Section 15.1.2.3.2. The determination of noncrystallographic symmetry

The self-rotation symmetry is now routinely solved by the use of a Patterson rotation function (Rossmann & Blow, 1962). The translation symmetry can be determined by a translation function (Crowther & Blow, 1967) when a search model, either an approximate structure of the protein to be determined or the structure of a homologous protein, is available. The searches of the Patterson rotation and translation functions are achieved typically using fast automatic methods, such as X-PLOR (Brünger et al., 1987) or AMoRe (Navaza, 1994). In cases where no search model is available or the Patterson translation function is unsolvable, either the whole electron-density map, or a region which is expected to contain a molecule, may be rotated using the rotation solution and used as a search model in a phased translation function (Read & Schierbeek, 1988).

Once the averaging operators are determined, the mask can be determined using the local density correlation function as developed by Vellieux et al. (1995). This is achieved by a systematic search for extended peaks in the local density correlation, which must be carried out over a volume of several unit cells in order to guarantee finding the whole molecule. The local correlation function distinguishes those volumes of crystal space which map onto similar density under transformation by the averaging operator. Thus, in the case of improper NCS, a local correlation mask will cover only one monomer. In the case of a proper symmetry, a local correlation mask will cover the whole complex (Fig. 15.1.2.4a,b).

Figure 15.1.2.4| top | pdf | Types of noncrystallographic symmetry and averaging calculation.

Special cases arise when there are combinations of crystallographic and noncrystallographic symmetries, of proper and improper symmetries, or when a noncrystallographic symmetry element maps a cell edge onto itself. In the latter case, the volume of matching density is infinite, and arbitrary limits must be placed upon the mask along one crystal axis.