Section 16.1.8.1. Utilizing Pattersons for better starts

When slightly heavier atoms such as sulfur are present, it is possible to start the Shake-and-Bake recycling procedure from a set of atomic positions that are consistent with the Patterson function. For large structures, the vectors between such atoms will correspond to Patterson densities around or even below the noise level, so classical methods of locating the positions of these atoms unambiguously from the Patterson are unlikely to succeed. Nevertheless, the Patterson function can still be used to filter sets of starting atoms. This filter is currently implemented as follows in SHELXD. First, a sharpened Patterson function (Sheldrick et al., 1993) is calculated, and the top 200 (for example) non-Harker peaks further than a given minimum distance from the origin are selected, in turn, as two-atom translation-search fragments, one such fragment being employed per solution attempt. For each of a large number of random translations, all unique Patterson vectors involving the two atoms and their symmetry equivalents are found and sorted in order of increasing Patterson density. The sum of the smallest third of these values is used as a figure of merit (PMF). Tests showed that although the globally highest PMF for a given two-atom search fragment may not correspond to correct atomic positions, nevertheless, by limiting the number of trials, some correct solutions may still be found. After all the vectors have been used as search fragments (e.g. after 200 attempts), the procedure is repeated starting again with the first vector. The two atoms may be used to generate further atoms using a full Patterson superposition minimum function or a weighted difference synthesis (in the current version of SHELXD, a combination of the two is used).

In the case of the small protein BPTI (Schneider, 1998), 15 300 attempts based on 100 different search vectors led to four final solutions with mean phase error less than 18°, although none of the globally highest PMF values for any of the search vectors corresponded to correct solutions. Table 16.1.8.2 shows the effect of using different two-atom search fragments for hirustasin, a previously unsolved 55-amino-acid protein containing five disulfide bridges first solved using SHELXD (Usón et al., 1999). It is not clear why some search fragments perform so much better than others; surprisingly, one of the more effective search vectors deviates considerably (1.69 Å) from the nearest true S–S vector.