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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Kk S, Persson F, Fritzsche J, Beech JP, Tegenfeldt JO, Westerlund F. Fluorescence Microscopy of Nanochannel-Confined DNA. Methods Mol Biol 2024; 2694:175-202. [PMID: 37824005 DOI: 10.1007/978-1-0716-3377-9_9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/13/2023]
Abstract
Stretching of DNA in nanoscale confinement allows for several important studies. The genetic contents of the DNA can be visualized on the single DNA molecule level, and the polymer physics of confined DNA and also DNA/protein and other DNA/DNA-binding molecule interactions can be explored. This chapter describes the basic steps to fabricate the nanostructures, perform the experiments, and analyze the data.
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Affiliation(s)
- Sriram Kk
- Department of Life Sciences, Chalmers University of Technology, Gothenburg, Sweden
| | | | - Joachim Fritzsche
- Department of Physics, Chalmers University of Technology, Gothenburg, Sweden
| | - Jason P Beech
- NanoLund and Department of Physics, Lund University, Lund, Sweden
| | | | - Fredrik Westerlund
- Department of Life Sciences, Chalmers University of Technology, Gothenburg, Sweden.
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3
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Lyu K, Zhao Y, Zhang M, Tang J, Zhang J, Liu Y, Bian X, Chen X, Chen H, Wang D. Tracking of Protein Adsorption on Poly(l-lactic acid) Film Surfaces: The Role of Molar Mass. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:13534-13545. [PMID: 37712535 DOI: 10.1021/acs.langmuir.3c01571] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/16/2023]
Abstract
Poly(l-lactic acid) (PLLA) has been extensively utilized as a biomaterial for various biomedical applications. The first and one of the most critical steps upon contact with biological fluids is the adsorption of proteins on the material's surface. Understanding the behavior of protein adsorption is vital for guiding the synthesis and preparation of PLLA for biomedical purposes. In this study, total internal reflection fluorescence microscopy was employed to investigate the adsorption of human serum albumin (HSA) on PLLA films with different molar masses. We found that molar mass affects HSA adsorption in such a way that it affects only the adsorption rate constants, but not the desorption rate constants. Additionally, we observed that HSA adsorption is spatially heterogeneous and exhibits many strong binding sites regardless of the molar mass of the PLLA films. We found that the free volume of PLLA plays a crucial role in determining its water uptake capacity and surface hydration, consequently impacting the adsorption of HSA.
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Affiliation(s)
- Kaixuan Lyu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
- School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei 230026, P. R. China
| | - Yuehua Zhao
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Miaomiao Zhang
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jilin Tang
- State Key Laboratory of Electroanalytical Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Jidong Zhang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Yanlong Liu
- Key Laboratory of Polymer Ecomaterials, Chinese Academy of Sciences, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Xinchao Bian
- Key Laboratory of Polymer Ecomaterials, Chinese Academy of Sciences, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Xuesi Chen
- Key Laboratory of Polymer Ecomaterials, Chinese Academy of Sciences, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Hongbo Chen
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
| | - Dapeng Wang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, P. R. China
- School of Applied Chemistry and Engineering, University of Science and Technology of China, Hefei 230026, P. R. China
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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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Chiarantoni P, Micheletti C. Linear Catenanes in Channel Confinement. Macromolecules 2023. [DOI: 10.1021/acs.macromol.3c00249] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
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6
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Chen Y, Tian X, Xu X, Xu WS, Chen J. Investigation of Markovian and Non-Markovian Search Processes of Monomers of a Rouse Chain Confined in a Spherical Cavity. Macromolecules 2023. [DOI: 10.1021/acs.macromol.2c01877] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Affiliation(s)
- Ye Chen
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun130022, P. R. China
- University of Science and Technology of China, Hefei230026, P. R. China
| | - Xiaofei Tian
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun130022, P. R. China
- University of Science and Technology of China, Hefei230026, P. R. China
| | - Xiaolei Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun130022, P. R. China
| | - Wen-Sheng Xu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun130022, P. R. China
- University of Science and Technology of China, Hefei230026, P. R. China
| | - Jizhong Chen
- School of Chemical Engineering and Light Industry, Guangdong University of Technology, Guangzhou510006, P. R. China
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7
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Tagliabue A, Micheletti C, Mella M. Tuning Knotted Copolyelectrolyte Conformations via Solution Properties. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c01933] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Affiliation(s)
- Andrea Tagliabue
- Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, 22100Como, Italy
- SISSA (Scuola Internazionale Superiore di Studi Avanzati), via Bonomea 265, 34136Trieste, Italy
| | - Cristian Micheletti
- SISSA (Scuola Internazionale Superiore di Studi Avanzati), via Bonomea 265, 34136Trieste, Italy
| | - Massimo Mella
- Dipartimento di Scienza ed Alta Tecnologia, Università degli Studi dell’Insubria, via Valleggio 11, 22100Como, Italy
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8
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Knot Factories with Helical Geometry Enhance Knotting and Induce Handedness to Knots. Polymers (Basel) 2022; 14:polym14194201. [PMID: 36236148 PMCID: PMC9572405 DOI: 10.3390/polym14194201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2022] [Revised: 09/25/2022] [Accepted: 10/05/2022] [Indexed: 11/06/2022] Open
Abstract
We performed molecular dynamics simulations of DNA polymer chains confined in helical nano-channels under compression in order to explore the potential of knot-factories with helical geometry to produce knots with a preferred handedness. In our simulations, we explore mutual effect of the confinement strength and compressive forces in a range covering weak, intermediate and strong confinement together with weak and strong compressive forces. The results find that while the common metrics of polymer chain in cylindrical and helical channels are very similar, the DNA in helical channels exhibits greatly different topology in terms of chain knottedness, writhe and handedness of knots. The results show that knots with a preferred chirality in terms of average writhe can be produced by using channels with a chosen handedness.
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9
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Zeng L, Reisner WW. Organized states arising from compression of single semiflexible polymer chains in nanochannels. Phys Rev E 2022; 105:064501. [PMID: 35854522 DOI: 10.1103/physreve.105.064501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Accepted: 04/11/2022] [Indexed: 06/15/2023]
Abstract
We use molecular dynamics simulation to probe the nonequilibrium physics of single nanochannel-confined semiflexible polymers in a homogeneous flow field. The flow field compresses the polymer against the end of the nanochannel, simulating an experiment of a nanochannel confined chain compressed against a slit barrier. The flow-based compression gives rise to a packing of the chain against the channel end that possesses a striking organization, consisting of interweaving of folds and circular coils. For stiff chains at low flow, we find that the organization is dominated by repeated hairpin folds. For stiff chains at higher flow, we observe that circular coils arise along with the folds, with folding and coiling domains becoming interwoven at the highest flow speeds. Chain organization is retained even when the chain persistence length is on order of the channel width. We show that the global polymer organization, consisting of a number of defined folds and coiled loops, arises from the minimization of the total chain free energy.
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Affiliation(s)
- Lili Zeng
- Department of Physics, McGill University, 3600 University Street, Montreal, Quebec H3A 2T8, Canada
| | - Walter W Reisner
- Department of Physics, McGill University, 3600 University Street, Montreal, Quebec H3A 2T8, Canada
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10
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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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11
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Tagliabue A, Micheletti C, Mella M. Tunable Knot Segregation in Copolyelectrolyte Rings Carrying a Neutral Segment. ACS Macro Lett 2021; 10:1365-1370. [PMID: 35549022 DOI: 10.1021/acsmacrolett.1c00453] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We use Langevin dynamics simulations to study the knotting properties of copolyelectrolyte rings carrying neutral segments. We show that by solely tuning the relative length of the neutral and charged blocks, one can achieve different combinations of knot contour position and size. Strikingly, the latter is shown to vary nonmonotonically with the length of the neutral segment; at the same time, the knot switches from being pinned at the block's edge to becoming trapped inside it. Model calculations relate both effects to the competition between two adversarial mechanisms: the energy gain of localizing one or more of the knot's essential crossings on the neutral segment and the entropic cost of such localization. Tuning the length of the neutral segment sets the balance between the two mechanisms and hence the number of localized essential crossings, which in turn modulates the knot's size. This general principle ought to be useful in more complex systems, such as multiblock copolyelectrolytes, to achieve a more granular control of topological constraints.
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Affiliation(s)
- Andrea Tagliabue
- Dipartimento di Scienza ed Alta Tecnologia, Universitá degli Studi dell’Insubria, via Valleggio 11, 22100, Como, Italy
| | - Cristian Micheletti
- SISSA (Scuola Internazionale Superiore di Studi Avanzati), via Bonomea 265, 34136, Trieste, Italy
| | - Massimo Mella
- Dipartimento di Scienza ed Alta Tecnologia, Universitá degli Studi dell’Insubria, via Valleggio 11, 22100, Como, Italy
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12
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Rusková R, Račko D. Channels with Helical Modulation Display Stereospecific Sensitivity for Chiral Superstructures. Polymers (Basel) 2021; 13:3726. [PMID: 34771282 PMCID: PMC8588256 DOI: 10.3390/polym13213726] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2021] [Revised: 10/23/2021] [Accepted: 10/23/2021] [Indexed: 01/03/2023] Open
Abstract
By means of coarse-grained molecular dynamics simulations, we explore chiral sensitivity of confining spaces modelled as helical channels to chiral superstructures represented by polymer knots. The simulations show that helical channels exhibit stereosensitivity to chiral knots localized on linear chains by effect of external pulling force and also to knots embedded on circular chains. The magnitude of the stereoselective effect is stronger for torus knots, the effect is weaker in the case of twist knots, and amphichiral knots do exhibit no chiral effects. The magnitude of the effect can be tuned by the so-far investigated radius of the helix, the pitch of the helix and the strength of the pulling force. The model is aimed to simulate and address a range of practical situations that may occur in experimental settings such as designing of nanotechnological devices for the detection of topological state of molecules, preparation of new gels with tailor made stereoselective properties, or diffusion of knotted DNA in biological conditions.
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Affiliation(s)
- Renáta Rusková
- Polymer Institute, Slovak Academy of Sciences, Dúbravská Cesta 3, 84541 Bratislava, Slovakia;
- Department of Plastics, Rubber and Fibres (IPM FCFT), Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 81237 Bratislava, Slovakia
| | - Dušan Račko
- Polymer Institute, Slovak Academy of Sciences, Dúbravská Cesta 3, 84541 Bratislava, Slovakia;
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13
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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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14
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Ma Z, Dorfman KD. Interactions between two knots in nanochannel-confined DNA molecules. J Chem Phys 2021; 155:154901. [PMID: 34686050 DOI: 10.1063/5.0067076] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Experimental data on the interaction between two knots in deoxyribonucleic acid (DNA) confined in nanochannels produced two particular behaviors of knot pairs along the DNA molecules: (i) widely separated knots experience an attractive interaction but only remain in close proximity for several seconds and (ii) knots tend to remain separated until one of the knots unravels at the chain end. The associated free energy profile of the knot-knot separation distance for an ensemble of DNA knots exhibits a global minimum when knots are separated, indicating that the separated knot state is more stable than the intertwined knot state, with dynamics in the separated knot state that are consistent with independent diffusion. The experimental observations of knot-knot interactions under nanochannel confinement are inconsistent with previous simulation-based and experimental results for stretched polymers under tension wherein the knots attract and then stay close to each other. This inconsistency is postulated to result from a weaker fluctuation-induced attractive force between knots under confinement when compared to the knots under tension, the latter of which experience larger fluctuations in transverse directions.
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Affiliation(s)
- Zixue Ma
- 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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15
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Park CB, Sung BJ. Effects of Packaging History on the Ejection of a Polymer Chain from a Small Confinement. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00857] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Affiliation(s)
- Chung Bin Park
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 04107, Republic of Korea
| | - Bong June Sung
- Department of Chemistry and Research Institute for Basic Science, Sogang University, Seoul 04107, Republic of Korea
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16
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Ma Z, Dorfman KD. Diffusion of Knotted DNA Molecules in Nanochannels in the Extended de Gennes Regime. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00143] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Zixue Ma
- Department of Chemical Engineering and Materials Science, University of Minnesota−Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
| | - Kevin D. Dorfman
- Department of Chemical Engineering and Materials Science, University of Minnesota−Twin Cities, 421 Washington Ave SE, Minneapolis, Minnesota 55455, United States
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17
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Gendron I, Savard K, Capaldi X, Liu Z, Zeng L, Reisner W, Capaldi L. Time-dependent knotting of agitated chains. Phys Rev E 2021; 103:032501. [PMID: 33862677 DOI: 10.1103/physreve.103.032501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2020] [Accepted: 02/19/2021] [Indexed: 11/07/2022]
Abstract
Agitated strings serve as macroscale models of spontaneous knotting, providing valuable insight into knotting dynamics at the microscale while allowing explicit analysis of the resulting knot topologies. We present an experimental setup for confined macroscale knot formation via tumbling along with a software interface to process complex knot data. Our setup allows characterization of knotting probability, knot complexity, and knot formation dynamics for knots with as many as 50 crossings. We find that the probability of knotting saturates below 80% within 100 s of the initiation of tumbling and that this saturation probability does not increase for chains above a critical length, an indication of nonequilibrium knot-formation conditions in our experiment. Despite the saturation in knot formation, we show that longer chains, while being more confined, will always tend to form knots of higher complexity since the free end can access a greater number of loops during tumbling.
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Affiliation(s)
- Ingrid Gendron
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Katherine Savard
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Xavier Capaldi
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Zezhou Liu
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Lili Zeng
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Walter Reisner
- Physics Department, McGill University, 3600 rue University, Montreal, Canada
| | - Luc Capaldi
- Department of Mechanical Engineering, University of Vermont, Burlington, Vermont 05405, USA
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18
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Zhu H, Tian F, Sun L, Wang S, Dai L. Revisiting the Non-monotonic Dependence of Polymer Knotting Probability on the Bending Stiffness. Macromolecules 2021. [DOI: 10.1021/acs.macromol.0c02640] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Haoqi Zhu
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Fujia Tian
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Liang Sun
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Simin Wang
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
| | - Liang Dai
- Department of Physics, City University of Hong Kong, Kowloon 999077, Hong Kong, P. R. China
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19
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Polson JM, Hastie CG. Free energy of a knotted polymer confined to narrow cylindrical and conical channels. Phys Rev E 2020; 102:052502. [PMID: 33327190 DOI: 10.1103/physreve.102.052502] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Accepted: 10/16/2020] [Indexed: 06/12/2023]
Abstract
Monte Carlo simulations are used to study the conformational behavior of a semiflexible polymer confined to cylindrical and conical channels. The channels are sufficiently narrow that the conditions for the Odijk regime are marginally satisfied. For cylindrical confinement, we examine polymers with a single knot of topology 3_{1}, 4_{1}, or 5_{1}, as well as unknotted polymers that are capable of forming S loops. We measure the variation of the free energy F with the end-to-end polymer extension length X and examine the effect of varying the polymer topology, persistence length P, and cylinder diameter D on the free-energy functions. Similarly, we characterize the behavior of the knot span along the channel. We find that increasing the knot complexity increases the typical size of the knot. In the regime of low X, where the knot/S-loop size is large, the conformational behavior is independent of polymer topology. In addition, the scaling properties of the free energy and knot span are in agreement with predictions from a theoretical model constructed using known properties of interacting polymers in the Odijk regime. We also examine the variation of F with the position of a knot in conical channels for various values of the cone angle α. The free energy decreases as the knot moves in a direction where the cone widens, and it also decreases with increasing α and with increasing knot complexity. The behavior is in agreement with predictions from a theoretical model in which the dominant contribution to the change in F is the change in the size of the hairpins as the knot moves to the wider region of the channel.
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Affiliation(s)
- James M Polson
- Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island, C1A 4P3, Canada
| | - Cameron G Hastie
- Department of Physics, University of Prince Edward Island, 550 University Ave., Charlottetown, Prince Edward Island, C1A 4P3, Canada
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