Braided biopolymer filament bundles produce topologically protected kinks

Bundles of stiff filaments are ubiquitous in the living world, found both in the cytoskeleton and in the extracellular medium. These bundles are typically held together by smaller cross-linking molecules. We demonstrate analytically, numerically and experimentally that such bundles can be kinked, i.e., have localized regions of high curvature that appear to be at least long-lived
metastable states. We find analytically three possible mechanisms of kink stabilization: the different trapped length of the filaments between two cross-links; the endpoint of the filament in the middle of the bundle; the braiding of the filaments in the bundle. For a high concentration of cross-links, last two effects lead to the topologically protected kinked state. Finally, we explore the transition of the metastable kinked state to the stable straight bundle state both numerically and analytically.