KIEs of Enzyme Catalyzed Reactions by Isotope Perturbation

The protocol described in Section 7.1.2 involves isotopic competition, but with the different isotopomers held in separate containers. Equations 7.10 to 7.13 apply equally well to a type of competition experiment known in biochemistry as the perturbation method for determining KIE s of reversible enzyme catalyzed reactions. The perturbation method differs from simultaneous non-competitive measurements in several important ways. One begins by mixing equilibrium concentrations of substrate and product but with one component (substrate or product) at a different isotopic composition than the other. Thus, the mixture is in chemical, but not isotopic equilibrium. At this stage no enzyme is present and the interconversion is 

In the discussions above we assumed the isotopomers being compared were in different containers. However, separate determinations of rate constants are also possible in a common container in the same solution. This obviously eliminates 

A slightly different example is the separate determination of rates of reaction of nC and 14C labeled methyl iodide with N,N-dimcthyl-/ -toluidine as illustrated in Fig. 7.3. Again the method takes advantage of the convenience of radiochemical analysis. If, as likely, the KIE of interest is ki2/ki4, it can be obtained to sufficiently good approximation by applying a modified Swain-Schaad rule, ln[ki2/ki4]/ln[kn/ki4] = [(12/14)/(11/14)]1/2 obtained from the law of the geometric mean (see Section 10.5). 

The most frequently used type of competitive study measures relative rates with both isotopomers present in the same solution. Instead of measuring individual 

Equations 7.17 and 7.18 show that KIEs can be obtained by comparing isotopic ratios of reactant or product with the initial isotope ratio of reactant as the reaction progresses. 

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