great Plate Count Anomaly". [ 1 ] The ichip instead cultures bacterial species within its soil environment. The soil is diluted in molten agar and nutrients such that only a single cell, on average, grows in the ichip's small compartments or wells, hence the term "isolation". The chip is then enclosed in a semipermeable plastic membrane and buried back in the dirt to allow in nutrients not available in the lab. [ 2 ] With this culturing method, about 50 to 60 percent of bacterial species are able to survive. [ 2 ] Notably, the bacterial species Eleftheria terrae , which makes the antibiotic teixobactin that has shown promise against many drug-resistant strains like methicillin-resistant Staphylococcus aureus , was discovered using the ichip in 2015. In addition to antibiotics, it is argued that anti-cancer agents, anti-inflammatory and immunosuppressives (which have previously been discovered from bacteria) as well as potential energy sources could be discovered. [ 1 ] The ichip was developed by the drug discovery company NovoBiotic Pharmaceuticals , founded by Kim Lewis and Slava Epstein. [ 2 ] | https://en.wikipedia.org/wiki/Isolation_chip |
In theoretical computer science , the term isolation lemma (or isolating lemma ) refers to randomized algorithms that reduce the number of solutions to a problem to one, should a solution exist.
This is achieved by constructing random constraints such that, with non-negligible probability, exactly one solution satisfies these additional constraints if the solution space is not empty.
Isolation lemmas have important applications in computer science, such as the Valiant–Vazirani theorem and Toda's theorem in computational complexity theory .
The first isolation lemma was introduced by Valiant & Vazirani (1986) , albeit not under that name.
Their isolation lemma chooses a random number of random hyperplanes, and has the property that, with non-negligible probability, the intersection of any fixed non-empty solution space with the chosen hyperplanes contains exactly one element. This suffices to show the Valiant–Vazirani theorem :
there exists a randomized polynomial-time reduction from the satisfiability problem for Boolean formulas to the problem of detecting whether a Boolean formula has a unique solution. Mulmuley, Vazirani & Vazirani (1987) introduced an isolation lemma of a slightly different kind:
Here every coordinate of the solution space gets assigned a random weight in a certain range of integers, and the property is that, with non-negligible probability, there is exactly one element in the solution space that has minimum weight. This can be used to obtain a randomized parallel algorithm for the maximum matching problem.
Stronger isolation lemmas have been introduced in the literature to fit different needs in various settings.
For example, the isolation lemma of Chari, Rohatgi & Srinivasan (1993) has similar guarantees as that of Mulmuley et al., but it uses fewer random bits.
In the context of the exponential time hypothesis , Calabro et al. (2008) prove an isolation lemma for k-CNF formulas .
Noam Ta-Shma [ 1 ] gives an isolation lemma with slightly stronger parameters, and gives non-trivial results even when the size of the weight domain is smaller than the number of variables.
It is remarkable that the lemma assumes nothing about the nature of the family F {\displaystyle {\mathcal {F}}} : for instance F {\displaystyle {\mathcal {F}}} may include all 2 n − 1 {\displaystyle 2^{n}-1} nonempty subsets. Since the weight of each set in F {\displaystyle {\mathcal {F}}} is between 1 {\displaystyle 1} and n N {\displaystyle nN} on average there will be ( 2 n − 1 ) / ( n N ) {\displaystyle (2^{n}-1)/(nN)} sets of each possible weight.
Still, with high probability , there is a unique set that has minimum weight.
Suppose we have fixed the weights of all elements except an element x . Then x has a threshold weight α , such that if the weight w ( x ) of x is greater than α , then it is not contained in any minimum-weight subset, and if w ( x ) ≤ α {\displaystyle w(x)\leq \alpha } , then it is contained in some sets of minimum weight. Further, observe that if w ( x ) < α {\displaystyle w(x)<\alpha } , then every minimum-weight subset must contain x (since, when we decrease w(x) from α , sets that do not contain x do not decrease in weight, while those that contain x do). Thus, ambiguity about whether a minimum-weight subset contains x or not can happen only when the weight of x is exactly equal to its threshold; in this case we will call x "singular". Now, as the threshold of x was defined only in terms of the weights of the other elements, it is independent of w(x) , and therefore, as w ( x ) is chosen uniformly from {1, …, N },
and the probability that some x is singular is at most n/N . As there is a unique minimum-weight subset iff no element is singular, the lemma follows.
Remark: The lemma holds with ≤ {\displaystyle \leq } (rather than =) since it is possible that some x has no threshold value (i.e., x will not be in any minimum-weight subset even if w ( x ) gets the minimum possible value, 1).
This is a restatement version of the above proof, due to Joel Spencer (1995). [ 2 ]
For any element x in the set, define
Observe that α ( x ) {\displaystyle \alpha (x)} depends only on the weights of elements other than x , and not on w ( x ) itself. So whatever the value of α ( x ) {\displaystyle \alpha (x)} , as w ( x ) is chosen uniformly from {1, …, N }, the probability that it is equal to α ( x ) {\displaystyle \alpha (x)} is at most 1/ N . Thus the probability that w ( x ) = α ( x ) {\displaystyle w(x)=\alpha (x)} for some x is at most n/N .
Now if there are two sets A and B in F {\displaystyle {\mathcal {F}}} with minimum weight, then, taking any x in A\B , we have
and as we have seen, this event happens with probability at most n/N . | https://en.wikipedia.org/wiki/Isolation_lemma |
An isolation valve is a valve in a fluid handling system that stops the flow of process media to a given location, usually for maintenance or safety purposes. [ 1 ] They can also be used to provide flow logic (selecting one flow path versus another), and to connect external equipment to a system. [ 2 ] A valve is classified as an isolation valve because of its intended function in a system, not because of the type of the valve itself. Therefore, many different types of valves can be classified as isolation valves.
To easily understand the concept of an isolation valve, one can think of the valves under a kitchen or bathroom sink in a typical household. These valves are normally left open so that the user can control the flow of water with the spigot above the sink, and does not need to reach under the counter to start or stop the water flow. However, if the spigot needs to be replaced (i.e. maintenance needs to take place on the system), the isolation valves are shut to stop the flow of water when the spigot is removed. In this system, the isolation valves and the spigot may even be the same type of valve. However, due to their function they are classified as the isolation valves and, in the case of the spigot, the control valves . As the isolation valve is intended to be operated infrequently and only in the fully on or fully off positions, they are often inferior quality globe valves . These less expensive styles lack a bonnet and stem seal in favor of threading the stem directly into the body. The stem is covered with a rubber washer and metal cap similar in appearance to a gland nut . Because they lack a stem seal they will leak unless fully closed and installed in the correct direction or fully open, causing the disk to compress the top washer against the stem.
Isolation valves can be in the normally open position (NO) or normally closed (NC). Normally open valves are located between pressure vessels , pumps , compressors , tanks, pressure sensors , liquid level measurement instrumentation and other components and allow fluids to flow between components, or to be connected to sensors. [ 3 ] The controlled closure of open valves enables the isolation of plant components for testing or maintenance of equipment, or allows flow of fluid to specific flow paths. [ 4 ] Normally closed valves are used to connect fluids and process components to other systems only when required. Vent and drain valves are examples of normally closed valves which are only opened when required to depressurise (vent) or drain fluids from a system.
Isolation valves must effectively stop the passage of fluids. [ 4 ] Gate valves , ball valves and plug valves are generally considered to provide tight and effective shut-off. Globe valves and Butterfly valves may not be tight shut-off due to wear on the plug or the seat, or due to their design, and may not be appropriate to provide effective isolation. [ 3 ]
Some valves are in a safety critical service and are secured, or otherwise locked, in an open or closed position. [ 5 ] Plant shutdown instrumentation must be effectively connected to the plant at all times, therefore the isolation valves associated with such equipment must be secured in the open position to prevent inadvertent movement or closure. [ 5 ] Securing mechanisms include car-seals, chain and padlocks and proprietary securing devices. Isolation valves in a flare, relief or vent system must ensure that a flow path is always available to the flare or vent. These valves are secured in the open position (LO). Drain valves that connect a high pressure system to a low pressure drain system are locked in the closed position (LC) to prevent potential over-pressurisation of the drain system. [ 3 ] Removal of locks from secured valves is only undertaken in specified and controlled conditions such as under a ‘ permit to work ’ system. Some relief or pressure relief valves are ‘paired’ to provide a duty and a standby valve, the associated isolation valves are interlock ed such that at least one relief valve is connected to the system being protected at all times. [ 5 ]
A single valve may provide effective isolation between the live plant and the system being maintained. However, for hazardous systems a more effective means of isolation is required. This may comprise a ‘ double block ’ consisting of two valves in series. Still more effective is a ‘ double block and bleed ’ comprising two isolation valves in series plus a bleed valve between them. The bleed valve enables the integrity of the valve on the hazardous side to be monitored. [ 5 ] | https://en.wikipedia.org/wiki/Isolation_valve |
An isolator is a two-port device that transmits microwave or radio frequency power in one direction only. The non-reciprocity observed in these devices usually comes from the interaction between the propagating wave and the material, which can be different with respect to the direction of propagation.
It is used to shield equipment on its input side, from the effects of conditions on its output side; for example, to prevent a microwave source being detuned by a mismatched load.
An isolator is a non- reciprocal device, with a non- symmetric scattering matrix . An ideal isolator transmits all the power entering port 1 to port 2, while absorbing all the power entering port 2, so that to within a phase-factor its S-matrix is
To achieve non-reciprocity, an isolator must necessarily incorporate a non-reciprocal material. At microwave frequencies, this material is usually a ferrite which is biased by a static magnetic field [ 1 ] but can be a self-biased material. [ 2 ] The ferrite is positioned within the isolator such that the microwave signal presents it with a rotating magnetic field, with the rotation axis aligned with the direction of the static bias field. The behaviour of the ferrite depends on the sense of rotation with respect to the bias field, and hence is different for microwave signals travelling in opposite directions. Depending on the exact operating conditions, the signal travelling in one direction may either be phase-shifted, displaced from the ferrite or absorbed.
Most common types of ferrite-based isolators are classified into four categories: terminated circulators, Faraday rotation isolators, field-displacement isolators, and resonance isolators. In all these kinds of devices, the observed non-reciprocity arises from the wave-material interaction which depends on the direction of propagation.
In this type the ferrite absorbs energy from the microwave signal travelling in one direction. A suitable rotating magnetic field is found in the dominant TE 10 mode of rectangular waveguide . The rotating field exists away from the centre-line of the broad wall, over the full height of the guide. However, to allow heat from the absorbed power to be conducted away, the ferrite does not usually extend from one broad-wall to the other, but is limited to a shallow strip on each face. For a given bias field, resonance absorption occurs over a fairly narrow frequency band, but since in practice the bias field is not perfectly uniform throughout the ferrite, the isolator functions over a somewhat wider band.
This type is superficially very similar to a resonance absorption isolator, but the magnetic biasing differs, and the energy from the backward travelling signal is absorbed in a resistive film or card on one face of the ferrite block rather than within the ferrite itself.
The bias field is weaker than that necessary to cause resonance at the operating frequency, but is instead designed to give the ferrite near-zero permeability for one sense of rotation of the microwave signal field. The bias polarity is such that this special condition arises for the forward signal; the backward signal sees the ferrite as an ordinary dielectric material (with little permeability, as the ferrite is already saturated by the bias field). Consequently, for the electromagnetic field of the forward signal, the ferrite has very low characteristic wave impedance , and the field tends to be excluded from the ferrite. This results in a null of the electric field of the forward signal on the surface of the ferrite where the resistive film is placed. Conversely for the backward signal, the electric field is strong over this surface and so its energy is dissipated in driving current through the film.
In rectangular waveguide the ferrite block will typically occupy the full height from one broad-wall to the other, with the resistive film on the side facing the centre-line of the guide.
A circulator is a non-reciprocal three- or four-port device, in which power entering any port is transmitted to the next port in rotation (only). So to within a phase-factor, the scattering matrix for a three-port circulator is
A two-port isolator is obtained simply by terminating one of the three ports with a matched load , which absorbs all the power entering it. The biased ferrite is part of the circulator and causes a differential phase-shift for signals travelling in different directions. The bias field is lower than that needed for resonance absorption, and so this type of isolator does not require such a heavy permanent magnet. Because the power is absorbed in an external load, cooling is less of a problem than with a resonance absorption isolator.
A last physical principle useful to design isolators is the Faraday rotation . When a linearly polarized wave propagates through ferrite having a magnetization aligned with the direction of propagation of the wave, the polarization plane will rotate along the propagation axis. This rotation may be used to create microwave devices as isolators, circulators, gyrators, etc. In rectangular waveguide topology, it also requires the implementation of circular waveguide sections which come out of the device plane.
Fox, A. G.; Miller, S. E.; Weiss, M. T. (January 1955). "Behaviour and applications of ferrites in the microwave region" (PDF) . Bell System Technical Journal . 34 (1). Bell Labs: 5– 103. doi : 10.1002/j.1538-7305.1955.tb03763.x .
Baden Fuller, A. J. (1969). Microwaves (1 ed.). Pergamon Press. ISBN 0-08-006616-X .
Baden Fuller, A. J. (1987). Ferrites at Microwave Frequencies . IEE electromagnetic waves series. Peter Peregrinus. ISBN 0-86341-064-2 . | https://en.wikipedia.org/wiki/Isolator_(microwave) |
Isolecithal ( Greek iso = equal, lekithos = yolk) refers to the even distribution of yolk in the cytoplasm of ova of mammals and other vertebrates , notably fishes of the families Petromyzontidae , Amiidae , and Lepisosteidae . [ 1 ] Isolecithal cells have two equal hemispheres of yolk. However, during cellular development, normally under the influence of gravity, some of the yolk settles to the bottom of the egg, producing an uneven distribution of yolky hemispheres. Such uneven cells are known as telolecithal and are common where there is sufficient yolk mass.
In the absence of a large concentration of yolk, four major cleavage types can be observed in isolecithal cells: radial holoblastic , spiral holoblastic, bilateral holoblastic, and rotational holoblastic cleavage. These holoblastic cleavage planes pass all the way through isolecithal zygotes during the process of cytokinesis . Coeloblastula is the next stage of development for eggs that undergo this radial cleavage. In mammals, because the isolecithal cells have only a small amount of yolk, they require immediate implantation onto the uterine wall to receive nutrients. [ citation needed ]
This cell biology article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isolecithal |
In organometallic chemistry , the isolobal principle (more formally known as the isolobal analogy ) is a strategy used to relate the structure of organic and inorganic molecular fragments in order to predict bonding properties of organometallic compounds. [ 1 ] Roald Hoffmann described molecular fragments as isolobal "if the number, symmetry properties, approximate energy and shape of the frontier orbitals and the number of electrons in them are similar – not identical, but similar." [ 2 ] One can predict the bonding and reactivity of a lesser-known species from that of a better-known species if the two molecular fragments have similar frontier orbitals, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Isolobal compounds are analogues to isoelectronic compounds that share the same number of valence electrons and structure. A graphic representation of isolobal structures, with the isolobal pairs connected through a double-headed arrow with half an orbital below, is found in Figure 1.
For his work on the isolobal analogy, Hoffmann was awarded the Nobel Prize in Chemistry in 1981, which he shared with Kenichi Fukui . [ 3 ] In his Nobel Prize lecture, Hoffmann stressed that the isolobal analogy is a useful, yet simple, model and thus is bound to fail in certain instances. [ 1 ]
To begin to generate an isolobal fragment, the molecule needs to follow certain criteria. [ 4 ] Molecules based around main group elements should satisfy the octet rule when all bonding and nonbonding molecular orbitals (MOs) are filled and all antibonding MOs are empty. For example, methane is a simple molecule from which to form a main group fragment. The removal of a hydrogen atom from methane generates a methyl radical. The molecule retains its molecular geometry as the frontier orbital points in the direction of the missing hydrogen atom. Further removal of hydrogen results in the formation of a second frontier orbital. This process can be repeated until only one bond remains to the molecule's central atom.
The isolobal fragments of octahedral complexes , such as type ML 6 , can be created in a similar fashion. Transition metal complexes should initially satisfy the eighteen electron rule , have no net charge, and their ligands should be two electron donors ( Lewis bases ). Consequently, the metal center for the ML 6 starting point must be d 6 . Removal of a ligand is analogous to the removal of hydrogen of methane in the previous example resulting in a frontier orbital, which points toward the removed ligand. Cleaving the bond between the metal center and one ligand results in a ML − 5 radical complex. In order to satisfy the zero-charge criteria the metal center must be changed. For example, a MoL 6 complex is d 6 and neutral. However, removing a ligand to form the first frontier orbital would result in a MoL − 5 complex because Mo has obtained an additional electron making it d 7 . To remedy this, Mo can be exchanged for Mn, which would form a neutral d 7 complex in this case, as shown in Figure 3. This trend can continue until only one ligand is left coordinated to the metal center.
Isolobal fragments of tetrahedral and octahedral molecules can be related. Structures with the same number of frontier orbitals are isolobal to one another. For example, the methane with two hydrogen atoms removed, CH 2 is isolobal to a d 8 ML 4 complex formed from an octahedral starting complex (Figure 4).
Any sort of saturated molecule can be the starting point for generating isolobal fragments. [ 5 ] [ 6 ] The molecule's bonding and nonbonding molecular orbitals (MOs) should be filled and the antibonding MOs empty. With each consecutive generation of an isolobal fragment, electrons are removed from the bonding orbitals and a frontier orbital is created. The frontier orbitals are at a higher energy level than the bonding and nonbonding MOs. Each frontier orbital contains one electron. For example, consider Figure 5, which shows the production of frontier orbitals in tetrahedral and octahedral molecules.
As seen above, when a fragment is formed from CH 4 , one of the sp 3 hybrid orbitals involved in bonding becomes a nonbonding singly occupied frontier orbital. The frontier orbital’s increased energy level is also shown in the figure. Similarly when starting with a metal complex such as d 6 -ML 6 , the d 2 sp 3 hybrid orbitals are affected. Furthermore, the t 2g nonbonding metal orbitals are unaltered.
The isolobal analogy has applications beyond simple octahedral complexes. It can be used with a variety of ligands, charged species and non-octahedral complexes. [ 7 ]
The isolobal analogy can also be used with isoelectronic fragments having the same coordination number, which allows charged species to be considered. For example, Re(CO) 5 is isolobal with CH 3 and therefore, [Ru(CO) 5 ] + and [Mo(CO) 5 ] − are also isolobal with CH 3 . Any 17-electron metal complex would be isolobal in this example.
In a similar sense, the addition or removal of electrons from two isolobal fragments results in two new isolobal fragments. Since Re(CO) 5 is isolobal with CH 3 , [Re(CO) 5 ] + is isolobal with CH + 3 . [ 8 ]
The analogy applies to other shapes besides tetrahedral and octahedral geometries. The derivations used in octahedral geometry are valid for most other geometries. The exception is square-planar because square-planar complexes typically abide by the 16-electron rule. Assuming ligands act as two-electron donors the metal center in square-planar molecules is d 8 . To relate an octahedral fragment, ML n , where M has a d x electron configuration to a square planar analogous fragment, the formula ML n −2 where M has a d x +2 electron configuration should be followed.
Further examples of the isolobal analogy in various shapes and forms are shown in figure 8. | https://en.wikipedia.org/wiki/Isolobal_principle |
Isomalathion is an impurity found in some batches of malathion . Whereas the structure of malation is, generically, RSP(S)(OCH 3 ) 2 , the connectivity of isomalathion is RSPO(SCH 3 )(OCH 3 ). It arises by heating malathion. Being significantly more toxic to humans than malathion, it has resulted in human poisonings. [ 1 ]
In 1976, numerous malaria workers in Pakistan were poisoned by isomalathion. [ 2 ] It is an inhibitor of carboxyesterase .
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isomalathion |
In chemistry , isomers are molecules or polyatomic ions with identical molecular formula – that is, the same number of atoms of each element – but distinct arrangements of atoms in space. [ 1 ] Isomerism refers to the existence or possibility of isomers.
Isomers do not necessarily share similar chemical or physical properties . Two main forms of isomerism are structural (or constitutional) isomerism, in which bonds between the atoms differ; and stereoisomerism (or spatial isomerism), in which the bonds are the same but the relative positions of the atoms differ.
Isomeric relationships form a hierarchy . Two chemicals might be the same constitutional isomer, but upon deeper analysis be stereoisomers of each other. Two molecules that are the same stereoisomer as each other might be in different conformational forms or be different isotopologues . The depth of analysis depends on the field of study or the chemical and physical properties of interest.
The English word "isomer" ( / ˈ aɪ s əm ər / ) is a back-formation from "isomeric", [ 2 ] which was borrowed through German isomerisch [ 3 ] from Swedish isomerisk ; which in turn was coined from Greek ἰσόμερoς isómeros , with roots isos = "equal", méros = "part". [ 4 ]
Structural isomers have the same number of atoms of each element (hence the same molecular formula ), but the atoms are connected in distinct ways. [ 5 ]
For example, there are three distinct compounds with the molecular formula C 3 H 8 O {\displaystyle {\ce {C3H8O}}} :
The first two isomers shown of C 3 H 8 O {\displaystyle {\ce {C3H8O}}} are propanols , that is, alcohols derived from propane . Both have a chain of three carbon atoms connected by single bonds, with the remaining carbon valences being filled by seven hydrogen atoms and by a hydroxyl group − OH {\displaystyle {\ce {-OH}}} comprising the oxygen atom bound to a hydrogen atom. These two isomers differ on which carbon the hydroxyl is bound to: either to an extremity of the carbon chain propan-1-ol (1-propanol, n -propyl alcohol, n -propanol; I ) or to the middle carbon propan-2-ol (2-propanol, isopropyl alcohol, isopropanol; II ). These can be described by the condensed structural formulas H 3 C − CH 2 − CH 2 OH {\displaystyle {\ce {H3C-CH2-CH2OH}}} and H 3 C − CH ( OH ) − CH 3 {\displaystyle {\ce {H3C-CH(OH)-CH3}}} .
The third isomer of C 3 H 8 O {\displaystyle {\ce {C3H8O}}} is the ether methoxyethane (ethyl-methyl-ether; III ). Unlike the other two, it has the oxygen atom connected to two carbons, and all eight hydrogens bonded directly to carbons. It can be described by the condensed formula H 3 C − CH 2 − O − CH 3 {\displaystyle {\ce {H3C-CH2-O-CH3}}} .
The alcohol "3-propanol" is not another isomer, since the difference between it and 1-propanol is not real; it is only the result of an arbitrary choice in the direction of numbering the carbons along the chain. For the same reason, "ethoxymethane" is the same molecule as methoxyethane, not another isomer.
1-Propanol and 2-propanol are examples of positional isomers , which differ by the position at which certain features, such as double bonds or functional groups , occur on a "parent" molecule (propane, in that case).
There are also three structural isomers of the hydrocarbon C 3 H 4 {\displaystyle {\ce {C3H4}}} :
In two of the isomers, the three carbon atoms are connected in an open chain, but in one of them ( propadiene or allene; I ) the carbons are connected by two double bonds , while in the other ( propyne or methylacetylene; II ) they are connected by a single bond and a triple bond . In the third isomer ( cyclopropene ; III ) the three carbons are connected into a ring by two single bonds and a double bond. In all three, the remaining valences of the carbon atoms are satisfied by the four hydrogens.
Again, note that there is only one structural isomer with a triple bond, because the other possible placement of that bond is just drawing the three carbons in a different order. For the same reason, there is only one cyclopropene, not three.
Tautomers are structural isomers which readily interconvert, so that two or more species co-exist in equilibrium such as
H − X − Y = Z ↽ − − ⇀ X = Y − Z − H {\displaystyle {\ce {H-X-Y=Z <=> X=Y-Z-H}}} . [ 6 ]
Important examples are keto-enol tautomerism and the equilibrium between neutral and zwitterionic forms of an amino acid .
Stereoisomers have the same atoms or isotopes connected by bonds of the same type, but differ in the relative positions of those atoms in space. Two broad types of stereoisomers exist, enantiomers and diastereomers. Enantiomers have identical physical properties but diastereomers do not. [ 7 ]
Two compounds are said to be enantiomers if their molecules are mirror images of each other and cannot be made to coincide only by rotations or translations – like a left hand and a right hand. The two shapes are said to be chiral .
A classic example is bromochlorofluoromethane ( CHFClBr {\displaystyle {\ce {CHFClBr}}} ). The two enantiomers can be distinguished, for example, by whether the path F ⟶ Cl ⟶ Br {\displaystyle {\ce {F->Cl->Br}}} turns clockwise or counterclockwise as seen from the hydrogen atom. In order to change one conformation to the other, at some point those four atoms would have to lie on the same plane – which would require severely straining or breaking their bonds to the carbon atom. The corresponding energy barrier between the two conformations is so high that there is practically no conversion between them at room temperature, and they can be regarded as different configurations.
The compound chlorofluoromethane CH 2 ClF {\displaystyle {\ce {CH2ClF}}} , in contrast, is not chiral; the mirror image of its molecule is also obtained by a half-turn about a suitable axis.
Another example of a chiral compound is 2,3-pentadiene H 3 C − CH = C = CH − CH 3 {\displaystyle {\ce {H3C-CH=C=CH-CH3}}} , a hydrocarbon that contains two overlapping double bonds. The double bonds are such that the three middle carbons are in a straight line, while the first three and last three lie on perpendicular planes. The molecule and its mirror image are not superimposable, even though the molecule has an axis of symmetry. The two enantiomers can be distinguished, for example, by the right-hand rule . This type of isomerism is called axial isomerism .
Enantiomers behave identically in chemical reactions, except when reacting with chiral compounds or in the presence of chiral catalysts , such as most enzymes . For this latter reason, the two enantiomers of most chiral compounds usually have markedly different effects and roles in living organisms. In biochemistry and food science , the two enantiomers of a chiral molecule – such as glucose – are usually identified and treated as very different substances.
Each enantiomer of a chiral compound typically rotates the plane of polarized light that passes through it. The rotation has the same magnitude but opposite senses for the two isomers, and can be a useful way of distinguishing and measuring their concentration in a solution. For this reason, enantiomers were formerly called "optical isomers". [ 8 ] [ 9 ] However, this term is ambiguous and is discouraged by the IUPAC . [ 10 ] [ 11 ]
Some enantiomer pairs (such as those of trans -cyclooctene ) can be interconverted by internal motions that change bond lengths and angles only slightly. Other pairs (such as CHFClBr) cannot be interconverted without breaking bonds, and therefore are different configurations.
Stereoisomers that are not enantiomers are called diastereomers . Some diastereomers may contain chiral centers , and some may not. [ 12 ]
A double bond between two carbon atoms forces the remaining four bonds (if they are single) to lie on the same plane, perpendicular to the plane of the bond as defined by its π orbital . If the two bonds on each carbon connect to different atoms, two distinct conformations are possible that differ from each other by a twist of 180 degrees of one of the carbons about the double bond.
The classical example is dichloroethene C 2 H 2 Cl 2 {\displaystyle {\ce {C2H2Cl2}}} , specifically the structural isomer Cl − HC = CH − Cl {\displaystyle {\ce {Cl-HC=CH-Cl}}} that has one chlorine bonded to each carbon. It has two conformational isomers, with the two chlorines on the same side or on opposite sides of the double bond's plane. They are traditionally called cis (from Latin meaning "on this side of") and trans ("on the other side of"), respectively, or Z and E in the IUPAC recommended nomenclature. Conversion between these two forms usually requires temporarily breaking bonds (or turning the double bond into a single bond), so the two are considered different configurations of the molecule.
More generally, cis – trans isomerism (formerly called "geometric isomerism") occurs in molecules where the relative orientation of two distinguishable functional groups is restricted by a somewhat rigid framework of other atoms. [ 13 ]
For example, in the cyclic alcohol inositol ( CHOH ) 6 {\displaystyle {\ce {(CHOH)6}}} (a six-fold alcohol of cyclohexane), the six-carbon cyclic backbone largely prevents the hydroxyl − OH {\displaystyle {\ce {-OH}}} and the hydrogen − H {\displaystyle {\ce {-H}}} on each carbon from switching places. Therefore, one has different configurational isomers depending on whether each hydroxyl is on "this side" or "the other side" of the ring's mean plane. Discounting isomers that are equivalent under rotations, there are nine isomers that differ by this criterion, and behave as different stable substances (two of them being enantiomers of each other). The most common one in nature ( myo -inositol) has the hydroxyls on carbons 1, 2, 3 and 5 on the same side of that plane, and can therefore be called cis -1,2,3,5- trans -4,6-cyclohexanehexol. And each of these cis - trans isomers can possibly have stable "chair" or "boat" conformations (although the barriers between these are significantly lower than those between different cis - trans isomers).
Cis and trans isomers also occur in inorganic coordination compounds , such as square planar MX 2 Y 2 {\displaystyle {\ce {MX2Y2}}} complexes and octahedral MX 4 Y 2 {\displaystyle {\ce {MX4Y2}}} complexes.
For more complex organic molecules, the cis and trans labels can be ambiguous. In such cases, a more precise labeling scheme is employed based on the Cahn-Ingold-Prelog priority rules . [ 14 ] [ 12 ]
Different isotopes of the same element can be considered as different kinds of atoms when enumerating isomers of a molecule or ion. The replacement of one or more atoms by their isotopes can create multiple structural isomers and/or stereoisomers from a single isomer.
For example, replacing two atoms of common hydrogen ( H 1 {\displaystyle {\ce {^1 H}}} ) by deuterium ( H 2 {\displaystyle {\ce {^2 H}}} , or D {\displaystyle {\ce {D}}} ) on an ethane molecule yields two distinct structural isomers, depending on whether the substitutions are both on the same carbon (1,1-dideuteroethane, HD 2 C − CH 3 {\displaystyle {\ce {HD2C-CH3}}} ) or one on each carbon (1,2-dideuteroethane, DH 2 C − CDH 2 {\displaystyle {\ce {DH2C-CDH2}}} ); as if the substituent was chlorine instead of deuterium. The two molecules do not interconvert easily and have different properties, such as their microwave spectrum . [ 15 ]
Another example would be substituting one atom of deuterium for one of the hydrogens in chlorofluoromethane ( CH 2 ClF {\displaystyle {\ce {CH2ClF}}} ). While the original molecule is not chiral and has a single isomer, the substitution creates a pair of chiral enantiomers of CHDClF {\displaystyle {\ce {CHDClF}}} , which could be distinguished (at least in theory) by their optical activity. [ 16 ]
When two isomers would be identical if all isotopes of each element were replaced by a single isotope, they are described as isotopomers or isotopic isomers. [ 17 ] In the above two examples if all D {\displaystyle {\ce {D}}} were replaced by H {\displaystyle {\ce {H}}} , the two dideuteroethanes would both become ethane and the two deuterochlorofluoromethanes would both become CH 2 ClF {\displaystyle {\ce {CH2ClF}}} .
The concept of isotopomers is different from isotopologs or isotopic homologs, which differ in their isotopic composition. [ 17 ] For example, C 2 H 5 D {\displaystyle {\ce {C2H5D}}} and C 2 H 4 D 2 {\displaystyle {\ce {C2H4D2}}} are isotopologues and not isotopomers, and are therefore not isomers of each other.
Another type of isomerism based on nuclear properties is spin isomerism , where molecules differ only in the relative spin magnetic quantum numbers m s of the constituent atomic nuclei. This phenomenon is significant for molecular hydrogen, which can be partially separated into two long-lived states described as spin isomers [ 18 ] or nuclear spin isomers: [ 19 ] parahydrogen, with the spins of the two nuclei pointing in opposite directions, and orthohydrogen, where the spins point in the same direction.
Isomers having distinct biological properties are common; for example, the placement of methyl groups . In substituted xanthines , theobromine , found in chocolate, is a vasodilator with some effects in common with caffeine ; but, if one of the two methyl groups is moved to a different position on the two-ring core, the isomer is theophylline , which has a variety of effects, including bronchodilation and anti-inflammatory action. Another example of this occurs in the phenethylamine -based stimulant drugs. Phentermine is a non-chiral compound with a weaker effect than that of amphetamine . It is used as an appetite-reducing medication and has mild or no stimulant properties. However, an alternate atomic arrangement gives dextromethamphetamine , which is a stronger stimulant than amphetamine.
In medicinal chemistry and biochemistry, enantiomers are a special concern because they may possess distinct biological activity . Many preparative procedures afford a mixture of equal amounts of both enantiomeric forms. In some cases, the enantiomers are separated by chromatography using chiral stationary phases. They may also be separated through the formation of diastereomeric salts . In other cases, enantioselective synthesis have been developed.
As an inorganic example, cisplatin (see structure above) is an important drug used in cancer chemotherapy, whereas the trans isomer (transplatin) has no useful pharmacological activity.
Isomerism was first observed in 1827, when Friedrich Wöhler prepared silver cyanate and discovered that, although its elemental composition of AgCNO {\displaystyle {\ce {AgCNO}}} was identical to silver fulminate (prepared by Justus von Liebig the previous year), [ 20 ] its properties were distinct. This finding challenged the prevailing chemical understanding of the time, which held that chemical compounds could be distinct only when their elemental compositions differ. (We now know that the bonding structures of fulminate and cyanate can be approximately described as O − N + {\displaystyle {\ce {O- N+}}} ≡ C − {\displaystyle {\ce {C-}}} and O = C = N − {\displaystyle {\ce {O=C=N-}}} , respectively.)
Additional examples were found in succeeding years, such as Wöhler's 1828 discovery that urea has the same atomic composition ( CH 4 N 2 O {\displaystyle {\ce {CH4N2O}}} ) as the chemically distinct ammonium cyanate . (Their structures are now known to be ( H 2 N − ) 2 C = O {\displaystyle {\ce {(H2N-)2C=O}}} and [ NH 4 + ] [ O = C = N − ] {\displaystyle {\ce {[NH+4][O=C=N^{-}]}}} , respectively.) In 1830 Jöns Jacob Berzelius introduced the term isomerism to describe the phenomenon. [ 4 ] [ 21 ] [ 22 ] [ 23 ]
In 1848, Louis Pasteur observed that tartaric acid crystals came into two kinds of shapes that were mirror images of each other. Separating the crystals by hand, he obtained two version of tartaric acid, each of which would crystallize in only one of the two shapes, and rotated the plane of polarized light to the same degree but in opposite directions. [ 24 ] [ 25 ] In 1860, Pasteur explicitly hypothesized that the molecules of isomers might have the same composition but different arrangements of their atoms. [ 26 ] | https://en.wikipedia.org/wiki/Isomer |
The isomeric shift (also called isomer shift) is the shift on atomic spectral lines and gamma spectral lines, which occurs as a consequence of replacement of one nuclear isomer by another. It is usually called isomeric shift on atomic spectral lines and Mössbauer isomeric shift respectively. If the spectra also have hyperfine structure the shift refers to the center of gravity of the spectra. The isomeric shift provides important information about the nuclear structure and the physical, chemical or biological environment of atoms. More recently the effect has also been proposed as a tool in the search for the time variation of fundamental constants of nature. [ 1 ]
The isomeric shift on atomic spectral lines is the energy or frequency shift in atomic spectra, which occurs when one replaces one nuclear isomer by another. The effect was predicted by Richard M. Weiner [ 2 ] in 1956, whose calculations showed that it should be measurable by atomic (optical) spectroscopy (see also [ 3 ] ). It was observed experimentally [ 4 ] for the first time in 1958. The theory of the atomic isomeric shift [ 2 ] [ 3 ] is also used in the interpretation of the Mössbauer isomeric shift.
The notion of isomer also appears in other fields such as chemistry and meteorology . Therefore, in the first publications devoted to this effect [ 3 ] [ 2 ] the name nuclear isomeric shift on spectral lines was used. Before the discovery of the Mössbauer effect , the isomeric shift referred exclusively to atomic spectra ; this explains the absence of the word atomic in the initial [ 2 ] [ 3 ] definition of the effect. Subsequently, the isomeric shift was also observed in gamma spectroscopy through the Mössbauer effect and was called Mössbauer isomeric shift . For further details on the history of the isomeric shift and the terminology used, see. [ 5 ] [ 6 ]
Atomic spectral lines are due to transitions of electrons between different atomic energy levels E , followed by emission of photons. Atomic levels are a manifestation of the electromagnetic interaction between electrons and nuclei. The energy levels of two atoms, the nuclei of which are different isotopes of the same element, are shifted one with respect to the other, despite the fact that the electric charges Z of the two isotopes are identical. This is so because isotopes differ by the number of neutrons, and therefore the masses and volumes of two isotopes are different; these differences give rise to the isotopic shift on atomic spectral lines.
In the case of two nuclear isomers, the number of protons and the number of neutrons are identical, but the quantum states and in particular the energy levels of the two nuclear isomers differ. This difference induces a difference in the electric charge distributions of two isomers and thus a difference δφ in the corresponding electrostatic nuclear potentials φ, which ultimately leads to a difference Δ E in the atomic energy levels. The isomeric shift on atomic spectral lines is then given by
where ψ is the wave function of the electron involved in the transition, e its electric charge, and the integration is performed over the electron coordinates.
The isotopic and the isomeric shift are similar in the sense that both are effects in which the finite size of the nucleus manifests itself and both are due to a difference in the electromagnetic interaction energy between the electrons and the nucleus of the atom. The isotopic shift had been known decades before the isomeric shift and provided useful but limited information about atomic nuclei. Unlike the isomeric shift, the isotopic shift was at first discovered in experiment and then interpreted theoretically (see also [ 7 ] ). While in the case of the isotopic shift the determination of the interaction energy between electrons and nuclei is a relatively simple electromagnetic problem, for isomers the problem is more involved, since it is the strong interaction, which accounts for the isomeric excitation of the nucleus and thus for the difference of charge distributions of the two isomeric states. This circumstance explains in part why the nuclear isomeric shift was not discovered earlier: the appropriate nuclear theory and in particular the nuclear shell model were developed only in the late 1940s and early 1950s. As to the experimental observation of this shift, it also had to await the development of a new technique, that permitted spectroscopy with isomers, which are metastable nuclei. This too happened only in the 1950s.
While the isomeric shift is sensitive to the internal structure of the nucleus, the isotopic shift is (in a good approximation) not. Therefore, the nuclear physics information that can be obtained from the investigation of the isomeric shift, is superior to what can be obtained from isotopic-shift studies. The measurements through the isomeric shift of e.g. the difference of nuclear radii of the excited and ground state constitute one of the most sensitive tests of nuclear models. Moreover, combined with the Mössbauer effect, the isomeric shift constitutes at present a unique tool in many other fields besides physics.
According to the nuclear shell model, there exists a class of isomers, for which, in a first approximation, it is sufficient to consider one single nucleon, called the "optical" nucleon, to get an estimate of the difference between the charge distributions of the two isomer states, the rest of the nucleons being filtered out . This applies in particular for isomers in odd-proton–even-neutron nuclei, with nearly closed shells. Indium -115, for which the effect was calculated, [ 2 ] is such an example. The result of the calculation was that the isomeric shift on atomic spectral lines, although rather small, turned out to be two orders of magnitude bigger than a typical natural line width, which constitutes the limit of optical measurability.
The shift measured three years later [ 4 ] in Hg-197 was quite close to that calculated for In-115, although in Hg-197, unlike in In-115, the optical nucleon is a neutron instead of a proton, and the electron–free-neutron interaction is much smaller than the electron—free-proton interaction. This is a consequence of the fact that the optical nucleons are not free, but bound particles. [ 2 ] Thus the results [ 4 ] could be explained [ 8 ] within the theory [ 2 ] by associating with the odd optical neutron an effective electric charge of Z / A .
The Mössbauer isomeric shift is the shift seen in gamma-ray spectroscopy when one compares two different nuclear isomeric states in two different physical, chemical or biological environments, and is due to the combined effect of the recoil-free Mössbauer transition between the two nuclear isomeric states and the transition between two atomic states in those two environments.
The isomeric shift on atomic spectral lines depends on the electron wave function ψ and on the difference δφ of electrostatic potentials φ of the two isomeric states.
For a given nuclear isomer in two different physical or chemical environments (different physical phases or different chemical combinations), the electron wave functions are also different. Therefore, on top of the isomeric shift on atomic spectral lines, which is due to the difference of the two nuclear isomer states, there will be a shift between the two environments (because of the experimental arrangement, these are called source (s) and absorber (a)). This combined shift is the Mössbauer isomeric shift, and it is described mathematically by the same formalism as the nuclear isomeric shift on atomic spectral lines, except that instead of one electron wave function, that in the source ψ s , one deals with the difference between the electron wave function in the source ψ s and the electron wave function in the absorber ψ a :
The first measurement of the isomeric shift in gamma spectroscopy with the help of the Mössbauer effect was reported [ 9 ] in 1960, two years after its first experimental observation in atomic spectroscopy. [ 4 ] By measuring this shift, one obtains important and extremely precise information, both about the nuclear isomer states and about the physical, chemical or biological environment of the atoms, represented by the electronic wave functions.
Under its Mössbauer variant, the isomeric shift has found important applications in domains as different as atomic physics , solid-state physics , nuclear physics , chemistry , biology , metallurgy , mineralogy , geology , and lunar research. For further literature, see also. [ 10 ]
The nuclear isomeric shift has also been observed in muonic atoms, [ 11 ] that is, atoms in which a muon is captured by the excited nucleus and makes a transition from an atomic excited state to the atomic ground state in a time shorter than the lifetime of the excited isomeric nuclear state. | https://en.wikipedia.org/wiki/Isomeric_shift |
In chemistry , isomerization or isomerisation is the process in which a molecule , polyatomic ion or molecular fragment is transformed into an isomer with a different chemical structure . [ 1 ] Enolization is an example of isomerization, as is tautomerization . [ 2 ]
When the activation energy for the isomerization reaction is sufficiently small, both isomers can often be observed and the equilibrium ratio will shift in a temperature-dependent equilibrium with each other. Many values of the standard free energy difference, Δ G ∘ {\displaystyle \Delta G^{\circ }} , have been calculated, with good agreement between observed and calculated data. [ 3 ]
Skeletal isomerization occurs in the cracking process, used in the petrochemical industry to convert straight chain alkanes to isoparaffins as exemplified in the conversion of normal octane to 2,5-dimethylhexane (an "isoparaffin"): [ 4 ]
Fuels containing branched hydrocarbons are favored for internal combustion engines for their higher octane rating . [ 5 ] Diesel engines however operate better with straight-chain hydrocarbons.
Trans-alkenes are about 1 kcal/mol more stable than cis-alkenes. An example of this effect is cis- vs trans-2-butene. The difference is attributed to unfavorable non-bonded interactions in the cis isomer. This effects helps to explain the formation of trans-fats in food processing. In some cases, the isomerization can be reversed using UV-light. The trans isomer of resveratrol converts to the cis isomer in a photochemical reaction . [ 6 ]
Terminal alkenes prefer to isomerize to internal alkenes:
The conversion essentially does not occur in the absence of metal catalysts. This process is employed in the Shell higher olefin process to convert alpha-olefins to internal olefins, which are subjected to olefin metathesis .
Isomerism is a major topic in sugar chemistry. Glucose , the most common sugar, exists in four forms.
Aldose-ketose isomerism , also known as Lobry de Bruyn–van Ekenstein transformation, provides an example in saccharide chemistry . [ citation needed ]
The compound with the formula (C 5 H 5 ) 2 Fe 2 (CO) 4 exists as three isomers in solution. In one isomer the CO ligands are terminal. When a pair of CO are bridging ,
cis and trans isomers are possible depending on the location of the C 5 H 5 groups . [ 7 ]
Another example in organometallic chemistry is the linkage isomerization of decaphenylferrocene, [(η 5 -C 5 Ph 5 ) 2 Fe] . [ 8 ] [ 9 ]
From the kinetic viewpoint , isomerizations can be classified into two categories. [ 10 ] Cases in the first category involve transformations between equivalent structures. Most chemical species are in principle susceptible to such processes. Many such cases involve fluxional molecules , such as the cyclohexane ring flip (chair inversion), the pyramidal inversion of ammonia, the Berry pseudorotation in pentacoordinate compounds (e.g. PF 5 , Fe(CO) 5 ), the Cope rearrangements of bullvalene or the Ray-Dutt / Bailar twists for the racemization of octahedral complexes with three bidentate chelate rings ( helical chirality ).
In the second broad category of isomerizations, the isomers are nonequivalent. Examples include tautomerizations ( keto-enol , lactam-lactim , amide-imidic , enamine-imine , nitroso-oxime , ketene-ynol , etc) in which one isomer is more stable than the other.
This scheme leads to the following system of differential rate equations : | https://en.wikipedia.org/wiki/Isomerization |
In mathematics, an isometry (or congruence , or congruent transformation ) is a distance -preserving transformation between metric spaces , usually assumed to be bijective . [ a ] The word isometry is derived from the Ancient Greek : ἴσος isos meaning "equal", and μέτρον metron meaning "measure". If the transformation is from a metric space to itself, it is a kind of geometric transformation known as a motion .
Given a metric space (loosely, a set and a scheme for assigning distances between elements of the set), an isometry is a transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between the elements in the original metric space.
In a two-dimensional or three-dimensional Euclidean space , two geometric figures are congruent if they are related by an isometry; [ b ] the isometry that relates them is either a rigid motion (translation or rotation), or a composition of a rigid motion and a reflection .
Isometries are often used in constructions where one space is embedded in another space. For instance, the completion of a metric space M {\displaystyle M} involves an isometry from M {\displaystyle M} into M ′ , {\displaystyle M',} a quotient set of the space of Cauchy sequences on M . {\displaystyle M.} The original space M {\displaystyle M} is thus isometrically isomorphic to a subspace of a complete metric space , and it is usually identified with this subspace.
Other embedding constructions show that every metric space is isometrically isomorphic to a closed subset of some normed vector space and that every complete metric space is isometrically isomorphic to a closed subset of some Banach space .
An isometric surjective linear operator on a Hilbert space is called a unitary operator .
Let X {\displaystyle X} and Y {\displaystyle Y} be metric spaces with metrics (e.g., distances) d X {\textstyle d_{X}} and d Y . {\textstyle d_{Y}.} A map f : X → Y {\textstyle f\colon X\to Y} is called an isometry or distance-preserving map if for any a , b ∈ X {\displaystyle a,b\in X} ,
An isometry is automatically injective ; [ a ] otherwise two distinct points, a and b , could be mapped to the same point, thereby contradicting the coincidence axiom of the metric d , i.e., d ( a , b ) = 0 {\displaystyle d(a,b)=0} if and only if a = b {\displaystyle a=b} . This proof is similar to the proof that an order embedding between partially ordered sets is injective. Clearly, every isometry between metric spaces is a topological embedding .
A global isometry , isometric isomorphism or congruence mapping is a bijective isometry. Like any other bijection, a global isometry has a function inverse .
The inverse of a global isometry is also a global isometry.
Two metric spaces X and Y are called isometric if there is a bijective isometry from X to Y .
The set of bijective isometries from a metric space to itself forms a group with respect to function composition , called the isometry group .
There is also the weaker notion of path isometry or arcwise isometry :
A path isometry or arcwise isometry is a map which preserves the lengths of curves ; such a map is not necessarily an isometry in the distance preserving sense, and it need not necessarily be bijective, or even injective. [ 5 ] [ 6 ] This term is often abridged to simply isometry , so one should take care to determine from context which type is intended.
The following theorem is due to Mazur and Ulam.
Theorem [ 7 ] [ 8 ] — Let A : X → Y be a surjective isometry between normed spaces that maps 0 to 0 ( Stefan Banach called such maps rotations ) where note that A is not assumed to be a linear isometry.
Then A maps midpoints to midpoints and is linear as a map over the real numbers R {\displaystyle \mathbb {R} } .
If X and Y are complex vector spaces then A may fail to be linear as a map over C {\displaystyle \mathbb {C} } .
Given two normed vector spaces V {\displaystyle V} and W , {\displaystyle W,} a linear isometry is a linear map A : V → W {\displaystyle A:V\to W} that preserves the norms:
for all v ∈ V . {\displaystyle v\in V.} [ 9 ] Linear isometries are distance-preserving maps in the above sense.
They are global isometries if and only if they are surjective .
In an inner product space , the above definition reduces to
for all v ∈ V , {\displaystyle v\in V,} which is equivalent to saying that A † A = Id V . {\displaystyle A^{\dagger }A=\operatorname {Id} _{V}.} This also implies that isometries preserve inner products, as
Linear isometries are not always unitary operators , though, as those require additionally that V = W {\displaystyle V=W} and A A † = Id V {\displaystyle AA^{\dagger }=\operatorname {Id} _{V}} (i.e. the domain and codomain coincide and A {\displaystyle A} defines a coisometry ).
By the Mazur–Ulam theorem , any isometry of normed vector spaces over R {\displaystyle \mathbb {R} } is affine .
A linear isometry also necessarily preserves angles, therefore a linear isometry transformation is a conformal linear transformation .
An isometry of a manifold is any (smooth) mapping of that manifold into itself, or into another manifold that preserves the notion of distance between points.
The definition of an isometry requires the notion of a metric on the manifold; a manifold with a (positive-definite) metric is a Riemannian manifold , one with an indefinite metric is a pseudo-Riemannian manifold . Thus, isometries are studied in Riemannian geometry .
A local isometry from one ( pseudo -) Riemannian manifold to another is a map which pulls back the metric tensor on the second manifold to the metric tensor on the first. When such a map is also a diffeomorphism , such a map is called an isometry (or isometric isomorphism ), and provides a notion of isomorphism ("sameness") in the category Rm of Riemannian manifolds.
Let R = ( M , g ) {\displaystyle R=(M,g)} and R ′ = ( M ′ , g ′ ) {\displaystyle R'=(M',g')} be two (pseudo-)Riemannian manifolds, and let f : R → R ′ {\displaystyle f:R\to R'} be a diffeomorphism. Then f {\displaystyle f} is called an isometry (or isometric isomorphism ) if
where f ∗ g ′ {\displaystyle f^{*}g'} denotes the pullback of the rank (0, 2) metric tensor g ′ {\displaystyle g'} by f {\displaystyle f} .
Equivalently, in terms of the pushforward f ∗ , {\displaystyle f_{*},} we have that for any two vector fields v , w {\displaystyle v,w} on M {\displaystyle M} (i.e. sections of the tangent bundle T M {\displaystyle \mathrm {T} M} ),
If f {\displaystyle f} is a local diffeomorphism such that g = f ∗ g ′ , {\displaystyle g=f^{*}g',} then f {\displaystyle f} is called a local isometry .
A collection of isometries typically form a group, the isometry group . When the group is a continuous group , the infinitesimal generators of the group are the Killing vector fields .
The Myers–Steenrod theorem states that every isometry between two connected Riemannian manifolds is smooth (differentiable). A second form of this theorem states that the isometry group of a Riemannian manifold is a Lie group .
Symmetric spaces are important examples of Riemannian manifolds that have isometries defined at every point.
3.11 Any two congruent triangles are related by a unique isometry. — Coxeter (1969) p. 39 [ 3 ]
3.51 Any direct isometry is either a translation or a rotation. Any opposite isometry is either a reflection or a glide reflection. | https://en.wikipedia.org/wiki/Isometry |
isomiRs (from iso- + miR ) are miRNA sequences that have variations with respect to the reference sequence. The term was coined by Morin et al in 2008. [ 1 ] It has been found that isomiR expression profiles can also exhibit race, population, and sex dependencies. [ 2 ]
There are four main variation types:
miRBase is considered to be the gold-standard miRNA database—it stores miRNA sequences detected by thousand of experiments. In this database each miRNA is associated with a miRNA precursor and with one or two mature miRNA (-5p and -3p). In the past it had always been said that the same miRNA precursor generates the same miRNA sequences. However, the advent of deep sequencing has now allowed researchers to detect a huge variability in miRNA biogenesis, meaning that from the same miRNA precursor many different sequences can be generated potentially have different targets, [ 3 ] [ 4 ] [ 5 ] or even lead to opposite changes in mRNA expression. [ 4 ]
The advent of sequencing has permitted scientists to elucidate a huge landscape of new miRNAs, to increase our knowledge of the biogenesis involved and to discover putative post-transcriptional editing processes in miRNAs ignored until now. These processes mostly generate variations of the current miRNAs that are annotated in miRBase in the 3' and 5' terminus and in minor frequencies, nucleotide substitution along the miRNA length. [ 6 ] [ 7 ] [ 8 ] [ 9 ] The variations are mainly generated by a shift of Drosha and Dicer in the cleavage site, but also by nucleotide additions at the 3'-end, [ 10 ] resulting in new sequences different from the annotated miRNA. These were named "isomiRs" by Morin et al., 2008. IsomiRs have been well established along different species in metazoa [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] and deeply described for the first time in human stem cells and human brain samples. [ 8 ] [ 9 ] Moreover, it has been proven that isomiRs are not caused by RNA degradation during sample preparation for next generation sequencing. [ 16 ] Some studies have tried to explain the miRNA diversity by structural bases of precursors but without clear results. [ 17 ] The functionality of adenylation or uridynilation at the 3'end (3'addition isomiRs) has been related to alterations in the miRNA-3'-UTR stability. [ 18 ] Furthermore, differential expression of isomiRs has been detected during development in D. melanogaster and Hippoglossus hippoglossus L., suggesting a biological function. [ 15 ] [ 19 ] | https://en.wikipedia.org/wiki/IsomiR |
An isomorph is an organism that does not change in shape during growth. The implication is that its volume is proportional to its cubed length, and its surface area to its squared length. This holds for any shape it might have; the actual shape determines the proportionality constants.
The reason why the concept is important in the context of the Dynamic Energy Budget (DEB) theory is that food ( substrate ) uptake is proportional to surface area, and maintenance to volume. Since volume grows faster than surface area, this controls the ultimate size of the organism. Alfred Russel Wallace wrote this in a letter to E. B. Poulton in 1865. [ 1 ] [ 2 ] The surface area that is of importance is the part that is involved in substrate uptake (e.g. the gut surface), which is typically a fixed fraction of the total surface area in an isomorph. The DEB theory explains why isomorphs grow according to the von Bertalanffy curve if food availability is constant.
Organisms can also change in shape during growth, which affects the growth curve and the ultimate size, see for instance V0-morphs and V1-morphs . Isomorphs can also be called V2/3-morphs.
Most animals approximate isomorphy, but plants in a vegetation typically start as V1-morphs , then convert to isomorphs, and end up as V0-morphs (if neighbouring plants affect their uptake). | https://en.wikipedia.org/wiki/Isomorph |
In chemistry , isomorphism has meanings both at the level of crystallography and at a molecular level. In crystallography , crystals are isomorphous if they have identical symmetry and if the atomic positions can be described with a set of parameters (unit cell dimensions and fractional coordinates) whose numerical values differ only slightly. [ 1 ]
Molecules are isomorphous if they have similar shapes. The coordination complexes tris(acetylacetonato)iron (Fe(acac) 3 ) and tris(acetylacetonato)aluminium (Al(acac) 3 ) are isomorphous. These compounds, both of D 3 symmetry have very similar shapes, as determined by bond lengths and bond angles. Isomorphous compounds give rise to isomorphous crystals and form solid solutions . [ 2 ] Historically, crystal shape was defined by measuring the angles between crystal faces with a goniometer . Whereas crystals of Fe(acac) 3 are deep red and crystals of Al(acac) 3 are colorless, a solid solution of the two, i.e. Fe 1−x Al x (acac) 3 will be deep or pale pink depending on the Fe/Al ratio, x.
Double sulfates , such as Tutton's salt , with the generic formula M I 2 M II (SO 4 ) 2 .6H 2 O, where M I is an alkali metal and M II is a divalent ion of Mg , Mn , Fe , Co , Ni , Cu or Zn , form a series of isomorphous compounds which were important in the nineteenth century in establishing the correct atomic weights of the transition elements. Alums , such as KAl(SO 4 ) 2 .12H 2 O, are another series of isomorphous compounds, though there are three series of alums with similar external structures, but slightly different internal structures. Many spinels are also isomorphous.
In order to form isomorphous crystals two substances must have the same chemical formulation (i.e., atoms in the same ratio), they must contain atoms which have corresponding chemical properties and the sizes of corresponding atoms should be similar. These requirements ensure that the forces within and between molecules and ions are approximately similar and result in crystals that have the same internal structure. Even though the space group is the same, the unit cell dimensions will be slightly different because of the different sizes of the atoms involved.
Mitscherlich's law of isomorphism , or the law of isomorphism , is an approximate law suggesting that crystals composed of the same number of similar elements tend to demonstrate isomorphism. [ 3 ]
Mitscherlich's law is named for German chemist Eilhard Mitscherlich , [ 4 ] who formulated the law and published it between 1819 and 1823. [ 5 ]
According to Ferenc Szabadváry , one of the clues that helped Berzelius determine the atomic weights of the elements was "the discovery of Mitscherlich that compounds which contain the same number of atoms and have similar structures, exhibit similar crystal forms (isomorphism)." [ 6 ] | https://en.wikipedia.org/wiki/Isomorphism_(crystallography) |
In mathematics , an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping . Two mathematical structures are isomorphic if an isomorphism exists between them. The word is derived from Ancient Greek ἴσος (isos) ' equal ' and μορφή (morphe) ' form, shape ' .
The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties (excluding further information such as additional structure or names of objects). Thus isomorphic structures cannot be distinguished from the point of view of structure only, and may often be identified. In mathematical jargon , one says that two objects are the same up to an isomorphism. A common example where isomorphic structures cannot be identified is when the structures are substructures of a larger one. For example, all subspaces of dimension one of a vector space are isomorphic and cannot be identified.
An automorphism is an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if there is only one isomorphism between the two structures (as is the case for solutions of a universal property ), or if the isomorphism is much more natural (in some sense) than other isomorphisms. For example, for every prime number p , all fields with p elements are canonically isomorphic, with a unique isomorphism. The isomorphism theorems provide canonical isomorphisms that are not unique.
The term isomorphism is mainly used for algebraic structures and categories . In the case of algebraic structures, mappings are called homomorphisms , and a homomorphism is an isomorphism if and only if it is bijective .
In various areas of mathematics, isomorphisms have received specialized names, depending on the type of structure under consideration. For example:
Category theory , which can be viewed as a formalization of the concept of mapping between structures, provides a language that may be used to unify the approach to these different aspects of the basic idea.
Let R + {\displaystyle \mathbb {R} ^{+}} be the multiplicative group of positive real numbers , and let R {\displaystyle \mathbb {R} } be the additive group of real numbers.
The logarithm function log : R + → R {\displaystyle \log :\mathbb {R} ^{+}\to \mathbb {R} } satisfies log ( x y ) = log x + log y {\displaystyle \log(xy)=\log x+\log y} for all x , y ∈ R + , {\displaystyle x,y\in \mathbb {R} ^{+},} so it is a group homomorphism . The exponential function exp : R → R + {\displaystyle \exp :\mathbb {R} \to \mathbb {R} ^{+}} satisfies exp ( x + y ) = ( exp x ) ( exp y ) {\displaystyle \exp(x+y)=(\exp x)(\exp y)} for all x , y ∈ R , {\displaystyle x,y\in \mathbb {R} ,} so it too is a homomorphism.
The identities log exp x = x {\displaystyle \log \exp x=x} and exp log y = y {\displaystyle \exp \log y=y} show that log {\displaystyle \log } and exp {\displaystyle \exp } are inverses of each other. Since log {\displaystyle \log } is a homomorphism that has an inverse that is also a homomorphism, log {\displaystyle \log } is an isomorphism of groups , i.e., R + ≅ R {\displaystyle \mathbb {R} ^{+}\cong \mathbb {R} } via the isomorphism log x {\displaystyle \log x} .
The log {\displaystyle \log } function is an isomorphism which translates multiplication of positive real numbers into addition of real numbers. This facility makes it possible to multiply real numbers using a ruler and a table of logarithms , or using a slide rule with a logarithmic scale.
Consider the group ( Z 6 , + ) , {\displaystyle (\mathbb {Z} _{6},+),} the integers from 0 to 5 with addition modulo 6. Also consider the group ( Z 2 × Z 3 , + ) , {\displaystyle \left(\mathbb {Z} _{2}\times \mathbb {Z} _{3},+\right),} the ordered pairs where the x coordinates can be 0 or 1, and the y coordinates can be 0, 1, or 2, where addition in the x -coordinate is modulo 2 and addition in the y -coordinate is modulo 3.
These structures are isomorphic under addition, under the following scheme: ( 0 , 0 ) ↦ 0 ( 1 , 1 ) ↦ 1 ( 0 , 2 ) ↦ 2 ( 1 , 0 ) ↦ 3 ( 0 , 1 ) ↦ 4 ( 1 , 2 ) ↦ 5 {\displaystyle {\begin{alignedat}{4}(0,0)&\mapsto 0\\(1,1)&\mapsto 1\\(0,2)&\mapsto 2\\(1,0)&\mapsto 3\\(0,1)&\mapsto 4\\(1,2)&\mapsto 5\\\end{alignedat}}} or in general ( a , b ) ↦ ( 3 a + 4 b ) mod 6. {\displaystyle (a,b)\mapsto (3a+4b)\mod 6.}
For example, ( 1 , 1 ) + ( 1 , 0 ) = ( 0 , 1 ) , {\displaystyle (1,1)+(1,0)=(0,1),} which translates in the other system as 1 + 3 = 4. {\displaystyle 1+3=4.}
Even though these two groups "look" different in that the sets contain different elements, they are indeed isomorphic : their structures are exactly the same. More generally, the direct product of two cyclic groups Z m {\displaystyle \mathbb {Z} _{m}} and Z n {\displaystyle \mathbb {Z} _{n}} is isomorphic to ( Z m n , + ) {\displaystyle (\mathbb {Z} _{mn},+)} if and only if m and n are coprime , per the Chinese remainder theorem .
If one object consists of a set X with a binary relation R and the other object consists of a set Y with a binary relation S then an isomorphism from X to Y is a bijective function f : X → Y {\displaystyle f:X\to Y} such that: [ 1 ] S ( f ( u ) , f ( v ) ) if and only if R ( u , v ) {\displaystyle \operatorname {S} (f(u),f(v))\quad {\text{ if and only if }}\quad \operatorname {R} (u,v)}
S is reflexive , irreflexive , symmetric , antisymmetric , asymmetric , transitive , total , trichotomous , a partial order , total order , well-order , strict weak order , total preorder (weak order), an equivalence relation , or a relation with any other special properties, if and only if R is.
For example, R is an ordering ≤ and S an ordering ⊑ , {\displaystyle \scriptstyle \sqsubseteq ,} then an isomorphism from X to Y is a bijective function f : X → Y {\displaystyle f:X\to Y} such that f ( u ) ⊑ f ( v ) if and only if u ≤ v . {\displaystyle f(u)\sqsubseteq f(v)\quad {\text{ if and only if }}\quad u\leq v.} Such an isomorphism is called an order isomorphism or (less commonly) an isotone isomorphism .
If X = Y , {\displaystyle X=Y,} then this is a relation-preserving automorphism .
In algebra , isomorphisms are defined for all algebraic structures . Some are more specifically studied; for example:
Just as the automorphisms of an algebraic structure form a group , the isomorphisms between two algebras sharing a common structure form a heap . Letting a particular isomorphism identify the two structures turns this heap into a group.
In mathematical analysis , the Laplace transform is an isomorphism mapping hard differential equations into easier algebraic equations.
In graph theory , an isomorphism between two graphs G and H is a bijective map f from the vertices of G to the vertices of H that preserves the "edge structure" in the sense that there is an edge from vertex u to vertex v in G if and only if there is an edge from f ( u ) {\displaystyle f(u)} to f ( v ) {\displaystyle f(v)} in H . See graph isomorphism .
In order theory , an isomorphism between two partially ordered sets P and Q is a bijective map f {\displaystyle f} from P to Q that preserves the order structure in the sense that for any elements x {\displaystyle x} and y {\displaystyle y} of P we have x {\displaystyle x} less than y {\displaystyle y} in P if and only if f ( x ) {\displaystyle f(x)} is less than f ( y ) {\displaystyle f(y)} in Q . As an example, the set {1,2,3,6} of whole numbers ordered by the is-a-factor-of relation is isomorphic to the set { O , A , B , AB } of blood types ordered by the can-donate-to relation. See order isomorphism .
In mathematical analysis, an isomorphism between two Hilbert spaces is a bijection preserving addition, scalar multiplication, and inner product.
In early theories of logical atomism , the formal relationship between facts and true propositions was theorized by Bertrand Russell and Ludwig Wittgenstein to be isomorphic. An example of this line of thinking can be found in Russell's Introduction to Mathematical Philosophy .
In cybernetics , the good regulator theorem or Conant–Ashby theorem is stated as "Every good regulator of a system must be a model of that system". Whether regulated or self-regulating, an isomorphism is required between the regulator and processing parts of the system.
In category theory , given a category C , an isomorphism is a morphism f : a → b {\displaystyle f:a\to b} that has an inverse morphism g : b → a , {\displaystyle g:b\to a,} that is, f g = 1 b {\displaystyle fg=1_{b}} and g f = 1 a . {\displaystyle gf=1_{a}.}
Two categories C and D are isomorphic if there exist functors F : C → D {\displaystyle F:C\to D} and G : D → C {\displaystyle G:D\to C} which are mutually inverse to each other, that is, F G = 1 D {\displaystyle FG=1_{D}} (the identity functor on D ) and G F = 1 C {\displaystyle GF=1_{C}} (the identity functor on C ).
In a concrete category (roughly, a category whose objects are sets (perhaps with extra structure) and whose morphisms are structure-preserving functions), such as the category of topological spaces or categories of algebraic objects (like the category of groups , the category of rings , and the category of modules ), an isomorphism must be bijective on the underlying sets . In algebraic categories (specifically, categories of varieties in the sense of universal algebra ), an isomorphism is the same as a homomorphism which is bijective on underlying sets. However, there are concrete categories in which bijective morphisms are not necessarily isomorphisms (such as the category of topological spaces).
Since a composition of isomorphisms is an isomorphism, since the identity is an isomorphism and since the inverse of an isomorphism is an isomorphism, the relation that two mathematical objects are isomorphic is an equivalence relation . An equivalence class given by isomorphisms is commonly called an isomorphism class . [ 2 ]
Examples of isomorphism classes are plentiful in mathematics.
However, there are circumstances in which the isomorphism class of an object conceals vital information about it.
Although there are cases where isomorphic objects can be considered equal, one must distinguish equality and isomorphism . [ 3 ] Equality is when two objects are the same, and therefore everything that is true about one object is true about the other. On the other hand, isomorphisms are related to some structure, and two isomorphic objects share only the properties that are related to this structure.
For example, the sets A = { x ∈ Z ∣ x 2 < 2 } and B = { − 1 , 0 , 1 } {\displaystyle A=\left\{x\in \mathbb {Z} \mid x^{2}<2\right\}\quad {\text{ and }}\quad B=\{-1,0,1\}} are equal ; they are merely different representations—the first an intensional one (in set builder notation ), and the second extensional (by explicit enumeration)—of the same subset of the integers. By contrast, the sets { A , B , C } {\displaystyle \{A,B,C\}} and { 1 , 2 , 3 } {\displaystyle \{1,2,3\}} are not equal since they do not have the same elements. They are isomorphic as sets, but there are many choices (in fact 6) of an isomorphism between them: one isomorphism is
while another is
and no one isomorphism is intrinsically better than any other. [ note 1 ] On this view and in this sense, these two sets are not equal because one cannot consider them identical : one can choose an isomorphism between them, but that is a weaker claim than identity and valid only in the context of the chosen isomorphism.
Also, integers and even numbers are isomorphic as ordered sets and abelian groups (for addition), but cannot be considered equal sets, since one is a proper subset of the other.
On the other hand, when sets (or other mathematical objects ) are defined only by their properties, without considering the nature of their elements, one often considers them to be equal. This is generally the case with solutions of universal properties .
For example, the rational numbers are formally defined as equivalence classes of pairs of integers, although nobody thinks of a rational number as a set (equivalence class). The universal property of the rational numbers is essentially that they form a field that contains the integers and does not contain any proper subfield. Given two fields with these properties, there is a unique field isomorphism between them. This allows identifying these two fields, since every property of one of them can be transferred to the other through the isomorphism. The real numbers that can be expressed as a quotient of integers form the smallest subfield of the reals. There is thus a unique isomorphism from this subfield of the reals to the rational numbers defined by equivalence classes. | https://en.wikipedia.org/wiki/Isomorphism_class |
Isomyosamine , also known as MyMD-1 or MYMD-1 , is a synthetic derivative of tobacco plant alkaloids being developed as a metabolic- and immunomodulator by MyMD Pharmaceuticals . To date, isomyosamine has been shown to suppress the production of IFN-γ , IL-2 , IL-10 , and TNF-α , and decrease the severity of experimental thyroiditis in a murine model. [ 1 ] Trials in humans are being planned, and some are underway, examining the potential benefits of isomyosamine in autoimmune diseases such as rheumatoid arthritis , and in sarcopenia and frailty . [ 2 ]
MyMD Pharmaceuticals claim that MYMD-1 is not immunosuppressive , and thus should not be associated with the dangerous side effects such as infections that are seen in currently used TNF-α inhibitors such as adalimumab . [ 3 ] While it is true that there currently is no evidence of immunosuppression in isomyosamine recipients, this has not yet been tested in large clinical trials. [ citation needed ]
One preliminary murine study comparing isomyosamine to rapamycin , the best-characterised drug slowing the progression of aging, reported an increase in lifespan in the isomyosamine cohort, indicating anti-aging activity. Isomyosamine's anti-proliferative effects were similar to those of rapamycin. [ 4 ]
A phase I randomised double-blind placebo-controlled trial on healthy volunteers examining the safety and pharmacokinetic properties of different amounts of isomyosamine found no serious adverse events , but 3 cases of mild dysgeusia in the highest-dose (600 mg) cohort. A preliminary decrease in TNF-α levels was reported in the lowest-dose (150 mg) cohort, but not in the placebo cohort. [ 5 ] | https://en.wikipedia.org/wiki/Isomyosamine |
An isonym , in botanical taxonomy , is a name of a taxon that is identical to another designation, and based on the same type , but published at a different time by different authors. [ 1 ] Citation from that source follows:
When the same name, based on the same type, has been published independently at different times by different authors, then only the earliest of these "isonyms" has nomenclatural status. The name is always to be cited from its original place of valid publication, and later isonyms may be disregarded.
That is, the later isonyms are to be discarded (they are not botanical names ), and only the first one is to be used (though it is not necessarily the accepted name for a taxon).
An exception is made for family names that have been conserved ; [ 2 ] the place of publication listed for those names is considered to be correct and the name valid (and legitimate [ 3 ] ), even if an earlier publication of the same name is discovered. | https://en.wikipedia.org/wiki/Isonym |
Isopentenyl pyrophosphate ( IPP , isopentenyl diphosphate , or IDP ) [ 1 ] is an isoprenoid precursor. IPP is an intermediate in the classical, HMG-CoA reductase pathway (commonly called the mevalonate pathway) and in the non-mevalonate MEP pathway of isoprenoid precursor biosynthesis. Isoprenoid precursors such as IPP, and its isomer DMAPP , are used by organisms in the biosynthesis of terpenes and terpenoids .
IPP is formed from acetyl-CoA via the mevalonate pathway (the "upstream" part), and then is isomerized to dimethylallyl pyrophosphate by the enzyme isopentenyl pyrophosphate isomerase . [ 2 ]
IPP can be synthesised via an alternative non-mevalonate pathway of isoprenoid precursor biosynthesis, the MEP pathway , where it is formed from ( E )-4-hydroxy-3-methyl-but-2-enyl pyrophosphate (HMB-PP) by the enzyme HMB-PP reductase (LytB, IspH). The MEP pathway is present in many bacteria , apicomplexan protozoa such as malaria parasites, and in the plastids of higher plants . [ 3 ] | https://en.wikipedia.org/wiki/Isopentenyl_pyrophosphate |
Isopeptag is a 16-amino acid peptide tag (TDKDMTITFTNKKDAE) that can be genetically linked to proteins without interfering with protein folding. [ 1 ] What makes the isopeptag different from other peptide tags is that it can bind its binding protein through a permanent and irreversible covalent bond . Other peptide tags generally bind their targets through weak non-covalent interactions, thus limiting their use in applications where molecules experience extreme forces. The isopeptag's covalent binding to its target overcomes these barriers and allows target proteins to be studied in harsher molecular environments.
The isopeptag was developed by dissecting the pilin protein (Spy0128) from Streptococcus pyogenes . Spy0128 contains two intramolecular isopeptide bonds , [ 2 ] and to generate the isopeptag one of these bonds was split by removing the last β-strand in the protein.
When the isopeptag is bound to a target protein, it spontaneously binds its binding partner through an isopeptide bond , an amide bond formed autocatalytically. The reaction is robust and occurs at various temperatures from 4-37 °C, a pH range of 5–8, and in the presence of commonly used detergents. Also, the reaction is independent of the redox state of the environment and can occur equally well in both reducing and oxidizing conditions. [ 1 ]
The covalent binding of the isopeptag to its binding partner can be used to permanently link proteins together in the complex environment of a bacterial cell, to target proteins of interest for cellular imaging, and to develop new protein structures. [ 1 ] | https://en.wikipedia.org/wiki/Isopeptag |
An isopeptide bond is a type of amide bond formed between a carboxyl group of one amino acid and an amino group of another. An isopeptide bond is the linkage between the side chain amino or carboxyl group of one amino acid to the α-carboxyl, α-amino group, or the side chain of another amino acid. In a typical peptide bond , also known as eupeptide bond, the amide bond always forms between the α-carboxyl group of one amino acid and the α-amino group of the second amino acid. Isopeptide bonds are rarer than regular peptide bonds. [ 1 ] Isopeptide bonds lead to branching in the primary sequence of a protein. Proteins formed from normal peptide bonds typically have a linear primary sequence .
Amide bonds, and thus isopeptide bonds, are stabilized by resonance ( electron delocalization ) between the carbonyl oxygen , the carbonyl carbon , and the nitrogen atom. The bond strength of an isopeptide bond is similar to that of a peptide due to the similar bonding type. The bond strength of a peptide bond is around 300 kJ/mol, or about 70 kcal/mol. [ 2 ]
Amino acids such as lysine , glutamic acid , glutamine , aspartic acid , and asparagine can form isopeptide bonds because they all contain an amino or carboxyl group on their side chain. For example, the formation of an isopeptide bond between the sidechains of lysine and glutamine is as follows:
The ε-amino group of lysine can also react with the α-carboxyl group of any other amino acid as in the following reaction:
Isopeptide bond formation is typically enzyme-catalyzed . [ 3 ] The reaction between lysine and glutamine, as shown above, is catalyzed by a transglutaminase . Another example of enzyme-catalyzed isopeptide bond formation is the formation of the glutathione molecule. Glutathione, a tripeptide , contains a normal peptide bond (between cysteine and glycine ) and an isopeptide bond (between glutamate and cysteine). The formation of the isopeptide bond between the γ-carboxyl group of glutamate and the α-amino group of cysteine is catalyzed by the enzyme γ-glutamylcysteine synthetase . [ 3 ] The isopeptide bond is formed instead of a eupeptide bond because intracellular peptidases [ 3 ] are unable to recognize this linkage and therefore do not hydrolyze the bond. An isopeptide bond can form spontaneously as observed in the maturation of the bacteriophage HK97 capsid . [ 4 ] In this case, the ε-amino group of lysine autocatalytically reacts with the side chain carboxamide group of asparagine . [ 4 ] Spontaneous isopeptide bond formation between lysine and asparagine also occurs in Gram-positive bacterial pili . [ 5 ]
Enzyme-generated isopeptide bonds have two main biological purposes: signaling and structure .
Biosignaling influences protein function, [ 6 ] chromatin condensation, [ 7 ] and protein-half life. [ 8 ] The biostructural roles of isopeptide bonds include blood clotting [ 9 ] (for wound healing), extracellular matrix upkeep, [ 10 ] the apoptosis pathway , [ 10 ] modifying micro-tubules , [ 11 ] and forming pathogenic pili [ 12 ] in bacteria. Isopeptide bonds contribute to the pathogenicity of Vibrio cholerae because the actin cross-linking domain (ACD) forms an intermolecular bond between the γ-carboxyl group of glutamate and the ε-amino group of lysine in actin . [ 13 ] This process stops actin polymerization in the host cell . [ 13 ]
For isopeptide bonds linking one protein to another for the purpose of signal transduction, the literature is dominated by ubiquitin and other similar proteins. Ubiquitin and its related proteins ( SUMO , Atg8 , Atg12 , etc.) all tend to follow relatively the same protein ligation pathway. [ 6 ]
The process of protein ligation by ubiquitin and ubiquitin-like proteins has three main steps. [ 6 ] In the initial step, the specific activating protein (E1 or E1-like protein) activates Ubiquitin by adenylating it with ATP . [ 6 ] Then the adenylated Ubiquitin can be transferred to a conserved cysteine using a thioester bond which is between the carboxyl group of the C-terminal glycine of the ubiquitin and the sulfur of the E1 cysteine. [ 6 ] [ 14 ] [ 8 ] The activating E1 enzyme then binds with and transfers the Ubiquitin to the next tier, the E2 enzyme which accepts the protein and once again forms a thioester with a conserved bond. The E2 acts to certain degree as an intermediary which then binds to E3 enzyme ligase for the final tier, which leads to the eventual transfer of the ubiquitin or ubiquitin related protein to a lysine site on the targeted protein, or more commonly for ubiquitin, onto ubiquitin itself to form chains of said protein. [ 14 ]
However, in final tier, there is also a divergence, in that depending on the type of E3 ligase, it may not actually be causing the conjugation. As there are the E3 ligases containing HECT domains, in which they continue this 'transfer chain' by accepting once again the ubiquitin via another conserved cysteine and then targeting it and transferring it to the desired target. Yet in case of RING finger domain containing that use coordination bonds with Zinc ions to stabilize their structures, they act more to direct the reaction. By that, it's meant that once the RING finger E3 ligase binds with the E2 containing the ubiquitin, it simply acts as a targeting device which directs the E2 to directly ligate the target protein at the lysine site. [ 14 ] [ 15 ]
Though in this case ubiquitin does represent other proteins related to it well, each protein obviously will have its own nuisances such as SUMO, which tends to be RING finger domain ligases, where the E3 simply acts as the targeting device to direct the ligation by the E2, and not actually performing the reaction itself such as the Ubiquitin E3-HECT ligases. [ 8 ] Thus while the internal mechanisms differ such as how proteins participate in the transfer chain, the general chemical aspects such as using thioesters and specific ligases for targeting remain the same.
The enzymatic chemistry involved in the formation of isopeptides for structural purposes is different from the case of ubiquitin and ubiquitin related proteins. In that, instead of sequential steps involving multiple enzymes to activate, conjugate and target the substrate. [ 16 ] The catalysis is performed by one enzyme and the only precursor step, if there is one, is generally cleavage to activate it from a zymogen. However, the uniformity that exists in the ubiquitin's case is not so here, as there are numerous different enzymes all performing the reaction of forming the isopeptide bond. [ citation needed ]
The first case is that of the sortases, an enzyme family that is spread throughout numerous gram positive bacteria. It has been shown to be an important pathogenicity and virulence factor. The general reaction performed by sortases involves using its own brand of the 'catalytic triad': i.e. using histidine, arginine, and cysteine for the reactive mechanism. His and Arg act to help create the reactive environment, and Cys once again acts as the reaction center by using a thioester help hold a carboxyl group until the amine of a Lysine can perform a nucleophilic attack to transfer the protein and form the isopeptide bond. An ion that can sometimes play an important although indirect role in the enzymatic reaction is calcium, which is bound by sortase. It plays an important role in holding the structure of the enzyme in the optimal conformation for catalysis. However, there are cases where calcium has been shown to be non-essential for catalysis to take place. [ 17 ]
Another aspect that distinguishes sortases in general is that they have a very specific targeting for their substrate, as sortases have generally two functions, the first is the fusing of proteins to the cell wall of the bacteria and the second is the polymerization of pilin. For the process of localization of proteins to the cell wall there is three-fold requirement that the protein contain a hydrophobic domain, a positively charged tail region, and final specific sequence used for recognition. [ 12 ] The best studied of these signals is the LPXTG, which acts as the point of cleavage, where the sortase attacks in between Thr and Gly, conjugating to the Thr carboxyl group. [ 17 ] Then the thioester is resolved by the transfer of the peptide to a primary amine, and this generally has a very high specificity, which is seen in the example of B. cereus where the sortase D enzyme helps to polymerize the BcpA protein via two recognition signals, the LPXTG as the cleavage and thioester forming point, and the YPKN site which acts as the recognition signal as where the isopeptide will form. [ 18 ] While the particulars may vary between bacteria, the fundamentals of sortase enzymatic chemistry remain the same. [ citation needed ]
The next case is that of Transglutaminases (TGases), which act mainly within eukaryotes for fusing together different proteins for a variety of reasons such as a wound healing or attaching proteins to lipid membranes. [ 19 ] [ 20 ] The TGases themselves also contain their own 'catalytic triad' with Histidine, Aspartate, and Cysteine. The roles of these residues are analogous or the same as the previously described Sortases, in that His and Asp play a supporting role in interacting with the target residue, while the Cys forms a thioester with a carboxyl group for a later nucleophilic attack by a primary amine, in this case due to interest that of Lysine. Though the similarities to sortase catalytically start to end there, as the enzyme and the family is dependent on calcium, which plays a crucial structural role in holding a tight conformation of the enzyme. The TGases, also have a very different substrate specificity in that they target specifically the middle Gln, in the sequence 'Gln-Gln-Val'. The general substrate specificity, i.e. the specific protein is due to the general structure of different TGases which targets them to the substrate. [ 19 ]
The specificity has been noted in TGases such that different TGases will react with different Gln's on the same protein, signifying that the enzymes have a very specific initial targeting. [ 21 ] It has also been shown to have some specificity as to which target Lysine it transfers the protein to, as in the case of Factor XIII, where the adjacent residue to the Lys decides whether the reaction will occur. [ 20 ] Thus while the TGases may initially seem like a eukaryotic sortase, they stand on their own as separate set of enzymes.
Another case of an isopeptide linking enzyme for structural purposes is the actin cross-linking domain (ACD) of the MARTX toxin protein generated by V. cholerae. While it has been shown that the ACD when performing the catalysis uses magnesium and ATP for the formation of the cross-links the specifics of the mechanism are uncertain. Though an interesting aspect of the cross-link formed in this case, is that it uses a non-terminal Glu to ligate to a non-terminal Lys, which seems to be rare in the process of forming an isopeptide bond. [ 13 ] Though the chemistry of ACD is still to be resolved, it shows that isopeptide bond formation is not dependent simply on Asp/Asn for non-terminal isopeptide linkages between proteins. [ citation needed ]
The final case to be looked is the curious case of the post translational modifications of microtubilin (MT). MT contains a wide array of post translational modifications; however the two of most regarded interest are polyglutamylation and polyglycylation. Both modifications are similar in the sense they are repeating stretches of the same amino acid fused to the side chain carboxyl group of glutamate at the c-terminal region of the MT. The enzymatic mechanisms are not fully fleshed out as not much is known about the polyglycating enzyme. In the case of polyglutamylation the exact mechanism is also unknown, but it does seem to be ATP-dependent. [ 22 ] Though again there is a lack of clarity in regard to the enzymatic chemistry, there is still valuable insight in the formation of isopeptide bonds using the R-group carboxyl of Glu in conjunction with the N-terminal amino of the modifying peptides. [ citation needed ]
Spontaneous isopeptide bond formation has been exploited in the development a peptide tag called SpyTag . SpyTag can spontaneously and irreversibly react with its binding partner (a protein termed SpyCatcher) through a covalent isopeptide bond. [ 23 ] This molecular tool may have applications for in vivo protein targeting, fluorescent microscopy, and irreversible attachment for a protein microarray . Following this, other Tag/Catcher systems were developed such as SnoopTag/SnoopCatcher [ 24 ] and SdyTag/SdyCatcher [ 25 ] that complement SpyTag/SpyCatcher. | https://en.wikipedia.org/wiki/Isopeptide_bond |
In mathematics , the isoperimetric dimension of a manifold is a notion of dimension that tries to capture how the large-scale behavior of the manifold resembles that of a Euclidean space (unlike the topological dimension or the Hausdorff dimension which compare different local behaviors against those of the Euclidean space).
In the Euclidean space , the isoperimetric inequality says that of all bodies with the same volume, the ball has the smallest surface area. In other manifolds it is usually very difficult to find the precise body minimizing the surface area, and this is not what the isoperimetric dimension is about. The question we will ask is, what is approximately the minimal surface area, whatever the body realizing it might be.
We say about a differentiable manifold M that it satisfies a d -dimensional isoperimetric inequality if for any open set D in M with a smooth boundary one has
The notations vol and area refer to the regular notions of volume and surface area on the manifold, or more precisely, if the manifold has n topological dimensions then vol refers to n -dimensional volume and area refers to ( n − 1)-dimensional volume. C here refers to some constant, which does not depend on D (it may depend on the manifold and on d ).
The isoperimetric dimension of M is the supremum of all values of d such that M satisfies a d -dimensional isoperimetric inequality.
A d -dimensional Euclidean space has isoperimetric dimension d . This is the well known isoperimetric problem — as discussed above, for the Euclidean space the constant C is known precisely since the minimum is achieved for the ball.
An infinite cylinder (i.e. a product of the circle and the line ) has topological dimension 2 but isoperimetric dimension 1. Indeed, multiplying any manifold with a compact manifold does not change the isoperimetric dimension (it only changes the value of the constant C ). Any compact manifold has isoperimetric dimension 0.
It is also possible for the isoperimetric dimension to be larger than the topological dimension. The simplest example is the infinite jungle gym , which has topological dimension 2 and isoperimetric dimension 3. See [1] for pictures and Mathematica code.
The hyperbolic plane has topological dimension 2 and isoperimetric dimension infinity. In fact the hyperbolic plane has positive Cheeger constant . This means that it satisfies the inequality
which obviously implies infinite isoperimetric dimension.
A simple integration over r (or sum in the case of graphs) shows that a d -dimensional isoperimetric inequality implies a d -dimensional volume growth , namely
where B ( x , r ) denotes the ball of radius r around the point x in the Riemannian distance or in the graph distance . In general, the opposite is not true, i.e. even uniformly exponential volume growth does not imply any kind of isoperimetric inequality. A simple example can be had by taking the graph Z (i.e. all the integers with edges between n and n + 1) and connecting to the vertex n a complete binary tree of height | n |. Both properties (exponential growth and 0 isoperimetric dimension) are easy to verify.
An interesting exception is the case of groups . It turns out that a group with polynomial growth of order d has isoperimetric dimension d . This holds both for the case of Lie groups and for the Cayley graph of a finitely generated group .
A theorem of Varopoulos connects the isoperimetric dimension of a graph to the rate of escape of random walk on the graph. The result states
Varopoulos' theorem: If G is a graph satisfying a d-dimensional isoperimetric inequality then
where p n ( x , y ) {\textstyle p_{n}(x,y)} is the probability that a random walk on G starting from x will be in y after n steps, and C is some constant. | https://en.wikipedia.org/wiki/Isoperimetric_dimension |
In mathematics , the isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations. Isoperimetric literally means "having the same perimeter ". Specifically, the isoperimetric inequality states, for the length L of a closed curve and the area A of the planar region that it encloses, that
and that equality holds if and only if the curve is a circle.
The isoperimetric problem is to determine a plane figure of the largest possible area whose boundary has a specified length. [ 1 ] The closely related Dido's problem asks for a region of the maximal area bounded by a straight line and a curvilinear arc whose endpoints belong to that line. It is named after Dido , the legendary founder and first queen of Carthage . The solution to the isoperimetric problem is given by a circle and was known already in Ancient Greece . However, the first mathematically rigorous proof of this fact was obtained only in the 19th century. Since then, many other proofs have been found.
The isoperimetric problem has been extended in multiple ways, for example, to curves on surfaces and to regions in higher-dimensional spaces. Perhaps the most familiar physical manifestation of the 3-dimensional isoperimetric inequality is the shape of a drop of water. Namely, a drop will typically assume a symmetric round shape. Since the amount of water in a drop is fixed, surface tension forces the drop into a shape which minimizes the surface area of the drop, namely a round sphere.
The classical isoperimetric problem dates back to antiquity. [ 2 ] The problem can be stated as follows: Among all closed curves in the plane of fixed perimeter, which curve (if any) maximizes the area of its enclosed region? This question can be shown to be equivalent to the following problem: Among all closed curves in the plane enclosing a fixed area, which curve (if any) minimizes the perimeter?
This problem is conceptually related to the principle of least action in physics , in that it can be restated: what is the principle of action which encloses the greatest area, with the greatest economy of effort? [ citation needed ] The 15th-century philosopher and scientist, Cardinal Nicholas of Cusa , considered rotational action, the process by which a circle is generated, to be the most direct reflection, in the realm of sensory impressions, of the process by which the universe is created. German astronomer and astrologer Johannes Kepler invoked the isoperimetric principle in discussing the morphology of the Solar System , in Mysterium Cosmographicum ( The Sacred Mystery of the Cosmos , 1596).
Although the circle appears to be an obvious solution to the problem, proving this fact is rather difficult. The first progress toward the solution was made by Swiss geometer Jakob Steiner in 1838, using a geometric method later named Steiner symmetrisation . [ 3 ] Steiner showed that if a solution existed, then it must be the circle. Steiner's proof was completed later by several other mathematicians.
Steiner begins with some geometric constructions which are easily understood; for example, it can be shown that any closed curve enclosing a region that is not fully convex can be modified to enclose more area, by "flipping" the concave areas so that they become convex. It can further be shown that any closed curve which is not fully symmetrical can be "tilted" so that it encloses more area. The one shape that is perfectly convex and symmetrical is the circle, although this, in itself, does not represent a rigorous proof of the isoperimetric theorem (see external links).
The solution to the isoperimetric problem is usually expressed in the form of an inequality that relates the length L of a closed curve and the area A of the planar region that it encloses. The isoperimetric inequality states that
and that the equality holds if and only if the curve is a circle. The area of a disk of radius R is πR 2 and the circumference of the circle is 2 πR , so both sides of the inequality are equal to 4 π 2 R 2 in this case.
Dozens of proofs of the isoperimetric inequality have been found. In 1902, Hurwitz published a short proof using the Fourier series that applies to arbitrary rectifiable curves (not assumed to be smooth). An elegant direct proof based on comparison of a smooth simple closed curve with an appropriate circle was given by E. Schmidt in 1938. It uses only the arc length formula, expression for the area of a plane region from Green's theorem , and the Cauchy–Schwarz inequality .
For a given closed curve, the isoperimetric quotient is defined as the ratio of its area and that of the circle having the same perimeter. This is equal to
and the isoperimetric inequality says that Q ≤ 1. Equivalently, the isoperimetric ratio L 2 / A is at least 4 π for every curve.
The isoperimetric quotient of a regular n -gon is
Let C {\displaystyle C} be a smooth regular convex closed curve. Then the improved isoperimetric inequality states the following
where L , A , A ~ 0.5 {\displaystyle L,A,{\widetilde {A}}_{0.5}} denote the length of C {\displaystyle C} , the area of the region bounded by C {\displaystyle C} and the oriented area of the Wigner caustic of C {\displaystyle C} , respectively, and the equality holds if and only if C {\displaystyle C} is a curve of constant width . [ 4 ]
Let C be a simple closed curve on a sphere of radius 1. Denote by L the length of C and by A the area enclosed by C . The spherical isoperimetric inequality states that
and that the equality holds if and only if the curve is a circle. There are, in fact, two ways to measure the spherical area enclosed by a simple closed curve, but the inequality is symmetric with the respect to taking the complement.
This inequality was discovered by Paul Lévy (1919) who also extended it to higher dimensions and general surfaces. [ 5 ]
In the more general case of arbitrary radius R , it is known [ 6 ] that
The isoperimetric inequality states that a sphere has the smallest surface area per given volume. Given a bounded open set S ⊂ R n {\displaystyle S\subset \mathbb {R} ^{n}} with C 1 {\displaystyle C^{1}} boundary, having surface area per ( S ) {\displaystyle \operatorname {per} (S)} and volume vol ( S ) {\displaystyle \operatorname {vol} (S)} , the isoperimetric inequality states
where B 1 ⊂ R n {\displaystyle B_{1}\subset \mathbb {R} ^{n}} is a unit ball . The equality holds when S {\displaystyle S} is a ball in R n {\displaystyle \mathbb {R} ^{n}} . Under additional restrictions on the set (such as convexity , regularity , smooth boundary ), the equality holds for a ball only. But in full generality the situation is more complicated. The relevant result of Schmidt (1949 , Sect. 20.7) (for a simpler proof see Baebler (1957) ) is clarified in Hadwiger (1957 , Sect. 5.2.5) as follows. An extremal set consists of a ball and a "corona" that contributes neither to the volume nor to the surface area. That is, the equality holds for a compact set S {\displaystyle S} if and only if S {\displaystyle S} contains a closed ball B {\displaystyle B} such that vol ( B ) = vol ( S ) {\displaystyle \operatorname {vol} (B)=\operatorname {vol} (S)} and per ( B ) = per ( S ) . {\displaystyle \operatorname {per} (B)=\operatorname {per} (S).} For example, the "corona" may be a curve.
The proof of the inequality follows directly from Brunn–Minkowski inequality between a set S {\displaystyle S} and a ball with radius ϵ {\displaystyle \epsilon } , i.e. B ϵ = ϵ B 1 {\displaystyle B_{\epsilon }=\epsilon B_{1}} . Indeed, vol ( A + B ϵ ) ≥ ( vol ( A ) 1 / n + vol ( B ϵ ) 1 / n ) n ≥ vol ( A ) + n vol ( A ) ( n − 1 ) / n ϵ vol ( B 1 ) 1 / n . {\displaystyle \operatorname {vol} (A+B_{\epsilon })\geq (\operatorname {vol} (A)^{1/n}+\operatorname {vol} (B_{\epsilon })^{1/n})^{n}\geq \operatorname {vol} (A)+n\operatorname {vol} (A)^{(n-1)/n}\epsilon \operatorname {vol} (B_{1})^{1/n}.} The isoperimetric inequality follows by subtracting vol ( A ) {\textstyle \operatorname {vol} (A)} , dividing by ϵ {\displaystyle \epsilon } , and taking the limit as ϵ → 0. {\displaystyle \epsilon \to 0.} ( Osserman (1978) ; Federer (1969 , §3.2.43)).
In full generality ( Federer 1969 , §3.2.43), the isoperimetric inequality states that for any set S ⊂ R n {\displaystyle S\subset \mathbb {R} ^{n}} whose closure has finite Lebesgue measure
where M ∗ n − 1 {\displaystyle M_{*}^{n-1}} is the ( n -1)-dimensional Minkowski content , L n is the n -dimensional Lebesgue measure, and ω n is the volume of the unit ball in R n {\displaystyle \mathbb {R} ^{n}} . If the boundary of S is rectifiable , then the Minkowski content is the ( n -1)-dimensional Hausdorff measure .
The n -dimensional isoperimetric inequality is equivalent (for sufficiently smooth domains) to the Sobolev inequality on R n {\displaystyle \mathbb {R} ^{n}} with optimal constant:
for all u ∈ W 1 , 1 ( R n ) {\displaystyle u\in W^{1,1}(\mathbb {R} ^{n})} .
Hadamard manifolds are complete simply connected manifolds with nonpositive curvature. Thus they generalize the Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , which is a Hadamard manifold with curvature zero. In 1970's and early 80's, Thierry Aubin , Misha Gromov , Yuri Burago , and Viktor Zalgaller conjectured that the Euclidean isoperimetric inequality
holds for bounded sets S {\displaystyle S} in Hadamard manifolds, which has become known as the Cartan–Hadamard conjecture .
In dimension 2 this had already been established in 1926 by André Weil , who was a student of Hadamard at the time.
In dimensions 3 and 4 the conjecture was proved by Bruce Kleiner in 1992, and Chris Croke in 1984 respectively.
Most of the work on isoperimetric problem has been done in the context of smooth regions in Euclidean spaces , or more generally, in Riemannian manifolds . However, the isoperimetric problem can be formulated in much greater generality, using the notion of Minkowski content . Let ( X , μ , d ) {\displaystyle (X,\mu ,d)} be a metric measure space : X is a metric space with metric d , and μ is a Borel measure on X . The boundary measure , or Minkowski content , of a measurable subset A of X is defined as the lim inf
where
is the ε- extension of A .
The isoperimetric problem in X asks how small can μ + ( A ) {\displaystyle \mu ^{+}(A)} be for a given μ ( A ). If X is the Euclidean plane with the usual distance and the Lebesgue measure then this question generalizes the classical isoperimetric problem to planar regions whose boundary is not necessarily smooth, although the answer turns out to be the same.
The function
is called the isoperimetric profile of the metric measure space ( X , μ , d ) {\displaystyle (X,\mu ,d)} . Isoperimetric profiles have been studied for Cayley graphs of discrete groups and for special classes of Riemannian manifolds (where usually only regions A with regular boundary are considered).
In graph theory , isoperimetric inequalities are at the heart of the study of expander graphs , which are sparse graphs that have strong connectivity properties. Expander constructions have spawned research in pure and applied mathematics, with several applications to complexity theory , design of robust computer networks , and the theory of error-correcting codes . [ 7 ]
Isoperimetric inequalities for graphs relate the size of vertex subsets to the size of their boundary, which is usually measured by the number of edges leaving the subset (edge expansion) or by the number of neighbouring vertices (vertex expansion). For a graph G {\displaystyle G} and a number k {\displaystyle k} , the following are two standard isoperimetric parameters for graphs. [ 8 ]
Here E ( S , S ¯ ) {\displaystyle E(S,{\overline {S}})} denotes the set of edges leaving S {\displaystyle S} and Γ ( S ) {\displaystyle \Gamma (S)} denotes the set of vertices that have a neighbour in S {\displaystyle S} . The isoperimetric problem consists of understanding how the parameters Φ E {\displaystyle \Phi _{E}} and Φ V {\displaystyle \Phi _{V}} behave for natural families of graphs.
The d {\displaystyle d} -dimensional hypercube Q d {\displaystyle Q_{d}} is the graph whose vertices are all Boolean vectors of length d {\displaystyle d} , that is, the set { 0 , 1 } d {\displaystyle \{0,1\}^{d}} . Two such vectors are connected by an edge in Q d {\displaystyle Q_{d}} if they are equal up to a single bit flip, that is, their Hamming distance is exactly one.
The following are the isoperimetric inequalities for the Boolean hypercube. [ 9 ]
The edge isoperimetric inequality of the hypercube is Φ E ( Q d , k ) ≥ k ( d − log 2 k ) {\displaystyle \Phi _{E}(Q_{d},k)\geq k(d-\log _{2}k)} . This bound is tight, as is witnessed by each set S {\displaystyle S} that is the set of vertices of any subcube of Q d {\displaystyle Q_{d}} .
Harper's theorem [ 10 ] says that Hamming balls have the smallest vertex boundary among all sets of a given size. Hamming balls are sets that contain all points of Hamming weight at most r {\displaystyle r} and no points of Hamming weight larger than r + 1 {\displaystyle r+1} for some integer r {\displaystyle r} . This theorem implies that any set S ⊆ V {\displaystyle S\subseteq V} with
satisfies
As a special case, consider set sizes k = | S | {\displaystyle k=|S|} of the form
for some integer r {\displaystyle r} . Then the above implies that the exact vertex isoperimetric parameter is
The isoperimetric inequality for triangles in terms of perimeter p and area T states that [ 13 ]
with equality for the equilateral triangle . This is implied, via the AM–GM inequality , by a stronger inequality which has also been called the isoperimetric inequality for triangles: [ 14 ] | https://en.wikipedia.org/wiki/Isoperimetric_inequality |
The isoplanatic patch is defined as an arbitrary area of the sky over which the path length of incoming electromagnetic waves (such as light or radio waves) only varies by a relatively small amount relative to their wavelength . [ 1 ] Typically this area is measured by angular size . Poor seeing or a larger telescope aperture will decrease the size of a patch. Thus, the patch size varies inversely with the Fried parameter and the telescope's angular resolution . In order to correct for atmospheric distortion, telescopes fitted with adaptive optics use a bright light source such as a laser to identify the properties of a patch in the area of interest.
This astronomy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isoplanatic_patch |
This page provides supplementary chemical data on isopropanol .
The handling of this chemical may incur notable safety precautions. It is highly recommend that you seek the Material Safety Datasheet ( MSDS ) for this chemical from a reliable source such as eChemPortal , and follow its directions.
Table data obtained from CRC Handbook of Chemistry and Physics 44th ed.
See also | https://en.wikipedia.org/wiki/Isopropyl_alcohol_(data_page) |
Isopropyl β- d -1-thiogalactopyranoside ( IPTG ) is a molecular biology reagent. This compound is a molecular mimic of allolactose , a lactose metabolite that triggers transcription of the lac operon , and it is therefore used to induce protein expression where the gene is under the control of the lac operator .
Like allolactose, IPTG binds to the lac repressor and releases the tetrameric repressor from the lac operator in an allosteric manner, thereby allowing the transcription of genes in the lac operon, such as the gene coding for beta-galactosidase , a hydrolase enzyme that catalyzes the hydrolysis of β-galactosides into monosaccharides. But unlike allolactose, the sulfur ( S ) atom creates a chemical bond which is non-hydrolyzable by the cell, preventing the cell from metabolizing or degrading the inducer . Therefore, its concentration remains constant during an experiment.
IPTG uptake by E. coli can be independent of the action of lactose permease , since other transport pathways are also involved. [ 1 ] At low concentration, IPTG enters cells through lactose permease, but at high concentrations (typically used for protein induction), IPTG can enter the cells independently of lactose permease. [ 2 ]
When stored as a powder at 4 °C or below, IPTG is stable for 5 years. It is significantly less stable in solution; Sigma recommends storage for no more than a month at room temperature. [ 3 ] IPTG is an effective inducer of protein expression in the concentration range of 100 μmol/L to 3.0 mmol/L . Typically, a sterile, filtered 1 mol/L solution of IPTG is added 1:1000 to an exponentially growing bacterial culture, to give a final concentration of 1 mmol/L. The concentration used depends on the strength of induction required, as well as the genotype of cells or plasmid used. If lacI q , a mutant that over-produces the lac repressor, is present, then a higher concentration of IPTG may be necessary. [ 4 ]
In blue-white screen , IPTG is used together with X-gal . Blue-white screen allows colonies that have been transformed with the recombinant plasmid rather than a non-recombinant one to be identified in cloning experiments. [ citation needed ] [ 5 ] | https://en.wikipedia.org/wiki/Isopropyl_β-D-1-thiogalactopyranoside |
Isoproturon ( IPU ) is a urea class selective herbicide , which has been used to control annual grasses and many broad leafed weeds in wheat , barley , rye and triticale . [ 5 ]
Isoproturon was introduced in 1971 [ 7 ] by Hoechst AG , (now AgrEvo GmbH), Rhône-Poulenc and Ciba-Geigy AG. [ 1 ] It was once one of the most widely used herbicides in the world, however it has suffered various bans, including the USA , and until 2016 was sold in 22 European countries. [ 8 ]
IPU is used in India. [ 9 ] In 2007, 624 tonnes (1,376,000 lb) was used, 2.6% of India's total herbicide consumption. [ 10 ]
Isoproturon was never registered in Australia. Agronomist Bill Crabtree estimates potential A$47 billion savings if IPU had been available since 1980. 4Farmers' attempt to register IPU is ongoing. [ 11 ] [ 12 ]
Isoproturon is used in the UK.
Isoproturon was banned in March 2007, taking effect in July 2009, due to its effects on the aquatic environment. [ 13 ]
By 2014 the ban was reversed. Lower concentration formulations, notably Blutron, with 250 g/L IPU and 50 g/L diflufenican , were for sale. Greater solubility allows lower concentrations of IPU and greater plant uptake -- lessening the residue left in the environment. [ 14 ]
Isoproturon's registration in the European Union is expired, though under EC Regulation 1107/2009 it is approved in the Netherlands and no other EU member nation. [ 7 ] The EU's ban took effect from the 30th of September 2016. [ 15 ]
The EU Commission, that also banned amitrole , did so only partially on endocrine disruption concerns, and other unclear grounds. If it had been for only endocrine disruption, it is likely exemptions would be available (for 'serious danger to plant health' or 'negligible exposure') under EU law. [ 15 ] The European Court of Justice ruled in December 2015 that the commission illegally broke their "clear, precise and unconditional obligation" to publish scientific criteria. [ 16 ]
Isoproturon is not registered in the United States. Presumably, it has never been registered.
Isoproturon is non-persistent in soil; very photochemically stable, and stable to acids and alkalis , [ 1 ] but under sustained ultraviolet light can degrade into some eleven products, [ 5 ] and can be hydrolytically cleaved by strong bases on heating. [ 1 ]
Degradation is mainly N -demethylation and oxidation of the ring-isopropyl group. Variations in order give rise to a few possible pathways, and the balance of demethylation and oxidation can allow selective activity of the herbicide. Both reactions may occur, making a typical degradation product of 2-(4-Aminophenyl)propan-2-ol (also called
Dimethyl-p-Aminobenzylalkohol), [ 5 ] which is an irritant and may be harmful if swallowed. [ 17 ]
Most isoproturon is expected to have degraded in soil after 6-28 days; the rate is temperature sensitive as the process is driven by enzymes and microbes. [ 1 ] In water, the DT 50 is 40 days, and in water sediments 149 days. [ 7 ]
Metabolism in plants usually follows the path beginning with isopropyl side chain oxidation. [ 5 ] White-rot fungus has the lignin -degrading enzymes lignin peroxidase and manganese peroxidase which are known to degrade isoproturon in vivo. [ 18 ]
Isoproturon is in the WHO 's toxicity class III: Slightly Hazardous. The oral LD 50 is 3350 mg/kg (mice), and percutaneously for rats is >2000 mg/kg. It is non-irritating to skin and eyes, as tested on rabbits. A dietary NOEL over 90 days for rates is 80 mg/kg, for dogs 50 mg/kg. [ 1 ] IPU is an endocrine disruptor . [ 7 ]
Isoproturon is not toxic to bees and birds but can harm fish, with LC 50 of 191 mg/L (carp), guppies 91 mg/L, and catfish just 9 mg/L. [ 1 ] The UK Environment Agency set a non-statutatory acceptable average water limit of 2 μg/L or 20 μg/L in one measurement. [ 7 ] In rats , the half life of ingested isoproturon is about 8 hours, excretion being 86% through urination. [ 5 ]
Technical grade isoproturon is >97% pure, and is then sold as an active ingredient in commercial formulations , usually as an SC, suspended concentrate, or WP, wettable powder. [ 1 ]
Diflufenican is a Class C2 (or Group 7) resistance class herbicide . [ 7 ]
IPU is synthesised from cumene , to which HNO 3 is reacted, forming p.nitrocumene. The nitrite group then is reacted with hydrogen to replace its two oxygen atoms. Phosgene is reacted to p.cumidine, which replaces one of phosgene's chlorine atoms, and then dimethyl amine completes the chain, replacing the other chlorine atom. An alternative route, involving the more direct combination of p.cumidine, urea and dimethyl amine, exists. [ 19 ]
Weeds controlled by IPU include annual grasses, such as black-twitch , common windgrass , common wild oat , and annual meadow grass . It is used in spring and winter to control many annual broad leaved weeds.
Isoproturon is used on crops such as wheat, rye, barley, triticale, [ 1 ] sugarcane, citrus, cotton, asparagus, [ 9 ] oilseed rape, peas, spring field beans, sugar beet, potatoes, carrots, brassicas and onions. [ 20 ] It is not used on durum wheat because of isoproturon's phytotoxicity to it, however it is nonphytotoxic to other cereals. [ 1 ]
Isoproturon's herbicide resistance class is class C2 (HRAC) or class 7 (WSSA). Black-twitch and lesser canary grass have shown resistant examples. [ 7 ] | https://en.wikipedia.org/wiki/Isoproturon |
Buoyant density centrifugation (also isopycnic centrifugation or equilibrium density-gradient centrifugation ) uses the concept of buoyancy to separate molecules in solution by their differences in density.
Historically a cesium chloride (CsCl) solution was often used, but more commonly used density gradients are sucrose or Percoll . This application requires a solution with high density and yet relatively low viscosity, and CsCl suits it because of its high solubility in water, high density owing to the large mass of Cs, as well as low viscosity and high stability of CsCl solutions. [ 1 ]
The sample is put on top of the solution, and then the tube is spun at a very high speed for an extended time, at times lasting days. The CsCl molecules become densely packed toward the bottom, so a continuous gradient of layers of different densities (and CsCl concentrations) form. Since the original solution was approximately the same density, they go to a level where their density and the CsCl density are the same, to which they form a sharp, distinctive band.
This method very sharply separates molecules, and is so sharp that it can even separate different molecular isotopes from one another. [ 2 ] It has been utilized in the Meselson-Stahl experiment .
Buoyant density of the majority of DNA is 1.7g/cm 3 [ 3 ] which is equal to the density of 6M CsCl solution. [ citation needed ] Buoyant density of DNA changes with its GC content . The term " satellite DNA " refers to small bands of repetitive DNA sequences with distinct base composition floating above (A+T rich) or below (G+C rich) the main component DNA. | https://en.wikipedia.org/wiki/Isopycnic_centrifugation |
Isorenieratene /ˌaɪsoʊrəˈnɪərətiːn/ is a carotenoid light-harvesting pigment produced exclusively by the genus Chlorobium , which are the brown-colored strains of the family of green sulfur bacteria ( Chlorobiaceae ). [ 1 ] Green sulfur bacteria are anaerobic photoautotrophic organisms, meaning they perform photosynthesis in the absence of oxygen using hydrogen sulfide in the following reaction:
H 2 S + CO 2 → SO 4 2− + organic compounds
Such anoxygenic photosynthesis requires reduced sulfur and light; thus, this metabolism occurs only in strictly photic and euxinic environments. Therefore, the discovery of isorenieratene and its derivatives in sediments and rocks are helpful biomarkers to identify euxinic water columns in the photic zone . [ 2 ]
Isorenieratene has the chemical formula C 40 H 48 . [ 3 ] It is a diaromatic carotenoid with a regularly-linked isoprenoid chain, except for a single tail-to-tail linkage in the middle of the molecule. Isorenieratene has a characteristic 1-alkyl-2,3,6-trimethyl substitution pattern on the aromatic rings , which helps identify the molecule. The nine conjugated double bonds on the isoprenoid backbone are all in the trans configuration and make the molecule highly reactive with reduced inorganic sulfur species. [ 4 ] The molecule is hydrophobic and insoluble in water, like most other carotenoids. Isorenieratene is generally non-toxic.
Isorenieratene was first discovered when isolated from the orange-colored sponge Reniera japonica. [ 5 ] Marine sponges are brilliantly colored due to the occurrence of several carotenoids and their association with symbionts such as bacteria or algae . Therefore, isorenieratene in sponges is assumed to originate from the symbiosis between sponges and green sulfur bacteria (Chlorobiaceae). [ 6 ]
Green sulfur bacteria live in euxinic environments, often at the chemocline , where the light flux is present but low. To increase their metabolic efficiency, they have developed a chlorosome , a membrane-bound antenna with bacteriochlorophyll c, d, or e. [ 7 ] The brown-colored strain of Chlorobiaceae has bacteriochlorophyll e in its chlorosome, which primarily makes isorenieratene. It is speculated that isorenieratene and other related carotenoids are adaptations that help organisms live under low-light conditions. [ 7 ] Green sulfur bacteria fix carbon through the reverse tricarboxylic acid cycle (TCA), resulting in the produced biomass , including isorenieratene, being anomalously enriched in carbon-13 ( 13 C) compared to other algal biomass by about 15 per mil. [ 8 ] δ 13 C of green sulfur bacteria biomass ranges between –9 and –21 per mil. Isorenieratene is relatively uncommon but of great significance when encountered. It is a powerful proxy for euxinic conditions in the photic zone both today and in the geologic record .
The combination of conditions in which green sulfur bacteria live and, thereby, where isorenieratene is found are limited today. Most of these locations are restricted water basins with highly stratified waters , allowing for anoxia development in the lower layers and H 2 S accumulation. The Black Sea is one such water basin where the hydrogen sulfide interface, or the chemocline , has moved up in the photic zone, and high concentrations of green sulfur bacteria and isorenieratene are found. [ 9 ] Other modern-day environments include meromictic lakes , restricted fjords , and some marine settings. Green sulfur bacteria are found to play a role in coral ecosystems and have been documented to live on coral and sponges as possible symbionts. [ 10 ]
Several cases have been found where green sulfur bacteria with bacteriochlorophyll e are abundant, but no isorenieratene was documented. Green sulfur bacteria were found to live near a deep-sea hydrothermal vent off the coast of Mexico ; [ 11 ] however, the bacteria are no longer doing photosynthesis at this depth, and no isorenieratene was isolated. In Fayetteville Green Lake (New York), green sulfur bacteria and bacteriochlorophyll e were abundant below the chemocline, yet the sediments lacked isorenieratene. [ 12 ] These unexpected absences of isorenieratene call for continued exploration of the microbial ecology of biomarker production in modern environments.
Isorenieratene is generally poorly-preserved because its structure is susceptible to alteration and degradation. Upon diagenesis and catagenesis , isorenieratene may be transformed and produce various related products that still indicate photic zone euxinia in the depositional environment. [ 13 ] The two main transformation processes are the saturation of double bonds to form isorenieratane and the rupture of the carbon chain resulting in smaller molecular fragments. Other alterations include sulphurization, cyclization , and aromatization . [ 13 ]
While euxinic conditions are rare today, In the early history of the Earth , these conditions were thought to be present in all oceans at depths of about 100 m (330 ft). The detection of isorenieratene and green sulfur bacteria in the mid-Proterozoic has been used as evidence for the long-term euxinic conditions remaining in oceans after the Great Oxygenation Event . For example, the 1.64-Gyr-old Barney Creek Formation in northern Australia hosts many biomarkers, including isorenieratene, that signify that these rocks were deposited in a marine basin with anoxic, sulphidic, and highly-stratified deep waters with colonies of green and purple sulfur bacteria . [ 14 ]
Isorenieratene derivatives have been identified in sedimentary rocks throughout the Paleozoic and Mesozoic, signifying that anoxygenic photosynthesis was a more common process in the past. [ 15 ] Isorenieratene derivatives have also been isolated from many petroleum source rocks, suggesting euxinic conditions and anoxia are favorable for preserving organic matter, leading to forming of petroleum reservoirs. [ 15 ] Additionally, the detection of isorenieratene derivatives during mass extinctions signifies that euxinic conditions may be common at such events. For example, the isolation of isorenieratene from rock units deposited during the Permian/Triassic Mass extinction , the deadliest mass extinction on Earth, was used as evidence for several pulses of widespread photic zone euxinia leading up to and during the extinction event. [ 16 ] | https://en.wikipedia.org/wiki/Isorenieratene |
In spectroscopy , an isosbestic point is a specific wavelength, wavenumber or frequency at which the total absorbance of a sample does not change during a chemical reaction or a physical change of the sample. The word derives from two Greek words: "iso", meaning "equal", and "sbestos", meaning "extinguishable". [ 1 ]
An isosbestic point corresponds to an absorbance A λ {\displaystyle A_{\lambda }} at a fixed wavelength λ {\displaystyle \lambda } that remains fixed [ 1 ] . The absorbance can be written as sum of absorbances of each species ( Beer–Lambert law ) A λ = ℓ ∑ i = 1 n ϵ i ( λ ) c i , {\displaystyle A_{\lambda }=\ell \sum _{i=1}^{n}\epsilon _{i}(\lambda )c_{i}\,,} where c i {\displaystyle c_{i}} the concentration of species i, ℓ {\displaystyle \ell } the optical path length.
By definition, an isosbestic point can be interpreted as a fixed linear combination of species concentrations, L = ∑ i n b i c i , d L d t = 0 , {\displaystyle L=\sum _{i}^{n}b_{i}c_{i},\ \ \ {\frac {dL}{dt}}=0\,,} i.e. an isobestic point is a conservation law. [ 2 ]
The IUPAC gold book [ 1 ] provides as an example the reaction A + B → c C + d D + e E , {\displaystyle A+B\rightarrow cC+dD+eE\,,} which will lead to an isosbestic point if ϵ A ( λ ) + ϵ B ( λ ) = c ϵ C ( λ ) + d ϵ D ( λ ) + e ϵ E ( λ ) , {\displaystyle \epsilon _{A}(\lambda )+\epsilon _{B}(\lambda )=c\ \epsilon _{C}(\lambda )+d\ \epsilon _{D}(\lambda )+e\ \epsilon _{E}(\lambda )\,,}
Isosbestic points can be observed in a variety of techniques [ 3 ] (for instance UV-VIS, IR, NMR). In UV-VIS, an isosbestic point is often interpreted as implying the occurrence of a single linearly independent reaction.
The simplest examples of isosbestic points involve only two species, but isosbestic points do not imply the participation of only two species (e.g. the IUPAC example involves 5 species), which is a common misconception [ 1 ] .
When an isosbestic plot is constructed by the superposition of the absorption spectra of two species (whether by using molar absorptivity for the representation, or by using absorbance and keeping the same molar concentration for both species), the isosbestic point corresponds to a wavelength at which these spectra cross each other.
A pair of substances can have several isosbestic points in their spectra.
When a 1-to-1 (one mole of reactant gives one mole of product ) chemical reaction (including equilibria ) involves a pair of substances with an isosbestic point, the absorbance of the reaction mixture at this wavelength remains invariant, regardless of the extent of reaction (or the position of the chemical equilibrium). This occurs because the two substances absorb light of that specific wavelength to the same extent, and the analytical concentration remains constant.
For the reaction:
the analytical concentration is the same at any point in the reaction:
The absorbance of the reaction mixture (assuming it depends only on X and Y) is:
But at the isosbestic point, both molar absorptivities are the same:
Hence, the absorbance
does not depend on the extent of reaction (i.e., on the particular concentrations of X and Y)
The requirement for an isosbestic point to occur in this example is that the two species involved are related linearly by stoichiometry, such that the absorbance is invariant at a certain wavelength. It can now also readily be seen that one should not expect an isosbestic point for two successive reactions:
As we then would need there to be a wavelength λ ∗ {\displaystyle \lambda ^{*}} at which all three spectra intersect simultaneously:
It would be very unlikely for three compounds to have extinction coefficients that are linearly related in this way by chance. [ 4 ]
In chemical kinetics , isosbestic points are used as reference points in the study of reaction rates , as the absorbance at those wavelengths remains constant throughout the whole reaction. [ 1 ]
Isosbestic points are used in medicine in a laboratory technique called oximetry to determine hemoglobin concentration, regardless of its saturation. Oxyhaemoglobin and deoxyhaemoglobin have (not exclusively) isosbestic points at 586 nm and near 808 nm.
Isosbestic points are also used in clinical chemistry , as a quality assurance method, to verify the accuracy in the wavelength of a spectrophotometer . This is done by measuring the spectra of a standard solution at two different pH conditions (above and below the p K a of the substance). The standards used include potassium dichromate (isosbestic points at 339 and 445 nm), bromothymol blue (325 and 498 nm) and congo red (541 nm). The wavelength of the isosbestic point determined does not depend on the concentration of the substance used, and so it becomes a very reliable reference.
One example of the use of isosbestic points in organic synthesis is seen in the photochemical A/D- corrin cycloisomerization ring closure reaction, which was the key step in the Eschenmoser / ETH Zürich vitamin B 12 total synthesis . [ 5 ] [ 6 ] The isosbestic points provide proof for a direct conversion of the seco-corrin complex to the metal-free corrin ligand without intermediary or side products (within the detection limits of UV/VIS spectroscopy ). [ 5 ] | https://en.wikipedia.org/wiki/Isosbestic_point |
An isoscape is a geological map of isotope distribution. It is a spatially explicit prediction of elemental isotope ratios (δ) that is produced by executing process-level models of elemental isotope fractionation or distribution in a geographic information system (GIS).
The word isoscape is derived from iso tope land scape and was first coined by Jason B. West. [ 1 ] [ 2 ]
Isoscapes of hydrogen , carbon , oxygen , nitrogen , strontium and sulfur [ 3 ] have been used to answer scientific or forensic questions regarding the sources, partitioning, or provenance of natural and synthetic materials or organisms via their isotopic signatures . These include questions about migration , Earth's element cycles , human water use , climate , archaeological reconstructions , forensic science , and pollution . Isoscapes of hydrogen and oxygen isotopes of precipitation, [ 4 ] [ 5 ] surface water, [ 6 ] groundwater, [ 7 ] [ 8 ] and tap water [ 9 ] have been developed to better understand the water cycle at regional to global scales.
This isotope -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isoscape |
Isoschizomers are pairs of restriction enzymes specific to the same recognition sequence . For example, SphI (CGTAC/G) and BbuI (CGTAC/G) are isoschizomers of each other. The first enzyme discovered which recognizes a given sequence is known as the prototype ; all subsequently identified enzymes that recognize that sequence are isoschizomers. Isoschizomers are isolated from different strains of bacteria and therefore may require different reaction conditions .
In some cases, only one out of a pair of isoschizomers can recognize both the methylated as well as unmethylated forms of restriction sites . In contrast, the other restriction enzyme can recognize only the unmethylated form of the restriction site.
This property of some isoschizomers allows identification of methylation state of the restriction site while isolating it from a bacterial strain .
For example, the restriction enzymes HpaII and MspI are isoschizomers, as they both recognize the sequence 5'-CCGG-3' when it is unmethylated. But when the second C of the sequence is methylated, only MspI can recognize it while HpaII cannot.
An enzyme that recognizes the same sequence but cuts it differently is a neoschizomer . Neoschizomers are a specific type (subset) of isoschizomer. For example, SmaI (CCC/GGG) and XmaI (C/CCGGG) are neoschizomers of each other. Similarly KpnI (GGTAC/C) and Acc65I (G/GTACC) are neoschizomers of each other.
An enzyme that recognizes a slightly different sequence, but produces the same ends is an isocaudomer . | https://en.wikipedia.org/wiki/Isoschizomer |
Isoserine is a non-proteinogenic α-hydroxy-β- amino acid , and an isomer of serine . Non-proteinogenic amino are not part of the genetic code of any known organism and are only present in proteins if added post-translationally . Isoserine has only been produced synthetically.
The first documented synthesis of isoserine in a laboratory setting was by Miyazawa et al., who published their results in 1976. [ 1 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isoserine |
In nuclear physics and particle physics , isospin ( I ) is a quantum number related to the up- and down quark content of the particle.
Isospin is also known as isobaric spin or isotopic spin .
Isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons .
The name of the concept contains the term spin because its quantum mechanical description is mathematically similar to that of angular momentum (in particular, in the way it couples ; for example, a proton–neutron pair can be coupled either in a state of total isospin 1 or in one of 0 [ 1 ] ). But unlike angular momentum, it is a dimensionless quantity and is not actually any type of spin .
Before the concept of quarks was introduced, particles that are affected equally by the strong force but had different charges (e.g. protons and neutrons) were considered different states of the same particle, but having isospin values related to the number of charge states. [ 2 ] A close examination of isospin symmetry ultimately led directly to the discovery and understanding of quarks and to the development of Yang–Mills theory . Isospin symmetry remains an important concept in particle physics.
To a good approximation the proton and neutron have the same mass: they can be interpreted as two states of the same particle. [ 2 ] : 141 These states have different values for an internal isospin coordinate. The mathematical properties of this coordinate are completely analogous to intrinsic spin angular momentum. The component of the operator, T ^ 3 {\displaystyle {\hat {T}}_{3}} , for this coordinate has eigenvalues + 1 / 2 and − 1 / 2 ; it is related to the charge operator, Q ^ {\displaystyle {\hat {Q}}} : Q ^ = e ( T ^ 3 + 1 2 ) {\displaystyle {\hat {Q}}=e\left({\hat {T}}_{3}+{\frac {1}{2}}\right)} which has eigenvalues e {\displaystyle e} for the proton and zero for the neutron. [ 2 ] : 144 For a system of n nucleons, the charge operator depends upon the mass number A: Q ^ = e ( T ^ 3 + 1 2 A ) {\displaystyle {\hat {Q}}=e\left({\hat {T}}_{3}+{\frac {1}{2}}A\right)} Isobars , nuclei with the same mass number like 40 K and 40 Ar, only differ in the value of the T ^ 3 {\displaystyle {\hat {T}}_{3}} eigenvalue. For this reason isospin is also called "isobaric spin".
The internal structure of these nucleons is governed by the strong interaction , but the Hamiltonian of the strong interaction is isospin invariant. As a consequence the nuclear forces are charge independent. Properties like the stability of deuterium can be predicted based on isospin analysis. [ 2 ] : 149 However,
this invariance is not exact and the quark model gives more precise results.
The charge operator can be expressed in terms of the projection of isospin T 3 {\displaystyle T_{3}} and hypercharge , Y {\displaystyle Y} : Q = 1 2 Y + T 3 , T 3 = T , T − 1 , . . . , − T . {\displaystyle Q={\frac {1}{2}}Y+T_{3},\ \ \ \ T_{3}=T,T-1,...,-T.} This is known as the Gell-Mann–Nishijima formula . The hypercharge is the center of splitting for the isospin multiplet: [ 2 ] : 187 1 2 Y = 1 2 ( Q min + Q max ) . {\displaystyle {\frac {1}{2}}Y={\frac {1}{2}}(Q_{\textrm {min}}+Q_{\textrm {max}}).} This relation has an analog in the weak interaction where T is the weak isospin .
In the modern formulation, isospin ( I ) is defined as a vector quantity in which up and down quarks have a value of I = 1 / 2 , with the 3rd-component ( I 3 ) being + 1 / 2 for up quarks, and − 1 / 2 for down quarks, while all other quarks have I = 0. Therefore, for hadrons in general, [ 3 ] where n u and n d are the numbers of up and down quarks respectively,
In any combination of quarks, the 3rd component of the isospin vector ( I 3 ) could either be aligned between a pair of quarks, or face the opposite direction, giving different possible values for total isospin for any combination of quark flavours. Hadrons with the same quark content but different total isospin can be distinguished experimentally, verifying that flavour is actually a vector quantity, not a scalar (up vs down simply being a projection in the quantum mechanical z axis of flavour space).
For example, a strange quark can be combined with an up and a down quark to form a baryon , but there are two different ways the isospin values can combine – either adding (due to being flavour-aligned) or cancelling out (due to being in opposite flavour directions). The isospin-1 state (the Σ 0 ) and the isospin-0 state (the Λ 0 ) have different experimentally detected masses and half-lives.
Isospin is regarded as a symmetry of the strong interaction under the action of the Lie group SU(2) , the two states being the up flavour and down flavour. In quantum mechanics , when a Hamiltonian has a symmetry, that symmetry manifests itself through a set of states that have the same energy (the states are described as being degenerate ). In simple terms, the energy operator for the strong interaction gives the same result when an up quark and an otherwise identical down quark are swapped around.
Like the case for regular spin, the isospin operator I is vector -valued: it has three components I x , I y , I z , which are coordinates in the same 3-dimensional vector space where the 3 representation acts. Note that this vector space has nothing to do with the physical space, except similar mathematical formalism. Isospin is described by two quantum numbers : I – the total isospin, and I 3 – an eigenvalue of the I z projection for which flavor states are eigenstates . In other words, each I 3 state specifies certain flavor state of a multiplet . The third coordinate ( z ), to which the "3" subscript refers, is chosen due to notational conventions that relate bases in 2 and 3 representation spaces. Namely, for the spin- 1 / 2 case, components of I are equal to Pauli matrices divided by 2, and so I z = 1 / 2 τ 3 , where
While the forms of these matrices are isomorphic to those of spin, these Pauli matrices only act within the Hilbert space of isospin, not that of spin, and therefore is common to denote them with τ rather than σ to avoid confusion.
Although isospin symmetry is actually very slightly broken, SU(3) symmetry is more badly broken, due to the much higher mass of the strange quark compared to the up and down. The discovery of charm , bottomness and topness could lead to further expansions up to SU(6) flavour symmetry, which would hold if all six quarks were identical. However, the very much larger masses of the charm, bottom, and top quarks means that SU(6) flavour symmetry is very badly broken in nature (at least at low energies), and assuming this symmetry leads to qualitatively and quantitatively incorrect predictions. In modern applications, such as lattice QCD , isospin symmetry is often treated as exact for the three light quarks (uds), while the three heavy quarks (cbt) must be treated separately.
Hadron nomenclature is based on isospin. [ 4 ]
In 1932, Werner Heisenberg [ 5 ] introduced a model for binding of the proton and the then newly discovered neutron (symbol n). His model resembled the bonding model for molecule Hydrogen ion, H 2 + : a single electron was shared by two protons.
Heisenberg's theory had several problems, most notable it incorrectly predicted the exceptionally strong binding energy of He 2+ , alpha particles . However, its equal treatment of the proton and neutron gained significance when several experimental studies showed these particles must bind almost equally. [ 6 ] : 39 In response, Eugene Wigner used Heisenberg's concept in his 1937 paper where he introduced the term "isotopic spin" to indicate how the concept is similar to spin in behavior. [ 7 ]
These considerations would also prove useful in the analysis of meson -nucleon interactions after the discovery of the pions in 1947. The three pions ( π + , π 0 , π − ) could be assigned to an isospin triplet with I = 1 and I 3 = +1, 0 or −1 . By assuming that isospin was conserved by nuclear interactions, the new mesons were more easily accommodated by nuclear theory.
As further particles were discovered, they were assigned into isospin multiplets according to the number of different charge states seen: 2 doublets I = 1 / 2 of K mesons ( K − , K 0 ), ( K + , K 0 ), a triplet I = 1 of Sigma baryons ( Σ + , Σ 0 , Σ − ), a singlet I = 0 Lambda baryon ( Λ 0 ), a quartet I = 3 / 2 Delta baryons ( Δ ++ , Δ + , Δ 0 , Δ − ), and so on.
The power of isospin symmetry and related methods comes from the observation that families of particles with similar masses tend to correspond to the invariant subspaces associated with the irreducible representations of the Lie algebra SU(2). In this context, an invariant subspace is spanned by basis vectors which correspond to particles in a family. Under the action of the Lie algebra SU(2), which generates rotations in isospin space, elements corresponding to definite particle states or superpositions of states can be rotated into each other, but can never leave the space (since the subspace is in fact invariant). This is reflective of the symmetry present. The fact that unitary matrices will commute with the Hamiltonian means that the physical quantities calculated do not change even under unitary transformation. In the case of isospin, this machinery is used to reflect the fact that the mathematics of the strong force behaves the same if a proton and neutron are swapped around (in the modern formulation, the up and down quark).
For example, the particles known as the Delta baryons – baryons of spin 3 / 2 – were grouped together because they all have nearly the same mass (approximately 1232 MeV/ c 2 ) and interact in nearly the same way.
They could be treated as the same particle, with the difference in charge being due to the particle being in different states. Isospin was introduced in order to be the variable that defined this difference of state. In an analogue to spin, an isospin projection (denoted I 3 ) is associated to each charged state; since there were four Deltas, four projections were needed. Like spin, isospin projections were made to vary in increments of 1. Hence, in order to have four increments of 1, an isospin value of 3 / 2 is required (giving the projections I 3 = + 3 / 2 , + 1 / 2 , − 1 / 2 , − 3 / 2 ). Thus, all the Deltas were said to have isospin I = 3 / 2 , and each individual charge had different I 3 (e.g. the Δ ++ was associated with I 3 = + 3 / 2 ).
In the isospin picture, the four Deltas and the two nucleons were thought to simply be the different states of two particles. The Delta baryons are now understood to be made of a mix of three up and down quarks – uuu ( Δ ++ ), uud ( Δ + ), udd ( Δ 0 ), and ddd ( Δ − ); the difference in charge being difference in the charges of up and down quarks (+ 2 / 3 e and − 1 / 3 e respectively); yet, they can also be thought of as the excited states of the nucleons.
Attempts have been made to promote isospin from a global to a local symmetry. In 1954, Chen Ning Yang and Robert Mills suggested that the notion of protons and neutrons, which are continuously rotated into each other by isospin, should be allowed to vary from point to point. To describe this, the proton and neutron direction in isospin space must be defined at every point, giving local basis for isospin. A gauge connection would then describe how to transform isospin along a path between two points.
This Yang–Mills theory describes interacting vector bosons, like the photon of electromagnetism. Unlike the photon, the SU(2) gauge theory would contain self-interacting gauge bosons. The condition of gauge invariance suggests that they have zero mass, just as in electromagnetism.
Ignoring the massless problem, as Yang and Mills did, the theory makes a firm prediction: the vector particle should couple to all particles of a given isospin universally . The coupling to the nucleon would be the same as the coupling to the kaons . The coupling to the pions would be the same as the self-coupling of the vector bosons to themselves.
When Yang and Mills proposed the theory, there was no candidate vector boson. J. J. Sakurai in 1960 predicted that there should be a massive vector boson which is coupled to isospin, and predicted that it would show universal couplings. The rho mesons were discovered a short time later, and were quickly identified as Sakurai's vector bosons. The couplings of the rho to the nucleons and to each other were verified to be universal, as best as experiment could measure. The fact that the diagonal isospin current contains part of the electromagnetic current led to the prediction of rho-photon mixing and the concept of vector meson dominance , ideas which led to successful theoretical pictures of GeV-scale photon-nucleus scattering.
The discovery and subsequent analysis of additional particles, both mesons and baryons , made it clear that the concept of isospin symmetry could be broadened to an even larger symmetry group, now called flavor symmetry . Once the kaons and their property of strangeness became better understood, it started to become clear that these, too, seemed to be a part of an enlarged symmetry that contained isospin as a subgroup. The larger symmetry was named the Eightfold Way by Murray Gell-Mann , and was promptly recognized to correspond to the adjoint representation of SU(3) . To better understand the origin of this symmetry, Gell-Mann proposed the existence of up, down and strange quarks which would belong to the fundamental representation of the SU(3) flavor symmetry.
In the quark model, the isospin projection ( I 3 ) followed from the up and down quark content of particles; uud for the proton and udd for the neutron. Technically, the nucleon doublet states are seen to be linear combinations of products of 3-particle isospin doublet states and spin doublet states. That is, the (spin-up) proton wave function , in terms of quark-flavour eigenstates, is described by [ 2 ]
| p ↑ ⟩ = 1 3 2 ( | d u u ⟩ | u d u ⟩ | u u d ⟩ ) ( 2 − 1 − 1 − 1 2 − 1 − 1 − 1 2 ) ( | ↓ ↑ ↑ ⟩ | ↑ ↓ ↑ ⟩ | ↑ ↑ ↓ ⟩ ) {\displaystyle \vert \mathrm {p} \uparrow \rangle ={\frac {1}{3{\sqrt {2}}}}\left({\begin{array}{ccc}\vert \mathrm {duu} \rangle &\vert \mathrm {udu} \rangle &\vert \mathrm {uud} \rangle \end{array}}\right)\left({\begin{array}{ccc}2&-1&-1\\-1&2&-1\\-1&-1&2\end{array}}\right)\left({\begin{array}{c}\left\vert \downarrow \uparrow \uparrow \right\rangle \\\left\vert \uparrow \downarrow \uparrow \right\rangle \\\left\vert \uparrow \uparrow \downarrow \right\rangle \end{array}}\right)}
and the (spin-up) neutron by
| n ↑ ⟩ = 1 3 2 ( | u d d ⟩ | d u d ⟩ | d d u ⟩ ) ( 2 − 1 − 1 − 1 2 − 1 − 1 − 1 2 ) ( | ↓ ↑ ↑ ⟩ | ↑ ↓ ↑ ⟩ | ↑ ↑ ↓ ⟩ ) . {\displaystyle \vert \mathrm {n} \uparrow \rangle ={\frac {1}{3{\sqrt {2}}}}\left({\begin{array}{ccc}\vert \mathrm {udd} \rangle &\vert \mathrm {dud} \rangle &\vert \mathrm {ddu} \rangle \end{array}}\right)\left({\begin{array}{ccc}2&-1&-1\\-1&2&-1\\-1&-1&2\end{array}}\right)\left({\begin{array}{c}\left\vert \downarrow \uparrow \uparrow \right\rangle \\\left\vert \uparrow \downarrow \uparrow \right\rangle \\\left\vert \uparrow \uparrow \downarrow \right\rangle \end{array}}\right).}
Here, | u ⟩ {\displaystyle \mathrm {\vert u\rangle } } is the up quark flavour eigenstate, and | d ⟩ {\displaystyle \mathrm {\vert d\rangle } } is the down quark flavour eigenstate, while | ↑ ⟩ {\displaystyle \left\vert \uparrow \right\rangle } and | ↓ ⟩ {\displaystyle \left\vert \downarrow \right\rangle } are the eigenstates of S z {\displaystyle S_{z}} . Although these superpositions are the technically correct way of denoting a proton and neutron in terms of quark flavour and spin eigenstates, for brevity, they are often simply referred to as "uud" and "udd". The derivation above assumes exact isospin symmetry and is modified by SU(2)-breaking terms.
Similarly, the isospin symmetry of the pions are given by:
| π + ⟩ = | u d ¯ ⟩ | π 0 ⟩ = 1 2 ( | u u ¯ ⟩ − | d d ¯ ⟩ ) | π − ⟩ = − | d u ¯ ⟩ . {\displaystyle {\begin{aligned}\vert \pi ^{+}\rangle &=\vert \mathrm {u{\overline {d}}} \rangle \\\vert \pi ^{0}\rangle &={\tfrac {1}{\sqrt {2}}}\left(\vert \mathrm {u{\overline {u}}} \rangle -\vert \mathrm {d{\overline {d}}} \rangle \right)\\\vert \pi ^{-}\rangle &=-\vert \mathrm {d{\overline {u}}} \rangle .\end{aligned}}}
Although the discovery of the quarks led to reinterpretation of mesons as a vector bound state of a quark and an antiquark, it is sometimes still useful to think of them as being the gauge bosons of a hidden local symmetry. [ 8 ]
In 1961 Sheldon Glashow proposed that a relation similar to the Gell-Mann–Nishijima formula for charge to isospin would also apply to the weak interaction : [ 9 ] [ 10 ] : 152 Q = T 3 + 1 2 Y w . {\displaystyle Q=T_{3}+{\frac {1}{2}}Y_{w}.} Here the charge Q {\displaystyle Q} is related to the projection of weak isospin T 3 {\displaystyle T_{3}} and the weak hypercharge Y w {\displaystyle Y_{w}} .
Isospin and weak isospin are related to the same symmetry but for different forces. Weak isospin is the gauge symmetry of the weak interaction which connects quark and lepton doublets of left-handed particles in all generations; for example, up and down quarks, top and bottom quarks, electrons and electron neutrinos. By contrast (strong) isospin connects only up and down quarks, acts on both chiralities (left and right) and is a global (not a gauge) symmetry. [ 11 ] | https://en.wikipedia.org/wiki/Isospin |
Classical Isosteres are molecules or ions with similar shape and often electronic properties. Many definitions are available. [ 1 ] but the term is usually employed in the context of bioactivity and drug development. Such biologically-active compounds containing an isostere is called a bioisostere . This is frequently used in drug design : [ 2 ] the bioisostere will still be recognized and accepted by the body, but its functions there will be altered as compared to the parent molecule.
Non-classical isosteres do not obey the above classifications, but they still produce similar biological effects in vivo . Non-classical isosteres may be made up of similar atoms, but their structures do not follow an easily definable set of rules.
The isostere concept was formulated by Irving Langmuir in 1919, [ 3 ] and later modified by Grimm. Hans Erlenmeyer extended the concept to biological systems in 1932. [ 4 ] [ 5 ] [ 6 ] Classical isosteres are defined as being atoms, ions and molecules that had identical outer shells of electrons, This definition has now been broadened to include groups that produce compounds that can sometimes have similar biological activities. Some evidence for the validity of this notion was the observation that some pairs, such as benzene , thiophene , furan , and even pyridine , exhibited similarities in many physical and chemical properties. | https://en.wikipedia.org/wiki/Isostere |
Isostructural chemical compounds have similar chemical structures . " Isomorphous " when used in the relation to crystal structures is not synonymous: in addition to the same atomic connectivity that characterises isostructural compounds, isomorphous substances crystallise in the same space group and have the same unit cell dimensions. [ 1 ] The IUCR definition [ 2 ] used by crystallographers is:
Two crystals are said to be isostructural, if they have the same structure, but not necessarily the same cell dimensions nor the same chemical composition, and with a 'comparable' variability in the atomic coordinates to that of the cell dimensions and chemical composition. For instance, calcite CaCO 3 , sodium nitrate NaNO 3 and iron borate FeBO 3 are isostructural. One also speaks of isostructural series, or of isostructural polymorphs or isostructural phase transitions. The term isotypic is synonymous with isostructural.
Examples include:
Many minerals are isostructural when they differ only in the nature of a cation.
Compounds which are isoelectronic usually have similar chemical structures. For example, methane , CH 4 , and the ammonium ion, NH 4 + , are isoelectric and are isostructural
as both have a tetrahedral structure. The C-H and N-H bond lengths are different and crystal structures are completely different because the ammonium ion only occurs in salts .
This condensed matter physics -related article is a stub . You can help Wikipedia by expanding it .
This crystallography -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isostructural |
Isotachophoresis ( ITP ) is a technique in analytical chemistry used for selective separation and concentration of ionic analytes . It is a form of electrophoresis ; charged analytes are separated based on ionic mobility , a quantity which tells how fast an ion migrates through an electric field .
In conventional ITP separations, a discontinuous buffer system is used. The sample is introduced between a zone of fast leading electrolyte (LE) and a zone of slow terminating (or: trailing) electrolyte (TE). Usually, the LE and the TE have a common counterion , but the co-ions (having charges with the same sign as the analytes of interest) are different: the LE is defined by co-ions with high ionic mobility , while the TE is defined by co-ions with low ionic mobility. The analytes of interest have intermediate ionic mobility. Application of an electric potential results in a low electrical field in the leading electrolyte and a high electrical field in the terminating electrolyte. Analyte ions situated in the TE zone will migrate faster than the surrounding TE co-ions, while analyte ions situated in the LE will migrate slower; the result is that analytes are focused at the LE/TE interface.
ITP is a displacement method: focusing ions of a certain kind displace other ions. If present in sufficient amounts, focusing analyte ions can displace all electrolyte co-ions, reaching a plateau concentration . Multiple analytes with sufficiently different ionic mobilities will form multiple plateau zones. Indeed, plateau mode ITP separations are readily recognized by stairlike profiles, each plateau of the stair representing an electrolyte or analyte zone having (from LE to TE) increasing electric fields and decreasing conductivities. In peak mode ITP, analytes amounts are insufficient to reach plateau concentrations, such analytes will focus in sharp Gaussian -like peaks. In peak mode ITP, analyte peaks will strongly overlap, unless so-called spacer compounds are added with intermediate ionic mobilities between those of the analytes; such spacer compounds are able to segregate adjacent analyte zones. [ 1 ]
A completed ITP separation is characterized by a dynamic equilibrium in which all coionic zones migrate with equal velocities. From this phenomenon ITP has obtained its name: iso = equal, tachos = speed, phoresis = migration.
Isotachophoresis is exactly equal to the steady-state-stacking step in discontinuous electrophoresis . [ 2 ]
A popular form of ITP is transient ITP (tITP). It alleviates the limitation of conventional ITP that it has limited separation capacity because of analyte zone overlap. In transient ITP, analytes are first concentrated by ITP, and then can be baseline separated by zone electrophoresis . Transient ITP is usually accomplished by dissolving the sample in the TE and sandwiching the sample/TE plug between LE zones - or vice versa: a sample/LE plug can also be sandwiched between TE zones. In the first case, analytes are focused at the front TE/LE interface. Meanwhile, the back of the TE plug becomes dissolved in the LE because the faster LE ions overcome the TE ions. When all of the TE ions are dissolved, the focusing process ceases and the analytes are separated according to the principles of zone electrophoresis.
tITP is nowadays more widespread than conventional ITP because it is easily implemented in capillary electrophoresis (CE) separations as a preconcentration step, making CE more sensitive while profiting from its powerful separation capacities. | https://en.wikipedia.org/wiki/Isotachophoresis |
Isothermal flow is a model of compressible fluid flow whereby the flow remains at the same temperature while flowing in a conduit. [ 1 ] In the model, heat transferred through the walls of the conduit is offset by frictional heating back into the flow. Although the flow temperature remains constant, a change in stagnation temperature occurs because of a change in velocity. The interesting part of this flow is that the flow is choked at 1 / k {\displaystyle 1/{\sqrt {k}}} and not at Mach number equal to one as in the case of many other model such as Fanno flow . This fact applies to real gases as well as ideal gases.
For the important practical case of a gas flow through a long tube, the model has applicability in situations where distance is relatively long and heat transfer is relatively rapid so temperature can be treated, for engineering purposes, as a constant. This model also has applicability as upper boundary to Fanno flow. | https://en.wikipedia.org/wiki/Isothermal_flow |
Isothermal microcalorimetry ( IMC ) is a laboratory method for real-time monitoring and dynamic analysis of chemical, physical and biological processes. Over a period of hours or days, IMC determines the onset, rate, extent and energetics of such processes for specimens in small ampoules (e.g. 3–20 ml) at a constant set temperature (c. 15 °C–150 °C).
IMC accomplishes this dynamic analysis by measuring and recording vs. elapsed time the net rate of heat flow (μJ/s = μW) to or from the specimen ampoule, and the cumulative amount of heat (J) consumed or produced.
IMC is a powerful and versatile analytical tool for four closely related reasons:
The IMC method of studying rates of processes is thus broadly applicable, provides real-time continuous data, and is sensitive. The measurement is simple to make, takes place unattended and is non-interfering (e.g. no fluorescent or radioactive markers are needed).
However, there are two main caveats that must be heeded in use of IMC:
In general, possible applications of IMC are only limited by the imagination of the person who chooses to employ it as an analytical tool and the physical constraints of the method. Besides the two general limitations (main caveats) described above, these constraints include specimen and ampoule size, and the temperatures at which measurements can be made. IMC is generally best suited to evaluating processes which take place over hours or days. IMC has been used in an extremely wide range of applications, and many examples are discussed in this article, supported by references to published literature. Applications discussed range from measurement of slow oxidative degradation of polymers and instability of hazardous industrial chemicals to detection of bacteria in urine and evaluation of the effects of drugs on parasitic worms. The present emphasis in this article is applications of the latter type—biology and medicine.
Calorimetry is the science of measuring the heat of chemical reactions or physical changes. Calorimetry is performed with a calorimeter .
Isothermal microcalorimetry (IMC) is a laboratory method for real-time, continuous measurement of the heat flow rate (μJ/s = μW) and cumulative amount of heat (J) consumed or produced at essentially constant temperature by a specimen placed in an IMC instrument. Such heat is due to chemical or physical changes taking place in the specimen. The heat flow is proportional to the aggregate rate of changes taking place at a given time. The aggregate heat produced during a given time interval is proportional to the cumulative amount of aggregate changes which have taken place.
IMC is thus a means for dynamic, quantitative evaluation of the rates and energetics of a broad range of rate processes, including biological processes. A rate process is defined here as a physical and/or chemical change whose progress over time can be described either empirically or by a mathematical model ( Bibliography : Glasstone, et al. 1941 and Johnson, et al. 1974 and rate equation ).
The simplest use of IMC is detecting that one or more rate processes are taking place in a specimen because heat is being produced or consumed at a rate that is greater than the detection limit of the instrument used. This can be a useful, for example, as a general indicator that a solid or liquid material is not inert but instead is changing at a given temperature. In biological specimens containing a growth medium, appearance over time of a detectable and rising heat flow signal is a simple general indicator of the presence of some type of replicating cells.
However, for most applications it is paramount to know, by some means, what process or processes are being measured by monitoring heat flow. In general this entails first having detailed physical, chemical and biological knowledge of the items placed in an IMC ampoule before it is placed in an IMC instrument for evaluation of heat flow over time. It is also then necessary to analyze the ampoule contents after IMC measurements of heat flow have been made for one or more periods of time. Also, logic-based variations in ampoule contents can be used to identify the specific source or sources of heat flow. When rate process and heat flow relationships have been established, it is then possible to rely directly on the IMC data.
What IMC can measure in practice depends in part on specimen dimensions, and they are necessarily constrained by instrument design. A given commercial instrument typically accepts specimens of up to a fixed diameter and height. Instruments accepting specimens with dimensions of up to ca. 1 or 2 cm in diameter x ca. 5 cm in height are typical. In a given instrument larger specimens of a given type usually produce greater heat flow signals, and this can augment detection and precision.
Frequently, specimens are simple 3 to 20 ml cylindrical ampoules (Fig. 1) containing materials whose rate processes are of interest—e.g. solids, liquids, cultured cells—or any combination of these or other items expected to result in production or consumption of heat. Many useful IMC measurements can be carried out using simple sealed ampoules, and glass ampoules are common since glass is not prone to undergoing heat-producing chemical or physical changes. However, metal or polymeric ampoules are sometimes employed. Also, instrument/ampoule systems are available which allow injection or controlled through-flow of gasses or liquids and/or provide specimen mechanical stirring.
Commercial IMC instruments allow heat flow measurements at temperatures ranging from ca. 15 °C – 150 °C. The range for a given instrument may be somewhat different.
IMC is extremely sensitive – e.g. heat from slow chemical reactions in specimens weighing a few grams, taking place at reactant consumption rates of a few percent per year, can be detected and quantified in a matter of days. Examples include gradual oxidation of polymeric implant materials and shelf life studies of solid pharmaceutical drug formulations ( Applications: Solid materials ).
Also the rate of metabolic heat production of e.g. a few thousand living cells, microorganisms or protozoa in culture in an IMC ampoule can be measured. The amount of such metabolic heat can be correlated (through experimentation) with the number of cells or organisms present. Thus, IMC data can be used to monitor in real time the number of cells or organisms present and the net rate of growth or decline in this number ( Applications: Biology and medicine ).
Although some non-biological applications of IMC are discussed ( Applications: Solid materials ) the present emphasis in this article is on the use of IMC in connection with biological processes ( Applications: Biology and medicine ).
A graphic display of a common type of IMC data is shown in Fig. 2. At the top is a plot of recorded heat flow (μJ/s = μW) vs. time from a specimen in a sealed ampoule, due to an exothermic rate process which begins, accelerates, reaches a peak heat flow and then subsides. Such data are directly useful (e.g. detection of a process and its duration under fixed conditions) but the data are also easily assessed mathematically to determine process parameters. For example, Fig. 2 also shows an integration of the heat flow data, giving accumulated heat (J) vs. time. As shown, parameters such as the maximum growth (heat generation) rate of the process, and the duration time of the lag phase before the process reaches maximum heat can be calculated from the integrated data. [ 1 ] Calculations using heat flow rate data stored as computer files are easily automated. Analyzing IMC data in this manner to determine growth parameters has important applications the life sciences ( Applications: Biology and medicine ). Also, heat flow rates obtained at a series of temperatures can be used to obtain the activation energy of the process being evaluated (Hardison et al. 2003). [ 2 ]
Lavoisier and Laplace are credited with creating and using the first isothermal calorimeter in ca. 1780 ( Bibliography: Lavoisier A & Laplace PS 1780 ). Their instrument employed ice to produce a relatively constant temperature in a confined space. They realized that when they placed a heat-producing specimen on the ice (e.g. a live animal), the mass of liquid water produced by the melting ice was directly proportional to the heat produced by the specimen. [ citation needed ]
Many modern IMC instrument designs stem from work done in Sweden in the late 1960s and early 1970s (Wadsö 1968, [ 3 ] Suurkuusk & Wadsö 1974 [ 4 ] ). This work took advantage of the parallel development of solid-state electronic devices—particularly commercial availability of small thermoelectric effect (Peltier-Seebeck) devices for converting heat flow into voltage—and vice versa. [ citation needed ]
In the 1980s, multi-channel designs emerged (Suurkuusk 1982), [ 5 ] which allow parallel evaluation of multiple specimens. This greatly increased the power and usefulness of IMC and led to efforts to fine-tune the method (Thorén et al. 1989). [ 6 ] Much of the further design and development done in the 1990s was also accomplished in Sweden by Wadsö and Suurkuusk and their colleagues. This work took advantage of the parallel development of personal computer technology which greatly augmented the ability to easily store, process and interpret heat flow vs. time data. [ citation needed ]
Instrument development work since the 1990s has taken further advantage of the continued development of solid-state electronics and personal computer technology. This has created IMC instruments of increasing sensitivity and stability, numbers of parallel channels, and even greater ability to conveniently record, store and rapidly process IMC data. In connection with wider use, substantial attention has been paid to creating standards for describing the performance of IMC instruments (e.g. precision, accuracy, sensitivity) and for methods of calibration (Wadsö and Goldberg 2001). [ 7 ]
Modern IMC instruments are actually semi-adiabatic—i.e. heat transfer between the specimen and its surroundings is not zero (adiabatic), because IMC measurement of heat flow depends on the existence of a small temperature differential—ca. 0.001 °C. [ 7 ] However, because the differential is so low, IMC measurements are essentially isothermal. Fig. 3. shows an overview of an IMC instrument which contains 48 separate heat flow measurement modules. One module is shown. The module's measuring unit is typically a Peltier-Seebeck device. The device produces a voltage proportional to the temperature difference between a specimen which is producing or consuming heat and a thermally inactive reference which is at the temperature of the heat sink. The temperature difference is in turn proportional to the rate at which the specimen is producing or consuming heat (see Calibration below). All the modules in an instrument use the same heat sink and thermostat and thus all produce data at the same set temperature. However, it is generally possible to start and stop measurements in each ampoule independently. In a highly parallel (e.g. 48-channel) instrument like the one shown in Fig. 3, this makes it possible to perform (start and stop) several different experiments whenever it is convenient to do so. [ citation needed ]
Alternatively, IMC instruments can be equipped with duplex modules which yield signals proportional to the heat flow difference between two ampoules. One of two such duplex ampoules is often a blank or control—i.e. a specimen which does not contain the material producing the rate process of interest, but whose content is otherwise identical to that which is in the specimen ampoule. This provides a means for eliminating minor heat-producing reactions which are not of interest—for example gradual chemical changes over a period of days in a cell culture medium at the measurement temperature. Many useful IMC measurements can be carried out using simple sealed ampoules. However, as mentioned above, instrument/ampoule systems are available which allow or even control flow of gasses or liquids to and/or from the specimens and/or provide specimen mechanical stirring. [ citation needed ]
Heat flow is usually measured relative to a reference insert, as shown in Fig. 3. This is typically a metal coupon that is chemically and physically stable at any temperature in the instrument's operating range and thus will not produce or consume heat itself. For best performance, the reference should have a heat capacity close to that of the specimen (e.g. IMC ampoule plus contents). [ citation needed ]
Commercial IMC instruments are often operated as heat conduction (hc) calorimeters in which heat produced by the specimen (i.e. material in an ampoule) flows to the heat sink , typically an aluminum block contained in a thermostat (e.g. constant temperature bath). As mentioned above, an IMC instrument operating in hc mode is not precisely isothermal because small differences between the set temperature and the specimen temperature necessarily exist—so that there is measurable heat flow. However, small variations in specimen temperature do not significantly affect heat sink temperature because the heat capacity of the heat sink is much higher than the specimen—usually ca. 100×. [ citation needed ]
Heat transfer between the specimen and the heat sink takes place through a Peltier-Seebeck device, allowing dynamic measurement of heat produced or consumed. In research-quality instruments, thermostat/heat sink temperature is typically accurate to < ±0.1 K and maintained within ca. < ±100 μK/24h. The precision with which heat sink temperature is maintained over time is a major determinant of the precision of the heat flow measurements over time. An advantage of hc mode is a large dynamic range. Heat flows of ca. 50,000 μW can be measured with a precision of ca. ±0.2 μW. Thus measuring a heat flow of ca. >0.2 μW above baseline constitutes detection of heat flow, although a more conservative detection of 10× the precision limit [ clarification needed ] is often used. [ citation needed ]
Some IMC instruments operate (or can also be operated) as power compensation (pc) calorimeters. In this case, in order to maintain the specimen at the set temperature, heat produced is compensated using a Peltier-Seebeck device. Heat consumed is compensated either by an electric heater or by reversing the polarity of the device (van Herwaarden, 2000). [ 8 ] If a given instrument is operated in pc mode rather than hc, the precision of heat flow measurement remains the same (e.g. ca. ±0.2 μW). The advantage of compensation mode is a smaller time constant – i.e. the time needed to detect a given heat flow pulse is ca.10X shorter than in conduction mode. The disadvantage is a ca. 10X smaller dynamic range compared to hc mode. [ citation needed ]
For operation in either hc or pc mode, routine calibration in commercial instruments is usually accomplished with built-in electric heaters. The performance of the electrical heaters can in turn be validated using specimens of known heat capacity or which produce chemical reactions whose heat production per unit mass is known from thermodynamics (Wadsö and Goldberg 2001). [ 7 ] In either hc or pc mode, the resulting signal is a computer-recordable voltage, calibrated to represent specimen μ W-range heat flow vs. time. Specifically, if no significant thermal gradients exist in the specimen, then P = e C [U + t (dU/dt)], where P is heat flow (i.e. μW), ε C is the calibration constant, U the measured potential difference across the thermopile, and t the time constant. Under steady-state conditions—for example during the release of a constant electrical calibration current, this simplifies to P = e C U. (Wadsö and Goldberg 2001). [ 7 ]
Many highly useful IMC measurements can be conducted in sealed ampoules (Fig. 1) which offer advantages of simplicity, protection from contamination and (where needed) a substantial margin of bio-safety for persons handling or exposed to the ampoules. A closed ampoule can contain any desired combination of solids, liquids, gasses or items of biologic origin. Initial gas composition in the ampoule head space can be controlled by sealing the ampoule in the desired gas environment. [ citation needed ]
However, there are also IMC instrument/ampoule designs which permit controlled flow of gas or liquid through the ampoule during measurement and/or mechanical stirring. Also, with proper accessories, some IMC instruments can be operated as ITC (isothermal titration calorimetry) instruments. The topic of ITC is covered elsewhere (see Isothermal titration calorimetry ). In addition some IMC instruments can record heat flow while the temperature is slowly changed (scanned) over time. The scanning rate has to be slow (ca. ± 2 °C/h ) in order to keep IMC-scale specimens (e.g. a few grams) sufficiently close to the heat sink temperature (< ca. 0.1 °C). Fast scanning of temperature is the province of differential scanning calorimetry (DSC) instruments which generally use much smaller specimens. Some DSC instruments can be operated in IMC mode, but the small ampoule (and therefore specimen) size needed for scanning limit the utility and sensitivity of DSC instruments used in IMC mode. [ citation needed ]
Heat flow rate (μJ/s = μW) measurements are accomplished by first setting an IMC instrument thermostat at a selected temperature and allowing the instrument's heat sink to stabilize at that temperature. If an IMC instrument operating at one temperature is set to a new temperature, re-stabilization at the new temperature setting may take several hours—even a day. As explained above, achievement and maintenance of a precisely stable temperature is fundamental to achieving precise heat flow measurements in the μW range over extended times (e.g. days). [ citation needed ]
After temperature stabilization, if an externally prepared ampoule (or some solid specimen of ampoule dimensions) is used, it is slowly introduced (e.g. lowered) into an instrument's measurement module, usually in a staged operation. The purpose is to ensure that by the time the ampoule/specimen is in the measurement position, its temperature is close to (within c. 0.001 °C) of the measurement temperature. This is so that any heat flow then measured is due to specimen rate processes rather than due to a continuing process of bringing the specimen to the set temperature. The time for introduction of a specimen in a 3–20 ml IMC ampoule into measurement position is ca. 40 minutes in many instruments. This means that heat flow from any processes which take place within a specimen during that the introduction period will not be recorded. [ citation needed ]
If an in-place ampoule is used, and some agent or specimen is injected, this also produces a period of instability, but it is on the order ca. 1 minute. Fig. 5 provides examples of both the long period needed to stabilize an instrument if an ampoule is introduced directly, and the short period of instability due to injection. [ citation needed ]
After the introduction process, specimen heat flow can be precisely recorded continuously, for as long as it is of interest. The extreme stability of research-grade instruments (< ±100 μK/24h ) means that accurate measurements can be (and often are) made for a period of days. Since the heat flow signal is essentially readable in real time, it serves as a means for deciding whether or not heat flow of interest is still occurring. Also, modern instruments store heat flow vs. time data as computer files, so both real-time and retrospective graphic display and mathematical analysis of data are possible. [ citation needed ]
As indicated below, IMC has many advantages as a method for analyzing rate processes, but there are also some caveats that must be heeded.
Any rate process can be studied—if suitable specimens will fit IMC instrument module geometry, and proceed at rates amenable to IMC methodology (see above). As shown under Applications , IMC is in use to quantify an extremely wide range of rate processes in vitro—e.g. from solid-state stability of polymers (Hardison et al. 2003) [ 2 ] to efficacy of drug compounds against parasitic worms (Maneck et al. 2011). [ 9 ] IMC can also determine the aggregate rate of uncharacterized, complex, or multiple interactions (Lewis & Daniels). [ 10 ] This is especially useful for comparative screening—e.g. the effects of different combinations of material composition and/or fabrication processes on overall physico-chemical stability.
IMC heat flow data are obtained as voltage fluctuations vs. time, stored as computer files and can be displayed essentially in real time—as the rate process is occurring. The heat flow-related voltage is continuous over time, but in modern instruments it is normally sampled digitally. The frequency of digital sampling can be controlled as needed—i.e. frequent sampling of rapid heat flow changes for better time resolution or slower sampling of slow changes in order to limit data file size.
IMC is sensitive enough to detect and quantify in short times (hours, days) reactions which consume only a few percent of reactants over long times (months). IMC thus avoids long waits often needed until enough reaction product has accumulated for conventional (e.g. chemical) assays. This applies to both physical and biological specimens (see Applications ).
At each combination of specimen variables and set temperature of interest, IMC provides direct determination of the heat flow kinetics and cumulative heat of rate processes. This avoids any need to assume that a rate process remains the same when temperature or other controlled variables are changed before an IMC measurement.
For comparisons of the effect of experimental variables (e.g. initial concentrations) on rate processes, IMC does not require development and use of chemical or other assay methods. If absolute data are required (e.g. quantity of product produced by a process), then assays can be conducted in parallel on specimens identical to those used for IMC (and/or on IMC specimens after IMC runs). The resultant assay data is used to calibrate the rate data obtained by IMC.
IMC does not require adding markers (e.g. fluorescent or radioactive substances) to capture rate processes. Unadulterated specimens can be used, and after an IMC run, the specimen is unchanged (except by the processes which have taken place). The post-IMC specimen can be subjected to any kind of physical, chemical, morphological or other evaluation of interest.
As indicated in the methodology description, when the IMC method of inserting a sealed ampoule is used, it is not possible to capture heat flow during the first ca. 40 minutes while the specimen is slowly being brought to the set temperature. In this mode therefore, IMC is best suited to studying processes which start slowly or occur slowly at a given temperature. This caveat also applies to the time before insertion—i.e. time elapsed between preparing a specimen (in which a rate process may then start) and starting the IMC insertion process (Charlebois et al. 2003). [ 11 ] This latter effect is usually minimized if the temperature chosen for IMC is substantially higher (e.g. 37 °C) than the temperature at which the specimen is prepared (e.g. 25 °C).
IMC captures the aggregate heat production or consumption resulting from all processes taking place within a specimen, including for example
Thus great care must be taken in experimental planning and design to identify all possible processes which may be taking place. It is often necessary to design and conduct preliminary studies intended to systematically determine if multiple processes are taking place and if so, their contributions to aggregate heat flow. One strategy, in order to eliminate extraneous heat flow data, is to compare heat flow for a specimen in which the rate process of interest is taking place with that from a blank specimen which includes everything in the specimen of interest—except the item which will undergo the rate process of interest. This can be directly accomplished with instruments having duplex IMC modules which report the net heat flow difference between two ampoules.
After a discussion of some special sources of IMC application information, several specific categories of IMC analysis of rate processes are covered, and recent examples (with literature references) are discussed in each category.
The Bibliography lists the four extensive volumes of the Handbook of Thermal Analysis and Calorimetry: Vol. 1 Principles and Practice (1998), Vol. 2 Applications to Inorganic and Miscellaneous Materials (2003), Vol. 3 Applications to Polymers and Plastics (2002), and Vol. 4 From Macromolecules to Man (1999). These constitute a prime source of information on (and literature references to) IMC applications and examples published prior to ca. 2000.
Some IMC instrument manufacturers have assembled application notes, and make them available to the public. The notes are often (but not always) adaptations of journal papers. An example is the Microcalorimetry Compendium Vol. I and II offered by TA Instruments, Inc. and listed in the Bibliography .
"Proteins" the first section of notes in Vol. I, is not of interest here, as it describes studies employing Isothermal titration calorimetry . The subsequent sections of Vol. I, Life & Biological Sciences and Pharmaceuticals contain application notes for both IMC and Differential scanning calorimetry . Vol. II of the compendium is devoted almost entirely to IMC applications. Its sections are entitled Cement, Energetics, Material and Other. A possible drawback to these two specific compendia is that none of the notes are dated. Although the compendia were published in 2009, some of the notes describe IMC instruments which were in use years ago and are no longer available. Thus, some of the notes, while still relevant and instructive, often describe studies done before 2000.
In general, possible applications of IMC are only limited by the imagination of the person who chooses to employ IMC as an analytical tool—within the previously described constraints presented by existing IMC instruments and methodology. This is because it is a universal means for monitoring any chemical, physical or biological rate process. Below are some IMC application categories with examples in each. In most categories, there are many more published examples than those mentioned and referenced. The categories are somewhat arbitrary and often overlap. A different set of categories might be just as logical, and more categories could be added.
IMC is widely used for studying the rates of formation of a variety of materials by various processes. It is best suited to study processes which occur slowly—i.e. over hours or days. A prime example is the study of hydration and setting reactions of calcium mineral cement formulations. One paper provides an overview (Gawlicki, et al. 2010) [ 12 ] and another describes a simple approach (Evju 2003). [ 13 ] Other studies focus on insights into cement hydration provided by IMC combined with IR spectroscopy (Ylmen et al. 2010) [ 14 ] and on using IMC to study the influence of compositional variables on cement hydration and setting times (Xu et al. 2011). [ 15 ]
IMC can also be conveniently used to study the rate and amount of hydration (in air of known humidity) of calcium minerals or other minerals. To provide air of known humidity for such studies, small containers of saturated salt solutions can be placed in an IMC ampoule along with a non-hydrated mineral specimen. The ampoule is then sealed and introduced into an IMC instrument. The saturated salt solution keeps the air in the ampoule at a known rH, and various common salt solutions provide humidities ranging from e.g. 32-100% rH. Such studies have been performed on μm size range calcium hydroxyapatite particles and calcium-containing bioactive glass "nano" particles (Doostmohammadi et al. 2011). [ 16 ]
IMC is well suited for rapidly quantifying the rates of slow changes in materials (Willson et al. 1995). [ 17 ] Such evaluations are variously described as studies of stability, degradation, or shelf life .
For example, IMC has been widely used for many years in shelf life studies of solid drug formulations in the pharmaceutical industry (Pikal et al. 1989, [ 18 ] Hansen et al. 1990, [ 19 ] Konigbauer et al. 1992. [ 20 ] ) IMC has the ability to detect slow degradation during simulated shelf storage far sooner than conventional analytical methods and without the need to employ chemical assay techniques. IMC is also a rapid, sensitive method for determining the often functionally crucial amorphous content of drugs such as nifedipine (Vivoda et al. 2011). [ 21 ]
IMC can be used for rapidly determining the rate of slow changes in industrial polymers. For example, gamma radiation sterilization of a material frequently used for surgical implants— ultra-high-molecular-weight polyethylene (UHMWPE)—is known to produce free radicals in the polymer. The result is slow oxidation and gradual undesirable embrittlement of the polymer on the shelf or in vivo. IMC could detect oxidation-related heat and quantified an oxidation rate of ca. 1% per year in irradiated UHMWPE at room temperature in air (Charlebois et al. 2003). [ 11 ] In a related study the activation energy was determined from measurements at a series of temperatures (Hardison et al. 2003). [ 2 ]
IMC is also of great utility in evaluating the "runaway potential" of materials which are significant fire or explosion hazards. For example, it has been used to determine autocatalytic kinetics of cumene hydroperoxide (CHP), an intermediate which is used in the chemical industry and whose sudden decomposition has caused a number of fires and explosions. Fig. 4 Shows the IMC data documenting thermal decomposition of CHP at 5 different temperatures (Chen et al. 2008). [ 22 ]
The term metabolismics can be used [ citation needed ] to describe studies of the quantitative measurement of the rate at which heat is produced or consumed vs. time by cells (including microbes) in culture, by tissue specimens, or by small whole organisms. As described subsequently, metabolismics can be useful as a diagnostic tool; especially in either (a) identifying the nature of a specimen from its heat flow vs. time signature under a given set of conditions, or (b) determining the effects of e.g. pharmaceutical compounds on metabolic processes, organic growth or viability. Metabolismics is related to metabolomics . The latter is the systematic study of the unique chemical fingerprints that specific cellular processes leave behind; i.e. the study of their small-molecule metabolite profiles. When IMC is used to determine metabolismics, the products of the metabolic processes studied are subsequently available for metabolomics studies. Since IMC does not employ biochemical or radioactive markers, the post-IMC specimens consist only of metabolic products and remaining culture medium (if any was used). If metabolismics and metabolomics are used together, they can provide a comprehensive record of a metabolic process taking place in vitro: its rate and energetics, and its metabolic products.
To determine metabolismics using IMC, there must of course be sufficient cells, tissue or organisms initially present (or present later if replication is taking place during IMC measurements) to generate a heat flow signal above a given instrument's detection limit. A landmark 2002 general paper on the topic of metabolism provides an excellent perspective from which to consider IMC metabolismic studies (see Bibliography , West, Woodruff and Brown 2002). It describes how metabolic rates are related and how they scale over the entire range from "molecules and mitochondria to cells and mammals". Importantly for IMC, the authors also note that while the metabolic rate of a given type of mammalian cell in vivo declines markedly with increasing animal size (mass), the size of the donor animal has no effect on the metabolic rate of the cell when cultured in vitro.
Mammalian cells in culture have a metabolic rate of ca. 30×10 −12 W/cell (Figs. 2 and 3 in Bibliography: West, Woodruff and Brown 2002 ). By definition, IMC instruments have a sensitivity of at least 1×10 −6 W (i.e. 1 μW). Therefore, the metabolic heat of ca. 33,000 cells is detectable. Based on this sensitivity, IMC was used to perform a large number of pioneering studies of cultured mammalian cell metabolismics in the 1970s and 1980s in Sweden. One paper (Monti 1990) [ 23 ] serves as an extensive guide to work done up until 1990. It includes explanatory text and 42 references to IMC studies of heat flow from cultured human erythrocytes , platelets , lymphocytes , lymphoma cells, granulocytes , adipocytes , skeletal muscle, and myocardial tissue. The studies were done to determine how and where IMC might be used as a clinical diagnostic method and/or provide insights into metabolic differences between cells from healthy persons and persons with various diseases or health problems.
Developments since ca. 2000 in IMC (e.g. massively parallel instruments, real-time, computer-based storage and analysis of heat flow data) have stimulated further use of IMC in cultured cell biology. For example, IMC has been evaluated for assessing antigen-induced lymphocyte proliferation (Murigande et al. 2009) [ 24 ] and revealed aspects of proliferation not seen using a conventional non-continuous radioactive marker assay method. IMC has also been applied to the field of tissue engineering . One study (Santoro et al. 2011) [ 25 ] demonstrated that IMC could be used to measure the growth (i.e. proliferation) rate in culture of human chondrocytes harvested for tissue engineering use. It showed that IMC can potentially serve to determine the effectiveness of different growth media formulations and also determine whether cells donated by a given individual can be grown efficiently enough to consider using them to produce engineered tissue.
IMC has also been used to measure the metabolic response of cultured macrophages to surgical implant wear debris. IMC showed that the response was stronger to μm size range particles of polyethylene than to similarly sized Co alloy particles (Charlebois et al. 2002). [ 26 ] A related paper covers the general topic of applying IMC in the field of synthetic solid materials used in surgery and medicine (Lewis and Daniels 2003). [ 10 ]
At least two studies have suggested IMC can be of substantial use in tumor pathology. In one study (Bäckman 1990), [ 27 ] the heat production rate of T-lymphoma cells cultured in suspension was measured. Changes in temperature and pH induced significant variations, but stirring rate and cell concentration did not. A more direct study of possible diagnostic use (Kallerhoff et al. 1996) [ 28 ] produced promising results. For the uro-genital tissue biopsy specimens studied, the results showed
"it is possible to differentiate between normal and tumorous tissue samples by microcalorimetric measurement based on the distinctly higher metabolic activity of malignant tissue. Furthermore, microcalorimetry allows a differentiation and classification of tissue samples into their histological grading."
As of 2012, IMC has not become widely used in cultured cell toxicology even though it has been used periodically and successfully since the 1980s. IMC is advantageous in toxicology when it is desirable to observe cultured cell metabolism in real time and to quantify the rate of metabolic decline as a function of the concentration of a possibly toxic agent. One of the earliest reports (Ankerst et al. 1986) [ 29 ] of IMC use in toxicology was a study of antibody-dependent cellular toxicity (ADCC) against human melanoma cells of various combinations of antiserum, monoclonal antibodies and also peripheral blood lymphocytes as effector cells. Kinetics of melanoma cell metabolic heat flow vs. time in closed ampoules were measured for 20 hours. The authors concluded that
"...microcalorimetry is a sensitive and particularly suitable method for the analysis of cytotoxicity kinetics."
IMC is also being used in environmental toxicology. In an early study (Thorén 1992) [ 30 ] toxicity against monolayers of alveolar macrophages of particles of MnO 2 , TiO 2 and SiO 2 (silica) were evaluated. IMC results were in accord with results obtained by fluorescein ester staining and microscopic image analysis—except that IMC showed toxic effects of quartz not discernable by image analysis. This latter observation—in accord with known alveolar effects—indicated to the authors that IMC was a more sensitive technique.
Much more recently (Liu et al. 2007), [ 31 ] IMC has been shown to provide dynamic metabolic data which assess toxicity against fibroblasts of Cr(VI) from potassium chromate. Fig. 5 shows baseline results determining the metabolic heat flow from cultured fibroblasts prior to assessing the effects of Cr(VI). The authors concluded that
"Microcalorimetry appears to be a convenient and easy technique for measuring metabolic processes...in...living cells. As opposed to standard bioassay procedures, this technique allows continuous measurements of the metabolism of living cells. We have thus shown that Cr(VI) impairs metabolic pathways of human fibroblasts and particularly glucose utilization."
Simple closed ampoule IMC has also been used and advocated for assessing the cultured cell toxicity of candidate surgical implant materials—and thus serve as a biocompatibility screening method. In one study (Xie et al. 2000) [ 32 ] porcine renal tubular cells in culture were exposed to both polymers and titanium metal in the form of "microplates" having known surface areas of a few cm 2 . The authors concluded that IMC
"...is a rapid method, convenient to operate and with good reproducibility. The present method can in most cases replace more time-consuming light and electron microscopic investigations for quantitating of adhered cells."
In another implant materials study (Doostmohammadi et al. 2011) [ 33 ] both a rapidly growing yeast culture and a human chondrocyte culture were exposed to particles (diam.< 50 μm) of calcium hydroxyapatite (HA) and bioactive (calcium-containing) silica glass. The glass particles slowed or curtailed yeast growth as a function of increasing particle concentration. The HA particles had much less effect and never entirely curtailed yeast growth at the same concentrations. The effects of both particle types on chondrocyte growth were minimal at the concentration employed. The authors concluded that
"The cytotoxicity of particulate materials such as bioactive glass and hydroxyapatite particles can be evaluated using the microcalorimetry method. This is a modern method for in vitro study of biomaterials biocompatibility and cytotoxicity which can be used alongside the old conventional assays."
Publications describing use of IMC in microbiology began in the 1980s (Jesperson 1982). [ 34 ] While some IMC microbiology studies have been directed at viruses (Heng et al. 2005) [ 35 ] and fungi (Antoci et al. 1997), [ 36 ] most have been concerned with bacteria. A recent paper (Braissant et al. 2010) [ 37 ] provides a general introduction to IMC metabolismic methods in microbiology and an overview of applications in medical and environmental microbiology. The paper also explains how heat flow vs. time data for bacteria in culture are an exact expression—as they occur over time—of the fluctuations in microorganism metabolic activity and replication rates in a given medium (Fig. 6).
In general, bacteria are about 1/10 the size of mammalian cells and produce perhaps 1/10 as much metabolic heat-i.e. ca. 3x10 −12 W/cell. Thus, compared to mammalian cells (see above) ca. 10X as many bacteria—ca. 330,000—must be present to produce detectable heat flow—i.e. 1 μW. [ 37 ] However, many bacteria replicate orders of magnitude more rapidly in culture than mammalian cells, often doubling their number in a matter of minutes (see Bacterial growth ). As a result, a small initial number of bacteria in culture and initially undetectable by IMC rapidly produce a detectable number. For example, 100 bacteria doubling every 20 minutes will in less than 4 hours produce >330,000 bacteria and thus an IMC-detectable heat flow. Consequently, IMC can be used for easy, rapid detection of bacteria in the medical field. Examples include detection of bacteria in human blood platelet products (Trampuz et al. 2007) [ 38 ] and urine (Bonkat et al. 2011) [ 39 ] and rapid detection of tuberculosis (Braissant et al. 2010, [ 40 ] Rodriguez et al. 2011 [ 41 ] ). Fig. 7 shows an example of detection times of tuberculosis bacteria as a function of the initial amount of bacteria present in a closed IMC ampoule containing a culture medium.
For microbes in growth media in closed ampoules, IMC heat flow data can also be used to closely estimate basic microbial growth parameters; i.e. maximum growth rate and duration time of the lag phase before maximum growth rate is achieved. This is an important special application of the basic analysis of these parameters explained previously ( Overview: Data Obtained ).
Unfortunately, the IMC literature contains some published papers in which the relation between heat flow data and microbial growth in closed ampoules has been misunderstood. However, in 2013 an extensive clarification was published, describing (a) details of the relation between IMC heat flow data and microbial growth, (b) selection of mathematical models which describe microbial growth and (c) determination of microbial growth parameters from IMC data using these models (Braissant et al. 2013). [ 42 ]
In a logical extension of the ability of IMC to detect and quantify bacterial growth, known concentrations of antibiotics can be added to bacterial culture, and IMC can then be used to quantify their effects on viability and growth. Closed ampoule IMC can easily capture basic pharmacologic information—e.g. minimum inhibitory concentration (MIC) of an antibiotic needed to stop growth of a given organism. In addition it can simultaneously provide dynamic growth parameters—lag time and maximum growth rate (see Fig. 2, Howell et al. 2011, Braissant et al. 2013), [ 1 ] [ 42 ] which assess mechanisms of action. Bactericidal action (see Bactericide ) is indicated by an increased lag time as a function of increasing antibiotic concentration, while bacteriostatic action (see Bacteriostatic agent ) is indicated by a decrease in growth rate with concentration. The IMC approach to antibiotic assessment has been demonstrated for a number of a types of bacteria and antibiotics (von Ah et al. 2009). [ 43 ] Closed ampoule IMC can also rapidly differentiate between normal and resistant strains of bacteria such as Staphylococcus aureus (von Ah et al. 2008, [ 44 ] Baldoni et al. 2009 [ 45 ] ). IMC has also been used to assess the effects of disinfectants on the viability of mouth bacteria adhered to dental implant materials (Astasov-Frauenhoffer et al. 2011). [ 46 ] In a related earlier study, IMC was used to measure the heat of adhesion of dental bacteria to glass (Hauser-Gerspach et al. 2008). [ 47 ]
Analogous successful use of IMC to determine the effects of antitumor drugs on tumor cells in culture within a few hours has been demonstrated (Schön and Wadsö 1988). [ 48 ] Rather than the closed-ampoule approach, an IMC setup was used which allowed drug injection into stirred specimens.
As of 2013, IMC has been used less widely in mammalian cell in vitro pharmacodynamic studies than in microbial studies.
It is possible to use IMC to perform metabolismic studies of living multicellular organisms—if they are small enough to be placed in IMC ampoules (Lamprecht & Becker 1988). [ 49 ] IMC studies have been made of insect pupa metabolism during ventilating movements (Harak et al. 1996) [ 50 ] and effects of chemical agents on pupal growth (Kuusik et al. 1995). [ 51 ] IMC has also proved effective in assessing the effects of aging on nematode worm metabolism (Braekman et al. 2002). [ 52 ]
IMC has also proved highly useful for in vitro assessments of the effects of pharmaceuticals on tropical parasitic worms (Manneck et al. 2011-1, [ 53 ] Maneck et al. 2011-2, [ 9 ] Kirchhofer et al. 2011). [ 54 ] An interesting feature of these studies is the use of a simple manual injection system for introducing the pharmaceuticals into sealed ampoules containing the worms. Also, IMC not only documents the general metabolic decline over time due to the drugs, but also the overall frequency of worm motor activity and its decline in amplitude over time as reflected in fluctuations in the heat flow data.
Because of its versatility, IMC can be an effective tool in the fields of plant and environmental biology. In an early study (Hansen et al. 1989), [ 55 ] the metabolic rate of larch tree clone tissue specimens was measured. The rate was predictive of long-term tree growth rates, was consistent for specimens from a given tree and was found to correlate with known variations in the long-term growth of clones from different trees.
Bacterial oxalotrophic metabolism is common in the environment, particularly in soils. Oxalotrophic bacteria are capable of using oxalate as a sole carbon and energy source. Closed-ampoule IMC was used to study metabolism of oxalotrophic soil bacteria exposed to both an optimized medium containing potassium oxalate as the sole carbon source and a model soil (Bravo et al. 2011). [ 56 ] Using an optimized medium, growth of six different strains of soil bacteria was easily monitored and reproducibly quantified and differentiated over a period days. IMC measurement of bacterial metabolic heat flow in the model soil was more difficult, but a proof of concept was demonstrated.
Moonmilk is a white, creamy material found in caves. It is a non-hardening, fine crystalline precipitate from limestone and is composed mainly of calcium and/or magnesium carbonates. Microbes may be involved in its formation. It is difficult to infer microbial activities in moonmilk from standard static chemical and microscopic assays of moonmilk composition and structure. Closed ampoule IMC has been used to solve this problem (Braissant, Bindscheidler et al. 2011). [ 57 ] It was possible to determine the growth rates of chemoheterotrophic microbial communities on moonmilk after the addition of various carbon sources simulating mixes that would be brought into contact with moonmilk due to snow melt or rainfall. Metabolic activity was high and comparable to that found in some soils.
Harris et al. (2012), [ 58 ] studying differing fertilizer input regimes, found that, when expressed as heat output per unit soil microbial biomass, microbial communities under organic fertilizer regimes produced less waste heat than those under inorganic regimes.
IMC has been shown to have diverse uses in food science and technology. An overview (Wadsö and Galindo 2009) [ 59 ] discusses successful applications in assessing vegetable cutting wound respiration, cell death from blanching, milk fermentation, microbiological spoilage prevention, thermal treatment and shelf life. Another publication (Galindo et al. 2005) [ 60 ] reviews the successful use of IMC for monitoring and predicting quality changes during storage of minimally processed fruits and vegetables.
IMC has also proven effective in accomplishing enzymatic assays for orotic acid in milk (Anastasi et al. 2000) [ 61 ] and malic acid in fruits, wines and other beverages and also cosmetic products (Antonelli et al. 2008). [ 62 ] IMC has also been used to assess the efficacy of anti-browning agents on fresh-cut potatoes (Rocculi et al. 2007). [ 63 ] IMC has also proven effective in assessing the extent to which low-energy pulsed electric fields (PEFs) affect the heat of germination of barley seeds—important in connection with their use in producing malted beverages (Dymek et al. 2012). [ 64 ] | https://en.wikipedia.org/wiki/Isothermal_microcalorimetry |
In chemical thermodynamics , isothermal titration calorimetry ( ITC ) is a physical technique used to determine the thermodynamic parameters of interactions in solution . [ 1 ] [ 2 ] ITC is the only technique capable comprehensively characterizing thermodynamic and even kinetic profile of the interaction by simultaneously determining binding constants ( K a {\displaystyle K_{a}} ), reaction stoichiometry ( n {\displaystyle n} ), enthalpy ( Δ H {\displaystyle \Delta H} ), Gibbs free energy ( Δ G {\displaystyle \Delta G} ) and entropy ( Δ S {\displaystyle \Delta S} ) within a single experiment. [ 3 ] [ 4 ] [ 5 ] [ 6 ] It consists of two cells which are enclosed in an adiabatic jacket. [ 7 ]
The compounds to be studied are placed in the sample cell, while the other cell, the reference cell, is used as a control and contains the buffer in which the sample is dissolved. [ 8 ] The technique quantifies the heat released or absorbed during the binding process by incrementally adding one reactant (via a syringe) to another (in the sample cell) while maintaining constant temperature and pressure. [ 3 ] [ 9 ] Heat-sensing devices within the ITC detect temperature variations between two cells, transmitting this information to heaters that adjust accordingly to restore thermal equilibrium between the cells. [ 3 ] This energy is converted into binding enthalpy using the information about concentrations of the reactants and the cell volume. [ 6 ] Compared to other calorimeters , ITC does not require any correctors since there is no heat exchange between the system and the environment. ITC is also highly sensitive with a fast response time and benefits from modest sample requirements. [ 6 ] While differential scanning calorimetry (DSC) can also provide direct information about the thermodynamic of binding interactions, ITC offers the added capability of quantifying the thermodynamics of metal ion binding to proteins. [ 5 ]
The history of ITC can be traced back to the 1930s when isothermal calorimetry was used to study chemical reactions . [ 10 ] In 1965 Christensen and Izatt introduced titration calorimetry as a method for simultaneously determining the equilibrium constant and enthalpy . [ 3 ] [ 11 ] The ITC technique was then developed by H. D. Johnston in 1968 as a part of his Ph.D. dissertation at Brigham Young University, [ 12 ] and was considered niche until introduced commercially by MicroCal Inc . in 1988. In 1978, Beaudette and Langerman conducted one of the earliest calorimetric binding studies using a small volume isoperibol titration calorimeter [ 11 ] and a decade later, in 1989, Wiseman, Williston, Brandts, and Lin demonstrated its application in biological systems , marking the beginning of titration calorimetry as a valuable tool for studying biological equilibria. [ 10 ] Originally, ITC was most often used to study the binding of small molecules (such as medicinal compounds) to larger macromolecules ( proteins , DNA etc.) in a label-free environment. [ 4 ] [ 13 ] [ 14 ] Its application has now broadened, aided by modern improvements, making it possible to measure the heat effects as small as 0.1 μcal (0.4 μJ) and determine the binding constants (K) as high as 10 8 –10 9 M −1 . [ 5 ] [ 11 ]
ITC is a quantitative technique that can determine the binding affinity ( K a {\displaystyle K_{a}} ), reaction enthalpy ( Δ H {\displaystyle \Delta H} ), and binding stoichiometry ( n {\displaystyle n} ) of the interaction between two or more molecules in solution. [ 15 ] This is achieved by measuring the enthalpies of a series of binding reactions caused by injections of a solution of one molecule to a reaction cell containing a solution of another molecule. [ 9 ] The enthalpy values are plotted over the molar ratios resulting from the injections. [ 16 ] From the plot, the molar reaction enthalpy Δ H {\displaystyle \Delta H} , the affinity constant ( K a {\displaystyle K_{a}} ) and the stochiometry are determined by curve fitting . [ 5 ] [ 15 ] The reaction's Gibbs free energy change ( Δ G {\displaystyle \Delta G} ) and entropy change ( Δ S {\displaystyle \Delta S} ) can be determined using the relationship:
(where R {\displaystyle R} is the gas constant and T {\displaystyle T} is the absolute temperature ).
For accurate measurements of binding affinity, the curve of the thermogram must be sigmoidal. A steep sigmoidal curve signals a strong binding whereas a less steep sigmoidal curve points to a weaker binding. [ 4 ] The profile of the curve is determined by the c-value, which is calculated using the equation:
where n {\displaystyle n} is the stoichiometry of the binding, K a {\displaystyle K_{a}} is the association constant and M {\displaystyle M} is the concentration of the molecule in the cell. [ 1 ] [ 17 ] [ 18 ] The c-value must fall between 1 and 1000, ideally between 10 and 100. In terms of binding affinity, it would be approximately from 1.0 × 10 3 {\displaystyle 1.0\times 10^{3}} ~ 10 7 {\displaystyle 10^{7}} within the limit range. [ 19 ] If it does not fall within the above range, the thermodynamic values obtained from the experiment are less robust to interpretation.
An isothermal titration calorimeter is composed of two identical cells made of a highly efficient thermally conducting and chemically inert material such as Hastelloy alloy or gold, surrounded by an adiabatic jacket. [ 1 ] [ 18 ] In this setup, one of the cells, the sample cell, holds the solution of one reactant, and the other cell, the reference cell, is filled with either a buffer or water. [ 3 ]
The second reactant, which has a higher concentration than the first, is placed in a syringe and gradually injected into the sample cell in small aliquots throughout the titration process. [ 7 ] This process is semi-automated and the sensitive thermopile/thermocouple circuits are used to detect temperature differences between the reference cell (filled with buffer or water) and the sample cell containing the macromolecule. [ 9 ] Prior to addition of ligand, a constant power (<1 mW) is applied to the reference cell. This directs a feedback circuit, activating a heater located on the sample cell. [ 17 ] During the experiment, ligand is titrated into the sample cell in precisely known aliquots, causing heat to be either taken up or evolved (depending on the nature of the reaction). [ 9 ] Measurements consist of the time-dependent input of power required to maintain equal temperatures between the sample and reference cells. [ 7 ] [ 12 ]
In an exothermic reaction, the temperature in the sample cell increases upon addition of ligand . This causes the feedback power to the sample cell to be decreased (remember: a reference power is applied to the reference cell) in order to maintain an equal temperature between the two cells. [ 7 ] In an endothermic reaction, the opposite occurs; the feedback circuit increases the power in order to maintain a constant temperature (isothermal operation). [ 1 ]
Observations are plotted as the power needed to maintain the reference and the sample cell at an identical temperature against time. [ 7 ] As a result, the experimental raw data consists of a series of spikes of heat flow (power), with every spike corresponding to one ligand injection. [ 15 ] These heat flow spikes/pulses are integrated with respect to time, giving the total heat exchanged per injection. [ 16 ] By integrating each peak from the baseline, the total heat associated with each injection is obtained, including both reaction-specific and non-reaction-related contributions. [ 3 ] The pattern of these heat effects as a function of the molar ratio [ligand]/[macromolecule] can then be analyzed to give the thermodynamic parameters of the interaction under study. [ 4 ]
In order to accurately and precisely measure the thermodynamic parameters using ITC, certain procedures must be followed, involving instrument set up, parameter configuation, sample loading, buffer selection, and instrument cleaning. [ 6 ] [ 11 ] [ 16 ] To obtain an optimum result, each injection should be given enough time for a reaction equilibrium to reach. [ 8 ] Degassing samples is often necessary in order to obtain good measurements as the presence of gas bubbles within the sample cell will lead to abnormal data plots in the recorded results. The entire experiment takes place under computer control. [ 6 ] [ 18 ]
Direct titration is performed most commonly with ITC to obtain the thermodynamic data, by binding two components of the reaction directly to each other. However, many of the chemical reactions and binding interactions may have higher binding affinity above what is desirable with the c-window. [ 7 ] To troubleshoot the limitation of c-window and conditions for certain binding interactions, various different methods of titration can be performed. [ 15 ] In some cases, simply doing a reverse titration of changing the samples between the injection syringe and sample cell can solve the issue, depending on the binding mechanism. However, the process of introducing a ligand to a macromolecule is distinct from the process of adding a macromolecule to a ligand. [ 15 ] While the binding equilibrium remains unchanged in both direct and reverse titrations, the route to equilibrium and the accessible binding states varies, particularly when one molecule possesses multiple binding sites for the other. [ 3 ] Most of the high or low affinity bindings require chelation or competitive titration. [ 15 ] This method is done by loading pre-bound complex solution in the sample cell and chelating one of the components out with a reagent of higher observed binding affinity within the desirable c-window.
In order to ensure optimum instrument stability, the ITC instrument should be powered on at least one day before use. Samples should ideally be pre-equilibrated to approximately 2°C below the target experimental temperature to reduce stabilization time after loading, although starting at the exact experimental temperature is also an option. [ 8 ] For instrument cleaning, sample cell should be rinsed with the experimental buffer and dried under vacuum, and any remaining rinsed solution should be discarded manually with a syringe. Then, the sample cell is filled with the experimental solution and the reference cell with either high-purity water or the same buffer. [ 4 ] To prevent air contamination, gas-tight Hamilton syringes are used, ensuring the needle is positioned near the bottom of the sample cell before dispensing the liquid slowly. [ 8 ] Experimental parameters such as the number of injections, initial injection volume, subsequent injection volumes, temperature, reference power, stirring speed, spacing, initial delay, and filter period should be adjusted according to the specific study. [ 7 ]
If the experiment is to be repeated, the syringe should be emptied, with the solution either discarded or saved for further analysis. Before refilling with the same solution, the syringe needle should be externally rinsed and dried with lint-free paper, without the need for an internal wash. [ 8 ] However, when switching to a different reagent or concentration, the syringe must be thoroughly washed, flushed with ethanol or methanol, and carefully dried under vacuum-using a ThermoVac for VP-ITC or the integrated vacuum systems in other models. The sample cell should be emptied using the loading syringe and rinsed multiple times with water. [ 11 ]
It is necessary to conduct a post-hoc analysis to determine the buffer or solvent-independent enthalpy from the experimental thermodynamics. The collected experimental data reflects not only the binding thermodynamics of the interaction of interest, but any contributing competing equilibria associated to it. [ 5 ] [ 15 ] [ 16 ] A post-hoc analysis can be performed to determine the buffer or solvent-independent enthalpy from the experimental thermodynamics, by simply going through the process of Hess’ law . [ 5 ] [ 10 ] [ 15 ] Below example shows a simple interaction between a metal ion (M) and a ligand (L). B represents the buffer used for this interaction and H + {\displaystyle {\ce {H+}}} represents protons .
M − B ↽ − − ⇀ M + B {\displaystyle {\ce {M - B <=> M + B}}} − Δ H MB {\displaystyle {\ce {-\Delta H_{MB}}}}
L − H ↽ − − ⇀ L + H + {\displaystyle {\ce {L - H <=> L + H+}}} − ( n H + ) Δ H L H {\displaystyle -(n_{H+})\Delta H_{LH}}
H + + B ↽ − − ⇀ H − B {\displaystyle {\ce {H+ + B <=> H - B}}} ( n H + ) Δ H B H {\displaystyle (n_{H+})\Delta H_{BH}}
M + L ↽ − − ⇀ M − L {\displaystyle {\ce {M + L <=> M - L}}} Δ H M L {\displaystyle \Delta H_{ML}}
Therefore,
Δ H I T C = − Δ H M B − ( n H + ) Δ H L H + ( n H + ) Δ H B H + Δ H M L {\displaystyle \Delta H_{ITC}=-\Delta H_{MB}-(n_{H+})\Delta H_{LH}+(n_{H+})\Delta H_{BH}+\Delta H_{ML}}
which can be further processed to calculate the enthalpy of metal-ligand interaction. [ 20 ] [ 21 ] Although this example is between a metal and a ligand , it is applicable to any ITC experiment, regarding binding interactions.
As a part of the analysis, a number of protons are required to calculate the solvent-independent thermodynamics. [ 15 ] This can be easily done by plotting a graph such as shown below.
The linear equation of this plot is the rearranged version of the equation above from the post-hoc analysis in a form of y = mx + b:
Δ H I T C = ( n H + ) Δ H B H + [ − Δ H M B − ( n H + ) Δ H L H + Δ H M L ] {\displaystyle \Delta H_{ITC}=(n_{H+})\Delta H_{BH}+[-\Delta H_{MB}-(n_{H+})\Delta H_{LH}+\Delta H_{ML}]}
Equilibrium constant of the reaction is also not independent from the other competing equilibria. [ 5 ] Competition would include buffer interactions and other pH-dependent reactions depending on the experimental conditions. [ 5 ] [ 15 ] The competition from species other than the species of interest is included in the competition factor, Q in the following equation: [ 21 ]
Q = Σ ( β n [ X ] n ) {\displaystyle Q=\Sigma (\beta _{n}[\mathrm {X} ]_{n})}
where, X {\displaystyle X} represents species such a buffer or protons, β {\displaystyle \beta } represents their equilibrium constant, when,
K M L = K I T C Q {\displaystyle K_{ML}=K_{ITC}Q}
For the past 30 years, isothermal titration calorimetry has been used in a wide array of fields, ranging from metal binding studies to drug discovery, and nanomaterials research. [ 9 ] [ 16 ] [ 22 ] [ 23 ] In the old days, this technique was used to determine fundamental thermodynamic values for basic small molecular interactions. [ 24 ] In recent years, ITC has been used in more industrially applicable areas, such as drug discovery and testing synthetic materials . [ 9 ] Although it is still heavily used in fundamental chemistry, the trend has shifted over to the biological side, where label-free and buffer independent values are relatively harder to achieve. [ 9 ] [ 25 ] [ 26 ]
Using the thermodynamic data from ITC, it is possible to deduce enzyme kinetics including proton or electron transfer , allostery and cooperativity , and enzyme inhibition . [ 8 ] [ 27 ] [ 28 ] [ 29 ] Modern ITC instruments can measure heat rates as small as 0.1 μcal/sec, allowing for the precise determination of reaction rates in the range of 10 −12 mol/sec and ITC can determine values for Km and kcat, in the ranges of 10 −2 –10 3 μM and 0.05–500 sec −1 , respectively. [ 11 ] ITC collects data over time that is useful for any kinetic experiments, but especially with the proteins due to constant aliquots of injections. [ 30 ] In terms of calculation, equilibrium constant and the slopes of binding can be directly utilized to determine the allostery and charge transfer, by comparing experimental data of different conditions ( pH , use of mutated peptide chain and binding sites, etc.). [ 11 ] Kinetic data obtained from ITC have been found to closely align with results from other purely kinetic methods, such as surface plasmon resonance. [ 3 ]
Membrane proteins and self-assembly properties of certain proteins can be studied under this technique, due to being a label-free calorimeter . [ 16 ] Membrane proteins are known to have difficulties with selection of proper solubilization and purification protocols. As ITC is a non-destructive calorimetric tool, it can be used as a detector to locate the fraction of protein with desired binding sites, by binding a known binding ligand to the protein. [ 16 ] [ 31 ] This feature also applies in studies of self-assembling proteins, especially in use of measuring thermodynamics of their structural transformation . [ 32 ]
ITC can provide insights into drug development by charactering the affinity, selectivity, ligand-induced conformational changes, and drug partitioning into membranes. [ 16 ] Binding affinity carries a huge importance in medicinal chemistry, as drugs need to bind to the protein effectively within a desired range. An exothermic binding process with a favorable enthalpy is considered a desirable characteristic for specific protein binders, as it indicates strong potential for optimization and high selectivity. [ 3 ] However, determining enthalpy changes and optimization of thermodynamic parameters are hugely difficult when designing drugs. [ 9 ] ITC troubleshoots this issue easily by deducing the binding affinity, enthalpic/entropic contributions and its binding stoichiometry.
Applying the ideas above, chirality of organometallic compounds can be deduced as well with this technique. [ 33 ] Each chiral compound has its own unique properties and binding mechanisms that are comparable to each other, which leads to differences in thermodynamic properties. By binding chiral solutions in a binding site can deduce the type of chirality and depending on the purpose, which chiral compound is more suitable for binding.
Binding metal ions to protein and other components of biological material is one of the most popular uses of ITC, since ovotransferrin to ferric iron binding study published by Lin et al. from MicroCal Inc. [ 34 ] This is due to some of the metal ions utilized in biological systems having d 10 electron configuration which cannot be studied with other common techniques such as UV-vis spectrophotometry or electron paramagnetic resonance . [ 19 ] [ 20 ] It is also closely related to biochemical and medicinal studies due to the large abundance of metal binding enzymes in biological systems. [ 35 ]
The technique has been well utilized in studying carbon nanotubes to determine thermodynamic binding interactions with biological molecules and graphene composite interactions. [ 36 ] Another notable use of ITC with carbon nanotubes is optimization of preparation of carbon nanotubes from graphene composite and polyvinyl alcohol (PVA) . PVA assembly process can be measured thermodynamically as mixing of the two ingredients is an exothermic reaction, and its binding trend can be easily observed by ITC.
ITC is increasingly utilized to study protein-nanoparticle interactions by providing key insights into binding affinity (in the form of association constant), interaction mechanisms (quantified through binding enthalpy, binding entropy, and Gibbs free energy), and binding stoichiometry. [ 22 ] These thermodynamic parameters from ITC can help assess structural modifications in proteins upon adsorption onto nanoparticle surfaces. [ 23 ]
One of the main limitations of ITC is that it is prone to allowing only moderate binding conformations to be detected, making it less effective for detecting very weak or extremely tight binding events. [ 16 ] Hence, it may struggle to provide accurate thermodynamic parameters for slow kinetic processes with long time constants, as these interactions may be masked by baseline noise and variability. [ 3 ] On the other hand, high-affinity interactions can be challenging to measure if they take several minutes or longer to fully develop, or if the measured signal depends on the reaction enthalpy. [ 37 ] When the binding enthalpy is close to zero, ITC may fail to generate meaningful interaction data, instead producing a series of small, uniform peaks that result in flat and uninformative thermograms. [ 3 ]
ITC is also susceptible to interference from unrelated heat signals, making it difficult to isolate and interpret the heat changes associated with the interaction of interest. [ 15 ] [ 16 ] Other limitations include solubility constraints, challenges in accurately determining protein concentration and the need to prepare the ligand in the same solution conditions as the protein for reliable measurements. [ 15 ] | https://en.wikipedia.org/wiki/Isothermal_titration_calorimetry |
Isothermal transformation diagrams (also known as time-temperature-transformation ( TTT ) diagrams ) are plots of temperature versus time (usually on a logarithmic scale ). They are generated from percentage transformation-vs time measurements, and are useful for understanding the transformations of an alloy steel at elevated temperatures.
An isothermal transformation diagram is only valid for one specific composition of material, and only if the temperature is held constant during the transformation, and strictly with rapid cooling to that temperature. Though usually used to represent transformation kinetics for steels, they also can be used to describe the kinetics of crystallization in ceramic or other materials. Time-temperature-precipitation diagrams and time-temperature-embrittlement diagrams have also been used to represent kinetic changes in steels.
Isothermal transformation ( IT ) diagram or the C-curve is associated with mechanical properties, microconstituents/microstructures, and heat treatments in carbon steels. Diffusional transformations like austenite transforming to a cementite and ferrite mixture can be explained using the sigmoidal curve; for example the beginning of pearlitic transformation is represented by the pearlite start (P s ) curve. This transformation is complete at P f curve. Nucleation requires an incubation time. The rate of nucleation increases and the rate of microconstituent growth decreases as the temperature decreases from the liquidus temperature reaching a maximum at the bay or nose of the curve. Thereafter, the decrease in diffusion rate due to low temperature offsets the effect of increased driving force due to greater difference in free energy . As a result of the transformation, the microconstituents, pearlite and bainite , form; pearlite forms at higher temperatures and bainite at lower.
Austenite is slightly undercooled when quenched below Eutectoid temperature. When given more time, stable microconstituents can form: ferrite and cementite. Coarse pearlite is produced when atoms diffuse rapidly after phases that form pearlite nucleate. This transformation is complete at the pearlite finish time (P f ).
However, greater undercooling by rapid quenching results in formation of martensite or bainite instead of pearlite. This is possible provided the cooling rate is such that the cooling curve intersects the martensite start temperature or the bainite start curve before intersecting the P s curve. The martensite transformation being a diffusionless shear transformation is represented by a straight line to signify the martensite start temperature. | https://en.wikipedia.org/wiki/Isothermal_transformation_diagram |
In organic chemistry , isothiocyanate is a functional group as found in compounds with the formula R−N=C=S . Isothiocyanates are the more common isomers of thiocyanates , which have the formula R−S−C≡N .
Many isothiocyanates from plants are produced by enzymatic conversion of metabolites called glucosinolates . A prominent natural isothiocyanate is allyl isothiocyanate , also known as mustard oils .
Cruciferous vegetables , such as bok choy , broccoli , cabbage , cauliflower , kale , and others, are rich sources of glucosinolate precursors of isothiocyanates. [ 1 ]
The N=C and C=S distances are 117 and 158 pm . [ 2 ] By contrast, in methyl thiocyanate , N≡C and C−S distances are 116 and 176 pm.
Typical bond angles for C−N=C in aryl isothiocyanates are near 165°. Again, the thiocyanate isomers are quite different with C−S−C angle near 100°. [ 3 ] In both isomers the SCN angle approaches 180°.
Allyl thiocyanate isomerizes to the isothiocyanate: [ 4 ]
Isothiocyanates can be prepared by treating organic dithiocarbamate salts with lead nitrate or tosyl chloride . [ 5 ] [ 6 ]
Isothiocyanates may also be accessed by the fragmentation reactions of 1,4,2-oxathiazoles. [ 7 ] This methodology has been applied to a polymer-supported synthesis of isothiocyanates. [ 8 ]
Isothiocyanates are weak electrophiles, susceptible to hydrolysis. In general, nucleophiles attack at carbon:
Electrochemical reduction gives thioformamides . [ 10 ] : 340
Isothiocyanates occur widely in nature and are of interest in food science and medical research . [ 1 ] Vegetable foods with characteristic flavors due to isothiocyanates include bok choy , broccoli , cabbage , cauliflower , kale , wasabi , horseradish , mustard , radish , Brussels sprouts , watercress , papaya seeds, nasturtiums , and capers . [ 1 ] These species generate isothiocyanates in different proportions, and so have different, but recognizably related, flavors. They are all members of the order Brassicales , which is characterized by the production of glucosinolates , and of the enzyme myrosinase , which acts on glucosinolates to release isothiocyanates. [ 1 ]
Phenyl isothiocyanate , is used for amino acid sequencing in the Edman degradation .
Isothiocyanate and its linkage isomer thiocyanate are ligands in coordination chemistry. Thiocyanate is a more common ligand . | https://en.wikipedia.org/wiki/Isothiocyanate |
In organic chemistry , isothiouronium is a functional group with the formula [RSC(NH 2 ) 2 ] + (R = alkyl , aryl ) and is the acid salt of isothiourea . The H centres can also be replaced by alkyl and aryl. Structurally, these cations resemble guanidinium cations. The CN 2 S core is planar and the C–N bonds are short. [ 1 ]
Salts comprising these cations are typically prepared by alkylation of thiourea :
Hydrolysis of isothiouronium salts gives thiols . [ 2 ]
Isothiouronium salts in which the sulfur has been alkylated, such as S -methylisothiourea hemisulfate (CAS number: 867-44-7), will convert amines into guanidinium groups. This approach is sometimes called the Rathke synthesis [ 3 ] after Bernhard Rathke [ 4 ] who first reported it in 1881. [ 5 ]
Chelating resins with isothiouronium groups are used to recover mercury and other noble metals including platinum from solutions. [ 6 ] | https://en.wikipedia.org/wiki/Isothiouronium |
Two nuclides are isotones if they have the same neutron number N , but different proton number Z . For example, boron-12 and carbon-13 nuclei both contain 7 neutrons , and so are isotones. Similarly, 36 S, 37 Cl, 38 Ar, 39 K, and 40 Ca nuclei are all isotones of 20 because they all contain 20 neutrons. Despite its similarity to the Greek for "same stretching", the term was formed by the German physicist K. Guggenheimer [ 1 ] by changing the "p" in " isotope " from "p" for "proton" to "n" for "neutron". [ 2 ]
The largest numbers of observationally stable nuclides exist for isotones 50 (five: 86 Kr, 88 Sr, 89 Y, 90 Zr, 92 Mo – noting also the primordial radionuclide 87 Rb) and 82 (six: 138 Ba, 139 La, 140 Ce, 141 Pr, 142 Nd, 144 Sm – noting also the primordial radionuclide 136 Xe). Neutron numbers for which there are no stable isotones are 19, 21, 35, 39, 45, 61, 89, 115, 123, and 127 or more (though 21, 142, 143, 146, and perhaps 150 have primordial radionuclides). In contrast, the proton numbers for which there are no stable isotopes are 43 , 61 , and 83 or more (83, 90 , 92 , and perhaps 94 have primordial radionuclides). [ 3 ] This is related to nuclear magic numbers , the number of nucleons forming complete shells within the nucleus, e.g. 2, 8, 20, 28, 50, 82, and 126. No more than one observationally stable nuclide has the same odd neutron number, except for 1 ( 2 H and 3 He), 5 ( 9 Be and 10 B), 7 ( 13 C and 14 N), 55 ( 97 Mo and 99 Ru), and 107 ( 179 Hf and 180m Ta). In contrast, all even neutron numbers from 6 to 124, except 84 and 86, have at least two observationally stable nuclides. Neutron numbers for which there is a stable nuclide and a primordial radionuclide are 27 ( 50 V), 65 ( 113 Cd), 81 ( 138 La), 84 ( 144 Nd), 85 ( 147 Sm), 86 ( 148 Sm), 105 ( 176 Lu), and 126 ( 209 Bi). Neutron numbers for which there are two primordial radionuclides are 88 ( 151 Eu and 152 Gd) and 112 ( 187 Re and 190 Pt).
The neutron numbers which have only one stable nuclide (compare: monoisotopic element for the proton numbers ) are: 0, 2, 3, 4, 9, 11, 13, 15, 17, 23, 25, 27, 29, 31, 33, 37, 41, 43, 47, 49, 51, 53, 57, 59, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 84, 85, 86, 87, 91, 93, 95, 97, 99, 101, 103, 105, 109, 111, 113, 117, 119, 121, 125, 126, and the neutron numbers which have only one significant naturally-abundant nuclide (compare: mononuclidic element for the proton numbers ) are: 0, 2, 3, 4, 9, 11, 13, 15, 17, 21, 23, 25, 29, 31, 33, 37, 41, 43, 47, 49, 51, 53, 57, 59, 63, 67, 69, 71, 73, 75, 77, 79, 83, 87, 91, 93, 95, 97, 99, 101, 103, 109, 111, 113, 117, 119, 121, 125, 142, 143, 146. | https://en.wikipedia.org/wiki/Isotone |
Isotopes are distinct nuclear species (or nuclides ) of the same chemical element . They have the same atomic number (number of protons in their nuclei ) and position in the periodic table (and hence belong to the same chemical element), but different nucleon numbers ( mass numbers ) due to different numbers of neutrons in their nuclei. While all isotopes of a given element have similar chemical properties, they have different atomic masses and physical properties. [ 1 ]
The term isotope is derived from the Greek roots isos ( ἴσος "equal") and topos ( τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the periodic table . [ 2 ] It was coined by Scottish doctor and writer Margaret Todd in a 1913 suggestion to the British chemist Frederick Soddy , who popularized the term. [ 3 ]
The number of protons within the atom's nucleus is called its atomic number and is equal to the number of electrons in the neutral (non-ionized) atom. Each atomic number identifies a specific element, but not the isotope; an atom of a given element may have a wide range in its number of neutrons . The number of nucleons (both protons and neutrons) in the nucleus is the atom's mass number , and each isotope of a given element has a different mass number.
For example, carbon-12 , carbon-13 , and carbon-14 are three isotopes of the element carbon with mass numbers 12, 13, and 14, respectively. The atomic number of carbon is 6, which means that every carbon atom has 6 protons so that the neutron numbers of these isotopes are 6, 7, and 8 respectively.
A nuclide is a species of an atom with a specific number of protons and neutrons in the nucleus, for example, carbon-13 with 6 protons and 7 neutrons. The nuclide concept (referring to individual nuclear species) emphasizes nuclear properties over chemical properties, whereas the isotope concept (grouping all atoms of each element) emphasizes chemical over nuclear. The neutron number greatly affects nuclear properties, but its effect on chemical properties is negligible for most elements. Even for the lightest elements, whose ratio of neutron number to atomic number varies the most between isotopes, it usually has only a small effect although it matters in some circumstances (for hydrogen, the lightest element, the isotope effect is large enough to affect biology strongly). The term isotopes (originally also isotopic elements , [ 4 ] now sometimes isotopic nuclides [ 5 ] ) is intended to imply comparison (like synonyms or isomers ). For example, the nuclides 12 6 C , 13 6 C , 14 6 C are isotopes (nuclides with the same atomic number but different mass numbers [ 6 ] ), but 40 18 Ar , 40 19 K , 40 20 Ca are isobars (nuclides with the same mass number [ 7 ] ). However, isotope is the older term and so is better known than nuclide and is still sometimes used in contexts in which nuclide might be more appropriate, such as nuclear technology and nuclear medicine .
An isotope and/or nuclide is specified by the name of the particular element (this indicates the atomic number) followed by a hyphen and the mass number (e.g. helium-3 , helium-4 , carbon-12 , carbon-14 , uranium-235 and uranium-239 ). [ 8 ] [ 9 ] When a chemical symbol is used, e.g. "C" for carbon, standard notation (now known as "AZE notation" because A is the mass number , Z the atomic number , and E for element ) is to indicate the mass number (number of nucleons) with a superscript at the upper left of the chemical symbol and to indicate the atomic number with a subscript at the lower left (e.g. 3 2 He , 4 2 He , 12 6 C , 14 6 C , 235 92 U , and 239 92 U ). [ 10 ] Because the atomic number is given by the element symbol, it is common to state only the mass number in the superscript and leave out the atomic number subscript (e.g. 3 He , 4 He , 12 C , 14 C , 235 U , and 239 U ). The letter m (for metastable) is sometimes appended after the mass number to indicate a nuclear isomer , a metastable or energetically excited nuclear state (as opposed to the lowest-energy ground state ), for example 180m 73 Ta ( tantalum-180m ).
The common pronunciation of the AZE notation is different from how it is written: 4 2 He is commonly pronounced as helium-four instead of four-two-helium, and 235 92 U as uranium two-thirty-five (American English) or uranium-two-three-five (British) instead of 235-92-uranium.
Some isotopes/nuclides are radioactive , and are therefore referred to as radioisotopes or radionuclides , whereas others have never been observed to decay radioactively and are referred to as stable isotopes or stable nuclides . For example, 14 C is a radioactive form of carbon, whereas 12 C and 13 C are stable isotopes. There are about 339 naturally occurring nuclides on Earth, [ 11 ] of which 286 are primordial nuclides , meaning that they have existed since the Solar System 's formation.
Primordial nuclides include 35 nuclides with very long half-lives (over 100 million years) and 251 that are formally considered as " stable nuclides ", [ 11 ] because they have not been observed to decay. In most cases, for obvious reasons, if an element has stable isotopes, those isotopes predominate in the elemental abundance found on Earth and in the Solar System. However, in the cases of three elements ( tellurium , indium , and rhenium ) the most abundant isotope found in nature is actually one (or two) extremely long-lived radioisotope(s) of the element, despite these elements having one or more stable isotopes.
Theory predicts that many apparently "stable" nuclides are radioactive, with extremely long half-lives (discounting the possibility of proton decay , which would make all nuclides ultimately unstable). Some stable nuclides are in theory energetically susceptible to other known forms of decay, such as alpha decay or double beta decay, but no decay products have yet been observed, and so these isotopes are said to be "observationally stable". The predicted half-lives for these nuclides often greatly exceed the estimated age of the universe, and in fact, there are also 31 known radionuclides (see primordial nuclide ) with half-lives longer than the age of the universe.
Adding in the radioactive nuclides that have been created artificially, there are 3,339 currently known nuclides . [ 12 ] These include 905 nuclides that are either stable or have half-lives longer than 60 minutes. See list of nuclides for details.
The existence of isotopes was first suggested in 1913 by the radiochemist Frederick Soddy , based on studies of radioactive decay chains that indicated about 40 different species referred to as radioelements (i.e. radioactive elements) between uranium and lead, although the periodic table only allowed for 11 elements between lead and uranium inclusive. [ 13 ] [ 14 ] [ 15 ]
Several attempts to separate these new radioelements chemically had failed. [ 16 ] For example, Soddy had shown in 1910 that mesothorium (later shown to be 228 Ra), radium ( 226 Ra, the longest-lived isotope), and thorium X ( 224 Ra) are impossible to separate. [ 17 ] Attempts to place the radioelements in the periodic table led Soddy and Kazimierz Fajans independently to propose their radioactive displacement law in 1913, to the effect that alpha decay produced an element two places to the left in the periodic table, whereas beta decay emission produced an element one place to the right. [ 18 ] [ 19 ] [ 20 ] [ 21 ] Soddy recognized that emission of an alpha particle followed by two beta particles led to the formation of an element chemically identical to the initial element but with a mass four units lighter and with different radioactive properties.
Soddy proposed that several types of atoms (differing in radioactive properties) could occupy the same place in the table. [ 15 ] For example, the alpha-decay of uranium-235 forms thorium-231, whereas the beta decay of actinium-230 forms thorium-230. [ 16 ] The term "isotope", Greek for "at the same place", [ 15 ] was suggested to Soddy by Margaret Todd , a Scottish physician and family friend, during a conversation in which he explained his ideas to her. [ 17 ] [ 22 ] [ 23 ] [ 24 ] [ 25 ] [ 26 ] He received the 1921 Nobel Prize in Chemistry in part for his work on isotopes. [ 27 ]
In 1914 T. W. Richards found variations between the atomic weight of lead from different mineral sources, attributable to variations in isotopic composition due to different radioactive origins. [ 16 ] [ 27 ]
The first evidence for multiple isotopes of a stable (non-radioactive) element was found by J. J. Thomson in 1912 as part of his exploration into the composition of canal rays (positive ions). [ 28 ] Thomson channelled streams of neon ions through parallel magnetic and electric fields, measured their deflection by placing a photographic plate in their path, and computed their mass to charge ratio using a method that became known as the Thomson's parabola method. Each stream created a glowing patch on the plate at the point it struck. Thomson observed two separate parabolic patches of light on the photographic plate (see image), which suggested two species of nuclei with different mass-to-charge ratios. He wrote "There can, therefore, I think, be little doubt that what has been called neon is not a simple gas but a mixture of two gases, one of which has an atomic weight about 20 and the other about 22. The parabola due to the heavier gas is always much fainter than that due to the lighter, so that probably the heavier gas forms only a small percentage of the mixture." [ 29 ]
F. W. Aston subsequently discovered multiple stable isotopes for numerous elements using a mass spectrograph . In 1919 Aston studied neon with sufficient resolution to show that the two isotopic masses are very close to the integers 20 and 22 and that neither is equal to the known molar mass (20.2) of neon gas. This is an example of Aston's whole number rule for isotopic masses, which states that large deviations of elemental molar masses from integers are primarily due to the fact that the element is a mixture of isotopes. Aston similarly showed in 1920 that the molar mass of chlorine (35.45) is a weighted average of the almost integral masses for the two isotopes 35 Cl and 37 Cl. [ 30 ] [ 31 ]
After the discovery of the neutron by James Chadwick in 1932, [ 32 ] the ultimate root cause for the existence of isotopes was clarified, that is, the nuclei of different isotopes for a given element have different numbers of neutrons, albeit having the same number of protons.
A neutral atom has the same number of electrons as protons. Thus different isotopes of a given element all have the same number of electrons and share a similar electronic structure. Because the chemical behaviour of an atom is largely determined by its electronic structure, different isotopes exhibit nearly identical chemical behaviour.
The main exception to this is the kinetic isotope effect : due to their larger masses, heavier isotopes tend to react somewhat more slowly than lighter isotopes of the same element. This is most pronounced by far for protium ( 1 H ), deuterium ( 2 H ), and tritium ( 3 H ), because deuterium has twice the mass of protium and tritium has three times the mass of protium. [ 33 ] These mass differences also affect the behavior of their respective chemical bonds, by changing the center of gravity ( reduced mass ) of the atomic systems. However, for heavier elements, the relative mass difference between isotopes is much less so that the mass-difference effects on chemistry are usually negligible. (Heavy elements also have relatively more neutrons than lighter elements, so the ratio of the nuclear mass to the collective electronic mass is slightly greater.) There is also an equilibrium isotope effect .
Similarly, two molecules that differ only in the isotopes of their atoms ( isotopologues ) have identical electronic structures, and therefore almost indistinguishable physical and chemical properties (again with deuterium and tritium being the primary exceptions). The vibrational modes of a molecule are determined by its shape and by the masses of its constituent atoms; so different isotopologues have different sets of vibrational modes. Because vibrational modes allow a molecule to absorb photons of corresponding energies, isotopologues have different optical properties in the infrared range.
Atomic nuclei consist of protons and neutrons bound together by the residual strong force . Because protons are positively charged, they repel each other. Neutrons, which are electrically neutral, stabilize the nucleus in two ways. Their copresence pushes protons slightly apart, reducing the electrostatic repulsion between the protons, and they exert an attractive nuclear force on each other and on protons. For this reason, one or more neutrons are necessary for two or more protons to bind into a nucleus. As the number of protons increases, so does the ratio of neutrons to protons necessary to ensure a stable nucleus (see graph at right). For example, although the neutron:proton ratio of 3 2 He is 1:2, the neutron:proton ratio of 238 92 U is greater than 3:2. A number of lighter elements have stable nuclides with the ratio 1:1 ( Z = N ). The nuclide 40 20 Ca (calcium-40) is observationally the heaviest stable nuclide with the same number of neutrons and protons. All stable nuclides heavier than calcium-40 contain more neutrons than protons.
Of the 80 elements with a stable isotope, the largest number of stable isotopes observed for any element is ten (for the element tin ). No element has nine or eight stable isotopes. Five elements have seven stable isotopes, eight have six stable isotopes, ten have five stable isotopes, nine have four stable isotopes, five have three stable isotopes, 16 have two stable isotopes (counting 180m 73 Ta as stable), and 26 elements have only a single stable isotope (of these, 19 are so-called mononuclidic elements , having a single primordial stable isotope that dominates and fixes the atomic weight of the natural element to high precision; 3 radioactive mononuclidic elements occur as well). [ 34 ] In total, there are 251 nuclides that have not been observed to decay. For the 80 elements that have one or more stable isotopes, the average number of stable isotopes is 251/80 ≈ 3.14 isotopes per element.
The proton:neutron ratio is not the only factor affecting nuclear stability. It depends also on evenness or oddness of its atomic number Z , neutron number N and, consequently, of their sum, the mass number A . Oddness of both Z and N tends to lower the nuclear binding energy , making odd nuclei, generally, less stable. This remarkable difference of nuclear binding energy between neighbouring nuclei, especially of odd- A isobars , has important consequences: unstable isotopes with a nonoptimal number of neutrons or protons decay by beta decay (including positron emission ), electron capture , or other less common decay modes such as spontaneous fission and cluster decay .
Most stable nuclides are even-proton-even-neutron, where all numbers Z , N , and A are even. The odd- A stable nuclides are divided (roughly evenly) into odd-proton-even-neutron, and even-proton-odd-neutron nuclides. Stable odd-proton-odd-neutron nuclides are the least common.
The 146 even-proton, even-neutron (EE) nuclides comprise ~58% of all stable nuclides and all have spin 0 because of pairing. There are also 24 primordial long-lived even-even nuclides. As a result, each of the 41 even-numbered elements from 2 to 82 has at least one stable isotope , and most of these elements have several primordial isotopes. Half of these even-numbered elements have six or more stable isotopes. The extreme stability of helium-4 due to a double pairing of 2 protons and 2 neutrons prevents any nuclides containing five ( 5 2 He , 5 3 Li ) or eight ( 8 4 Be ) nucleons from existing long enough to serve as platforms for the buildup of heavier elements via nuclear fusion in stars (see triple alpha process ).
Only five stable nuclides contain both an odd number of protons and an odd number of neutrons. The first four "odd-odd" nuclides occur in low mass nuclides, for which changing a proton to a neutron or vice versa would lead to a very lopsided proton-neutron ratio ( 2 1 H , 6 3 Li , 10 5 B , and 14 7 N ; spins 1, 1, 3, 1). The only other entirely "stable" odd-odd nuclide, 180m 73 Ta (spin 9), is thought to be the rarest of the 251 stable nuclides, and is the only primordial nuclear isomer , which has not yet been observed to decay despite experimental attempts. [ 35 ]
Many odd-odd radionuclides (such as the ground state of tantalum-180) with comparatively short half-lives are known. Usually, they beta-decay to their nearby even-even isobars that have paired protons and paired neutrons. Of the nine primordial odd-odd nuclides (five stable and four radioactive with long half-lives), only 14 7 N is the most common isotope of a common element. This is the case because it is a part of the CNO cycle . The nuclides 6 3 Li and 10 5 B are minority isotopes of elements that are themselves rare compared to other light elements, whereas the other six isotopes make up only a tiny percentage of the natural abundance of their elements.
53 stable nuclides have an even number of protons and an odd number of neutrons. They are a minority in comparison to the even-even isotopes, which are about 3 times as numerous. Among the 41 even- Z elements that have a stable nuclide, only two elements (argon and cerium) have no even-odd stable nuclides. One element (tin) has three. There are 24 elements that have one even-odd nuclide and 13 that have two odd-even nuclides. Of 35 primordial radionuclides there exist four even-odd nuclides (see table at right), including the fissile 235 92 U . Because of their odd neutron numbers, the even-odd nuclides tend to have large neutron capture cross-sections, due to the energy that results from neutron-pairing effects. These stable even-proton odd-neutron nuclides tend to be uncommon by abundance in nature, generally because, to form and enter into primordial abundance, they must have escaped capturing neutrons to form yet other stable even-even isotopes, during both the s-process and r-process of neutron capture, during nucleosynthesis in stars . For this reason, only 195 78 Pt and 9 4 Be are the most naturally abundant isotopes of their element.
48 stable odd-proton-even-neutron nuclides, stabilized by their paired neutrons, form most of the stable isotopes of the odd-numbered elements; the very few odd-proton-odd-neutron nuclides comprise the others. There are 41 odd-numbered elements with Z = 1 through 81, of which 39 have stable isotopes ( technetium ( 43 Tc ) and promethium ( 61 Pm ) have no stable isotopes). Of these 39 odd Z elements, 30 elements (including hydrogen-1 where 0 neutrons is even ) have one stable odd-even isotope, and nine elements: chlorine ( 17 Cl ), potassium ( 19 K ), copper ( 29 Cu ), gallium ( 31 Ga ), bromine ( 35 Br ), silver ( 47 Ag ), antimony ( 51 Sb ), iridium ( 77 Ir ), and thallium ( 81 Tl ), have two odd-even stable isotopes each. This makes a total 30 + 2(9) = 48 stable odd-even isotopes.
There are also five primordial long-lived radioactive odd-even isotopes, 87 37 Rb , 115 49 In , 187 75 Re , 151 63 Eu , and 209 83 Bi . The last two were only recently found to decay, with half-lives greater than 10 18 years.
Actinides with odd neutron number are generally fissile (with thermal neutrons ), whereas those with even neutron number are generally not, though they are fissionable with fast neutrons . All observationally stable odd-odd nuclides have nonzero integer spin. This is because the single unpaired neutron and unpaired proton have a larger nuclear force attraction to each other if their spins are aligned (producing a total spin of at least 1 unit), instead of anti-aligned. See deuterium for the simplest case of this nuclear behavior.
Only 195 78 Pt , 9 4 Be , and 14 7 N have odd neutron number and are the most naturally abundant isotope of their element.
Elements are composed either of one nuclide ( mononuclidic elements ), or of more than one naturally occurring isotopes. The unstable (radioactive) isotopes are either primordial or postprimordial. Primordial isotopes were a product of stellar nucleosynthesis or another type of nucleosynthesis such as cosmic ray spallation , and have persisted down to the present because their rate of decay is very slow (e.g. uranium-238 and potassium-40 ). Post-primordial isotopes were created by cosmic ray bombardment as cosmogenic nuclides (e.g., tritium , carbon-14 ), or by the decay of a radioactive primordial isotope to a radioactive radiogenic nuclide daughter (e.g. uranium to radium ). A few isotopes are naturally synthesized as nucleogenic nuclides, by some other natural nuclear reaction , such as when neutrons from natural nuclear fission are absorbed by another atom.
As discussed above, only 80 elements have any stable isotopes, and 26 of these have only one stable isotope. Thus, about two-thirds of stable elements occur naturally on Earth in multiple stable isotopes, with the largest number of stable isotopes for an element being ten, for tin ( 50 Sn ). There are about 94 elements found naturally on Earth (up to plutonium inclusive), though some are detected only in very tiny amounts, such as plutonium-244 . Scientists estimate that the elements that occur naturally on Earth (some only as radioisotopes) occur as 339 isotopes ( nuclides ) in total. [ 36 ] Only 251 of these naturally occurring nuclides are stable, in the sense of never having been observed to decay as of the present time. An additional 35 primordial nuclides (to a total of 286 primordial nuclides), are radioactive with known half-lives, but have half-lives longer than 100 million years, allowing them to exist from the beginning of the Solar System. See list of nuclides for details.
All the known stable nuclides occur naturally on Earth; the other naturally occurring nuclides are radioactive but occur on Earth due to their relatively long half-lives, or else due to other means of ongoing natural production. These include the afore-mentioned cosmogenic nuclides , the nucleogenic nuclides, and any radiogenic nuclides formed by ongoing decay of a primordial radioactive nuclide, such as radon and radium from uranium.
An additional ~3000 radioactive nuclides not found in nature have been created in nuclear reactors and in particle accelerators. Many short-lived nuclides not found naturally on Earth have also been observed by spectroscopic analysis, being naturally created in stars or supernovae . An example is aluminium-26 , which is not naturally found on Earth but is found in abundance on an astronomical scale.
The tabulated atomic masses of elements are averages that account for the presence of multiple isotopes with different masses. Before the discovery of isotopes, empirically determined noninteger values of atomic mass confounded scientists. For example, a sample of chlorine contains 75.8% chlorine-35 and 24.2% chlorine-37 , giving an average atomic mass of 35.5 atomic mass units .
According to generally accepted cosmology theory , only isotopes of hydrogen and helium, traces of some isotopes of lithium and beryllium, and perhaps some boron, were created at the Big Bang , while all other nuclides were synthesized later, in stars and supernovae, and in interactions between energetic particles such as cosmic rays, and previously produced nuclides. (See nucleosynthesis for details of the various processes thought responsible for isotope production.) The respective abundances of isotopes on Earth result from the quantities formed by these processes, their spread through the galaxy, and the rates of decay for isotopes that are unstable. After the initial coalescence of the Solar System , isotopes were redistributed according to mass, and the isotopic composition of elements varies slightly from planet to planet. This sometimes makes it possible to trace the origin of meteorites .
The atomic mass ( m r ) of an isotope (nuclide) is determined mainly by its mass number (i.e. number of nucleons in its nucleus). Small corrections are due to the binding energy of the nucleus (see mass defect ), the slight difference in mass between proton and neutron, and the mass of the electrons associated with the atom, the latter because the electron:nucleon ratio differs among isotopes.
The mass number is a dimensionless quantity . The atomic mass, on the other hand, is measured using the atomic mass unit based on the mass of the carbon-12 atom. It is denoted with symbols "u" (for unified atomic mass unit) or "Da" (for dalton ).
The atomic masses of naturally occurring isotopes of an element determine the standard atomic weight of the element. When the element contains N isotopes, the expression below is applied for the average atomic mass m ¯ a {\displaystyle {\overline {m}}_{a}} :
m ¯ a = m 1 x 1 + m 2 x 2 + . . . + m N x N {\displaystyle {\overline {m}}_{a}=m_{1}x_{1}+m_{2}x_{2}+...+m_{N}x_{N}}
where m 1 , m 2 , ..., m N are the atomic masses of each individual isotope, and x 1 , ..., x N are the relative abundances of these isotopes.
Several applications exist that capitalize on the properties of the various isotopes of a given element. Isotope separation is a significant technological challenge, particularly with heavy elements such as uranium or plutonium. Lighter elements such as lithium, carbon, nitrogen, and oxygen are commonly separated by gas diffusion of their compounds such as CO and NO. The separation of hydrogen and deuterium is unusual because it is based on chemical rather than physical properties, for example in the Girdler sulfide process . Uranium isotopes have been separated in bulk by gas diffusion, gas centrifugation, laser ionization separation, and (in the Manhattan Project ) by a type of production mass spectrometry . | https://en.wikipedia.org/wiki/Isotope |
Isotope-ratio mass spectrometry ( IRMS ) is a specialization of mass spectrometry , in which mass spectrometric methods are used to measure the relative abundance of isotopes in a given sample. [ 1 ] [ 2 ]
This technique has two different applications in the earth and environmental sciences. The analysis of ' stable isotopes ' is normally concerned with measuring isotopic variations arising from mass-dependent isotopic fractionation in natural systems. On the other hand, radiogenic isotope analysis [ 3 ] involves measuring the abundances of decay-products of natural radioactivity, and is used in most long-lived radiometric dating methods.
The isotope-ratio mass spectrometer (IRMS) allows the precise measurement of mixtures of naturally occurring isotopes. [ 4 ] Most instruments used for precise determination of isotope ratios are of the magnetic sector type. This type of analyzer is superior to the quadrupole type in this field of research for two reasons. First, it can be set up for multiple-collector analysis, and second, it gives high-quality 'peak shapes'. Both of these considerations are important for isotope-ratio analysis at very high precision and accuracy. [ 3 ]
The sector-type instrument designed by Alfred Nier was such an advance in mass spectrometer design that this type of instrument is often called the 'Nier type'. In the most general terms the instrument operates by ionizing the sample of interest, accelerating it over a potential in the kilo-volt range, and separating the resulting stream of ions according to their mass-to-charge ratio (m/z). Beams with lighter ions bend at a smaller radius than beams with heavier ions. The current of each ion beam is then measured using a ' Faraday cup ' or multiplier detector.
Many radiogenic isotope measurements are made by ionization of a solid source, whereas stable isotope measurements of light elements (e.g. H, C, O) are usually made in an instrument with a gas source. In a "multicollector" instrument, the ion collector typically has an array of Faraday cups , which allows the simultaneous detection of multiple isotopes. [ 5 ]
Measurement of natural variations in the abundances of stable isotopes of the same element is normally referred to as stable isotope analysis. This field is of interest because the differences in mass between different isotopes leads to isotope fractionation , causing measurable effects on the isotopic composition of samples, characteristic of their biological or physical history.
As a specific example, the hydrogen isotope deuterium (heavy hydrogen) is almost double the mass of the common hydrogen isotope. Water molecules containing the common hydrogen isotope (and the common oxygen isotope, mass 16) have a mass of 18. Water incorporating a deuterium atom has a mass of 19, over 5% heavier. The energy to vaporise the heavy water molecule is higher than that to vaporize the normal water so isotope fractionation occurs during the process of evaporation. Thus a sample of sea water will exhibit a quite detectable isotopic-ratio difference when compared to Antarctic snowfall.
Samples must be introduced to the mass spectrometer as pure gases, achieved through combustion, gas chromatographic feeds, [ 6 ] or chemical trapping. By comparing the detected isotopic ratios to a measured standard , an accurate determination of the isotopic make up of the sample is obtained. For example, carbon isotope ratios are measured relative to the international standard for C. The C standard is produced from a fossil belemnite found in the Peedee Formation , which is a limestone formed in the Cretaceous period in South Carolina , U.S.A. The fossil is referred to as VPDB (Vienna Pee Dee Belemnite) and has 13 C: 12 C ratio of 0.0112372. Oxygen isotope ratios are measured relative the standard , V-SMOW (Vienna Standard Mean Ocean Water).
It is critical that the sample be processed before entering the mass spectrometer so that only a single chemical species enters at a given time. Generally, samples are combusted or pyrolyzed and the desired gas species (usually hydrogen (H 2 ), nitrogen (N 2 ), carbon dioxide (CO 2 ), or sulfur dioxide (SO 2 )) is purified by means of traps, filters, catalysts and/or chromatography.
The two most common types of IRMS instruments are continuous flow [ 7 ] and dual inlet. In dual inlet IRMS, purified gas obtained from a sample is alternated rapidly with a standard gas (of known isotopic composition ) by means of a system of valves, so that a number of comparison measurements are made of both gases. In continuous flow IRMS, sample preparation occurs immediately before introduction to the IRMS, and the purified gas produced from the sample is measured just once. The standard gas may be measured before and after the sample or after a series of sample measurements. While continuous-flow IRMS instruments can achieve higher sample throughput and are more convenient to use than dual inlet instruments, the yielded data is of approximately 10-fold lower precision.
A static gas mass spectrometer is one in which a gaseous sample for analysis is fed into the source of the instrument and then left in the source without further supply or pumping throughout the analysis. This method can be used for 'stable isotope' analysis of light gases (as above), but it is particularly used in the isotopic analysis of noble gases (rare or inert gases) for radiometric dating or isotope geochemistry . Important examples are argon–argon dating and helium isotope analysis.
Several of the isotope systems involved in radiometric dating depend on IRMS using thermal ionization of a solid sample loaded into the source of the mass spectrometer (hence thermal ionization mass spectrometry , TIMS). These methods include rubidium–strontium dating , uranium–lead dating , lead–lead dating , potassium-calcium dating , and samarium–neodymium dating .
When these isotope ratios are measured by TIMS, mass-dependent fractionation occurs as species are emitted by the hot filament. Fractionation occurs due to the excitation of the sample and therefore must be corrected for accurate measurement of the isotope ratio. [ 8 ]
There are several advantages of the TIMS method. It has a simple design, is less expensive than other mass spectrometers, and produces stable ion emissions. It requires a stable power supply, and is suitable for species with a low ionization potential, such as strontium (Sr), and lead (Pb).
The disadvantages of this method stem from the maximum temperature achieved in thermal ionization. The hot filament reaches a temperature of less than 2500°C, leading to the inability to create atomic ions of species with a high ionization potential, such as osmium (Os), and tungsten (Hf-W). Though the TIMS method can create molecular ions instead in this case, species with high ionization potential can be analyzed more effectively with MC-ICP-MS.
An alternative approach used to measure the relative abundance of radiogenic isotopes when working with a solid surface is secondary-ion mass spectrometry (SIMS). This type of ion-microprobe analysis normally works by focusing a primary (oxygen) ion beam on a sample in order to generate a series of secondary positive ions that can be focused and measured based on their mass/charge ratios.
SIMS is a common method used in U-Pb analysis, as the primary ion beam is used to bombard the surface of a single zircon grain in order to yield a secondary beam of Pb ions. The Pb ions are analyzed using a double focusing mass spectrometer that comprises both an electrostatic and magnetic analyzer. This assembly allows the secondary ions to be focused based on their kinetic energy and mass-charge ratio in order to be accurately collected using a series of Faraday cups. [ 10 ]
A major issue that arises in SIMS analysis is the generation of isobaric interference between sputtered molecular ions and the ions of interest. This issue occurs with U–Pb dating as Pb ions have essentially the same mass as HfO 2 + . [ 11 ] In order to overcome this problem, a sensitive high-resolution ion microprobe ( SHRIMP ) can be used. A SHRIMP is a double-focusing mass spectrometer that allows for a large spatial separation between different ion masses based on its relatively large size. For U-Pb analysis, the SHRIMP allows for the separation of Pb from other interfering molecular ions, such as HfO 2 + .
An MC-ICP-MS instrument is a multiple collector mass spectrometer with a plasma source. MC-ICP-MS was developed to improve the precision achievable by ICP-MS during isotope-ratio measurements. Conventional ICP-MS analysis uses a quadrupole analyser, which only allows single-collector analysis. Due to the inherent instability of the plasma, this limits the precision of ICP-MS with a quadrupole analyzer to around 1%, which is insufficient for most radiogenic isotope systems.
Isotope-ratio analysis for radiometric dating has normally been determined by TIMS. However, some systems (e.g. Hf-W and Lu-Hf) are difficult or impossible to analyse by TIMS, due to the high ionization potential of the elements involved. Therefore, these methods can now be analysed using MC-ICP-MS.
The Ar-ICP produces an ion-beam with a large inherent kinetic energy distribution, which makes the design of the mass-spectrometer somewhat more complex than it is the case for conventional TIMS instruments. First, different from Quadrupole ICP-MS systems, magnetic sector instruments have to operate with a higher acceleration potential (several 1000 V) in order to minimize the energy distribution of the ion beam. Modern instruments operate at 6-10kV.
The radius of deflection of an ion within a magnetic field depends on the kinetic energy and the mass/charge ratio of the ion (strictly, the magnet is a momentum analyzer not just a mass analyzer). Because of the large energy distribution, ions with similar mass/charge ratio can have very different kinetic energies and will thus experience different deflection for the same magnetic field. In practical terms one would see that ions with the same mass/charge ratio focus at different points in space. However, in a mass-spectrometer one wants ions with the same mass/charge ratio to focus at the same point, e.g. where the detector is located. In order to overcome these limitations, commercial MC-ICP-MS are double-focusing instruments. In a double-focusing mass-spectrometer ions are focused due to kinetic energy by the ESA (electro-static-analyzer) and kinetic energy + mass/charge (momentum) in the magnetic field. Magnet and ESA are carefully chosen to match the energy focusing properties of one another and are arranged so that the direction of energy focusing is in opposite directions. To simplify, two components have an energy focus term, when arranged properly, the energy term cancels out and ions with the same mass/charge ratio focus at the same point in space. It is important to note, double-focusing does not reduce the kinetic energy distribution and different kinetic energies are not filtered or homogenized. Double-focusing works for single as well as multi-collector instruments. In single collector instruments ESA and magnet can be arranged in either forward geometry (first ESA then magnet) or reversed geometry (magnet first then ESA), as only point-to-point focusing is required. In multi-collector instruments, only forward geometry (ESA then magnet) is possible due to the array of detectors and the requirements of a focal plane rather than a focal point.
For isotopes occurring at extremely low levels, accelerator mass spectrometry (AMS) can be used. For example, the decay rate of the radioisotope 14 C is widely used to date organic materials, but this approach was once limited to relatively large samples no more than a few thousand years old. AMS extended the range of 14 C dating to about 60,000 years BP, and is about 10 6 times more sensitive than conventional IRMS.
AMS works by accelerating negative ions through a large (mega-volt) potential, followed by charge exchange and acceleration back to ground. During charge exchange, interfering species can be effectively removed. In addition, the high energy of the beam allows the use of energy-loss detectors, that can distinguish between species with the same mass/charge ratio. Together, these processes allow the analysis of extreme isotope ratios above 10 12 .
Moving wire IRMS is useful for analyzing carbon-13 ratios of compounds in a solution, such as after purification by liquid chromatography . The solution (or outflow from the chromatography) is dried onto a nickel or stainless steel wire. After the residue is deposited on the wire, it enters a furnace where the sample is converted to CO 2 and water by combustion. The gas stream finally enters a capillary, is dried, ionized, and analyzed. [ 12 ] This process allows a mixture of compounds to be purified and analyzed continuously, which can decrease the analysis time by a factor of four. [ 12 ] Moving wire IRMS is quite sensitive, and samples containing as little as 1 nano mole of carbon can yield precise (within 1‰) results. [ 13 ] | https://en.wikipedia.org/wiki/Isotope-ratio_mass_spectrometry |
Isotope analysis is the identification of isotopic signature , abundance of certain stable isotopes of chemical elements within organic and inorganic compounds . Isotopic analysis can be used to understand the flow of energy through a food web , to reconstruct past environmental and climatic conditions, to investigate human and animal diets, for food authentification, and a variety of other physical, geological, palaeontological and chemical processes. Stable isotope ratios are measured using mass spectrometry , which separates the different isotopes of an element on the basis of their mass-to-charge ratio .
Isotopic oxygen is incorporated into the body primarily through ingestion at which point it is used in the formation of, for archaeological purposes, bones and teeth . The oxygen is incorporated into the hydroxylcarbonic apatite of bone and tooth enamel .
Bone is continually remodelled throughout the lifetime of an individual. Although the rate of turnover of isotopic oxygen in hydroxyapatite is not fully known, it is assumed to be similar to that of collagen ; approximately 10 years. Consequently, should an individual remain in a region for 10 years or longer, the isotopic oxygen ratios in the bone hydroxyapatite would reflect the isotopic oxygen ratios present in that region.
Teeth are not subject to continual remodelling and so their isotopic oxygen ratios remain constant from the time of formation. The isotopic oxygen ratios, then, of teeth represent the ratios of the region in which the individual was born and raised. Where deciduous teeth are present, it is also possible to determine the age at which a child was weaned . Breast milk production draws upon the body water of the mother, which has higher levels of 18 O due to the preferential loss of 16 O through sweat, urine, and expired water vapour.
While teeth are more resistant to chemical and physical changes over time, both are subject to post-depositional diagenesis . As such, isotopic analysis makes use of the more resistant phosphate groups, rather than the less abundant hydroxyl group or the more likely diagenetic carbonate groups present.
Isotope analysis has widespread applicability in the natural sciences . These include numerous applications in the biological , earth and environmental sciences .
Archaeological materials, such as bone, organic residues, hair, or sea shells, can serve as substrates for isotopic analysis. Carbon , nitrogen and zinc isotope ratios are used to investigate the diets of past people; these isotopic systems can be used with others, such as strontium or oxygen, to answer questions about population movements and cultural interactions, such as trade. [ 1 ]
Carbon isotopes are analysed in archaeology to determine the source of carbon at the base of the foodchain. Examining the 12 C / 13 C isotope ratio, it is possible to determine whether animals and humans ate predominantly C3 or C4 plants. [ 2 ] Potential C3 food sources include wheat , rice , tubers , fruits , nuts and many vegetables , while C4 food sources include millet and sugar cane. [ 3 ] Carbon isotope ratios can also be used to distinguish between marine, freshwater, and terrestrial food sources. [ 4 ] [ 5 ]
Carbon isotope ratios can be measured in bone collagen or bone mineral ( hydroxylapatite ), and each of these fractions of bone can be analysed to shed light on different components of diet. The carbon in bone collagen is predominantly sourced from dietary protein, while the carbon found in bone mineral is sourced from all consumed dietary carbon, included carbohydrates, lipids, and protein. [ 6 ]
Nitrogen isotopes can be used to infer soil conditions, with enriched δ15N used to infer the addition of manure . A complication is that enrichment also occurs as a result of environmental factors, such as wetland denitrification , salinity , aridity , microbes , and clearance . [ 7 ] δ13C and δ15N measurements on medieval manor soils has shown that stable isotopes can differentiate between crop cultivation and grazing activities, revealing land use types such as cereal production and the presence of fertilization practices at historical sites. [ 8 ]
To obtain an accurate picture of palaeodiets, it is important to understand processes of diagenesis that may affect the original isotopic signal. It is also important for the researcher to know the variations of isotopes within individuals, between individuals, and over time. [ 1 ]
Isotope analysis has been particularly useful in archaeology as a means of characterization. Characterization of artifacts involves determining the isotopic composition of possible source materials such as metal ore bodies and comparing these data to the isotopic composition of analyzed artifacts. A wide range of archaeological materials such as metals, glass and lead-based pigments have been sourced using isotopic characterization. [ 9 ] Particularly in the Bronze Age Mediterranean, lead isotope analysis has been a useful tool for determining the sources of metals and an important indicator of trade patterns. Interpretation of lead isotope data is, however, often contentious and faces numerous instrumental and methodological challenges. [ 10 ] Problems such as the mixing and re-using of metals from different sources, limited reliable data and contamination of samples can be difficult problems in interpretation.
All biologically active elements exist in a number of different isotopic forms, of which two or more are stable. For example, most carbon is present as 12 C, with approximately 1% being 13 C. The ratio of the two isotopes may be altered by biological and geophysical processes, and these differences can be utilized in a number of ways by ecologists.
The main elements used in isotope ecology are carbon, nitrogen, oxygen, hydrogen and sulfur, but also include silicon, iron, and strontium. [ 11 ]
Stable isotopes have become a popular method for understanding aquatic ecosystems because they can help scientists in understanding source links and process information in marine food webs. These analyses can also be used to a certain degree in terrestrial systems. Certain isotopes can signify distinct primary producers forming the bases of food webs and trophic level positioning. The stable isotope compositions are expressed in terms of delta values (δ) in permil (‰), i.e. parts per thousand differences from a standard . They express the proportion of an isotope that is in a sample. The values are expressed as:
where X represents the isotope of interest (e.g., 13 C ) and R represents the ratio of the isotope of interest and its natural form (e.g., 13 C/ 12 C). [ 12 ] Higher (or less negative) delta values indicate increases in a sample's isotope of interest, relative to the standard , and lower (or more negative) values indicate decreases. The standard reference materials for carbon, nitrogen, and sulfur are Pee Dee Belamnite limestone, nitrogen gas in the atmosphere, and Cañon Diablo meteorite respectively. Analysis is usually done using a mass spectrometer, detecting small differences between gaseous elements. Analysis of a sample can cost anywhere from $30 to $100. [ 12 ] Stable isotopes assist scientists in analyzing animal diets and food webs by examining the animal tissues that bear a fixed isotopic enrichment or depletion vs. the diet. Muscle or protein fractions have become the most common animal tissue used to examine the isotopes because they represent the assimilated nutrients in their diet. The main advantage to using stable isotope analysis as opposed to stomach content observations is that no matter what the status is of the animal's stomach (empty or not), the isotope tracers in the tissues will give us an understanding of its trophic position and food source. [ 13 ] The three major isotopes used in aquatic ecosystem food web analysis are 13 C, 15 N and 34 S . While all three indicate information on trophic dynamics , it is common to perform analysis on at least two of the previously mentioned three isotopes for better understanding of marine trophic interactions and for stronger results.
The ratio of 2 H, also known as deuterium , to 1 H has been studied in both plant and animal tissue. Hydrogen isotopes in plant tissue are correlated with local water values but vary based on fractionation during photosynthesis , transpiration, and other processes in the formation of cellulose. A study on the isotope ratios of tissues from plants growing within a small area in Texas found tissues from CAM plants were enriched in deuterium relative to C4 plants. [ 14 ] Hydrogen isotope ratios in animal tissue reflect diet, including drinking water, and have been used to study bird migration [ 15 ] and aquatic food webs. [ 16 ] [ 17 ]
Carbon isotopes aid us in determining the primary production source responsible for the energy flow in an ecosystem. The transfer of 13 C through trophic levels remains relatively the same, except for a small increase (an enrichment < 1 ‰). Large differences of δ 13 C between animals indicate that they have different food sources or that their food webs are based on different primary producers (i.e. different species of phytoplankton, marsh grasses.) Because δ 13 C indicates the original source of primary producers, the isotopes can also help us determine shifts in diets, both short term, long term or permanent. These shifts may even correlate to seasonal changes, reflecting phytoplankton abundance. [ 13 ] Scientists have found that there can be wide ranges of δ 13 C values in phytoplankton populations over a geographic region. While it is not quite certain as to why this may be, there are several hypotheses for this occurrence. These include isotopes within dissolved inorganic carbon pools (DIC) may vary with temperature and location and that growth rates of phytoplankton may affect their uptake of the isotopes. δ 13 C has been used in determining migration of juvenile animals from sheltered inshore areas to offshore locations by examining the changes in their diets. A study by Fry (1983) studied the isotopic compositions in juvenile shrimp of south Texas grass flats. Fry found that at the beginning of the study the shrimp had isotopic values of δ 13 C = -11 to -14‰ and 6-8‰ for δ 15 N and δ 34 S. As the shrimp matured and migrated offshore, the isotopic values changed to those resembling offshore organisms (δ 13 C= -15‰ and δ 15 N = 11.5‰ and δ 34 S = 16‰). [ 18 ]
While there is no enrichment of 34 S between trophic levels, the stable isotope can be useful in distinguishing benthic vs. pelagic producers and marsh vs. phytoplankton producers. [ 13 ] Similar to 13 C, it can also help distinguish between different phytoplankton as the key primary producers in food webs. The differences between seawater sulfates and sulfides (c. 21‰ vs -10‰) aid scientists in the discriminations. Sulfur tends to be more plentiful in less aerobic areas, such as benthic systems and marsh plants, than the pelagic and more aerobic systems. Thus, in the benthic systems, there are smaller δ 34 S values. [ 13 ]
Nitrogen isotopes indicate the trophic level position of organisms (reflective of the time the tissue samples were taken). There is a larger enrichment component with δ 15 N because its retention is higher than that of 14 N. This can be seen by analyzing the waste of organisms. [ 13 ] Cattle urine has shown that there is a depletion of 15 N relative to the diet. [ 19 ] As organisms eat each other, the 15 N isotopes are transferred to the predators. Thus, organisms higher in the trophic pyramid have accumulated higher levels of 15 N ( and higher δ 15 N values) relative to their prey and others before them in the food web. Numerous studies on marine ecosystems have shown that on average there is a 3.2‰ enrichment of 15 N vs. diet between different trophic level species in ecosystems. [ 13 ] In the Baltic sea, Hansson et al. (1997) found that when analyzing a variety of creatures (such as particulate organic matter (phytoplankton), zooplankton , mysids , sprat, smelt and herring,) there was an apparent fractionation of 2.4‰ between consumers and their apparent prey. [ 20 ]
In addition to trophic positioning of organisms, δ 15 N values have become commonly used in distinguishing between land derived and natural sources of nutrients. As water travels from septic tanks to aquifers, the nitrogen rich water is delivered into coastal areas. Waste-water nitrate has higher concentrations of 15 N than the nitrate that is found in natural soils in near shore zones. [ 21 ] For bacteria, it is more convenient for them to uptake 14 N as opposed to 15 N because it is a lighter element and easier to metabolize. Thus, due to bacteria's preference when performing biogeochemical processes such as denitrification and volatilization of ammonia, 14 N is removed from the water at a faster rate than 15 N, resulting in more 15 N entering the aquifer. 15 N is roughly 10-20‰ as opposed to the natural 15 N values of 2-8‰. [ 21 ] The inorganic nitrogen that is emitted from septic tanks and other human-derived sewage is usually in the form of NH 4 + {\displaystyle {\ce {NH4+}}} . Once the nitrogen enters the estuaries via groundwater, it is thought that because there is more 15 N entering, that there will also be more 15 N in the inorganic nitrogen pool delivered and that it is picked up more by producers taking up N. Even though 14 N is easier to take up, because there is much more 15 N, there will still be higher amounts assimilated than normal. These levels of δ 15 N can be examined in creatures that live in the area and are non migratory (such as macrophytes , clams and even some fish). [ 20 ] [ 22 ] [ 23 ] This method of identifying high levels of nitrogen input is becoming a more and more popular method in attempting to monitor nutrient input into estuaries and coastal ecosystems. Environmental managers have become more and more concerned about measuring anthropogenic nutrient inputs into estuaries because excess in nutrients can lead to eutrophication and hypoxic events , eliminating organisms from an area entirely. [ 24 ]
Analysis of the ratio of 18 O to 16 O in the shells of the Colorado Delta clam was used to assess the historical extent of the estuary in the Colorado River Delta prior to construction of upstream dams. [ 25 ]
A recent development in forensic science is the isotopic analysis of hair strands. Hair has a recognisable growth rate of 9-11mm [ 26 ] per month or 15 cm per year. [ 27 ] Human hair growth is primarily a function of diet, especially drinking water intake. [ citation needed ] The stable isotopic ratios of drinking water are a function of location, and the geology that the water percolates through. 87 Sr, 88 Sr and oxygen isotope variations are different all over the world. These differences in isotopic ratio are then biologically 'set' in our hair as it grows and it has therefore become possible to identify recent geographic histories by the analysis of hair strands. For example, it could be possible to identify whether a terrorist suspect had recently been to a particular location from hair analysis. This hair analysis is a non-invasive method which is becoming very popular in cases that DNA or other traditional means are bringing no answers. [ citation needed ]
Isotope analysis can be used by forensic investigators to determine whether two or more samples of explosives are of a common origin. Most high explosives contain carbon, hydrogen, nitrogen and oxygen atoms and thus comparing their relative abundances of isotopes can reveal the existence of a common origin. Researchers have also shown that analysis of the 12 C/ 13 C ratios can locate the country of origin for a given explosive. [ citation needed ]
Stable isotopic analysis has also been used in the identification of drug trafficking routes. Isotopic abundances are different in morphine grown from poppies in south-east Asia versus poppies grown in south-west Asia. The same is applied to cocaine that is derived from Bolivia and that from Colombia. [ 28 ]
Stable isotopic analysis has also been used for tracing the geographical origin of food, [ 29 ] timber, [ 30 ] and in tracing the sources and fates of nitrates in the environment. [ 31 ] [ 32 ]
In isotope hydrology , stable isotopes of water ( 2 H and 18 O) are used to estimate the source, age, and flow paths of water flowing through ecosystems. The main effects that change the stable isotope composition of water are evaporation and condensation . [ 33 ] Variability in water isotopes is used to study sources of water to streams and rivers, evaporation rates, groundwater recharge, and other hydrological processes. [ 34 ] [ 35 ] [ 36 ]
The ratio of 18 O to 16 O in ice and deep sea cores is temperature dependent, and can be used as a proxy measure for reconstructing climate change . During colder periods of the Earth's history (glacials) such as during the ice ages , 16 O is preferentially evaporated from the colder oceans, leaving the slightly heavier and more sluggish 18 O behind. Organisms such as foraminifera which combine oxygen dissolved in the surrounding water with carbon and calcium to build their shells therefore incorporate the temperature-dependent 18 O to 16 O ratio. When these organisms die, they settle out on the sea bed, preserving a long and invaluable record of global climate change through much of the Quaternary . [ 37 ] Similarly, ice cores on land are enriched in the heavier 18 O relative to 16 O during warmer climatic phases ( interglacials ) as more energy is available for the evaporation of the heavier 18 O isotope. The oxygen isotope record preserved in the ice cores is therefore a "mirror" of the record contained in ocean sediments. [ 38 ]
Oxygen isotopes preserve a record of the effects of the Milankovitch cycles on climate change during the Quaternary, revealing an approximately 100,000-year cyclicity in the Earth's climate . [ 39 ] | https://en.wikipedia.org/wiki/Isotope_analysis |
Isotope analysis has many applications in archaeology , from dating sites and artefacts , determination of past diets and migration patterns and for environmental reconstruction. [ 1 ]
Information is determined by assessing the ratio of different isotopes of a particular element in a sample. The most widely studied and used isotopes in archaeology are carbon, oxygen, nitrogen, strontium and calcium. [ 2 ]
An isotope is an atom of an element with an abnormal number of neutrons, changing their atomic mass. [ 2 ] Isotopes can be subdivided into stable and unstable or radioactive. Unstable isotopes decay at a predictable rate over time. [ 2 ] The first stable isotope was discovered in 1913, and most were identified by the 1930s. [ 2 ] Archaeology was relatively slow to adopt the study of isotopes. Whereas chemistry, biology and physics, saw a rapid uptake in applications of isotope analysis in the 1950s and 1960s, following the commercialisation of the mass spectrometer. [ 2 ] It wasn't until the 1970s, with the publication of works by Vogel and Van Der Merwe (1977) and DeNiro and Epstein (1978; 1981) that isotopic analysis became a mainstay of archaeological study. [ 3 ] [ 4 ] [ 5 ]
Carbon is present in all biological material including skeletal remains, charcoal and food residues and plays an integral role in the dating of materials, through radiocarbon dating. [ 6 ] The ratio of different carbon isotopes naturally fluctuates over time, and, by analysing the composition of carbon dioxide (CO 2 ) in ancient air bubbles trapped in ice cores, a chronological record of these fluctuations can be constructed. [ 7 ] Primary producers (such as grasses) absorb and sequester CO 2 during photosynthesis, these plants are then eaten by consumers (such as cows, and later humans) which inherit this same CO 2 signature. Therefore, by matching the carbon isotope ratios from a sample to ratios from the ice core record, the sample can be assigned to a broad period. [ 6 ] [ 1 ] After death, an organism no longer absorbs CO 2 , 14 C's instability causes its concentration to decrease over time [ 8 ] The predictable rate at which this occurs is known as an element's decay rate.
Oxygen and nitrogen occur in the form of different isotopes which vary in their proportions geospatially and climatically. [ 9 ] [ 10 ] Oxygen is absorbed into the body in the form of H 2 O and is used in the growth of tissues. As with carbon, oxygen isotopic ratio variances can be attributed to specific locations and the proportion of O isotopes can therefore contribute to the reconstruction of past climates, understanding of diets and water consumption, seasonality, mobility patterns, life history and elements of culture. [ 9 ] [ 10 ]
Strontium is naturally deposited in hydroxyapatite, the mineral component of bones and teeth, following its consumption in food and water. [ 11 ] Each locale has a unique Sr isotope ratio and, therefore, the ratio found in a bone or enamel sample can be cross referenced against a record of environmental Sr ratios and assigned to a region. [ 11 ] Dental enamel forms in childhood, therefore, Sr extracted from dental enamel reflects the environment in which an individual lived during infancy and childhood. Bone, however, is constantly being renewed and can therefore be used to infer the adult diet and location of the individual. [ 11 ] As such, if the Sr ratios are the analogous in the bones and teeth, it can be inferred that an individual remained in the same general region throughout their life. [ 2 ] If the ratios differ, the individual's birthplace and death place can be mapped, allowing inference of their movements. [ 1 ] This has been applied to determine the functionality and significance of Stonehenge, finding that both the visitors and cattle used in feasting travelled great distances, with Sr ratios attributed to both Scotland and Wales. [ 12 ] [ 13 ]
Alongside strontium, dietary calcium is deposited in bones teeth, however Ca is more readily deposited than Sr in humans and animals who consume primarily or exclusively plants. [ 1 ] Therefore, the greater the Ca:Sr ratio in sample, the more herbivorous the animal was likely to be.
Before the isotopes can be separated and a ratio can be determined, the desired component of the tissue must be isolated. Such components include collagen, carbonate and apatite. [ 1 ] Each component requires different means of isolation, and methods must be further specialised to account for the varied levels of decay and contamination which may occur as a result of taphonomy. [ 2 ]
In the case of collagen, there are three main modes of isolation:
The latter is most effective in the instance of very poorly preserved bone, although it also faces an increased risk of contamination by other organic matter. [ 2 ] Consequently, the supposedly isolated sample should be analysed and only tested if the readings fall within an acceptable range; most mass spectrometers now include a gas analyser as well as a combustion chamber to streamline this process. [ 2 ] [ 20 ]
Mass spectrometry is used to separate and measure distinct isotopes present in a sample. Archaeologists typically employ isotope ratio mass spectrometers or IRMSs, consisting of an inlet system, ion source, mass analyser and multiple ion detectors. [ 2 ]
The sample is usually introduced into the mass spectrometer as a gas, with oxygen and carbon being introduced as carbon dioxide. [ 2 ]
Strontium is too unstable to be easily handled in gas form, instead, it is evaporated and ionised in a vacuum. This use of a solid source is referred to as thermal ionisation mass spectrometry or TIMS. [ 2 ] More recently, strontium isotopes have been at the centre of discussion and investigation into the use of laser ablation inductively coupled mass spectrometry (ICP-MS), which is also of interest due to its less invasive nature. [ 2 ]
Electron bombardment ionises the gas, allowing the molecules to be focused into a beam which is then split by mass into smaller beams - forming a "mass spectrum". [ 2 ] The relative intensities of the different beams is then measured in the ion collector and relayed as isotope ratios. [ 2 ]
Plants can be characterised by the ratio of carbon isotopes they sequester, due to alterations in the evolution of photosynthetic biochemical pathways. [ 21 ] So-called C3 plants fix CO 2 into a 3-carbon molecule and have a greater proportion of 12 C, whereas C4 plants fix it into a 4-carbon molecule, and have a carbon isotope signature with higher 13 C. [ 1 ] This signature translates across trophic levels and can be used to determine the diets of people and animals. Isotopic analysis has been used to illuminate the diets of the different species of the Paranthropus genus. It was determined that P. boisei had a reduced ratio of C3:C4, meaning they likely consumed a greater proportion of grasses and sedges than trees, shrubs and temperature grasses. [ 22 ] [ 1 ] P. aethiopicus showed a similar trend, [ 23 ] whereas P. robustus was a generalist, with a broader dietary niche. [ 24 ] Furthermore, carbon isotope analysis shows that around 2.37 million years ago, hominins displayed a widespread shift to favour C4 plants. [ 24 ]
Ötzi is a Neolithic man who, in 1991, was found in an Alpine glacier between Austria and Italy. [ 25 ] [ 26 ] Ötzi is exceptionally well preserved since his body was dehydrated and encapsulated in glacial ice. [ 27 ] Radiocarbon dating gave an age of approximately 5,200 years old. TIMS, ICP-MS and gas mass spectrometry have all been applied to the strontium, lead, and oxygen isotopes [ 28 ] in Ötzi's bones and teeth. His teeth indicated a likely birth and early childhood near to where the Eisack and Rienz rivers confluence. [ 27 ] In his adulthood, however, Ötzi's bones suggest that he moved to the lower Vinschgau and Etsch valley. [ 27 ] More recent isotopic data, gathered from his gut contents, provides yet another timescale and hint that Ötzi's movement could be attributable to seasonal migration. [ 29 ]
The earliest compelling evidence for human habitation of the Americas comes from the Clovis complex, between 11,050 and 10,800 14 C yr B.P. [ 30 ] However, a series of human tracks were identified at White Sands National Park, New Mexico, which have been dated contentiously dated to between 23,000 and 21,000 years ago - during the Last Glacial Maximum. [ 31 ] [ 32 ] Alongside anatomically modern humans, the trackway shows impressions created by a Columbian mammoth and a giant ground sloth. [ 31 ] The upper biostratigraphic limit for when the impressions were made could therefore be determined by consideration of the extinction dates of mammoths and ground sloths. [ 31 ] More precise dates were able to be gained via radiocarbon dating of ditch grass ( ruppia cirrhosa ) embedded in the prints. [ 32 ] These seeds produced a date of 23,000-21,000 years ago. [ 32 ]
However, 14 C dates are not infallible, and this remains a topic of debate. A recent counterproposal posits that the trackways were, in fact, created by the Clovis culture and the pre-existing proposed dates of first habitation should not be moved. [ 33 ] False dates may have been produced as older strata containing the seeds could have been eroded and displaced onto the damp clay, before being impressed in by footsteps. [ 33 ] Alternatively, aquatic plants like ditch grass reflect the 14 C levels in their environment when living, if 14 C was deficient in the habitat, this could imply a false date. [ 33 ] | https://en.wikipedia.org/wiki/Isotope_analysis_in_archaeology |
Isotope dilution analysis is a method of determining the quantity of chemical substances. In its most simple conception, the method of isotope dilution comprises the addition of known amounts of isotopically enriched substance to the analyzed sample. Mixing of the isotopic standard with the sample effectively "dilutes" the isotopic enrichment of the standard and this forms the basis for the isotope dilution method. Isotope dilution is classified as a method of internal standardisation , because the standard (isotopically enriched form of analyte) is added directly to the sample. In addition, unlike traditional analytical methods which rely on signal intensity, isotope dilution employs signal ratios. Owing to both of these advantages, the method of isotope dilution is regarded among chemistry measurement methods of the highest metrological standing. [ 1 ]
Isotopes are variants of a particular chemical element which differ in neutron number . All isotopes of a given element have the same number of protons in each atom . The term isotope is formed from the Greek roots isos ( ἴσος "equal") and topos ( τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the periodic table .
Analytical application of the radiotracer method is a forerunner of isotope dilution. This method was developed in the early 20th century by George de Hevesy for which he was awarded the Nobel Prize in Chemistry for 1943.
An early application of isotope dilution in the form of radiotracer method was determination of the solubility of lead sulphide and lead chromate in 1913 by George de Hevesy and Friedrich Adolf Paneth . [ 2 ] In the 1930s, US biochemist David Rittenberg pioneered the use of isotope dilution in biochemistry enabling detailed studies of cell metabolism. [ 3 ]
Isotope dilution is analogous to the mark and recapture method, commonly used in ecology to estimate population size.
For instance, consider the determination of the number of fish ( n A ) in a lake. For the purpose of this example, assume all fish native to the lake are blue. On their first visit to the lake, an ecologist adds five yellow fish ( n B = 5). On their second visit, the ecologist captures a number of fish according to a sampling plan and observes that the ratio of blue-to-yellow (i.e. native-to-marked) fish is 10:1. The number of fish native to the lake can be calculated using the following equation:
This is a simplified view of isotope dilution but it illustrates the method's salient features. A more complex situation arises when the distinction between marked and unmarked fish becomes fuzzy. This can occur, for example, when the lake already contains a small number of marked fish from previous field experiments; and vice versa, where the amount of marked fish added contains a small number of unmarked fish. In a laboratory setting, an unknown (the "lake") may contain a quantity of a compound that is naturally present in major ("blue") and minor ("yellow") isotopic forms. A standard that is enriched in the minor isotopic form may then be added to the unknown, which can be subsequently analyzed. Keeping to the fish analogy, the following expression can be employed:
where, as indicated above, n A and n B represent the number of fish in the lake and the number of fish added to the lake, respectively; R A is the ratio of the native-to-marked fish in the lake prior to the addition of marked fish; R B is the ratio of the native-to-marked fish in the amount of marked fish added to the lake; finally, R AB is the ratio of the native-to-marked fish captured during the second visit.
Isotope dilution is almost exclusively employed with mass spectrometry in applications where high-accuracy is demanded. For example, all National Metrology Institutes rely significantly on isotope dilution when producing certified reference materials. In addition to high-precision analysis, isotope dilution is applied when low recovery of the analyte is encountered. In addition to the use of stable isotopes, radioactive isotopes can be employed in isotope dilution which is often encountered in biomedical applications, for example, in estimating the volume of blood .
Consider a natural analyte rich in isotope i A (denoted as A), and the same analyte, enriched in isotope j A (denoted as B). Then, the obtained mixture is analyzed for the isotopic composition of the analyte, R AB = n ( i A) AB / n ( j A) AB . If the amount of the isotopically enriched substance ( n B ) is known, the amount of substance in the sample ( n A ) can be obtained: [ 4 ]
Here, R A is the isotope amount ratio of the natural analyte, R A = n ( i A) A / n ( j A) A , R B is the isotope amount ratio of the isotopically enriched analyte, R B = n ( i A) B / n ( j A) B , R AB is the isotope amount ratio of the resulting mixture, x ( j A) A is the isotopic abundance of the minor isotope in the natural analyte, and x ( j A) B is the isotopic abundance of the major isotope in the isotopically enriched analyte.
For elements with only two stable isotopes, such as boron, chlorine, or silver, the above single dilution equation simplifies to the following:
In a typical gas chromatography analysis, isotopic dilution can decrease the uncertainty of the measurement results from 5% to 1%. It can also be used in mass spectrometry (commonly referred to as isotopic dilution mass spectrometry or IDMS), in which the isotopic ratio can be determined with precision typically better than 0.25%. [ 5 ]
In a simplified manner, the uncertainty of the measurement results is largely determined from the measurement of R AB :
From here, we obtain the relative uncertainty of n A , u r ( n A ) = u ( n A )/ n A :
The lowest relative uncertainty of n A corresponds to the condition when the first derivative with respect to R AB equals zero. In addition, it is common in mass spectrometry that u ( R AB )/ R AB is constant and therefore we can replace u ( R AB ) with R AB . These ideas combine to give
Solving this equation leads to the optimum composition of the blend AB, i.e., the geometric mean between the isotopic compositions of standard (A) and spike (B):
This simplified equation was first proposed by De Bievre and Debus numerically [ 4 ] and later by Komori et al. [ 6 ] and by Riepe and Kaiser analytically. [ 7 ] It has been noted that this simple expression is only a general approximation and it does not hold, for example, in the presence of Poisson statistics [ 8 ] or in the presence of strong isotope signal ratio correlation. [ 9 ]
The single dilution method requires the knowledge of the isotopic composition of the isotopically enriched analyte ( R B ) and the amount of the enriched analyte added ( n B ). Both of these variables are hard to establish since isotopically enriched substances are generally available in small quantities of questionable purity. As a result, before isotope dilution is performed on the sample, the amount of the enriched analyte is ascertained beforehand using isotope dilution. This preparatory step is called the reverse isotope dilution and it involves a standard of natural isotopic-composition analyte (denoted as A*). First proposed in the 1940s [ 10 ] and further developed in the 1950s, [ 11 ] reverse isotope dilution remains an effective means of characterizing a labeled material.
Reverse isotope dilution analysis of the enriched analyte:
Isotope dilution analysis of the analyte:
Since isotopic composition of A and A* are identical, combining these two expressions eliminates the need to measure the amount of the added enriched standard ( n B ):
Double dilution method can be designed such that the isotopic composition of the two blends, A+B and A*+B, is identical, i.e. , R AB = R A*B . This condition of exact-matching double isotope dilution simplifies the above equation significantly: [ 12 ]
To avoid contamination of the mass spectrometer with the isotopically enriched spike, an additional blend of the primary standard (A*) and the spike (B) can be measured instead of measuring the enriched spike (B) directly. This approach was first put forward in the 1970s and developed in 2002. [ 13 ]
Many analysts do not employ analytical equations for isotope dilution analysis. Instead, they rely on building a calibration curve from mixtures of the natural primary standard (A*) and the isotopically enriched standard (the spike, B). Calibration curves are obtained by plotting measured isotope ratios in the prepared blends against the known ratio of the sample mass to the mass of the spike solution in each blend. Isotope dilution calibration plots sometimes show nonlinear relationships and in practice polynomial fitting is often performed to empirically describe such curves. [ 14 ]
When calibration plots are markedly nonlinear, one can bypass the empirical polynomial fitting and employ the ratio of two linear functions (known as Padé approximant ) which is shown to describe the curvature of isotope dilution curves exactly. [ 15 ] | https://en.wikipedia.org/wiki/Isotope_dilution |
Kinetic isotope effect is observed when molecules containing heavier isotopes of the same elements (for example, deuterium for hydrogen ) engage in a chemical reaction at a slower rate. Deuterium- reinforced lipids can be used for protecting living cells by slowing the chain reaction of lipid peroxidation . [ 1 ] The lipid bilayer of the cell and organelle membranes contain polyunsaturated fatty acids (PUFA) are key components of cell and organelle membranes. Any process that either increases oxidation of PUFAs or hinders their ability to be replaced can lead to serious disease. Correspondingly, drugs that stop the chain reaction of lipid peroxidation have preventive and therapeutic potential.
The mass of the atoms forming a chemical bond affects the bond’s strength. When two different isotopes of the same element exist, the heavier ones form stronger bonds. Stronger bonds make bond cleavage reactions run more slowly, leading to the kinetic isotope effect (KIE), a well-studied concept in physical chemistry. [ 2 ] To illustrate this with an example from soccer, if one of the two identical soccer balls is filled up with air and another one with water, they will look identical on the ground, but a stronger kick would be required to send the water-filled ball the same distance as the air-filled one. Of the two stable isotopes of hydrogen (H), deuterium ( 2 H) is twice as heavy as protium ( 1 H), giving the largest kinetic isotope effect of all stable (non-radioactive) atoms.
The KIE is sometimes applied in another context in drug development, modulating drug properties in a favorable/patient-friendly way ( deuterated drugs ). Small molecules used as drugs are recognized as “foreign” to the body, and an organism’s defense systems often mount a response. Typically, drug metabolism alters the drug molecule through oxidation into derivatives that are easier to excrete, reducing the drug’s half-life . This can be slowed down by deuteration , hence improving pharmacokinetics and pharmacodynamics .
PUFAs are highly prone to oxidative damage through a purely chemical, non-enzymatic chain reaction. With tight packaging of PUFAs in membranes, the oxidation of a single PUFA molecule rapidly leads to a chain reaction resulting in oxidation of hundreds to thousands of adjacent PUFA molecules. Cell and organelle membranes contain small quantities of antioxidants such as vitamin E , and enact complex mechanisms to delete and replace oxidized PUFAs to maintain normal membrane function. However, in certain disease states, the natural PUFA maintenance system is not able to cope with disease-related increased levels of oxidation or decreased levels of repair. Once a PUFA molecule has been oxidized it is irreversibly damaged and must be
removed from the membrane and excreted.
One method to reduce the rate of PUFA oxidation is to replace a portion of the dietary PUFAs with reinforced PUFAs of identical chemical structure to natural PUFA, but more resistant to oxidation. [ 3 ] Those hydrogen atoms that are most prone to oxidation are replaced with deuterium atoms. This change has no discernible impact on the normal biochemical properties of D-PUFAs – their distribution within the human body remains unchanged, they undergo all the normal enzyme catalysed PUFA reactions, they function normally in all cell and organelle membranes, but once the levels of these D-PUFAs in various membranes reach a concentration of about 15-20%, all non-enzymatic chain oxidation stops including that of the normal, nondeuterated PUFAs. The result is the stabilization of cell membranes, even in the face of excess oxidative stress or diminished membrane repair, such as those elicited by disease states.
Several biomolecules, including PUFAs and some amino acids, cannot be made by human beings and must be supplied in the diet. These molecules are termed “essential dietary components” and serve as building blocks that are incorporated into larger structures such as proteins and cell membranes. PUFA membrane components are particularly vulnerable to damage (oxidation) by reactive oxygen species (ROS) as part of both normal and pathological
metabolism. Unlike catabolic oxidation of drugs, or oxidative damage to DNA or proteins (which occurs stoichiometrically ), oxidation of PUFAs is particularly pernicious, proceeding through a non-enzymatic lipid peroxidation chain reaction (LPO), whereby a single ROS species can initiate a runaway autoxidation process that does not need any additional ROS to propagate. [ 4 ]
LPO may damage hundreds to thousands of PUFA residues in PUFA-rich neuronal , mitochondrial and retinal membranes. The chain oxidation proceeds inexorably through multiple steps, destroying lipid membranes and generating highly reactive toxic secondary products that damage numerous biomolecules, such as proteins and DNA , irreversibly. This makes LPO one of the most detrimental processes that occur in the body. LPO is not controlled by enzymes , so evolution could not have provided a straightforward solution. Antioxidants cannot efficiently stop the incipient chain reaction because their maximal achievable concentration in lipid membranes is orders of magnitude lower than the PUFA concentration (typically, 1 tocopherol moiety per 2000 PUFA residues in a bilayer). Numerous neuronal and retinal diseases have LPO in their etiology. [ 4 ] To put things in perspective, the brain makes up 1.5–2% of body weight yet consumes about a fifth of the body’s total energy output. A quarter of this 20%, i.e. 5% of the total body energy expenditure, is used by the brain to recycle damaged lipids in neuronal membranes. [ 5 ]
The concept of using D-PUFAs to inhibit LPO has been tested in numerous cell and animal
models, including:
The D-PUFAs are currently undergoing clinical trials in several human indications. [ 10 ] [ 11 ]
In general, reinforced by deuterium polyunsaturated fatty acids ( D-PUFA ) drugs: | https://en.wikipedia.org/wiki/Isotope_effect_on_lipid_peroxidation |
Isotope electrochemistry is a field within electrochemistry concerned with various topics like electrochemical separation of isotopes, electrochemical estimation of isotopic exchange equilibrium constants , [ 1 ] electrochemical kinetic isotope effect , electrochemical isotope sensors, etc.
It is an active domain of investigation. It overlaps with many other domains of both theoretical and practical importance like nuclear engineering , radiochemistry , electrochemical technology, geochemistry, sensors and instrumentation.
This isotope -related article is a stub . You can help Wikipedia by expanding it .
This electrochemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isotope_electrochemistry |
Isotope fractionation describes fractionation processes that affect the relative abundance of isotopes, a phenomena that occurs (and so advantage is taken of it) in the study geochemistry , [ 1 ] biochemistry, [ 2 ] food science, [ 3 ] and other fields. Normally, the focus is on stable isotopes of the same element. Isotopic fractionation can be measured by isotope analysis , using isotope-ratio mass spectrometry , [ 1 ] nuclear magnetic resonance methods ( specialised techniques , [ 2 ] [ 3 ] ) cavity ring-down spectroscopy , [ not verified in body ] etc., to measure ratios of isotopes , important tools to understand geochemical and biological systems, past and present. [ not verified in body ] For example, biochemical processes cause changes in ratios of stable carbon isotopes incorporated into biomass. [ not verified in body ]
Stable isotopes partitioning between two substances A and B can be expressed by the use of the isotopic fractionation factor (alpha):
where R is the ratio of the heavy to light isotope (e.g., 2 H/ 1 H or 18 O/ 16 O). Values for alpha tend to be very close to 1. [ 1 ] [ 4 ]
There are four types of isotope fractionation (of which the first two are normally most important): equilibrium fractionation , kinetic fractionation , mass-independent fractionation (or non-mass-dependent fractionation), and transient kinetic isotope fractionation . [ citation needed ]
Isotope fractionation occurs during a phase transition , when the ratio of light to heavy isotopes in the involved molecules changes. As Carol Kendall of the USGS states in an information page for the USGS Isotope Tracers Project, " water vapor condenses (an equilibrium process ), the heavier water isotopes ( 18 O and 2 H) become enriched in the liquid phase while the lighter isotopes ( 16 O and 1 H) tend toward the vapor phase". [ 1 ] | https://en.wikipedia.org/wiki/Isotope_fractionation |
Isotope geochemistry is an aspect of geology based upon the study of natural variations in the relative abundances of isotopes of various elements . Variations in isotopic abundance are measured by isotope-ratio mass spectrometry , and can reveal information about the ages and origins of rock, air or water bodies, or processes of mixing between them.
Stable isotope geochemistry is largely concerned with isotopic variations arising from mass-dependent isotope fractionation , whereas radiogenic isotope geochemistry is concerned with the products of natural radioactivity .
For most stable isotopes, the magnitude of fractionation from kinetic and equilibrium fractionation is very small; for this reason, enrichments are typically reported in "per mil" ( ‰ , parts per thousand). [ 1 ] These enrichments (δ) represent the ratio of heavy isotope to light isotope in the sample over the ratio of a standard . That is,
Carbon has two stable isotopes , 12 C and 13 C, and one radioactive isotope, 14 C .
The stable carbon isotope ratio, δ 13 C , is measured against Vienna Pee Dee Belemnite (VPDB) [ clarification needed ] . [ 2 ] The stable carbon isotopes are fractionated primarily by photosynthesis (Faure, 2004). The 13 C/ 12 C ratio is also an indicator of paleoclimate: a change in the ratio in the remains of plants indicates a change in the amount of photosynthetic activity, and thus in how favorable the environment was for the plants. During photosynthesis, organisms using the C 3 pathway show different enrichments compared to those using the C 4 pathway , allowing scientists not only to distinguish organic matter from abiotic carbon, but also what type of photosynthetic pathway the organic matter was using. [ 1 ] Occasional spikes in the global 13 C/ 12 C ratio have also been useful as stratigraphic markers for chemostratigraphy , especially during the Paleozoic . [ 3 ]
The 14 C ratio has been used to track ocean circulation, among other things.
Nitrogen has two stable isotopes, 14 N and 15 N. The ratio between these is measured relative to nitrogen in ambient air . [ 2 ] Nitrogen ratios are frequently linked to agricultural activities. Nitrogen isotope data has also been used to measure the amount of exchange of air between the stratosphere and troposphere using data from the greenhouse gas N 2 O . [ 4 ]
Oxygen has three stable isotopes, 16 O, 17 O, and 18 O. Oxygen ratios are measured relative to Vienna Standard Mean Ocean Water (VSMOW) or Vienna Pee Dee Belemnite (VPDB). [ 2 ] Variations in oxygen isotope ratios are used to track both water movement, paleoclimate, [ 1 ] and atmospheric gases such as ozone and carbon dioxide . [ 5 ] Typically, the VPDB oxygen reference is used for paleoclimate, while VSMOW is used for most other applications. [ 1 ] Oxygen isotopes appear in anomalous ratios in atmospheric ozone, resulting from mass-independent fractionation . [ 6 ] Isotope ratios in fossilized foraminifera have been used to deduce the temperature of ancient seas. [ 7 ]
Sulfur has four stable isotopes, with the following abundances: 32 S (0.9502), 33 S (0.0075), 34 S (0.0421) and 36 S (0.0002). These abundances are compared to those found in Cañon Diablo troilite . [ 5 ] Variations in sulfur isotope ratios are used to study the origin of sulfur in an orebody and the temperature of formation of sulfur–bearing minerals as well as a biosignature that can reveal presence of sulfate reducing microbes. [ 8 ] [ 9 ]
Radiogenic isotopes provide powerful tracers for studying the ages and origins of Earth systems. [ 10 ] They are particularly useful to understand mixing processes between different components, because (heavy) radiogenic isotope ratios are not usually fractionated by chemical processes.
Radiogenic isotope tracers are most powerful when used together with other tracers: The more tracers used, the more control on mixing processes. An example of this application is to the evolution of the Earth's crust and Earth's mantle through geological time.
Lead has four stable isotopes : 204 Pb, 206 Pb, 207 Pb, and 208 Pb.
Lead is created in the Earth via decay of actinide elements , primarily uranium and thorium .
Lead isotope geochemistry is useful for providing isotopic dates on a variety of materials. Because the lead isotopes are created by decay of different transuranic elements, the ratios of the four lead isotopes to one another can be very useful in tracking the source of melts in igneous rocks , the source of sediments and even the origin of people via isotopic fingerprinting of their teeth, skin and bones.
It has been used to date ice cores from the Arctic shelf, and provides information on the source of atmospheric lead pollution .
Lead–lead isotopes has been successfully used in forensic science to fingerprint bullets, because each batch of ammunition has its own peculiar 204 Pb/ 206 Pb vs 207 Pb/ 208 Pb ratio.
Samarium – neodymium is an isotope system which can be utilised to provide a date as well as isotopic fingerprints of geological materials, and various other materials including archaeological finds (pots, ceramics).
147 Sm decays to produce 143 Nd with a half life of 1.06x10 11 years.
Dating is achieved usually by trying to produce an isochron of several minerals within a rock specimen. The initial 143 Nd/ 144 Nd ratio is determined.
This initial ratio is modelled relative to CHUR (the Chondritic Uniform Reservoir), which is an approximation of the chondritic material which formed the Solar System . CHUR was determined by analysing chondrite and achondrite meteorites.
The difference in the ratio of the sample relative to CHUR can give information on a model age of extraction from the mantle (for which an assumed evolution has been calculated relative to CHUR) and to whether this was extracted from a granitic source (depleted in radiogenic Nd), the mantle, or an enriched source.
Rhenium and osmium are siderophile elements which are present at very low abundances in the crust. Rhenium undergoes radioactive decay to produce osmium. The ratio of non-radiogenic osmium to radiogenic osmium throughout time varies.
Rhenium prefers to enter sulfides more readily than osmium. Hence, during melting of the mantle, rhenium is stripped out, and prevents the osmium–osmium ratio from changing appreciably. This locks in an initial osmium ratio of the sample at the time of the melting event. Osmium–osmium initial ratios are used to determine the source characteristic and age of mantle melting events.
Natural isotopic variations amongst the noble gases result from both radiogenic and nucleogenic production processes. Because of their unique properties, it is useful to distinguish them from the conventional radiogenic isotope systems described above.
Helium-3 was trapped in the planet when it formed. Some 3 He is being added by meteoric dust, primarily collecting on the bottom of oceans (although due to subduction , all oceanic tectonic plates are younger than continental plates). However, 3 He will be degassed from oceanic sediment during subduction , so cosmogenic 3 He is not affecting the concentration or noble gas ratios of the mantle .
Helium-3 is created by cosmic ray bombardment, and by lithium spallation reactions which generally occur in the crust. Lithium spallation is the process by which a high-energy neutron bombards a lithium atom, creating a 3 He and a 4 He ion. This requires significant lithium to adversely affect the 3 He/ 4 He ratio.
All degassed helium is lost to space eventually, as it is less dense than the atmosphere and thus steadily rises until subject to charge exchange escape . Thus, it is assumed the helium content and ratios of Earth's atmosphere have remained essentially stable.
It has been observed that 3 He is present in volcano emissions and oceanic ridge samples. How 3 He is stored in the planet is under investigation, but it is associated with the mantle and is used as a marker of material of deep origin.
Due to similarities in helium and carbon in magma chemistry, outgassing of helium requires the loss of volatile components ( water , carbon dioxide ) from the mantle, which happens at depths of less than 60 km. However, 3 He is transported to the surface primarily trapped in the crystal lattice of minerals within fluid inclusions .
Helium-4 is created by radiogenic production (by decay of uranium / thorium -series elements ). The continental crust has become enriched with those elements relative to the mantle and thus more He 4 is produced in the crust than in the mantle.
The ratio ( R ) of 3 He to 4 He is often used to represent 3 He content. R usually is given as a multiple of the present atmospheric ratio ( Ra ).
Common values for R/Ra :
3 He/ 4 He isotope chemistry is being used to date groundwaters , estimate groundwater flow rates, track water pollution, and provide insights into hydrothermal processes, igneous geology and ore genesis .
Isotopes in the decay chains of actinides are unique amongst radiogenic isotopes because they are both radiogenic and radioactive. Because their abundances are normally quoted as activity ratios rather than atomic ratios, they are best considered separately from the other radiogenic isotope systems.
Uranium is well mixed in the ocean, and its decay produces 231 Pa and 230 Th at a constant activity ratio (0.093). The decay products are rapidly removed by adsorption on settling particles, but not at equal rates. 231 Pa has a residence equivalent to the residence time of deep water in the Atlantic basin (around 1000 yrs) but 230 Th is removed more rapidly (centuries). Thermohaline circulation effectively exports 231 Pa from the Atlantic into the Southern Ocean , while most of the 230 Th remains in Atlantic sediments. As a result, there is a relationship between 231 Pa/ 230 Th in Atlantic sediments and the rate of overturning: faster overturning produces lower sediment 231 Pa/ 230 Th ratio, while slower overturning increases this ratio. The combination of δ 13 C and 231 Pa/ 230 Th can therefore provide a more complete insight into past circulation changes.
Tritium was released to the atmosphere during atmospheric testing of nuclear bombs. Radioactive decay of tritium produces the noble gas helium-3 . Comparing the ratio of tritium to helium-3 ( 3 H/ 3 He) allows estimation of the age of recent ground waters . A small amount of tritium is also produced naturally by cosmic ray spallation and spontaneous ternary fission in natural uranium and thorium, but due to the relatively short half-life of tritium and the relatively small quantities (compared to those from anthropogenic sources) those sources of tritium usually play only a secondary role in the analysis of groundwater. | https://en.wikipedia.org/wiki/Isotope_geochemistry |
Isotope hydrology [ 1 ] is a field of geochemistry and hydrology that uses naturally occurring stable and radioactive isotopic techniques to evaluate the age and origins of surface and groundwater and the processes within the atmospheric hydrologic cycle . [ 2 ] Isotope hydrology applications are highly diverse, and used for informing water-use policy , mapping aquifers , conserving water supplies, assessing sources of water pollution , investigating surface-groundwater interaction, refining groundwater flow models, and increasingly are used in eco-hydrology to study human impacts on all dimensions of the hydrological cycle and ecosystem services .
Water molecules carry unique isotopic "fingerprints", based in part on differing ratios of the oxygen and hydrogen isotopes that constitute the water molecule. Isotopes are atoms of the same element that have a different number of neutrons in their nuclei.
Air , freshwater and seawater contain mostly oxygen-16 ( 16 O). Oxygen-18 ( 18 O) occurs in approximately one oxygen atom in every five hundred and has a slightly higher mass than oxygen-16, as it has two extra neutrons. From a simple energy and bond breakage standpoint this results in a preference for evaporating the lighter 16 O containing water and leaving more of the 18 O water behind in the liquid state (called isotope fractionation ). Thus seawater tends to contain more 18 O than rain and snow.
Dissolved ions in surface and groundwater water also contain useful isotopes for hydrological investigations. Dissolved species like sulfate and nitrate contain differing ratios of 34-S to 32-S or 15-N to 14-N, and are often diagnostic of pollutant sources. Natural radioisotopes like tritium (3-H) and radiocarbon ( 14-C ) are also used as natural clocks to determine the residence times of water in aquifers, rivers, and the oceans.
The most commonly used isotope application in hydrology uses hydrogen and oxygen isotopes to evaluate sources or age of water, ice or snow. Isotopes in ice cores help to reveal conditions of past climate. Higher average global temperature would provide more energy and thus an increase the atmospheric 18 O content of rain or snow, so that lower than modern amounts of 18 O in groundwater or ice layer imply the water or ice represents a period of cooler climatic eras or even ice ages . [ 3 ]
Another application involves the separation of groundwater flow and baseflow from streamflow in the field of catchment hydrology (i.e. a method of hydrograph separation). Since precipitation in each rain or snowfall event has a specific isotopic signature , and subsurface water can be identified by well sampling, the composite signature in the stream is an indicator the proportion of the streamflow comes from overland flow and what portion comes from subsurface flow . [ 4 ] [ 5 ]
Stable isotopes in the water molecule are also useful in tracing the sources (or proportion of sources) of water that plants use. [ 6 ] [ 7 ] [ 8 ]
The isotope hydrology program at the International Atomic Energy Agency works to aid developing states to create a detailed portrait of Earth's water resources. [ 9 ]
In Ethiopia , Libya , Chad , Egypt and Sudan , the International Atomic Energy Agency used radioisotope techniques to help local water policy identify and conserve fossil water .
The International Atomic Energy Agency maintains a publicly accessible global network and isotopic database for Earth's rainfall and rivers. [ 10 ] | https://en.wikipedia.org/wiki/Isotope_hydrology |
A medical isotope is an isotope used in medicine . The first uses of isotopes in medicine were in radiopharmaceuticals , and this is still the most common use. However more recently, separated stable isotopes have come into use.
Radioactive isotopes are used in medicine for both treatment and diagnostic scans. The most common isotope used in diagnostic scans is Technetium-99m , used in approximately 85% of all nuclear medicine diagnostic scans worldwide. It is used for diagnoses involving a large range of body parts and diseases such as cancers and neurological problems. [ 1 ] Another well-known radioactive isotope used in medicine is Iodine-131 , which is used as a radioactive label for some radiopharmaceutical therapies or the treatment of some types of thyroid cancer. [ 2 ]
Examples of non-radioactive medical isotopes are:
This medical treatment –related article is a stub . You can help Wikipedia by expanding it .
This nuclear physics or atomic physics –related article is a stub . You can help Wikipedia by expanding it .
This isotope -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isotopes_in_medicine |
Isotopic analysis by nuclear magnetic resonance refers to overarching set of methodologies to precisely quantify differences in isotopic content at each atom of a molecule , and thus to measure the specific natural isotope fractionation for each site of the molecule. [ not verified in body ] One such method, SNIF-NMR —the corresponding English of the original French acronym, which abbreviates site-specific natural isotopic fractionation nuclear magnetic resonance [ 1 ] [ 2 ] [ 3 ] —is an analytical method developed to detect over-sugaring of wine and enrichment of grape musts . [ not verified in body ] As of this date, [ when? ] its main use has been to check the authenticity of foodstuffs such as wines , spirits , [ not verified in body ] fruit juice , honey , sugar , and vinegar , and to control the naturality [ clarification needed ] of flavorant and odorant molecules such as vanillin , benzaldehyde , raspberry ketone , and anethole . [ not verified in body ] The SNIF-NMR method in particular has been adopted by the International Organisation of Vine and Wine (OIV) and the European Union as an official method for wine analysis, by the Association of Official Agricultural Chemists (AOAC) as an official method for analysis of fruit juices, maple syrup , vanillin, and by the European Committee for Standardization (CEN) for analysis of vinegar. [ not verified in body ]
The atoms hydrogen , oxygen , and carbon co-exist naturally in specific proportions with their stable isotopes , 2H (or D), 18O and 13C respectively, in different proportions as shown in the figure. [ citation needed ]
The amount and distribution of the different isotopes in a molecule is influenced in for natural products by: [ 7 ]
A phenomenon known as natural isotopic fractionation (see figure) means that an isotopic fingerprint composed of ratios of isotopes at each atom of a molecule can be determined to provide information on the origin—botanical, synthetic, geographical—of the molecule or product. [ citation needed ]
SNIF-NMR is built on the principle of natural isotopic fractionation . [ citation needed ] NMR of two nuclei are routinely used for assessing for food authenticity:
The SNIF-NMR is applied on purified molecules; therefore, preparative steps are required before instrumental analysis. For example, for the SNIF-NMR of ethanol, according to official methods, preparative steps include:
followed by NMR acquisition, and interpretation of the results, and report regarding sample authenticity.
At each step of the SNIF-NMR sample preparation and analysis, efforts are made to avoid parasite isotopic fractionation . Control measures such as determining the alcoholic strength of the intermediate products of the analysis (fermented juice or distillate) are performed on each sample.
The isotopic ratios of a molecule can also be determined by isotope ratio mass spectrometry (IRMS), sample quantity for IRMS is much lower than for NMR, and there is the possibility of coupling the mass spectrometer to a chromatographic system to enable on-line purification or analyses of several components of a complex mixture. However the sample is burnt after a physical transformation such as combustion or pyrolysis . Therefore, it gives a mean value of the concentration of the isotope studied between all sites of the molecule. IRMS is the official AOAC technique used for the average ratio 13 C/ 12 C (or δ 13 C) of sugars or ethanol, and the official CEN and OIV method for the 18O/16O in water .
The SNIF-NMR method (Site-Specific Natural Isotope Fractionation studied by Nuclear Magnetic Resonance) is able to determine, to a high level of accuracy, the isotopic ratios for each of the sites of the molecule, which enables a better discrimination. For example, for ethanol (CH 3 CH 2 OH), the three ratios ((D/H)CH 3 , (D/H)CH 2 and (D/H) OH ) can be obtained.
Ethanol molecules obtained after complete fermentation of the sugar coexists with 3 naturally monodeuterated isotopomers (CH 2 D-CH 2 -OH, CH 3 -CHDOH and-CH 3 -CH 2 OD). Their presence can then be quantified with relative precision. [ 8 ] In the presented 2 H-NMR spectrum, peaks correspond to one of the three observed isotopomers of ethanol.
In the AOAC official method, the ratios of (D/H)CH 3 and (D/H)CH 2 are calculated by comparison with an Internal standard, tetramethylurea (TMU), with a certified (D/H) value. [ citation needed ]
The figure summarizes the principles of interpretation applied: [ citation needed ]
Values obtained on a test sample are then compared with the values of authentic, databased sample data. [ citation needed ]
AOAC Official Method for detecting the addition of sugar in a fruit juice [ 6 ] or in maple syrup. It is the only reliable method to detect addition of C3 sugar (ex: beet sugar ).
SNIF-NMR is the official method of the OIV to determine the authentication of wine origin, [ citation needed ] and as of this date, [ when? ] is the only method to detect C3 sugar addition (like beet sugar). [ citation needed ]
The isotopic parameters of both water and ethanol are related to the humidity and temperature of the growing region of the plant . Therefore, considerations of meteorological data of the region and of the year help to make a diagnosis. In the case of wine and fruits, the isotopic parameters of ethanol have been shown to respond even to subtle environmental variations and they efficiently characterize the region of production. [ 8 ] [ 9 ]
Since 1991, an isotopic data bank is built in the Joint Research Centre of the European Commission (EC-JRC) concerning wines of all European members. The database contains several thousand entries for European wines, [ 10 ] [ full citation needed ] and is maintained and updated every year. [ citation needed ] This database is accessible for all official public laboratories. Private companies involved in food and beverage controls have also collected authentic samples and built up specific data banks. [ 11 ]
Thus, by comparing the specific natural isotope fractionation corresponding to each site of a molecule of ethanol of wine with that of a molecule known and referenced in a database. The geographical origin, botany and method of production of the ethanol molecule and thus the authenticity of wine can be checked. [ 12 ]
The origins of vinegars obtained by bacterial or chemical oxidation of ethanol resulting from the fermentation of various sugars can be identified by the 2 H-SNIF-NMR. It allows to control the quality of vinegar and to determine if it comes from sugar cane, wine, malt, cider, and alcohol or from a chemical synthesis. [ 13 ] [ page needed ]
As of this date, [ when? ] 2 H-SNIF-NMR is the official AOAC method for determining the natural vanillin. [ citation needed ]
The abundance of five monodeuterated isotopomers for vanillin can be measured by 2 H-SNIF-NMR. [ citation needed ] Data for vanillin are shown in the figure; all observable sites for which the site specific deuterium concentrations can be measured are referenced with a number. [ citation needed ]
As for wine or fruit, the interpretation of results regarding origin is done by comparison of the isotopic parameters of the sample analyzed with those from a group of referenced molecules of known origin. [ citation needed ] Origins of vanillin are well discriminated using 2 H-NMR data; in particular, vanillin ex-bean can well be distinguished from the other sources (see next figure). [ citation needed ]
Additionally, this method is the only one to discriminate between natural and biosynthetic sources of vanillin. [ 14 ]
The naturality [ clarification needed ] of different aroma can also be checked using SNIF-NMR: for example for anethole, abundance of only six monodeuterated isotopomers can be measured by 2 H-SNIF-NMR that allows differentiating the botanical origins fennel, star anise or pine. [ 15 ] [ full citation needed ]
The SNIF-NMR applied to benzaldehyde can detect adulterated bitter almond and cinnamon oils. It is demonstrated that the site specific deuterium contents of benzaldehyde allow the determination of the origin of the molecule: synthetic (ex- toluene and ex- benzal chloride ), natural (ex-kernels from apricots , peaches , cherries and ex-bitter almond) and semisynthetic (ex- cinnamaldehyde extracted from cinnamon). [ 16 ] [ full citation needed ] Other applications have also been published, including for raspberry ketone, [ 17 ] [ verification needed ] heliotropine, [ citation needed ] etc.
Optimization of technique parameters have enabled to reach better accuracy for the 13 C NMR measurements. [ 18 ]
The 13 C-SNIF-NMR method is called method “new frontier” because it is the first analytical method that can differentiate sugars coming from C4-metabolism plants (cane, maize, etc.) and some crassulacean acid metabolism plants (CAM-metabolism) like pineapple or agave . [ 19 ]
This method can also be applied to tequila products, where it can differentiate authentic 100% agave tequila, misto tequila (made from at least 51% agave), and products made from a larger proportion of cane or maize sugar and therefore not complying with the legal definition of tequila. [ 19 ] | https://en.wikipedia.org/wiki/Isotopic_analysis_by_nuclear_magnetic_resonance |
Isotopic labeling (or isotopic labelling ) is a technique used to track the passage of an isotope (an atom with a detectable variation in neutron count) through chemical reaction , metabolic pathway , or a biological cell . [ 1 ] The reactant is 'labeled' by replacing one or more specific atoms with their isotopes. The reactant is then allowed to undergo the reaction. The position of the isotopes in the products is measured to determine what sequence the isotopic atom followed in the reaction or the cell's metabolic pathway. The nuclides used in isotopic labeling may be stable nuclides or radionuclides . In the latter case, the labeling is called radiolabeling .
In isotopic labeling, there are multiple ways to detect the presence of labeling isotopes; through their mass , vibrational mode , or radioactive decay . Mass spectrometry detects the difference in an isotope's mass, while infrared spectroscopy detects the difference in the isotope's vibrational modes. Nuclear magnetic resonance detects atoms with different gyromagnetic ratios. The radioactive decay can be detected through an ionization chamber or autoradiographs of gels.
An example of the use of isotopic labeling is the study of phenol (C 6 H 5 OH) in water by replacing common hydrogen ( protium ) with deuterium ( deuterium labeling ). Upon adding phenol to deuterated water (water containing D 2 O in addition to the usual H 2 O ), a hydrogen-deuterium exchange is observed to affect phenol's hydroxyl group (resulting in C 6 H 5 OD), indicating that phenol readily undergoes hydrogen-exchange reactions with water. Mainly the hydroxyl group is affected—without a catalyst, the other 5 hydrogen atoms are much slower to undergo exchange—reflecting the difference in chemical environments between the hydroxyl hydrogen and the aryl hydrogens. [ 2 ]
An isotopic tracer , (also "isotopic marker" or "isotopic label"), is used in chemistry and biochemistry to help understand chemical reactions and interactions. In this technique, one or more of the atoms of the molecule of interest is substituted for an atom of the same chemical element , but of a different isotope (like a radioactive isotope used in radioactive tracing ). Because the labeled atom has the same number of protons, it will behave in almost exactly the same way as its unlabeled counterpart and, with few exceptions, will not interfere with the reaction under investigation. The difference in the number of neutrons , however, means that it can be detected separately from the other atoms of the same element.
Nuclear magnetic resonance (NMR) and mass spectrometry (MS) are used to investigate the mechanisms of chemical reactions. NMR and MS detects isotopic differences, which allows information about the position of the labeled atoms in the products' structure to be determined. With information on the positioning of the isotopic atoms in the products, the reaction pathway the initial metabolites utilize to convert into the products can be determined. Radioactive isotopes can be tested using the autoradiographs of gels in gel electrophoresis . The radiation emitted by compounds containing the radioactive isotopes darkens a piece of photographic film , recording the position of the labeled compounds relative to one another in the gel.
Isotope tracers are commonly used in the form of isotope ratios. By studying the ratio between two isotopes of the same element, we avoid effects involving the overall abundance of the element, which usually swamp the much smaller variations in isotopic abundances. Isotopic tracers are some of the most important tools in geology because they can be used to understand complex mixing processes in earth systems. Further discussion of the application of isotopic tracers in geology is covered under the heading of isotope geochemistry .
Isotopic tracers are usually subdivided into two categories: stable isotope tracers and radiogenic isotope tracers. Stable isotope tracers involve only non-radiogenic isotopes and usually are mass-dependent. In theory, any element with two stable isotopes can be used as an isotopic tracer. However, the most commonly used stable isotope tracers involve relatively light isotopes, which readily undergo fractionation in natural systems. See also isotopic signature . A radiogenic isotope tracer [ 4 ] involves an isotope produced by radioactive decay , which is usually in a ratio with a non-radiogenic isotope (whose abundance in the earth does not vary due to radioactive decay).
Stable isotope labeling involves the use of non-radioactive isotopes that can act as tracers used to model several chemical and biochemical systems. The chosen isotope can act as a label on that compound that can be identified through nuclear magnetic resonance (NMR) and mass spectrometry (MS). Some of the most common stable isotopes are 2 H, 13 C, and 15 N, which can further be produced into NMR solvents , amino acids , nucleic acids , lipids , common metabolites and cell growth media . [ 6 ] The compounds produced using stable isotopes are either specified by the percentage of labeled isotopes (that is, 30% uniformly labeled 13 C glucose contains a mixture that is 30% labeled with 13 carbon isotope and 70% naturally labeled carbon) or by the specifically labeled carbon positions on the compound (that is, 1- 13 C glucose which is labeled at the first carbon position of glucose).
A network of reactions adopted from the glycolysis pathway and the pentose phosphate pathway is shown in which the labeled carbon isotope rearranges to different carbon positions throughout the network of reactions. The network starts with fructose 6-phosphate (F6P), which has 6 carbon atoms with a label 13 C at carbon positions 1 and 2. 1,2- 13 C F6P becomes two glyceraldehyde 3-phosphate (G3P), one 2,3- 13 C T3P and one unlabeled T3P. The 2,3- 13 C T3P can now be reacted with sedoheptulose 7-phosphate (S7P) to form an unlabeled erythrose 4-phosphate (E4P) and a 5,6- 13 C F6P. The unlabeled T3P will react with the S7P to synthesize unlabeled products. [ 5 ] The figure demonstrates the use of stable isotope labeling to discover the carbon atom rearrangement through reactions using position specific labeled compounds.
Metabolic flux analysis (MFA) using stable isotope labeling is an important tool for explaining the flux of certain elements through the metabolic pathways and reactions within a cell . An isotopic label is fed to the cell, then the cell is allowed to grow utilizing the labeled feed. For stationary metabolic flux analysis the cell must reach a steady state (the isotopes entering and leaving the cell remain constant with time) or a quasi-steady state (steady state is reached for a given period of time). [ 7 ] The isotope pattern of the output metabolite is determined. The output isotope pattern provides valuable information, which can be used to find the magnitude of flux , rate of conversion from reactants to products , through each reaction. [ 8 ]
The figure demonstrates the ability to use different labels to determine the flux through a certain reaction. Assume the original metabolite, a three carbon compound, has the ability to either split into a two carbon metabolite and one carbon metabolite in one reaction then recombine or remain a three carbon metabolite. If the reaction is provided with two isotopes of the metabolite in equal proportion, one completely labeled (blue circles), commonly known as uniformly labeled, and one completely unlabeled (white circles). The pathway down the left side of the diagram does not display any change in the metabolites, while the right side shows the split and recombination. As shown, if the metabolite only takes the pathway down the left side, it remains in a 50–50 ratio of uniformly labeled to unlabeled metabolite. If the metabolite only takes the right side new labeling patterns can occur, all in equal proportion. Other proportions can occur depending on how much of the original metabolite follows the left side of the pathway versus the right side of the pathway. Here the proportions are shown for a situation in which half of the metabolites take the left side and half the right, but other proportions can occur. [ 9 ] These patterns of labeled atoms and unlabeled atoms in one compound represent isotopomers . By measuring the isotopomer distribution of the differently labeled metabolites, the flux through each reaction can be determined. [ 10 ]
MFA combines the data harvested from isotope labeling with the stoichiometry of each reaction, constraints , and an optimization procedure resolve a flux map. The ir reversible reactions provide the thermodynamic constraints needed to find the fluxes. A matrix is constructed that contains the stoichiometry of the reactions. The intracellular fluxes are estimated by using an iterative method in which simulated fluxes are plugged into the stoichiometric model. The simulated fluxes are displayed in a flux map, which shows the rate of reactants being converted to products for each reaction. [ 8 ] In most flux maps, the thicker the arrow, the larger the flux value of the reaction. [ 11 ]
Any technique in measuring the difference between isotopomers can be used. The two primary methods, nuclear magnetic resonance (NMR) and mass spectrometry (MS), have been developed for measuring mass isotopomers in stable isotope labeling.
Proton NMR was the first technique used for 13 C-labeling experiments. Using this method, each single protonated carbon position inside a particular metabolite pool can be observed separately from the other positions. [ 12 ] This allows the percentage of isotopomers labeled at that specific position to be known. The limit to proton NMR is that if there are n carbon atoms in a metabolite, there can only be at most n different positional enrichment values, which is only a small fraction of the total isotopomer information. Although the use of proton NMR labeling is limiting, pure proton NMR experiments are much easier to evaluate than experiments with more isotopomer information.
In addition to Proton NMR , using 13 C NMR techniques will allow a more detailed view of the distribution of the isotopomers. A labeled carbon atom will produce different hyperfine splitting signals depending on the labeling state of its direct neighbors in the molecule. [ 12 ] A singlet peak emerges if the neighboring carbon atoms are not labeled. A doublet peak emerges if only one neighboring carbon atom is labeled. The size of the doublet split depends on the functional group of the neighboring carbon atom. If two neighboring carbon atoms are labeled, a doublet of doublets may degenerate into a triplet if the doublet splittings are equal.
The drawbacks to using NMR techniques for metabolic flux analysis purposes is that it is different from other NMR applications because it is a rather specialized discipline. An NMR spectrometer may not be directly available for all research teams. The optimization of NMR measurement parameters and proper analysis of peak structures requires a skilled NMR specialist. Certain metabolites also may require specialized measurement procedures to obtain additional isotopomer data. In addition, specially adapted software tools are needed to determine the precise quantity of peak areas as well as identifying the decomposition of entangled singlet, doublet, and triplet peaks.
As opposed to nuclear magnetic resonance, mass spectrometry (MS) is another method that is more applicable and sensitive to metabolic flux analysis experiments. MS instruments are available in different variants. Different from two-dimensional nuclear magnetic resonance ( 2D-NMR ), the MS instruments work directly with hydrolysate . [ 12 ]
In gas chromatography-mass spectrometry ( GC-MS ), the MS is coupled to a gas chromatograph to separate the compounds of the hydrolysate. The compounds eluting from the GC column are then ionized and simultaneously fragmented. The benefit in using GC-MS is that not only are the mass isotopomers of the molecular ion measured but also the mass isotopomer spectrum of several fragments, which significantly increases the measured information.
In liquid chromatography-mass spectrometry ( LC-MS ), the GC is replaced with a liquid chromatograph. [ 13 ] The main difference is that chemical derivatization is not necessary. Applications of LC-MS to MFA, however, are rare.
In each case, MS instruments divide a particular isotopomer distribution by its molecular weight. All isotopomers of a particular metabolite that contain the same number of labeled carbon atoms are collected in one peak signal. Because every isotopomer contributes to exactly one peak in the MS spectrum, the percentage value can then be calculated for each peak, yielding the mass isotopomer fraction. [ 12 ] For a metabolite with n carbon atoms, n+1 measurements are produced. After normalization, exactly n informative mass isotopomer quantities remain. [ 12 ]
The drawback to using MS techniques is that for gas chromatography, the sample must be prepared by chemical derivatization in order to obtain molecules with charge. There are numerous compounds used to derivatize samples. N,N-Dimethylformamide dimethyl acetal (DMFDMA) [ 14 ] and N-(tert-butyldimethylsilyl)-N-methyltrifluoroacetamide (MTBSTFA) [ 15 ] are two examples of compounds that have been used to derivatize amino acids.
In addition, strong isotope effects observed affect the retention time of differently labeled isotopomers in the GC column. Overloading of the GC column also must be prevented. [ 15 ]
Lastly, the natural abundance of other atoms than carbon also leads to a disturbance in the mass isotopomer spectrum. For example, each oxygen atom in the molecule might also be present as a 17 O isotope and as a 18 O isotope. A more significant impact of the natural abundance of isotopes is the effect of silicon with a natural abundance of the isotopes 29 Si and 30 Si. Si is used in derivatizing agents for MS techniques. [ 12 ]
Radioisotopic labeling is a technique for tracking the passage of a sample of substance through a system. The substance is "labeled" by including radionuclides in its chemical composition. When these decay , their presence can be determined by detecting the radiation emitted by them. Radioisotopic labeling is a special case of isotopic labeling.
For these purposes, a particularly useful type of radioactive decay is positron emission . When a positron collides with an electron, it releases two high-energy photons traveling in diametrically opposite directions. Suppose the positron is produced within a solid object. In that case, it will travel as little as 0.5 millimeters, up to 6 mm. [ 16 ] If both of these photons can be detected, the location of the decay event can be determined very precisely.
Strictly speaking, radioisotopic labeling includes only cases where radioactivity is artificially introduced by experimenters, but some natural phenomena allow similar analysis to be performed. In particular, radiometric dating uses a closely related principle.
The use of stable isotope tracers to study mineral nutrition and metabolism in humans was first reported in the 1960s. [ 17 ] While radioisotopes had been used in human nutrition research for several decades prior, stable isotopes presented a safer option, especially in subjects for which there is elevated concern about radiation exposure, e.g. pregnant and lactating women and children. Other advantages offered by stable isotopes include the ability to study elements having no suitable radioisotopes and to study long-term tracer behavior. [ 18 ] [ 19 ] Thus the use of stable isotopes became commonplace with the increasing availability of isotopically enriched materials and inorganic mass spectrometers. The use of stable isotopes instead of radioisotopes does have several drawbacks: larger quantities of tracer are required, having the potential of perturbing the naturally existing mineral; analytical sample preparation is more complex and mass spectrometry instrumentation more costly; the presence of tracer in whole bodies or particular tissues cannot be measured externally. [ 20 ] Nonetheless, the advantages have prevailed making stable isotopes the standard in human studies.
Most of the minerals that are essential for human health and of particular interest to nutrition researchers have stable isotopes, some well-suited as biological tracers because of their low natural abundance. [ 18 ] [ 20 ] Iron , zinc , calcium , copper , magnesium , selenium and molybdenum are among the essential minerals having stable isotopes to which isotope tracer methods have been applied. Iron, zinc and calcium in particular have been extensively studied.
Aspects of mineral nutrition/metabolism that are studied include absorption (from the gastrointestinal tract into the body), distribution, storage, excretion and the kinetics of these processes. Isotope tracers are administered to subjects orally (with or without food, or with a mineral supplement) and/or intravenously. Isotope enrichment is then measured in blood plasma, erythrocytes, urine and/or feces. [ 21 ] [ 22 ] Enrichment has also been measured in breast milk [ 23 ] and intestinal contents. Tracer experiment design sometimes differs between minerals due to differences in their metabolism. For example, iron absorption is usually determined from incorporation of tracer in erythrocytes whereas zinc or calcium absorption is measured from tracer appearance in plasma, urine or feces. [ 24 ] [ 25 ] The administration of multiple isotope tracers in a single study is common, permitting the use of more reliable measurement methods and simultaneous investigations of multiple aspects of metabolism.
The measurement of mineral absorption from the diet, often conceived of as bioavailability , is the most common application of isotope tracer methods to nutrition research. Among the purposes of such studies are the investigations of how absorption is influenced by type of food (e.g. plant vs animal source, breast milk vs formula), other components of the diet (e.g. phytate ), disease and metabolic disorders (e.g. environmental enteric dysfunction ), the reproductive cycle, quantity of mineral in diet, chronic mineral deficiency , subject age and homeostatic mechanisms. When results from such studies are available for a mineral, they may serve as a basis for estimations of the human physiological and dietary requirements of the mineral. [ 26 ] [ 27 ]
When tracer is administered with food for the purpose of observing mineral absorption and metabolism, it may be in the form of an intrinsic or extrinsic label. [ 28 ] [ 29 ] An intrinsic label is isotope that has been introduced into the food during its production, thus enriching the natural mineral content of the food, whereas extrinsic labeling refers to the addition of tracer isotope to the food during the study. Because it is a very time-consuming and expensive approach, intrinsic labeling is not routinely used. Studies comparing measurements of absorption using intrinsic and extrinsic labeling of various foods have generally demonstrated good agreement between the two labeling methods, supporting the hypothesis that extrinsic and natural minerals are handled similarly in the human gastrointestinal tract.
Enrichment is quantified from the measurement of isotope ratios , the ratio of the tracer isotope to a reference isotope, by mass spectrometry. Multiple definitions and calculations of enrichment have been adopted by different researchers. [ 30 ] Calculations of enrichment become more complex when multiple tracers are used simultaneously. Because enriched isotope preparations are never isotopically pure, i.e. they contain all the element's isotopes in unnatural abundances, calculations of enrichment of multiple isotope tracers must account for the perturbation of each isotope ratio by the presence of the other tracers. [ 30 ]
Due to the prevalence of mineral deficiencies and their critical impact on human health and well-being in resource-poor countries, the International Atomic Energy Agency has recently published detailed and comprehensive descriptions of stable isotope methods to facilitate the dissemination of this knowledge to researchers beyond western academic centers. [ 24 ] [ 31 ]
In proteomics , the study of the full set of proteins expressed by a genome , identifying diseases biomarkers can involve the usage of stable isotope labeling by amino acids in cell culture (SILAC), that provides isotopic labeled forms of amino acid used to estimate protein levels. [ 32 ] In protein recombinant, manipulated proteins are produced in large quantities and isotope labeling is a tool to test for relevant proteins. The method used to be about selectively enrich nuclei with 13 C or 15 N or deplete 1 H from them. The recombinant would be expressed in E.coli with media containing 15 N- ammonium chloride as a source of nitrogen. [ 33 ] The resulting 15 N labeled proteins are then purified by immobilized metal affinity and their percentage estimated. In order to increase the yield of labeled proteins and cut down the cost of isotope labeled media, an alternative procedure primarily increases the cell mass using unlabeled media before introducing it in a minimal amount of labeled media. [ 34 ] Another application of isotope labeling would be in measuring DNA synthesis, that is cell proliferation in vitro . Uses H 3 -thymidine labeling to compare pattern of synthesis (or sequence) in cells. [ 35 ]
Isotopic tracers are used to examine processes in natural systems, especially terrestrial and aquatic environments. In soil science 15 N tracers are used extensively to study nitrogen cycling, whereas 13 C and 14 C, stable and radioisotopes of carbon respectively, are used for studying turnover of organic compounds and fixation of CO 2 by autotrophs . For example, Marsh et al. (2005) used dual labeled ( 15 N- and 14 C) urea to demonstrate utilization of the compound by ammonia oxidizers as both an energy source (ammonia oxidation) and carbon source (chemoautotrophic carbon fixation). [ 36 ] Deuterated water is also used for tracing the fate and ages of water in a tree [ 37 ] or in an ecosystem. [ 38 ]
Tracers are also used extensively in oceanography to study a wide array of processes. The isotopes used are typically naturally occurring with well-established sources and rates of formation and decay. However, anthropogenic isotopes may also be used with great success. The researchers measure the isotopic ratios at different locations and times to infer information about the physical processes of the ocean.
The ocean is an extensive network of particle transport. Thorium isotopes can help researchers decipher the vertical and horizontal movement of matter. 234 Th has a constant, well-defined production rate in the ocean and a half-life of 24 days. This naturally occurring isotope has been shown to vary linearly with depth. Therefore, any changes in this linear pattern can be attributed to the transport of 234 Th on particles. For example, low isotopic ratios in surface water with very high values a few meters down would indicate a vertical flux in the downward direction. Furthermore, the thorium isotope may be traced within a specific depth to decipher the lateral transport of particles. [ 39 ]
Circulation within local systems, such as bays, estuaries, and groundwater, may be examined with radium isotopes. 223 Ra has a half-life of 11 days and can occur naturally at specific locations in rivers and groundwater sources. The isotopic ratio of radium will then decrease as the water from the source river enters a bay or estuary. By measuring the amount of 223 Ra at a number of different locations, a circulation pattern can be deciphered. [ 40 ] This same exact process can also be used to study the movement and discharge of groundwater. [ 41 ]
Various isotopes of lead can be used to study circulation on a global scale. Different oceans (i.e. the Atlantic, Pacific, Indian, etc.) have different isotopic signatures. This results from differences in isotopic ratios of sediments and rocks within the different oceans. [ 42 ] Because the different isotopes of lead have half-lives of 50–200 years, there is not enough time for the isotopic ratios to be homogenized throughout the whole ocean. Therefore, precise analysis of Pb isotopic ratios can be used to study the circulation of the different oceans. [ 43 ]
Isotopes with extremely long half-lives and their decay products can be used to study multi-million year processes, such as tectonics and extreme climate change. For example, in rubidium–strontium dating , the isotopic ratio of strontium ( 87 Sr/ 86 Sr) can be analyzed within ice cores to examine changes over the earth's lifetime. Differences in this ratio within the ice core would indicate significant alterations in the earth's geochemistry. [ 43 ]
The aforementioned processes can be measured using naturally occurring isotopes. Nevertheless, anthropogenic isotopes are also extremely useful for oceanographic measurements. Nuclear weapons tests released a plethora of uncommon isotopes into the world's oceans. 3 H, 129 I, and 137 Cs can be found dissolved in seawater, while 241 Am and 238 Pu are attached to particles. The isotopes dissolved in water are particularly useful in studying global circulation. For example, differences in lateral isotopic ratios within an ocean can indicate strong water fronts or gyres. [ 44 ] Conversely, the isotopes attached to particles can be used to study mass transport within water columns. For instance, high levels of Am or Pu can indicate downwelling when observed at great depths, or upwelling when observed at the surface. [ 45 ] | https://en.wikipedia.org/wiki/Isotopic_labeling |
The isotopic resonance hypothesis (IsoRes) [ 1 ] [ 2 ] postulates that certain isotopic compositions of chemical elements affect kinetics of chemical reactions involving molecules built of these elements. The isotopic compositions for which this effect is predicted are called resonance isotopic compositions.
Fundamentally, the IsoRes hypothesis relies on a postulate that less complex systems exhibit faster kinetics than equivalent but more complex systems. Furthermore, system's complexity is affected by its symmetry (more symmetric systems are simpler), and symmetry (in general meaning) of reactants may be affected by their isotopic composition.
The term “resonance” relates to the use of this term in nuclear physics, where peaks in the dependence of a reaction cross section upon energy are called “resonances”. Similarly, a sharp increase (or decrease) in the reaction kinetics as a function of the average isotopic mass of a certain element is called here a resonance.
The concept of isotopes developed from radioactivity. The pioneering work on radioactivity by Henri Becquerel , Marie Curie and Pierre Curie was awarded the Nobel Prize in Physics in 1903 . Later Frederick Soddy would take radioactivity from physics to chemistry and shed light on the nature of isotopes, something with rendered him the Nobel Prize in Chemistry in 1921 (awarded in 1922).
The question of stable, non-radioactive isotopes was more difficult and required the development by Francis Aston of a high-resolution mass spectrograph, which allowed the separation of different stable isotopes of one and the same element. Francis Aston was awarded the 1922 Nobel Prize in Chemistry for this achievement. With his enunciation of the whole-number rule, Aston solved a problem that had riddled chemistry for a hundred years. The understanding was that different isotopes of a given element would be chemically identical.
It was discovered in the 1930s by Harold Urey in 1932 (awarded the Nobel Prize in Chemistry in 1934). [ citation needed ] It was early on found that the deuterium content had a profound effect on chemistry and biochemistry.
In the linear approximation, the effect of isotopic substitution is proportional to the mass ratio of the heavy and light isotope. Thus chemical and biological effects of heavier isotopes of the “biological” atoms C, N and O are expected to be much smaller since the mass ratios for the normal to heavier isotopes are much closer to unity than the factor two for hydrogen to deuterium. However, it has been reported in 1930s, [ 3 ] and then again in 1970s [ 4 ] [ 5 ] and 1990s, [ 6 ] as well as recently, [ 7 ] that relatively small changes in the content of the heavy isotope of hydrogen, deuterium, has profound effects on biological systems. These strong nonlinear effects could not be fully rationalized based on the known concepts of the isotopic effects. These and other observations make it possible that isotopes have a much more profound importance than could ever have been imagined by the pioneers.
In 2011 Roman Zubarev formulated the isotope resonance hypothesis. [ 1 ] [ 2 ] It originated in the following, unexpected observation. Define ΔM m = M mono - M nom , where M mono is the monoisotopic mass (e.g. O = 15.994915 Da ) and M nom is the nominal (integer) mass, i.e., the number of nucleons (e.g. 16 O = 16). ΔM m is a constant in the whole Universe. Define ΔM is = M av - M mono , where M av is the average isotopic mass (e.g. O = 15.999 Da on Earth). Obviously ΔM is depends on the precise isotopic composition for a given molecule. Finally define NMD = 1000ΔM m /M nom and NIS = 1000ΔM is /M nom , where NMD [in units of ‰] and NIS [in units of ‰] are the normalized isotopic defect and shift, respectively. If NIS is plotted as a function of NMD for a large number of terrestrial peptides, one would anticipate a homogenous distribution of data points (as in Fig. 1B). This is not what was found by Zubarev's team, [ 1 ] instead they found band gap in the distribution with a narrow line in the middle (Fig. 1A).
This serendipitous discovery led Zubarev to formulate the isotope resonance hypothesis. [ 2 ]
As an example of isotopic symmetry (in compositional, and not in geometrical sense) affecting the kinetics of physic-chemical processes, see mass independent isotope fractionation in ozone O 3 .
According to the IsoRes hypothesis, there are certain resonance isotopic compositions at which terrestrial organisms thrive best. Curiously, average terrestrial isotopic compositions are very close to a resonance affecting a large class of amino acids and polypeptides, the molecules of outmost importance for life. [ 1 ] Thus, the IsoRes hypothesis suggests that early life on Earth was aided, perhaps critically, by the proximity to an IsoRes. In contrast, there is no strong resonance for then atmosphere of Mars, which led to a prediction that life could not have originated on Mars and that the planet is probably sterile. [ 8 ]
One would expect that enrichment of heavy isotopes leads to progressively slower reactions, but the IsoRes hypothesis suggests that there exist certain resonance compositions for which kinetics increases even for higher abundances of heavy stable isotopes. For example, at 9.5% 13 C, 10.9% 15 N and 6.6% 18 O (when all three elements are 10-35 times enriched compared to their natural abundances) and normal deuterium composition (150 ppm or 0.015%), a very strong resonance (Fig. 1C) is predicted (“super-resonance”). [ 8 ] Yet another nontrivial prediction of the IsoRes hypothesis is that at ≈250-350 ppm deuterium content, the terrestrial resonance becomes “perfect”, and the rates of biochemical reactions and growth of terrestrial organisms further increase. This prediction seems to be matched by at least some experimental observations. [ 8 ] [ 9 ]
The IsoRes hypothesis has been tested experimentally by means of growth of E. coli and found to be supported by extremely strong statistics (p << 10 −15 ). [ 8 ] Particular strong evidence of faster growth was found for the “super-resonance”.
Fig. 1. 2D plot of molecular masses of 3000 E. coli tryptic peptides. A – terrestrial isotopic compositions (red arrow shows the line representing the resonance); B – 18 O abundance is increased by 20%, which destroyed the terrestrial resonance; C – isotopic compositions of the “super-resonance”, where all dots (molecules) are perfectly aligned. Adapted from ref. 4. | https://en.wikipedia.org/wiki/Isotopic_resonance_hypothesis |
An isotopic signature (also isotopic fingerprint ) is a ratio of non-radiogenic ' stable isotopes ', stable radiogenic isotopes , or unstable radioactive isotopes of particular elements in an investigated material. The ratios of isotopes in a sample material are measured by isotope-ratio mass spectrometry against an isotopic reference material . This process is called isotope analysis .
The atomic mass of different isotopes affect their chemical kinetic behavior, leading to natural isotope separation processes.
For example, different sources and sinks of methane have different affinity for the 12 C and 13 C isotopes, which allows distinguishing between different sources by the 13 C/ 12 C ratio in methane in the air. In geochemistry , paleoclimatology and paleoceanography this ratio is called δ 13 C . The ratio is calculated with respect to Pee Dee Belemnite (PDB) standard :
Similarly, carbon in inorganic carbonates shows little isotopic fractionation, while carbon in materials originated by photosynthesis is depleted of the heavier isotopes. In addition, there are two types of plants with different biochemical pathways; the C3 carbon fixation , where the isotope separation effect is more pronounced, C4 carbon fixation , where the heavier 13 C is less depleted, and Crassulacean Acid Metabolism (CAM) plants, where the effect is similar but less pronounced than with C 4 plants. Isotopic fractionation in plants is caused by physical (slower diffusion of 13 C in plant tissues due to increased atomic weight) and biochemical (preference of 12 C by two enzymes: RuBisCO and phosphoenolpyruvate carboxylase ) factors. [ 2 ] The different isotope ratios for the two kinds of plants propagate through the food chain , thus it is possible to determine if the principal diet of a human or an animal consists primarily of C 3 plants ( rice , wheat , soybeans , potatoes ) or C 4 plants ( corn , or corn-fed beef ) by isotope analysis of their flesh and bone collagen (however, to obtain more accurate determinations, carbon isotopic fractionation must be also taken into account, since several studies have reported significant 13 C discrimination during biodegradation of simple and complex substrates). [ 3 ] [ 4 ] Within C3 plants processes regulating changes in δ 13 C are well understood, particularly at the leaf level, [ 5 ] but also during wood formation. [ 6 ] [ 7 ] Many recent studies combine leaf level isotopic fractionation with annual patterns of wood formation (i.e. tree ring δ 13 C) to quantify the impacts of climatic variations and atmospheric composition [ 8 ] on physiological processes of individual trees and forest stands. [ 9 ] The next phase of understanding, in terrestrial ecosystems at least, seems to be the combination of multiple isotopic proxies to decipher interactions between plants, soils and the atmosphere, and predict how changes in land use will affect climate change. [ 10 ] Similarly, marine fish contain more 13 C than freshwater fish, with values approximating the C 4 and C 3 plants respectively.
The ratio of carbon-13 and carbon-12 isotopes in these types of plants is as follows: [ 11 ]
Limestones formed by precipitation in seas from the atmospheric carbon dioxide contain normal proportion of 13 C. Conversely, calcite found in salt domes originates from carbon dioxide formed by oxidation of petroleum , which due to its plant origin is 13 C-depleted. The layer of limestone deposited at the Permian extinction 252 Mya can be identified by the 1% drop in 13 C/ 12 C.
Nitrogen-15 , or 15 N, is often used in agricultural and medical research, for example in the Meselson–Stahl experiment to establish the nature of DNA replication . [ 12 ] An extension of this research resulted in development of DNA-based stable-isotope probing, which allows examination of links between metabolic function and taxonomic identity of microorganisms in the environment, without the need for culture isolation. [ 13 ] [ 14 ] Proteins can be isotopically labelled by cultivating them in a medium containing 15 N as the only source of nitrogen, e.g., in quantitative proteomics such as SILAC .
Nitrogen-15 is extensively used to trace mineral nitrogen compounds (particularly fertilizers ) in the environment. [ 15 ] When combined with the use of other isotopic labels, 15 N is also a very important tracer for describing the fate of nitrogenous organic pollutants . [ 16 ] [ 17 ] Nitrogen-15 tracing is an important method used in biogeochemistry .
The ratio of stable nitrogen isotopes, 15 N/ 14 N or δ 15 N , tends to increase with trophic level , such that herbivores have higher nitrogen isotope values than plants , and carnivores have higher nitrogen isotope values than herbivores. Depending on the tissue being examined, there tends to be an increase of 3-4 parts per thousand with each increase in trophic level. [ 18 ] The tissues and hair of vegans therefore contain significantly lower δ 15 N than the bodies of people who eat mostly meat. Similarly, a terrestrial diet produces a different signature than a marine-based diet. Isotopic analysis of hair is an important source of information for archaeologists , providing clues about the ancient diets and differing cultural attitudes to food sources. [ 19 ]
A number of other environmental and physiological factors can influence the nitrogen isotopic composition at the base of the food web (i.e. in plants) or at the level of individual animals. For example, in arid regions, the nitrogen cycle tends to be more 'open' and prone to the loss of 14 N, increasing δ 15 N in soils and plants. [ 20 ] This leads to relatively high δ 15 N values in plants and animals in hot and arid ecosystems relative to cooler and moister ecosystems. [ 21 ] Furthermore, elevated δ 15 N have been linked to the preferential excretion of 14N and reutilization of already enriched 15N tissues in the body under prolonged water stress conditions or insufficient protein intake. [ 22 ] [ 23 ]
δ 15 N also provides a diagnostic tool in planetary science as the ratio exhibited in atmospheres and surface materials "is closely tied to the conditions under which materials form". [ 24 ]
Oxygen occurs naturally in three variants, but 17 O is so rare that it is very difficult to detect (~0.04% abundant). [ 25 ] The ratio of 18 O / 16 O in water depends on the amount of evaporation the water experienced (as 18 O is heavier and therefore less likely to vaporize). As the vapor tension depends on the concentration of dissolved salts, the 18 O/ 16 O ratio shows correlation on the salinity and temperature of water. As oxygen is incorporated into the shells of calcium carbonate -secreting organisms, such sediments provide a chronological record of temperature and salinity of the water in the area.
The oxygen isotope ratio in the atmosphere varies predictably with time of year and geographic location; e.g. there is a 2% difference between 18 O-rich precipitation in Montana and 18 O-depleted precipitation in Florida Keys. This variability can be used for approximate determination of geographic location of origin of a material; e.g. it is possible to determine where a shipment of uranium oxide was produced. The rate of exchange of surface isotopes with the environment has to be taken in account. [ 26 ]
The oxygen isotopic signatures of solid samples (organic and inorganic) are usually measured with pyrolysis and mass spectrometry . [ 27 ] Improper or prolonged storage of samples can lead to inaccurate measurements. [ 27 ]
Sulfur has four stable isotopes, 32 S , 33 S, 34 S, and 36 S, of which 32 S is the most abundant by a large margin due to the fact it is created by the very common 12 C in supernovas . Sulfur isotope ratios are almost always expressed as ratios relative to 32 S due to this major relative abundance (95.0%). Sulfur isotope fractionations are usually measured in terms of δ 34 S due to its higher abundance (4.25%) compared to the other stable isotopes of sulfur , though δ 33 S is also sometimes measured. Differences in sulfur isotope ratios are thought to exist primarily due to kinetic fractionation during reactions and transformations.
Sulfur isotopes are generally measured against standards; prior to 1993, the Canyon Diablo troilite standard (abbreviated to CDT ), which has a 32 S: 34 S equal to 22.220, was used as both a reference material and the zero point for the isotopic scale. Since 1993, the Vienna-CDT standard has been used as a zero point, and there are several materials used as reference materials for sulfur isotope measurements . Sulfur fractionations by natural processes measured against these standards have been shown to exist between −72‰ and +147‰, [ 28 ] [ 29 ] as calculated by the following equation:
δ S 34 s a m p l e = ( S 34 / 32 S sample S 34 / 32 S s t a n d a r d − 1 ) ⋅ 1000 {\displaystyle \delta {\ce {^{34}S}}_{\mathrm {sample} }=\left({\frac {{\ce {^{34}S/^{32}S}}_{{\ce {sample}}}}{{\ce {^{34}S/^{32}S}}_{\mathrm {standard} }}}-1\right)\cdot 1000}
As a very redox-active element, sulfur can be useful for recording major chemistry-altering events throughout Earth's history , such as marine evaporites which reflect the change in the atmosphere's redox state brought about by the Oxygen Crisis . [ 32 ] [ 33 ]
Lead consists of four stable isotopes : 204 Pb, 206 Pb, 207 Pb, and 208 Pb. Local variations in uranium / thorium / lead content cause a wide location-specific variation of isotopic ratios for lead from different localities. Lead emitted to the atmosphere by industrial processes has an isotopic composition different from lead in minerals. Combustion of gasoline with tetraethyllead additive led to formation of ubiquitous micrometer-sized lead-rich particulates in car exhaust smoke ; especially in urban areas the man-made lead particles are much more common than natural ones. The differences in isotopic content in particles found in objects can be used for approximate geolocation of the object's origin. [ 26 ]
The 14 C isotope is important in distinguishing between materials made from modern sources of carbon and ancient sources of carbon. Cosmic rays transform 14 N to radioactive 14 C, which subsequently decays over the course of tens of thousands of years. Shielded from cosmic radiation underground, fossil fuels like coal or petroleum exhibit 14 C levels below detectable limits. However, carbon circulating in the surface biosphere maintains a measurable amount of 14 C. Thus, materials synthesized from fossil fuel sources can be differentiated from those made with modern materials by the absence/presence of 14 C. Federal regulators use this technique to encourage and monitor the incorporation of renewable biofeedstocks into transportation fuels. [ 34 ]
Hot particles , radioactive particles of nuclear fallout and radioactive waste , also exhibit distinct isotopic signatures. Their radionuclide composition (and thus their age and origin) can be determined by mass spectrometry or by gamma spectrometry . For example, particles generated by a nuclear blast contain detectable amounts of 60 Co and 152 Eu . The Chernobyl accident did not release these particles but did release 125 Sb and 144 Ce . Particles from underwater bursts will consist mostly of irradiated sea salts. Ratios of 152 Eu / 155 Eu, 154 Eu/ 155 Eu, and 238 Pu / 239 Pu are also different for fusion and fission nuclear weapons , which allows identification of hot particles of unknown origin.
Uranium has a relatively constant isotope ratio in all natural samples with ~0.72% 235 U , some 55 ppm 234 U (in secular equilibrium with its parent nuclide 238 U ), and the balance made up by 238 U . Isotopic compositions that diverge significantly from those values are evidence for the uranium having been subject to depletion or enrichment in some fashion or of (part of it) having participated in a nuclear fission reaction. While the latter is almost as universally due to human influence as the former two, the natural nuclear fission reactor at Oklo , Gabon was detected through a significant diversion of 235 U concentration in samples from Oklo compared to those of all other known deposits on earth. Given that 235 U is a material of proliferation concern then as now every IAEA -approved supplier of Uranium fuel keeps track of the isotopic composition of uranium to ensure none is diverted for nefarious purposes. It would thus become apparent quickly if another Uranium deposit besides Oklo proves to have once been a natural nuclear fission reactor.
In archaeological studies, stable isotope ratios have been used to track diet within the time span formation of analyzed tissues (10–15 years for bone collagen and intra-annual periods for tooth enamel bioapatite) from individuals; "recipes" of foodstuffs (ceramic vessel residues); locations of cultivation and types of plants grown (chemical extractions from sediments); and migration of individuals (dental material). [ citation needed ]
With the advent of stable isotope ratio mass spectrometry , isotopic signatures of materials find increasing use in forensics , distinguishing the origin of otherwise similar materials and tracking the materials to their common source. For example, the isotope signatures of plants can be to a degree influenced by the growth conditions, including moisture and nutrient availability. In case of synthetic materials, the signature is influenced by the conditions during the chemical reaction. The isotopic signature profiling is useful in cases where other kinds of profiling, e.g. characterization of impurities , are not optimal. Electronics coupled with scintillator detectors are routinely used to evaluate isotope signatures and identify unknown sources.
A study was published demonstrating the possibility of determination of the origin of a common brown PSA packaging tape by using the carbon, oxygen, and hydrogen isotopic signature of the backing polymer, additives, and adhesive . [ 35 ]
Measurement of carbon isotopic ratios can be used for detection of adulteration of honey . Addition of sugars originated from corn or sugar cane (C4 plants) skews the isotopic ratio of sugars present in honey, but does not influence the isotopic ratio of proteins; in an unadulterated honey the carbon isotopic ratios of sugars and proteins should match. [ 36 ] As low as 7% level of addition can be detected. [ 37 ]
Nuclear explosions form 10 Be by a reaction of fast neutrons with 13 C in the carbon dioxide in air. This is one of the historical indicators of past activity at nuclear test sites. [ 38 ]
Isotopic fingerprints are used to study the origin of materials in the Solar System. [ 39 ] For example, the Moon 's oxygen isotopic ratios seem to be essentially identical to Earth's. [ 40 ] Oxygen isotopic ratios, which may be measured very precisely, yield a unique and distinct signature for each Solar System body. [ 41 ] Different oxygen isotopic signatures can indicate the origin of material ejected into space. [ 42 ] The Moon's titanium isotope ratio ( 50 Ti/ 47 Ti) appears close to the Earth's (within 4 ppm). [ 43 ] [ 44 ] In 2013, a study was released that indicated water in lunar magma was 'indistinguishable' from carbonaceous chondrites and nearly the same as Earth's, based on the composition of water isotopes. [ 39 ] [ 45 ]
Isotope biogeochemistry has been used to investigate the timeline surrounding life and its earliest iterations on Earth . Isotopic fingerprints typical of life, preserved in sediments, have been used to suggest, but do not necessarily prove, that life was already in existence on Earth by 3.85 billion years ago. [ 46 ]
Sulfur isotope evidence has also been used to corroborate the timing of the Great Oxidation Event , during which the Earth's atmosphere experienced a measurable rise in oxygen (to about 9% of modern values [ 47 ] ) for the first time about 2.3–2.4 billion years ago. Mass-independent sulfur isotope fractionations are found to be widespread in the geologic record before about 2.45 billion years ago, and these isotopic signatures have since ceded to mass-dependent fractionation, providing strong evidence that the atmosphere shifted from anoxic to oxygenated at that threshold. [ 48 ]
Modern sulfate-reducing bacteria are known to favorably reduce lighter 32 S instead of 34 S, and the presence of these microorganisms can measurably alter the sulfur isotope composition of the ocean. [ 32 ] Because the δ 34 S values of sulfide minerals is primarily influenced by the presence of sulfate-reducing bacteria , [ 49 ] the absence of sulfur isotope fractionations in sulfide minerals suggests the absence of these bacterial processes or the absence of freely available sulfate. Some have used this knowledge of microbial sulfur fractionation to suggest that minerals (namely pyrite ) with large sulfur isotope fractionations relative to the inferred seawater composition may be evidence of life. [ 50 ] [ 51 ] This claim is not clear-cut, however, and is sometimes contested using geologic evidence from the ~3.49 Ga sulfide minerals found in the Dresser Formation of Western Australia, which are found to have δ 34 S values as negative as −22‰. [ 52 ] Because it has not been proven that the sulfide and barite minerals formed in the absence of major hydrothermal input, it is not conclusive evidence of life or of the microbial sulfate reduction pathway in the Archean. [ 53 ] | https://en.wikipedia.org/wiki/Isotopic_signature |
Isotopocules are isotopically substituted molecules , which differ only in their isotopic composition or their isotopes' intramolecular position. [ 1 ] "Isotopocule" is also an umbrella term for the more specific terms " isotopologue " and " isotopomer ", coined by Jan Kaiser and Thomas Röckmann in 2008. [ 2 ] [ 3 ]
This physical chemistry -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isotopocule |
In chemistry , isotopologues (also spelled isotopologs ) are molecules that differ only in their isotopic composition. [ 1 ] They have the same chemical formula and bonding arrangement of atoms , but at least one atom has a different number of neutrons than the parent.
An example is water , whose hydrogen -related isotopologues are: "light water" (HOH or H 2 O ), " semi-heavy water " with the deuterium isotope in equal proportion to protium (HDO or 1 H 2 HO ), " heavy water " with two deuterium atoms ( D 2 O or 2 H 2 O ); and "super-heavy water" or tritiated water ( T 2 O or 3 H 2 O , as well as HTO [ 1 H 3 HO] and DTO [ 2 H 3 HO] , where some or all of the hydrogen is the radioactive tritium isotope). Oxygen -related isotopologues of water include the commonly available form of heavy-oxygen water ( H 2 18 O ) and the more difficult to separate version with the 17 O isotope. Both elements may be replaced by isotopes, for example in the doubly labeled water isotopologue D 2 18 O . Altogether, there are 9 different stable water isotopologues, [ 2 ] and 9 radioactive isotopologues involving tritium, [ 3 ] for a total of 18. However only certain ratios are possible in mixture, due to prevalent hydrogen swapping.
The atom(s) of the different isotope may be anywhere in a molecule, so the difference is in the net chemical formula. If a compound has several atoms of the same element, any one of them could be the altered one, and it would still be the same isotopologue. When considering the different locations of the same isotope, the term isotopomer , first proposed by Seeman and Paine in 1992, is used. [ 4 ] [ 5 ] Isotopomerism is analogous to constitutional isomerism or stereoisomerism of different elements in a structure. Depending on the formula and the symmetry of the structure, there might be several isotopomers of one isotopologue. For example, ethanol has the molecular formula C 2 H 6 O . Mono-deuterated ethanol, C 2 H 5 DO or C 2 H 5 2 HO , is an isotopologue of it. The structural formulas CH 3 −CH 2 −O−D and CH 2 D−CH 2 −O−H are two isotopomers of that isotopologue.
Singly substituted isotopologues may be used for nuclear magnetic resonance experiments, where deuterated solvents such as deuterated chloroform (CDCl 3 or C 2 HCl 3 ) do not interfere with the solutes' 1 H signals, and in investigations of the kinetic isotope effect .
In the field of stable isotope geochemistry , isotopologues of simple molecules containing rare heavy isotopes of carbon, oxygen, hydrogen, nitrogen, and sulfur are used to trace equilibrium and kinetic processes in natural environments and in Earth's past .
Measurement of the abundance of clumped isotopes (doubly substituted isotopologues) of gases has been used in the field of stable isotope geochemistry to trace equilibrium and kinetic processes in the environment inaccessible by analysis of singly substituted isotopologues alone.
Currently measured doubly substituted isotopologues include:
Because of the relative rarity of the heavy isotopes of C, H, and O, isotope-ratio mass spectrometry (IRMS) of doubly substituted species requires larger volumes of sample gas and longer analysis times than traditional stable isotope measurements, thereby requiring extremely stable instrumentation. Also, the doubly-substituted isotopologues are often subject to isobaric interferences, as in the methane system where 13 CH 5 + and 12 CH 3 D + ions interfere with measurement of the 12 CH 2 D 2 + and 13 CH 3 D + species at mass 18. A measurement of such species requires either very high mass resolving power to separate one isobar from another, [ 13 ] or modeling of the contributions of the interfering species to the abundance of the species of interest. These analytical challenges are significant: The first publication precisely measuring doubly substituted isotopologues did not appear until 2004, though singly substituted isotopologues had been measured for decades previously. [ 14 ]
As an alternative to more conventional gas source IRMS instruments, tunable diode laser absorption spectroscopy has also emerged as a method to measure doubly substituted species free from isobaric interferences, and has been applied to the methane isotopologue 13 CH 3 D.
When a light isotope is replaced with a heavy isotope (e.g., 13 C for 12 C), the bond between the two atoms will vibrate more slowly, thereby lowering the zero-point energy of the bond and acting to stabilize the molecule. [ 15 ] An isotopologue with a doubly substituted bond is therefore slightly more thermodynamically stable, which will tend to produce a higher abundance of the doubly substituted (or “clumped”) species than predicted by the statistical abundance of each heavy isotope (known as a stochastic distribution of isotopes). This effect increases in magnitude with decreasing temperature, so the abundance of the clumped species is related to the temperature at which the gas was formed or equilibrated. [ 16 ] By measuring the abundance of the clumped species in standard gases formed in equilibrium at known temperatures, the thermometer can be calibrated and applied to samples with unknown abundances.
The abundances of multiply substituted isotopologues can also be affected by kinetic processes. As for singly substituted isotopologues, departures from thermodynamic equilibrium in a doubly-substituted species can implicate the presence of a particular reaction taking place. Photochemistry occurring in the atmosphere has been shown to alter the abundance of 18 O 2 from equilibrium, as has photosynthesis . [ 17 ] Measurements of 13 CH 3 D and 12 CH 2 D 2 can identify microbial processing of methane and have been used to demonstrate the significance of quantum tunneling in the formation of methane, as well as mixing and equilibration of multiple methane reservoirs . Variations in the relative abundances of the two N 2 O isotopologues 14 N 15 N 18 O and {{sup>15}}N 14 N 18 O can distinguish whether N 2 O has been produced by bacterial denitrification or by bacterial nitrification .
Multiple substituted isotopologues may be used for nuclear magnetic resonance or mass spectrometry experiments, where isotopologues are used to elucidate metabolic pathways in a qualitative (detect new pathways) or quantitative (detect quantitative share of a pathway) approach. A popular example in biochemistry is the use of uniform labelled glucose (U- 13 C glucose), which is metabolized by the organism under investigation (e. g. bacterium, plant, or animal) and whose signatures can later be detected in newly formed amino acid or metabolically cycled products.
Resulting from either naturally occurring isotopes or artificial isotopic labeling , isotopologues can be used in various mass spectrometry applications.
The relative mass spectral intensity of natural isotopologues, calculable from the fractional abundances of the constituent elements, is exploited by mass spectrometry practitioners in quantitative analysis and unknown compound identification:
A compound tagged by replacing specific atoms with the corresponding isotopes can facilitate the following mass spectrometry methods: | https://en.wikipedia.org/wiki/Isotopologue |
Isotopomers or isotopic isomers are isomers which differ by isotopic substitution , and which have the same number of atoms of each isotope but in a different arrangement. For example, CH 3 OD and CH 2 DOH are two isotopomers of monodeuterated methanol .
The molecules may be either structural isomers (constitutional isomers) or stereoisomers depending on the location of the isotopes. Isotopomers have applications in areas including nuclear magnetic resonance spectroscopy , reaction kinetics , and biochemistry .
Isotopomers or isotopic isomers are isomers with isotopic atoms, having the same number of each isotope of each element but differing in their positions in the molecule. The result is that the molecules are either constitutional isomers or stereoisomers solely based on isotopic location. The term isotopomer was first proposed by Seeman and Paine in 1992 to distinguish isotopic isomers from isotopologues (isotopic homologues). [ 1 ] [ 2 ]
In nuclear magnetic resonance spectroscopy , the highly abundant 12 C isotope does not produce any signal whereas the comparably rare 13 C isotope is easily detected. As a result, carbon isotopomers of a compound can be studied by carbon-13 NMR to learn about the different carbon atoms in the structure. Each individual structure that contains a single 13 C isotope provides data about the structure in its immediate vicinity. A large sample of a chemical contains a mixture of all such isotopomers, so a single spectrum of the sample contains data about all carbons in it. Nearly all of the carbon in normal samples of carbon-based chemicals is 12 C, with only about 1% abundance of 13 C, so there is only about a 1% abundance of the total of the singly-substituted isotopologues , and exponentially smaller amounts of structures having two or more 13 C in them. The rare case where two adjacent carbon atoms in a single structure are both 13 C causes a detectable coupling effect between them as well as signals for each one itself. The INADEQUATE correlation experiment uses this effect to provide evidence for which carbon atoms in a structure are attached to each other, which can be useful for determining the actual structure of an unknown chemical.
In reaction kinetics , a rate effect is sometimes observed between different isotopomers of the same chemical. This kinetic isotope effect can be used to study reaction mechanisms by analyzing how the differently massed atom is involved in the process. [ 4 ]
In biochemistry , differences between the isotopomers of biochemicals such as starches is of practical importance in archaeology. They offer clues to the diet of prehistoric humans that lived as long ago as Paleolithic times. [ citation needed ] This is because naturally occurring carbon dioxide contains both 12 C and 13 C. Monocots , such as rice and oats , differ from dicots , such as potatoes and tree fruits , in the relative amounts of 12 CO 2 and 13 CO 2 that they incorporate into their tissues as products of photosynthesis . When tissues of such subjects are recovered, usually tooth or bone, the relative isotopic content can give useful indications of the main source of the staple foods of the subjects of the investigations.
A cumomer is a set of isotopomers sharing similar properties and is a concept that relates to metabolic flux analysis . The concept was developed in 1999. [ 5 ] [ 6 ] In a metabolic cascade, many molecules will contain the same pattern of isotope labelling. In order to simplify the analysis of such cascades, molecules with identically labelled atoms are aggregated into a virtual molecule called a cumomer (a conflation of cumulative and isotopomer ). [ 5 ] | https://en.wikipedia.org/wiki/Isotopomer |
Isotricha is a genus of protozoa (single-celled organisms) which are commensals of the rumen of ruminant animals. They are approximately 150 μm (0.0059 in) long. [ 1 ]
Species include: [ 2 ]
This ciliate -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isotricha |
In physiology , isotropic bands (better known as I bands ) are the lighter bands of skeletal muscle cells (a.k.a. muscle fibers ). Isotropic bands contain only actin -containing thin filaments . [ 1 ] The thin filaments are placed between 2 myosin filaments and contain only the actin filaments of neighboring sarcomeres . Bisecting the I band and serving as an anchoring point for the two adjacent actin filaments is the Z disc. During muscle contraction, the I band will shorten, while an A band will maintain its width. [ 2 ]
The darker bands within skeletal muscle, known as anisotropic bands (A bands), encompass both thick and thin filaments and constitute the central region of the sarcomere, extending across the H-zone. Collectively, the A bands and the I bands create the distinctive striped appearance of skeletal muscle tissue. [ 3 ] Tropomyosin, a protein, shields the myosin-binding sites, hindering actin from binding to myosin. It attaches to troponin , which secures it in place. During muscle relaxation, the troponin-tropomyosin complex inhibits myosin heads from binding to the active sites on actin microfilaments. Troponin also possesses a calcium ion binding site. These two regulatory proteins cooperate in response to calcium levels, overseeing sarcomere contraction. During muscle contraction, tropomyosin shifts to expose the myosin-binding site on an actin filament, allowing the interaction between actin and myosin microfilaments to occur. The initiation of contraction involves calcium ions binding to troponin, prompting a reaction that displaces tropomyosin from the actin filament binding sites. Consequently, myosin heads can attach to these exposed sites, forming cross-bridges and initiating muscle contraction. [ 4 ] | https://en.wikipedia.org/wiki/Isotropic_bands |
An isotropic beacon is a hypothetical type of transmission beacon that emits a uniform EM signal in all directions for the purposes of communication with extraterrestrial intelligence . [ 1 ]
An isotropic beacon can be any transmitter that emits a uniform electromagnetic field. However, the term is most commonly used to describe a transmitter used by a civilization to call attention to itself over interstellar distances to extraterrestrial creatures. The isotropic beacon uses the Kardashev scale. The Kardashev scale is a method of measuring a civilization's level of technological advancement based on the amount of energy it is able to use. The measure was proposed by Soviet astronomer Nikolai Kardashev in 1964. The Kardashev scale has three designated categories, which are a Type I civilization, also called a planetary civilization, that can use and store all of the energy available on its planet. A Type II civilization, also called a stellar civilization, can use and control energy at the scale of its planetary system. A Type III civilization, also called a galactic civilization, can control energy at the scale of its entire host galaxy. [ citation needed ] Project Cyclops is and was one of the first looks at the theoretical framework of what it would take to create such a device. [ citation needed ]
This astrobiology -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isotropic_beacon |
Isotropic formulations are thermodynamically stable microemulsions possessing lyotropic liquid crystal properties. [ 1 ] They inhabit a state of matter and physical behaviour somewhere between conventional liquids and that of solid crystals . [ 2 ] Isotropic formulations are amphiphillic , exhibiting selective synchronicity with both the water and lipid phases of the substrate to which they are applied. [ 3 ] Most recently, isotropic formulations have been used extensively in dermatology for drug delivery . [ 4 ]
While it is well established that the skin provides an ideal site for the administration of local and systemic drugs , it presents a formidable barrier to the permeation of most substances. [ 5 ] Isotropic formulations have been used to deliver drugs locally and systemically via the skin appendages, intercellular and transcellular routes. [ 6 ] | https://en.wikipedia.org/wiki/Isotropic_formulations |
In fluid dynamics , an isotropic helicoid is a shape that is helical , so it rotates as it moves through a fluid , and yet is isotropic , so that its rotation and drag are the same for all orientations of the particle. It was first proposed by Lord Kelvin in 1871, who described a specific geometry with twelve vanes placed around a sphere. [ 1 ] As of 2021, such a phenomenon has yet to be proven by researchers. [ 2 ]
This geometry-related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isotropic_helicoid |
In the geometry of quadratic forms , an isotropic line or null line is a line for which the quadratic form applied to the displacement vector between any pair of its points is zero. An isotropic line occurs only with an isotropic quadratic form , and never with a definite quadratic form .
Using complex geometry , Edmond Laguerre first suggested the existence of two isotropic lines through the point ( α , β ) that depend on the imaginary unit i : [ 1 ]
Laguerre then interpreted these lines as geodesics :
In the complex projective plane , points are represented by homogeneous coordinates ( x 1 , x 2 , x 3 ) {\displaystyle (x_{1},x_{2},x_{3})} and lines by homogeneous coordinates ( a 1 , a 2 , a 3 ) {\displaystyle (a_{1},a_{2},a_{3})} . An isotropic line in the complex projective plane satisfies the equation: [ 2 ]
In terms of the affine subspace x 3 = 1 , an isotropic line through the origin is
In projective geometry, the isotropic lines are the ones passing through the circular points at infinity .
In the real orthogonal geometry of Emil Artin , isotropic lines occur in pairs:
Isotropic lines have been used in cosmological writing to carry light. For example, in a mathematical encyclopedia, light consists of photons : "The worldline of a zero rest mass (such as a non-quantum model of a photon and other elementary particles of mass zero) is an isotropic line." [ 4 ] For isotropic lines through the origin, a particular point is a null vector , and the collection of all such isotropic lines forms the light cone at the origin.
Élie Cartan expanded the concept of isotropic lines to multivectors in his book on spinors in three dimensions . [ 5 ] | https://en.wikipedia.org/wiki/Isotropic_line |
In condensed matter physics and continuum mechanics , an isotropic solid refers to a solid material for which physical properties are independent of the orientation of the system. While the finite sizes of atoms and bonding considerations ensure that true isotropy of atomic position will not exist in the solid state, it is possible for measurements of a given property to yield isotropic results, either due to the symmetries present within a crystal system , or due to the effects of orientational averaging over a sample (e.g. in an amorphous solid or a polycrystalline metal). Isotropic solids tend to be of interest when developing models for physical behavior of materials, as they tend to allow for dramatic simplifications of theory; for example, conductivity in metals of the cubic crystal system can be described with single scalar value, rather than a tensor . [ 1 ] Additionally, cubic crystals are isotropic with respect to thermal expansion [ 2 ] and will expand equally in all directions when heated. [ 3 ]
Isotropy should not be confused with homogeneity , which characterizes a system’s properties as being independent of position, rather than orientation. Additionally, all crystal structures, including the cubic crystal system, are anisotropic with respect to certain properties, and isotropic to others (such as density ). [ 4 ] The anisotropy of a crystal’s properties depends on the rank of the tensor used to describe the property, as well as the symmetries present within the crystal. The rotational symmetries within cubic crystals, for example, ensure that the dielectric constant (a 2nd rank tensor property) will be equal in all directions, whereas the symmetries in hexagonal systems dictate that the measurement will vary depending on whether the measurement is made within the basal plane . [ 5 ] Due to the relationship between the dielectric constant and the optical index of refraction, it would be expected for cubic crystals to be optically isotropic, and hexagonal crystals to be optically anisotropic; Measurements of the optical properties of cubic and hexagonal CdSe confirm this understanding. [ 6 ]
Nearly all single crystal systems are anisotropic with respect to mechanical properties, with Tungsten being a very notable exception, as it is a cubic metal with stiffness tensor coefficients that exist in the proper ratio to allow for mechanical isotropy. In general, however, cubic crystals are not mechanically isotropic. However, many materials, such as structural steel , tend to be encountered and utilized in a polycrystalline state. Due to random orientation of the grains within the material, measured mechanical properties tend to be averages of the values associated with different crystallographic directions, with the net effect of apparent isotropy. As a result, it is typical for parameters such as the Young's Modulus to be reported independent of crystallographic direction. [ 7 ] Treating solids as mechanically isotropic greatly simplifies analysis of deformation and fracture (as well as of the elastic fields produced by dislocations [ 8 ] ). However, preferential orientation of grains (called texture) can occur as a result of certain types of deformation and recrystallization processes, which will create anisotropy in mechanical properties of the solid. [ 7 ]
This condensed matter physics -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isotropic_solid |
In physics and geometry , isotropy (from Ancient Greek ἴσος ( ísos ) ' equal ' and τρόπος ( trópos ) ' turn, way ' ) is uniformity in all orientations . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix a- or an- , hence anisotropy . Anisotropy is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement , and an isotropic field exerts the same action regardless of how the test particle is oriented.
Within mathematics , isotropy has a few different meanings:
In the study of mechanical properties of materials , "isotropic" means having identical values of a property in all directions. This definition is also used in geology and mineralogy . Glass and metals are examples of isotropic materials. [ 3 ] Common anisotropic materials include wood (because its material properties are different parallel to and perpendicular to the grain) and layered rocks such as slate .
Isotropic materials are useful since they are easier to shape, and their behavior is easier to predict. Anisotropic materials can be tailored to the forces an object is expected to experience. For example, the fibers in carbon fiber materials and rebars in reinforced concrete are oriented to withstand tension.
In industrial processes, such as etching steps, "isotropic" means that the process proceeds at the same rate, regardless of direction. Simple chemical reaction and removal of a substrate by an acid, a solvent or a reactive gas is often very close to isotropic. Conversely, "anisotropic" means that the attack rate of the substrate is higher in a certain direction. Anisotropic etch processes, where vertical etch-rate is high but lateral etch-rate is very small, are essential processes in microfabrication of integrated circuits and MEMS devices.
An isotropic antenna is an idealized "radiating element" used as a reference ; an antenna that broadcasts power equally (calculated by the Poynting vector ) in all directions. The gain of an arbitrary antenna is usually reported in decibels relative to an isotropic antenna, and is expressed as dBi or dB(i).
In cells (a.k.a. muscle fibers ), the term "isotropic" refers to the light bands ( I bands ) that contribute to the striated pattern of the cells.
While it is well established that the skin provides an ideal site for the administration of local and systemic drugs, it presents a formidable barrier to the permeation of most substances. [ 4 ] Recently, isotropic formulations have been used extensively in dermatology for drug delivery. [ 5 ] | https://en.wikipedia.org/wiki/Isotropy |
In immunology , antibodies ( immunoglobulins (Ig) ) are classified into several types called isotypes or classes .
The variable (V) regions near the tip of the antibody can differ from molecule to molecule in countless ways, allowing it to specifically target an antigen (or more exactly, an epitope ).
In contrast, the constant (C) regions only occur in a few variants, which define the antibody's class.
Antibodies of different classes activate distinct effector mechanisms in response to an antigen (triggering different elements of the innate immune system ).
They appear at different stages of an immune response, differ in structural features, and in their location around the body. [ 1 ]
Isotype expression reflects the maturation stage of a B cell . Naive B cells express IgM and IgD isotypes with unmutated variable genes, which are produced from the same initial transcript following alternative splicing. Expression of other antibody isotypes (in humans: IgG, IgA, and IgE) occurs via a process of class switching after antigen exposure. [ 2 ] Class switching is mediated by the enzyme AID ( activation-induced cytidine deaminase ) and occurs after the B cell binds an antigen through its B cell receptor. Class-switching usually requires interaction with a T helper cell . [ 3 ] [ 4 ]
In humans , there are five heavy chain isotypes α,δ,γ,ε,μ, corresponding to five antibody isotypes:
There are also two light chain isotypes κ and λ; however, there is no significant difference in function between the two. Thus an antibody isotype is determined by the constant regions of the heavy chains only. [ 1 ]
IgM is first expressed as a monomer on the surface of immature B cells. Upon antigenic stimulation, IgM+ B cells secrete pentameric IgM antibody formed by five Ig monomers which are linked via disulfide bonds. The pentamer also contains a polypeptide J-chain, which links two of the monomers and facilitates secretion at mucosal surfaces. The pentameric structure of IgM antibodies makes them efficient at binding antigens with repetitive epitopes (e.g. bacterial capsule, viral capsid) and activation of complement cascade. As IgM antibodies are expressed early in a B cell response, they are rarely highly mutated and have broad antigen reactivity thus providing an early response to a wide range of antigens without the need for T cell help. [ 5 ]
IgD isotypes are expressed on naive B cells as they leave bone marrow and populate secondary lymphoid organs. The levels of surface expression of IgD isotype has been associated with differences in B cell activation status but their role in serum is poorly understood. [ 6 ]
The IgG, IgE and IgA antibody isotypes are generated following class-switching during germinal centre reaction and provide different effector functions in response to specific antigens. IgG is the most abundant antibody class in the serum and it is divided into 4 subclasses based on differences in the structure of the constant region genes and the ability to trigger different effector functions. Despite the high sequence similarity (90% identical on the amino acid level), each subclass has a different half-life, a unique profile of antigen binding and distinct capacity for complement activation. IgG1 antibodies are the most abundant IgG class and dominate the responses to protein antigens. Impaired production of IgG1 is observed in some cases of immunodeficiency and is associated with recurrent infections. [ 7 ] The IgG responses to bacterial capsular polysaccharide antigens are mediated primarily via IgG2 subclass, and deficiencies in this subclass result in susceptibility to certain bacterial species. [ 8 ] IgG2 represents the major antibody subclass reacting to glycan antigens but IgG1 and IgG3 subclasses have also been observed in such responses, particularly in the case of protein-glycan conjugates. [ 9 ]
IgG3 is an efficient activator of pro-inflammatory responses by triggering the classical complement pathway. [ 10 ] It has the shortest half-life compared to the other IgG subclasses [ 11 ] and is frequently present together with IgG1 in response to protein antigens after viral infections. [ 12 ] IgG4 is the least abundant IgG subclass in the serum and is often generated following repeated exposure to the same antigen or during persistent infections.
IgA antibodies are secreted in the respiratory or the intestinal tract and act as the main mediators of mucosal immunity. [ 13 ] They are monomeric in the serum, but appear as a dimer termed secretory IgA (sIgA) at mucosal surfaces. The secretory IgA is associated with a J-chain and another polypeptide chain called the secretory component. [ 14 ] IgA antibodies are divided into two subclasses that differ in the size of their hinge region. [ 15 ] IgA1 has a longer hinge region which increases its sensitivity to bacterial proteases. [ 16 ] Therefore, this subclass dominates the serum IgA, while IgA2 is predominantly found in mucosal secretions. Complement fixation by IgA is not a major effector mechanism at the mucosal surface but IgA receptor is expressed on neutrophils which may be activated to mediate antibody-dependent cellular cytotoxicity. [ 17 ] sIgA has also been shown to potentiate the immune response in intestinal tissue by uptake of antigen together with the bound antibody by dendritic cells. [ 18 ]
IgE antibodies are present at lowest concentrations in peripheral blood but constitute the main antibody class in allergic responses through the engagement of mast cells, eosinophils and Langerhans cells. [ 19 ] Responses to specific helminths are also characterised with elevated levels of IgE antibodies. [ 20 ] | https://en.wikipedia.org/wiki/Isotype_(immunology) |
In chemistry , isovalent or second order hybridization is an extension of orbital hybridization , the mixing of atomic orbitals into hybrid orbitals which can form chemical bonds, to include fractional numbers of atomic orbitals of each type (s, p, d). It allows for a quantitative depiction of bond formation when the molecular geometry deviates from ideal bond angles.
Only bonding with 4 equivalent substituents results in exactly sp 3 hybridization. For molecules with different substituents, we can use isovalent hybridization to rationalize the differences in bond angles between different atoms. In the molecule methyl fluoride for example, the HCF bond angle (108.73°) is less than the HCH bond angle (110.2°). [ 1 ] This difference can be attributed to more p character in the C−F bonding and more s character in the C−H bonding orbitals. The hybridisation of bond orbitals is determined by Bent's rule : "Atomic s character concentrates in orbitals directed toward electropositive substituents".
The bond length between similar atoms also shortens with increasing s character. For example, the C−H bond length is 110.2 pm in ethane , 108.5 pm in ethylene and 106.1 pm in acetylene , with carbon hybridizations sp 3 (25% s), sp 2 (33% s) and sp (50% s) respectively.
To determine the degree of hybridization of each bond one can utilize a hybridization parameter ( λ ). For hybrids of s and p orbitals, this is the coefficient ( λ ) {\displaystyle (\lambda )} multiplying the p orbital when the hybrid orbital is written in the form ( s + λ p ) {\displaystyle (s+\lambda p)} . The square of the hybridization parameter equals the hybridization index ( n ) of an sp n orbital. [ 2 ] [ 3 ] [ 4 ] n = λ 2 {\displaystyle n=\lambda ^{2}} .
The fractional s character of orbital i is 1 1 + λ i 2 {\displaystyle {\frac {1}{1+\lambda _{i}^{2}}}} , and the s character of all the hybrid orbitals must sum to one, so that ∑ i 1 1 + λ i 2 = 1 {\displaystyle \sum _{i}{\frac {1}{1+\lambda _{i}^{2}}}=1}
The fractional p character of orbital i is λ i 2 1 + λ i 2 {\displaystyle {\frac {\lambda _{i}^{2}}{1+\lambda _{i}^{2}}}} , and the p character of all the hybrid orbitals sums to the number of p orbitals involved in the formation of hybrids:
These hybridization parameters can then be related to physical properties like bond angles. Using the two bonding atomic orbitals i and j we are able to find the magnitude of the interorbital angle. The orthogonality condition implies the relation known as Coulson's theorem: [ 5 ]
For two identical ligands the following equation can be utilized:
The hybridization index cannot be measured directly in any way. However, one can find it indirectly by measuring specific physical properties. Because nuclear spins are coupled through bonding electrons, and the electron penetration to the nucleus is dependent on s character of the hybrid orbital used in bonding, J- coupling constants determined through NMR spectroscopy is a convenient experimental parameter that can be used to estimate the hybridization index of orbitals on carbon. The relationships for one-bond 13 C- 1 H and 13 C- 13 C coupling are
where 1 J X-Y is the one-bond NMR spin-spin coupling constant between nuclei X and Y and χ S (α) is the s character of orbital α on carbon, expressed as a fraction of unity.
As an application, the 13 C- 1 H coupling constants show that for the cycloalkanes , the amount of s character in the carbon hybrid orbital employed in the C-H bond decreases as the ring size increases. The value of 1 J 13 C- 1 H for cyclopropane, cyclobutane and cyclopentane are 161, 134, and 128 Hz, respectively. This is a consequence of the fact that the C-C bonds in small, strained rings (cyclopropane and cyclobutane) employ excess p character to accommodate their molecular geometries (these bonds are famously known as ' banana bonds '). In order to conserve the total number of s and p orbitals used in hybridization for each carbon, the hybrid orbital used to form the C-H bonds must in turn compensate by taking on more s character. [ 2 ] [ 4 ] [ 7 ] Experimentally, this is also demonstrated by the significantly higher acidity of cyclopropane (p K a ~ 46) compared to, for instance, cyclohexane (p K a ~ 52). [ 4 ] [ 8 ] [ 9 ] | https://en.wikipedia.org/wiki/Isovalent_hybridization |
Isovaleryl-CoA (also known as 3-methylbutyryl-CoA) is a metabolic intermediate formed during the catabolism of the branched-chain amino acid, Leucine . It is a short-chain acyl-CoA thioester that plays a key role in mitochondrial energy metabolism. The compound is converted into 3-methylcrotonyl-CoA by the enzyme isovaleryl-CoA dehydrogenase (IVD), a flavoprotein that catalyzes the third step in the leucine degradation pathway. [ 1 ] Deficiency of this enzyme activity results in the accumulation of isovaleryl-CoA and related metabolites, leading to a rare autosomal recessive disorder known as isovaleric acidemia , characterized by metabolic crises, developmental delays, and a distinctive odor due to isovaleric acid buildup. [ 2 ] [ 3 ] The metabolism of isovaleryl-CoA is vital for proper amino acid utilization and energy homeostasis in humans. [ 4 ]
The enzyme, Isovaleryl-CoA dehydrogenase (IVD) , part of the family of acyl-CoA dehydogenases (ACDs) , is activated through the substrate binding of Isovaleryl-CoA , within the hydrophobic pocket tailored to accommodate its branched alkyl chain . Upon substrate binding, conformational changes position the thioester group for hydride transfer to the flavin adenine dinucleotide (FAD) cofactor. This starts the dehydrogenation process, in which two hydrogen atoms are abstracted from the β and γ carbon atoms of isovaleryl-CoA, leading to the formation of a trans-double bond. [ 1 ] This enzymatic step results in the conversion of isovaleryl-CoA (3-methylbutyryl-CoA) into 3-methylcrotonyl-CoA , marking the third reaction in the leucine degradation pathway in the Mitochondria. [ 2 ]
IVD funcions as part of the electron transport flavoprotein (ETF) system , passing electrons from FADH₂ to ETF, which would then transport those electrons to the electron transport chain . The electron transport chain establishes a gradient by pushing protons into the inner mitochondrial membrane , contributing to ATP synthesis. The conversion of isovaleryl-CoA into 3-methylcrotonyl-CoA is thus not only central to leucine metabolism but also links amino acid catabolism to oxidative phosphorylation . [ 1 ] [ 4 ]
Following this transformation, 3-methylcrotonyl-CoA, is carboxylated to form 3-methylglutaconyl-CoA , then is hydrated and cleaved into acetyl-CoA and acetoacetate - two energy rich molecules that enter tricarboxylic acid (TCA) cycle and ketone body production [ 2 ] [ 3 ]
This biochemistry article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Isovaleryl-CoA |
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