Two-state approach to stochastic hair bundle dynamics.
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.
Max-Planck-Institut für Physik Komplexer Systeme, Nöthnitzer Strasse 38, Dresden, Germany.
Diana
D
Clausznitzer
Benjamin
B
Lindner
Frank
F
Jülicher
Pascal
P
Martin
D000818:Animals; D006198:Hair Cells, Auditory / Q000502:physiology*; D040542:Mechanotransduction, Cellular / Q000502:physiology; D008959:Models, Neurological; D009991:Oscillometry; D010812:Physical Stimulation / Q000379:methods; D011892:Rana catesbeiana / Q000502:physiology; D013269:Stochastic Processes