Origin of the right-handed twist of beta-sheets of poly(LVal) chains

The energies of three- and five-chain antiparallel and parallel beta-sheets were minimized. Each chain consisted of six L-valine residues with CH3CO and NHCH3 end groups; the chains were considered to be equivalent, but all dihedral angles of a given chain were allowed to vary independently during energy minimization. The minimum-energy structures had a considerable right-handed twist, as observed in globular proteins. This right-handed twist is due primarily to intrachain nonbonded interactions. Such interactions between the C gamma 1H3 group of the ith residue and the C gamma 2H3 group of the (i + 2)th residue of the same chain favor a twist of either handedness over the flat structure. However, many small intrastrand pair-wise interatomic interactions involving the C gamma 1H3 and C gamma 2H3 groups, especially the interactions of these groups with the O and amide H atoms of the neighboring peptide groups, make the right-handed twisted structure energetically more favorable than the left-handed one. The intrastrand side-chain torsional energy plays a small additional role in favoring the right-twisted structure over both the flat and the left-twisted structures. The interstrand interactions favor flat structures, but they are not strong enough to overcome the intrastrand interactions that favor the twisted structure; they only decrease somewhat the extent of the right-handed twist of the beta-sheets.