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arXiv · 1309.3957

Autocatalysis in Reaction Networks

Abhishek Deshpande·Manoj Gopalkrishnan
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Abstract

The persistence conjecture is a long-standing open problem in chemical reaction network theory. It concerns the behavior of solutions to coupled ODE systems that arise from applying mass-action kinetics to a network of chemical reactions. The idea is that if all reactions are reversible in a weak sense, then no species can go extinct. A notion that has been found useful in thinking about persistence is that of "critical siphon." We explore the combinatorics of critical siphons, with a view towards the persistence conjecture. We introduce the notions of "drainable" and "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 networks are persistent. Our results clarify that the difficulties in proving the persistence conjecture are essentially due to competition between drainable and self-replicable siphons.

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Abhishek Deshpande, Manoj Gopalkrishnan. 2014-08-06. Autocatalysis in Reaction Networks. https://doi.org/10.1007/s11538-014-0024-x

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