Determination of multiple torsion-angle constraints in U-¹³C,¹⁵N-labeled peptides: 3D ¹H-¹⁵N-¹³C-¹H dipolar chemical shift NMR spectroscopy in rotating solids

We demonstrate constraint of peptide backbone and side-chain conformation with 3D ¹H-¹⁵N-¹³C-¹H dipolar chemical shift, magic-angle spinning NMR experiments. In these experiments, polarization is transferred from ¹⁵N[i] by ramped SPECIFIC cross polarization to the ¹³C^α[i], ¹³C^β[i], and ¹³C^α[i - 1] resonances and evolves coherently under the correlated ¹H-¹⁵N and ¹H-¹³C dipolar couplings. The resulting set of frequency-labeled ¹⁵N¹H-¹³C¹H dipolar spectra depend strongly upon the molecular torsion angles π[i], χ1[/], and ψ[i - 1]. To interpret the data with high precision, we considered the effects of weakly coupled protons and differential relaxation of proton coherences via an average Liouvillian theory formalism for multispin clusters and employed average Hamiltonian theory to describe the transfer of ¹⁵N polarization to three coupled ¹³C spins (¹³C^α[i], ¹³C^β[i], and ¹³C^α[i - 1]). Degeneracies in the conformational solution space were minimized by combining data from multiple ¹⁵N¹H-¹³C¹H line shapes and analogous data from other 3D ¹H-¹³C^α-¹³C-¹H (χ1), ¹⁵N-¹³C^α-¹³ C′-¹⁵N (ψ), and ¹H-¹⁵N[i]-¹⁵N[i + 1]-¹H (φ, ψ) experiments. The method is demonstrated here with studies of the uniformly ¹³C,¹⁵N-labeled solid tripeptide N-formyl-Met-Leu-Phe-OH, where the combined data constrains a total of eight torsion angles (three φ, three χ1, and two ψ): φ(Met) = -146°, ψ(Met) = 159°, χ1(Met) = -85°, φ(Leu) = -90°, ψ(Leu) = -40°, χ1(Leu) = -59°, φ(Phe) = -166°, and χ1(Phe) = 56°. The high sensitivity and dynamic range of the 3D experiments and the data analysis methods provided here will permit immediate application to larger peptides and proteins when sufficient resolution is available in the ¹⁵N-¹³C chemical shift correlation spectra.