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 informati on on protein structure and dynamics in the solid and solution states. Unfo rtunately, the methods available for determining the orientation of the CSA tensor experimentally have inherent limitations. Rotation studies of a sin gle crystal provide complete information but are tedious and limited in app licability. Solid-state NMR studies on powder samples can be applied to a g reater range of samples but suffer from ambiguities in the results obtained . Density functional gauge-including-atomic-orbitals (GIAO) calculations of the orientations of N-15 CSA tensors in peptides are presented here as an independent source of confirmation for these studies. A comparison of the c alculated N-15 CSA orientations with the available experimental values from single-crystal and powder studies shows excellent agreement after a partia l, constrained optimization of some of the crystal structures used in the c alculation. The results from this study suggest that the orientation as wel l as the magnitudes of N-15 CSA tensors may vary from molecule to molecule. The calculated alpha (N) angle varies from 0 degrees to 24 degrees with th e majority in the 10 degrees to 20 degrees range and the PN angle varies fr om 17 degrees to 24 degrees in good agreement with most of the solid-state NMR experimental results. Hydrogen bonding is shown to have negligible effe ct on the orientation of N-15 CSA tensor in accordance with recent theoreti cal predictions. Furthermore, it is demonstrated that the orientation of th e N-15 CSA can be calculated accurately with much smaller basis sets than i s needed to calculate the chemical shift, suggesting that the routine appli cation of ab initio calculations to the determination of N-15 CSA tensor or ientations in large biomolecules might be possible.