A model of protocell based on the introduction of a semi-permeable membrane in a stochastic model of catalytic reaction networks

The theoretical characterization of the self-organizing molecular structures emerging from ensembles of distinct interacting chemicals turns to be very important in revealing those dynamics that led to the transition from the non-living to the living matter as well as in the design of artificial protocells [12, 13, 14]. In this work we aim at studying the role of a semi-permeable membrane, i.e. a very simple protocell description, in the dynamics of a stochastic model describing randomly generated catalytic reaction sets (CRSs) of molecules. Catalytic reaction sets are networks composed of different molecules interacting together leading to the formation of several reaction pathways. In particular, molecules are representation of molecular species formed by a concatenation of letters (bricks) from a finite alphabet. Reaction pathways are formed by two kinds of reaction only, namely condensation, where two molecular species are glued together in order to create a longer species and cleavage where a molecular species is divided in two shorter species, Figure 1, Filisetti et al. [3, 4]. We present here only a brief summary of the principal characteristics and a description of the new features. An assumption of the model is that each reaction needs a catalyst to occur; hence spontaneous reactions are neglected at this stage of the model. To create the reaction scheme, the molecular species involved in the reactions are randomly chosen at the beginning of the simulation according to a fixed probability p that a random species catalyzes a random reaction. In accordance with both the species and the reactions created, in different realizations