Envelope skeletonization as a means to determine monomer masks and non-crystallographic symmetry relationships: application in the solution of the structure of fibrinogen fragment D

1999 ◽  
Vol 55 (2) ◽  
pp. 458-463 ◽  
Author(s):  
Glen Spraggon
Keyword(s):  
Three Dimensional ◽  
Real Space ◽  
Reciprocal Space ◽  
Structure Solution ◽  
Crystallographic Symmetry ◽  
Translation Component ◽  
Rotation Function ◽  
Molecular Envelope

An algorithm is described which utilizes the solvent mask generated by the solvent-flattening technique to calculate a monomer molecular envelope. In the case where non-crystallographic symmetry (NCS) is present in the crystal and self-rotation angles are known from a self-rotation function, the resultant monomer envelopes can be used to search for the translation component of the NCS element by a three-dimensional search in real space. In the absence of self-rotation angles, the monomer envelope may be used to derive the NCS operators by reciprocal-space techniques. Thus, an automatic procedure for averaging directly from the solvent-flattening stage can be implemented. The procedure was instrumental in the structure solution of fibrinogen fragment D, which is presented as an example.

Orientation Relationships and Interfaces Between Low Symmetry Phases in The Yttria-Alumina System

1994 ◽  
Vol 357 ◽  
Author(s):  
R. S. Hay
Keyword(s):  
Monoclinic Phase ◽  
Three Dimensional ◽  
Real Space ◽  
Reciprocal Space ◽  
High Symmetry ◽  
Orientation Relationships ◽  
Yttrium Aluminum ◽  
High Resolution Tem ◽  
Interphase Boundaries ◽  
Definition Of

AbstractInterphase boundaries and orientation relationships for yttria - yttrium-aluminum monoclinic and yttrium-aluminum monoclinic - yttrium-aluminum perovskite eutectics were observed by standard and high resolution TEM techniques. Three and five orientation relationships were found for each system, respectively. These eutectics all had a monoclinic phase and therefore had little potential for high symmetry overlap. In many cases low index planes with similer spacings or spacing multiples were parallel. However, presence of a monoclinic phase made definition of a three-dimensional low index near-CSL very difficult, so a combination of planes corresponding to reciprocal-space directions and zones corresponding to real-space directions were often needed for a geometric description of the orientation relationship. In general, two planes and the real-space direction corresponding to the zone for these planes described the orientation relationships. The disregistry between reciprocal-space coincidence sites was not localized by dislocations large enough to be visible.

scholarly journals 6D electron microscopy: combining real-space and reciprocal-space tomography

2014 ◽  
Vol 70 (a1) ◽  
pp. C368-C368 ◽  
Author(s):  
Alexander Eggeman ◽  
Robert Krakow ◽  
Paul Midgley
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Real Space ◽  
Dark Field ◽  
Reciprocal Space ◽  
Data Set ◽  
Wide Range ◽  
The Matrix ◽  
Precession Electron Diffraction ◽  
Tilt Series

STEM and TEM-based tomography has been used widely to study the 3D morphology of a wide range of materials. Similarly reciprocal space tomography in which a tilt-series of diffraction patterns are acquired offers a powerful method for the analysis of the atomic structure of crystalline materials. The natural progression is to combine these techniques into a complete three dimensional morphology and crystallography data set, allowing both features to be studied simultaneously. Using a tilt series of scanning precession electron diffraction measurements from a commercially available Ni-base superalloy as an example, the complete reciprocal lattice orientation for a number of components embedded within the matrix could be determined. It was straightforward to identify reciprocal lattice vectors that allowed dark-field images representing each phase to be produced post-acquisition. In turn these were combined using geometric tomography methods to yield a 3-D tomogram of the superalloy. Imaging these phases using conventional ADF STEM tomography would potentially be challenging given the compositional similarity between the different phases. From the combined dataset the spatial distribution of the component phases could be easily recovered but more importantly the orientational relationships between these different components could be unambiguously determined. In this way the thermo-mechanical history of the sample could be inferred from the arrangement of coherent and semi-coherent interfaces and a previously unreported crystallographic registry between metal carbide (MC) and the matrix f.c.c. phases could been identified. The possibilities for development and applications of this technique will be discussed further.

EDMA: a computer program for topological analysis of discrete electron densities

2012 ◽  
Vol 45 (3) ◽  
pp. 575-580 ◽  
Author(s):  
Lukáš Palatinus ◽  
Siriyara Jagannatha Prathapa ◽  
Sander van Smaalen
Keyword(s):  
Computer Program ◽  
Electron Density ◽  
Critical Points ◽  
Topological Analysis ◽  
Three Dimensional ◽  
Real Space ◽  
Principal Curvatures ◽  
Electron Densities ◽  
Structure Solution ◽  
Aperiodic Crystals

EDMAis a computer program for topological analysis of discrete electron densities according to Bader's theory of atoms in molecules. It locates critical points of the electron density and calculates their principal curvatures. Furthermore, it partitions the electron density into atomic basins and integrates the volume and charge of these atomic basins.EDMAcan also assign the type of the chemical element to atomic basins based on their integrated charges. The latter feature can be used for interpretation ofab initioelectron densities obtained in the process of structure solution. A particular feature ofEDMAis that it can handle superspace electron densities of aperiodic crystals in arbitrary dimensions.EDMAfirst generates real-space sections at a selected set of phases of the modulation wave, and subsequently analyzes each section as an ordinary three-dimensional electron density. Applications ofEDMAto model electron densities have shown that the relative accuracy of the positions of the critical points, the electron densities at the critical points and the Laplacian is of the order of 10−4or better.

scholarly journals How to assign a (3 + 1)-dimensional superspace group to an incommensurately modulated biological macromolecular crystal

2017 ◽  
Vol 50 (4) ◽  
pp. 1200-1207 ◽  
Author(s):  
Jason Porta ◽  
Jeff Lovelace ◽  
Gloria E. O. Borgstahl
Keyword(s):  
Crystal Structure ◽  
Three Dimensional ◽  
Real Life ◽  
Group Symmetry ◽  
Protein Crystal ◽  
3D Space ◽  
Structure Solution ◽  
Crystallographic Symmetry ◽  
Aperiodic Crystals ◽  
Periodic Crystal

Periodic crystal diffraction is described using a three-dimensional (3D) unit cell and 3D space-group symmetry. Incommensurately modulated crystals are a subset of aperiodic crystals that need four to six dimensions to describe the observed diffraction pattern, and they have characteristic satellite reflections that are offset from the main reflections. These satellites have a non-integral relationship to the primary lattice and requireqvectors for processing. Incommensurately modulated biological macromolecular crystals have been frequently observed but so far have not been solved. The authors of this article have been spearheading an initiative to determine this type of crystal structure. The first step toward structure solution is to collect the diffraction data making sure that the satellite reflections are well separated from the main reflections. Once collected they can be integrated and then scaled with appropriate software. Then the assignment of the superspace group is needed. The most common form of modulation is in only one extra direction and can be described with a (3 + 1)D superspace group. The (3 + 1)D superspace groups for chemical crystallographers are fully described in Volume C ofInternational Tables for Crystallography. This text includes all types of crystallographic symmetry elements found in small-molecule crystals and can be difficult for structural biologists to understand and apply to their crystals. This article provides an explanation for structural biologists that includes only the subset of biological symmetry elements and demonstrates the application to a real-life example of an incommensurately modulated protein crystal.

Imaging of strain and lattice orientation by quick scanning X-ray microscopy combined with three-dimensional reciprocal space mapping

2014 ◽  
Vol 47 (2) ◽  
pp. 762-769 ◽  
Author(s):  
Gilbert André Chahine ◽  
Marie-Ingrid Richard ◽  
Roberto Arturo Homs-Regojo ◽  
Thu Nhi Tran-Caliste ◽  
Dina Carbone ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Continuous Mapping ◽  
Real Space ◽  
Reciprocal Space ◽  
Data Sets ◽  
Two Dimensional ◽  
Reciprocal Space Mapping ◽  
X Ray ◽  
Study Materials ◽  
User Friendly

Numerous imaging methods have been developed over recent years in order to study materials at the nanoscale. Within this context, scanning X-ray diffraction microscopy has become a routine technique, giving access to structural properties with sub-micrometre resolution. This article presents an optimized technique and an associated software package which have been implemented at the ID01 beamline (ESRF, Grenoble). A structural scanning probe microscope with intriguing imaging qualities is obtained. The technique consists in a two-dimensional quick continuous mapping with sub-micrometre resolution of a sample at a given reciprocal space position. These real space maps are made by continuously moving the sample while recording scattering images with a fast two-dimensional detector for every point along a rocking curve. Five-dimensional data sets are then produced, consisting of millions of detector images. The images are processed by the user-friendly X-ray strain orientation calculation software (XSOCS), which has been developed at ID01 for automatic analysis. It separates tilt and strain and generates two-dimensional maps of these parameters. At spatial resolutions of typically 200–800 nm, this quick imaging technique achieves strain sensitivity below Δa/a= 10−5and a resolution of tilt variations down to 10−3° over a field of view of 100 × 100 µm.

Traditional direct phasing procedures

2013 ◽  
Author(s):  
Carmelo Giacovazzo
Keyword(s):  
Crystal Structure ◽  
Least Squares ◽  
Fourier Transforms ◽  
Direct Methods ◽  
Real Space ◽  
Reciprocal Space ◽  
Interatomic Distances ◽  
Patterson Function ◽  
Structure Solution ◽  
Phase Extension

Which phasing methods can be included in the category direct methods, and which require a different appellation? Originally, direct phasing was associated with those approaches which were able to derive phases directly from the diffraction moduli, without passing through deconvolution of the Patterson function. Since a Patterson map provides interatomic distances, and therefore lies in ‘direct space’, direct methods were also referred to as reciprocal space methods, and Patterson techniques as real-space methods. Historically, direct methods use 3-,4-, . . . , n-phase invariants and 1-2-, . . . phase seminvariants via the tangent formula or its modified algorithms. Since the 1950s, about a half a century of scientific effort has fallen under the above definition. Such approaches are classified here as traditional direct methods. Today, the situation is more ambiguous, because: (i) modern direct methods programs involve steps operating both in reciprocal space and in direct space, the latter mainly devoted to phase extension and refinement (see Chapter 8); (ii) in the past decade, new phasing methods for crystal structure solution (see Chapter 9) have been developed, based on the properties of Fourier transforms, which again work both in direct and in reciprocal space. Should they therefore be considered to be outside the direct methods category or not? Our choice is as follows. Direct methods are all of the approaches which allow us to derive phases from diffraction amplitudes, without passing through a Patterson function deconvolution. Thus, we also include in this category, charge flipping and VLD (vive la difference), here classified as non-traditional direct methods; their description is postponed to Chapter 9. In accordance with the above assumptions, in this chapter we will shortly illustrate traditional direct phasing procedures, with particular reference to those which are current and in regular use today: mainly the tangent procedures (see Section 6.2) and the cosine least squares technique, which is the basic tool of the shake and Bake method (see Section 6.4).

FraGen: a computer program for real-space structure solution of extended inorganic frameworks

2012 ◽  
Vol 45 (4) ◽  
pp. 855-861 ◽  
Author(s):  
Yi Li ◽  
Jihong Yu ◽  
Ruren Xu
Keyword(s):  
Three Dimensional ◽  
Computation Time ◽  
Optimization Method ◽  
Real Space ◽  
Space Structure ◽  
Parallel Tempering ◽  
Global Optimization Method ◽  
Cell Parameters ◽  
Density Maps ◽  
Structure Solution

TheFraGen(framework generator) program has been developed for real-space structure solution. It has been designed especially for the generation of extended inorganic frameworks in a given unit cell.FraGenis based on the parallel tempering global optimization method. Various restraints can be introduced intoFraGen, such as restraints on bonding geometry, relative reflection intensities and three-dimensional density maps. The basic inputs forFraGenare the space group and cell parameters. The number of unique atoms is not a necessary input, since it can be estimated from certain constraints.FraGenalso has the ability to exit unpromising simulation cycles to save computation time for promising ones. Program features, methods and three examples are demonstrated. TheFraGenprogram for the Windows platform is available from the authors upon request.

An Image Reconstruction System Applied to High Voltage Microscopy

1975 ◽  
Vol 33 ◽  
pp. 292-293
Author(s):  
D. E. Johnson
Keyword(s):  
High Voltage ◽  
Prior Information ◽  
Block Diagram ◽  
Three Dimensional ◽  
Real Space ◽  
Two Dimensional ◽  
Efficient Manner ◽  
Fourier Methods ◽  
Tilt Series ◽  
Methods Of Reconstruction

Increased specimen penetration; the principle advantage of high voltage microscopy, is accompanied by an increased need to utilize information on three dimensional specimen structure available in the form of two dimensional projections (i.e. micrographs). We are engaged in a program to develop methods which allow the maximum use of information contained in a through tilt series of micrographs to determine three dimensional speciman structure.In general, we are dealing with structures lacking in symmetry and with projections available from only a limited span of angles (±60°). For these reasons, we must make maximum use of any prior information available about the specimen. To do this in the most efficient manner, we have concentrated on iterative, real space methods rather than Fourier methods of reconstruction. The particular iterative algorithm we have developed is given in detail in ref. 3. A block diagram of the complete reconstruction system is shown in fig. 1.

Ab initio structure determination of cytochrome c6 by combined reciprocal space-real space approach

2003 ◽  
Vol 218 (1) ◽  
Author(s):  
K. Chowdhury ◽  
S. Ghosh ◽  
M. Mukherjee
Keyword(s):  
Cytochrome C ◽  
Ab Initio ◽  
Structure Determination ◽  
Direct Method ◽  
Real Space ◽  
Reciprocal Space ◽  
Cytochrome C6 ◽  
Ab Initio Structure ◽  
Space Approach

AbstractThe direct method program SAYTAN has been applied successfully to redetermine the structure of cytochrome c

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