Noise-induced mixing and multimodality in reaction networks

Tomislav Plesa, Radek Erban, Hans G Othmer

Research output: Contribution to journalArticle

Abstract

We analyse a class of chemical reaction networks under mass-action kinetics involving multiple time scales, whose deterministic and stochastic models display qualitative differences. The networks are inspired by gene-regulatory networks and consist of a slow subnetwork, describing conversions among the different gene states, and fast subnetworks, describing biochemical interactions involving the gene products. We show that the long-term dynamics of such networks can consist of a unique attractor at the deterministic level (unistability), while the long-term probability distribution at the stochastic level may display multiple maxima (multimodality). The dynamical differences stem from a phenomenon we call noise-induced mixing, whereby the probability distribution of the gene products is a linear combination of the probability distributions of the fast subnetworks which are 'mixed' by the slow subnetworks. The results are applied in the context of systems biology, where noise-induced mixing is shown to play a biochemically important role, producing phenomena such as stochastic multimodality and oscillations.

Original languageEnglish (US)
Pages (from-to)887-911
Number of pages25
JournalEuropean Journal of Applied Mathematics
Volume30
Issue number5
DOIs
StatePublished - Oct 1 2019

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Reaction Network
Multimodality
Probability Distribution
Genes
Probability distributions
Gene
Chemical Reaction Networks
Multiple Time Scales
Gene Regulatory Network
Deterministic Model
Systems Biology
Stochastic Model
Linear Combination
Attractor
Stochastic models
Kinetics
Oscillation
Chemical reactions
Interaction

Keywords

  • Chemical reaction networks
  • gene-regulatory networks
  • perturbation theory
  • stochastic dynamics

Cite this

Noise-induced mixing and multimodality in reaction networks. / Plesa, Tomislav; Erban, Radek; Othmer, Hans G.

In: European Journal of Applied Mathematics, Vol. 30, No. 5, 01.10.2019, p. 887-911.

Research output: Contribution to journalArticle

Plesa, Tomislav ; Erban, Radek ; Othmer, Hans G. / Noise-induced mixing and multimodality in reaction networks. In: European Journal of Applied Mathematics. 2019 ; Vol. 30, No. 5. pp. 887-911.
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