A general class of iterative projection algorithms is described and proposed as a tool for phasing in protein crystallography in order to improve the radius of convergence over that of conventional density-modification algorithms. Their relationship to conventional density modification is described. The common iterative projection algorithms, their convergence properties and their application to protein crystallography are described. These algorithms offer the possibility of protein structure determination starting with only information on the molecular envelope and low-order non-crystallographic symmetry.
Iterative projection algorithms (IPAs) are a promising tool for protein crystallographic phase determination. Although related to traditional density-modification algorithms, IPAs have better convergence properties, and, as a result, can effectively overcome the phase problem given modest levels of structural redundancy. This is illustrated by applying IPAs to determine the electron densities of two protein crystals with fourfold non-crystallographic symmetry, starting with only the experimental diffraction amplitudes, a low-resolution molecular envelope and the position of the non-crystallographic axes. The algorithm returns electron densities that are sufficiently accurate for model building, allowing automated recovery of the known structures. This study indicates that IPAs should find routine application in protein crystallography, being capable of reconstructing electron densities starting with very little initial phase information.
An algorithm is described for determining macromolecular envelopes from crystal diffraction amplitudes measured from a solvent contrast variation series. The method uses solvent contrast variation data that have been preprocessed to represent the structure-factor amplitudes of the envelope. The amplitudes are phased using an iterative projection algorithm that incorporates connectivity and compactness constraints on the envelope. The algorithm is tested by simulation on two protein envelopes and shown to be effective even in the absence of the very low resolution data, which are difficult to access experimentally.
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