Patterson-oriented automatic structure determination. Utilizing Patterson peaks

Pavelčík, F.; Kuchta, Ľ.; Sivý, J.

doi:10.1107/s010876739200374x

Cited by 26 publications

(21 citation statements)

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“…To derive a single image of the structure from a Patterson map it is necessary to apply a deconvolution process. Quite effective are the implication transformations (see Pavelčík, 1988;Pavelčík et al, 1992, and literature quoted therein): they are symmetry operations which transform a region of the Patterson map defined via specific symmetry rules into a function whose maxima may coincide with the atomic positions. A typical implication transformation is…”

Section: The Variance Component Th 1 and The Concept Of Map Variancementioning

confidence: 99%

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Estimation of the variance in any point of an electron-density map for any space group

Giacovazzo¹,

Mazzone²,

Comunale³

2011

Acta Cryst Sect A

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In a recent paper [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218] a mathematical expression of the variance at any point of the unit cell has been described. The formulas were derived in P1 for any type of Fourier synthesis (observed, difference and hybrid) under the following hypothesis: the current phases are distributed on the trigonometric circle about the correct values according to von Mises distributions. This general hypothesis allows the variance expressions to be valid at any stage of the phasing process. In this paper the method has been extended to any space group, no matter whether centric or acentric. The properties of the variance generated by space-group symmetry are described; in particular it is shown that the variance is strictly connected with the implication transformations, which are basic for Patterson deconvolution. General formulas simultaneously taking into account phase uncertainty and measurement errors have been obtained, valid no matter what the quality of the model.

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Section: The Variance Component Th 1 and The Concept Of Map Variancementioning

confidence: 99%

“…(b) By combining the symmetry minimum function with superposition techniques (Pavelčík, 1988;Pavelčík et al, 1992;Sheldrick, 1992, and more recently Caliandro, Carrozzini, Cascarano, De Caro, Giacovazzo, Mazzone & Siliqi, 2008). These last authors were able to solve ab initio proteins up to 7890 atoms in the asymmetric unit.…”

Section: Figurementioning

confidence: 99%

Estimation of the variance in any point of an electron-density map for any space group

Giacovazzo¹,

Mazzone²,

Comunale³

2011

Acta Cryst Sect A

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“…In this paper we suggest applying the C 0 map to the Patterson deconvolution process, with particular interest in its integration with implication transformation (Simpson et al, 1965;Pavelčík et al, 1992) and superposition methods (Buerger, 1959;Richardson & Jacobson, 1987;Sheldrick, 1992). Implication transformation and Patterson superposition methods are traditionally applied to structures containing heavy atoms.…”

Section: Introductionmentioning

confidence: 99%

On the use of theCmap in Patterson deconvolution procedures

et al. 2012

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The cross-correlation function between the target and a model electron density, denoted as the C map, has been crystallographically characterized. In particular, a study of its interatomic vectors and of their relation with the Patterson vectors has been undertaken. Since the C map is not available during the phasing process, the C' map, its centric modification, is considered. It may be computed at any stage of the phasing process and shows properties that are very useful for the crystal structure determination process. It has been combined with the implication transformation method and with vector-superposition techniques for performing the Patterson deconvolution and obtaining an initial model for dual-space recycling. While Patterson methods are traditionally considered to be more efficient for structures containing heavy atoms, the C map extends their potential to light-atom structures (i.e. containing atoms not heavier than O).

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“…(ii) Patterson deconvolution techniques (Buerger, 1959), eventually based on the implication transformations and on superposition techniques (Richardson & Jacobson, 1987;Pavelčík et al, 1992). In the evolved form they proved to be highly competitive both for ab initio protein phasing (Burla et al, 2005(Burla et al, , 2006Caliandro et al, 2008) and for finding the substructure in multiple-wavelength anomalous scattering (MAD) techniques (Burla et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

Estimates of triplet invariants given a model structure

et al. 2012

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The triplet structure invariant is estimated via the method of joint probability distribution functions when a model structure is available. The six-variate probability distribution function P(E h , E k , E ÀhÀk , E ph , E pk , E p,ÀhÀk ) is studied under the condition that imperfect isomorphism between the target and model structures exist. The results are compared with those available in the literature, which were obtained under the condition of perfect isomorphism. It is shown that the new formalism is more suitable for real cases, where perfect isomorphism is very rare.

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Patterson-oriented automatic structure determination. Utilizing Patterson peaks

Cited by 26 publications

References 1 publication

Estimation of the variance in any point of an electron-density map for any space group

Estimation of the variance in any point of an electron-density map for any space group

On the use of theCmap in Patterson deconvolution procedures

Estimates of triplet invariants given a model structure

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