|Phase Improvement and Interpretation Manual
Phase Improvement and
Interpretation Manual - Basics
||© 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,
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pursuant to a valid written licence from GPhL.
||(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.
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
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).
- linear constraints
Modification of electron density at a single grid point in the map
is independent of all other grid points. This is true for
solvent flattening, solvent flipping, histogram
matching and non-crystallographic symmetry (NCS)
averaging. These methods get a better map directly from the
- non-linear constraints
Especially for Sayre's equation the resulting density at a
specific grid point is not independent of the surrounding grid
- structure factor constraints
The measured structure factor amplitudes are obviously constraints
that the resulting (modified) electron density has to follow.
- phase constraints
If experimental phase information (ideally in the form of
Hendrickson-Lattmann coefficients) is available, these can be used
as constraints too. Usually, there is also a weight
(figure-of-merit, Sim weight) associated with these
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.
For successful density modification a good estimate of the initial phase
quality is important. Some factors include:
- overall resolution of phase information
What are the high and low resolution limits of the (experimental)
phases? Good low resolution phases are especially helpful, since
these define mainly the solvent envelope.
- resolution limits of reliable phases information
Although phases might be available to high resolution, only lower
resolution phases are of good quality. This is easily visible
through the figure-of-merit: is there a resolution where it
Any differences between the overall resolution of the data and
this reliable resolution should be taken into account in
the density modification protocol/strategy.
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
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.
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
The electron density in the solvent region is inverted using a
kflip = ( solvent content - 1 ) / solvent content
(Abrahams & Leslie, 1996; )
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,
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.
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).
Electron density modification is a cyclic procedure that will go through
the various steps for a defined number of cycles:
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
- calculating electron density map
- modifying density in real space
- calculating structure factors from modified map
- combining modified phases with experimental phases
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 &
Last modification: 25.07.06