{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T23:01:31Z","timestamp":1790895691723,"version":"4.1.0"},"reference-count":52,"publisher":"The Royal Society","issue":"136","license":[{"start":{"date-parts":[[2017,11,22]],"date-time":"2017-11-22T00:00:00Z","timestamp":1511308800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/royalsocietypublishing.org\/licence"},{"start":{"date-parts":[[2017,11,22]],"date-time":"2017-11-22T00:00:00Z","timestamp":1511308800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"crossref","award":["EP\/M017982\/1"],"award-info":[{"award-number":["EP\/M017982\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100011199","name":"FP7 Ideas: European Research Council","doi-asserted-by":"crossref","award":["247333"],"award-info":[{"award-number":["247333"]}],"id":[{"id":"10.13039\/100011199","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/100011199","name":"FP7 Ideas: European Research Council","doi-asserted-by":"crossref","award":["682754"],"award-info":[{"award-number":["682754"]}],"id":[{"id":"10.13039\/100011199","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2017,11,30]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>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 \u2018follower-force\u2019 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 \u2018two-link\u2019 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.<\/jats:p>","DOI":"10.1098\/rsif.2017.0491","type":"journal-article","created":{"date-parts":[[2017,11,22]],"date-time":"2017-11-22T05:10:19Z","timestamp":1511327419000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":100,"title":["Spontaneous oscillations of elastic filaments induced by molecular motors"],"prefix":"10.1098","volume":"14","author":[{"given":"Gabriele","family":"De Canio","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8916-2545","authenticated-orcid":false,"given":"Eric","family":"Lauga","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2645-0598","authenticated-orcid":false,"given":"Raymond E.","family":"Goldstein","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2017,11,22]]},"reference":[{"key":"2026022415245937600_RSIF20170491C1","volume-title":"Osservazione microscopiche sulla tremella e sulla circulazione del fluido in una planto acquaguola","author":"Corti","year":"1774"},{"key":"2026022415245937600_RSIF20170491C2","doi-asserted-by":"crossref","DOI":"10.1098\/rsfs.2015.0030","article-title":"A physical perspective on cytoplasmic streaming","volume":"5","author":"Goldstein","year":"2015","journal-title":"Interface Focus"},{"key":"2026022415245937600_RSIF20170491C3","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/BF02524260","article-title":"Microtubule disassembly enhances reversible cytochalasin-dependent disruption of actin bundles in characean internodes","volume":"214","author":"Foissner","year":"2000","journal-title":"Protoplasma"},{"key":"2026022415245937600_RSIF20170491C4","doi-asserted-by":"crossref","first-page":"14 132","DOI":"10.1073\/pnas.1302736110","article-title":"Cytoplasmic streaming in plant cells emerges naturally by microfilament self-organization","volume":"110","author":"Woodhouse","year":"2013","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2026022415245937600_RSIF20170491C5","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1242\/dev.115.4.923","article-title":"Reorganization of the cytoskeleton during Drosophila oogenesis: implications for axis specification and intercellular transport","volume":"115","author":"Theurkauf","year":"1992","journal-title":"Development"},{"key":"2026022415245937600_RSIF20170491C6","doi-asserted-by":"crossref","first-page":"15 109","DOI":"10.1073\/pnas.1203575109","article-title":"Cytoplasmic streaming in drosophila oocytes varies with kinesin activity and correlates with the microtubule cytoskeleton architecture","volume":"109","author":"Ganguly","year":"2012","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2026022415245937600_RSIF20170491C7","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1016\/j.neuron.2010.09.039","article-title":"Molecular motors in neurons: transport mechanisms and roles in brain function, development, and disease","volume":"68","author":"Hirokawa","year":"2010","journal-title":"Neuron"},{"key":"2026022415245937600_RSIF20170491C8","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1103\/PhysRevLett.75.176","article-title":"Spiral defects in motility assays: a measure of motor protein force","volume":"75","author":"Bourdieu","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"2026022415245937600_RSIF20170491C9","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1016\/S0006-3495(96)79585-1","article-title":"Directional loading of the kinesin motor molecule as it buckles a microtubule","volume":"70","author":"Gittes","year":"1996","journal-title":"Biophys. J."},{"key":"2026022415245937600_RSIF20170491C10","doi-asserted-by":"crossref","first-page":"1736","DOI":"10.1083\/jcb.100.5.1736","article-title":"Gliding movement of and bidirectional transport along single native microtubules from squid axoplasm: evidence for an active role of microtubules in cytoplasmic transport","volume":"100","author":"Allen","year":"1985","journal-title":"J. Cell Biol."},{"key":"2026022415245937600_RSIF20170491C11","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevE.82.016309","article-title":"Dynamics of a semiflexible polar filament in Stokes flow","volume":"82","author":"Young","year":"2010","journal-title":"Phys. Rev. E"},{"key":"2026022415245937600_RSIF20170491C12","doi-asserted-by":"crossref","first-page":"7181","DOI":"10.1039\/C5SM01683E","article-title":"Self-propelled worm-like filaments: spontaneous spiral formation, structure, and dynamics","volume":"11","author":"Isele-Holder","year":"2015","journal-title":"Soft Matter"},{"key":"2026022415245937600_RSIF20170491C13","doi-asserted-by":"crossref","first-page":"2157","DOI":"10.1039\/C5SM02574E","article-title":"Forced desorption of semiflexible polymers, adsorbed and driven by molecular motors","volume":"12","author":"Chaudhuri","year":"2016","journal-title":"Soft Matter"},{"key":"2026022415245937600_RSIF20170491C14","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/j.physd.2015.10.022","article-title":"On complex, curved trajectories in microtubule gliding","volume":"318\u2013319","author":"Gosselin","year":"2016","journal-title":"Phys. D"},{"key":"2026022415245937600_RSIF20170491C15","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1016\/j.bpj.2016.03.036","article-title":"A mechanism for cytoplasmic streaming: kinesin-driven alignment of microtubules and fast fluid flows","volume":"110","author":"Monteith","year":"2016","journal-title":"Biophys. J."},{"key":"2026022415245937600_RSIF20170491C16","doi-asserted-by":"crossref","DOI":"10.1088\/1367-2630\/aa5f80","article-title":"Filament actuation by an active colloid at low Reynolds number","volume":"19","author":"Laskar","year":"2017","journal-title":"New J. Phys."},{"key":"2026022415245937600_RSIF20170491C17","author":"De Canio"},{"key":"2026022415245937600_RSIF20170491C18","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1115\/1.3629660","article-title":"On the stability of elastic systems subjected to nonconservative forces","volume":"31","author":"Herrmann","year":"1964","journal-title":"J. Appl. Mech."},{"key":"2026022415245937600_RSIF20170491C19","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1006\/jsvi.2000.3137","article-title":"Dynamic stability of columns subjected to follower loads: a survey","volume":"238","author":"Langthjem","year":"2000","journal-title":"J. Sound Vib."},{"key":"2026022415245937600_RSIF20170491C20","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1115\/1.1849170","article-title":"Controversy associated with the so-called \u2018follower forces\u2019: critical overview","volume":"58","author":"Elishakoff","year":"2005","journal-title":"Appl. Mech. Rev."},{"key":"2026022415245937600_RSIF20170491C21","doi-asserted-by":"crossref","DOI":"10.1098\/rsif.2016.0523","article-title":"Steady dynein forces induce flutter instability and propagating waves in mathematical models of flagella","volume":"13","author":"Bayly","year":"2016","journal-title":"J. R. Soc. Interface"},{"key":"2026022415245937600_RSIF20170491C22","doi-asserted-by":"crossref","first-page":"923","DOI":"10.1083\/jcb.120.4.923","article-title":"Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape","volume":"120","author":"Gittes","year":"1993","journal-title":"J. Cell Biol."},{"key":"2026022415245937600_RSIF20170491C23","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1016\/0092-8674(94)90060-4","article-title":"Force and velocity measured for single kinesin molecules","volume":"77","author":"Svoboda","year":"1994","journal-title":"Cell"},{"key":"2026022415245937600_RSIF20170491C24","volume-title":"Elasticity and geometry: from hair curls to the non-linear response of shells","author":"Audoly","year":"2010"},{"key":"2026022415245937600_RSIF20170491C25","doi-asserted-by":"crossref","first-page":"1094","DOI":"10.1103\/PhysRevLett.75.1094","article-title":"Nonlinear dynamics of stiff polymers","volume":"75","author":"Goldstein","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"2026022415245937600_RSIF20170491C26","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1242\/jeb.32.4.802","article-title":"The propulsion of sea-urchin spermatozoa","volume":"32","author":"Gray","year":"1955","journal-title":"J. Exp. Biol."},{"key":"2026022415245937600_RSIF20170491C27","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1017\/S002211207000215X","article-title":"The motion of long slender bodies in a viscous fluid part 1. General theory","volume":"44","author":"Cox","year":"1970","journal-title":"J. Fluid Mech."},{"key":"2026022415245937600_RSIF20170491C28","doi-asserted-by":"crossref","first-page":"8169","DOI":"10.1039\/c1sm05503h","article-title":"High-speed propulsion of flexible nanowire motors: theory and experiments","volume":"7","author":"Pak","year":"2011","journal-title":"Soft Matter"},{"key":"2026022415245937600_RSIF20170491C29","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1137\/1018040","article-title":"Flagellar hydrodynamics","volume":"18","author":"Lighthill","year":"1976","journal-title":"SIAM Rev."},{"key":"2026022415245937600_RSIF20170491C30","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1098\/rspa.1953.0048","article-title":"The self-propulsion of microscopic organisms through liquids","volume":"217","author":"Hancock","year":"1953","journal-title":"Proc. R. Soc. Lond. A"},{"key":"2026022415245937600_RSIF20170491C31","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1017\/S0022112076000475","article-title":"Slender-body theory for slow viscous flow","volume":"75","author":"Keller","year":"1976","journal-title":"J. Fluid Mech."},{"key":"2026022415245937600_RSIF20170491C32","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/S0006-3495(79)85281-9","article-title":"Flagellar hydrodynamics. a comparison between resistive-force theory and slender-body theory","volume":"25","author":"Johnson","year":"1979","journal-title":"Biophys. J."},{"key":"2026022415245937600_RSIF20170491C33","doi-asserted-by":"crossref","first-page":"3879","DOI":"10.1103\/PhysRevLett.80.3879","article-title":"Flexive and propulsive dynamics of elastica at low Reynolds number","volume":"80","author":"Wiggins","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"2026022415245937600_RSIF20170491C34","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1016\/S0006-3495(98)74029-9","article-title":"Trapping and wiggling: elastohydrodynamics of driven microfilaments","volume":"74","author":"Wiggins","year":"1998","journal-title":"Biophys. J."},{"key":"2026022415245937600_RSIF20170491C35","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.108.038103","article-title":"Fluctuations, dynamics, and the stretch-coil transition of single actin filaments in extensional flows","volume":"108","author":"Kantsler","year":"2012","journal-title":"Phys. Rev. Lett."},{"key":"2026022415245937600_RSIF20170491C36","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.99.058303","article-title":"Stretch-coil transition and transport of fibers in cellular flows","volume":"99","author":"Young","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"2026022415245937600_RSIF20170491C37","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.87.198301","article-title":"Instability of elastic filaments in shear flow yields first-normal-stress differences","volume":"87","author":"Becker","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"2026022415245937600_RSIF20170491C38","volume-title":"A first course in the numerical analysis of differential equations","author":"Iserles","year":"1996"},{"key":"2026022415245937600_RSIF20170491C39","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1017\/jfm.2015.115","article-title":"Transport and buckling dynamics of an elastic fibre in a viscous cellular flow","volume":"769","author":"Quennouz","year":"2015","journal-title":"J. Fluid Mech."},{"key":"2026022415245937600_RSIF20170491C40","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1146\/annurev.fl.09.010177.002011","article-title":"Fluid mechanics of propulsion by cilia and flagella","volume":"9","author":"Brennen","year":"1977","journal-title":"Annu. Rev. Fluid Mech."},{"key":"2026022415245937600_RSIF20170491C41","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139178938","volume-title":"Nonlinear solid mechanics: bifurcation theory and material instability","author":"Bigoni","year":"2012"},{"key":"2026022415245937600_RSIF20170491C42","volume-title":"Theory of elasticity","author":"Landau","year":"1986"},{"key":"2026022415245937600_RSIF20170491C43","doi-asserted-by":"crossref","DOI":"10.1063\/1.4771606","article-title":"Buckling transitions of an elastic filament in a viscous stagnation point flow","volume":"24","author":"Guglielmini","year":"2012","journal-title":"Phys. Fluids"},{"key":"2026022415245937600_RSIF20170491C44","doi-asserted-by":"crossref","first-page":"4962","DOI":"10.1039\/C4SM02395A","article-title":"Effects of thermal noise on the transitional dynamics of an inextensible elastic filament in stagnation flow","volume":"11","author":"Deng","year":"2015","journal-title":"Soft Matter"},{"key":"2026022415245937600_RSIF20170491C45","volume-title":"Methodus lnveniendi Lineas Curvas Maximi Minimive Proprietate Gaudentes (Appendix, De curvis elasticis)","author":"Euler","year":"1774"},{"key":"2026022415245937600_RSIF20170491C46","volume-title":"Theory of elastic stability","author":"Timoshenko","year":"1970","edition":"2nd edn"},{"key":"2026022415245937600_RSIF20170491C47","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF02008828","article-title":"Die Knicklast des einseitig eingespannten, tangential gedr\u00fcckten Stabes","volume":"3","author":"Beck","year":"1952","journal-title":"Z. Angew. Math. Phys."},{"key":"2026022415245937600_RSIF20170491C48","first-page":"49","article-title":"Die stabilit\u00e4tskriterien der elastomechanik","volume":"20","author":"Ziegler","year":"1952","journal-title":"Arch. Appl. Mech."},{"key":"2026022415245937600_RSIF20170491C49","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/0771-050X(80)90013-3","article-title":"A family of embedded Runge-Kutta formulae","volume":"6","author":"Dormand","year":"1980","journal-title":"J. Comput. Appl. Math."},{"key":"2026022415245937600_RSIF20170491C50","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1017\/S0022112075000614","article-title":"Hydromechanics of low-Reynolds-number flow. 2. Singularity method for Stokes flows","volume":"67","author":"Chwang","year":"1975","journal-title":"J. Fluid Mech."},{"key":"2026022415245937600_RSIF20170491C51","doi-asserted-by":"crossref","first-page":"4600","DOI":"10.1016\/j.jcp.2008.01.032","article-title":"The method of images for regularized Stokeslets","volume":"227","author":"Ainley","year":"2008","journal-title":"J. Comput. Phys."},{"key":"2026022415245937600_RSIF20170491C52","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/BF02353701","article-title":"Fundamental singularities of viscous flow. Part 1. Image systems in vicinity of a stationary no-slip boundary","volume":"8","author":"Blake","year":"1974","journal-title":"J. Eng. Math."}],"container-title":["Journal of The Royal Society Interface"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rsif.2017.0491","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/full-xml\/10.1098\/rsif.2017.0491","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/rsif\/article-pdf\/doi\/10.1098\/rsif.2017.0491\/471405\/rsif.2017.0491.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/royalsocietypublishing.org\/rsif\/article-pdf\/doi\/10.1098\/rsif.2017.0491\/471405\/rsif.2017.0491.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T20:25:14Z","timestamp":1771964714000},"score":1,"resource":{"primary":{"URL":"https:\/\/royalsocietypublishing.org\/rsif\/article\/14\/136\/20170491\/64852\/Spontaneous-oscillations-of-elastic-filaments"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,22]]},"references-count":52,"journal-issue":{"issue":"136","published-print":{"date-parts":[[2017,11,30]]}},"URL":"https:\/\/doi.org\/10.1098\/rsif.2017.0491","relation":{},"ISSN":["1742-5689","1742-5662"],"issn-type":[{"value":"1742-5689","type":"print"},{"value":"1742-5662","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,22]]},"assertion":[{"value":"2017-07-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-10-30","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-11-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"20170491"}}