How to take advantage of non-crystallographic symmetry in molecular replacement: `locked' rotation and translation functions

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Abstract
Many protein molecules form assemblies that obey point-group symmetry. These assemblies are often situated at general positions in the unit cell such that the point-group symmetry of the assembly becomes non-crystallographic symmetry (NCS) in the crystal. The presence of NCS places significant constraints on structure determination by the molecular-replacement method. The locked rotation and translation functions have been developed to take advantage of the presence of NCS in this structure determination, which generally requires four steps. (i) The locked self-rotation function is used to determine the orientation of the NCS assembly in the crystal, relative to a pre-defined `standard' orientation of this NCS point group. (ii) The locked cross-rotation function is used to determine the orientation of one monomer of the assembly in the standard orientation. This calculation requires only the structure of the monomer as the search model. (iii) The locked translation function is used to determine the position of this monomer relative to the center of the assembly. Information obtained from steps (ii) and (iii) will produce a model of the entire assembly centered at the origin of the coordinate system. (iv) An ordinary translation function is used to determine the center of the assembly in the crystal unit cell, using as the search model the structure of the entire assembly produced in step (iii). The locked rotation and translation functions simplify the structure-determination process in the presence of NCS. Instead of searching for each monomer separately, the locked calculations search for a single rotation or translation. Moreover, the locked functions reduce the noise level in the calculation, owing to the averaging over the NCS elements, and increase the signals as all monomers of the assembly are taken into account at the same time.

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