Theoretical studies on the origin of β-sheet twisting

Right-handed twisting is a fundamental structural feature of beta -pleated sheets in globular proteins which is critical for their geometry and function. The origin of this twisting is poorly understood and has represented a challenge for theoretical chemistry for almost 30 years. Density functional theory using the B3LYP exchange-correlation functional and the split-valence 6-31G** basis set has been utilized to investigate the structure and conformational transitions of single and double-stranded antiparallel beta -sheet models to determine the driving force for the right-handed twisting. Right-handed twisting is found to be an intrinsic property of a peptide main chain because of the difference in rotational potentials around N(sp(2))-C-alpha(sp(3)) and C(sp(2))-C-alpha(sp(3)) bonds. The difference arises from a tendency of the single C-alpha(sp(3))-C(sp(2)) bonds to eclipse the lone pair of atoms N(sp(2)), which results in decreasing absolute values of dihedral angles phi but not psi. This tendency is suppressed by hydrogen bonding between adjacent CO and NH groups within single beta -strands, and released only when these bonds are disrupted by the interstrand CO . . . HN hydrogen bonding. The results obtained constitute the following paradigm of the origin of alpha -sheet twist: although right-handed twisting of beta -sheets in globular proteins is an inherent property of the peptide backbone within single beta -strands, it is unleashed by the interstrand hydrogen bonding in multistranded beta -sheets. The observed pleating, right-handed twisting, skewed mutual orientation of beta -strands, and intrinsic conformational variability of double-stranded antiparallel beta -sheet motifs in globular proteins are explained from the first principles.