The Problem of $\delta $-Meeting on a 3-Dimensional Ball

1978 ◽  
Vol 23 (1) ◽  
pp. 190-195 ◽  
Author(s):  
M. M. Lutsenko
Keyword(s):  
3 Dimensional ◽  
Dimensional Ball

scholarly journals A topological analysis of difference topology experiments of condensin with Topoisomerases II

2019 ◽  
Author(s):  
Soojeong Kim ◽  
Isabel K. Darcy
Keyword(s):  
Simple Model ◽  
Experimental Technique ◽  
Topological Analysis ◽  
Simple Experiment ◽  
Dna Complexes ◽  
3 Dimensional ◽  
Model Protein ◽  
Summary Statement ◽  
Mu Transpososome ◽  
Dimensional Ball

ABSTRACTAn experimental technique called difference topology combined with the mathematics of tangle analysis has been used to unveil the structure of DNA bound by the Mu transpososome. However, difference topology experiments can be difficult and time-consuming. We discuss a modification that greatly simplifies this experimental technique. This simple experiment involves using a topoisomerase to trap DNA crossings bound by a protein complex and then running a gel to determine the crossing number of the knotted product(s). We develop the mathematics needed to analyze the results and apply these results to model the topology of DNA bound by 13S condensin and by the condensin MukB.SUMMARY STATEMENTTangles are used to model protein-DNA complexes: A 3-dimensional ball represents protein while strings embedded in this ball represent protein-bound DNA. We use this simple model to analyze experimental results.

Artin’s braids, braids for three space, and groups Γn4 and Gnk

2019 ◽  
Vol 28 (10) ◽  
pp. 1950063
Author(s):  
S. Kim ◽  
V. O. Manturov
Keyword(s):  
Fundamental Group ◽  
Configuration Space ◽  
Point Of View ◽  
Group Homomorphism ◽  
Delaunay Triangulations ◽  
3 Dimensional ◽  
Pachner Moves ◽  
Dimensional Ball ◽  
Three Space

We construct a group [Formula: see text] corresponding to the motion of points in [Formula: see text] from the point of view of Delaunay triangulations. We study homomorphisms from pure braids on [Formula: see text] strands to the product of copies of [Formula: see text]. We will also study the group of pure braids in [Formula: see text], which is described by a fundamental group of the restricted configuration space of [Formula: see text], and define the group homomorphism from the group of pure braids in [Formula: see text] to [Formula: see text]. At the end of this paper, we give some comments about relations between the restricted configuration space of [Formula: see text] and triangulations of the 3-dimensional ball and Pachner moves.

scholarly journals The depth of centres of maps on dendrites

1998 ◽  
Vol 64 (1) ◽  
pp. 44-53 ◽  
Author(s):  
Hisao Kato
Keyword(s):  
Ordinal Number ◽  
Unit Interval ◽  
Finite Tree ◽  
3 Dimensional ◽  
Countable Ordinal ◽  
Dimensional Ball

AbstractXiong proved that if f: I → I is any map of the unit interval I, then the depth of the centre of f is at most 2, and Ye proved that for any map f: T → T of a finite tree T, the depth of the centre of f is at most 3. It is natural to ask whether the result can be dendrites. In this note, we show that there is dendrite D such that for any countable ordinal number λ there is a map f: D →D such that the depth of centre of f is λ. As a corollary, we show that for any countable ordinal number λ there is a map (respectively a homeomorphism) f of a 2-dimensional ball B2 (respectively a 3-dimensional ball B3) such that the depth of centre of f is λ.

scholarly journals Wavelets on the 3-dimensional Ball

PAMM ◽  
2005 ◽  
Vol 5 (1) ◽  
pp. 775-776 ◽  
Author(s):  
V. Michel
Keyword(s):  
3 Dimensional ◽  
Dimensional Ball

Three-Dimensional Reconstruction Using Stereo Pairs from Serial Thick Sections

1977 ◽  
Vol 35 ◽  
pp. 562-563
Author(s):  
Robert Glaeser ◽  
Thomas Bauer ◽  
David Grano
Keyword(s):  
Three Dimensional ◽  
Dimensional Structure ◽  
Serial Sections ◽  
Thin Sections ◽  
3 Dimensional ◽  
Transmission Electron ◽  
Freeze Dried ◽  
Dimensional Reconstruction ◽  
Stereo Imagery ◽  
Whole Mounts

In transmission electron microscopy, the 3-dimensional structure of an object is usually obtained in one of two ways. For objects which can be included in one specimen, as for example with elements included in freeze- dried whole mounts and examined with a high voltage microscope, stereo pairs can be obtained which exhibit the 3-D structure of the element. For objects which can not be included in one specimen, the 3-D shape is obtained by reconstruction from serial sections. However, without stereo imagery, only detail which remains constant within the thickness of the section can be used in the reconstruction; consequently, the choice is between a low resolution reconstruction using a few thick sections and a better resolution reconstruction using many thin sections, generally a tedious chore. This paper describes an approach to 3-D reconstruction which uses stereo images of serial thick sections to reconstruct an object including detail which changes within the depth of an individual thick section.

Structural preservation and absolute contrast of catalase crystal sections prepared with tannic acid

1983 ◽  
Vol 41 ◽  
pp. 448-449
Author(s):  
C.W. Akey ◽  
M. Szalay ◽  
S.J. Edelstein
Keyword(s):  
Tannic Acid ◽  
Beef Heart ◽  
X Rays ◽  
Screw Axis ◽  
General Applicability ◽  
Thin Sections ◽  
Beef Liver ◽  
3 Dimensional ◽  
Dimensional Reconstruction ◽  
Structural Preservation

Three methods of obtaining 20 Å resolution in sectioned protein crystals have recently been described. They include tannic acid fixation, low temperature embedding and grid sectioning. To be useful for 3-dimensional reconstruction thin sections must possess suitable resolution, structural fidelity and a known contrast. Tannic acid fixation appears to satisfy the above criteria based on studies of crystals of Pseudomonas cytochrome oxidase, orthorhombic beef liver catalase and beef heart F1-ATPase. In order to develop methods with general applicability, we have concentrated our efforts on a trigonal modification of catalase which routinely demonstrated a resolution of 40 Å. The catalase system is particularly useful since a comparison with the structure recently solved with x-rays will permit evaluation of the accuracy of 3-D reconstructions of sectioned crystals.Initially, we re-evaluated the packing of trigonal catalase crystals studied by Longley. Images of the (001) plane are of particular interest since they give a projection down the 31-screw axis in space group P3121. Images obtained by the method of Longley or by tannic acid fixation are negatively contrasted since control experiments with orthorhombic catalase plates yield negatively stained specimens with conditions used for the larger trigonal crystals.

Deviations from Ideal Decagonal Symmetry in Electron Diffraction Patterns of the “Decagonal” Phase in the Al-Co-Cu Alloy System

1991 ◽  
Vol 49 ◽  
pp. 914-915
Author(s):  
Atul S. Ramani ◽  
Earle R. Ryba ◽  
Paul R. Howell
Keyword(s):  
Electron Microscope ◽  
Alloy System ◽  
Nominal Composition ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Decagonal Phase ◽  
Cu Alloy ◽  
Transmission Electron ◽  
Lattice Periodicity ◽  
Diffraction Patterns

The “decagonal” phase in the Al-Co-Cu system of nominal composition Al65CO15Cu20 first discovered by He et al. is especially suitable as a topic of investigation since it has been claimed that it is thermodynamically stable and is reported to be periodic in the dimension perpendicular to the plane of quasiperiodic 10-fold symmetry. It can thus be expected that it is an important link between fully periodic and fully quasiperiodic phases. In the present paper, we report important findings of our transmission electron microscope (TEM) study that concern deviations from ideal decagonal symmetry of selected area diffraction patterns (SADPs) obtained from several “decagonal” phase crystals and also observation of a lattice of main reflections on the 10-fold and 2-fold SADPs that implies complete 3-dimensional lattice periodicity and the fundamentally incommensurate nature of the “decagonal” phase. We also present diffraction evidence for a new transition phase that can be classified as being one-dimensionally quasiperiodic if the lattice of main reflections is ignored.

A Novel Reconstitution Method for Inducing the Formation of Regular 2-Dimensional Arrays of Membrane Proteins and Lipids

1988 ◽  
Vol 46 ◽  
pp. 152-153 ◽  
Author(s):  
A. Engel ◽  
A. Holzenburg ◽  
K. Stauffer ◽  
J. Rosenbusch ◽  
U. Aebi
Keyword(s):  
Membrane Proteins ◽  
Flow Rate ◽  
Lipid Membranes ◽  
Functional Characterization ◽  
Dimensional Structure ◽  
Electron Crystallography ◽  
Peltier Element ◽  
Protein Ratio ◽  
Precise Control ◽  
3 Dimensional

Reconstitution of solubilized and purified membrane proteins in the presence of phospholipids into vesicles allows their functions to be studied by simple bulk measurements (e.g. diffusion of differently sized solutes) or by conductance measurements after transformation into planar membranes. On the other hand, reconstitution into regular protein-lipid arrays, usually forming at a specific lipid-to-protein ratio, provides the basis for determining the 3-dimensional structure of membrane proteins employing the tools of electron crystallography.To refine reconstitution conditions for reproducibly inducing formation of large and highly ordered protein-lipid membranes that are suitable for both electron crystallography and patch clamping experiments aimed at their functional characterization, we built a flow-dialysis device that allows precise control of temperature and flow-rate (Fig. 1). The flow rate is generated by a peristaltic pump and can be adjusted from 1 to 500 ml/h. The dialysis buffer is brought to a preselected temperature during its travel through a meandering path before it enters the dialysis reservoir. A Z-80 based computer controls a Peltier element allowing the temperature profile to be programmed as function of time.

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