Tables for
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

International Tables for Crystallography (2006). Vol. F, ch. 15.1, p. 311   | 1 | 2 |

Section 15.1.1. Introduction

K. Y. J. Zhang,a K. D. Cowtanb* and P. Mainc

aDivision of Basic Sciences, Fred Hutchinson Cancer Research Center, 1100 Fairview Ave N., Seattle, WA 90109, USA,bDepartment of Chemistry, University of York, York YO1 5DD, England, and cDepartment of Physics, University of York, York YO1 5DD, England
Correspondence e-mail:

15.1.1. Introduction

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Density modification is a technique for improving the quality of an approximate electron-density map based on some conserved features of the correct electron-density map. These conserved features are independent of the unknown fine detail of the structural conformation. They are often expressed as constraints on the electron density in various forms, either in real or reciprocal space. Since the structure-factor amplitudes are known, these constraints restrict the values of phases and can therefore be used for phase improvement.

The structure-factor amplitudes and phases are independent of each other if we know nothing about the electron density. Therefore, the phases are indeterminable given only the amplitudes (Baker, Krukowski & Agard, 1993[link]). The information about the electron density provides the missing link between structure-factor amplitudes and phases. It is only through the knowledge of the chemical or physical properties of the electron density that the phases can be retrieved. Density modification is usually the most straightforward application of the constraints on electron density. However, this is only a matter of convenience in implementation. Sometimes the constraints can be more readily implemented in reciprocal space on structure factors.

Density-modification methods are usually implemented as an iterative procedure that alternates between density modification in real space and phase combination in reciprocal space. This paradigm was first proposed by Hoppe & Gassmann (1968)[link] in their `phase correction' method. This approach takes advantage of the particular properties of the constraints and uses them in a way that is most convenient to implement.

Density-modification methods usually require an initial map with substantial phase information. In most cases, these phases are obtained from multiple isomorphous replacement (MIR) or multiwavelength anomalous dispersion (MAD), but it is also possible to improve maps from other sources, such as molecular replacement. The amount of information in the initial map is dependent on phase accuracy, data resolution and completeness. As more powerful constraints are incorporated, the density modification can be initiated from lower-resolution maps with less accurate phases. Ab initio phasing would be achieved if a density-modification method could start from a map generated from random phases. Therefore, density modification can potentially lead to ab initio phasing methods, although it does not seek direct solution to the phase problem as its immediate goal.

There are two major components in a density-modification procedure. One is the type of electron-density constraints. The other is the way the constraints are exploited. These two components combined determine the phasing power of the procedure. In this chapter, we will review various electron-density constraints and the way they are exploited for phase improvement.


Baker, D., Krukowski, A. E. & Agard, D. A. (1993). Uniqueness and the ab initio phase problem in macromolecular crystallography. Acta Cryst. D49, 186–192.Google Scholar
Hoppe, W. & Gassmann, J. (1968). Phase correction, a new method to solve partially known structures. Acta Cryst. B24, 97–107.Google Scholar

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