  Heterogeneity in gene expression across isogenic cell populations can give
rise to phenotypic diversity, even when cells are in homogenous environments.
This diversity arises from the discrete, stochastic nature of biochemical
reactions, which naturally arise due to the very small numbers of genes, RNA,
or protein molecules in single cells. Modern measurements of single
biomolecules have created a vast wealth of information about the fluctuations
of these molecules, but a quantitative understanding of these complex,
stochastic systems requires precise computational tools. In this article, we
present modern tools necessary to model variability in biological system and to
compare model results to experimental data. We review the Chemical Master
Equation and approaches to solve for probability distributions of discrete
numbers of biomolecules. We discuss how to fit probability distributions to
single-cell data using likelihood based approaches. Finally, we provide
examples of fitting discrete stochastic models to single-molecule fluorescent
in-situ hybridization data that quantifies RNA levels across populations of
cells in bacteria and yeast.
