Determination of relative tensor orientations by γ-encoded chemical shift anisotropy/heteronuclear dipolar coupling 3D NMR spectroscopy in biological solids

Abstract

In this paper, we present 3D chemical shift anisotropy (CSA)/dipolar coupling correlation experiments, based on γ-encoded R-type symmetry sequences. The γ-encoded correlation spectra are exquisitely sensitive to the relative orientation of the CSA and dipolar tensors and can provide important structural and dynamic information in peptides and proteins. We show that the first-order (m = ±1) and second-order (m = ±2) Hamiltonians in the R-symmetry recoupling sequences give rise to different correlation patterns due to their different dependencies on the crystallite orientation. The relative orientation between CSA and dipolar tensors can be determined by fitting the corresponding correlation patterns. The orientation of ¹⁵N CSA tensor in the quasi-molecular frame is determined by the relative Euler angles, α_NH and β_NH, when the combined symmetry schemes are applied for orientational studies of ¹H–¹⁵N dipolar and ¹⁵N CSA tensors. The correlation experiments introduced here work at moderate magic angle spinning frequencies (10–20 kHz) and allow for simultaneous measurement of multiple sites of interest. We studied the orientational sensitivity of γ-encoded symmetry-based recoupling techniques numerically and experimentally. The results are demonstrated on [¹⁵N]-N-acetyl-valine (NAV) and N-formyl-Met-Leu-Phe (MLF) tripeptide.