Hair cells perform the mechanoelectrical transduction of
sound signals in the auditory and
vestibular systems of vertebrates. The part of the
hair cell essential for this transduction is the so-called
hair bundle. In vitro experiments on
hair cells from the
sacculus of the American bullfrog have shown that the
hair bundle comprises
active elements capable of producing periodic deflections like a relaxation oscillator. Recently, a continuous nonlinear
stochastic model of the
hair bundle motion [Nadrowski, Proc. Natl. Acad. Sci. U.S.A. 101, 12195 (2004)] has been shown to reproduce the experimental data in
stochastic simulations faithfully. Here, we demonstrate that a binary filtering of the
hair bundle's deflection (experimental data and continuous
hair bundle model) does not change significantly the spectral
statistics of the spontaneous as well as the periodically driven
hair bundle motion. We map the continuous
hair bundle model to the
FitzHugh-Nagumo model of
neural excitability and discuss the bifurcations between different regimes of the system in terms of the latter model. Linearizing the nullclines and assuming perfect time-scale separation between the variables we can map the FitzHugh-Nagumo system to a simple two-state model in which each of the states corresponds to the two possible values of the binary-filtered
hair bundle trajectory. For the two-state model, analytical expressions for the power spectrum and the susceptibility can be calculated [Lindner and Schimansky-Geier,
Phys. Rev. E 61, 6103 (2000)] and show the same features as seen in the experimental data as well as in simulations of the continuous
hair bundle model.
