Orientation of Amide-Nitrogen-15 Chemical Shift Tensors in Peptides:  A Quantum Chemical Study

Abstract

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.

Density functional calculations of 15N chemical shifts in solvated dipeptides

“…σ 33 is the most shielded component and lies approximately in the peptide plane; the projection of NH bond onto the plane of σ 22 and σ 33 forms an angle α with σ 33 . This definition of the angles is taken from (Brender et al 2001). Table 1 Bond lengths (in Å) used for calculations in gas phase (in vacuo), continuum-only, and cluster/continuum models for N-methylacetamide a NMA_vac refers to the NMA molecule structure optimized in vacuum b NMA_cont refers to NMA's molecular structure optimized in continuum-only model c NMA+3w refers to the optimized structure of NMA and three water molecules from the first coordination shell within the polarized continuum model.…”

How Does an Amide-15N Chemical Shift Tensor Vary in Peptides?

“…Tensor orientations were calculated from the Gaussian 98 output using the rotational matrix equation reported in a recent publication. 43 The orientation is related to the molecular frame by three Euler angles α, β, and γ, where α represents the angle between the most shielded axis δ 33 and the projection of the N-H bond onto the δ 33 -δ 22 plane; β, the angle between the least shielded axis δ 11 and the N-H bond; and γ, the angle between δ 11 and its projection onto the peptide plane. Thus, the CSA tensor can be completely described by six parameters: three principal shift values (δ 11 , δ 22 , δ 33 ) and three orientation angles (α, β, γ).…”

“…25,27,30,43 Discrepancies between the calculated and experimental shift values can be attributed to one or more possible factors. 43 There may be differences between the structures used in the crystallographic and experimental studies, an insufficient basis set may have been used in the calculations, or intermolecular interactions may have been improperly included.…”

Chemical Shift Anisotropy and Offset Effects in Cross Polarization Solid-State NMR Spectroscopy

“…8a and 8c; differences in time courses persist even with as many as 15,000 random orientations in powder averaging. Thus, in principle the relative orientation of the tensors, PM , is important (especially in high magnetic fields where the CSA span is larger) (33)(34)(35), though there could be regions of magnitudes of ω and d P where its effect is minimal (see Figs. 8a and 8c).…”