Rods-on-string idealization captures semiflexible filament dynamics

Abstract

We present an approach to modeling the two-dimensional Brownian dynamics of semiflexible filaments in the worm-model description as uniform, isotropic, and continuously flexible. Experimental observations increasingly show that the mechanical behavior of semiflexible filament networks departs from conventional knowledge. A force-balance-based dynamic simulation of the filament networks has multiple advantages as an approach to understanding their anomalous mechanics. However, a major disadvantage is the difficulty of capturing filament hydrodynamics and bending mechanics in a computationally efficient and physically consistent manner. To that end, we propose a strategy for modeling semiflexible filaments which involves idealizing a semiflexible filament as a contiguous string of flexible rods, and considering the Brownian forces on it as Einsteinian-like point normal and tangential forces. By idealizing the filament as a string of rods, we avoid the complex hydrodynamic treatment involved in beads-on-string idealizations, and implement large-deflection beam mechanics and filament inextensibility in a natural manner, while reducing the computational size of the problem. By considering the Brownian forces as point normal and tangential forces, we decompose the Brownian forces on straight and curved segments into a combination of classical resultant forces and couples whose distribution is shown to be governed by the rod diffusion coefficients. The decomposition allows solution of the Euler beam equations to second-order continuity between segments and fifth-order continuity within segments. We show that the approach is physically consistent by capturing multiple Brownian phenomena ranging from the rigid to the semiflexible limit: the translational and rotational diffusion of rigid rods; the thermal fluctuation of semirigid cantilever filaments; and the shape, bending, and time relaxation of freely diffusing, semiflexible actin filaments.