Control of Subpopulation Fractions in a Population of Bistable Cells

Bistable genetic circuits have long been studied in systems and synthetic biology, with notable recent work focused on controlling the phenotypic composition of populations with such circuits. Here, we build on previous literature to theoretically characterize a mechanism by which cells with bistable circuits can use quorum sensing to drive the population to arbitrary phenotypic compositions. We in particular investigate the ability of a proportional controller to accomplish this task on ideal and non-ideal plants, providing performance guarantees and, under additional assumptions, guarantees of almost-global convergence to a desirable population equilibrium.