  Hair cells conduct auditory transduction in vertebrates. In lower vertebrates
such as frogs and turtles, due to the active mechanism in hair cells, hair
bundles(stereocilia) can be spontaneously oscillating or quiescent. Recently,
the amplitude death phenomenon has been proposed [K.-H. Ahn, J. R. Soc.
Interface, {\bf 10}, 20130525 (2013)] as a mechanism for auditory transduction
in frog hair-cell bundles, where sudden cessation of the oscillations arises
due to the coupling between non-identical hair bundles. The gating of the ion
channel is intrinsically stochastic due to the stochastic nature of the
configuration change of the channel. The strength of the noise due to the
channel gating can be comparable to the thermal Brownian noise of hair bundles.
Thus, we perform stochastic simulations of the elastically coupled hair
bundles. In spite of stray noisy fluctuations due to its stochastic dynamics,
our simulation shows the transition from collective oscillation to amplitude
death as inter-bundle coupling strength increases. In its stochastic dynamics,
the formation of the amplitude death state of coupled hair bundles can be seen
as a sudden suppression of the displacement fluctuation of the hair bundles as
the coupling strength increases. The enhancement of the signal-to-noise ratio
through the amplitude death phenomenon is clearly seen in the stochastic
dynamics. Our numerical results demonstrate that the multiple number of
transduction channels per hair bundle is an important factor to the amplitude
death phenomenon, because the phenomenon may disappear for a small number of
transduction channels due to strong gating noise.
