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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Becerra D, Klotz AR, Hall LM. Single-molecule analysis of solvent-responsive mechanically interlocked ring polymers and the effects of nanoconfinement from coarse-grained simulations. J Chem Phys 2024; 160:114906. [PMID: 38511659 DOI: 10.1063/5.0191295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2023] [Accepted: 03/02/2024] [Indexed: 03/22/2024] Open
Abstract
In this study, we simulate mechanically interlocked semiflexible ring polymers inspired by the minicircles of kinetoplast DNA (kDNA) networks. Using coarse-grained molecular dynamics simulations, we investigate the impact of molecular topological linkage and nanoconfinement on the conformational properties of two- and three-ring polymer systems in varying solvent qualities. Under good-quality solvents, for two-ring systems, a higher number of crossing points lead to a more internally constrained structure, reducing their mean radius of gyration. In contrast, three-ring systems, which all had the same crossing number, exhibited more similar sizes. In unfavorable solvents, structures collapse, forming compact configurations with increased contacts. The morphological diversity of structures primarily arises from topological linkage rather than the number of rings. In three-ring systems with different topological conformations, structural uniformity varies based on link types. Extreme confinement induces isotropic and extended conformations for catenated polymers, aligning with experimental results for kDNA networks and influencing the crossing number and overall shape. Finally, the flat-to-collapse transition in extreme confinement occurs earlier (at relatively better solvent conditions) compared to non-confined systems. This study offers valuable insights into the conformational behavior of mechanically interlocked ring polymers, highlighting challenges in extrapolating single-molecule analyses to larger networks such as kDNA.
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Affiliation(s)
- Diego Becerra
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, USA
| | - Alexander R Klotz
- Department of Physics and Astronomy, California State University, Long Beach, California 90840, USA
| | - Lisa M Hall
- William G. Lowrie Department of Chemical and Biomolecular Engineering, The Ohio State University, Columbus, Ohio 43210, USA
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3
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Staňo R, Likos CN, Egorov SA. Mixing Linear Polymers with Rings and Catenanes: Bulk and Interfacial Behavior. Macromolecules 2023; 56:8168-8182. [PMID: 37900098 PMCID: PMC10601540 DOI: 10.1021/acs.macromol.3c01267] [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: 06/28/2023] [Revised: 09/11/2023] [Indexed: 10/31/2023]
Abstract
We derive and parameterize effective interaction potentials between a multitude of different types of ring polymers and linear chains, varying the bending rigidity and solvent quality for the former species. We further develop and apply a density functional treatment for mixtures of both disconnected (chain-ring) and connected (chain-polycatenane) mixtures of the same, drawing coexistence binodals and exploring the ensuing response functions as well as the interface and wetting behavior of the mixtures. We show that worsening of the solvent quality for the rings brings about a stronger propensity for macroscopic phase separation in the linear-polycatenane mixtures, which is predominantly of the demixing type between phases of similar overall particle density. We formulate a simple criterion based on the effective interactions, allowing us to determine whether any specific linear-ring mixture will undergo a demixing phase separation.
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Affiliation(s)
- Roman Staňo
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
- Vienna
Doctoral School in Physics, University of
Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Christos N. Likos
- Faculty
of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria
| | - Sergei A. Egorov
- Department
of Chemistry, University of Virginia, Charlottesville, Virginia 22901, United States
- Erwin
Schrödinger International Institute for Mathematics and Physics, Boltzmanngasse 9, 1090 Vienna, Austria
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4
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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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5
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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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6
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Sleiman JL, Burton RH, Caraglio M, Gutierrez Fosado YA, Michieletto D. Geometric Predictors of Knotted and Linked Arcs. ACS POLYMERS AU 2022; 2:341-350. [PMID: 36254317 PMCID: PMC9562465 DOI: 10.1021/acspolymersau.2c00021] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
Inspired by how certain proteins “sense”
knots and
entanglements in DNA molecules, here, we ask if local geometric features
that may be used as a readout of the underlying topology of generic
polymers exist. We perform molecular simulations of knotted and linked
semiflexible polymers and study four geometric measures to predict
topological entanglements: local curvature, local density, local 1D
writhe, and nonlocal 3D writhe. We discover that local curvature is
a poor predictor of entanglements. In contrast, segments with maximum
local density or writhe correlate as much as 90% of the time with
the shortest knotted and linked arcs. We find that this accuracy is
preserved across different knot types and also under significant spherical
confinement, which is known to delocalize essential crossings in knotted
polymers. We further discover that nonlocal 3D writhe is the best
geometric readout of the knot location. Finally, we discuss how these
geometric features may be used to computationally analyze entanglements
in generic polymer melts and gels.
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Affiliation(s)
- Joseph L. Sleiman
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Robin H. Burton
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Michele Caraglio
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Yair Augusto Gutierrez Fosado
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Davide Michieletto
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
- MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh EH4 2XU, United Kingdom
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7
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Amici G, Caraglio M, Orlandini E, Micheletti C. Topological Friction and Relaxation Dynamics of Spatially Confined Catenated Polymers. ACS Macro Lett 2022; 11:1-6. [PMID: 35574798 PMCID: PMC8772382 DOI: 10.1021/acsmacrolett.1c00594] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2021] [Accepted: 12/03/2021] [Indexed: 11/30/2022]
Abstract
We study catenated ring polymers confined inside channels and slits with Langevin dynamics simulations and address how the contour position and size of the interlocked or physically linked region evolve with time. We show that the catenation constraints generate a drag, or topological friction, that couples the contour motion of the interlocked regions. Notably, the coupling strength decreases as the interlocking is made tighter, but also shorter, by confinement. Though the coupling strength differs for channel and slit confinement, the data outline a single universal curve when plotted against the size of the linked region. Finally, we study how the relaxation kinetics changes after one of the rings is cut open and conclude that considering interlocked circular polymers is key for isolating the manifestations of topological friction. The results ought to be relevant for linked biomolecules in experimental or biological confining conditions.
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Affiliation(s)
- Giulia Amici
- Scuola
Internazionale Superiore di Studi Avanzati - SISSA, via Bonomea 265, 34136 Trieste, Italy
| | - Michele Caraglio
- Institut
für Theoretische Physik, Universität
Innsbruck, Technikerstraße 21A, A-6020 Innsbruck, Austria
| | - Enzo Orlandini
- Department
of Physics and Astronomy, University of
Padova, Via Marzolo 8, I-35100 Padova, Italy
| | - Cristian Micheletti
- Scuola
Internazionale Superiore di Studi Avanzati - SISSA, via Bonomea 265, 34136 Trieste, Italy
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8
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Polson JM, Garcia EJ, Klotz AR. Flatness and intrinsic curvature of linked-ring membranes. SOFT MATTER 2021; 17:10505-10515. [PMID: 34755161 DOI: 10.1039/d1sm01307f] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Recent experiments have elucidated the physical properties of kinetoplasts, which are chain-mail-like structures found in the mitochondria of trypanosome parasites formed from catenated DNA rings. Inspired by these studies, we use Monte Carlo simulations to examine the behavior of two-dimensional networks ("membranes") of linked rings. For simplicity, we consider only identical rings that are circular and rigid and that form networks with a regular linking structure. We find that the scaling of the eigenvalues of the shape tensor with membrane size are consistent with the behavior of the flat phase observed in self-avoiding covalent membranes. Increasing ring thickness tends to swell the membrane. Remarkably, unlike covalent membranes, the linked-ring membranes tend to form concave structures with an intrinsic curvature of entropic origin associated with local excluded-volume interactions. The degree of concavity increases with increasing ring thickness and is also affected by the type of linking network. The relevance of the properties of linked-ring model membranes to those observed in kinetoplasts is discussed.
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Affiliation(s)
- James M Polson
- Department of Physics, University of Prince Edward Island, Charlottetown, Prince Edward Island, C1A 4P3, Canada.
| | - Edgar J Garcia
- Department of Physics and Astronomy, California State University, Long Beach, California, 90840, USA
| | - Alexander R Klotz
- Department of Physics and Astronomy, California State University, Long Beach, California, 90840, USA
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9
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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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10
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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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11
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Soh BW, Doyle PS. Equilibrium Conformation of Catenated DNA Networks in Slitlike Confinement. ACS Macro Lett 2021; 10:880-885. [PMID: 35549205 DOI: 10.1021/acsmacrolett.1c00299] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
A kinetoplast is a planar network of catenated DNA rings with topology that resembles that of chain mail armor. In this work, we use single-molecule experiments to probe the conformation of kinetoplasts confined to slits. We find that the in-plane size of kinetoplasts increases with degree of confinement, akin to the slitlike confinement of linear DNA. The change in kinetoplast size with channel height is consistent with the scaling prediction from a Flory-type approach for a 2D polymer. With an increase in extent of confinement, the kinetoplasts appear to unfold and take on more uniform circular shapes, in contrast to the broad range of conformations observed for kinetoplasts in bulk.
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Affiliation(s)
- Beatrice W. Soh
- 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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12
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13
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Ranjbar HA, Nourany M, Mollavali M, Noormohammadi F, Jafari S. Stimuli‐responsive polyurethane bionanocomposites of poly(ethylene glycol)/poly(ε‐caprolactone) and [poly(ε‐caprolactone)‐grafted‐] cellulose nanocrystals. POLYM ADVAN TECHNOL 2020. [DOI: 10.1002/pat.5062] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
| | - Mohammad Nourany
- Polymer Engineering and Color Technology Amirkabir University of Technology Tehran Iran
| | - Majid Mollavali
- Department of Chemical Engineering, Faculty of Engineering Ardakan University Ardakan Iran
| | - Fatemeh Noormohammadi
- Polymer Engineering and Color Technology Amirkabir University of Technology Tehran Iran
| | - Safora Jafari
- Polymer Engineering and Color Technology Amirkabir University of Technology Tehran Iran
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14
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Soh BW, Doyle PS. Deformation Response of Catenated DNA Networks in a Planar Elongational Field. ACS Macro Lett 2020; 9:944-949. [PMID: 35648605 DOI: 10.1021/acsmacrolett.0c00360] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
A kinetoplast is a complex catenated DNA network that bears resemblance to a two-dimensional polymeric system. In this work, we use single-molecule experiments to study the transient and steady-state deformation of kinetoplasts in a planar elongational field. We demonstrate that kinetoplasts deform in a stagewise manner and undergo transient deformation at large strains, due to conformational rearrangements from an intermediate metastable state. Kinetoplasts in an elongational field achieve a steady-state deformation that depends on strain rate, akin to the deformation of linear polymers. We do not observe an abrupt transition between the nondeformed and deformed states of a kinetoplast, in contrast to the coil-stretch transition for a linear polymer.
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Affiliation(s)
- Beatrice W. Soh
- 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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