The Saupe matrix describing protein alignment in a liquid crystalline medium contains five independent elements, enabling the generation of up to five linearly independent alignment conditions. Measurement of internuclear residual dipolar couplings (RDCs) by NMR spectroscopy under these conditions, orthogonal in five-dimensional alignment space, provides access to the amplitude, asymmetry, and direction of motions of the internuclear vector. It is demonstrated for the small protein domain GB3 (56 residues) that suitably orthogonal alignment conditions can be generated in a single liquid crystalline medium of Pf1 phage, by generating a series of conservative mutants that have negligible impact on the time-averaged backbone structure of the domain. Mutations involve changes in the charge of several solvent-exposed sidechains, as well as extension of the protein by either an N- or C-terminal His-tag peptide, commonly used for protein purification. These protein mutants map out the five-dimensional alignment space, providing unique insights into the structure and dynamics.? 3JHN,Ha, 3JHN,Cb, and 3JHN,C′ couplings, all related to the backbone torsion angle phi, were measured for GB3. Measurements were carried out using both previously published methods, and novel sequences based on the multiple quantum principle, which limit attenuation of experimental couplings caused by finite life times of the spin states of passive spins. High reproducibility between the multiple quantum and conventional approaches confirms the accuracy of the measurements. With few exceptions, close agreement between 3JHN,Ha, 3JHN,Cb, and 3JHN,C′and values predicted by their respective Karplus equations is observed. For the three types of couplings, up to 20% better agreement is obtained when fitting the experimental couplings to a dynamic ensemble NMR structure, which has a phi angle root-mean-square spread of 8.64 and was previously calculated on the basis of a very extensive set of residual dipolar couplings, than for any single static NMR structure. Fits of 3J couplings to a 1.1-Ǻ X-ray structure, with hydrogens added in idealized positions, are 40-90% worse. Approximately half of the improvement when fitting to the NMR structures relates to the amide proton deviating from its idealized, in-peptide-plane position, indicating that the positioning of hydrogens relative to the backbone atoms is one of the factors limiting the accuracy at which the backbone torsion angle phi can be extracted from 3J couplings. Introducing an additional, residue-specific variable for the amplitude of phi angle fluctuations does not yield a statistically significant improvement when fitting to a set of dynamic Karplus curves, pointing to a homogeneous behavior of these amplitudes.
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