Vector-Search Methods in Molecular Replacement
Carmen Álvarez-Rúa, Javier Borge and Santiago García-Granda.
Departamento de Química Física y Analítica
Facultad de Química. Universidad de Oviedo
C/ Julián Clavería, 8. 33006 Oviedo. SPAIN
OVIONE is a computer program that uses a vector-search rotation function for
macromolecular crystal-structure determination by the molecular-replacement
In order to determine the orientation of the search model in the crystal
unit cell, a vector set obtained from the model is rotated through the
asymmetric unit of the angular space. In each angular position an Image
Seeking Function is evaluated. This function acts as a criterion of fit
between the vector set from the search model and the observed Patterson map
of the target structure, and it is expected to attain a maximum value at the
correct orientation of the search model.
The rotation search is followed by a refinement of the highest peaks of the
rotation function, that is also carried out in Patterson space.
The use of ISFs (Image Seeking Functions) (Buerger, 1959) as rotation
functions was proposed for the first time by Nordman (Nordman & Nakatsu, 1963),
who used these functions as a criterion of fit between vector sets and Patterson
maps. A new ISF proposed by Nordman, the ``weighted minimum-average
function'' (Nordman, 1966; Schilling, 1970) was later implemented for the
determination of the orientation of a known molecular fragment in the
program ORIENT (Beurskens et al., 1987) included in the DIRDIF system
(Beurskens et al., 1999), and widely used in crystallography of small
The same function has now been implemented in OVIONE (Álvarez-Rúa
et al., 2000), with some modifications that allow the use of this
methodology in macromolecular crystallography (Borge et al., 2000).
The rotation function algorithm in the program consists of the following
- First, a calculated Patterson map of the search model is
computed and a set of intramolecular vectors (the self-vector set) is
extracted from it.
- An observed Patterson map is calculated from experimental data
of the target crystal.
- An statistical analysis is performed to check if the problem
presents the adequate conditions for the Image Seeking Function to work
- In the next step, the rotation search is carried out. Currently,
two ISFs are implemented in the program: the ``weighted minimum-average
function'' (Nordman & Schilling, 1970) and the ``weighted sum function''
- Finally, a refinement of the highest peaks of the rotation
function is carried out by means of a minimization algorithm known as the
``downhill simplex method'' (Nelder & Mead, 1965).
Details about the methodology implemented in the program can be found at the
OVIONE home page1
together with some examples of application of the method.
The results of the program are written to an output file which contains the
list of the Euler angles that represent the possible orientations of the
search model. If required by the user, the program also rotates the atomic
coordinates of the search model according to the highest peak from the
rotation (and refinement) process and writes the result in a PDB-formatted
Since the molecular replacement process does not finish once the orientation
of the model is determined (except for crystals with P1 symmetry) some
procedures have been developped which act as an interface with other
translation function programs, such as the version of AMoRe incorporated in
the CCP4 package.
The last release of the program (OVIONE 1.1; March 2001) presents some new
technical features, mainly:
- The amount of physical memory required by the program has been
substantially reduced, which allows the treatment of proteins of bigger
- If required by the user, the observed Patterson map is now
written to disk and stored. The program is able to read in again this map.
This can be useful and time-saving in case the program is run
several times, for instance, with different search models.
- In the same way, the self-vector set can be now calculated and stored.
This avoids having to repeat the self-vector set selection process, which is one
of the most time-consuming steps of the algorithm, in case the user wants to rerun
the program under the same conditions, but using, for example, a finer angular grid
around a possible orientation of the search model.
The authors wish to thank CCP4 for permission to incorporate in OVIONE some
routines from the CCP4/Daresbury Laboratory libraries. Professor M. G.
Rossmann is also thanked for allowing us to use some FFT routines
from the Purdue Library of Programs.
This work was partially supported by CICYT (BQU2000-0219).
Álvarez-Rúa, C., Borge, J. & García-Granda, S. (2000). J. Appl.
Cryst. 33, 1436-1444.
Beurskens, P. T., Beurskens, G., Strumpel, M. & Nordman, C. E. (1987).
Patterson and Pattersons. Fifty years of the Patterson function,
edited by J. P. Glusker, B. K. Patterson & M. Rossy, pp. 356-367. New York:
Oxford University Press.
Beurskens, P. T., Beurskens, G., de Gelder, R.,
García-Granda, S., Gould, R. O., Israël, R. & Smits, J. M. M. (1999).
The DIRDIF-99 program system. Crystallography Laboratory, University of
Nijmegen, The Netherlands.
Borge, J., Álvarez-Rúa, C. \& García-Granda, S. (2000). Acta Cryst. D56, 735-746.
Buerger, M. J. (1959). Vector space and its application in crystal
structure investigation. New York: John Wiley & Sons, Inc.
Nelder, J. A. & Mead, R. (1965). Computer Journal 7,
Nordman, C. E. (1966). Trans. Am. Crystallogr. Assoc. 2,
Nordman, C. E. (1972). Acta Cryst. A28, 134-143.
Nordman, C. E. & Nakatsu, K. (1963). J. Am. Chem. Soc.
Nordman, C. E. & Schilling, J. W. (1970). Crystallographic
Computing, edited by F. R. Ahmed, pp. 110-114. Copenhagen: Munksgaard.
Schilling, J. W. (1970). Crystallographic Computing, edited by F.
R. Ahmed, pp. 115-123. Copenhagen: Munksgaard.