Dependency graphs and mass conservation in reaction systems

Reaction systems is a new mathematical formalism inspired by the biological cell, which focuses on an abstract set-based representation of chemical reactions via facilitation and inhibition. In this article we focus on the property of mass conservation for reaction systems. We show that conservation of sets gives rise to a relation between the species, which we capture in the concept of the conservation dependency graph. We then describe an application of this relation to the problem of listing all conserved sets. We further give a sufficient negative polynomial criterion which can be used for proving that a set is not conserved. Finally, we present a simulator of reaction systems, which also includes an implementation of the algorithm for listing the conserved sets of a given reaction system.