Spontaneous low-frequency voltage oscillations in frog saccular hair cells

Abstract

Spontaneous membrane voltage oscillations were found in 27 of 130 isolated frog saccular hair cells. Voltage oscillations had a mean peak-to-peak amplitude of 23 mV and a mean oscillatory frequency of 4.6 Hz. When compared with non-oscillatory cells, oscillatory cells had significantly greater hyperpolarization-activated and lower depolarization-activated current densities. Two components, the hyperpolarization-activated cation current, I_h, and the K⁺-selective inward-rectifier current, I_K1, contributed to the hyperpolarization-activated current, as assessed by the use of the I_K1-selective inhibitor Ba²⁺ and the I_h-selective inhibitor ZD-7288. Five depolarization-activated currents were present in these cells (transient I_BK, sustained I_BK, I_DRK, I_A, and I_Ca), and all were found to have significantly lower densities in oscillatory cells than in non-oscillatory cells (revealed by using TEA to block I_BK, 4-AP to block I_DRK, and prepulses at different voltages to isolate I_A). Bath application of either Ba²⁺ or ZD-7288 suppressed spontaneous voltage oscillations, indicating that I_h and I_K1 are required for generating this activity. On the contrary, TEA or Cd²⁺ did not inhibit this activity, suggesting that I_BK and I_Ca do not contribute. A mathematical model has been developed to test the interpretation derived from the pharmacological and biophysical data. This model indicates that spontaneous voltage oscillations can be generated when the electrophysiological features of oscillatory cells are used. The oscillatory behaviour is principally driven by the activity of I_K1 and I_h, with I_A playing a modulatory role. In addition, the model indicates that the high densities of depolarization-activated currents expressed by non-oscillatory cells help to stabilize the resting membrane potential, thus preventing the spontaneous oscillations.

Hair cells of the inner ear transduce movements of their hair bundle into electrical signals. Such a process involves the opening of mechanotransduction channels, hair cell depolarization, and basolateral synaptic release, resulting in a modulation of the rate of action potential discharge of the postsynaptic, afferent nerve fibres. When stimulated with depolarizing currents, the membrane potential of several types of hair cells undergoes damped sinusoidal oscillations, usually referred to as electrical resonance. In lower vertebrates this process contributes to frequency discrimination of the sensory organ (reviewed in Fettiplace & Fuchs, 1999). This electrical response to injected current is mainly determined by the interplay between a voltage-activated Ca²⁺ current and voltage- or Ca²⁺-activated K⁺ currents (Hudspeth & Lewis, 1988b; Wu et al. 1995). In addition, many lower vertebrate hair cells display spontaneous fluctuations of their resting membrane potential in the absence of external stimuli (Crawford & Fettiplace, 1980; Ashmore, 1983; Ospeck et al. 2001), and this activity has sometimes been linked to periodic interval histograms in the spontaneous firing of afferent fibres (Manley, 1979; Crawford & Fettiplace, 1980; Temchin, 1988). This spontaneous activity is usually found to be poorly coherent, to have a low peak-to-peak voltage amplitude (up to 10 mV) and high frequency (in the range 11–85 Hz in a frog saccular semi-intact preparation, Ashmore, 1983). In frog basilar papilla hair cells it has been found that this incoherent and low-amplitude spontaneous activity arises from the interaction of voltage-activated Ca²⁺ and Ca²⁺-activated K⁺ currents (Ospeck et al. 2001), as found for the stimulus-evoked electrical resonance. Here we present a novel form of spontaneous voltage oscillations recorded from ∼20% of isolated frog saccular hair cells. This activity differs markedly from that previously described, having higher coherence and voltage amplitude, lower oscillatory frequency, and different ionic basis.

The present investigation focused on the characterization of the spontaneous voltage oscillations, and the underlaying ionic basis. Because of the dissociated cell preparation, we did not address their functional role. Frog saccular hair cells possess a variety of voltage-activated conductances. Four depolarization-activated currents (the voltage-activated Ca²⁺ (I_Ca) and K⁺ (I_DRK) currents, and the transient (I_BKT) and sustained (I_BKS) BK currents) are thought to underlie their electrical resonance (Ashmore, 1983; Lewis & Hudspeth, 1983; Armstrong & Roberts, 1998; Catacuzzeno et al. 2003a,b). An additional fast transient voltage-activated K⁺ current (I_A) has been reported, but its physiological role is questionable, due to its high degree of inactivation at the resting potential (Hudspeth & Lewis, 1988a; Catacuzzeno et al. 2003b). Two hyperpolarization-activated currents, the K⁺-selective, inward-rectifier (I_K1) and the cation-selective (I_h) currents have also been reported, and are thought to contribute to setting the resting membrane potential (Holt & Eatock, 1995). Our electrophysiological data and modelling study show that the activity of I_K1, I_h, and I_A shapes the spontaneous voltage oscillations, while the other depolarization-activated currents have a stabilizing action on the membrane potential of non-oscillatory cells, thus preventing the spontaneous oscillations.

Methods

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 has been previously described (Holt et al. 2001; Catacuzzeno et al. 2003a). Briefly, the saccular epithelium was removed from the organ, and incubated for 3 min in low-Ca²⁺ solution containing 0.25 mg ml⁻¹ protease VIII (P-5380, Sigma). The epithelium was then transferred to a low-calcium solution containing 0.5 mg ml⁻¹ 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.

Electrophysiology

Voltage responses and macroscopic currents were recorded under current-clamp and voltage-clamp mode, respectively, using the perforated-patch method (Horn & Marty, 1988). Borosilicate pipettes (Hilgenberg GmbH, Malsfeld, Germany), pulled with a programmable puller (PUL-100; WPI, Sarasota, FL, USA) were used. Their resistance ranged between 3 and 6 MΩ 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⁻¹ 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 approximately every 40 min, and kept at 0°C in the dark. A series resistance, R_s, of 20–30 MΩ (measured using the Membrane Test routine of the pClamp software by applying 5 mV voltage steps, 5 ms in duration, from a holding potential of −70 mV) was usually achieved within 15 min of attaining the cell-attached configuration. The following findings indicated that the only current that could potentially activate within the 5-ms step of the voltage pulse around −70 mV, the fast activating I_K1, did not introduce a measurable bias in the estimation of R_s: (i) no significant difference was found in the mean R_s estimated in cells with, and in cells without I_K1; (ii) in four cells where R_s was assessed before and after the simultaneous block of I_K1 and I_h (using Ba²⁺ and ZD-7288), no significant difference was found; (iii) good capacitive compensation was always verified by assessing the magnitude of current transients at the beginning of a depolarizing step. Although at least 50% of the R_s was compensated, a significant uncompensated R_s component remained (ranging between 10 and 15 MΩ), 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 due to R_s by subtracting I R_s (i.e. the amount of voltage drop across R_s, where I is the current being measured):

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 (DigiData1200 interface; Axon Instruments Inc., Union City, CA, USA), or alternatively amplified and digitized with the EPC-10 amplifier (Heka Electronik, Germany). The pClamp software package (version 7.0; Axon Instruments Inc.) or the PULSE software (Heka Electronik, Germany) were 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 3 kHz and sampled at 25–50 μs point⁻¹. All recordings and procedures were performed at room temperature (18–22°C). All frog saccular hair cells studied here were first monitored under current-clamp mode, with no applied current, to assess whether they oscillated. Recording was then switched to the voltage-clamp mode to assess the biophysical and/or pharmacological properties of the voltage-activated currents. The cells used in this study had a clear cylindrical or club-shaped morphology. Cells with round-shaped morphology and grainy appearance, usually associated with unhealthy or deteriorated conditions, were discarded. The cell membrane capacitance measured 11.3 ± 2.1 pF (mean ± s.d.; n = 18; range 9.0–15.7 pF) in oscillatory cells, and 12.8 ± 3.1 pF (mean ± s.d.; n = 35; range 6.8–17.0 pF) in non-oscillatory cells. These values are not significantly different (P > 0.05).

Solutions and pharmacological agents

The low-Ca²⁺ solution used during the dissociation procedure contained (mm): 130 NaCl, 2.5 KCl, 0.8 CaCl₂, 5 MgCl₂, 5 MOPS, 2 EGTA, 3 glucose, 5 pyruvic acid, 1 Na-ascorbate. The physiological salt solution (PSS) used during recordings contained (mm): 112 Na⁺, 2 K⁺, 1.8 Ca²⁺, 0.7 Mg²⁺, 119 Cl⁻, 3 d-glucose, 5 MOPS. Solutions containing TEA were prepared by equimolar substitution for NaCl. The standard pipette solution contained (mm): 114 K⁺, 114 aspartate, 0.08 Ca²⁺, 4 Cl⁻, 2 Mg²⁺, 5 MOPS, 1 EGTA. The intracellular solution was chosen to be slightly hypotonic to assist the perforated-patch recording. All solutions were adjusted to a pH of 7.25. All reagents were from Sigma (St Louis, MO, USA), with the exception of ZD-7288 which was obtained from Tocris (Tocris Cookson Inc., UK).

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 4.1. The χ² statistic was used as an indicator of the quality of the fit (Dempster, 1993). χ² 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 (d.f.) 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). Normalized power spectra and autocorrelation functions on spontaneous voltage oscillations were assessed by using built-in functions of Microcal Origin 4.1. Modelling of membrane potential changes was performed with programs implemented in C, solving eqns (A1)–(A30) by a fourth-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 change the simulated curves appreciably. Assessment of current densities at specified membrane potentials was done by taking into account voltage errors due to series resistance. Specifically, current estimation was made by linear interpolation between the current points at the two closest voltages on the corrected I–V relationship. Results are expressed as mean ± s.e.m., unless stated otherwise. Statistical differences between means were analysed using the t test which does not assume equal variances. Where appropriate the significance level of probability (P) for the difference between mean values is given.

Results

Current clamp recordings

Under current-clamp mode with no applied command current, about 20% of the saccular hair cells tested (27 out of 130) displayed spontaneous voltage oscillations, an example of which is shown in Fig. 1A. The peak-to-peak amplitude of these oscillations ranged from 9.1 to 33.6 mV, with a mean of 23 ± 6.3 mV (mean ± s.d.; n = 27), and the oscillatory frequency (defined as the peak frequency in the power spectrum, cf. Fig. 1B) varied from 2.3 to 11.3 Hz, with a mean of 4.6 ± 1.9 Hz (mean ± s.d.; n = 27). The oscillatory activity was usually strongly coherent, as demonstrated by the autocorrelation function shown in the inset of Fig. 1B. There was some variability in the shape of voltage oscillations. In some cells the depolarizing and hyperpolarizing phases displayed markedly different rates, whereas in other cells voltage oscillations had a more sinusoidal shape, with similar rates in both depolarizing and hyperpolarizing directions.

Figure 1. Features of spontaneous voltage oscillations in frog saccular hair cells.

A, current-clamp recording of a frog saccular hair cell showing spontaneous membrane voltage oscillations at rest. B, normalized power spectrum and autocorrelation function (inset) for the voltage recording shown in A. C, voltage traces obtained from an oscillatory cell upon injection of the indicated holding current. D, plot of the oscillatory frequency (circles) and peak-to-peak voltage amplitude (squares) versus the injected current for the cell shown in C. E, current-clamp recording of a non-oscillatory cell at rest. The trace in the lower part of the panel represents a time and voltage expansion of a portion of the recording, showing the presence of small voltage fluctuations. F, normalized power spectrum and autocorrelation function (inset) for the voltage trace shown in E.

The oscillatory activity appeared to be a property of the resting state of the cell, its peak-to-peak amplitude being maximal with no applied command current, and decreasing upon application of both positive and negative injected currents. An example of this feature is shown in Fig. 1C and D, where an oscillatory cell was subjected to different holding currents. It can be seen that oscillations could be discerned only for zero and ±10 pA holding currents, vanishing completely at more positive or negative injected currents. Figure 1C and D also show that the oscillatory frequency decreases slightly with increasing positive injected currents. This small voltage dependence, seen in all oscillatory cells tested (n = 5), is contrary to that observed for the electrical resonance recorded from the same preparation (Catacuzzeno et al. 2003a), suggesting that distinct mechanisms underpin these two forms of electrical response.

Three morphologically different cell populations have been described in the frog saccular epithelium, differing in the length to apical width (LAD) ratio (Chabbert, 1997). The electrophysiological recordings presented in this study were made on central cylindrical (LAD lower than 4.5) and central club-shaped (LAD of 4.5–8) cells, both located in the central part of the saccular macula. We found a significant correlation between the incidence of spontaneous oscillatory activity and cell shape, with 70% (14 out of 20) of the central club-shaped cells, but only about 14% (9 out of 64) of central cylindrical cells displaying spontaneous oscillations.

In most saccular hair cells lacking spontaneous voltage oscillations, fluctuations of the membrane potential of smaller amplitude and much higher frequency were present (Fig. 1E). This activity resembles the resting resonance described in frog saccular (Ashmore, 1983) and basilar papilla (Ospeck et al. 2001) hair cells, and could be readily discriminated from the spontaneous voltage oscillations, having much smaller peak-to-peak voltage amplitudes, higher characteristic frequencies and lower coherence (Fig. 1F). Despite the presence of these voltage fluctuations, we refer to these cells as non-oscillatory, to distinguish them from those displaying coherent and high-amplitude spontaneous oscillatory activity, which is the focus of this study.

Voltage-clamp recordings

To understand the ionic basis of the spontaneous voltage oscillations, we compared the characteristics of voltage-activated currents of 18 oscillatory cells with those found in 35 non-oscillatory cells (i.e. cells showing either a stable resting membrane potential, or the small voltage fluctuations shown in Fig. 1E). Both depolarization- and hyperpolarization-activated currents were found to be markedly different in amplitude and temporal shape in these two cell populations (Fig. 2). In oscillatory cells 100 ms depolarizing voltage steps from a holding potential of −70 mV evoked, after a small blip of inward current, fully sustained outward currents (Fig. 2A, upper current traces). In non-oscillatory cells this protocol evoked a partially inactivating outward current with a more complex shape (Fig. 2B, upper current traces). The amplitude of these currents differed markedly, with a mean current density at −30 mV (measured at the end of the 100 ms depolarizing step) of 32.6 ± 4.3 pA pF⁻¹ in oscillatory cells (n = 18) and of 76.5 ± 6.1 pA pF⁻¹in non-oscillatory cells (n = 35; Fig. 2D). These current densities are significantly different (P < 0.01). A second, marked difference in current amplitude was found for the hyperpolarization-activated currents in the two cell populations (Fig. 2A and B, lower current traces). Mean current densities recorded on stepping to −120 mV were −80.8 ± 5.3 pA pF⁻¹in oscillatory cells (n = 18) and −30.5 ± 3.9 pA pF⁻¹ in non-oscillatory cells (n = 35; Fig. 2D; P < 0.01). The correlation between voltage-activated current amplitudes and the oscillatory activity is illustrated in Fig. 2C, where the current density at −30 mV is plotted against the current density at −120 mV for individual cells. Oscillatory cells are clustered in the lower-right quadrant of the plot, corresponding to high hyperpolarization- and low depolarization-activated current densities. A further difference in the macroscopic currents of the two cell populations is shown in Fig. 2D. The mean I–V relationships show that the flat region around the zero-current potential is more extended in oscillatory cells compared to non-oscillatory cells, due to a higher activation threshold for depolarization-activated currents. This behaviour is highlighted in the inset of Fig. 2D, where an expansion of the mean I–V relationships around the oscillatory voltage range (indicated by the grey bar) is made. Whereas the depolarization-activated currents of non-oscillatory cells slightly activate in the depolarized region of the oscillatory range, those of oscillatory cells activate at more depolarized membrane potentials, suggesting that their contribution to the oscillatory activity is minimal.

Figure 2. Macroscopic currents of oscillatory and non-oscillatory cells.

A and B, families of current traces obtained by either depolarizing (upper current trace families) or hyperpolarizing (lower current trace families) voltage pulses from a holding potential of −70 mV, in 10 mV steps, for an oscillatory (A) and a non-oscillatory (B) cell. The voltage traces in the upper part of each panel represent the resting current-clamp behaviour of the corresponding cells. C, plot of the current density at −30 mV versus current density at −120 mV for 53 saccular hair cells. Each cell was tested for the presence of spontaneous voltage oscillations under current-clamp mode, and oscillatory and non-oscillatory cells are indicated in the plot by closed and open symbols, respectively. D, mean current density versus voltage relationship assessed from 18 oscillatory and 35 non-oscillatory cells. Inset, expansion of the mean I–V relationships in the voltage range of the oscillations. The grey bar indicates the mean minimum and maximum voltages found in the 18 oscillatory cells. Where not shown, s.e.m. values are smaller than the symbol size.

Dissection of ionic currents in oscillatory and non-oscillatory cells

Pharmacological dissection and biophysical protocols were applied in order to identify the current components responsible for the observed differences in the total current amplitude in oscillatory and non-oscillatory cells. The voltage protocols adopted for current dissection were in accordance with previous studies on the same preparation (Holt & Eatock, 1995; Armstrong & Roberts, 1998, 2001; Catacuzzeno et al. 2003a,b).

Hyperpolarization-activated currents

Two hyperpolarization-activated currents have been reported in frog saccular hair cells, I_K1 and I_h (Holt & Eatock, 1995). To pharmacologically dissect these currents we either used 100 μm Ba²⁺, an agent shown to be highly selective for I_K1 over I_h in these cells (Holt & Eatock, 1995), or 100 μm ZD-7288, a selective inhibitor of I_h in both cardiac pacemaker and neuronal preparations (BoSmith et al. 1993; Gasparini & DiFrancesco, 1997). In all oscillatory cells tested, 100 μm Ba²⁺ strongly inhibited the hyperpolarization-activated currents (Fig. 3A). The slowly activating inward current remaining after application of Ba²⁺ was irreversibly suppressed by the addition of ZD-7288 (100 μm) to the bathing solution (Fig. 3A). In the presence of both Ba²⁺ and ZD-7288, only a small, time independent, leakage current was recorded (see Fig. 3A and C). These results indicate that both I_K1 and I_h are present in oscillatory cells. The effect of 100 μm Ba²⁺ on non-oscillatory cells was much more variable. The two extremes, where the Ba²⁺-sensitive current was virtually absent (left traces), and where it was of comparable magnitude to that found in oscillatory cells (right traces), are shown in Fig. 3B. Similarly to oscillatory cells, all non-oscillatory cells possessed a Ba²⁺-insensitive and ZD-7288-sensitive component of the hyperpolarization-activated current, and a leakage current (Fig. 3B). I_K1 and I_h, identified using these pharmacological manipulations, were measured for several cells belonging to both populations. The mean results are presented in Fig. 3D. Significant differences were found for both I_h and I_K1 in the two cell populations at −120 mV of applied potential. In particular, the Ba²⁺-sensitive component was markedly higher in oscillatory cells, suggesting that the principal difference in the hyperpolarization-activated current found in the two cell populations is due to different mean I_K1 densities.

Figure 3. Pharmacological dissection of the hyperpolarization-activated currents in oscillatory and non-oscillatory cells.

A,B, current traces obtained with hyperpolarizing steps from −60 mV to −120 mV in an oscillatory (A) and two non-oscillatory (B) cells, in control conditions, and after bath application of 100 μm Ba²⁺ or 100 μm Ba²⁺ plus 100 μm ZD-7288, in succession. C, I–V relationship of an oscillatory cell taken under control conditions (•), in the presence of 100 μm Ba²⁺ (▪), and in the presence of 100 μm Ba²⁺ +100 μm ZD-7288 (□). D, bar histogram of the I_K1 and I_h components of the inward current at −120 mV obtained from 8 oscillatory and 12 non-oscillatory cells. **P < 0.01.

Depolarization-activated currents

Frog saccular hair cells have been previously shown to possess five depolarization-activated currents: I_BKS, I_BKT, I_DRK, I_A and I_Ca (Hudspeth & Lewis, 1988a; Armstrong & Roberts, 1998, 2001; Catacuzzeno et al. 2003a,b). We assessed the contribution of each of these components in both oscillatory and non-oscillatory cells. I_DRK was assessed using 1 mm 4-AP, previously shown to be selective for this current (Armstrong & Roberts, 1998; Catacuzzeno et al. 2003b; cf. Fig. 4A and B). I_BKS and I_BKT were determined from the sustained and peak TEA (6 mm)-sensitive components (at this concentration TEA has been shown to block BK but not K_v currents in these cells; Armstrong & Roberts, 1998; Catacuzzeno et al. 2003b; cf. Fig. 4A and B). I_Ca was estimated from the inward peak current in the presence of both TEA (6 mm) and 4-AP (1 mm; cf. Fig. 4A and B). Finally, I_A was assessed as the difference between currents evoked by depolarizing pulses following a 200 ms prepulse to either −50 mV or −110 mV (cf. Fig. 4C and D and Catacuzzeno et al. 2003b). The results of these procedures are shown in Fig. 4E. It can be seen that all the depolarization-activated currents recorded from oscillatory cells are of lower magnitude than those of non-oscillatory cells, and these differences are particularly high for I_DRK, I_BKT and I_Ca. The I_A density we recorded for non-oscillatory cells is significantly higher than that we have reported previously for cylindrical hair cells from the same preparation (Catacuzzeno et al. 2003b). Differences in the composition of the extracellular solution (for example the low Ca²⁺ concentration used in our previous study) may be the reason for such a difference.

Figure 4. Pharmacological dissection of the depolarization-activated currents in oscillatory and non-oscillatory cells.

A and B, current traces recorded from an oscillatory (A) and a non-oscillatory (B) cell, both stimulated with a depolarizing step to −30 mV from a holding potential of −70 mV, in control conditions, after bath application of 4-AP (1 mm), and TEA (6 mm) plus 4-AP (1 mm), in succession. C,D, current traces of an oscillatory (C) and a non-oscillatory (D) cell obtained by a 100 ms depolarizing pulse to −30 mV preceded by a 200 ms prepulse to either −110 mV or −50 mV. TEA (6 mm) was present throughout the experiments to block the BK current and thus reduce voltage errors related to series resistance. E, bar histogram showing the depolarization-activated current densities in oscillatory and non-oscillatory cells. Sustained BK current was assessed from the TEA-sensitive current density at 50 ms from the beginning of the depolarizing step to −30 mV from a holding potential of −70 mV. The transient BK current was assessed as the difference between the peak (at 2 ms) and sustained (at 50 ms) TEA-sensitive current density. I_DRK was estimated from the 4-AP-sensitive current at −30 mV (from experiments similar to those shown in A and B). The number of cells used for each estimation is reported. **P < 0.01. Inset, mean, normalized (at −20 mV) I–V relationships for I_BKS, assessed as the TEA-sensitive component at 50 ms from the beginning of the depolarizing step, in 7 oscillatory and 11 non-oscillatory cells.

The mean, normalized I–V relationships for the TEA-sensitive component in the two cell populations is displayed in the inset of Fig. 4E. It is apparent that, in addition to a lower current density, the I_BKS of oscillatory cells also have a more depolarized threshold of activation. This feature explains the more depolarized activation threshold of the total voltage-activated current in oscillatory cells (cf. Fig. 2D).

Pharmacology of spontaneous voltage oscillations

The actions of inhibitors of voltage-activated ion currents were then tested in current-clamp mode, to evaluate the contribution of each conductance to spontaneous oscillatory activity. In four oscillatory cells, bath application of 100 μm Ba²⁺ abolished voltage oscillations, accompanied by a marked membrane potential depolarization (Fig. 5A). An inhibitory effect on the oscillatory activity was also observed following bath application of the I_h-selective inhibitor ZD-7288 (100 μm, n = 4; Fig. 5B). In presence of ZD-7288, the hair cell resting potential became bistable, with sudden jumps between hyperpolarized (∼–85 mV) and relatively depolarized (∼–50 mV) levels (Fig. 5B, right trace). However, such activity did not display any dominant frequency, typical of oscillatory activity. Bath application of 6 mm TEA, which inhibits most of the depolarization-activated K⁺ current in oscillatory cells (cf. Fig. 4), did not inhibit voltage oscillations (n = 5; Fig. 5C), in accordance with a threshold of BK current activation in these cells not overlapping with the oscillatory voltage range (cf. Fig. 4E). In three out of five cells tested, TEA significantly reduced the oscillatory frequency, and slightly increased the peak-to-peak amplitude (cf. Fig. 5C). This effect may be due to the small, but significant, blocking action of TEA on I_K1 (data not shown; see also Goodman & Art, 1996). The possibility of a contribution of I_BK to the oscillatory activity can be dismissed since in two oscillatory cells bath application of 100 μm Cd²⁺ (that blocks voltage-activated Ca²⁺ influx and the consequent activation of I_BK; Armstrong & Roberts, 2001; Catacuzzeno et al. 2003a), did not significantly affect voltage oscillations (Fig. 5D). This result also suggests that I_Ca is not essential for the oscillatory activity. Interestingly, in about half of non-oscillatory cells (five out of nine), TEA application resulted in the appearance of membrane potential instability (Fig. 5F), suggesting that I_BK has a stabilizing role on the membrane potential in these cells. In three out of five hair cells, voltage oscillations with an amplitude comparable to those seen in oscillatory cells were recorded (Fig. 5F); in the remaining two cells all-or-none action potentials were superimposed on these voltage oscillations (data not shown). Together, these results indicate that I_K1 and I_h are central players in the generation of the spontaneous voltage oscillations. Due to the lack of selective inhibitors of I_A, we could not pharmacologically probe the contribution of this current to the oscillatory activity. We have, however, addressed this issue using a modelling approach, as described in the Model results section, and found that this current plays a modulatory role on the amplitude and frequency of voltage oscillations.

Figure 5. Sensitivity of the oscillatory activity to inhibitors of voltage-activated currents.

A–E, effect of bath application of 100 μm Ba²⁺ (A), 100 μm ZD-7288 (B), 6 mm TEA (C), 100 μm Cd²⁺ (D) or 100 μm gentamicin (E) on the oscillatory activity. F, voltage activity at the resting membrane potential of a non-oscillatory cell in control conditions and after addition of 6 mm TEA, showing the appearance of an oscillatory activity after drug application.

Previous studies on frog saccular hair cells have described spontaneous hair bundle oscillations with frequencies comparable to those observed here for spontaneous voltage oscillations (Martin & Hudspeth, 1999; Martin et al. 2003). To test the hypothesis that an oscillatory mechanotrasduction current originating from hair bundle oscillations may contribute to the oscillatory voltage activity, we assessed the effect of gentamicin (100 μm), an agent known to inhibit bundle motility (Martin et al. 2003). Gentamicin had no action on either the frequency or the amplitude of the voltage oscillations (n = 2; Fig. 5E), suggesting that changes in the mechanotransduction current due to spontaneous bundle movements are not responsible for the voltage oscillations. Moreover, oscillatory bundle movements would not be expected in the 1.8 mm external [Ca²⁺] we employed (Martin et al. 2003).

Biophysical study of I_K1 and I_h

The results reported above suggest that I_K1 and I_h are the principal currents responsible for the generation of the spontaneous voltage oscillations. To better understand the role of these currents during voltage oscillations we assessed their biophysical properties, and built approximate kinetic models that will be used in the next section to model the voltage oscillatory activity. Although a biophysical description of both these currents in frog saccular hair cells has been previously reported (Holt & Eatock, 1995), we considered it necessary to reassess their main properties because of differences in cell isolation and recording method. The study of Holt & Eatock (1995) used hair cells isolated with the proteolytic enzyme papain, which has subsequently been demonstrated to alter the properties of several ion currents in this preparation (Armstrong & Roberts, 1998; Catacuzzeno et al. 2003a). In addition, Holt & Eatock (1995) used the whole-cell configuration, while we used the perforated patch, which will preserve the intracellular factors likely to modulate these currents (for example cAMP for I_h, or Mg²⁺ and polyamines for I_K1; see for example, Ishihara et al. 2002; Accili et al. 2002).

I_K1

I_K1 was studied in both oscillatory and non-oscillatory cells in the presence of 100 μm ZD-7288 in the bathing solution to block I_h, whose activation range overlaps with that of I_K1. Figure 6A shows a typical family of current traces evoked by stepping the membrane voltage, from a holding potential of −70 mV, from −170 to −60 mV. The reversal potential of the current was estimated from the intersection of the instantaneous and steady-state I–V relationships (data not shown), a procedure that eliminates the leak contribution (cf. Holt & Eatock, 1995). The mean reversal potential obtained on three hair cells was −95 ± 4 mV, close to the K⁺ equilibrium potential under our recording conditions (−103 mV), suggesting that I_K1 is very selective for K⁺. Figure 6B shows the mean, normalized I–V relationship of the Ba²⁺-sensitive current, showing that I_K1 carries a small, but significant, outward current at membrane potentials positive to the K⁺ equilibrium potential. The data could be well fitted by a simple two-state kinetic model with voltage slope of 11 mV and V_½ of −110 mV (solid line in Fig. 6B; an ohmic instantaneous conductance was considered).

Figure 6. Biophysical study of I_K1.

A, family of current traces obtained by voltage pulses from −170 to −60 mV in 10 mV steps from a holding potential of −70 mV. The bath solution contained 100 μm ZD-7288 to remove I_h. B, mean, normalized I–V relationship (taken at 100 ms from the beginning of the depolarizing steps) obtained from four cells similar to that shown in A. Data points were obtained by measuring the current amplitude at the end of the hyperpolarizing steps at different membrane potentials. Current amplitudes were leak corrected by subtracting currents obtained after addition of the I_K1 blocker Ba²⁺ (100 μm) at the end of the experiment. The continuous line is a fit of the I–V data with the relationship I_K1 = A (V + 95)/(1 + exp((V − V_½)/k)), giving V_½ = −110.8 mV, and k = 11 mV. Inset, mean, normalized I–V relationship showing a wider membrane potential range. C, plots showing the fit of I_K1 activation (upper plot) and deactivation (lower plot) time courses with mono-exponential and bi-exponential functions, respectively. Open symbols represent experimental points and the continuous lines the fits. D, plot of the activation (closed symbols) and deactivation (open symbols) time constants versus membrane potential for I_K1. Data were obtained from three different recordings similar to those shown in panel C. The continuous lines represent the fit of the experimental data with the exponential relationship τ = τ(0 mV) exp((V – V₀)/V_T) + K_T. The best fit parameters were: fast deactivation time constant: K_T = 0.04 ms, V_T = −43.8 mV, V₀ = −120 mV, τ(0 mV) = 0.7 ms; slow deactivation time constant: K_T = 0.04 ms, V_T = −28 mV, V₀ = −120 mV, τ(0 mV) = 14.1 ms; activation time constant: K_T = 0.17 ms, V_T = 30.5 mV, V₀ = −80 mV, τ(0 mV) = 7.5 ms. Inset, plot of the fractional contribution of the fast deactivation time constant (a_fast) versus membrane potential. The continuous line represents the fit of the experimental data with a linear relationship of the form a_fast = mV + q. The best fit parameters are m = 0.0042 mV⁻¹ and q = 1.03.

The activation time course of I_K1 upon hyperpolarizing steps from a holding potential of −70 mV was mono-exponential, after a small, but significant, instantaneous component (Fig. 6C, upper current traces). The time constant of activation decreased from 2.15 ± 0.75 ms at −120 mV to 0.59 ± 0.09 ms at −170 mV. This voltage dependence could be well described by an exponential relationship of the form

with best fit parameters: τ(0 mV) = 7.5 ms, V₀ = −80 mV, V_T = 30.5 mV, and K_T = 0.17 ms (Fig. 6D, closed symbols and superimposed solid line). The deactivation time course at potentials more positive than the current reversal potential was bi-exponential (Fig. 6C, lower current trace family). Both τ_fast and τ_slow were voltage dependent, measuring 0.38 ± 0.17 ms and 4.8 ± 0.24 ms at −90 mV, and 0.23 ± 0.14 ms and 1.96 ± 0.66 ms at −65 mV, respectively (see open symbols in Fig. 6D). The deactivation time constants as functions of voltage could be well described by exponential relationships, with the following best fit parameters. τ_fast: K_T = 0.04 ms, V_T = −43.8 mV, V₀ = −120 mV and τ(0 mV) = 0.7 ms; τ_slow: K_T = 0.04 ms, V_T = −28 mV, V₀ = −120 mV and τ(0 mV) = 14.1 ms. The relative contribution of the fast to the slow component (a_fast) was also slightly voltage dependent (see inset to Fig. 6D).

I_h

I_h was studied in presence of 100 μm Ba²⁺ to eliminate I_K1 (cf. Fig. 7A). The I_h reversal potential, obtained by extrapolation from a linear fit of the instantaneous ZD-7288-sensitive I–V relationship, had a mean value of −44.8 ± 1.2 mV (n = 3; data not shown). We found that a modified Hodgkin–Huxley (HH) model, already proposed to describe I_h in papain-isolated frog saccular hair cells (Holt & Eatock, 1995), could adequately reproduce the main features of this current. This model considers three independent activation gates, two of which need to be in the permissive state to open the channel, as summarized by the following kinetic scheme:

Figure 7. Biophysical study of I_h.

A, family of current traces obtained by hyperpolarizing voltage pulses from −140 to −60 mV in 10 mV steps from a holding potential of −60 mV. The bath solution contained 100 μm Ba²⁺ to remove I_K1, 6 mm TEA and 1 mm 4-AP to remove the depolarization-activated currents. B, mean steady-state I–V relationship obtained from four cells similar to that shown in A, by measuring currents at the end of the hyperpolarizing steps at different membrane potentials. Current amplitudes were leak corrected by subtracting currents obtained after addition of the I_h blocker ZD-7288. The solid line represents the fit of the steady-state I–V with the relationship: I_h(SS) = g_h (V – E_K) [3P_inf² (1 − P_inf) + P_inf³], with P_inf = 1/(1 + exp((V − V_½)/k)). The best fit parameters were V_½ = −87 mV, k = 16.7 mV. C, plots showing the fit of I_h activation (upper plot) and deactivation (lower plot) time courses with the equation: I_h = A + B (3p² (1 − p) + p³), with p = p_i + (p_inf − p_i) exp(−t/τ). Open symbols represent experimental points and the solid lines the fits. The activation time courses were obtained by stepping the membrane potential from −80 to −140 mV, in 10 mV steps. The deactivation time courses were obtained by preconditioning the membrane potential to −120 mV, before stepping the voltage from −90 to −65 mV, in 5 mV steps. The holding potential was −60 mV. D, plot of the activation (open symbols) and deactivation (closed symbols) time constants versus membrane potential for I_h. Data were obtained from three recordings similar to those shown in C. The solid line represents the fit of the experimental data with the relationship τ = P₁ + P₂ exp(−[(V − P₃)/P₄]². The best fit parameters were: P₁ = 63.7 ms, P₂ = 135.7 ms, P₃ = −91.4 mV and P₄ = 21.2 mV

scheme (1)

where α and β are the rate constants for each independent gate to switch into the permissive or non-permissive state, respectively. Figure 7B shows a mean, normalized I–V relationship of the ZD-7288-sensitive current component. The solid line in Fig. 7B shows the fit of the experimental data with a relationship derived from scheme 1, considering a Boltzmann-shaped voltage dependence for each independent gate (see figure legend for details), and a ohmic instantaneous conductance. The fit gave a single-gate activation V_½ of −87 mV and a slope factor (k) of 16.7 mV. The modified HH model is also sufficient to describe the activation and deactivation kinetics of I_h, as shown by the fits for a representative family of I_h (Fig. 7C, activation and deactivation). The resulting time constants showed a bell-shaped voltage dependence (Fig. 7D).

Model results

Simulation of spontaneous voltage oscillations

To assess the role of the voltage-activated currents in the spontaneous oscillatory activity, we implemented a biophysical simulation based on the results reported in this study, as well as published data. Figures 3 and 4 show that only a subset of the voltage-dependent currents found in frog saccular hair cells are potentially active within the voltage range experienced during the spontaneous oscillations, namely I_K1, I_h, and I_A. As for the other currents, I_DRK, I_BKT, and I_Ca were found to be of negligible amplitude in oscillatory cells, while I_BKS showed an activation threshold beyond the voltage range of the oscillations (cf. Fig. 4). Based on these data, oscillatory cells were modelled by a single-compartment model in which only I_K1, I_h, I_A and a leakage current were included. The kinetic descriptions of these currents were either based on the experimental results reported in this paper (I_K1 and I_h), or in Catacuzzeno et al. (2003b) (I_A; cf. Appendix for details), and the current densities were those found experimentally in oscillatory cells (cf. Figs 3 and 4, and Table 1). As shown on Fig. 8A, left, the model predicts spontaneous voltage oscillations with peak-to-peak voltage amplitude and frequency of 28 mV and 3.4 Hz, respectively, well within the range recorded experimentally.

Table 1.

Permeability values for oscillatory and non-oscillatory cells used in the model

	Non-oscillatory cell model	Oscillatory cell model
gca (nS)	3.2	—
PDRKa (l s−1)b	6.4 × 10−14	—
PA (l s−1)	1.5 × 10−13	3 × 10−14
gK1 (nS)	7.3	28
ghc (nS)	1.5	2.2
PBKS (l s−1)	2 × 10−13	—
PBKTd (l s−1)	14 × 10−13	—

Parameter values were estimated from the pharmacological data reported in Figs 3 and 4 on oscillatory and non-oscillatory cells, respectively.

^aTaken as 1.2 times the 4-AP-sensitive component estimated in Fig. 4E, given that 20% of I_DRK is insensitive to this blocker (Catacuzzeno et al. 2003b).

^bUnits of permeability as in Nygren et al. (1997).

^cThe partial current activation at the time of estimation (100 ms) was taken into account using the data of Fig. 7D.

^dEstimated by simulating I_BKT with the model reported in the Appendix, and choosing a value that could adequately reproduce the peak TEA-sensitive current found in Fig. 4E.

Figure 8. Modelling the spontaneous voltage oscillations in frog saccular hair cells.

A, simulated resting voltage activity under current-clamp mode obtained with a single-compartment model containing all the major ion conductances found to be active within the oscillatory voltage range (cf. Appendix). The left voltage trace was generated using current densities similar to those found in oscillatory cells, while the right trace was obtained with current densities similar to those found in non-oscillatory cells (see Table 1). B, plots of the peak-to-peak voltage amplitude (upper plot) and oscillatory frequency (lower plot) of the simulated voltage oscillations as a function of the indicated conductance or permeability parameter, showing the effect of varying the I_A, I_K1 or I_h density on the oscillatory properties. In each plot all the other conductance parameters were set according to the oscillatory cell model (cf. Table 1). C, temporal plot of the activity of I_h, I_K1, and I_A during an oscillation. The model parameters used were as for the simulated left trace of A. D, plot of the open probability of each current included in the oscillatory model (indicated) as a function of the membrane potential experienced by the cell during the oscillatory activity. Model parameters used were the same as for the simulated left trace of A. E, simulated oscillatory activity obtained by multiplying the activation time constant of I_h (τ_h) by a factor ≤ 1 (indicated).

To understand the relevance of each current to the oscillatory activity, we modelled the effect of varying I_K1, I_h and I_A densities on the oscillatory voltage amplitude and frequency. Figure 8B shows that the oscillatory activity disappears when I_K1 and I_h conductances were reduced below about 22 and 1.5 nS, respectively, indicating that these currents are essential to establish the oscillatory activity (Fig. 8B, solid and dashed lines). Voltage oscillations also disappear with excessively high I_K1 or I_h densities. This is consistent with our unpublished data indicating that a relatively constant I_K1/I_h ratio is required to generate and maintain oscillations. I_A however, is not necessary for establishing the oscillatory activity (Fig. 8B, dotted lines), but it does contribute to the temporal shape of the voltage changes. Specifically, an increase in I_A density results in higher frequency and smaller amplitude oscillations.

The model also allows visualization of the temporal changes in the activity of the voltage-gated currents (I_h, I_K1 and I_A; cf. Fig. 8C), and understanding of their interplay to generate voltage oscillations. At the peak depolarization (first dashed line in Fig. 8C), I_K1 is at its minimum activity, whereas I_h, because of its slower kinetics (cf. Fig. 7), is still decreasing. This delayed deactivation of I_h helps to hyperpolarize the membrane potential. Membrane hyperpolarization is enhanced by a I_K1-based regenerative process (K⁺ efflux through I_K1 further hyperpolarizes the membrane potential, further increasing I_K1 activity), until the peak hyperpolarization is reached (second dashed line in Fig. 8C). At the peak hyperpolarization I_K1 is at its maximum activity, whereas the slower I_h is still increasing. This delayed activation of I_h, together with I_K1 deactivation, acts to depolarize the membrane potential until it reaches the peak depolarization of a new oscillatory cycle. Figure 8C also shows that during the depolarization of the voltage oscillation I_A is also activated, albeit to a minor degree. This small, but significant, I_A permeability helps to determine the rate of voltage changes, and the peak amplitude reached by the oscillation (cf. also Fig. 8B).

The relevance of the slow kinetics of I_h in generating voltage oscillations is perhaps better described in Fig. 8D which shows the activity (P_o) of the three current components as a function of the membrane voltage experienced by the cell during voltage oscillations. Because of its slow kinetics, I_h displays a marked hysteresis, with changes in activity during the hyperpolarizing and depolarizing phases of the oscillation following very different trajectories. This hysteresis gives rise to the delayed feedback mechanism required for spontaneous voltage oscillations to occur (cf. Fig. 8C). In accordance, an increase in the activation rate of I_h (obtained by multiplying its activation time constant by a factor lower than one) results in the progressive reduction of the amplitude of voltage oscillations, until it fades (Fig. 8E). This effect is specific for I_h, since a reduced model in which only I_h kinetics were considered (assuming instantaneous gating for all other currents) was still capable of generating an oscillatory activity (data not shown).

We also tested whether the properties and densities of the currents found in non-oscillatory cells were compatible with a stable resting potential. The pharmacological results reported in Figs 3 and 4 indicated that all the voltage-activated currents found in non-oscillatory cells are potentially active near the resting membrane potential. In modelling the non-oscillatory cells, we thus included all the voltage-activated currents found in frog saccular hair cells, namely I_K1, I_h, I_A, I_BKS, I_BKT, I_DRK, I_Ca, and a leakage current. The kinetic descriptions of the additional currents were taken from the experimental results reported in this paper (I_BKT and I_BKS, cf. also supplemental data), or in Catacuzzeno et al. (2003b) (I_DRK and I_Ca; cf. Appendix), and the current densities were those found experimentally in non-oscillatory cells (cf. Figs 3 and 4, and Table 1). As shown on Fig. 8A, right, a stable membrane potential was obtained, in accordance with the experimental results. It can be seen from Fig. 8A that our non-oscillatory cell model does not demonstrate the much smaller amplitude and higher-frequency voltage fluctuations sometimes seen in these cells (cf. Ashmore, 1983; Fig. 1E). This is because in our theoretical description of the electrical activity we did not introduce the stochastic opening and closing of ion channels, that is likely to be the origin of this ‘noisy’ activity (White et al. 1998; Ospeck et al. 2001; our unpublished observations). Finally, we verified that the non-oscillatory cell model, containing the full set of voltage-dependent currents described in frog saccular hair cells, was able to generate electrical resonance in response to depolarizing current steps (data not shown).

The stabilizing role of the depolarization-activated currents on the membrane potential of non-oscillatory cells

The model indicates that I_K1 and I_h, when present at appropriate amplitudes, are primarily responsible for the spontaneous oscillations. Some non-oscillatory cells, however, possess hyperpolarization-activated currents with amplitude and composition similar to oscillatory cells (cf. Fig. 3). How do these cells display a stable resting membrane potential? The findings that: (i) non-oscillatory cells possess large depolarization-activated currents that are active within the oscillatory voltage range (cf. Figs 2D and 4E), and (ii) blocking I_BK with TEA produces electrical instability in some non-oscillatory cells (cf. Fig. 5F), would suggest that the depolarization-activated currents might exert a stabilizing effect on the membrane potential. We tested this hypothesis by modelling the effects of varying the depolarization-activated currents in a non-oscillatory cell with hyperpolarization-activated currents capable of generating oscillatory activity (as used in the oscillatory model; see Fig. 8A). Figure 9A shows simulated voltage traces in which the amplitude of all the depolarization-activated currents was progressively increased, without altering the amplitude of the hyperpolarization-activated currents. Specifically, we set the amplitude of each depolarization-activated current to a fraction f of their mean value in non-oscillatory cells. Thus, f = 0 corresponds to a cell totally lacking depolarization-activated currents, while f = 1 corresponds to a cell possessing the mean depolarization-activated current amplitude of non-oscillatory cells (cf. Table 1). This simulation clearly shows that increasing the depolarization-activated current amplitude results in the suppression of oscillations, i.e. stabilization of the resting membrane potential. The simulation further shows that ∼75% of the mean current amplitudes of non-oscillatory cells was sufficient to completely eliminate the oscillations (Fig. 9B). This action is mainly due to the stabilizing effect of I_BK, since an oscillatory activity reappeared when I_BK was individually decreased in a model in which f = 1 for all the other depolarization-activated conductances (see inset of Fig. 9B).

Figure 9. Stabilizing role of the depolarization-activated currents on the membrane potential of non-oscillatory cells.

A, simulated voltage traces showing the effect of increasing the depolarization-activated currents in a non-oscillatory cell having appropriate hyperpolarization-activated current amplitudes to generate an oscillatory activity (the same used in the oscillatory cell model, cf. Table 1). All the depolarization-activated current amplitudes were set equal to a fraction f of their mean values in non-oscillatory cells (cf. Table 1, non-oscillatory cell model). B, plot of the simulated oscillatory amplitude as a function of the parameter f obtained by running a series of simulations similar to those shown in panel A. Inset, plot showing the effect of varying either I_BKS + I_BKT, I_Ca, I_DRK or I_A on the voltage oscillatory peak-to-peak amplitude, while leaving the other current amplitudes at their mean values in non-oscillatory cells (cf. Table 1, non-oscillatory cell model). When varying I_Ca, U in eqn (A26) was appropriately modified to keep the coupling between Ca²⁺ and BK channels unaltered.

Discussion

The main finding of this study is the presence of high-amplitude spontaneous voltage oscillations in about 20% of isolated frog saccular hair cells, having centre frequency of 2–11 Hz, and peak-to-peak voltage amplitude in the range of 9–33 mV. These spontaneous oscillations are thus tuned to frequencies lower than the preferred excitatory frequencies of afferent saccular fibres (typically from 20 to 120 Hz; reviewed in Smotherman & Narins, 2000). We also found that in the majority of non-oscillatory cells, the depolarization-activated currents, present at substantially higher density as compared to those of oscillatory cells, help to stabilize the resting membrane potential.

We found a significant correlation between the presence of voltage oscillations and cell morphology, most oscillatory cells being found to have LAD ratios typical of central club-shaped cells. This result suggests that morphologically distinct saccular hair cells possess distinct electrical behaviours, thus supporting the notion of the existence of functionally different hair cells in the submammalian vertebrate sensory epithelia (Chabbert, 1997; Guth et al. 1998).

Ionic basis of spontaneous voltage oscillations

Both the experimental and modelling studies reported in this paper indicate that spontaneous voltage oscillations require the activity of the two hyperpolarization-activated currents present in this preparation, I_K1 and I_h. First, the voltage-clamp data reported in Figs 2 and 3 indicate that a strong correlation exists between the oscillatory activity and the presence of high densities of both I_K1 and I_h. Second, both ZD-7288 and low Ba²⁺ concentrations, selective blockers of I_h and I_K1, respectively, inhibit the oscillatory activity (cf. Fig. 5). Third, a mathematical model incorporating the kinetics and amplitude of I_K1 and I_h of oscillatory cells faithfully reproduces the spontaneous oscillations, and a reduction of either I_K1 or I_h density induces their disappearance (cf. Fig. 8). The model results depicted in Fig. 8 also indicate that I_A is not required for oscillatory activity. This current, however, appeared to modulate the oscillatory properties, with higher I_A densities resulting in faster and smaller voltage oscillations (cf. Fig. 8B).

An important feature for the generation of spontaneous voltage oscillations is the slow kinetics of I_h. As our experiments and simulations show (cf. Figs 7 and 8), I_h kinetics appeared to be slow as compared to the rate of membrane voltage changes during the oscillation. This results in a substantial hysteresis of I_h activity, conferring on the system a memory of the previous oscillatory cycle, a requirement for generating the oscillatory activity. This is confirmed by the model results shown in Fig. 8E, indicating that faster I_h kinetics result in the suppression of voltage oscillations. Thus, I_h has kinetic properties appropriate for the generation of spontaneous voltage oscillations. Accordingly, I_h is important in several forms of spontaneous electrical activity with frequencies of several hertz, such as the rhythmic discharge of cardiac muscle cells (reviewed in Accili et al. 2002), and the subthreshold voltage fluctuations observed in neuronal tissues (Dickson et al. 2000).

Our data further show that the depolarization-activated currents counteract the oscillatory activity. Indeed, oscillatory cells possess smaller depolarization-activated currents, which in addition activate at more depolarized membrane potentials than for non-oscillatory cells (cf. Figs 2 and 4). Moreover, pharmacological block of I_BK resulted in the appearance of an electrical instability in a group of non-oscillatory cells (Fig. 5E). Our simulation of voltage oscillations showed that an increase in the depolarization-activated currents resulted in a reduction of the oscillatory voltage amplitude, until it disappears completely (cf. Fig. 9). These observations explain why some cells with hyperpolarization-activated current amplitudes consistent with generating oscillatory activity had a stable membrane potential (cf. Fig. 3B).

Comparison with previous studies

To our knowledge, spontaneous voltage oscillations of the type described in this paper have not been previously reported in frog saccular hair cells. On isolated frog saccular neuroepithelia Ashmore (1983) reported a spontaneous voltage activity displaying high-frequency (11–85 Hz) and low-amplitude (noise variances over 0.249–3.54 mV²). A similar high-frequency and low-amplitude spontaneous activity was recorded from frog basilar papilla hair cells (Ospeck et al. 2001). Both these spontaneous activities differ profoundly from that described here. Rather, they resemble the small voltage fluctuations we observed in most non-oscillatory hair cells (cf. Fig. 1E and F). Another type of voltage activity, spontaneous spikes observed either at rest or upon current injection, has been reported for several mature lower vertebrates, including frog saccular hair cells, as well as in immature mammalian hair cells (Hudspeth & Corey, 1977; Fuchs et al. 1988; Sugihara & Furukawa, 1989; Kros et al. 1998). In addition to their very different time course, these spontaneous spikes appear to differ from our oscillations in the underlying ionic basis, as they are believed to result from the interplay between a delayed rectifier K⁺ current and voltage-activated Na⁺ and/or Ca²⁺ current (Sugihara & Furukawa, 1989; Marcotti et al. 2003).

There may be several reasons as to why the spontaneous voltage oscillations described here have not been previously observed. Papain, which has been used in most studies as a dissociating enzyme (Lewis & Hudspeth, 1983; Hudspeth & Lewis, 1988a,b; Roberts et al. 1990; Holt & Eatock, 1995) may alter the electrophysiological properties of the hair cells (cf. Armstrong & Roberts, 1998). It is worth noting that depolarization-activated currents are much larger in hair cells dissociated with papain compared to those dissociated with protease VIII. (Catacuzzeno et al. 2003a). This large outward K⁺ current would stabilize the membrane voltage, and thus prevent voltage oscillations. Voltage oscillations have not, however, been reported for the semi-intact (in situ) preparation, where current-clamp recordings have also been carried out (Ashmore, 1983; Armstrong & Roberts, 1998). A possible reason could be that in situ the spontaneous voltage oscillations are prevented by the stabilizing effect on the membrane potential exerted by the mechanotransducer cationic current or the ACh-induced K⁺ current, both of which are likely to be absent in our preparation (cf. Holt et al. 2001). We are not inclined, however, to believe that our enzymatic dissociation procedure causes our apparently distinct results. In a previous investigation, analysing outward BK and K_V currents, as well as the electrical resonance in protease VIII-dissociated hair cells, we showed that their general electrophysiological properties were very similar to those reported in the semi-intact preparation (Catacuzzeno et al. 2003a). Another possible explanation may be related to the type of hair cells. Spontaneous voltage oscillations are mostly confined to a specific cell type, the central club-shaped saccular hair cells. These cells represent a relatively small proportion of frog saccular hair cells in the intact epithelium (Chabbert, 1997), and they have possibly been overlooked in previous investigations. Moreover, the recording conditions may be crucial. Indeed, these cells appear unique in the frog saccule with regard to their Ca²⁺ regulation, since they have been found to express calbindin-28D instead of parvalbumin 3 as their main mobile Ca²⁺ buffer (Edmonds et al. 2000; Heller et al. 2002). The depolarized shift we observed in I_BK activation for these cells would agree with their Ca²⁺ buffering power being stronger (Edmonds et al. 2000), a feature that would be lost in ruptured whole-cell recordings.

Functional significance

Except for a row of presumably immature club-like hair cells at the periphery of the macula, the frog saccule does not display any regional heterogeneity in its hair cell properties (Chabbert, 1997), unlike most other hair cell organs. The two main cell types (central club-shaped and central cylindrical) are intermingled, apparently at random. So far as we are aware there are no data available regarding the afferent or efferent innervation patterns of these two cell populations. Whereas this indicates the requirement for further physiological and morphological data for a clear functional interpretation of spontaneous oscillations, several hypotheses may be proposed.

Spontaneous voltage oscillations could represent an electrical phenotype of immature frog saccular hair cells. Lower vertebrates are known to continuously produce new hair cells (Corwin & Oberholtzer, 1997). In the toad saccule, the peripheral elongated cells are thought to be the immature ‘growing pool’ of the macula, but about 10% of the cell population in more central regions was also labelled by mitotic indicators, possibly indicating an additional intramacular hair cell turnover (Corwin, 1985). Besides their shape, oscillatory hair cells share other properties with developing hair cells. First, developing hair cells transiently display different Ca²⁺ buffers from mature hair cells (Dechesne et al. 1994). Moreover, during their development, inner hair cells from the mammalian cochlea show progressively larger I_Ca and I_BK (Beutner & Moser, 2001; Kros et al. 1998), transiently display low-frequency voltage spikes (Kros et al. 1998) and receive an efferent innervation which activates the α₉ ACh receptor and in turn the SK current (Glowatzki & Fuchs, 2000). The small I_Ca and I_BK (cf. Fig. 4E), large I_SK (Chabbert, 1997), unique Ca²⁺ buffer (Edmonds et al. 2000) and low-frequency voltage oscillations (although not identical to those found in immature mouse hair cells) found in central club-shaped hair cells are congruent with an immature stage in development.

If they release transmitter, oscillatory hair cells could cyclically modulate the firing pattern of the afferent nerve fibre contacting them. Interestingly, single-unit recordings in few frog saccular afferents exhibit regular spontaneous activity (Christenses-Dalsgaard & Jorgensen, 1988; Christensen-Dalsgaard & Narins, 1993), as also observed in other lower vertebrate hair cell organs (Manley, 1979; Crawford & Fettiplace, 1980; Temchin, 1988). We do not know, however, whether the small Ca²⁺ influx (due to the low I_Ca density and the hyperpolarized range of voltage oscillations) occurring during the depolarizing phase of the spontaneous oscillations is sufficient to trigger neurotransmitter release. Interestingly, a recent study on frog saccular hair cells reports a non-L Ca²⁺ channel with an activation V_½ within the voltage range of our spontaneous oscillations (Rodriguez-Contreras & Yamoah, 2001).

Another possible role for the spontaneous voltage oscillations may be found in the interaction with the spontaneous voltage oscillations at similar frequency stemming from the mechanotransducer current, and the consequent reinforcement of the spontaneous hair bundle motility. The hair bundle of frog saccular hair cells undergoes spontaneous oscillatory movements at frequencies close to, although slightly higher than, those we found for spontaneous voltage oscillations (Martin & Hudspeth, 1999; Martin et al. 2003). An important step in the bundle oscillatory cycle appears to be the Ca²⁺ influx through mechanotransducer channels (Choe et al. 1998; Ricci et al. 2000, 2002; Martin et al. 2003; Vilfan & Duke, 2003). Spontaneous voltage oscillations could modulate bundle motility by cyclically modulating the driving force for Ca²⁺ influx, thus amplifying alterations in intracellular Ca²⁺ during the oscillatory cycle. The finding that changes in membrane potential have been shown to evoke bundle movements (Assad & Corey, 1992; Denk & Webb, 1992; Ricci et al. 2000, 2002; Bozovic & Hudspeth, 2003) supports this proposal.

Appendix

Modelling the oscillatory cells

Voltage oscillations were modelled by numerically solving the following current-clamp equation:

where V is the membrane voltage, C_m is the cell membrane capacitance, and I_ion is the total ion current passing through the membrane. In the oscillatory cell model I_ion is given by

where I_L is the leakage current.

The currents included in eqn (A2) were modelled as follows.

I_K1 modelling

I_K1 was modelled, using the experimental data from this study (Fig. 6), by a combination of two different activation gates, according to the following relationship:

where g_K1 is the maximal K1 conductance, m_K1f and m_K1s are the fast and slow gates, respectively, and a_fast is the contribution of the fast gate to the overall I_K1 gating. a_fast was considered to be 0.7 (see Fig. 6D). The temporal evolution of the two gates is described by the following differential equations:

with

and

where V_½ and k are the I_K1 half activation voltage and steepness, respectively.

I_h modelling

I_h was modelled, in accordance with the experimental data obtained from this study (Fig. 7), using a modified HH model with three independent activation gates, assuming that only two need to enter the m state to open the channel (scheme 1; Holt & Eatock, 1995). This gives:

where g_h is the maximal h conductance and E_h its reversal potential. m_h(V, t) was assessed from

with m_h(V, ∞) and τ_h(V) given by the relationships:

and

I_A and I_L modelling

Both these currents were modelled as in Catacuzzeno et al. (2003b).

Modelling the non-oscillatory cells

Non-oscillatory cells were modelled by numerically solving eqn (A1). In this case I_ion also incorporates I_Ca, I_BKS, I_BKT and I_DRK, given their sensible activation and substantial current density within the oscillatory voltage range (see Figs 2 and 4). Namely

I_K1, I_h, I_A and I_L were modelled as described above for the oscillatory cell model. A description of the other currents included in the non-oscillatory cell model follows.

I_BKS and I_BKT modelling

The following five-state linear scheme was used to model the activation of both I_BKS and I_BKT (Hudspeth & Lewis, 1988a)

Scheme 2

Identical activation schemes were used for both I_BKS and I_BKT since a previous study showed identical activation kinetics for both currents (Armstrong & Roberts, 2001). The voltage dependence of the Ca²⁺-dependent transitions in scheme 2 is given by

where j = 1, 2 and 3. β_c is voltage independent, whereas α_c voltage dependence is given by

The following series of differential equations was used to find the probability of encountering the channels in each of the five states

O₂ + O₃ gives the total open probability for I_BKS. Thus

where P_BKS is the maximal sustained BK current permeability, K_i and K_o are the intracellular and extracellular K⁺ concentrations, and F, R, and T have their usual meanings.

Ion permeation through BK channels was described using the GHK relationship, instead of the more common ohmic relationship, since this allowed a much better reproduction of the experimental, TEA-sensitive, I–V relationship (cf. Fig. 4E, see below). I_BKT has an additional term (h_BKT) taking into account inactivation

where P_BKT is the maximal transient BK current permeability. h_BKT is described by the following differential equation

with h_BKT and τ_BKT (V) given by

and

The steady-state and kinetic parameters of I_BKT inactivation are estimated in the supplemental data. The Ca²⁺ concentration used to assess the Ca²⁺-dependent transition rates in scheme 2 is given by solving the following differential equation (Hudspeth & Lewis, 1988a):

where z and F have their usual meanings. C_vol, ɛ, and K_s were taken from Hudspeth & Lewis (1988a). The buffering capacity of the intracellular solution (U in eqn (A26)) was determined by fitting the steady-state I_BKS − V relationship of non-oscillatory cells (cf. Fig. 4E) with the above-described model at steady state, using the following relationship

where

and

The free parameters of the fit have the following values: U = 0.005 and P_BKS= 2e⁻¹³. g_Ca, estimated from the data reported in Fig. 4E, was 3.2 nS. All the other parameters were taken from Hudspeth & Lewis (1988a) for BK currents, and from Catacuzzeno et al. (2003b) for Ca²⁺ currents. The U-value was found to be lower than that used in Hudspeth & Lewis (1988a; see Table 2), in accordance with a higher intracellular buffering capability in our perforated-patch recordings (see Roberts, 1993).

Table 2.

Kinetic and steady-state parameters used to model the electrical activity of frog saccular hair cells

IBK		IK1		Ih
Parameter	Value	Parameter	Value	Parameter	Value
k−1	300 s−1	EK	−95 mV	Eh	−45 mV
k−2	5000 s−1	Steady-state activation		Steady-state activation
k−3	1500 s−1	V½	−110 mV	V½	−87 mV
K1(0)	6 μm	k	11 mV	k	16.7 mV
K2(0)	45 μm	Activation kinetics		Activation kinetics
K3(0)	20 μm	τK1f(0)	0.7 ms	P1	63.7 ms
δ1	0.2	V0f	−120 mV	P2	135.7 ms
δ2	0	VTf	−43.8 mV	P3	−91.4 mV
δ3	0.2	KTf	0.04 ms	P4	21.2 mV
αC(0)	450 s−1	τK1s(0)	14.1 ms
VA	33 mV	V0s	−120 mV	Casm
βC	1000 s−1	VTs	−28 mV	U	0.005
Inactivation		KTs	0.04 ms	ɛ	3.4e−5
V½	−61.6 mV			Cvo	1.25 pl
KBKT	3.65 mV	IL		Ks	2800 s−1
P1	2.1 ms	gL	0.1 nS	ZCa	2.0
P2	9.4 ms	EL	0 mV
P3	−66.9 mV			Cell capacitance
P4	17.7 mV			Cm	10 pF

I_DRK and I_Ca modelling

Both these currents were modelled as in Catacuzzeno et al. (2003b).

Supplementary material

The online version of this paper can be accessed at:

DOI: 10.1113/jphysiol.2004.072652/

http://jp.physoc.org/cgi/content/full/jphysiol.2004.072652/DC1 and contains supplementary material entitled: Biophysical study of I_BKT inactivation.