Solving stochastic gene expression models using queueing theory: a tutorial review

TL;DR

This paper reviews an alternative queueing theory approach to modeling stochastic gene expression, offering analytical solutions and bounds that could solve complex models difficult to address with traditional methods.

Contribution

It introduces queueing theory as a novel analytical framework for stochastic gene expression, providing new formulas and bounds for model distributions.

Findings

Analytical expressions for stationary and non-stationary distributions of mRNA/protein levels.

Bounds on the Fano factor for gene expression models.

Queueing theory can solve complex models previously intractable.

Abstract

Stochastic models of gene expression are typically formulated using the chemical master equation, which can be solved exactly or approximately using a repertoire of analytical methods. Here, we provide a tutorial review of an alternative approach based on queueing theory that has rarely been used in the literature of gene expression. We discuss the interpretation of six types of infinite server queues from the angle of stochastic single-cell biology and provide analytical expressions for the stationary and non-stationary distributions and/or moments of mRNA/protein numbers, and bounds on the Fano factor. This approach may enable the solution of complex models which have hitherto evaded analytical solution.