Average orientation Another validation comes from the MF parameters (ϕav,θav) which represent the polar angles of the average orientation of the C–C bond within the frame of the ubiquitin reference structure. It is expected that for those methyl groups with low mobility (high order parameter), the average orientation lies close to the corresponding orientation defined from the electron density in the reference crystal structure, especially if those are well-defined and unaffected by the crystal packing effects. It would also be expected that for more mobile methyl groups, this correlation would weaken due to the nature of the averaging effect of second order tensors explained earlier in the Materials and Methods section. Figure 3b shows the relationship between the order parameter and the angle between the average orientation defined from the X-ray structure (pdb code:1ubi). There is indeed a strong tendency for the MFA to yield a similar orientation of C–C bonds relative to the crystal structure for the more rigid methyl groups. Except for A28 and L69, all methyl groups with  > 0.45 are predicted within 20° of the reference. Conversely, for all other methyl groups with lower order parameter, an even distribution of angles is observed within the allowed range from 0° to 90°, due to the averaging properties of second order tensors.