The expression of kinetic isotope effects during the time course of enzyme-catalyzed reactions

Abstract

Because of the progressive isotopic enrichment of substrate during the time course of an enzymatic reaction, the kinetic isotope effect calculated from the enrichment in a substrate (the preferred measurement for isotope effects of less than 1.05) or the depletion in a product (the more common measurement) varies with time and thus must be corrected. Bigeleisen and Wolfsberg ( Adv. Phys. Chem. 1, 15–76, 1958) derived a correctional equation for irreversible first-order uncatalyzed reactions, whose validity for an enzyme-catalyzed reaction is examined in this work. The primary finding is that, if significant depletion of a second substrate occurs during the course of an enzymatic reaction, then the expression of an isotope effect will change extensively in a manner which is not anticipated by the correctional equation. This was demonstrated in a single time-course assay of the oxidation of tritiated NADH by pyruvate beef heart lactate dehydrogenase, in which the corrected isotope effect varied from 1.39 at the start of the reaction to 1.8 at 95% reaction. High concentrations of pyruvate inhibit the isotope effect with an apparent K I of 358 ± 24 μ m. The inhibition arises because pyruvate is the second substrate to bind and its value agrees with the apparent K m of 379 ± 88 μ m, as expected. Separate tritium isotope effects extrapolate to 2.64 ± 0.05 at zero pyruvate and 1.01 ± 0.05 at infinite pyruvate. When the concentration of pyruvate was well in excess of that of NADH, so as to minimize the effect of depletion of pyruvate, the correctional equation was found to be valid for up to 85% of the oxidation of tritiated NADH. An analysis of standard errors over the complete time course shows a minimum at 50% of reaction and maxima near 0 and 100%. Hence, the precision of competitive isotope effects is greatly increased by choosing conditions under which the correctional equation applies and allowing the reaction to proceed halfway, avoiding the more common practice of restricting measurements to the period of initial velocity. Computer simulations suggest that the correction may remain a reasonable approximation for up to 50% of an approach to equilibrium in reactions more reversible than that of lactate dehydrogenase.