How much backbone motion in ubiquitin is required to account for dipolar coupling data measured in multiple alignment media as assessed by independent cross-validation?

The magnitude of backbone internal motions in the small protein ubiquitin that needs to be invoked to account for dipolar coupling data measured in multiple alignment media is investigated using an intuitively straightforward approach. This involves simultaneous refinement of the coordinates (against NOE, torsion angle, and dipolar coupling restraints) and optimization of the magnitudes and orientations of the alignment tensors; by means of torsion angle simulated annealing and Cartesian space minimization. We show that N-H dipolar couplings in 11 different alignment media and N-C', H-N-C', and Calpha-C' dipolar coupling in two alignment media can be accounted for, at approximately the level of uncertainty in the experimental data, by a single structure representation. Extension to a two-member ensemble representation which provides the simplest description of anisotropic motions in the form of a two-site jump model (in which the overall calculated dipolar couplings are the averages of the calculated dipolar couplings of the individual ensemble members), results in modest, but significant, improvements in dipolar coupling R-factors for both the working set of couplings used in the refinement and for the free cross-validated set of Calpha-Halpha dipolar couplings recorded in two alignment media. Extensions to larger ensemble sizes do not result in any R-factor improvement for the cross-validated C(x-H(x dipolar couplings. With a few notable exceptions, the amplitudes of the anisotropic motions are small, with S-2(jump) order parameters greater than or equal to0.8. Moreover, the structural impact of those few residues that do exhibit larger amplitude motions (S2(jump) ranging from 0.3 to 0.8) is minimal and can readily be accommodated by very small backbone atomic rms shifts (<0.5 Angstrom) because of compensatory changes in phi and psi backbone torsion angles. In addition, evidence for correlated motions of N-H bond vectors is observed. For most practical applications, however, refinement of NMR structures against dipolar couplings using a single structure representation is adequate and will not adversely impact coordinate accuracy within the limits of the NMR method.