Section 11.3.6.2. Finding possible space groups

Inspection of the table rating the likelihood of each of the 44 lattice types usually reveals a rather limited set of possible space groups. Furthermore, the absence of parity-changing symmetry operators required for protein crystals restricts the number of possible space groups to 65 instead of 230. Any space group can be tested by repeating only the final steps of data processing. These steps include a comparison of symmetry-related reflection intensities, as well as a refinement of the parameters controlling the diffraction pattern after reindexing the reflections by the appropriate transformation. Low r.m.s. deviations between the observed and refined spot positions, as well as small R factors for symmetry-related reflection intensities, indicate that the constraints imposed by the tentatively chosen space group are satisfied. The space group with highest symmetry compatible with the data is almost certainly correct if the data set is sufficiently complete and redundant, which requires that each symmetry element relates a sufficient number of reflections to one another.

For the example of a 1.5° oscillation data film given above, space-group determination consists of the following steps. Inspection of Table 11.3.6.1 indicates that lattice characters 10, 13, 14 and 34, besides the triclinic characters 31 and 44, are approximately compatible with the observed diffraction pattern. The highest lattice symmetry is orthorhombic (character 13, Bravais type oC), which limits the possible space groups for protein crystals to either or C222. Processing of all films in the data set was completed in space group P1 using the cell constants shown for lattice character 44. To test whether the crystal has space-group symmetry C222 and conventional cell constants , the final steps of data processing were repeated after reindexing the reflections by the transformation , , as specified for lattice character 13. Note that the transformation also provides a simple tool for correcting the indices if all reflections are misindexed by a constant. The results clearly show that the crystal has space-group symmetry . The presence of the axis was deduced from the rather weak intensities observed for reflections of type .