# Behavior of Active Polymer Knots

## TL;DR

This paper studies how active forces affect polymer knots, revealing new behaviors like knot tightening and breathing, which could be relevant to biopolymers like DNA.

## Contribution

The study reveals novel behaviors of active polymer knots, including activity-induced stretching and knot breathing, supported by simulations and an approximate theory.

## Key findings

- Active force significantly tightens knots through an activity-induced stretching effect.
- Active polymer knots exhibit knot breathing, switching between loose and tight states.
- Activity-induced shrinkage is counteracted in long chains by segment reallocation between knotted and unknotted regions.

## Abstract

We investigate active polymer knots
using Brownian dynamics simulations.
We find the interplay of active force, chain connectivity, and knotting
leads to several unexpected phenomena. First, active force significantly
tightens knots through activity-induced stretching effect. The magnitude
of the stretching effect differs greatly in and out of the knot core,
probably because knotting modifies the arrangement of monomers and
thus affects the stretching effect. We develop an approximate theory
to quantify the dependence of the knot size on Péclet number Pe, which describes the activity strength. Second, active
polymer knots significantly differ dynamically from nonactive polymer
knots under tension. For example, active polymers exhibit knot breathing,
i.e., switching between a very loose knot and a very tight knot, which
is absent in nonactive knot under tension. Third, activity can shrink
the conformations of very short chains, and knotting appears to enhance
this activity-induced shrinkage. Fourth, in long knotted chains, activity-induced
shrinkage vanishes because activity can reallocate segments from the
knotted to the unknotted portion. This reallocation enlarges the overall
conformation, counteracting the shrinkage effect. These results may
have biological implications, considering that active force, chain
connectivity, and knotting exist in biopolymers, such as DNA.