DIRECT-SPACE METHODS IN PHASE EXTENSION AND PHASE DETERMINATION .3. PHASE REFINEMENT USING SAYRES EQUATION

An algorithm is described for refining a set of phases to agree with t he Sayre equation. All operations are carried out using Fourier transf orms with modest computer-store requirements even for very large syste ms. The procedure is tested with two moderate-sized proteins, one cont aining heavy atoms, and is found to give good refinement with data at more than atomic resolution (1.17 Angstrom) and useful, if less good, refinement when the data resolution is lower (1.5 Angstrom). It is con cluded that at atomic resolution, or slightly below, the Sayre equatio n still has something to offer both for phase refinement and phase ext ension, especially if used cautiously with weighted multiple isomorpho us replacement phases acting as a constraint on the phase changes. Eve n when the Sayre equation on its own refines phases badly, or not at a ll, it may still make an important contribution in conjunction with ot her real-space refinement procedures.