A mean field approach to determine the statistics of bundles of wormlike chains

Crosslinked bundles of macromolecules play an important role in a variety of biologically relevant systems, including the flagella that provide locomotion and the microtubules and actin filaments that compose the cytoskeleton. In this talk, I describe a novel method of studying the statistics of weakly-bending, weakly-shearing bundles of stiff polymers using a mean field approach. I show that the imposition of the constraints of inextensibility and inter-filament separation on average leads to an analytically tractable free energy determined by a single wormlike Hamiltonian coupled to an effective Hamiltonian of a cylindrically confined chain, the latter representing the crosslinking between filaments. This gives rise to a bundle free energy that deviates from a typical wormlike chain, depending on a deflection length that couples the filament stiffness and bundle radius. The free energy of an intrinsically twisted bundle is determined for stiff bundles as well, which produces a significant change in the dependence of the free energy on filament stiffness and cross-sectional width. This mean field approach provides new insight into the statistics of bundled macromolecules with a variety of geometric constraints, useful in a number of biological contexts.