Conformation of a semiflexible filament in a quenched random potential

Motivated by the observation of the storage of excess elastic free energy, prestress, in cross-linked semiflexible networks, we consider the problem of the conformational statistics of a single semiflexible polymer in a quenched random potential. The random potential, which represents the effect of cross-linking to other filaments, is assumed to have a finite correlation length ξ and mean strength V_{0}. We examine statistical distribution of curvature in filament with thermal persistence length ℓ_{P} and length L_{0} in the limit in which ℓ_{P}≫L_{0}. We compare our theoretical predictions to finite-element Brownian dynamics simulations. Finally, we comment on the validity of replica field techniques in addressing these questions.