Cluster analysis for phasing with molecular replacement: a feasibility study

Molecular replacement can fail to find a solution, namely a unique orientation and position of a search model, even when many search models are tested under various conditions. Simultaneous use of the results of these searches may help in the solution of such difficult structures. A closeness between the peaks of several calculated rotation functions may identify the model orientation. The largest and most compact cluster of such peaks usually corresponds to models which are oriented similarly to the molecule under study. A search for the optimal translation may be more problematic and both individual translation functions and straightforward cluster analysis in the space of geometric parameters such as rotation angles and translation vectors may give no result. An improvement may be obtained by performing cluster analysis of the peaks of several translation functions in phase-set space. In this case, the Fourier maps computed using the observed structure-factor magnitudes and the phases calculated from differently positioned models are compared. Again, as a rule, the largest and the most compact cluster corresponds to the correct solution. The result of the updated procedure is no longer a single search model but an averaged Fourier map.