Abstract Simulation of Reaction Networks

Abstract

Reaction networks model reactions between a finite set of species. These networks can be associated with different semantics, depending on the type of analysis and the phenomena under study. The standard continuous semantics is given by a system of differential equations based on the kinetic expressions of the reactions. To simulate a network under this semantics, the full knowledge of the kinetic laws of each reaction and the initial concentrations of each species is necessary. Since in empirical settings the quantitative information about the reactions can be partially or totally unknown, the challenge is to introduce new semantics that can still be applied. In this direction, a recent approach in the state of the art concerning Reaction Networks proposes a qualitative abstraction that is too coarse to properly capture the time-course continuous behaviour. Starting from the ideas of this approach, in this paper we first introduce the causal continuous semantics for Reaction Networks to capture their continuous-time dynamics, preserving the causality hidden inside each transition. Later, we introduce the differential sign semantics to abstract in a qualitative way the behaviour of a system under the causal continuous semantics. We show that our new method, based on abstract interpretation, yields appropriate Boolean transition graphs that refine those provided by the previous approach.