InternationalSpace-group symmetryTables for Crystallography Volume A Edited by M. I. Aroyo © International Union of Crystallography 2016 |
International Tables for Crystallography (2016). Vol. A, ch. 1.6, pp. 126-127
## Section 1.6.5.2. Space-group determination in macromolecular crystallography H. D. Flack
^{b} |

For macromolecular crystallography, succinct descriptions of space-group determination have been given by Kabsch (2010*a*,*b*, 2012) and Evans (2006, 2011). Two characteristics of macromolecular crystals give rise to variations on the small-molecule procedures described above.

The first characteristic is the large size of the unit cell of macromolecular crystals and the variation of the cell dimensions from one crystal to another. This makes the determination of the Bravais lattice by cell reduction problematic, as small changes of cell dimensions give rise to differences in the assignment. Kabsch (2010*a*,*b*, 2012) uses a `quality index' from each of Niggli's 44 lattice characters to come to a best choice. Grosse-Kunstleve *et al.* (2004) and Sauter *et al.* (2004) have found that some commonly used methods to determine the Bravais lattice are susceptible to numerical instability, making it possible for high-symmetry Bravais lattice types to be improperly identified. Sauter *et al.* (2004, 2006) find from practical experience that a deviation δ as high as 1.4° from perfect alignment of direct and reciprocal lattice rows must be allowed to construct the highest-symmetry Bravais type consistent with the data. Evans (2006) uses a value of 3.0°. The large unit-cell size also gives rise to a large number of reflections in the asymmetric region of reciprocal space, and taken with the tendency of macromolecular crystals to decompose in the X-ray beam, full-sphere data sets are uncommon. This means that confirmation of the Laue class by means of values of *R*_{int} (*R*_{merge}) are rarer than with small-molecule crystallography, although Kabsch (2010*b*) does use a `redundancy-independent *R* factor'. Evans (2006, 2011) describes methods very similar to those given as the second stage in Section 1.6.2.1. The conclusion of Sauter *et al.* (2006) and Evans (2006) is that *R*_{int} values as high as 25% must be permitted in order to assemble an optimal set of operations to describe the diffraction symmetry. Another interesting procedure, accompanied by experimental proof, has been devised by Sauter *et al.* (2006). They show that it is clearer to calculate *R*_{merge} values individually for each potential symmetry operation of a target point group rather than comparing *R*_{merge} values for target point groups globally. According to Sauter *et al.* (2006) the reason for this improvement lies in the lack of intensity data relating some target symmetry operations.

The second characteristic of macromolecular crystals is that the compound is known, or presumed, to be chiral and enantiomerically pure, so that the crystal structure is chiral. This limits the choice of space group to the 65 Sohncke space groups containing only translations, pure rotations or screw rotations. For ease of use, these have been typeset in bold in Tables 1.6.4.2–1.6.4.30.

For the evaluation of protein structures, Poon *et al.* (2010) apply similar techniques to those described in Section 1.6.2.3. The major tactical objective is to identify pairs of α-helices that have been declared to be symmetry-independent in the structure solution but which may well be related by a rotational symmetry of the crystal structure. Poon *et al.* (2010) have been careful to test their methodology against generated structural data before proceeding to tests on real data. Their results indicate that some 2% of X-ray structures in the Protein Data Bank potentially fit in a higher-symmetry space group. Zwart *et al.* (2008) have studied the problems of under-assigned translational symmetry operations, suspected incorrect symmetry and twinned data with ambiguous space-group choices, and give illustrations of the uses of group–subgroup relations.

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