International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

International Tables for Crystallography (2006). Vol. F. ch. 21.1, p. 503   | 1 | 2 |

Section 21.1.7.2.5. Noncrystallographic symmetry

G. J. Kleywegta*

aDepartment of Cell and Molecular Biology, Uppsala University, Biomedical Centre, Box 596, SE-751 24 Uppsala, Sweden
Correspondence e-mail: gerard@xray.bmc.uu.se

21.1.7.2.5. Noncrystallographic symmetry

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Molecules that are related by noncrystallographic symmetry exist in very similar, but not identical, physical environments. This implies that their structures are expected to be quite similar, although different relative domain orientations and local variations may occur (e.g. owing to different crystal-packing interactions; Kleywegt, 1996[link]). Many criteria have been developed to quantify the differences between (NCS) related models. Some, such as the r.m.s. distance (e.g. on all atoms, backbone atoms or Cα atoms) are based on distances between equivalent atoms, measured after a (to some extent arbitrary; Kleywegt, 1996[link]) structural superpositioning operation has been performed. Others are based on a comparison of torsion angles, be it of main-chain ϕ, ψ angles [e.g. Δϕ, Δψ plot (Korn & Rose, 1994[link]); multiple-model Ramachandran plot (Kleywegt, 1996[link]); σ(ϕ), σ(ψ) plot (Kleywegt, 1996[link]); circular variance (Allen & Johnson, 1991[link]) plots of ϕ and ψ (G. J. Kleywegt, unpublished results); Euclidian ϕ, ψ distances (Carson et al., 1994[link]) or pseudo-energy values (Carson et al., 1994[link])] or side-chain χ1, χ2 angles [e.g. multiple-model χ1, χ2 plot (Kleywegt, 1996[link]); σ(χ1), σ(χ2) plots (Kleywegt, 1996[link]); circular variance (Allen & Johnson, 1991[link]) plots of χ1 and χ2 (G. J. Kleywegt, unpublished results); Euclidian χ1, χ2 distances (Carson et al., 1994[link]) or pseudo-energy values (Carson et al., 1994[link])]. Still other methods are based on analysing differences in contact-surface areas (Abagyan & Totrov, 1997[link]), temperature factors (Kleywegt, 1996[link]) or the geometry of the Cα backbone alone (Flocco & Mowbray, 1995[link]; Kleywegt, 1996[link]). Many of these methods can also be used to compare the structures of related molecules in different crystals or crystal forms (e.g. complexes, mutants).

References

First citation Abagyan, R. A. & Totrov, M. M. (1997). Contact area difference (CAD): a robust measure to evaluate accuracy of protein models. J. Mol. Biol. 268, 678–685.Google Scholar
First citation Allen, F. H. & Johnson, O. (1991). Automated conformational analysis from crystallographic data. 4. Statistical descriptors for a distribution of torsion angles. Acta Cryst. B47, 62–67.Google Scholar
First citation Carson, M., Buckner, T. W., Yang, Z., Narayana, S. V. L. & Bugg, C. E. (1994). Error detection in crystallographic models. Acta Cryst. D50, 900–909.Google Scholar
First citation Flocco, M. M. & Mowbray, S. L. (1995). Cα-based torsion angles: a simple tool to analyze protein conformational changes. Protein Sci. 4, 2118–2122.Google Scholar
First citation Kleywegt, G. J. (1996). Use of non-crystallographic symmetry in protein structure refinement. Acta Cryst. D52, 842–857.Google Scholar
First citation Korn, A. P. & Rose, D. R. (1994). Torsion angle differences as a means of pinpointing local polypeptide chain trajectory changes for identical proteins in different conformational states. Protein Eng. 7, 961–967.Google Scholar








































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