Abstract Simulation of Reaction Networks via Boolean Networks

We propose to simulate chemical reaction networks with the deterministic semantics abstractly, without any precise knowledge on the initial concentrations. For this, the concentrations of species are abstracted to Booleans stating whether the species is present or absent, and the derivatives of the concentrations are abstracted to signs saying whether the concentration is increasing, decreasing, or unchanged. We use abstract interpretation over the structure of signs for mapping the ODEs of a reaction network to a Boolean network with nondeterministic updates. The abstract state transition graph of such Boolean networks can be computed by finite domain constraint programming over the finite structure of signs. Constraints on the abstraction of the initial concentrations can be added naturally, leading to an abstract simulation algorithm that produces only the part of the abstract state transition graph that is reachable from the abstraction of the initial state. We prove the soundness of our abstract simulation algorithm, and show its applicability to reaction networks in the SBML format from the BioModels database.