Error thresholds for RNA replication in the presence of both point mutations and premature termination errors

We consider a spatial model of replication in the RNA World in which polymerase ribozymes use neighbouring strands as templates. Point mutation errors create parasites that have the same replication rate as the polymerase. We have shown previously that spatial clustering allows survival of the polymerases as long as the error rate is below a critical error threshold. Here, we additionally consider errors where a polymerase prematurely terminates replication before reaching the end of the template, creating shorter parasites that are replicated faster than the functional polymerase. In well-known experiments where Qβ RNA is replicated by an RNA polymerase protein, the virus RNA is rapidly replaced by very short non-functional sequences. If the same thing were to occur when the polymerase is a ribozyme, this would mean that termination errors could potentially destroy the RNA World. In this paper, we show that this is not the case in the RNA replication model studied here. When there is continued generation of parasites of all lengths by termination errors, the system can survive up to a finite error threshold, due to the formation of travelling wave patterns; hence termination errors are important, but they do not lead to the inevitable destruction of the RNA World by short parasites. The simplest assumption is that parasite replication rate is inversely proportional to the strand length. In this worst-case scenario, the error threshold for termination errors is much lower than for point mutations. We also consider a more realistic model in which the time for replication of a strand is the sum of a time for binding of the polymerase, and a time for polymerization. When the binding step is considered, termination errors are less serious than in the worst case. In the limit where the binding time is dominant, replication rates are equal for all lengths, and the error threshold for termination is the same as for point mutations.