Noise-induced multistability in chemical systems: Discrete versus continuum modeling

Area of Science:

• Chemical kinetics
• Stochastic processes
• Computational chemistry

Background:

• Noisy chemical dynamics are often modeled using the chemical master equation (CME) or the chemical Fokker-Planck equation (CFPE).
• The CFPE is a continuum approximation of the discrete CME.
• Recent studies suggested the CFPE could capture noise-induced multistability, a phenomenon where system behavior shifts with decreasing size.

Purpose of the Study:

• To investigate the limitations of the chemical Fokker-Planck equation (CFPE) in capturing noise-induced multistability.
• To identify specific chemical systems where the CFPE's predictions diverge from the chemical master equation (CME).

Main Methods:

• Analysis of stochastic chemical kinetics using both the chemical master equation (CME) and the chemical Fokker-Planck equation (CFPE).
• Comparison of predicted probability distributions for simple chemical systems across different system sizes.

Main Results:

• The chemical Fokker-Planck equation (CFPE) does not universally capture noise-induced multistability predicted by the chemical master equation (CME).
• Specific simple chemical systems were identified where the CME predicts noise-induced multistability, but the CFPE predicts monostability across all system sizes.

Conclusions:

• The CFPE's continuum approximation can lead to inaccuracies in predicting stochastic phenomena like noise-induced multistability.
• Careful consideration of model approximations is crucial when studying noisy chemical dynamics, especially for systems exhibiting critical transitions.