Side chain dynamics in unfolded protein states: An NMR based ²H spin relaxation study of Δ131Δ

NMR relaxation data on disordered proteins can provide insight into both structural and dynamic properties of these molecules. Because of chemical shift degeneracy in correlation spectra, detailed sitespecific analyses of side chain dynamics have not been possible. Here, we present new experiments for the measurement of side chain dynamics in methyl-containing residues in unfolded protein states. The pulse schemes are similar to recently proposed methods for measuring deuterium spin relaxation rates in ¹³CH₂D methyl groups in folded proteins.¹ However, because resolution in ¹H-¹³C correlation maps of unfolded proteins is limiting, relaxation data are recorded as a series of ¹H-¹⁵N spectra. The methodology is illustrated with an application to the study of side chain dynamics in Δ131Δ, a large disordered fragment of staphylococcal nuclease containing residues 1-3 and 13-140 of the wide-type protein. A good correlation between the order parameters of the symmetry axes of the methyl groups and the backbone ¹H-¹⁵N bond vectors of the same residue is observed. Simulations establish that such a correlation is only possible if the unfolded state is comprised of an ensemble of structures which are not equiprobable. A motional model, which combines wobbling-in-a-cone and Gaussian axial fluctuations, is proposed to estimate _χ1 torsion angle fluctuations, σ_χ1, of Val and Thr residues on the basis of the backbone and side chain order parameters. Values of σ_χ1 are approximately 10° larger than what has previously been observed in folded proteins. Of interest, the value of σ_χ1 for Val 104 is considerably smaller than for other Val or Thr residues, suggesting that it may be part of a hydrophobic cluster. Notably large ¹⁵N transverse relaxation rates are observed in this region. To our knowledge, this is the first time that side chain dynamics in an unfolded state have been studied in detail by NMR.