Effective rate constants and general isotope effect equations for steady state enzymatic reactions with multiple isotope-sensitive steps

Abstract

In the theoretical treatment of apparent isotope effects corresponding to one-step perturbations, the nonisotopic rate constants are commonly collected as commitments. Such a collection is not possible where a multistep perturbation occurs. However, the multistep perturbations can be treated if the nonisotopic rate constants are collected as effective rate constants, each of which is defined as the rate constant of a kinetic step times the overall equilibrium constant of the steps preceding that kinetic step. If all of the steps are isotope-sensitive, the isotopic equation, written as a ratio of the apparent isotope effect to the overall rate, will be simply a sum of the ratios of intrinsic isotope effect to effective rate constant from all of the steps. Isotopic equations for reactions in which not all of the steps are isotope-sensitive are then obtained by setting the intrinsic kinetic isotope effects and the equilibrium isotope effects of the isotope-insensitive steps to equal one. Designed for treatment of isotope effects derived from single isotopic labelings, the method can also be extended to isotope effects from multiple isotopic labelings. Perturbation of kinetic barriers by equilibrium isotope effects is also discussed.