Structural Transitions and Soft Modes in Frustrated DNA Crystals

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.

7 pages, 3 figures (revised version)

References in corpus (4)

• Phase Behavior of Columnar DNA Assemblies
• Positional, Reorientational and Bond Orientational Order in DNA Mesophases
• Statistical mechanics of columnar DNA assemblies
• Frustrated Polyelectrolyte Bundles and T=0 Josephson-Junction Arrays

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• Multiple phase transitions in the $XY$ model with nematic-like couplings
• Phase diagrams of antiferromagnetic $XY$ model on a triangular lattice with higher-order interactions
• Energetic preference and topological constraint effects on the formation of DNA twisted toroidal bundles
• XY model with competing higher-order interactions
• Generalized $XY$ model with competing antiferromagnetic and antinematic interactions