Computer control of gene expression: Robust setpoint tracking of protein mean and variance using integral feedback

TL;DR

This paper demonstrates how to use proportional-integral feedback control to robustly regulate both the mean and variance of protein levels in a stochastic gene expression system, ensuring stability and precise setpoint tracking.

Contribution

It introduces a control strategy that achieves global and local robust regulation of protein mean and variance using PI controllers and additional inputs, with proven stability conditions.

Findings

PI control can globally track protein mean levels to desired values.

Controlling both mean and variance requires an additional control input.

Existence of PI controllers that stabilize all equilibria within the admissible region.

Abstract

Protein mean and variance levels in a simple stochastic gene expression circuit are controlled using proportional integral feedback. It is shown that the protein mean level can be globally and robustly tracked to any desired value using a simple PI controller that satisfies explicit sufficient conditions. Controlling both the mean and variance on the other hand requires the use of an additional control input, chosen here as the mRNA degradation rate. Local robust tracking of mean and variance is proved to be achievable using multivariable PI control, provided that the reference point satisfies necessary conditions imposed by the system. Even more importantly, it is shown that there exist PI controllers that locally, robustly and simultaneously stabilize all the equilibrium points inside the admissible region. Simulation examples illustrate the results.