Section 26.1.3.5.1. Absorption corrections

Although absorption of X-rays by protein crystals is low compared with crystals having a preponderance of heavier atoms, corrections for absorption are required in order to give F values that are sufficiently precise for calculation of the relatively small changes due to the introduction of heavy atoms or anomalous dispersion. The mounting of protein crystals within a glass capillary, normally with a small amount of mother liquor between the crystal and the capillary wall, presents a complicated situation for absorption calculations. Although Wells (1960) wrote a computer program to deal with the situation, a severe impediment to the use of theoretical methods of correcting for absorption results from the very great difficulty in obtaining precise measurements of the mounted crystal, the liquid meniscus and the capillary-tube walls. An alternative approach was to use a semi-empirical method and, for low-resolution lysozyme studies, Furnas' (1957) method had been employed, as described above.

Despite the fact that the method of Furnas had been successful in improving the agreement between symmetry-related reflections in the earlier studies, the implicit assumption that the absorption depended upon the mean direction of the incident and reflected X-ray beams became clearly less valid as the Bragg angle increased. We therefore implemented a development of the method in which the absorption correction applied to any reflection was given by the mean of the two values for the directions of the incident and reflected beams (North et al., 1968).

Although the method was easy to apply and was of significant value, as judged by the improved agreement between symmetry-related reflections, it nevertheless provided only a partial correction for absorption, because of the assumption that absorption is dependent solely on the directions of the incident and reflected beams. The limitations of this assumption are particularly important where precise values are required for Friedel pairs of reflections in order to make use of anomalous-scattering differences in phase determination. Fig. 26.1.3.5 shows two contrasting situations that can arise when the environment of a crystal is asymmetrical because of its mounting. The Friedel pair of reflections shown in Fig. 26.1.3.5(a) would suffer similar absorptions, whereas the pair shown in Fig. 26.1.3.5(b) would have significant differences because of the location of the mother liquor. In the 2 Å structure determination of lysozyme, an approximate correction was made for this effect. From Fig. 26.1.3.5, it is clear that the absorption error arising from the asymmetric distribution of the mother liquor is 0 for reflections with h = 0 and becomes increasingly great as h increases. The assumption was made, therefore, that the required correction was a function only of h and the reflections hkL with constant L were divided into groups with constant h and −h. The ratios were then plotted against h, as shown in Fig. 26.1.3.6.

Figure 26.1.3.5| top | pdf | Asymmetric mounting of a protein crystal with its mother liquor in a capillary tube. Anomalous-scattering differences would be seriously affected in (b) but not in (a). Reproduced with permission from North et al. (1968). Copyright (1968) International Union of Crystallography.

Figure 26.1.3.6| top | pdf | Plot of the ratio against h. In this example, a linear correction may be safely applied to equalize the average intensities in opposite rows (North et al., 1968).

Such plots were frequently found to be linear, and the corresponding linear correction was then applied to each row on the more highly absorbed side in order to bring its mean intensity up to that of the other. Where the plots were not linear, so that a simple form of correction was not applicable, the entire set of measurements was usually rejected.