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Issue 28, 2018
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Characterising knotting properties of polymers in nanochannels

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Using a lattice model of polymers in a tube, we define one way to characterise different configurations of a given knot as either “local” or “non-local”, based on a standard approach for measuring the “size” of a knot within a knotted polymer chain. The method involves associating knot-types to subarcs of the chain, and then identifying a knotted subarc with minimal arclength; this arclength is then the knot-size. If the resulting knot-size is small relative to the whole length of the chain, then the knot is considered to be localised or “local”; otherwise, it is “non-local”. Using this definition, we establish that all but exponentially few sufficiently long self-avoiding polygons (closed chains) in a tubular sublattice of the simple cubic lattice are “non-locally” knotted. This is shown to also hold for the case when the same polygons are subject to an external tensile force, as well as in the extreme case when they are as compact as possible (no empty lattice sites). We also provide numerical evidence for small tube sizes that at equilibrium non-local knotting is more likely than local knotting, regardless of the strength of the stretching or compressing force. The relevance of these results to other models and recent experiments involving DNA knots is also discussed.

Graphical abstract: Characterising knotting properties of polymers in nanochannels

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The article was received on 09 Apr 2018, accepted on 26 Jun 2018 and first published on 28 Jun 2018

Article type: Paper
DOI: 10.1039/C8SM00734A
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Soft Matter, 2018,14, 5775-5785

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    Characterising knotting properties of polymers in nanochannels

    N. R. Beaton, J. W. Eng, K. Ishihara, K. Shimokawa and C. E. Soteros, Soft Matter, 2018, 14, 5775
    DOI: 10.1039/C8SM00734A

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