The structure of a protein is built from its electron density map which could be calculated by a Fourier transform. The magnitudes of the Fourier coefficients are recorded by the X-ray diffraction pattern of the protein crystal. The phases of the Fourier coefficients are lost. Solving the phase problem is crucial for building the model of a protein structure. 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. Density modifications are then imposed through the histogram matching technique in the protein region, and the hybrid input–output algorithm in the solvent region. Starting from random initial phases, after thousands of iterations the calculated protein mask evolves into the correct shape and the phases converge to the correct values with an average error of  for high-resolution data for several protein crystals with high solvent content. With the use of non-crystallographic symmetry and other density constraints, the method has been extended to phase protein crystals with less than 50% solvent fraction. The new phasing algorithm can supplement and enhance the traditional refinement tools.

Hongxing He works on developing computational algorithms for structural biology. He was a postdoc in physics at the University of Houston and the Texas Center for Superconductivity. He earned his Ph.D. in physics from the University of Houston in 2015, and the M.S. and B.S. in physics from Nanjing University.