Shaping Pulses to Control Bistable Biological Systems

TL;DR

This paper develops a method to control bistable biological systems using shaped pulses, enabling switching between states without real-time feedback, with applications demonstrated in synthetic biology.

Contribution

It introduces an efficient algorithm for pulse-based control of monotone bistable systems, extending to uncertain models and combining pulse and event-based control strategies.

Findings

Efficient computation of switching pulses for bistable systems.

Extension of control methods to systems with parametric uncertainty.

Successful induction of oscillations using pulse and event-based control.

Abstract

In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation for pulse-based control comes from applications in synthetic biology, where it is generally difficult to implement real-time feedback control systems due to technical limitations in sensors and actuators. We show that for monotone bistable systems, the estimation of the set of all pulses that switch the system reduces to the computation of one non-increasing curve. We provide an efficient algorithm to compute this curve and illustrate the results with a genetic bistable system commonly used in synthetic biology. We also extend these results to models with parametric uncertainty and provide a number of examples and counterexamples that demonstrate the power and limitations of the current theory. In order to show the full potential of the framework, we consider the problem of inducing oscillations in a monotone biochemical system using a combination of temporal pulses and event-based control. Our results provide an insight into the dynamics of bistable systems under external inputs and open up numerous directions for future investigation.