Noncrystallographic

Noncrystallographic is an adjective used in crystallography and structural biology to describe symmetry operations or relationships that are not part of a crystal’s space group. In crystals, the arrangement of atoms is constrained by translational symmetry; any symmetry operation that maps the crystal lattice onto itself is crystallographic. Noncrystallographic symmetry (NCS) refers to symmetry relating multiple copies of a molecule within the same crystal that does not extend to the lattice. As a result, NCS cannot generate an entire crystal from a single molecule, but it can relate positions of molecules or subunits within the asymmetric unit.

Common examples include relationships between subunits in multimeric proteins, where twofold, threefold, fourfold, or fivefold rotations relate copies that are not lattice symmetries. In viruses, icosahedral arrangements are often described as noncrystallographic with respect to the crystal lattice because icosahedral symmetry is incompatible with translational periodicity.

In structure determination, recognizing NCS provides useful constraints. NCS averaging can improve electron density maps and refine models more accurately, but if the symmetry relations are broken by conformational changes or disorder, refinement can become more complex and may reveal multiple states.

Related concepts include crystallographic symmetry, space groups, and the asymmetric unit. Noncrystallographic symmetry is distinct from true crystallographic symmetry in that it does not describe the entire crystal lattice, yet it remains a valuable tool for interpreting and refining molecular structures within crystals.