Symmetry and designability for lattice protein models

Native protein folds often have a high degree of symmetry. We study therelationship between the symmetries of native proteins, and theirdesignabilities -- how many different sequences encode a given nativestructure. Using a two-dimensional lattice protein model based onhydrophobicity, we find that those native structures that are encoded by thelargest number of different sequences have high symmetry. However only certainsymmetries are enhanced, e.g. x/y-mirror symmetry and $180^o$ rotation, whileothers are suppressed. If it takes a large number of mutations to destabilizethe native state of a protein, then, by definition, the state is highlydesignable. Hence, our findings imply that insensitivity to mutation implieshigh symmetry. It appears that the relationship between designability andsymmetry results because protein substructures are also designable. Nativeprotein folds may therefore be symmetric because they are composed of repeateddesignable substructures.Comment: 13 pages, 10 figure