Chaotic Behavior of Oscillatory Hair Cells

Abstract

The inner ear is capable of detecting sounds that elicit motions below the stochastic noise levels. Hair cells are the specialized sensory cells essential for the hearing process. They convert mechanical energy from incoming sound into currents by opening and closing mechanically sensitive ion channels, in response to the induced deflections. Hair cells of certain species are also known to oscillate without external stimulation. The role of these spontaneous oscillations is not understood, but they are believed to be a signature of an underlying active mechanism. As this active process constitutes one of the most important open topics in auditory research, a deeper understanding of spontaneous motility could have important implications on understanding the extreme sensitivity of hearing. The motion of spontaneously oscillating hair cell bundles has been described with a number of theoretical models. Hair cells have been shown to flicker between the oscillatory and quiescent states; this phenomenon was modeled with dynamic feedback acting on an internal control parameter that determines the dynamic state of the cell. This simulation was also able to predict a range of values for the Lyapunov exponent, which quantifies the level of chaos in a dynamical system. A positive Lyapunov exponent was predicted, indicating chaotic motion. We will present on experimental measurements of spontaneous hair bundle oscillations, which were obtained from the sacculus of the American bullfrog. Using the delay-coordinate technique, the phase space of the oscillator was reconstructed, allowing for estimation of the Lyapunov exponent. These estimates were consistent with predictions based of the feedback model. A lower Lyapunov exponent was found during mechanical stimulation, indicating that the detection of sound reduces the level of chaos in the hair cell.