Motif frequency and evolutionary search times in RNA populations.

RNA molecules, through their dual identity as sequence and structure, are an appropriate experimental and theoretical model to study the genotype-phenotype map and evolutionary processes taking place in simple replicator populations. In this computational study, we relate properties of the sequence-structure map, in particular the abundance of a given secondary structure in a random pool, with the number of replicative events that an initially random population of sequences needs to find that structure through mutation and selection. For common structures, this search process turns out to be much faster than for rare structures. Furthermore, search and fixation processes are more efficient in a wider range of mutation rates for common structures, thus indicating that evolvability of RNA populations is not simply determined by abundance. We also find significant differences in the search and fixation processes for structures of same abundance, and relate them with the number of base pairs forming the structure. Moreover, the influence of the nucleotide content of the RNA sequences on the search process is studied. Our results advance in the understanding of the distribution and attainability of RNA secondary structures. They hint at the fact that, beyond sequence length and sequence-to-function redundancy, the mutation rate that permits localization and fixation of a given phenotype strongly depends on its relative abundance and global, in general non-uniform, distribution in sequence space.