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Structure determination of macromolecules often depends on phase improvement and phase extension by use of real-space averaging of electron density related by noncrystallographic symmetry. Although techniques for such procedures have been described previously [Bricogne (1976). Acta Cryst. A32, 832-847; Johnson (1978). Acta Cryst. B34, 576-577], modern computer architecture and experience with these methods have suggested changes and improvements. Two unit cells are considered: (1) the p-cell corresponding to the actual crystal structure(s) being determined (there would be more than one of these if the molecule crystallizes in more than one crystal form) and (2) the h-cell corresponding to the molecule in a standard orientation with respect to which the molecular symmetry axes are defined. Averaging can proceed entirely within the p-cell, referring to the h-cell only in as far as knowledge of the molecular symmetry is required. It is also possible to place the averaged molecule back into the h-cell, where it can be used to redefine the molecular envelope or for displaying a suitably chosen asymmetric unit of the molecule. Techniques are discussed for automatically selecting a molecular envelope which is consistent with packing considerations within the p-cell and which retains the symmetry of the molecular point group. The electron density map to be averaged is divided into bricks for storage in virtual memory. Roughly as many bricks as there are noncrystallographic asymmetric units per crystallographic asymmetric unit need to be retained in memory at one time. This procedure minimizes paging problems and avoids double sorting. Use of eight-point interpolation permits storing the map at grid points separated by no more than 1/2.5 of the resolution limit to obtain rapid convergence.
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