A geometric parameterization 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 many key structural and functional roles. Previous work has produced classification systems for turn backbone geometry at multiple levels of precision, but these all 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 local coordinate system that implicitly aligns turns, together with a simple geometric parameterization for turn backbone shape that describes modes of structural variation not explicitly captured by existing systems. These modes are shown to be meaningful by the demonstration of clear relationships between parameter values and the electrostatic energy of the beta-turn H-bond, the overrepresentation of key side-chain motifs, and the structural contexts of turns. Geometric turn parameters, which complement existing Ramachandran-space classifications, can be used to tune turn structures for compatibility with particular side-chain interactions or contexts, and they should prove valuable in applications, such as protein design, where an enhanced Euclidean-space description 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 parameters and demonstrate their utility.