Patterson-guided ab initio analysis of structures with helical symmetry

Patterson maps, which have a peak for intermolecular vectors between two molecules linked by a pseudo-translation, are widely used for structure solution. However, these maps may contain other peaks that indicate additional important information. In particular, if a molecule has internal symmetry, the Patterson maps may have a peak even when the relation between two molecules is other than a pure translation. A special and frequent case is a crystal that consists of molecules with pseudo-helical symmetry, like RNA or DNA, packed more or less parallel to each other. For such pairs of molecules, the Patterson peak does not simply link the molecular centres but is shifted along the helical axis. The shift is proportional to the rotation between the two molecules. The known step of the helix may be sufficient to obtain a system of linear equations whose solution gives an approximate position for the molecule. This technique may provide crucial information when molecular replacement fails to find a solution or suggests a number of candidates. Instead of repeating numerous molecular-replacement trials varying the model, a model may be positioned directly in place and be modified and refined directly. This Patterson-based search for molecular position has been tested with several solved crystals and has assisted in structure solution of RNA duplexes containing Homo sapiens cytoplasmic or mito­chondrial ribosomal decoding sites (A sites).