Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/wiley/mathematical-aspects-of-molecular-replacement-i-algebraic-properties-oaaguJk27z
References (68)
-
D. Jamrog, Yin Zhang, G. Phillips (2003)
SOMoRe: a multi-dimensional search and optimization approach to molecular replacement.Acta crystallographica. Section D, Biological crystallography, 59 Pt 2
-
(1990)
Lectures on Crystallographic Groups, Aarhus Universitet Matematisk Institut Lecture Series -
G. Chirikjian (2010)
Group theory and biomolecular conformation: I. Mathematical and computational modelsJournal of Physics: Condensed Matter, 22
-
H. Hilton (2010)
Mathematical Crystallography and the Theory of Groups of MovementsNature, 69
-
(1980)
Acta Cryst. A36 -
P. Nagy, K. Strambach (2002)
Loops in Group Theory and Lie Theory -
(1999)
Smooth Quasigroups and Loops. Dordrecht: Kluwer and USA -
R. Evarestov, V. Smirnov (1993)
Site symmetry in crystals -
(1968)
Acta Cryst. A24 -
F. Hirshfeld (1968)
Symmetry in the generation of trial structuresActa Crystallographica Section A, 24
-
(2010)
J. Phys. Condens. Matter -
(2008)
Acta Cryst. A64 -
G. Jogl, X. Tao, Yingwu Xu, L. Tong (2001)
COMO: a program for combined molecular replacement.Acta crystallographica. Section D, Biological crystallography, 57 Pt 8
-
BY Navaza (1994)
AMoRe: an automated package for molecular replacementActa Crystallographica Section A, 50
-
E. Lattman, W. Love (1970)
A rotational search procedure for detecting a known molecule in a crystal. ErrataActa Crystallographica Section B Structural Crystallography and Crystal Chemistry, 26
-
(2001)
Biomolecular Crystallography: Principles, Practice -
(1963)
Mathematical Crystallography and the Theory -
(1962)
Acta Cryst -
(2008)
Foundations of Crystallography with Computer -
(2010)
Representations of Crystallographic Space Groups, Commission on Mathematical and Theoretical Crystallography -
(1970)
Acta Cryst. B26 -
M. Nespolo (2008)
Does mathematical crystallography still have a role in the XXI century?Acta crystallographica. Section A, Foundations of crystallography, 64 Pt 1
-
G. Rhodes (1993)
Crystallography Made Crystal Clear -
Jonathan Smith (2006)
Quasigroups and Loops -
A. Weinstein (1996)
Groupoids: Unifying Internal and External Symmetry A Tour through Some Examples -
R. Bruck (1971)
A Survey of Binary Systems -
H. Pflugfelder (1990)
Quasigroups and loops : introduction -
E. Lattman, P. Loll (2008)
Protein Crystallography: A Concise Guide -
(2010)
Acta Cryst. D66 -
(2008)
Protein Crystallography: a Concise -
(1968)
J. Mol. Biol -
(2006)
Acta Cryst. D62 -
W. Kandasamy (2003)
Smarandache loops -
(2003)
Acta Cryst. D59 -
(1994)
Collaborative Computational Project, Number Acta Cryst. D50 -
C. Bradley, A. Cracknell (1972)
The mathematical theory of symmetry in solids;: Representation theory for point groups and space groups, -
S. Sheriff, H. Klei, M. Davis (1999)
Implementation of a six-dimensional search using the AMoRe translation function for difficult molecular-replacement problemsJournal of Applied Crystallography, 32
-
(1994)
Acta Cryst. A50 -
M. Rossmann, D. Blow (1962)
The detection of sub‐units within the crystallographic asymmetric unitActa Crystallographica, 15
-
M. Senechal (1980)
A simple characterization of the subgroups of space groupsActa Crystallographica Section A, 36
-
R. Evarestov, V. Smirnov (1993)
Site Symmetry in Crystals: Theory and Applications -
G. Burns, A. Glazer, A. Maradudin (1979)
Space groups for solid state scientists -
B. Matthews (1968)
Solvent content of protein crystals.Journal of molecular biology, 33 2
-
Collaborative Computational (1994)
The CCP4 suite: programs for protein crystallography.Acta crystallographica. Section D, Biological crystallography, 50 Pt 5
-
Stephanie Wukovitz, T. Yeates (1995)
Why protein crystals favour some space-groups over othersNature Structural Biology, 2
-
Representations of Crystallographic Space Groups -
Jay Jeong, E. Lattman, G. Chirikjian (2006)
A method for finding candidate conformations for molecular replacement using relative rotation between domains of a known structure.Acta crystallographica. Section D, Biological crystallography, 62 Pt 4
-
Carolyn Brock (2019)
International Tables for CrystallographyInternational Tables for Crystallography
-
R. Caliandro, B. Carrozzini, G. Cascarano, C. Giacovazzo, A. Mazzone, D. Siliqi (2009)
Molecular replacement: the probabilistic approach of the program REMO09 and its applications.Acta crystallographica. Section A, Foundations of crystallography, 65 Pt 6
-
G. Chirikjian, A. Kyatkin, Ac Buckingham (2000)
Engineering Applications of Noncommutative Harmonic Analysis: With Emphasis on Rotation and Motion Groups -
Jonathan Smith (2006)
An Introduction to Quasigroups and Their Representations -
R. Bryan (2000)
Crystallography made crystal clear (2nd edition) . By Gale Rhodes. London: Academic Press, 2000. Pp. xix + 269 + 21 colour plates. Price £29.95 (paperback) ISBN 012 587072 8. -
Notices Of The -
Michael Rossmann (2001)
Molecular replacement ± historical background -
T. Hahn (2006)
International Tables for Crystallography: Space-group symmetry -
A. Vagin, A. Teplyakov (2010)
Molecular replacement with MOLREP.Acta crystallographica. Section D, Biological crystallography, 66 Pt 1
-
B. Iversen (1990)
Lectures on crystallographic groups -
(2009)
Acta Cryst. A65 -
W. Miller (1972)
Symmetry groups and their applications -
(2001)
Beitr. Algebr. Geom -
M. Julian (2008)
Foundations of Crystallography with Computer Applications -
(2001)
Acta Cryst. D57 -
B. Rupp (2009)
Biomolecular Crystallography: Principles, Practice, and Application to Structural Biology -
M. Ladd (1989)
Symmetry in molecules and crystals -
L. Sabinin (1999)
Smooth Quasigroups and Loops -
P. Engel, P. Engel (1986)
Geometric Crystallography: An Axiomatic Introduction to Crystallography -
HA Kuyong (2007)
FOR CRYSTALLOGRAPHIC GROUPS OF -
(2011)
Chirikjian Mathematical aspects of molecular replacement
- Publisher
- Wiley
- Copyright
- Copyright © 2011 Wiley Subscription Services, Inc., A Wiley Company
- ISSN
- 0108-7673
- eISSN
- 1600-5724
- DOI
- 10.1107/S0108767311021003
- pmid
- 21844648
- Publisher site
- See Article on Publisher Site
Abstract
Molecular replacement (MR) is a well established method for phasing of X‐ray diffraction patterns for crystals composed of biological macromolecules of known chemical structure but unknown conformation. In MR, the starting point is known structural domains that are presumed to be similar in shape to those in the macromolecular structure which is to be determined. A search is then performed over positions and orientations of the known domains within a model of the crystallographic asymmetric unit so as to best match a computed diffraction pattern with experimental data. Unlike continuous rigid‐body motions in Euclidean space and the discrete crystallographic space groups, the set of motions over which molecular replacement searches are performed does not form a group under the operation of composition, which is shown here to lack the associative property. However, the set of rigid‐body motions in the asymmetric unit forms another mathematical structure called a quasigroup, which can be identified with right‐coset spaces of the full group of rigid‐body motions with respect to the chiral space group of the macromolecular crystal. The algebraic properties of this space of motions are articulated here.
Journal
Acta Crystallographica Section A Foundations of Crystallography – Wiley
Published: Jan 1, 2011
Keywords: ; ; ; ;