Geometric Predictors of Knotted and Linked Arcs

TL;DR

This study investigates local geometric features in polymers to predict topological entanglements, finding that local density and writhe are highly effective indicators, with non-local 3D writhe being the best predictor.

Contribution

It identifies specific geometric measures, especially local density and 3D writhe, as reliable predictors of polymer entanglements, advancing understanding of topology sensing in polymers.

Findings

Local density and writhe predict entanglements with up to 90% accuracy.

Non-local 3D writhe is the most effective geometric indicator.

Predictive accuracy holds across different knot types and confinement conditions.

Abstract

Inspired by how certain proteins "sense" knots and entanglements in DNA molecules, here we ask if there exist local geometric features that may be used as a read-out of the underlying topology of generic polymers. We perform molecular simulations of knotted and linked semiflexbile polymers and study four geometric measures to predict topological entanglements: local curvature, local density, local 1D writhe and non-local 3D writhe. We discover that local curvature is a poor predictor of entanglements. In contrast, segments with maximum local density or writhe correlate as much as 90% of the time with the shortest knotted and linked arcs. We find that this accuracy is preserved across different knot types and also under significant spherical confinement, which is known to delocalise essential crossings in knotted polymers. We further discover that non-local 3D writhe is the best geometric read-out of knot location. Finally, we discuss how these geometric features may be used to computationally analyse entanglements in generic polymer melts and gels.