  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.
