Fitness Landscapes Arising from the Sequence-Structure Maps of Biopolymers

Fitness landscapes are an important concept in molecular evolution since evolutionary adaptation as well as {\it in vitro} selection of biomolecules can be viewed as a hill-climbing-like process. Global features of landscapes can be described by statistical measures such as correlation functions or the fraction of neutral (equally fit) neighbors. Simple spin-glass-like landscape models borrowed from statistical physics lend themselves to detailed mathematical analysis but lack several basic features of natural landscapes. Biologically relevant landscape models are based on the assumption that genotypes give rise to phenotypes that are evaluated by their environment and hence determine the genotype's fitness. In the case of {\it in vitro} evolution of biopolymers the phenotypes are the three dimensional shapes of the molecules. A large degree of neutrality, giving rise to neutral networks and shape space covering, is a generic feature of RNA and polypeptide sequence-structure maps. These properties are inherited by the fitness landscapes independent of the details of the structure-to-fitness evaluation. Neutrality qualitatively changes the dynamics of evolution. While rugged landscapes without neutral neighbors lead to localized populations, trapping in local optima, and the existence of a critical replication rate beyond which sequence information is lost, we find diffusion in sequence space and ever-lasting innovation of novel mutants on landscapes arising from RNA or protein folding.