Worm-like Polymer Loops and Fourier Knots

TL;DR

This paper demonstrates that Fourier sum-generated curves can model worm-like polymer loops, revealing insights into their physical properties and topological similarities with other polymer models.

Contribution

It introduces a Fourier-based method to generate curves that accurately represent worm-like polymer loops and explores their physical and topological properties.

Findings

Fourier-generated curves match physical worm-like loops.

Larger persistence length observed from global measures.

Topological properties are similar to other polymer models.

Abstract

Every smooth closed curve can be represented by a suitable Fourier sum. We show that the ensemble of curves generated by randomly chosen Fourier coefficients with amplitudes inversely proportional to spatial frequency (with a smooth exponential cutoff), can be accurately mapped on the physical ensemble of worm-like polymer loops. We find that measures of correlation on the scale of the entire loop yield a larger persistence length than that calculated from the tangent-tangent correlation function at small length scales. The conjecture that physical loops exhibit additional rigidity on scales comparable to the entire loop due to the contribution of twist rigidity, can be tested experimentally by determining the persistence length from the local curvature and comparing it with that obtained by measuring the radius of gyration of dsDNA plasmids. The topological properties of the ensemble randomly generated worm-like loops are shown to be similar to that of other polymer models.