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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. 25.2, pp. 701-702
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Phase combination, either during density-modification procedures or to make use of partial structure information, is carried out by the BNDRY program (batch). For standard phase combination, two structure-factor files are input. The first file, called the `anchor' phase set, contains structure-factor information along with phase probability distributions in the form of A, B, C, D coefficients and usually corresponds to MIR, SIR, or MAD phases. The other file contains only `calculated' structure-factor amplitudes and phases and is usually obtained either from Fourier inversion of a modified electron-density map or from a structure-factor calculation based on atomic coordinates from a partial structure. Common reflections in both files are identified, and the `calculated' amplitudes are scaled to those in the anchor set by least squares. For phase combination, a variety of options are available, with the most important described below.
The scaled data are sorted into bins according to d spacing, and a three-term polynomial is fitted to the mean values of ![[|F^{2}_{\rm obs} - F^{2}_{\rm calc}|]](/teximages/fach25o2/fach25o2fi50.svg)
as a function of resolution. For each reflection, a unimodal phase probability distribution is constructed using a modification (Bricogne, 1976![[link]](/graphics/greenarr.gif)
) of the Sim (1959) weighting scheme via ![[P(\varphi_{P}) = k \exp \left[{2F_{\rm obs} F_{\rm calc} \cos (\varphi_{P} - \varphi_{\rm calc}) \over \langle | F_{\rm obs}^{2} - F_{\rm calc}^{2}|\rangle}\right], \eqno(25.2.1.29)]](/teximages/fach25o2/fach25o2fd29.svg)
where the average in the appropriate resolution range is determined from the polynomial. This distribution is cast in the A, B, C, D form with ![[\eqalignno{ A &= W \cos (\varphi_{\rm calc}), &\cr B &= W \sin (\varphi_{\rm calc}), &\cr C &= 0 &\cr D &= 0\;\;{\rm and}&\cr W &= {2F_{\rm obs} F_{\rm calc} \over \langle |F_{\rm obs}^{2} - F_{\rm calc}^{2}|\rangle}. &(25.2.1.30)\cr}]](/teximages/fach25o2/fach25o2fd30.svg)
Phase combination with the anchor set then proceeds according to equation (25.2.1.10), and the combined distributions are integrated to give a new phase and figure of merit for each reflection.
As an alternative to the procedure above, in the BNDRY program the weights, W, used when constructing the unimodal probability distributions in equations (25.2.1.30) can be computed according to ![[W = {2\sigma_{A} E_{\rm tot} E_{\rm par} \over 1 - \sigma_{A}}, \eqno(25.2.1.31)]](/teximages/fach25o2/fach25o2fd31.svg)
where ![[E_{\rm tot}]](/teximages/dach2o2/dach2o2fi211.svg)
and ![[E_{\rm par}]](/teximages/fach25o2/fach25o2fi52.svg)
are normalized structure-factor amplitudes for the observed and calculated structure factors, respectively, and ![[\sigma_{A}]](/teximages/fach15o2/fach15o2fi19.svg)
is determined by the procedure described by Read (1986). For acentric reflections, equation (25.2.1.31) is used whereas for centric reflections, W is one half the value given by equation (25.2.1.31).
Normally, the distributions constructed for the calculated phases are combined with those for the anchor set with full weight in equation (25.2.1.10). However, in BNDRY, one can supply a damping factor in the range 0–1 to down-weight the contributions of the anchor set. The damping factor simply multiplies the distribution coefficients such that a factor of 1 (default) indicates no damping, and values less than one place more emphasis on the map-inverted or partial structure phases. If set to zero, the calculated phases are accepted as they are, since there is effectively no phase combination with the anchor set.
If phase extension is requested during the phase combination step, an additional file (prepared by the interactive program MISSNG) is also supplied to the BNDRY program. This file contains unique reflections absent from the anchor set but for which observed amplitudes (and possibly phase probability distribution coefficients) are available. Phase combination then proceeds exactly as above, except that for any extended reflections lacking phase probability information, the calculated phases are accepted as they are. Phase extension is required when phasing purely by SAS methods as it is the only way to phase centric reflections. As a final option, phase and amplitude extension is possible, in which case both the calculated amplitude and phase are accepted as they are for reflections having only indices provided on the extension file. This is sometimes desirable to include low-resolution reflections that may have been obscured by the beam stop.
References
Bricogne, G. (1976). Methods and programs for direct-space exploitation of geometric redundancies. Acta Cryst. A32, 832–846.Google Scholar
Read, R. J. (1986). Improved Fourier coefficients for maps using phases from partial structures with errors. Acta Cryst. A42, 140–149.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, 813–814.Google Scholar
