Stochastic modeling of gene expression, protein modification, and polymerization

TL;DR

This paper reviews minimal stochastic models for key cellular processes like gene expression, protein modification, and polymerization, highlighting analytic tools that offer efficient alternatives to simulations.

Contribution

It introduces and discusses analytic methods such as generating functions and eigenfunction expansions for solving stochastic models of cellular processes.

Findings

Analytic tools provide efficient solutions to stochastic models.

Methods extend to complex models beyond minimal cases.

Offers insights into fluctuations in cellular processes.

Abstract

Many fundamental cellular processes involve small numbers of molecules. When numbers are small, fluctuations dominate, and stochastic models, which account for these fluctuations, are required. In this chapter, we describe minimal stochastic models of three fundamental cellular processes: gene expression, protein modification, and polymerization. We introduce key analytic tools for solving each model, including the generating function, eigenfunction expansion, and operator methods, and we discuss how these tools are extended to more complicated models. These analytic tools provide an elegant, efficient, and often insightful alternative to stochastic simulation.