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An iterative transform method is proposed for solving the phase problem in protein crystallography. In each iteration, a weighted average electron-density map is constructed to define an estimated protein mask. Solvent flattening is then imposed through the hybrid input-output algorithm [Fienup (1982). Appl. Opt. 21, 2758-2769]. Starting from random initial phases, after thousands of iterations the mask evolves into the correct shape and the phases converge to the correct values with an average error of 30-40° for high-resolution data for several protein crystals with high solvent content. With the use of non-crystallographic symmetry, the method could potentially be extended to phase protein crystals with less than 50% solvent fraction. The new phasing algorithm can supplement and enhance the traditional refinement tools.

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