Figure 7 models the result of the grid search. For the MFA-based model, we generated 200 structures satisfying the relative rotamer populations and represented the overall isotropic order parameter as a normal distribution of deviations around each of the χ angles. The figure gives a sense of how the RDC-based MFA data can roughly reproduce the same dominant rotameric conformations as those present in the different ensembles for all types of residues. Furthermore, the majority of missing rotamers in the ensembles are also excluded or very rare in the results of the grid search. This result is quite remarkable considering that the ensemble conformations are largely driven by distance and J-coupling restraints as well as hydrophobic packing energy during minimization, whereas the MFA models are purely and uniquely based on orientation restraints.
Fig. 7 Eight representative examples of methyl bearing ubiquitin side chain heterogeneity from average structure (pdb:1d3z), from backrub-ensemble (brub), from dynamic ensembles (pdb:1xqq, 2nr2, 2k39) and from ensembles generated by rotamer model-fitting of the average spherical harmonics resulting from the Model-free Analysis (MFA). Backbone is shown in black, Cβ–Cγ1 (Cβ–Cγ2), Cγ–Cδ (Cβ–Cγ2) and Cγ–Cδ1 (Cγ–Cδ2) bonds are in red (green) for valines, isoleucines, and leucines, respectively. In the MFA rotamer construction of leucines, the small scale fluctuation order parameter is entirely represented in χ2. Side chains are aligned based on N, Cα,Cβ and C′ positions