Multiple Isotope Effects, Different Steps

It is not always possible to determine intrinsic isotope effects. However, other useful information about the reaction can still be obtained. Above we assumed a single rate determining step sensitive to each isotope substitution. More frequently, however, the isotope sensitivity is found in different steps. Studies with multiple isotope effects can be used to determine the sequence of steps. To illustrate, a more complicated reaction scheme is needed  

As a first example we discuss a mechanism in which the formation of the enzyme-intermediate complex, El, is sensitive to hydrogen isotopic substitution, while the next step characterized by rate constants ks and k6 exhibits a carbon kinetic isotope effect. Expressions for the three kinetic isotope effects that can be determined experimentally are  

A second example (where the step sensitive to carbon isotope substitution precedes the one sensitive to hydrogen substitution) can be treated similarly. If we assume that the conversion of ES to El in scheme 11.49 (the step involving k3 and k4) is characterized by a carbon KIE, while the following step (El to EP) exhibits an hydrogen KIE, the equations corresponding to Equations 11.50 and 11.51 are  

Equations 11.51 and 11.53 hold for even more complicated mechanisms even though more rate constants enter Equations 11.50 and 11.52. The isotope sensitive steps are not necessarily consecutive. Application of Equations 11.50 through 11.53 is illustrated later in this chapter. 

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Note that the weighting factors correspond to the common H-isotopomer in the H/D and H/T isotope effects, and expressions for w are different for the serial and parallel cases. The equations in Eq. (11.11), developed by Northrop [49, 50], have proved to be useful in obtaining intrinsic kinetic isotope effects in enzymatic reactions with multiple rate-limiting steps that partially mask the full effect of an isotope-sensitive step. 

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