Direct methods with single isomorphous replacement data. I. Reduction of systematic errors

A new strategy for employing three phase triples invariant estimates from Hauptman's single isomorphous replacement (SIR) and anomalous dispersion (SAS)joint probability distribution formulae is outlined which produces a single unique phase-invariant solution in the case where the positions of the heavy-atom scatterers is known. A similar but non-identical result is obtained for the phase invariants of a structure for which a molecularreplacement solution has been obtained. It is important to note that the values of the individual native/derivative phases can be determined directly from the probability distribution formulae without having to utilize the phaseinvariant estimates in an active way. Elimination of the multisolution aspect of utilizing phase-invariant estimates should have important repercussions with regard to phasing macromolecular sets of derivatized data. Trial calculations based on experimentally measured 2.5A data for three derivatives of cytochrome %5o are encouraging. The average of the three SIR maps resolves a number of structural ambiguities seen in the published multiple isomorphous replacement (MIR) map obtained from eight derivatives.

Section: Discussion Of Resultsmentioning

confidence: 77%

TDSIR phasing: direct use of phase-invariant distributions in macromolecular crystallography

Langs

Guo²,

Hauptman³

1995

“…Recently, the full probabilistic integration of DM with any number and type of isomorphous data sets has been accomplished (Peschar & Schenk, 1991). Although test results (Furey, Chandrasekhar, Dyda & Sax 1990) exist which suggest that DM may be applicable in solving protein structures ab initio, the full potential of DM in this respect seems not to have been realized as yet.…”

Section: Introductionmentioning

confidence: 99%

On the doublet phase sums of isomorphous data sets

Kyriakidis¹,

Peschar²,

Schenk³

1993

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.

“…Incorporating such information into (1) and (2) a posteriori [that is, after the mathematical form of (1) and (2) has been ®xed on assuming F H unknown] is an unreliable way for improving their ef®ciency. Extensive tests made by Furey et al (1990) suggest that the procedure is not able to eliminate the bias towards`unresolved SIR values'. Further contributions by Fan & Gu (1985), Fan et al (1990) and Liu et al (1999) show that the bias may be overcome in favourable cases by a supplementary direct procedure combining Sim and Cochran distributions.…”

Section: Introductionmentioning

confidence: 99%

Direct methods and isomorphous replacement. The triplet invariant estimate when heavy atoms are located

Giacovazzo

Siliqi²,

2002

The probabilistic theory of the three-phase structure invariants for isomorphous pairs has been generalized to the case in which a heavy-atom structure model is available. The rigorous method of joint probability distributions has been applied: it is able to handle errors in measurements and in the heavy-atom structure model, as well as the lack of isomorphism. The conclusive formulas have been successfully applied to experimental data. NotationF p jF p j expi0 p : structure factor of the protein F d jF d j expi0 d : structure factor of the isomorphous derivative F H F d À F p : structure factor of the heavy-atom structure (i.e. the atoms added to the native protein)pseudo-normalized structure factor of the derivative (normalized with respect to the native protein structure) E H : pseudo-normalized structure factor of the heavy-atom structure (normalized with respect to the native protein structure) IntroductionThe probability theory of the three-phase structure invariants for isomorphous pairs was initiated by Hauptman (1982;Hauptman et al., 1982) who derived the joint probability distributionThe Hauptman approach was revisited by Giacovazzo et al. (1988), who derived an ef®cient and simple formula for estimating the triplet phase È p . Their conclusive expression may be written asd j are the structure-factor moduli of the protein and of the derivative, respectively, normalized with respect to the heavy-atom structure. The formulas (2) and (3a) were implemented into a direct-methods procedure aimed at phasing protein structure factors without any information on the heavy-atom positions (Giacovazzo,