Gaussian random energy model and Dyson’s model for the origin of metabolism

The equivalence between Dyson’s model for a population of prebiotic mutually catalytic molecules and the Gaussian random energy model is established. It is shown that, within the mean field approximation, the mathematical expression for the function that describes the autocatalytic capability of the whole system is completely determined by the nature of the interaction potential (or the force field) between the monomers. Our results along with those previously obtained by Abbott [J. Mol. Evol. 27, 513 (1988)] on the replication of an autocatalytic system lead us to suggest that spin-glass theory is an appropriate model for the investigation of the origins of both metabolism and replication.