Noise-induced mixing and multimodality in reaction networks

Journal article

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.

Authors: Plesa, T; Erban, R; Othmer, H

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: European Journal of Applied Mathematics
• Volume: 30
• Issue: 5
• Pages: 887-911
• Publication date: 2018-09-18
• Acceptance date: 2018-07-25
• DOI: 10.1017/S0956792518000517
• EISSN: 1469-4425
• ISSN: 0956-7925
• Keywords: perturbation theory; stochastic dynamics; gene-regulatory networks; chemical reaction networks