Symmetry and designability for lattice protein models

Native protein folds often have a high degree of symmetry. We study the relationship between the symmetries of native proteins, and their designabilities—how many different sequences encode a given native structure. Using a two-dimensional lattice protein model based on hydrophobicity, we find that those native structures that are encoded by the largest number of different sequences have high symmetry. However only certain symmetries are enhanced, e.g., x/y-mirror symmetry and 180° rotation, while others are suppressed. If there are many possible mutations which leave the native state of a particular protein stable, then, by definition, the state is highly designable. Hence, our findings imply that insensitivity to mutation implies high symmetry. It appears that the relationship between designability and symmetry results because protein substructures are also designable. Native protein folds may therefore be symmetric because they are composed of repeated designable substructures.