Total rotation range for anomalous-dispersion data

Dauter, Z.; Wilson, K. S.

doi:10.1107/97809553602060000671

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. 9.1, p. 186 | 1 | 2 |

Section 9.1.7.2. Total rotation range for anomalous-dispersion data

Z. Dauter^a ^* and K. S. Wilson^b

^a National Cancer Institute, Brookhaven National Laboratory, NSLS, Building 725A-X9, Upton, NY 11973, USA, and ^bStructural Biology Laboratory, Department of Chemistry, University of York, York YO10 5DD, England
Correspondence e-mail: dauter@bnl.gov

9.1.7.2. Total rotation range for anomalous-dispersion data

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In the presence of anomalous-scattering centres, Friedel's law breaks down and the intensities of the two halves of the reciprocal sphere are no longer equivalent. Strictly speaking, reflections related by a centre of symmetry or mirror relation cease to have equal intensities, but those related by pure rotation preserve their equivalence. The non-equivalent pairs of reflections are known as Bijvoet pairs. In macromolecular crystallography, it is often highly desirable to record the intensity differences between the Bijvoet mates to provide information on the position of anomalous scatterers, usually to be exploited in phasing procedures (Part 14 ). The anomalous signal should also be retained for so-called native data, for example, in the discrimination between water and ions in the surface solvent shell.

This implies that the intensities of the unique reflections have to be measured for both hemispheres of reciprocal space. In the general (triclinic) case, this requires the rotation of the crystal by a wider rotation range. At very low resolution, the surface of the Ewald sphere can be approximated by a plane. In this case, rotation of the lower half of the Ewald sphere will cover a full hemisphere of data, and the upper half the remaining centrosymmetrically related hemisphere. At high resolution, the surface of the Ewald sphere increasingly deviates from planarity by θ on each side (Fig. 9.1.7.6). To record complete anomalous data for such a triclinic crystal therefore requires it to be rotated by $[180^{\circ} + 2\theta_{\max}]$ from a random starting position. This will measure each Bijvoet mate at least once. However, only after a total rotation of 360° will the average multiplicity reach a value of two.

Figure 9.1.7.6| top | pdf |

For data containing an anomalous signal, when both Bijvoet mates have to be measured, 180° rotation of a triclinic crystal is not sufficient and at least an additional $[2\theta_{\max}]$ is required.

Similar reasoning applies to higher-symmetry space groups. Intensity data for two asymmetric units related by a centre of symmetry or a mirror need to be recorded. For some cases, the total range remains the same for completeness of anomalous data as for native. However, in several symmetries or orientations, the total range must again be increased by either $[\theta_{\max}]$ or $[2\theta_{\max}]$ (Table 9.1.7.2).

References

International Tables for Crystallography (2006). Vol. F. ch. 9.1, p. 186