Origin of self-replicating biopolymers: autocatalytic feedback can jump-start the RNA world

Life is based on biopolymers that have the ability to replicate themselves. Here we consider how a self-replicating RNA system may have originated. We consider a reaction system in which polymerization is possible by the addition of an activated monomer to the end of a chain. We suppose that a small fraction of polymers longer than some minimum length L have the ability to act as polymerase ribozymes. Polymerization can occur spontaneously at a slow rate and can also be catalyzed by polymerase ribozymes, if these ribozymes exist. The system contains autocatalytic feedback: increasing the polymerization rate causes the ribozyme concentration to increase, which causes the polymerization rate to further increase. For an infinite volume, the dynamics are deterministic. There are two stable states: a 'dead' state with a very low concentration of ribozymes and a polymerization rate almost equal to the spontaneous rate, and a 'living' state with a high concentration of ribozymes and a high rate of polymerization occurring via ribozyme catalysis. In a finite volume, such as the interior of a lipid vesicle or other small compartment, the reaction dynamics is stochastic and concentration fluctuations can occur. Using a stochastic simulation, we show that if a small number of ribozymes is initially formed spontaneously, this can be enough to drive the system from the dead to the living state where ribozyme-catalyzed synthesis of large numbers of additional ribozymes occurs. This transition occurs most easily in volumes of intermediate size.