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

International Tables for Crystallography (2012). Vol. F, ch. 15.3, pp. 409-410   | 1 | 2 |

Section Phase-extension schemes

K. D. Cowtan,a* K. Y. J. Zhangb and P. Mainc

aDepartment of Chemistry, University of York, York YO1 5DD, England,bDivision of Basic Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N., Seattle, WA 90109, USA, and cDepartment of Physics, University of York, York YO1 5DD, England
Correspondence e-mail: Phase-extension schemes

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When performing phase extension, the order in which the structure factors are included will affect the final accuracy of the extended phases. The phases obtained from previous cycles of phase extension will be included in the calculation of new phases for the unphased structure factors in the next cycle. A reflection with more accurately determined phases might enhance the phase-extension power of the original set of reflections, whereas a reflection with less accurately determined phases might corrupt the phase-extension power of the original set of reflections and make the phase extension deteriorate quickly. The factors that might affect phase extension are the structure-factor amplitudes, the resolution shell and the figure of merit. Based on the above considerations, the following phase-extension schemes are provided in DM:

  • (1) Extension by resolution shell: This performs phase extension in resolution steps, starting from the low-resolution data, and extends the phase to the high-resolution limit of the data or that specified by the user. Structure factors are related by the reciprocal-space density-modification function that is dominated by low-resolution terms, as shown by equation ([link] ) and Fig.[link] in Chapter 15.1. This means that only structure factors in a small region of reciprocal space are related. Thus, when initial phases are only available at low resolution, phase extension is performed by inclusion of successive resolution shells. In the case of fourfold or higher NCS, this can allow extension to 2 Å starting from initial phasing at 6 Å or worse.

  • (2) Extension in structure-factor amplitude steps: In this mode, those reflections with larger amplitudes are added first, gradually extending to those reflections with smaller amplitudes in many steps. The contribution of a reflection to the electron density is proportional to the square of its structure-factor amplitude according to Parseval's theorem, as shown in equation ([link]. This favours the protocol of extending the stronger reflections first so that they can be more reliably estimated. These stronger reflections will be used to phase relatively weaker subsequent reflections.

  • (3) Extension in figure-of-merit step: To extend phases for those structure factors with experimentally measured, albeit less accurate, phases and figures of merit, the reflections can be added in order of their figure of merit, starting from the highest to the lowest. It is advantageous to use the more reliably estimated phases with higher figure of merit to phase those reflections with lower figure of merit. This can be useful when working with initial phasing from multiwavelength anomalous diffraction (MAD) or molecular replacement (MR) sources.

  • (4) Automatic mode: This combines the previous three extension schemes. The program automatically works out the optimum combination of the above three schemes according to the density-modification mode, the phase-combination mode and the nature of the input reflection data. The automatic mode is the default and is the recommended mode of choice unless specific circumstances warrant a different choice.

  • (5) All reflection mode: One advantage of the reflection-omit and perturbation-γ methods is that the strength of extrapolation of a structure-factor amplitude is a good indicator of the reliability of its corresponding phase. As a result, a phase-extension scheme is unnecessary in reflection-omit calculations; all reflections may be included from the first cycle.

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