Eliminating fast reactions in stochastic simulations of biochemical networks: a bistable genetic switch

TL;DR

This paper investigates how to effectively simplify stochastic biochemical network simulations by removing fast reactions, focusing on a bistable genetic switch, and highlights which reactions can be safely eliminated without losing accuracy.

Contribution

It evaluates coarse-graining strategies in stochastic simulations of a bistable genetic switch, identifying which reactions can be safely removed and emphasizing the importance of using the chemical master equation.

Findings

Protein-protein interactions can be safely eliminated.

Protein-DNA interactions should not be eliminated.

Using the chemical master equation is crucial for accurate coarse-graining.

Abstract

In many stochastic simulations of biochemical reaction networks, it is desirable to ``coarse-grain'' the reaction set, removing fast reactions while retaining the correct system dynamics. Various coarse-graining methods have been proposed, but it remains unclear which methods are reliable and which reactions can safely be eliminated. We address these issues for a model gene regulatory network that is particularly sensitive to dynamical fluctuations: a bistable genetic switch. We remove protein-DNA and/or protein-protein association-dissociation reactions from the reaction set, using various coarse-graining strategies. We determine the effects on the steady-state probability distribution function and on the rate of fluctuation-driven switch flipping transitions. We find that protein-protein interactions may be safely eliminated from the reaction set, but protein-DNA interactions may not. We also find that it is important to use the chemical master equation rather than macroscopic rate equations to compute effective propensity functions for the coarse-grained reactions.