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. We previously 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, and providing access to anisotropic parameters such as the 13C, 15N and 1H chemical shielding tensors. Rather than modifying the charge distribution to alter protein alignment, we have demonstrated that for detergent-solubilized systems it is also possible to change alignment by altering the detergent and lipid composition of the sample. Combining these technologies, we have engaged in a modelfree study of the sidechain conformational distributions in a small model protein, GB3. We find that the RDC data are compatible with a single narrow distribution of sidechain chi1 angles for only about 40% of the residues. For more than half of the residues, populations greater than 10% for a second rotamer are observed, and four residues require sampling of three rotameric states to fit the RDC data. In virtually all cases, sampled chi11 values are found to center closely around ideal g-, g+ and t rotameric angles, even though no rotamer restraint is used when deriving the sampled angles. The root-mean-square difference between experimental 3JHH couplings and those predicted by the Haasnoot-parameterized, motion-adjusted Karplus equation reduces from 2.05 Hz to 0.75 Hz when using the new rotamer analysis instead of the 1.1- X-ray structure as input for the dihedral angles. A comparison between observed and predicted 3JHH values suggests that the root-mean-square amplitude of chi1 angle fluctuations within a given rotamer well is ca 20. The quantitatively defined sidechain rotamer equilibria obtained from our study set new benchmarks for evaluating improved molecular dynamics force fields, and also will enable further development of quantitative relations between sidechain chemical shift and structure. In a separate but related approach, we use the measurement of multiple three-bond J couplings as a new method to define the root-mean-square amplitude of backbone phi angle fluctuations. Although for most folded proteins, these fluctuations are too small (<15 deg) to be detectable by this method, for intrinsically disordered proteins an accurate, residue-specific estimate can be made. This approach has been used to study two amyloidogenic proteins, alpha-synuclein and Abeta peptides.
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