THE DIFFERENTIAL GEOMETRY OF SCROLL WAVES

Traveling waves of excitation organize physical, chemical, and biological systems in space and time. In the biological context they serve to communicate information rapidly over long distances and to coordinate the activity of tissues and organs. An example of particular beauty, complexity and importance is the three-dimensional rotating scroll wave observed in the Belousov–Zhabotinskii reaction and in the ventricle of the heart. A scroll wave rotates around a filamentous phase singularity that weaves through the three-dimensional medium. At any instant of time the geometry of the scroll wave can be reduced to the spatial arrangement of a ribbon whose edges are the singular filament and the tip of the scroll wave. This ribbon, when it closes on itself, must satisfy the topological constraint L = Tw + Wr, where L is the linking number of the two edges of the ribbon, Tw is the total twist of the ribbon, and Wr is the writhing number of the singular filament. We discuss the origin of this equation and its implications for scroll wave statics and dynamics.

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Conformation of Ribosomes from Escherichia Coli

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051062 ◽

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.

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Structural organization of escherichia coli ribosomes as determined by immuno electron microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100081693 ◽

1978 ◽

Vol 36 (2) ◽

pp. 166-167 ◽

Cited By ~ 1

Author(s):

G. Stöffler ◽

R.W. Bald ◽

J. Dieckhoff ◽

H. Eckhard ◽

R. Lührmann ◽

...

Keyword(s):

Electron Microscopy ◽

Escherichia Coli ◽

Ribosomal Proteins ◽

Structural Organization ◽

Three Dimensional ◽

Ribosomal Subunit ◽

Spatial Arrangement ◽

Small Subunit ◽

Antibody Binding ◽

Immuno Electron Microscopy

A central step towards an understanding of the structure and function of the Escherichia coli ribosome, a large multicomponent assembly, is the elucidation of the spatial arrangement of its 54 proteins and its three rRNA molecules. The structural organization of ribosomal components has been investigated by a number of experimental approaches. Specific antibodies directed against each of the 54 ribosomal proteins of Escherichia coli have been performed to examine antibody-subunit complexes by electron microscopy. The position of the bound antibody, specific for a particular protein, can be determined; it indicates the location of the corresponding protein on the ribosomal surface.The three-dimensional distribution of each of the 21 small subunit proteins on the ribosomal surface has been determined by immuno electron microscopy: the 21 proteins have been found exposed with altogether 43 antibody binding sites. Each one of 12 proteins showed antibody binding at remote positions on the subunit surface, indicating highly extended conformations of the proteins concerned within the 30S ribosomal subunit; the remaining proteins are, however, not necessarily globular in shape (Fig. 1).

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Petiole-Lamina Transition Zone: A Functionally Crucial but Often Overlooked Leaf Trait

Plants ◽

10.3390/plants10040774 ◽

2021 ◽

Vol 10 (4) ◽

pp. 774

Author(s):

Max Langer ◽

Thomas Speck ◽

Olga Speck

Keyword(s):

Transition Zone ◽

Three Dimensional ◽

Spatial Arrangement ◽

Body Plan ◽

The Body ◽

Vascular Bundles ◽

Cross Sectional ◽

Thin Sections ◽

Transition Zones ◽

The Cross

Although both the petiole and lamina of foliage leaves have been thoroughly studied, the transition zone between them has often been overlooked. We aimed to identify objectively measurable morphological and anatomical criteria for a generally valid definition of the petiole–lamina transition zone by comparing foliage leaves with various body plans (monocotyledons vs. dicotyledons) and spatial arrangements of petiole and lamina (two-dimensional vs. three-dimensional configurations). Cross-sectional geometry and tissue arrangement of petioles and transition zones were investigated via serial thin-sections and µCT. The changes in the cross-sectional geometries from the petiole to the transition zone and the course of the vascular bundles in the transition zone apparently depend on the spatial arrangement, while the arrangement of the vascular bundles in the petioles depends on the body plan. We found an exponential acropetal increase in the cross-sectional area and axial and polar second moments of area to be the defining characteristic of all transition zones studied, regardless of body plan or spatial arrangement. In conclusion, a variety of terms is used in the literature for describing the region between petiole and lamina. We prefer the term “petiole–lamina transition zone” to underline its three-dimensional nature and the integration of multiple gradients of geometry, shape, and size.

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INTERACTIVE VISUALIZATION TECHNOLOGY IN AUGMENTED REALITY

Bulletin of the Korkyt Ata Kyzylorda University ◽

10.52081/bkaku.2021.v58.i3.080 ◽

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.

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Protein-protein docking using learned three-dimensional representations

10.1101/738690 ◽

2019 ◽

Cited By ~ 1

Author(s):

Georgy Derevyanko ◽

Guillaume Lamoureux

Keyword(s):

Protein Interactions ◽

Network Architecture ◽

Protein Complexes ◽

Three Dimensional ◽

Spatial Arrangement ◽

Protein Docking ◽

Protein Protein Interactions ◽

Translational Invariance ◽

Shape Complementarity ◽

Spatial Features

AbstractProtein-protein interactions are determined by a number of hard-to-capture features related to shape complementarity, electrostatics, and hydrophobicity. These features may be intrinsic to the protein or induced by the presence of a partner. A conventional approach to protein-protein docking consists in engineering a small number of spatial features for each protein, and in minimizing the sum of their correlations with respect to the spatial arrangement of the two proteins. To generalize this approach, we introduce a deep neural network architecture that transforms the raw atomic densities of each protein into complex three-dimensional representations. Each point in the volume containing the protein is described by 48 learned features, which are correlated and combined with the features of a second protein to produce a score dependent on the relative position and orientation of the two proteins. The architecture is based on multiple layers of SE(3)-equivariant convolutional neural networks, which provide built-in rotational and translational invariance of the score with respect to the structure of the complex. The model is trained end-to-end on a set of decoy conformations generated from 851 nonredundant protein-protein complexes and is tested on data from the Protein-Protein Docking Benchmark Version 4.0.

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Three-dimensional electron microscopy of ribosomal chromatin in two higher plants: a cytochemical, immunocytochemical, and in situ hybridization approach.

Journal of Histochemistry & Cytochemistry ◽

10.1177/39.11.1918926 ◽

1991 ◽

Vol 39 (11) ◽

pp. 1495-1506 ◽

Cited By ~ 22

Author(s):

P M Motte ◽

R Loppes ◽

M Menager ◽

R Deltour

Keyword(s):

Electron Microscopy ◽

In Situ Hybridization ◽

Spatial Organization ◽

Higher Plants ◽

Three Dimensional ◽

Spatial Arrangement ◽

Thin Sections ◽

Cytoplasmic Dna ◽

Immunocytochemical Techniques

We report the 3-D arrangement of DNA within the nucleolar subcomponents from two evolutionary distant higher plants, Zea mays and Sinapis alba. These species are particularly convenient to study the spatial organization of plant intranucleolar DNA, since their nucleoli have been previously reconstructed in 3-D from serial ultra-thin sections. We used the osmium ammine-B complex (a specific DNA stain) on thick sections of Lowicryl-embedded root fragments. Immunocytochemical techniques using anti-DNA antibodies and rDNA/rDNA in situ hybridization were also applied on ultra-thin sections. We showed on tilted images that the OA-B stains DNA throughout the whole thickness of the section. In addition, very low quantities of cytoplasmic DNA were stained by this complex, which is now the best DNA stain used in electron microscopy. Within the nucleoli the DNA was localized in the fibrillar centers, where large clumps of dense chromatin were also visible. In the two plant species intranucleolar chromatin forms a complex network with strands partially linked to chromosomal nucleolar-organizing regions identified by in situ hybridization. This study describes for the first time the spatial arrangement of the intranucleolar chromatin in nucleoli of higher plants using high-resolution techniques.

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Maintenance of Oscillations in Three-Dimensional Traveling Waves in Plane Poiseuille Flows

Moscow University Mechanics Bulletin ◽

10.3103/s0027133018340040 ◽

2018 ◽

Vol 73 (4) ◽

pp. 91-96 ◽

Cited By ~ 1

Author(s):

V. O. Pimanov

Keyword(s):

Traveling Waves ◽

Three Dimensional ◽

Poiseuille Flows

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Divergent Design of Mechanical Metamaterials Clan Deducted from Arc-serpentine Curve

10.21203/rs.3.rs-753485/v1 ◽

2021 ◽

Author(s):

Shengli Mi ◽

Hongyi Yao ◽

Xiaoyu Zhao ◽

Wei Sun

Keyword(s):

Thick Plate ◽

Three Dimensional ◽

Spatial Arrangement ◽

Design Strategies ◽

Shape Morphing ◽

Mechanical Metamaterials ◽

Unit Cells ◽

Combinatorial Principles ◽

Composite Curve ◽

Typical Design

Abstract The exotic properties of mechanical metamaterials are determined by their unit-cells' structure and spatial arrangement, in analogy with the atoms of conventional materials. Companioned with the mechanism of structural or cellular materials1–5, the ancient wisdom of origami6–11 and kirigami12–16 and the involvement of multiphysics interaction2,17,18 enrich the programable mechanical behaviors of metamaterials, including shape-morphing8,12,14,16,19, compliance4,5,8,17,20, texture2,18,21, and topology11,18,22−25. However, typical design strategies are mainly convergent, which transfers various structures into one family of metamaterials that are relatively incompatible with the others and do not fully bring combinatorial principles3,10,26 into play. Here, we report a divergent strategy that designs a clan of mechanical metamaterials with diverse properties derived from a symmetric curve consisting of serpentines and arcs. We derived this composite curve into planar and cubic unit-cells and modularized them by attaching magnetics. Moreover, stacking each of them yields two- and three-dimensional auxetic metamaterials, respectively. Assembling with both modules, we achieved three thick plate-like metamaterials separately with flexibility, in-plane buckling, and foldability. Furthermore, we demonstrated that the hybrid of paradox properties is possible by combining two of the above assembles. We anticipate that this divergent strategy paves the path of building a hierarchical library of diverse combinable mechanical metamaterials and making conventional convergent strategies more efficient to various requests. Main

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