In-silico feedback control of a MIMO synthetic Toggle Switch via Pulse-Width Modulation

The genetic toggle switch is a MIMO control system that can be controlled by varying the concentrations of two inducer molecules, aTc and IPTG, to achieve a desired level of expression of the two genes it comprises. It has been shown in Lugagne et al., Nature Communication (2017) that this can be accomplished through an open-loop external control strategy where the two inputs are selected as mutually exclusive periodic pulse waves of appropriate amplitude and duty-cycle. In this paper, we use a recently derived average model of the genetic toggle switch subject to these inputs to synthesize new feedback control approaches that adjust the inputs duty-cycle in real-time via two different possible strategies, a model-based hybrid PI-PWM approach and a so-called Zero-Average dynamics (ZAD) controller. The controllers are validated in-silico via both deterministic and stochastic simulations (SSA) illustrating the advantages and limitations of each strategy.