Randomness, structural uniqueness, modularity and neutral evolution in sequence space of model proteins

The genotype-phenotype map for short chains of a protein-like hetero-polymer model has been characterised [10, 12]. Hydrophobic-Polar (HP) sequences on a square lattice, their structures and partition functions have been exhaustively enumerated and analysed. Homologous sequences folding uniquely into the same structure are interconnected by point mutations. These neutral nets arrange in superfunnel topology as they are centred around prototype sequences which tolerate the largest number of neutral mutations, are thermodynamically most stable, and correspond to what is known as consensus sequences of real protein families. This work briefly summarises the superfunnel concept and reports new results on the non-randomness of sequences, modularity and well-definedness of structures, and variations of sequence positions in nets. Essentially, these features vary smoothly along evolutionarily plausible trajectories and can be qualitatively related to experimental evidence from real world proteins. In summary, results can be understood in the context of the designing-out principle and structural isolation in shape space. The resulting picture offers a unified perspective on evolutionary design, thermodynamic and mutational stability.