In this work we present the mathematical formulation of a Master equation that pertains to a single cell and takes into account the major sources of heterogeneity, namely stochasticity in reaction, division, and DNA duplication. The formulation also takes into account cell growth and respects the discrete nature of the molecular contents. We further extend the framework to cell populations and develop Monte Carlo algorithms for the simulation of the stochastic processes considered here. Using this approach we demonstrate the effect of each source of heterogeneity on the overall phenotypic variability for the two-promoter system used experimentally by Elowitz et al. (2002) to quantify intrinsic versus extrinsic noise.
Elowitz, M. B., A. J. Levine, E. D. Siggia and P. S. Swain (2002). "Stochastic gene expression in a single cell." Science 297 (5584): 1183-1186