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Separation of Geometrical and Topological Entanglement in Confined Polymers Driven out of Equilibrium

  • Davide Michieletto*
    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 Molecular Medicine, University of Edinburgh, North Crewe Road, Edinburgh, EH4 2XU, United Kingdom
    *E-mail: [email protected]
  • Enzo Orlandini
    Enzo Orlandini
    Dipartimento di Fisica e Astronomia and Sezione INFN, Universitá degli Studi di Padova, I-35131 Padova, Italy
  • Matthew S. Turner
    Matthew S. Turner
    Department of Physics and Centre for Complexity Science, University of Warwick, Coventry, CV4 7AL, U.K.
    Department of Chemical Engineering, Kyoto University, Kyoto, Japan
  • , and 
  • Cristian Micheletti
    Cristian Micheletti
    SISSA (Scuola Internazionale Superiore di Studi Avanzati), Via Bonomea 265, 34136 Trieste, Italy
Cite this: ACS Macro Lett. 2020, 9, 8, 1081–1085
Publication Date (Web):July 14, 2020
https://doi.org/10.1021/acsmacrolett.0c00366
Copyright © 2020 American Chemical Society

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    Abstract

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    We use Brownian dynamics simulations and advanced topological profiling methods to characterize the out-of-equilibrium evolution of self-entanglement in linear polymers confined into nanochannels and under periodic compression. By introducing suitable observables, we can distinguish two main forms of entanglement that we term geometrical and topological. The latter is measured by the number of (essential) crossings of the physical knot detected after a suitable bridging of the chain termini. The former is instead measured as the average number of times a linear chain appears to cross itself when viewed under all projections and is irrespective of the physical knotted state. The key discovery of our work is that these two forms of entanglement are uncoupled and evolve with distinct dynamics. While geometrical entanglement is typically in phase with the compression–elongation cycles and it is primarily sensitive to its force f, the topological measure is mildly sensitive to cyclic modulation but strongly depends on both compression force f and duration k. The findings could assist the interpretation of experiments using fluorescence molecular tracers to track physical knots in polymers. Furthermore, we identify optimal regions in the experimentally controllable parameter space in which to obtain more/less topological and geometrical entanglement; this may help designing polymers with targeted topology.

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    Cited By

    This article is cited by 8 publications.

    1. Andrea Tagliabue, Cristian Micheletti, Massimo Mella. Tuning Knotted Copolyelectrolyte Conformations via Solution Properties. Macromolecules 2022, 55 (23) , 10761-10772. https://doi.org/10.1021/acs.macromol.2c01933
    2. Andrea Tagliabue, Cristian Micheletti, Massimo Mella. Tunable Knot Segregation in Copolyelectrolyte Rings Carrying a Neutral Segment. ACS Macro Letters 2021, 10 (11) , 1365-1370. https://doi.org/10.1021/acsmacrolett.1c00453
    3. Lili Zeng, Xavier Capaldi, Zezhou Liu, Walter W. Reisner. Transient physics in the compression and mixing dynamics of two nanochannel-confined polymer chains. Physical Review E 2024, 109 (2) https://doi.org/10.1103/PhysRevE.109.024501
    4. Renáta Rusková, Dušan Račko. Knot Formation on DNA Pushed Inside Chiral Nanochannels. Polymers 2023, 15 (20) , 4185. https://doi.org/10.3390/polym15204185
    5. Jan Rothörl, Sarah Wettermann, Peter Virnau, Aniket Bhattacharya. Knot formation of dsDNA pushed inside a nanochannel. Scientific Reports 2022, 12 (1) https://doi.org/10.1038/s41598-022-09242-5
    6. Renáta Rusková, Dušan Račko. Knot Factories with Helical Geometry Enhance Knotting and Induce Handedness to Knots. Polymers 2022, 14 (19) , 4201. https://doi.org/10.3390/polym14194201
    7. Davide Michieletto, Yair A G Fosado, Elias Melas, Marco Baiesi, Luca Tubiana, Enzo Orlandini. Dynamic and facilitated binding of topoisomerase accelerates topological relaxation. Nucleic Acids Research 2022, 50 (8) , 4659-4668. https://doi.org/10.1093/nar/gkac260
    8. Peter Cifra, Tomáš Bleha. Piston Compression of Semiflexible Ring Polymers in Channels. Macromolecular Theory and Simulations 2021, 30 (5) https://doi.org/10.1002/mats.202100027

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