Time-dependent corrections to effective rate and event statistics in Michaelis-Menten kinetics

TL;DR

This paper extends the geometric phase concept to noncyclic stochastic kinetics, revealing how time-dependent parameter changes cause corrections to Michaelis-Menten law, with implications for biological reaction modeling.

Contribution

It introduces a noncyclic geometric phase in stochastic kinetics and demonstrates its impact on reaction rates under time-varying conditions.

Findings

Noncyclic geometric phase causes corrections to Michaelis-Menten law.

Time-dependent parameters significantly alter reaction kinetics.

Geometric correction affects biological reaction outcomes.

Abstract

We generalize the concept of the geometric phase in stochastic kinetics to a noncyclic evolution. Its application is demonstrated on kinetics of the Michaelis-Menten reaction. It is shown that the nonperiodic geometric phase is responsible for the correction to the Michaelis-Menten law when parameters, such as a substrate concentration, are changing with time. We apply these ideas to a model of chemical reactions in a bacterial culture of a growing size, where the geometric correction qualitatively changes the outcome of the reaction kinetics.