Cells use various regulatory motifs, including feedforward loops, to control the intrinsic noise that arises in gene expression at low copy numbers. Here we study one such system, which is broadly inspired by the interaction between an mRNA molecule and an antagonistic mi-croRNA molecule encoded by the same gene. The two reaction species are synchronously produced, individually degraded, and the second species (microRNA) exerts an antagonistic pressure on the first species (mRNA). Using linear-noise approximation, we show that the noise in the first species, which we quantify by the Fano factor, is sub-Poissonian, and exhibits a nonmonotonic response both to the species lifetime ratio and to the strength of the antagonistic interaction. Additionally, we use the Chemical Reaction Network Theory to prove that the first species distribution is Poissonian if the first species is much more stable than the second. Finally, we identify a special parametric regime, supporting a broad range of behaviour, in which the distribution can be analytically described in terms of the confluent hypergeometric limit function. We verify our analysis against large-scale kinetic Monte Carlo simulations. Our results indicate that, subject to specific physiological constraints, optimal parameter values can be found within the mRNA-microRNA motif that can benefit the cell by lowering the gene-expression noise.
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 theabsence 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 moderatelevels 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.
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