Stochastic curvature of enclosed semiflexible polymers

The conformational states of a semiflexible polymer enclosed in a compact domain of typical size a are studied as stochastic realizations of paths defined by the Frenet equations under the assumption that stochastic "curvature" satisfies a white noise fluctuation theorem. This approach allows us to derive the Hermans-Ullman equation, where we exploit a multipolar decomposition that allows us to show that the positional probability density function is well described by a telegrapher's equation whenever 2a/ℓ_{p}>1, where ℓ_{p} is the persistence length. We also develop a Monte Carlo algorithm for use in computer simulations in order to study the conformational states in a compact domain. In addition, the case of a semiflexible polymer enclosed in a square domain of side a is presented as an explicit example of the formulated theory and algorithm. In this case, we show the existence of a polymer shape transition similar to the one found by Spakowitz and Wang [Phys. Rev. Lett. 91, 166102 (2003)PRLTAO0031-900710.1103/PhysRevLett.91.166102] where in this case the critical persistence length is ℓ_{p}^{*}≃a/8 such that the mean-square end-to-end distance exhibits an oscillating behavior for values ℓ_{p}>ℓ_{p}^{*}, whereas for ℓ_{p}<ℓ_{p}^{*} it behaves monotonically increasing.