An ab initio quantum chemical investigation of carbon-13 NMR shielding tensors in glycine, alanine, valine, isoleucine, serine, and threonine: Comparisons between helical and sheet tensors, and the effects of (χ1) on shielding

The carbon-13 nuclear magnetic resonance shielding surfaces for the isotropic and anisotropic shielding components, σ₁₁, σ₂₂, and σ₃₃, for C(α) in N-formylglycine amide, and C(α) and C(β) 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 C(α) 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 - 31-37 ppm). However, for each of the C(β) substituted amino acids (valine, isoleucine, serine, and threonine) our results for C(α) 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 tenser breadths for sheet residues over helical ones, and a change in tenser orientation. On average, the sheet residues have |σ₃₃ - σ₁₁| ~ 34 ppm, while on average the helical value is only ~22 ppm. For each C(β) substituted amino acid, the results for C(α) also show that |σ₂₂ - σ₁₁|(sheet >> |σ₂₂ - σ₁₁|(helix). For C(β), 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 C(α) tenser 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 ¹³C(α) shielding tenser, results which can be confirmed in some cases with data on C(β) (and C(γ)). 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 tenser elements.