International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by E. Arnold, D. M. Himmel and M. G. Rossmann © International Union of Crystallography 2012 |
International Tables for Crystallography (2012). Vol. F, ch. 11.4, p. 292
Section 11.4.10.3. Merging and signal validation^{a}UT Southwestern Medical Center at Dallas, 5323 Harry Hines Boulevard, Dallas, TX 75390–9038, USA, and ^{b}Department of Molecular Physiology and Biological Physics, University of Virginia, 1300 Jefferson Park Avenue, Charlottesville, VA 22908, USA |
Symmetry-related scaled measurements I(hkl) and their uncertainty estimates σ_{E} are used to obtain merged intensities by a standard weighted averaging formula:This allows for calculations of validation statistics, called goodness-of-fit or normalized χ^{2}, for each unique index:where n represents the number of observations of a given unique index. This χ^{2} statistic is then averaged in resolution shells or over intensity bins or batch number. If the error model accounts properly for all effects, the χ^{2} statistic should fluctuate around a value of unity. If χ^{2} values depart from this expectation it may indicate a number of possibilities, e.g. various problems at earlier stages (poorly edited beam-stop shadow, hardware failures, mistakes in processing or other source of outliers etc.), inadequacy of the error model or variations in the structure factors within the symmetry-related observations. The instrumental problems or mistakes in processing should be corrected. The effects that cannot be corrected may be handled by adjusting the error model. However, if the more detailed analysis eliminates the obvious source for such problems, then the most likely source of discrepancies between symmetry-related measurements results from violation of Friedel symmetry. SCALEPACK calculates merging statistics both for the Bijvoet pairs merged together and separately. Differences in χ^{2} values between these two merging outputs are very reliable estimates of anomalous signal strength. When a more detailed analysis eliminates the obvious reasons for high χ^{2} values, the most likely remaining source of error is non-isomorphism (Borek et al., 2007, 2010).
References
Borek, D., Cymborowski, M., Machius, M., Minor, W. & Otwinowski, Z. (2010). Diffraction data analysis in the presence of radiation damage. Acta Cryst. D66, 426–436.Borek, D., Ginell, S. L., Cymborowski, M., Minor, W. & Otwinowski, Z. (2007). The many faces of radiation-induced changes. J. Synchrotron Rad. 14, 24–33.