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

Abstract

We present a stochastic model motivated by gene expression which incorporates unspecific interactions between proteins and binding sites. We focus on characterizing the distribution of free (i.e. unbound) protein molecules in a cell. Although it cannot be expressed in a closed form, we present three different approaches to obtain it: stochastic simulation algorithms, system of ODEs and quasi-steadystate solution. Additionally we use a large-system-size scaling to derive statistical measures of approximate distribution of the amount of free protein, such as the Fano factor. Intriguingly, we report that while in the absence of or in the excess of decoy binding sites the Fano factor is equal to one (suggestive of Poissonian fluctuations), in the intermediate regimes of moderate levels of binding sites the Fano factor is greater than one (suggestive of super-Poissonian fluctuations). We support and illustrate all of our results with numerical simulations.