On the doublet phase sums of isomorphous data sets

Abstract

The role of the doublet phase sum present among isomorphous data sets is investigated in connection with the triplet-phase-sum statistics. Several probabilistic and algebraic techniques are discussed to estimate the doublets. The combination of an algebraic estimation technique and a new difference Patterson synthesis, the maxima of which are used to improve iteratively the doublet phase sums, is shown to be successful. Test results for large model structures and idealized protein data show that this technique reduces the triplet-phase-sum errors to a level small enough for ab initio direct-methods applications.

On direct-methods phase information from differences between isomorphous structure factors

“…An important goal of the paper is the derivation of a new expression to estimate the triplet phase sums present among isomorphous data. It will be shown that the new procedure, supplemented by optimal doublet phase-sum estimates that use difference Patterson information [Kyriakidis, Peschar & Schenk (1993b), from now on referred to as KPS2], leads to far better results than obtainable by other j.p.d.-based expressions (Hauptman, 1982a, b;Giacovazzo, 1983;Giacovazzo, Cascarano & Zheng, 1988;Fortier & Nigam, 1989;Peschar & Schenk, 1991;hereafter P&S), in particular if the DR is small (Kyriakidis, Peschar & Schenk, 1993a; from now on KPS 1). In contrast with other DM techniques, the final triplet distributions in the SAS and 2DW cases seem to be of sufficient quality to be used in a normal DM procedure.…”

The Estimation of Four-Phase Structure Invariants Using the Single Difference of Isomorphous Structure Factors

“…In Kyriakidis et al (1993b), it was shown that algebraically based estimates of doublet phase sums can be useful to get correct estimates of triplet phase sums present among isomorphous data sets; in particular, if the estimation of the doublet phase sums are based on vector information from a special difference Patterson synthesis. For the benefit of the current paper, the two algebraic approaches in Kyriakidis et al (1993b) have been tested: (a) the algebraic doublet estimation (ALG) and (b) the algebraic estimation improved by difference-Patterson vectors (PAT). For SAS and 2DW data, the ALG doublet estimation depends only on the imaginary dispersion correction of the anomalous scatterers.…”

“…The expression for a structure factor with a phase restriction 0/zr is with fj~ =f:n-fjh. Because of anomalous scattering, the phase ~0 n will deviate slightly from its phase restriction ~0r: ~0 n ~ q9 r -t-~H" From (47), lEVI = 21Fn 1211 -cos(2~n)] so the same functional form is obtained as for general reflections [see (13) in Kyriakidis et al, 1993b]:…”

On Integrating the Techniques of Direct Methods with Anomalous Dispersion. IV. A Simplified Perturbation Treatment for SAS Phasing

“…We think that the SAS perturbation treatment offers the advantages of a simple formulation and a clear physical picture of the SAS phase effect as a positive origin shift for the three-phase invariant distribution. Before concluding, however, we wish to acknowledge that other workers (Fan, Han, Qian & Yao, 1984;Hao & Fan, 1988;Kyriakidis, Peschar & Schenk, 1993) have developed other approaches to SAS phasing using phase 'doublets' to resolve the Harker-construction ambiguity and/or to estimate three-phase invariants. The power of these methods has been convincingly demonstrated in the recent ab initio redetermination of the structure of the selenobiotin binding core of the protein streptavidin via a SAS direct-methods procedure (Sha, Liu, Gu, Fan, Ke, Yao & Woolfson, 1995).…”