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 acessibility can be used to define a relation of nearness among pheno types, independently of their similarity. Because of neutrality, pheno types denote equivalence classes of genotypes. The definition of neigh borhood relations among phenotypes relies, therefore, on the statistic s of neighborhood relations among equivalence classes of genotypes in genotype space. The folding of RNA sequences (genotypes) into secondar y structures (phenotypes) is an ideal case to implement these concepts . We study the extent to which the folding of RNA sequences induces a ''statistical topology'' on the set of minimum free energy secondary s tructures. The resulting nearness relation suggests a notion of ''cont inuous'' structure transformation. We can, then, rationalize major tra nsitions in evolutionary trajectories at the level of RNA structures b y identifying those transformations which are irreducibly discontinuou s. This is shown by means of computer simulations. The statistical top ology organizing the set of RNA shapes explains why neutral drift in s equence space plays a key role in evolutionary optimization. (C) 1998 Academic Press.