Translation functions for the positioning of a well oriented molecular fragment

Abstract

The application of Patterson methods to the solution of molecular structures with approximately equal atoms is usually limited by the translation function. The literature on translation functions for the positioning of a correctly oriented molecular fragment is surveyed and summarized. Similarities and differences in the published functions are discussed. Variations of these functions have been tested, with the goal of finding the function that will give the best results for small search fragments and that can be used in routine X-ray analyses of small and medium sized structures. We find that well known reciprocal-space correlation functions (which are shown to be closely related to the residual R 2 ), which make use of Fast Fourier Transform techniques, are fast and reliable. Best results are obtained when all symmetry elements are used simultaneously, and geometrically unacceptable positions are rejected. Test results show that for small fragments (containing less than 10% of the scattering matter of the asymmetric unit) one should use all observed reflections (including weak reflections) and the correlation function to be used should take care of the reciprocal space equivalent of sharpening, origin removal, and subtraction of intramolecular vectors. A computer program for the automatic positioning of a correctly oriented molecular fragment is described. § 1. IntroductionIn structure determination processes using direct methods to solve the phase problem, it often occurs that the resulting structural information is

Structure solution by iterative peaklist optimization and tangent expansion in space group P1

“…Beurskens et al (1987) have also observed that the correlation coefficient is more effective when all data are used.…”

“…The first of these is the series of spectacular successes that Weeks, DeTitta, Miller & Hauptman (1993), DeTitta, Weeks, Thuman, Miller & Hauptman (1994) and Weeks, DeTitta, Hauptman, Thuman & Miller (1994) have achieved with a related real/reciprocal space recycling scheme, in which phases are refined to minimize a function of the estimated cosines of structure invariants, followed by E-map calculation, peaksearch and calculating new phases based on the top N peaks (where N is the number of unique atoms expected). Alternation between real and reciprocal space was also always a fundamental feature of the DIRDIF system; see, for example, Beurskens, Gould, Bruins Slot & Bosman (1987). The second important development is the enormous increase in computer number-crunching power over the last few years, which makes it possible to employ 'brute force' algorithms which would have been out of the question a few years ago.…”

The reliability indexR2as a versatile tool in structure analysis of inorganic and small molecular compounds

“…Often, strategies have been changed based on experience. Usually, the structural fragment to be completed is obtained by either heavy-atom Patterson interpretation techniques (subprogram PATTY; Admiraal et al, 1992) or by vector-search methods (subprogram ORIENT; Beurskens, followed by reciprocalspace correlation methods (subprogram TRACOR; Beurskens, Gould et al, 1987). At the start of the cyclic expansion procedure, most atoms of the fragment (partial structure) are assumed to be in approximately correct positions.…”

An efficient molecular-replacement translation function based on the evaluation of direct-methods phase invariants

“…Various techniques to determine translation solutions exist and include vector search methods (Nordman & Schilling, 1970), electron-density convolutions (Rossmann & Blow, 1962), Patterson correlation functions (Vand & Pepinsky, 1956) and computing the crystallo-0108-7673/92/020172-03503.00 graphic residual on a grid encompassing the searched space (Booth, 1945;Bhuiya & Stanley, 1964). An up-to-date and thorough review of the literature by Beurskens and co-workers is highly recommended to those who wish to become more familiar with these established methods (Beurskens, Gould, Bruins Slot & Bosman, 1987). …”