Self-regulation in a stochastic model of chemical self-replication

In this article, we provide an analysis of noise propagation in a stochastic minimal model of chemical self-replication, where a given species can duplicate itself normally. A feedback from the end product on the source, acting as an inhibitor transcription factor, is considered. Stochasticity involves the intrinsic noise affecting gene expression, which is assumed to happen in bursts. The use of a stochastic approach is a novelty within such a framework. The investigation involves the role of the feedback: how it impacts noise attenuation with respect to different modeling choices of stochastic transcription, and with respect to different strengths of the feedback action. The quantification of noise propagation is measured by means of the so called metabolic noise, that is, the coefficient of variation of the end product. Computations are carried out numerically, according to the stochastic simulation algorithm (SSA) properly adapted for the proposed stochastic hybrid systems, as well as analytically: the latter has been achieved by exploiting the linear approximation of the nonlinear terms involved, since otherwise there are no closed loop solutions for the first- and second-order moments. In such a way, noise propagation may be linked to the model parameters, with the SSA aiming at validating the approximated formulas. Results confirm the noise reduction paradigm with feedback.