A pattern-recognition approach to the phase problem: Application to the X-ray diffraction study of biological membranes and model systems

Luzzati, Vittorio; Tardieu, A.; Taupin, D.

doi:10.1016/0022-2836(72)90335-x

Cited by 61 publications

(35 citation statements)

References 15 publications

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“…Also in case of all studies of nonlamellar phospholipid mesophases we are aware of, be it inverted hexagonal, ripple, cubic (e.g. [111,112,113]) or the rhombohedral phase, the assumption of centrosymmetry has been made and yielded reasonable structural results. It has been attempted to motivate this by the fact that nonlamellar mesophases are obtained by phase transitions from symmetric lipid bilayers, and centrosymmetry should somehow be conserved [114].…”

Section: The Phase Problemmentioning

confidence: 99%

See 1 more Smart Citation

Stalk structures in lipid bilayer fusion studied by x-ray diffraction

Aeffner¹

2012

Göttingen Series in X-Ray Physics

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Section: The Phase Problemmentioning

confidence: 99%

“…The structures ρ( r ) obtained after reconstruction must be compatible with so-me general features due to the physico-chemical properties of lipid mesophases [113]: As a result of the powerful hydrophobic effect, water and hydrocarbon do not mix. The obtained structures must be composed of continuous lipid monolayers [115], i.e.…”

mentioning

confidence: 98%

Stalk structures in lipid bilayer fusion studied by x-ray diffraction

Aeffner¹

2012

Göttingen Series in X-Ray Physics

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“…Luzzati, Tardieu & Taupin (1972) used the lamellar reflexions up to the 9th and obtained the density profile with a resolution of about 6.7 A. Lesslauer, Cain & Blasie (1972) used the lamellar reflexions up to the 10th together with diffraction data from the dispersions and obtained the density profile with a resolution of about 6 A.…”

Section: Discussionmentioning

confidence: 99%

Structures of uranyl-decorated lecithin and lecithin–cholesterol bilayers

K¹,

Yamaguchi²,

Inoko³

et al. 1976

Acta Crystallogr Sect B

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Dipalmitoyl lecithin and dipalmitoyl lecithin-cholesterol bilayers are capable of binding about the same number of uranyl ions as lecithin molecules. Dispersions of the uranyl-decorated bilayers give very distinct continuous X-ray diffraction peaks up to the seventh order. Electron density projection onto the normal to the membrane is obtained with a resolution of about 6.5 ~. It gives two high peaks separated by 48/~, indicating that uranyl ions are bound at the surfaces of membranes in both lecithin and lecithin--cholesterol bilayers.

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“…Possible solutions, generated from the permuted starting phase terms, were sought in the multiple list after calculating all possible potential maps and testing the flatness of the density distribution. This test was made using the figure of merit suggested by Luzzati, Tardieu & Taupin (1972), i.e. q = lAp4), where Ap = p -Pavg" When the F000 term is set to 0.0 for calculation of the potential map, Pavg = 0.0.…”

Section: Phase Determinationmentioning

confidence: 99%

“…The phase determination employed a multisolution approach, also via the Sayre (1952) equation. The optimal structure solution was identified by a figure of merit used in early X-ray studies of amphiphile mesophases (Luzzati, Tardieu & Taupin, 1972), later proposed for macromolecules (Luzzati, Mariani & Delacroix, 1988).…”

Section: Introductionmentioning

confidence: 99%

Direct Phasing in Protein Electron Crystallography – Phase Extension and the Prospects forAb InitioDeterminations

Dorset

1996

Acta Cryst Sect A

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Zonal diffraction amplitudes and crystallographic phases, derived from an averaged electron micrograph of two-dimensionally crystalline E. coli Omp F outer membrane porin (plane group p31m, a=72A), embedded in glucose, were used as a model data set to test the feasibility of direct phase extension and ab initio direct phase determination. If 17 phase terms derived from e.g. a 10A (diffraction) resolution image are expanded to 6 ,h, by the Sayre-Hughes equation, the unknown phases are found with reasonable accuracy (mean error 43 ° for 25 reflections). This, however, is not the most optimal starting point. As a function of initial image resolution, the accuracy of the phase extension to 6 A is approximately a parabolic function. That is, an optimal basis resolution, found at 11 A (i. e. 14 defined reflections), produces a least mean error of 18 ° for 28 new reflections. In addition, ab initio phase determination is possible via a multisolution technique, using a test for density flatness as a figure of merit. The success of the determination, again, is sensitive to the size of the starting basis set generated from the permuted unknown reflections. If an annealing step is used to improve the basis set, the test for flatness will identify which reflections should be changed in phase. However, this figure of merit is not absolutely reliable for finding the exact value of the unknown phases.

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A pattern-recognition approach to the phase problem: Application to the X-ray diffraction study of biological membranes and model systems

Cited by 61 publications

References 15 publications

Stalk structures in lipid bilayer fusion studied by x-ray diffraction

Stalk structures in lipid bilayer fusion studied by x-ray diffraction

Structures of uranyl-decorated lecithin and lecithin–cholesterol bilayers

Direct Phasing in Protein Electron Crystallography – Phase Extension and the Prospects forAb InitioDeterminations

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