# Twist-bend coupling, twist waves and the shape of DNA loops

## TL;DR

This paper combines analytical and numerical methods to study the shape and dynamics of short DNA loops, revealing twist oscillations caused by twist-bend coupling due to DNA's groove asymmetry, and demonstrates their robustness against thermal fluctuations.

## Contribution

It introduces a simple analytical variational shape that accurately models DNA loops and elucidates the role of twist-bend coupling in their shape and dynamics.

## Key findings

- Twist oscillations are observed in DNA loops due to twist-bend coupling.
- The analytical model reproduces loop energy with high accuracy.
- Twist waves are stable against thermal fluctuations and exhibit diffusive motion.

## Abstract

By combining analytical and numerical calculations, we investigate the minimal-energy shape of short DNA loops of approximately $100$ base pairs (bp). We show that in these loops the excess twist density oscillates as a response to an imposed bending stress, as recently found in DNA minicircles and observed in nucleosomal DNA. These twist oscillations, here referred to as twist waves, are due to the coupling between twist and bending deformations, which in turn originates from the asymmetry between DNA major and minor grooves. We introduce a simple analytical variational shape, that reproduces the exact loop energy up to the fourth significant digit, and is in very good agreement with shapes obtained from coarse-grained simulations. We, finally, analyze the loop dynamics at room temperature, and show that the twist waves are robust against thermal fluctuations. They perform a normal diffusive motion, whose origin is briefly discussed.