Ab initio phasing based on topological restraints: automated determination of the space group and the number of molecules in the unit cell

The connectivity-based phasing method has been demonstrated to be capable of finding molecular packing and envelopes even for difficult cases of structure determination, as well as of identifying, in favorable cases, secondary-structure elements of protein molecules in the crystal. This method uses a single set of structure factor magnitudes and general topological features of a crystallographic image of the macromolecule under study. This information is expressed through a number of parameters. Most of these parameters are easy to estimate, and the results of phasing are practically independent of these parameters when they are chosen within reasonable limits. By contrast, the correct choice for such parameters as the expected number of connected regions in the unit cell is sometimes ambiguous. To study these dependencies, numerous tests were performed with simulated data, experimental data and mixed data sets, where several reflections missed in the experiment were completed by computed data. This paper demonstrates that the procedure is able to control this choice automatically and helps in difficult cases to identify the correct number of molecules in the asymmetric unit. In addition, the procedure behaves abnormally if the space group is defined incorrectly and therefore may distinguish between the rotation and screw axes even when high-resolution data are not available.