Use of anomalous-scattering data in heavy-atom location

Matthews, B. W.

doi:10.1107/97809553602060000685

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

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International Tables for Crystallography (2006). Vol. F. ch. 14.1, p. 297 | 1 | 2 |

Section 14.1.11. Use of anomalous-scattering data in heavy-atom location

B. W. Matthews^a ^*

^aInstitute of Molecular Biology, Howard Hughes Medical Institute and Department of Physics, University of Oregon, Eugene, OR 97403, USA
Correspondence e-mail: brian@uoxray.uoregon.edu

14.1.11. Use of anomalous-scattering data in heavy-atom location

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A relation exactly analogous to equation (14.1.10.1) can be used to approximate the anomalous heavy-atom scattering amplitude, namely, $[\hfil\hfil|F_{H}''| \simeq {\textstyle{1 \over 2}}| F_{PH+} - F_{PH-}|\eqno(14.1.11.1)]$ (see Fig. 14.1.7.1b). As noted above, if all the heavy atoms are the same, $[F_{H} = k F_{H}'']$ . Thus, a Patterson function with coefficients $[(F_{PH+} - F_{PH-})^{2}]$ should also show the desired heavy-atom–heavy-atom vector peaks (Blow, 1957; Rossmann, 1961).

For each individual reflection, however, and as is also the case for phase determination, the information that is provided by the isomorphous-replacement difference $[(|F_{PH}| - |F_{P}|)]$ is exactly complementary to that provided by the anomalous-scattering measurement $[(|F_{PH+}| - |F_{PH-}|)]$ . By combining both sets of experimental measurements, it is possible to obtain a much better estimate of the heavy-atom scattering, $[|F_{H}|]$ , for every reflection (Kartha & Parthasarathy, 1965a,b; Matthews, 1966a; Singh & Ramaseshan, 1966). One formulation (Matthews, 1966a) can be written as $[{F_{H}^{2} = F_{P}^{2} + F_{PH}^{2} - 2F_{P}F_{PH} \{1 - [wk(F_{PH+} - F_{PH-})/2F_{P}^{2}\}^{1/2},} \eqno(14.1.11.2)]$ where $[F_{PH} = (F_{PH+} + F_{PH-})/2]$ and w is a weighting factor (from 0 to 1) that is an estimate of the relative reliability of the measurements of $[(F_{PH+} - F_{PH-})]$ compared with $[(F_{PH} - F_{P})]$ .

References

Blow, D. M. (1957). X-ray analysis of haemoglobin: determination of phase angles by isomorphous substitution. PhD thesis, University of Cambridge.Google Scholar

Kartha, G. & Parthasarathy, R. (1965a). Combination of multiple isomorphous replacement and anomalous dispersion data for protein structure determination. I. Determination of heavy-atom positions in protein derivatives. Acta Cryst. 18, 745–749.Google Scholar

Kartha, G. & Parthasarathy, R. (1965b). Combination of multiple isomorphous replacement and anomalous dispersion data for protein structure determination. II. Correlation of the heavy-atom positions in different isomorphous protein crystals. Acta Cryst. 18, 749–753.Google Scholar

Matthews, B. W. (1966a). The determination of the position of the anomalously scattering heavy atom groups in protein crystals. Acta Cryst. 20, 230–239.Google Scholar

Rossmann, M. G. (1961). The position of anomalous scatterers in protein crystals. Acta Cryst. 14, 383–388.Google Scholar

Singh, A. K. & Ramaseshan, S. (1966). The determination of heavy atom positions in protein derivatives. Acta Cryst. 21, 279–280.Google Scholar

International Tables for Crystallography (2006). Vol. F. ch. 14.1, p. 297