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We present a maximum entropy framework to separate intrinsic and extrinsiccontributions to noisy gene expression solely from the profile of expression.We express the experimentally accessible probability distribution of the copynumber of the gene product (mRNA or protein) by accounting for possiblevariations in extrinsic factors. The distribution of extrinsic factors isestimated using the maximum entropy principle. Our results show that extrinsicfactors qualitatively and quantitatively affect the probability distribution ofthe gene product. We work out, in detail, the transcription of mRNA from aconstitutively expressed promoter in {\it E. coli}. We suggest that thevariation in extrinsic factors may account for the observed {\it wider thanPoisson} distribution of mRNA copy numbers. We successfully test our frameworkon a numerical simulation of a simple gene expression scheme that accounts forthe variation in extrinsic factors. We also make falsifiable predictions, someof which are tested on previous experiments in {\it E. coli} while others needverification. Application of the current framework to more complex situationsis also discussed.

Quantifying extrinsic noise in gene expression using the maximum entropy framework