A new qualitative control strategy for the genetic Toggle Switch

Abstract

Genetic positive feedback loops are essential for cell decision making and cell differentiation. They are traditionally described by a two-dimensional smooth non-linear differential system composed of Hill functions. The bistability of this classic model properly captures the decision properties of these biological motifs. This paper designs a new control strategy based on the measurement and control of a unique gene within the loop, in order to stabilize the system around its unstable fixed point. The quantized nature of genetic measurements and the new synthetic control approaches available in biology encourage the use of a piecewise constant control law. A specific partitioning of the state space and the study of successive repelling regions allow to prove global convergence and global stability for the resulting system. The same strategy is shown to be efficient as well in the more realistic context in which measurements are considered possibly uncertain. This new control strategy is compared with a real biological experiment that was implemented for the Toggle Switch with the same stabilization objective, but for which both genes were measured and controlled.