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 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 (2)

• A geometric approach to the Global Attractor Conjecture
• A Projection Argument for Differential Inclusions, with Applications to Persistence of Mass-Action Kinetics

Cited by in corpus (4)

• Thermodynamic Bounds on Symmetry Breaking in Linear and Catalytic Biochemical Systems
• Unstable Cores are the source of instability in chemical reaction networks
• Maximum likelihood estimation of log-affine models using detailed-balanced reaction networks
• Computational Complexity of Atomic Chemical Reaction Networks