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Polymers 2017, 9(2), 55; doi:10.3390/polym9020055

Entropic Interactions between Two Knots on a Semiflexible Polymer

1
Department of Physics, Johannes Gutenberg University Mainz, Staudinger Weg 9, 55128 Mainz, Germany
2
Graduate School Materials Science in Mainz, 55128 Mainz, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Martin Kröger
Received: 30 December 2016 / Revised: 27 January 2017 / Accepted: 31 January 2017 / Published: 9 February 2017
(This article belongs to the Special Issue Semiflexible Polymers)
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Abstract

Two knots on a string can either be separated or intertwined, and may even pass through each other. At the microscopic scale, such transitions may occur spontaneously, driven by thermal fluctuations, and can be associated with a topological free energy barrier. In this manuscript, we study the respective location of a trefoil ( 3 1 ) and a figure-eight ( 4 1 ) knot on a semiflexible polymer, which is parameterized to model dsDNA in physiological conditions. Two cases are considered: first, end monomers are grafted to two confining walls of varying distance. Free energy profiles and transition barriers are then compared to a subset of free chains, which contain exactly one 3 1 and one 4 1 knot. For the latter, we observe a small preference to form an intertwined state, which can be associated with an effective entropic attraction. However, the respective free energy barrier is so small that we expect transition events to occur spontaneously and frequently in polymers and DNA, which are highly knotted for sufficient strain lengths. View Full-Text
Keywords: knots; DNA; free energy barriers knots; DNA; free energy barriers
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Richard, D.; Stalter, S.; Siebert, J.T.; Rieger, F.; Trefz, B.; Virnau, P. Entropic Interactions between Two Knots on a Semiflexible Polymer. Polymers 2017, 9, 55.

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