The Journal of Neuroscience, June 1, 2003, 23(11):4533-4548
Previous Article | Next Article 
Spontaneous Oscillation by Hair Bundles of the Bullfrog's Sacculus
Pascal Martin,
D. Bozovic,
Y. Choe, and
A. J. Hudspeth
Howard Hughes Medical Institute and Laboratory of Sensory Neuroscience,
The Rockefeller University, New York, New York 10021-6399
 |
Abstract
|
|---|
One prominent manifestation of mechanical activity in hair cells is
spontaneous otoacoustic emission, the unprovoked emanation of sound by an
internal ear. Because active hair bundle motility probably constitutes the
active process of nonmammalian hair cells, we investigated the ability of hair
bundles in the bullfrog's sacculus to produce oscillations that might underlie
spontaneous otoacoustic emissions. When maintained in the normal ionic milieu
of the ear, many bundles oscillated spontaneously through distances as great
as 80 nm at frequencies of 550 Hz. Whole-cell recording disclosed that
the positive phase of movement was associated with the opening of transduction
channels. Gentamicin, which blocks transduction channels, reversibly arrested
oscillation; drugs that affect the cAMP phosphorylation pathway and might
influence the activity of myosin altered the rate of oscillation. Increasing
the Ca 2+ concentration rendered oscillations faster and smaller
until they were suppressed; lowering the Ca 2+ concentration
moderately with chelators had the opposite effect. When a bundle was offset
with a stimulus fiber, oscillations were transiently suppressed but gradually
resumed. Loading a bundle by partial displacement clamping, which simulated
the presence of the accessory structures to which a bundle is ordinarily
attached, increased the frequency and diminished the magnitude of oscillation.
These observations accord with a model in which oscillations arise from the
interplay of the hair bundle's negative stiffness with the activity of
adaptation motors and with Ca 2+-dependent relaxation of gating
springs.
Key words: adaptation; amplification; auditory system; mechanoelectrical transduction; negative stiffness; vestibular system
 |
Introduction
|
|---|
The ear is mechanically active. Whether spontaneous or evoked by sound,
otoacoustic emissions constitute the most striking evidence that
energy-consuming elements within the inner ear can produce work. The ear's
ability to deliver metabolically powered forces results in mechanical
amplification: for sound stimuli near threshold, the active process augments
vibrations in the mammalian cochlea by >100-fold, thus countering the
dissipation caused by viscous drag in the fluid of the inner ear.
Amplification of faint stimuli is closely associated with sharp frequency
selectivity, because each portion of a receptor organ acts as a highly tuned
mechanical resonator that responds preferentially at a natural frequency.
Finally, the response of the ear to stimuli of increasing magnitude grows
nonlinearly; the basilar membrane of the chinchilla, for example, represents
six decades of sound pressure by only two orders of magnitude of vibration
(Ruggero et al., 1997
).
Otoacoustic emissions, amplification, frequency selectivity, and compressive
nonlinearity represent four essential characteristics of the active process
that enhances detection of mechanical stimuli by the vertebrate inner ear (for
review, see Manley, 2000
,
2001
).
Although amplification in the mammalian cochlea is widely believed to
involve membrane-based electromotility by outer hair cells (reviewed in
Dallos, 1992
;
Nobili et al., 1998
), the
receptor organs of amphibians, reptiles, and birds are not endowed with
electromotile cells (He et al.,
2003
). The ears of nonmammalian tetrapods nevertheless display all
four characteristics of the active process (for review, see
Manley and Köppl, 1998
;
Manley, 2000
,
2001
). The alternative
mechanism proposed to underlie the active process in those animals, and
perhaps in mammals as well, is active hair bundle motility (for review, see
Hudspeth, 1997
;
Hudspeth et al., 2000
;
Fettiplace et al., 2001
). This
process displays the four hallmarks of the active process
(Martin and Hudspeth, 2001
). A
bundle can oscillate spontaneously
(Crawford and Fettiplace,
1985
; Howard and Hudspeth,
1987a
; Denk and Webb,
1992
; Benser et al.,
1996
; Martin and Hudspeth,
1999
,
2001
; Martin et al.,
2000
,
2001
), a behavior that might
underlie spontaneous otoacoustic emissions. The power expended by an
oscillating bundle can be funneled into a weak sinusoidal stimulus to amplify
the input (Martin and Hudspeth,
1999
,
2001
). The sensitivity of a
bundle is tuned, with the greatest responsiveness at its natural frequency
(Martin et al., 2001
).
Finally, the response of a hair bundle at its natural frequency displays a
compressive nonlinearity (Martin and
Hudspeth, 2001
).
The four characteristics that define the aural active process are
signatures of a dynamical system operating near a Hopf bifurcation
(Choe et al., 1998
;
Camalet et al., 2000
;
Eguíluz et al., 2000
;
Jülicher et al., 2001
;
Martin et al., 2001
). Such an
oscillatory instability may emerge from the interplay of the negative
stiffness of a hair bundle (Martin et al.,
2000
) with the molecular motors responsible for mechanical
adaptation (for review, see Hudspeth and
Gillespie, 1994
; Eatock,
2000
; Holt and Corey,
2000
). To strengthen the evidence that this mechanism can mediate
active hair bundle movements, we have examined the effects of treatments that
affect the mechanical properties of a bundle and the adaptation motor on the
ability of a hair cell to oscillate spontaneously.
 |
Materials and Methods
|
|---|
Experimental preparation. Experiments were performed at a room
temperature of
21°C on saccular hair cells from the bullfrog Rana
catesbeiana. Each internal ear was dissected in oxygenated standard
saline solution containing (in mM): 110 Na +, 2 K
+, 4 Ca 2+, 122 Cl -, 3 D-glucose,
and 5 HEPES. After dissection from the labyrinth, the saccular macula was
mounted over a 1 mm hole in a plastic coverslip and secured around the edges
of its basal aspect with tissue-compatible acrylic adhesive (Isodent; Ellman
International, Hewlett, NY). While the basolateral surface remained in contact
with standard saline solution, the otolithic membrane was loosened by a 30 min
exposure of the apical surface to 40 µg/ml protease type XXIV in
N-methyl-D-glucamine (NMDG) endolymph
containing (in mM): 2 Na +, 3 K +, 0.25 Ca
2+, 110 NMDG, 111 Cl -, 3D-glucose, and 5
HEPES. The otolithic membrane was then lifted from the hair bundles, and the
coverslip was secured in a two-compartment experimental chamber
(Martin and Hudspeth,
1999
).
During most experiments, the standard saline solution in the lower
compartment was not exchanged. The upper compartment ordinarily contained
oxygenated NMDG endolymph; except when specifically indicated, the results
presented here were obtained in the presence of this solution. Some
experiments instead used artificial endolymph containing (in mM): 2
Na +, 118 K +, 0.25 Ca 2+, 118 Cl
-, 3 D-glucose, and 5 HEPES. Each solution had a pH of
7.3 and an osmotic strength of
230 mmol/kg.
Enzymes, drugs, and other chemicals were obtained from Sigma (St. Louis,
MO).
Kinociliary dissection. After control recordings had been made,
kinocilia were detached from individual hair bundles with a horizontally
mounted glass microelectrode (Hudspeth and
Jacobs, 1979
). The tip of the electrode was situated about halfway
up the bundle and insinuated between the kinocilium and the remainder of the
bundle. Moving the electrode upward then severed the filamentous connections
between the kinociliary bulb and the five tallest stereocilia
(Hillman and Lewis, 1971
;
Jacobs and Hudspeth, 1990
).
While additional mechanical recordings were made with the stimulus fiber
resting atop the stereociliary cluster, the electrode was used to hold the
loosened kinocilium flat against the epithelial surface.
Iontophoresis of Ca2+ and drugs.
Iontophoresis was used to apply several substances to hair bundles during
measurement of their spontaneous oscillation and stiffness. In each instance,
a coarse microelectrode, whose resistance would have been
5 M
if
filled with 3 M KCl, was fabricated with a patch-electrode puller
(L/M-3P-A; List Electronic, Darmstadt, Germany). After having been bent
through an angle of
45° in its tapered region, the electrode was
filled with 2.5 M CaCl2, 350 mM disodium ATP,
or 500 mM gentamicin sulfate. The tip of the pipette was then
situated over the hair cell under investigation,
3 µm above the top of
the bundle, and oriented toward the bundle. An appropriate holding current was
used in each instance to minimize diffusive release of the contents of the
electrode under control conditions.
Tight-seal electrical recording. We used the perforated patch
recording technique with a voltage-clamp amplifier (Axopatch 200B; Axon
Instruments, Union City, CA) to measure transduction currents in spontaneously
oscillating hair cells. Tight-seal electrodes were drawn with a pipette puller
(L/M-3P-A, List Electronic), bent to permit an orthogonal approach to the
apical surface of a cell, and heat-polished to give resistances of 510
M
. The tip of each recording electrode was positioned with a Huxley
micromanipulator on the apical surface of a hair cell opposite the kinocilium
(Holton and Hudspeth,
1986
).
Each recording pipette was tip-filled for
1 sec with a solution
containing (in mM): 110 Cs +, 3 Mg 2+, 20
spermine, 114 Cl -, 40 SO4 2-, and 5 HEPES.
The pipette was then back-filled with an identical solution supplemented with
260 µM amphotericin B that had been dissolved in DMSO, whose
concentration in the internal solution was 2% (v/v). When used in the presence
of artificial endolymph, this internal solution produced a
liquidjunction potential of
0 mV. A polycationic molecule,
spermine, was included in the internal solution because of the difficulty in
creating tight seals on the apical membrane of hair cells
(Holton and Hudspeth, 1986
).
The presence of spermine permitted the formation of tight seals within several
seconds of applied suction. Like its precursor spermidine, this polyamine
occurs in cytoplasm at a concentration of
1 mM as an important
counterion to RNA (Igarashi and Kashiwagi,
2000
). The transduction currents measured in the presence of
spermine did not differ in magnitude from those recorded from isolated hair
cells (Jaramillo and Hudspeth,
1991
; Assad and Corey,
1992
; Shepherd and Corey,
1994
; Walker and Hudspeth,
1996
; Lumpkin and Hudspeth,
1998
), for which no special treatment is required to make tight
seals. Moreover, control recordings earlier demonstrated no untoward effects
of lower concentrations of spermine and spermidine
(Holton and Hudspeth, 1986
).
Because the membrane potential of a hair cell was held either at the resting
potential ascertained under current-clamp conditions or at -70 mV,
transduction currents were always inward and it is improbable that a cation
such as spermine would have significantly blocked transduction channels.
Microscopic apparatus. Experiments were conducted under an upright
microscope (MPS; Zeiss, Jena, Germany) equipped with a 100 W mercury
illuminator, an infrared-reflecting hot mirror (K43-842; Edmund Industrial
Optics, Barrington, NJ), and a broadband green interference filter (500
± 40 nm, half-width at half-maximal transmittance; K46-157; Edmund
Industrial Optics). The image formed by a 40x water immersion objective
lens of numerical aperture 0.75 was further magnified by a 1.6x relay
lens. Observations by eye and video microscopy were made with differential
interference contrast optics. To increase the signal reaching the photodiodes,
the analyzer was relocated from the microscope tube to the eyepiece assembly;
moreover, during measurements of hair bundle motion, the polarizer was
removed.
Because spontaneous hair bundle movements were sometimes too small or too
fast to be detected directly by eye, we also used video microscopy to locate
spontaneously active bundles. The image provided by the microscope was relayed
through a projection eyepiece of 125 mm focal length or by a 1.5x
telescope to a charge-coupleddevice camera whose field of view
encompassed several hair bundles. Its output was directed to a video image
processor (Argus-20; Hamamatsu Photonics, Hamamatsu City, Japan). To highlight
hair bundle oscillations, we digitally subtracted from each frame the running
average of several consecutive frames.
Mechanical stimulation. Mechanical stimuli were delivered by a
flexible glass fiber whose tip was attached to the kinociliary bulb of an
individual hair bundle. Fibers were fabricated from borosilicate capillaries
of 1.2 mm diameter (TW120-3, World Precision Instruments). Each capillary was
first reduced with an electrode puller (P-80/PC; Sutter Instruments, Novato,
CA) and then pulled finer in a direction perpendicular to its shank with a 120
V solenoid (Howard and Hudspeth,
1988
). We found that a fiber of
500 nm in diameter was best
for attachment to the kinociliary bulb. The fiber was trimmed with iridectomy
scissors to a length of 100400 µm. To enhance optical contrast, we
coated the fiber with an
100 nm layer of gold-palladium (Hummer VI;
Anatech, Alexandria, VA). The stiffness and drag coefficient of the fiber
were, respectively, 80400 µN · m-1 and
40110 nN · sec · m-1, as determined by power
spectral analysis of Brownian motion of the tip of the fiber in water. The
fiber behaved as a first-order low-pass mechanical filter with a cutoff
frequency of 0.21.6 kHz.
The fiber was secured by its base to a stack-type piezoelectric actuator
(P835.10; Physik Instrumente) driven by a matched power supply (P-870; Physik
Instrumente); this actuator provided displacements up to ±1 µm with
a bandwidth of 5 kHz. The piezoelectric actuator was in turn mounted on a
Huxley micromanipulator, which allowed fine positioning of the tip of the
fiber with a submicrometer resolution. The fiber was used both to apply
stimuli at the top of a hair bundle and to report bundle movements. Holding
the base of the fiber at a fixed position permitted accurate measurement of
the spontaneous motion of the bundle.
Displacement monitor. The tip of the fiber was imaged at a
magnification of 1000x on a dual photodiode (UV-140-2; EG&G
Electro-Optics, Salem, MA). A pair of preamplifiers directly attached to the
photodiodes provided current-to-voltage conversion with a gain of
107. After the difference between the electrical signals from the
two photodiodes had been computed, the displacement monitor yielded an output
linearly proportional to the displacement of the tip of the fiber with a
resolution of
1 nm. To allow centering of the image of the fiber on the
detector, the dual photodiode and preamplifier were mounted on a two-axis
linear stage equipped with a stepping motor microdrive and controller (B-05
and PMC100; Newport, Irvine, CA). The photometric apparatus was placed on an
independent platform mounted above the air table holding the microscope.
For calibration purposes, the photometric system was additionally secured
to a piezoelectric stimulator. Each experimental record was calibrated by
imposing a 20 µm offset pulse on the dual photodiode. Because of the
optical magnification of the imaging system, the resultant output signal from
the photodiodes was equivalent to that attributable to a 20 nm displacement of
the stimulus fiber. The photodiode offset system was in turn calibrated with a
heterodyne interferometer (OFV3001; Polytec GmbH, Waldbronn, Germany).
Displacement-clamp measurements. We used negative feedback to
ensure that the bundle position, X(t), matched a command
position, XC(t)
(Jaramillo and Hudspeth, 1993
;
Benser et al., 1996
). The
feedback signal, obtained by comparing the position of the bundle to the
command signal, provided the input to the piezoelectric stimulator that moved
the base of the fiber by a distance
(t). It follows that:
 | (1) |
in which
(
) defines the gain
of the clamp circuit at the angular frequency
, and tildes denote the
Fourier transforms of variables. In addition to proportional gain, which does
not depend on frequency, we added integral gain to counter slow drifts in the
position of the bundle and differential gain to dampen high-frequency
components of the movement of the bundle. To prevent instabilities, the
feedback signal sent to the piezoelectric stimulator was further filtered
using a single-pole low-pass filter. The complex gain function thus assumes
the form:
 | (2) |
in which the scaling factor A
10, and the corner frequencies
1 = 400 sec-1;
2 = 3
sec-1;
3 = 10,000 sec-1; and
4 = 1000 sec-1. Before each experiment, the
magnitudes of the proportional gain GP, the integral gain
GI, and the derivative gain GD were
set manually to bring the spontaneous oscillation of a bundle to a complete
halt; the maximal values of the respective gains were GP =
12.5, GI = 77, and GD = 50. We then
applied a 100 nm test command pulse and adjusted the gain of the clamp to
achieve the bundle movement that reflected the command most faithfully. For
the partial-displacement-clamp experiments, the gain of the clamp was
controlled electrically by the computer. The clamp circuit was able to track
command steps with a time constant of
1 msec.
For measurements of the negative stiffness of a hair bundle, we recorded
the forces necessary to displace the bundle through various distances under
displacement-clamp control and plotted the relation between displacement and
applied force (Martin et al.,
2000
).
We used partial displacement clamping to study the effect of varying
elastic loads on the spontaneous oscillation of a bundle. In this procedure,
the movement imposed on the base of the stimulus fiber opposed but did not
completely arrest that of a spontaneously oscillating bundle. More
specifically, the signal sent to the piezoelectric stimulator consisted of
only a fraction of the feedback required to clamp the bundle completely.
Neglecting viscous components, the force, FSF, exerted by
the stimulus fiber against the hair bundle was proportional to the deflection
of the fiber:
 | (3) |
in which KSF represents the stiffness of the stimulus
fiber. In combination with Equation 1 for XC = 0, the
Fourier transform of Equation 3 yields:
 | (4) |
in which
EFF(
) =
KSF[1 +
(
)] defines the impedance of
the fiber at angular frequency
.
Because|
EFF| exceeds
KSF at any frequency, the clamp circuit effectively
stiffened the fiber in the frequency range over which the feedback circuit
operated. Although the impedance of the fiber depended on frequency, it
remained approximately constant at frequencies from a few hertz to
50 Hz
with the parameter settings used in these experiments. Because most of the
spectral power of the oscillation of a bundle lay within this frequency band,
the fiber effectively provided a linear stiffness.
Data collection and analysis. Stimulation and recording were
performed under the control of a computer (P6400 GX1; Dell Computer Corp.,
Round Rock, TX) running LabVIEW software, version 5.0 (National Instruments,
Austin, TX). Stimulus commands and experimental control signals were provided
by a dedicated interface (AT-AO-10; National Instruments). Before sampling,
responses were low-pass-filtered with an eight-pole Bessel antialiasing filter
adjusted to a half-power frequency of 1 kHz. A multipurpose interface card
(PCI-MIO-16E-1; National Instruments) conducted signal acquisition and
analog-to-digital conversion with a precision of 12 bits and a sampling rate
of 2.5 kHz.
To characterize the spontaneous oscillation of a hair bundle, we computed
its power spectrum and fitted it with a Lorentzian function
(Martin et al., 2001
). The
peak frequency of the best fit defined the frequency of the oscillation, and
the half-width of the Lorentzian at half its maximal value described the
extent of frequency fluctuation.
Data were analyzed with Mathematica, version 4.0 (Wolfram Research, Inc.,
Champaign, IL) and Matlab, version 6.0 (The MathWorks, Natick, MA).
 |
Results
|
|---|
Spontaneous hair bundle oscillation
When mounted in a two-compartment experimental chamber with artificial
endolymph or NMDG endolymph bathing the apical surface and standard saline
solution contacting the basolateral aspect, the saccular macula from a
bullfrog remained healthy for several hours. In most preparations, hair
bundles were observed by eye to undergo spontaneous oscillations. In
occasional preparations, all of the dozen or so hair bundles within a
microscopic field of view could be seen to oscillate. The movements could also
be documented by video microscopy. Slow-motion replay revealed fast bundle
strokes that looked like instant jumps for a video acquisition rate of 30
frames per second; after each stroke, the bundle remained nearly still before
it leapt back in the opposite direction. Subtraction of successive video
frames clearly revealed the two components of the motion of a hair bundle in
each direction (Fig. 1).

View larger version (121K):
[in this window]
[in a new window]
|
Figure 1. Spontaneous oscillation of hair bundles from the bullfrog's sacculus. The
center panel shows one frame from a video movie of a microscopic field
encompassing two hair bundles; the arrowhead marks the kinociliary bulb of the
upper bundle. Subtraction of this frame from that antecedent produced the
false-color image shown at the left, in which it is apparent that the
medium-sized bottom hair bundle moved during the 33 msec interval. A similar
subtraction of the following frame yielded the right panel, which demonstrates
abrupt motion of the large top hair bundle. Movement of a hair bundle toward
its tall edge, and thus toward the kinocilium, to the right, is defined as
positive in sign and is displayed as an upward deflection in all subsequent
figures.
|
|
We monitored the movement of an individual hair bundle by attaching the
distal end of a fine glass fiber to the top of its kinocilium and projecting
an enlarged image of the tip of the fiber onto a dual photodiode. Although
loading a hair bundle with a fiber affects the amplitude and frequency of the
oscillation (see below), the use of a very flexible fiber minimized this
interference and allowed accurate measurement of the dynamical behavior of a
bundle.
Different bundles were observed to oscillate spontaneously at frequencies
of 550 Hz with a peak-to-peak magnitude of motion as great as 80 nm but
most commonly
25 nm (Fig.
2). There was no rigorous correlation between the frequency and
magnitude of spontaneous movements by different hair bundles. Two hair bundles
that oscillated at frequencies almost an order of magnitude apart displayed
movements of similar magnitudes (Fig.
2A,G). The slow oscillations were often the largest,
however, especially for a given hair bundle. We sometimes observed an
oscillation that reversibly changed its behavior within short periods. A hair
bundle that initially oscillated at
44 Hz, for instance, displayed
movements at
28 Hz 1 min later before almost doubling its frequency to
53 Hz after another 1 min had elapsed (data not shown). Correspondingly,
the amplitude of oscillation increased from 18 to 30 nm before returning to 16
nm. Some bundles produced movements of almost metronomic regularity
(Fig. 2A,B); others
moved sporadically and occasionally halted for variable intervals
(Fig. 2C).

View larger version (40K):
[in this window]
[in a new window]
|
Figure 2. Varieties of spontaneous hair bundle oscillations. A, For a common
pattern of regular low-frequency movement, in this instance at 6 ± 2
Hz, the rms magnitude was 18 nm. B, This bundle produced a highly
regular, relatively high-frequency oscillationat 27 ± 3 Hz with an 18
nm rms magnitude. C, Some bundles showed variations in oscillation
frequency or even occasional pauses in their motion. In this example, the
oscillation occurred at 18 ± 9 Hz, and its rms magnitude was 13 nm.
D, The spontaneous movement of this bundle was irregular both in
frequency, 6 ± 3 Hz, and in waveform. Its rms magnitude was 12 nm. Even
for a hair bundle capable of regular oscillation, a similar pattern could
occur when the recording fiber was poorly attached to the bundle. E,
Low-frequency oscillations, especially large ones, displayed two clear
components during each phase of movement. In each half-cycle, a fast stroke of
movement in one direction concluded with a slower component in the same
direction. This oscillation was characterized by an exceptionally large rms
magnitude of 30 nm and a frequency of 9 ± 4 Hz. F,
Low-frequency oscillations could be relatively rectilinear. The rms magnitude
of this oscillation was 16 nm, and the frequency was 11 ± 3 Hz.
G, The waveform of a relatively high-frequency oscillation, here 53
± 6 Hz, could not be parsed into fast and slow components. The rms
magnitude of this oscillation was 15 nm.
|
|
Particularly for hair bundles that moved regularly and at relatively low
frequencies, it was apparent that each cycle of spontaneous oscillation
comprised movements on two time scales
(Martin et al., 2000
), a
behavior typical of a relaxation oscillation
(Strogatz, 1994
). In each
half-cycle, a rapid stroke was followed by a slow excursion in the same
direction (Fig. 2E).
The fast component generally consisted of a displacement lasting no more than
5 msec. The shape of the slower component varied from cell to cell. In some
instances, the movement was nearly exponential
(Fig. 2E). On other
occasions, the bundle was almost stationary during this component
(Fig. 2F). Finally,
the trajectory was often more complex and sometimes even nonmonotonic
(Fig. 2D,G). Moreover,
the waveforms of the positively and the negatively directed slow components
were often dissimilar (Fig.
2C,D).
Relation of channel open probability to spontaneous oscillation
By making tight-seal voltage-clamp recordings, we were able to measure
changes in transduction current associated with the movement of hair bundles.
In 10 spontaneously oscillatory hair cells, but not static ones, the current
displayed well defined oscillations
100 pA in peak-to-peak magnitude.
Like spontaneous hair bundle displacements, slow current oscillations
alternated between rapid transitions and relatively static intervals (data not
shown).
We were able to make simultaneous tight-seal electrical recordings and
mechanical measurements from one hair cell and therefore to examine the
relation of transduction channel gating to bundle movement. The transduction
current was highly correlated with the phase of spontaneous bundle movement.
Positive bundle motion corresponded to an increase in the inward transduction
current, whereas negatively directed motion coincided with decreased current
(Fig. 3A). Within the
temporal resolution of the mechanical and electrical recording techniques, the
rapid components of bundle movement and the quick steps in transduction
current occurred simultaneously. Because the current oscillations were
eliminated by saturating mechanical stimuli, they represented the activity of
mechanoelectrical transduction channels.

View larger version (23K):
[in this window]
[in a new window]
|
Figure 3. Correlation of spontaneous hair bundle oscillation with channel open
probability. A, Positive movements of a hair bundle (top record) were
associated with inward transduction current, shown as a downward deflection
(bottom record). This hair cell was voltage-clamped at -70 mV in artificial
endolymph. At the relatively high oscillation frequency of 100 Hz, the
bundle did not display distinct slow and fast phases of movement. B,
The application of saturating mechanical stimuli defined the range of open
probabilities during spontaneous bundle oscillation. Bundle movements were
recorded in the absence of stimulation and during positive and negative
offsets that were large enough to saturate the mechanoelectrical transduction
process (top records). The corresponding records of transduction current
(bottom records) demonstrate that the large stimuli completely closed or
opened the transduction channels, thereby abolishing oscillation. The
transduction current in the absence of stimulation corresponded to open
probabilities ranging from 0.13 to 0.70. The base of the stimulus fiber, whose
stiffness was 80 µN · m-1, was displaced by ±1000
nm to produce the saturating deflections.
|
|
By applying large mechanical stimuli of both polarities to the hair bundle,
we were able to determine the maximal transduction current with all channels
open and the zero current with all channels shut
(Fig. 3B). Comparison
of these values with the extreme values of the transduction current measured
during spontaneous oscillation revealed that the open probability varied
between 0.13 and 0.70 in this spontaneously active cell.
On excitation with current pulses, a hair cell from the bullfrog's sacculus
displays damped oscillations of its membrane potential, a phenomenon termed
electrical resonance. Hair cells are also capable of spontaneous electrical
oscillation in the absence of stimulation. Because changing the membrane
potential of a hair cell evokes bundle movements
(Assad and Corey, 1992
;
Denk and Webb, 1992
; Ricci et
al., 2000
,
2002
;
Bozovic and Hudspeth, 2003
), we
were concerned that hair bundle oscillation might have been the result, rather
than the source, of an electrical oscillation in the soma of the hair cell.
Our observation that hair bundle oscillations remain under voltage-clamp
circumstances demonstrates that electrical resonance is not involved in their
production.
Effect of gentamicin on spontaneous oscillation
An oscillatory hair bundle evinces a peculiar mechanical feature: its
displacementforce relation, obtained by measuring the external force
required to move the bundle through various distances, displays a region of
negative stiffness (Martin et al.,
2000
). According to the gatingspring model of
mechanoelectrical transduction (Corey and
Hudspeth, 1983
) (for review, see
Markin and Hudspeth, 1995
;
Hudspeth et al., 2000
), direct
mechanical gating of transduction channels is expected to reduce the stiffness
of a bundle over a limited range of positions
(Howard and Hudspeth, 1988
).
For suitable values of the parameters of the model, this gating compliance can
be great enough to dominate the other elastic components of the bundle and to
render the stiffness of the bundle negative
(Denk et al., 1992
) (for
review, see Markin and Hudspeth,
1995
). Aminoglycoside antibiotics are known to block transduction
channels (Kroese et al.,
1989
). By preventing channel gating, these drugs abolish gating
compliance (Howard and Hudspeth,
1988
) and should thus eliminate the negative stiffness of
spontaneously oscillating bundles.
A spontaneously active hair bundle characteristically displayed a region of
negative stiffness encompassing a displacement range of
20 nm
(Fig. 4A). When the
solution bathing the apical hair cell surface was replaced by artificial
endolymph containing 60 µM gentamicin, the bundle instead
behaved as a Hookean spring throughout the range of deflections explored. The
region of negative stiffness of the hair bundle was restored by exchanging the
bath with gentamicin-free endolymph.

View larger version (20K):
[in this window]
[in a new window]
|
Figure 4. The effect of transduction channel blockage by the aminoglycoside
antibiotic gentamicin. A, An oscillatory hair bundle initially
displayed a region of negative stiffness in the displacementforce
relation measured by displacement clamping (filled circles). When the solution
bathing the hair bundle was replaced by artificial endolymph containing 60
µM gentamicin, the region of negative stiffness vanished; the
displacementforce relation became linear throughout the range of
deflections explored (open circles). This effect was reversible in that
negative stiffness was restored by returning gentamicin-free endolymph to the
bath (diamonds). The fiber was detached from the tip of the bundle to allow
successive bath exchanges. B, During each of three iontophoretic
applications of gentamicin to the same hair bundle, the spontaneous
oscillation vanished transiently. Because gentamicin blocks transduction
channels in the open position, the bundle initially moved in the positive
direction. When the drug encountered a bundle that was lurching in the
negative direction, the bundle reversed abruptly and moved in the positive
direction (top record). In contrast, very little positive motion resulted from
applying the drug when the hair bundle was on the verge of jumping in the
negative direction (center record). When the iontophoretic current was small
enough, the hair bundle ceased oscillating but displayed rapid, noisy bundle
movements. This noisy motion likely corresponded to channel clatter as the
gentamicin molecules alternately blocked and unblocked the channels. The
holding current was -0.2 nA; the expulsion currents were +2 nA for the top two
traces and +1 nA for the bottom trace. The 1 sec iontophoretic pulse is
indicated below the experimental records.
|
|
Active mechanical biasing of a hair bundle into its unstable region of
negative stiffness can explain spontaneous oscillations
(Martin et al., 2000
). By
eliminating negative stiffness, aminoglycosides would be expected to remove
one of the conditions necessary for spontaneous oscillation. On iontophoretic
application of gentamicin near the top of an oscillatory hair bundle, we found
that the movements reversibly disappeared
(Fig. 4B). Gentamicin
arrested the hair bundle in a positive position, where most transduction
channels are likely to be open (Fig.
3). This observation thus confirms the previous inference that
gentamicin blocks transduction channels in an open state
(Denk et al., 1992
;
Jaramillo and Hudspeth, 1993
).
By blocking Ca 2+ entry through open transduction channels,
gentamicin should also interfere indirectly with the myosin-based molecular
motors that effect adaptation to sustained stimuli
(Eatock et al., 1987
;
Hacohen et al., 1989
). After
the initial blockage, a hair bundle often moved slowly in the negative
direction, a phenomenon attributable to mechanical adaptation when Ca
2+ entry was interrupted (Denk
et al., 1992
; Jaramillo and
Hudspeth, 1993
).
Effect of pharmacological agents on spontaneous oscillation
If spontaneous hair bundle oscillation involves the shape of the
displacementforce relation of the bundle and the activity of adaptation
motors, drugs that affect either would be expected to influence oscillation.
Substances that interfere with the cAMP second messenger pathway evoke a shift
of the transduction currentdisplacement curve
(Ricci and Fettiplace, 1997
;
Géléoc and Corey,
2001
) and are therefore suitable reagents with which to perturb
oscillation. A wealth of information suggests that the molecular motors
responsible for adaptation of the mechanoelectricaltransduction process
are based on myosin molecules (for review, see
Hudspeth and Gillespie, 1994
;
Gillespie and Corey, 1997
;
Eatock, 2000
;
Holt and Corey, 2000
).
Substances that interfere with force production by myosin would thus be
expected to affect oscillation. An example is butanedione monoxime, which
places myosin II molecules in a weakly bound state
(Herrmann et al., 1992
;
Seow et al., 1997
;
Tesi et al., 2002
). Although
the effect of this substance on other myosin isozymes remains uncertain
(Cramer and Mitchison, 1995
;
Ostap, 2002
;
Titus, 2003
), butanedione
monoxime lowers the open probability of transduction channels in hair cells
(Wu et al., 1999
) and may
therefore affect adaptation motors.
Used at a concentration of 100 µM, forskolin, an activator of
adenylate cyclase, consistently lowered the oscillation frequency in each of
the four hair cells examined (Fig.
5A). Sp-adenosine 3',5'-cyclic
monophosphorothioate (Sp-cAMPS; 500 µM) and 8-bromo-cAMP
(8-Br-cAMP; 100 µM), membrane-permeant analogs of cAMP that
activate cAMP-dependent protein kinases, had similar effects in one and two
cells, respectively (data not shown). 3-Isobutyl 1-methylxanthine (IBMX; 500
µM), an inhibitor of cAMP phosphodiesterases, also reduced the
frequency of oscillation in each of the two cells studied
(Fig. 5B). Rp-cAMPS
(500 µM), a membrane-permeant inhibitor of cAMP-dependent
protein kinases, had the opposite effect in each of three hair cells: in the
presence of the drug, the oscillation frequency increased appreciably
(Fig. 5C). Finally,
okadaic acid, an inhibitor of some protein phosphatases, slowed oscillation in
both of the cells exposed to the drug at a concentration of 5 µM
(Fig. 5D). As
expected, the myosin inhibitor butanedione monoxime (10 mM)
suppressed oscillation altogether in all four cells tested
(Fig. 5E). In the many
instances in which we were able to record bundle movements after control
endolymph solution had been restored, we found that the oscillation
frequencies returned to nearly their initial values.

View larger version (27K):
[in this window]
[in a new window]
|
Figure 5. Effects of pharmacological agents on spontaneous hair bundle oscillation.
In each instance, a control record is shown at the left, and a record in the
presence of the drug is shown at the right; the corresponding recovery record
is not illustrated. A, Forskolin lowered the frequency of spontaneous
oscillation to one-third, from 33 ± 17 to 9 ± 4 Hz. The rms
magnitude of the oscillation was relatively unaffected, falling from 11 to 10
nm. When the drug was removed, the frequency recovered to 24 ± 7 Hz
with a magnitude of 9 nm. B, In the presence of isobutyl
methylxanthine, the frequency of an oscillation fell from 23 ± 4 to 10
± 3 Hz; the magnitude declined from 16 to 11 nm. C,
Rp-adenosine 3',5'-cyclic monophosphorothioate increased the
oscillation frequency from 5 ± 2 to 10 ± 8 Hz, whereas the
magnitude of oscillation declined from 18 to 14 nm. Restoring the control
solution restored the frequency to 4 ± 3 Hz with a magnitude of 17 nm.
D, The spontaneous oscillation of a hair bundle exposed to okadaic
acid declined in frequency from 13 ± 3 to 5 ± 2 Hz; the
magnitude fell from 20 to 16 nm. During recovery, the oscillation frequency
rose to 12 ± 4 Hz with a magnitude of 7 nm. E, Oscillation at
7 ± 3 Hz with a magnitude of 13 nm was abolished by butanedione
monoxime. All experiments were conducted with artificial endolymph.
|
|
Because each drug was applied by changing the solution contained in the
upper compartment of the recording chamber, it was necessary to detach the
stimulus fiber to prevent disruption of the recorded hair bundle by
turbulence. This procedure might have affected an oscillation by damaging the
bundle, offsetting its position, or affecting the strength or exact site of
coupling between the fiber and bundle. However, although drugs other than
butanedione monoxime could change the frequency of an oscillation by as much
as threefold, the magnitude of oscillation during treatment remained within
30% of the control value. If this magnitude is determined by the shape of the
displacementforce relation of the bundle
(Martin at al, 2000
), these
observations suggest that hair bundles primarily retained their mechanical
integrity throughout the experiment. In the cases of forskolin, 3-isobutyl
1-methylxanthine, and okadaic acid, the oscillation became slower and smaller
on drug application. Because simply detaching and reattaching the fiber never
produced these effects, the observed changes may safely be ascribed to the
effects of the various drugs on the oscillation motor. Finally, to ensure that
a bundle was not significantly offset after solution changes, we subjected
most hair bundles to a range of static offsets both under control conditions
and during drug exposure and compared the frequency ranges of the consequent
oscillations. These control experiments confirmed in each instance that the
effects of the drugs on oscillation frequency were legitimate.
Effect of Ca 2+ on spontaneous oscillation
Ca 2+ mediates both of the processes proposed to power
mechanical amplification by hair bundles, activity of the adaptation motor
(Eatock et al., 1987
;
Hacohen et al., 1989
) (for
review, see Hudspeth and Gillespie,
1994
; Gillespie and Corey,
1997
; Eatock,
2000
; Holt and Corey,
2000
) and rapid transduction channel reclosure
(Howard and Hudspeth, 1988
;
Crawford et al., 1991
;
Benser et al., 1996
; Ricci et
al., 2000
,
2002
) (for review, see
Hudspeth et al., 2000
;
Fettiplace et al., 2001
). Ca
2+ also reversibly affects the stiffness of a hair bundle
(Marquis and Hudspeth, 1997
)
and the open probability of transduction channels at rest
(Corey and Hudspeth, 1983
;
Hacohen et al., 1989
).
Finally, Ca 2+ modulates the frequency of spontaneous otoacoustic
emissions (Manley and Kirk,
2002
). We therefore tested the effects of different extracellular
Ca 2+ concentrations on spontaneous hair bundle motion.
Varying the Ca 2+ concentration by exchange of the solution
bathing the apical surface of the saccular macula produced systematic changes
in spontaneous oscillation. Raising the Ca 2+ concentration from
the control value of 250 µM resulted in an increase in frequency
and a decrease in amplitude of the oscillation of the bundle, whereas reducing
the concentration had the opposite effect (data not shown). When the Ca
2+ concentration exceeded
1 mM, or when it fell
below
100 µM, the oscillations disappeared. This effect was
reversible, however, because reimposing a Ca 2+ concentration near
250 µM restored well defined bundle oscillations.
We performed additional experiments in which we used iontophoresis to
rapidly raise or lower the Ca 2+ concentration near the
stereociliary tips while keeping the glass fiber attached to the kinociliary
bulb. Transiently elevating the concentration with a Ca
2+-containing electrode had three consistent and reversible
effects: a hair bundle displayed a net movement in the negative direction; the
amplitude of oscillation declined; and the frequency of oscillation increased
(Fig. 6A). For small
to moderate levels of iontophoresis, it was noteworthy that the increase in
oscillation frequency involved principally a shortening of the slow component
of movement in the positive direction. For a given bundle, the fastest
oscillation that we could elicit by Ca 2+ iontophoresis occurred at
approximately twice the frequency of the control movement. The oscillation
amplitude was not as strongly affected, decreasing by
20%.

View larger version (41K):
[in this window]
[in a new window]
|
Figure 6. Effect of extracellular Ca 2+ concentration on spontaneous hair
bundle oscillation. A, When a spontaneously oscillating hair bundle
was exposed to the Ca 2+ expelled from an iontophoretic pipette,
the increased Ca 2+ concentration offset the bundle by -7 nm and
decreased the rms magnitude of the movement from 18 to 16 nm. The frequency of
oscillation also rose from 17 ± 8 to 34 ±6Hz, primarily by
shortening of the positive phase of motion. The 1 sec iontophoretic pulse is
indicated below the experimental record in this and the subsequent records.
The holding current was -15 nA, and the expulsion current was +10 nA.
B, Although the largest Ca 2+ ejections suppressed
rhythmic hair bundle activity, fast, erratic movements remained. These spikes
lasted no more than a few milliseconds and were characterized by peak-to-peak
magnitudes up to 80% those of the unperturbed bundle oscillation. Before
application of the 0.7 sec iontophoretic pulse, the spontaneous oscillation of
this bundle was characterized by an rms magnitude of 12 nm and a frequency of
42 ± 6 Hz. The pulse caused a static bundle deflection of -4 nm. The
holding current was -15 nA, and the expulsion current was +30 nA. C,
Ca 2+ expelled by a ramp of iontophoretic current initially
accelerated and eventually suppressed spontaneous bundle oscillation. Fast,
spiky movements of relatively large magnitudes remained. The 1.25 sec linear
ramp of iontophoretic current commenced at the dot. The holding current was
-15 nA, and the maximal expulsion current was +60 nA. The greatest hair bundle
offset induced by Ca 2+ iontophoresis was -18 nm. D, An
0.7-sec iontophoretic pulse of ATP decreased the local Ca 2+
concentration around a hair bundle, causing a net movement of +5 nm and
prolonging the positive phase of oscillation. The spontaneous oscillation of
the bundle increased slightly in rms magnitude, from 18 to 20 nm, whereas its
frequency fell nearly by half, from 17 ± 4 to 10 ± 3 Hz. The
holding current was +5 nA, and the maximal expulsion current was -15 nA.
E, A greater reduction of the Ca 2+ concentration,
effected by the iontophoretic application of an 0.7 sec ATP pulse, further
prolonged the slow component of positive bundle movement but left the negative
phase unchanged. The holding current was +5 nA, and the expulsion current was
-20 nA. F, Even greater reduction of the Ca 2+
concentration suppressed the oscillation, originally 14 nm in rms magnitude
and 21 ± 4 Hz in frequency, and caused a bundle offset of +6.5 nm. The
noisy displacement fluctuations that persisted had an rms magnitude of 7 nm.
The holding current was +0.5 nA, and the expulsion current was -40 nA.
|
|
The greatest increases in Ca 2+ concentration attained by
iontophoresis suppressed rhythmic hair bundle activity
(Fig. 6B). However,
erratic, rapid movements lasting no more than 12 msec persisted.
Because these spikes were distinct from the background noise apparent under
control conditions during the slow components of oscillation, they probably
represented residual active bundle motion. At the conclusion of the
iontophoretic pulse, the oscillation resumed progressively, further
demonstrating the relation among movement amplitude, frequency, and the
duration of the positive phase of bundle movement. The use of iontophoretic
pulses of varying intensity or the application of a ramp of iontophoretic
current disclosed that a progressive increase in Ca 2+
concentration evokes graded effects (Fig.
6C).
We were also able to lower transiently the local Ca 2+
concentration around a hair bundle by iontophoresis of a chelator. Because
carboxylate Ca 2+ chelators damage the transduction process by
breaking tip links (Assad et al.,
1991
; Crawford et al.,
1991
; Marquis and Hudspeth,
1997
), we elected to use ATP to sequester Ca 2+ (for
review, see Fabiato and Fabiato,
1979
). The effects of applying this nucleotide were opposite those
of Ca 2+ iontophoresis. For low to modest levels of iontophoresis,
the bundle displayed an offset in the positive direction and a graded slowing
of spontaneous oscillations dominated by protraction of their slow component
of positive motion (Fig.
6D,E). The ATP ejected by stronger iontophoretic currents
entirely suppressed oscillations, producing a significant bundle excursion in
the positive direction (Fig.
6F).
Effect of bundle position on spontaneous oscillation
By applying step displacements at the base of a flexible stimulus fiber, we
analyzed the effect on a spontaneously oscillating hair bundle of deflecting
its top by distances up to ±200 nm. Large offsets completely but
reversibly suppressed the oscillation (data not shown). For bundle
displacements smaller than
150 nm in either direction, however, a bundle
remained quiescent only transiently (Fig.
7). During this period, the hair bundle relaxed slowly in the
direction of the stimulus with a time course characteristic of mechanical
adaptation (Eatock et al.,
1987
; Hacohen et al.,
1989
). After the bundle position had attained a plateau and
adaptation had presumably concluded, the oscillation eventually resumed.

View larger version (32K):
[in this window]
[in a new window]
|
Figure 7. Effect of offset on spontaneous hair bundle oscillation. The center record
demonstrates an unperturbed bundle oscillation at a frequency of 7 ± 3
Hz with an rms magnitude of 27 nm. From top to bottom, the remaining records
show the effect of offsetting the tip of the bundle by +140, +85, -95, and
-160 nm. In each instance, after having been suppressed for a period of
adaptation, the oscillation resumed. After the largest offsets, the magnitude
of oscillation grew progressively from zero. Positive offsets shortened the
negative phase of bundle movement, whereas negative offsets had the opposite
effect. Offsets thus perturbed the symmetry of the oscillation. The stiffness
of the fiber was 130 µN · m-1.
|
|
The recovery of oscillation during a protracted displacement could be
abrupt for small bundle offsets but was graded for larger ones. In the latter
case, oscillation grew progressively over the course of a few cycles from zero
amplitude to a steady-state level and correspondingly decreased its frequency.
The recovery was not complete, however, in that the oscillation was
consistently faster than at rest when the bundle was offset in the positive
direction and slower when it was displaced in the negative direction. In
contradistinction to the effect of changes in Ca 2+ concentration
near the stereociliary tips, bundle offset affected primarily the slow
component of negative movement. The symmetry of oscillation was modified in
such a way that a bundle displayed spiky movements in one direction when it
was offset in the other.
Effect of mechanical load on spontaneous oscillation
When attached to the flexible glass fibers used in this study, most hair
bundles oscillated at frequencies near 10 Hz. These frequencies lie near the
bottom of the range of 5150 Hz that is characteristic of saccular nerve
fibers (Koyama et al., 1982
;
Yu et al., 1991
) and
presumably of the corresponding hair cells. Although several aspects of in
vitro recording might have perturbed the oscillation frequency, one
condition whose effect could readily be tested was the elastic load against
which the hair bundle operated.
While recording spontaneous bundle oscillations, we used varying degrees of
negative feedback, or partial displacement clamping, to increase the effective
stiffness of the stimulus fiber attached to a bundle. When the stiffness of
the fiber rose, the magnitude of the oscillation of a bundle
characteristically declined as the frequency of spontaneous oscillation
increased (Fig. 8A). A
sufficiently great increase in the effective stiffness of the stimulus fiber
suppressed well defined bundle oscillations altogether
(Fig. 8B).

View larger version (43K):
[in this window]
[in a new window]
|
Figure 8. Effect of mechanical load on hair bundle oscillation. As a bundle
oscillated spontaneously, partial displacement clamping was abruptly activated
during the 1.2 sec epoch at the center of each record. Because the movement of
the base of the fiber opposed that of the hair bundle, activating the clamp
system increased the effective impedance of the fiber above its actual value
of 152 µN · m-1. A, The hair bundle oscillated
spontaneously at 5 Hz with an rms magnitude of 33 nm. The effective stiffness
of the fiber during partial displacement clamping increased to 260 µN
· m-1 (top record), then to 490 µN ·
m-1 (middle record), and finally to 690 µN ·
m-1 (bottom record). The increasing load raised the frequency of
oscillation successively to 9 ± 3, then to 12 ± 4, and finally
to 18 ± 10 Hz. The rms magnitude of oscillation correspondingly
decreased to 22, then to 14, and finally to 12 nm. B, Another hair
bundle, contacted by the same fiber as in A, oscillated spontaneously
at 21 Hz with an rms magnitude of 18 nm. During partial displacement clamping,
the effective stiffness of the fiber rose to 750 µN · m-1
(top record), then to 1070 µN · m-1 (middle record), and
finally to 1390 µN · m-1 (bottom record). The oscillation
frequency increased to 34 ± 9 and then to 41 ± 20 Hz, whereas
the rms magnitude decreased to 10 and then to 9 nm. The greatest effective
stiffness of the fiber suppressed well defined hair bundle oscillations,
leaving noisy bundle movements with an rms magnitude of 7 nm.
|
|
The effect of mechanical load on the frequency and amplitude of spontaneous
hair bundle oscillation bears on the status of unstimulated bundles in
vivo. Like those in most acousticolateralis organs, a hair bundle of the
bullfrog's sacculus is normally attached to an accessory structure. In the
intact ear, the bulbous tip of the single kinocilium in the bundle is linked
by numerous filaments to the compact layer of the otolithic membrane
(Hillman and Lewis, 1971
;
Jacobs and Hudspeth, 1990
;
Kachar et al., 1990
). The
polycrystalline otoconia that surmount this structure constitute an inertial
mass whose movement relative to the skull signals acceleration. Although the
mechanical properties of the otolithic membrane are complex
(Benser et al., 1993
), the
structure exhibits a steady-state stiffness of 1400 ± 800 µN
· m-1 for each of the
2500 attached hair bundles. The
present results suggest that the stiffness of the otolithic membrane is
comparable with the minimal load required to suppress spontaneous
oscillation.
Role of the kinocilium in spontaneous oscillation
In addition to the clustered stereocilia that mediate mechanoelectrical
transduction (Hudspeth and Jacobs,
1979
), every hair bundle, at least during its development,
includes a single kinocilium. Because it contains an axoneme, or 9 + 2 array
of microtubules adorned with dynein motor molecules, a kinocilum is capable of
performing mechanical work. A kinocilium can oscillate spontaneously
(Bowen, 1931
) and can move in
response to electrical stimulation
(Rüsch and Thurm, 1990
).
Because this organelle has been suggested to contain the motor molecules
responsible for hair bundle oscillation (Camalet et al.,
1999
,
2000
), we wished to determine
its role in the process.
A kinocilium may be detached from the stereociliary cluster by
microdissection with the tip of a microelectrode
(Hudspeth and Jacobs, 1979
).
We selected hair bundles that displayed robust spontaneous oscillations in
artificial endolymph solution. After the kinocilium had been detached from
each of five such bundles, all continued their active movements
(Fig. 9). Even flattening the
kinocilium against the apical surface of the hair cell and holding it pointed
away from the stereociliary cluster with the dissecting electrode did not
arrest spontaneous movements. In most instances, the magnitude of the
oscillation increased slightly after dissection. This response might indicate
that a kinocilium imposes a load on the stereociliary cluster
(Crawford and Fettiplace,
1985
). The change after dissection might alternatively stem from
repositioning of the stimulus fiber at the top of a bundle, slightly farther
from the apical surface of the cell than the control point of attachment at
the kinociliary bulb.

View larger version (29K):
[in this window]
[in a new window]
|
Figure 9. Persistence of spontaneous hair bundle oscillation after kinociliary
detachment. A, A hair bundle initially displayed spontaneous
oscillations at 10 ± 6 Hz with a magnitude of 16 nm (top record). After
the kinocilium had been disconnected from the contiguous stereocilia and
flattened against the epithelial surface with a glass microelectrode, the
bundle continued to oscillate at 11 ± 4 Hz (bottom record). In this
instance, the magnitude of oscillation increased to 26 nm. B, Another
hair bundle, which originally oscillated at 9 ± 3 Hz with a magnitude
of 12 nm (top record), survived microsurgery with oscillations at 10 ±
4 Hz and 16 nm in magnitude (bottom record).
|
|
Model for spontaneous hair bundle oscillation
To ascertain whether our understanding of the principal features of
spontaneous hair bundle oscillation accords with the present experimental
findings, we developed a model for oscillations and tested its performance in
simulations of several experimental conditions. More specifically, we
assembled equations to represent hair bundle mechanics, mechanoelectrical
transduction and the flow of ionic current, adaptation of the transduction
process, and Ca 2+-dependent channel reclosure. We did not include
the effects of noise in the model. These equations, their origins and
justifications, and other features of the model are described in the
Appendix.
The model yields simulated oscillations resembling those observed
experimentally. In particular, adjustment of parameter values within a range
that accords with other measurements readily produces oscillations of
frequencies extending throughout and beyond the observed range of 550
Hz and of peak-to-peak magnitudes up to 70 nm. The oscillation waveforms
resemble those of actual bundle movements
(Fig. 10A,B). Each
phase of the slower oscillations is bipartite, with a rapid initial component
followed by a slow relaxation. As for actual oscillations, the slow components
may be approximately exponential, essentially flat, or even nonmonotonic.

View larger version (52K):
[in this window]
[in a new window]
|
Figure 10. Simulations of spontaneous hair bundle oscillations and effects of
experimental procedures. Each record was produced by the model described in
Appendix, with most of the parameter values shown in
Table 1. Record D was
produced with exactly the values in Table
1; the values that were altered for other records are provided in
the captions below. All the records have a common distance scale, but the time
scales vary so that each record may be compared with the corresponding
experimental trace. Except when indicated, each record's the total length of
each record is 2 sec. A, A high-frequency spontaneous oscillation
produced by the model displays symmetry of its positive and negative phases
(compare with Fig. 2
B). CMAX = 0.31 µm ·
sec-1; SMAX = 420 km · sec-1
· N-1; kOFF,M = 50 ·
103 sec-1; kOFF,RE = 75 ·
103 sec -1; E ø = 70
zJ; and XSP = 272 nm. B, Each phase of a large
low-frequency modeled oscillation comprises a fast component followed by a
slow movement in the same direction (compare with
Fig. 2 E). d
= 9 nm; CMAX = 0.15 µm · sec-1;
SMAX = 390 km · sec-1 ·
N-1; kON,M = 1.1 · 109
sec-1 · M-1; kOFF,M = 80
· 103 sec-1; RE,MAX = 1200
µN · m-1; RE,MIN = 200 µN ·
m-1; kOFF,RE = 75 · 103
sec-1; E ø = 65 zJ; and record
length = 500 msec. C, The response of the model to an elevation of
the extracellular Ca 2+ concentration was mimicked by evaluating
the response to a 10 nA rectangular pulse of iontophoretic current, indicated
beneath the record, with a transfer number of 0.1 for Ca 2+. Ca
2+ accelerates the oscillations but renders them smaller (compare
with Fig. 6 A).
CMAX = 0.22 µm · sec-1;
SMAX = 220 km · sec-1 ·
N-1;kOFF,M =50 ·
103sec-1; RE,MIN =200 µN ·
m-1; E ø=54 zJ; and
XSP = 178 nm. D, The response to iontophoretic
application of a Ca 2+ chelator, indicated below the trace, was
modeled by reducing the extracellular Ca 2+ concentration. The
removal of Ca 2+ slows oscillations and slightly augments their
amplitude (compare with Fig. 6
D). E, Modeling an increase in the load imposed
by the stimulus fiber from 152 to 490 µN · m-1 during the
middle portion of the record produces smaller and faster oscillations (compare
with Fig. 8 A, middle
record). CMAX = 0.06 µm · sec-1;
SMAX = 110 km · sec-1 ·
N-1; kOFF,M = 80 · 103
sec-1; RE,MIN = 200 µN · m-1;
kOFF,RE = 75 · 103 sec-1;
E ø = 68 zJ; XSP = 251
nm; and record length = 2.5 sec.
|
|
Changing the extracellular Ca 2+ concentration affects simulated
oscillations as it does actual bundle movements. In particular, an abrupt
increase in Ca 2+ concentration, similar to that during
iontophoretic application of the ion, accelerates oscillations by shortening
the slow component of positive motion and reduces their magnitude
(Fig. 10C). A
comparable concentration decrease, which mimics the effect of iontophoretic
ejection of a Ca 2+ chelator, slows oscillations by prolonging the
slow component of positive movement and augments their size
(Fig. 10D).
The formulation of the model for the mechanism of Ca
2+-dependent channel reclosure was meant to encompass the
experimental observation that the amplitude of oscillation changes in response
to alterations of the extracellular Ca 2+ concentration. If each
cycle of oscillation represents a trajectory around the
displacementresponse relation
(Martin et al., 2000
), its
amplitude can be changed only by adjusting the shape of the relation. In the
present model, Ca 2+ entry into the stereociliary cytoplasm relaxes
a component of the gating spring, thus reducing the magnitude of negative
stiffness and shortening the oscillatory trajectory. The response of the model
to simulated Ca 2+ exposure captures this aspect of the
experimental result.
The model also recapitulates the effects of increasing the mechanical load
on a hair bundle. As the stiffness of the fictive stimulus fiber increases,
oscillation becomes faster and smaller
(Fig. 10E) until it
is wholly suppressed.
Modeling readily simulates the effects of pharmacological reagents on
spontaneous hair bundle oscillation. Reducing the rate of adaptation motor
climbing lowers the frequency of oscillation by prolonging the negative phase
of movement. Such a change would occur in response to substances that promote
protein phosphorylation, such as forskolin, IBMX, 8-Br-cAMP, Sp-cAMP, and
okadaic acid. Increasing the climbing rate of the motor recapitulates the
effect of Rp-cAMP, which presumably reduces phosphorylation, by accelerating
oscillation. Not surprisingly, eliminating or greatly reducing the motility of
a myosin-based motor, as might be effected by butanedione monoxime, suppresses
oscillations (data not shown).
Modeling affords an opportunity to gain insight into complex physiological
processes by examining the behavior of parameters whose values cannot be
measured experimentally. For an oscillation 78 nm in peak-to-peak magnitude
(