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.

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.

4f-Electron Density Distribution in Crystals of CeB6 at 165 K and its Analysis Based on the Crystal Field Theory

1997 ◽  
Vol 53 (1) ◽  
pp. 143-152 ◽  
Author(s):  
K. Tanaka ◽  
Y. Kato ◽  
Y. Onuki
Keyword(s):  
Field Theory ◽  
Density Distribution ◽  
Electron Density ◽  
Crystal Field ◽  
Electron Density Distribution ◽  
Kondo Effect ◽  
Crystal Field Theory ◽  
X Ray ◽  
Deformation Density ◽  
Density Map

4f-Electron density in single crystals of CeB6, cerium hexaboride, was measured at 165 K by X-ray diffractometry. Significant peaks 2.0 e Å−3 high were found along the \langle100\rangle directions at 0.41 Å from Ce on the deformation density map. Analysis based on the crystal field theory removed the peaks, confirming that they were due to the Ce 4f-electrons on the t 1u -orbital. The deformation density in the B6 octahedron was also markedly improved by the analysis and coincides qualitatively with a theoretical molecular orbital (MO) calculation. It also coincides with the model deformation density map of CaB6 composed of only light atoms. These facts guarantee the accuracy of the intensity measurement for the present study. Since Ce3+ has only one 4f-electron, a highly accurate intensity measurement is necessary to detect its 4f-electron density distribution. A ψ-scan technique was therefore employed to avoid multiple diffraction (MD) and to measure the intensities at ω and χ angles with minimum fluctuation of temperature at the sample position. Relativistic radial functions for orbitals of Ce3+ and the corresponding scattering factors, which take the aspherical electron density distribution of 4f-electrons into account, were used for the analysis. CeB6 is a typical dense Kondo material. The Kondo effect occurs in CeB6 from low temperature to above room temperature. X-ray analysis of the f-electron density based on atomic orbitals (AO) revealed that 1.5 (2) electrons are donated from B6 to Ce and a total of 2.5 (2) electrons localize on the 4f-orbital. κ values are consistent with the 4f-orbitals being highly contracted and thus stabilized. These may be related to the Kondo effect.

Electron Density Distribution in LiB3O5 at 293 K

1997 ◽  
Vol 53 (6) ◽  
pp. 870-879 ◽  
Author(s):  
C. Le Hénaff ◽  
N. K. Hansen ◽  
J. Protas ◽  
G. Marnier
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Electron Density Distribution ◽  
X Ray Diffraction ◽  
X Ray ◽  
Hartree Fock ◽  
Density Maps ◽  
Symmetry Constraints ◽  
Net Charges ◽  
Good Agreement

The electron density distribution in lithium triborate LiB3O5 has been studied at room temperature by X-ray diffraction using Ag K \alpha radiation up to 1.02 Å−1 [1439 unique reflections with I > 3\sigma(I)]. Conventional refinements with a free-atom model yield R(F) = 0.0223, wR(F) = 0.0299, S = 1.632. Atom charge refinements show that the lithium should be considered a monovalent ion. Multipolar refinements were undertaken up to fourth order, imposing local non-crystallographic symmetry constraints in order to avoid phase problems leading to meaningless multipole populations due to the non-centrosymmetry of the structure (space group: Pn a21). The residual indices decreased to: R(F) = 0.0147, wR(F) = 0.0193, S = 1.106. The net charges are in good agreement with what can be expected in borate chemistry. Deformation density maps are analysed in terms of \sigma and \pi bonding. The experimental electron distribution in the p z orbitals of triangular B atoms and surrounding O atoms has been analysed by introducing idealized hybridized states. In parallel, the electron density has been determined from ab initio Hartree–Fock calculations on fragments of the structure. Agreement with the X-ray determination is very good and confirms the nature of bonding in the crystal. The amount of transfer of \pi electrons from the oxygen to the triangular B atoms is estimated to be 0.22 electrons by theory.

Phase improvement and extension

2013 ◽  
Author(s):  
Carmelo Giacovazzo
Keyword(s):  
Ab Initio ◽  
Electron Density ◽  
Model Building ◽  
Special Treatment ◽  
Fourier Synthesis ◽  
Density Maps ◽  
Phase Extension ◽  
Density Map ◽  
The Fourier Transform ◽  
Electron Density Map

The descriptions of the various types of Fourier synthesis (observed, difference, hybrid) and of their properties, given in Chapter 7, suggest that electron density maps are not only a tool for depicting the distribution of the electrons in the target structure, but also a source of information which may be continuously exploited during the phasing process, no matter whether ab initio or non-ab initio methods were used for deriving the initial model. Here, we will describe two important techniques based on the properties of electron density maps. (i) The recursive approach for phase extension and refinement called EDM (electron density modification). Such techniques have dramatically improved the efficiency of phasing procedures, which usually end with a limited percentage of phased reflections and non-negligible phase errors. EDM techniques allow us to extend phase assignment and to improve phase quality. The author is firmly convinced that practical solution of the phase problem for structures with Nasym up to 200 atoms in the asymmetric unit may be jointly ascribed to direct methods and to EDM techniques. (ii) The AMB (automated model building) procedures; these may be considered to be partly EDM techniques and they are used for automatic building of molecular models from electron density maps. Essentially, we will refer to proteins; the procedures used for small to medium-sized molecules have already been described in Section 6.3.5. Two new ab initio phasing approaches, charge flipping and VLD, essentially based on the properties of the Fourier transform, belong to the EDM category, and since they require a special treatment, they will be described later in Chapter 9. Phase extension and refinement may be performed in reciprocal and in direct space. We described the former in Section 6.3.6; here, we are just interested in direct space procedures, the so-called EDM (electron density modification) techniques. Such procedures are based on the following hypothesis: a poor electron density map, ρ, may be modified by a suitable function, f , to obtain a new map, say ρmod, which better approximates the true map: . . . ρmod (r) = f [ρ(r)]. (8.1) . . . If function f is chosen properly, more accurate phases can be obtained by Fourier inversion of ρmod, which may in turn be used to calculate a new electron density map.

X-Ray Characterization of Ag Impurities in Na1-xAgxCl

2008 ◽  
Vol 278 ◽  
pp. 33-44 ◽  
Author(s):  
Ramachandran Saravanan ◽  
K.S. Syed Ali ◽  
M. Prema Rani ◽  
R. Saravanan
Keyword(s):  
Density Distribution ◽  
Electron Density ◽  
Electron Density Distribution ◽  
Entropy Method ◽  
Data Sets ◽  
Density Profiles ◽  
X Ray ◽  
Density Maps ◽  
Electron Density Profiles

The alkali halide Na1-xAgxCl, with two different compositions (x = 0.03 and 0.10), was studied with regard to the Ag impurities in terms of the bonding and electron density distribution. X-ray single crystal data sets have been used for the purpose. The present analysis focused on the electron density distribution and hence the interaction between the atoms is clearly revealed by maximum entropy method (MEM) and multipole analyses. The bonding in these systems has been studied using two-dimensional MEM electron density maps on the (100) and (110) planes and onedimensional electron density profiles along the [100], [110] and [111] directions. The mid-bond electron densities between atoms in these systems are found to be 0.175 e/Å3 and 0.183 e/Å3, respectively, for Na0.97Ag0.03Cl and Na0.90Ag0.10Cl. Multipole analysis of the structure has been performed for these two systems, with respect to the expansion/contraction of the ion involved.

A protocol for searching the most probable phase-retrieved maps in coherent X-ray diffraction imaging by exploiting the relationship between convergence of the retrieved phase and success of calculation

2017 ◽  
Vol 24 (5) ◽  
pp. 1024-1038 ◽  
Author(s):  
Yuki Sekiguchi ◽  
Saki Hashimoto ◽  
Amane Kobayashi ◽  
Tomotaka Oroguchi ◽  
Masayoshi Nakasako
Keyword(s):  
Diffraction Pattern ◽  
Electron Density ◽  
Figure Of Merit ◽  
X Ray Diffraction ◽  
X Ray ◽  
Density Maps ◽  
Diffraction Imaging ◽  
Density Map ◽  
Diffraction Patterns ◽  
Electron Density Map

Coherent X-ray diffraction imaging (CXDI) is a technique for visualizing the structures of non-crystalline particles with size in the submicrometer to micrometer range in material sciences and biology. In the structural analysis of CXDI, the electron density map of a specimen particle projected along the direction of the incident X-rays can be reconstructed only from the diffraction pattern by using phase-retrieval (PR) algorithms. However, in practice, the reconstruction, relying entirely on the computational procedure, sometimes fails because diffraction patterns miss the data in small-angle regions owing to the beam stop and saturation of the detector pixels, and are modified by Poisson noise in X-ray detection. To date, X-ray free-electron lasers have allowed us to collect a large number of diffraction patterns within a short period of time. Therefore, the reconstruction of correct electron density maps is the bottleneck for efficiently conducting structure analyses of non-crystalline particles. To automatically address the correctness of retrieved electron density maps, a data analysis protocol to extract the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a single diffraction pattern is proposed. Through monitoring the variations of the phase values during PR calculations, the tendency for the PR calculations to succeed when the retrieved phase sets converged on a certain value was found. On the other hand, if the phase set was in persistent variation, the PR calculation tended to fail to yield the correct electron density map. To quantify this tendency, here a figure of merit for the variation of the phase values during PR calculation is introduced. In addition, a PR protocol to evaluate the similarity between a map of the highest figure of merit and other independently reconstructed maps is proposed. The protocol is implemented and practically examined in the structure analyses for diffraction patterns from aggregates of gold colloidal particles. Furthermore, the feasibility of the protocol in the structure analysis of organelles from biological cells is examined.

Classification and assessment of retrieved electron density maps in coherent X-ray diffraction imaging using multivariate analysis

2016 ◽  
Vol 23 (1) ◽  
pp. 312-323 ◽  
Author(s):  
Yuki Sekiguchi ◽  
Tomotaka Oroguchi ◽  
Masayoshi Nakasako
Keyword(s):  
Diffraction Pattern ◽  
Electron Density ◽  
Phase Retrieval ◽  
Dimensional Space ◽  
X Ray Diffraction ◽  
X Ray ◽  
Density Maps ◽  
Diffraction Imaging ◽  
Density Map ◽  
Electron Density Map

Coherent X-ray diffraction imaging (CXDI) is one of the techniques used to visualize structures of non-crystalline particles of micrometer to submicrometer size from materials and biological science. In the structural analysis of CXDI, the electron density map of a sample particle can theoretically be reconstructed from a diffraction pattern by using phase-retrieval (PR) algorithms. However, in practice, the reconstruction is difficult because diffraction patterns are affected by Poisson noise and miss data in small-angle regions due to the beam stop and the saturation of detector pixels. In contrast to X-ray protein crystallography, in which the phases of diffracted waves are experimentally estimated, phase retrieval in CXDI relies entirely on the computational procedure driven by the PR algorithms. Thus, objective criteria and methods to assess the accuracy of retrieved electron density maps are necessary in addition to conventional parameters monitoring the convergence of PR calculations. Here, a data analysis scheme, named ASURA, is proposed which selects the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a diffraction pattern. Each electron density map composed ofJpixels is expressed as a point in aJ-dimensional space. Principal component analysis is applied to describe characteristics in the distribution of the maps in theJ-dimensional space. When the distribution is characterized by a small number of principal components, the distribution is classified using thek-means clustering method. The classified maps are evaluated by several parameters to assess the quality of the maps. Using the proposed scheme, structure analysis of a diffraction pattern from a non-crystalline particle is conducted in two stages: estimation of the overall shape and determination of the fine structure inside the support shape. In each stage, the most accurate and probable density maps are objectively selected. The validity of the proposed scheme is examined by application to diffraction data that were obtained from an aggregate of metal particles and a biological specimen at the XFEL facility SACLA using custom-made diffraction apparatus.

The structure of carboxypeptidase A. VIII. Atomic interpretation at 0.2 nm resolution, a new study of the complex of glycyl-L-tyrosine with CPA, and mechanistic deductions

1970 ◽  
Vol 257 (813) ◽  
pp. 177-214 ◽  
Keyword(s):  
Electron Density ◽  
Model Building ◽  
Ester Bond ◽  
Terminal Residue ◽  
Binding Residue ◽  
Density Maps ◽  
The Subject ◽  
Density Map ◽  
Electron Density Map ◽  
Hydrolysis Of

Bovine pancreatic carboxypeptidase Aa (CPA),J the subject of these studies, is a zinc containing enzyme of molecular weight 34 600, which catalyses the hydrolysis of polypeptides and esters at the C-terminal peptide or ester bond. Experiments to date have shown that in order to be hydrolysed, the substrate must contain a C-terminal residue in the l configuration, with the carboxyl group free and α to the peptide or ester bond which is to be cleaved. In addition, the reaction is favoured if the C-terminal residue is aromatic. Our crystallographic studies of CPA have yielded electron density maps of the native enzyme at 0.6 nm (Lipscomb, Coppola, Hartsuck, Ludwig, Muirhead, Searl & Steitz 1966), 0.28 nm (Ludwig, Hartsuck, Steitz, Muirhead, Coppola, Reeke & Lipscomb 1967) and 0.20 nm resolution (Reeke, Hartsuck, Ludwig, Quiocho, Steitz & Lipscomb 1967; Lipscomb, Hartsuck, Reeke, Quiocho, Bethge, Ludwig, Steitz, Muirhead & Coppola 1968). Concurrently, a study of the binding of a number of substrates and inhibitors at 0.6 nm resolution was under way (Steitz, Ludwig, Quiocho & Lipscomb 1967). Subsequently, the most promising of these complexes, that of glycyl-L-tyrosine with CPA, was carried to atomic resolution (Reeke et al. 1967; Lipscomb et al. 1968). Even though chemical sequence is not available for several of the binding and catalytic groups of the enzyme, we have been able to deduce the identity of the binding residue Arg-145 and the catalytic residue Glu-270 (Reeke et al. 1967), to describe the mode of binding of Gly-Tyr, to extrapolate these conclusions to the binding of polypeptides, and to propose a mechanism, with certain ambiguities, for the action of the enzyme (Lipscomb et al. 1968). We have now completed the detailed atomic interpretation of the 0.20 nm electron density map, supplying residue identifications where the primary sequence is not available, and have subjected the resulting atomic coordinates to a model building procedure (Diamond 1966) which forces them to conform to standard bond distances and angles. The improved coordinates have been entered in a structure factor calculation, which gave a standard crystallographic R factor of 0.44.

scholarly journals Machine learning to estimate the local quality of protein crystal structures

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ikuko Miyaguchi ◽  
Miwa Sato ◽  
Akiko Kashima ◽  
Hiroyuki Nakagawa ◽  
Yuichi Kokabu ◽  
...  
Keyword(s):  
Electron Density ◽  
Protein Structures ◽  
Three Dimensional ◽  
Protein Crystal ◽  
Low Resolution ◽  
X Ray Crystallography ◽  
Density Maps ◽  
Local Quality ◽  
Density Map ◽  
Electron Density Map

AbstractLow-resolution electron density maps can pose a major obstacle in the determination and use of protein structures. Herein, we describe a novel method, called quality assessment based on an electron density map (QAEmap), which evaluates local protein structures determined by X-ray crystallography and could be applied to correct structural errors using low-resolution maps. QAEmap uses a three-dimensional deep convolutional neural network with electron density maps and their corresponding coordinates as input and predicts the correlation between the local structure and putative high-resolution experimental electron density map. This correlation could be used as a metric to modify the structure. Further, we propose that this method may be applied to evaluate ligand binding, which can be difficult to determine at low resolution.

A study on α-RuCl3 crystal structure by scanning tunneling microscopy

1989 ◽  
Vol 47 ◽  
pp. 30-31
Author(s):  
H.-J. Cantow ◽  
H. Hillebrecht ◽  
S. Magonov ◽  
H. W. Rotter ◽  
G. Thiele
Keyword(s):  
Crystal Structure ◽  
Density Distribution ◽  
Scanning Tunneling Microscopy ◽  
Electron Density ◽  
Structure Determination ◽  
Electron Density Distribution ◽  
Scanning Tunneling ◽  
Monoclinic Space Group ◽  
Tunneling Microscopy ◽  
X Ray

From X-ray analysis, the conclusions are drawn from averaged molecular informations. Thus, limitations are caused when analyzing systems whose symmetry is reduced due to interatomic interactions. In contrast, scanning tunneling microscopy (STM) directly images atomic scale surface electron density distribution, with a resolution up to fractions of Angstrom units. The crucial point is the correlation between the electron density distribution and the localization of individual atoms, which is reasonable in many cases. Thus, the use of STM images for crystal structure determination may be permitted. We tried to apply RuCl3 - a layered material with semiconductive properties - for such STM studies. From the X-ray analysis it has been assumed that α-form of this compound crystallizes in the monoclinic space group C2/m (AICI3 type). The chlorine atoms form an almost undistorted cubic closed package while Ru occupies 2/3 of the octahedral holes in every second layer building up a plane hexagon net (graphite net). Idealizing the arrangement of the chlorines a hexagonal symmetry would be expected. X-ray structure determination of isotypic compounds e.g. IrBr3 leads only to averaged positions of the metal atoms as there exist extended stacking faults of the metal layers.

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