Effects of cross-links on motor-mediated filament organization

Cross-links and molecular motors play an important role in the organization of cytoskeletal filament networks. Here, we incorporate the effect of cross-links into our model of polar motor-filament organization (Aranson and Tsimring 2005 Phys. Rev. E 71 050901), through suppressing the relative sliding of filaments in the course of motor-mediated alignment. We show that this modification leads to a nontrivial macroscopic behavior, namely the oriented state exhibits a transverse instability in contrast to the isotropic instability that occurs without cross-links. This transverse instability leads to the formation of dense extended bundles of oriented filaments, similar to the recently observed structures in actomyosin. This model can be also applied to situations with two oppositely directed motor species or motors with different processing speeds.