Modeling stochastic gene expression in growing cells

Gene expression is an inherently noisy process. Fluctuations arise at many points in the expression of a gene, as all the salient reactions such as transcription, translation, and mRNA degradation are stochastic processes. The fluctuations become important when the cellular copy numbers of the relevant molecules (mRNA or proteins) are low. For regulated genes, a computational complication arises from the fact that protein synthesis rates depend on the concentrations of the transcription factors that regulate the corresponding genes. Because of the growing cell volume, such rates are effectively time-dependent. We deal with the effects of volume growth computationally using a rather simple method: the growth of the cell volume is incorporated in our simulations by stochastically adding small volume elements to the cell volume. As an application of this method we study a gene circuit with positive autoregulation that exhibits bistability. We show how the region of bistability becomes diminished by increasing the effect of noise via a reduced copy number of the regulatory protein. Cell volume determines the region of bistability for different noise strengths. The method is general and can also be applied to other cases where synthesis rates of proteins are regulated and an appropriate analytical description is difficult to achieve.