Shaping space: the possible and the attainable in RNA genotype-phenotype mapping.

Understanding which phenotypes are accessible from which genotypes is fundamental for understanding the evolutionary process. This notion of accessibility can be used to define a relation of nearness among phenotypes, independently of their similarity. Because of neutrality, phenotypes denote equivalence classes of genotypes. The definition of neighborhood relations among phenotypes relies, therefore, on the statistics of neighborhood relations among equivalence classes of genotypes in genotype space. The folding of RNA sequence (genotypes) into secondary structures (phenotypes) is an ideal case to implement these concepts. We study the extent to which the folding of RNA sequence induces a "statistical topology" on the set of minimum free energy secondary structures. The resulting nearness relation suggests a notion of "continuous" structure transformation. We can, then rationalize major transitions in evolutionary trajectories at the level of RNA structures by identifying those transformations which are irreducibly discontinuous. This is shown by means of computer simulations. The statistical topology organizing the set of RNA shapes explains why neutral drift in sequence space plays a key role in evolutionary optimization.