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 (1)H-(15)N-(13)C-(1)H dipolar chemical shift, magic-angle spinning NMR experiments. In these experiments, polarization is transferred from (15)Ni by ramped SPECIFIC cross polarization to the (13)C(alpha)i, (13)C(beta)i, and (13)C(alpha)i - 1 resonances and evolves coherently under the correlated (1)H-(15)N and (1)H-(13)C dipolar couplings. The resulting set of frequency-labeled (15)N(1)H-(13)C(1)H dipolar spectra depend strongly upon the molecular torsion angles phii, chi1i, and psii - 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 (15)N polarization to three coupled (13)C spins ((13)C(alpha)i, (13)C(beta)i, and (13)C(alpha)i - 1). Degeneracies in the conformational solution space were minimized by combining data from multiple (15)N(1)H-(13)C(1)H line shapes and analogous data from other 3D (1)H-(13)C(alpha)-(13)C(beta)-(1)H (chi1), (15)N-(13)C(alpha)-(13)C'-(15)N (psi), and (1)H-(15)Ni-(15)Ni + 1-(1)H (phi, psi) experiments. The method is demonstrated here with studies of the uniformly (13)C,(15)N-labeled solid tripeptide N-formyl-Met-Leu-Phe-OH, where the combined data constrains a total of eight torsion angles (three phi, three chi1, and two psi): phi(Met) = -146 degrees, psi(Met) = 159 degrees, chi1(Met) = -85 degrees, phi(Leu) = -90 degrees, psi(Leu) = -40 degrees, chi1(Leu) = -59 degrees, phi(Phe) = -166 degrees, and chi1(Phe) = 56 degrees. 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 (15)N-(13)C chemical shift correlation spectra.