The Relation Between the Phase of the Electron Wave (Which is Lost When an Em Image is Recorded) and the Preserved Crystallographic Structure Factor Phases

1997 ◽  
Vol 3 (S2) ◽  
pp. 1027-1028
Author(s):  
Sven Hovmöller ◽  
Xiaodong Zou
Keyword(s):  
Electron Microscopy ◽  
General Solution ◽  
Structure Factor ◽  
Crystallographic Structure ◽  
Phase Problem ◽  
Electron Wave ◽  
X Ray ◽  
Patterson Function ◽  
X Ray Crystallography ◽  
Mathematical Problems

The phase problem in X-ray crystallography is one of the most interesting and most studied mathematical problems that exist. There is still today no general solution of the phase problem, but partial solutions have resulted in at least 8 Nobel Prizes, even though one of the most prominent solutions, the Patterson function, was not awarded the Prize.It has frequently been claimed that there should be a phase problem also in electron microscopy. It may be more correct to say that there is no phase problem, only a phase confusion problem in electron microscopy. The phase confusion problem has arisen since the word phase is used for (at least) two very different physical entities in the field of electron microscopy. When crystallographers speak about phases, they mean the crystallographic structure factor phases, while physicists mean the wave front phases. In order to resolve the phase confusion problem, it is necessary to define clearly which phases are meant.

Bridging the resolution gap between x-ray crystallography and electron microscopy

1994 ◽  
Vol 52 ◽  
pp. 92-93
Author(s):  
P. L. Stewart ◽  
S. D. Fuller ◽  
R. M. Burnett
Keyword(s):  
Electron Microscopy ◽  
Transfer Function ◽  
Electron Micrographs ◽  
Structural Information ◽  
Crystallographic Structure ◽  
Contrast Transfer Function ◽  
X Ray ◽  
X Ray Crystallography ◽  
Intact Virus

While x-ray crystallography provides atomic resolution structures of proteins and small viruses, electron microscopy can provide complementary structural information on larger assemblies. A significant computational challenge is faced in bridging the resolution gap between the two techniques. X-ray crystallographic data is collected in the range of 2-10 Å, while image reconstructions from electron micrographs are at a resolution of 25-35 Å. A further problem is that density derived from cryo-electron micrographs is distorted by the contrast transfer function of the microscope, whichaccentuates certain resolution bands.A novel combination of electron microscopy and x-ray crystallography has revealed the various structural components forming the capsid of human type 2 adenovirus. An image reconstruction of the intact virus (Fig. 1), derived from cryo-electron micrographs, was deconvolved with an approximate contrast transfer function to mitigate microscope distortions (Fig. 2). A model capsid was calculated from 240 copies of the crystallographic structure of the major capsid protein and filtered to the correct resolution (Fig. 3).

Electron microscopy of rabbit FC crystals

1983 ◽  
Vol 41 ◽  
pp. 730-731
Author(s):  
Robert A. Grant ◽  
Laura L. Degn ◽  
Wah Chiu ◽  
John Robinson
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
High Resolution Electron Microscopy ◽  
Molecular Replacement ◽  
X Ray ◽  
X Ray Crystallography ◽  
Resolution Electron ◽  
Replacement Technique ◽  
Hydrated Crystal ◽  
Molecular Structure Analysis

Proteolytic digestion of the immunoglobulin IgG with papain cleaves the molecule into an antigen binding fragment, Fab, and a compliment binding fragment, Fc. Structures of intact immunoglobulin, Fab and Fc from various sources have been solved by X-ray crystallography. Rabbit Fc can be crystallized as thin platelets suitable for high resolution electron microscopy. The structure of rabbit Fc can be expected to be similar to the known structure of human Fc, making it an ideal specimen for comparing the X-ray and electron crystallographic techniques and for the application of the molecular replacement technique to electron crystallography. Thin protein crystals embedded in ice diffract to high resolution. A low resolution image of a frozen, hydrated crystal can be expected to have a better contrast than a glucose embedded crystal due to the larger density difference between protein and ice compared to protein and glucose. For these reasons we are using an ice embedding technique to prepare the rabbit Fc crystals for molecular structure analysis by electron microscopy.

scholarly journals Structure of the Lassa Virus Nucleoprotein Revealed by X-ray Crystallography, Small-angle X-ray Scattering, and Electron Microscopy

2011 ◽  
Vol 286 (44) ◽  
pp. 38748-38756 ◽  
Author(s):  
Linda Brunotte ◽  
Romy Kerber ◽  
Weifeng Shang ◽  
Florian Hauer ◽  
Meike Hass ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Small Angle ◽  
Lassa Virus ◽  
X Ray ◽  
X Ray Crystallography ◽  
X Ray Scattering ◽  
Ray Scattering

scholarly journals The Use of Connected Masks for Reconstructing the Single Particle Image from X-Ray Diffraction Data. II. The Dependence of the Accuracy of the Solution on the Sampling Step of Experimental Data

2015 ◽  
Vol 10 (2) ◽  
pp. 508-525 ◽  
Author(s):  
Н.Л. Лунина ◽  
N.L. Lunina
Keyword(s):  
Experimental Data ◽  
Particle Image ◽  
Expected Improvement ◽  
Problem Solution ◽  
Phase Problem ◽  
X Ray Diffraction ◽  
Sampling Step ◽  
X Ray ◽  
X Ray Crystallography ◽  
Grid Points

Advances in the methodology of the X-ray diffraction experiments leads to a possibility to register the rays scattered by large isolated biological particles (viruses and individual cells) but not only by crystalline samples. The experiment with an isolated particle provides researchers with the intensities of the scattered rays for the continuous spectrum of scattering vectors. Such experiment gives much more experimental data than an experiment with a crystalline sample where the information is limited to a set of Bragg reflections. This opens up additional opportunities in solving underlying problem of X-ray crystallography, namely, calculating phase values for the scattered waves needed to restore the structure of the object under study. In practice, the original continuous diffraction pattern is sampled, reduced to the values at grid points in the space of scattering vectors (in the reciprocal space). The sampling step determines the amount of the information involved in solving the phase problem and the complexity of the necessary calculations. In this paper, we investigate the effect of the sampling step on the accuracy of the phase problem solution obtained by the method proposed earlier by the authors. It is shown that an expected improvement of the accuracy of the solution with the reducing the sampling step continues even after crossing the Nyquist limit defined as the inverse of the double size of the object under study.

scholarly journals Howard Flack and the Flack Parameter

Chemistry ◽  
2020 ◽  
Vol 2 (4) ◽  
pp. 796-804
Author(s):  
David John Watkin ◽  
Richard Ian Cooper
Keyword(s):  
Structure Determination ◽  
Standard Uncertainty ◽  
Crystallographic Structure ◽  
X Ray ◽  
Original Algorithm ◽  
X Ray Crystallography ◽  
Chiral Materials

The Flack Parameter is now almost universally reported for all chiral materials characterized by X-ray crystallography. Its elegant simplicity was an inspired development by Howard Flack, and although the original algorithm for its computation has been strengthened by other workers, it remains an essential outcome for any crystallographic structure determination. As with any one-parameter metric, it needs to be interpreted in the context of its standard uncertainty.

scholarly journals Architectural plasticity of AMPK revealed by electron microscopy and X-ray crystallography

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Yan Ouyang ◽  
Li Zhu ◽  
Yifang Li ◽  
Miaomiao Guo ◽  
Yang Liu ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
X Ray ◽  
X Ray Crystallography ◽  
Architectural Plasticity
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