Reversible Reaction at the Active Site

We start with the case when chemical conversion at the active site is reversible. By assuming the initial product concentration to be negligible we may neglect the reversibility of product binding  

Using the steady-state approximation for the concentrations of complexes ES and EP  

Taking ratios of the apparent rate constants for light and heavy species we obtain  

As before, the assumption that binding processes do not introduce appreciable isotope fractionation, i.e., Hki = Hk2 = Hks, allows the simplification of Equation 11.35  

Equation 11.36 recognizes that Hk3/Hk4 corresponds to the equilibrium isotope effect, hK3/4 for the step containing rate constants k3 and k4. The rate ratio k4/k.5 is the commitment for catalysis for the reaction that proceeds from products to substrates, and therefore is called the reverse commitment to catalysis, Cr. Also cf = k3/k2 is the forward commitment to catalysis. Since we have assumed that these steps are the only isotope sensitive ones, HK3/4 corresponds to the overall equilibrium isotope effect, HK. 

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