INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Several studies have described voltage-sensitive, outwardly rectifying K⁺ conductances in vestibular hair cells (Correia et al. 1989; Marcotti et al. 1999; Masetto et al. 1994; Ohmori 1984; Rennie and Correia 1994; Rüsch and Eatock 1996; Rüsch et al. 1998). Although voltage responses to injected currents have also been described (Baird 1994; Correia and Lang 1990; Correia et al. 1989; Eatock et al. 1998; Griguer et al. 1993; Rennie et al. 1996; Ricci and Correia 1999; Weng and Correia 1999), the roles of these conductances in shaping afferent responses are far from certain.

A possible reason for this lack of certainty is the choice of testing stimuli, which have been of short duration compared with many signals involved in vestibular transduction. In addition, controlled currents have been presented in the absence of background currents so that the resting potential serves as a baseline. There is reason to believe that hair cells normally operate around potentials more depolarized than the resting potential. In particular, afferents have a resting discharge (Fernández and Goldberg 1976a; Goldberg and Fernández 1971; Lowenstein and Sand 1936), which in turn is the result of neurotransmitter release from hair cells (Rossi et al. 1994; Xue et al. 2002). Resting potentials of vestibular hair cells are more hyperpolarized than the voltages needed to trigger the Ca²⁺ conductances underlying quantal neurotransmission (Bao et al. 1999; Martini et al. 2000; Prigioni et al. 1992). This implies that transducer currents are active at rest and serve to depolarize the hair cell.

A goal of our research has been to determine how voltage-sensitive currents in hair cells are related to the diversity in response properties of vestibular afferents. In the case of the turtle posterior crista, bouton fibers innervating the neuroepithelium near the planum and near the nonsensory torus differ in several of their firing properties, including their discharge regularity and their rotational gains and phases (Brichta and Goldberg 2000). Furthermore, the gains and phases of calyx-bearing afferents are lower than those of bouton afferents having a similarly irregular discharge. This and the preceding paper (Brichta et al. 2002) were designed to answer two questions. Could the large differences in discharge properties of bouton afferents located near the planum and torus be related to differences in the electrophysiology of the hair cells they innervate? Could differences in the currents of type I and II hair cells be responsible for differences between calyx-bearing and bouton afferents? In the preceding paper, preliminary answers to these questions were provided by voltage-clamp experiments.

Here, we used injected currents to continue the analysis. We first used brief current steps to compare responses of type I hair cells with those of type II hair cells selectively harvested from different regions of the neuroepithelium. To extend the studies to lower frequencies and to determine the influence of background depolarizations, we next superimposed sinusoidal currents over a broad frequency range on steady depolarizing currents. Results differed from those obtained with brief voltage and current steps because background currents resulted in a slow inactivation of outward K⁺ conductances, similar to that described in other hair-cell organs (Correia and Lang 1990; Marcotti et al. 1999; Rennie et al. 2001; Russo et al. 1996). As had been reported in the pigeon cristae (Correia and Lang 1990) and as we confirmed with long-duration voltage clamps, inactivation was more prominent in rapidly activating type II cells than in type I cells.

To provide a theoretical context for our results, we used a linearized Hodgkin-Huxley theory developed by others (Ashmore and Attwell 1985; Detwiler et al. 1980; Mauro et al. 1970). An advantage of the theory is that it allows a quantitative comparison of the responses to voltage clamps and to sinusoidal currents. Another benefit is that the theory identifies those features of outwardly rectifying K⁺ conductances that determine the tuning quality of the responses to current steps (Art and Fettiplace 1987; Ashmore and Attwell 1985).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Preparative methods were identical to those used previously (Brichta et al. 2002). Briefly, red-eared turtles were decapitated, the posterior ampulla on one side was excised, the neuroepithelium was exposed, and an enzymatic dissociation procedure was used to harvest hair cells from one of three regions (planum, torus, or central zone). The chamber containing the isolated hair cells was placed on the sliding stage of an inverted microscope (Zeiss Axiovert 100) and continually perfused at a rate of 500 µl/min with a standard external solution. Hair cells were examined at ×600 with Nomarski optics and were recorded in the ruptured-patch, whole cell mode with patch pipettes connected to an Axopatch 200A amplifier (Axon Instruments, Foster City, CA). All procedures were done at 22°C, and both external and pipette solutions were identical to the standard solutions described in the preceding paper.

A cell selected for recording was photographed for later morphological classification. Next, the series resistance (R_S) and membrane capacitances (C_M) were determined with 3-ms voltage clamps. A standard 200-ms voltage-clamp series was then run (see Brichta et al. 2002) with the capacitative transient canceled and the series resistance, which was typically 5-15 M, compensated 70-90%. Two controlled-current protocols were run either on the same or separate cells. Currents were delivered in the "fast" mode of the amplifier as this minimized undesirable current transients. The first protocol was a standard current-clamp series. Current was stepped from zero to each of 10 values (50, 20, 10, 0, 10, 20, 50, 100, 200, and 500 pA) for 200 ms and then returned to zero. Voltages were filtered at 3 kHz and were sampled every 0.6 ms. Current traces were similarly sampled to insure that uncontrolled transients were not present.

In the second protocol, sinusoidal currents (0.1-100 Hz) usually of ±25-pA amplitude were introduced on a background current (usually 50 pA). Frequencies were spaced 1/2 decade apart. The number of points per cycle ranged from 1,024 at 0.1 Hz to 64 at 10-100 Hz. Currents and voltages were sorted into 32 equally spaced bins, and values for successive cycles after the first were averaged into a single cycle. A least-squares analysis was used to determine the best-fitting sinusoids for the current input and the voltage output, from which gains and phases were calculated. Gains were expressed in units of mV/pA (=1,000 M), and positive phases indicated that voltage led current.

Long-term inactivation was studied in voltage-clamp mode with 60-s steps to 47 mV from a holding potential of 67 mV. Sampling was done every 5 ms. Once every 500 ms, a 10-mV, 25-ms hyperpolarizing pulse was delivered to measure conductance.

In all cases, voltage was corrected for a junction potential of +7 mV and voltage-current curves were corrected for the uncompensated series resistances in voltage clamp and for the entire series resistance in current clamp.

Results are expressed as means ± SE unless otherwise stated.

Theory

The goal of this section is to present a linearized version of the Hodgkin-Huxley equations for outwardly rectifying K⁺ currents (Ashmore and Attwell 1985; Detwiler et al. 1980; Mauro et al. 1970). Let the membrane be at a definite potential () with an associated K⁺ current (_K) and an instantaneous (high-frequency) conductance (_HF). The three variables are related by

(1)

where v_K is the K⁺ equilibrium potential. For small variations, i_K and v, we can ignore second-order terms and

(2)

where '_HF = d_HF/dv at v = . The slope (low-frequency) conductance is

(3)

For an outwardly rectifying current in the voltage range  > v_K, both '_HF and (  v_K), the two terms in the last expression on the right side of Eq. 3, are positive. Hence, the expression is positive and _LF > _HF.

The variation in i for a voltage step v can be expressed as

(4)

where Î(s) and (s) are, respectively, the Laplace transforms of i_K and v, and H(s) is a transfer function describing the frequency dependence of the transition between the low-frequency (_LF) and high-frequency (_HF) conductances. From the form of Eq. 4, H(s) = 1 when |s|  0 and H(s) = 0 when |s|  . A second-order equation meeting these conditions is

(5)

where _K1 = 1/_K1 and _K2 = 1/_K2. The suitability of Eq. 5 is seen from the response, i(t), to a voltage step, v. Inverting Eq. 5 gives

(6)

Equation 6 provides a good fit to our activation data (Brichta et al. 2002, Fig. 7).

The conductance of the channel, when expressed as a Laplace transform, is

(7)

where K = _LF/_HF. When K  1, (s)  _HF, a constant equal to the instantaneous conductance. (s) can be expressed as the sum of two terms, only one of which is time-invariant. Leak conductances contribute to the time-invariant term, _HF.

As we are mainly interested in the voltage produced by an injected current, we consider the impedance, (s) = 1/(s) = (s)/Î(s), as a complex gain. When the membrane capacitance, C_M, is added to the circuit, the impedance becomes

(8)

where ₁ = _HF/C_M is the reciprocal of ₁, the effective membrane time constant at the particular voltage, . Many features of the system are easier to deduce with first-order channel kinetics where H(s)  _K1/(s + _K1) and

(9)

Behavior depends on the roots of the characteristic equation, s² + (_Ki + ₁)s + K_K1a. The system is overdamped when the two roots are real and distinct, critically damped when they are real and equal, and underdamped when they are a complex conjugate pair. Damping increases as K decreases toward unity. When the conductance ratio, K  1, (s)  1/[ C_M(s + ₁) ], the impedance of a passive or RC circuit. From Eq. 3, such passive behavior occurs when '_HF  0, which can happen when _HF approaches its upper limit at large depolarizations or is dominated by a leak (voltage-independent) conductance. Critical damping occurs when K = L, where

(10)

with T = _K1/₁ = _K1HF/C_M.

We first consider the second-order model in the absence of C_M (ionic current only). Sinusoidal currents result in a phase lead that reaches a maximum

(11)

at a frequency, f_MAX = (1/2_K)K^1/2 (Fig. 1A1, ). At lower frequencies, phase approaches zero because the sinusoidal variation in current is so slow that the voltage can reach a quasi-steady state predicted by the slope conductance (_LF). Phase also approaches zero for very high frequencies because current variations are so much faster than activation kinetics that the conductance will not vary from _HF. As frequency increases, gain (impedance) grows from 1/_LF to 1/_HF (Fig. 1A, ). Adding C_M results in a second pole with a corner frequency, f_C = 1/2₁ (Fig. 1, A and A1 ). Introducing the additional pole of the third-order model affects gain and phase only slightly (Fig. 1, A and A1 ).

View larger version (26K): [in this window] [in a new window]   Fig. 1. Top: Bode plotsgains (A) and phases (A1) vs. frequencycalculated from linearized Hodgkin-Huxley theory with the following parameters: activation rate constants (K1 and K2), 62.8 and 628 s1; steady-state (LF) and instantaneous (HF) conductances, 50 and 10 nS; capacitance (C), 10 pF. Four versions of the model are shown (see key): 2nd- and 3rd-order models with and without capacitance (ionic only). When activation was 1st-order, the rate constant was 62.8 s1. Middle: effects of varying activation rate constants on Bode plotsgains (B) and phases (B1) vs. frequency. In all calculations, HF = 10 nS, LF = 50 nS, CM = 10 pF. Third-order model with K1 of 10, 100, and 1,000 s1 (see key); K2 was set to 10 times K1 in all cases. Increasing K1 shifts the maximal gains and phase leads to higher frequencies and narrows the tuning curve. Bottom: effects of varying the ratio, K = LF/HF, on Bode plotsgains (C1) and phases (C2) vs. frequency. All parameters are as in A and A1 except LF = 10, 30, and 100 nS with K =1, 3, and 10 (see key). Tuning becomes sharper as K increases.

The pole associated with C_M can interact with channel kinetics. As _K approaches ₁, the increase in gain (Fig. 1B) and the corresponding phase lead (Fig. 1B1) become progressively restricted along the frequency axis and tuning becomes sharper. Tuning is characterized by a best frequency (BF), where the gain is maximum, and a bandwidth (BW) defined by the two points at which gain is attenuated by 3 dB from maximum. A conventional measure of tuning sharpness is the dimensionless ratio, Q = BF/BW. In Fig. 1B, as _K1 increases from 10 to 1,000 rad/s while ₁ is kept at 1,000 rad/s, the best frequency increases from 14.5 to 340 Hz and Q increases from 0.16 to 1.4. For fixed values of _K and ₁, tuning increases in parallel with the ratio, K = _HF/_LF. This is illustrated in Fig. 1, C and C1, where Q increases from 0 to 1.55 as K increases from 1 to 10; for the particular parameters used, critical damping occurs at K = 4.5.

Step responses, S(t), provide a convenient empirical test of damping (Fig. 2A). Except when K = 1, the initial part of the response will overshoot its steady-state value. When the system is overdamped, which for the parameters of Fig. 2A occurs when K < 1.8, the voltage approaches its final value exponentially from above. Slight underdamping at K = 3 results in only a small (2-3%) undershooting of the final value. As K is increases to 10, clear oscillations occur. Step responses are affected by two other variables, channel kinetics and current-step amplitude. The slower the kinetics, the more overdamped the response (Fig. 2B). This can be explained by an increase in _K1, leading to increases in T and L. As current-step size is increased, the response can be underdamped at one step size (Fig. 2C, 30 mV) but overdamped for either smaller or larger steps (Fig. 2C, 50 and 10 mV). The reasons are as follows. When current (and voltage) decrease from optimal, there is a decrease in K and an increase in _K. The increase in _K usually outweighs any increase in ₁ and results in an increase in T and L. Increasing current (and voltage) beyond optimal lowers K more rapidly than it does T (and L), the decrease in T being limited by both _K and ₁ reaching near-minimal values.

View larger version (9K): [in this window] [in a new window]   Fig. 2. Step responses calculated from linearized 2nd-order Hodgkin-Huxley theory. A: influence of K = LF/HF. Activation rate constant, K1 = 200 s-1; K is varied by setting LF = 10, 30 and 100 nS, while keeping HF = 10 nS. Critical damping occurs at K =1.8, but even at K =3 there is only a slight undershoot, 2.3% of the steady-state value. Modest oscillations, amounting to 1 1/2 cycles occur at K =10. B: expected step responses for various kinds of hair cells based on typical parameters obtained from voltage-clamp responses. Responses are scaled inversely proportional to LF with steady-state amplitude of fast type II cell being set to unity. For all cells, CM = 10 pF. Type I: LF = 100 nS, HF = 20 nS, K1 = 20 s-1; slow type II: LF = 50 nS, HF = 20 nS, K1 = 50 s-1; fast type II: LF = 20 nS, HF = 4 nS, K1 = 200 s-1. C: effects of current amplitude and steady-state voltage on step responses for a single cell whose instantaneous conductance was calculated from a steady-state Boltzmann activation curve HF = gMAX/{1 + exp[(V  V1/2)/VS]} + gL with gMAX = 30 nS, gL = 1 nS, V1/2 = 35 mV, VS = 5 mV, and CM = 14 pF. Activation time constant, 30, 7.5, and 5 ms for steady-state voltages, V, of 50, 30 and 10 mV, respectively. For graphical simplicity, all responses are plotted with a steady-state value of unity.

The following procedures were used to estimate parameters at a particular voltage, , from voltage-clamp data. C_M was estimated by fitting exponentials to brief (3-ms) voltage clamps. Conductances were obtained from steady-state I-V curves. _LF was calculated as a slope conductance at , while _HF was obtained as a chord conductance between and v_K = 87 mV. For both conductances, we subtracted the corresponding leak conductance obtained when the current was deactivated. Activation time constants, _K1 and _K2, were determined by fitting equation 6 to activation data (see, for example, Brichta et al. 2002, Fig. 7, B-D).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

Hair cells were classified based on the outwardly rectifying currents they displayed (Brichta et al. 2002). Cells with a slow, noninactivating, outward rectifying current active at voltages more negative than 57 mV were considered to have I_K,L. In all cases, we verified that the current could be deactivated by hyperpolarizations to 100 mV. If a cell had I_K,L, it was classified as type I. In most, although not in all cases, cells with I_K,L had constricted necks so their morphology was consistent with their classification as type I. Cells whose outward currents only activated more positive than 57 mV were considered type II. In addition to their having a more depolarized activation range than type I cells, almost all peripheral type II cells had outward currents with faster activation kinetics and relatively small maximal whole cell conductances. Such type II cells could also be distinguished by the lack of a constricted neck and by conspicuous inward currents. Although some central type II cells had slow activation, the other criteria served to distinguish them from type I cells.

Type II cells were classified by their half-activation (t_1/2) times on being depolarized from a holding potential of 67 to 37 mV. Cells were called fast if t_1/2 < 7.5 ms, intermediate if t_1/2 was between 7.5 and 15 ms, and slow if t_1/2 > 15 ms.

Responses to brief current clamps

We used brief (200-ms) current steps to compare various hair cells in terms of their steady-state voltage-current (V-I) and impedance-current (Z-I) curves and their resonant properties as indicated by the presence of ringing in current-clamp responses.

VOLTAGE-CURRENT AND IMPEDANCE-CURRENT CURVES. Because of the presence of I_{K, L}, type I hair cells have more hyperpolarized resting potentials and lower impedances than do type II hair cells. As a result, more outward current is needed to depolarize a type I cell to a given voltage. This is seen in Fig. 3, which compares current-clamp responses for the two kinds of hair cells. Results for individual hair cells are shown above (Fig. 3, A and B); population results, below (Fig. 3, C and D).

View larger version (27K): [in this window] [in a new window]   Fig. 3. Voltage responses to 200-ms current steps ranging from 50 to 500 pA. A and B: voltage-current (V-I) curves for a type I hair cell (A) and a type II hair cell (B) with individual voltage responses in insets. For the type I cell, depolarization to 50 mV () is not reached with a 500-pA current, whereas for the type II cell a 170-pA current suffices (). C and D: mean V-I and impedance-current (Z-I) curves for 20 type I cells (C) and for 19 central, 16 planum, and 6 torus type II cells plotted separately and collectively (D); error bars are SE. Impedances were measured from the slopes of the V-I curves taken during the last 5 ms of current steps. Most type I cells have such low impedances that large currents (>500 pA) are needed to depolarize the cells to 50 mV from their resting potential; smaller currents (20-100 pA) will depolarize type II cells to the same level. V-I and Z-I curves are similar for planum and torus cells.

RESONANT PROPERTIES OF HAIR CELLS. Hair cells from vibratory and auditory organs of nonmammalian vertebrates show marked oscillatory responses to current steps (for review, see Fettiplace and Fuchs 1999). In contrast, most vestibular hair cells show modestly underdamped responses (Baird 1994; Correia and Lang 1990; Eatock et al. 1998; Weng and Correia 1999). The same was true for our hair cells. Typical current-step responses are shown for three hair cells, a fast type II (Fig. 4A), a slow type II (Fig. 4B), and a type I hair cell (Fig. 4C). Responses were reasonably well fit by equations from the third-order linearized Hodgkin-Huxley theory (Eq. 8; Fig. 4D). Such fits were used to determine the best frequency (BF) and tuning quality (Q) of individual hair cells.

View larger version (13K): [in this window] [in a new window]   Fig. 4. Responses to 200-ms current steps of 3 hair cells. The first 50 ms of each response is shown. Currents (pA) are stated to the right of each trace. A: over a limited voltage range of currents (50-100 pA), a fast type II cell shows an underdamped response consisting of 1 1/2 cycles. B: in a type II central cell with slow activation kinetics, it is unclear whether the responses are underdamped or overdamped. C: responses of a type I cell are overdamped. D: recorded voltages () for the 3 cells of A-C are fit by linearized 2nd-order Hodgkin-Huxley theory (). Currents were 50 (top), 20 (middle), and 100 pA (bottom). Vertical calibrations, 5 (top and middle) and 10 mV (bottom). Horizontal calibrations, all records, 20 ms.

Responses to sinusoidal currents

Type II hair cells harvested from the peripheral zone near the planum or near the torus have similar responses to 200-ms current steps. On this basis, we suggested that the large differences in discharge between afferents innervating these two regions could not be accounted for by their basolateral currents. As a further test of this suggestion, we used sinusoidal stimuli similar to those used in our afferent studies (Brichta and Goldberg 2000). A larger than expected difference in the responses of type I and type II hair cells was observed. Because the difference can be related to the fact that the sinusoidal currents were presented on a constant depolarizing current, we first turn to the need for the latter.

BACKGROUND CURRENT. We have justified the use of a background current by considering the need for Ca²⁺ currents and neurotransmitter release under resting conditions. Other more pragmatic reasons also suggested the use of a background current. One reason had to do with outward rectification. For most of our hair cells, whether type I or type II, only a fraction of their outward currents was activated at the resting potential. As a result, without the presence of a background current, responses to sinusoidal stimuli were asymmetric. An example is provided by a type I cell (Fig. 5A). In its response to sinusoidal currents, the cell has a hyperpolarizing response more than 15 times larger than its depolarizing response. This may be contrasted with the almost linear behavior of afferents to rotation sinusoids. In addition, the large nonlinearity would preclude a linear analysis of the responses. Introduction of a background current, presented as a step just before the sinusoid, eliminates the problem in type I cells but introduces a feature in type II cells that is not paralleled in afferent discharge.

View larger version (22K): [in this window] [in a new window]   Fig. 5. Responses to sinusoidal currents with and without background currents. A: a type I cell. Traces with (top) and without (bottom) a 200-pA depolarizing current step. The current step eliminates much of the response asymmetry (outward rectification) and leads to a more sinusoidal voltage response. B: a fast type II cell harvested near the planum. A 200-pA current step initially depolarizes the cell by 23 mV. Over the next 40 s, the depolarization increases by 28 mV, and the sinusoidal gain increases threefold. C: a fast type II cell was presented with a persistent holding current of 47.5 pA. Both the superimposed sinusoidal current (top) and the voltage response (bottom) are asymmetric, being smaller in the depolarizing direction. The response (voltage) asymmetry is more pronounced than the stimulus (current) asymmetry. Sinusoidal currents: 0.5 Hz, ±100 pA (A); 0.3 Hz, ±100 pA (B); 1.0 Hz, ±23.9 pA (C).

GAIN AND PHASE. Traces occurring over several cycles were averaged into 32-point single-cycle displays. This was done for both current input and voltage output. By fitting sine waves to both curves, we were able to calculate gains and phases. Displays based on responses to 1-Hz sinusoids are shown for two fast type II cells (Fig. 6, A and B) and a type I cell (Fig. 6C). Several differences can be noted between type I and type II cells. First, background currents, which were comparable in Fig. 6, B and C, resulted in more positive voltages in the type II cells. Second, even though the amplitudes of sinusoidal currents were similar in all three cases, the type II peak-to-peak voltage responses were about 40 mV, while the corresponding type I response was <4 mV. In short, the type II impedances were >10 times larger than the type I impedance. Third, voltage was in phase with current for the type II cells, but led current by 25-30° in the type I cell.

View larger version (18K): [in this window] [in a new window]   Fig. 6. Voltage responses to 1-Hz sinusoidal currents presented on background currents. Voltages and currents over several cycles (256 points/cycle) are averaged into a single cycle (32 points/cycle). Curves are least-squares sinusoidal fits. A: a fast type II cell from the planum. Background current of 19.5 pA (dashed horizontal line) gives rise to a background voltage of 43.4 mV (unbroken horizontal line). The peak depolarization of 23.5 pA leads to a depolarizing response of 14.9 mV; the hyperpolarizing values are 17.8 pA and 21.4 mV. The average impedance is 870 M, with a depolarizing impedance of 635 M and a hyperpolarizing impedance of 1,200 M. B: a fast type II cell from the torus; 950 M (average), 800 M (depolarizing), and 1,050 M (hyperpolarizing impedance). C: a type I hair cell; 69.5 M (average), 62.2 M (depolarizing), and 75.2 M (hyperpolarizing impedance).

View larger version (22K): [in this window] [in a new window]   Fig. 7. Bode plots for 2 hair cells. A and B: a type I hair cell. Background current, 46 pA; sinusoidal current, ± 23.6 pA. Data () are fit by 3 curves. Best fit: Bode plots predicted from linearized 2nd-order Hodgkin-Huxley theory (text Eq. 9) with parameters chosen to give best fit. VC fit: calculated from same version of linearized theory with parameters obtained from 200-ms voltage clamps. RC fit: best fit assuming only a voltage-independent current. There is a peak in the gain curve between 10 and 30 Hz and in the phase curve between 3 and 10 Hz. The peaks reflect an active conductance. The actual low-frequency gain is 47 M as compared with a gain of 27 M predicted from voltage clamps. C and D: a central fast type II hair cell. Background current, 19.8 pA; sinusoidal current, ±23.5 pA. Gains and phases are well fit by passive curve (RC fit). There are no peaks corresponding to the predictions from short voltage clamps (VC fit). Furthermore, the actual impedance is 10 times higher than the impedance predicted from voltage-clamp data and more than 20 times higher than the actual impedance of the type I cell (A).

View larger version (23K): [in this window] [in a new window]   Fig. 8. Bode plots for 10 type I hair cells (A and B), for 6 slow type II hair cells (C and D), and for 10 fast type II cells (E and F). Gain curves are to the left and phase curves to the right. A and B: with 2 exceptions, type I cells show peaks in their gain and phase curves, The exceptions (dashed lines) were almost fully activated, which implies that the ratio, K = LF/HF, approached unity. Under these conditions, linearized Hodgkin-Huxley theory predicts that gain and phase curves should lack peaks. C and D: all of the gain and phase curves for slow type II cells show peaks. E and F: fast type II cells have high-impedances and their gain and phase curves resemble those of RC filters. Results are similar for fast type II cells obtained from the central zone (n = 1) or from the peripheral zone near the torus (n = 4) or near the planum (n = 5).

Long-term inactivation

One difficulty in interpreting the results of the preceding section was our inability to depolarize type I hair cells to the same extent as type II cells (cf. Fig. 6, B and C). To overcome this difficulty, we sometimes used larger background currents of 100 or 200 pA in type I cells without affecting the results. It, nevertheless, seemed important to study long-term inactivation under more controlled conditions.

This was done in voltage clamp by holding each cell at 67 mV and then stepping to 47 mV for 60 s before returning to 67 mV. Throughout the trial, responses to brief hyperpolarizing pulses provided independent estimates of conductance. Results are shown for three hair cells in Fig. 9 with original traces to the left and conductance measurements to the right. The type I cell shows a 20% conductance decrease over the 60-s voltage step, while the conductance of the fast type II cell is almost completely inactivated. In this respect, the slow type II cell is intermediate in its behavior. For 13 cells, the conductance curves during the step to 47 mV, excluding the first 1 s of the step, were fit by a single exponential. There was no evidence that time constants differed for the three groups. The average time constant was 10.7 ± 2.3 s for the 13 cells.

View larger version (31K): [in this window] [in a new window]   Fig. 9. Left: Voltage clamps in which each hair cell was stepped from 67 to 47 mV for 60 s and then returned to 67 mV. Every 0.5 s a 25-ms hyperpolarizing (10 mV) step was introduced to measure the conductance, which is plotted to the right. The type I cell (top) shows minimal long-term inactivation. The fast type II cell (bottom) shows almost complete inactivation. The slow type II cell (middle) shows intermediate behavior. The declines in conductance are fit with exponential functions (smooth curves) in all three cases; time constants were 14 (top), 9.4 (middle), and 6.9 s (bottom).

Statistics bearing on long-term inactivation are summarized in Table 3. Type I cells show no inactivation at 1 s and 25% inactivation at 60 s. In contrast, fast type II cells show, on average, 78% inactivation, about half of which takes place in the first second. Slow type II cells resemble type I cells in showing little inactivation during the first second, but resemble fast type II cells in showing a >50% conductance decline between 1 and 60 s. The latter observation is an indication that fast and slow inactivation are not tightly coupled. Further evidence comes from fast type II cells, which show no correlation between the two kinds of inactivation. Overall, the difference in gains of fast type II and type I cells after a 60-s depolarization is 25-fold, similar to the 20-fold difference seen with sinusoids.