  The hair cells of the vertebrate inner ear convert mechanical stimuli to
electrical signals. Two adaptation mechanisms are known to modify the ionic
current flowing through the transduction channels of the hair bundles: a rapid
process involves calcium ions binding to the channels; and a slower adaptation
is associated with the movement of myosin motors. We present a mathematical
model of the hair cell which demonstrates that the combination of these two
mechanisms can produce `self-tuned critical oscillations', i.e. maintain the
hair bundle at the threshold of an oscillatory instability. The characteristic
frequency depends on the geometry of the bundle and on the calcium dynamics,
but is independent of channel kinetics. Poised on the verge of vibrating, the
hair bundle acts as an active amplifier. However, if the hair cell is
sufficiently perturbed, other dynamical regimes can occur. These include slow
relaxation oscillations which resemble the hair bundle motion observed in some
experimental preparations.
