Foamlike properties in networks of bundled semiflexible polymers

Abstract

We simulate large systems of mutually attractive semiflexible polymers such as actin filaments in quasi-two dimensions with recently developed event-chain Monte Carlo and molecular dynamics techniques. An isotropic initial state generically evolves into a network of bundles of polymers, which slowly coarsens over time. This explains why networks of bundles are frequently observed in cytoskeletal systems, although one single polymer bundle appears to have a lower free energy. The resulting structure aims to minimize the overall bundle length, which gives rise to properties reminiscent of foams. We apply laws and relations characterizing the structure of foams to the polymer bundle networks. While the empirical Feltham law, as well as the Aboav-Weaire relation, apply to our system, Plateau's law is not followed due to anisotropy and bending stiffness. The coarsening dynamics of the bundle networks are found to be very sensitive with respect to details of the polymer interactions and to deviate from a pure power-law growth of the mean enclosed area, albeit qualitative resemblance to foams remains. We develop a scaling theory capturing the observed coarsening process based on a solidlike friction law for polymer motion in a bundle.