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Computational and Mathematical Biophysics

(formerly Molecular Based Mathematical Biology)

Editor-in-Chief: Wei, Guowei

Ed. by Mitchell, Julie / Zhao, Shan

Covered by MathSciNet and Zentralblatt Math (zbMATH)

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2544-7297
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Modeling repulsive forces on fibres via knot energies

Simon Blatt
  • Corresponding author
  • Workgroup Applied Analysis, Karlsruhe Institute of Technology, Kaiserstraße 89-93, 76133 Karlsruhe, Germany
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Philipp Reiter
Published Online: 2014-12-01 | DOI: https://doi.org/10.2478/mlbmb-2014-0004

Abstract

Modeling of repulsive forces is essential to the understanding of certain bio-physical processes, especially for the motion of DNA molecules. These kinds of phenomena seem to be driven by some sort of “energy” which especially prevents the molecules from strongly bending and forming self-intersections. Inspired by a physical toy model, numerous functionals have been defined during the past twenty-five years that aim at modeling self-avoidance. The general idea is to produce “detangled” curves having particularly large distances between distant strands. In this survey we present several families of these so-called knot energies. It turns out that they are quite similar from an analytical viewpoint. We focus on proving self-avoidance and existence of minimizers in every knot class. For a suitable subfamily of these energies we show how to prove that these minimizers are even infinitely differentiable.

Keywords: repulsive forces; knot energies; molecular biology

MSC 2010: 53A04; 57M25; 26A33; 46N60; 92C40

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About the article

Received: 2013-07-31

Accepted: 2014-04-09

Published Online: 2014-12-01

Published in Print: 2014-01-01


Citation Information: Computational and Mathematical Biophysics, Volume 2, Issue 1, Pages 56–72, ISSN (Online) 2544-7297, DOI: https://doi.org/10.2478/mlbmb-2014-0004.

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© 2019 Simon Blatt, Philipp Reiter, published by Sciendo. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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