Orientation of amide-nitrogen-15 chemical shift tensors in peptides: a quantum chemical study

Knowledge of the orientation of the nitrogen-15 chemical shift anisotropy (CSA) tensor is critical for a variety of experiments that provide information on protein structure and dynamics in the solid and solution states. Unfortunately, the methods available for determining the orientation of the CSA tensor experimentally have inherent limitations. Rotation studies of a single crystal provide complete information but are tedious and limited in applicability. Solid-state NMR studies on powder samples can be applied to a greater range of samples but suffer from ambiguities in the results obtained. Density functional gauge-including-atomic-orbitals (GIAO) calculations of the orientations of (15)N CSA tensors in peptides are presented here as an independent source of confirmation for these studies. A comparison of the calculated (15)N CSA orientations with the available experimental values from single-crystal and powder studies shows excellent agreement after a partial, constrained optimization of some of the crystal structures used in the calculation. The results from this study suggest that the orientation as well as the magnitudes of (15)N CSA tensors may vary from molecule to molecule. The calculated alpha(N) angle varies from 0 degrees to 24 degrees with the majority in the 10 degrees to 20 degrees range and the beta(N) angle varies from 17 degrees to 24 degrees in good agreement with most of the solid-state NMR experimental results. Hydrogen bonding is shown to have negligible effect on the orientation of (15)N CSA tensor in accordance with recent theoretical predictions. Furthermore, it is demonstrated that the orientation of the (15)N CSA can be calculated accurately with much smaller basis sets than is needed to calculate the chemical shift, suggesting that the routine application of ab initio calculations to the determination of (15)N CSA tensor orientations in large biomolecules might be possible.