Geometric descriptors for beta turns.

Beta turns, in which the protein backbone abruptly changes direction over four amino acid residues, are the most common type of protein secondary structure after alpha helices and beta sheets and play key structural and functional roles. Previous work has produced classification systems for turn geometry at multiple levels of precision, but these operate in backbone dihedral-angle (Ramachandran) space, and the absence of a local Euclidean-space coordinate system and structural alignment for turns, or of any systematic Euclidean-space characterization of turn backbone shape, presents challenges for the visualization, comparison and analysis of the wide range of turn conformations and the design of turns and the structures that incorporate them. This work derives a turn-local coordinate system that implicitly aligns turns, together with a set of geometric descriptors that characterize the bulk BB shapes of turns and describe modes of structural variation not explicitly captured by existing systems. These modes are shown to be meaningful by the demonstration of clear relationships between descriptor values and the electrostatic energy of the beta-turn H-bond, the overrepresentations of key side-chain motifs, and the structural contexts of turns. Geometric turn descriptors complement Ramachandran-space classifications, and they can be used to select turn structures for compatibility with particular side-chain interactions or contexts. Potential applications include protein design and other tasks in which an enhanced Euclidean-space characterization of turns may improve understanding or performance. The web-based tools ExploreTurns, MapTurns, and ProfileTurn, available at www.betaturn.com, incorporate turn-local coordinates and turn descriptors and demonstrate their utility.