Buckling, bundling, and pattern formation:: From semi-flexible polymers to assemblies of interacting filaments

Semiflexible polymers and filaments play an important role in biological and chemical physics. Single filaments are characterized by a certain bending rigidity which governs their persistence length and buckling instabilities. Attractive mutual interactions of filaments in bundles or the attractive interaction with an adhesive substrate lead to equilibrium phase transitions, such as bundling and adsorption. Finally, on the level of active systems consisting of many interacting filaments, we discuss cooperative ordering effects in non-equilibrium systems such as motility assays. In motility assays filaments are adsorbed and driven by motor proteins, which are anchored to a planar two-dimensional substrate. The interaction with motor proteins leads to enhanced ordering of filaments. Motility assays containing patterns of adsorbed motors, i.e., stripes of low motor density with increasing widths can be used to sort filaments according to their lengths.