The Annals of Applied Probability

Stochastically-induced bistability in chemical reaction systems

John K. McSweeney and Lea Popovic

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We study a stochastic two-species chemical reaction system with two mechanisms. One mechanism consists of chemical interactions which govern the overall drift of species amounts in the system; the other mechanism consists of resampling, branching or splitting which makes unbiased perturbative changes to species amounts. Our results show that in a system with a large but bounded capacity, certain combinations of these two types of interactions can lead to stochastically-induced bistability. Depending on the relative magnitudes of the rates of these two sets of interactions, bistability can occur in two distinct ways with different dynamical signatures.

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Ann. Appl. Probab., Volume 24, Number 3 (2014), 1226-1268.

First available in Project Euclid: 23 April 2014

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Primary: 60J27: Continuous-time Markov processes on discrete state spaces 60J28: Applications of continuous-time Markov processes on discrete state spaces 60J60: Diffusion processes [See also 58J65] 60F10: Large deviations 60F17: Functional limit theorems; invariance principles 92C45: Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) [See also 80A30] 92C37: Cell biology 80A30: Chemical kinetics [See also 76V05, 92C45, 92E20]

Reaction networks chemical reactions resampling bistability Markov chains large deviations stochastic switching scaling limits


McSweeney, John K.; Popovic, Lea. Stochastically-induced bistability in chemical reaction systems. Ann. Appl. Probab. 24 (2014), no. 3, 1226--1268. doi:10.1214/13-AAP946.

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