Chiral knots display symmetry breaking in helical confinement

Chiral knots display symmetry breaking in helical confinement


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ISBN: ISBN 978-80-972360-7-6

Chiral knots display symmetry breaking in helical confinement

Renáta Rusková1 Dušan Račko1
1Ústav Polymérov SAV, Bratislava, Slovensko

Topological knots naturally occur on DNA due to conformational moves [1] or activity of molecular machines [2]. Around half of knots are chiral including the simplest and most abundant trefoil knot. In some bacteria, occurrence of chiral knots is preferred over the achiral ones [3] and in some one form of chiral knots is more abundant [4]. Experimentally, it was successful to separate chiral knots through 2D-gel electrophoresis, where their structure was altered by negative supercoiling [4]. In general, we know that chirality plays an important role in biological systems, yet there are still mysteries to uncover, especially regarding interaction of chiral molecules towards various environments. In this work, we observe differences between right- and left-handed forms of trefoil knots and their interplay with various confinements (cylinder, toroid, helix) through molecular dynamics simulations in ESPResSo. Simulations in cylinder provided general information about behaviour of knots in confined system, their size and shape properties, which we divided into two categories – geometrical properties independent of chirality and topological parameters influenced by handedness of the knot. Toroid confinement represents a system curved in space in one dimension. Such curving, however, was not enough to enhance distinguishability of chiral knots and they had similar topological properties as in cylinder. Right-handed helix, on the other hand, strongly influenced knot topology and induced symmetry breaking for chiral knots. Right-handed knot was delocalized and compressed at its centre, while the left-handed knot expanded its main loop towards confinement wall, making it more localized, spherical and better fitting in the helix. Different topological behaviour of chiral knots as well as introduced asymmetry visible on radius of curvature indicates that helical confinement is suitable for distinguishing and direct separation of right- and left-handed forms of knots.


The work was supported by the Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic No. VEGA 2/0102/20 “Molecular dynamics simulations of topologically constrained and confined polymers”. Work is also part of European Topology Interdisciplinary Action COST 17 139.


1. Uehara, E. and T. Deguchi, Characteristic length of the knotting probability revisited. Journal of physics. Condensed matter : an Institute of Physics journal, 2015. 27: p. 354104.
2. Valdés, A., et al., Transcriptional supercoiling boosts topoisomerase II-mediated knotting of intracellular DNA. Nucleic Acids Research, 2019. 47(13): p. 6946-6955.
3. Arsuaga, J., et al., DNA knots reveal a chiral organization of DNA in phage capsids. Proceedings of the National Academy of Sciences of the United States of America, 2005. 102: p. 9165-9.
4. Valdés, A., et al., Quantitative disclosure of DNA knot chirality by high-resolution 2D-gel electrophoresis. Nucleic Acids Research, 2019. 47(5): p. e29-e29.