A Modular Criterion for Persistence of Chemical Reaction Networks

In this technical note we investigate the interplay between structure and dynamics of Chemical Reaction Networks by exploiting the formalism of Petri Nets. More specifically we point out how decomposition of a network into smaller concurrent subunits may affect systems dynamics. We show in the case of State Machine Decomposable Nets (SMD nets) that under some additional topological conditions none of the chemical species involved will tend to disappear in the course of the reaction. From a purely Petri Net theoretic point of view, we present novel modular conditions to guarantee that supports of minimal P-semiflows coincide with minimal siphons of a net.