On the choice of the model cell and the integration volume in the use of the rotation function
Résumé
In the general case where there is only one molecule in the asymmetric unit, and in the absence of non-crystallographic symmetry, molecular-replacement (MR) techniques can be used to solve an unknown crystal structure from a closely related known molecular model. The procedure comprises two stages in order to find (i) the orientation of the model in the crystal, and (ii) the position of the well oriented model relative to the crystallographic symmetry elements. The most widely used rotation function R(θ) [Rossmann & Blow (1962). Acta Cryst. 15, 24—31], for stage (i), correlates the rotated central portion U of the Patterson function of the observed crystal with the calculated Patterson function of the proposed model. The calculation of the Patterson function of the model is performed in an arbitrary celi of sufficient size to prevent the overlap of intramolecular vectors from adjacent origins. Tollin & Rossmann [Acta Cryst. (1966), 21, 872—876] have proposed a criterion for the choice of the cell; this criterion is in fact sufficient but not necessary: after a discussion on the shape and the size of U, it is shown in this paper that the volume of the cell can be generally halved for the very same resulting map and, as a consequence, the computing time is also halved. Moreover, the size of the cell, even over-reduced, has a relatively weak influence on the ultimate conclusion ofthe MR calculation.
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