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It is known from the wave-like motion of microtubules in motility assays thatthe piconewton forces that motors produce can be sufficient to bend thefilaments. In cellular phenomena such as cytosplasmic streaming, molecularmotors translocate along cytoskeletal filaments, carrying cargo which entrainsfluid. When large numbers of such forced filaments interact through thesurrounding fluid, as in particular stages of oocyte development in$Drosophila~melanogaster$, complex dynamics are observed, but the detailedmechanics underlying them has remained unclear. Motivated by theseobservations, we study here perhaps the simplest model for these phenomena: anelastic filament, pinned at one end, acted on by a molecular motor treated as apoint force. Because the force acts tangential to the filament, no matter whatits shape, this "follower-force" problem is intrinsically non-variational, andthereby differs fundamentally from Euler buckling, where the force has a fixeddirection, and which, in the low Reynolds number regime, ultimately leads to astationary, energy-minimizing shape. Through a combination of linear stabilitytheory, analytical study of a solvable simplified "two-link" model, andnumerical studies of the full elastohydrodynamic equations of motion weelucidate the Hopf bifurcation that occurs with increasing forcing of afilament, leading to flapping motion analogous to the high Reynolds numberoscillations of a garden hose with a free end.

Spontaneous Oscillations of Elastic Filaments Induced by Molecular Motors