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 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. 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 predicted a positive Lyapunov exponent for innate bundle motility, indicating the presence of chaos. We will present 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 number of state variables required for modeling the system. Using Poincaré maps, we observed a quasiperiodic transition from low dimensional chaos to order, as the amplitude of an applied mechanical stimulus was increased. This transition was accompanied by a reduction in Kolmogorov entropy, a quantity used to determine the degree of disorder in a dynamical system.