Treatment of structure-factor data and scaling

Wodak, S. J.; Vagin, A. A.; Richelle, J.; Das, U.; Pontius, J.; Berman, H. M.

doi:10.1107/97809553602060000708

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. 21.2, pp. 510-511 | 1 | 2 |

Section 21.2.3.1.1.1. Treatment of structure-factor data and scaling

S. J. Wodak,^a ^* A. A. Vagin,^b J. Richelle,^b U. Das,^b J. Pontius^b and H. M. Berman^c

^aUnité de Conformation de Macromolécules Biologiques, Université Libre de Bruxelles, avenue F. D. Roosevelt 50, CP160/16, B-1050 Bruxelles, Belgium, and EMBL–EBI, Wellcome Trust Genome Campus, Hinxton, Cambridge CB10 1SD, England, ^bUnité de Conformation de Macromolécules Biologiques, Université Libre de Bruxelles, avenue F. D. Roosevelt 50, CP160/16, B-1050 Bruxelles, Belgium, and ^cDepartment of Chemistry, Rutgers University, 610 Taylor Road, Piscataway, NJ 08854-8087, USA
Correspondence e-mail: shosh@ucmb.ulb.ac.be

21.2.3.1.1.1. Treatment of structure-factor data and scaling

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SFCHECK reads in the structure-factor data written in mmCIF format. It then performs the following operations: Reflections are excluded if they are systematically absent, negative, or have flagged σ values (99.9). Equivalent reflections are merged. The amplitudes of missing reflections are approximated by taking the average value for the corresponding resolution shell.

From the model coordinates read from the PDB (or mmCIF) atomic coordinates file, SFCHECK calculates structure factors and scales them to the observed structure factors. The scaling factor, S, is computed using a smooth cutoff for low-resolution data (Vaguine et al., 1999) (Table 21.2.3.1). This involves the calculation of the observed and calculated overall B factors from the standard deviations of the Gaussian fitted to the Patterson origin peaks [see Table 21.2.3.1 and Vaguine et al. (1999)]. In addition, SFCHECK also estimates the overall anisotropy of the data, following the approach of Sheriff & Hendrickson (1987), and applies the anisotropic scaling after the Patterson scaling is performed (Murshudov et al., 1998).

Table 21.2.3.1| top | pdf |
Parameters computed for the analysis of the structure-factor data

The first column lists the parameter, the second column gives the formula or definition of the parameter and the third column contains a short description of the meaning of the parameters when warranted.

Parameter	Formula/definition	Meaning
Completeness (%)	Percentage of the expected number of reflections for the given crystal space group and resolution
B_overall (Patterson)	$[8\pi^{2} \sigma_{\rm Patt}/(2)^{1/2}]$ ^†	Overall B factor
R_stand(F)	$[\langle \sigma (F)\rangle/\langle F \rangle]$ ^‡	Uncertainty of the structure-factor amplitudes
Optical resolution	$[(\sigma_{\rm Patt}^{2} + \sigma_{\rm sph}^{2})^{1/2}]$ ^† ^§	Expected minimum distance between two resolved atomic peaks
Expected optical resolution	Optical resolution computed considering all reflections
$[\hbox{CC}_{F}]$	$[\displaystyle{\langle F_{\rm obs} F_{\rm calc}\rangle - \langle F_{\rm obs}\rangle\langle F_{\rm calc}\rangle \over \left[(\langle F_{\rm obs}^{2} \rangle - \langle F_{\rm obs}\rangle^{2}) (\langle F_{\rm calc}^{2}\rangle - \langle F_{\rm calc}\rangle^{2})\right]^{1/2}}]$	Correlation coefficient between the observed and calculated structure-factor amplitudes
S	$[\left\{{\textstyle\sum\displaystyle (F_{\rm obs} f_{\rm cutoff})^{2} \over \textstyle\sum\displaystyle \left[F_{\rm calc} \exp (- B_{\rm diff}^{\rm overall} s^{2}) f_{\rm cutoff}\right]^{2}}\right\}^{1/2}]$ ^¶	Factor applied to scale $[F_{\rm calc}]$ to $[F_{\rm obs}]$
$[f_{\rm cutoff}]$	$[1 - \exp (- B_{\rm off} s^{2})]$ ^††	Function applied to obtain a smooth cutoff for low-resolution data

^† $[\sigma_{\rm Patt}]$ is the standard deviation of the Gaussian fitted to the Patterson origin peak.
^‡F is the structure-factor amplitude, and $[\sigma({F})]$ is the structure-factor standard deviation. The brackets denote averages.
^§ $[\sigma _{\rm sph}]$ is the standard deviation of the spherical interference function, which is the Fourier transform of a sphere of radius $[1/d_{\min}]$ , with $[d_{\rm min}]$ being the minimum d spacing.
^¶ $[B_{\rm diff}^{\rm overall} = B_{\rm obs}^{\rm overall} - B_{\rm calc}^{\rm overall}]$ is added to the calculated overall B factor, $[B_{\rm overall}]$ , so as to make the width of the calculated Patterson origin peak equal to the observed one; s is the magnitude of reciprocal-lattice vector.
^†† $[B_{\rm off} = 4 d_{\rm max}^{2}]$ , where s and $[d_{\rm max}]$ , respectively, are the magnitude of the reciprocal-lattice vector and the maximum d spacing.

To assess the quality of the structure-factor data, the program computes four additional quantities (see Table 21.2.3.1 for details): the completeness of the data, the uncertainty of the structure-factor amplitudes, the optical resolution and the expected optical resolution. The latter two quantities represent the expected minimum distance between two resolved atomic peaks in the electron-density map when the latter is computed with the set of reflections specified by the authors and with all the reflections, respectively.

References

Murshudov, G. N., Davies, G. J., Isupov, M., Krzywda, S. & Dodson, E. J. (1998). The effect of overall anisotropic scaling in macromolecular refinement. Newsletter on protein crystallography, pp. 37–42. Warrington: Daresbury Laboratory.Google Scholar

Sheriff, S. & Hendrickson, W. A. (1987). Description of overall anisotropy in diffraction from macromolecular crystals. Acta Cryst. A43, 118–121.Google Scholar

Vaguine, A. A., Richelle, J. & Wodak, S. J. (1999). SFCHECK: a unified set of procedures for evaluating the quality of macromolecular structure-factor data and their agreement with the atomic model. Acta Cryst. D55, 191–205.Google Scholar

International Tables for Crystallography (2006). Vol. F. ch. 21.2, pp. 510-511