Reaction-Path Statistical Mechanics of Enzymatic Kinetics

TL;DR

This paper develops a reaction-path statistical mechanics framework to analyze single-molecule enzymatic kinetics, revealing phase-separation-like behavior in unbinding events through large deviation theory.

Contribution

It introduces a novel nonequilibrium ensemble based on reaction path entropy to quantify enzyme kinetics without explicit boundary conditions.

Findings

Identifies bimodal unbinding behavior at finite timescales.

Demonstrates phase-separation-like phenomena in enzyme unbinding.

Provides a method to calculate enzymatic reaction timescales without boundary conditions.

Abstract

We introduce a reaction-path statistical mechanics formalism based on the principle of large deviations to quantify the kinetics of single-molecule enzymatic reaction processes under the Michaelis-Menten mechanism, which exemplifies an out-of-equilibrium process in the living system. Our theoretical approach begins with the principle of equal a priori probabilities and defines the reaction path entropy to construct a new nonequilibrium ensemble as a collection of possible chemical reaction paths. As a result, we evaluate a variety of path-based partition functions and free energies using the formalism of statistical mechanics. They allow us to calculate the timescales of a given enzymatic reaction, even in the absence of an explicit boundary condition that is necessary for the equilibrium ensemble. We also consider the large deviation theory under a closed-boundary condition of the fixed observation time to quantify the enzyme-substrate unbinding rates. The result demonstrates the presence of a phase-separation-like, bimodal behavior in unbinding events at a finite timescale, and the behavior vanishes as its rate function converges to a single phase in the long-time limit.