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.? A novel iterative procedure is described which allows both the orientation and dynamics of internuclear bond vectors to be determined from direct interpretation of NMR dipolar couplings, measured under at least three orthogonal alignment conditions. With the five orthogonal alignments available from the above mentioned mutation procedure, the approach also yields information on the degree of motional anisotropy and the direction in which the largest amplitude internal motion of each bond vector takes place. The method is demonstrated for the backbone 15N-1H, 13Ca-1Ha, and 13Ca-13C′ interactions in the previously well studied protein domain GB3, dissolved in a liquid crystalline suspension of filamentous phage Pf1. Alignment variation is achieved by using conservative mutations of charged surface residues. Results indicate remarkably uniform backbone dynamics, with amplitudes that agree well with those of previous 15N relaxation studies for most residues involved in elements of secondary structure, but larger amplitude dynamics than found by 15N relaxation for residues in loop and turn regions. In agreement with a previous analysis of dipolar couplings, the N-H bonds in the second beta-strand, which is involved in antibody recognition, show elevated dynamics with largest amplitudes orthogonal to the chain direction.
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