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Postponing production exponentially enhances the molecular memory of a stochastic switch

Part of: Approximations and expansions Markov processes Physiological, cellular and medical topics

Published online by Cambridge University Press:  12 January 2021

PAVOL BOKES Open the ORCID record for PAVOL BOKES [Opens in a new window]
PAVOL BOKES*
Affiliation:
Comenius University, Bratislava, Slovakia email: [email protected]
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Abstract

Delayed production can substantially alter the qualitative behaviour of feedback systems. Motivated by stochastic mechanisms in gene expression, we consider a protein molecule which is produced in randomly timed bursts, requires an exponentially distributed time to activate and then partakes in positive regulation of its burst frequency. Asymptotically analysing the underlying master equation in the large-delay regime, we provide tractable approximations to time-dependent probability distributions of molecular copy numbers. Importantly, the presented analysis demonstrates that positive feedback systems with large production delays can constitute a stable toggle switch even if they operate with low copy numbers of active molecules.

Keywords

Stochastic gene expressionburstingproduction delaychemical master equationlinear noise approximationsystem-size expansionFokker–Planck equationWKB approximationlarge deviationsexponential asymptoticsasymptotic matching

MSC classification

Primary: 92C40: Biochemistry, molecular biology
Secondary: 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 60J28: Applications of continuous-time Markov processes on discrete state spaces
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 1 , February 2022 , pp. 182 - 199
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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