On integrating the techniques of direct methods and isomorphous replacement. A new probabilistic formula for triplet invariants

Giacovazzo, Carmelo; Cascarano, G.; Chao-De, Zheng

doi:10.1107/s0108767387008377

Cited by 25 publications

(9 citation statements)

References 7 publications

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“…The distribution presented by Giacovazzo, Cascarano & Zheng Chao-de (1988) [their equation (3)] is also readily obtained from (3.2). Indeed, the only differences between the two distributions are in the atomic scattering factors, which are real in the former case and complex in the latter.…”

Section: Dhkl = Chkl + Ish'klmentioning

confidence: 87%

“…The It should be noted that in the case of Z~ the expression on the fight-hand side is an approximation only. Its validity [see Fortier, Weeks & Hauptman (1984a) and Giacovazzo, Cascarano & Zheng Chao-de (1988)] depends upon: (a) the total number of atoms in the complete structure unit cell; (b) the difference between the number of atoms in the partial and complete structures; and (c) the dependence of the scattering factors on the Bragg angle. The approximation is used here for the sake of comparison with the distribution presented by Giacovazzo (1983b).…”

Section: Case 3 Calculated Data Of a Partial Structure And Observed mentioning

confidence: 99%

“…Through the use of the method of joint probability distributions, formulae have been obtained to estimate the value of two-and three-phase structure invariants for the cases of isomorphous replacement (Hauptman, 1982a;Giacovazzo, Cascarano & Zheng Chao-de, 1988;Srinivasan & Parthasarathy, 1976), anomalous dispersion (Hauptman, 1982b;Giacovazzo, 1983a) and partial/complete structure (Beurskens, Prick, Doesburg & Gould, 1979;Srinivasan & Parthasarathy, 1976;Giacovazzo, 1983b;Sim, 1959). T-a the present paper, it is shown that the joint probability distributions are isomorphous: that is, they have the same functional form and differ only in individual atomic scattering factors.…”

Section: Introductionmentioning

confidence: 99%

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On the probabilistic theory of isomophous data sets: general joint distributions for the SIR, SAS and partial/complete structure cases

Fortier

Nigam²

1989

Acta Cryst Sect A

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By characterizing isomorphism in reciprocal space [ i.e. diffraction data sets are isomorphous if they have the same geometry (the same reciprocal-lattice unit cell) and the same symmetry] it is shown that the diffraction data of a native protein and of its heavyatom derivatives, the calculated data of a partial structure and the observed data of its associated complete structure, and the Friedel-pair data of an anomalously scattering crystal structure all belong to the more general class of isomorphous data sets. Their joint probability distributions for two-and threephase structure invariants are shown to be isomorphous: they have the same functional form and differ only in individual atomic scattering factors. General joint probability distributions, which can be used for any isomorphous data pairs, are presented.

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Section: Dhkl = Chkl + Ish'klmentioning

confidence: 87%

Section: Case 3 Calculated Data Of a Partial Structure And Observed mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the probabilistic theory of isomophous data sets: general joint distributions for the SIR, SAS and partial/complete structure cases

Fortier

Nigam²

1989

Acta Cryst Sect A

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“…• Statistical analysis of structure factor • Initial phase estimation * Completing and refining the structure Two popular methods exist for phase estimation -the Patterson method and "so called" direct methods [5,6,8,9,10]. The Patterson method is based on calculating maps using the Patterson]unction with squares of the structure factor amplitudes as coefficients.…”

Section: Problem Definitionmentioning

confidence: 99%

On the scalability of parallel triplet generation for protein crystallography

Ramamurthy

York

Giacovazzo³

1996

Proceedings of the 1996 ACM Symposium on Applied Computing - SAC '96

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The phase problem of X-ray crystallography is well-known and a number of methods have been developed to solve it. The discovery of invariants and semi-invariants is almost always the first step in the solution and triplet invariants have proved extremely useful. In this work we present a fast parallel method for triplet generation that works for moderate-sized proteins. Variations of the algorithm and implementations for two popular models of parallel computation, SIMD and SPMD, are described. Performance results are given for implementations on the MasPar MP-1 and two networks of workstations (NoWs). Nearly linear scalability is achieved and the method has been used for structures involving more than 3000 reflections and more than 8 million triplets.

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“…The probability distribution of the three-phase structure invariants (3PSIs) based on a combination of direct methods with single isomorphous replacement (SIR) data was pioneered by Hauptman (1982) and subsequently by Giacovazzo et al (1988). Recently, the probabilistic approaches of the fourphase structure invariants (4PSIs) in the SIR case were initiated by Kyriakidis et al (1996) and Giacovazzo & Siliqi (1996a,b).…”

Section: Introductionmentioning

confidence: 99%

Estimation of individual phases from the four-phase structure invariants in the single isomorphous replacement case

Liu

Wang

2001

Acta Cryst Sect A

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The probability distribution of the four-phase invariants in the case of single isomorphous replacement has been developed to estimate some individual phases. An example of its application to obtain the phases having special values of 0, % or AE%/2 is given for a known protein structure in space group P2 1 2 1 2 1 . The phasing procedure includes the determination of starting phases and an iterative calculation. The initial values of starting phases, which are required by the formula, can be obtained from the estimate of one-phase seminvariants and by specifying the origin and enantiomorph. In addition, the calculations lead to two sets of possible phases for each type of re¯ection by assigning arbitrarily an initial phase value. The present method provides a possibility for the multisolution technique to increase greatly the number of known phases while keeping the number of the trials quite small.

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On integrating the techniques of direct methods and isomorphous replacement. A new probabilistic formula for triplet invariants

Abstract: The mathematical technique recently used [Hauptman (1982 suggest that the formula is quite efficient for picking up triplet cosines near 0 or rr.

Cited by 25 publications

References 7 publications

On the probabilistic theory of isomophous data sets: general joint distributions for the SIR, SAS and partial/complete structure cases

On the probabilistic theory of isomophous data sets: general joint distributions for the SIR, SAS and partial/complete structure cases

On the scalability of parallel triplet generation for protein crystallography

Estimation of individual phases from the four-phase structure invariants in the single isomorphous replacement case

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