Solid-state NMR and quantum chemical investigations of ¹³C ^α shielding tensor magnitudes and orientations in peptides: Determining φ and ψ torsion angles

We report the experimental determination of the ¹³C ^α chemical shift tensors of Ala, Leu, Val, Phe, and Met in a number of polycrystalline peptides with known X-ray or de novo solid-state NMR structures. The 700 Hz dipolar coupling between ¹³C^α and its directly bonded ¹⁴N permits extraction of both the magnitude and the orientation of the shielding tensor with respect to the C ^α-N bond vector. The chemical shift anisotropy (CSA) is recoupled under magic-angle spinning using the SUPER technique (Liu et al., J. Magn. Reson. 2002, 155, 15-28) to yield quasi-static chemical shift powder patterns. The tensor orientation is extracted from the ¹³C- ¹⁴N dipolar modulation of the powder line shapes. The magnitudes and orientations of the experimental ¹³C^α chemical shift tensors are found to be in good accord with those predicted from quantum chemical calculations. Using these principal values and orientations, supplemented with previously measured tensor orientations from ¹³C-¹⁵N and ¹³C-¹H dipolar experiments, we are able to predict the (φ, ψ, χ₁) angles of Ala and Val within 5.8° of the crystallographic values. This opens up a route to accurate determination of torsion angles in proteins based on shielding tensor magnitude and orientation information using labeled compounds, as well as the structure elucidation of noncrystalline organic compounds using natural abundance ¹³C NMR techniques.