Exact protein distributions for stochastic models of gene expression using partitioning of Poisson processes

TL;DR

This paper introduces a novel method leveraging Poisson process partitioning to derive exact analytical protein distributions in stochastic gene expression models, enabling precise quantification of cellular noise and phenotypic variability.

Contribution

It presents a new mapping technique that simplifies the analysis of complex gene expression models, providing exact solutions for protein distributions including regulatory effects.

Findings

Exact steady-state and time-dependent distributions derived for basic gene expression models

Extension of the method to models with post-transcriptional regulation

Applicable to a wide range of stochastic gene expression models

Abstract

Stochasticity in gene expression gives rise to fluctuations in protein levels across a population of genetically identical cells. Such fluctuations can lead to phenotypic variation in clonal populations, hence there is considerable interest in quantifying noise in gene expression using stochastic models. However, obtaining exact analytical results for protein distributions has been an intractable task for all but the simplest models. Here, we invoke the partitioning property of Poisson processes to develop a mapping that significantly simplifies the analysis of stochastic models of gene expression. The mapping leads to exact protein distributions using results for mRNA distributions in models with promoter-based regulation. Using this approach, we derive exact analytical results for steady-state and time-dependent distributions for the basic 2-stage model of gene expression. Furthermore, we show how the mapping leads to exact protein distributions for extensions of the basic model that include the effects of post-transcriptional and post-translational regulation. The approach developed in this work is widely applicable and can contribute to a quantitative understanding of stochasticity in gene expression and its regulation.