Low Frequency Entrainment of Oscillatory Bursts in Hair Cells

Sensitivity of mechanical detection by the inner ear is dependent upon a highly nonlinear response to the applied stimulus. Here we show that a system of differential equations that support a subcritical Hopf bifurcation, with a feedback mechanism that tunes an internal control parameter, captures a wide range of experimental results. The proposed model reproduces the regime in which spontaneous hair bundle oscillations are bistable, with sporadic transitions between the oscillatory and the quiescent state. Furthermore, it is shown, both experimentally and theoretically, that the application of a high-amplitude stimulus to the bistable system can temporarily render it quiescent before recovery of the limit cycle oscillations. Finally, we demonstrate that the application of low-amplitude stimuli can entrain bundle motility either by mode-locking to the spontaneous oscillation or by mode-locking the transition between the quiescent and oscillatory states.