Carbon-13 NMR shielding in the twenty common amino acids: Comparisons with experimental results in proteins

We have used ab initio quantum chemical techniques to compute the ¹³C^α and ¹³C^β shielding surfaces for the 14 amino acids not previously investigated (R. H. Havlin et al., J. Am. Chem. Soc. 1997, 119, 11951-11958) in their most popular conformations. The spans Ω = σ₃₃ - σ₁₁) of all the tensors reported here are large (≈34 ppm) and there are only very minor differences between helical and sheet residues. This is in contrast to the previous report in which Val, Ile, and Thr were reported to have large (∼12 ppm) differences in Ω between helical and sheet geometries. Apparently, only the β-branched (β-disubstituted) amino acids have such large CSA span (Ω) differences; however, there are uniformly large differences in the solution-NMR-determined CSA (Δσ* = σ_orth - σ_par) between helices and sheets in all amino acids considered. This effect is overwhelmingly due to a change in shielding tensor orientation. With the aid of such shielding tensor orientation information, we computed Δσ* values for all the amino acids in calmodulin/M13 and ubiquitin. For ubiquitin, we find only a 2.7 ppm rmsd between theory and experiment for Δσ* over an ∼45 ppm range, a 0.96 slope, and an R² = 0.94 value when using an average solution NMR structure. We also report C^β shielding tensor results for these same amino acids, which reflect the small isotropic chemical shift differences seen experimentally, together with similar C^β shielding tensor magnitudes and orientations. In addition, we describe the results of calculations of C^α, C^β, C^γ1, C^γ2, and C^δ shifts in the two isoleucine residues in bovine pancreatic trypsin inhibitor and the four isoleucines in a cytochrome c and demonstrate that the side chain chemical shifts are strongly influenced by Χ₂ torsion angle effects. There is very good agreement between theory and experiment using either X-ray or average solution NMR structures. Overall, these results show that both C^α backbone chemical shift anisotropy results as well as backbone and side chain ¹³C isotropic shifts can now be predicted with good accuracy by using quantum chemical methods, which should facilitate solution structure determination/refinement using such shielding tensor surface information.