The secondary structure of folded RNA sequences is a good model to map phenotype onto genotype, as represented by the RNA sequence. Computational studies of the evolution of ensembles of RNA molecules towards target secondary structures yield valuable clues to the mechanisms behind adaptation of complex populations. We have investigated the effect of microscopic mutations on the phenotype of RNA molecules during the computational evolution and adaptation of large populations. We calculate the distribution of the effects of mutations on fitness, the relative fractions of beneficial and deleterious mutations and the corresponding selection coefficients for populations evolving under different mutation rates. Two different situations are explored: the mutation-selection equilibrium (optimized population) and the dynamics during adaptation towards a goal structure (adapting population).
The ratio between the number of beneficial and deleterious mutations experienced by a population of RNA sequences increases with the value of the mutation rate m at which evolution proceeds. In contrast, the selective value of mutations remains almost constant, independent of m, indicating that adaptation occurs through an increase in the amount of beneficial mutations, with little variations in the average effect they have on fitness. Statistical analyses of the
distribution of fitness effects reveal that small effects, either beneficial or deleterious, are well described by a Pareto distribution. These results are robust under changes in the fitness landscape, remarkably when, in addition to selecting a target secondary structure, specific subsequences or low-energy folds are required.
Our study has been extended to the analysis of the effect of single mutations in the secondary structure of viroids and other natural RNAs. Previous studies identified a large abundance of mild effects on fitness. Here we show that the distribution of fitness effect for viroids and a few selected larger genomes is also consistent with a distribution with a fat-tail (Pareto-like or Lognormal). In the light of our results, we hypothesize that the topology of the fitness landscape of RNA secondary structure is well characterized by algebraically decaying functions as far as the (small) effects of mutations in fitness are considered. Our results support the idea that the conformational order observed in evolved RNA structures results not from evolutionary optimization but from constraints intrinsic to the RNA folding process.