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Updated: Jun 18, 2026

The Use of Chemostats in Microbial Systems Biology
Published on: October 14, 2013
Thermodynamic limit of a nonequilibrium steady state: Maxwell-type construction for a bistable biochemical system
1School of Mathematical Sciences and Centre for Computational Systems Biology, Fudan University, Shanghai 200433, People's Republic of China. gehao@fudan.edu.cn
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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