Title: In-silico Feedback Control of a MIMO Synthetic Toggle Switch via Pulse-Width Modulation,
Abstract: The synthetic toggle switch, first proposed by Gardner & Collins [1] 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 [2] 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