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. 11.5, pp. 238241
Section 11.5.7. Experimental results^{a}Department of Biological Sciences, Purdue University, West Lafayette, IN 479071392, USA 
If scale factors are to make physical sense, their behaviour with respect to the frame number has to be in accordance with the known changes in the beam intensity, crystal condition and detector response.
The scaling of a ϕX174 procapsid data set (Dokland et al., 1997) was performed using methods 1 and 2 as described here and using SCALEPACK (Otwinowski & Minor, 1997) (Fig. 11.5.7.1). Graphs (a) and (b) in Fig. 11.5.7.1 have four segments corresponding to four synchrotron beam `fills'. All three methods give scale factors within 5% of each other (Figs. 11.5.7.1c and d). However, for the first and last frame of each `fill' the results can differ by as much as 15%. Both method 1 and SCALEPACK produce physically wrong results in that the scale factors of these frames look like outliers compared to the scale factors of the neighbouring frames. By contrast, method 2 provides consistent scale factors for these frames. Although the algorithm used by SCALEPACK for scaling frames with partial reflections has never been disclosed, the similar results obtained by method 1 and SCALEPACK suggest that SCALEPACK might be using an algorithm similar to that of method 1 (Fig. 11.5.7.1d).
Attempts at scaling a data set of a frozen crystal of HRV14 (Rossmann et al., 1985, 1997) failed with method 1 as a result of gaps in the rotation range for the first 20 frames, causing singularity of the normal equations matrix. When frames without useful neighbours were excluded, the cubic symmetry of the crystal was sufficient for successful scaling. In contrast, method 2 did not have any problems with the whole data set, and the results obtained with method 2 showed greater consistency than those obtained with method 1 or SCALEPACK (Fig. 11.5.7.2).

Linear scale factor as a function of frame number for an HRV14 data set (Rossmann et al., 1985, 1997). 
The accuracy and robustness of method 2 is also demonstrated by the scaling results for a Sindbis virus capsid protein (SCP), residues 114–264 (Choi et al., 1991, 1996). The behaviour of the scale factor with respect to the frame number reflects the anisotropy of the thin plateshaped crystal (Fig. 11.5.7.3). For the first 40 frames (frame numbers 0 to 39), evennumbered frames have higher scale factors than oddnumbered frames. Data collection was stopped after frame number 39 and restarted. After frame number 39, oddnumbered frames have higher scale factors than evennumbered frames. This effect presumably relates to the use of the two alternating image plates with slightly different sensitivities in the Raxis camera used in the data collection.
In order to determine the limits of tolerance that can be permitted when method 1 is used, the R factor was examined as a function of the sumofpartialities for the ϕX174 procapsid data (Fig. 11.5.7.4). Reflections with sumofpartialities of were used. The R factor changes sharply when the sumofpartialities is outside . Hence, were acceptable limits of tolerance for this data set.
The behaviour of the R factor versus frame number (Fig. 11.5.7.5) is more monotonic when method 1 is used compared to method 2. In method 1, the dataquality estimates for neighbouring frames are strongly correlated because the full reflections used in the statistics are obtained by summing partials from consecutive frames. By contrast, in method 2 every frame produces estimates of full reflection intensities independently of the neighbouring frames. Therefore, the R factors per frame calculated after scaling with method 2 truly represent the data quality for individual frames.
The relationship between observed and calculated partialities (Fig. 11.5.7.6) deviates from the ideal line , especially for the smaller calculated partialities where . This suggests errors in the measurements of or the calculations of . The latter may be improved by a post refinement of the orientation matrix and crystal mosaicity (Rossmann et al., 1979).
Refinement of the effective mosaicity can show both the anisotropic nature of the crystal (Fig. 11.5.7.7) as well as the impact of radiation damage. The effective mosaicity is the convolution of the mosaic spread of the crystal, the beam divergence and the wavelength divergence of the incident Xray beam. Hence, Xray diffraction data collected at a synchrotronradiation source necessitate the differentiation of the effective mosaicity in the horizontal and vertical planes. A more general approach is the introduction of six parameters reflecting the anisotropic effective mosaicity.
The quality of anomalousdispersion data can be assessed by calculation of the average scatter, expression (11.5.6.6). The ratios and should be larger than unity for significant anomalous data (Fig. 11.5.7.8). Note the much larger ratios for the scatter among measurements of for data measured at the absorption edge of Se, as opposed to measurements remote from the edge. The decreasing values of the ratios with resolution are due to the decrease of value, thus causing the error in the measurement of to approach the difference in intensity of Bijvoet opposites.
References
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