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

International Tables for Crystallography (2006). Vol. F, ch. 14.1, p. 296   | 1 | 2 |

Section 14.1.8. The phase probability distribution for anomalous scattering

B. W. Matthewsa*

aInstitute of Molecular Biology, Howard Hughes Medical Institute and Department of Physics, University of Oregon, Eugene, OR 97403, USA
Correspondence e-mail:

14.1.8. The phase probability distribution for anomalous scattering

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From Fig.[link], it can be seen that the most probable phase angle will be the one for which [\varepsilon_{+} = \varepsilon_{-}]. At any other phase angle, there will be an `anomalous-scattering lack of closure' which we define to be [(\varepsilon_{+} - \varepsilon_{-})]. The value of [(\varepsilon_{+} - \varepsilon_{-})] can readily be calculated as a function of ϕ (Matthews, 1966b[link]; Hendrickson, 1979[link]). Thus, if the r.m.s. error in [(\varepsilon_{+} - \varepsilon_{-})] is [E'], and the distribution of error is assumed to be Gaussian, then from measurements of anomalous scattering, the probability [P_{\rm ano}(\varphi)] of phase ϕ being the true phase of [{\bf F}_{P}] can be estimated using an equation exactly analogous to equation ([link]).


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Vector diagrams illustrating lack of closure in the anomalous-scattering method.

An example of an anomalous-scattering phase probability distribution is shown by the dotted curve in Fig.[link]. The asymmetry of the distribution arises from the fact that [P_{\rm ano}(\varphi)] is the phase probability distribution for [F_{P}] rather than that of [F_{PH}], which would be symmetrical about the phase of [F_{H}'']. The overall probability distribution obtained by combining the anomalous-scattering data with the previous isomorphous-replacement data (Fig.[link]) is given by [P(\varphi) = N P_{\rm iso} (\varphi) P_{\rm ano}(\varphi) \eqno(] and is illustrated in Fig.[link].


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Combination of isomorphous replacement and anomalous-scattering phase probabilities for a single isomorphous replacement. [P_{\rm iso} (\varphi)] is drawn as a solid line, [P_{\rm ano} (\varphi)] as a dotted line, and the combined probability distribution is drawn as a dotted-and-dashed line.


Hendrickson, W. A. (1979). Phase information from anomalous-scattering measurements. Acta Cryst. A35, 245–247.Google Scholar
Matthews, B. W. (1966b). The extension of the isomorphous replacement method to include anomalous scattering measurements. Acta Cryst. 20, 82–86.Google Scholar

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