dorsal/arxiv
View SchemaPhysical Aspects of Axonemal Beating and Swimming
| Authors | Sebastien Camalet, Frank Julicher |
|---|---|
| Categories | |
| ArXiv ID | physics/0003101 |
| URL | https://arxiv.org/abs/physics/0003101 |
| DOI | 10.1088/1367-2630/2/1/324 |
| Journal | New Journal of Physics 2, 24 (2000) |
Abstract
We discuss a two-dimensional model for the dynamics of axonemal deformations driven by internally generated forces of molecular motors. Our model consists of an elastic filament pair connected by active elements. We derive the dynamic equations for this system in presence of internal forces. In the limit of small deformations, a perturbative approach allows us to calculate filament shapes and the tension profile. We demonstrate that periodic filament motion can be generated via a self-organization of elastic filaments and molecular motors. Oscillatory motion and the propagation of bending waves can occur for an initially non-moving state via an instability termed Hopf bifurcation. Close to this instability, the behavior of the system is shown to be independent of microscopic details of the axoneme and the force-generating mechanism. The oscillation frequency however does depend on properties of the molecular motors. We calculate the oscillation frequency at the bifurcation point and show that a large frequency range is accessible by varying the axonemal length between 1 and 50$\mu$m. We calculate the velocity of swimming of a flagellum and discuss the effects of boundary conditions and externally applied forces on the axonemal oscillations.
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"abstract": "We discuss a two-dimensional model for the dynamics of axonemal deformations\ndriven by internally generated forces of molecular motors. Our model consists\nof an elastic filament pair connected by active elements. We derive the dynamic\nequations for this system in presence of internal forces. In the limit of small\ndeformations, a perturbative approach allows us to calculate filament shapes\nand the tension profile. We demonstrate that periodic filament motion can be\ngenerated via a self-organization of elastic filaments and molecular motors.\nOscillatory motion and the propagation of bending waves can occur for an\ninitially non-moving state via an instability termed Hopf bifurcation. Close to\nthis instability, the behavior of the system is shown to be independent of\nmicroscopic details of the axoneme and the force-generating mechanism. The\noscillation frequency however does depend on properties of the molecular\nmotors. We calculate the oscillation frequency at the bifurcation point and\nshow that a large frequency range is accessible by varying the axonemal length\nbetween 1 and 50$\\mu$m. We calculate the velocity of swimming of a flagellum\nand discuss the effects of boundary conditions and externally applied forces on\nthe axonemal oscillations.",
"arxiv_id": "physics/0003101",
"authors": [
"Sebastien Camalet",
"Frank Julicher"
],
"categories": [
"physics.bio-ph"
],
"doi": "10.1088/1367-2630/2/1/324",
"journal_ref": "New Journal of Physics 2, 24 (2000)",
"title": "Physical Aspects of Axonemal Beating and Swimming",
"url": "https://arxiv.org/abs/physics/0003101"
},
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