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We present a stochastic model motivatedВ by gene expression which incorporates unspecific interactionsВ between proteins and binding sites. WeВ focus on characterizing the distribution of free (i.e.В unbound) protein molecules in a cell. Although itВ cannot be expressed in a closed form, we presentВ three different approaches to obtain it: stochastic simulationВ algorithms, system of ODEs and quasi-steadystateВ solution. Additionally we use a large-system-sizeВ scaling to derive statistical measures of approximateВ distribution of the amount of free protein, such as theВ Fano factor. Intriguingly, we report that while in the absence of or in the excess of decoy binding sites theВ Fano factor is equal to one (suggestive of PoissonianВ fluctuations), in the intermediate regimes of moderateВ levels of binding sites the Fano factor is greater thanВ one (suggestive of super-Poissonian fluctuations). WeВ support and illustrate all of our results with numericalВ simulations.

Non-monotonicity of Fano factor in a stochastic model for protein expression with sequesterisation at decoy binding sites