Structural Transitions and Soft Modes in Frustrated DNA Crystals

TL;DR

This paper investigates the structural phase transitions and elastic properties of frustrated DNA crystals, revealing that frustration leads to highly anisotropic and soft in-plane elastic responses due to symmetry and coupling effects.

Contribution

It introduces a Landau-Ginzburg free energy framework for DNA crystal phase transitions, highlighting the role of frustration in elastic anisotropy and soft modes.

Findings

Frustrated DNA crystals show highly anisotropic elastic responses.

Coupling between backbone displacements and in-plane order influences elasticity.

Frustration causes increased softness to shear deformations.

Abstract

Relying on symmetry considerations appropriate for helical biopolymers such as DNA and filamentous actin, we argue that crystalline packings of mutually repulsive helical macromolecules fall principally into two categories: unfrustrated (hexagonal) and frustrated (rhombohedral). For both cases, we construct the Landau-Ginzburg free energy for the 2D columnar-hexagonal to 3D crystalline phase transition, including the coupling between molecular displacements {\it along} biopolymer backbone to displacements in the plane of hexagonal order. We focus on the distinct elastic properties that emerge upon crystallization of helical arrays due to this coupling. Specifically, we demonstrate that frustrated states universally exhibit a highly anisotropic in-plane elastic response, characterized by an especially soft compliance to simple-shear deformations and a comparatively large resistance to those deformations that carry the array from the low- to high-density crystalline states of DNA.