Contents - Max-Planck-Institut für Physik komplexer Systeme

2.8 Coupling Virtual and Real Hair Bundles in a Hybrid Experiment
KAI DIERKES, FRANK JÜLICHER, BENJAMIN LINDNER
Active amplification in hearing. Humans possess an
extraordinary ability to detect complex sound stimuli
and to analyze their spectral and temporal fine structure.
It has been recognized that the human sense of
hearing relies on an active nonlinear process boosting
vibrations within the cochlea [1], i.e. the inner ear organ
responsible for the coding of auditory signals into patterns
of neural activity. Spontaneous otoacoustic emissions,
i.e. sounds emanating from the ear canal even
in the absence of any external auditory stimulus, constitute
a striking manifestation of this active amplifier.
As of today, its exact biophysical implementation, however,
remains elusive.
Two processes on a cellular scale have been suggested
to play the key role in auditory amplification [2]. On
the one hand, there is the ability of outer hair cells to
undergo length changes in response to modulations of
their transmembrane potential (electromotility). On the
other hand, hair bundles, which also constitute the universal
mechano-transducers in the inner ear, can generate
active forces and even perform spontaneous oscillations
(hair-bundle motility).
The hair-bundle amplifier. The hair bundle is a tuft
of a few tens to a few hundreds stiff finger-like protrusions,
termed stereocilia, emanating from the surface
of specialized sensory hair cells. Upon deflection,
minute geometric rearrangements within the hair
bundle lead to the opening and closing of mechanically
gated ion channels. In this way, the hair bundle
transduces mechanical stimuli (deflections) into electrical
signals (ionic currents).
Next to operating as mere transducers, hair bundles
from the bullfrog’s sacculus have been shown to exhibit
many features reminiscent of the auditory amplifier.
Even in the absence of external stimulation,
hair bundles can perform noisy spontaneous oscillations
[3]. The forces necessary for these oscillations
to occur are produced by calcium-regulated molecular
motors, which operate on the inside of stereocilia. Most
importantly, hair bundles can amplify weak periodic
stimuli in a frequency-dependent manner [4]. In particular,
for intermediate driving amplitudes, a nonlinear
decay of sensitivity is observed, similar to the one
characteristic for cochlear responses [4].
However, noise limits the extent of amplification a single
hair bundle can achieve [5]. Noise stems from
thermal interactions with the bathing fluid, stochastic
opening of the mechanically gated ion channels, and a
fluctuating component of force production by molecular
motors. The operation of a single hair bundle therefore
does not suffice to quantitatively account for the
operation of the whole cochlea.
Coupled hair bundles. Hair bundles in vivo are often
found to be attached to overlying elastic structures,
such as tectorial or otolithic membranes. This suggests
the possibility that coupling of hair bundles plays a role
to enhance the properties of hair-bundle mediated amplification.
A
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Real-time
simulation
Figure 1: Coupling a hair bundle to two cyber clones by dynamic
force clamp. (A) Schematic representation of a system of three coupled
hair bundles. A hair bundle (blue) is connected to one neighbor
on each side (orange and red) by identical springs. Relative movements
of the hair bundles induce coupling forces. (B) Experimental
realization. A single hair bundle is monitored. Two cyber clones,
substituting the two flanking hair bundles in (A), are simulated on
the computer. In real-time coupling forces and possibly also external
periodic forces are computed and exerted by means of a glass fiber
that was attached to the hair bundle’s tip. We adjusted cyber-clone
parameters such that our stochastic simulation would mimic the dynamics
of the hair bundle used during the experiment, i.e. in particular
its frequency, amplitude and quality of oscillation. Adopted
from [9].
Contributions of our group. In earlier studies, we approached
this hypothesis from a theoretical point of
view. On the basis of an existing biophysical description
of stochastic hair-bundle dynamics [5], we investigated
the effect of elastic coupling [6]. In our simulations,
we found that elastic coupling could induce synchronization
among hair bundles and lead to an effective
noise reduction. The latter manifested itself in an
increased phase coherence of spontaneous oscillations
and an enhancement of nonlinear amplification. In particular,
we observed a sharpend frequency tuning and
a pronounced increase in sensitivity to weak amplitude
stimulation. An analysis of the response characteristics
of a generic noisy oscillator helped to further understand
the detrimental effect of noise in this particular
context [7, 8].
56 Selection of Research Results
B