title: Autocatalysis in reaction networks.
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 toward 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 nonautocatalytic 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.
authors.affiliation: Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad, India, deshabhi123@gmail.com.
authors.forename: Abhishek
authors.initials: A
authors.lastname: Deshpande
authors.forename: Manoj
authors.initials: M
authors.lastname: Gopalkrishnan
mesh_terms: D000465:Algorithms; D002384:Catalysis; D007700:Kinetics; D055641:Mathematical Concepts; D008956:Models, Chemical; D058615:Synthetic Biology; D049490:Systems Biology