Control of negative feedback loops in genetic networks

The oscillator made of a negative loop of two genes is one of the most classical motifs of genetic networks. We give solutions to control such an oscillator by modifying the synthesis rates. Our models are given by piecewise affine systems, and the control is qualitative, taking only two values. Thus, the necessary measurements for implementing this control only depend on the fact that some gene is expressed or not. Our first goal is to obtain sustained oscillations. Then we study the control by a sliding mode for negative ODE loops in general, to suppress sustained or damped oscillations. Finally, we introduced a general idea for creating sustained oscillations in systems with damped oscillations following a particular cycle of domains.