Title: Initial condition issue in the Turnover time Statistics of Enzyme Molecules at Mesoscopic Concentrations
Author: In-Chun Jeong
In this study we investigate the dependence of a system’s enzymatic turnover time distribution on the number of enzymes and on the microscopic reaction dynamics of the enzyme-substrate complex. Recently it has come to light that enzyme kinetics, for example, the mean catalytic rate of a system of enzymes, at physiologically relevant mesoscopic concentrations does not satisfy the Michaelis-Menten (MM) equation, even though the individual enzyme reaction obeys the MM mechanism. However, this case can only occur at the first enzymatic turnover event in an N-enzyme system, under which all given enzymes synchronously start catalysis at time 0, meaning the system is not in the steady-state condition. Here we modify the initial condition and define the mean enzymatic turnover time, satisfying the MM equation at any concentration of enzymes in the steady-state, as long as each catalytic reaction occurs in a manner consistent with the MM mechanism. We confirm our theory through stochastic simulation results and a comparison between theoretical and experimental data.