A Logic for Checking the Probabilistic Steady-State Properties of Reaction Networks Article - Août 2017

Vincent Picard, Anne Siegel, Jérémie Bourdon

Vincent Picard, Anne Siegel, Jérémie Bourdon, « A Logic for Checking the Probabilistic Steady-State Properties of Reaction Networks  », Journal of Computational Biology, août 2017, pp. 1—12. ISSN 1066-5277

Abstract

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 observa- tions 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.

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