Enabling equivalence and its cover relation for reaction systems

Abstract

A reaction system consists of a background set of entities and a set of reactions. Reactions are specified by three sets of entities: reactants, inhibitors, and products. A reaction is enabled by a state (a subset of entities), if all its reactants are present in that state and none of its inhibitors. The result of a set of reactions on a given state is a new state that consists of the products of the reactions that were enabled at the original state. In this paper, we further investigate enabling equivalence. This relation equates two sets of reactions for which the states that enable all their reactions simultaneously, are the same and, moreover, their results on those states are the same. From the point of view of enabling equivalence, sets of reactions act as if they were a single (combined) reaction. We show how combined reactions characterize enabling equivalence classes. Furthermore, enabling equivalence induces a partial order in the form of a cover relation on its equivalence classes. The resulting partially ordered set turns out to be a lattice and we demonstrate how this lattice relates to the enabling cover relation introduced earlier for single reactions.