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Previous Article | Next Article
Volume 17, Number 6, Issue of March 15, 1997 pp. 2212-2226
Copyright ©1997 Society for NeuroscienceAcetylcholine, Outer Hair Cell Electromotility, and the Cochlear Amplifier
Peter Dallos1, David Z. Z. He1, Xi Lin1, István Sziklai2, Samir Mehta1, and Burt N. Evans1 1 Auditory Physiology Laboratory (The Hugh Knowles Center), Departments of Neurobiology and Physiology and Communication Sciences and Disorders, The Institute for Neuroscience, Northwestern University, Evanston, Illinois 60208, and 2 Department of Otolaryngology, Semmelweis University, Budapest, Hungary, H-1083
ABSTRACT
ABSTRACT
The dominant efferent innervation of the cochlea terminates on outer hair cells (OHCs), with acetylcholine (ACh) being its principal neurotransmitter. OHCs respond with a somatic shape change to alterations in their membrane potential, and this electromotile response is believed to provide mechanical feedback to the basilar membrane. We examine the effects of ACh on electromotile responses in isolated OHCs and attempt to deduce the mechanism of ACh action. Axial electromotile amplitude and cell compliance increase in the presence of the ligand. This response occurs with a significantly greater latency than membrane current and potential changes attributable to ACh and is contemporaneous with Ca2+ release from intracellular stores. It is likely that increased axial compliance largely accounts for the increase in motility. The mechanical responses are probably related to a recently demonstrated slow efferent effect. The implications of the present findings related to commonly assumed efferent behavior in vivo are considered.
Key words: cochlea; efferent; acetylcholine; outer hair cell; electromotility; cell stiffness; calcium; effects of ACh on outer hair cell; cochlear amplifier; microchamber technique; patch-clamp technique; dose-response curves
INTRODUCTION
Its first examination showed inhibitory effects during electrical stimulation of the efferent nerve bundle (Galambos, 1956
; Wiederhold and Kiang, 1970
The largest effect is obtained with electrical stimulation of medial olivocochlear fibers, which provide the efferent innervation of cochlear outer hair cells (OHCs). Whether measured in the compound response of the afferent nerve trunk (Galambos, 1956
Acetylcholine (ACh) is the principal efferent neurotransmitter in the cochlea (for review, see Eybalin, 1993
9) of the nicotinic AChR family has been cloned recently (Elgoyhen et al., 1994
Because ACh binds to receptors at the synaptic pole of the cell, the response is a rapid influx of Ca2+ through nonspecific cation channels opened by the ligand. This results in the opening of calcium-dependent potassium channels, yielding an increase in the input conductance of the cell and the efflux of K+, which hyperpolarizes the cell by a few millivolts. The currents are activated rapidly, and the potential change reaches a peak in <100 msec (Housley and Ashmore, 1991
Electrical stimulation of the olivocochlear bundle affects only the medial efferents, and thus the effects are on OHCs (Guinan, 1996
OHC electromotility is a membrane potential-dependent (Santos-Sacchi and Dilger, 1988
L-V) of the OHC is nonlinear (Evans et al., 1989
Interestingly, ACh invariably produces increased gain and magnitude of the motile response in isolated OHCs (Sziklai and Dallos, 1993
OHC electromotility has been studied with either the whole-cell patch technique (Hamill et al., 1981
Care and use of animals have been approved by the Northwestern University Institutional Review Board and by the National Institutes of Health.
Some of these results have been published previously (Dallos et al., 1996).
MATERIALS AND METHODS
Cell isolation. OHCs were obtained from the cochleae of young albino guinea pigs euthanized with sodium pentobarbital. Appropriate segments of the organ of Corti were isolated from second, third, and fourth turns of the cochlea. After light enzymatic digestion for 15 min (1 mg/ml Type IV Collagenase, Sigma, St. Louis, MO) and gentle pipetting, cells were transferred to small plastic chambers filled with enzyme-free culture medium. The normal medium was Leibovitz's L-15 (Life Technologies, Gaithersburg, MD), supplemented with 15 mM HEPES or HBSS (Life Technologies) and adjusted to pH 7.35, 300 mOsm.
A Zeiss inverted microscope with 16× objective was used for these experiments. Cell length and diameter changes, or displacement of the driven fiber, were measured by the change in the current of a photodiode when the magnified image of the ciliated pole of the cell, a full diameter, or the edge of fibers was projected onto it through a rectangular slit. The position of the slit in front of the photodiode was adjustable so that the image of the object could always be projected to the photodiode without moving the cell or the fiber. The position of the image in the slit was monitored by a video camera behind it. Two slit-photodiode assemblies were used for simultaneous length and diameter change measurements. Photocurrent response was calibrated to displacement units by moving the slit to a fixed distance in front of the photodiode at the beginning of each trial. The photodiode measurement system, including postfiltering, had a corner frequency (3 dB down) of 1100 Hz. With some averaging, movement amplitudes as low as 10 nm could be detected routinely. In most experiments, 10-20 averages of trials were preset. Experiments were performed at room temperature (20 ± 4°C) and videotaped with a Panasonic video recorder.
Drug application. ACh was delivered by pressure ejection from a micropipette (tip diameter 2-3 µm) positioned ~20 µm from the synaptic pole of the cell. The duration and strength of the pressure pulse were controlled (Lin et al., 1993
Microchamber methods (Fig. 1A). Healthy-appearing isolated OHCs (no obvious signs of hair bundle damage, granularity, swelling, or nucleus translocation) were drawn gently part of the way into a close-fitting glass pipette, the microchamber, with their ciliated pole inside. The microchamber was fabricated from 2 mm thin-wall glass tubing (Glass Company of America) by a two-stage microelectrode puller (Narashige, Tokyo, Japan) and heat-polished to an aperture diameter close to that of a hair cell (~8-9 µm). The microchamber, with an access resistance of ~0.4-0.5 M , was mounted in an electrode holder that was held on a three-dimensional (3-D) micromanipulator (Leitz, Wetzlar, Germany). The position and height of the microchamber in the bath were readily adjustable with the micromanipulator. By moving the microchamber, cells in the bath could be picked up easily. The experimental bath, which contained the isolated OHCs, was placed on the stage of an inverted microscope (Zeiss). An Ag/AgCl ground electrode was installed in the bath. The internal medium (L-15) of the microchamber was connected to the voltage command generator through an Ag/AgCl wire inside the microchamber. The suction port of the microchamber holder was connected to a micrometer-driven syringe to provide positive or negative pressure to draw in or expel the cells. The inserted cell and the microchamber formed a resistive seal (4-6 M
Fig. 1. A, Video image showing the experimental setup for microchamber measurements. The OHC is inserted into the microchamber with its synaptic pole outside. Fractional cell length outside the chamber is designated with q. The diameter of the cell and its cuticular plate are imaged via rectangular slits on photodiodes. The photocurrents are proportional to diameter and length changes, respectively. Command voltage (Vc) is delivered between electrolytes inside and surrounding the microchamber. ACh is delivered to the synaptic pole of the cell. B, Video image showing the experimental setup for measuring electromotility with the whole-cell patch technique. Cell length changes are measured as in A, and ACh is delivered to the synaptic pole. C, Video image showing the experimental setup for stiffness measurements and for constrained electromotility measurement. A piezo-driven glass fiber is brought up against the synaptic pole of the cell. The cell is inserted into a microchamber with ciliary pole inside and q = 0.8-0.9. ACh is delivered to the synaptic pole, and its displacement is measured as in A.
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Voltage-clamp methods (Fig. 1B). OHCs were bathed in HBSS. Their membrane potentials were clamped using the standard whole-cell voltage-clamp technique (Hamill et al., 1981
Stiffness measurement (Fig. 1C). Glass fibers were pulled from molten glass (1.5 mm) by a microforge (Stoelting, Chicago, IL). The tapered fiber was 4-6 mm in length and 1-2 µm in tip diameter. We did not measure the actual stiffness of the fiber, but it was desirable that the compliance of the fiber be of the same order as that of the cells. This was ascertained by noting that the compression of the cell and the displacement of the fiber were approximately the same. The glass fiber was attached to an electrical piezo actuator, which was mounted on a 3-D micromanipulator (Narashige). OHCs were inserted ~20% into the microchamber with their ciliated pole inside, and the glass fiber was brought into contact with the excluded synaptic pole of the cell. The fiber was placed perpendicular to the long axis of the OHC in such a way that the lateral motions of the fiber would compress or relax the cell. Free fiber and cell-loaded fiber motions (fiber-driven cell compression) were measured by focusing the driven pole of the cell through a slit on a photodiode. Data acquisition was performed using an IBM-compatible computer. The probe stimulus was a series of 5 Hz sinusoidal voltage bursts with a duration of 500 msec.
Fluorescence measurements. Isolated OHCs were loaded with an adjusted final concentration of 75 µM chlortetracycline (CTC; Sigma) (Caswell, 1971
In all the experiments, ACh (Sigma) was perfused slowly into the bath without disturbing the position of the plated cells. A 1 mM stock solution was added to the experimental bath to obtain a final solution concentration of 150 µM. The volume of the experimental bath was ~0.25 ml, and the volume of the chemicals containing culture medium was adjusted to obtain the appropriate concentration. In some experiments, atropine sulfate (MW 676.8; Sigma) was applied to achieve a final concentration of 100 µM.
First, fluorescence of OHCs was measured. Readings were taken to obtain control curves with respect to the extinction of the fluorescence as a function of time. In the second series of experiments, after 1 min of baseline readings, ACh was added to the bath. Readings were taken at intervals for 2 min after addition of the ACh. Finally, in the last set of experiments, atropine was added to the bath. After the atropine was allowed to diffuse through the bath, the same procedure as in series 2 was followed.
EXPERIMENTAL RESULTS
Motile response under current and voltage clamp
It is our experience that immediately after whole-cell recording conditions are established, the zero current potential is low (average,25 mV; SD = 9.8 mV in 10 cells), but on equilibration with the content of the recording pipette the cell hyperpolarizes to an average value of
Fig. 2. A, Example of membrane potential from a cell clamped to zero membrane current during the delivery of an ACh puff. B, Example of membrane current waveforms from an isolated OHC (cell length L = 60 µm) under voltage clamp. The cell was held at
[View Larger Version of this Image (23K GIF file)]
In Figure 2A, the ACh-evoked membrane potential change is shown over time when the net whole-cell current was clamped at 0 nA. The membrane rapidly hyperpolarizes and shows some subsequent repolarization during the persistence of the ligand. Both the control and post-ACh time patterns and I-V curves (Fig. 2B) resemble those published by others for OHCs (Housley and Ashmore, 1991
Electromotile responses were measured with the whole-cell voltage-clamp method in 14 OHCs. Three examples are presented in Figure 3; an additional example has been published (Dallos et al., 1996, their Fig. 2). Pressure ejection of ACh onto the synaptic pole of the cell produced a significant effect on electromotile response in 10 cases. The other four cells showed very small change in motile response. Figure 3 depicts a sequence of responses to bipolar square-pulse stimuli (top row). In the left-hand column electromotile response waveforms are shown. In the center column these are repeated after ACh application. From the steady-state portion of the response waveforms, 
Fig. 3. Motility data for three cells stimulated in the whole-cell voltage-clamp mode. Holding potential is at
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Dose-response relations and antagonists
To rule out nonspecific effects on motility attributable to the ligand, we obtained dose-response curves in eight cells. These measurements were made in the microchamber, and the ligand was delivered as in Figure 1A. Delivery was with a puffer pipette, and the pipette was removed, refilled, and replaced between each sequence of measurements for the different doses. Care was taken to position the pipette tip at the same location vis-à-vis the synaptic pole of the cell. Representative data from one cell are shown in Figure 4A. In Figure 4B the data points give the mean normalized response (along with 2 SD) for eight cells. The smooth curve is a fit by the following form of the Hill equation: LAch = 100/[1 + (KD/[Ach])n]. Values are KD = 21.3 µM and n = 1.6.
Fig. 4. A, Representative motile response waveforms from one cell obtained when different ACh concentrations are applied to the synaptic pole of the cell. Electrical driving signal is a 10 Hz sinusoid. B, Normalized dose-response curve obtained from eight OHCs. Data points are mean values; error bars represent 2 SD. The smooth curve is the Hill equation with half-activating concentration of 21.3 µM and slope of 1.6. C, Normalized antagonizing effect of strychnine on increased motility evoked by 100 µM ACh in six hair cells. Data points are mean values; error bars represent 2 SD. Fifty percent reduction is seen at 0.015 µM.
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Sziklai et al. (1996) Length versus radius change
The electromotile response of OHCs consists of axial (
It is reasonable to assume that any influence (by ACh) that occurs before the activation of the motility motors is expressed equally in
Our results are summarized readily. In no case did we find constancy of 
Fig. 5. Simultaneously measured change in cell length and diameter for 10 OHCs. Reference condition is pre-ACh; experimental condition is after application of 30 µM ACh. Dotted line represents theoretical condition of equal percentage of length and diameter change. Experimental arrangement is as in Figure 1A.
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Effect of calcium
Removal of Ca2+ from the medium that surrounds the synaptic pole of the cell completely inhibits the ACh effect. This is demonstrated in Figure 6. The top trace gives axial motile response to square-pulse electrical stimulus in normal medium. The middle trace depicts the response when the medium is calcium-free and contains 30 µM ACh. This response is identical to the first: lack of calcium has no effect on electromotility, but it blocks the effects of ACh. This is apparent from the bottom trace, which depicts the response in normal medium in the presence of ACh. Clearly, response magnitude is increased roughly twofold relative to the first two conditions.
Fig. 6. Example of square-pulse electrical stimulation (top trace: stimulus waveform, Vc = ±50 mV) of an isolated OHC in the microchamber, as in Figure 1A. Cell exclusion, q = 0.2; here the displacement of the included, ciliated pole is measured. Total pulse duration: 60 msec. Cell contraction is plotted down. Second trace, Control response in normal medium. Third trace, Response in the presence of 30 µM ACh in Ca2+-free medium (containing 5 mM EGTA). Bottom trace, Response in normal medium in the presence of 30 µM ACh.
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The square-pulse responses shown in Figure 6 present an opportunity to examine the effect of ACh on the transient motile response versus time-dependent response components. As described previously (Hallworth et al., 1993 Time course of responses
To assess whether the motility changes seen here are attributable to the ionotropic or metabotropic action of ACh, we endeavored to compare the time courses of different events. Figure 7A represents an overview of findings. The top trace serves as time calibration. Here the substance-delivery pipette was brought to a distance of 20 µm from the synaptic pole of the cell, and 130 mM KCl was pressure-ejected from it. The OHC was current-clamped, and the zero-current membrane potential was monitored. Time course of depolarization represents the speed of delivery of the substance ejected from the pipette. In six trials, using different cells, we found that the mean time value to peak depolarization is 147.5 msec (SD = 28.1 msec). The center traces give three examples of the time courses seen in experiments in which the OHCs were current-clamped to 0 nA and the membrane potential was monitored after ACh delivery. The mean response time, measured to the peak of membrane hyperpolarization and adjusted for ligand delivery time, was 213 msec (SD = 127 msec) for 10 cells. This is similar to that discernible in the data of Blanchet et al. (1996)
Fig. 7. A, Results of whole-cell patch recordings. Top trace is calibration of the time course of ligand delivery. Depolarization of cell on pressure ejection of 130 mM KCl from the delivery pipette (20 mV vertical scale bar). The next three traces show time course of membrane hyperpolarization from the indicated zero current potential (membrane potential) for three OHCs in response to 50 µM ACh (2 mV vertical scale bar). B, Results of microchamber experiments. Continuous electrical stimulation of the cell with 100 Hz sinusoidal voltage elicited sinusoidal electromotile response. Peak-to-peak amplitude of this response was measured in consecutive 100 msec intervals and plotted as individual data points for three cells. Dotted horizontal line is the average pre-ACh motility amplitude. ACh (50 µM) delivery starts at time 0. Note logarithmic time scales.
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In Figure 7B the time course of motility change is shown for three cells. Here a 100 Hz continuous sinusoidal command voltage was delivered to the microchamber, and the ensuing motile response was monitored before, during, and after ACh delivery. Peak-to-peak responses were averaged off-line from consecutive 100 msec segments of the time record. Data points represent these averages. It is apparent from the figure that the first appearance of a change in motility (increase) occurred ~6-7 sec after the start of the ACh puff. Time constants ranged from 12 to 30 sec. It is unclear whether the decreased motility seen in the response of one cell, beginning at 250 msec, is a result of the hyperpolarization of the cell or simply of variability. The prominent increase in motility, however, occurs after a significant latency of the order of 10 sec. These results suggest that the increased electromotile response (Sziklai et al., 1996 Calcium release from internal stores
In these experiments, the brightest fluorescent signal was observed consistently in the infranuclear region and the subcuticular region, as well as in some subcellular structures, presumably mitochondria. Similar to the findings of Ikeda and Takasaka (1993)
As with most fluorochromes, the fluorescent signal strength decreases over time because of factors such as photobleaching and leakage. Therefore, control curves were measured that indicated that the decrease in fluorescence over time was approximately linear. Data representing mean + 2 SD from seven control experiments are indicated in Figure 8 by the filled circles and error bars. To reduce the decay in fluorescence, the light source was activated only when readings were to be taken from the OHC. Normalized plots of the change in fluorescence after application of ACh are seen in Figure 8 for five cells. On the addition of ACh, at time 0, a significant decrease in fluorescence was measured. The decline was steep in the beginning, and then the slope began to asymptote to a value measured before the addition of the ligand (linear decay). In the pre-ACh portion of the curves, the data best conform to a linear fit, and the slopes in this region are the same as those of control curves. On addition of ACh, however, there is a clear deviation from linearity in all cases; the post-ACh portion of the curves can be fit with exponentials having an average time constant of 42 sec. Application of 100 µM atropine essentially arrested the influence of ACh (data from three experiments are indistinguishable from control curves and hence are not shown). Atropine was added before the application of ACh to block AChRs. 
Fig. 8. Five examples of decreased fluorescence on gradual application of 150 µM ACh to the bath, starting at time 0. Fluorescence values are normalized to that measured at time 0. Heavy data points represent mean control values (no ACh) for seven cells to indicate the background decline of fluorescence, presumably attributable to photobleaching. Error bars represent 2 SD. Note that pre-ACh experimental and control results are similar.
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Time-dependent volume changes
A great deal of attention had been paid to the influence on electromotile responses of cell turgor changes brought about by alterations of osmolarity (Brownell and Shehata, 1990
Fig. 9. A, Motile response measured in the microchamber over time before and during the delivery of 50 µM ACh. Bars represent response magnitudes averaged over 16 sec periods with 300 msec long, 50 Hz sinusoidal electrical stimuli having a repetition rate of 3/sec. Cell length is 61 µm, q = 0.8. B, Simultaneous volume change measured off-line from the videotaped image of the cell.
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The first detectable change in motility amplitude occurs at ~30 sec after ACh delivery (the plot has 15 sec resolution), whereas the first detectable volume change is seen in excess of 3 min. The dead time for volume changes induced by hypotonic challenge was 210 sec in the data of Ratnanather et al. (1996) Constrained motility and axial stiffness
In Figure 10, the results of an experiment are shown in which the effects of ACh on the axial stiffness of the cell and its loaded axial motility are studied. Similar experiments, in which complete data sets were obtained in a given cell, were performed on seven cells. Furthermore, stiffness changes attributable to ACh were monitored in 14 additional cells, whereas changes in loaded electromotile response were measured in eight cells. The cells were inserted into the microchamber with their ciliated poles first, so that ~80-90% was outside the chamber. A piezo-driven glass fiber was brought up against the synaptic pole (Fig. 1C). Unloaded and loaded fiber motion and unloaded and loaded motility were measured with and without ACh in the bath. The top single trace is the motion of the fiber when it does not contact the cell. The left three traces are control, and the right three traces are corresponding responses in the presence of 50 µM ACh. In this example we first note that on pushing the fiber against the cell, its amplitude decreased to ~40% (Fig. 10, bottom left vs top single trace). Consequently, in this case the stiffness of the fiber is ~66% of that of the cell. Without the mechanical load by the fiber, electromotile amplitude increased ~100% when ACh was applied (Fig. 10, second row). The corresponding change in the loaded condition is 62% (Fig. 10, third row). In the fourth row of the figure the axial motion of the cell is shown as driven by the fiber. Here the cell is not stimulated electrically. On application of ACh the amplitude increased by 62% (the mean change is 69.4%; SD = 20.5% in 7 cells). This implies that the stiffness of the cell decreased because of ACh to ~36% of its original value. A quantitative comparison of ACh results, as manifested in changed electromotile amplitude and stiffness, provides a consistency check on the model of ACh effect. This is considered in the Discussion.
Fig. 10. Experiment as in Figure 1C. Top trace is displacement of free fiber driven by a piezoelectric actuator. Second trace, Electromotile response of the cell without the fiber loading it. Third trace, As above but with the fiber attached to the cell. Fourth trace, Loaded fiber motion driven by the piezoelectric actuator. Left column gives control conditions; right column provides corresponding data after application of 50 µM ACh. Cell length is 60 µm.
[View Larger Version of this Image (28K GIF file)]
THEORETICAL RESULTS
Length versus radius changes
The electromotile response of OHCs consists of a prominent axial component (
In previous publications we proposed a simple model for fast electromotility of OHCs, as expressed in microchamber measurements (Dallos et al., 1991 (
] is different from that in the circumferential direction [
where a and b are constants and do is the elementary displacement of the motor in the
![&PHgr;(&dgr;V)=d<SUB><UP>o</UP></SUB>{[1+exp(<UP>−a</UP>&dgr;V+<UP>b</UP>)]<SUP>−1</SUP>−[1+exp(<UP>b</UP>)]<SUP>−1</SUP>},](img001.gif)
(1)
Let us denote the length of the segment of the cell whose motility was monitored in these experiments as L, the global longitudinal stiffness as Ka, and the elementary axial stiffness (connecting individual motor elements) as ka. If the linear density of molecular motors is Na in the axial and Nc in the circumferential dimensions, the number of motors summing their axial displacements is LNa (Fig. 11A). The treatment ignores the mechanical partitioning of the cell by the microchamber, a practice valid for either small or large exclusion index, as in Figures 5 and 6. Here the excluded synaptic portion is devoid of motility motors (Dallos et al., 1991 where r is the radius of the cell. The above can be understood by considering that the sum of motor displacements is LNa
(2) rkaNc/LNa, whereas the global stiffness parallel with the motors and elementary stiffnesses is Ka. One may similarly express the radius change (
where kc is the elementary stiffness and Kc is the global stiffness in the circumferential direction. The total circumferential length change is 2
(3) In line with our heuristic argument, the ratio
(4) 
Fig. 11. A, Mechanical equivalent circuit of the nonpartitioned cell. B, Mechanical equivalent circuit of cell partitioned in the microchamber. Cell membrane is attached at the orifice of the microchamber. Symbols:
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Expressed in terms of the elementary (ka) and global (Ka) axial stiffnesses, the total longitudinal stiffness of the measured portion of cell is: The above ignores the mechanical partitioning of the cell by the microchamber, which is permissible for the almost fully extruded cells in our stiffness measurement experiments. Results indicate that
(5) Interaction of cell stiffness and damping
The above argument assumed that damping of OHCs is insignificant and that the cell can be modeled as a pure compliance. We now briefly consider how damping would influence response dynamics.
Consider the equivalent mechanical circuit of a nonpartitioned cell (Fig. 11A). The aggregate of motors is in series with the aggregate of elementary stiffness elements (ka) and is parallel with the aggregate of elementary damping elements (da). This complex works against a load comprising the global stiffness (Ka) and damping (Da) of the cell. Assuming that da = 0 (the justification for this is developed below), the input stiffness of the cell is expressed by Equation 5. The motile response may be computed from the following transfer function for the linear case: This system has a single time constant:
(6) The combination of Equations 5 and 7 yields a simple relation between
(7) , Da, and KL:
We did not make absolute stiffness measurements; however, these are available from the literature. Hallworth (1995) recently summarized various measurements of the axial stiffness of the OHCs (KL). Although different experimenters obtain a rather broad range of values, KL = 10
(8) 3 N/m is representative. With the assumption that motor density is the same in axial and circumferential directions (Na = Nc), all constants are now estimated except Ka, ka, and Da. The first two, however are related via Equation 5. Taking an approximate resting value of Ka = 2 10
It is of interest to consider transient and steady-state responses in partitioned cells. Sziklai et al. (1996)
(9)
![=<FR><NU>[qK<SUB><UP>a</UP></SUB>LN<SUB><UP>a</UP></SUB>+2&pgr;rk<SUB><UP>a</UP></SUB>N<SUB><UP>c</UP></SUB>+s(qD<SUB><UP>a</UP></SUB>LN<SUB><UP>a</UP></SUB>+2&pgr;rd<SUB><UP>a</UP></SUB>N<SUB><UP>c</UP></SUB>)]L(1−q)N<SUB><UP>a</UP></SUB></NU><DE>(k<SUB><UP>a</UP></SUB>+sd<SUB><UP>a</UP></SUB>)[K<SUB><UP>a</UP></SUB>LN<SUB><UP>a</UP></SUB>+2&pgr;rk<SUB><UP>a</UP></SUB>N<SUB>c</SUB>+s(D<SUB><UP>a</UP></SUB>LN<SUB><UP>a</UP></SUB>+2&pgr;rd<SUB><UP>a</UP></SUB>N<SUB><UP>c</UP></SUB>]</DE></FR>](img010.gif)
This transfer function posesses one zero and two real poles. The step response derived from it does not have an instantaneous transient step component, in contrast to all available microchamber data (Fig. 6). If the elementary damping is neglected (da = 0), the transfer function reduces to that shown in Equation 10:
(10) When the cell is partitioned mechanically by the microchamber, the two cell segments both possess arrays of elementary stiffness and damping elements, assumed to be associated with the elementary molecular motors. The two cell segments are also connected by some global internal stiffness and damping (Fig. 11B). If the elementary damping is negligible, analysis of the equivalent mechanical circuit reveals that the frequency response of either cell segment is all-pass (Eq. 10). This mirrors the all-pass (lag-lead network) nature of the electrical partitioning of the cell membrane in the microchamber. Previously we assumed that the frequency response of electromotility measured in the microchamber could be completely accounted for by the electrical properties of the cell membrane and that the mechanical properties of the cell were unlikely to influence the response (Dallos and Evans, 1995
Equation 10 can provide one additional useful result. For a fully inserted cell (q = 0), the equation reduces to a form identical to that derived for the patched whole cell (Eq. 6). The function has a single pole; hence its step response is a single exponential. This result reflects the fact that for a fully inserted cell there is no longer mechanical partitioning; however, in the microchamber there is still electrical partitioning (Dallos and Evans, 1995
Analysis suggests that there are two ways to achieve joint changes seen in both the initial rise (the transient response) and the steady-state plateau attributable to ACh. As we have shown before (Sziklai et al., 1996
Are the measured stiffness changes sufficient to explain low-frequency changes in electromotility? In other words, does a given measured change in Ka provide quantitative agreement with the change in where Kfiber is the stiffness of the driving fiber and Kcell is the axial stiffness of the cell (KL in Eq. 5). Denote the ratio of cell deflection driven by the fiber in the presence and in the absence of ACh as A2. Then one can compute the following relationship:
(11) Next, one measures the ratio of electromotile responses under fiber load in the presence of and without ACh as A3. Then with the assumption that elementary stiffness does not change (see above) and that global stiffness change is solely responsible for the change in axial motility, one can express:
(12)
This is a powerful prediction, which seems to be fulfilled. From Figure 10 one measures A1 = 0.4, A2 = 1.6, and A3 = 1.6. From similar data obtained in four cells, we compute the average A2 as 1.52 and the average A3 as 1.54.
(13)
Finally, one more internal check is available. If A4 is the ratio of unloaded motility with and without ACh, then, again assuming that only the global cell stiffness changes: The right-hand side of the equation is already available from Equation 12 and yields a value of 2.5. The measured A4 is 2.2, giving acceptable agreement. It is concluded that the global axial stiffness decrease attributable to ACh can account for the low-frequency change in electromotile response.
(14)
DISCUSSION
Mechanism of the ACh effect
Figure 2 shows that I-V curves obtained by us, with or without ACh, are similar to those of others (Housley and Ashmore, 1991
Nonspecific effects of the ligand can be ruled out by the demonstration of a well defined dose-response relation (Fig. 4A,B), showing half-activation concentration and Hill coefficient similar to those found by others using ACh-activated membrane current as an index. Thus our values ar
