Spontaneous oscillations displayed by hair bundles of the bullfrog sacculus have complex temporal profiles, not fully captured by single limit-cycle descriptions. Quiescent intervals are typically interspersed with oscillations, leading to a bursting-type behavior. Temporal characteristics of the oscillation are strongly affected by imposing a mechanical load or by the application of a steady-state deflection to the resting position of the bundle. Separate spectral components of the spontaneous motility are differently affected by increases in the external calcium concentration. We use numerical modeling to explore the effects of internal parameters on the oscillatory profiles, and to reproduce the experimental modulation induced by mechanical or ionic manipulation.

We explore mode-locking of spontaneous oscillations of saccular hair cell bundles to periodic mechanical deflections. A simple dynamic systems framework is presented that captures the main features of the experimentally observed behavior in the form of an Arnold Tongue. We propose that the phase-locking transition can proceed via different bifurcations. At low stimulus amplitudes F, the transition to mode-locking as a function of the stimulus frequency ω has the character of a saddle-node bifurcation on an invariant circle. At higher stimulus amplitudes, the mode-locking transition has the character of a supercritical Andronov-Hopf bifurcation.