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.

Determining the topology of stable protein–DNA complexes

2013 ◽  
Vol 41 (2) ◽  
pp. 601-605 ◽  
Author(s):  
Isabel K. Darcy ◽  
Mariel Vazquez
Keyword(s):  
Present Article ◽  
Experimental Technique ◽  
Topological Structure ◽  
Reaction Pathway ◽  
Dna Supercoiling ◽  
Dna Complexes ◽  
Nucleoprotein Complex ◽  
Mu Transpososome ◽  
Dna Complex

Difference topology is an experimental technique that can be used to unveil the topological structure adopted by two or more DNA segments in a stable protein–DNA complex. Difference topology has also been used to detect intermediates in a reaction pathway and to investigate the role of DNA supercoiling. In the present article, we review difference topology as applied to the Mu transpososome. The tools discussed can be applied to any stable nucleoprotein complex.

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 Mechanical unfolding of a simple model protein goes beyond the reach of one-dimensional descriptions

2014 ◽  
Vol 141 (13) ◽  
pp. 135102 ◽  
Author(s):  
R. Tapia-Rojo ◽  
S. Arregui ◽  
J. J. Mazo ◽  
F. Falo
Keyword(s):  
Simple Model ◽  
One Dimensional ◽  
Model Protein

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

scholarly journals Forces driving cell sorting in Hydra

2017 ◽  
Author(s):  
Olivier Cochet-Escartin ◽  
Tiffany T. Locke ◽  
Winnie H. Shi ◽  
Robert E. Steele ◽  
Eva-Maria S. Collins
Keyword(s):  
Cell Sorting ◽  
Single Cells ◽  
Cell Types ◽  
Biological Organization ◽  
3 Dimensional ◽  
Physical Mechanisms ◽  
Summary Statement ◽  
Endodermal Cells

AbstractCell sorting, whereby a heterogeneous cell mixture organizes into distinct tissues, is a fundamental patterning process in development. So far, most studies of cell sorting have relied either on 2-dimensional cellular aggregates, in vitro situations that do not have a direct counterpart in vivo, or were focused on the properties of single cells. Here, we report the first multiscale experimental study on 3-dimensional regenerating Hydra aggregates, capable of reforming a full animal. By quantifying the kinematics of single cell and whole aggregate behaviors, we show that no differences in cell motility exist among cell types and that sorting dynamics follow a power law. Moreover, we measure the physical properties of separated tissues and determine their viscosities and surface tensions. Based on our experimental results and numerical simulations, we conclude that tissue interfacial tensions are sufficient to explain Hydra cell sorting. Doing so, we illustrate D’Arcy Thompson’s central idea that biological organization can be understood through physical principles, an idea which is currently re-shaping the field of developmental biology.Summary statementHydra regenerates after dissociation into single cells. We show how physical mechanisms can explain the first step of regeneration, whereby ectodermal and endodermal cells sort out to form distinct tissue layers.

Sign in / Sign up

Export Citation Format

Share Document