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Mini Course 1: Stochastic biochemical reaction networks with absolute concentration robustness

We will first introduce time-continuous Markov chains arising in chemical reaction networks, with special emphasis on specific models occurring in the cellular processing system. The course will next focus on structural sources of robustness in biochemical reaction networks. A protein is absolute robust when its equilibrium concentration is independent of the total concentration of other proteins. In the deterministic setting, the structural properties of the reaction network suffice often to induce absolute robustness of some species. When the dynamics are modeled as stochastic mass-action kinetics, such systems often get absorbed by a set of states, so that the system is undergoing an extinction event. We will explain recent results that give conditions ensuring that the process settle down to a quasi-stationary distribution, and characterize species having a quasi-stationary Poisson distribution centered around the deterministic mean.