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A space-group graph showing all subgroups of space group P1211 (2a, b, c). Specifically, two distinct P21 subgroups are available with equal unit-cell parameters, related by an origin shift of ¼. See text and Table 2 ▶ for details.
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fig3: A space-group graph showing all subgroups of space group P1211 (2a, b, c). Specifically, two distinct P21 subgroups are available with equal unit-cell parameters, related by an origin shift of ¼. See text and Table 2 ▶ for details.

Mentions: An interesting crystallographic pathology can arise when pseudocentring is present. An example is given by Isupov & Lebedev (2008 ▶). In this case, the space group is P21 with a pseudotranslation (x + ½, y, z). Consider two P21 cells stacked side by side on the bc face of the unit cell. The resulting symmetry is described by the universal Hermann–Mauguin symbol P1211 (2a, b, c). A full list of symmetry operators in this setting is shown in Table 2 ▶. From this set of operators, a number of subgroups can be constructed (Fig. 3 ▶). Operators not used in the construction of the subgroup can be regarded as NCS operators. If operators A and B are designated as crystallographic symmetry, the space group is P21 and operators C and D are NCS operators. If, however, operators A and D are designated to be crystallo­graphic, the space group is P21 with an origin shift of (¼, 0, 0) and B and C are NCS operators. Both choices produce initially reasonable R values, but only choice one is correct and eventually leads to the best model.

Surprises and pitfalls arising from (pseudo)symmetry

Zwart PH, Grosse-Kunstleve RW, Lebedev AA, Murshudov GN, Adams PD - Acta Crystallogr. D Biol. Crystallogr. (2007)

Bottom Line: When more than a single molecule is present in the asymmetric unit, various pathological situations such as twinning, modulated crystals and pseudo translational or rotational symmetry can arise.The presence of pseudosymmetry can lead to uncertainties about the correct space group, especially in the presence of twinning.The main concepts are illustrated with several examples from the literature and the Protein Data Bank.

Affiliation: Berkeley Center for Structural Biology, Lawrence Berkeley National Laboratory, One Cyclotron Road, Building 6R2100, Berkeley, CA 94720, USA. phzwart@lbl.gov

ABSTRACT
It is not uncommon for protein crystals to crystallize with more than a single molecule per asymmetric unit. When more than a single molecule is present in the asymmetric unit, various pathological situations such as twinning, modulated crystals and pseudo translational or rotational symmetry can arise. The presence of pseudosymmetry can lead to uncertainties about the correct space group, especially in the presence of twinning. The background to certain common pathologies is presented and a new notation for space groups in unusual settings is introduced. The main concepts are illustrated with several examples from the literature and the Protein Data Bank.

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