A Compositional Semantics of Reaction Systems with Restriction

Reaction systems are an abstract model of interactions among biochemical reactions, developed around two opposite mechanisms: facilitation and inhibition. The evolution of a Reaction System is driven by the external objects which are sent into the system by the environment at each step. In this paper, we propose the Reaction Algebra, a calculus resembling reaction systems extended with a restriction operator. Restriction increases the expressiveness of the calculus by allowing the modeling of hidden entities, such as those contained in membranes. We define a compositional semantics and a behavioral equivalence for the Reaction Algebra, in order to enable the modular description of biological systems.