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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. 15.2, p. 327
Section 15.2.4. Figure-of-merit weighting for model phases
a
Department of Haematology, University of Cambridge, Wellcome Trust Centre for Molecular Mechanisms in Disease, CIMR, Wellcome Trust/MRC Building, Hills Road, Cambridge CB2 2XY, England |
Blow & Crick (1959)![[link]](/graphics/greenarr.gif)
and Sim (1959) showed that the electron-density map with the least r.m.s. error is calculated from centroid structure factors. This conclusion follows from Parseval's theorem, because the centroid structure factor (its probability-weighted average value or expected value) minimizes the r.m.s. error of the structure factor. Since the structure-factor distribution ![[p({\bf F}\hbox{;}\ {\bf F}_{C})]](/teximages/fach15o2/fach15o2fi39.svg)
is symmetrical about ![[{\bf F}_{C}]](/teximages/fach15o2/fach15o2fi20.svg)
, the expected value of F will have the same phase as , but the averaging around the phase circle will reduce its magnitude if there is any uncertainty in the phase value (Fig. 15.2.4.1). We treat the reduction in magnitude by applying a weighting factor called the figure of merit, m, which is equivalent to the expected value of the cosine of the phase error.
![[Figure 15.2.4.1]](/figures/Fafig15o2o4o1thm.gif) | Figure-of-merit weighted model-phased structure factor, obtained as the probability-weighted average over all possible phases. |
References
Blow, D. M. & Crick, F. H. C. (1959). The treatment of errors in the isomorphous replacement method. Acta Cryst. 12, 794–802.Google Scholar
Sim, G. A. (1959). The distribution of phase angles for structures containing heavy atoms. II. A modification of the normal heavy-atom method for non-centrosymmetrical structures. Acta Cryst. 12, 813–815.Google Scholar
