Qualitative Control of Genetic Networks: the Bistable Switch Example

The control of a generic model for a genetic network is studied using piecewise affine differential systems. It is assumed that the state measurements are qualitative (each variable is at high or low concentration) and that the possible input values are also qualitative (no control, high or low value). The advantage of this approach is to obtain control laws which can be implemented in the laboratory, using only qualitative knowledge of the system's variables. Exact solutions are given for the problem of controlling the bistable switch to either of its steady states.