Effect of bending rigidity on the knotting of a polymer under tension

TL;DR

This study uses computational modeling to explore how a polymer's bending rigidity influences knot formation under tension, revealing a minimum free-energy cost at specific rigidity levels and knot localization preferences.

Contribution

It introduces a detailed analysis of the relationship between bending rigidity and knotting behavior, highlighting a non-zero rigidity optimal point and localization effects.

Findings

Minimum free-energy cost at non-zero bending rigidity

Power-law dependence of rigidity minimum on tension

Knots localize in regions with optimal rigidity

Abstract

A coarse-grained computational model is used to investigate how the bending rigidity of a polymer under tension affects the formation of a trefoil knot. Thermodynamic integration techniques are applied to demonstrate that the free-energy cost of forming a knot has a minimum at non-zero bending rigidity. The position of the minimum exhibits a power-law dependence on the applied tension. For knotted polymers with non-uniform bending rigidity, the knots preferentially localize in the region with a bending rigidity that minimizes the free-energy.