Laboratory of Macromolecular Crystallography
This is a review of the works carried out in LMC of the IMPB RAS. Information on other papers in this field
may be found in the original papers listed below.
The use of the connectivity properties of high-density regions for solution of
the phase problem in macromolecular crystallography.
(1999-2002)
This project was developed in close collaboration with the crystallographic
laboratory of the University of Nancy I ( LCM3B, Nancy, France; PI
Prof.A.G.Urzhumtsev). The goal of the project was to estimate to what extent
topological properties of high electron density regions may be used for
ab-initio phasing. This type of additional information on the studied object was
further incorporated into a general scheme of low-resolution ab-initio phasing.
The traditional goal of the first stage of determining a macromolecular
structure is to find the function ρ(x,y,z), which presents the
distribution of electron density in the crystal of a studied object. This
function is periodical in the three space directions and may be presented as a
three-dimensional Fourier series
(1)
In crystallography, the complex coefficients
F(h,k,l)exp[i φ(h,k,l)] are referred to as
structure factors while real values of F(h,k,l) and
φ(h,k,l) are called magnitudes and phases, respectively. In a
conventional X-ray experiment one can only determine the magnitudes
F(h,k,l). The problem of restoring the phase values is called the
phase problem of X-ray crystallography. Obviously, some additional information
on the studied object must be attracted to solve this problem. Once approximate
phase values have been found, they (together with experimental magnitudes) may
be used to calculate an approximate density distribution by formula (1). If a
finite number of structure factors only are used to calculate the series (1)
they say that the Fourier synthesis of a finite resolution is calculated. The
synthesis resolution depends on the number of structure factors used. The more
terms in the series (1) are used the more fine details may be recognised in
analysing this synthesis.
Additional information may be presented in terms of properties of the electron
density distribution ρ(x,y,z) or in terms of its Fourier
syntheses (1) [1,5]. Such properties may be non-specific for an object under
study, but reflect general properties of a class of objects. For example, in
studies of low-resolution Fourier syntheses for protein crystals, one can see
that the region of the highest synthesis values usually splits into a number of
globular isolated regions corresponding to different protein molecules in the
crystal. The number of such regions is equal to the number of molecules in the
unit cell. The picture is different if the Fourier synthesis was calculated with
wrong phases (but still true magnitudes). It follows from this observation that
the demand to have the prescribed number of equal isolated components in the
region of the highest synthesis values may serve as an additional limitation for
admissible phases.
A preliminary restriction on the number of connected components may be used to
choose the optimal phase set out of a number of alternative sets [2]. This
limitation may also be used in the framework of the general procedure for
ab-initio solution of the phase problem [1,3,4]. This approach includes several
steps:
- a number of phase sets are generated randomly; these sets are used
(together with the observed magnitudes) to calculate the corresponding Fourier
syntheses; connectivity analysis of high values regions is performed for these
syntheses;
- if the results of the connectivity analysis are agreeable then the tested
phase set is selected as admissible for further work;
- the selected sets are divided into groups of close sets (clusters) and an
averaging procedure is applied to every cluster producing a small number of
alternative solutions of the phase problem (only one cluster is usually revealed
when working with the connectivity based selection criteria).
The examination of properly phased middle-resolution syntheses shows that
usually, high-values region reveals a small number of long continuous chains
corresponding to the polypeptide chain in the protein. Otherwise, if the phases
are wrong this region breaks down into a large number of small "drops". So, the
number of connected components of the high-synthesis-values region may be used
as an additional phase selection criterion.
Connectivity based restrictions were successfully used in the study of
Low-Density Lipoprotein particle (LDL) [6].
March, 24, 2003
V.Lunin
Publications
The full texts of papers
- Lunin, V.Yu., Urzhumtsev, A.G. & Skovoroda, T.A. (1990). "Direct
low-resolution phasing from electron-density histograms in protein
crystallography". Acta Cryst., A46, 540-544.
- Lunin, V.Y., Lunina, N.L. & Urzhumtsev, A.G. (1999). "Seminvariant density
decomposition and connectivity analysis and their application to very low
resolution macromolecular phasing". Acta Cryst., A55, 916-925.
- Lunin, V.Y., Lunina, N.L. & Urzhumtsev, A.G. (2000). "Connectivity
properties of high-density regions and ab initio phasing at low resolution".
Acta Cryst., A56, 375-382.
- Lunin, V.Y., Lunina, N.L., Petrova, T.E., Skovoroda, T.P., Urzhumtsev, A.G.
& Podjarny, A.D. (2000). "Low-resolution ab initio phasing: problems and
advances". Acta Cryst., D56, 1223-1232.
- Urzhumtsev, A.G., Lunina, N.L., Skovoroda, T.P., Podjarny, A.D. & Lunin,
V.Y. (2000). "Density constraints and low-resolution phasing". Acta
Cryst., D56, 1233-1244.
- Lunin, V.Y., Lunina, N.L., Ritter, S., Frey, I., Berg, A., Diderichs, K.,
Podjarny, A.D., Urzhumtsev, A. & Baumstark M.W. (2001). "Low-resolution data
analysis for low-density lipoprotein particle". Acta Cryst., D57,
108-121.
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