Section 21.1.7.2.5. Noncrystallographic symmetry

Molecules that are related by noncrystallographic symmetry exist in very similar, but not identical, physical environments. This implies that their structures are expected to be quite similar, although different relative domain orientations and local variations may occur (e.g. owing to different crystal-packing interactions; Kleywegt, 1996). Many criteria have been developed to quantify the differences between (NCS) related models. Some, such as the r.m.s. distance (e.g. on all atoms, backbone atoms or C^α atoms) are based on distances between equivalent atoms, measured after a (to some extent arbitrary; Kleywegt, 1996) structural superpositioning operation has been performed. Others are based on a comparison of torsion angles, be it of main-chain φ, ψ angles [e.g. Δφ, Δψ plot (Korn & Rose, 1994); multiple-model Ramachandran plot (Kleywegt, 1996); σ(φ), σ(ψ) plot (Kleywegt, 1996); circular variance (Allen & Johnson, 1991) plots of φ and ψ (G. J. Kleywegt, unpublished results); Euclidian φ, ψ distances (Carson et al., 1994) or pseudo-energy values (Carson et al., 1994)] or side-chain χ₁, χ₂ angles [e.g. multiple-model χ₁, χ₂ plot (Kleywegt, 1996); σ(χ₁), σ(χ₂) plots (Kleywegt, 1996); circular variance (Allen & Johnson, 1991) plots of χ₁ and χ₂ (G. J. Kleywegt, unpublished results); Euclidian χ₁, χ₂ distances (Carson et al., 1994) or pseudo-energy values (Carson et al., 1994)]. Still other methods are based on analysing differences in contact-surface areas (Abagyan & Totrov, 1997), temperature factors (Kleywegt, 1996) or the geometry of the C^α backbone alone (Flocco & Mowbray, 1995; Kleywegt, 1996). Many of these methods can also be used to compare the structures of related molecules in different crystals or crystal forms (e.g. complexes, mutants).