Autocatalysis in Reaction Networks

作者：Deshpande Abhishek; Gopalkrishnan Manoj^*

来源：Bulletin of Mathematical Biology, 2014, 76(10): 2570-2595.

DOI：10.1007/s11538-014-0024-x

• Critical siphons
• Persistence
• Reaction network
• Autocatalysis
• Petri net

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 %26quot;critical siphon.%26quot; We explore the combinatorics of critical siphons, with a view toward the persistence conjecture. We introduce the notions of %26quot;drainable%26quot; and %26quot;self-replicable%26quot; (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.

• 出版日期2014-10