Synchronization in near-membrane reaction models of protocells

In this paper a new model of growing and dividing protocells is described, whose main features are (i) an autocatalytic set of “genetic memory molecules” (GMMs) whose reactions happen in a thin aqueous phase shell near the membrane and (ii) a lipid container that grows according to the amphiphilic production stimulated by the GMMs. Synchronization occur when the container growth rate is equal to the GMMs self-replicative one: the behavior of this model is compared with a previous version where reactions occur in the whole internal aqueous volume. Analytical results and simulations has shown that synchronization emerges in both models for the same set of kinetic equations, the main difference being only in the time scale of the process. Moreover the introduction of finite rates in the transmembrane diffusion permits the emergence of synchronization for a significantly wide set of parameters, enough to allow the protocell evolvability (defined as the capability of cumulating novelties, by maintaining the already present capabilities).