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Polymers 2017, 9(6), 196; doi:10.3390/polym9060196

Efficient Sampling of Knotting-Unknotting Pathways for Semiflexible Gaussian Chains

1
International School for Advanced Studies (SISSA), Physics Area via Bonomea 265, I-34136 Trieste, Italy
2
Institut de Physique Théorique, CEA, CNRS, UMR3681, F-91191 Gif-sur-Yvette, France
3
Beijing Computational Science Research Center, No.10 East Xibeiwang Road, 100193 Beijing, China
*
Authors to whom correspondence should be addressed.
Academic Editors: Andrzej Stasiak and Dusan Racko
Received: 10 May 2017 / Revised: 17 May 2017 / Accepted: 19 May 2017 / Published: 29 May 2017
(This article belongs to the Special Issue Knotted and Catenated Polymers)
View Full-Text   |   Download PDF [1235 KB, uploaded 31 May 2017]   |  

Abstract

We propose a stochastic method to generate exactly the overdamped Langevin dynamics of semi-flexible Gaussian chains, conditioned to evolve between given initial and final conformations in a preassigned time. The initial and final conformations have no restrictions, and hence can be in any knotted state. Our method allows the generation of statistically independent paths in a computationally efficient manner. We show that these conditioned paths can be exactly generated by a set of local stochastic differential equations. The method is used to analyze the transition routes between various knots in crossable filamentous structures, thus mimicking topological reconnections occurring in soft matter systems or those introduced in DNA by topoisomerase enzymes. We find that the average number of crossings, writhe and unknotting number are not necessarily monotonic in time and that more complex topologies than the initial and final ones can be visited along the route. View Full-Text
Keywords: knots, Langevin bridges, reconnection paths knots, Langevin bridges, reconnection paths
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Micheletti, C.; Orland, H. Efficient Sampling of Knotting-Unknotting Pathways for Semiflexible Gaussian Chains. Polymers 2017, 9, 196.

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