Noise-induced multistability in chemical systems: Discrete vs Continuum modeling

TL;DR

This paper compares discrete and continuum models of noisy chemical systems, revealing that the continuum approximation can miss noise-induced multistability predicted by the discrete approach, especially at small system sizes.

Contribution

It demonstrates that the chemical Fokker-Planck equation may fail to capture noise-induced multistability present in the chemical master equation, highlighting limitations of continuum models.

Findings

CME predicts noise-induced multistability at small system sizes.

CFPE fails to capture multistability, remaining unimodal.

Discrepancies depend on system size and model approximation.

Abstract

The noisy dynamics of chemical systems is commonly studied using either the chemical master equation (CME) or the chemical Fokker-Planck equation (CFPE). The latter is a continuum approximation of the discrete CME approach. We here show that the CFPE may fail to capture the CME's prediction of noise-induced multistability. In particular we find a simple chemical system for which the CME's marginal probability distribution changes from unimodal to multimodal as the system-size decreases below a critical value, while the CFPE's marginal probability distribution is unimodal for all physically meaningful system sizes.