In-Silico Proportional-Integral Moment Control of Stochastic Gene Expression

In-silico control of complex stochastic biological systems is a promising area of cybergenetics, which provides enabling theoretical and practical tools for the real-time control of living cells with digital computers. We demonstrate here that simple proportional-integral control laws can be used to control both the mean and the variance of the expression product of a simple gene expression network. Extensions to more general unimolecular networks, networks with input delay, and to a gene expression network involving protein dimerization are also provided. Notably, no moment closure method is used for dealing with the network with dimerization. The obtained results are illustrated by simulations.