Computer control of gene expression: Robust setpoint tracking of protein mean and variance using integral feedback
This work provides a theoretical framework for robust setpoint tracking in synthetic biology, enabling precise control of gene expression noise for biotechnological applications.
The paper demonstrates that proportional integral feedback can robustly control both the mean and variance of protein expression in a stochastic gene circuit, with global tracking for mean and local robust tracking for both mean and variance using multivariable PI control.
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.