Analysis and Control of Gene Regulation Network Models Using Kinetic Semi-Discretization

In this paper the exogenous control of gene reg-ulatory networks is investigated through the semi-discretized partial integro-differential equation (PIDE) describing the time-evolution of the network's probability density function. With an appropriate finite volume method the semi-discretized system is a mass-conservative linear compartmental model, and thus it preserves most qualitative properties of the solution of the PIDE, namely, it is nonnegative and mass conservative. These advantages combined with the newly investigated mesh-invariance of control allows us to efficiently determine the reachability set. The possibilities of this framework are demon-strated through an illustrative example from literature.