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Transient kinetic isotope fractionation
Transient kinetic isotope effects (or fractionation) occur when the reaction leading to isotope fractionation does not follow pure first-order kinetics and therefore isotopic effects cannot be described with the classical equilibrium fractionation equations or with steady-state kinetic fractionation equations (also known as the Rayleigh equation).〔Mariotti A., J.C. Germon, P. Hubert, P. Kaiser, R. Letolle, A. Tardieux, P. Tardieux, (1981), Experimental determination of nitrogen kinetic isotope fractionation – Some principles – Illustration for the denitrification and nitrification processes, Plant and Soil 62(3), 413–430.〕 In these instances, the general equations for biochemical isotope kinetics (GEBIK) and the general equations for biochemical isotope fractionation (GEBIF) can be used.
The GEBIK and GEBIF equations are the most generalized approach to describe isotopic effects in any chemical, catalytic reaction and biochemical reactions because they can describe isotopic effects in equilibrium reactions, kinetic chemical reactions and kinetic biochemical reactions.〔Maggi F. and W. J. Riley, (2010), Mathematical treatment of isotopologue and isotopomer speciation and fractionation in biochemical kinetics, Geochim. Cosmochim. Acta, 〕 In the latter two cases, they can describe both stationary and non-stationary fractionation (i.e., variable and inverse fractionation). In general, isotopic effects depend on the number of reactants and on the number of combinations resulting from the number of substitutions in all reactants and products. Describing with accuracy isotopic effects, however, depends also on the specific rate law used to describe the chemical or biochemical reaction that produces isotopic effects. Normally, regardless of whether a reaction is purely chemical or whether it involves some enzyme of biological nature, the equations used to describe isotopic effects base on first-order kinetics. This approach systematically leads to isotopic effects that can be described by means of the Rayleigh equation. In this case, isotopic effects will always be expressed as a constant, hence will not be able to describe isotopic effects in reactions where fractionation and enrichment are variable or inverse during the course of a reaction. Most chemical reactions do not follow first-order kinetics; neither biochemical reactions can normally be described with first-order kinetics. To properly describe isotopic effects in chemical or biochemical reactions, different approaches must be employed such as the use of Michaelis–Menten reaction order (for chemical reactions) or coupled Michaelis–Menten and Monod reaction orders (for biochemical reactions). However, conversely to Michaelis–Menten kinetics, GEBIK and GEBIF equations are solved under the hypothesis of non-steady state. This characteristic allows GEBIK and GEBIF to capture ''transient'' isotopic effects.
==Mathematical description of transient kinetic isotope effects==
The GEBIK and GEBIF equations are introduced here below.
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