SURFACE REACTION MODELS OF PROTOCELLS

We present some improved versions of a previous model10 to describe a class of genericprotocells hypotheses, inspired by the \u201cLos Alamos bug\u201d hypothesis but which, due totheir abstraction level, can be applied to a wider set of detailed protocell hypotheses. Inthe present paper we address in particular the question of generic non-linear growth lawfor the container and a general non-linear replication law for the self-replicatingmolecules. Our technique, combining a continuous-time formalism, for the growthbetween two successive protocell divisions, and a discrete map, relating the quantity ofself-replicating molecules in successive generations, allows one to derive severalproperties in an analytical way. It can thus be shown that, under fairly generalassumptions, the two growth rates synchronise, so that the lipid container doubles its sizewhen the quantity of self-replicating molecules has also doubled \u2013 thus giving rise toexponential growth of the population of protocells. Such synchronization had beenpostulated a priori in previous models of protocells, while it is here an emergentproperty