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How to assign a (3 + 1)‐dimensional superspace group to an incommensurately modulated biological macromolecular crystal
Author(s) -
Porta Jason,
Lovelace Jeff,
Borgstahl Gloria E. O.
Publication year - 2017
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576717007294
Subject(s) - superspace , aperiodic graph , crystallography , crystal structure , crystallographic point group , group (periodic table) , diffraction , macromolecule , lattice (music) , chemistry , physics , theoretical physics , mathematics , quantum mechanics , combinatorics , biochemistry , supersymmetry , acoustics
Periodic crystal diffraction is described using a three‐dimensional (3D) unit cell and 3D space‐group symmetry. Incommensurately modulated crystals are a subset of aperiodic crystals that need four to six dimensions to describe the observed diffraction pattern, and they have characteristic satellite reflections that are offset from the main reflections. These satellites have a non‐integral relationship to the primary lattice and require q vectors for processing. Incommensurately modulated biological macromolecular crystals have been frequently observed but so far have not been solved. The authors of this article have been spearheading an initiative to determine this type of crystal structure. The first step toward structure solution is to collect the diffraction data making sure that the satellite reflections are well separated from the main reflections. Once collected they can be integrated and then scaled with appropriate software. Then the assignment of the superspace group is needed. The most common form of modulation is in only one extra direction and can be described with a (3 + 1)D superspace group. The (3 + 1)D superspace groups for chemical crystallographers are fully described in Volume C of International Tables for Crystallography . This text includes all types of crystallographic symmetry elements found in small‐molecule crystals and can be difficult for structural biologists to understand and apply to their crystals. This article provides an explanation for structural biologists that includes only the subset of biological symmetry elements and demonstrates the application to a real‐life example of an incommensurately modulated protein crystal.