New proteinlike properties of cubic lattice models

An analysis of the sequences associated with each of the 60 highly designable structures found in a $3\times 3\times 3$ cubic lattice model of proteins [H. Li et al., Science 273, 666 (1996)] reveals that 99% of them belong to a “neutral island,” entirely described by a single-mutation walk in sequence space. In each island, five hydrophobic sites are almost perfectly conserved, corresponding to the unique five-hydrophobic-residue sequence able to accommodate a three-dimensional hydrophobic core formed by the center of the cube together with the four neighboring centers of face. This happens to reflect the peculiar topologies of the 60 preferred structures. Other properties of the model appear to match specific properties of natural proteins, either structural or evolutionary ones.