The kinetic isotope method

This technique has been developed for studying sequential reactions by Gal and co-workers. Theory and earlier results were summarised in a book, describing it as a dynamic method that utihsed the temporal changes of specific (or molar) radioactivities of assumed intermediates. 

When a small portion of labelled X is introduced, the changes of the specific activity of X(a) and that of Y(6) as a function of time, can be described by the following equations 

In case c (i.e., when another intermediate enters between X and Y)  

The kinetic isotope method was also applied to study whether the stepwise or direct route is valid for the dehydrogenation of the cyclohexane ring.[bi4,67] mentioned before, plotting specific radioactivities as a function of the contact time confirmed the predominance of direct pathway on Re and the stepwise dehydrogenation on chromia. 

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Calculations according to the kinetic isotope method for the mixture of inactive -hexane and -hexene showed that 92-97% of the total... 

M. B. Neiman and D. Gal, The Kinetic Isotope Method and Its Application, Akademic Kiado, Budapest, 1971. 

The kinetic-isotope method is distinctly different from the tracer method. Here we make use of the fact that isotopic substitution leads to changes in rate constants which in some cases can be satisfactorily correlated with the reaction mechanism. 

Neiman MB, Gal D, The Kinetic Isotope Method and Its Applications, Akademiai Kiado, Budapest — Elsevier, Amsterdam, 1971. 

The mechanism of the low-temperature oxidation of methane has also been studied following the kinetic isotopic method By adding known portions of H[ " C)HO and CO to the methane-air mixture and measuring the changes with time of the specific activities of formaldehyde and carbon monoxide in the mixture, it has been established that formaldehyde is the unique precursor of carbon monoxide and the oxidation of methane proceeds according to equation 227. A suggestion has been made that... 

Applications of the kinetic isotopic method to the study of gas-phase oxidations of alkanes as well as liquid-phase oxidation of cyclohexane (equation 229) are presented in a monograph by Neiman and Gal . ... 

Conceptually, the simplest way to measure a kinetic isotope effect (KIE) is to use a non-competitive method, in which two separate kinetic runs are carried out, each starting with a different isotopomer of the reactant. The rate constants for both species are determined and the kinetic isotope effect (KIE) is the ratio of the two rate constants. This procedure is frequently referred to as the direct method . 

An alternative to the three isotope method is to use an enriched isotope tracer in experiments that are run in parallel to those involving normal isotope compositions under identical run conditions. Use of enriched isotope tracers to evaluate the kinetics of isotopic exchange has a long history (e.g.. Mills and Urey 1940). The extent of exchange toward isotopic equilibrium may be defined as ... 

As logical as this diagnostic method is, one needs to realize its lack of absolute applicability. The observed magnitude of the kinetic isotopic effect is not great, and the aforementioned statement of independence of the electron affinity from the increase in molecular mass of the substrate is not obvious. This postulate should be proved in each case. Benzophenone, taken as an isotopic mixture of C=0 and C=0 gives a mixture of anion-radicals with a decreased proportion of C=0 isotomer when reduced with potassium in HMPA (Stevenson et al. 1987b). In effect, this means that for the heavier isotopomer of benzophenone, the electron affinity is smaller. 

The value of the kinetic isotope effect method lies mainly in the possibility of making a substitution within tlve reactive center of the molecule, while still retaining the original type of the read ion, thus allowing the cancellation of many poorly defined quantities in the absolute rate equations and permitting a direct comparison between the measured and calculated values of the relative rate constants. Since the magnitude of these latter values depends on the hypothetical transition state model, a diagnostic means is provided by the method for the experimental verification of the nature of tlie transition state in question. 

The rate coefficient of a reactive process is a transport coefficient of interest in chemical physics. It has been shown from linear response theory that this coefficient can be obtained from the reactive flux correlation function of the system of interest. This quantity has been computed extensively in the literature for systems such as proton and electron transfer in solvents as well as clusters [29,32,33,56,71-76], where the use of the QCL formalism has allowed one to consider quantum phenomena such as the kinetic isotope effect in proton transfer [31], Here, we will consider the problem of formulating an expression for a reactive rate coefficient in the framework of the QCL theory. Results from a model calculation will be presented including a comparison to the approximate methods described in Sec. 4. 

A less well developed, but potentially less intrusive alternative is to block acidic sites with deuterium and to use the kinetic isotope effect to prevent lithiation.35 43 If the substrate can be polylithiated, the use of dianions (with the last formed anion being likely to be the most reactive) may give the required selectivity this method works well in the halogen-metal exchange area (section 3.1). 

In the application of this method it should be pointed out that mobility of the adsorbed phase on a nonuniform surface will yield results that are equivalent to those of a uniform surface. However, making use of information obtained from the kinetics of adsorption and from studies employing the differential isotopic method, these difficulties can frequently be resolved. 

Various kinetic methods in the enzyme catalysis has been described elsewhere (Likhtenshtein, 1988a Gates, 1991 Bugg, 1997 Comish-Bowden, 1995, 2001 Varfolomeev and Gurevich, 1998) Fersht,1999 Gutfreund,. 1995 Hammes, 2000 Leninger et al.1993 ). In this section we concentrate on recent developments in methods of the kinetic isotope effect, transition state analoges, and nanosecond temperature jump techniques. 

The kinetic isotope effect is a substantial shortcoming of methods based on stopping the polymerization by tritium-labelled Bronsted acids, such as alcohols and... 

Jones has studied the kinetic isotope effect in the chlorination of H2 and HT inducing the reaction with visible radiation and also with tritium p-particles. He found the same isotope effect with either method. The reactions and quantity of interest are... 

The enzyme mechanism of NA of influenza virus has been investigated by kinetic isotope methods, NMR, and a molecular dynamics simulation of the enzyme-substrate complex. 

Recent theoretical investigations clearly favor the [3 + 2] mechanism [27, 62], The calculation of the respective transition states using DFT methods show significantly lower activation barriers for the [3 + 2] addition compared with the [2 + 2] reaction path. Subsequently, these results were also supported by the theoretical and experimental determination of the kinetic isotope effect of the AD reaction [28]. 

We hope to apply this method in the near future for enzymatic active centres. Replacement of the polar solvent with a fluctuating macromolecular environment, such as an enzyme, is methodologically a straightforward step but requires a lot of coding efforts. Quantum treatment of the nuclear motion is essential for calculation of the kinetic isotope effects that are of vital importance for enzymology. Very recently the H/D kinetic isotope effect h/ d = 80 was simulated with what is in excellent agreement with the experiment [36]. 

We believe that the preceding resonance and steric arguments explain the differences in the reaction rates of the studied monomers, between themselves and the diffusion controlled limit. Because of the lack of H atom data for addition reactions at the diffusion controlled limit we wish to reserve judgement on the kinetic isotope effect. However, it appears that for these reported reactions there is little if any mass effect between H and Mu. Once the kinetic isotope effect is understood. Mu data observed directly by MSR methods could replace the more difficult... 

Our interest in McArdle s disease and vitamin B6 metabolism is stimulated by consideration of the consequences of the loss of the major, slowly metabolizing pool of vitamin B6 in the body. It is conceivable that the whole body phosphorylase-derived pool acts as a buffer to compensate for day-to-day variation in vitamin B6 intake. It will therefore be important to assess the rate of degradation of phosphorylase in the human, and the stable isotope method we have developed is directly applicable to this problem. Analysis of the same kinetics in McArdle s patients will define the role of muscle phosphorylase in the compartmen-talization of vitamin B6. 

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