On the frequency limit and phase of outer hair cell motility: effects of the membrane filter

Whole-cell voltage clamp and displacement-measuring photodiode techniques were used to study electrophysiological and mechanical properties of the guinea pig outer hair cell (OHC). OHCs demonstrate a voltage-mechanical response (V-M) function that can be fit by a two state Boltzmann relation, where the cell normally rests near the hyperpolarizing saturation region (-70 to -90 mV). The voltage at half- maximal length change (Vh) is depolarized relative to the resting potential, and this ensures that for symmetrical sinusoidal voltage stimulation about the resting potential, AC and DC mechanical responses will be generated. Analysis of OHC motility using pure tone voltage bursts from 11 to 3200 Hz demonstrates both AC and DC mechanical responses. By exploiting the frequency-dependent current-voltage phase separation that is characteristic of an RC-dominated system under voltage clamp, it is demonstrated that OHC motility follows the phase of AC transmembrane voltage and not that of current. For voltage stimulation across frequencies in the acoustic range, the motility cutoff frequency corresponds to the cutoff frequency of the imposed transmembrane voltage. Frequency cutoffs approaching 1 kHz have been measured but are clamp time constant limited. These observations are congruent with the voltage dependency hypothesis of OHC motility. In addition, the DC component of the mechanical response is shown to be frequency independent, but to decrease in magnitude disproportionately compared to the AC component as the magnitude of the driving voltage decreases. This is predicted from the form of the V-M function, whose level dependent DC nonlinearity is a consequence of the resting potential being displaced from Vh. The net effect is that the mechanical DC: AC ratio approaches zero for small AC voltages. Taken together, these findings question the ability of the OHC mechanical response to influence organ of Corti micromechanics at high acoustic frequencies where a tuned amplification of basilar membrane motion is hypothesized.

Whole-cell voltage clamp and displacement-measuring photodiode techniques were used to study electrophysiological and mechanical properties of the guinea pig outer hair cell (OHC). OHCs demonstrate a voltage-mechanical response (V-M) function that can be fit by a two state Boltzmann relation, where the cell normally rests near the hyperpolarizing saturation region (-70 to -90 mV). The voltage at halfmaximal length change (V,) is depolarized relative to the resting potential, and this ensures that for symmetrical sinusoidal voltage stimulation about the resting potential, AC and DC mechanical responses will be generated. Analysis of OHC motility using pure tone voltage bursts from 11 to 3200 Hz demonstrates both AC and DC mechanical responses. By exploiting the frequency-dependent currentvoltage phase separation that is characteristic of an RCdominated system under voltage clamp, it is demonstrated that OHC motility follows the phase of AC transmembrane voltage and not that of current. For voltage stimulation across frequencies in the acoustic range, the motility cutoff frequency corresponds to the cutoff frequency of the imposed transmembrane voltage. Frequency cutoffs approaching 1 kHz have been measured but are clamp time constant limited. These observations are congruent with the voltage dependency hypothesis of OHC motility. In addition, the DC component of the mechanical response is shown to be frequency independent, but to decrease in magnitude disproportionately compared to the AC component as the magnitude of the driving voltage decreases. This is predicted from the form of the V-M function, whose level dependent DC nonlinearity is a consequence of the resting potential being displaced from V,. The net effect is that the mechanical DC: AC ratio approaches zero for small AC voltages. Taken together, these findings question the ability of the OHC mechanical response to influence organ of Corti micromechanits at high acoustic frequencies where a tuned amplification of basilar membrane motion is hypothesized.
Hair cells transduce mechanical stimuli into electrical signals by modulating a standing transduction current in response to stereocilia displacement; this current induces a receptor poten-tial across the basolateral membrane of the cell, the depolarizing phase of which may promote the release of neurotransmitter (Hudspeth, 1989). Although evidence had accumulated that some type of interaction between outer (OHCs) and inner hair cells (IHCs) of the organ of Corti promoted the highly selective and sensitive responses of the mammalian auditory system to highfrequency acoustic stimulation (Dallos and Harris, 1978;Harrison and Evans, 1979;Brown and Nuttall, 1984), a potential mechanism for such an interaction remained obscure until recently. Following the discovery that the OHC is capable of electrically evoked mechanical responses (Brownell et al., 1985), a reevaluation of the classical concepts of mammalian hearing has been underway. Current theories concerning the basis of a cochlear amplifier envision an acoustically evoked cycle by cycle feedback process between OHC and basilar membrane (Geisler and Shari, 1990;Robles et al., 199 1;Ruggero and Rich, 199 1). That is, in viva, the acoustically evoked electrical responses of the OHC should effect rapid length changes of these cells that modify the mechanical input to the IHC-the receptor cell that receives up to 95% of the afferent innervation (Spoendlin, 1988).
We have previously shown that under whole-cell voltage clamp, blocking the known ionic conductances of the OHC does not interfere with the cell's mechanical response, and we proposed that transmembrane potential was the driving force responsible for OHC motility (Santos-Sacchi and Dilger, 1988). Although the molecular basis of OHC motility remains to be determined, the physiological consequences of its voltage dependence are readily discernible. For example, the voltage dependence suggests that AC motility magnitude and phase characteristics should be governed by the attenuation effects of the OHC membrane (RC) filter. Any feedback contribution of the OHC to basilar membrane mechanics will be dependent upon these magnitude and phase characteristics. I report here that an analysis of OHC motility in response to step and AC voltage stimuli confirms the voltage dependency hypothesis, since the frequency extent and phase of motility are dependent upon the extent and phase of the imposed transmembrane voltage. Furthermore, while the effects of the membrane filter influence the AC mechanical component directly, the DC component is indirectly susceptible. Indeed, the DC component is far more susceptible than the AC component. These results are important for understanding the possible contribution of OHC motility in peripheral auditory processing.
Preliminary reports of this work have been presented previously (Santos-Sacchi, 1990, 199 la).

Materials and Methods
General. Guinea pigs were overdosed with pentobarbital. The temporal bones were removed, and OHCs were isolated nonenzymatically from The Journal of Neuroscience, May 1992May , T2(5) 1907 the cochleas by gentle pipetting of the isolated top two turns of the organ Corp., NJ; output filtered at 30 Hz) across the image of the cuticular of Corti. The cell enriched supematant was then transferred to a 700 ~1 plate (apical end of the cell) at a monitor magnification of 2800 x (Sanperfusion chamber, and cells were permitted to settle onto the cover tos- Sacchi, 1989). Fast OHC movements elicited by voltage clamp with glass bottom. All experiments were performed at room temperature short-duration stimuli (below video detection) were measured with a (-23°C). A Nikon Diaphot inverted microscope with Hoffmann optics differential photodiode (PD) onto which the image of the cuticular plate was used to observe the cells during electrical recording. All experiments from the microscope was proiected. Placement of the PD was accomwere taped with a Panasonic AG6300 video recorder. A modified Leibovitz medium (NaCl,142.2 mM;KCI,5.37 mM;CaCl,,1.25 mM;MgCl,,1.48 mM;HEPES,5.0 mM;dextrose,5.0 mM; pH 7.2) was used as the normal perfusate. Modifications to the extracellular medium are noted in figure captions, with NaCl adjusted to maintain osmolarity (300 mOsm). Extracellular solutions were changed via two methods. A chamber perfusion system permitted the fluid in the whole chamber to be constantly exchanged with fresh medium (0.1-l ml/min). A more rapid and direct perfusion system was used to perfuse single cells selectively under voltage clamp, during continuous exchange of bulk medium via chamber perfusion. The device is a four-barreled glass pipette tapered to about 100 rrn and fitted with a polyethylene sleeve at the tip to permit fluid flow from a single port with a small dead volume. Solutions were fed to the pipette under gravity control and rapidly switched with solenoid valves. The tip of the pipette was brought to within 50 pm of the cell being studied, and the flow of solution was adjusted so as not to perturb the cell physically.
Electrical recording. OHCs were whole-cell voltage clamped with a Dagan patch-clamp amplifier at holding potentials between -70 and -80 mV, similar to potentials recorded in vivo (Dallos et al., 1982). Pipette solutions were composed of 140 mM KC1 or CsCl, 5 or 10 mM EGTA, 2 mk MgCl,, and 5 mM HEPES buffered to pH 7.2. Gigohm seals were obtained at the nuclear level of the cell membrane, and electrode capacitance was compensated prior to whole-cell recording. Voltage steu studies were net-formed with an Axolab 1100 A/D and D/A board(Axon Instruments, Foster City, CA) with associated software @LAMP).
AC studies were performed using a digital signal processing board with custom-written software (DSP-16; Ariel Corp., Highland Park, NJ) capable of delivering and analyzing pure tone or swept frequency stimuli. Data were saved to disk for off-line analysis.
For most experiments, ionic conductances were blocked. Under these conditions, the cell clamp can be modeled most simply as an electrode resistance (R,) in series with a parallel combination of the membrane resistance (R,) and capacitance (C,). These component values were estimated at the holding potential from current records in response to -10 mV voltage steps, and were accounted for during analysis, so that actual voltages imposed upon the cell are known (Marty and Neher, 1983). Care was taken to maintain low series resistance values during recording by delivering transient positive or negative pressure into the electrode to maintain an unobstructed orifice; electronic series resistance compensation was employed as well. The program CLAMPEX (Axon Instruments, Foster City, CA) was modified to provide a continuous display of clamp time constant, cell capacitance and resistance, and series resistance between data collections. The magnitude and phase of the transmembrane voltage (I',,,), predicted from the command voltage (I',), were obtained using the estimated component values by modeling the impedance (Z,,) of the cell clamp with the software package MATLAB (Mathworks, Natick, MA): (2) v, = IZ,. ( In some cases, an absolute delay (I = I . e+, where t is the delay in seconds) was included in the model so that the predicted phase plots coincided (as determined by eye) with those of the measured current and mechanical response plots. Typically, this was required when series resistance compensation was used, and may be the result of delays introduced as a result of the compensation feedback. OHC motility measures. OHC mechanical responses and currents were simultaneously measured in response to step or sinusoidal voltage stimuli. For steady state movements (voltage steps > 100 msec), length changes were analyzed off the video monitor during playback by placing differential optoresistors or a position-sensitive detector (Hamamatsu plished remotely by a computer-controlled micromanipulator, so as not to perturb whole-cell recording. The PD was backlit by two fiber optic beams projected through the microscope's camera port onto a 30% mirrored glass coverslip base of the perfusion chamber, and reflected back to a CCD video camera via a 90" prism to allow PD placement during simultaneous cell visualization on a mixed video-computer monitor (Matrox Corp., Dorval, Quebec, Canada). Backlighting was not required after calibration of the PD's position on the monitor. The frequency response of the PD system was measured by driving an onbiased light-emitting diode (LED) and had a 3 dB rolloff at 6 kHz ( Fig.  1). The validity of the PD system was verified by measuring the movements of a glass probe driven by a piezoelectric bimorph (Fig. 1, insets). Sinusoidal voltage bursts (onset and offset linearly ramped) of frequencies ranging from 11.7 to 320 1 Hz were delivered to OHCs under voltage clamp. PD output and whole-cell currents were filtered at 10 kHz (12 dB/octave) and collected simultaneously using a sampling rate of 20 kHz for AC analysis or up to 50 kHz for step analysis. Responses were averaged 200 times. Fundamental magnitude and phase of the mechanical responses were measured by fast Fourier transformation (FFT) of the central portion of the digitized waveforms using the software package MATLAB. Mechanical responses were corrected for the phase and magnitude characteristics of the PD system. Absolute calibration of cell movements was determined by measuring off the video monitor the cell movement in response to a large steady state depolarizing voltage stimulus (Santos-Sacchi, 1989).
Motility estimates using a photodiode technique rely upon intensity measures of the projected image of the OHC's cuticular plate. The problems with such a technique have been addressed by Clark et al. (1990). In the present study, care was taken to maintain the position of the cells within the bounds of the differential photodiode; in order to check this, cells were visualized on a video monitor during data collection. While magnitude measures may be affected by changes in image intensity, phase measures should not. Similar cutoff frequencies of the mechanical responses were obtained from phase and magnitude data, indicating that the image intensity did not change during the data collection period, typically about 5 min.
The mechanical response AL (v) was fit with a Boltzmann function: where AL.,,, and AL,,, are the fitted maximum and minimum length changes from the resting state, b is the voltage slope factor, and V, is the voltage at half-maximal length change.

Results
The OHC changes length when its transmembrane potential is altered. Figure 2A demonstrates the V-M function for an isolated OHC using step voltage commands from a holding potential of -68.4 mV. The function follows a saturating Boltzmann relation, such that the mechanical response is larger in the depolarizing (shortening) direction near the cell's normal resting potential. This is a consequence of the holding potential being displaced from V,. For this cell, a maximum slope of about 2 1 nm/mV at -26 mV is calculated (Fig. 2B). Responses as large as 30 nm/mV have been observed (Santos-Sacchi and Dilger, 1988).
The OHC membrane possesses a nonlinear charge movement that is correlated in time and voltage dependence with induced length changes (Ashmore, 1989;Santos-Sacchi, 1990, 199 1 b); this nonlinear charge probably represents the movement of membrane-bound voltage sensors responsible for the cell's voltage-dependent mechanical response. Figure 3 demonstrates that the kinetics of the charge movement are such that the time Frequency (Hz) Figure 1. Characteristics of the movement measurement system. Frequency response of differential PD output (open circles, averaged 200x) in response to off-centered LED emission elicited by sine wave bursts. Cutoff frequency was 6 kHz. Insets, Outputs from PD in response to simulated cell movement. The tip of a glass microelectrode shank was melted to a sphere of about 15 pm; transmitted light produced a bright area in the sphere's center! which was used to mimic the bright OHC cuticular plate observed under Hoffmann optics. The artificial cell was attached to a piezoelectric brmorph and moved using various voltage waveform inputs to test the linearity and frequency following capability of the PD measurement system. a, PD output measured in response to bimorph movements produced by fixed incremental voltage steps (filtered to avoid bimorph resonance at 2 kHz). Linearity is good. Response filtered at 800 Hz. Calibration vertical, 0.1 pm; horizontal, 2 msec. b, PD output (noisy truces) in response to bimorph voltage stepped through a filter of 100 Hz (top truce) and 300 Hz (bottom truce). Simultaneously recorded voltage (solid truces) corresponds faithfully to the PD output. Maximum excursion is about 1 pm. Pulse width is 5 msec. c, Bimorph was stimulated with sinusoidal voltage bursts (156 Hz). Two truces on top are measured voltage; corresponding two truces on bottom are PD output (filtered at 800 Hz). Excellent frequency following is apparent. Stimulus and response traces on right demonstrate that the measurement system is capable of detecting DC offsets.
constant of the voltage-clamp amplifier limits their study under whole-cell configuration. That is, the time constant of nonlinear capacitive current decay follows changes in the time constant of the clamp amplifier, indicating that the kinetics are faster than the fastest clamp speed presently attainable. Measures of OHC mechanical response induced by voltage steps indicate a similar trend (Fig. 4A). In this case, an OHC was stepped from a holding potential near -70 mV to about 40 mV, while the clamp time constant was modified between 0.8 and 0.52 msec with series resistance feedback compensation. Both movement onset and offset are directly correlated with clamp time constant. Note that fitted single exponentials of the movement onset appear faster than the clamp time constant. This is due to the fact that the voltage steps are saturating, and is consistent with model simulations based on the OHC's V-M function (see Discussion). It was noted by Ashmore (1987) that delays in mechanical response onset occurred following voltage step onset. The insets in Figure 4A illustrate that clamp time constant modifications do not appear to influence the mechanical response onset, which occurred within 40 Fsec of stimulus onset in this case. In other cells, however, delays were observed up to about 100 psec (Fig.  4B). It is conceivable that alterations of cell turgor that occur during whole-cell voltage clamp may underlie this delay phenomenon (Santos-Sacchi, 199 1 b). Figure 4C illustrates the mechanical response of an OHC driven by a voltage step depolarization of about 5 msec in duration, with one of the fastest clamp time constants attained, 0.14 msec. The onset of the mechanical response is rapid (onset 7 of a double exponential fit, 0.240 msec); a maximum velocity of 6.5 mm/set is calcu-lated, which is about 3.5 times faster than previous estimates of OHC velocity (Ashmore, 1987). The form of the V-M function ( Fig. 2A) indicates that the mechanical response will include both AC and DC components when a sinusoidal voltage command is delivered about the holding potential. Such mechanical rectification has been demonstrated with low-frequency sinusoidal stimuli (Evans et al., 1989;Santos-Sacchi, 1989). Figure 5 illustrates this phenomenon as a function of stimulus frequency. Sinusoidal voltage command stimuli of frequencies ranging from 11.7 to 320 1 Hz elicit AC and DC mechanical responses. Figure 5A documents the rectified nature of the V-M function of this cell based on the response from an 11.7 Hz transmembrane voltage stimulus. Mechanical rectification is also apparent at higher stimulus frequencies, as reflected in the DC mechanical components present in the raw data (Fig. 5B). The measured reduction in magnitude of the mechanical response as frequency increases is not inherent in the OHC, but is due to limitations of the voltageclamp amplifier. That is, command voltage magnitude decreases with increasing frequency because of the voltage clamp's limited frequency response;' therefore, voltage dependent AC mechanical responses roll o@as well (see below). As command voltage magnitude decreases (due to the clamp time constant), there is a disproportionate decrease in the mag-  Evans et al. (1990) obtain similar V-M functions (see Fig. 5A, solid triangles), they report a linear correspondence between AC and DC mechanical responses as voltage magnitude is altered. However, Figure 5C exemplifies the nonlinear correspondence inherent in the V-M function by plotting the ratio of DC to AC mechanical response as a function of AC voltage magnitude. The measured ratio (open circles) decreases as the stimulating voltage magnitude decreases, and is well predicted (solid line) from the V-M function of this cell (Fig. 5A). This observation indicates that the form of the V-M function measured at 11.7 Hz is preserved at higher frequencies; that is, the nature of the function is frequency independent.
The top panels of Figure 6, A and B, examine the magnitude of the mechanical response fundamental (obtained by FFT) and compare it to the voltage delivered to the cell as predicted from the clamp time constant, before (top panel, Fig. 6A) and after (top panel, Fig. 6B) series resistance compensation. The cutoff frequency of the cell's mechanical response increased following compensation of the series resistance. The mechanical response rolloff roughly follows the rolloff of the transmembrane voltage, demonstrating that the mechanical response can follow rapid voltage fluctuations quite faithfully (fcUtoff -1 kHz). This is inmarked contrast to the limited frequency response (fcutoff -60 Hz) reported by Ashmore (1987; see thick line in top panels of Fig. 6A,B). The analysis of phase data presents a more robust test of the voltage dependence hypothesis. In an RC-dominated system, such as the OHC under voltage clamp, as voltage command frequency is increased, an asymptotic phase separation of 1.57 radians (90") will develop between injected current and voltage. Voltage phase will lag that of current. The clamp time constant, R, 1) R,C,, dictates the resultant frequency dependence of the separation. The bottom panels in Figure 6, indeed, demonstrate that the mechanical response follows the phase of the induced transmembrane voltage and not that of the transmembrane current. Similar data on the magnitude and phase of current, voltage, and motility obtained from four additional cells, each with a different clamp time constant, are presented in Figure 7. In all, an asymptotic phase separation between motility and injected transmembrane current is reached [ 1.66 + 0.18 radians at 625 Hz (mean + SD; n = 6 cells)], as would be expected for a voltage driven process. This is strong evidence favoring the voltage dependence hypothesis of OHC motility.2 The relationship of the mechanical response time constant (i.e., cutofffrequency) to that of the voltage clamp is summarized for five cells in Figure 8. The frequency response of OHC motility is positively correlated with the speed of the voltage clamp.
2 It should be noted that the measured current phase consists of both a resistive and capacitive component, and that at high frequencies the capacitive component dominates. However, the current through membrane-resistive elements is always in phase with transmembrane voltage. Nevertheless, alterations of the resistive currents by means of various ionic blocking agents do not interfere with voltageinduced mechanical responses (Santos-Sacchi and Dilger, 1988;Santos-Sacchi, 1989, 1991b. For two OHCs (circles and diamonds), mechanical responses were obtained before and after series resistance compensation; mechanical response cutoff frequency paralleled the resulting changes in clamp speed. There is, however, a trend for the mechanical response fundamental to roll off at lower frequencies than the applied transmembrane voltage. This phenomenon may be a consequence of the nonlinear V-M function, as a similar trend is also found with model simulations (solid line, Fig. 8).

Discussion
The data presented here provide insight into the mechanism and potential significance of OHC motility. The observation  Figure 5. OHC AC and DC mechanical responses elicited by AC voltage stimulation. A, Voltage versus movement for an 11.7 Hz voltage stimulus. Voltage is the estimated intracellular potential obtained from the command potential corrected for series resistance and phase shifted to minimize phase differences between it and movement response. The solid line is a fit to a portion of a Boltzmann function with V, = -30.5 mV and b = 3 1 mV. For comparison, the data (solid triangles) of Evans et al. (1990) based on step commands about the authors' estimated resting potential of -60 mV were scaled and superimposed (see Results and Discussion). Inset, Movement response waveform smoothed with five point running average. Peak-to-peak (PkPk) response is about 1 pm. B, Photodiode output indicating the movement of the OHC in response to voltage sine wave bursts of varying frequency. The movement consists of an AC and DC response, both of which decrease as a function of frequency; this results from the decrease of the magnitude of voltage stimulation due to the voltage-clamp time constant. DC responses can be observed above 3 kHz but decrease in magnitude disproportionately compared to AC response magnitude. C, Ratio of DC movement to AC PkPk movement versus PkPk voltage stimulus corrected for the frequency-dependent attenuating effects of series resistance, Measures are from the raw data shown in B. Data were obtained by visually determining PkPk movement response and DC movement response (difference between baseline and half-PkPk response). The solid line is the predicted ratio based upon the movement versus voltage response for 11.7 Hz as in A. Note the greater susceptibility of the DC response to reduction of driving voltage magnitude. That is, the DC:AC ratio is not constant as a function of driving voltage magnitude.
1912 Santos-Sacchi l OHC Mechanical Frequency Response movement within the membrane of the OHC (indicative of membrane-bound voltage sensors) corroborates this concept (Ashmore, 1989;Santos-Sacchi, 1990, I99 1 b). Similarities between characteristics of the nonlinear charge movement and motility, including voltage dependence (V,, b), susceptibility to charge screening, and reversible block by gadolinium ions, indicate that the estimated 4000 voltage sensors/cLm2 control OHC length through an equal number of associated elemental motors (Santos- Sacchi, 199 1 b). Assuming that the motors are equally distributed within the membrane along the extent of the subsurface cisternae, it is calculated that each elemental motor would contribute an effective unit displacement of about 1 nm in the longitudinal direction. The actual displacement vector may not be purely longitudinal (Dallos et al.,199 lb). Ultimately, the dependence of OHC motility on transmembrane voltage and the form of the V-M function will determine the physiological significance of OHC motility.
Velocity and frequency response of OHC motility An important indicator for evaluating the significance of OHC motility in inner ear function is its frequency response. Certainly, there will be a point at which the OHC will be unable physically to follow an imposed transmembrane AC voltage, and a determination of this cutoff frequency will permit a more realistic assessment of the OHC's mechanical influence in the high-frequency region of the cochlea. Unfortunately, the maximum velocity and the frequency extent of OHC motility are as yet undetermined, due to the speed limitations imposed by the voltage-clamp amplifier. Thus, the current maximum OHC velocity measured during a step response (6.5 mm/set; Fig. 4C), or estimated from the AC data [ Fig. 6B, (AL w) 4 mm/set at 1250 Hz] is likely to be an underestimate. Indeed, the OHC mechanical response probably extends beyond the widest frequency response measured, which approached a 1 kHz cutoff.
It is interesting to note that although the speed of the mechanical response follows changes in the speed of the imposed voltage, the time constants of each are not necessarily equal. In fact, in Figure 4 it was illustrated that the mechanical on-response can have an apparent time constant faster than that of the imposed voltage; contrarily, the off-response can be slower than the imposed voltage. This is not unusual for a nonlinear system, and the same effects are simulated for a model V-M function in Figure 9. It is clear that despite a constant membrane potential time course, level-dependent changes in the apparent time constant of the mechanical response arise. Mechanical response saturation at the extremes of the V-M function accounts for much of these effects. The tendency for the mechanical frequency response to roll off sooner than the imposed voltage frequency response (Fig. 8) may also reflect the effects of the nonlinear V-M function. If the resting potential (holding potential) were equal to V, and the stimulus amplitude were very small, the time course of the mechanical response would more closely mirror that of the driving voltage.
Despite their limitations, the measurements of velocity and frequency response reported here more closely reflect OHC mechanical response capabilities than previous measures (Ashmore, 1987), and are useful in evaluating some timely issues. For example, electrically evoked otoacoustic emissions recorded from the ear canal, presumably due to the activity of OHCs, have been measured in pass bands up to several kHz (Hubbard and Mountain, 1990). These investigators have suggested, based on Ashmore's (1987) mechanical frequency response data, that the OHC length changes are too low pass to account for such high-frequency phenomena. Clearly, the data presented here suggest that OHC length changes may be significant at those acoustic frequencies where electrically evoked otoacoustic emissions occur. Ashmore's (1987) observation that OHC motility was extremely low pass was probably due to the very slow clamp time constants achieved in that study (see footnote 3 of Santos-Sacchi, 1989). Since the in viva receptor potential will provide the OHC motility driving force, the effectiveness of evoked AC mechanical events in influencing organ of Corti micromechanics at high frequencies can be evaluated to a first approximation by an assessment of OHC receptor potential characteristics. Thus, it is known that OHC AC receptor potentials for cells with high characteristic frequencies (> 15 kHz) are quite small due to the cell's RC time constant Cf;uto,r -1.2 kHz); AC potentials of about 15 PV have been recorded in these cells near auditory threshold (Russell et al., 1986). Consequently, it has been argued that evoked AC movements of an OHC with a resting potential of -70 mV are much smaller (-20 dB) than basilar membrane movements near auditory threshold (Santos-Sacchi, 1989; but see Santos-Sacchi, 199 1 b).
The present velocity estimates, though clamp limited, appear incompatible with the electro-osmotic theory of OHC motility proposed by Brownell and Kachar (1986). The rate of movement is far greater than that attributable to an electro-osmotic mechanism; experiments on a variety of preparations indicate the maximum velocity achievable is 1 pm/set per V/cm (Mc-Laughlin and Mathias, 1985). The steady state voltage drop across the membrane of the OHC in Figure 4C was 107 mV. The maximum field strength along a cell of'70 Frn, assuming that the total imposed voltage drops across the length of the cell (which is unlikely, since space-clamp estimates indicate little longitudinal decay) would be 15.3 V/cm. Thus, an electro-osmotic based velocity of 15.3 pm/set is predicted, over 2 orders of magnitude smaller than the observed maximum velocity. Iwasa and Kachar (1,989) employed the same argument against an electro-osmotic mechanism, although the disparity between their velocity measures and electro-osmotic estimates were not as great as those reported here. Furthermore, an electro-osmotic mechanism would predict that the velocity, not the displacement, of OHC motility would be in phase with voltage. This is in conflict with the phase data reported here. It should be noted that velocities associated with electro-osmosis are derived for DC mechanical response Voltage-dependent OHC motility, analyzed under whole-cell voltage clamp, is well characterized by a two-state Boltzmann function, whose I', is offset in the depolarizing direction relative to the normal resting potential of the cell. A mechanical DC nonlinearity is not inherent in the V-M function but is expressed only due to this voltage offset. This concept differs from the contention of Dallas et al. (1991 b), who suggest, based on DC responses measured at very small stimulus levels, that the DC component is the result ofan essential nonlinearity ofthe OHC's stochastic motor. Clearly, however, should the cell's resting potential and Vh superimpose, then no DC mechanical component would arise.
The normal resting potential in vivo is near -70 mV (Dallos et al., 1982;Russell and Sellick, 1983). V, of the V-M function ranged from about -40 mV to -20 mV, which to a large extent is dependent upon membrane surface charge and agents that affect the resultant surface potential (Santos-Sacchi, 199 1 b). Thus, a DC mechanical response appears ensured under normal in vivo conditions4 and is dependent on the many factors governing 4 Actually, V, is not known for the i n viva situation. Unfortunately, the traditional i n vitro whole-cell technique modifies both intra-and extracellular environments, so that biochemical conditions (e.g., membrane surface charge screening, phosphorylations, etc.) existing in vitro may not represent those in viva Thus, OHC resting membrane potential and membrane surface potential. The effects of resting potential on the sum of elemental motor contributions, that is, on the observable OHC mechanical response, can be complex. For example, whereas shifts of the normal resting potential toward V, will reduce the DC component, the peak-to-peak component can grow. It is interesting to note that noise-induced threshold shift, which produces a depolarization of the OHC (Cody and Russell, 1985) should affect both AC and DC mechanical response production. It is demonstrated here that the OHC DC mechanical response is a frequency-independent consequence of the V-M function. The persistence of the DC mechanical response above 3 kHz is the first demonstration that the mechanical rectification extends to physiologically important frequencies. Previous studies have reported DC responses at frequencies between 10 and 200 Hz (Evans et al., 1989;Santos-Sacchi, 1989). It is conceivable that DC mechanical responses of OHCs could provide a bias that may change mechanical characteristics (e.g., stiffness) of the organ of Corn-basilar membrane complex, leading in some manner to enhanced tuning. At first thought, this may appear to alleviate some of the problems associated with the membrane filtering effects on the high-frequency AC mechanical response. However, the DC nonlinearity is highly stimulus level dependent, greatly diminishing with level. Consequently, as the AC voltage stimulus is reduced (e.g., due to the membrane filter), the DC mechanical response magnitude declines much more precipitously than the AC mechanical response. Figure 10 demonstrates this inherent outcome of such a V-M function in a model AC simulation. DC mechanical components are vanishingly small at low stimulus levels. Evans et al. (1990, 199 1) have reported significant DC mechanical responses at low AC stimulation levels. The superposition of their data (from Evans et al., 1990, their Fig. 2) onto the AC data in Figure 2A indicates that the form of their V-M function in the voltage range shown is remarkably similar to the form obtained in the present study under voltage clamp. This is of interest since their stimulus delivery technique (a partitioning microchamber) differs from the whole-cell technique used here. However, while they may have control over the voltage imposed across the membrane of the OHC, their technique permits neither the control of the resting membrane potential nor the control of the intracellular environment (e.g., pH). Calculation of the DC:AC ratio predicted by their V-M function presents essentially the same result as that calculated for the voltage-clamp data reported here. It is surprising, therefore, that they detect a linear modification in both the AC and DC mechanical components as stimulus magnitude is changed.
The inability to control resting potential and/or intracellular environment with the microchamber technique may underlie their observation; for example, the resting potential along the V-M function or V, may be changing as a function of stimulus level. DC responses necessarily change when resting voltage shifts relative to V,. Relatedly, Evans et al. (1991) presented data that they interpreted to indicate that the DC component was vulnerable to repeated voltage stimulations. These data may it is very difficult extrapolating to in vim conditions. It should be noted, however, that DC mechanical resoonses of the basilar membrane i n viva, presumably due to the effects of OHCs, have been measured at high sound pressure levels @Page, 1987). Obviously, it is important to obtain V, estimates i n viva. Since the voltage dependence of nonlinear capacitance in the OHC is similar to that of the cell's mechanical response (Santos-Sacchi, 199 1 b), inferences concerning the mechanical response V, may be made from in viva estimates of voltage-dependent capacitance.  AC ratio (D) clearly indicates that the DC response is more susceptible to voltage magnitude alterations.
1916 Sat-doe-Sacchi-OHC Mechanical Frequency Response mV),' the DC mechanical response would be 18 fm. Clearly, it is difficult to imagine the significance of such DC displacements when basilar membrane motions at threshold are estimated to be near 350 pm in the guinea pig (Sellick et al., 1982) and 2000 pm in the chinchilla (Robles et al., 1986)." It is important to note, however, that hair cells are capable of generating DC receptor potentials that are not susceptible to the attenuation effects of the cell's RC time constant (Dallos et al., 1982;Russell and Sellick, 1983). Such DC potentials generated at high acoustic frequencies should induce movements of the OHC. However, whereas IHCs produce significant DC potentials at the characteristic frequency threshold in the high-frequency region of the cochlea, OHCs do not (Russell et al., 1986). Thus, the occurrence of rapid, stimulus related DC mechanical responses that are physiologically significant at auditory threshold is not readily envisioned.
In summary, this report demonstrates the widest mechanical frequency response of the OHC measured to date, and shows that the mechanical rectification due to the V-M function extends well into the kilohertz range. These results attest to the unique nature of the OHC's motility mechanism among known cellular mechanisms of movement. Nevertheless, the results confirm theLvoltage dependency hypothesis of OHC motility, and the limitations that this dependency imposes in vivo remain to be reconciled with current concepts of OHC performance in the high-frequency region of the mammalian inner ear.