Quantifying the effect of extrinsic factors in noisy gene expression

We present a maximum entropy framework to separate the intrinsic and the extrinsic contributions to noisy gene expression solely from the profile of expression. We express the experimentally accessible histogram of mRNA copy numbers by accounting for possible variations in global extrinsic factors. The distribution of extrinsic factors is estomated using the maximum entropy principle. Our results show that extrinsic factors quantitatively and qualitatively affect the histogram. Specifically, we suggest that the cell to cell variation in extrinsic factors accounts for the wider that Poisson distribution of mRNA copy numbers. We successfully test our framework on a numerical simulation of a simple gene expression scheme that accounts for the variation in extrinsic factors. We also make falsifiable predictions, some of which are tested on previous experiments in E. coli while others need verification. Application of the current method to understanding noise in mRNA production in eukaryotes and protein production is also discussed.