Structure of β-sheets: Origin of the right-handed twist and of the increased stability of antiparallel over parallel sheets

Abstract

The energies of two and three-chain antiparallel and parallel β-sheets have been minimized. The chains were considered to be equivalent. In each case, chains consisting of four and of eight l-alanine residues, respectively, with CH 3CO- and -NHCH 3 end groups were examined. Computations were carried out both for chains constrained to have a regular structure (i.e. the same φ and ψ dihedral angles for each residue) and for chains in which the regularity constraint was relaxed. All computed minimum-energy β-sheets were found to have a right-handed twist, as observed in proteins. As in the case of right-handed α-helices, it is the intrastrand non-bonded interaction energy that plays the key role in forcing β-sheets of l-amino acid residues to adopt a right-handed twist. The non-bonded energy contribution favoring the right-handed twist is the result of many small pairwise interatomic interactions involving the C βH 3 groups. Polyglycine β-sheets, lacking the C βH 3 side-chains, are not twisted. The twist of the poly- l-alanine sheet diminishes as the number of residues per chain increases, in agreement with observations. The twist of the four-residue chain increases somewhat (because of interstrand non-bonded interactions, also involving the C βH 3 groups) in going from a single chain to a two-chain antiparallel structure, but then decreases slightly in going from a two-chain to a three-chain structure. β-Sheets in observed protein structures sometimes have a larger twist than those in the structures computed here. This may be due to irregularities in amino acid sequence and in hydrogenbonding patterns in the observed sheets, or to long-range interactions in proteins. The minimized energies of parallel β-sheets are considerably higher than those of the corresponding antiparallel β-sheets, indicating that parallel β-sheets are intrinsically less stable. This finding about the two kinds of β-sheets agrees with suggestions based on analyses of β-sheets observed in proteins. The energy difference between antiparallel and parallel β-sheets is due to closer packing of the chains and a more favorable alignment of the peptide dipoles in the antiparallel structures. The hydrogen-bond geometry in the computed antiparallel structures is very close to that proposed by Arnott et al. (1967) for the β-form of poly- l-alanine.