Electron microscopy at 1-Å resolution by entropy maximization and likelihood ranking

Dong, Wei; Baird, T.; Fryer, J. R.; Gilmore, C. J.; MacNicol, David D.; Bricogne, G.; Smith, David J.; O’Keefe, Michael A.; Hovmöller, Sven

doi:10.1038/355605a0

Cited by 86 publications

(40 citation statements)

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“…Whenever the crystal size is too small for single crystal X-ray diffraction and X-ray powder diffraction is unsuited for structural analysis, electron crystallography may be the answer to the problem. reported for membrane proteins [1][2][3], organic molecules [4][5][6], and inorganic compounds [7][8][9]. Further advantages of electron crystallography versus X-ray diffraction appear evident when dealing with modulated structures, where one immediately gains information about the modulation wave-vector [10,11].…”

Section: Introductionmentioning

confidence: 99%

A practical method to detect and correct for lens distortion in the TEM

et al. 2006

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A practical, offline method for experimental detection and correction for projector lens distortion in the transmission electron microscope (TEM) operating in high-resolution (HR) and selected area electron diffraction (SAED) modes is described. Typical TEM works show that, in the simplest case, the distortion transforms on the recording device, which would be a circle into an ellipse. The first goal of the procedure described here is to determine the elongation and orientation of the ellipse. The second goal is to correct for the distortion using an ordinary graphic program. The same experimental data set may also be used to determine the actual microscope magnification and the rotation between SAED patterns and HR images.The procedure may be helpful in several quantitative applications of electron diffraction and HR imaging, for instance while performing accurate lattice parameter determination, or while determining possible metrical deviations (cell edges and angles) from a given symmetry. r

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Section: Introductionmentioning

confidence: 99%

A practical method to detect and correct for lens distortion in the TEM

et al. 2006

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“…An adaptation of the likelihood criterion to intensity data corrupted by overlap (Bricogne, 1991b) also enabled MICE to successfully tackle the ab initio determination of small inorganic structures from powder diffraction data (Gilmore, K. Henderson & Bricogne, 1991;Shanldand, Gilmore, Bricogne & Hashizume, 1992). Another related application has been in electron crystallography (Dong, Baird, Fryer, Gilmore, MacNicol, Bricogne, Smith, O'Keefe & Hovmoller, 1992) where MICE was able to extend initial phases to 3 A resolution for a projection of perchlorocoronene, obtained from electron micrographs by image-processing techniques, to the full set of 1 A resolution amplitudes measured by electron diffraction. In macromolecular crystallography Charles Carter and co-workers have shown at this meeting (Xiang, Carter, Bricogne & Gilmore, 1993) that MICE can be used to carry out phase extension very effectively by entropy maximization to maximum likelihood, a technique which yields results far superior to conventional solvent flattening when some initial phase information is available together with a sufficiently good molecular envelope.…”

Section: O Introductionmentioning

confidence: 99%

Direct phase determination by entropy maximization and likelihood ranking: status report and perspectives

Bricogne

1993

Acta Crystallogr D Biol Crystallogr

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105

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A new multisolution phasing method based on entropy maximization and likelihood ranking, proposed for the specific purpose of extending probabilistic direct methods to the field of macromolecules, has been implemented in two different computer programs and applied to a wide variety of problems. The latter comprise the determination of small crystal structures from X-ray diffraction data obtained from single crystals or from powders, and from electron diffraction data partially phased by image processing of electron micrographs, the ab initio generation and ranking of phase sets for small proteins; and the improvement of poor quality phases for a larger protein at medium resolution under constraint of solvent flatness. These applications show that the primary goal of this new method -namely increasing the accuracy and sensitivity of probabilistic phase indications compared with conventional direct methods -has been achieved. The main components of the method are (1) a tree-directed search through a space of trial phase sets; (2) the saddlepoint method for calculating joint probabilities of structure factors, using entropy maximization; (3) likelihood-based scores to rank trial phase sets and prune the search tree; (4) efficient schemes, based on error-correcting codes, for sampling trial phase sets; (5) a statistical analysis of the scores for automatically selecting reliable phase indications. They have been implemented to varying degrees of completeness in a computer program (BUSTER) and tested on two small structures as well as on the small protein crambin. The main obstructions to successful ab initio phasing in the latter case seem to reside in the accumulation of phase sampling errors and in the lack of a properly defined molecular envelope, both of which can be remedied within the methods proposed. A review of the Bayesian statistical theory encompassing all phasing procedures, proposed earlier as an extension of the initial theory, shows that the techniques now available in BUSTER bring closer a number of major enhancements of standard macromolecular phasing techniques, namely isomorphous replacement, molecular replacement, solvent flattening and non-crystallographic symmetry averaging. The gradual implementation of the successive stages of this 'Bayesian programme' should lead to an increasingly integrated, effective and dependable phasing procedure for macromolecular structure determination.

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“…A direct approach based on interpretation of lattice images projected along axes where the atom strings are well separated is necessarily limited by the point resolution of the electron microscope, although new techniques such as side-band holography (Lichte, 1992), phase extension by direct methods adapted from X-ray crystallography (Dong et al, 1992) and processing of through-focal sequences (Coene, Janssen, Op de Beeck & Van Dyck, 1992) are reducing the resolution limit towards 1 A. Nevertheless, a resolution of 1 ,~, is insufficient to infer the threedimensional structure of even a moderately complex crystal, quite apart from the problem of dealing with ©1995 International Union of Crystallography Printed in Great Britain -all rights reserved dynamical coupling between beams diffracted around a major zone axis.…”

Section: Introductionmentioning

confidence: 99%

Structure determination of a rhombohedral Al–Ge phase by CBED and X-ray powder diffraction

Vincent¹,

Exelby²

1995

Acta Cryst Sect A

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A new approach to the problem of crystal structure determination by electron diffraction is described based upon the intensities of higher-order Laue-zone (HOLZ) reflections in convergent-beam electron diffraction (CBED) patterns. Along a major zone axis, a subset of symmetry-related atoms may project into separate string potentials associated with localized Bloch states. In a quasi-kinematic limit, the amplitudes of HOLZ excess lines diffracted from the Bloch states are proportional to the partial structure factors for these atoms. If a structure is unknown, the Bloch states cannot be calculated but it is shown that the conditional Patterson transform of the HOLZ intensities around suitable axes may include narrow correlation peaks that identify interatomic vectors. This approach was tested by analysis of a metastable A1-Ge phase with space group R3c. A transform of HOLZ intensities measured around the c axis showed peaks displaced by only 0.21 A from the screw axes, consistent with Ge atoms in the 18(e) positions. Although A1 atoms were not visible in the Patterson maps, the crystal structure with nominal composition A16Ge 5 was identified as isostructural with the Zn4Sb 3 phase by comparison of observed and calculated X-ray powder intensities.

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Electron microscopy at 1-Å resolution by entropy maximization and likelihood ranking

Cited by 86 publications

References 0 publications

A practical method to detect and correct for lens distortion in the TEM

A practical method to detect and correct for lens distortion in the TEM

Direct phase determination by entropy maximization and likelihood ranking: status report and perspectives

Structure determination of a rhombohedral Al–Ge phase by CBED and X-ray powder diffraction

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