Noise-induced Mixing and Multimodality in Reaction Networks

TL;DR

This paper investigates how noise-induced mixing in multiscale chemical reaction networks can lead to multimodal distributions despite deterministic unistability, revealing important biological implications.

Contribution

It introduces the concept of noise-induced mixing in multiscale reaction networks and demonstrates its role in generating stochastic multimodality and oscillations.

Findings

Deterministic models show unistability, stochastic models can be multimodal.

Noise-induced mixing causes probability distributions to be linear combinations of subnetworks.

Biochemical phenomena like stochastic oscillations are explained by this mechanism.

Abstract

We analyze a class of chemical reaction networks under mass-action kinetics and 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 novel 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.