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Protein mean and variance levels in a simple stochastic gene expressioncircuit are controlled using proportional integral feedback. It is shown thatthe protein mean level can be globally and robustly tracked to any desiredvalue using a simple PI controller that satisfies explicit sufficientconditions. Controlling both the mean and variance on the other hand requiresthe use of an additional control input, chosen here as the mRNA degradationrate. Local robust tracking of mean and variance is proved to be achievableusing multivariable PI control, provided that the reference point satisfiesnecessary conditions imposed by the system. Even more importantly, it is shownthat there exist PI controllers that locally, robustly and simultaneouslystabilize all the equilibrium points inside the admissible region. Simulationexamples illustrate the results.

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