Dynamic Disorder-Driven Substrate Inhibition and Bistability in a Simple Enzymatic Reaction

Conformations and catalytic rates of enzymes (biological catalysts) fluctuate over a wide range of time scales. Recent experimental and theoretical investigations demonstrated case studies where the enzymatic catalysis rate follows the Michaelis-Menten (MM) rate law despite molecular fluctuations. In this paper, we investigate deviations from MM law and their effects oil the dynamical behavior of the enzymatic network. We consider a simple kinetic scheme for a single substrate enzymatic reaction in which the product release step is treated explicitly. We examine how conformational fluctuations affect the underlying rate law ill the quasi-static limit when conformational dynamics is very slow in one of the states. Our numerical results and analytically solvable model indicate that slow conformational fluctuations of the enzyme substrate complex lead to non-MM behavior, substrate inhibition, and possible bistability of the reaction network.