International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by E. Arnold, D. M. Himmel and M. G. Rossmann © International Union of Crystallography 2012 
International Tables for Crystallography (2012). Vol. F, ch. 16.1, pp. 419420
Section 16.1.8. Utilizing Pattersons for better starts
G. M. Sheldrick,^{a} C. J. Gilmore,^{b} H. A. Hauptman,^{c}^{‡} C. M. Weeks,^{c}^{*} R. Miller^{c} and I. Usón^{d}
^{a}Lehrstuhl für Strukturchemie, GeorgAugustUniversität Göttingen, Tammannstrasse 4, D37077 Göttingen, Germany,^{b}Department of Chemistry, University of Glasgow, Glasgow G12 8QQ, UK,^{c}Hauptman–Woodward Medical Research Institute, Inc., 700 Ellicott Street, Buffalo, NY 14203–1102, USA, and ^{d}Institució Catalana de Recerca i Estudis Avançats at IBMBCSIC, Barcelona Science Park. Baldiri Reixach 15, 08028 Barcelona, Spain 
When slightly heavier atoms such as sulfur are present, it is possible to start recycling procedures 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) nonHarker peaks further than a given minimum distance from the origin are selected, in turn, as twoatom translationsearch 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 twoatom search fragment may not correspond to correct atomic positions, nevertheless, by limiting the number of trials, some correct solutions may still be found. The twoatom vectors are chosen by biased random sampling that favours the vectors corresponding to higher Patterson values. The two atoms may be used to generate further atoms using a full Patterson superposition minimum function or a weighted difference synthesis.
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 16.1.8.1 shows the effect of using different twoatom search fragments for hirustasin, a previously unsolved 55aminoacid 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.

References
Schneider, T. R. (1998). Personal communication.Sheldrick, G. M., Dauter, Z., Wilson, K. S., Hope, H. & Sieker, L. C. (1993). The application of direct methods and Patterson interpretation to highresolution native protein data. Acta Cryst. D49, 18–23.
Usón, I., Sheldrick, G. M., de La Fortelle, E., Bricogne, G., di Marco, S., Priestle, J. P., Grütter, M. G. & Mittl, P. R. E. (1999). The 1.2 Å crystal structure of hirustasin reveals the intrinsic flexibility of a family of highly disulphide bridged inhibitors. Structure, 7, 55–63.