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1 Division of Neuroscience, Baylor College of Medicine, Houston, Texas 77030 2 The Bobby R. Alford Department of Otorhinolaryngology and Communicative Sciences, Baylor College of Medicine, Houston, Texas 77030
Submitted 4 October 2002; accepted in final form 24 June 2003
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ABSTRACT |
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INTRODUCTION |
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). This difference can be seen in the frequency dependence of responses to sinusoidal head movements. Below 2 Hz, the highest frequency examined, the response gain tends to rise with frequency for striolar afferents and remain flat with frequency for extrastriolar afferents.
Such differences in afferent responses can arise at any preceding stage, from the macromechanical response of the utricular accessory structures (otoconia and gel layer) to hair cell synaptic transmission. [Goldberg et al. (1984) showed that differences in afferent response dynamics are unlikely to reflect differences in spike generation in the afferent nerve.] Holt et al. (1997, 1998, 1999) found that transduction currents in mouse utricular hair cells adapt to step bundle deflections with a time course that, in the frequency domain, causes the currents to increase with stimulus frequency over the range from DC to 5 Hz (high-pass filtering). Whether this behavior varies with hair cell location in the sensory epithelium was not determined. In the present study, we asked whether the transduction stage contributes to regional variation in the response kinetics of utricular afferents, by comparing the responses of extrastriolar and striolar hair cells to step bundle deflections. We also compared the responses of the two morphologically distinct hair cell types, type I and type II, that are found in the vestibular organs of all amniotes.
In previous studies in which bundles were deflected with a fluid jet (Holt et al. 1997, 1998, 1999), adaptation of mouse utricular hair cells was slower than that evoked in frog saccular (Shepherd and Corey 1994) and turtle cochlear hair cells (Ricci et al. 1998) by deflecting bundles with stiff probes. It was not clear whether this difference arose from physiological or technical differences in the experiments. The former seemed plausible because the rodent utricle operates down to lower frequencies than do the turtle cochlea and frog saccule. Turtle auditory afferents have best frequencies between about 30 and 700 Hz (Crawford and Fettiplace 1980). The frog saccule differs from mammalian otolith organs in that it is designed to detect relatively high-frequency substrate vibrations (Narins and Lewis 1984); frog saccular afferents have best frequencies between 20 and 300 Hz. Although the upper end of the rodent utricle's frequency range is not established, chinchilla utricular afferents produce robust responses to stimulus frequencies from 2 Hz down to steady state (Goldberg et al. 1990a).
Technical differences in the stimulus method may also have affected the time course of adaptation. Stiff probes apply displacement steps, clamping bundle position, whereas fluid jets apply force steps. Adaptation is known to be accompanied by stiffness changes in the bundle (Howard and Hudspeth 1987). By Hooke's law, a stiffness change during a force step will change bundle displacement; thus fluid-jet stimuli are more complex in terms of bundle displacement. To permit comparisons with published frog and turtle data obtained with stiff probes, we stimulated mouse utricular hair bundles with stiff probes. To eliminate the possibility of technical differences affecting the results obtained from different hair cell organs, we used identical methods to record from frog saccular hair cells. To investigate the differences between fluid-jet and stiff-probe stimulation, we recorded with both methods from individual mouse utricular hair cells.
Experiments on in vitro preparations of hair cells of the frog saccule and turtle cochlea have provided evidence for two Ca2+-dependent processes that affect the decay of transduction current in response to step bundle deflections (Eatock 2000; Holt and Corey 2000; Howard and Hudspeth 1987; Wu et al. 1999). Whether these processes are referred to as adapting or amplifying mechanisms depends on the experimental conditions. In millimolar external Ca2+, the fast and slow components cause decay (adaptation) of the transduction current with time constants of milliseconds or less and of tens of milliseconds, respectively. When Ca2+ bathing the bundle is lowered to endolymph levels (50–100 µM), both components may be seen to act as tuning mechanisms (Choe et al. 1998; Howard and Hudspeth 1988; Martin et al. 2000; Ricci et al. 1998; reviewed in Fettiplace et al. 2001 and Hudspeth et al. 2000). Experimentally this is seen as the transformation of the step response from one that simply decays after a peak to one that undergoes a damped oscillation. It is hypothesized that the fast component reflects channel closure in response to Ca2+ binding to a site on or near the transduction channel (Choe et al. 1998; Crawford et al. 1991; Howard and Hudspeth 1987). The slow component has been modeled as a myosin-driven movement of the transduction channel and associated gating spring along the stereocilium, which tends to restore tension on the gating spring toward resting levels (Assad and Corey 1992; Howard and Hudspeth 1987; Shepherd and Corey 1994). The gating springs contribute a substantial fraction of the total bundle stiffness (Howard and Hudspeth 1988; Ricci et al. 2002; van Netten 1997) and their relaxation during the slow process decreases the total bundle stiffness.
The responses of mouse utricular hair cells to fluid-jet steps (Holt et al. 1997) and the data we present here for a stiff probe with a 1-ms rise time are both consistent with the slow component. We show that a faster stiff probe reveals a fast component in both mouse utricular hair cells and frog saccular hair cells.
In hair cells of the turtle cochlea and frog saccule, the rate of decay of transduction current during a step decreases strongly with increasing step size. In the turtle cochlea, this change has been explained as an increase in the amplitude of the slow kinetic component with increasing positive displacement (Wu et al. 1999). In the frog saccule, this change has been interpreted in terms of the effects of adaptation on the instantaneous and steady-state current–displacement [I(X)] relations. The decay of the transduction current reflects a shift in the hair cell's instantaneous I(X) relation in the direction of the imposed deflection (Corey and Hudspeth 1983; Eatock et al. 1987). Thus adaptation acts to realign the instantaneous operating range with the steady bundle position. In the frog saccule, the steady-state shift of the instantaneous I(X) relation is a constant percentage (about 80%) of the adapting step. As described by Shepherd and Corey (1994), this behavior produces a steady-state operating range that is 5-fold broader than the instantaneous operating range. Here we report that in many mouse utricular hair cells, in contrast, the percentage shift increases with size of the adapting step, with dramatic effects on the steady-state relation.
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METHODS |
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MOUSE UTRICLE. Semi-intact preparations of the mouse utricle were made as described previously (Holt et al. 1997; Rüsch and Eatock 1996a). Procedures involving animals were approved by the animal care committee of Baylor College of Medicine. Briefly, utricles of early postnatal mice [postnatal days (P) 0–10, birth = P0; ICR outbred strain, Charles River Laboratories, Wilmington, MA] were exposed by opening the medial wall of the otic capsule, then bathed for 20 min in standard extracellular solution (below) containing 100 µg/ml protease type XXVII (Sigma, St. Louis, MO). The protease facilitates removal of the otoconia and otolithic membrane overlying the hair bundles. The utricle was then dissected out, mounted in an experimental chamber, and viewed on an upright microscope (Axioskop FS; Zeiss, Oberkochen, Germany) with water-immersion objectives (x40 or x63) with differential interference contrast optics (Fig. 1). All preparations and recording were done at room temperature (22–25°C).
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The extracellular solution for dissection and perfusion contained (in mM): 144 NaCl, 0.7 NaH2PO4, 5.8 KCl, 1.3 CaCl2, 0.9 MgCl2, 5.6 D-glucose, 10 HEPES-NaOH, vitamins and minerals as in Eagle's MEM; pH 7.4, about 320 mmol/kg. The recording pipette contained (in mM): 140 KCl, 0.1 CaCl2, 10 EGTA-KOH, 3.5 MgCl2, 2.5 Na2ATP, 5 HEPES-KOH, 0.1 Li-GTP, 0.1 Na-cAMP; pH 7.4, about 290 mmol/kg. The free Ca2+ concentration is estimated as 710 pM by MaxChelator software (WEBMAXC Standard; http://www.stanford.edu/~cpatton/maxc.html; Bers et al. 1994).
CELL TYPE. Hair cells were classified as type I if they were innervated by a partial or full calyx terminal (Wersäll 1956; see Fig. 1) or if the type I–specific conductance, gK,L, was present (Correia and Lang 1990; Ricci et al. 1996; Rüsch and Eatock 1996a). Before P8, a hair cell in the mouse utricle that does not have gK,L can be either a type II cell or an immature type I cell (Rüsch et al. 1998). In a previous study (Holt et al. 1997) and the present study, such cells showed no systematic variation with age between P0 and P10 in the time course of adaptation or other transduction properties (linear regression of the adaptation time constant 
A as a function of age yielded r2 = 0.07; n = 18; data in Table 1). For simplicity, then, we refer to all hair cells lacking gK,L and calyces (partial or complete) as "type II".
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CELL REGION. Hair cells were also classified as either striolar or extrastriolar. The striola, an arclike strip running approximately through the middle of the sensory epithelium, differs from the extrastriola in many morphological features (Lindeman 1973; Lysakowski and Goldberg 1997; Rüsch et al. 1998). Based on data from the chinchilla utricle (Fernández et al. 1990), we classified hair cells as striolar if they were within 6 cells of the line of hair bundle reversal. Recent data from Zeh et al. (1999), in which regions were classified according to patterns of calretinin staining, suggest that the striola in the mouse utricle is about 7 cells wide, rather than 12. Our "striolar" sample therefore includes hair cells from what Fernández et al. (1990) called the "juxtastriola," a strip about 5 hair cells wide around the striola. We classified hair cells as extrastriolar if they were within 12 hair cells of the edge of the sensory epithelium. This is in reasonable agreement with the calretinin staining study of Zeh et al. (1999).
FROG SACCULE. Some experiments were performed on hair cells in a semi-intact epithelium of the frog saccule. Leopard frogs (Rana pipiens; Kons Direct, Germantown, WI), were deeply anesthetized by chilling, double pithed, and decapitated. The saccules were dissected out and treated with 50 µg/ml protease type XXIV (Sigma) in extracellular solution (below) for 20 min. The otolithic membrane was removed and the preparation mounted as for the mouse utricle. The extracellular solution for dissection and perfusion contained (in mM): 120 NaCl, 2 KCl, 4 CaCl2, 5 CsCl, 3 D-glucose, 5 HEPES; pH 7.25, about 250 mmol/kg. The recording pipette contained (in mM): 120 CsCl, 0.1 CaCl2, 10 EGTA, 2 MgCl2, 2 Na2ATP, 5 HEPES; pH 7.25, about 290 mmol/kg. Again, all procedures were done at room temperature.
Recording
Pipettes were pulled from R6 glass (Garner Glass, Claremont, CA) and coated with sylgard (Dow Corning, Midland, MI). Their resistances in standard solutions were 3–5 M
. Positive pressure was applied to the recording pipette as it was lowered into the epithelium and advanced toward the hair cell of interest; the outflow of pipette solution cleaned the pipette tip and the cell's basolateral membrane. The positive pressure was released just before making contact with the membrane, then suction was applied to form a seal and rupture the membrane, entering whole cell voltage clamp mode. The currents were amplified with an Axopatch 200A or 200B amplifier (Axon Instruments, Union City, CA). Hair cells were voltage clamped at –64 mV, near the mean resting potential for type II and neonatal cells in this preparation (–66 mV; Rüsch et al. 1998). Voltage-clamp protocols and stimulus waveforms were controlled by pClamp 8.0 software (Axon Instruments). Currents were low-pass filtered at a corner frequency fc of 2–10 kHz (8-pole Bessel filter) and digitized at 10–100 kHz (>2 x fc) with a 12-bit acquisition board (Digidata 1200; Axon Instruments) and stored on disk. Data analysis and fitting were done with Origin 6.0 (Microcal Software, Northampton, MA), which uses a Levenberg-Marquardt least-squares fitting algorithm. Results are presented as means ± SE. Comparisons of transduction and adaptation properties across cells were tested for significance with the Student's t-test.
Stimulation
Transduction currents were elicited by hair bundle displacements effected with either a stiff probe or a fluid jet.
STIFF PROBE. Borosilicate pipettes (Sutter Instrument Company, San Rafael, CA) were pulled to a final diameter of 1–2 µm and mounted on a piezoelectric bimorph (Corey and Hudspeth 1980). The stiff probe was brought into contact with the short edge of the hair bundle and used to push or pull the bundle to deliver positive or negative step displacements, respectively (Figs. 1B, 3A). The probe was driven by voltage protocols generated with pClamp 8.0 and the Digidata 1200 and low-pass filtered by an 8-pole Bessel filter (Model 902; Frequency Devices, Haverhill, MA), with fc below the probe's resonant frequency. Probe displacement as a function of applied voltage was calibrated from videotaped images of the displacements evoked by 1-s voltage steps. For each new probe, the waveform of probe movement in response to a voltage step was recorded with a photodiode. According to these recordings, stimulus "creep" (further movement in the direction of the applied step, after the step onset) was <10% of the initial step, as found in other studies (Corey and Hudspeth 1980). For the probes used for comparisons of type I and type II cells and hair cells from different regions, input voltages were usually filtered at fc = 500 Hz, giving a 10–90% rise time of 1 ms. For comparison with the fluid jet stimulus, we slowed the rise time to 2 ms by filtering at 200 Hz. To deliver faster stimuli (rise time 
200 µs), we increased the probe's resonant frequency by making it lighter and filtered the voltage input at 1.5–2.5 kHz.
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FLUID JET. We used a fast pressure-clamp system (McBride and Hamill 1995) to deliver suction or pressure steps to the back of a wide-bore (10-µm) pipette filled with extracellular solution (Holt et al. 1997). The fluid-jet pipette was placed tens of microns from the hair bundle. Piezoelectric valves, driven by the output of the Digidata 1200 board, controlled a mixture of vacuum and air that was supplied to the back of the pipette. The feedback circuit included a strain gauge that measured the pressure at the back of the pipette. The waveform shown for the fluid jet stimulus (Fig. 3B) is the output of the strain gauge, calibrated by measuring steady-state displacement near the top of the bundle from videotaped images of bundle movement during 1-s fluid-jet steps. This method does not reveal dynamic changes in bundle position that may occur as a result of adaptation (Howard and Hudspeth 1987; see Hair bundle model, below, and Fig. 3D).
Stimulus protocols and data analysis
Figure 2 illustrates how we measured properties of transduction and adaptation from the transduction currents evoked by families of step displacements of the hair bundle. Steps were 100, 350, or 400 ms.
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TIME COURSE OF ADAPTATION. By adaptation, we mean the decay of the transduction current during step deflections of the bundle. Decays were fit with single-exponential or double-exponential functions (Eqs. 1 and 2) (Fig. 2A)
 | (1) |
 | (2) |
A or fast and slow are the time constants of each term, and ISS is the current level at steady state. Percent decay of the transducer current was measured at steady state [100 x (peak current – ISS)/(peak current)].
CURRENT–DISPLACEMENT RELATIONS. We generated instantaneous and steady-state current–displacement relations [I(X) relations] from the peak currents and ISS values, respectively, evoked by families of steps. Examples of instantaneous I(X) relations are shown in Fig. 2C. I(X) relations were fit with a second-order Boltzmann function (Eq. 3)
 | (3) |
From the Boltzmann fits of I(X) relations, we took the resting open probability (P0, the percentage of the maximum current at resting bundle position, X = 0) and the operating range [the range of displacements corresponding to growth of the I(X) relation from 10 to 90% of Imax]. We refer to the operating range of the instantaneous I(X) relation as ORinst. For between-cell comparisons of the time constants of decay and percent decay of the transducer current, we fit the responses to X1/2, which is the displacement corresponding to the half-maximal response (Imax/2) (Fig. 2A).
ADAPTIVE SHIFT OF THE INSTANTANEOUS i(x) RELATION. In hair cells of the frog saccule (Assad and Corey 1992; Eatock et al. 1987) and mouse utricle (Holt et al. 1997), adaptation of the transduction current during a step reflects a shift of the instantaneous I(X) relationship along the displacement axis. To measure this shift, we applied families of test steps before and 250 ms after the onset of the adapting step (Fig. 2B). The percent shift is the shift of the I(X) relation expressed as a percentage of the adapting step. Note that this is the same as the "extent of adaptation" used in studies of frog saccular hair cells (Shepherd and Corey 1994) and is strongly correlated with, but not identical to, the percent decay of the transducer current.
In some cases, the steady-state I(X) relation was fit with a stretched version of the instantaneous I(X) relation
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), the stretch required to fit the steady-state I(X) relation is related to the percentage shift, according to the following equation
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Hair bundle model
The motor model of hair cell adaptation (Assad and Corey 1992; Howard and Hudspeth 1987) predicts that the transduction current decay evoked by a force step will be slower than that evoked by a displacement step to the same steady-state displacement. To illustrate this, we used a simple version of the model, consisting of two parallel Hookean springs and a motor element (illustrated in Fig. 3D). One spring represents the stiffness of the stereociliary pivots and the other spring represents the stiffness of the gating springs, hypothetical elastic elements that apply force to the mechanosensitive transduction channels. The adaptation motor is in series with the gating springs. After the onset of a displacement or force step toward the tall edge of the bundle (a positive step), the adaptation motor moves in such a way as to reduce the stretch across the gating springs. If XS(t) is the stereociliary (bundle) displacement at time t and XM(t) is the position of the motor, then the displacement applied to the gating springs at time t is [XS(t) – XM(t)]. The forces sensed by the springs are
 | (6) |
 | (7) |
 | (8) |
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The movement of the adaptation motor is modeled as a single exponential process that acts to restore a target force, FG
= KG(XS – XM), across the gating spring
 | (9) |
and XM are the target positions of the bundle and the motor and XM is the intrinsic time constant of the motor. After each 
t, XS is updated as XS(t + t) = (FT + KGXM)/(KS + KG).
According to the model, the time constant of the operating range shift evoked by a displacement step is the intrinsic time constant of the motor (Assad and Corey 1992). For small steps that do not saturate the instantaneous operating range, the time constant of the operating range shift and the time constant of transduction current decay are similar. Therefore for our simulation we assigned to XM the average time constant of transduction current decay for stiff-probe bundle displacements evoking half-maximal responses (30 ms; Table 1). This value is similar to the time constant of the operating range shift measured for stiff-probe displacements of mouse utricular hair bundles (25 ms; Holt et al. 1997). We used t = 1 ms or 0.1 ms.
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RESULTS |
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We performed a series of experiments to determine whether transduction and adaptation properties map onto location or cell type in the utricular sensory epithelium. The hair bundles were deflected with a stiff glass probe with a 10–90% step rise time of 1 ms.
We fit the time course of adaptation to steps at half-maximal displacements (X1/2) with a single-exponential function (Eq. 1; Fig. 2A). The fit provided the time constant of adaptation A and the percent decay at steady state. There were no systematic differences across cell types and cell locations (Table 1). The mean A was 30 ± 2 ms (range 9–75 ms; normal distribution) and the mean percent decay at steady state was 76 ± 3%. In the frequency domain, a monoexponential adaptation process acts like a high-pass filter with fc(Hz) = 1/(2
A) (A in s). For our sample, fc had a mean value of 5 Hz and ranged from 2 to 18 Hz. If percent decay is similar in vivo to its average value here, then about 25% of the peak response would be available to report steady head position and head movements below 0.1 Hz.
Instantaneous I(X) relations were generated and fit as illustrated in Fig. 2 and described in METHODS. Again, no systematic differences were seen in the parameters obtained from fits of the instantaneous I(X) relations: Imax, P0, or ORinst.
The large variability in ORinst (749 ± 59 nm; Table 1) probably reflects variation both in bundle height and in the position of the probe along the rake of the bundle (Fig. 1F). Hair bundles in early postnatal mouse utricles range in height from 8 to 15 µm (Géléoc et al. 1997; Holt et al. 1997). The lower the probe, the larger the angular bundle deflection for a given horizontal probe displacement and the smaller the apparent operating range. Operating ranges 2 standard errors away from the mean can be explained by differences of just 1–2 µm in the probe height along the rake of the bundle, which is within the expected variability of our probe placement.
We applied test protocols as illustrated in Fig. 2B to measure the percent shift of the instantaneous I(X) relation at 250 ms (approximately steady state) for step sizes that ranged from 0.4 to 1.4 times the initial ORinst. Percent shift also did not vary systematically with either cell type or cell location.
There were also no significant differences in any property when results were compared for a particular cell type across regions, although the sample sizes were small (type II cells: 7 extrastriolar, 8 striolar, 3 unknown; type I cells: 5 extrastriolar, 11 striolar, 2 unknown).
Adaptation is faster with a stiff probe than with a fluid jet
For type II cells, the mean A in the present study is half that obtained previously with a fluid-jet stimulus (61 ± 8 ms; 28 cells; Holt et al. 1999). The fluid jet provides a force step rather than a displacement step, and has a slower rise time: 2–3 ms versus 1 ms for the experiments summarized in Table 1. Wu et al. (1999) showed that A in turtle cochlear hair cells increases with the rise time of deflections effected by a stiff probe. To investigate the relative importance of stimulus rise time and stimulus type (displacement vs. force step) in setting A, we compared the responses of individual cells to a fluid jet and to a stiff probe with two rise times. The input to the probe was filtered so that its rise time would be either 1 or 2 ms, closer to the rise time of the fluid jet (mean rise time 2.82 ± 0.03 ms, n = 9 experiments).
As shown for one cell in Fig. 3A, slowing the rise time of the displacement step to 2 ms had no effect on adaptation time course. Mean A values were 32 ± 5 and 34 ± 6 ms for the 1- and 2-ms rise times, respectively (n = 9 cells; P = 0.75, paired t-test). When the same hair bundles were deflected with the fluid jet, however, the mean A was significantly slower and had a larger variance, 90 ± 23 ms (P = 0.02 for a pairwise comparison with the data from the 2-ms probe, Fig. 3C). The percent decay of the transducer current was slightly smaller with the fluid jet (70 ± 5%) than with the 2-ms probe stimulus (82 ± 4%; P = 0.02). During individual experiments, A was similar for stiff-probe deflections given before and after the fluid jet stimulus (Fig. 3B), showing that the slowness of the decay in response to the fluid jet did not reflect bundle damage.
Thus, in this comparison, the type of stimulus, rather than its rise time, affected the measured properties of adaptation (shortening the rise time below 1 ms affects adaptation time course, below). During a fluid jet step, the bundle position depends on bundle stiffness, which may vary dynamically as a result of transduction and adaptation processes (Hudspeth et al. 2000). Note that any effects of such stiffness changes on bundle position are not shown in our stimulus traces, which represent the pressure output of the fluid jet calibrated by the steady-state bundle deflection recorded on videotape.
We made a simple mechanical model of the bundle similar to that of Assad and Corey (1992), with two parallel springs corresponding to the passive bundle springs and the gating springs and an adaptation motor in series with the gating spring (see METHODS). For a displacement step, the bundle displacement XS is constant and the force across the gating springs FG changes exponentially with the time constant of motor movement XM (Fig. 3D). Thus for a step that is small relative to the instantaneous I(X) relation, the open probability of the transduction channels and the transduction current decay with the same time constant XM. For a force step, the total force FT is constant but the motor movement reduces FG, causing a proportional increase in the force across the stereociliary pivots FS (Eq. 8). As a consequence, XS = FS/KS increases with time (i.e., the bundle creeps forward) (Fig. 3D). A change in XS changes the force across the gating spring (the input to the motor), so that the motor continues to move, slowing the rate of transduction current decay.
With this model, the ratio of the time courses of the motor movement in the force step and displacement step conditions equals the ratio of the summed stiffnesses over the stereociliary stiffness. Thus for approximately equal KG and KS, as found by Howard and Hudspeth (1988) and Ricci et al. (2002), the time course of the relaxation during a force step is twice that during a displacement step. The 2-fold difference between our mean time constant for all cells and that obtained in the fluid jet study by Holt et al. (1997) is consistent with the gating springs contributing about half of the bundle stiffness. In the sample for which we have both fluid jet and stiff probe data, linear regression of stiff-probe A against fluid-jet A yields a slope of 0.3 (Fig. 3C). This slope and the ratio of the mean A values (34/90) are consistent with the gating springs contributing almost two-thirds of the total bundle stiffness. In the simulation shown in Fig. 3D, we set the time constant of the adaptation motor equal to the mean time constant of transduction current decay (30 ms; Table 1). To triple the time constant of motor movement during a force step relative to a displacement step, we set KG = 2KS.
Another difference between the fluid-jet data and the stiffprobe data is the rounded onset of the fluid-jet response (Fig. 3A; also see examples in Holt et al. 1997; Fig. 2). In Géléoc et al. (1997), a similar rounded onset was seen in both the transduction currents and the hair bundle motion evoked by fluid-jet steps. Such rounding may reflect low-pass filtering of the force stimulus by passive bundle mechanics, such that bundle deflection takes longer than the fluid velocity step illustrated in the stimulus trace. In Géléoc et al. (1997), rounding of the onset response was much less evident for the stiffer bundles of mouse outer hair cells, consistent with a faster mechanical response time.
The 9 cells in this study consisted of 5 type I cells and 4 type II cells; 7 were from the striolar region. In this small sample, as in the total data set (Table 1), adaptation rates were similar for type I and type II cells. In contrast, in the fluid-jet study of Holt et al. (1998), only 6 of 14 type I cells showed any response decay during 100- to 300-ms steps, and for these 6 cells, the mean A was very large (230 ± 39 ms). It is not clear why the two studies differ in this regard. The average postnatal ages of the type I cells were not significantly different [4.9 ± 0.6 days, n = 18, in the present study vs. 5.9 ± 0.6 days, n = 14 in Holt et al. (1998); P = 0.3]; furthermore, A did not change systematically from P0 to P10 (r2 = 0.09 for type I cells in the present study). Although it is possible that the two studies sampled from different epithelial regions (region was not specified in the earlier study), there is no indication in our data of strong regional differences. Type I cells from the striola and extrastriola adapted with mean A values of 26 ± 4 ms (n = 10) and 32 ± 8 ms (n = 6), respectively (P > 0.4). A third possibility is that distinct subsets of type I cells (e.g., with different bundle morphologies) were selected in the two studies.
A faster step revealed two components of transduction current decay
In hair cells, the fastest time constants of adaptation (<1 ms) have been measured in the turtle cochlea with a stiff probe with a rise time of about 100 µs (Ricci and Fettiplace 1997). To determine whether our measured A values were slowed by stimulus rise times in the 1- to 2-ms range, we built a stiff probe with a rise time of 200 µs. The decay of the transduction current was faster for the faster stiff probe. If we fit the response at X1/2 with a single-exponential function, the mean A was significantly shorter: 18 ± 3 ms (n = 44) versus 30 ± 2 ms (n = 36) for the 1-ms probe (Table 1) (data from different sets of experiments). This would not be expected for a single exponential process and suggests that the faster probe revealed an additional fast component. Moreover, at X1/2 the decay was better fit by a double-exponential function than by a single-exponential function in 90% (41/44) of cells, as judged by eye and by 
2 value (Fig. 4A). Although the increased number of free parameters would be expected to produce better fits, our data for small-to-intermediate stimuli showed a clear early fast component that is not accommodated by single-exponential fits. At X1/2, the average fast and slow time constants from the double-exponential fits, fast and slow, were 5.2 ± 0.7 ms (range 0.8–22.8 ms) and 45.6 ± 4.5 ms (range 6.3–171.2 ms). The adaptation time course did not vary systematically with transduction current amplitude. Linear regressions of A versus Imax had r2 values of 0.028 (fast probe) and 0.023 (1-ms probe).
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Because the faster probe completed the step faster than the time constant of the fast component, the average Imax value obtained with the fast probe was significantly greater than that obtained with the 1-ms probe (Table 1): 199 ± 10 versus 155 ± 16 pA, P = 0.02. Assuming a reversal potential of +3 mV for the transduction channels (Kros et al. 1992), the mean Imax for the 1-ms probe corresponds to an average maximum conductance (gmax) of 3.1 ± 0.3 nS, similar to that obtained by Géléoc et al. (1997) in their study of hair cells in cultured neonatal mouse saccules and utricles. For the single-channel conductance that Géléoc et al. (1997) calculated for mouse cochlear hair cells, 112 pS, the average gmax corresponds to 28 transduction channels per bundle. The maximum transduction current we recorded was 450 pA, or 6.7 nS and 60 channels. For hair bundles of neonatal mouse saccules and utricles, Géléoc et al. (1997) found an average of 38 ± 2 stereocilia with 31 ± 2 potential tip links (n = 15 bundles). Thus our average and largest peak currents correspond to 0.9 and 1.9 transduction channels per tip link, respectively.
We also examined the transduction currents evoked in frog saccular hair cells by the fast stiff probe for evidence of two decay components. Although a fast component has been described in responses to deflections imposed by flexible fibers (Benser et al. 1996; Howard and Hudspeth 1987), its time course has not been characterized for a displacement step. Again, at X1/2, double-exponential fits of transduction current decays were better than single-exponential fits in 4 of the 5 cells tested (Fig. 4B). At X1/2, the mean time constant from the single-exponential fit A was 3.0 ± 0.8 ms, and the mean fast and slow values were 2.3 ± 1.0 and 18.1 ± 3.9 ms, respectively. The slow component has a similar time course to the adaptation previously reported for the responses of frog saccular hair cells to bundle displacement (20–30 ms; Shepherd and Corey 1994). The use of a faster probe in our experiments, revealed an additional fast component.
As in the turtle cochlea (Wu et al. 1999), the fast component was most prominent for small displacements in both frog and mouse hair cells. This tendency can be seen in Fig. 4A, where the largest step has a negligible fast component. Figure 5 shows the effects of bundle displacement on the time constants (A), the size of the slow component as a fraction of the total decay (B), and the percent decay (C). Note that the displacement axis is 3-fold broader for the mouse data, reflecting the relative sizes of the operating ranges expressed in terms of bundle displacements partway up the rake of the bundle (Fig. 1). In both cells, the fractional amplitude of the slow component grew from 0.1 to 0.2 for the smallest step to 1.0 for the largest steps (Fig. 5B).
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Percent shift of the operating range increases with adapting step size in mouse utricular hair cells
With increasing displacement, fast decreased, slow increased, and the percent decay at steady state decreased markedly in frog saccular hair cells (Fig. 5, A and C). Similar changes in slow and percent decay with step size occur in turtle cochlear hair cells (Wu et al. 1999). This can be understood in terms of the slow adaptation process. In frog hair cells, the adaptive shift of the instantaneous I(X) relation (Fig. 2C) is a constant 80% of the adapting step (Shepherd and Corey 1994). As shown schematically in Fig. 6A, as adapting step size increases (arrows), the 80% shifted operating range lies increasingly negative to the imposed bundle position. As a result, the percent decay of the transduction current decreases with adapting step size (Figs. 5C, 7A). For very large steps (not shown), the 80% shift is not large enough to bring the ORinst into register with the new bundle position, and therefore there is no decay in the transduction current.
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Figure 6A shows schematically how a constant percent shift produces a steady-state I(X) relation (gray curve) that is a stretched version of the instantaneous I(X) relation (Shepherd and Corey 1994). We confirmed this behavior in 5 frog saccular hair cells (Fig. 7A). The mean ORinst was 280 ± 32 nm. To fit the steady-state I(X) relations, the instantaneous relations were stretched by s = 5.6 ± 1.0 (Eq. 4). This corresponds to a percentage shift of 82 ± 2% (Eq. 5), in agreement with the 80% reported by Shepherd and Corey (1994).
In mouse utricular hair cells, the average percent shift of the instantaneous I(X) relation was 86% (Table 1). If the mouse cells behaved like frog cells, then the steady-state I(X) relations would be fit by stretching the instantaneous I(X) relation about 7-fold (Eq. 5). Instead, the mean steady-state operating range was not significantly larger than ORinst: 1181 ± 224 versus 762 ± 49 nm (n = 37; P = 0.06). This reflects the fact that fewer than half of the mouse steady-state I(X) relations could be fit by stretching the instantaneous I(X) relations. Two examples that could be fit are shown in Fig. 7B. In many of these cases, the steady-state currents were so small that very large stretch factors (>20) were required (Fig. 7B, right panel). In contrast, in 26/37 (70%) of the mouse cells, the steady-state I(X) relations saturated at current levels far below the Imax values of the instantaneous I(X) relations (Fig. 7C). Correspondingly, the percent decay did not decrease with increasing displacement; in some cases, it increased with displacement (see the mouse hair cell data in Fig. 5C).
Because frog and mouse hair cells differ in how percent decay changes with adapting step size, we investigated whether percent decay in mouse cells follows directly from percent shift of the instantaneous operating range (ORinst) as it does in frog cells. Figure 8B shows that this is the case. Figure 8B also shows, however, that the percent shift increased with step size (4% per ORinst, r2 = 0.51; Fig. 8, B and C). This is in contrast to the frog data, where the percent shift was constant (80%) over a large range of step sizes (Shepherd and Corey 1994). [For mouse data obtained with the slower probe, which covered a smaller range of step sizes (0.4–1.4 x ORinst; Table 1), the percent shift also tended to increase with step size: 12% per ORinst, r2 = 0.19.] Figure 6B shows schematically how a percent shift that increases with displacement affects the steady-state operating range. This explains why steady-state I(X) relations of mouse cells were not fit by stretching the instantaneous I(X) relations (Fig. 7C) and why the percent decay did not decrease with step size (Fig. 5C): the ORinst shifted to align with the new bundle position even for very large adapting steps.
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For very large adapting steps, small reductions in Imax may also contribute to compression of the steady-state I(X) relation. For 5 cells in which instantaneous I(X) relations were measured in the presence of multiple adapting steps, the mean instantaneous Imax for the largest adapting steps [mean size = (3.8 ± 0.7) x ORinst] was 90.58 ± 0.01% of the initial (preadapted) instantaneous Imax. In Fig. 8B, there was a 12% decrease in Imax for the largest (2.7-µm) step. In contrast, there was no compression for adapting steps the size of the instantaneous operating range [mean (1.0 ± 0.2) x ORinst]; for these, the mean instantaneous Imax was 99 ± 1% of the preadapted instantaneous Imax.
In addition, for very large adapting steps, reductions in the slope of the instantaneous I(X) relation contribute to compression of the steady-state I(X) relation. For steps over twice the initial ORinst, ORinst increased by 28 ± 12% (range: 5 to 77%). For example, in Fig. 8B, the instantaneous I(X) relations obtained initially and after adaptation to the largest step had ORinst values of 0.99 and 1.75 µm, respectively. The broader ORinst reflects a more gradual positive saturation and more current at displacements negative to the adapting displacement. Similar shape changes were seen in the ORinst of an isolated frog saccular hair cell when its bundle was subjected to a large adapting step by a stiff probe (see Fig. 11C in Assad and Corey 1992). Large adapting steps delivered by fluid jet also caused broadening and compression of ORinst in a previous study of mouse utricular hair cells (Holt et al. 1997). Thus large displacements may recruit distinct processes that affect transduction.
Figure 9 compares the instantaneous and steady-state operating ranges of a mouse utricular hair cell and a frog saccular hair cell. What stands out is the high instantaneous sensitivity and small ORinst of the frog saccular bundle. In vivo, the stimulus is likely to be applied near the tip of the bundle, so that the operating range as we measure it is relevant to thinking about the normal input to the hair cells. The high instantaneous sensitivity of the frog saccular hair cells befits their role in detecting minuscule, high-frequency substrate vibrations (Narins and Lewis 1984). The utricular afferents of mammals are reported to be insensitive to vibrations (Fernández and Goldberg 1976). The difference in instantaneous sensitivity between the frog and mouse hair cells may reflect differences in bundle geometry more than intrinsic differences in the gating springs or channel sensitivity (Géléoc et al. 1997; Holt et al. 1997). For a given displacement X at a height above the base of the bundle h, the extension of tip links is approximated by X
, where = (interstereociliary distance)/h. For neonatal mouse utricular hair bundles, has been estimated as 0.047 (Holt et al. 1997), just one-third its average value in frog saccular hair cells (0.14; Jacobs and Hudspeth 1990). This difference can therefore account for the 2.9-fold difference in our mean ORinst values for mouse utricular and frog saccular hair cells: 749 ± 59 nm (n = 31; Table 1) and 280 ± 32 nm (n = 5). To convert to angular deflections, we assume that the probe was halfway up the bundle and use average bundle heights of 6.7 µm (frog saccule; Jacobs and Hudspeth 1990) and 13.2 µm (mouse utricle; Holt et al. 1997), yielding operating ranges of 4.8 and 6.5° angular deflection, respectively.
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Our estimate for mouse utricular bundles is more than 3 times the estimate by Géléoc et al. (1997) for mouse utricular and saccular bundles stimulated with fluid jets (2.0 ± 0.6°, n = 5). The mean bundle height in their sample (9.3 µm) is shorter than the value we used (13.2 µm), possibly because they included saccular bundles in their study. Our estimates will err on the large side if our probe was positioned more than halfway up the bundle. The mean ORinst that we obtained with the fluid jet (1996 ± 436 nm, n = 8) was about twice that obtained with the stiff probe (1010 ± 173 nm, n = 9). Because we measured fluid-jet displacement by focusing on the bundle tip, this comparison suggests that the stiff probe was about halfway up the bundle. However, the displacements used to measure ORinst for the fluid jet were actually steady-state displacements (see METHODS), which may have included significant forward creep relative to the onset displacement as a result of adaptation (see Fig. 3D). Correcting for such a creep would place the probe closer to the bundle tip and reduce the instantaneous operating range by as much as one-third.
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DISCUSSION |
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Adaptation is sensitive to stereociliary Ca2+ levels and presumably to temperature. In our experiments, the bundles were bathed in 1.3 mM Ca2+ and the pipette solution contained 10 mM EGTA. Endolymphatic Ca2+ is on the order of 10–100 µM (Bosher and Warren 1978; Corey and Hudspeth 1983; Crawford et al. 1991) and stereociliary Ca2+ buffering may be equivalent to 1 mM BAPTA or less (Ricci et al. 1998; Roberts 1993). The low external Ca2+ in vivo might be expected to substantially slow the Ca2+-dependent adaptation processes. For low-frequency turtle cochlear hair cells, adaptation rates in in vivo-like conditions (70 µM apical Ca2+ and endogenous Ca2+ buffering) were one-third those obtained in conditions similar to ours (1 mM apical Ca2+ and 10 mM EGTA in the pipette) (Ricci et al. 1998). In mouse utricular hair cells, however, these effects may be offset in vivo by the effects of increased temperature on adaptation rate.
The slow adaptation that we have measured is roughly consistent with the frequency dependence of responses from chinchilla utricular afferents with irregular and intermediate spontaneous discharge (Goldberg et al. 1990a), which tend to innervate the striolar and juxtastriolar zones of the macula (Goldberg et al. 1990b). For such afferents, the response gain rises from its steady-state value to a value 2- to 10-fold higher at 2 Hz, with no sign of leveling off. Both the steady-state response and the rise in gain with frequency 2 Hz are expected from our hair cell data. The steady-state transduction current for the mouse utricular cells was about 25% of the peak current (Table 1). Such currents can strongly depolarize type II hair cells, even after activation of their outwardly rectifying K+ conductances (Rüsch and Eatock 1996b; Fig. 3 in Eatock 2000; Vollrath and Eatock, unpublished results). Therefore the fully adapted current is adequate to carry low-frequency signals.
The response gains of afferents that innervate the extrastriola are constant with head movement frequency 2 Hz (Goldberg et al. 1990b). We therefore hypothesized that a population of extrastriolar hair cells would not adapt to bundle deflections. Instead, we found that virtually all hair cells adapted, with no systematic differences in transduction and adaptation properties between hair cells of different type or location. There are at least two kinds of explanation.
First, the regional variation in afferent data may arise at sites other than the transduction channel, including bundle mechanics and voltage-gated conductances. Bundle morphology varies with hair cell type and location in mammalian vestibular epithelia (Bagger-Sjöbäck and Takumida 1988; Denman-Johnson and Forge 1999; Lim 1976; Rüsch et al. 1998), and the otoconia and otolithic gel of the striola and extrastriola differ (Lindeman 1973; Xue and Peterson 2002). The mechanical consequences of these regional variations would not be revealed in experiments in which bundles are deflected by rigid probes. There is also regional variation in the outwardly rectifying K+ currents that repolarize the type II hair cell's membrane after a depolarizing current step: inactivation kinetics are faster in the extrastriola than in the striola (Holt et al. 1999; Vollrath and Eatock, unpublished observations). Inactivation of outward K+ current may offset adaptation of the transduction current, such that the receptor potential adapts less than the transduction current.
The second kind of explanation is that regional variation in mechanotransduction does occur in vivo, but that the conditions of our experiments did not reveal it. Possible factors include:
1. The immaturity of our preparation. The first week or so after birth is a time of dramatic changes in bundle morphology (Denman-Johnson and Forge 1999), Ca2+-binding proteins (Dechesne et al. 1993, 1994) and voltage-gated conductances of rodent vestibular hair cells (Rüsch et al. 1998). Although we did not record from hair cells with frankly immature bundles, it remains possible that the mechanosensitive apparatus had not fully differentiated in our preparation.
2. Whole cell recording conditions. The ruptured-patch recording configuration may eliminate between-cell variations that arise through different concentrations or types of intracellular Ca2+ buffers. Ca2+ concentration inside the stereocilia sets the rate of adaptation and other properties such as the slope of the I(X) relation and the resting open probability of the transduction channel (Assad et al. 1989; Crawford et al. 1991; Eatock et al. 1987; Ricci et al. 1998). In vestibular epithelia, Ca2+ binding proteins vary with hair cell type, location, and stage of development (Baird et al. 1997; Dechesne et al. 1994). At present the properties of Ca2+ buffers in mouse vestibular hair cells are not known. Previous experiments on mouse vestibular hair cells used lower EGTA concentrations in the internal solution, for estimated free Ca2+ concentrations of 170 nM (Holt et al. 1997, 2002) and 10 nM (Géléoc et al. 1997), versus 710 pM in our experments and 130 pM in the experiments on frog saccular hair cells (Shepherd and Corey 1994). Evidence from turtle cochlear hair cells (Ricci et al. 1998) suggests that the fast component is relatively impervious to the pipette's Ca2+ buffer, possibly because it is mediated by Ca2+ binding on or close to the channel. The adaptation time constants of turtle cochlear hair cells, which appear to principally reflect the fast component, are similar for 1 and 10 mM EGTA, 0.1 mM BAPTA, and the endogenous buffer as measured in perforated-patch whole cell recordings. The slow component, however, may be mediated by Ca2+ binding at a more distant site from the channel (e.g., on calmodulin associated with myosin) and therefore may be more sensitive to changes in internal Ca2+ buffers.
3. The stimulation method. The otolithic gel layer that normally delivers the stimulus to hair bundles is likely to be less stiff than the probes used in our experiments (Benser et al. 1993). Thus the transduction current decay may be slowed by micromechanical rearrangements within the bundle (reflecting gating, Ca2+ reclosure, and myosin-dependent movements of the gating springs; see Hudspeth et al. 2000 for a review). As discussed next, such an effect is seen on switching from a stiff probe to a fluid jet.
Fluid jet versus stiff probe
Use of the fluid jet increased A about 3-fold over its value with the stiff probe in the same cell (Fig. 3C). The critical difference is not rise time, and therefore is likely to be that the fluid jet delivers a force step rather than a displacement step. Howard and Hudspeth (1987) showed that slow adaptation to a positive bundle deflection is accompanied by a decrease in bundle stiffness, and argued that the loss of stiffness reflects the relaxation of force across the gating springs during adaptation. When the bundle is coupled to a relatively flexible glass fiber, which is then stepped to a new position, the bundle first jumps forward, reflecting the instantaneous bundle stiffness, then "creeps" further forward with the same time course as slow adaptation reduces the tension on the gating springs. A similar result may be expected in the case of the fluid jet, and indeed, such forward creep is evident in recordings by Géléoc et al. (1997) of mouse vestibular bundle displacement during fluid-jet steps (see their Fig. 2). The corresponding transduction currents did not decay, but the lack of creep in the transduction current indicates that some adaptation occurred. Moreover, the 50-ms steps may have been too short to clearly reveal slow adaptation, the only type that we saw with fluid-jet stimuli. This is illustrated in our fluid-jet responses of Fig. 3: although decay of the transduction current is clear when 320 ms of the step response is shown (Fig. 3A), it is not at all obvious over the first 50 ms (Fig. 3B).
In our cells, the use of a force step rather than a displacement step tripled the mean time course of transduction current decay. For a simple two-spring model of the bundle, this result is consistent with gating spring stiffness being two-thirds of the total bundle stiffness. The one cell in our sample for which the fluid-jet A did not exceed the stiff-probe A had a relatively fast A (Fig. 3C). It is possible that in this one case the fast adaptation component predominated, so that there was little myosin-mediated creep.
Two components of transduction current decay
In most mouse utricular hair cells, the fast probe revealed two kinetic components of decay in response to step displacements, which may correspond to the fast and slow processes that have been identified in other hair cells. The slow component has the same time course as a component that was recently shown to be mediated by myosin-1c (Holt et al. 2002). The faster component in mouse utricular cells resembles the fast adaptation in the turtle cochlea and the "twitch" of the frog saccular bundles in two ways: it occurs on a similar time scale and is most prominent for small displacements. In turtle, this process does not depend on myosin motors (Wu et al. 1999) and is postulated to reflect Ca2+-mediated reclosure of transduction channels (Crawford et al. 1989; Fettiplace et al. 2001). Ricci et al. (2002) found evidence that the relative importance of the two components is influenced by the steady position of the turtle bundle. Depolarization evokes bundle movements by changing intracellular Ca2+. At the resting bundle position, depolarization evoked forward movements, reflecting the fast Ca2+ feedback process. In the presence of a steady bias of the bundle toward the kinocilium, this movement reversed and slowed, consistent with the slow Ca2+ feedback process.
In frog, it has been proposed that the twitch is mediated either by Ca2+-mediated channel reclosure (Choe et al. 1998; Howard and Hudspeth 1987) or by an interaction between channel gating and the same myosin motors that are believed to mediate slow adaptation (Martin et al. 2000). The latter possibility was ruled out by the results of Holt et al. (2002), who blocked myosin-1c in mouse utricular hair cells. This eliminated slow adaptation but revealed a fast component in a subset of cells, with the same time constant as the fast component that we have measured. Thus mouse utricular hair cells have a fast component that is independent of the slow adaptation motor.
In turtle cochlea and frog saccule, one or both processes tune the transduction current to the acoustic and vibrational best frequencies, respectively, of the hair cells (Fettiplace et al. 2001; Hudspeth et al. 2000). With intracellular and apical Ca2+ at in vivo levels, both fast and slow components can participate in resonances (Benser et al. 1996; Martin et al. 2000; Ricci et al. 1998, 2000). The fast and slow values that we measured in frog saccular hair cells correspond to low-pass corner frequencies of about 80 and 8 Hz, respectively, within the range of best frequencies of frog saccular afferents (Narins and Lewis 1984). With similar methods, we measured fast and slow values in mouse utricular hair cells corresponding to corner frequencies of about 30 and 3.5 Hz. Although in vivo conditions may change these time courses, it is not clear in which direction (see DISCUSSION of temperature and Ca2+ effects, above).
The slow component as measured is clearly in the frequency range of head movements (Wilson and Melvill Jones 1979), whereas the fast component is above the frequency range traditionally associated with the vestibular system. There is, however, energy at frequencies up to 20 Hz in human angular head movements during natural locomotion (Grossman et al. 1988). Recent work on otolith-driven and canal-driven reflexes in monkeys (Angelaki 1998; Huterer and Cullen 2002; Minor et al. 1999) and the responses of chinchilla canal afferents (Hullar and Minor 1999) also has revealed robust vestibular afferent signals for stimuli up to 25 Hz. A resonance in the hair cell transduction process at some tens of Hertz may serve to amplify stimuli that are low-pass filtered by the inertia of the head.
Extent of adaptation as a function of step size
The resting tension on the mechanosensitive channel, and therefore open probability, has been modeled as a Ca2+-regulated balance between slipping and climbing of a transduction complex (gating spring, channel, and adaptation motor) relative to the actin core of the stereocilium (Assad and Corey 1992; Howard and Hudspeth 1987). This motor model explains the shift of the instantaneous operating range in the direction of the applied step. To explain why the shift in frog saccular hair cells is about 80% of the applied step rather than 100%, Shepherd and Corey (1994) modified the model by adding a linear extent spring in parallel with the adaptation motor. Because the shift is a constant percentage of the adapting step in the frog cells, the stiffness of the extent spring was assumed constant for adapting steps of different size.
In most mouse utricular hair cells, in contrast, the percent shift of the instantaneous I(X) relation increased with large steps (Fig. 8C). As a result, mouse utricular hair cells can report novel stimuli over a very broad range of background stimuli (Fig. 6B). This result is accommodated by modifying the Shepherd and Corey (1994) model such that the stiffness of the extent spring decreases as steps get larger. Such nonlinear behavior is seen in titin, the giant elastic protein that dominates myocardial passive stiffness (for review, see Granzier and Labeit 2002). Another possible mechanism is tilting of the cuticular plate, a structure just below the apical surface of the hair cell into which the stereocilia insert. Each stereocilium is anchored in the cuticular plate by a subset of its actin filaments (the stereociliary "rootlet"). The cuticular plate contains filamentous actin, at cross angles to the rootlets (DeRosier and Tilney 1989), and other proteins, including myosins (Dumont et al. 2002; Hasson et al. 1997). Transduction stimuli lead to increases in Ca2+ at the base of the bundle (Ohmori 1988), which might interact with cuticular plate proteins to change the attitude or stiffness of the hair bundle.
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DISCLOSURES |
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Present address of M. A. Vollrath: Department of Neurobiology, Harvard Medical School, 220 Longwood Ave., Boston, MA 02115 (E-mail: mvollrath{at}hms.harvard.edu).
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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Address for reprint requests and other correspondence: R. A. Eatock, Department of Otolaryngology, Rm. NA-511, Baylor College of Medicine, One Baylor Plaza, Houston, TX 77030 (E-mail: eatock{at}bcm.tmc.edu).
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ABSTRACT
INTRODUCTION
) and during (
) adapting step, and fit with 2nd-order Boltzmann function (Eq. 3; solid curves). Instantaneous I(X) relation shifted by 89% of the 400-nm adapting step (arrow). P0 = 0.13; Imax = 405 pA; operating range, ORinst = 568 nm.
1 ms (Wu et al. 1999
) and steady-state (
), however, differs in shape from relations for smaller adapting steps and has a 12% smaller Imax and 77% broader ORinst. C: percent shift of instantaneous I(X) relation, normalized to ORinst, for adapting steps of different amplitudes, in 5 mouse vestibular hair cells (4 utricular cells plus crista cell from A, 
). On average, percent shift increased with step size by 4% per ORinst (from linear regression, thick gray line; r2 = 0.51).