A Polyaddition Model for the Prebiotic Polymerization of RNA and RNA-Like Polymers.

Implicit in the RNA world hypothesis is that prebiotic RNA synthesis, despite occurring in an environment without biochemical catalysts, produced the long RNA polymers which are essential to the formation of life. In order to investigate the prebiotic formation of long RNA polymers, we consider a general solution of functionally identical monomer units that are capable of bonding to form linear polymers by a step-growth process. Under the assumptions that (1) the solution is well-mixed and (2) bonding/unbonding rates are independent of polymerization state, the concentration of each length of polymer follows the geometric Flory-Schulz distribution. We consider the rate dynamics that produce this equilibrium; connect the rate dynamics, Gibbs free energy of bond formation, and the bonding probability; solve the dynamics in closed form for the representative special case of a Flory-Schulz initial condition; and demonstrate the effects of imposing a maximum polymer length. Afterwards, we derive a lower bound on the error introduced by truncation and compare this lower bound to the actual error found in our simulation. Finally, we suggest methods to connect these theoretical predictions to experimental results.

Computational Models of Polymer Synthesis Driven by Dehydration/Rehydration Cycles: Repurination in Simulated Hydrothermal Fields.

Cycles of biologically relevant reactions are an alternative to an origin of life emerging from a steady state away from equilibrium. The cycles involve a rate at which polymers are synthesized and accumulate in microscopic compartments called protocells, and two rates in which monomers and polymers are chemically degraded by hydrolytic reactions. Recent experiments have demonstrated that polymers are synthesized from mononucleotides and accumulate during cycles of hydration and dehydration, which means that the rate of polymer synthesis during the dehydrated phase of the cycle is balanced (but not dominated) by the rate of polymer hydrolysis during the hydrated phase of the cycle. Furthermore, depurination must be balanced by the reverse process of repurination. Here we describe a computational model that was inspired by experimental results, can be generalized to accommodate other reaction parameters, and has qualitative predictive power.