Conditions for emergent synchronization in protocells.

In this paper we study general protocell models, called Surface Reactions Models, aiming to understand the synchronization of genetic material and container productions, a necessary condition to assure sustainable growth in protocells.Synchronization has been proved to be an emergent property in many relevant protocell models , assuming both linear and nonlinear law for the replications rates. While in those previous studies the replicators were assumed to compete forresources, without any direct interaction among them, here we improve the model by allowing linear interaction between replicators: catalysis and/or inhibition.Extending some techniques introduced in, we are able to give a quite general analytical answer about the synchronization phenomenon in this more general context.We also report on the results of numerical simulations to support the theory, where applicable, and allow to investigate cases which are not amenable to analytical calculations . A short comment on preliminary results concerning fully nonlinearmodels is presented in the conclusions