Catalysis in Reaction Networks

TL;DR

This paper explores catalytic reaction networks, showing that weakly-reversible networks with critical siphons are catalytic, and connects these concepts to autocatalytic networks with implications for chemical and molecular systems.

Contribution

It introduces the concept of catalytic networks, proves that weakly-reversible networks with critical siphons are catalytic, and conjectures a characterization involving autocatalytic networks.

Findings

Weakly-reversible networks with critical siphons are catalytic.

New proofs for the persistence of certain atomic and normal networks.

Conjecture linking critical siphons and autocatalytic networks.

Abstract

We define catalytic networks as chemical reaction networks with an essentially catalytic reaction pathway: one which is on in the presence of certain catalysts and off in their absence. We show that examples of catalytic networks include synthetic DNA molecular circuits that have been shown to perform signal amplification and molecular logic. Recall that a critical siphon is a subset of the species in a chemical reaction network whose absence is forward invariant and stoichiometrically compatible with a positive point. Our main theorem is that all weakly-reversible networks with critical siphons are catalytic. Consequently, we obtain new proofs for the persistence of atomic event-systems of Adleman et al., and normal networks of Gnacadja. We define autocatalytic networks, and conjecture that a weakly-reversible reaction network has critical siphons if and only if it is autocatalytic.