Local squaring functions

Simple modifications to the Sayre squaring method determine a class of functional atomic form constraints representing the likelihood that a particular atomic form occupies a localized volume of the unit cell. The functional formulation, as opposed to the traditional structure-factor equation formulation, facilitates modeling multiple atom types and integrating atomic form information into established density-modification routines. Two complementary methods of phase refinement are considered. The first method constructs an atomic resolution probabilistic filter from the atomic form functions. The probabilistic filter is used to modify density throughout the unit cell, in both the solvent and macromolecular regions of the unit cell. The second method exploits the automated map interpretation aspects of the atomic form functions. A simple iterative phase-refinement procedure alternating the two methods successively is applied to three small metalloproteins, with significant phase improvements beyond that obtained with conventional density modification or refinement in accordance with reciprocal-space squaring equations.