Equilibrium Size Distribution of Twisted Biopolymer Bundles

Using a continuum elastic model of hexagonal filament packing, we demonstrate that molecular-scale chirality strongly affects the equilibrium properties of aggregates, or bundles, of biopolymers, such as DNA and F-actin. We show that biopolymers tend to form bundles with long-range, chiral stress patterns, twisting or braiding helically around the central bundle axis. Due to the build-up of elastic stress on the outer surface, the cohesive energy of chiral filament bundles has a non-monotonic dependence on filament number. As a consequence, we demonstrate for two cases--bundles with 1) columnar-hexagonal order and 2) columnar-solid order--that a stable phase of dispersed bundles is thermodynamically stable below the point of bulk condensation and below a critical surface energy for the bundle exterior. This work suggests that the large characteristic radius biopolymer bundles observed in {\it in vitro} studies of is not a product of some mysterious long-range force or kinetic limitations of bundle growth, but rather in-plane elastic stresses which result from the local preference for the chiral packing of filaments.