Dipolar waves as NMR maps of protein structure

The anisotropy of nuclear spin interactions results in a unique mapping of structure to the resonance frequencies and split tings observed in NMR spectra, however, the determination of molecular structure from experimentally measured spectral parameters is complicated by angular ambiguities resulting from the symmetry properties of dipole-dipole and chemical shift interactions. This issue can be addressed through the periodicity inherent in secondary structure elements, which can be used as an index of topology. Distinctive wheel-like patterns are observed in two-dimensional ¹H-¹⁵N heteronuclear dipolar/¹⁵N chemical shift PISEMA (polarization inversion spin-exchange at the magic angle) spectra of helical membrane proteins in highly aligned lipid bilayer samples. One-dimensional dipolar waves are an extension of two-dimensional PISA (polarity index slant angle) wheels to map protein structure in NMR spectra of both highly and weakly aligned samples. Dipolar waves describe the periodic wavelike variations of the magnitudes of the static heteronuclear dipolar couplings as a function of residue number in the absence of chemical shift effects. Weakly aligned samples of proteins display these same effects, primarily as residual dipolar couplings (RDCs), in solution NMR spectra. The corresponding properties of the RDCs in solution NMR spectra of weakly aligned helices represent a convergence of solid-state and solution NMR approaches to structure determination.