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Can Polymer Helicity Affect Topological Chirality of Polymer Knots?
[Image: see text] We investigate the effect of helicity in isolated polymers on the topological chirality of their knots with computer simulations. Polymers are described by generic worm-like chains (WLC), where helical conformations are promoted by chiral coupling between segments that are neighbor...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
American Chemical Society
2023
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9948535/ https://www.ncbi.nlm.nih.gov/pubmed/36706453 http://dx.doi.org/10.1021/acsmacrolett.2c00600 |
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author | Zhao, Yani Rothörl, Jan Besenius, Pol Virnau, Peter Daoulas, Kostas Ch. |
author_facet | Zhao, Yani Rothörl, Jan Besenius, Pol Virnau, Peter Daoulas, Kostas Ch. |
author_sort | Zhao, Yani |
collection | PubMed |
description | [Image: see text] We investigate the effect of helicity in isolated polymers on the topological chirality of their knots with computer simulations. Polymers are described by generic worm-like chains (WLC), where helical conformations are promoted by chiral coupling between segments that are neighbors along the chain contour. The sign and magnitude of the coupling coefficient u determine the sense and strength of helicity. The corrugation of the helix is adjusted via the radius R of a spherical, hard excluded volume around each WLC segment. Open and compact helices are, respectively, obtained for R that is either zero or smaller than the length of the WLC bond, and R that is a few times larger than the bond length. We use a Monte Carlo algorithm to sample polymer conformations for different values of u, spanning the range from achiral polymers to chains with well-developed helices. Monitoring the average helix torsion and fluctuations of chiral order as a function of u, for two very different chain lengths, demonstrates that the coil–helix transition in this model is not a phase transition but a crossover. Statistical analysis of conformations forming the simplest chiral knots, 3(1), 5(1), and 5(2), demonstrates that topological mirror symmetry is broken—knots formed by helices with a given sense prefer one handedness over the other. For the 3(1) and 5(1) knots, positive helical sense favors positive handedness. Intriguingly, an opposite trend is observed for 5(2) knots, where positive helical sense promotes negative handedness. We argue that this special coupling between helicity and topological chirality stems from a generic mechanism: conformations where some of the knot crossings are found in “braids” formed by two tightly interwoven sections of the polymer. |
format | Online Article Text |
id | pubmed-9948535 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | American Chemical Society |
record_format | MEDLINE/PubMed |
spelling | pubmed-99485352023-02-24 Can Polymer Helicity Affect Topological Chirality of Polymer Knots? Zhao, Yani Rothörl, Jan Besenius, Pol Virnau, Peter Daoulas, Kostas Ch. ACS Macro Lett [Image: see text] We investigate the effect of helicity in isolated polymers on the topological chirality of their knots with computer simulations. Polymers are described by generic worm-like chains (WLC), where helical conformations are promoted by chiral coupling between segments that are neighbors along the chain contour. The sign and magnitude of the coupling coefficient u determine the sense and strength of helicity. The corrugation of the helix is adjusted via the radius R of a spherical, hard excluded volume around each WLC segment. Open and compact helices are, respectively, obtained for R that is either zero or smaller than the length of the WLC bond, and R that is a few times larger than the bond length. We use a Monte Carlo algorithm to sample polymer conformations for different values of u, spanning the range from achiral polymers to chains with well-developed helices. Monitoring the average helix torsion and fluctuations of chiral order as a function of u, for two very different chain lengths, demonstrates that the coil–helix transition in this model is not a phase transition but a crossover. Statistical analysis of conformations forming the simplest chiral knots, 3(1), 5(1), and 5(2), demonstrates that topological mirror symmetry is broken—knots formed by helices with a given sense prefer one handedness over the other. For the 3(1) and 5(1) knots, positive helical sense favors positive handedness. Intriguingly, an opposite trend is observed for 5(2) knots, where positive helical sense promotes negative handedness. We argue that this special coupling between helicity and topological chirality stems from a generic mechanism: conformations where some of the knot crossings are found in “braids” formed by two tightly interwoven sections of the polymer. American Chemical Society 2023-01-27 /pmc/articles/PMC9948535/ /pubmed/36706453 http://dx.doi.org/10.1021/acsmacrolett.2c00600 Text en © 2023 The Authors. Published by American Chemical Society https://creativecommons.org/licenses/by/4.0/Permits the broadest form of re-use including for commercial purposes, provided that author attribution and integrity are maintained (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Zhao, Yani Rothörl, Jan Besenius, Pol Virnau, Peter Daoulas, Kostas Ch. Can Polymer Helicity Affect Topological Chirality of Polymer Knots? |
title | Can Polymer
Helicity Affect Topological Chirality
of Polymer Knots? |
title_full | Can Polymer
Helicity Affect Topological Chirality
of Polymer Knots? |
title_fullStr | Can Polymer
Helicity Affect Topological Chirality
of Polymer Knots? |
title_full_unstemmed | Can Polymer
Helicity Affect Topological Chirality
of Polymer Knots? |
title_short | Can Polymer
Helicity Affect Topological Chirality
of Polymer Knots? |
title_sort | can polymer
helicity affect topological chirality
of polymer knots? |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9948535/ https://www.ncbi.nlm.nih.gov/pubmed/36706453 http://dx.doi.org/10.1021/acsmacrolett.2c00600 |
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