Noncrystallographic symmetry

Definition

A symmetry relationship between similar subunits within the crystallographic asymmetric unit.

Discussion

The phrase 'noncrystallographic symmetry' is used because the operation required to superimpose one subunit on another is similar to a symmetry operation, but it operates only over a local volume, and the symmetry may be inexact because the subunits are in different environments.

1. In quasicrystals there may be local symmetries (e.g. fivefold or tenfold rotational axes) that are incapable of tiling space through the application of normal lattice translations.

2. In biological crystallography, the 'subunit' can be a molecular aggregate, a single molecule, a monomer unit of an oligomeric molecule, or a fragment of a molecule.

The word 'similar' is used because protein subunits in different environments are never identical. At the very least, surface side chains are differently ordered, and solvation is different because of different interactions with adjacent subunits.