Twist and shear in β-sheets and β-ribbons

The structures of the beta-sheets and the beta-ribbons have been analysed using high-resolution protein structure data. Systematic asymmetries measured in both parallel and antiparallel beta-structures include the sheet twist and the strand shear. In order to determine the origin of these asymmetries, numerous interactions and correlations were examined. The strongest correlations are observed for residues in antiparallel beta-sheets and beta-ribbons that form non-H-bonded pairs. For these residues, the sheet twist is correlated to the backbone phi angle but not to the psi angle. Our analysis supports the existence of an inter-strand C(alpha)H(alpha)...O weak H-bond, which, together with the CO...HN H-bond, constitutes a bifurcated H-bond that links neighbouring beta-strands. Residues of beta-sheets and beta-ribbons in high-resolution protein structures form a distinct region of the Ramachandran plot, which is determined by the formation of the bifurcated H-bond, the formation of an intra-strand O...H(alpha) non-bonded polar interaction, and an intra-strand O...C(beta) steric clash. Using beta-strands parameterised by phi-psi values from the allowed beta-sheet region of the Ramachandran plot, the shear and the right-hand twist can be reproduced in a simple model of the antiparallel and parallel beta-ribbon that models the bifurcated H-bonds specifically. The conformations of interior residues of beta-sheets are shown to be subsets of the conformations of residues of beta-ribbons.