Detecting Autocatalytic, Self-sustaining Sets in Chemical Reaction Systems
Wim Hordijk and Mike Steel
Journal of Theoretical Biology 227(4), 451-461, 2004.
The ability of systems of molecular reactions to be simultaneously autocatalytic and sustained by some ambient `food source' of simple molecules may have been an essential step in the origin of life. In this paper we first describe a polynomial-time algorithm that determines whether any given set of molecules, reactions and catalysations contains a subsystem that is both autocatalytic and able to be sustained from a given subset of the molecules. We also describe some combinatorial properties of this algorithm, and show how it can be used to find irreducible auto-catalysing and sustaining subsystems. In the second part of the paper we use the algorithm to investigate random catalytic networks - in particular a model described by Kauffman. Using simulations and some analytic techniques we investigate the rate of catalysis that is required for the emergence of autocatalytic and sustaining subsystems.