Radial Distribution Function for Semiflexible Polymers Confined in Microchannels

An analytic expression is derived for the distribution G(~ R) of the end-to-end distance ~ R of semiflexible polymers in external potentials to elucidate the effect of confinement on the mechanical and statistical properties of biomolecules. For parabolic confinement the result is exact whereas for realistic potentials a self-consistent ansatz is developed, so that G(~ R) is given explicitly even for hard wall confinement. The theoretical result is in excellent quantitative agreement with fluorescence microscopy data for actin filaments confined in rectangularly shaped microchannels. This allows an unambiguous determination of persistence length LP and the dependence of statistical properties such as Odijk’s deflection length λ on the channel width D. It is shown that neglecting the effect of confinement leads to a significant overestimation of bending rigidities for filaments. Bending of semiflexible macromolecules such as actin filaments play a crucial role for the mechanical properties of cells [1]. In general, the motion of biopolymers such as DNA or actin filaments takes place in gels or cytoplasm where sterical constraints forces a single molecule to bend in addition to the bending constantly induced by thermal motion. Advances in microfluidic techniques and in the direct visualization of actin filaments [2, 3, 4, 5, 6] make it nowadays possible to study experimentally the interplay of thermal fluctuations and confinement in controlled environments. Although the dynamics of single biomolecules can be measured for almost 20 years by fluorescence microscopy in simple confining geometries [7, 8, 9, 10] as well as