Locating a Local Symmetry Axis from Patterson Map Cross Vectors: Application to Crystal Data from GroEl, GTP Cyclohydrolase I and the Proteosome

The cross vectors of the native Patterson map are shown to exhibit non-crystallographic symmetry in the case of local axes parallel to one another. This information can be used to determine the translation component of such axes. A program is described to search for this cross vector, and is tested on low-resolution data from crystals of the tetradecameric GroEL molecule, the decameric GTP cyclohydrolase I and the tetradecameric proteosome. For GroEL, the function produces a packing arrangement optimal for sevenfold symmetry, and is in agreement with the dimensions of the molecule as given by electron microscopy data and the recently determined crystal structure. Positioning of local axes is confirmed by two high-resolution crystal structure analyses: the fivefold axis in cyclohydrolase I and the sevenfold axis in the proteosome. Implications for the location of heavy-atom positions are discussed for these two cases.