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Chapter 1

Phase Improvement and
Interpretation Manual - Basics

Copyright    © 2001-2006 by Global Phasing Limited
  All rights reserved.
  This software is proprietary to and embodies the confidential technology of Global Phasing Limited (GPhL). Possession, use, duplication or dissemination of the software is authorised only pursuant to a valid written licence from GPhL.
Documentation    (2001-2006)  Clemens Vonrhein



Most of the time, the best electron density map for building and interpretation of a structure is obtained after phase improvement and some sort of automatic interpretation. The various tools for phase improvement are described in this document.

Real space

The physical and chemical assumptions used for improving an initial electron density are (obviously) features of the real space. Therefore, the modifications of phases (and amplitudes) are done mostly in real space through changes in an electron density map. This map is then transformed (via Fourier transform) into (modified) phases and amplitudes.

Restraints and constraints

Density modification methods usually use constraints on electron density. Various classes can be used: To get an electron density that fulfils all constraints at the same time (if more than one is used) a system of equations can be used (Main, 1990).

Solvent content

One of the most important parameters for most density modification methods is the fraction of the unit cell (or asymmetric unit) that is considered as solvent. The most often used way to calculate the solvent content is via the Matthews parameter (Matthews, 1968):
Vsolvent = 1.0 - ( 1.23 / Vm )

with: Vm = V / ( M * Z )

      M  =  molecular weight of protein [daltons]
      V  =  volume of unit cell [Å3]
      Z  =  no. of molecules in unit cell
The mayor problem here is, that the correct number of molecules in the unit cell might not be known. This could be due to uncertainty in the space group (therefore the correct number of asymmetric units is unknown) or in the number of molecules per asymmetric unit (especially with large unit cells). All additional information (self rotation functions, native Patterson functions, biochemical data etc) should be taken into consideration.

Quality of initial phases

For successful density modification a good estimate of the initial phase quality is important. Some factors include:

Non-crystallographic symmetry (NCS)

If the asymmetric unit contains more than one identical molecule, this information can be used for NCS averaging. The type of arrangement within the asymmetric unit can be of various types (proper or improper, closed or open etc). Ways of finding the NCS operators include:

Solvent envelope

One of the most important factors for a successful phase improvement is the distinction between protein and solvent region. The solvent content used in this procedure doesn't have to be the physical solvent content of the crystal. Especially when starting from poor or very incomplete phase information some trial-and-error might be required to find the solvent content best suited for improving the initial electron density.

The solvent envelope can be determined using a variety of methods, e.g.


We will give a short description of the various methods used for modifying electron density in real space.

Solvent flattening

Since the density in the solvent region of a crystal should be relatively flat (as compared to the protein region) we can set all grid points in the solvent to a constant value. Additionally, since density in the protein region should be positive, all grid points in the protein region are usually constrained to be positive (density truncation).

Solvent flipping

The electron density in the solvent region is inverted using a flipping factor
kflip = ( solvent content - 1 ) / solvent content
(Abrahams & Leslie, 1996; )

Histogram matching

The distribution of electron density in an ideal electron density map is dependent on resolution and temperature factor but independent of the actual structure in the crystal. Therefore, the experimental density can be modified so that its distribution resembles that of an ideal electron density (Zhang & Main, 1990a; Zhang & Main, 1990b)

NCS averaging

To perform density modification using NCS averaging a mask defining the region of the asymmetric unit that is repeated within the asymmetric unit and the operators describing the transformations have to be known.

The masks can cover either a monomer or a multimer (in case of closed proper local symmetry). It can be generated through auto-correlation (Schuller, 1996), from bones or a PDB file or completely manual. Care should be taken to avoid overlap between masks if several masks (e.g. for different domains, chains) are being used.

Since NCS averaging is mostly used in conjunction with other density modification steps (e.g. solvent flattening), the NCS mask(s) and the solvent envelope are not independent of each other: the NCS masks is probably only valid within the protein region and should not contain too much solvent region. This allows for consistency checks to validate either the solvent envelope and.or the NCS mask.


A macromolecular crystal should contain continuous stretches of density. This could potentially be used to improve the connectivity of the map and therefore improve the phases.

Various attempts have been made to include this knowledge into density modification procedures (Wilson & Agard, 1993; Baker et al, 1993; Bystroff et al, 1993; see also documentation of DM). Although some have proved very efficient it is not (yet) a routine method for phase improvement.

Sayre's equation

This is a non-linear constraint that is useful only at higher resolution. It takes neighbouring grid points into account, ie the atomicity of the map (Sayre, 1952; Main, 1990; Zhang & Main, 1990b).

Cyclic method

Electron density modification is a cyclic procedure that will go through the various steps for a defined number of cycles:
  1. calculating electron density map
  2. modifying density in real space
  3. calculating structure factors from modified map
  4. combining modified phases with experimental phases
Since running electron density modification protocols for too many cycles usually degrades the quality of the phases again (after the initial improvements), it is important to have a good convergence criteria. This could include e.g. a real space free residual or a free R-factor.

The combination of modified phases with experimental phases has to be done with great care: since the modified phases are not independent of the initial experimental ones (from which the initial unmodified map was calculated) a proper weighting scheme has to be adopted (Read, 1986; Cowtan & Main, 1996; Roberts & Brünger, 1995). Phase information is described as phase probability (Rossmann & Blow, 19961) in form of Hendrickson-Lattmann coefficients (Hendrickson & Lattmann, 1970)

Last modification: 25.07.06