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.
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.
R
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
We define catalytic
A
as chemical reaction networks
R
"on "
on
R
"off "
off
A
examples of catalytic networks include
R
happen to be examples of catalytic networks
. 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
R
We
Consequently, we
D
"
D
"
A
a
R
networks have
network has
R
they are
it is