Local neutral networks help maintain inaccurately replicating ribozymes.

The error threshold of replication limits the selectively maintainable genome size against recurrent deleterious mutations for most fitness landscapes. In the context of RNA replication a distinction between the genotypic and the phenotypic error threshold has been made; where the latter concerns the maintenance of secondary structure rather than sequence. RNA secondary structure is treated as a proxy for function. The phenotypic error threshold allows higher per digit mutation rates than its genotypic counterpart, and is known to increase with the frequency of neutral mutations in sequence space. Here we show that the degree of neutrality, i.e. the frequency of nearest-neighbour (one-step) neutral mutants is a remarkably accurate proxy for the overall frequency of such mutants in an experimentally verifiable formula for the phenotypic error threshold; this we achieve by the full numerical solution for the concentration of all sequences in mutation-selection balance up to length 16. We reinforce our previous result that currently known ribozymes could be selectively maintained by the accuracy known from the best available polymerase ribozymes. Furthermore, we show that in silico stabilizing selection can increase the mutational robustness of ribozymes due to the fact that they were produced by artificial directional selection in the first place. Our finding offers a better understanding of the error threshold and provides further insight into the plausibility of an ancient RNA world.