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International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F. ch. 15.1, p. 316
Section 15.1.2.3.1. Introduction
a
Division of Basic Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N., Seattle, WA 90109, USA,bDepartment of Chemistry, University of York, York YO1 5DD, England, and cDepartment of Physics, University of York, York YO1 5DD, England |
Noncrystallographic symmetry (NCS) arises in crystals when there are two or more of the same molecules in one asymmetric unit. Such symmetries are local, since they only apply within a sub-region of a single unit cell. A fivefold axis, for example, must be noncrystallographic, since it is not possible to tessellate objects with fivefold symmetry. Since the symmetry does not map the crystal lattice back onto itself, the individual molecules that are related by the noncrystallographic symmetry will be in different environments; therefore, the symmetry relationships are only approximate.
Noncrystallographic symmetries provide phase information by the following means. Firstly, the related regions of the map may be averaged together, increasing the ratio of signal to noise in the map. Secondly, since the asymmetric unit must be proportionally larger to hold multiple copies of the molecule, the number of independent diffraction amplitudes available at any resolution is also proportionally larger. This redundancy in sampling the molecular transform leads to additional phase information which can be used for phase improvement.
