scholarly journals A moment invariant for evaluating the chirality of three-dimensional objects

2010 ◽  
Vol 8 (54) ◽  
pp. 144-151 ◽  
Author(s):  
Johan Hattne ◽  
Victor S. Lamzin
Keyword(s):  
Electron Density ◽  
Three Dimensional ◽  
Peptide Fragments ◽  
Moment Invariant ◽  
Three Dimensional Objects ◽  
Density Maps ◽  
Wide Range ◽  
Polypeptide Backbone ◽  
Dimensional Object ◽  
Electron Density Map

Chirality is an important feature of three-dimensional objects and a key concept in chemistry, biology and many other disciplines. However, it has been difficult to quantify, largely owing to computational complications. Here we present a general chirality measure, called the chiral invariant (CI), which is applicable to any three-dimensional object containing a large amount of data. The CI distinguishes the hand of the object and quantifies the degree of its handedness. It is invariant to the translation, rotation and scale of the object, and tolerant to a modest amount of noise in the experimental data. The invariant is expressed in terms of moments and can be computed in almost no time. Because of its universality and computational efficiency, the CI is suitable for a wide range of pattern-recognition problems. We demonstrate its applicability to molecular atomic models and their electron density maps. We show that the occurrence of the conformations of the macromolecular polypeptide backbone is related to the value of the CI of the constituting peptide fragments. We also illustrate how the CI can be used to assess the quality of a crystallographic electron density map.

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 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.

scholarly journals Application of Photopolymer Materials in Holographic Technologies

Polymers ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2020 ◽  
Author(s):  
Nadezhda Vorzobova ◽  
Pavel Sokolov
Keyword(s):  
3D Printing ◽  
Periodic Structures ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Polymer Materials ◽  
Solar Concentrators ◽  
Three Dimensional Objects ◽  
Wide Range ◽  
Material Fabrication ◽  
Dimensional Object

The possibility of the application of acrylate compositions and Bayfol HX photopolymers in holographic technologies is considered. The holographic characteristics of materials, their advantages, and limitations in relation to the tasks of obtaining holographic elements based on periodic structures are given. The conditions for obtaining controlled two and multichannel diffraction beam splitters are determined with advantages in terms of the simplicity of the fabrication process. The diffraction and selective properties of volume and hybrid periodic structures by radiation incidence in a wide range of angles in three-dimensional space are investigated, and new properties are identified that are of interest for the development of elements of holographic solar concentrators with advantages in the material used and the range of incidence angles. A new application of polymer materials in a new method of holographic 3D printing for polymer objects with arbitrary shape fabrication based on the projection of a holographic image of the object into the volume of photopolymerizable material is proposed, the advantage of which, relative to additive 3D printing technologies, is the elimination of the sequential synthesis of a three-dimensional object. The factors determining the requirements for the material, fabrication conditions, and properties of three-dimensional objects are identified and investigated.

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.

scholarly journals Brickworxbuilds recurrent RNA and DNA structural motifs into medium- and low-resolution electron-density maps

2015 ◽  
Vol 71 (3) ◽  
pp. 697-705 ◽  
Author(s):  
Grzegorz Chojnowski ◽  
Tomasz Waleń ◽  
Paweł Piątkowski ◽  
Wojciech Potrzebowski ◽  
Janusz M. Bujnicki
Keyword(s):  
Nucleic Acid ◽  
Electron Density ◽  
Three Dimensional ◽  
Real Space ◽  
Density Peaks ◽  
Density Maps ◽  
Resolution Electron ◽  
Fragment Library ◽  
Electron Density Map ◽  
Recurrent Motifs

Brickworxis a computer program that builds crystal structure models of nucleic acid molecules using recurrent motifs including double-stranded helices. In a first step, the program searches for electron-density peaks that may correspond to phosphate groups; it may also take into account phosphate-group positions provided by the user. Subsequently, comparing the three-dimensional patterns of the P atoms with a database of nucleic acid fragments, it finds the matching positions of the double-stranded helical motifs (A-RNA or B-DNA) in the unit cell. If the target structure is RNA, the helical fragments are further extended with recurrent RNA motifs from a fragment library that contains single-stranded segments. Finally, the matched motifs are merged and refined in real space to find the most likely conformations, including a fit of the sequence to the electron-density map. TheBrickworxprogram is available for download and as a web server at http://iimcb.genesilico.pl/brickworx.

A Comparison of Two Algorithms for Electron-Density Map Improvement by Introduction of Atomicity: Skeletonization, and Map Sorting Followed by Refinement

1998 ◽  
Vol 54 (1) ◽  
pp. 81-85 ◽  
Author(s):  
F. M. D. Vellieux
Keyword(s):  
Electron Density ◽  
Initial Density ◽  
Acta Cryst ◽  
Density Maps ◽  
Resolution Electron ◽  
Crystallographic Symmetry ◽  
Density Map ◽  
Ornithine Transcarbamoylase ◽  
Electron Density Map ◽  
Pseudo Atom

A comparison has been made of two methods for electron-density map improvement by the introduction of atomicity, namely the iterative skeletonization procedure of the CCP4 program DM [Cowtan & Main (1993). Acta Cryst. D49, 148–157] and the pseudo-atom introduction followed by the refinement protocol in the program suite DEMON/ANGEL [Vellieux, Hunt, Roy & Read (1995). J. Appl. Cryst. 28, 347–351]. Tests carried out using the 3.0 Å resolution electron density resulting from iterative 12-fold non-crystallographic symmetry averaging and solvent flattening for the Pseudomonas aeruginosa ornithine transcarbamoylase [Villeret, Tricot, Stalon & Dideberg (1995). Proc. Natl Acad. Sci. USA, 92, 10762–10766] indicate that pseudo-atom introduction followed by refinement performs much better than iterative skeletonization: with the former method, a phase improvement of 15.3° is obtained with respect to the initial density modification phases. With iterative skeletonization a phase degradation of 0.4° is obtained. Consequently, the electron-density maps obtained using pseudo-atom phases or pseudo-atom phases combined with density-modification phases are much easier to interpret. These tests also show that for ornithine transcarbamoylase, where 12-fold non-crystallographic symmetry is present in the P1 crystals, G-function coupling leads to the simultaneous decrease of the conventional R factor and of the free R factor, a phenomenon which is not observed when non-crystallographic symmetry is absent from the crystal. The method is far less effective in such a case, and the results obtained suggest that the map sorting followed by refinement stage should be by-passed to obtain interpretable electron-density distributions.

scholarly journals INTERACTIVE VISUALIZATION TECHNOLOGY IN AUGMENTED REALITY

2021 ◽  
Vol 58 (3) ◽  
pp. 137-142
Author(s):  
A.O. Dauitbayeva ◽  
◽  
A.A. Myrzamuratova ◽  
A.B. Bexeitova ◽  
◽  
...  
Keyword(s):  
Virtual Reality ◽  
Augmented Reality ◽  
User Interfaces ◽  
Three Dimensional ◽  
Spatial Arrangement ◽  
Linear Perspective ◽  
Three Dimensional Objects ◽  
Visualization Technology ◽  
Image Volume ◽  
Dimensional Object

This article is devoted to the issues of visualization and information processing, in particular, improving the visualization of three-dimensional objects using augmented reality and virtual reality technologies. The globalization of virtual reality has led to the introduction of a new term "augmented reality"into scientific circulation. If the current technologies of user interfaces are focused mainly on the interaction of a person and a computer, then augmented reality with the help of computer technologies offers improving the interface of a person and the real world around them. Computer graphics are perceived by the system in the synthesized image in connection with the reproduction of monocular observation conditions, increasing the image volume, spatial arrangement of objects in a linear perspective, obstructing one object to another, changing the nature of shadows and tones in the image field. The experience of observation is of great importance for the perception of volume and space, so that the user "completes" the volume structure of the observed representation. Thus, the visualization offered by augmented reality in a real environment familiar to the user contributes to a better perception of three-dimensional object.

Early Motion Processes and the Kinetic Depth Effect

1989 ◽  
Vol 41 (1) ◽  
pp. 183-198 ◽  
Author(s):  
George Mather
Keyword(s):  
Depth Perception ◽  
Short Range ◽  
Three Dimensional ◽  
Visual Display ◽  
Depth Effect ◽  
Temporal Properties ◽  
Early Motion ◽  
Wide Range ◽  
Dimensional Object ◽  
Inter Frame

It has been known for over 30 years that motion information alone is sufficient to yield a vivid impression of three-dimensional object structure. For example, a computer simulation of a transparent sphere, the surface of which is randomly speckled with dots, gives no impression of depth when presented as a stationary pattern on a visual display. As soon as the sphere is made to rotate in a series of discrete steps or frames, its 3-D structure becomes apparent. Three experiments are described which use this stimulus, and find that depth perception in these conditions depends crucially on the spatial and temporal properties of the display: 1. Depth is seen reliably only for between-frame rotations of less than 15°, using two-frame and four-frame sequences. 2. Parametric observations using a wide range of frame durations and inter-frame intervals reveal that depth is seen only for inter-frame intervals below 80 msec and is optimal when the stimulus can be sampled at intervals of about 40–60 msec. 3. Monoptic presentation of two frames of the stimulus is sufficient to yield depth, but the impression is destroyed by dichoptic presentation. These data are in close agreement with the observed limits of direction perception in experiments using “short-range” stimuli. It is concluded that depth perception in the motion display used in these experiments depends on the outputs of low-level or “short-range” motion detectors.

The Research of Collision Detection Based on OBB in Vega Prime

2012 ◽  
Vol 220-223 ◽  
pp. 2803-2808
Author(s):  
Xiao Ping Wang ◽  
Xiu Cheng Dong
Keyword(s):  
Early Warning ◽  
Collision Detection ◽  
Line Segment ◽  
Three Dimensional ◽  
Trend Line ◽  
Three Dimensional Objects ◽  
Bounding Box ◽  
Object Based ◽  
Early Warning Mechanism ◽  
Dimensional Object

Collision detection in Vega Prime is based on the simple line segment, and collision detection based on bounding box is not realized. By studying the composition of three-dimensional object based on Oriented Bounding Box (OBB), we define a collision detection class, which inherits from vpIsector. After finding out all vertices of geometry in object, we connect these vertices one by one and constitute a tend line. The trend line constitutes our bounding box based on OBB. Now, our collision detection is based on three-dimensional objects, but not the simple line segment. At the same time, we can control the efficiency of collision detection by increasing or decreasing the number of collision lines on the actual demand. Additionally, on this basis, we have made the further application. By adjusting parameter, we can get a bounding box with early warning mechanism or collision tolerance.

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