  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.
