Feedback control of stochastic gene switches using PIDE models

Abstract

Achieving control of gene regulatory circuits is one of the goals of synthetic biology, as a way to regulate cellular functions for useful purposes (in biomedical, environmental or industrial applications). The inherent stochastic nature of gene expression makes it challenging to control the behavior of gene regulatory networks, and increasing efforts are being devoted in the field to address different control problems.In this work, we combine the efficient modeling of stochastic gene regulatory networks by means of Partial Integro-Differential Equations with feedback control, in order to keep protein levels at the target (pre-defined) stationary probability distribution. In particular, we achieve the closedloop stabilization of bi-modal toggle-switches in the stochastic regime within the region of low probability (around the minimum located between the two modes of the uncontrolled system).