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. 16.2, p. 348   | 1 | 2 |

Section 16.2.3.1. The random-atom model

G. Bricognea*

aLaboratory of Molecular Biology, Medical Research Council, Cambridge CB2 2QH, England
Correspondence e-mail: gb10@mrc-lmb.cam.ac.uk

16.2.3.1. The random-atom model

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The standard setting of probabilistic direct methods (Hauptman & Karle, 1953[link]; Bertaut, 1955a[link],b[link]; Klug, 1958[link]) uses implicitly as its starting point a source of random atomic positions. This can be described in the terms introduced in Section 16.2.2.1[link] by using a continuous alphabet [{\cal A}] whose symbols s are fractional coordinates x in the asymmetric unit of the crystal, the uniform measure μ being the ordinary Lebesgue measure [\hbox{d}^{3}{\bf x}]. A message of length N generated by that source is then a random N-equal-atom structure.

References

First citation Bertaut, E. F. (1955a). La méthode statistique en cristallographie. I. Acta Cryst. 8, 537–543.Google Scholar
 First citation Bertaut, E. F. (1955b). La méthode statistique en cristallographie. II. Quelques applications. Acta Cryst. 8, 544–548.Google Scholar
 First citation Hauptman, H. & Karle, J. (1953). The solution of the phase problem: I. The centrosymmetric crystal. ACA Monograph No. 3. Pittsburgh: Polycrystal Book Service.Google Scholar
 First citation Klug, A. (1958). Joint probability distribution of structure factors and the phase problem. Acta Cryst. 11, 515–543.Google Scholar








































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