Sensitivity of Projections of Backbone ¹³ C ^α / ¹⁵ N Chemical Shielding Along Covalent Bonds to Protein Secondary Structure—An Ab Initio Study

Statistical analysis of backbone ¹³C^α and ¹⁵N chemical shielding tensors (CST) computed using the DFT-GIAO method is presented for 40 alanine residues located centrally in three-residue segments extracted from α-helical and β-sheet regions of 12 proteins with high-resolution crystal structures. Our results show that the projections of ¹³C^α shielding along the three covalent bond directions, C^α-C^β, C^α-H^α, and C^α-N, exhibit significantly higher sensitivity to secondary structure than the principal components. The increased sensitivity is due to the changes in the orientation of ¹³C^α CST in the molecular frame of the two secondary structures. Similarly, the projections of backbone amide ¹⁵N shielding along the covalent bonds N-H, N-C^α and along the normal direction to the peptide plane have a reasonably higher sensitivity to the secondary structure than the principal components. Unlike ¹³C^α nuclei, the orientation of amide ¹⁵N CST in the molecular frame is found to be invariant in the two secondary structures. The calculated amide ¹⁵N chemical shielding anisotropies (CSA) are larger in helix than in sheet structure, consistent with the experimental ¹⁵N chemical shift studies reported in the literature. Furthermore, two-dimensional correlation plots of backbone ¹³C^α and ¹⁵N CSA parameters show a clear distinction between the two major secondary structure elements.