Spontaneous oscillations of elastic filaments induced by molecular motors. Issue 136 (22nd November 2017)

• Record Type: Journal Article
• Authors: De Canio, Gabriele; Lauga, Eric; Goldstein, Raymond E.
• Is Part Of: Journal of the Royal Society interface. Volume 14:Issue 136(2017)
• Publication Date: 2017-11-22
• Subjects: cytoskeleton -- molecular motors -- buckling instability -- flapping dynamics; Physical sciences -- Research -- Periodicals; Life sciences -- Research -- Periodicals; Interdisciplinary research -- Periodicals; 570.5
• DOI: 10.1098/rsif.2017.0491
• Languages: English
• ISSNs: 1742-5689

Abstract

Abstract : It is known from the wave-like motion of microtubules in motility assays that the piconewton forces that motors produce can be sufficient to bend the filaments. In cellular phenomena such as cytosplasmic streaming, molecular motors translocate along cytoskeletal filaments, carrying cargo which entrains fluid. When large numbers of such forced filaments interact through the surrounding fluid, as in particular stages of oocyte development in Drosophila melanogaster, complex dynamics are observed, but the detailed mechanics underlying them has remained unclear. Motivated by these observations, we study here perhaps the simplest model for these phenomena: an elastic filament, pinned at one end, acted on by a molecular motor treated as a point force. Because the force acts tangential to the filament, no matter what its shape, this 'follower-force' problem is intrinsically non-variational, and thereby differs fundamentally from Euler buckling, where the force has a fixed direction, and which, in the low-Reynolds-number regime, ultimately leads to a stationary, energy-minimizing shape. Through a combination of linear stability theory, analytical study of a solvable simplified 'two-link' model and numerical studies of the full elastohydrodynamic equations of motion, we elucidate the Hopf bifurcation that occurs with increasing forcing of a filament, leading to flapping motion analogous to the high-Reynolds-number oscillations of a garden hose with a free end.