INFINITE NON-CRYSTALLOGRAPHIC SYMMETRIES IN CRYSTALS OF A GLOBULAR PROTEIN

The monomeric enzyme 6-phospho-beta-galactosidase crystallized in thre e forms, all of which can be considered as fiber associations when jud ged from the packing contacts. In one case the internal fiber symmetry is a row of parallel twofold axes that are displaced by a' along the fiber axis. In the crystal, these twofold axes are non-crystallographi c, but they define the x axis by a = 2a'. Antiparallel and asymmetric fiber association along y and z, respectively, results in space group P2(1). The two other crystal forms contain fibers with internal 2(1) a xes (translation c') defining the z axis by c=2c'. Antiparallel fiber association results in sheets with internal twofold and 2(1) axes defi ning the yz plane. These sheets associate along x in two ways; in one case the internal sheet symmetry becomes crystallographic, while it re mains non-crystallographic in the other. All non-crystallographic fibe r symmetries run infinitely through the crystal. In one case they caus e exact systematic absences that mimic space group P2(1)2(1)2(1) inste ad of the actual P2(1)2(1)2. The relationship between contact areas an d local symmetries is discussed.