Metastable tight knots in a worm-like polymer

TL;DR

This paper predicts that in semi-flexible polymers like DNA, knots form metastable, compact configurations due to a balance of bending energy and entropy, which diffuse along the chain without spreading.

Contribution

It introduces a theoretical model for metastable knot configurations in worm-like chains, aligning with recent experimental observations on DNA.

Findings

Knot size depends on topological invariants.

Knot configurations are metastable and diffuse without spreading.

Model agrees with experimental data on knotted DNA.

Abstract

Based on an estimate of the knot entropy of a worm-like chain we predict that the interplay of bending energy and confinement entropy will result in a compact metastable configuration of the knot that will diffuse, without spreading, along the contour of the semi-flexible polymer until it reaches one of the chain ends. Our estimate of the size of the knot as a function of its topological invariant (ideal aspect ratio) agrees with recent experimental results of knotted dsDNA. Further experimental tests of our ideas are proposed.