Resolution of sub-element length scales in Brownian dynamics simulations of biopolymer networks with geometrically exact beam finite elements

Networks of crosslinked biopolymer filaments such as the cytoskeleton are the subject of intense research. Oftentimes, mechanics on the scale of single monomers ( ~ 5 n m ) govern the mechanics of the entire network ( ~ 10 μ m ). Until now, one either resolved the small scales and lost the big (network) picture or focused on mechanics above the single-filament scale and neglected the molecular architecture. Therefore, the study of network mechanics influenced by the entire spectrum of relevant length scales has been infeasible so far. We propose a method that reconciles both small and large length scales without the otherwise inevitable loss in either numerical efficiency or geometrical (molecular) detail. Both explicitly modeled species, filaments and their crosslinkers, are discretized with geometrically exact beam finite elements of Simo-Reissner type. Through specific coupling conditions between the elements of the two species, mechanical joints can be established anywhere along a beam's centerline, enabling arbitrary densities of chemical binding sites. These binding sites can be oriented to model the monomeric architecture of polymers. First, we carefully discuss the method and then demonstrate its capabilities by means of a series of numerical examples.