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Open AccessArticle

Role of Bending Energy and Knot Chirality in Knot Distribution and Their Effective Interaction along Stretched Semiflexible Polymers

Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
Department of Physics, Faculty for Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia
Department of Theoretical Physics, J. Stefan Institute, SI-1000 Ljubljana, Slovenia
Computational Physics Group, University of Vienna, Sensengasse 8, 1090 Vienna, Austria
Author to whom correspondence should be addressed.
Academic Editor: Martin Kröger
Polymers 2016, 8(10), 347;
Received: 16 July 2016 / Revised: 25 August 2016 / Accepted: 15 September 2016 / Published: 22 September 2016
(This article belongs to the Special Issue Semiflexible Polymers)
Knots appear frequently in semiflexible (bio)polymers, including double-stranded DNA, and their presence can affect the polymer’s physical and functional properties. In particular, it is possible and indeed often the case that multiple knots appear on a single chain, with effects which have only come under scrutiny in the last few years. In this manuscript, we study the interaction of two knots on a stretched semiflexible polymer, expanding some recent results on the topic. Specifically, we consider an idealization of a typical optical tweezers experiment and show how the bending rigidity of the chain—And consequently its persistence length—Influences the distribution of the entanglements; possibly more importantly, we observe and report how the relative chirality of the otherwise identical knots substantially modifies their interaction. We analyze the free energy of the chain and extract the effective interactions between embedded knots, rationalizing some of their pertinent features by means of simple effective models. We believe the salient aspect of the knot–knot interactions emerging from our study will be present in a large number of semiflexible polymers under tension, with important consequences for the characterization and manipulation of these systems—Be they artificial or biologica in origin—And for their technological application. View Full-Text
Keywords: semiflexible polymers; dsDNA; knots; chirality; topology semiflexible polymers; dsDNA; knots; chirality; topology
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MDPI and ACS Style

Najafi, S.; Podgornik, R.; Potestio, R.; Tubiana, L. Role of Bending Energy and Knot Chirality in Knot Distribution and Their Effective Interaction along Stretched Semiflexible Polymers. Polymers 2016, 8, 347.

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