Free energy and extension of a semiflexible polymer in cylindrical confining geometries

We consider a long, semiflexible polymer with persistence length P and contour length L fluctuating in a narrow cylindrical channel of diameter D. In the regime D < P < L the free energy of confinement Delta F and the length of the channel R-parallel to occupied by the polymer are given by Odijk's relations Delta F/R-parallel to=A(o)k(B)TP(-1/3)D(-2/3) and R-parallel to=L[1-alpha(o)(D/P)(2/3)], where A(o) and alpha(o) are dimensionless amplitudes. Using a simulation algorithm inspired by the pruned enriched Rosenbluth method, which yields results for very long polymers, we determine A(o) and alpha(o) and the analogous amplitudes for a channel with a rectangular cross section. For a semiflexible polymer confined to the surface of a cylinder, the corresponding amplitudes are derived with an exact analytic approach. The results are relevant for interpreting experiments on biopolymers in microchannels or microfluidic devices.