arXiv1999
The aims of this paper are to propose, construct and analyse microscopic kinetic models for the emergence of long chains of RNA from monomeric beta-D-ribonucleotide precursors in prebiotic circumstances. Our theory starts out from similar but more general chemical assumptions to those of Eigen, namely that catalytic replication can lead to a large population of long chains. In particular, our models incorporate the possibility of (i) direct chain growth, (ii) template-assisted synthesis and (iii) catalysis by RNA replicase ribozymes, all with varying degrees of efficiency. However, in our models the reaction mechanisms are kept `open'; we do not assume the existence of closed hypercycles which sustain a population of long chains. Rather it is the feasibility of the initial emergence of a self-sustaining set of RNA chains from monomeric nucleotides which is our prime concern. We confront directly the central nonlinear features of the problem, which have often been overlooked in previous studies. Our detailed microscopic kinetic models lead to kinetic equations which are generalisations of the Becker-Doring system (BD) for the step-wise growth of clusters or polymer chains; they lie within a general theoretical framework which has recently been successfully applied to a wide range of complex chemical problems. In fact, the most accurate model we consider has BD aggregation terms, together with a general Smoluchowski fragmentation term to model the competing hydrolysis of RNA polymer chains. We conclude that, starting from reasonable initial conditions of monomeric nucleotide concentrations within a prebiotic soup and in an acceptable timescale, it is possible for a self-replicating subset of polyribonucleotide chains to be selected, while less efficient replicators become extinct.