Symmetry and designability for lattice protein models

Native protein folds often have a high degree of symmetry. We study the rel ationship between the symmetries of native proteins, and their designabilit ies-how many different sequences encode a given native structure. Using a t wo-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 degrees rotation, while others are supp ressed. If there are many possible mutations which leave the native state o f a particular protein stable, then, by definition, the state is highly des ignable. Hence, our findings imply that insensitivity to mutation implies h igh symmetry. It appears that the relationship between designability and sy mmetry results because protein substructures are also designable. Native pr otein folds may therefore be symmetric because they are composed of repeate d designable substructures. (C) 2000 American Institute of Physics. [S0021- 9606(00)50842-3].