Theoretical Studies on the Origin of β-sheet Twisting

Right-handed twisting is a fundamental structural feature of β-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 β-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 α (sp 3 ) and C(sp 2 )−C α (sp 3 ) bonds. The difference arises from a tendency of the single C α (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 φ but not ψ. This tendency is suppressed by hydrogen bonding between adjacent CO and NH groups within single β-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 β-sheet twist: although right-handed twisting of β-sheets in globular proteins is an inherent property of the peptide backbone within single β-strands, it is unleashed by the interstrand hydrogen bonding in multistranded β-sheets. The observed pleating, right-handed twisting, skewed mutual orientation of β-strands, and intrinsic conformational variability of double-stranded antiparallel β-sheet motifs in globular proteins are explained from the first principles.