Balancing Cell Populations Endowed with a Synthetic Toggle Switch via Adaptive Pulsatile Feedback Control

The problem of controlling cells endowed with a genetic toggle switch has been recently highlighted as a benchmark problem in synthetic biology. It has been shown that a carefully selected periodic forcing can balance a population of such cells in an undifferentiated state. The effectiveness of these control strategies, however, can be hindered by the presence of stochastic perturbations and uncertainties typically observed in biological systems and is therefore not robust. Here, we propose the use of feedback control strategies to enhance robustness and performance of the balancing action by selecting in real-time both the amplitude and the duty-cycle of the pulsatile inputs affecting the toggle switch behavior. We show, via in silico experiments and realistic agent-based simulations, the effectiveness of the proposed strategies even in the presence of uncertainties, stochastic effects, cell growth, and inducer diffusion. In so doing, we confirm previous observations made in the literature about coherence of the population when pulsatile forcing inputs are used, but, contrary to what was proposed in the past, we leverage feedback control techniques to endow the balancing strategy with unprecedented robustness and stability properties. We compare via in silico experiments different external control solutions and show their advantages and limitations from an in vivo implementation viewpoint.