Threshold dynamics of a stochastic Keizer’s model with stochastic incidence

In this paper, we incorporate stochastic incidence of a chemical reaction into the standard Keizer’s open chemical reaction. We prove that a positive stationary distribution (PSD) for the associated chemical master equation exists and is globally asymptotically stable. We present threshold dynamics of the stochastic Keizer’s model in term of the profile of the PSD for both finite and infinite volume size V . This establishes a sharp link between deterministic Keizer’s model and the stochastic model. In this way, we resolve Keizer’s paradox from a new perspective. This simple model reveals that such stochastic incidence incorporated, though negligible when V goes to infinity, may play an indispensable role in the stochastic formulation for irreversible biochemical reactions.