Nonequilibrium phase transition in a mesoscopic biochemical system: From stochastic to nonlinear dynamics and beyond

TL;DR

This paper develops a mathematical framework to analyze nonequilibrium phase transitions in biochemical systems, revealing characteristics similar to equilibrium phase transitions and connecting stochastic and deterministic dynamics across different time scales.

Contribution

It introduces a rigorous large deviation-based approach to study phase transitions in biochemical systems, linking stochastic and nonlinear dynamics with biological processes.

Findings

Identification of a nonequilibrium steady-state phase transition with classic features

Matching of bifurcation cusp with tricritical point

Three distinct time scales in molecular signaling, network dynamics, and cellular evolution

Abstract

A rigorous mathematical framework for analyzing the chemical master equation (CME) with bistability, based on the theory of large deviation, is proposed. Using a simple phosphorylation-dephosphorylation cycle with feedback as an example, we show that a nonequilibrium steady-state (NESS) phase transition occurs in the system which has all the characteristics of classic equilibrium phase transition: Maxwell construction, discontinuous fraction of phosphorylation as a function of the kinase activity, and Lee-Yang's zero for the generating function. The cusp in nonlinear bifurcation theory matches the tricritical point of the phase transition. The mathematical analysis suggests three distinct time scales, and related mathematical descriptions, of (i) molecular signaling, (ii) biochemical network dynamics, and (iii) cellular evolution. The (i) and (iii) are stochastic while (ii) is deterministic.