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The constraints of correct electron-density distribution, solvent flatness, correct local shape of the electron density and equal molecules are combined in an integrated procedure for macromolecular phase refinement and extension. These constraints on electron densities are satisfied simultaneously by solving a system of non-linear equations. The electron-density solution is further filtered by a phase combination procedure. The non-crystallographic symmetry operations are refined by a rotation and translation space search and a least-squares minimization method, thereby reducing the chance of introducing systematic phase errors during averaging. The effect of each constraint on phase refinement and extension is examined. The constraints are found to work synergistically in phase improvement. Test results on 2Zn insulin are presented.
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