To this end, we chose several residues, for which MFA data were available with comparatively small experimental errors for both their methyl groups (Cγ1 and Cγ2 for valines, Cγ2 and Cδ1 for isoleucines and Cδ1 and Cδ2 for leucines), each acting as individual probes directly on the χ1 or χ2 angles. To model these side chain motions, we assume that their mechanism is dominated by rotameric jumps and fast libration fluctuation around equilibrium positions. As described in the Materials and Methods section, a grid search was performed on all population factors p representing the occupancy of each of the three (Val) or nine (Ile, Leu) possible combinations of ideal [gauche+ (60°), trans (180°), gauche− (-60°)] rotameric pairs for χ1 (V, I, L) and χ2 (I, L). In addition, we include isotropic order parameter terms,  and , to account for small scale fluctuations around each χ angle. Table 4 lists the average results for all solutions within 10% of the overall minimum of the squared sum of difference [ssd, (9)] of the grid search and compares them to the statistics from different ensembles.