674 research outputs found
Order-by-Disorder in the XY Pyrochlore Antiferromagnet Revisited
We investigate the properties of the XY pyrochlore antiferromagnet with local
planar anisotropy. We find the ground states and show that the
configurational ground state entropy is subextensive. By computing the free
energy due to harmonic fluctuations and by carrying out Monte Carlo
simulations, we confirm earlier work indicating that the model exhibits thermal
order-by-disorder leading to low temperature long-range order consisting of
discrete magnetic domains. We compute the spin wave spectrum and show that
thermal and quantum fluctuations select the same magnetic structure. Using
Monte Carlo simulations, we find that the state selected by thermal
fluctuations in this XY pyrochlore antiferromagnet can survive the addition of
sufficiently weak nearest-neighbor pseudo-dipolar interactions to the spin
Hamiltonian. We discuss our results in relation to the Er2Ti2O7 pyrochlore
antiferromagnet.Comment: 13 pages, 6 figure
Modelling of crowded polymers elucidate effects of double-strand breaks in topological domains of bacterial chromosomes.
Using numerical simulations of pairs of long polymeric chains confined in microscopic cylinders, we investigate consequences of double-strand DNA breaks occurring in independent topological domains, such as these constituting bacterial chromosomes. Our simulations show a transition between segregated and mixed state upon linearization of one of the modelled topological domains. Our results explain how chromosomal organization into topological domains can fulfil two opposite conditions: (i) effectively repulse various loops from each other thus promoting chromosome separation and (ii) permit local DNA intermingling when one or more loops are broken and need to be repaired in a process that requires homology search between broken ends and their homologous sequences in closely positioned sister chromatid
Structural motifs of biomolecules
Biomolecular structures are assemblies of emergent anisotropic building
modules such as uniaxial helices or biaxial strands. We provide an approach to
understanding a marginally compact phase of matter that is occupied by proteins
and DNA. This phase, which is in some respects analogous to the liquid crystal
phase for chain molecules, stabilizes a range of shapes that can be obtained by
sequence-independent interactions occurring intra- and intermolecularly between
polymeric molecules. We present a singularityfree self-interaction for a tube
in the continuum limit and show that this results in the tube being positioned
in the marginally compact phase. Our work provides a unified framework for
understanding the building blocks of biomolecules.Comment: 13 pages, 5 figure
Metastable tight knots in a worm-like polymer
Based on an estimate of the knot entropy of a worm-like chain we predict that
the interplay of bending energy and confinement entropy will result in a
compact metastable configuration of the knot that will diffuse, without
spreading, along the contour of the semi-flexible polymer until it reaches one
of the chain ends. Our estimate of the size of the knot as a function of its
topological invariant (ideal aspect ratio) agrees with recent experimental
results of knotted dsDNA. Further experimental tests of our ideas are proposed.Comment: 4 pages, 3 figure
Gel Electrophoresis of DNA Knots in Weak and Strong Electric Fields
Gel electrophoresis allows to separate knotted DNA (nicked circular) of equal
length according to the knot type. At low electric fields, complex knots being
more compact, drift faster than simpler knots. Recent experiments have shown
that the drift velocity dependence on the knot type is inverted when changing
from low to high electric fields. We present a computer simulation on a lattice
of a closed, knotted, charged DNA chain drifting in an external electric field
in a topologically restricted medium. Using a simple Monte Carlo algorithm, the
dependence of the electrophoretic migration of the DNA molecules on the type of
knot and on the electric field intensity was investigated. The results are in
qualitative agreement with electrophoretic experiments done under conditions of
low and high electric fields: especially the inversion of the behavior from low
to high electric field could be reproduced. The knot topology imposes on the
problem the constrain of self-avoidance, which is the final cause of the
observed behavior in strong electric field.Comment: 17 pages, 5 figure
Effects of supercoiling on enhancer-promoter contacts.
Using Brownian dynamics simulations, we investigate here one of possible roles of supercoiling within topological domains constituting interphase chromosomes of higher eukaryotes. We analysed how supercoiling affects the interaction between enhancers and promoters that are located in the same or in neighbouring topological domains. We show here that enhancer-promoter affinity and supercoiling act synergistically in increasing the fraction of time during which enhancer and promoter stay in contact. This stabilizing effect of supercoiling only acts on enhancers and promoters located in the same topological domain. We propose that the primary role of recently observed supercoiling of topological domains in interphase chromosomes of higher eukaryotes is to assure that enhancers contact almost exclusively their cognate promoters located in the same topological domain and avoid contacts with very similar promoters but located in neighbouring topological domains
Subknots in ideal knots, random knots, and knotted proteins.
We introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the chain by means of a spatially robust closure protocol. We characterize the sets of observed subknot types in global knots taking energy-minimized shapes such as KnotPlot configurations and ideal geometric configurations. We compare the sets of observed subknots to knot types obtained by changing crossings in the classical prime knot diagrams. Building upon this analysis, we study the sets of subknots in random configurations of corresponding knot types. In many of the knot types we analyzed, the sets of subknots from the ideal geometric configurations are found in each of the hundreds of random configurations of the same global knot type. We also compare the sets of subknots observed in open protein knots with the subknots observed in the ideal configurations of the corresponding knot type. This comparison enables us to explain the specific dispositions of subknots in the analyzed protein knots
3D visualization software to analyze topological outcomes of topoisomerase reactions.
The action of various DNA topoisomerases frequently results in characteristic changes in DNA topology. Important information for understanding mechanistic details of action of these topoisomerases can be provided by investigating the knot types resulting from topoisomerase action on circular DNA forming a particular knot type. Depending on the topological bias of a given topoisomerase reaction, one observes different subsets of knotted products. To establish the character of topological bias, one needs to be aware of all possible topological outcomes of intersegmental passages occurring within a given knot type. However, it is not trivial to systematically enumerate topological outcomes of strand passage from a given knot type. We present here a 3D visualization software (TopoICE-X in KnotPlot) that incorporates topological analysis methods in order to visualize, for example, knots that can be obtained from a given knot by one intersegmental passage. The software has several other options for the topological analysis of mechanisms of action of various topoisomerases
Tight open knots
The most tight conformations of prime knots are found with the use of the
SONO algorithm. Their curvature and torsion profiles are calculated. Symmetry
of the knots is analysed. Connections with the physics of polymers are
discussed.Comment: 11 pages, 8 figure
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