High Resolution Microscopy of Multi-Layered Biological Crystals

1982 ◽  
Vol 40 ◽  
pp. 80-83
Author(s):  
H.A. Cohen ◽  
T.W. Jeng ◽  
W. Chiu
Keyword(s):  
High Resolution ◽  
Low Dose ◽  
Three Dimensional ◽  
Data Interpretation ◽  
Two Dimensional ◽  
Biological Objects ◽  
Density Maps ◽  
Density Map ◽  
Complex Crystal ◽  
High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

Electron Crystallographic Determination of the Structure of Bacteriorhodopsin

1990 ◽  
Vol 48 (1) ◽  
pp. 90-91
Author(s):  
R. Henderson ◽  
J.M. Baldwin ◽  
T.A. Ceska ◽  
E. Beckman ◽  
F. Zemlin ◽  
...  
Keyword(s):  
High Resolution ◽  
Proton Pump ◽  
Three Dimensional ◽  
Atomic Resolution ◽  
Two Dimensional ◽  
New Methods ◽  
Density Map ◽  
Diffraction Patterns

The light driven proton pump bacteriorhodopsin (bR) occurs naturally as two-dimensional crystals. A three-dimensional density map of the structure, at near atomic resolution, has been obtained by studying the crystals using electron cryo-microscopy to obtain diffraction patterns and high resolution micrographs (1).New methods have been developed for analysing micrographs from tilted specimens, incorporating the methods previously developed for untilted specimens that enable large areas to be analysed and corrected for distortions. Data from 72 images, from both tilted and untilted specimens, have been analysed to produce the phases of 2700 independent Fourier components of the structure. The amplitudes of these components have been accurately measured from 150 diffraction patterns. Together, these data represent about half of the full three-dimensional transform to 3.5 Å. The distribution of the data which is included in the map is shown in fig. 1. For specimen tilts up to around 20° the data is essentially complete. For higher tilts the data is more sparsely sampled, and is at present about half complete.

Electron-density maps

2002 ◽  
Author(s):  
David Blow
Keyword(s):  
Fourier Transform ◽  
Electron Density ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Unit Cell ◽  
Density Maps ◽  
Wave Cycle ◽  
Density Map ◽  
The Fourier Transform ◽  
Electron Density Map

When everything has been done to make the phases as good as possible, the time has come to examine the image of the structure in the form of an electron-density map. The electron-density map is the Fourier transform of the structure factors (with their phases). If the resolution and phases are good enough, the electron-density map may be interpreted in terms of atomic positions. In practice, it may be necessary to alternate between study of the electron-density map and the procedures mentioned in Chapter 10, which may allow improvements to be made to it. Electron-density maps contain a great deal of information, which is not easy to grasp. Considerable technical effort has gone into methods of presenting the electron density to the observer in the clearest possible way. The Fourier transform is calculated as a set of electron-density values at every point of a three-dimensional grid labelled with fractional coordinates x, y, z. These coordinates each go from 0 to 1 in order to cover the whole unit cell. To present the electron density as a smoothly varying function, values have to be calculated at intervals that are much smaller than the nominal resolution of the map. Say, for example, there is a protein unit cell 50 Å on a side, at a routine resolution of 2Å. This means that some of the waves included in the calculation of the electron density go through a complete wave cycle in 2 Å. As a rule of thumb, to represent this properly, the spacing of the points on the grid for calculation must be less than one-third of the resolution. In our example, this spacing might be 0.6 Å. To cover the whole of the 50 Å unit cell, about 80 values of x are needed; and the same number of values of y and z. The electron density therefore needs to be calculated on an array of 80×80×80 points, which is over half a million values. Although our world is three-dimensional, our retinas are two-dimensional, and we are good at looking at pictures and diagrams in two dimensions.

scholarly journals On inertial-range scaling laws

1996 ◽  
Vol 306 ◽  
pp. 167-181 ◽  
Author(s):  
John C. Bowman
Keyword(s):  
Steady State ◽  
High Resolution ◽  
Scaling Laws ◽  
State Energy ◽  
Three Dimensional ◽  
Inertial Range ◽  
Energy Spectra ◽  
Two Dimensional ◽  
Unified Framework ◽  
Asymptotic Nature

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's k−5/3 scaling is derived for the energy inertial range. A related modification is found to Kraichnan's logarithmically corrected two-dimensional enstrophy-range law that removes its unexpected divergence at the injection wavenumber. The significance of these corrections is illustrated with steady-state energy spectra from recent high-resolution closure computations. Implications for conventional numerical simulations are discussed. These results underscore the asymptotic nature of inertial-range scaling laws.

scholarly journals Point-group symmetry detection in three-dimensional charge density of biomolecules

2019 ◽  
Vol 36 (7) ◽  
pp. 2237-2243
Author(s):  
Cyril F Reboul ◽  
Simon Kiesewetter ◽  
Dominika Elmlund ◽  
Hans Elmlund
Keyword(s):  
Charge Density ◽  
Single Particle ◽  
Statistical Tests ◽  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Density Maps ◽  
Point Groups ◽  
Density Map

Abstract Motivation No rigorous statistical tests for detecting point-group symmetry in three-dimensional (3D) charge density maps obtained by electron microscopy (EM) and related techniques have been developed. Results We propose a method for determining the point-group symmetry of 3D charge density maps obtained by EM and related techniques. Our ab initio algorithm does not depend on atomic coordinates but utilizes the density map directly. We validate the approach for a range of publicly available single-particle cryo-EM datasets. In straightforward cases, our method enables fully automated single-particle 3D reconstruction without having to input an arbitrarily selected point-group symmetry. When pseudo-symmetry is present, our method provides statistics quantifying the degree to which the 3D density agrees with the different point-groups tested. Availability and implementation The software is freely available at https://github.com/hael/SIMPLE3.0.

FRACTAL DIMENSIONALITY OF PORE AND GRAIN VOLUME OF A SILICICLASTIC MARINE SAND

2000 ◽  
Vol 11 (08) ◽  
pp. 1555-1559 ◽  
Author(s):  
A. H. REED ◽  
R. B. PANDEY ◽  
D. L. LAVOIE
Keyword(s):  
Weight Loss ◽  
High Resolution ◽  
Pore Volume ◽  
Three Dimensional ◽  
Fractal Dimensionality ◽  
Ct Images ◽  
Spatial Distributions ◽  
Two Dimensional ◽  
Linear Gradient ◽  
Marine Sand

Three-dimensional (3D) spatial distributions of pore and grain volumes were determined from high-resolution computer tomography (CT) images of resin-impregnated marine sands. Using a linear gradient extrapolation method, cubic three-dimensional samples were constructed from two-dimensional CT images. Image porosity (0.37) was found to be consistent with the estimate of porosity by water weight loss technique (0.36). Scaling of the pore volume (Vp) with the linear size (L), V ~ LD provides the fractal dimensionalities of the pore volume (D = 2.74 ± 0.02) and grain volume (D = 2.90 ± 0.02) typical for sedimentary materials.

High Resolution Synchrotron X-Ray Diffraction Tomography Of Large-Grained Samples

1996 ◽  
Vol 437 ◽  
Author(s):  
D.P. Piotrowski ◽  
S.R. Stock ◽  
A. Guvenilir ◽  
J.D. Haase ◽  
Z.U. Rek
Keyword(s):  
Spatial Distribution ◽  
High Resolution ◽  
Three Dimensional ◽  
Polycrystalline Materials ◽  
Diffraction Tomography ◽  
Two Dimensional ◽  
X Ray Diffraction ◽  
Image Storage ◽  
X Ray ◽  
Dimensional Distribution

AbstractIn order to understand the macroscopic response of polycrystalline structural materials to loading, it is frequently essential to know the spatial distribution of strain as well as the variation of micro-texture on the scale of 100 μm. The methods must be nondestructive, however, if the three-dimensional evolution of strain is to be studied. This paper describes an approach to high resolution synchrotron x-ray diffraction tomography of polycrystalline materials. Results from model samples of randomly-packed, millimeter-sized pieces of Si wafers and of similarly sized single-crystal Al blocks have been obtained which indicate that polychromatic beams collimated to 30 μm diameter can be used to determine the depth of diffracting volume elements within ± 70 μm. The variation in the two-dimensional distribution of diffracted intensity with changing sample to detector separation is recorded on image storage plates and used to infer the depth of diffracting volume elements.

Interactive visualization of electron density slices

2005 ◽  
Vol 38 (3) ◽  
pp. 563-565 ◽  
Author(s):  
Filipe R. N. C. Maia ◽  
Abraham Szöke ◽  
Warren DeLano ◽  
David van der Spoel
Keyword(s):  
High Resolution ◽  
Quantum Chemistry ◽  
Electron Density ◽  
Three Dimensional ◽  
Structure Model ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Molecular Visualization ◽  
Density Maps ◽  
Quantum Chemistry Calculations

A new tool has been developed to aid in the visualization of electron density in crystals or from quantum chemistry calculations. It displays the fine details of the electron density on a plane and the three-dimensional model of the molecule at the same time. The program enables the user to examine the details of weak or irregular features. Such features frequently occur in low-resolution maps, where they determine the correct tracing of a protein backbone. In high-resolution maps, solvent regions are difficult or impossible to observe using isosurfaces. The tool has been integrated into an existing molecular visualization package (PyMol) making it possible to observe and interact both with a structure model and the electron density slices freely, simultaneously and independently. This visualization model fills a gap in the visualization methods available to crystallographers and others who work with electron density maps.

scholarly journals Building brain network in electron density map determined by micro-CT

2014 ◽  
Vol 70 (a1) ◽  
pp. C1752-C1752
Author(s):  
Rino Saiga ◽  
Susumu Takekoshi ◽  
Naoya Nakamura ◽  
Akihisa Takeuchi ◽  
Kentaro Uesugi ◽  
...  
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Model Building ◽  
Three Dimensional ◽  
Brain Network ◽  
X Ray ◽  
Density Maps ◽  
Density Map ◽  
Electron Density Map

In macromolecular crystallography, an electron density distribution is traced to build a model of the target molecule. We applied this method to model building for electron density maps of a brain network. Human cerebral tissue was stained with heavy atoms [1]. The sample was then analyzed at the BL20XU beamline of SPring-8 to obtain a three-dimensional map of X-ray attenuation coefficients representing the electron density distribution. Skeletonized wire models were built by placing and connecting nodes in the map [2], as shown in the figure below. The model-building procedures were similar to those reported for crystallographic analyses of macromolecular structures, while the neuronal network was automatically traced by using a Sobel filter. Neuronal circuits were then analytically resolved from the skeletonized models. We suggest that X-ray microtomography along with model building in the electron density map has potential as a method for understanding three-dimensional microstructures relevant to biological functions.

Sign in / Sign up

Export Citation Format

Share Document