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

• Published in: Journal of computational physics Vol. 303; pp. 185 - 202
• Main Authors: Müller, Kei W., Meier, Christoph, Wall, Wolfgang A.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.12.2015
• Subjects: Architecture; Binding sites; Biopolymer networks; Biopolymers; Brownian dynamics simulations; Crosslinking; Cytoskeleton; Filaments; Geometrically exact beam finite elements; Mathematical analysis; Mathematical models; Networks; Polymer physics; Geometrically exact beam finite elements; Biopolymer networks; Cytoskeleton; Polymer physics; Brownian dynamics simulations
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2015.09.038

Networks of crosslinked biopolymer filaments such as the cytoskeleton are the subject of intense research. Oftentimes, mechanics on the scale of single monomers (∼5 nm) govern the mechanics of the entire network (∼10 μm). 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. •We model crosslinked biopolymer networks with Brownian dynamics beam finite elements.•Decoupling chemical and mechanical resolution, we boost computational efficiency.•Our approach allows for network simulations reaching the scale of eukaryotic cells.•We account for polar and chiral polymers and filament-linker reaction kinetics.•We simulate the evolution, rheology, and effects of chirality of large networks.