Before revision:  We say a reaction network is " saturated " if it satisfies such an expectation. We prove that the associated dynamical systems of saturated networkshave no relevant siphons , and are therefore permanent. Saturated networks generalize normal networks by Gnacadja, atomic event-systems by Adleman et al. and constructive networks by Shinar et al.
After revision:  We say a reaction network is " saturated " in the presence of certain catalysts and "off" in their absence. We show that synthetic DNA molecular circuits that have been shown to perform signal amplification and molecular logic happen to be examples of catalytic networks. Our main theorem is that all weakly-reversible networks with critical siphons are catalytic. We obtain new proofs for the persistence of atomic event-systems by Adleman et al. and constructive networks by Shinar et al.