SUFFICIENT CONDITIONS FOR EMERGENT SYNCHRONIZATION IN PROTOCELL MODELS

In this paper, we study general protocell models aiming to understand the synchronizationphenomenon of genetic material and container productions, a necessary condition to ensure sustainablegrowth in protocells and eventually leading to Darwinian evolution when applied to a population ofprotocells.Synchronization has been proved to be an emergent property in many relevant protocell models inthe class of the so-called surface reaction models, assuming both linear- and non-linear dynamics forthe involved chemical reactions. We here extend this analysis by introducing and studying a new classof models where the relevant chemical reactions are assumed to occur inside the protocell, in contrastwith the former model where the reaction site was the external surface.While in our previous studies, the replicators were assumed to compete for resources,without any direct interaction among them, we here improve both models by allowing linearinteraction between replicators: catalysis and/or inhibition. Extending some techniques previouslyintroduced, we are able to give a quite general analytical answer about the synchronizationphenomenon in this more general context. We also report on results of numerical simulations tosupport the theory, where applicable, and allow the investigation of cases which are not amenable toanalytical calculations.