Perspectives on protein evolution from simple exact models

Understanding the evolution of biopolymers is important to rationalise the directed and undirected design of functional molecules. Large scale experiments or detailed computational studies are often impractical. Therefore, simple model systems, such as RNA secondary structure and lattice proteins have been adapted to study general statistical and topological features of genotype (sequence) to phenotype (structure) maps. We review findings from such models that address aspects of thermodynamic and mutational robustness, neutral evolution and recombination of proteins. We compare various modelling approaches, and discuss their generality, parameter dependency and experimental verifications of their predictions. The most striking observation is the universal emergence of neutral nets--sets of phenotypically identical genotypes that are interconnected by series of point mutations. However, fast adaptation by point mutations appears to be problematic for proteins. This may explain why proteins appear to be more specific while RNA is rather versatile. This could even be the reason why RNA had to evolve before proteins. Similar principles of biological organisation are reflected in sequence and structure databases of real proteins. Insights gained from modelling are useful for designing more efficient database organisation and search strategies.