Proportional-integral control of stochastic gene regulatory networks

We consider the problem of controlling gene expression in a stochastic genetic regulatory network. We introduce a general class of network designs that achieve this task, and that could be implemented in a synthetic biological setting. For our system, we describe the dynamics of the means and covariances of the gene products, and show that their steady states can be prescribed and tuned. We demonstrate the ideas with a series of examples and also discuss how the network design could be implemented with molecular mechanisms such as transcription factors and kinases.