Facilitation in reaction systems

Reaction systems is a formal model of computation which originated as a model of interactions between biochemical reactions in the living cell. These interactions are based on two mechanisms, facilitation and inhibition, and this is well reflected in the formulation of reaction systems. In this paper, we investigate the facilitation aspect of reaction systems, where the products of a reaction may facilitate other reactions by providing some of their reactants. This aspect is formalized through positive dependency graphs which depict explicitly such facilitating interactions. The focus of the paper is on demonstrating how structural properties of reaction systems defined through the properties of their positive dependency graphs influence the behavioural properties of (suitable subclasses of) reaction systems, which, as usual, are defined through their transition graphs.