Detection and use of pseudo-translation in determination of protein structures

Two types of pseudo-translation symmetry, pseudo-twofold translational symmetry and pseudo-body-centered symmetry, have been found in protein crystals of chorismate mutase and cyclophilin C. Statistics on diffraction intensity from these two crystals showed that the presence of pseudo-translations in atomic space yielded a distribution of systematically strong and weak reflections at low resolution. The diffraction pattern resulting from pseudo-translational symmetry was apparently similar to that from true crystallographic symmetry at 4 Å resolution, but was distinct at high resolution. Pseudo-translation can be detected by comparing the average magnitudes of certain parity groups of reflections in three-dimensional hkl space. Based on the structures of chorismate mutase and cyclophilin C, the ratio of >1.2 for the average magnitudes of parity groups is sufficient to indicate the existence of pseudo-translation. Although pseudo-translation often makes structure determination more difficult, the additional information of pseudo-translation has been used successfully in the structure determination of chorismate mutase by multiple isomorphous replacement and of cyclophilin C by molecular replacement. Thus, examination of pseudo-translation is recommended at an early stage of structure determination.