Evolving reaction systems

Reaction systems were introduced as a formal model of interactions between biochemical reactions. These interactions, which are based on two mechanisms: facilitation and inhibition, determine the functioning of the living cell. Processes taking place in a reaction system A are driven by the fixed set A of available reactions provided by A. In this paper we generalize this setup: as a process progresses from a state W to its successor W′, the set of available reactions may change from A in W to A′ in W′. This new framework of evolving reaction systems is introduced and studied in this paper. Also, the notion of enabling equivalence between sets of reactions and the notion of a transformation of a set of reactions are introduced and thoroughly studied.