Knotted and Catenated Polymers

A special issue of Polymers (ISSN 2073-4360).

Deadline for manuscript submissions: closed (31 May 2017) | Viewed by 43159

Special Issue Editors

Center for Integrative Genomic, Faculty of Biology and Medicine, University of Lausanne, CH-1015 Lausanne, Switzerland
Interests: DNA structure and topology; DNA recombination; DNA replication; DNA repair; knotted and catenated polymers; structure of chromosomes and knotted proteins; DNA supercoiling and enhancer-promoter interactions
Polymer Institute, Slovak Academy of Sciences, Dubravska cesta 9, 845 41 Bratislava, Slovakia
Interests: computer simulations; molecular simulations; DNA; DNA topology; DNA and condensed matter, polymers and material modelling
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Special Issue Information

Dear Colleagues,

Interest in polymer knotting and catenation is shared by chemists, physicists, biologists, and mathematicians.

Chemists are frequently interested in synthesis of particular knots or catenanes, such as the work of researchers distinguished with the Nobel Prize in Chemistry in 2016. Physicists are interested, for example, in aspects, such as the influence of polymer length, polymer crowding, or specific spatial confinement of the probability of knotting and catenation. Biologists try to understand how DNA knots and catenanes are formed, and then efficiently disentangled in living cells, or how certain proteins always fold into knotted native structures. Mathematicians are interested in topological classification of polymeric knots and catenanes with such interesting aspects as how to define a knot type in case of linear polymers.

This Special Issue of Polymers is intended to present the research of scientists working in various fields but all having very keen interest in polymer knotting and catenation. This Special Issue will help to increase the visibility of the covered disciplines among a broad readership, and of individual contributions among colleagues in the field. We invite research articles, topical reviews, as well as communications, for this Special Issue on polymer knotting and catenation.

Prof. Andrzej Stasiak

Prof. Dusan Racko

Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Polymers is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Polymers
  • Knots
  • Catenanes
  • Synthesis
  • Supramolecular chemistry
  • Chemical topology
  • Nanotechnology
  • Polymer physics
  • Statistical physics
  • Topology
  • Manifolds
  • Constrained polymer
  • Confinement
  • Semiflexible polymers
  • Polymer stiffness
  • Ring polymers
  • Entanglement
  • Condensed matter
  • Complex systems
  • Soft matter
  • Living matter
  • Molecular biology
  • Biophysics
  • Bioinformatics
  • DNA topology
  • DNA knots
  • DNA topoisomerases
  • Knotted proteins
  • Protein folding
  • Protein knots
  • Molecular simulations
  • Molecular modeling
  • Monte Carlo
  • Molecular Dynamics
  • Coarse-grained models
  • High Performance Computing

Published Papers (7 papers)

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Research

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7110 KiB  
Article
Topological Models for Open-Knotted Protein Chains Using the Concepts of Knotoids and Bonded Knotoids
by Dimos Goundaroulis, Neslihan Gügümcü, Sofia Lambropoulou, Julien Dorier, Andrzej Stasiak and Louis Kauffman
Polymers 2017, 9(9), 444; https://doi.org/10.3390/polym9090444 - 13 Sep 2017
Cited by 42 | Viewed by 7175
Abstract
In this paper we introduce a method that offers a detailed overview of the entanglement of an open protein chain. Further, we present a purely topological model for classifying open protein chains by also taking into account any bridge involving the backbone. To [...] Read more.
In this paper we introduce a method that offers a detailed overview of the entanglement of an open protein chain. Further, we present a purely topological model for classifying open protein chains by also taking into account any bridge involving the backbone. To this end, we implemented the concepts of planar knotoids and bonded knotoids. We show that the planar knotoids technique provides more refined information regarding the knottedness of a protein when compared to established methods in the literature. Moreover, we demonstrate that our topological model for bonded proteins is robust enough to distinguish all types of lassos in proteins. Full article
(This article belongs to the Special Issue Knotted and Catenated Polymers)
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11585 KiB  
Article
Are There Knots in Chromosomes?
by Jonathan T. Siebert, Alexey N. Kivel, Liam P. Atkinson, Tim J. Stevens, Ernest D. Laue and Peter Virnau
Polymers 2017, 9(8), 317; https://doi.org/10.3390/polym9080317 - 02 Aug 2017
Cited by 32 | Viewed by 7818
Abstract
Recent developments have for the first time allowed the determination of three-dimensional structures of individual chromosomes and genomes in nuclei of single haploid mouse embryonic stem (ES) cells based on Hi–C chromosome conformation contact data. Although these first structures have a relatively low [...] Read more.
Recent developments have for the first time allowed the determination of three-dimensional structures of individual chromosomes and genomes in nuclei of single haploid mouse embryonic stem (ES) cells based on Hi–C chromosome conformation contact data. Although these first structures have a relatively low resolution, they provide the first experimental data that can be used to study chromosome and intact genome folding. Here we further analyze these structures and provide the first evidence that G1 phase chromosomes are knotted, consistent with the fact that plots of contact probability vs sequence separation show a power law dependence that is intermediate between that of a fractal globule and an equilibrium structure. Full article
(This article belongs to the Special Issue Knotted and Catenated Polymers)
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1927 KiB  
Article
Mechanical Pulling of Linked Ring Polymers: Elastic Response and Link Localisation
by Michele Caraglio, Cristian Micheletti and Enzo Orlandini
Polymers 2017, 9(8), 327; https://doi.org/10.3390/polym9080327 - 01 Aug 2017
Cited by 21 | Viewed by 4342
Abstract
By using Langevin dynamics simulations, we study how semiflexible rings that are topologically linked respond to mechanical stretching. We use both constant-force and constant-velocity pulling protocols and map out how the mechanical tension affects observables related to metric quantities such as the longitudinal [...] Read more.
By using Langevin dynamics simulations, we study how semiflexible rings that are topologically linked respond to mechanical stretching. We use both constant-force and constant-velocity pulling protocols and map out how the mechanical tension affects observables related to metric quantities such as the longitudinal extension or span, and topology-related ones such as the length of the linked portion. We find that the average extension of linked rings, once divided by that of a single equivalent ring, is nonmonotonic in the applied force. We show that this remarkable feature becomes more prominent as the link complexity is increased, and originates from the different stretching compliance of the linked portion and the rest of the rings’ contour. By comparing the results of different pulling protocols, we also establish the best one for telling apart different types of links from their tensile response. Full article
(This article belongs to the Special Issue Knotted and Catenated Polymers)
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2316 KiB  
Article
Structural Behavior of a Semiflexible Polymer Chain in an Array of Nanoposts
by Zuzana Benková, Lucia Rišpanová and Peter Cifra
Polymers 2017, 9(8), 313; https://doi.org/10.3390/polym9080313 - 28 Jul 2017
Cited by 10 | Viewed by 4356 | Correction
Abstract
The structural properties of a flexible and semiflexible circular chain confined in an array of parallel nanoposts with a square lattice cross-sectional projection were studied using coarse-grained molecular dynamics simulations. To address the effect of the circular topology, a comparison with linear analogs [...] Read more.
The structural properties of a flexible and semiflexible circular chain confined in an array of parallel nanoposts with a square lattice cross-sectional projection were studied using coarse-grained molecular dynamics simulations. To address the effect of the circular topology, a comparison with linear analogs was also carried out. In the interpretation of the chain structural properties, the geometry of the post array is considered as a combination of a channel approximating the interstitial volume with the diameter dc and a slit approximating the passage aperture with the width wp. The number of interstitial volumes occupied by a chain monotonically increases with the decreasing ratio dc/wp regardless of the way the geometry of the post array is varied. However, depending on how the array geometry is modified, the chain span along the posts displays a monotonic (constant post separation) or a non-monotonic behavior (constant passage width) when plotted as a function of the post diameter. In the case of monotonic trend, the width of interstitial spaces increases with the increasing chain occupation number, while, in the case of non-monotonic trend, the width of interstitial spaces decreases with the increasing chain occupation number. In comparison with linear topology, for circular topology, the stiffness affects more significantly the relative chain extension along the posts and less significantly the occupation number. The geometrical parameters of the post arrays are stored in the single-chain structure factors. The characteristic humps are recognized in the structure factor which ensue from the local increase in the density of segments in the circular chains presented in an interstitial volume or from the correlation of parallel chain fragments separated by a row of posts. Although the orientation correlations provide qualitative information about the chain topology and the character of confinement within a single interstitial volume, information about the array periodicity is missing. Full article
(This article belongs to the Special Issue Knotted and Catenated Polymers)
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1235 KiB  
Article
Efficient Sampling of Knotting-Unknotting Pathways for Semiflexible Gaussian Chains
by Cristian Micheletti and Henri Orland
Polymers 2017, 9(6), 196; https://doi.org/10.3390/polym9060196 - 29 May 2017
Cited by 2 | Viewed by 3914
Abstract
We propose a stochastic method to generate exactly the overdamped Langevin dynamics of semi-flexible Gaussian chains, conditioned to evolve between given initial and final conformations in a preassigned time. The initial and final conformations have no restrictions, and hence can be in any [...] Read more.
We propose a stochastic method to generate exactly the overdamped Langevin dynamics of semi-flexible Gaussian chains, conditioned to evolve between given initial and final conformations in a preassigned time. The initial and final conformations have no restrictions, and hence can be in any knotted state. Our method allows the generation of statistically independent paths in a computationally efficient manner. We show that these conditioned paths can be exactly generated by a set of local stochastic differential equations. The method is used to analyze the transition routes between various knots in crossable filamentous structures, thus mimicking topological reconnections occurring in soft matter systems or those introduced in DNA by topoisomerase enzymes. We find that the average number of crossings, writhe and unknotting number are not necessarily monotonic in time and that more complex topologies than the initial and final ones can be visited along the route. Full article
(This article belongs to the Special Issue Knotted and Catenated Polymers)
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Review

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16690 KiB  
Review
To Tie or Not to Tie? That Is the Question
by Pawel Dabrowski-Tumanski and Joanna I. Sulkowska
Polymers 2017, 9(9), 454; https://doi.org/10.3390/polym9090454 - 16 Sep 2017
Cited by 44 | Viewed by 8201
Abstract
In this review, we provide an overview of entangled proteins. Around 6% of protein structures deposited in the PBD are entangled, forming knots, slipknots, lassos and links. We present theoretical methods and tools that enabled discovering and classifying such structures. We discuss the [...] Read more.
In this review, we provide an overview of entangled proteins. Around 6% of protein structures deposited in the PBD are entangled, forming knots, slipknots, lassos and links. We present theoretical methods and tools that enabled discovering and classifying such structures. We discuss the advantages and disadvantages of the non-trivial topology in proteins, based on available data about folding, stability, biological properties and evolutionary conservation. We also formulate intriguing and challenging questions on the border of biophysics, bioinformatics, biology and mathematics, which arise from the discovery of an entanglement in proteins. Finally, we discuss possible applications of entangled proteins in medicine and nanotechnology, such as the chance to design super stable proteins, whose stability could be controlled by chemical potential. Full article
(This article belongs to the Special Issue Knotted and Catenated Polymers)
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11561 KiB  
Review
Ring Polymers: Threadings, Knot Electrophoresis and Topological Glasses
by Davide Michieletto, Davide Marenduzzo, Enzo Orlandini and Matthew S. Turner
Polymers 2017, 9(8), 349; https://doi.org/10.3390/polym9080349 - 08 Aug 2017
Cited by 23 | Viewed by 6213
Abstract
Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these systems arise due to topological interactions between [...] Read more.
Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these systems arise due to topological interactions between polymers, or between the polymers and the environment, and it is often challenging to describe this quantitatively. Here we review recent research which suggests that a key role is played by inter-ring threadings (or penetrations), which become more abundant as the ring size increases. As we discuss, the physical consequences of such threadings are far-reaching: for instance, they lead to a topologically-driven glassy behaviour of ring polymer melts under pinning perturbations, while they can also account for the shape of experimentally observed patterns in two-dimensional gel electrophoresis of DNA knots. Full article
(This article belongs to the Special Issue Knotted and Catenated Polymers)
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