Strengthened translation functions. An automated method for the positioning of a correctly oriented fragment by translation functions inDIRDIFFourier space

Some applications of the phased translation function in macromolecular structure determination

“…The mathematical basis of the PTF has been described elsewhere (Colman, Fehlhammer & Bartels, 1976;Doesburg & Beurskens, 1983;Read & Schierbeek, 1988). The principle of the function is best visualized in real space.…”

“…The use of the PTF with calculated phases from partial structures was described by Doesburg & Beurskens (1983), who applied the method to small molecules. The oriented model is at first arbitrarily positioned in the unit cell.…”

“…Thus, more than one symmetry position must be used to obtain a complete solution to the translation for many space groups. In practice, Doesburg & Beurskens (1983) used difference coefficients, (Fobs--Fcalc ) exp (27riaealc), to remove the contribution of the phasing model. These coefficients, containing information essentially on the symmetry-related molecules only, are thus used as F(h) in (2).…”

New probabilistic formulas for finding the positions of correctly oriented atomic groups

“…The position of the fragment with respect to the symmetry elements of the space group is usually achieved by: (a) translation functions in the vector space (Braun, Hornstra & Leenhouts, 1969;Huber, 1965;Nordman & Nakatsu, 1963) or in the reciprocal space (Tollin, 1966;Crowther & Blow, 1967;Karle, 1972;Langs, 1975;Harada, Lifchitz, Berthou & Jolles, 1981); or (b) special direct-methods procedures. Among these it is worth noting: (bl) a modified tangent formula (Karle, 1968) is used to recycle in P1 phases derived from the known fragment; (b2) reflection data are expanded in the space group P1 (Doesburg & Beurskens, 1983;Bruins Slot & Beurskens, 1984) and coefficients for Fourier synthesis are obtained by direct methods on difference structure factors. The position of the fragment relative to symmetry elements is deduced from the maximum of a suitable translation function; (b3) the correctly oriented but randomly positioned atomic groups are introduced as prior information in the probabilistic approach aimed at estimating triplet invariant phases (Main, 1976).…”

Structure of enprofylline: 3,7-dihydro-3-propyl-1H-purine 2,6-dione

“…A search fragment, C5N40 2 [formula (I), with R = H], was retrieved from the literature (Mercer & Trotter, 1978). The subsequent TRADIR (Doesburg & Beurskens, 1983) and DIRDIF runs failed to give the solution; instead DIRDIF Fourier maps gave a multiple image of the structure, in which many well defined molecular fragments could be recognized. From these, the following possibilities became apparent:…”