Design of a long-term memory genetic toggle switch inspired by chromatin modification circuits

Abstract

A genetic toggle switch, a bistable gene-regulatory network, has many biotechnology applications, from environmental sensing to therapeutics. In order for a toggle switch to be practically useful, it should be able to maintain either of its states for a sufficiently long time. While a number of bistable circuit designs have appeared, it remains a challenge to control the duration of memory of the two states due to the presence of noise. To address this problem, we propose a bacterial toggle switch design that is inspired by a chromatin modification circuit ubiquitous in mammalian systems. We specifically propose a bacterial implementation based on two DNA invertases, in which each invertase is auto-catalyzing its own expression while also catalyzing the other invertase’s repression. We perform a mathematical analysis of the time to memory loss of the circuit’s stable states in a simplified stochastic model of the system. Our analysis shows that we can increase the time to memory loss by increasing the expression rates of the invertases, allowing to design the circuit for longterm memory. As a comparison, we also analyze two additional designs based on invertases, a published one, and a simpler version of our design. We demonstrate that for these circuits, there is no design parameter that allows to extend the time to memory loss, thereby highlighting structural properties of our design necessary for long-term memory. We validate the theoretical findings by stochastic simulations of the full set of reactions describing the circuits. More broadly, our results provide criteria for designing long-term memory toggle switches in bacteria.