Shaping pulses to control bistable biological systems

In this paper, we present a framework for shaping pulses to control biological systems, and specifically systems in synthetic biology. By shaping we mean computing the magnitude and the length of a pulse, application of which results in reaching the desired control objective. Hence the control signals have only two parameters, which makes these signals amenable to wetlab implementations. We focus on the problem of switching between steady states in a bistable system. We show how to estimate the set of the switching pulses, if the trajectories of the controlled system can be bounded from above and below by the trajectories of monotone systems. We then generalise this result to systems with parametric uncertainty under some mild assumptions on the set of admissible parameters, thus providing some robustness guarantees. We illustrate the results on some example genetic circuits.