Solid-State NMR and Quantum Chemical Investigations of 13Cα Shielding Tensor Magnitudes and Orientations in Peptides:  Determining φ and ψ Torsion Angles

We report the experimental determination of the 13Cα 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 13Cα and its directly bonded 14N permits extraction of both the magnitude and the orientation of the shielding tensor with respect to the Cα−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 13Cα 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.