A key step in the emergence of early life was the formation of a set of reactions that is (i) self-sustaining (all reactions involve reactants that are either produced by other reactions or are available in the environment) and (ii) autocatalytic (each reaction is catalyzed by some molecule produced by the system). Mathematical, algorithmic and stochastic techniques can help define, analyse, classify and search for these self-sustaining autocatalytic system in large chemical reaction networks. It is also possible to compute the probability of such systems forming in simple polymer models, as a function of the catalysis rate, and to determine their size when they first arise. In this talk, I will provide an overview of some of our earlier and more recent results in this area.
Joint work with Wim Hordijk, Elchanan Mossel and others.