Molecular Distributions in Gene Regulatory Dynamics

TL;DR

This paper analytically computes the stationary molecular distributions in gene regulatory systems under stochastic noise, revealing key parameters influencing system behavior and offering an alternative to simulations.

Contribution

It provides an analytical framework for understanding stochastic gene regulation dynamics, linking deterministic and stochastic behaviors through key parameters.

Findings

Analytical expressions for stationary densities under noise

Identification of parameters controlling system states

Bursts and degradation noise are indistinguishable analytically

Abstract

We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in degradation rates arising from low numbers of molecules. We have compared our results with an analysis of the same model systems (either inducible or repressible operons) in the absence of any stochastic effects, and shown the correspondence between behaviour in the deterministic system and the stochastic analogs. We have identified key dimensionless parameters that control the appearance of one or two steady states in the deterministic case, or unimodal and bimodal densities in the stochastic systems, and detailed the analytic requirements for the occurrence of different behaviours. This approach provides, in some situations, an alternative to computationally intensive stochastic simulations. Our results indicate that, within the context of the simple models we have examined, bursting and degradation noise cannot be distinguished analytically when present alone.