Section 9.1.10. Lysozyme as an example

Tetragonal hen egg-white lysozyme (Chapter 26.1 and Blake et al., 1967), crystallizing in the space group with cell dimensions and , is used here as a model system to illustrate some of the points made above, based on Dauter (1999). The example involves a set of two consecutive blocks of images with a crystal-to-detector distance of 243 mm, a wavelength of 0.92 Å, a resolution of 2.7 Å, an oscillation range of 1.5° and a crystal mosaicity around 0.5°. These images are shown in Fig. 9.1.10.1(a–f).

Figure 9.1.10.1| top | pdf | Images recorded from a crystal of lysozyme. (a–d) Four consecutive exposures with the crystal fourfold axis parallel to the X-ray beam. (e–f) Two successive exposures 90° away, when the fourfold axis lies vertically in the plane of the image. The crystal [110] direction is parallel to the rotation axis, horizontal in the plane of the images.

The first four images, (a–d), were exposed with the tetragonal fourfold c axis lying approximately along the direction of the beam. On these images, the reflections within each lune are arranged in a square grid, reflecting the tetragonal symmetry with . The squares are oriented with their diagonals in the horizontal and vertical directions of the image, as the crystal was mounted with its [110] direction along the spindle rotation axis. Indeed, at the end of image (a) and the start of image (b), the c axis lay almost perfectly along the beam, and the zero-layer lune almost disappears behind the beam-stop shadow, since the corresponding (hk0) plane in reciprocal space is tangential to the Ewald sphere at the origin of the reciprocal lattice.

The lunes are widely spaced with clear gaps between them, because the third cell dimension, c, which is perpendicular to the detector plane, is relatively short, 37.2 Å. Images (e–f), exposed at an angle on the rotation spindle roughly 90° away from (a–d), have a quite different appearance, despite the rotation range per image being the same. Each lune is less densely populated by reflections, but the number of lunes is larger and the gaps between them much smaller. This arises from the lunes now being parallel to the (hhl) family of planes, as the vector is now parallel to the beam. The interplanar spacing within this family is less than for those on images (a–d), hence at high resolution, close to the edge of the detector window, the lunes overlap on images (e–f). The reflections, however, do not overlap, as the crystal orientation is diagonal; the lunes are sparsely populated, with large separation between adjacent spots, so the reflections on successive lunes fit between one another. It should be noted that the density of reflections in different regions of the reciprocal lattice is constant, and that the total number of reflections recorded on an image depends only on the rotation range, not on the crystal orientation.

The zero-layer lune containing reflections with indices hk0 is especially evident on exposures (c–d) directly above the centre of the image. With such a lune close to the centre, the reciprocal lattice shows minimal distortion owing to its projection onto the detector plane, and the lune appears as a `pseudoprecession' pattern. The systematic absence of every second reflection, with odd index, along the h00 and 0k0 lines indicates the presence of twofold screw axes of symmetry along the crystal axes a and b. Images (e–f), 90° away, have the hhl lune at the centre and, although it is less well separated from higher lunes, the presence of a fourfold screw axis along c is confirmed by the presence of only every fourth reflection on the 00l line. This allows the identification of the space group as or its enantiomorph, . In general, the positions of the reflections define only the Bravais lattice, and it is symmetry of the intensity pattern which reflects the point group. Thus, further confirmation that the symmetry belongs to point group P422 rather than P4 comes from the symmetric relation of the intensity distribution on either side of each lune in images (a–d). This is equivalent to the earlier use of precession photography for space-group elucidation.

Close inspection shows that the reflections at the edges of the lune are also present on the adjacent image. The rotation range was 1.5°, and the mosaicity was estimated at 0.5°, and thus about one-sixth of the reflections are partially recorded at each edge of the lune, giving one-third partially recorded terms in total. The lack of sharpness at the edge of the lunes confirms a substantial level of mosaicity.