Modeling Stochastic Gene Expression in Growing Cells

Abstract

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, mRNA degradation etc. are stochastic processes. The flucatuations become important when the cellular copy numbers of the relevant molecules (mRNA or proteins) are low. We investigate different sources of noise in gene expression by considering several models in which protein synthesis and partitioning of proteins during cell dividision are described in either a stochastic or a deterministic way. 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 compuationally 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 diminshed 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 strength. The method is general and can also be applied to other cases where synthesis of proteins are regulated and an appropriate analytical description is difficult to achieve.