Autocatalysis in Reaction Networks
arXiv:1309.3957 · doi:10.1007/s11538-014-0024-x
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.
v4: 29 pages, 1 figure, Theorem 5.3.3 strengthened to all consistent reaction networks; v3: 28 pages, 1 figure, minor revisions; v2: 27 pages, 1 figure, new introduction and related work sections replacing sections in v1; v1:27 pages, 1 figure
References in corpus (7)
- A model for the emergence of cooperation, interdependence and structure in evolving networks
- Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model
- A geometric approach to the Global Attractor Conjecture
- On the Mathematics of the Law of Mass Action
- Catalysis in Reaction Networks
- The origin of large molecules in primordial autocatalytic reaction networks
- A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics
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