The reversibility of stochastic reaction model and its relationship with multistability.

In this paper, we study the reversibility of the chemical master equation model. We will give an easily verifiable necessary and sufficient condition for the chemical master equation model to satisfy the Kolmogorov's cycle criterion. Next we prove that the quasi-potential, which plays a key role in the problem of exit from a domain, can be expressed by the potential function of some vector field in a line integral provided its existence. We then explore the relationship among the path independence of the line integral, the reversibility of the chemical master equation model and the reversibility of the deterministic model. As an application of our results, we find a non-trivial class of chemical systems that may exhibit multistability, and the transitions between steady states can be explicitly described.