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Entropic Interactions between Two Knots on a Semiflexible Polymer

Trapping a Knot into Tight Conformations by Intra-Chain Repulsions

by 1 and 1,2,*
BioSystems and Micromechanics IRG, Singapore-MIT Alliance for Research and Technology Centre, Singapore 117543, Singapore
Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), Cambridge, MA 02139, USA
Author to whom correspondence should be addressed.
Academic Editor: Martin Kröger
Polymers 2017, 9(2), 57;
Received: 31 December 2016 / Revised: 7 February 2017 / Accepted: 8 February 2017 / Published: 10 February 2017
(This article belongs to the Special Issue Semiflexible Polymers)
Knots can occur in biopolymers such as DNA and peptides. In our previous study, we systematically investigated the effects of intra-chain interactions on knots and found that long-range repulsions can surprisingly tighten knots. Here, we use this knowledge to trap a knot into tight conformations in Langevin dynamics simulations. By trapping, we mean that the free energy landscape with respect to the knot size exhibits a potential well around a small knot size in the presence of long-range repulsions, and this potential can well lead to long-lived tight knots when its depth is comparable to or larger than thermal energy. We tune the strength of intra-chain repulsion such that a knot is weakly trapped. Driven by thermal fluctuations, the knot can escape from the trap and is then re-trapped. We find that the knot switches between tight and loose conformations—referred to as “knot breathing”. We use a Yukawa potential to model screened electrostatic interactions to explore the relevance of knot trapping and breathing in charged biopolymers. We determine the minimal screened length and the minimal strength of repulsion for knot trapping. We find that Coulomb-induced knot trapping is possible to occur in single-stranded DNA and peptides for normal ionic strengths. View Full-Text
Keywords: knot; polymer; diffusion; Langevin dynamics simulation knot; polymer; diffusion; Langevin dynamics simulation
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MDPI and ACS Style

Dai, L.; Doyle, P.S. Trapping a Knot into Tight Conformations by Intra-Chain Repulsions. Polymers 2017, 9, 57.

AMA Style

Dai L, Doyle PS. Trapping a Knot into Tight Conformations by Intra-Chain Repulsions. Polymers. 2017; 9(2):57.

Chicago/Turabian Style

Dai, Liang, and Patrick S. Doyle. 2017. "Trapping a Knot into Tight Conformations by Intra-Chain Repulsions" Polymers 9, no. 2: 57.

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