Showing papers by "Frank Jülicher published in 2000"

Auditory sensitivity provided by self-tuned critical oscillations of hair cells

Abstract: We introduce the concept of self-tuned criticality as a general mechanism for signal detection in sensory systems. In the case of hearing, we argue that active amplification of faint sounds is provided by a dynamical system that is maintained at the threshold of an oscillatory instability. This concept can account for the exquisite sensitivity of the auditory system and its wide dynamic range as well as its capacity to respond selectively to different frequencies. A specific model of sound detection by the hair cells of the inner ear is discussed. We show that a collection of motor proteins within a hair bundle can generate oscillations at a frequency that depends on the elastic properties of the bundle. Simple variation of bundle geometry gives rise to hair cells with characteristic frequencies that span the range of audibility. Tension-gated transduction channels, which primarily serve to detect the motion of a hair bundle, also tune each cell by admitting ions that regulate the motor protein activity. By controlling the bundle's propensity to oscillate, this feedback automatically maintains the system in the operating regime where it is most sensitive to sinusoidal stimuli. The model explains how hair cells can detect sounds that carry less energy than the background noise.

Generic aspects of axonemal beating

Abstract: 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

Actively contracting bundles of polar filaments.

Abstract: We introduce a phenomenological model to study the properties of bundles of polar filaments which interact via active elements. The stability of the homogeneous state, the attractors of the dynamics in the unstable regime, and the tensile stress generated in the bundle are discussed. We find that the interaction of parallel filaments can induce unstable behavior and is responsible for active contraction and tension in the bundle. The interaction between antiparallel filaments leads to filament sorting. Our model could apply to simple contractile structures in cells such as stress fibers.

Physical Aspects of Axonemal Beating and Swimming

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.