Section 16.1.8.4. Choosing a refinement strategy

Variations in the computational details of the dual-space loop can make major differences in the efficacy of SnB and SHELXD. Recently, several strategies were combined in SHELXD and applied to a 148-atom P1 test structure (Karle et al., 1989) with the results shown in Fig. 16.1.8.3. The CPU time requirements of parameter-shift (PS) and tangent-formula expansion (TE) are similar, both being slower than no phase refinement (NR). In real space, the random-omit-map strategy (RO) was slightly faster than simple peak picking (PP) because fewer atoms were used in the structure-factor calculations. Both of these procedures were much faster than iterative peaklist optimization (PO). The original SHELXD algorithm (TE + PO) performs quite well in comparison with the SnB algorithm (PS + PP) in terms of the percentage of correct solutions, but less well when the efficiency is compared in terms of CPU time per solution. Surprising, the two strategies involving random omit maps (PS + RO and TE + RO), which had been calculated to give reference curves, are much more effective than the other algorithms, especially in terms of CPU efficiency. Indeed these two runs appear to approach a 100% success rate as the number of cycles becomes large. The combination of random omit maps and Karle-type tangent expansion appears to be even more effective (Fig. 16.1.8.4) for gramicidin A, a structure (Langs, 1988). It should be noted that conventional direct methods incorporating the tangent formula tend to perform better in than in P1, perhaps because there is less risk of a uranium-atom pseudosolution.

Figure 16.1.8.3| top | pdf | (a) Success rates and (b) cost effectiveness for several dual-space strategies as applied to a 148-atom P1 structure. The phase-refinement strategies are: (PS) parameter-shift reduction of the minimal-function value, (TE) Karle-type tangent expansion (holding the top 40% highest fixed) and (NR) no phase refinement but Sim (1959) weights applied in the E map (these depend on and so cannot be employed after phase refinement). The real-space strategies are: (PP) simple peak picking using peaks, (PO) peaklist optimization (reducing peaks to ), and (RO) random omit maps (also reducing peaks to ). A total of about 10 000 trials of 400 internal loop cycles each were used to construct this diagram.

Figure 16.1.8.4| top | pdf | Success rates for the 317-atom structure of gramicidin A.

Subsequent tests using SHELXD on several other structures have shown that the use of random omit maps is much more effective than picking the same final number of peaks from the top of the peak list. However, it should be stressed that it is the combination TE + RO that is particularly effective. A possible special case is when a very small number of atoms is sought (e.g. Se atoms from MAD data). Preliminary tests indicate that peaklist optimization (PO) is competitive in such cases because the CPU time penalty associated with it is much smaller than when many atoms are involved.

With hindsight, it is possible to understand why the random omit maps provide such an efficient search algorithm. In macromolecular structure refinement, it is standard practice to omit parts of the model that do not fit the current electron density well, to perform some refinement or simulated annealing (Hodel et al., 1992) on the rest of the model to reduce memory effects, and then to calculate a new weighted electron-density map (omit map). If the original features reappear in the new density, they were probably correct; in other cases the omit map may enable a new and better interpretation. Thus, random omit maps should not lead to the loss of an essentially correct solution, but enable efficient searching in other cases. It is also interesting to note that the results presented in Figs. 16.1.8.3 and 16.1.8.4 show that it is possible, albeit much less efficiently, to solve both structures using random omit maps without the use of any phase relationships based on probability theory (curves NR + RO).