Equilibrium and Non-equilibrium Reaction Schemes for Prebiotic Polymerization of Ribonucleotides

The RNA World theory for the origin of life requires polymers to be generated initially by abiotic reactions. Experiments have studied polymerization of 5′-monophosphates, 2′,3′-cyclic phosphates, and 5′-triphosphates. We consider theoretical models of polymerization in solution illustrating the differences between these cases. We consider (i) a basic model where all monomers undergo reversible joining and breaking; (ii) a model where 2′,3′-cyclic phosphates can join, and breaking regenerates the cyclic phosphate; (iii) a model where 5′-triphosphates can join irreversibly, in addition to the joining and breaking of 2′,3′-cyclic phosphates. In cases (i) and (ii) there is an equilibrium steady state with balance between making and breaking bonds. In case (iii) there is a circular reaction flux in which monomers are activated by an external phosphate source, activated monomers form polymers, and polymers break to release non-activated monomers. The mean length can be calculated as a function of concentration. In case (iii), the mean length switches from a low-concentration regime controlled by the 5′-triphosphates to a high-concentration regime controlled by the 2′,3′-cyclic phosphates. The circular reaction flux is reminiscent of a metabolism. If formation of 5’-triphosphates was already in place for RNA synthesis, ATP could subsequently been coopted for metabolism.