Finite-element Brownian dynamics simulations of biopolymer filament bundles and networks

Cross-linked, semiflexible filaments form bundles and networks, which are ubiquitous, load-bearing structures in the cytoskeleton and extracellular matrix. We perform large-scale numerical simulations of such complex, three-dimensional fibrous systems in order to explore their fundamental mechanical properties. This is enabled by our efficient, mesoscopic modeling approach, which uses nonlinear beam finite elements to model the filaments, and additionally includes stochastic thermal forces and viscous drag to account for their Brownian dynamics. The random binding and unbinding of cross-linker molecules is based on given reaction rates and a preferred binding length and orientation.

In our latest work, we investigate topological defects in self-assembled bundles that lead to metastable, yet long-lived, disordered configurations [1]. As it turns out, such defects can produce localized, sharp bends in the bundles that are reminiscent of the crimped patterns typically observed in collagen fibers. Our simulations also show that missing cross links in the vicinity of the defects cause a significant reduction of the bundle's local bending modulus. This in turn challenges the simple understanding of a filament bundle as a single thicker and thus stiffer filament. Using simulations on longer time scales finally allows us to investigate the dynamics of defects as they move along the bundles and interact with each other. Motivated by this work, we intend to study the frequency-dependent mechanical properties of transiently cross-linked fiber bundles. A final overview of our other projects aims to outline the high versatility and performance of the applied research code BACI [2] and thereby inspire further applications.

[1] V. Slepukhin, M. Grill, Q. Hu, E. Botvinick, W. Wall, A. Levine, Disordered biopolymer filament bundles: Topological defects and kinks, In preparation.
[2] BACI: A comprehensive multi-physics simulation framework, https://baci.pages.gitlab.lrz.de/website