Generic aspects of axonemal beating

By S. Camalet, Frank Jülicher. 2000

243 citations recorded by the source corpus.

We study the dynamics of an elastic rod-like filament in two dimensions, driven by internally generated forces. This situation is motivated by cilia and flagella which contain an axoneme. These hair-like appendages of many cells are used for swimming and to stir surrounding fluids. Our approach characterizes the general physical mechanisms that govern the behaviour of axonemes and the properties of the bending waves generated by these structures. Starting from the dynamic equations of a filament pair in the presence of internal forces we use a perturbative approach to systematically calculate filament shapes and the tension profile. We show that periodic filament motion can be generated by a self-organization of elastic filaments and internal active elements, such as molecular motors, via a dynamic instability termed Hopf bifurcation. Close to this instability, the behaviour of the system is shown to be independent of many microscopic details of the active system and only depends on phenomenological parameters such as the bending rigidity, the external viscosity and the filament length. Using a two-state model for molecular motors as an active system, we calculate the selected oscillation frequency at the bifurcation point and show that a large frequency range is accessible by varying the axonemal length between 1 and 50 µm. We discuss the effects of the boundary conditions and externally applied forces on the axonemal wave forms and calculate the swimming velocity for the case of free boundary conditions.

Subfields: Biomedical Engineering, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f5b5bc65ab8885aa87c0a5c5bf446e3320165e7a

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In Biomedical Engineering

In Condensed Matter Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Experimental Investigations of Elastic Tail Propulsion At Low Reynolds Number (2006, methodology): “Local mechanical equilibrium along the rod, leads to a pair of coupled, nonlinear partial differential equations of motion, as shown in [16]:”
Nonequilibrium physics in biology (2019, background): “ella (Camalet and Jülicher, 2000).”
Mammalian Sperm Motility: Observation and Theory (2011, methodology): “…as discussed by Lindemann & Leisch (2010), dynein cross-bridge cycle regulation with active shear forces controlled by the sliding displacement via a self-organization model (Camalet & Julicher 2000, Riedel-Kruse et al. 2007), and Lindemann’s (1994a,b, 2004) geometric clutch control framework.”
The hydrodynamics of swimming microorganisms (2008, background): “Since the oscillations arise spontaneously in this model, the calculation of the beating filament shape amounts to solving an eigenvalue problem [92, 93].”