A Logic for Checking the Probabilistic Steady-State Properties of Reaction Networks

Designing probabilistic reaction models and determining their stochastic kinetic parameters are major issues in systems biology. To assist in the construction of reaction network models, we introduce a logic that allows one to express asymptotic properties about the steady-state stochastic dynamics of a reaction network. Basically, the formulas can express properties on expectancies, variances, and covariances. If a formula encoding for experimental observations on the system is not satisfiable, then the reaction network model can be rejected. We demonstrate that deciding the satisfiability of a formula is NP-hard, but we provide a decision method based on solving systems of polynomial constraints. We illustrate our method on a toy example.