Section 11.5.7.1. Variation of scale factors versus frame number

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).

Figure 11.5.7.1| top | pdf | Linear scale factors as a function of frame number for a φX174 data set (Dokland et al., 1997). Results from (a) method 1 and method 2, (b) SCALEPACK. Comparison of (c) method 2 versus method 1, and (d) SCALEPACK versus method 1.

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).

Figure 11.5.7.2| top | pdf | 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 plate-shaped crystal (Fig. 11.5.7.3). For the first 40 frames (frame numbers 0 to 39), even-numbered frames have higher scale factors than odd-numbered frames. Data collection was stopped after frame number 39 and restarted. After frame number 39, odd-numbered frames have higher scale factors than even-numbered frames. This effect presumably relates to the use of the two alternating image plates with slightly different sensitivities in the R-axis camera used in the data collection.

Figure 11.5.7.3| top | pdf | Linear scale factor determined by method 2 as a function of frame number for an SCP(114–264) data set (Choi et al., 1991, 1996). The sine-like pattern reflects the anisotropy of a thin plate-shaped crystal.