Abstract
The sustained growth of a population of protocells which undergo symmetrical division (where each individual splits into two equal daughter protocells) requires synchronization between the two processes of (i) duplication of the genetic material and (ii) fission of the lipid container. It has however been observed that one often encounters uneven division, where daughters of different sizes may be generated. Here we analyze the case of asymmetrical division, where each protocell has exactly two daughters of different sizes. In this case no true synchronization is possible, and we introduce the notion of homogeneous growth which guarantees that sustained population growth is possible. We consider different abstract models of protocells growth and reproduction and we show by simulation that homogeneous growth is encountered, both in Surface Reaction Models, where the replicators are located in the membrane, and in Internal Reaction Models where they are found in the internal water phase, under a broad set of different kinetic equations. We argue that, when there are different kinds of replicators, it is legitimate to identify the “chemical signature” of the protocell with the set of the ratios between the quantities of these replicators at fission time: it is shown that, in the case of linear kinetic equations, the ratios and therefore the chemical identity are conserved through generations.