  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.
