It is a common expectation in chemistry that a chemical transformation which takes place in the presence of a catalyst must also take place in its absence , though perhaps at a much slower rate. 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. Our result is independent of the specific rates,and the deficiency of the network. The question of permanence for weakly-reversible reaction networks remains an important and long-standing open problem .
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. We define "catalytic networks" as 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 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 of Adleman et al. , and normal networks of Gnacadja. We define "autocatalytic networks," and conjecture that weakly-reversible reaction networks have critical siphons if and only if they are autocatalytic .
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It is a common expectation in chemistry that a chemical transformation which takes place in the presence of a catalyst must also take place in its absence , though perhaps at a much slower rate. We say a reaction network
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. We define "catalytic networks" as networks with an essentially catalytic reaction pathway: one which
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saturated
on
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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,
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
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by
of
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and constructive networks by Shinar et al. Our result is independent of the specific rates,and the deficiency of the network. The question of permanence for
, and normal networks of Gnacadja. We define "autocatalytic networks," and conjecture that
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remains an important and long-standing open problem
have critical siphons if and only if they are autocatalytic