The strong phase object approximation may allow extending crystallographic phases of dynamical electron diffraction patterns of 3D protein nano-crystals

Abrahams, Jan Pieter

doi:10.1524/zkri.2010.1216

Cited by 8 publications

(3 citation statements)

References 23 publications

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“…By allowing significant phase fluctuations with arbitrary κ|ψ|, (3) and ( 4) is an improvement over the weak-phase-object approximation e iκψ ≈ 1 + iκψ (5) often used in cryo-electron microscopy (cryo-EM) [1,34,41]. Following the nomenclature in [41,89], we call (3) and (4) the strong-phase-object approximation, noting, however, that f is a complex-valued function in general (thus e iκψ not a 'phase' object per se).…”

Section: Forward Modelmentioning

confidence: 99%

3D tomographic phase retrieval and unwrapping

Fannjiang

2023

Inverse Problems

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This paper develops uniqueness theory for 3D phase retrieval with finite, discrete measurement data for strong phase objects and weak phase objects, including: (i) Unique determination of (phase) projections from diffraction patterns—General measurement schemes with coded and uncoded apertures are proposed and shown to ensure unique reduction of diffraction patterns to the phase projection for a strong phase object (respectively, the projection for a weak phase object) in each direction separately without the knowledge of relative orientations and locations. (ii) Uniqueness for 3D phase unwrapping—General conditions for unique determination of a 3D strong phase object from its phase projection data are established, including, but not limited to, random tilt schemes densely sampled from a spherical triangle of vertexes in three orthogonal directions and other deterministic tilt schemes. (iii) Uniqueness for projection tomography—Unique determination of an object of n 3 voxels from generic n projections or n + 1 coded diffraction patterns is proved. This approach of reducing 3D phase retrieval to the problem of (phase) projection tomography has the practical implication of enabling classification and alignment, when relative orientations are unknown, to be carried out in terms of (phase) projections, instead of diffraction patterns. The applications with the measurement schemes such as single-axis tilt, conical tilt, dual-axis tilt, random conical tilt and general random tilt are discussed.

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Section: Forward Modelmentioning

confidence: 99%

3D tomographic phase retrieval and unwrapping

Fannjiang

2023

Inverse Problems

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“…As it turned out, the individual diffraction patterns provided a challenge as the relative orientation of the crystal lattice for each pattern was unknown, so merging diffraction data from multiple crystals was difficult. Data processing methods were then developed (Jiang et al, 2009) (Abrahams, 2010), before improved detectors yielded better signal-to-noise ratios (SNR) (Nederlof et al, 2011). Reducing electron dosage (to 0.1 e − Å −2 s −1 ) prevented degradation and acquired more diffraction patterns per crystal (Nederlof et al, 2013), allowing patterns to be orientated.…”

Section: Electron Crystallographymentioning

confidence: 99%

Illuminating the Secrets of Crystals - Microcrystal Electron Diffraction in Structural Biology

Barringer

Meier²

2018

Preprint

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An exploration of the crystallographic theory of the relatively novel method of Microcrystal Electron Diffraction (MicroED), via comparison to X-ray crystallography at the theoretical and practical level as it applies to biological macromolecules. We then attempt to outline the limitations and challenges that the technique currently faces in structural biology, and suggest future areas of study that may improve and optimize the technique.

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“…When the indices and their corresponding intensity are known, methods from X-ray crystallography can be used to reconstruct the 3D lattice of intensities in reciprocal space. Phase recovery of electron diffraction (Abrahams, 2010) may be facilitated by dynamical scattering effects but requires knowledge of the orientation parameters for each recorded intensity, which means that standard X-ray crystallography data integration software may not be used for this purpose. Subsequent iterative refinement is essential for determining the atomic structure and may involve correction for dynamical scattering.…”

Section: Introductionmentioning

confidence: 99%

Image Processing and Lattice Determination for Three-Dimensional Nanocrystals

et al. 2011

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Three-dimensional nanocrystals can be studied by electron diffraction using transmission cryo-electron microscopy. For molecular structure determination of proteins, such nanosized crystalline samples are out of reach for traditional single-crystal X-ray crystallography. For the study of materials that are not sensitive to the electron beam, software has been developed for determining the crystal lattice and orientation parameters. These methods require radiation-hard materials that survive careful orienting of the crystals and measuring diffraction of one and the same crystal from different, but known directions. However, as such methods can only deal with well-oriented crystalline samples, a problem exists for three-dimensional (3D) crystals of proteins and other radiation sensitive materials that do not survive careful rotational alignment in the electron microscope. Here, we discuss our newly released software AMP that can deal with nonoriented diffraction patterns, and we discuss the progress of our new preprocessing program that uses autocorrelation patterns of diffraction images for lattice determination and indexing of 3D nanocrystals.

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The strong phase object approximation may allow extending crystallographic phases of dynamical electron diffraction patterns of 3D protein nano-crystals

Cited by 8 publications

References 23 publications

3D tomographic phase retrieval and unwrapping

3D tomographic phase retrieval and unwrapping

Illuminating the Secrets of Crystals - Microcrystal Electron Diffraction in Structural Biology

Image Processing and Lattice Determination for Three-Dimensional Nanocrystals

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