Anisotropic small amplitude peptide plane dynamics in proteins from residual dipolar couplings

The effect of small amplitude anisotropic peptide plane motion on residual dipolar couplings (RDC) measured in proteins has been investigated. RDC averaging effects in the presence of GAF (Gaussian axial fluctuation) motions are found to vary strongly depending on the peptide plane orientation. Even low amplitude dynamics can significantly affect derived alignment tensor parameters if this motion is not taken into account. An analytical description of averaged N-H-N RDCs is introduced that includes basic GAF-like motion. The averaging depends on the orientation of the peptide plane (alpha, beta, gamma) in the alignment frame and on the motional amplitude (sigma). This expression is used to investigate the presence of anisotropic reorientational dynamics in proteins by incorporating sigma as an additional parameter into the alignment tensor analysis. Average GAF amplitudes (sigma(av)) are determined for secondary structural elements from single experimental N-H-N RDC data sets from five different proteins, in combination with high-resolution structural models. This yields statistically significant improvement over the static description, and detects sigma(av), values ranging from 14.4 to 17.0degrees for the different proteins. A higher value of sigma(av) = 20degrees from loop regions was found using two independent sets of N-H-N RDC in the protein lysozyme, for which a very high-resolution structure is available. Comparison of fitting behavior over 13 structures from lysozyme of crystal diffraction resolution ranging from 0.9 to 2.1 Angstrom indicates a small spread of motional amplitudes, demonstrating that the method is robust up to this level of resolution. A combined definition of C-alpha-C' and N-H-N RDC under the influence of GAF motions allows simultaneous fitting of both RDC. Application to three proteins leads to similar sigma(av) values and a more significant improvement with respect to the static model. Using the GAF model to describe conformationally averaged RDC is important for two reasons: a more accurate definition of the alignment tensor magnitude can be derived, and the method can be used to detect average small amplitude motions in protein backbones from readily accessible data, on time scales not easily sampled by other NMR techniques.