Theoretical Study of the Effective Chemical Shielding Anisotropy (CSA) in Peptide Backbone, Rating the Impact of CSAs on the Cross-Correlated Relaxations in L-Alanyl-L-alanine

The dependence of the effective chemical shielding anisotropy (effective CSA, Delta sigma(eff)) on the T and p peptide backbone torsion angles was calculated in the L-alanyl-L-alanine (LALA) peptide using the DFT method. The effects of backbone conformation, molecular charge including the cation, zwitterion, and anion forms of the LALA peptide, and the scaling taking into account the length of the dipolar vector were calculated for the effective CSAs in order to assess their structural behaviors and to predict their magnitudes which can be probed for the beta-sheet and alpha-helix backbone conformations via measurement of the cross-correlated relaxation rates (CCR rates). Twenty different CSA-DD cross-correlation mechanisms involving the amide nitrogen and carbonyl carbon chemical shielding tensors and the C(alpha)H(alpha) (alpha-carbon group), NH(N) (amide group), C(alpha)H(N), NH(alpha), C'H(alpha), and C'H(N) (alpha = alpha 1, alpha 2) dipolar vectors were investigated. The X-C(alpha)H(alpha) (X = N, C'; alpha = alpha 1, alpha 2) cross-correlations, which had already been studied experimentally, exhibited overall best performance of the calculated effective CSAs in the LALA molecule; they spanned the largest range of values upon variation of the psi and phi torsions and depended dominantly on only one of the two backbone torsion angles. The X-NH(N) (X = N, C') cross-correlations, which had been also probed experimentally, depended on both backbone torsions, which makes their structural assignment more difficult. The N-NH(alpha 2) and N-C'H(alpha 1) cross-correlations were found to be promising for the determination of various backbone conformations due to the large calculated range of the scaled effective CSA values and due to their predominant dependence on the psi and phi torsions, respectively. The 20 calculated dependencies of effective CSAs on the two backbone torsion angles can facilitate the structural interpretation of CCR rates.