1
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Caraglio M, Micheletti C, Orlandini E. Unraveling the Influence of Topology and Spatial Confinement on Equilibrium and Relaxation Properties of Interlocked Ring Polymers. Macromolecules 2024; 57:3223-3233. [PMID: 38616813 PMCID: PMC11008367 DOI: 10.1021/acs.macromol.3c02203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Revised: 02/27/2024] [Accepted: 03/01/2024] [Indexed: 04/16/2024]
Abstract
We use Langevin dynamics simulations to study linked ring polymers in channel confinement. We address the in- and out-of-equilibrium behavior of the systems for varying degrees of confinement and increasing topological and geometrical complexity of the interlocking. The main findings are three. First, metric observables of different link topologies collapse onto the same master curve when plotted against the crossing number, revealing a universal response to confinement. Second, the relaxation process from initially stretched states is faster for more complex links. We ascribe these properties to the interplay of several effects, including the dependence of topological friction on the link complexity. Finally, we show that transient forms of geometrical entanglement purposely added to the initial stressed state can leave distinctive signatures in force-spectroscopy curves. The insight provided by the findings could be leveraged in single-molecule nanochannel experiments to identify geometric entanglement within topologically linked rings.
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Affiliation(s)
- Michele Caraglio
- Institut
für Theoretische Physik, Universität
Innsbruck, Technikerstraße 21A, Innsbruck A-6020, Austria
| | - Cristian Micheletti
- Scuola
Internazionale Superiore di Studi Avanzati—SISSA, Via Bonomea 265, Trieste 34136, Italy
| | - Enzo Orlandini
- Department
of Physics and Astronomy, University of
Padova, Via Marzolo 8, Padova I-35100, Italy
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2
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Ubertini MA, Rosa A. Spatial Organization of Slit-Confined Melts of Ring Polymers with Nonconserved Topology: A Lattice Monte Carlo Study. Macromolecules 2023; 56:7860-7869. [PMID: 37841537 PMCID: PMC10569094 DOI: 10.1021/acs.macromol.3c01320] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Revised: 09/08/2023] [Indexed: 10/17/2023]
Abstract
We present Monte Carlo computer simulations for melts of semiflexible randomly knotted and randomly concatenated ring polymers on the fcc lattice and in slit confinement. Through systematic variation of the slit width at fixed melt density, we explore the influence of confinement on single-chain conformations and interchain interactions. We demonstrate that confinement makes chains globally larger and more elongated while enhancing both contacts and knottedness propensities. As for multichain properties, we show that ring-ring contacts decrease with the confinement, yet neighboring rings overlap more as confinement grows. These aspects are accompanied by a marked decrease in the links formed between pairs of neighboring rings. In connection with the quantitative relation between links and entanglements in polymer melts recently established by us [Ubertini M. A.; Rosa A.Macromolecules2023, 56, 3354-3362], we propose that confinement can be used to set polymer networks that act softer under mechanical stress and suggest a viable experimental setup to validate our results.
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Affiliation(s)
- Mattia Alberto Ubertini
- Scuola Internazionale Superiore
di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Angelo Rosa
- Scuola Internazionale Superiore
di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
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3
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Chang LH, Ghosh S, Papale A, Luppino JM, Miranda M, Piras V, Degrouard J, Edouard J, Poncelet M, Lecouvreur N, Bloyer S, Leforestier A, Joyce EF, Holcman D, Noordermeer D. Multi-feature clustering of CTCF binding creates robustness for loop extrusion blocking and Topologically Associating Domain boundaries. Nat Commun 2023; 14:5615. [PMID: 37699887 PMCID: PMC10497529 DOI: 10.1038/s41467-023-41265-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Accepted: 08/28/2023] [Indexed: 09/14/2023] Open
Abstract
Topologically Associating Domains (TADs) separate vertebrate genomes into insulated regulatory neighborhoods that focus genome-associated processes. TADs are formed by Cohesin-mediated loop extrusion, with many TAD boundaries consisting of clustered binding sites of the CTCF insulator protein. Here we determine how this clustering of CTCF binding contributes to the blocking of loop extrusion and the insulation between TADs. We identify enrichment of three features of CTCF binding at strong TAD boundaries, consisting of strongly bound and closely spaced CTCF binding peaks, with a further enrichment of DNA-binding motifs within these peaks. Using multi-contact Nano-C analysis in cells with normal and perturbed CTCF binding, we establish that individual CTCF binding sites contribute to the blocking of loop extrusion, but in an incomplete manner. When clustered, individual CTCF binding sites thus create a stepwise insulation between neighboring TADs. Based on these results, we propose a model whereby multiple instances of temporal loop extrusion blocking create strong insulation between TADs.
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Affiliation(s)
- Li-Hsin Chang
- Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell (I2BC), 91198, Gif-sur-Yvette, France
- MRC Molecular Haematology Unit, MRC Weatherall Institute of Molecular Medicine, Radcliffe Department of Medicine, University of Oxford, and National Institute of Health Research, Blood and Transplant Research Unit in Precision Cellular Therapeutics, OX3 9DS, Oxford, UK
| | - Sourav Ghosh
- Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell (I2BC), 91198, Gif-sur-Yvette, France
- Department of Pathology and Laboratory Medicine, Western University, N6A3K7, London, ON, Canada
| | - Andrea Papale
- École Normale Supérieure, IBENS, Université PSL, 75005, Paris, France
| | - Jennifer M Luppino
- Department of Genetics, Penn Epigenetics Institute, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA
| | - Mélanie Miranda
- Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell (I2BC), 91198, Gif-sur-Yvette, France
| | - Vincent Piras
- Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell (I2BC), 91198, Gif-sur-Yvette, France
| | - Jéril Degrouard
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides (LPS), 91405, Orsay, France
| | - Joanne Edouard
- Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell (I2BC), 91198, Gif-sur-Yvette, France
| | - Mallory Poncelet
- Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell (I2BC), 91198, Gif-sur-Yvette, France
| | - Nathan Lecouvreur
- Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell (I2BC), 91198, Gif-sur-Yvette, France
| | - Sébastien Bloyer
- Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell (I2BC), 91198, Gif-sur-Yvette, France
| | - Amélie Leforestier
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides (LPS), 91405, Orsay, France
| | - Eric F Joyce
- Department of Genetics, Penn Epigenetics Institute, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA, USA
| | - David Holcman
- École Normale Supérieure, IBENS, Université PSL, 75005, Paris, France
- Churchill College, University of Cambridge, CB3 0DS, Cambridge, UK
| | - Daan Noordermeer
- Université Paris-Saclay, CEA, CNRS, Institute for Integrative Biology of the Cell (I2BC), 91198, Gif-sur-Yvette, France.
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4
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Mao R, Dorfman KD. Diffusion of knots in nanochannel-confined DNA molecules. J Chem Phys 2023; 158:2890486. [PMID: 37184024 DOI: 10.1063/5.0151025] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2023] [Accepted: 05/03/2023] [Indexed: 05/16/2023] Open
Abstract
We used Langevin dynamics simulations without hydrodynamic interactions to probe knot diffusion mechanisms and the time scales governing the evolution and the spontaneous untying of trefoil knots in nanochannel-confined DNA molecules in the extended de Gennes regime. The knot untying follows an "opening up process," wherein the initially tight knot continues growing and fluctuating in size as it moves toward the end of the DNA molecule before its annihilation at the chain end. The mean knot size increases significantly and sub-linearly with increasing chain contour length. The knot diffusion in nanochannel-confined DNA molecules is subdiffusive, with the unknotting time scaling with chain contour length with an exponent of 2.64 ± 0.23 to within a 95% confidence interval. The scaling exponent for the mean unknotting time vs chain contour length, along with visual inspection of the knot conformations, suggests that the knot diffusion mechanism is a combination of self-reptation and knot region breathing for the simulated parameters.
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Affiliation(s)
- Runfang Mao
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
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5
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Wettermann S, Datta R, Virnau P. Influence of ionic conditions on knotting in a coarse-grained model for DNA. Front Chem 2023; 10:1096014. [PMID: 36733610 PMCID: PMC9887150 DOI: 10.3389/fchem.2022.1096014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2022] [Accepted: 12/23/2022] [Indexed: 01/18/2023] Open
Abstract
We investigate knotting probabilities of long double-stranded DNA strands in a coarse-grained Kratky-Porod model for DNA with Monte Carlo simulations. Various ionic conditions are implemented by adjusting the effective diameter of monomers. We find that the occurrence of knots in DNA can be reinforced considerably by high salt conditions and confinement between plates. Likewise, knots can almost be dissolved completely in a low salt scenario. Comparisons with recent experiments confirm that the coarse-grained model is able to capture and quantitatively predict topological features of DNA and can be used for guiding future experiments on DNA knots.
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6
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Zhu Y, Zhu H, Tian F, Qiu Q, Dai L. Quantifying the effects of slit confinement on polymer knots using the tube model. Phys Rev E 2022; 105:024501. [PMID: 35291068 DOI: 10.1103/physreve.105.024501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 01/27/2022] [Indexed: 06/14/2023]
Abstract
Knots can spontaneously form in DNA, proteins, and other polymers and affect their properties. These knots often experience spatial confinement in biological systems and experiments. While confinement dramatically affects the knot behavior, the physical mechanisms underlying the confinement effects are not fully understood. In this work, we provide a simple physical picture of the polymer knots in slit confinement using the tube model. In the tube model, the polymer segments in the knot core are assumed to be confined in a virtual tube due to the topological restriction. We first perform Monte Carlo simulation of a flexible knotted chain confined in a slit. We find that with the decrease of the slit height from H=+∞ (the 3D case) to H=2a (the 2D case), the most probable knot size L_{knot}^{*} dramatically shrinks from (L_{knot}^{*})_{3D}≈140a to (L_{knot}^{*})_{2D}≈26a, where a is the monomer diameter of the flexible chain. Then we quantitatively explain the confinement-induced knot shrinking and knot deformation using the tube model. Our results for H=2a can be applied to a polymer knot on a surface, which resembles DNA knots measured by atomic force microscopy under the conditions that DNA molecules are weakly absorbed on the surface and reach equilibrium 2D conformations. This work demonstrates the effectiveness of the tube model in understanding polymer knots.
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Affiliation(s)
- Yongjian Zhu
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Haoqi Zhu
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Fujia Tian
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Qiyuan Qiu
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Kowloon, Hong Kong, 999077, China and Shenzhen Research Institute, City University of Hong Kong, Shenzhen 518057, China
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7
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Orlandini E, Micheletti C. Topological and physical links in soft matter systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2021; 34:013002. [PMID: 34547745 DOI: 10.1088/1361-648x/ac28bf] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2021] [Accepted: 09/21/2021] [Indexed: 06/13/2023]
Abstract
Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.
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Affiliation(s)
- Enzo Orlandini
- Department of Physics and Astronomy, University of Padova and Sezione INFN, Via Marzolo 8, Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, Trieste, Italy
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8
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Halun J, Karbowniczek P, Kuterba P, Danel Z. Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations. ENTROPY 2021; 23:e23020242. [PMID: 33669820 PMCID: PMC7922339 DOI: 10.3390/e23020242] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/15/2020] [Revised: 02/06/2021] [Accepted: 02/08/2021] [Indexed: 12/03/2022]
Abstract
The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with f=4 arms in a Θ-solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with N=300, 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries.
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Affiliation(s)
- Joanna Halun
- Institute of Nuclear Physics, Polish Academy of Sciences, 31-342 Cracow, Poland
- Correspondence:
| | - Pawel Karbowniczek
- Institute of Physics, Cracow University of Technology, 30-084 Cracow, Poland; (P.K.); (Z.D.)
| | - Piotr Kuterba
- Faculty of Physics, Astronomy and Applied Computer Sciences, Jagiellonian University in Cracow, 30-348 Cracow, Poland;
| | - Zoriana Danel
- Institute of Physics, Cracow University of Technology, 30-084 Cracow, Poland; (P.K.); (Z.D.)
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9
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Ahmadian Dehaghani Z, Chubak I, Likos CN, Ejtehadi MR. Effects of topological constraints on linked ring polymers in solvents of varying quality. SOFT MATTER 2020; 16:3029-3038. [PMID: 32129365 DOI: 10.1039/c9sm02374g] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
We investigate the effects of topological constraints in catenanes composed of interlinked ring polymers on their size in a good solvent as well as on the location of their θ-point when the solvent quality is worsened. We mainly focus on poly[n]catenanes consisting of n ring polymers each of length m interlocked in a linear fashion. Using molecular dynamics simulations, we study the scaling of the poly[n]catenane's radius of gyration in a good solvent, assuming in general that Rg∼mμnν and we find that μ = 0.65 ± 0.02 and ν = 0.60 ± 0.01 for the range of n and m considered. These findings are further rationalized with the help of a mean-field Flory-like theory yielding the values of μ = 16/25 and ν = 3/5, consistent with the numerical results. We show that individual rings within catenanes feature a surplus swelling due to the presence of NL topological links. Furthermore, we consider poly[n]catenanes in solvents of varying quality and we demonstrate that the presence of topological links leads to an increase of its θ-temperature in comparison to isolated linear and ring chains with the following ordering: T > T > T. Finally, we show that the presence of links similarly raises the θ-temperature of a single linked ring in comparison to an unlinked one, bringing its θ-temperature close to the one of a poly[n]catenane.
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10
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Gooneie A, Hufenus R. Polymeric Solvation Shells around Nanotubes: Mesoscopic Simulation of Interfaces in Nanochannels. Macromolecules 2019. [DOI: 10.1021/acs.macromol.9b01657] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Affiliation(s)
- Ali Gooneie
- Laboratory of Advanced Fibers, Empa, Swiss Federal Laboratories for Materials Science and Technology, Lerchenfeldstrasse 5, CH-9014 St. Gallen, Switzerland
| | - Rudolf Hufenus
- Laboratory of Advanced Fibers, Empa, Swiss Federal Laboratories for Materials Science and Technology, Lerchenfeldstrasse 5, CH-9014 St. Gallen, Switzerland
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11
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Cardelli C, Tubiana L, Bianco V, Nerattini F, Dellago C, Coluzza I. Heteropolymer Design and Folding of Arbitrary Topologies Reveals an Unexpected Role of Alphabet Size on the Knot Population. Macromolecules 2018. [DOI: 10.1021/acs.macromol.8b01359] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Chiara Cardelli
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Luca Tubiana
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Valentino Bianco
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Francesca Nerattini
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Christoph Dellago
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Ivan Coluzza
- CIC biomaGUNE, Paseo Miramon 182, 20014 San Sebastian, Spain
- IKERBASQUE,
Basque
Foundation for Science, Maria Diaz de Haro 3, 48013 Bilbao, Spain
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12
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Bleha T, Cifra P. Correlation anisotropy and stiffness of DNA molecules confined in nanochannels. J Chem Phys 2018; 149:054903. [PMID: 30089382 DOI: 10.1063/1.5034219] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The anisotropy of orientational correlations in DNA molecules confined in cylindrical channels is explored by Monte Carlo simulations using a coarse-grained model of double-stranded (ds) DNA. We find that the correlation function ⟨C(s)⟩⊥ in the transverse (confined) dimension exhibits a region of negative values in the whole range of channel sizes. Such a clear-cut sign of the opposite orientation of chain segments represents a microscopic validation of the Odijk deflection mechanism in narrow channels. At moderate-to-weak confinement, the negative ⟨C(s)⟩⊥ correlations imply a preference of DNA segments for transverse looping. The inclination for looping can explain a reduction of stiffness as well as the enhanced knotting of confined DNA relative to that detected earlier in bulk at some channel sizes. Furthermore, it is shown that the orientational persistence length Por fails to convey the apparent stiffness of DNA molecules in channels. Instead, correlation lengths P∥ and P⊥ in the axial and transverse directions, respectively, encompass the channel-induced modifications of DNA stiffness.
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Affiliation(s)
- Tomáš Bleha
- Polymer Institute, Slovak Academy of Sciences, 84541 Bratislava, Slovakia
| | - Peter Cifra
- Polymer Institute, Slovak Academy of Sciences, 84541 Bratislava, Slovakia
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13
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
| | - Patrick S. Doyle
- BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts 02139, United States
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14
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Affiliation(s)
- Iurii Chubak
- Faculty of Physics, University of Vienna, Vienna, Austria
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15
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Tubiana L, Polles G, Orlandini E, Micheletti C. KymoKnot: A web server and software package to identify and locate knots in trajectories of linear or circular polymers. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2018; 41:72. [PMID: 29884956 DOI: 10.1140/epje/i2018-11681-0] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2018] [Accepted: 05/18/2018] [Indexed: 06/08/2023]
Abstract
The KymoKnot software package and web server identifies and locates physical knots or proper knots in a series of polymer conformations. It is mainly intended as an analysis tool for trajectories of linear or circular polymers, but it can be used on single instances too, e.g. protein structures in PDB format. A key element of the software package is the so-called minimally interfering chain closure algorithm that is used to detect physical knots in open chains and to locate the knotted region in both open and closed chains. The web server offers a user-friendly graphical interface that identifies the knot type and highlights the knotted region on each frame of the trajectory, which the user can visualize interactively from various viewpoints. The dynamical evolution of the knotted region along the chain contour is presented as a kymograph. All data can be downloaded in text format. The KymoKnot package is licensed under the BSD 3-Clause licence. The server is publicly available at http://kymoknot.sissa.it/kymoknot/interactive.php .
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Affiliation(s)
- Luca Tubiana
- Computational Physics Department, University of Vienna, Sensengasse 8/10, 1090, Vienna, Austria.
| | - Guido Polles
- Molecular and Computational Biology, Department of Biological Sciences, University of Southern California, 90089, Los Angeles, CA, USA
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia and Sezione INFN, Università di Padova, Via Marzolo 8, 35131, Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, Via Bonomea 265, I-34136, Trieste, Italy
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16
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Liebetreu M, Ripoll M, Likos CN. Trefoil Knot Hydrodynamic Delocalization on Sheared Ring Polymers. ACS Macro Lett 2018; 7:447-452. [PMID: 35619341 DOI: 10.1021/acsmacrolett.8b00059] [Citation(s) in RCA: 34] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
The behavior of unknotted and trefoil-knotted ring polymers under shear flow is here examined by means of mesoscopic simulations. In contrast to most polymers, ring polymers in a hydrodynamic solvent at high shear rates do not get shortened in the vorticity direction. This is a consequence of the backflow produced by the interaction of the sheared solvent with the end-free polymer topology. The extended structures of the ring in the vorticity-flow plane, when they are aligned in a constant velocity plane, favor ring contour fluctuations. This variety of conformations largely suppresses the tank-treading type of rotation with extended conformations in favor of the tumbling type of rotations, where stretched and collapsed conformations alternate. The extension of trefoil knots is also enhanced, so that the knots become delocalized. We anticipate that these effects, which disappear in the absence of hydrodynamic interactions, will have a crucial impact on the rheological properties of concentrated ring solutions, and will also influence the behavior of more complicated systems such as mixtures of polymers with different topologies.
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Affiliation(s)
- Maximilian Liebetreu
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Marisol Ripoll
- Forschungszentrum Jülich, Institute of Complex Systems, Theoretical Soft Matter and Biophysics, 52425 Jülich, Germany
| | - Christos N. Likos
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
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17
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Cheong GK, Li X, Dorfman KD. Evidence for the extended de Gennes regime of a semiflexible polymer in slit confinement. Phys Rev E 2018; 97:022502. [PMID: 29479576 PMCID: PMC5823612 DOI: 10.1103/physreve.97.022502] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
We use off-lattice, pruned-enriched Rosenbluth method (PERM) simulations to compute the confinement free energy of a real wormlike chain of effective width w and persistence length lp in a slit of height H. For slit heights much larger than the persistence length of the polymer and much smaller than the thermal blob size, the excess free energy of the confined chain is consistent with a modified version of the scaling theory for the extended de Gennes regime in a channel that reflects the blob statistics in slit confinement. Explicitly, for channel sizes [Formula: see text], the difference between the confinement free energy of the real chain and that of an ideal chain scales like w/H.
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Affiliation(s)
- Guo Kang Cheong
- Department of Chemical Engineering and Materials Science, University of Minnesota – Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - Xiaolan Li
- Department of Chemical Engineering and Materials Science, University of Minnesota – Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota – Twin Cities, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, USA
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18
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Sassi AS, Assenza S, De Los Rios P. Shape of a Stretched Polymer. PHYSICAL REVIEW LETTERS 2017; 119:037801. [PMID: 28777625 DOI: 10.1103/physrevlett.119.037801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2015] [Indexed: 06/07/2023]
Abstract
The shape of a polymer plays an important role in its interactions with surrounding molecules. We characterize the shape and the orientational properties of a polymer chain under tension in a good solvent, a physical condition that is often realized both in single-molecule experiments and in vivo. Our findings reveal the existence of hitherto unobserved universal laws encompassing polymers with different rigidities and including the possible presence of excluded-volume effects, showing that both shape and orientation are solely determined by the force contribution to the free energy. In doing so, they also provide a simple way to retrieve these quantities from the knowledge of the force-versus-extension curve.
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Affiliation(s)
- Alberto S Sassi
- Laboratoire de Biophysique Statistique, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Salvatore Assenza
- Laboratoire de Biophysique Statistique, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Paolo De Los Rios
- Laboratoire de Biophysique Statistique, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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19
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Coronel L, Orlandini E, Micheletti C. Non-monotonic knotting probability and knot length of semiflexible rings: the competing roles of entropy and bending energy. SOFT MATTER 2017; 13:4260-4267. [PMID: 28573303 DOI: 10.1039/c7sm00643h] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
We consider self-avoiding rings of up to 1000 beads and study, by Monte Carlo techniques, how their equilibrium knotting properties depend on the bending rigidity. When the rings are taken from the rigid to fully-flexible limit, their average compactness increases, as expected. However, this progressive compactification is not parallelled by a steady increase of the abundance of knots. In fact the knotting probability, Pk, has a prominent maximum when the persistence length is a few times larger than the bead size. At similar bending rigidities, the knot length has, instead, a minimum. We show that the observed non-monotonicity of Pk arises from the competition between two effects. The first one is the entropic cost of introducing a knot. The second one is the gain in bending energy due to the presence of essential crossings. These, in fact, constrain the knotted region and keep it less bent than average. The two competing effects make knots maximally abundant when the persistence length is 5-10 times larger than the bead size. At such intermediate bending rigidities, knots in the chains of 500 and 1000 beads are 40 times more likely than in the fully-flexible limit.
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Affiliation(s)
- Lucia Coronel
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
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20
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Japaridze A, Orlandini E, Smith KB, Gmür L, Valle F, Micheletti C, Dietler G. Spatial confinement induces hairpins in nicked circular DNA. Nucleic Acids Res 2017; 45:4905-4914. [PMID: 28201616 PMCID: PMC5605231 DOI: 10.1093/nar/gkx098] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2016] [Revised: 01/25/2017] [Accepted: 02/06/2017] [Indexed: 01/05/2023] Open
Abstract
In living cells, DNA is highly confined in space with the help of condensing agents, DNA binding proteins and high levels of supercoiling. Due to challenges associated with experimentally studying DNA under confinement, little is known about the impact of spatial confinement on the local structure of the DNA. Here, we have used well characterized slits of different sizes to collect high resolution atomic force microscopy images of confined circular DNA with the aim of assessing the impact of the spatial confinement on global and local conformational properties of DNA. Our findings, supported by numerical simulations, indicate that confinement imposes a large mechanical stress on the DNA as evidenced by a pronounced anisotropy and tangent-tangent correlation function with respect to non-constrained DNA. For the strongest confinement we observed nanometer sized hairpins and interwound structures associated with the nicked sites in the DNA sequence. Based on these findings, we propose that spatial DNA confinement in vivo can promote the formation of localized defects at mechanically weak sites that could be co-opted for biological regulatory functions.
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Affiliation(s)
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia and Sezione INFN, Universita di Padova, Via Marzolo 8, 35131 Padova, Italy
| | | | - Lucas Gmür
- Laboratory of Physics of Living Matter, EPFL, 1015 Lausanne, Switzerland
| | - Francesco Valle
- Consiglio Nazionale delle Ricerche (CNR), Istituto per lo Studio dei Materiali Nanostrutturati (ISMN), Via P.Gobetti 101, Bologna 40129, Italy
| | - Cristian Micheletti
- SISSA - Scuola Internazionale Superiore di Studi Avanzati and CNR-IOM Democritos, Via Bonomea 265, 34136 Trieste, Italy
| | - Giovanni Dietler
- Laboratory of Physics of Living Matter, EPFL, 1015 Lausanne, Switzerland
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21
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Japaridze A, Muskhelishvili G, Benedetti F, Gavriilidou AFM, Zenobi R, De Los Rios P, Longo G, Dietler G. Hyperplectonemes: A Higher Order Compact and Dynamic DNA Self-Organization. NANO LETTERS 2017; 17:1938-1948. [PMID: 28191853 DOI: 10.1021/acs.nanolett.6b05294] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Bacterial chromosome has a compact structure that dynamically changes its shape in response to bacterial growth rate and growth phase. Determining how chromatin remains accessible to DNA binding proteins, and transcription machinery is crucial to understand the link between genetic regulation, DNA structure, and topology. Here, we study very large supercoiled dsDNA using high-resolution characterization, theoretical modeling, and molecular dynamics calculations. We unveil a new type of highly ordered DNA organization forming in the presence of attractive DNA-DNA interactions, which we call hyperplectonemes. We demonstrate that their formation depends on DNA size, supercoiling, and bacterial physiology. We compare structural, nanomechanic, and dynamic properties of hyperplectonemes bound by three highly abundant nucleoid-associated proteins (FIS, H-NS, and HU). In all these cases, the negative supercoiling of DNA determines molecular dynamics, modulating their 3D shape. Overall, our findings provide a mechanistic insight into the critical role of DNA topology in genetic regulation.
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Affiliation(s)
- Aleksandre Japaridze
- Laboratory of Physics of Living Matter, Ecole Polytechnique Fédérale de Lausanne , 1015 Lausanne, Switzerland
| | - Georgi Muskhelishvili
- Jacobs University , D-28759 Bremen, Germany
- Agricultural University of Georgia , 0159 Tbilisi, Georgia
| | - Fabrizio Benedetti
- Center for Integrative Genomics, University of Lausanne , 1015 Lausanne, Switzerland
- Vital-IT, SIB Swiss Institute of Bioinformatics , 1015 Lausanne, Switzerland
| | - Agni F M Gavriilidou
- Laboratory of Organic Chemistry, Department of Chemistry and Applied Biosciences, ETH Zurich , 8093 Zurich, Switzerland
| | - Renato Zenobi
- Laboratory of Organic Chemistry, Department of Chemistry and Applied Biosciences, ETH Zurich , 8093 Zurich, Switzerland
| | - Paolo De Los Rios
- Vital-IT, SIB Swiss Institute of Bioinformatics , 1015 Lausanne, Switzerland
- Laboratoire de Biophysique Statistique, Ecole Polytechnique Fédérale de Lausanne , 1015 Lausanne, Switzerland
| | - Giovanni Longo
- Laboratory of Physics of Living Matter, Ecole Polytechnique Fédérale de Lausanne , 1015 Lausanne, Switzerland
- Istituto di Struttura della Materia, Consiglio Nazionale delle Ricerche , Rome, Italy
| | - Giovanni Dietler
- Laboratory of Physics of Living Matter, Ecole Polytechnique Fédérale de Lausanne , 1015 Lausanne, Switzerland
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22
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Jain A, Dorfman KD. Simulations of knotting of DNA during genome mapping. BIOMICROFLUIDICS 2017; 11:024117. [PMID: 28798853 PMCID: PMC5533507 DOI: 10.1063/1.4979605] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2017] [Accepted: 03/21/2017] [Indexed: 05/28/2023]
Abstract
Genome mapping involves the confinement of long DNA molecules, in excess of 150 kilobase pairs, in nanochannels near the circa 50 nm persistence length of DNA. The fidelity of the map relies on the assumption that the DNA is linearized by channel confinement, which assumes the absence of knots. We have computed the probability of forming different knot types and the size of these knots for long chains (approximately 164 kilobase pairs) via pruned-enriched Rosenbluth method simulations of a discrete wormlike chain model of DNA in channel sizes ranging from 35 nm to 60 nm. Compared to prior simulations of short DNA in similar confinement, these long molecules exhibit both complex knots, with up to seven crossings, and multiple knots per chain. The knotting probability is a very strong function of channel size, ranging from 0.3% to 60%, and rationalized in the context of Odijk's theory for confined semiflexible chains. Overall, the knotting probability and knot size obtained from these equilibrium measurements are not consistent with experimental measurements of the properties of anomalously bright regions along the DNA backbone during genome mapping experiments. This result suggests that these events in experiments are either knots formed during the processing of the DNA prior to injection into the nanochannel or regions of locally high DNA concentration without a topological constraint. If so, knots during genome mapping are not an intrinsic problem for genome mapping technology.
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Affiliation(s)
- Aashish Jain
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
| | - Kevin D Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota-Twin Cities, 421 Washington Ave. SE, Minneapolis, Minnesota 55455, USA
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23
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Abstract
Long, flexible physical filaments are naturally tangled and knotted, from macroscopic string down to long-chain molecules. The existence of knotting in a filament naturally affects its configuration and properties, and may be very stable or disappear rapidly under manipulation and interaction. Knotting has been previously identified in protein backbone chains, for which these mechanical constraints are of fundamental importance to their molecular functionality, despite their being open curves in which the knots are not mathematically well defined; knotting can only be identified by closing the termini of the chain somehow. We introduce a new method for resolving knotting in open curves using virtual knots, which are a wider class of topological objects that do not require a classical closure and so naturally capture the topological ambiguity inherent in open curves. We describe the results of analysing proteins in the Protein Data Bank by this new scheme, recovering and extending previous knotting results, and identifying topological interest in some new cases. The statistics of virtual knots in protein chains are compared with those of open random walks and Hamiltonian subchains on cubic lattices, identifying a regime of open curves in which the virtual knotting description is likely to be important.
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24
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Affiliation(s)
- G. D’Adamo
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
| | - E. Orlandini
- Dipartimento
di Fisica e Astronomia, Università di Padova and Sezione INFN, Via Marzolo 8, I-35100 Padova, Italy
| | - C. Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
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25
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Coil-helix-globule transition for self-attractive semiflexible ring chains. POLYMER 2017. [DOI: 10.1016/j.polymer.2016.12.075] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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26
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Marenda M, Orlandini E, Micheletti C. Sorting ring polymers by knot type with modulated nanochannels. SOFT MATTER 2017; 13:795-802. [PMID: 28058437 DOI: 10.1039/c6sm02551j] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
In this theoretical study we discuss a novel method for sorting ring polymers according to their topological, knotted state. The proposed approach harnesses the rich dynamical behaviour of polymers confined inside spatially-modulated nanochannels. The longitudinal mobility of the rings is shown to have two key properties that are ideally suited for knot sorting. First, at fixed topology, the mobility has an intriguing oscillatory dependence on chain length. Second, the mobility ranking of different knot types is inverted upon increasing the chain length. We show that this complex interplay of channel geometry, chain length and topology can be rationalised within a simple theoretical framework based on Fick-Jacobs's diffusive theory. The results and the interpretative scheme ought to be useful for designing microfluidic devices with optimal topological sorting capabilities.
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Affiliation(s)
- Mattia Marenda
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia "Galileo Galilei", sezione CNISM, Università degli Studi di Padova, via Marzolo 8, I-35131 Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
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27
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28
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Ziebarth JD, Gardiner AA, Wang Y, Jeong Y, Ahn J, Jin Y, Chang T. Comparison of Critical Adsorption Points of Ring Polymers with Linear Polymers. Macromolecules 2016. [DOI: 10.1021/acs.macromol.6b01925] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- Jesse D. Ziebarth
- Department
of Chemistry, The University of Memphis, Memphis, Tennessee 38154, United States
| | - Abigail Anne Gardiner
- Department
of Chemistry, The University of Memphis, Memphis, Tennessee 38154, United States
| | - Yongmei Wang
- Department
of Chemistry, The University of Memphis, Memphis, Tennessee 38154, United States
| | - Youncheol Jeong
- Division of Advanced Materials
Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Junyoung Ahn
- Division of Advanced Materials
Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Ye Jin
- Division of Advanced Materials
Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
| | - Taihyun Chang
- Division of Advanced Materials
Science and Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 37673, Korea
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29
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Benková Z, Námer P, Cifra P. Comparison of a stripe and slab confinement for ring and linear macromolecules in nanochannel. SOFT MATTER 2016; 12:8425-8439. [PMID: 27722460 DOI: 10.1039/c6sm01507g] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
The combined effects of the channel asymmetry and the closed chain topology on the chain extension, structure factor, and the orientation correlations were studied using coarse-grained molecular dynamics simulations for moderate chain lengths. These effects are related to applications in linearization experiments with a DNA molecule in nanofluidic devices. According to the aspect ratio, the channels are classified as a stripe or slabs. The chain segments do not have any freedom to move in the direction of the narrowest stripe size, being approximately the same size as the segment size. The chains of both ring and linear topologies are extended more in a stripe than in a slab; this effect is strengthened for a ring. For a ring in a stripe, the extension-confinement strength dependence leads to effective Flory exponents even larger than 3/4, which is characteristic for a self-avoiding two-dimensional chain. While the chain extension-confinement strength dependence for both topologies conforms to the de Gennes regime in a stripe, a linear chain undergoes gradual transition to the pseudoideal regime as the slab height increases in the slab-like confinement. For a confined circle, the onset of the pseudoideal regime is shifted to larger slab heights. The structure factor confirms the absence of the pseudoideal and extended de Gennes regime in a stripe and the transition from the extended to the pseudoideal regime of a circular and linear chain upon increasing the slab heights.
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Affiliation(s)
- Zuzana Benková
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia. and LAQV@REQUIMTE, Department of Chemistry and Biochemistry, Faculty of Sciences, University of Porto, Rua do Campo Alegre 687, 4168-007 Porto, Portugal
| | - Pavol Námer
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia.
| | - Peter Cifra
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia.
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30
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D'Adamo G, Dietler G, Micheletti C. Tuning knot abundance in semiflexible chains with crowders of different sizes: a Monte Carlo study of DNA chains. SOFT MATTER 2016; 12:6708-6715. [PMID: 27443238 DOI: 10.1039/c6sm01327a] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We use stochastic simulation techniques to sample the conformational space of linear semiflexible polymers in a crowded medium and study how the knotting properties depend on the crowder size and concentration. The abundance of physical knots in the chains, which for definiteness we model on 10 kb long DNA filaments, is shown to have a non-monotonic, unimodal dependence on the colloid diameter, dc. The maximum incidence of knots occurs when dc is about equal to half of the gyration radius of the isolated chain. The degree of enhancement of knots grows rapidly with the solution density and can be very conspicuous relative to the case of isolated chains with no crowders. For instance, at 30% volume fraction the relative increase is more than fourfold. This dramatic enhancement is shown to originate from the depletion-induced chain compaction over multiple and concurring length scales. The same effect accounts for the variations of the knot length that accompany the changes in knotting probability. The findings suggest that crowded media could be viably used as a passive physical means for controlling and modulating the incidence and length of knots in DNA and other types of semiflexible polymers.
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Affiliation(s)
- Giuseppe D'Adamo
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
| | - Giovanni Dietler
- Institut de Physique des Systèmes Biologiques, Ecole Polytechnique Fédérale de Lausanne, BSP, CH-1015 Lausanne, Switzerland
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy.
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31
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Ziebarth JD, Wang Y. Interactions of complex polymers with nanoporous substrate. SOFT MATTER 2016; 12:5245-5256. [PMID: 27263839 DOI: 10.1039/c6sm00768f] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
With the advance of polymer synthesis, polymers that possess unique architectures such as stars or cyclic chains, and unique chemical composition distributions such as block copolymers or statistical copolymers have become frequently encountered. Characterization of these complex polymer systems drives the development of interactive chromatography where the adsorption of polymers on the porous substrate in chromatography columns is finely tuned. Liquid Chromatography at the Critical Condition (LCCC) in particular makes use of the existence of the Critical Adsorption Point (CAP) of polymers on solid surfaces and has been successfully applied to characterization of complex polymer systems. Interpretation and understanding of chromatography behaviour of complex polymers in interactive chromatography motivates theoretical/computational studies on the CAP of polymers and partitioning of these complex polymers near the CAP. This review article covers the theoretical questions encountered in chromatographic studies of complex polymers.
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Affiliation(s)
- Jesse D Ziebarth
- Department of Chemistry, The University of Memphis, Memphis, Tennessee, USA.
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32
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Dai L, Renner CB, Doyle PS. The polymer physics of single DNA confined in nanochannels. Adv Colloid Interface Sci 2016; 232:80-100. [PMID: 26782150 DOI: 10.1016/j.cis.2015.12.002] [Citation(s) in RCA: 73] [Impact Index Per Article: 9.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2015] [Revised: 12/01/2015] [Accepted: 12/01/2015] [Indexed: 11/17/2022]
Abstract
In recent years, applications and experimental studies of DNA in nanochannels have stimulated the investigation of the polymer physics of DNA in confinement. Recent advances in the physics of confined polymers, using DNA as a model polymer, have moved beyond the classic Odijk theory for the strong confinement, and the classic blob theory for the weak confinement. In this review, we present the current understanding of the behaviors of confined polymers while briefly reviewing classic theories. Three aspects of confined DNA are presented: static, dynamic, and topological properties. The relevant simulation methods are also summarized. In addition, comparisons of confined DNA with DNA under tension and DNA in semidilute solution are made to emphasize universal behaviors. Finally, an outlook of the possible future research for confined DNA is given.
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Affiliation(s)
- Liang Dai
- BioSystems and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602, Singapore
| | - C Benjamin Renner
- Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, United States
| | - Patrick S Doyle
- BioSystems and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, 138602, Singapore; Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, United States.
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33
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Li B, Sun ZY, An LJ, Wang ZG. Influence of Topology on the Free Energy and Metric Properties of an Ideal Ring Polymer Confined in a Slit. Macromolecules 2015. [DOI: 10.1021/acs.macromol.5b02026] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Bing Li
- State Key Laboratory of Polymer Physics and Chemistry,
Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China
| | - Zhao-Yan Sun
- State Key Laboratory of Polymer Physics and Chemistry,
Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China
- Xinjiang
Laboratory of Phase Transitions and Microstructures in Condensed Matters,
College of Physical Science and Technology, Yili Normal University, Yining, 835000, China
| | - Li-Jia An
- State Key Laboratory of Polymer Physics and Chemistry,
Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China
| | - Zhen-Gang Wang
- State Key Laboratory of Polymer Physics and Chemistry,
Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China
- Division
of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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34
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Vargas-Lara F, Stavis SM, Strychalski EA, Nablo BJ, Geist J, Starr FW, Douglas JF. Dimensional reduction of duplex DNA under confinement to nanofluidic slits. SOFT MATTER 2015; 11:8273-8284. [PMID: 26353028 DOI: 10.1039/c5sm01580d] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
There has been much interest in the dimensional properties of double-stranded DNA (dsDNA) confined to nanoscale environments as a problem of fundamental importance in both biological and technological fields. This has led to a series of measurements by fluorescence microscopy of single dsDNA molecules under confinement to nanofluidic slits. Despite the efforts expended on such experiments and the corresponding theory and simulations of confined polymers, a consistent description of changes of the radius of gyration of dsDNA under strong confinement has not yet emerged. Here, we perform molecular dynamics (MD) simulations to identify relevant factors that might account for this inconsistency. Our simulations indicate a significant amplification of excluded volume interactions under confinement at the nanoscale due to the reduction of the effective dimensionality of the system. Thus, any factor influencing the excluded volume interaction of dsDNA, such as ionic strength, solution chemistry, and even fluorescent labels, can greatly influence the dsDNA size under strong confinement. These factors, which are normally less important in bulk solutions of dsDNA at moderate ionic strengths because of the relative weakness of the excluded volume interaction, must therefore be under tight control to achieve reproducible measurements of dsDNA under conditions of dimensional reduction. By simulating semi-flexible polymers over a range of parameter values relevant to the experimental systems and exploiting past theoretical treatments of the dimensional variation of swelling exponents and prefactors, we have developed a novel predictive relationship for the in-plane radius of gyration of long semi-flexible polymers under slit-like confinement. Importantly, these analytic expressions allow us to estimate the properties of dsDNA for the experimentally and biologically relevant range of contour lengths that is not currently accessible by state-of-the-art MD simulations.
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Affiliation(s)
- Fernando Vargas-Lara
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
| | - Samuel M Stavis
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Elizabeth A Strychalski
- Biosystems and Biomaterials Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Brian J Nablo
- Semiconductor and Dimensional Metrology Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Jon Geist
- Semiconductor and Dimensional Metrology Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Francis W Starr
- Department of Physics and Department of Molecular Biology and Biochemistry, Wesleyan University, Middletown, CT 06459, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA.
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35
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Caraglio M, Micheletti C, Orlandini E. Stretching Response of Knotted and Unknotted Polymer Chains. PHYSICAL REVIEW LETTERS 2015; 115:188301. [PMID: 26565504 DOI: 10.1103/physrevlett.115.188301] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2015] [Indexed: 06/05/2023]
Abstract
Recent theoretical and experimental advances have clarified the major effects of knotting on the properties of stretched chains. Yet, how knotted chains respond to weak mechanical stretching and how this behavior differs from the unknotted case are still open questions and we address them here by profiling the complete stretching response of chains of hundreds of monomers and different topology. We find that the ratio of the knotted and unknotted chain extensions varies nonmonotonically with the applied force. This surprising feature is shown to be a signature of the crossover between the well-known high-force stretching regime and the previously uncharacterized low-force one. The observed differences of knotted and unknotted chain response increases with knot complexity and are sufficiently marked that they could be harnessed in single-molecule contexts to infer the presence and complexity of physical knots in micron-long biomolecules.
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Affiliation(s)
- Michele Caraglio
- Dipartimento di Fisica e Astronomia Università di Padova and sezione CNISM, Via Marzolo 8, I-35131 Padova, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia Università di Padova and sezione INFN, Via Marzolo 8, I-35131 Padova, Italy
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36
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Suma A, Orlandini E, Micheletti C. Knotting dynamics of DNA chains of different length confined in nanochannels. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2015; 27:354102. [PMID: 26291786 DOI: 10.1088/0953-8984/27/35/354102] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
Langevin dynamics simulations are used to characterize the typical mechanisms governing the spontaneous tying, untying and the dynamical evolution of knots in coarse-grained models of DNA chains confined in nanochannels. In particular we focus on how these mechanisms depend on the chain contour length, Lc, at a fixed channel width D = 56 nm corresponding to the onset of the Odijk scaling regime where chain backfoldings and hence knots are disfavoured but not suppressed altogether. We find that the lifetime of knots grows significantly with Lc, while that of unknots varies to a lesser extent. The underlying kinetic mechanisms are clarified by analysing the evolution of the knot position along the chain. At the considered confinement, in fact, knots are typically tied by local backfoldings of the chain termini where they are eventually untied after a stochastic motion along the chain. Consequently, the lifetime of unknots is mostly controlled by backfoldings events at the chain ends, which is largely independent of Lc. The lifetime of knots, instead, increases significantly with Lc because knots can, on average, travel farther along the chain before being untied. The observed interplay of knots and unknots lifetimes underpins the growth of the equilibrium knotting probability of longer and longer chains at fixed channel confinement.
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Affiliation(s)
- Antonio Suma
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
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37
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Affiliation(s)
- Giuseppe D’Adamo
- SISSA, International School for Advanced
Studies, via Bonomea 265, I-34136 Trieste, Italy
| | - Cristian Micheletti
- SISSA, International School for Advanced
Studies, via Bonomea 265, I-34136 Trieste, Italy
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38
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Li B, Sun ZY, An LJ. Effects of topology on the adsorption of singly tethered ring polymers to attractive surfaces. J Chem Phys 2015; 143:024908. [DOI: 10.1063/1.4926775] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Bing Li
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China and Graduate School of the Chinese Academy of Sciences, Beijing 10039, People’s Republic of China
| | - Zhao-Yan Sun
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China and Graduate School of the Chinese Academy of Sciences, Beijing 10039, People’s Republic of China
| | - Li-Jia An
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China and Graduate School of the Chinese Academy of Sciences, Beijing 10039, People’s Republic of China
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39
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Chen W, Zhao H, Liu L, Chen J, Li Y, An L. Effects of excluded volume and hydrodynamic interaction on the deformation, orientation and motion of ring polymers in shear flow. SOFT MATTER 2015; 11:5265-5273. [PMID: 26053427 DOI: 10.1039/c5sm00837a] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
A ring polymer is a classical model to explore the behaviors of biomacromolecules. Compared with its linear counterpart in shear flow, the ring polymer should be more sensitive to excluded volume and hydrodynamic interaction attributed to the absence of chain ends. We carried out multiparticle collision dynamics combined with molecular dynamics simulation to study the effects of excluded volume and hydrodynamic interaction on the behaviors of ring polymers in shear flow. The results show that in the absence of the strong excluded volume interaction, the ring polymer prefers a two-strand linear conformation with high deformation and orientation in the flow-gradient plane, and the tank-treading motion is nearly negligible. Ring polymers without excluded volume show no significant difference from linear polymers in the scaling exponents for the deformation, orientation and tumbling motion. We also observed that the hydrodynamic interaction could efficiently slow down the relaxation of ring polymers while the scaling exponents against the Weissenberg number have rarely been affected.
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Affiliation(s)
- Wenduo Chen
- Key Laboratory of Synthetic Rubber & Laboratory of Advanced Power Sources, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, 5625 Renmin Street, Changchun, P. R. China130022.
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40
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Chen W, Li Y, Zhao H, Liu L, Chen J, An L. Conformations and dynamics of single flexible ring polymers in simple shear flow. POLYMER 2015. [DOI: 10.1016/j.polymer.2015.03.034] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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41
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Renner CB, Doyle PS. Stretching self-entangled DNA molecules in elongational fields. SOFT MATTER 2015; 11:3105-3114. [PMID: 25693945 DOI: 10.1039/c4sm02738h] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present experiments of self-entangled DNA molecules stretching under a planar elongational field, and their stretching dynamics are compared to identical molecules without entanglements. Self-entangled molecules stretch in a stage-wise fashion, persisting in an "arrested" state for decades of strain prior to rapidly stretching, slowing down the stretching dynamics by an order of magnitude compared to unentangled molecules. Self-entangled molecules are shown to proceed through a transient state where one or two ends of the molecule are protruding from an entangled, knotted core. This phenomenon sharply contrasts with the wide array of transient configurations shown here and by others for stretching polymers without entanglements. The rate at which self-entangled molecules stretch through this transient state is demonstrably slower than unentangled molecules, providing the first direct experimental evidence of a topological friction. These experimental observations are shown to be qualitatively and semi-quantitatively reproduced by a dumbbell model with two fitting parameters, the values of which are reasonable in light of previous experiments of knotted DNA.
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Affiliation(s)
- C Benjamin Renner
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
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42
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Affiliation(s)
- Liang Dai
- BioSystems
and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore 138602
| | - C. Benjamin Renner
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Patrick S. Doyle
- BioSystems
and Micromechanics (BioSyM) IRG, Singapore-MIT Alliance for Research and Technology (SMART) Centre, Singapore 138602
- Department
of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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43
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Benková Z, Námer P, Cifra P. Stripe to slab confinement for the linearization of macromolecules in nanochannels. SOFT MATTER 2015; 11:2279-2289. [PMID: 25651783 DOI: 10.1039/c4sm02382j] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We investigated the recently suggested advantageous analysis of chain linearization experiments with macromolecules confined in a stripe-like channel (Huang and Battacharya, EPL, 2014, 106, 18004) using Monte Carlo simulations. The enhanced chain extension in a stripe, which is due to the significant excluded volume interactions between the monomers in two dimensions, weakens considerably on transition to an experimentally feasible slit-like channel. Based on the chain extension-confinement strength dependence and the structure factor behavior for a chain in a stripe, we infer the excluded volume regime (de Gennes regime) typical for two-dimensional systems. On widening of the stripe in a direction perpendicular to the stripe plane, i.e. on the transition to the slab geometry, the advantageous chain extension decreases and a Gaussian regime is observed for not very long semiflexible chains. The evidence for pseudo-ideality in confined chains is based on four indicators: the extension curves, variation of the extension with the persistence length P, estimated limits for the regimes in the investigated systems, and the structure factor behavior. The slab behavior can be observed when the two-dimensional stripe (originally of a one-monomer thickness) reaches a reduced thickness D larger than approximately D/P ≈ 0.2 in the third dimension. This maximum height of a slab at which the advantage of a stripe is retained is very low and has implications for DNA linearization experiments.
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Affiliation(s)
- Zuzana Benková
- Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 845 41 Bratislava, Slovakia.
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Abstract
We present Brownian dynamics simulations of initially knotted double-stranded DNA molecules untying in elongational flows. We show that the motions of the knots are governed by a diffusion-convection equation by deriving scalings that collapse the simulation data. When being convected, all knots displace nonaffinely, and their rates of translation along the chain are topologically dictated. We discover that torus knots "corkscrew" when driven by flow, whereas nontorus knots do not. We show that a simple mechanism can explain a coupling between this rotation and the translation of a knot, explaining observed differences in knot translation rates. These types of knots are encountered in nanoscale manipulation of DNA, occur in biology at multiple length scales (DNA to umbilical cords), and are ubiquitous in daily life (e.g., hair). These results may have a broad impact on manipulations of such knots via flows, with applications to genomic sequencing and polymer processing.
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Affiliation(s)
- C. Benjamin Renner
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Patrick S. Doyle
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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Micheletti C, Orlandini E. Knotting and Unknotting Dynamics of DNA Strands in Nanochannels. ACS Macro Lett 2014; 3:876-880. [PMID: 35596352 DOI: 10.1021/mz500402s] [Citation(s) in RCA: 55] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
The self-knotting dynamics of DNA strands confined in nanochannels is studied with Brownian simulations. The model DNA chains are several microns long and placed inside channels that are 50-300 nm wide. This width range covers the transition between different metric scaling regimes and the concomitant drop of DNA knotting probability for channel widths below ∼75 nm. We find that knots typically originate from deep looping and backfoldings of the chain ends. Upon lowering the channel width, backfoldings become shallower and rarer and the lifetime of knots decreases while that of unknots increases. This lifetimes interplay causes the dramatic reduction of knots incidence for increasing confinement. The results can aid the design of nanochannels capable of harnessing the self-knotting dynamics to quench or relax the DNA topological state as desired.
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Affiliation(s)
- Cristian Micheletti
- SISSA, International School for Advanced Studies, via Bonomea 265, I-34136 Trieste, Italy
| | - Enzo Orlandini
- Dipartimento
di Fisica, Sezione CNISM, and Università di Padova, via Marzolo 8, I-35131 Padova, Italy
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Poier P, Likos CN, Matthews R. Influence of Rigidity and Knot Complexity on the Knotting of Confined Polymers. Macromolecules 2014; 47:3394-3400. [PMID: 24882882 PMCID: PMC4037316 DOI: 10.1021/ma5006414] [Citation(s) in RCA: 53] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2014] [Revised: 05/05/2014] [Indexed: 02/01/2023]
Abstract
We employ computer simulations and thermodynamic integration to analyze the effects of bending rigidity and slit confinement on the free energy cost of tying knots, ΔFknotting, on polymer chains under tension. A tension-dependent, nonzero optimal stiffness κmin exists, for which ΔFknotting is minimal. For a polymer chain with several stiffness domains, each containing a large amount of monomers, the domain with stiffness κmin will be preferred by the knot. A local analysis of the bending in the interior of the knot reveals that local stretching of chains at the braid region is responsible for the fact that the tension-dependent optimal stiffness has a nonzero value. The reduction in ΔFknotting for a chain with optimal stiffness relative to the flexible chain can be enhanced by tuning the slit width of the 2D confinement and increasing the knot complexity. The optimal stiffness itself is independent of the knot types we considered, while confinement shifts it toward lower values.
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Affiliation(s)
- Peter Poier
- Faculty of Physics, University of Vienna , Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Christos N Likos
- Faculty of Physics, University of Vienna , Boltzmanngasse 5, A-1090 Vienna, Austria
| | - Richard Matthews
- Faculty of Physics, University of Vienna , Boltzmanngasse 5, A-1090 Vienna, Austria
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47
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Tubiana L. Computational study on the progressive factorization of composite polymer knots into separated prime components. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:052602. [PMID: 25353821 DOI: 10.1103/physreve.89.052602] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2013] [Indexed: 06/04/2023]
Abstract
Using Monte Carlo simulations and advanced knot localization methods, we analyze the length and distribution of prime components in composite knots tied on freely jointed rings. For increasing contour length, we observe the progressive factorization of composite knots into separated prime components. However, we observe that a complete factorization, equivalent to the "decorated ring" picture, is not obtained even for rings of contour lengths N ≃ 3 N(0), about tens of times the most probable length of the prime knots tied on the rings. The decorated ring hypothesis has been used in the literature to justify the factorization of composite knot probabilities into the knotting probabilities of their prime components. Following our results, we suggest that such a hypothesis may not be necessary to explain the factorization of the knotting probabilities, at least when polymers excluding volume is not relevant. We rationalize the behavior of the system through a simple one-dimensional model in which prime knots are replaced by slip links randomly placed on a circle, with the only constraint being that the length of the loops has the same distribution as that of the length of the corresponding prime knots.
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Affiliation(s)
- Luca Tubiana
- Department of Theoretical Physics, Jožef Stefan Institute, Jamova cesta 39, SI-1000 Ljubljana (Slovenia) and SISSA-Scuola Internazionale Superiore di Studi Avanzati Via Bonomea 265, 34136 Trieste, Italy
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48
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Santalla SN, Rodríguez-Laguna J, Cuerno R. Circular Kardar-Parisi-Zhang equation as an inflating, self-avoiding ring polymer. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:010401. [PMID: 24580156 DOI: 10.1103/physreve.89.010401] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2013] [Indexed: 06/03/2023]
Abstract
We consider the Kardar-Parisi-Zhang equation for a circular interface in two dimensions, unconstrained by the standard small-slope and no-overhang approximations. Numerical simulations using an adaptive scheme allow us to elucidate the complete time evolution as a crossover between a short-time regime with the interface fluctuations of a self-avoiding ring or two-dimensional vesicle, and a long-time regime governed by the Tracy-Widom distribution expected for this geometry. For small-noise amplitudes, scaling behavior is only of the latter type. Large noise is also seen to renormalize the bare physical parameters of the ring, akin to analogous parameter renormalization for equilibrium three-dimensional membranes. Our results bear particular importance on the relation between relevant universality classes of scale-invariant systems in two dimensions.
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Affiliation(s)
- Silvia N Santalla
- Departamento de Física and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Carlos III de Madrid, Leganés, Spain
| | - Javier Rodríguez-Laguna
- ICFO-Institut de Ciències Fotòniques, Castelldefels, Spain and Departamento de Matemáticas and GISC, Universidad Carlos III de Madrid, Leganés, Spain
| | - Rodolfo Cuerno
- Departamento de Matemáticas and GISC, Universidad Carlos III de Madrid, Leganés, Spain
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49
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Chen W, Chen J, Liu L, Xu X, An L. Effects of Chain Stiffness on Conformational and Dynamical Properties of Individual Ring Polymers in Shear Flow. Macromolecules 2013. [DOI: 10.1021/ma401137c] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Wenduo Chen
- State Key Laboratory of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Jizhong Chen
- State Key Laboratory of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Lijun Liu
- State Key Laboratory of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Xiaolei Xu
- State Key Laboratory of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
| | - Lijia An
- State Key Laboratory of Polymer
Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, People’s Republic of China
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50
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Orlandini E, Micheletti C. Knotting of linear DNA in nano-slits and nano-channels: a numerical study. J Biol Phys 2013; 39:267-75. [PMID: 23860873 PMCID: PMC3662413 DOI: 10.1007/s10867-013-9305-0] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2012] [Accepted: 02/07/2013] [Indexed: 12/23/2022] Open
Abstract
The amount and type of self-entanglement of DNA filaments is significantly affected by spatial confinement, which is ubiquitous in biological systems. Motivated by recent advancements in single DNA molecule experiments based on nanofluidic devices and by the introduction of algorithms capable of detecting knots in open chains, we investigate numerically the entanglement of linear, open DNA chains confined inside nano-slits. The results regard the abundance, type, and length of occurring knots and are compared with recent findings for DNA inside nano-channels. In both cases, the width of the confining region, D, spans the 30 nm-1 μm range and the confined DNA chains are 1-4 μm long. It is found that the knotting probability is maximum for slit widths in the 70-100 nm range. However, over the considered DNA contour lengths, the maximum incidence of knots remains below 20%, while for channel confinement it tops 50%. Further differences of the entanglement are seen for the average contour length of the knotted region, which drops significantly below D ~100 nm for channel-confinement, while it stays approximately constant for slit-like confinement. These properties ought to reverberate in different kinetic properties of linear DNA depending on confinement and could be detectable experimentally or exploitable in nano-technological applications.
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Affiliation(s)
- Enzo Orlandini
- />Dipartimento di Fisica e Astronomia and Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
| | - Cristian Micheletti
- />SISSA - Scuola Internazionale Superiore di Studi Avanzati and CNR-IOM Democritos, Via Bonomea 265, 34136 Trieste, Italy
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