The carbon-13 nuclear magnetic resonance shielding surfaces for the isotropic and anisotropic shielding components, σ11, σ22, and σ33, for Cα in N-formylglycine amide, and Cα and Cβ in N-formylalanine amide, N-formylvaline amide (χ1 = 180°, −60°, 60°), N-formylisoleucine amide (all χ1 = −60° conformers), N-formyl serine amide (χ1 = 74.3°), and N-formylthreonine amide (χ1 = 180°, −60°, 60°) have been computed at the Hartree−Fock level by using large, locally dense basis sets. The results for Cα in glycine and alanine show the expected ∼4−5 ppm increase in isotropic shielding of sheet over helical geometries, and the overall breadths of the shielding tensors are very similar for both helical and sheet fragments (|σ33 − σ11| ∼ 31−37 ppm). However, for each of the Cβ substituted amino acids (valine, isoleucine, serine, and threonine) our results for Cα indicate not only the expected ∼4−5 ppm increase in shielding of sheet fragments over helical ones but also a large increase in the overall tensor breadths for sheet residues over helical ones, and a change in tensor orientation. On average, the sheet residues have |σ33 − σ11| ∼ 34 ppm, while on average the helical value is only ∼22 ppm. For each Cβ substituted amino acid, the results for Cα also show that |σ22 − σ11|(sheet) ≫ |σ22 − σ11|(helix). For Cβ, the helical and sheet tensor breadths are in general much more similar for a given amino acid, although the actual magnitudes vary widely from one amino acid to another. Since the individual Cα tensor elements, σ11, σ22, and σ33, are all quite sensitive to not only the backbone torsion angles, φ, ψ, but also to the side chain torsion angle, χ1, as well, these results suggest that it will in many instances be possible to deduce both backbone (φ,ψ) and side chain (χ1) torsion angles from an experimental determination of the three principal elements of the 13Cα shielding tensor, results which can be confirmed in some cases with data on Cβ (and Cγ). Such an approach, based on quantum chemical calculations, should be useful in determining the structures of both crystalline, noncrystalline, and potentially even soluble peptides and proteins, as well as in refining their structures, using shielding tensor elements.

A simple method for the determination of backbone dihedral angles in peptides and proteins is presented. The chemical-shift anisotropies (CSA) of the central alanine α-carbon in powdered crystalline tripeptides, whose structures have been determined previously by X-ray crystallography, were measured by cross-polarization magic-angle-spinning nuclear magnetic resonance. The experimental CSA values were correlated with ab initio chemical-shielding calculations over Ramanchandran φ/ψ space on an N-formyl-l-alanine amide fragment. Using this correlation, φ/ψ probability surfaces for one of the tripeptides were calculated based only on the α-carbon CSA, allowing a prediction of backbone angles. Dihedral angles predicted by these calculations fall within ±12° of the values determined by crystallography. This approach should be useful in the determination of solid-state protein structure.