Noise-induced mixing and multimodality in reaction networks

Tomislav Plesa, Radek Erban, Hans G. Othmer

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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
Issue number5
StatePublished - Oct 1 2019

Bibliographical note

Funding Information:
This work was supported by NIH Grant number 29123 and a Visiting Research Fellowship from Merton College, Oxford, awarded to Hans Othmer. Radek Erban would also like to thank the Royal Society for a University Research Fellowship.

Publisher Copyright:
© Cambridge University Press 2018.


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


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