Amplitudes of Protein Backbone Dynamics and Correlated Motions in a Small α/β Protein: Correspondence of Dipolar Coupling and Heteronuclear Relaxation Measurements

Abstract

Backbone residual dipolar coupling (N−H, Cα−Hα, N−C‘, and Cα-C‘) data collected in five different media on the B3 IgG binding domain of streptococcal protein G (GB3) have been analyzed by simultaneous refinement of the coordinates and optimization of the magnitudes and orientations of the alignment tensors using single and multiple structure representations. We show, using appropriate error analysis, that agreement between observed and calculated dipolar couplings at the level of experimental uncertainty is obtained with a two-structure (N_e = 2) ensemble representation which represents the simplest equilibrium description of anisotropic motions. The data permit one to determine the magnitude of the anisotropic motions along the four different backbone bond vectors in terms of 〈S²(jump)〉 order parameters. The order parameters, 〈 (jump)〉, for the N−H bond vectors are in qualitative agreement with the generalized order parameters, (relaxation), derived from ¹⁵N relaxation measurements, with a correlation coefficient of 0.84. (relaxation) can be regarded as the product of an anisotropic order parameter, corresponding to 〈 (jump)〉 derived from the residual dipolar couplings, and an axially symmetric order parameter, (axial), corresponding to bond librations which are expected to be essentially uniform along the polypeptide chain. The current data indicate that the average value of (axial) is ∼0.9. The close correspondence of 〈 (jump)〉 and (relaxation) indicates that any large-scale displacements from the mean coordinate positions on time scales longer than the rotational correlation time are rare and hence do not perturb the observed dipolar couplings. Analysis of a set of 100 N_e = 2 ensembles reveals the presence of some long-range correlated motions of N−H and Cα−Hα vectors involving residues far apart in the sequence but close together in space. In addition, direct evidence is obtained for ubiquitous crankshaft motions along the entire length of the polypeptide backbone manifested by the anticorrelation of the backbone torsion angles φ_i and ψ_i-1.