The Annals of Applied Probability

Stochastically-induced bistability in chemical reaction systems

John K. McSweeney and Lea Popovic

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 23 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1398258100

Digital Object Identifier
doi:10.1214/13-AAP946

Mathematical Reviews number (MathSciNet)
MR3199985

Zentralblatt MATH identifier
1308.60095

Subjects
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]

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

Citation

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. https://projecteuclid.org/euclid.aoap/1398258100


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