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.
Bibliographical noteFunding 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.
© Cambridge University Press 2018.
- Chemical reaction networks
- gene-regulatory networks
- perturbation theory
- stochastic dynamics