# Plectoneme dynamics and statistics in braided polymers

## TL;DR

This paper investigates the formation, dynamics, and statistics of plectonemes in braided polymers using simulations and analytics, revealing phase transitions, kinetic behaviors, and a stochastic theory for twist-writhe coupling.

## Contribution

It introduces a new order parameter and a stochastic field theory to explain plectoneme behavior and phase transitions in braided polymers.

## Key findings

- Identification of phase boundary via plectonemic fraction
- Observation of phase separation kinetics and plectonemic hopping
- Development of a stochastic model explaining coarsening laws

## Abstract

Braids composed of two interwoven polymer chains exhibit a buckling transition whose origin has been explained through the onset of plectonemic structures. Here we study, by a combination of simulation and analytics, the dynamics of plectoneme formation and their statistics in steady state. The introduction of an order parameter, the plectonemic fraction, allows us to map out the phase boundary between the straight braid phase and the plectonemic one. We then monitor the formation and the growth of plectonemes, observing events typical of phase separation kinetics for liquid-gas systems (fusion, fission, 1D Ostwald ripening), but also of DNA supercoiling dynamics (plectonemic hopping). Finally, we propose a stochastic field theory for the coupled dynamics of twist and local writhe which explains the phenomenology found with Brownian dynamics simulations as well the power laws underlying the coarsening of plectonemes.