Stochastic Modeling of Single Molecule Michaelis Menten Kinetics

TL;DR

This paper introduces a stochastic formalism for modeling single enzyme kinetics on a 2D lattice, capturing substrate diffusion and reaction dynamics, and explaining experimental turnover time distributions.

Contribution

It presents a novel decoupled stochastic model that accurately reproduces turnover time distributions in single enzyme systems with disorder and diffusion effects.

Findings

Model reproduces Monte Carlo simulation results

Explains experimental turnover time distributions

Applicable to normal and anomalous diffusion

Abstract

We develop an general formalism of single enzyme kinetics in two dimension where substrates diffuse stochastically on a square lattice in presence of disorder. The dynamics of the model could be decoupled effectively to two stochastic processes, (a) the substrate arrives at the enzyme site in intervals which fluctuates in time and (b) the enzymatic reaction takes place at that site stochastically. We argue that distribution of arrival time is a two parameter function specified by the substrate and the disorder densities, and that it correctly reproduce the distribution of turnover time obtained from Monte-Carlo simulations of single enzyme kinetics in two dimension, both in absence and presence of disorder. The decoupled dynamics model is simple to implement and generic enough to describe both normal and anomalous diffusion of substrates. It also suggests that the diffusion of substrates in the single enzyme systems could explain the different distributions of turnover time observed in recent experiments.