Time-optimal control of piecewise affine bistable gene-regulatory networks: preliminary results

In this preliminary work we give a geometric characterization of the time-optimal trajectories for piecewise affine bistable switch. Such hybrid models play major role in systems biology, as they can expressively account behaviors simple gene-regulatory networks. A key example these biological circuits is genetic toggle switch, which optimality state switch has not been studied to present day. The main result prove that optimal control strategy bang-bang feedback law. opposition previous works, show transition between states should pass by an undifferentiated state, well known cell biology playing fate differentiation cells. We conclude showing numerical simulations illustrating structure different scenarios.