Before revision:  Using this, we show that a reaction network has critical siphons iff it has "drainable" or "self-replicable" siphons. Further, if the minimal siphons of a reaction network are not drainable , then the dynamics is persistent. Consequently, we obtain a new, elementary proof for the persistence of non-catalytic weakly-reversible chemical reaction networks .
After revision:  Using this, we show that a reaction network has critical siphons iff it has "drainable" or "self-replicable" (or autocatalytic) siphons. We show that: every minimal critical siphon is either drainable or self-replicable; reaction networks without drainable siphons are persistent; and non-autocatalytic weakly-reversible chemical reaction networks .