Thermodynamic Limit of a Nonequilibrium Steady-State: Maxwell-Type Construction for a Bistable Biochemical System

TL;DR

This paper investigates the thermodynamic limit of a bistable biochemical system, revealing a Maxwell-like construction that determines the dominant steady state and highlights the stochastic nature of stability in biological contexts.

Contribution

It introduces a Maxwell-type construction for selecting the stable steady state in a nonequilibrium biochemical system using a chemical master equation approach.

Findings

Bistability disappears in the stochastic model when fluctuations are sufficiently low but not negligible.

A Maxwell-like construction determines the dominant steady state in the thermodynamic limit.

Stability concepts in cell biology are fundamentally stochastic, not purely deterministic.

Abstract

We show that the thermodynamic limit of a bistable phosphorylation-dephosphorylation cycle has a selection rule for the "more stable" macroscopic steady state. The analysis is akin to the Maxwell construction. Based on the chemical master equation approach, it is shown that, except at a critical point, bistability disappears in the stochastic model when fluctuation is sufficiently low but unneglectable. Onsager's Gaussian fluctuation theory applies to the unique macroscopic steady state. With initial state in the basin of attraction of the "less stable" steady state, the deterministic dynamics obtained by the Law of Mass Action is a metastable phenomenon. Stability and robustness in cell biology are stochastic concepts.