Time?optimal control of piecewise affine bistable gene?regulatory networks

We study the minimal-time problem for a piecewise affine bistable switch. Motivated by applications in synthetic biology and biotechnology, aim is to minimize time needed this system achieve transitions between its two stable steady states. The latter represents possible states of genetic toggle switch, flip-flop device playing fundamental role biocomputing gene therapy. Results show that time-optimal transition should pass an undifferentiated state, which well known cell importance fate differentiation cells. In order characterize capacity transitions, we provide lower bound on minimal time, whose knowledge becomes relevant when considering realistic systems involving subsystems evolving different scales. Then, numerical simulations optimal trajectories illustrating structure bang-bang control scenarios.