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

Introduction

OVIONE is a computer program that uses a vector-search rotation function for macromolecular crystal-structure determination by the molecular-replacement method.

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.

Methodology

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 molecules.

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 steps:

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 properly.
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'' (Nordman, 1972).
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).

Availability

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 file.

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 size.
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.

Acknowledgements

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).

References

     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, 308-313.
     Nordman, C. E. (1966). Trans. Am. Crystallogr. Assoc. 2, 29-38.
     Nordman, C. E. (1972). Acta Cryst. A28, 134-143.
     Nordman, C. E. & Nakatsu, K. (1963). J. Am. Chem. Soc. 85, 353-354.
     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.

¹http://www11.uniovi.es/~mr/ovione/ovione_main.html

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