Successive instabilities in elastic filaments driven by molecular motors

Active microfilaments are ubiquitous in cellular and sub-cellular processes that involve motility and cargo transport. Examples include the beating motion of cilia and flagella, the formation of the mitotic spindle during cell division, and cytoskeleton-driven motility.  In these systems, molecular motors bind to microtubules, exerting axial forces along these filaments. Experimental assays have demonstrated that motor-driven microtubules exhibit rich dynamical behaviors from straight to curled configurations. Here, we theoretically investigate the dynamic instabilities of elastic filaments, with free-ends, due to a single follower force. Using the resistive force theory at low Reynolds number, and a combination of numerical techniques with linear stability analysis, we show the existence of five distinct regimes of filament behavior, including a buckled state with locked curvature similar to experimental observations.