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Voltage-Gated Outward K Currents in Frog Saccular Hair Cells

Dipartimento di Biologia Cellulare e Molecolare, Università di Perugia, I-06123 Perugia, Italy

Submitted 28 March 2003; accepted in final form 4 September 2003

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX DISCLOSURES ACKNOWLEDGMENTS REFERENCES

 
A biophysical analysis of the voltage-gated K (K_v) currents of frog saccular hair cells enzymatically isolated with bacterial protease VIII was carried out, and their contribution to the cell electrical response was addressed by a modeling approach. Based on steady-state and kinetic properties of inactivation, two distinct K_v currents were found: a fast inactivating I_A and a delayed rectifier I_DRK. I_A exhibited a strongly hyperpolarized inactivation V_1/2 (-83 mV), a relatively rapid single exponential recovery from inactivation (_rec of 100 ms at -100 mV), and fast activation and deactivation kinetics. I_DRK showed instead a less-hyperpolarized inactivation V_1/2 (-48 mV), a slower, double-exponential recovery from inactivation (_rec1 490 ms and _rec2 4,960 ms at -100 mV), and slower activation and deactivation kinetics. Steady-state activation gave a V_1/2 and a k of -46.2 and 8.2 mV for I_A and -48.3 and 4.2 mV for I_DRK. Both currents were not appreciably blocked by bath application of 10 mM TEA, but were inhibited by 4-AP, with I_DRK displaying a higher sensitivity. I_DRK also showed a relatively low affinity to linopirdine, being half blocked at 50 µM. Steady-state and kinetic properties of I_DRK and I_A were described by 2nd- and 3rd-order Hodgkin–Huxley models, respectively. The goodness of our quantitative description of the K_v currents was validated by including I_A and I_DRK in a theoretical model of saccular hair cell electrical activity and by comparing the simulated responses with those obtained experimentally. This thorough description of the I_DRK and I_A will contribute toward understanding the role of these currents in the electrical response on this preparation.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX DISCLOSURES ACKNOWLEDGMENTS REFERENCES

 
Sensory epithelia of inner ear organs transduce mechanical stimuli into electrical responses, a process involving the highly specialized hair cells. In many hair cells of lower vertebrates, injection of depolarizing currents evokes damped voltage oscillations, whose frequency and quality factor are tuned to the frequency selectivity and sharpness of the sensory organ (Crawford and Fettiplace 1981; Fettiplace and Fuchs 1999). The characteristics of the oscillatory response vary among tissues and are strictly dependent on the types of ion currents present in each specific hair cell. In general, the interplay between depolarizing currents (i.e., mechanotransducing nonselective cation currents and Ca currents) and repolarizing currents (i.e., K_v currents, inward-rectifying K and large-conductance Ca-activated K (BK) currents) shapes the oscillatory response. At least 2 types of K_v current have been described in hair cells, differing primarily in their inactivation properties. The transient K_v current (I_A) exhibits relatively fast inactivation kinetics, and a steady-state inactivation midpoint V_1/2 of -80 to -90 mV (Griguer et al. 1993; Hudspeth and Lewis 1988a; Lang and Correia 1989; Lewis and Hudspeth 1983; Masetto et al. 1994; Murrow and Fuchs 1990; Smotherman and Narins 1999a, b). At the normal resting potential of the hair cell I_A will be mostly unavailable, and its relevance to the cell's electrical behavior has been questioned (Hudspeth and Lewis 1988a; Murrow and Fuchs 1990; Smotherman and Narins 1999a; but see Masetto et al. 1994). The other K_v conductance, reported for several hair cell preparations, displays slow and sometimes incomplete inactivation. Its inactivation V_1/2 varies among hair cells by as much as 40 mV (range from -50 to -90 mV), suggesting that the molecular counterpart of this current is not uniform among different hair cells. This current is usually referred to as delayed rectifier K current (I_DRK; Fuchs and Evans 1990; Goodman and Art 1996; Lang and Correia 1989; Marcotti et al. 1999; Masetto et al. 1994; Smotherman and Narins 1999a; Sugihara and Furukawa 1995). In the tissues where this current is available at physiologically relevant membrane potentials, its role in the control of the electrical response has been proposed and supported by pharmacological tests (Armstrong and Roberts 1998; Goodman and Art 1996).

The frog sacculus has been extensively used as an experimental model to investigate the role of basolateral ion channels in the electrical response of hair cells (Ashmore 1983; Holt and Eatock 1995; Hudspeth and Lewis 1988a, b; Lewis and Hudspeth 1983). Most studies have used papain-dissociated frog saccular hair cells, where 2 ion conductances are activated in response to depolarizing pulses from the resting potential: a voltage-gated Ca current and a BK current (Holt and Eatock 1995; Hudspeth and Lewis 1988a; Lewis and Hudspeth 1983; Roberts et al. 1990). An additional fast-inactivating I_A was also reported, but was recruited only if depolarizations were preceded by hyperpolarizing conditioning pulses, indicating that this current was normally not functional at the cell's resting potential (Hudspeth and Lewis 1988a; Lewis and Hudspeth 1983). There was no evidence for I_DRK in these papain-dissociated hair cells. Accordingly, both experimental data and modeling studies indicated that the interplay between voltagegated Ca currents and BK currents was sufficient to account for the electrical responses recorded from these cells (Holt and Eatock 1995; Hudspeth and Lewis 1988b). The frequency response of these papain-dissociated hair cells (80–160 Hz; Armstrong and Roberts 1998; Holt and Eatock 1995; Lewis and Hudspeth 1983) was, however, markedly higher than the frequency range the organ in situ is tuned for (20–100 Hz; Koyama et al. 1982; Lewis 1988; Yu et al. 1991). This discrepancy led a number of investigators to conclude that the electrical characteristics of these cells were not major determinants in frequency discrimination (Eatock et al. 1993; Lewis 1988).

Recently it was found that papain alters the electrophysiological properties of saccular hair cells. Frog saccular hair cells in undissociated (in situ) epithelial preparations, subjected to neither enzymatic treatment nor mechanical cell dissociation, possess a transient IBTX-sensitive BK current and a sustained (or slowly inactivating) 4-AP–sensitive K_v current, in addition to the A- and sustained BK currents (Armstrong and Roberts 1998). In situ hair cells display in addition a resonant frequency response matching the tuning frequency range of the organ in vivo (Armstrong and Roberts 1998), stimulating intense interest in these newly reported K currents. However, whereas the partially inactivating BK current has been the subject of extensive investigation (Armstrong and Roberts 2001), the sustained, 4-AP–sensitive K_v current has, to our knowledge, been neglected.

We recently reported that the isolation of frog saccular hair cells with the bacterial protease VIII instead of papain preserves the pattern of outward K currents and the electrical response of the undissociated (in situ) hair cells (Catacuzzeno et al. 2003). This isolation procedure has allowed us to investigate the biophysical properties of the K_v currents of frog saccular hair cells to a level of detail required to model the electrical response of these cells.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX DISCLOSURES ACKNOWLEDGMENTS REFERENCES

 
Hair cell preparation

Frogs (Rana esculenta) obtained from local suppliers were chilled and decapitated according to the Animal Experimentation guidelines of the University of Perugia. The dissociation of hair cells was described previously (Catacuzzeno et al. 2003; Holt et al. 2001). Briefly, the saccular epithelium was removed from the organ, and incubated for 3 min in a low-Ca solution containing 0.25 mg/ml protease VIII (P-5380, Sigma). The epithelium was then transferred to a low-calcium solution containing 0.5 mg/ml BSA for 15 min to stop the enzymatic reaction, and subsequently into a petri dish where the hair cells were mechanically dissociated by gently rubbing the saccular epithelium with a fine tungsten filament. For electrophysiological recordings hair cells were transferred to concanavalin A–coated petri dishes to allow cell adhesion. The experiments described in this study were all carried out on cylindrical hair cells, the most abundant cell type in this preparation (Chabbert 1997).

Electrophysiology

Macroscopic currents were recorded using the perforated-patch method (Horn and Marty 1988). Borosilicate pipettes (Hilgenberg GmbH, Malsfeld, Germany), pulled with a programmable puller (PUL-100; WPI, Sarasota, FL) were used. Their resistance ranged between 3 and 6 M when filled with standard pipette solution. Electrical access to the cytoplasm was obtained by adding amphotericin B to the pipette solution. Stock solutions of amphotericin B (A-4888, Sigma; 50 mg/ml in DMSO) were stored at -20°C for a maximum of 8 h. The working solution of amphotericin B (4 µl of stock per ml of pipette solution) was prepared about every 40 min and kept at 0°C in the dark. A series resistance R_s of 20–30 M (measured using the Membrane Test routine of the pClamp software) was usually achieved within 15 min of attaining the cell-attached configuration. Although at least 50% of the R_s was compensated, a significant uncompensated R_s component remained (ranging between 10 and 15 M), which would introduce significant errors in the applied (command) voltage, V_com, when large currents were recorded. V_com was thus always corrected for errors attributed to R_s by subtracting IR_s (i.e., the amount of voltage drop across R_s, where I is the current being measured): V_real = V_com - IR_s. The voltage applied was also corrected for the liquid junction potential, estimated to be -13 mV under our recording conditions using the method developed by Neher (1992). Currents were amplified with a List EPC-7 amplifier (List Medical Instruments, Darmstadt, Germany), and digitized with a 12-bit A/D converter (DigiData 1200 interface; Axon Instruments, Union City, CA). The pClamp software package (version 7.0; Axon Instruments) was used on a Compaq Pentium PC for generating the command voltage pulses, recording and archiving the currents, and preliminary analysis of the data. For on-line data collection, current signals were normally filtered at 5 kHz and sampled at 25–50 µs/point. All recordings and procedures were performed at room temperature (18–22°C).

Solutions and pharmacological agents

The low-Ca solution used for the cell dissociation procedure contained (in mM): 110 Na, 2 K, 0.05 Ca, 110 Cl, 3 D-glucose, 5 HEPES. The physiological salt solution (PSS) used for current clamp experiments contained (in mM): 112 Na, 2 K, 1.8 Ca, 0.7 Mg, 119 Cl, 3 D-glucose, 5 MOPS. Frog saccular hair cells possess a variety of ion currents, including voltage-gated K and Ca currents, Ca-activated K (mainly BK) currents, and hyperpolarization-activated currents (Armstrong and Roberts 1998, 2001; Catacuzzeno et al. 2003; Holt and Eatock 1995; Hudspeth and Lewis 1988a; Lewis and Hudspeth 1983; Roberts et al. 1990). To isolate the K_v current from the Ca current and the coupled BK current under voltage-clamp the external Ca was lowered to 100 µM (replaced with Mg), and the Ca channel blocker Cd (100 µM) was added to the bath solution. Under these conditions, the Ca current and the BK current were fully suppressed, as indicated by the lack of effect on the macroscopic outward current of the BK channel blocker IBTX (200 nM; n = 4), and reduction of external Ca to 10 µM (n = 4). Previous studies on hair cells have demonstrated that millimolar concentrations of Cd significantly affected steady-state properties of K_v currents (Smotherman and Narins 1999a, b). Although we also observed an effect of millimolar Cd on K_v current gating on our preparation, dedicated experiments clearly indicated that the low-Cd concentration we used (100 µM) had no effect on the steady-state current parameters (n = 6). To exclude the possibility that hyperpolarization-activated currents could make a significant contribution in the voltage range tested only hair cells with high membrane resistance at -90 mV (R_m > 1 G) were used. Solutions containing 4-AP and TEA were prepared by equimolar substitution for NaCl. The standard pipette solution contained (in mM): 114 K, 114 aspartate, 0.08 Ca, 4 Cl, 2 Mg, 5 MOPS, 1 EGTA. All solutions were adjusted to a pH of 7.25. All reagents were from Sigma (St. Louis, MO), with the exception of IBTX, which was obtained from Alomone Labs (Israel).

Data analysis

The time course of the current, as well as kinetic and steady-state parameters were fitted with the indicated equations by using the Simplex algorithm incorporated in Microcal Origin v 4.1. The ² statistic was used as an indicator of the quality of the fit (Dempster 1993). Unless otherwise indicated, ² values for the fits to the experimental data shown in the RESULTS section correspond to levels of significance probability lower than 0.05 (the degrees of freedom being given by n_obs - n_p, where n_obs is the number of experimental points used in the fitting procedure and n_p is the number of free parameters). A comparison of the ² values was used to ascertain the order of the Hodgkin–Huxley model (N) chosen to describe I_A and I_DRK. The number of exponential components necessary to fit the inactivation time courses was determined by comparing the sums of squares generated for the different fits, using the quantity F = (S_f - S_g)(n - k_g)/(S_gk_f), where S_f, S_g, and k_f, k_g are, respectively, the residual sum of squares and number of parameters for each consecutive model (i.e., f and g), and n is the number of points in the data set (cf. Dempster 1993). The higher-order model g was accepted if the quantity F was higher than the value of the f-distribution with k_f and n - k_g degrees of freedom for a level of significance probability of 0.05.

Results are expressed as means ± SE. Statistical differences between means were analyzed using the t-test, which does not assume equal variances. Where appropriate the significance level of probability (P) for the difference between mean values are given.

Hodgkin–Huxley modeling of the K_v currents

In this study we describe the 2 K_v currents, I_A and I_DRK, with the Hodgkin–Huxley model (Hodgkin and Huxley 1952). This formalism assumes that an ion channel has one or more independent gates, each of which can reside in a permissive (m) or in a nonpermissive ("1 - m") state, according to the following kinetic scheme

where and are the transition rates from "1 - m" to m and from m to "1 - m", respectively. The probability P_o, that the channel is in the open (conductive) state, assumed to happen when all gates are in the m state, is given by

(1)

where m_i(V, t) is the probability of the ith gate being in the m state, with i extending over all the independent gates considered. The change over time of m_i(V, t) is described by

or, alternatively

(2)

where m_i(V, ), the steady-state probability of the ith gate being in the m state, and _i(V), the relaxation time constant of the kinetic scheme, are related to and by the relationships

If membrane voltage does not change with time (i.e. under voltage-clamp conditions) Eq. 2 can be analytically solved to give (Connor and Stevens 1971)

(3)

where m₀ is the probability of m at t = 0.

MODELING THE I_DRK. Using the formalism described above, I_DRK could be modeled using 2 equal and independent activation gates, giving

(4)

where P_DRK is the maximal K permeability through DRK channels; V is the membrane voltage; K_i and K_o are the intracellular and extracellular K concentrations, respectively; and R, T, and F have their usual meanings. m_DRK(V, t) was assessed from Eq. 2 using the experimentally determined m_DRK(V, ) and _DRK(V). In particular, their voltage dependency was described by

(5)

and

(6)

with

Equation (4) neglects I_DRK inactivation because 1) its kinetics are too slow (the fastest inactivation time constant was 3.6 s) to appreciably affect the current and voltage changes within the time range examined in our modeling (t 1.2 s); and 2) given the relatively depolarized inactivation V_1/2 ( -48 mV) and high voltage sensitivity (k 4.5 mV), it is assumed that this current is fully available within the physiological range of resting membrane potentials of saccular hair cells (-70 to -60 mV; Armstrong and Roberts 1998; Catacuzzeno et al. 2003).

MODELING THE I_A. I_A was described by a combination of 3 activation gates and 2 inactivation gates, according to the following relationship

(7)

where P_A is the maximal K permeability through A channels. m_A(V, t), h₁(V, t), and h₂(V, t) were computed according to Eq. 2, with

(8)

(9)

(10)

(11)

and _2(h) = 300 ms at all membrane potentials. a₁(V) was found to follow a Boltzmann-like relationship

(12)

All the parameters in the right-hand side of Eqs. 5, 6, and 8–12 were determined experimentally, and are presented in Table 1.

Modeling the electrical response of hair cells

The electrical (voltage) response in the absence of BK currents (i.e., in the presence of IBTX) was modeled by solving the following current-clamp equation, that includes all the other major ion currents of this preparation

(13)

where I_com(t) is the current flowing through the model circuit; C_m is the cell membrane capacitance; I_Ca(V, t) is the voltage-gated Ca current; I_K1(V, t) and I_h(V, t) are the hyperpolarization-activated K and cation currents, respectively; and I_L(V) is the leakage current. I_A(V, t) and I_DRK(V, t) were modeled according to Eqs. 4–12 described above. The other currents were modeled using the parameters taken from published results for this preparation (Armstrong and Roberts 1998; Holt and Eatock 1995; Hudspeth and Lewis 1988a). A brief description of these currents can be found in the APPENDIX.

Modeling of membrane potential changes was performed with programs implemented in C, solving Eqs. 2, 4–13, and A1–A7 by a 4th-order Runge–Kutta algorithm (Press et al. 1992) with a fixed step size of 10 µs. A 10 times reduction in the time step used for the computation did not appreciably change the simulated curves. The current parameters reported in Table 1 were used. P_DRK, P_A, g_h, and C_m were estimated from the same saccular hair cell used to compare the simulated versus experimental electrical response. In particular P_DRK and P_A were estimated by assessing the early and late inactivating current by applying inactivation protocols similar to that shown in Fig. 1, and g_h was assessed from the current amplitude at the K equilibrium potential. Finally g_Ca and g_k1 were adjusted by visual inspection until a well reproducible voltage response was obtained. For the assessment of I_DRK and I_A activity during electrical (oscillatory) response of a saccular hair cell (cf. Fig. 11), Eqs. 4 and 7 were solved using a voltage trajectory experimentally recorded from a saccular hair cell bathed in PSS.

View larger version (32K): [in this window] [in a new window]   FIG. 1. Kv current of frog saccular hair cells consists of 2 components. A: family of currents evoked with depolarizing steps from -70 to +30 mV, in 10-mV steps, from a holding potential of -90 mV. B: mean current density vs. voltage relationships obtained from experiments on 10 different cells, similar to that shown in A. Current amplitudes were assessed either at peak (closed symbols) or at 1.2 s from beginning of depolarizing pulse (open symbols). C: family of currents evoked with depolarizing steps to -10 mV, after 30-s conditioning pulses from -120 to -20 mV, in 10-mV steps. Dashed line represents zero current level. D: plot of current density vs. conditioning potential assessed for peak (closed symbols) and sustained current (measured at 1.2 s from beginning of depolarizing pulse; open symbols) for cell shown in C. Solid line represents best fit of peak current densities with double Boltzmann relationship (Eq. 14). Best-fit parameters are a = 0.055 nA/pF, V1/2(a) = -87.7 mV, ka = 3.33 mV, b = 0.0376 nA/pF, V1/2(b) = -49.0 mV, kb = 4.08 mV, and c = 0.0101 nA/pF. Dotted line represents best fit of sustained current densities with Boltzmann relationship as follows: I = a/{1 + exp[(V - V1/2)/k]} + b. Best-fit parameters are a = 0.028 nA/pF, V1/2 = -49.8 mV, k = 4.05 mV, and b = 0.0087 nA/pF.

View larger version (15K): [in this window] [in a new window]   FIG. 11. Contribution of IDRK and IA to electrical activity of frog saccular hair cells. A: voltage traces obtained in response to current injection (100 pA) on a saccular hair cell held in PSS external solution and after addition of 1 mM 4-AP. B: estimated open probability of IA and IDRK (top plot) during a membrane potential trajectory obtained from a current-clamp experiment of a saccular hair cell stimulated with a 20-pA depolarizing current step (bottom plot).

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX DISCLOSURES ACKNOWLEDGMENTS REFERENCES

 
Two distinct K_v currents are present in frog saccular hair cells

Under the conditions used to isolate the voltage-gated K_v current (cf. METHODS), 1.2-s depolarizing pulses from -70 to +30 mV, from a holding potential of -90 mV, evoked voltage-gated outward currents characterized by a relatively fast but incomplete inactivation (Fig. 1, A and B), suggesting the presence of multiple current components. To explore this possibility, steady-state inactivation protocols, consisting of a series of 30-s prepulses from -120 to -20 mV, in steps of 10 mV, followed by a test pulse to -10 mV were applied (Fig. 1C). With very negative prepulses (< -90 mV), the test current at -10 mV rapidly reached a peak and then declined to about 50% by the end of the pulse. With less negative prepulse voltages the evoked current would progressively decrease its inactivating component, until at a prepulse voltage of -60 mV no transient component could be recorded. In contrast, within the prepulse range -120 to -60 mV, the sustained component was unaltered (Fig. 1C). Further depolarization of the prepulse now resulted in a progressive decrease of the noninactivating component that reached about 10% of the peak current with a prepulse of -20 mV. Figure 1D shows current density versus conditioning voltage for the cell shown in Fig. 1C. Current densities were measured at the peak, and after 1.2 s from the beginning of the depolarizing pulse, when current inactivation had stabilized. The decrease in peak current versus prepulse voltage was described by 2 distinct phases (closed symbols, Fig. 1D), indicating the presence of at least 2 inactivation processes with different stabilities. Data were well fitted (solid line) by the following double Boltzmann function

(14)

This behavior was observed in all cells tested (n = 10), with mean values for half inactivation voltage and voltage steepness for the 2 Boltzmann components: V_1/2(a) = -83 ± 1.7 mV, V_1/2(b) = -48.6 ± 2.0 mV, k_a = 3.9 ± 0.2 mV, and k_b = 4.5 ± 0.3 mV (mean ± SE). a, b, and c, the current density amplitudes of the 2 inactivating components, and of the noninactivating portion of the current had mean values of 39 ± 5, 40 ± 8, and 10.1 ± 1.5 pA/pF, respectively. Current densities taken at 1.2 s from the beginning of the depolarizing pulse inactivated with a single phase (open symbols, Fig. 1D). The data points were well fitted by a single Boltzmann component (dotted line) with a mean V_1/2 of -48.7 ± 1.9 mV and k of 4.8 ± 0.4 mV, values not significantly different from those of the inactivating component with more depolarized V_1/2, as measured at the peak current (P > 0.1). The noninactivating component was 11.2 ± 1.8 pA/pF. These results indicate the presence of 2 outward K_v currents principally distinguished by their inactivation parameters. Specifically, a fast inactivating K current I_A, already described in papain-dissociated saccular hair cells, and in other hair cell preparations (Griguer et al. 1993; Hudspeth and Lewis 1988a; Lang and Correia 1989; Lewis and Hudspeth 1983; Masetto et al. 1994; Murrow and Fuchs 1990; Smotherman and Narins 1999a, b), and a slowly activating and inactivating K current I_DRK, similar in appearance to the delayed rectifier K current observed in undissociated (in situ) saccular hair cells (Armstrong and Roberts 1998) and in chick and turtle basilar papilla (Fuchs and Evans 1990; Goodman and Art 1996).

All hair cells probed with the above protocol exhibited a significant noninactivating residual current that persisted even at the most depolarized conditioning pulses (c in Eq. 14). Most of this residual current appeared to originate from incomplete inactivation of I_DRK, attributed to insufficient prepulse duration. Cells held at -10 mV for more than 30 s displayed a residual, holding current smaller than that observed in the inactivation protocol shown above (cf. Fig. 5A). In addition the inactivation time course of I_DRK revealed a very slow exponential component ( 20 s, at -30 mV; cf. Fig. 4, D and E), that would be consistent with an incomplete inactivation for 30-s conditioning pulses used in the inactivation protocol.

View larger version (15K): [in this window] [in a new window]   FIG. 5. Steady-state activation of IA. A: family of IA currents isolated by applying pulse protocol illustrated below that allowed isolation of IA. B: plot of mean K permeability vs. voltage obtained from 5 different experiments, 3 of which were similar to that shown in A and 2 obtained by subtracting current traces obtained from holding potential of -70 and -100 mV. Permeability of IA was obtained as ratio between peak current and driving force for K ions, taken as V(F2/RT)(Ki - Ko e-FV/RT)/(1 - e-FV/RT). Solid line represents best fit of experimental data with Boltzmann relationship PA = PA(max)/{1 + exp[-(V - V1/2)/k]}. Parameters obtained are PA(max) = 1.07 x 10-13 L/s, V1/2 = -46.2 mV, and k = 8.2 mV. Dotted line represents best fit of experimental data with relationship PA = PA(max)/{1 + exp[-(V - V1/2)/k]}3, with best-fit parameters PA(max) = 1.08 x 10-13 L/s, V1/2 = -61 mV, and k = 10.7 mV. Dashed line represents steady-state inactivation of IA assessed in Fig. 1 [scaled to match PA(max)].

View larger version (25K): [in this window] [in a new window]   FIG. 4. Activation and inactivation kinetics of IDRK. A: family of currents evoked with depolarizing steps from -50 to +30 mV, from holding potential of -60 mV. Smooth, black lines are best fits to data with a 2nd-order Hodgkin–Huxley model. B: tail (deactivating) currents obtained by repolarizing membrane at varying voltages (from -50 to -85 mV, in 5-mV steps), after IDRK had been activated with a 400-ms voltage step to -10 mV. Holding potential was -60 mV. Smooth lines are best fits to data with a single-exponential function. C: plot of mean activation (closed symbols) and deactivation time constants (x2, open symbols) vs. membrane potential, obtained from 8 experiments similar to those shown in A and B. Solid line represents best fit of experimental data with Eq. 6. Best-fit parameters are P1 = 0.00323 s-1; P2 = -20.9209 mV; P3 = 0.003 s-1; P4 = 1,466.97 s-1; P5 = 5.96571 mV; P6 = 0.00928 s-1. D: family of current traces evoked by long (60-s) depolarizing steps at -30, -10, and +10 mV, from holding potential of -90 mV. Current decay in time interval 1–60 s was fitted with double-exponential function I = Af exp(-t/f) + As exp(-t/s) + Ainf (superimposed smooth lines). Best-fit parameters are as follows: trace at -30 mV: f = 4,421 ms, Af = 0.147 nA, s = 20,424 ms, As = 0.395 nA, Ainf = 0.06 nA; trace at +10 mV: f = 4,106 ms, Af = 0.264 nA, s = 34,305 ms, As = 0.575 nA, Ainf = 0.119 nA. E: plot of mean inactivation time constant vs. voltage obtained from 8 experiments similar to that shown in D. Fast component vs. voltage could be fitted by constant function of 3,623 ms. Slow component was fitted with relationship: s = s(0) exp(V/k). Best-fit parameters are s(0) = 24,252 ms and k = 103 mV. F: plot of fractional amplitude of fast exponential component vs. voltage. Data were fitted with relationship af /(af + as) = A0 exp(V/k) + A1. Best-fit parameters are A0 = 0.288, A1 = 0.242, and k = 85.6 mV.

RECOVERY FROM INACTIVATION. Further evidence for the presence of 2 distinct K_v current components in saccular hair cells comes from their different rate of recovery from inactivation. Figure 2A shows current traces obtained from a voltage protocol that allows measurement of recovery from inactivation of the total K_v current. The current was first inactivated by holding the cell at -10 mV. A subsequent repolarizing step to -100 mV of variable duration was then applied to allow recovery of the K_v current, the amount of which was assessed by a final 1.2-s depolarizing test pulse. For short repolarizing pulses (300 ms) the recovered current evoked by the test pulse inactivated almost completely (Fig. 2A; t = 30, 100, and 300 ms). Increasing the duration of the repolarizing pulse revealed the presence and increased the amplitude of the sustained current. This complex behavior of recovery from inactivation of the K_v current provides further evidence for the presence of 2 distinct K_v current components, the I_A and I_DRK.

View larger version (34K): [in this window] [in a new window]   FIG. 2. Recovery from inactivation of IDRK and IA. A: family of currents evoked with pulse protocol illustrated below. Cell was held at holding potential of -10 mV to fully inactivate Kv current. Membrane was then repolarized at -100 mV for varying times (30, 100, 300, 1,000, and 3,000 ms; indicated in figure), and finally depolarized to -10 mV to evaluate amount of Kv current recovered from inactivation. B: plot of recovery from inactivation of Kv current vs. repolarizing pulse duration for peak current (squares) and current at 1.2 s from beginning of pulse at -10 mV (circles). Data points for recovery at 1.2 s were fitted with a double-exponential function as follows: frec(1.2) = a[1 - exp(-t/1)] + (1 - a)[1 - exp(-t/2)]. Best-fit parameters are a = 0.62, 1 = 527 ms, and 2 = 6,147 ms. Data points of peak current recovery could be fitted with triple-exponential function: frec(peak) = a[1 - exp(-t/1)] + b[1 - exp(-t/2)] + (1 - a - b)[1 - exp(-t/3)], where 1 and 2 were held fixed to values found from fit of recovery data at 1.2 s. Best-fit free parameters are a = 0.33, b = 0.059, and 3 = 87 ms. Inset: plot showing recovery functions over 0- to 50-ms interval for IDRK and IA obtained from fit described above. C: current traces evoked by 1.2-s depolarizations to +40 mV, after hyperpolarizing cell to -100 mV for varying times, from holding potential of -60 mV (which inactivated IA). D: plot of mean fractional recovery from inactivation vs. repolarizing prepulse duration assessed for peak currents at +40 mV from 4 experiments similar to that shown in C. Data points were fitted by a single-exponential function having time constant of 102.6 ms (solid line).

The rates of recovery from inactivation of the I_A and I_DRK shown in Fig. 2A were assessed by measuring the current amplitudes at the peak and at 1.2 s, respectively (Fig. 2B). Recovery of the I_DRK, measured at 1.2 s, when I_A had fully inactivated, was fitted by a double-exponential function, with mean time constants of 491 ± 22 and 4,964 ± 1,183 ms, with the fractional contribution of the fast component being of 0.53 ± 0.09 (n = 3). The rate of recovery of the peak current, used to assess the recovery of I_A, but also containing the I_DRK, was described by the sum of 3 exponentials, 2 of which are associated with the sustained I_DRK. The additional 3rd exponential component resulting from the rate of recovery of I_A is much faster, having a time constant of 90 ± 15 ms (n = 3). The fast, single-exponential recovery from inactivation of I_A was confirmed by applying the stimulation protocol illustrated in Fig. 2C. Cells were held at -60 mV, a potential that will fully inactivate I_A, but not alter I_DRK (cf. Fig. 1). Recovery of I_A was achieved by subjecting the cells to a -100-mV hyperpolarizing pulse of variable duration, and assessed by applying a depolarizing pulse to +40 mV. As shown in Fig. 2D, peak current versus hyperpolarizing pulse duration could be described by a single-exponential function (solid line) with a time constant of 102.6 ms (n = 3), a value close to that determined in Fig. 2, A and B. Based on the observed differences on steady-state and recovery from inactivation, the 2 outward K_v current components can be isolated and their kinetic and pharmacological features studied in detail.

The I_DRK

STEADY-STATE ACTIVATION. The properties of I_DRK were studied by stepping from a holding potential of -70 mV (where virtually all the I_A is inactivated; cf. Fig. 1, C and D). Under these conditions depolarizing pulses from -70 to +30 mV evoked currents showing little or no inactivation during the first few hundred milliseconds (Fig. 3A) as expected for I_DRK. The voltage dependency of steady-state I_DRK activation was determined from tail currents measured immediately after repolarization to -60 mV (Fig. 3A). Tail current amplitudes increased with depolarization up to about -30 mV (Fig. 3B). For depolarizations more positive than -30 mV, tail current amplitudes tended to decrease. In the voltage range -70 to -30 mV experimental data could be fitted by a Boltzmann relationship (solid line, Fig. 3B) with an activation V_1/2 of -48.3 mV and a slope factor k of 4.19 mV. Possible explanations for the observed tail current reduction at the more depolarized potentials include the presence of a fast, voltage-dependent inactivation gating or a voltage-dependent block of I_DRK by an unknown intracellular component. We did not investigate this aspect further. Superimposing the steady-state I_DRK activation and inactivation curve (Fig. 3B; dashed line, from Fig. 1D) reveals that the 2 processes develop over the same voltage range.

View larger version (17K): [in this window] [in a new window]   FIG. 3. Steady-state activation of IDRK. A: family of currents evoked by depolarizing steps from -70 to +30 mV, from holding potential of -70 mV. Holding potential was chosen to obtain a nearly complete steady-state inactivation of IA. B: plot of mean normalized tail currents (taken 250 µs after beginning of repolarizing pulse) vs. voltage obtained from 8 different experiments similar to that shown in A. Solid line represents best fit of experimental data (in voltage range -70 to -30 mV) with Boltzmann relationship Itail = Itail(max)/{1 + exp[-(V - V1/2)/k]} + b. Parameters obtained are Itail(max) = 1.002, V1/2 = -48.3 mV, k = 4.19 mV, and b = -0.0133. Dashed line represents mean steady-state inactivation curve of IDRK assessed as shown in Fig. 1D.

ACTIVATION AND INACTIVATION KINETICS. The activation time course of the current in response to depolarizing steps was sigmoidal, and could be well described by a Hodgkin–Huxley model with 2 activation gates over the voltage range examined (Fig. 4A, smooth lines). Deactivation time courses followed a single-exponential function (Fig. 4B). The calculated time constants for activation and deactivation ranged from 2.7 ± 0.09 ms at +40 mV to 40 ± 6 ms at -55 mV (n = 8), and displayed a bell-shaped voltage sensitivity (Fig. 4C).

Inactivation of I_DRK was very slow, requiring long duration depolarizing pulses to chart its progress (Fig. 4D). In all cells tested (n = 8) the inactivation time course approximated a double-exponential function (Fig. 4D, smooth lines). The fast time constant was voltage independent over the voltage range -30 to +10 mV, and had a mean value of 3.6 ± 0.3 s (Fig. 4E). The slow component had a small, but significant, voltage dependency, increasing from 20 ± 2 s at -30 mV to 29 ± 3 s at +10 mV (P < 0.05; n = 8; Fig. 4E). The amplitudes of the 2 fitted exponentials were also weakly, but not significantly, voltage dependent (P > 0.1; Fig. 4F), with the fast exponential component giving a fractional contribution of 0.53 ± 0.12 at -30 mV and of 0.41 ± 0.13 at +10 mV.

The I_A

I_A was isolated from I_DRK by 2 different methods, both giving similar results. The 1st method takes advantage of the faster time course of I_A recovery from inactivation, as compared to I_DRK (cf. Fig. 2). Hair cells were held at a holding potential of -10 mV at which both K_v currents were fully inactivated. I_A could be essentially isolated by applying depolarizing test pulses, preceded by a 100-ms conditioning pulse to -100 mV, sufficient to recover almost exclusively the I_A (cf. inset of Fig. 2B). This protocol is shown in Fig. 5A, where a family of outward currents showing a high degree of inactivation were recorded. The 2nd method was to evoke outward K currents from 2 different holding potentials, -70 and -100 mV, and revealed I_A by subtraction of the resulting current traces. A pharmacological isolation was not available because of the lack of selective I_DRK inhibitors (cf. next section).

STEADY-STATE ACTIVATION. The voltage dependency of I_A activation was obtained by plotting the peak K permeability at different voltages, as estimated from experiments similar to that shown in Fig. 5A (n = 3), or alternatively using the subtraction protocol (n = 2). I_A activated over a wider voltage range than that needed for I_DRK, indicating a smaller voltage dependency of gating (Fig. 5B). Data points fitted by a Boltzmann relationship gave a V_1/2 of -46.2 mV and a voltage steepness k of 8.2 mV (n = 5, solid line). The dotted line in Fig. 5B shows a fit of the experimental data with a 3rd-power Boltzmann relationship, giving a V_1/2 of -61 mV and a k of 10.7 mV. Comparison of the I_A activation and inactivation (dashed line, from Fig. 1D) curves shows that no significant overlap is observed, indicating that I_A is not available within its activation voltage range.

ACTIVATION AND INACTIVATION KINETICS. The time course of I_A activation was fitted by a 3rd-order Hodgkin–Huxley model (Fig. 6A, smooth lines). The goodness of fit was poor for the higher voltage range examined (P > 0.05, ² test), and was not improved by increasing the order, suggesting that current activation at high voltages deviates from a simplified independent particle model. The resulting time constants were well described by single-exponential functions of voltage with values decreasing from 5.2 ± 1.8 ms at -50 mV to 1.5 ± 0.4 ms at +10 mV (open symbols and solid line in Fig. 6C). Deactivation kinetics were assessed from the time course of the tail currents obtained in response to varying repolarizing voltages after a 20-ms depolarization to +40 mV (the remainder of the pulse protocol was as outlined above). Tail currents had a single-exponential time course (Fig. 6B), with time constants increasing with voltage from 8.2 ± 1.3 ms at -75 mV to 13.3 ± 1.9 ms at -55 mV (Fig. 6C, closed symbols). Inactivation of I_A during depolarizing pulses followed a double-exponential time course (Fig. 7A, smooth lines). Both time constants were voltage independent over the voltage range examined, and had mean values of 75 ± 10 and 322 ± 48 ms (Fig. 7C, open symbols). The relative contribution of the fast exponential component changed with voltage, increasing at negative voltages (inset of Fig. 7C). At membrane potentials lower than -30 mV, current decay was described by a single-exponential function in all cells examined (applying a further component did not improve the fit). Inactivation rates at membrane potentials lower than the threshold for activation of I_A were determined by evaluating the changes in peak current at +30 mV, following a conditioning prepulse of variable duration (50, 100, 300, 1,000 ms) at different subthreshold voltages (from -120 to -60 mV), from a holding potential of -90 mV. Figure 7B illustrates a typical experiment. Peak currents versus prepulse duration plots were described by a single-exponential function at all voltages examined (Fig. 7D), with the time constants showing a bell-shaped dependency on voltage (Fig. 7C, closed symbols).

View larger version (15K): [in this window] [in a new window]   FIG. 6. Activation and deactivation kinetics of IA. A: family of currents obtained in response to following pulse protocol, devised to isolate IA. Cell was held at holding potential of -10 mV to fully inactivate both IA and IDRK. Cell was then hyperpolarized to -100 mV for 50 ms to allow sole recovery of IA, which was subsequently activated by depolarizing pulses from -50 to +10 mV. Solid lines represent a 3rd-order Hodgkin–Huxley model fit to currents. B: family of currents obtained by repolarizing membrane from -55 to -75 mV, in 5-mV steps, after activation of IA with a depolarizing pulse to +40 mV. Isolation of IA was obtained with a pulse protocol as described in A. C: plot of mean activation (open symbols) and deactivation (x3, closed symbols) time constant vs. voltage obtained from 3 different cells by applying activation and deactivation protocols as described in A and B. Solid lines represent best fits to experimental data with Eq. 9. Best-fit parameters are a = 0.48 ms, b = -23.1 mV, and c = 1.14 ms for activation time constants, and a = 173.6 ms, b = 17.9 mV, and c = 5.4 ms for deactivation time constants.

View larger version (31K): [in this window] [in a new window]   FIG. 7. Inactivation kinetics of IA. A: family of currents obtained by depolarizing membrane from -50 to +30 mV, in 10-mV steps. To isolate IA, cells were held at holding potential of -10 mV to fully inactivate both IA and IDRK. Membrane was then hyperpolarized to -100 mV for 50 ms to allow sole recovery of IA. Superimposed solid lines are single-exponential (-50 and -40 mV) or double-exponential (from -30 to +30 mV) fits of decaying portion of current traces. B: families of currents obtained with 1.2-s depolarizing pulses to +30 mV, after a conditioning pulse to varying voltages (from -120 to -60 mV, in 10-mV steps) and for variable durations (50, 100, 300, and 1,000 ms, as indicated in figure). Holding potential was -90 mV. C: plot of mean inactivation time constants vs. test voltage obtained from 8 different cells by applying pulse protocols described in A (open symbols; n = 5) and B and D (closed symbols; n = 3). Solid line represents best fit of data points with Eq. 11, with C1 = 74 ms; C2 = 321.5 ms; C3 = -82 mV; C4 = 15.5 mV. Inset: plot of mean fractional amplitude of fast vs. voltage. Smooth line represents fit of data points with Eq. 12, with Ca = 0.54, V1/2(a) = -21.5 mV, and ka = 15.6 mV. D: plot of peak current at +30 mV vs. conditioning pulse duration for varying conditioning voltages. Cell is same as that used in B. Solid lines represent best fit of data points with single-exponential functions. Resulting time constants at varying conditioning voltages are: 61.6 ms at -120 mV; 85 ms at -110 mV; 127.4 ms at -100 mV; 388 ms at -80 mV; 169.4 ms at -70 mV; 103 ms at -60 mV.

Pharmacology of the K_v currents

Pharmacological tests on K_v currents used a voltage protocol consisting of 2 successive depolarizing steps, the 1st from a holding potential of -60 mV that would activate only the I_DRK, the 2nd preceded by a 100-ms hyperpolarization to -120 mV, allowing I_A to recover from inactivation (Fig. 8A). The effects of the blocking agents on I_DRK were evaluated from the steady-state current activated by both depolarizing steps to +40 mV, whereas the effects on I_A were evaluated from the peak current recovered after the hyperpolarizing step. Both current components were insensitive to 10 mM TEA (n = 5; P > 0.1; Fig. 8, A and E, top traces). In contrast, 4-AP blocked both K currents (Fig. 8A, bottom traces), but with different affinities. 4-AP at 1 mM blocked most of the I_DRK (the fractional inhibition of the steady-state current being 0.78 ± 0.06 at a membrane potential of -20 mV; n = 3; Fig. 8B), whereas it did not alter I_A. This is clearly shown by point-by-point subtraction of current traces, in control conditions and in the presence of 1 mM 4-AP (Fig. 8C), showing that 1 mM 4-AP–sensitive current does not possess fast inactivation. A 10-fold higher concentration of 4-AP was required to block I_A (Fig. 8B, bottom traces and Fig. 8E). The mean fractional inhibition of the peak current by 10 mM 4-AP was 0.54 ± 0.06 (n = 3). This higher concentration of 4-AP also increased the rate of inactivation of I_A (Fig. 8B). In 2 of the 3 cells tested a substantial steady-state current remained even at 10 mM 4-AP (the mean fractional inhibition of the steady-state current with 1 mM 4-AP was not significantly different from that observed with 10 mM 4-AP; P > 0.1; cf. Fig. 8, B and E), suggesting that a small 4-AP–insensitive, sustained current may contribute to I_DRK.

View larger version (36K): [in this window] [in a new window]   FIG. 8. Pharmacology of the Kv currents. A, B, D: representative current records showing effect of 10 mM TEA (A), 1 and 10 mM 4-AP (B), and 5, 10, and 50 µM linopirdine (D) on Kv current of frog saccular hair cells. Stimulation protocol consisted of repeated stimuli of 2 depolarizing steps separated by a 100-ms repolarization pulse to -120 mV to selectively recover IA (A and B) or of a single depolarizing step to 0 mV (D). Holding potential was -60 mV. C: families of currents obtained by applying depolarizing steps from -80 mV to +30 mV, in 10-mV steps, from holding potential of -90 mV, in control conditions (top panel), and after addition of 1 mM 4-AP to bath (middle panel). Family of currents in bottom panel is point-by-point subtraction of current traces in 1 mM 4-AP from current traces in control conditions. E: bar histogram showing mean blocking efficacy of TEA, 4-AP, and linopirdine on IDRK and IA. Blocking efficacy on IDRK was assessed from current amplitude at end of 1.2-s-long depolarizing pulse before and after addition of agent. Blocking efficacy on IA was evaluated from difference in IA before and after addition of drug. IA in control and test conditions was assessed from current amplitudes of 2nd and 1st depolarizing pulses, measured 20 ms from beginning of each pulse.

We also tested the inhibitory effect of linopirdine on I_DRK. This agent, a relatively selective inhibitor of the KCNQ channel family, has been reported to block both a delayed rectifier current component of gerbil and pigeon type II hair cells (Rennie et al. 2001), and mammalian inner and outer hair cells (Marcotti and Kros 1999; Oliver et al. 2003) with high affinity (IC₅₀ 5 µM). At 5 µM, linopirdine did not inhibit the I_DRK significantly (Fig. 8, D and E), whereas higher concentrations (10 and 50 µM) produced a significant block (Fig. 8, D and E).

Model results

The validity of the quantitative description of the I_A and I_DRK was tested by modeling both the macroscopic K_v currents and the electrical response of saccular hair cell. Figure 9 compares the experimental K_v currents obtained by depolarizing steps from -50 to -10 mV from holding potentials of -90 and -60 mV (left traces), with simulated current traces obtained for these voltage protocols (right traces). P_A and P_DRK for the modeled traces were adjusted to match those observed in the experimental traces, whereas the kinetic and steady-state parameters of the 2 currents were taken from the results presented above, summarized in Table 1 (see METHODS for details). The model provides a good simulation of the kinetics of the current over the voltage and time ranges examined, suggesting that this formalism can be an adequate starting point for modeling K_v currents of saccular hair cells.

View larger version (25K): [in this window] [in a new window]   FIG. 9. Modeling of the Kv current of frog saccular hair cells. Experimental (left) and modeled (right) currents obtained by applying depolarizing steps from -50 to -10 mV, in 10-mV steps, from holding potentials of -90 mV (top traces), or -60 mV (bottom traces). IA and IDRK were modeled by assuming a 2nd- and 3rd-order Hodgkin–Huxley model, respectively (cf. METHODS).

We further verified whether the quantitative description of the K_v currents could reproduce the electrical response of these cells under experimental conditions where the K_v currents are the principal repolarizing current (i.e., in the absence of BK current activity, achieved using 150 nM IBTX). Left-hand traces in Fig. 10 depict the two main types of voltage response we observed upon depolarizing current steps in the presence of 150 nM IBTX, both being qualitatively distinct from the electrical response obtained in the same preparation under control conditions (Catacuzzeno et al. 2003; Fig. 11A). Four out of the 10 cells tested responded with repetitive spiking activity at frequencies of a few tens of Hertz (Fig. 10, top left trace). This response appears similar to those obtained in undissociated saccular hair cells in the presence of TEA, an effective inhibitor of BK channels (Armstrong and Roberts 1998). The remainder responded with an isolated voltage inflection (Fig. 10, bottom left traces). The different voltage response seems related to the I_DRK density, given that discharging cells were found to have a significantly lower I_DRK than cells responding with an isolated hump (P < 0.05). Both types of electrical response could, however, be well reproduced by our model (see Fig. 10B, right-hand traces). Saccular hair cell membrane was modeled as an RC circuit containing the I_A and I_DRK investigated in this study, together with inward rectifier (I_K1 and I_h) and voltage-gated Ca currents (I_Ca) modeled according to the experimental data obtained previously in these cells (Armstrong and Roberts 1998; Holt and Eatock 1995; Lewis and Hudspeth 1988a; cf. APPENDIX). These results indicate that a Hodgkin–Huxley formalism of the I_A and I_DRK can be used in future investigation of saccular hair cell electrical activity.

View larger version (37K): [in this window] [in a new window]   FIG. 10. Modeling of electrical response of frog saccular hair cells. Experimental (left) and modeled (right) voltage responses of frog saccular hair cells over different time and current domains. Experimental traces, obtained in physiological salt solution (PSS) plus 150 nM IBTX to eliminate contribution of BK current to electrical response, are typical electrical responses of frog saccular hair cells under these conditions. Simulated electrical responses were obtained by modeling IA and IDRK using parameters reported in this study, and modeling other currents using published results (cf. APPENDIX for details). Cell-specific parameters used are reported in Table 1. Other parameters used in simulation were: top trace: PDRK = 4.2 10-14 L/s, PA = 1.08 10-13 L/s, gCa = 2.0 nS, gK1 = 3.0 nS, Cm = 16 pF; bottom trace: PDRK = 2.4 10-13 L/s, PA = 1.65 10-13 L/s, gCa = 1.1 nS, gK1 = 42 nS, Cm = 20 pF.

Contribution of K_v currents to the electrical response of frog saccular hair cells

The contribution of I_DRK to the electrical response of these cells was tested using 4-AP. 4-AP at 1 mM blocks most of the I_DRK, but does not alter I_A (cf. Fig. 8), or any of the other ion currents present in these cells (Armstrong and Roberts 1998). As shown in Fig. 11A, injection of depolarizing currents into hair cells bathed in PSS (with BK currents not blocked) resulted in a highly damped oscillatory voltage response, in agreement with previous reports (Armstrong and Roberts 1998; Catacuzzeno et al. 2003). Addition of 1 mM 4-AP to the external solution caused a complete loss of the oscillatory response (Fig. 11A) in 5 out of the 11 cells examined. In the remaining 6 cells the damped oscillatory response remained after 4-AP addition. The variability of the action of 4-AP on the oscillatory voltage response is likely to result from the marked variability in the contribution of I_BK versus I_DRK currents to the outward current in these cells (Armstrong and Roberts 1998; Catacuzzeno et al. 2003). These results suggest an important role for I_DRK in modulating the electrical behaviour of frog saccular hair cells.

In the absence of available selective inhibitors, the contribution of I_A to the oscillatory response was addressed by a modeling approach. Modeled I_A and I_DRK were voltage-clamped using as a template the electrical response of a saccular hair cell bathed in PSS. The time changes in open probability (P_o) during the electrical response were then assessed for I_DRK and I_A (Fig. 11B). It can be seen that I_DRK displays a significant activity (0.13 < P_o < 0.21), confirming its contribution to the electrical response. The observation that I_A activity remained extremely low (about 3 orders of magnitude smaller than I_DRK; cf. inset of Fig. 11B), attributed to I_A channels remaining in the inactivated state at the membrane potentials encountered during the electrical response (cf. Fig. 1), indicates that I_A does not contribute significantly to the cell's electrical activity.

	DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX DISCLOSURES ACKNOWLEDGMENTS REFERENCES

 
General

In spite of the functional relevance of K_v currents in the electrical response of frog saccular hair cells, their major biophysical properties have remained largely unexplored. This situation has most likely arisen from the distortion of the K_v currents associated with the commonly used papain-based enzymatic isolation procedure. Using an isolation method that we showed to preserve the in situ properties of the K_v currents (Catacuzzeno et al. 2003), we have attempted to provide a quantitative description of these currents, a prerequisite to understanding their role in shaping the electrical response of hair cells. Based on steady-state and kinetic properties of inactivation, 2 distinct K_v currents could be discerned: a fast inactivating I_A, and a delayed rectifier I_DRK. I_A exhibited a strongly hyperpolarized inactivation V_1/2 (-83 mV; Fig. 1), a relatively rapid single-exponential recovery from inactivation (_rec of 100 ms at -100 mV; Fig. 2), and fast activation and deactivation kinetics (Fig. 6). I_DRK showed instead a less-hyperpolarized inactivation V_1/2 (-48 mV; Fig. 1), a slower, double-exponential recovery from inactivation (_rec1 490 ms and _rec2 4960 ms at -100 mV; Fig. 2), and slower activation and deactivation kinetics (Fig. 4). The inactivation time course of both I_A and I_DRK was double exponential, suggesting that multiple channel types participate in each current component, or alternatively that these currents have complex inactivation gating. Both current components were not significantly inhibited by TEA up to a concentration of 10 mM, but were blocked by 4-AP, with I_DRK being more sensitive than I_A to this agent (Fig. 8).

Both these currents have already been reported in a variety of auditory and vestibular hair cell preparations. Slowly activating and inactivating I_DRK have been studied in hair cells of many inner ear organs, including turtle and chick cochleas, goldfish sacculus, frog semicircular canals (SCC) and basilar papilla, and pigeon semicircular canals (Fuchs and Evans 1990; Goodmann and Art 1996; Lang and Correia 1989; Masetto et al. 1994; Smotherman and Narins 1999a; Sugihara and Furukawa 1995). In frog sacculus, the I_DRK has only been reported to be present, no investigation being carried out to define its major properties (Armstrong and Roberts 1998; Catacuzzeno et al. 2003). The I_DRK we studied here shares several properties with the slowly inactivating K currents of goldfish oscillatory type saccular hair cells (Sugihara and Furukawa 1995) and turtle and chick cochlear hair cells (Fuchs and Evans 1990; Goodman and Art 1996), that is, high sensitivity to 4-AP, slow inactivation rate, activation range -60 to -20 mV, and inactivation V_1/2 -50 mV. It differs from the I_DRK of frog SCCs and from frog basilar papilla (another auditory organ of the frog). In both preparations it has been reported to have an inactivation V_1/2 -90 mV, that is, about 40 mV more hyperpolarized than the I_DRK studied here (Masetto et al. 1994; Smotherman and Narins 1999a). The I_DRK of frog SCC hair cells differed also for being insensitive to 4-AP concentrations as high as 10 mM (Marcotti et al. 1999; Masetto et al. 1994). Notably, this comparison shows that hair cells deriving from functionally similar and spatially very close inner ear organs from the same species (such as frog basilar papilla and sacculus) possess different K_v channels underlying I_DRK.

Fast transient I_A has been found in many hair cells, including frog SCCs, basilar and amphibian papilla, chick cochleas, mouse utricle and pigeon SCCs (Griguer et al. 1993; Lang and Correia 1989; Lennan et al. 1999; Masetto et al. 1994; Murrow and Fuchs 1990; Smotherman and Narins 1999a, b). I_A has been also reported in frog saccular hair cells isolated with papain (Hudspeth and Lewis 1988a; Lewis and Hudspeth 1983), indicating that this current, unlike the I_DRK, is not sensitive to the proteolytic action of this agent. We found a good match between the properties of frog saccular I_A reported here, and those of hair cells from other inner ear organs. Hair cell I_A always shows a relatively hyperpolarized inactivation V_1/2, and the major inactivation time constant usually less than a few hundred milliseconds. The voltage dependency of steady-state activation is also low. The I_A of frog saccular hair cells appeared to have a relatively low sensitivity to 4-AP, with 10 mM giving a fractional peak current block of 0.54. In this respect it differs from I_A in other frog auditory organs, such as the amphibian papilla where 1 mM 4-AP suppressed nearly all the I_A (Smotherman and Narins 1999b).

Because very few studies have addressed the expression of cloned K channel subunits in hair cells, it is not possible to identify the molecular counterparts of the K_v currents we have reported here. Recent pharmacological and biochemical evidence has suggested that the I_DRK found in several hair cells belongs to the KCNQ family (Kharkovets et al. 2000; Kubisch et al. 1999; Marcotti and Kros 1999; Oliver et al. 2003; Rennie et al. 2001), whose general electrophysiological properties include a relatively slow activation kinetics (_act 12 ms at +40 mV), a double-exponential inactivation time course (_inact 300 ms and 4 s), and inactivation V_1/2 -90 mV (Rennie et al. 2001). I_DRK showing all the properties of the mammalian KCNQ current was reported in frog SCC hair cells (Marcotti et al. 1999), providing electrophysiological evidence of the association of this hair cell I_DRK with the KCNQ family. The I_DRK we described here displays biophysical properties not matching those possessed by hair cell KCNQ current. Our pharmacological tests, giving a half block for I_DRK by linopirdine of about 50 µM, seem to further support the notion that neither of the K_v currents described here belongs to the KCNQ channel family. The IC₅₀ values reported for linopirdine block of cloned KCNQ channels (KCNQ1–3) are in fact markedly lower (<10 µM; Schnee and Brown 1998; Wang et al. 2000) than our value, and IC₅₀ even lower (0.6–5 µM) were reported on hair cells for K_v channels identified as KCNQ (Marcotti et al. 1999; Oliver et al. 2003; Rennie et al. 2001). In contrast, expressed KCNQ4 channels have been found to be not very sensitive to block by linopirdine (Kubisch et al. 1999; Sogaard et al. 2001). Our results with linopirdine therefore cannot be conclusive. Future tests with the more selective KCNQ channel antagonist XE991 (Wang et al. 1998) will provide more definitive evidence concerning the identity of the channel.

Kinetic modeling

We have provided a quantitative description of the K_v currents of frog saccular hair cells using a Hodgkin–Huxley formalism (Figs. 4, 6, and 7). Hodgkin–Huxley modeling of I_A in other preparations usually assumed 4 independent gating particles (Huguenard and McCormick 1992; Lockery and Spitzer 1992; but see Bekkers 2000), as was done in the original description of this current (Connor and Stevens 1971). In our study a 3rd-order model seemed to provide a better description of the data (Figs. 5 and 6). With regard to the I_DRK, a 2nd-order Hodgkin–Huxley model seemed to provide a good description of its main features, as also found for other hair cells I_DRK currents (Wu et al. 1995).

The Hodgkin–Huxley approach has been shown to have limitations in describing subtle properties of K_v current gating (Horrigan et al. 1999; Koren et al. 1990; Stefani et al. 1994; Zagotta and Aldrich 1990; Zagotta et al. 1994). Accordingly we found that at relatively depolarized potentials the fit of I_A activation time course deviated significantly from the experimental data (Fig. 6). In addition, the voltage dependency of the activation time constant required a segmental approach (Fig. 6). The Hodgkin–Huxley formalism, however, proved adequate for modeling the electrical response in a large number of cell preparations, including hair cells (Holt and Eatock 1995; Hudspeth and Lewis 1988a; Wu et al. 1995). Accordingly, our modeling results indicate that the electrical response of frog saccular hair cells could be well reproduced based on the Hodgkin–Huxley description of the K_v currents, under experimental conditions where these currents represented the main repolarizing currents (Figs. 9 and 10).

Functional role of the K_v currents

Several biophysical properties of the I_DRK we described here will assign an important role to this current in the electrical responses of frog saccular hair cells; that is, the I_DRK inactivation V_1/2 and k, found to be about -50 and 4.5 mV, respectively, indicate that a large fraction of the total I_DRK is available at the resting potential of these cells (-60 to -70 mV; Armstrong and Roberts 1998; Catacuzzeno et al. 2003), and thus may well contribute in shaping the receptor potential of saccular hair cells. Accordingly, relatively low concentrations of 4-AP that would selectively block this current, markedly altered the electrical response in many cells (cf. Fig. 11; Armstrong and Roberts 1998). Another feature of the I_DRK described here that would speak for an important role of this current in generating the electrical response is its voltage dependency of activation. We estimated a voltage steepness of activation k of 4.2 mV, a value unusually high for a sustained K_v current, which would translate into a significant change in I_DRK activation upon only a few millivolts change of the cell membrane potential. The frequency of hair cell electrical resonance has been usually found to be strictly dependent on the kinetics of the outward K current, with faster currents giving high frequency voltage oscillations (Fettiplace and Fuchs 1999; Goodman and Art 1996; Smotherman and Narins 1999b). I_DRK activation time course was at least 10 times lower than those of the BK current in many hair cells. Assuming that the slow kinetic I_DRK contributes significantly to the electrical response, these cells are expected to resonate at frequencies significantly lower than those observed on hair cells possessing the faster kinetic BK currents as the sole K current component. This is indeed the case of papain-dissociated hair cells where the I_DRK has been removed by the enzymatic treatment (frequency response 100–160 Hz; Catacuzzeno et al. 2003; Holt and Eatock 1995; Hudspeth and Lewis 1988b; Lewis and Hudspeth 1983). By contrast, the undissociated in situ preparation or hair cells subjected to isolation procedures that preserve the I_DRK resonate at lower frequencies, between 20 and 100 Hz (Armstrong and Roberts 1998; Catacuzzeno et al. 2003).

A contribution of I_A to the electrical response is unlikely because of its highly hyperpolarized inactivation V_1/2. This is suggested by our modeling results (cf. Fig. 11), which indicate a very low activity of I_A attributed to its high degree of inactivation at the membrane potentials encountered by the cell during the electrical response. These results suggest that of the 2 K_v currents, only I_DRK could significantly contribute to the electrical activity observed in saccular hair cells. However, efferent stimulation has been shown to hyperpolarize frog saccular hair cells by as much as 20 mV (Holt et al. 2001). Such a hyperpolarization could release a significant fraction of I_A inactivation, and the resulting increase in outward K current would diminish the amplitude of the receptor potential. Similar to what has been proposed for I_A in the chick cochlea and amphibian papilla (Murrow and Fuchs 1990; Smotherman and Narins 1999b), we think that this current may act in conjunction with efferent stimulation to modulate the receptor potential under inhibitory conditions.

	APPENDIX

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX DISCLOSURES ACKNOWLEDGMENTS REFERENCES

 
Modeling of the electrical response of frog saccular hair cells required the inclusion of the major ion currents operating in these cells under our recording conditions. In addition to the I_DRK and I_A described in this study the model included several other currents whose kinetic description and parameters were taken from the literature. A brief description of these currents follows.

Leakage current

The leakage current was modeled as I_L(V) = g_L(V - E_L), where g_L is the leakage conductance and E_L is its reversal potential.

K₁ current

The K₁ current was modeled using a single activation gate (Holt and Eatock 1995)

(A1)

where g_K1 is the maximal conductance for this current and m_K1(V, t) was assessed from Eq. 2 with

(A2)

and

(A3)

The h current

The h current was modeled using a modified Hodgkin–Huxley model with 3 independent activation gates, assuming that only 2 need to enter the m state to open the channel (Holt and Eatock 1995). This gives

(A4)

where g_h is the maximal h conductance. m_h(V, t) was assessed from Eq. 2 with m_h(V, ) and _h(V) given by relationships having the form of Eqs. A2 and A3.

Ca current

The Ca current has been shown to require a model with 3 independent activation gates (Armstrong and Roberts 1998; Hudspeth and Lewis 1988), giving

(A5)

where g_Ca is the maximal Ca conductance and E_Ca is the reversal potential for Ca ions. As for the other currents, m_Ca(V, t) can be assessed from Eq. 2. Model parameters of this current have already been published for papain-dissociated saccular hair cells (Holt and Eatock 1995; Hudspeth and Lewis 1988a). However, the papain-based cell dissociation has been demonstrated to alter the steady-state and kinetic properties of this current (Armstrong and Roberts 1998). For this reason we assessed m_Ca(V, ) and _Ca(V), as well as E_Ca, from the I–V, and _Ca versus voltage data reported by Armstrong and Roberts (1998) for undissociated saccular hair cell Ca current (symbols in Fig. A1, A and B). The experimental I–V data were well fitted (solid line in Fig. A1A) using the relationship: I_Ca/I_max = g_Ca(V - E_Ca)m_Ca(V, )³, with

(A6)

and the _Ca versus voltage data were well fitted (solid line in Fig. A1B) when _Ca(V) had the following form

(A7)

The parameters of the fit can be found in Table 1.

View larger version (10K): [in this window] [in a new window]   FIG. A1. Modeled Ca current. Normalized I–V (A) and activation time constant (m) vs. voltage (B) relationships (solid lines) for voltage-gated Ca current used in this study to model electrical activity of frog saccular hair cells. Curves were computed assuming a 3rd-order Hodgkin–Huxley model (see text for details), with parameters reported in Table 1. Symbols are experimental data from Armstrong and Roberts (1998).

	DISCLOSURES

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX DISCLOSURES ACKNOWLEDGMENTS REFERENCES

 
This work was supported by grant Cofin 2002058113 from the Italian Ministero dell'Università e della Ricerca Scientifica e Tecnologica.

	ACKNOWLEDGMENTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION APPENDIX DISCLOSURES ACKNOWLEDGMENTS REFERENCES

 
We thank S. Harper (University of Dundee) and W. Nonner (University of Miami) for useful comments on the manuscript.

	FOOTNOTES

 
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

Address for reprint requests and other correspondence: L. Catacuzzeno, Dipartimento di Biologia Cellulare e Molecolare, Università di Perugia, Via Pascoli 1, I-06123 Perugia, Italy (E-mail: fabiolab{at}unipg.it).

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