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We discuss a two-dimensional model for the dynamics of axonemal deformationsdriven by internally generated forces of molecular motors. Our model consistsof an elastic filament pair connected by active elements. We derive the dynamicequations for this system in presence of internal forces. In the limit of smalldeformations, a perturbative approach allows us to calculate filament shapesand the tension profile. We demonstrate that periodic filament motion can begenerated via a self-organization of elastic filaments and molecular motors.Oscillatory motion and the propagation of bending waves can occur for aninitially non-moving state via an instability termed Hopf bifurcation. Close tothis instability, the behavior of the system is shown to be independent ofmicroscopic details of the axoneme and the force-generating mechanism. Theoscillation frequency however does depend on properties of the molecularmotors. We calculate the oscillation frequency at the bifurcation point andshow that a large frequency range is accessible by varying the axonemal lengthbetween 1 and 50$\mu$m. We calculate the velocity of swimming of a flagellumand discuss the effects of boundary conditions and externally applied forces onthe axonemal oscillations.Comment: 14 pages, 8 figures, REVTE

Generic aspects of axonemal beating