  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 are long-lived metastable states. We
propose three possible mechanisms of kink stabilization: a difference in
trapped length of the filament segments between two cross links; a dislocation
where the endpoint of a filament occurs within the bundle, and the braiding of
the filaments in the bundle. At a high concentration of cross links, the last
two effects lead to the topologically protected kinked states. Finally, we
explore numerically and analytically the transition of the metastable kinked
state to the stable straight bundle.
