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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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Cifra P, Bleha T. Pressure of Linear and Ring Polymers Confined in a Cavity. J Phys Chem B 2023; 127:4646-4657. [PMID: 37192395 DOI: 10.1021/acs.jpcb.3c01585] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
Nanoscale confinement of polymers in a cavity is central to a variety of biological and nanotechnology processes. Using the discrete WLC model we simulate the compression of flexible and semiflexible polymers of linear and ring topology in a closed cavity. Simulation reveals that polymer pressure inside the cavity increases with the chain stiffness but is practically unaffected by the chain topology. For flexible polymers, the computed dependence of pressure on the cavity size and polymer concentration is consistent with the scaling behavior expected for bulk polymers in a good solvent. However, the scaling behavior of semiflexible polymers is only in partial agreement with the theory prediction, with discrepancies arising from a continuous transition between regimes in chains of moderate lengths. The computed segment density profiles endorse the propensity of semiflexible polymers to concentrate beneath the cavity surface and thus elevate the pressure. The compaction of polymers by compression into the disordered globule or growing toroidal structure is documented.
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Affiliation(s)
- Peter Cifra
- Polymer Institute, Slovak Academy of Sciences, 84541 Bratislava, Slovakia
| | - Tomáš Bleha
- Polymer Institute, Slovak Academy of Sciences, 84541 Bratislava, Slovakia
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3
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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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Polson JM, MacLennan RG. Entropic force of cone-tethered polymers interacting with a planar surface. Phys Rev E 2022; 106:024501. [PMID: 36109988 DOI: 10.1103/physreve.106.024501] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2022] [Accepted: 07/29/2022] [Indexed: 06/15/2023]
Abstract
Computer simulations are used to characterize the entropic force of one or more polymers tethered to the tip of a hard conical object that interact with a nearby hard flat surface. Pruned-enriched Rosenbluth method Monte Carlo simulations are used to calculate the variation of the conformational free energy F of a hard-sphere polymer with respect to the cone-tip-to-surface distance h from which the variation of the entropic force f≡|dF/dh| with h is determined. We consider the following cases: a single freely jointed tethered chain, a single semiflexible tethered chain, and several freely jointed chains of equal length each tethered to the cone tip. The simulation results are used to test the validity of a prediction by Maghrebi et al. [Maghrebi et al., Europhys. Lett. 96, 66002 (2011)0295-507510.1209/0295-5075/96/66002; Phys. Rev. E 86, 061801 (2012)1539-375510.1103/PhysRevE.86.061801] that f∝(γ_{∞}-γ_{0})h^{-1}, where γ_{0} and γ_{∞} are universal scaling exponents for the partition function of the tethered polymer for h=0 and h=∞, respectively. The measured functions f(h) are generally consistent with the predictions, with small quantitative discrepancies arising from the approximations employed in the theory. In the case of multiple tethered polymers, the entropic force per polymer is roughly constant, which is qualitatively inconsistent with the predictions.
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Affiliation(s)
- James M Polson
- Department of Physics, University of Prince Edward Island, 550 University Avenue, Charlottetown, Prince Edward Island, Canada C1A 4P3
| | - Roland G MacLennan
- Department of Physics, University of Prince Edward Island, 550 University Avenue, Charlottetown, Prince Edward Island, Canada C1A 4P3
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Confinement anisotropy drives polar organization of two DNA molecules interacting in a nanoscale cavity. Nat Commun 2022; 13:4358. [PMID: 35902565 PMCID: PMC9334635 DOI: 10.1038/s41467-022-31398-x] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2021] [Accepted: 06/15/2022] [Indexed: 11/08/2022] Open
Abstract
There is growing appreciation for the role phase transition based phenomena play in biological systems. In particular, self-avoiding polymer chains are predicted to undergo a unique confinement dependent demixing transition as the anisotropy of the confined space is increased. This phenomenon may be relevant for understanding how interactions between multiple dsDNA molecules can induce self-organized structure in prokaryotes. While recent in vivo experiments and Monte Carlo simulations have delivered essential insights into this phenomenon and its relation to bacteria, there are fundamental questions remaining concerning how segregated polymer states arise, the role of confinement anisotropy and the nature of the dynamics in the segregated states. To address these questions, we introduce an artificial nanofluidic model to quantify the interactions of multiple dsDNA molecules in cavities with controlled anisotropy. We find that two dsDNA molecules of equal size confined in an elliptical cavity will spontaneously demix and orient along the cavity poles as cavity eccentricity is increased; the two chains will then swap pole positions with a frequency that decreases with increasing cavity eccentricity. In addition, we explore a system consisting of a large dsDNA molecule and a plasmid molecule. We find that the plasmid is excluded from the larger molecule and will exhibit a preference for the ellipse poles, giving rise to a non-uniform spatial distribution in the cavity that may help explain the non-uniform plasmid distribution observed during in vivo imaging of high-copy number plasmids in bacteria.
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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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Teng Y, Andersen NT, Chen JZY. Statistical Properties of a Slit-Confined Wormlike Chain of Finite Length. Macromolecules 2021. [DOI: 10.1021/acs.macromol.1c00759] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Affiliation(s)
- Yue Teng
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Nigel T. Andersen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Jeff Z. Y. Chen
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Sunday DF, Dolejsi M, Chang AB, Richter LJ, Li R, Kline RJ, Nealey PF, Grubbs RH. Confinement and Processing Can Alter the Morphology and Periodicity of Bottlebrush Block Copolymers in Thin Films. ACS NANO 2020; 14:17476-17486. [PMID: 33225683 DOI: 10.1021/acsnano.0c07777] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Bottlebrush block copolymers (BBCPs) are intriguing architectural variations on linear BCPs with highly tunable structure. Confinement can have a significant impact on polymer assembly, giving rise to changes in morphology, assembly kinetics, and properties like the glass transition. Given that confinement leads to significant changes in the persistence length of bottlebrush homopolymers, it is reasonable to expect that BBCPs will see significant changes in their structure and periodicity relative to the bulk morphology. Understanding how confinement influences assembly will be important for designing BBCPs for thin film applications including membranes, integrated photonic structures, and potentially BCP lithography. In order to study the effects of confinement on BBCP conformation and morphology, a blade coating was used to prepare films with continuous variation in film thickness. Unlike thin films of linear BCPs, islands/holes were not observed, and instead mixtures of parallel and perpendicular morphologies emerge after annealing. The lamellar periodicity (L0) of the morphologies is found to be thickness dependent, increasing L0 with decreasing film thickness for blade coated films. Films coated out of tetrahydrofuran (THF) resulted in a single well-defined lamellar periodicity, verified through atomic force microscopy (AFM) and grazing incidence small-angle X-ray scattering (GISAXS), which increases dramatically from the bulk value (30.6 nm) and continues to increase as the film thickness decreases. The largest observed L0 was 65.5 nm, and this closely approaches the estimated upper limit of 67 nm corresponding to a fully extended backbone in a bilayer arrangement. Films coated out of propylene glycol methyl ether acetate (PGMEA) resulted in a mixture of perpendicular lamellae and a smaller, likely cylindrical morphology. The lamellar portion of the film shows the same thickness dependence as the lamellae observed in the THF coated films. The scaling of the lamellar L0 with respect to film thickness follows predictions for confined semiflexible polymers with weak excluded volume interactions and can be related to models for confinement of DNA. Spin coated films shows the same reduction in periodicity, although at very different film thicknesses. This result suggests that the material has shallow free-energy barriers to transitioning between different L0 and morphologies, a property that could be taken advantage of for patterning diverse structures with a single material.
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Affiliation(s)
- Daniel F Sunday
- Materials Science and Engineering Division, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Moshe Dolejsi
- Institute for Molecular Engineering, University of Chicago, 5801 S Ellis Ave, Chicago, Illinois 60637, United States
| | - Alice B Chang
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
| | - Lee J Richter
- Materials Science and Engineering Division, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Ruipeng Li
- National Synchrotron Light Source II, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - R Joseph Kline
- Materials Science and Engineering Division, National Institute of Standards and Technology, 100 Bureau Drive, Gaithersburg, Maryland 20899, United States
| | - Paul F Nealey
- Institute for Molecular Engineering, University of Chicago, 5801 S Ellis Ave, Chicago, Illinois 60637, United States
| | - Robert H Grubbs
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States
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