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

Abstract

The energies of three-and five-chain antiparallel and parallel .8-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 righthanded twist is due primarily to intrachain nonbonded interactions. Such interactions between the Ct'H3 group of the ith residue and the Cy2H3 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 CY1H3 and Cy2H3 groups, especially the interactions of these groups with the 0 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 fl-sheets.We recently showed that minimum-energy structures of 1-sheets consisting of poly(LAla) chains have a right-handed twist addition to the earlier-demonstrated role of the backbone) in producing the right-handed twist. COMPUTATIONAL METHODSComputations were carried out on a single polypeptide chain and on parallel and antiparallel three-and five-stranded 13-sheets. Each chain had the composition CH3CO-(L-Val)6-NHCH3. The residue geometry and energy parameters were those of the ECEPP algorithm [empirical conformational energy program for peptides (6)] (see ref. 1 for further computational details).Generation of 13-Sheets. For a 13-sheet with equivalent strands, the first chain can be generated by using the ECEPP algorithm, and then all the other chains can be generated by iterative rotational and translational operations on the preceding chain; i.e., the ith chain can be generated from the (i-l)th chain by the following equation:where ri and ri-1 are the coordinates of corresponding atoms in the ith and (i-l)th chains, respectively, T = (t1,t2,t3) is a translational vector, and Qi is the following Euler rotational operator (1), as observed in globular proteins (2). As in the case of righthanded a-helices (3), it is the intrastrand nonbonded interaction energy that plays the key role in forcing 13-sheets of L-amino acids to adopt a right-handed twist. The nonbonded energy contribution favoring the right-handed twist is the result of many small intrastrand pair-wise interatomic interactions involving the CPH3 groups; interstrand nonbonded interactions, also involving the C"H3 groups, contribute somewhat, but less so, in influencing the twist....

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