Global least-squares determination of Eulerian angles from single electron diffraction patterns of tilted crystals

2000 ◽  
Vol 33 (4) ◽  
pp. 1088-1101 ◽  
Author(s):  
Eva Dimmeler ◽  
Rasmus R. Schröder
Keyword(s):  
Electron Diffraction ◽  
Least Squares ◽  
Three Dimensional ◽  
Test Sample ◽  
Single Electron ◽  
Dimensional Structure ◽  
Diffraction Spot ◽  
Linear Fit ◽  
Diffraction Patterns

Three-dimensional structure determination using electron diffraction of crystalline samples necessitates the determination of the Eulerian angles of tilted samples. For experimental tilt series, even with approximately known tilt, the resolution of the final three-dimensional reconstructions is reduced as a result of the large errors of the refined tilt angles and crystal axes positions. The presented new least-squares procedure determines the orientation of the crystal with very high accuracy from a single electron diffraction pattern. Instead of evaluating the averaged pattern geometry, each diffraction spot position is individually included in an analytical non-linear fit. This procedure is very stable against potential experimental errors, as demonstrated by Monte Carlo simulations. As a test sample, a three-dimensional microcrystal of an organic crystal compound was used. Contrary to the conventional method, which produced erroneous Miller indices for some reflections, the indexing obtained with the new algorithm was more consistent for each individual pattern. Preliminary data from frozen hydrated protein crystals, the samples of which are beam sensitive and for which only a few patterns can be recorded from a single crystal, indicate that the new angle determination promises to be particularly beneficial under such conditions.

Determination of Tilt Parameters in Electron Diffraction Patterns of 3D-Microcrystals

1997 ◽  
Vol 3 (S2) ◽  
pp. 1049-1050
Author(s):  
E. Dimmeler ◽  
K.C. Holmes ◽  
R.R. Schröder
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Diffraction Spot ◽  
Spot Intensity ◽  
Crystal Face ◽  
Ewald Sphere ◽  
Exact Determination ◽  
Current Experimental Data ◽  
Diffraction Patterns

Electron crystallography of thin three-dimensional (3D) protein crystals requires very exact determination of tilt angles and spot profiles to obtain correct merging of diffraction spot amplitudes. The reciprocal lattice of 3D microcrystals consists of ellipsoidal spot profiles which are very extended in the direction normal to the crystal face (z*). To extrapolate from the intensity measured in a section to the total spot intensity, two features need to be known very exactly: 1. the orientation of reciprocal lattice relative to the Ewald sphere, 2. the 3D-shape of the spot cloud.Fig. 1 shows a tilt series of one frozen hydrated catalase crystal, in the order of recording. The third diffraction pattern gives the highest resolution because it is untilted and therefore the electrons have the shortest path length. In the current experimental data taken at 120 keV electron energy inelastic scattering within the crystal leads to a dramatic loss of elastic information in highly tilted patterns.

EDIFF: a program for automated unit-cell determination and indexing of electron diffraction data

2011 ◽  
Vol 44 (5) ◽  
pp. 1132-1136 ◽  
Author(s):  
Linhua Jiang ◽  
Dilyana Georgieva ◽  
Jan Pieter Abrahams
Keyword(s):  
Electron Diffraction ◽  
Diffraction Data ◽  
Three Dimensional ◽  
Unit Cell ◽  
Electron Diffraction Data ◽  
Cell Determination ◽  
Diffraction Patterns ◽  
Inorganic Molecules ◽  
User Friendly

EDIFFis a new user-friendly software suite for unit-cell determination of three-dimensional nanocrystals from randomly oriented electron diffraction patterns with unknown independent orientations. It can also be used for three-dimensional cell reconstruction from diffraction tilt series. In neither case is exact knowledge of the angular relationship between the patterns required. The unit cell can be validated and the crystal system assigned.EDIFFcan index the reflections in electron diffraction patterns. Thus,EDIFFcan be employed as a first step in reconstructing the three-dimensional atomic structure of organic and inorganic molecules and of proteins from diffraction data. An example illustrates the viability of theEDIFFapproach.

scholarly journals Three-dimensional electron crystallography of protein microcrystals

eLife ◽  
2013 ◽  
Vol 2 ◽  
Author(s):  
Dan Shi ◽  
Brent L Nannenga ◽  
Matthew G Iadanza ◽  
Tamir Gonen
Keyword(s):  
Electron Diffraction ◽  
Protein Structures ◽  
Three Dimensional ◽  
Electron Diffraction Data ◽  
Electron Crystallography ◽  
Electron Dose ◽  
Tilt Series ◽  
Diffraction Patterns ◽  
A New Technique

We demonstrate that it is feasible to determine high-resolution protein structures by electron crystallography of three-dimensional crystals in an electron cryo-microscope (CryoEM). Lysozyme microcrystals were frozen on an electron microscopy grid, and electron diffraction data collected to 1.7 Å resolution. We developed a data collection protocol to collect a full-tilt series in electron diffraction to atomic resolution. A single tilt series contains up to 90 individual diffraction patterns collected from a single crystal with tilt angle increment of 0.1–1° and a total accumulated electron dose less than 10 electrons per angstrom squared. We indexed the data from three crystals and used them for structure determination of lysozyme by molecular replacement followed by crystallographic refinement to 2.9 Å resolution. This proof of principle paves the way for the implementation of a new technique, which we name ‘MicroED’, that may have wide applicability in structural biology.

scholarly journals Protein Crystallography: Getting in on the Ground Floor

2014 ◽  
Vol 70 (a1) ◽  
pp. C931-C931
Author(s):  
Brian Matthews
Keyword(s):  
Three Dimensional ◽  
Protein Crystal ◽  
Dimensional Structure ◽  
Three Dimensional Structure ◽  
Egg White Lysozyme ◽  
Isomorphous Replacement ◽  
Hen Egg White ◽  
Diffraction Patterns ◽  
Dorothy Crowfoot Hodgkin

The first diffraction pattern from crystals of a protein was obtained by Desmond Bernal and Dorothy Crowfoot Hodgkin in 1934. As early as 1939, Bernal described how such diffraction patterns might be used to determine the complete three-dimensional structure of a protein. It was not until 1954, however, that Max Perutz showed how isomorphous replacement could be used to determine the phases for crystalline hemoglobin. Using this approach, Kendrew and coworkers described the three-dimensional structure of myoglobin in 1960. In 1965, David Phillips' group determined the structure of hen egg-white lysozyme. Then, in 1967, three different protein crystal structures were reported. Macromolecular crystallography had come of age. The talk will touch on some of these early events and include reminiscences of work at the MRC Lab in David Blow's group leading up to the successful determination of the alpha-chymotrypsin structure.

scholarly journals MicroED: Three Dimensional Electron Crystallography of Protein Micro-Crystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C1063-C1063
Author(s):  
Tamir Gonen
Keyword(s):  
Electron Diffraction ◽  
Protein Structures ◽  
Three Dimensional ◽  
Electron Diffraction Data ◽  
Molecular Replacement ◽  
Electron Crystallography ◽  
Electron Dose ◽  
Tilt Series ◽  
Diffraction Patterns

We demonstrate that it is feasible to determine high-resolution protein structures by electron crystallography of three-dimensional crystals in an electron cryo-microscope (CryoEM). Lysozyme microcrystals were frozen on an electron microscopy grid, and electron diffraction data collected to 1.7Å resolution. We developed a data collection protocol to collect a full-tilt series in electron diffraction to atomic resolution. A single tilt series contains up to 90 individual diffraction patterns collected from a single crystal with tilt angle increment of 0.1 - 10and a total accumulated electron dose less than 10 electrons per angstrom squared. We indexed the data from three crystals and used them for structure determination of lysozyme by molecular replacement followed by crystallographic refinement to 2.9Å resolution. In this seminar I will present our initial proof of principle study and highlight the major advances since the first publication.

Conformation of Ribosomes from Escherichia Coli

1974 ◽  
Vol 32 ◽  
pp. 210-211
Author(s):  
M. Boublik ◽  
W. Hellmann ◽  
F. Jenkins
Keyword(s):  
Binding Sites ◽  
Ribosomal Proteins ◽  
Fluorescent Dyes ◽  
Protein Biosynthesis ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Dimensional Structure ◽  
Complete Understanding ◽  
And Function

The present knowledge of the three-dimensional structure of ribosomes is far too limited to enable a complete understanding of the various roles which ribosomes play in protein biosynthesis. The spatial arrangement of proteins and ribonuclec acids in ribosomes can be analysed in many ways. Determination of binding sites for individual proteins on ribonuclec acid and locations of the mutual positions of proteins on the ribosome using labeling with fluorescent dyes, cross-linking reagents, neutron-diffraction or antibodies against ribosomal proteins seem to be most successful approaches. Structure and function of ribosomes can be correlated be depleting the complete ribosomes of some proteins to the functionally inactive core and by subsequent partial reconstitution in order to regain active ribosomal particles.

scholarly journals Determination of the alpha-actinin-binding site on actin filaments by cryoelectron microscopy and image analysis.

1994 ◽  
Vol 126 (2) ◽  
pp. 433-443 ◽  
Author(s):  
A McGough ◽  
M Way ◽  
D DeRosier
Keyword(s):  
Image Analysis ◽  
Smooth Muscle ◽  
Binding Sites ◽  
Actin Filaments ◽  
Three Dimensional ◽  
Actin Binding ◽  
Dimensional Structure ◽  
Outer Face ◽  
Actin Binding Domain

The three-dimensional structure of actin filaments decorated with the actin-binding domain of chick smooth muscle alpha-actinin (alpha A1-2) has been determined to 21-A resolution. The shape and location of alpha A1-2 was determined by subtracting maps of F-actin from the reconstruction of decorated filaments. alpha A1-2 resembles a bell that measures approximately 38 A at its base and extends 42 A from its base to its tip. In decorated filaments, the base of alpha A1-2 is centered about the outer face of subdomain 2 of actin and contacts subdomain 1 of two neighboring monomers along the long-pitch (two-start) helical strands. Using the atomic model of F-actin (Lorenz, M., D. Popp, and K. C. Holmes. 1993. J. Mol. Biol. 234:826-836.), we have been able to test directly the likelihood that specific actin residues, which have been previously identified by others, interact with alpha A1-2. Our results indicate that residues 86-117 and 350-375 comprise distinct binding sites for alpha-actinin on adjacent actin monomers.

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