Conditions for emergent synchronization in protocells

A major aspect of the dynamics of a populations of protocells, is that, in order to assure sustainable growth, the genetic material and container productions must be synchronized if they are coupled. In a previous work [10] we have shown that such synchronization is 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 for resources, without any direct interaction among them, here we address a similar question in the case where the replicators interact in a linear way (due to the fact that the protocell divides into two when a certain critical size is reached, the overall model is definitely nonlinear). Using the technique introduced in [10], we are able to give a quite general analytical answer about the synchronization phenomenon even in the presence of interactions. 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 nonlinear models is presented in the conclusions.