Chapter 15.1 Phase improvement by iterative density modification

Crystallography of biological macromolecules

First Online Edition (2006)

Part 15. Density modification and phase combination

  1. K. Y. J. Zhang1,
  2. K. D. Cowtan2,
  3. P. Main3

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000687

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Zhang, K. Y. J., Cowtan, K. D. and Main, P. 2006. Phase improvement by iterative density modification. International Tables for Crystallography. F:15:15.1:311–324.

Author Information

  1. 1

    Division of Basic Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N., Seattle, WA 90109, USA

  2. 2

    Department of Chemistry, University of York, York YO1 5DD, England

  3. 3

    Department of Physics, University of York, York YO1 5DD, England

Publication History

  1. Published Online: 1 JAN 2006


Density modification is a method for improving phase estimates arising from sources such as MIR/MAD and molecular replacement. This is achieved by use of chemical knowledge concerning the properties of well phased electron-density maps, including such features as solvent flatness, atomic composition and noncrystallographic symmetry. The calculation is performed iteratively, with alternating stages of map modification in real space and phase weighting in reciprocal space.


  • Sayre’s equation;
  • Sim weighting;
  • atomicity;
  • automated convolution method for molecular-boundary identification;
  • conjugate-gradient method;
  • constraints;
  • density modification;
  • diagonal-approximation method;
  • electron-density averaging;
  • histogram matching;
  • molecular-boundary identification by automated convolution method;
  • noncrystallographic symmetry;
  • nonlinear constraints;
  • phase combination;
  • phase improvement;
  • refinement;
  • reflection-omit method;
  • scaling;
  • skeletonization;
  • solvent flattening;
  • solvent flipping;
  • weighting