Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations

Abstract

The chemical master equation and the stochastic simulation algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled for through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise in a growing population. We find that the solution of the chemical master equation - including static extrinsic noise - exactly agrees with the one of the agent-based formulation when a simple condition on the network's topology is met. We illustrate this result for a range of common gene expression networks. When these conditions are not met, we demonstrate using analytical solutions of the agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the effective master equation. Surprisingly, the latter distorts total noise in gene regulatory networks by at most 8% independently of network parameters. Our results highlight the accuracy of extrinsic noise modelling within the chemical master equation framework.

Poisson representation: a bridge between discrete and continuous models of stochastic gene regulatory networks

“…Interface 20: 20230467 rate. The model couples gene expression dynamics to cell size dynamics and cell cycle events [62][63][64][65][66], and is described as follows (see figure 2e for an illustration).…”