Analysis of noise-induced bistability in Michaelis Menten single-step enzymatic cycle

TL;DR

This paper investigates noise-induced bistability in a Michaelis Menten enzymatic cycle, analyzing conditions for bimodality and how coupling with other reactions can induce bistability in biological systems.

Contribution

It provides a detailed comparison of discrete and continuous models for enzymatic cycles and identifies conditions under which stochastic bistability can occur.

Findings

Bimodality does not occur in the basic enzymatic cycle model.

Coupling with enzyme production can induce bistability under specific conditions.

System size influences the emergence of stochastic bistability.

Abstract

In this paper we study noise-induced bistability in a specific circuit with many biological implications, namely a single-step enzymatic cycle described by Michaelis Menten equations with quasi-steady state assumption. We study the system both with a Master Equation formalism, and with the Fokker-Planck continuous approximation, characterizing the conditions in which the continuous approach is a good approximation of the exact discrete model. An analysis of the stationary distribution in both cases shows that bimodality can not occur in such a system. We discuss which additional requirements can generate stochastic bimodality, by coupling the system with a chemical reaction involving enzyme production and turnover. This extended system shows a bistable behaviour only in specific parameter windows depending on the number of molecules involved, providing hints about which should be a feasible system size in order that such a phenomenon could be exploited in real biological systems.