The geometrical origin of the strain-twist coupling in double helices

TL;DR

This paper explores the geometric basis of strain-twist coupling in double helices, revealing universal overwinding behavior below a specific pitch angle and identifying zero-twist structures independent of material properties.

Contribution

It introduces a geometric explanation for strain-twist coupling in helices, identifying a universal zero-twist angle and its implications for biological structures.

Findings

Overwinding occurs when the pitch angle is below 39.4 degrees.

Zero-twist angle is independent of mechanical properties.

Estimates of overwinding in DNA, chromatin, and RNA are provided.

Abstract

The geometrical coupling between strain and twist in double helices is investigated. Overwinding, where strain leads to further winding, is shown to be a universal property for helices, which are stretched along their longitudinal axis when the initial pitch angle is below the zero-twist angle (39.4 deg). Unwinding occurs at larger pitch angles. The zero-twist angle is the unique pitch angle at the point between overwinding and unwinding, and it is independent of the mechanical properties of the double helix. This suggests the existence of zero-twist structures, i.e. structures that display neither overwinding, nor unwinding under strain. Estimates of the overwinding of DNA, chromatin, and RNA are given.