Infinite non-crystallographic symmetries in crystals of a globular protein

The monomeric enzyme 6-phospho-beta-galactosidase crystallized in three forms, all of which can be considered as fiber associations when judged 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-crystallographic, 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) axes (translation c') defining the z axis by c = 2c'. Antiparallel fiber association results in sheets with internal twofold and 2(1) axes defining the yz plane. These sheets associate along x in two ways; in one case the internal sheet symmetry becomes crystallographic, while it remains non-crystallographic in the other. All non-crystallographic fiber symmetries run infinitely through the crystal. In one case they cause exact systematic absences that mimic space group P2(1)2(1)2(1) instead of the actual P2(1)2(1)2. The relationship between contact areas and local symmetries is discussed.