Chiral Symmetry Breaking and Elastic Response of Frustrated Polyelectrolyte Bundles

We present a model for hexagonal aggregates of charged, cylindrical macromolecules (DNA, microtubules, F-actin, {\it etc.}) in the presence of multivalent counterions at low temperature. Using the Wigner crystal picture of the neutralizing charge condensed onto the rod-like macromolecules, we establish a one-to-one mapping between the statistical mechanics of the charged bundle system and those governing the $T=0$ properties of a two-dimensional, frustrated Josephson junction array. We find that the superconducting phase of the {\it quantum} system corresponds to the low-temperature phase of our {\it classical} bundle system, where the condensed counterions are ordered in three dimensions, while the insulating phase corresponds to the phase where one-dimensional phonon fluctuations destroy long-range order of the condensed charge. Remarkably, the mapping makes the prediction that the transition to the charge-ordered state should be accompanied by a spontaneous breaking of chiral symmetry (even in the absence of any molecular chirality). Finally, we exploit the well-studied critical properties of the electromagnetic response of the two-dimensional {\it quantum} system to deduce the elastic response of the {\it classical} charged-rod bundle system.