Theoretical study of the conditional non-monotonic off rate dependence of catalytic reaction rates in single enzymes in the presence of conformational fluctuations

Abstract

In ordinary Michaelis–Menten kinetics of enzyme-catalyzed reactions, the enzymatic velocity decreases with the increase in the off dissociation rate constant of the enzyme-substrate complex. In this work, we study the role of the off dissociation rate constants in single-molecule enzymatic reactions in which both the free enzyme and the enzyme-substrate complex undergo slow conformational fluctuations. By applying our theoretical formalism, we calculate the enzymatic velocity and show that there can be an increase in the reaction velocity with the off rate constant dependence which is not very intuitive. From our analytical calculations, we can establish a region of the parameter space and subsequently explore a range of substrate concentration where the enzymatic velocity is accelerated with an increase in the off rate constant. Further, we study the role of the substrate unbinding rate constants on the randomness parameter, which is a measure of the dynamic disorder present in the system.