Abstract
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.
Highlights
The RNA world hypothesis maintains that RNA molecules, being capable of both performing functions and storing information, were the first self-replicating molecules in the origin of life [1,2].Deamer et al [3] have advanced a specific theory that outlines the importance of RNA to the origins of life
The dynamics of the system are determined by the rate constants k + and k −, which are a function of the experimental conditions; the effect of pH and salt cofactors on hydrolysis have been studied in depth, e.g., by Oivanen et al [35], the effects of the same on synthesis rates have remained obscure
Since the Flory-Schulz distribution of polymer length which is the solution to the system of reaction Equation (9) includes a non-zero expected concentration for polymers longer than any finite d, it is impossible for the truncated probability distribution which is the solution to (13) to be identical to the infinite-dimensional solution
Summary
Department of Computer Engineering, University of California, Santa Cruz, CA 95064, USA Center for Studies in Physics and Biology, The Rockefeller University, New York, NY 10065, USA These authors contributed equally to this work. Received: 16 December 2019; Accepted: 26 January 2020; Published: 2 February 2020
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