Signatures of combinatorial regulation in intrinsic biological noise

Gene expression is controlled by the action of transcription factors that bind to DNA and influence the rate at which a gene is transcribed. The quantitative mapping between the regulator concentrations and the output of the gene is known as the cis-regulatory input function (CRIF). Here, we show how the CRIF shapes the form of the joint probability distribution of molecular copy numbers of the regulators and the product of a gene. Namely, we derive a class of fluctuation-based relations that relate the moments of the distribution to the derivatives of the CRIF. These relations are useful because they enable statistics of naturally arising cell-to-cell variations in molecular copy numbers to substitute for traditional manipulations for probing regulatory mechanisms. We demonstrate that these relations can distinguish super- and subadditive gene regulatory scenarios (molecular analogs of AND and OR logic operations) in simulations that faithfully represent bacterial gene expression. Applications and extensions to other regulatory scenarios are discussed.