Exact control of genetic networks in a qualitative framework: The bistable switch example

Abstract

A qualitative method to control piecewise affine differential systems is proposed and explored for application to genetic regulatory networks. This study considers systems whose outputs and inputs are of a qualitative form, well suited to experimental devices: the measurements indicate whether the variables are "strongly" or "weakly" expressed, that is, only the region of the state space where trajectories evolve at each instant can be known. The control laws are piecewise constant functions in each region and in time, and are only allowed to take three qualitative values corresponding to no control (u = 1), high synthesis rates (u = umax) or low synthesis rates (u = umin). The problems of controlling the bistable switch to each of its steady states is considered. Exact solutions are given to asymptotically control the system to either of its two stable steady states. Two approximate solutions are suggested to the problem of controlling the system to the unstable steady state: either control to a neighborhood of the state, or in the form of a periodic cycle that passes through the state.

Applying differential dynamic logic to reconfigurable biological networks

“…In practice, this may lead to the calculation of, for instance, basins of attraction or control strategies. These are very promising perspectives for the analysis of piecewise linear systems: in fact, many regulatory questions can be posed in terms of finding a trajectory that will lead from one specific domain to another [24,27]. A similar case is presented in Example 4.3, where the objective was to highly express both proteins.…”

Hybrid Control of a Bioreactor With Quantized Measurements

“…Following [8], [9], a solution of System (1) under Control We first consider System (1) when a constant dilution rate D is applied in the whole space (i.e. u(t) = D, ∀t ≥ 0).…”

In-silico feedback control of a MIMO synthetic Toggle Switch via Pulse-Width Modulation

“…For example, Pulse-Shaping Control [3]- [5] and a Reinforcement Learning control approach [6] were both proposed to drive the system from a stable equilibrium to the other. Moreover, Stochastic Motion Planning [7] and Piecewise Linear Switched Control [8] were used to stabilize the circuit around its unstable equilibrium. In all these cases though the results are only tested in-silico and no experimental validation is provided.…”