Effects of side-chain orientation on the 13C chemical shifts of antiparallel β-sheet model peptides

The dependence of the 13C chemical shift on side-chain orientation was investigated at the density functional level for a two-strand antiparallel β-sheet model peptide represented by the amino acid sequence Ac-(Ala)3-X-(Ala)12-NH2 where X represents any of the 17 naturally occurring amino acids, i.e., not including alanine, glycine and proline. The dihedral angles adopted for the backbone were taken from, and fixed at, observed experimental values of an antiparallel β-sheet. We carried out a cluster analysis of the ensembles of conformations generated by considering the side-chain dihedral angles for each residue X as variables, and use them to compute the 13C chemical shifts at the density functional theory level. It is shown that the adoption of the locally-dense basis set approach for the quantum chemical calculations enabled us to reduce the length of the chemical-shift calculations while maintaining good accuracy of the results. For the 17 naturally occurring amino acids in an antiparallel β-sheet, there is (i) good agreement between computed and observed 13Cα and 13Cβ chemical shifts, with correlation coefficients of 0.95 and 0.99, respectively; (ii) significant variability of the computed 13Cα and 13Cβ chemical shifts as a function of χ1 for all amino acid residues except Ser; and (iii) a smaller, although significant, dependence of the computed 13Cα chemical shifts on χξ (with ξ ≥ 2) compared to χ1 for eleven out of seventeen residues. Our results suggest that predicted 13Cα and 13Cβ chemical shifts, based only on backbone (φ,ψ) dihedral angles from high-resolution X-ray structure data or from NMR-derived models, may differ significantly from those observed in solution if the dihedral-angle preferences for the side chains are not taken into account