Modeling homopolymer self-replication: implications for early competition.

We start showing that the rate equation for a homopolymer self-replication may be written as being proportional to mbetapGamma with beta=1 and Gamma=1/2, where m is the monomer concentration and p is the homopolymer total concentration (double helices plus isolated strands). With such values for the exponents beta and Gamma, we examine analytically the asymptotic behavior of our model previously proposed for studying the early polymer evolution. In this model, polymers compete for activated monomers carried into the system under a constant flux. Time changes on their concentrations are determined by the reactions of: spontaneous generation of dimers through non-instructed junction of two monomers; ligation among free monomers and polymers at the end of their chains, so that they can extend their sizes; template-instructed synthesis by which polymers with lengths above a length threshold can catalyse the formation of other polymers; and decomposition of all species. We find out that if the monomer flux intensity is "low" (lesser than the decomposition rate constants), dimer is the dominant species. Under a "high" flux (greater than the template-instructed synthesis rate constant), the longest self-replicating species prevails. For a "middle" flux (between "low" and "high"), the shortest self-replicating polymer is the winner. Whatever the flux intensity, all polymer species ever coexist.