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

Hao Ge and Hong Qian
Phys. Rev. Lett. 103, 148103 – Published 2 October 2009

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 an 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 emergent stochastic concepts.

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  • Received 14 April 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.148103

©2009 American Physical Society

Authors & Affiliations

Hao Ge1,* and Hong Qian2,1,†

  • 1School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai 200433, People’s Republic of China
  • 2Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA

  • *gehao@fudan.edu.cn
  • qian@amath.washington.edu

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Vol. 103, Iss. 14 — 2 October 2009

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