Section 18.2.7. Ensemble models

In cases of conformational variability or discrete disorder, there is not one single correct solution to the global minimization of equation (18.2.3.1). Rather, the X-ray diffraction data represent a spatial and temporal average over all conformations that are assumed by the molecule. Ensembles of structures, which are simultaneously refined against the observed data, may thus be a more appropriate description of the diffraction data. This has been used for some time when alternate conformations are modelled locally. Alternate conformations can be generalized to global conformations (Gros et al., 1990; Kuriyan et al., 1991; Burling & Brünger, 1994), i.e., the model is duplicated n-fold, the calculated structure factors corresponding to each copy of the model are summed, and this composite structure factor is refined against the observed X-ray diffraction data. Each member of the family is chemically `invisible' to all other members. The optimal number, n, can be determined by cross validation (Burling & Brünger, 1994; Burling et al., 1996).

An advantage of a multi-conformer model is that it directly incorporates many possible types of disorder and motion (global disorder, local side-chain disorder, local wagging and rocking motions). Furthermore, it can be used to detect automatically the most variable regions of the molecule by inspecting the atomic r.m.s. difference around the mean as a function of residue number. Thermal factors of single-conformer models may sometimes be misleading because they underestimate the degree of motion or disorder (Kuriyan et al., 1986), and, thus, the multiple-conformer model can be a more faithful representation of the diffraction data. A disadvantage of the multi-conformer model is that it introduces many more parameters in the refinement.

Although there are some similarities between averaging structure factors of individually refined structures and performing multi-conformer refinement, there are also fundamental differences. For example, multi-start averaging seeks to improve the calculated electron-density map by averaging out the noise present in the individual models, each of which is still a good representation of the diffraction data. This method is most useful at the early stages of refinement when the model still contains errors. In contrast, multi-conformer refinement seeks to create an ensemble of structures at the final stages of refinement which, taken together, best represent the data. It should be noted that each individual conformer of the ensemble does not necessarily remain a good description of the diffraction data, since the whole ensemble is refined against the data. Clearly, multi-conformer refinement requires a high observable-to-parameter ratio.