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The Journal of Neuroscience, January 1, 2002, 22(1):44-52
Mechanisms of Active Hair Bundle Motion in Auditory Hair
Cells
A. J.
Ricci1,
A. C.
Crawford2, and
R.
Fettiplace3
1 Neuroscience Center, Louisiana State University
Health Sciences Center, New Orleans, Louisiana 70112, 2 Department of Physiology, University of Cambridge,
Cambridge CB2 3EG, United Kingdom, and 3 Department of
Physiology, University of Wisconsin Medical School, Madison, Wisconsin
53706
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ABSTRACT |
Sound stimuli vibrate the hair bundles on auditory hair cells, but
the resulting motion attributable to the mechanical stimulus may
be modified by forces intrinsic to the bundle, which drive it actively.
One category of active hair bundle motion has properties similar to
fast adaptation of the mechanotransducer channels and is explicable if
gating of the channels contributes significantly to the mechanics of
the hair bundle. To explore this mechanism, we measured hair bundle
compliance in turtle auditory hair cells under different conditions
that alter the activation range of the channel.
Force-displacement relationships were nonlinear, possessing a maximum
slope compliance when approximately one-half of the transducer channels
were open. When the external calcium concentration was reduced from 2.8 to 0.25 mM, the position of maximum compliance was shifted
negative, reflecting a comparable shift in the transducer channel
activation curve. Assuming that the nonlinearity represents the
compliance attributable to channel gating, a single-channel gating
force of 0.25 pN was calculated. By comparing bundle displacements with
depolarization with and without an attached flexible fiber, the force
contributed by each channel was independently estimated as 0.47 pN.
These results are consistent with fast active bundle movements
resulting from changes in mechanotransducer channel gating. However,
several observations revealed additional components of hair bundle
motion, with slower kinetics and opposite polarity to the fast movement but also linked to transducer adaptation. This finding argues for
multiple mechanisms for controlling hair bundle position in auditory
hair cells.
Key words:
adaptation; cochlear amplifier; hair cell; hair bundle movements; mechanosensitive channel; stereociliary
bundle
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INTRODUCTION |
In the vertebrate inner ear, sound
stimuli are detected by auditory hair cells through submicrometer
displacements of their mechanically sensitive hair bundles. Evidence
has accumulated that motion of the hair bundle driven by the external
acoustic stimulus can be modified and augmented by energy supplied by
the hair cell (Hudspeth, 1997 ; Fettiplace et al., 2001). Such action might serve to increase auditory sensitivity by amplifying the hair
bundle vibrations to incoming sounds, especially those near threshold.
Spontaneous oscillations of the bundle are one manifestation of the
active process (Crawford and Fettiplace, 1985; Rüsch and Thurm,
1990; Denk and Webb, 1992; Martin and Hudspeth, 1999; Martin et al.,
2000). Another is force generation by the bundle in response to
stimulation with a flexible glass fiber (Crawford and Fettiplace, 1985;
Howard and Hudspeth, 1987, 1988; Benser et al., 1996; Ricci et al.,
2000). The cellular reactions subserving the active process are not
fully understood, but multiple mechanisms will probably be needed to
explain all results, which display a wide range of kinetics.
We observed recently active bundle movements in turtle hair cells on a
millisecond time course synchronous with fast adaptation of the
mechanotransducer channels. We proposed that these bundle movements,
like adaptation, result from calcium directly closing the
mechanotransducer channels (Ricci et al., 2000). The movements can
be explained (Howard and Hudspeth, 1988) if a significant portion of
the hair bundle stiffness depends on channel gating: as the channels
open or close in response to changes in intracellular calcium, they
exert force on the bundle, causing it to move. The contribution of
channel gating to hair bundle mechanics, known as the "gating
compliance," may comprise as much as 50% of the total compliance of
the bundle in frog hair bundles (Howard and Hudspeth, 1988). The
remaining compliance, the nongating compliance, is partly attributable
to flexure of the actin filaments in the ankles of the stereocilia
(Crawford and Fettiplace, 1985; Howard and Ashmore, 1986). An aim of
the present experiments was to determine whether the gating compliance
in turtle hair cells is sufficient to account for the active bundle movements.
Active hair bundle movements have also been reported in response to
changes in membrane potential (Crawford and Fettiplace, 1985; Assad et
al., 1989; Rüsch and Thurm, 1990; Denk and Webb, 1992). Such
movements may be secondary to a reduction in calcium influx as the
membrane potential approaches the calcium equilibrium potential.
Depolarizations positive to 0 mV evoke a sustained deflection of the
bundle accompanied by an outward current thought to represent the
opening of mechanotransducer channels by reduced intracellular calcium.
However, the evoked movements differ in both time scale and polarity
between preparations. Fast millisecond responses are associated with
motion of the hair bundle toward the kinocilium (Ricci et al., 2000),
whereas slower displacements lasting tens or hundreds of milliseconds
have the opposite polarity (Assad and Corey, 1992). The different
polarities imply the operation of two independent mechanisms. Here we
show that both processes can be observed in a single hair cell.
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MATERIALS AND METHODS |
Preparation and recording. The method of recording
from hair cells in the auditory papilla of the red-eared turtle was
identical to that described previously (Ricci and Fettiplace, 1997).
Turtles (Trachemys scripta elegans; carapace length, 75-125
mm) were decapitated, and the cochlea was dissected out, opened, and
incubated in saline (in mM: 125 NaCl, 4 KCl, 2.8 CaCl2, 2.2 MgCl2, 2 Na
pyruvate, 8 glucose, and 10 Na-HEPES, pH 7.6) containing up to 0.06 mg/ml protease (type XXIV; Sigma, St. Louis, MO). The tectorial
membrane was then removed to expose the hair bundles. The preparation
was mounted in a Perspex chamber on the stage of a Zeiss (Oberkochen, Germany) Axioskop FS microscope and viewed through a 63×
water-immersion objective (0.9 numerical aperture). The recording
chamber was perfused with standard saline containing (in
mM): 130 NaCl, 0.5 KCl, 2.8 CaCl2, 2.2 MgCl2, 2 Na
pyruvate, 8 glucose, and 10 Na-HEPES, pH 7.6. The upper surface of the
hair cell epithelium and the hair bundles were independently perfused
with a solution similar in composition to standard saline with
Na+ as the major monovalent ion and with
either normal (2.8 mM) or reduced (0.25 mM) Ca2+
concentration. Perfusion of the hair cell apical surface with a
K+-rich saline to fully mimic endolymph
was not attempted in the present experiments. However, it is worth
noting that exposure of the hair bundle to such a
K+-based solution may result in a more
pronounced gating compliance and active bundle movements closer to
those occurring in vivo (Martin and Hudspeth, 1999).
Whole-cell currents were measured with an Axopatch 200A amplifier (Axon
Instruments, Foster City, CA) connected to a patch pipette
filled with an intracellular solution containing (in
mM): 125 CsCl, 3 Na2ATP, 2 MgCl2, 1 EGTA, and 10 Cs-HEPES, pH 7.2. After
applying up to 70% series resistance compensation, electrode access
resistances were 1-5 M , and recording time constants were 10-100
µsec. All measurements were begun at a holding potential of  80 mV.
Unless otherwise indicated, measurements are quoted as the mean ± 1 SD, and the responses shown are averages of from 5-25
presentations. Cells studied were located between 0.5 and 0.7 of the
distance along the basilar papilla from the low-frequency end.
Experiments were performed at 19-23°C.
Hair bundle displacement. Hair bundles were stimulated with
a flexible glass fiber cemented to a piezoelectric bimorph (Crawford and Fettiplace, 1985). The bimorph was driven differentially with voltage steps, filtered with an eight-pole Bessel filter at 2 kHz to
produce a 10-90% voltage rise time of ~0.2 msec. Fibers were
constructed and calibrated as described previously (Ricci et al., 2000)
and had a mechanical stiffness between 0.7 and 3.3 mN/m. Before an
experiment, the flexible fiber was acid-cleaned to help it stick to the
hair bundle membrane, ensuring that the bundle followed motion of the fiber.
The apparatus for measuring hair bundle motion was similar to that
described previously (Crawford and Fettiplace, 1985; Ricci et al.,
2000). The secondary image of the bundle was projected through the
camera port of the Axioskop onto a pair of photodiodes (Centronics LD
2-5) at a magnification of ~700×. The photodiodes were themselves
mounted on a piezoelectric bimorph, sinusoidal deflections of which
were used to calibrate the photodiode signals (Art et al., 1986). The
bundle image was centered on the photodiode junction, and its lateral
motion was always less than the total width of one photodiode (0.5 mm).
The difference between the signals from the two diodes should therefore
be proportional to the displacement of the image (Crawford and
Fettiplace, 1985). The proportionality constant was determined for each
hair bundle by measuring the photocurrent produced by small sinusoidal
vibrations, 60 nm peak-to-peak, of the photodiodes across the image of
the bundle.
For stimulating a hair bundle, the flexible glass fiber was attached to
the neural face of the bundle between 0.3 and 0.5 of the distance up
the bundle from the epithelial surface. At this position, the fiber was
several times more compliant than the hair bundle, and so
the stimulus delivered on deflecting the fiber was approximately a
force step. The magnitude of the force was calculated from the
compliance of the fiber and the difference between the displacements of
the end of the fiber fixed to the piezoelectric bar and the free end of
the fiber that was attached to the bundle (Crawford and Fettiplace,
1985). The displacement of the tip of the fiber at which it touches the
bundle was calculated from the motion of the top of the bundle, deduced
from the photodiode signal. Assuming that the hair bundles
pivot about their base (Flock et al., 1977; Crawford and Fettiplace,
1985), motion of the end of the fiber will be  times the motion of
the top of the bundle, where is the fractional distance up the
bundle of the point of attachment of the fiber. The value of
, which fell between 0.3 and 0.5, was measured at the end of each
experiment. If the displacement of the piezoelectric bimorph was
y, the deflection of the top of the hair bundle was
x, and the stiffness of the fiber was
KF, then the force
F delivered at the point of contact
of the fiber with the bundle was calculated as follows: F = KF · (y x). To estimate the stiffness of the bundle, the
effective force at the tip of the bundle,
FB, was then approximated as follows:
FB = F. From recording the unhindered
motion of the flexible fiber in solution, it was estimated that the
combined stimulation and imaging systems had a time constant of
0.2-0.3 msec. The bundle displacement, x, and hence force,
FB, was taken at a time coinciding
with the peak of the current for a small stimulus producing an adapting
response. This was between 0.5 and 1 msec after deflecting the fixed
end of the fiber.
Hair bundle motion was analyzed in terms of the gating spring model of
mechanotransduction (Howard and Hudspeth, 1988; Markin and Hudspeth,
1995; van Netten and Kros, 2000). In this model, gating of the
mechanotransducer channels contributes to the mechanical stiffness of
the bundle, which declines over the range of displacements at which the
channels are opening. The model predicts a relationship between the
force, FB, applied to the bundle and
bundle displacement x given as follows:
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(1)
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where KS is the combined
stiffness of the stereociliary pivot, and the gating spring,
po, is the probability of opening of the mechanotransducer channels, N is the number of
mechanotransducer channels in the bundle, and z is the
gating force per channel (the decrease in the gating spring force that
occurs when the channel opens). Fo is
a constant chosen to make FB zero at
the resting position of the bundle. In a two-state channel scheme in
which the mechanotransducer channels can occupy either a single closed
or open state, po is described as
follows:
![p<SUB><UP>o</UP></SUB>=1/(1+<UP>exp</UP>{<UP>−</UP>[z(x−x<SUB><UP>o</UP></SUB>)/kT]},](/content/vol22/issue1/fulltext/44/img002.gif)
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(2)
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and the slope stiffness of the hair bundle,
KB, is given as follows:
![K<SUB><UP>B</UP></SUB>=K<SUB><UP>S</UP></SUB>−K<SUB><UP>c</UP></SUB>/{<UP>cosh</UP>[(x−x<SUB><UP>o</UP></SUB>)/&kgr;]}<SUP>2</SUP>](/content/vol22/issue1/fulltext/44/img003.gif)
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(3)
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where Kc is
Nz2/4kT and  = 2kT/z. is a space constant reflecting the
broadness of the stiffness minimum. Equation 3 was used to fit the hair
bundle stiffness measurements and to determine the space constant to evaluate z, the gating force per channel. It should be
noted that the value of z calculated by this method is the
force expressed at the tip of the bundle and therefore depends on the
geometry of the bundle. This analysis assumes that gating of the
mechanotransducer channel can be described by a scheme with single open
and closed states. As noted previously (Corey and Hudspeth, 1983;
Crawford et al., 1989), a two-state channel scheme poorly describes the
current-displacement relationship in some hair cells, and a
three-state scheme, two closed states and one open state, provides a
better fit. However, it was not felt that this deviation was sufficient
to warrant a more complex analysis of the gating compliance, which
requires extra assumptions about channel gating (Markin and Hudspeth,
1995; van Netten and Kros, 2000).
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RESULTS |
Gating compliance
A principal aim of the experiments was to determine whether hair
cells displaying active bundle movements also possessed a prominent
gating compliance, such that gating of the mechanotransducer channel
made a significant contribution to the compliance of the hair bundle.
One indication of the active bundle movements was the presence of a
recoil in the displacement response to a force step with a time course
similar to adaptation of the transducer current (Ricci et al., 2000).
The force-displacement relationship in such cells was nonlinear and
possessed a point of inflection, corresponding to the minimum
stiffness, when approximately one-half of the transducer channels were
open. Figure 1 shows an example in which
there was an approximately fourfold reduction in stiffness from 12 mN/m
for large positive or negative displacements to a minimum of 3 mN/m
over the region in which the open probability changed most. In 10 cells, the limiting stiffness for large positive and negative
displacements was 3.3 ± 1.7 mN/m (mean ± SD), and this
stiffness declined over the gating range to a minimum of 1.4 ± 0.4 mN/m. These values are more than three times the bundle stiffnesses
reported for frog saccular hair cells (Howard and Hudspeth, 1988),
which probably reflects more intact gating springs. However, the
fractional reduction is similar and indicates that, in turtle auditory
hair cells, as in frog hair cells, 50-60% of the compliance of the
bundle may be contributed by the gating process. The reduction in
stiffness varied between 0.6 and 9 mN/m across cells and was
proportional to the maximum size of the transducer current, which
ranged from 0.2 to 1.1 nA. This correlation is expected if the
reduction in stiffness is a consequence of gating of the
mechanotransducer channels.
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Figure 1.
Nonlinear compliance of the hair bundle.
A, The stereociliary bundle of a hair cell was
stimulated with a flexible fiber, delivering a family of force steps
(top) that generated mechanotransducer currents
(middle) and associated bundle displacements
(bottom). The largest force step was 175 pN.
B, The force-displacement relationship
(top) and the current-displacement relationship
(bottom, filled circles) were derived
from the records in A, measurements of both
mechanotransducer current and bundle displacement being taken 0.5 msec
after commencing the force step (see Materials and Methods). Hair
bundle stiffness was calculated by differentiating the
force-displacement results and is plotted against displacement
(bottom, open circles). The
force-displacement results are fitted with Equation 1, and the bundle
stiffness-displacement results are fitted with Equation 3, with
Ks = 13.5 mN/m,
Kc = 10.8 mN/m,
xo = 47 nm, and z = 0.27 pN.
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The force-displacement relationships were used to obtain the slope
stiffness of the bundle, which, when plotted against displacement, could be fitted by Equation 3 (Figs. 1,
2). From these fits, the gating force per
channel, z, was calculated as described in Materials and
Methods. Measurements on 10 cells gave a mean z of 0.25 ± 0.03 pN, which is similar to values reported for other preparations (Markin and Hudspeth, 1995; van Netten and Kros, 2000). The mechanical sensitivity of the hair cells in these experiments was inferred from
the plot of the mechanotransducer current divided by its maximum value
(I/Imax) against bundle
displacement. The plot was fit over its steepest region with a straight
line that had a mean inverse slope of 44 ± 19 nm. The slope
provides a measure of the operating range of the mechanotransducer
channels. It was used to obtain an independent estimate for
z, the gating force per channel (Markin and Hudspeth, 1995)
of 0.37 ± 0.16 pN, which is similar to the value inferred from
the stiffness-displacement relationship.
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Figure 2.
Simultaneous shifts in the mechanotransducer
channel activation and gating compliance. A, Reducing
the extracellular calcium concentration from 2.8 to 0.25 mM
caused leftward shifts in the channel activation (top)
and in the bundle stiffness-displacement relationship
(bottom). The channel activation relationship is plotted
as the mechanotransducer current, I, normalized to its
maximum value, Imax, where
Imax = 0.95 nA (2.8 mM
calcium; open circles) and 1.014 nA (0.25 mM
calcium; filled circles). The bundle
stiffness-displacement relationships were fitted with Equation 3, with
Ks = 8.0 mN/m,
Kc = 4.0 mN/m,
xo = 30 nm, and z = 0.23 pN (2.8 mM calcium) and with
Ks = 9.3 mN/m,
Kc = 3.0 mN/m,
xo = 18 nm, and z = 0.31 pN. B, A 30 nm sustained displacement of the hair
bundle toward the kinocilium caused rightward shifts in the channel
activation (top) and in the bundle
stiffness-displacement relationship (bottom). The
channel activation curve and hair bundle mechanics were assayed with a
test stimulus 3 msec in duration starting 5 msec after the onset of the
adapting step. Mechanotransducer currents, I, normalized
to an Imax of 0.85 nA in both conditions.
The bundle stiffness-displacement relationships were fitted with
Equation 3, with Ks = 6.7 mN/m,
Kc = 2.0 mN/m,
xo = 20 nm, and z = 0.23 pN (control; open circles) and with
Ks = 5.5 mN/m,
Kc = 2.5 mN/m,
xo = 44 nm, and z = 0.23 pN. In both A and B, the
arrows indicate the bundle position for half-activation
of the channels (top) and for minimum stiffness of the
bundle (bottom).
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Effects of calcium on hair bundle mechanics
The active bundle movements are thought to be driven by a rise or
fall in intracellular calcium acting via a change in the probability of
opening of the mechanotransducer channels. A key test of this mechanism
for the active movements is to alter the gating compliance by
manipulating calcium within the stereocilia. Lowering extracellular
calcium should reduce stereociliary calcium, whereas sustained bundle
deflection toward the kinocilium should increase stereociliary calcium.
Figure 2 shows the results of these procedures, each of which altered
the range of bundle positions over which the mechanotransducer channels
were activated. Lowering external calcium translated the activation
curve to the left, corresponding to a displacement away from the
kinocilium, whereas an excitatory adaptive step shifted the activation
curve to the right, toward the kinocilium. These shifts in the
activation curve along the displacement axis were accompanied by
equivalent shifts in the stiffness-displacement relationship, assayed
from the bundle position at which the stiffness was a minimum. The
bundle position for minimum stiffness is indicated by the
arrows in Figure 2. Reducing the external calcium from 2.8 to 0.25 mM translated the position of minimum
stiffness by 40 ± 15 nm (n = 5). For both cells
in Figure 2, the shift in the bundle position for the stiffness minimum
was similar to that for half-activation of the mechanotransducer channels. The correlation between the electrical and mechanical parameters is shown in Figure 3. These
results demonstrate that the nonlinear behavior of turtle auditory hair
bundle attributable to gating compliance can be changed by procedures
that might be expected to alter intracellular calcium. A similar effect
on the gating compliance of frog saccular hair cells has been reported previously (Howard and Hudspeth, 1988).
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Figure 3.
Correlation between mechanotransducer channel
activation and hair bundle mechanics. The bundle position for minimum
stiffness, Kmin, is plotted against
that for half-activation of the channels (see arrows in
Fig. 2). control are measurements in 2.8 mM
extracellular calcium (open circles; each
symbol is a different hair cell); adapted
are in similar conditions to controls, except with a sustained bundle
displacement of between 30 and 150 nm toward the kinocilium
(filled triangles); low Ca are in
0.25 mM extracellular calcium (filled
circles). Line is a least-squares fit with slope
1.15, intercept 0.6 nm, and regression coefficient 0.95.
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The effects of reducing extracellular calcium took several minutes to
stabilize because of the speed of the perfusion system, and we
therefore had no information about how fast these changes occurred.
However, for small bundle displacements, adaptation was rapid, and the
decline in the mechanotransducer current and the shift in the
activation curve of the channel were complete in, at most, 5 msec.
There were suggestions that manipulating intracellular calcium had
other effects besides those attributable to shifts in channel gating.
Thus, in all cells studied, lowering extracellular calcium produced a
small increase in the nongating stiffness, and adaptation caused a
small decrease in the nongating stiffness. In five cells, the limiting
stiffness (the stiffness for displacements in which the probability of
channel opening was ~0 or 1) was 3.0 ± 0.5 mN/m (mean ± 1 SEM) in 2.8 mM external calcium, and it increased to
4.8 ± 1.3 mN/m in 0.25 mM external calcium. In nine
other cells, a limiting stiffness of 3.5 ± 0.5 mN/m was reduced
to 2.8 ± 0.6 mN/m by a positive adapting step. These changes,
although small, were significant at the 0.05 level in a two-tailed
t test. An increase in bundle stiffness on reducing extracellular calcium has been reported previously for frog saccular hair cells (Marquis and Hudspeth, 1997). The origin of these
effects is unknown, but, because they occur with adaptation, they are likely to be a consequence of changes in intracellular calcium.
Estimate of force generated by the active process
Depolarization of the hair cell positive to 0 mV, which opens
transducer channels probably by lowering bundle calcium, also elicits
active bundle movements. Such movements are accompanied by the
simultaneous development of an outward current flowing through newly
opened channels (Ricci et al., 2000). This behavior provided a means of
determining the magnitude of force generated by the active process.
Figure 4 shows that a depolarizing
voltage step to +60 mV from the holding potential of 80 mV caused a
sustained displacement of the free-standing bundle toward the
kinocilium. When the flexible fiber was placed against the tip of the
bundle, on its kinocilial side, the amplitude of the active movement
was reduced because the bundle now had to perform work against the stiffness of the fiber. The evoked displacement was restored to its
original size on detaching the fiber. The force produced by the active
process was then inferred from the reduction in movement caused by the
fiber multiplied by the stiffness of the fiber. In Figure
4A, a fiber with a stiffness of 3.3 mN/m reduced the bundle movement by 8 nm, so the bundle produced a force of 26 pN.
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Figure 4.
Force generated by active movement of the hair
bundle. A, Three averaged bundle displacements produced
by depolarizing voltage steps from 80 to +60 mV, in the presence
(fiber on) or absence (fiber
off) of a flexible fiber attached to the tip of the
bundle. Positive displacements are toward the kinocilium.
Superimposed movements of the free bundle (fiber
off) are measurements before attachment of the fiber and
after its removal. The force generated is 26.4 pN, the product of the
difference is peak motion with and without the fiber (8 nm) and the
stiffness of the fiber (3.3 mN/m). B, Collected
results in 12 cells of the force generated by active bundle
motion plotted against the mechanotransducer current activated during a
depolarization to +60 or +80 mV (for method of measurement, see Ricci
et al., 2000, their Fig. 7). All currents have been corrected to a
holding potential of +80 mV, assuming a reversal potential for the
transducer current of 0 mV. Straight line is a
least-squares fit, with slope 0.056 pN/pA and regression coefficient
0.84.
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We showed previously that the displacement of the free-standing bundle
attributable to depolarization was proportional to the amount of
outward current activated and, hence, number of channels opened (Ricci
et al., 2000, their Fig. 7). In the present experiments, the
force attributable to the active process also increased with the size
of transducer current activated (Fig. 4B). The
results have been fitted with a straight line, the slope of which can
be used directly to determine the gating force per channel. The linear
relationship depicted assumes that the bundles assayed all have the
same height and stereociliary complement. There are likely to be small
differences in both parameters with hair cell location (Hackney et al.,
1993), but, because recordings were made at a restricted range of
locations (see Materials and Methods), the variations would be within
the scatter of the results. After correcting for differences in
membrane potential between experiments, the current should be
proportional to the number of mechanotransducer channels opened.
Assuming that these channels have a unitary conductance of 106 pS
(Crawford et al., 1991) and a linear current-voltage
relationship, the slope of the fitted line in Figure
4B can be expressed as a force of 0.47 pN per
transducer channel. This value is comparable with the gating force per
channel deduced from the force-displacement relationships (0.25 pN;
see above). Such agreement would be expected if the active bundle motion stems from gating of the mechanotransducer channel.
Two components of the active response
The hair bundle movement caused by depolarization (Fig. 4) (Ricci
et al., 2000) was of the opposite polarity to that reported for frog
saccular hair cells under comparable stimulus conditions (Assad et al.,
1989). Thus, depolarization to +80 mV produced a sustained bundle
displacement toward the kinocilium in turtle but away from the
kinocilium in the frog, the amplitude of the motion being similar in
the two cases. The simplest explanation for this discrepancy is that
different mechanisms underlie the active movements in turtle and frog.
A frequently observed aspect of our measurements was that the
displacement would reach a peak and then decline slightly or sag during
the depolarization. If the sag was present, at the end of the voltage
step, the bundle would overshoot its original position before returning
slowly to rest (Figs. 4A,
5A). This behavior occurred in
free-standing bundles and was more prominent at larger
depolarizations, suggesting the recruitment of a second component in
the movement of reverse polarity. The reduction in displacement with
time was most obvious if the voltage step was lengthened, and sometimes
the reversed component would bring the bundle back to its original
position. The time course of the second component was slow, and, when
fitted with a single exponential, it had a time constant ranging
between 100 and 300 msec (mean of 163 ± 95 msec;
n = 4). These time constants are 100 times slower than
that of the initial movement, which was simultaneous to fast
adaptation. The relaxation in bundle position was not accompanied by a
decline in the current, signifying channel closure, but was associated
with a small slow growth of the outward current. It must therefore
reflect a secondary increase in the opening of the mechanotransducer
channels. These results indicate that two components of active bundle
movement arise in turtle auditory hair cells.
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Figure 5.
Sags in the bundle displacement produced by
depolarization. A, A depolarizing step to +40 mV caused
an increase in outward current as a result of opening of
mechanotransducer channels (middle) and a sustained
displacement of the bundle toward the kinocilium
(bottom). When the depolarization was increased to +80
mV, the bundle displacement was not maintained but sagged back toward
the resting position, and, on return to the holding potential, the
bundle overshot its original position before slowly returning to rest.
Despite the sag in the bundle displacement at +80 mV, the current
increased slightly. The very fast transient at the onset of the
depolarization is unrelated to transducer channel gating (Ricci et al.,
2000). B, A pronounced sag in the movement for a longer,
500 msec, depolarizing step in which the bundle went past its resting
position during the depolarization. Note that the sag in the bundle
movement was not accompanied by a decline in the current.
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Polarity of active bundle motion depends on bundle position
Reversal of the polarity of response to a depolarizing voltage
step could also be achieved by a sustained deflection of the hair
bundle toward the kinocilium (Fig. 6). In
a free-standing bundle, or one in which the flexible fiber had been
brought into contact with the bundle without perturbing its position,
a depolarization from 80 to +60 or +80 mV caused an
initial movement toward the kinocilium, as described above. This will
be referred to as the normal response. However, if the fiber was then
displaced in the direction of the kinocilium, the response
to the depolarization diminished, and, for sustained movements of 90 nm
of more, it was reversed. The mean bundle displacement needed to
reverse the response in seven cells was 167 ± 67 nm. When the
fiber was pulled back, restoring the hair bundle to its original
position, the polarity of the displacement response was returned to
normal. The reversal is unlikely to be an artifact of a change in
position of the image of the bundle on the photodiode because the small transient at the onset of the response did not reverse. The origin of
this early instantaneous component is unknown, but it is unlikely to be
related to gating of the mechanotransducer channels because it is
insensitive to streptomycin (Ricci et al. al., 2000). In many of the
experiments, the offset in bundle position slightly increased the
steady inward current, presumably because of an increase in
po for the mechanotransducer channels.
Furthermore, the outward current during the step was larger, implying
that more mechanotransducer channels opened. A possible explanation for
the increase in the number of channels opened by depolarization with a
positive bundle deflection is shown in Figure 6B.
This explanation requires that the mechanotransducer channels are
significantly adapted by the imposed bundle displacement, implying that
the resting calcium concentration within the stereocilia was
elevated.
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Figure 6.
Polarity of active bundle motion depends on bundle
position. A, Depolarization to +60 mV produced an
outward current and a displacement toward the kinocilium when delivered
at the resting position of the bundle (trace 1). With a
sustained displacement of the bundle toward the kinocilium by the
attached flexible fiber, an outward current still occurred, but the
polarity of the bundle motion was reversed and slowed (trace
2). When the bundle was restored to its original position, the
polarity of bundle motion for the depolarizing step returned to normal
(trace 3). Note that the outward current was larger when
the bundle was displaced toward the kinocilium (trace
2) than when in its unperturbed position
(traces 1, 3).
B, Theoretical activation curves for the
mechanotransducer channels at 80, +80, and 80 mV with a sustained
bundle offset, XOFF. In response to
depolarization from 80 to +80 mV, there is an increase in the
probability of opening of the transducer channels
(I1), causing an outward current. If
the bundle is displaced toward the kinocilium by
XOFF, then the activation curve
shifts to the right because of channel adaptation. In response to the
same depolarization, there is now a larger increase in the probability
of opening of the transducer channels
(I2), causing a greater outward
current. The activation curve at +80 mV is the same for the two
conditions because the channels do not adapt at positive holding
potentials.
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The reversed displacement response had a slower time course than the
normal response at both the onset and offset of the voltage step. The
onset of the displacement could be fit with a single exponential,
which, in seven cells, had a time constant of 3.8 ± 1.7 msec for
the normal polarity and 17.8 ± 7.4 msec for reversed polarity.
This slowing was also evident in the current response, which showed a
particularly slow return to the baseline at the end of the voltage
step. It has been argued previously that the decline in current at the
end of the voltage step is a manifestation of adaptation of the
mechanotransducer channels (Assad and Corey 1992; Ricci et al., 2000).
Thus, as the membrane potential is stepped back to 80 mV, the
electrochemical gradient driving calcium into the stereocilia is
increased, so calcium enters the stereocilium to promote adaptation.
The slowing of adaptation during sustained bundle deflection may be
attributable to a rise in resting stereociliary calcium or may reflect
a displacement sensitivity to the process. The phenomenon is probably
related to the slowing of adaptation seen with larger displacement
steps in a family of mechanotransducer currents, such as those in
Figure 1A (see also Wu et al., 1999, their Fig. 1).
It is unclear whether the slower reversed response to depolarization
reflects the recruitment of a separate mechanism or whether it is
attributable to modification of the normal response by the elevated
intracellular calcium. The reversed response showed the same dependence
on membrane potential as the normal response, growing for
depolarizations positive to 0 mV and then eventually saturating (Ricci
et al., 2000). This suggests that the reversed response, like the
normal response, is also controlled by changes in intracellular
calcium. When the bundle was deflected incrementally during
presentation of depolarizing voltage steps, it was possible to observe
at intermediate bundle positions a biphasic movement that may represent
the transition from the normal to reversed response (Fig.
7). To demonstrate that the intermediate
responses (Fig. 7, traces 2, 3) were a mixture of
the normal (N) and reversed (R) responses (Fig. 7, traces 1,
4), N and R were each fit with single time constants
for their onset and offset. The onset and offset time constants were
3.3 and 1.5 msec, respectively, for the normal response and 10.3 and 14 msec for the reversed response. The intermediate responses could then
be described by a linear sum of N and R. For example, trace
2 was well described by adding 0.63 N and 0.37 R, whereas
trace 3 was obtained by adding 0.31 N and 0.69 R. The
results imply the mixing of two distinct processes, the normal response
diminishing and the reversed response growing, as the bundle is biased
toward the kinocilium.
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Figure 7.
Depolarization produces two components of bundle
motion. Depolarization to +60 mV produced an outward current and a
displacement toward the kinocilium when delivered at the resting
position of the bundle (trace 1). When the bundle was
displaced incrementally toward the kinocilium by the attached flexible
fiber (traces 2-4), the bundle motion became
biphasic and then reversed polarity. Superimposed current records are
shown for the four positions, with the corresponding bundle motions
shown below. The normal response (trace 1; N) and the
reversed response (trace 4; R) were fitted with
single-exponential onsets and decays. The onset and offset time
constants were 3.3 and 1.5 msec, respectively, for N, and 10.3 and 14 msec, respectively, for R. Linear combinations of N and R
[aN + (1 a)R] were calculated
to best describe the intermediate responses: a = 0.63 for trace 2, and a = 0.31 for
trace 3. This suggests the mixing of two distinct
processes. For all responses, the smooth theoretical lines are
superimposed on the noisy experimental records. A negative step
corresponding to a small fast component unrelated to gating of the
mechanotransducer channels has been subtracted from each averaged
displacement record.
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DISCUSSION |
The mechanotransducer channel as the source of the
active movement
Motion of the stereociliary bundle of the hair cell to a force
stimulus is governed by its mechanical compliance. This compliance has
a passive component attributable to the flexibility of the stereociliary ankles and the stiffness of the gating springs, and an
active component, the gating compliance, linked to the opening
and closing of the mechanotransducer channels (Howard and Hudspeth,
1988). The relative importance of the gating compliance may differ in
different end organs (Russell et al., 1992; van Netten and Khanna,
1994; Géléoc et al., 1997). We described previously for
turtle auditory hair cells a fast active bundle motion associated with
the gating of the transducer channels, which is most simply explained
if the gating compliance makes a substantial contribution to bundle
mechanics (Ricci et al., 2000, their Fig. 12). Here we presented
several lines of evidence supporting this mechanism. (1) The
force-displacement relationship of the hair bundle was nonlinear and
possessed a point of inflection, corresponding to the maximum
compliance, when approximately one-half of the transducer channels were
open. This analysis is consistent with a gating compliance that
contributes a significant proportion (50-60%) of the total compliance
of the bundle. (2) The nonlinearity in the force-displacement
relationship of the bundle occurred over a similar range of open
probabilities to the active motion; both the fast recoil in bundle
displacement to a force step and the bundle compliance were largest for
open probabilities of 0.4-0.6. (3) The nonlinearity in the
force-displacement relationship of the bundle, like the active bundle
motion, was sensitive to changing intracellular calcium by lowering
extracellular calcium concentration or superimposing stimuli on an
adapting step. (4) A single-channel gating force of 0.25 pN, derived on
the gating spring hypothesis (Howard and Hudspeth, 1988), was
comparable with that of 0.47 pN obtained by independent measurements on
the force produced by the bundle for a depolarizing voltage step. To
account for the fast active bundle movements, the nonlinearity in the
force-displacement relationship should shift rapidly with channel
gating. In support of this notion, the shifts in open probability and
bundle stiffness for an adapting step occurred as quickly as they could
be monitored, which was within 5 msec. Together, these pieces of
evidence support the idea that the nonlinearity in the
force-displacement relationship is attributable to the gating
compliance and that its fast translation along the displacement axis as
the channel opens and closes can account for the fast active bundle motion.
Because force generation by the bundle is linked to gating of the
mechanotransducer channels, it operates at frequencies within the
auditory range. For example, the fast recoil that follows adaptation in
turtle hair cells has a time constant between 0.3 and 3 msec,
corresponding to a frequency range of 50-500 Hz (Ricci et al., 2000).
Such speed would enable it to amplify hair bundle movements, thereby
increasing auditory sensitivity. The amount of force produced by the
hair bundle will be primarily determined by two factors: the
number of mechanotransducer channels and the bundle geometry. The
gating force per channel exerted at the tip of the bundle will be
smaller than at the channel by a geometrical gain,  , equal to the
ratio of the inter-stereociliary spacing divided by the average
stereociliary height in the bundle (Howard et al., 1988). For
turtle auditory hair cells in the mid-frequency range, = 0.06 (Hackney et al., 1993), and the average value for gating force at the
tip of the bundle from the two methods is 0.36 pN per channel.
Therefore, the force at the channel itself is on the order of 6 pN.
Assuming that the gating force at the channel is similar in all hair
cells, the force generated by the bundle will become larger with an
increase in the number of mechanotransducer channels per bundle and a
decrease in bundle height (increasing ). In turtle hair cells, both
parameters vary with the characteristic frequency of the cell (Hackney
et al., 1993; Ricci and Fettiplace, 1997), in a manner that makes the
force larger in cells tuned to higher frequencies. The increase in
active force generation by hair bundles of cells at higher frequency
may be needed to offset the viscous load on the bundles, which will
also become more prominent at higher frequencies.
Multiple components of force generation
Our experiments demonstrate that other types of active bundle
movement can also be observed in turtle auditory hair cells, and these
movements are slower and of opposite polarity to the fast movements
that were the main focus of the previous study (Ricci et al., 2000).
Whereas these fast movements have time constants of ~1 msec, slower
movements with time constants of 10-20 msec (Figs. 6, 7) and 150 msec
(Fig. 5) are seen under certain conditions. The time course of the slow
movements was variable across cells, but it is unclear whether such
intrinsic variability can explain the 10-fold difference in mean values
observed under the two experimental circumstances in Figures 5-7, and
more than one slower process may be involved. The slow movements are of
the same polarity and amplitude as those reported for frog saccular
hair cells, in which motion of free-standing bundles could also be
produced by depolarizing voltage steps (Assad and Corey, 1992). Those
movements had a mean time constant of 193 msec for depolarization to
+80 mV and 56 msec for repolarization to 80 mV. Faster displacements
may have been missed in their experiments because of the limited
sampling imposed by the 30 Hz frame rate of the camera used for imaging the bundle. Indeed, other methods of stimulation have demonstrated both
fast and slow active movements in frog hair bundles (Howard and
Hudspeth, 1987; Denk and Webb, 1992; Benser et al., 1996). For example,
analysis of spontaneous hair bundle motion revealed two temporal
distributions with time constants of ~1.5 and 15 msec, respectively
(Denk and Webb, 1992). These values are similar to two of the kinetic
components for turtle hair bundles. Thus, it seems likely that multiple
mechanisms of active bundle motion and adaptation are a general feature
of mechanotransduction in all hair cells.
In both the present results and those of Assad and Corey (1992), the
slow bundle displacement produced by depolarization was directed away
from the kinocilium. However, a decline of the inward transducer
current denoting adaptation always occurred at the end of depolarizing
step (Figs. 5, 6A, 7A) despite the
polarity of the bundle movement. The underlying mechanisms of the fast and slow processes must therefore differ, although both lead to closure
of the mechanotransducer channels. However, why, as is clear from
Figure 7, does the fast movement disappear if the bundle is pushed
toward the kinocilium? One idea (Wu et al., 1999) sees the state of the
mechanotransducer channels as determined by a balance between the
tension in the gating springs that favors opening and the binding of
intracellular calcium to an intracellular site that causes channel
closure. When all of the calcium sites are occupied, the likelihood of
channel closure is maximal and constant. At this point, increasing
tension in the gating springs will still promote channel opening, and
large enough displacements must eventually overcome any action of
intracellular calcium to close the channels: hence, the disappearance
of fast movements when the bundle is biased toward the kinocilium. This
explanation might also account for the disappearance of the fast
component of current adaptation with large stimuli (Wu et al., 1999,
their Fig. 1).
The results in Figures 6 and 7 indicate that the slower component
possesses a displacement sensitivity that would make it most important
for large bundle deflections toward the kinocilium. In line with this
observation, adaptation in turtle hair cells in response to stepping
the bundle becomes slower for larger stimuli, which has been
interpreted as being attributable to the recruitment of a second
component of adaptation (Wu et al., 1999). This additional component
had a time constant in the same range of 10-20 msec as the
reversed-polarity bundle movements. Moreover, it depended on the
concentration of internal calcium buffer, implying that it, too, was
controlled by intracellular calcium. Thus, two calcium-controlled processes both result in closure of the mechanotransducer channels but
cause bundle motions of opposite polarity.
It has been argued that the slow adaptation in the mechanotransducer
currents of frog hair cells reflects the operation of a motor, powered
by an unconventional myosin, which tensions the tip links (Assad and
Corey, 1992; Hudspeth and Gillespie, 1994). This motor is also
regulated by intracellular calcium. Thus, a fall in intracellular
calcium occurring during depolarization will have two effects on bundle
position. On a millisecond time scale, the drop in calcium directly
opens mechanotransducer channels, causing a movement of the bundle
toward the kinocilium (Ricci et al., 2000). Over tens or hundreds of
milliseconds, the reduced intracellular calcium will activate the
myosin motor applying tension to the tip links to pull the bundle away
from the kinocilium (Assad and Corey, 1992). More experiments are
needed to show that the slower reversal in polarity of the bundle
movement reported here involves the myosin motor.
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FOOTNOTES |
Received May 4, 2001; revised Oct. 12, 2001; accepted October 12, 2001.
This work was supported by National Institute on Deafness and Other
Communicative Disorders Grants RO1 DC 01362 (to R.F.) and RO1 DC 03896 (to A.J.R.) and a Deafness Research Foundation grant (to A.J.R.).
Correspondence should be addressed to Robert Fettiplace,
185 Medical Sciences Building, 1300 University Avenue, Madison, WI 53706. E-mail:fettiplace{at}physiology.wisc.edu.
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ABSTRACT
INTRODUCTION
