INTRODUCTION

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The hyperpolarization-activated inward current (I_h; usually referred to as I_f in heart) has been implicated in the pacemaking of both single-cell and network rhythmicity (for recent reviews, see DiFrancesco 1993; Lüthi and McCormick 1998; Pape 1996). Typically, this current acts to promote depolarization after a hyperpolarizing event. This, in combination with Ca²⁺ currents, functions to induce low-threshold rhythmic discharge in a number of neurons and thus contributes to brain rhythm generation (Llinás and Jahnsen 1982; Lüthi et al. 1998; McCormick and Pape 1990; Steriade and Llinás 1988; Steriade et al. 1993). In contrast to Ca²⁺-dependent oscillations, numerous studies have shown that some, mainly cortical, neuronal populations can generate Na⁺-dependent rhythmic subthreshold membrane potential oscillations that are thought also to be implicated in the genesis of cortical rhythms (Alonso and Llinas 1989; reviewed by Connors and Amitai 1997). The role of near-threshold conductances, including I_h, in the generation of these Na⁺-dependent subthreshold oscillatory events is less clear.

A prominent case of Na⁺-dependent subthreshold oscillatory activity is observed in the principal neurons from entorhinal cortex (EC) layer II (Alonso and Klink 1993; Alonso and Llinás 1989). These glutamatergic neurons, named by Cajal as the stellate cells (SCs) (Ramon y Cajal 1902), funnel most of the neocortical input to the hippocampal formation via the perforant pathway (for review, see Dolorfo and Amaral 1998) and appear to be generators of limbic theta rhythm (Alonso and García-Austt 1987a,b; Buzsáki 1996; Dickson et al. 1995). In vitro current-clamp studies have shown that the current-voltage relationship of EC layer II SCs is extremely nonlinear, displaying robust inward rectification in both the depolarizing and hyperpolarizing direction. Inward rectification in the depolarizing direction is generated by a persistent subthreshold Na⁺ current (I_NaP) (Magistretti and Alonso 1999; Magistretti et al. 1999) (for a recent review on I_NaP, see also Crill 1996) that has been shown to be necessary for the development of the robust theta frequency subthreshold oscillations that the SCs display (Alonso and Klink 1993; Alonso and Llinás 1989). On the other hand, the time-dependent inward rectification in the hyperpolarizing direction is affected by extracellular Cs⁺ but not Ba²⁺ and thus is likely to be generated by the nonspecific cationic current I_h (Klink and Alonso 1993). Given the properties and role of I_h in pacemaking in other excitable cells, it was proposed that this current also could contribute to the genesis of subthreshold oscillations in SCs (Alonso and Llinás 1989; Klink and Alonso 1993: White et al. 1995) although the exact nature of this role was not specified.

Using the whole cell patch-clamp technique in the EC slice preparation, the aim of the present study was to characterize the specific properties of I_h in the SCs and to examine the role of this current in the generation of subthreshold membrane potential oscillations in these cells. In addition, a simplified biophysical simulation based on the voltage- and current-clamp data was used to study the interactions between I_h and I_NaP in the generation of such oscillations. Our results indicate that the dynamic interplay between the gating and kinetic properties of I_h and I_NaP is essential for the generation of rhythmic subthreshold oscillations by the SCs. Given the key position of the SCs in the temporal lobe memory system, modulation of I_h in the SCs may have major implications for the control of population dynamics in the entorhinal network and in the memory processes it carries out. Some of these results have been presented previously in abstract form (Dickson and Alonso 1996, 1998; Fransén et al. 1998).

	METHODS

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General

Brain slices were prepared from male Long-Evans rats (100-250 g, i.e., 30-60 days of age) as previously described (Alonso and Klink 1993). Briefly, animals were decapitated quickly, and the brain was removed rapidly from the cranium, blocked, and placed in a cold (4°C) Ringer solution (pH 7.4 by saturation with 95% O₂-5% CO₂) containing (in mM) 124 NaCl, 5 KCl, 1.25 NaH₂PO₄, 2 CaCl₂, 2 MgSO₄, 26 NaHCO₃, and 10 glucose. Horizontal slices of the retrohippocampal region were cut at 350-400 µm on a vibratome (Pelco Series 1000, Redding, CA) and were transferred to an incubation chamber in which they were kept submerged for 1 h at room temperature (24°C). Slices were transferred, one at a time, to a recording chamber and were superfused with Ringer solution, also at room temperature. The chamber was located on the stage of an upright, fixed-stage microscope (Axioskop, Zeiss) equipped with a water immersion objective (×40-63: long-working distance), Nomarski optics, and a near-infrared charge-coupled device (CCD) camera (Sony XC-75). With this equipment, stellate and pyramidal-like cells could be distinguished based on their shape, size, and position within layer II of the medial entorhinal cortex (Fig. 1A) (Klink and Alonso 1997). Stellate cells (SCs) were selected for whole cell recording.

View larger version (47K): [in this window] [in a new window]   Fig. 1. Basic electrophysiological profile of entorhinal cortex (EC) layer II stellate cells (SCs) under whole cell current-clamp recording conditions. A: digitized photomicrograph demonstrating the visualization of a patched SC. - - -, approximate border between layers I and II. B: V-I relationship of the SC in A demonstrating robust time-dependent inward rectification in the hyperpolarizing direction. C: action potential from (D2) (*) at an expanded time and voltage scale. Note the fast-afterhyperpolarization/depolarizing afterpotential/medium afterhyperpolarization (fast-AHP/DAP/medium-AHP) sequence characteristic of these cells. D: subthreshold membrane potential oscillations (1 and 2) and spike clustering (3) develop at increasingly depolarized membrane potential levels positive to about 55 mV. Autocorrelation function (inset in 1) demonstrates the rhythmicity of the subthreshold oscillations.

Recording

Patch pipettes (4-7 M) were filled with (in mM) 140-130 gluconic acid (potassium salt: K-gluconate), 5 NaCl, 2 MgCl₂, 10 N-2-hydroxyethylpiperazine-N-2-ethanesulfonic acid (HEPES), 0.5 ethylene glycol-bis(-aminoethyl ether)-N,N,N',N'-tetraacetic acid (EGTA), 2 ATP (ATP Tris salt), and 0.4 GTP (GTP Tris salt), pH 7.25 with KOH. In additional experiments performed to assess the contribution of chloride ions to I_h, a modified intracellular solution was made containing (in mM) 120 K-gluconate, 10 KCl, 5 NaCl, 2 MgCl2, 10 HEPES, 0.5 EGTA, 2 ATP-Tris, and 0.4 GTP-Tris, pH 7.25 with KOH. The liquid junction potential was estimated following the technique of Neher (1992). In brief, the offset was zeroed while recording the potential across the patch pipette and a commercial salt-bridge ground electrode (MERE 2, WPI, Sarasota, FL) when the chamber was filled with the same intracellular solution as used in the pipette. After zeroing, the chamber solution was replaced with the extracellular recording solution, and the potential recorded was used as an estimate of the liquid junction potential. Using this method, we recorded a value between 2 and 3 mV. Membrane potential values reported herein do not contain this correction.

Tight seals (>1 G) were formed on cell bodies of selected EC layer II SCs, and whole cell recordings were made by rupturing the cell membrane with negative pressure. Both current- and voltage-clamp recordings were made with an Axopatch 1D patch-clamp amplifier (Axon Instruments, Foster City, CA). For current-clamp recordings, the low-pass filter (3dB) was set at 10 kHz, whereas for voltage clamp, it was set at 2 kHz. All current- and some voltage-clamp experiments were stored by PCL coding on VHS tape (Neurocorder, Neurodata, New York), and all voltage-clamp experiments were stored on computer by digital sampling at 4 kHz, using pClamp software (V6.0, Axon Instruments). Data stored on VHS tape was digitized and plotted off-line by sampling at 20 kHz using Axoscope software (V1.1, Axon Instruments).

The identification of neurons as SCs was confirmed by current-clamp recordings demonstrating the presence of robust inward rectification with hyperpolarizing current pulses in addition to the presence of subthreshold membrane potential oscillations at depolarized levels (Fig. 1, B and C) (Alonso and Klink 1993). SCs fulfilling the following criteria were considered acceptable for further analysis: stable membrane potential less than 50 mV, input resistance >75 M, overshooting spike, and a balanced series resistance <20 M compensated between 60 and 80%.

Solutions

Various salts and drugs were added directly to the perfusate from concentrated stock solutions during experiments. Divalent cations such as Ba²⁺, Co²⁺, or Cd²⁺ were added to a modified Ringer solution without phosphates or sulfates. To isolate I_h to compute activation curves using the tail current method (see RESULTS), the following solution was used (in mM): 80 NaCl, 40 tetraethylammonium chloride (TEA-Cl), 5 KCl, 4 4-aminopyridine (4-AP), 2 MgCl₂, 2 BaCl₂, 2 CoCl₂, 1 CaCl₂, 0.2 CdCl₂, 26 NaH₂CO₃, and 10 glucose and 1 µM tetrodotoxin (TTX). Lowering the extracellular concentration of sodium ions (NaCl) was achieved using equimolar N-methyl-D-glucamine substitution in a no phosphate/sulfate Ringer solution. Alterations in the concentration of potassium ions (KCl) was achieved in the same way in a no phosphate/sulfate Ringer solution with a consistent concentration (119 mM) of NaCl. To prevent the influence of synaptic transmission on the subthreshold membrane behavior in current-clamp recordings, 6-cyano-7-nitoquinoxaline-2,3-dione (CNQX: 10 µM), DL2-amino-5-phosphonopentanoic acid (AP-5: 50 µM), bicuculline methiodide (BMI: 10 µM), and 2-hydroxysaclofen (2-OH saclofen:100 µM) were added to the Ringer solution. To block I_h, CsCl (1-6 mM) or ZD7288 (100 µM) was added directly to the Ringer solution. All salts were purchased from BDH (Toronto, CA), whereas TEA-Cl, 4-AP, TTX, and BMI were purchased from Sigma (St. Louis, MO). CNQX, AP-5, 2-OH-saclofen, and ZD7288 were purchased from Tocris Cookson (UK).

Analysis

Traces were plotted and measurements made with the use of pClamp (Clampfit) and Origin (Microcal, Northampton, MA) software packages. Curve fitting of subtracted traces was conducted with pClamp software. The fittings were made from a time point 15 ms after the application of the hyperpolarizing voltage step so as to minimize any capacitive or membrane charging transients. All curve-fitting procedures were optimized using the least sum of squares method. The standard deviation between the fit and the data were used to estimate the goodness of the fit. Autocorrelational analysis was conducted with Matlab (Mathworks, Natick, MA). Spectral (Fourier) analysis was conducted using both Origin and Matlab.

Biophysical simulation

A simple Hodgkin-Huxley model was assumed for describing I_h activation and deactivation. We applied the basic relationship

(1)

where

(2)

and m is the probability of the activating particle to be in the permissive position. Because I_h activation and deactivation could be properly fitted with double-exponential functions, Eq. 2 was applied separately to each exponential component, whereas Eq. 1 was extended to
Conductance values were derived from amplitude coefficient (A_i) values by applying the relationship: G_hi(V,t) = A_i(V,t)/(V  V_h), where the index i is either 1 or 2. The functions describing m_i(V) were derived directly from G_hi(V) activation curves. The transitions of the activating particle, m_i, were schematized as the following first-order kinetic reaction:
from which it follows

(3)

where

(4)

(5)

Numerical values for the rate constants, _i and _i, were derived from the experimental values of time constants of activation and deactivation (_i) and from the m_i curves by applying Eqs. 4 and 5. Rate-constant plots were best fitted with the empiric function
After obtaining the analytic functions appropriately describing the voltage dependence of rate constants, the changes in I_h during various simulated current-clamp protocols were numerically reconstructed on the basis of the Eqs. 1 and 2 and Eq. 3 in its differential form.

The basic equations used for describing I_NaP were the same as used for I_h (see preceding text, Eqs. 1 and 2). G_NaP(V) was modeled according to the voltage-dependence data reported by Magistretti and Alonso (1999). I_NaP activation was assumed to be instantaneous.

Kinetic and voltage-dependence parameters concerning I_h and I_NaP were used in a simplified model of an EC SC aimed at reproducing the subthreshold oscillatory behavior of membrane potential in these same neurons. In this model, the neuron was considered as monocompartmental, and its membrane conductance consisted of G_h, G_NaP, and a linear leakage conductance (G_l) whose current reversed at the equilibrium potential for K⁺. The parameters of the equations describing conductance kinetics and voltage dependence were given the same numerical values as returned by the analysis of the relevant experimental data (see RESULTS). Na⁺ and K⁺ reversal potentials had the theoretical (Nernst) values calculated for the ionic conditions employed in our current-clamp experiments (V_Na = +87 mV, V_K = 83 mV). The reversal potential for I_h (V_h = 20 mV) and the amplitude ratio between the fast and slow kinetic components of G_h (G_h1Max /G_h2Max = 1.85) also matched exactly the experimentally observed average values. Only the absolute values of maximal conductances (G_Max) were adjusted until a good concordance between simulations and experimental observations was achieved. In the simulations here illustrated, G_hMax, G_NaPMax, and G_lMax equaled 98.0, 17.4, and 78.0 pS/pF, respectively. These values compared reasonably, namely within a factor of 2, with the experimentally measured values.

Numeric solution of the differential equations was achieved by the use of a one-step Euler integration method. The integration step size was 0.25 ms. Preliminary tests on the adequacy of this integration method were carried out by reducing the step size by 25 times, which revealed an optimal convergence. The simulation programs were compiled using QuickBASIC 4.5 (Microsoft). Data were analyzed using Origin.

	RESULTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION REFERENCES

The results presented in this study were based on a database of 131 EC layer II SCs intracellularly recorded under whole cell patch conditions and met the criteria specified in METHODS. The studied neurons were identified as SCs by their gross morphological characteristics (Klink and Alonso 1993) as afforded by direct visualization of their somata and proximal dendrites (Fig. 1A) but mainly by their characteristic electrophysiological properties (Alonso and Klink 1993; Alonso and Llinás 1989) (Fig. 1, B-D). Indeed, as illustrated in Fig. 1, patched SCs demonstrated qualitatively the same electroresponsive properties that distinguish SCs recorded with sharp electrodes. First, the patched SCs demonstrated robust time-dependent inward rectification in the hyperpolarizing direction. As shown in Fig. 1B, the membrane voltage responses to hyperpolarizing current pulses did not monotonically reach a steady value but displayed, after a certain delay, large amplitude "sags" back to more depolarized values. Second, the action potential of the patched SCs also demonstrated the characteristic fast after hyperpolarization (arrowhead Fig. 1C) followed by a depolarizing afterpotential and a medium after hyperpolarization. Finally, and most importantly, patched SCs also developed rhythmic subthreshold membrane potential oscillations and demonstrated cluster discharge when depolarized with DC current in the membrane potential range between 55 and 50 mV (Fig. 1D, 1-3). At an average membrane potential of 52 ± 1 mV, the peak frequency of these membrane potential oscillations as determined by Fourier analysis averaged 3.1 ± 0.7 Hz (n = 12). The SCs had an average resting membrane potential of 55 ± 3 mV and an input resistance of 113 ± 40 M.

Although not further treated, in some instances, neurons other than SCs were recorded from. Pyramidal-like cells of EC layer II (n = 10), could be distinguished from SCs based on their pyramidal shape and their limited expression of time-dependent inward rectification (Klink and Alonso 1993). Layer III pyramidal cells (n = 3) were distinguishable based on their qualitatively smaller size, their high-input resistance (217 ± 67 M) and the absence of time-dependent inward rectification (Dickson et al. 1997).

Hyperpolarization-activated, time-dependent inward rectification in SCs corresponded to a slow, noninactivating inward current

As illustrated for a typical SC in Fig. 2, the depolarizing sags that developed on membrane hyperpolarization in current-clamp conditions (A, ) were paralleled by the development of a slow inward current on step hyperpolarization under voltage-clamp conditions (B, ). Note that the time course and amplitude of this inward relaxation was overtly voltage dependent (see following text). In all cases, analysis of the subthreshold input-output relations under current-clamp revealed that the steady-state voltage-current (V-I) curve (Fig. 2C; ) showed a marked upward bending over the entire voltage range (60 to 120). Similarly, analysis of input-output relations under voltage-clamp revealed that the steady-state current-voltage curve (ssI-V; Fig. 2D, ) showed a robust inward shift, as compared with the instantaneous current-voltage curve (Fig. 2D, ), that grew steadily with membrane hyperpolarization. The slow inward current relaxations were associated with a membrane-conductance increase because the instantaneous current flowing at the break of the hyperpolarizing commands was larger than that recorded on first jumping to the command potential (see Fig. 4A). Thus SCs do possess a robust time-dependent hyperpolarization activated conductance (G_h).

View larger version (34K): [in this window] [in a new window]   Fig. 2. Characterization of inward rectification in the SCs. A: in current-clamp conditions, hyperpolarizing current pulses evoke voltage responses with a robust time-dependent depolarizing sag (). B: in the same neuron, under voltage-clamp conditions, hyperpolarizing voltage steps evoke a slow inward current (Ih) that grows in amplitude and rate of activation with increasing hyperpolarization. C: peak and steady-state V-I plot ( and , respectively) derived from the data in A. Time-dependent inward rectification is graphically represented as the depolarizing shift between peak and steady-state potential readings. D: instantaneous and steady-state I-V plot ( and , respectively) derived from the data in B. Time-dependent inward rectification is apparent as the negative difference in the holding current between the instantaneous and steady-state measurements. All traces shown were obtained in the standard Ringer solution.

Pharmacological block of inward rectification

In addition to a time-dependent inward rectifier such as I_h, many neurons also possess a fast inward rectifier K⁺ current (I_Kir) (reviewed by Hille 1992). It has been shown that in many cells bath application of Ba²⁺ and Cs⁺ can be used to pharmacologically dissect I_h from I_Kir because Ba²⁺ blocks I_Kir and not I_h, whereas Cs⁺ blocks both I_Kir and I_h (Hagiwara et al. 1976, 1978). In agreement with this, in all SCs tested (n = 8), bath application of Ba²⁺ (0.5-2 mM) had no effect on I_h (Fig. 3, A-C), although it did block the small inward bending of the instantaneous I-V relationship that was always observed at potentials negative to about 80 mV in control conditions (Fig. 3C, squares). This Ba²⁺ effect suggests the presence of a minor I_Kir in the SCs. In contrast to Ba²⁺, in all SCs tested (n = 10), bath application of Cs⁺ (1-6 mM) always produced a substantial decrease in I_h (though never a complete I_h block). This decrease was assessed by expressing the percentage decrease in the difference between the instantaneous and steady-state current at potentials between 60 and 80 mV before and after application of Cs⁺ (cf. Ishii et al. 1999). It was dose dependent and ranged from 60 to 75% for a concentration of 2 mM Cs⁺ (n = 5) that produced close to maximal effects.

View larger version (33K): [in this window] [in a new window]   Fig. 3. Effects of extracellular Ba2+ and ZD7288 on Ih. A and B: current responses evoked by a series of voltage-clamp steps in control conditions (A) and during superfusion with 2 mM Ba2+ (B). C: I-V plot of both the instantaneous ( and ) and steady-state ( and ) current responses from A and B. Note that Ba2+ did not block time-dependent inward rectification (generated by Ih) though it did appear to affect fast inward rectification (apparent as the negative bending of the instantaneous current plot at potentials negative to 80 mV). D-F: current responses evoked by a series of voltage-clamp steps in control conditions (D), in the presence of 100 µM ZD7288 (E) and during further addition of 2 mM Ba2+ (F). G: I-V plot of both the instantaneous ( and ) and steady-state ( and ) current responses from (D, control) and (E, +ZD7288). H: I-V plot of both the instantaneous ( and ) and steady-state ( and ) current responses from (E, +ZD7288) and (F, +Ba2+). Note that ZD7288 completely abolished time-dependent inward rectification and that Ba2+ abolished the remaining, minor, fast inward rectification. All recordings were carried out in the presence of 1 µM TTX and 2 mM Co2+.

Given that Cs⁺ produced only a partial block of I_h in the SCs, we assessed the effects of the novel bradycardic agent ZD7288, which has been reported to be a potent blocker of I_h in other cells (BoSmith et al. 1993; Harris and Constanti 1995; Maccaferri and McBain 1996; Williams et al. 1997). As illustrated in Fig. 3 (D and E), in all cases tested (n = 9), bath application of ZD7288 (>10 min; 100 µM) always resulted in a complete and irreversible block of I_h. When the cells were held at 60 mV (about resting level), application of ZD7288 always resulted in an outward shift of the holding current (mean =138 ± 52 pA, n = 5), indicating that G_h is active at the resting membrane potential (see following text). Significantly, ZD7288 did not abolish the small inward shift of the instantaneous I-V relation below 80 mV (Fig. 3G) and thus whereas ZD7288 fully blocked I_h, it did not affect I_Kir. Although small, the remaining fast inward rectification, however, could be blocked fully by the further addition of Ba²⁺ that also caused a decrease in slope conductance due to its blocking action on leak currents (n = 3; Fig. 3, F and H).

Activation of I_h

We estimated the activation curve of the membrane conductance underlying I_h (G_h) by applying two different protocols (Fig. 4). In the first protocol, a modified Ringer solution (as specified in METHODS) was used. The activation curve of G_h was estimated from the peak amplitude of the tail currents recorded at about 40 mV (n = 8) or at about 60 mV (n = 5) after a series of hyperpolarizing voltage-clamp steps from a holding potential in the range of 45 to 30 mV (Fig. 4, A-C). When stepping back to 60 mV, the zero current level was the tail current amplitude after the most depolarized voltage step (at least 40 mV). Tail current amplitudes were normalized to the maximal value (I_max) and plotted as a function of the membrane potential during the hyperpolarizing prepulse. In all cases (n = 13), the data were well fitted with a Boltzmann equation of the form
where V_m is the membrane potential of the prepulse, V_1/2 the membrane potential at which G_h is half activated, k a slope factor, and I is the amplitude of the tail current recorded after the prepulse. The tail current analysis yielded an activation range of G_h between 45 and 115 mV, a mean value for V_1/2 of 77 ± 5 mV and a slope factor (k) of 11.2 ± 1.8 (Fig. 4C).

View larger version (30K): [in this window] [in a new window]   Fig. 4. Activation curve for the conductance Gh. A: incremental hyperpolarizing voltage-clamp steps increase the amount of Ih that is activated as well as the amplitude of the tail currents that follow (inset). B: tail currents from A shown at an expanded time and current scale. Tail current amplitude measurements were taken at the time indicated by the empty circle and broken line. C: plot of the activation curve of Gh. Filled circles, averaged activation curve for 13 SCs. Individual experiments first were fitted with Boltzmann functions and the interpolated values for the steps at each 10-mV increment were used to compute the average value. Small open circles, data derived from cell in A. Line, best Boltzmann fit to the average (see RESULTS) where the half activation voltage and slope factor were found to be 77 ± 5 mV and 11.2 ± 1.8, respectively. D: Gh activation curves also were estimated in four cells from Ih-V relations where Ih was isolated by subtracting ZD7288 I-V curves from control I-V curves obtained through slow ramp protocols (inset, see RESULTS for details). As can be seen, the Gh activation curve obtained in this manner (noisy line) and its Boltzmann fit (dotted line) largely overlap the activation curve obtained from tail current analysis (continuous line; same as in C). Tail current protocols were conducted using the specialized solution described in METHODS, and ramp protocols were conducted in solution containing 1 µM TTX, 2 mM Co2+, and 2 mM Ba2+.

For comparison, in four cells we applied slow (<10 mV/s) 100 mV hyperpolarizing voltage ramps from a holding potential of 30 mV in control and after block of I_h with ZD7288 (Fig. 4D). In these experiments, 1 µM TTX, 2 mM Co²⁺, and 2 mM Ba²⁺ were added to the control Ringer. Subtraction of the ZD7288 I-V curve from the control curve yielded the steady-state I_h I-V relationship from which we estimated G_h according to the formula G_h= I_h/(V_m  V_h) where V_h is the reversal potential for I_h estimated to be 21 mV (see following text, Fig. 6). The resulting values were normalized to the maximal conductance (G_max; 10.4 ± 2.3 nS) and plotted against V_m. In all cases the curves were well fitted with a Boltzmann equation as in the preceding text. This ramp analysis yielded a V_1/2 of 76 ± 4 mV and a slope factor of 12.1 ± 2, which were not significantly different to those obtained by tail current analysis by two-tailed t-tests [t(15) = 0.36, P > 0.05; t(15) = 0.85, P > 0.05].

Time course of activation and deactivation

As stated previously, the rate of activation of I_h increased sharply with hyperpolarization (e.g., Fig. 2B). This qualitative observation was further explored in a more quantitative manner. To maximize the accuracy of our kinetic analysis, we isolated I_h by subtracting from control current traces evoked by hyperpolarizing voltage-clamp steps, the current traces evoked to the same potentials in the presence of the selective I_h blocker ZD7288 (n = 5; Fig. 5A). Over the whole voltage range tested, the I_h current relaxations were best fitted with a double exponential function of the form
where I_h(t) is the amplitude of the current at time t, C is a constant, and A₁, and A₂ reflect the amplitude coefficients of the fast (₁) and slow (₂) time constants, respectively. Attempts to fit the subtracted traces with a single exponential function were judged to be unsuccessful based on visual inspection and by comparison of the standard deviations of the fits using single or double exponential functions (not shown). Both the first and second time constants were found to be voltage dependent, as shown in Fig. 5, C and D, becoming faster with increased hyperpolarization. The first time constant ranged between 78 ± 12 and 39 ± 6 ms for voltage steps to 70 and 110 mV, respectively. The second time constant ranged between 372 ± 39 and 164 ± 45 ms for the same voltage steps. The ratio of the amplitude coefficients for the first (A₁) and second (A₂) time constants increased from 1 at 70 mV to just over 2 at 110 mV.

View larger version (24K): [in this window] [in a new window]   Fig. 5. Activation and deactivation kinetics of Ih. Ih was isolated by subtraction of ZD7288 current traces from control current traces recorded in the presence of 1 µM TTX, 2 mM Co2+, and 2 mM Ba2+. A: averaged (n = 5) Ih traces ( · · · ) evoked by hyperpolarizing steps from 60 mV. Ih activation time course was well fitted by a double-exponential decay function (, see RESULTS for details). B: averaged (n = 5) Ih traces ( · · · ) evoked by depolarizing steps from 60 mV (same collection of cells as in A). Ih deactivation time course was also well fitted by an incremental asymptotic double-exponential function (, see RESULTS for details). C and D: plots of the 1st and 2nd time constants of activation and deactivation as a function of membrane potential. Kinetics of activation of Ih () can be seen to be voltage dependent with both the 1st (C) and 2nd (D) time constants decreasing with hyperpolarization. Kinetics of deactivation of Ih () also can be seen to be voltage dependent with both the 1st (C) and 2nd (D) time constants decreasing with depolarization.

An equivalent method as the one described in the preceding text was conducted to study the rate of deactivation of I_h isolated with the use of ZD7288 (Fig. 5B). Isolated I_h current traces evoked by depolarizing voltage steps from a holding potential of 60 mV were also well fitted by a double-exponential function. As for the time constants of activation, both the first and second time constants of deactivation were found to be voltage dependent, becoming faster with increasing depolarization (Fig. 5, C and D). The first time constant of deactivation ranged from 23 ± 9 to 58 ± 13 ms for voltage steps to 40 and 50 mV, respectively. The second time constant of deactivation ranged between 241 ± 38 and 326 ± 58 ms for the same voltage steps. The amplitude of the fast time constant was roughly 1.25 that of the slower, and this ratio remained constant over the voltage range tested.

Reversal of I_h

Estimation of the reversal potential of I_h was achieved by two different methods, which took advantage of the fact that at 80 mV, G_h was strongly activated and did not show time-dependent inactivation (Fig. 6, A and B). In all experiments, the superfusing Ringer solution contained 1 µM TTX, 2 mM CoCl₂, and 2 mM BaCl₂. Thus in the first method, we estimated the reversal potential of I_h (V_h) from the intersection of the instantaneous (chord) current-voltage relationships recorded at holding potentials of 80 and 40 mV (i.e., in the presence and absence of I_h; Fig. 6C) (Mayer and Westbrook 1983). In 17 neurons examined, this method provided an average value for V_h of 21 ± 5mV.

View larger version (15K): [in this window] [in a new window]   Fig. 6. Reversal potential of Ih. Extrapolated reversal potential of Ih (Vh) was estimated by 2 different approaches. A-C: SCs were held at 40 and 80 mV (A and B, respectively) and the instantaneous I-V relations constructed. Vh was estimated from the intersection of the extrapolated I-V relations derived from both holding potentials (C). D and E: SCs were held at 80 mV, and the instantaneous I-V relation was constructed in control conditions (D) and during Ih block with ZD7288 (E). Vh was estimated from the intersection of the extrapolated I-V relations derived in both conditions (F). All recordings were conducted in a solution containing 1 µM TTX, 2 mM Co2+, and 2 mM Ba2+.

To support the preceding estimation, we used a second method in which we took advantage of the fact that I_h is selectively and fully blocked by ZD7288 (see preceding text). Chord conductance measurements were made from voltage steps from a holding potential of 80 mV before and after block of I_h using ZD7288 and the instantaneous I/V relationships in both conditions were constructed (Fig. 6, D-F). In eight neurons examined, the average voltage at which the linear fits for both plots intersected, i.e., the reversal potential for I_h, was 22 ± 6 mV, a value that was not significantly different from that found with the tail current analysis method above [t(23) = 0.44, P > 0.05].

Ionic basis of I_h

The fact that in the SCs I_h reverses at about 20 mV suggests that, as in other neurons (Crepel and Penit-Soria 1986; Halliwell and Adams 1982; Mayer and Westbrook 1983; McCormick and Pape 1990; Spain et al. 1987; Takahashi 1990), this hyperpolarization-activated inward current might be carried by a mixture of both Na⁺ and K⁺ ions. Indeed, increasing the extracellular concentration of K⁺ ([K⁺]_o) (Fig. 7) produced an increase in I_h (with no change in the G_h activation curve; not shown) as well as an increase in instantaneous conductance. As expected for K⁺ being an important carrier for I_h, an increase in [K⁺]_o from 1 to 10 mM produced an average positive shift in V_h of 10 ± 4mV (n = 4, Fig. 7D).

View larger version (23K): [in this window] [in a new window]   Fig. 7. Ih is increased and Vh shifted in a depolarized direction in raised [K+]o. A: Ih was evoked by hyperpolarizing voltage steps from a holding potential of 40 mV in a control Ringer solution containing 1 mM [K+]o. B: increasing the concentration of [K+]o markedly increased the amplitude of Ih evoked at the same potential levels. C: washing with 1 mM [K+]o reversed this increase. D: cells were held at 40 and 80 mV (top and bottom left, respectively) and the instantaneous I-V relations were constructed in both 1 and 10 mM [K+]o. Right: Vh in both 1 mM (, , and ) and 10 mM [K+]o (, , and - - -) was estimated from the intersection of the extrapolated I/V relations constructed from 40 ( and ) and 80 mV ( and ). Note that in this cell changing the [K+]o from 1 to 10 mM shifted the extrapolated Vh from 24 to 17 mV. All recordings were conducted in a solution containing 1 µM TTX, 2 mM Co2+, and 2 mM Ba2+.

On the other hand, reductions in the concentration of extracellular Na⁺ from control levels (151 mM) to 26 mM reversibly reduced the amplitude of I_h (Fig. 8) without changing the activation properties of the conductance underlying this current (not shown). Concomitant with this reduction, V_h shifted in the hyperpolarizing direction by an average of 21 ± 5mV (n = 5). These results indicate that Na⁺ ions also largely contribute to I_h.

View larger version (28K): [in this window] [in a new window]   Fig. 8. Ih is decreased and its reversal potential shifted in a hyperpolarized direction in lowered [Na+]o. A: Ih was evoked by hyperpolarizing voltage steps from a holding potential of 40 mV in a control Ringer solution (151 mM [Na+]o). B: lowering [Na+]o to 26 mM (substitution with N-methyl-D-glucamine) diminished the amplitude of Ih evoked at the same potential levels. C: washing with control Ringer reversed this reduction. D: cells were held at 40 and 80 mV (top and bottom left, respectively) and the instantaneous I-V relations constructed in both 151 mM [Na+]o (control) and 26 mM [Na+]o (low Na+). Right: Vh in both 151 mM [Na+]o (, , and ) and 26 mM [Na+]o (, , and - - -) was estimated from the intersection of the extrapolated I-V relations constructed from 40 ( and ) and 80 mV ( and ). Note that in this cell changing the [Na+]o from 151 to 26 mM shifted the extrapolated Vh from 19.8 to 45.9 mV. All recordings were conducted in a solution containing 1 µM TTX, 2 mM Co2+, and 2 mM Ba2+.

Finally, a number of neurons (5) were recorded using a modified intracellular solution containing an additional 10 mM Cl in the pipette solution (see METHODS). Although in these cases, the chloride reversal potential was theoretically shifted by ~20 mV in a positive direction, no significant difference was observed in either the average reversal potential [23 ± 6 mV; t(20) = 1.48, P > 0.05] or the activation properties of I_h (not shown). Thus using the Goldman-Hodgkin-Katz equation and an estimated V_h of 21.5 mV, we calculated a permeability (conductance) ratio for Na⁺ and K⁺ (pNa⁺/pK⁺) of ~0.4 for I_h in the SCs.

Role of I_h in membrane potential oscillations

Given the overlap between the activation range of G_h (threshold at about 45 mV), and the voltage range at which subthreshold membrane potential oscillations occur in SCs (60 to 50 mV), we sought to define the involvement of I_h in these oscillations by exploring the effects on them of Cs⁺, ZD7288 and Ba²⁺. Because these agents, particularly Cs⁺ and Ba²⁺, greatly enhance spontaneous synaptic events, we carried out this analysis during synaptic transmission block with CNQX (10 µM), AP5 (50 µM), bicuculline (10 µM), and 2-OH-saclofen (100 µM). In line with a role of I_h in the generation of the rhythmic subthreshold oscillations, we observed that the addition of Cs⁺ (1-2 mM; n = 4) to the superfusate resulted in a progressive disruption (and slow-down) of the oscillations. However, as previously reported (Klink and Alonso 1993), some trains of subthreshold oscillatory activity could consistently be observed in the presence of Cs⁺. This result might be interpreted as suggestive that, in addition to I_h, another conductance operating in the subthreshold range, such as the M current, may play a major role in the generation of the rhythmic subthreshold oscillations by the SCs. Alternatively, it also might be that the expression of subthreshold oscillatory activity by the SCs is rather insensitive to the level of I_h expression and that a major decrease in I_h is necessary to abolish the oscillations. To explore these possibilities, we first tested the effects of the more potent I_h blocker ZD7288. In all cells, application of 50-100 µM ZD7288 always resulted in membrane hyperpolarization (9 ± 4 mV; n = 8) concomitant with the block of the typical depolarizing voltage sag evoked by hyperpolarizing current pulses. Similarly to Cs⁺, ZD7288 always produced a progressive disruption of the oscillations, though, in contrast to what was observed with Cs⁺, this disruption always proceeded to a complete block (Fig. 9, A-C). Although these data suggest that, indeed, a major block of I_h is necessary to completely abolish the oscillations, it could be argued that the blocking effect of ZD7288 might have been due to a nonselective action of the drug on another conductance operating in the oscillatory range. To exclude this possibility, we performed a series of voltage-clamp experiments in which we examined the effects of ZD7288 on the outward current relaxations evoked by a series of depolarizing voltage-clamp steps from 60 mV (about resting level) to the voltage range where subthreshold oscillations develop (55 to 50 mV; Fig. 10A) and up to the G_h activation threshold (45 mV). These experiments were conducted in the presence of 1 µM TTX and 2 mM Co²⁺. As shown in Fig. 10, B-D, ZD7288 (100 µM) always caused a robust outward shift in the holding current and a complete and selective block of both the outward current relaxations in response to membrane depolarization as well as the associated tail currents on return to the holding potential (n = 4). In contrast, there was a nearly perfect overlap between the traces at 45 mV, the threshold for activation of I_h, before and after ZD7288. This indicates that, in the voltage range from 60 to 45 (which includes the voltage range at which the membrane potential oscillations occur) the action of ZD7288 was specific for I_h. Thus the block of the oscillations by ZD7288 cannot be attributed to a nonspecific effect of the drug.

View larger version (18K): [in this window] [in a new window]   Fig. 9. Effects of ZD7288 and Ba2+ on subthreshold oscillations. A and D: in control Ringer solution containing synaptic blockers (see METHODS), DC depolarization elicited rhythmic subthreshold membrane potential oscillations in 2 different cells. B: in the cell shown in A, the subthreshold oscillatory activity was abolished after application of 50 µM ZD7288. Inset in B shows the membrane responses to a 0.1-nA hyperpolarizing pulse before and after ZD7288 application, demonstrating a full block of time-dependent inward rectification. C: autocorrelation analysis of membrane potential in the just-subthreshold range before and after application of ZD7288 ( and - - -, respectively). Note lack of rhythmical oscillatory activity after drug application. E: in the cell shown in D, the oscillations were still present after application of 1 mM Ba2+; however, they were increased markedly in amplitude (from 3.6 to 4.5 mV: peak to peak), and reduced in frequency (from 2.1 to 1.1 Hz). Inset in D shows the membrane response to a hyperpolarizing pulse of 0.1-nA demonstrating a large increase in input resistance without block of time-dependent inward rectification. F: autocorrelation analysis of membrane potential in the just-subthreshold range before and after application of Ba2+ ( and - - -, respectively). Note the longer period of rhythmical oscillatory activity after Ba2+ application.

View larger version (21K): [in this window] [in a new window]   Fig. 10. Blocking effect of ZD7288 on the subthreshold membrane potential oscillations can be attributed to the blocking action of this drug on Ih. A: subthrehold oscillations in the SCs develop on DC depolarization to the voltage range between about 55 to 50 mV. B: voltage-clamp experiment in the same cell showing outward current relaxations (corresponding to Ih deactivation) during depolarizing voltage steps through the oscillatory voltage level (55, 50, and 45 mV), as well as inward current relaxations (corresponding to Ih activation) on return to the holding potential (60 mV). C: addition of 100 µM ZD7288 eliminated Ih and thus caused a robust outward shift in the holding current and the concomitant disappearance of the outward current relaxations on depolarization as well as the inward current relaxations on return to the holding potential. D: superimposition of traces in B and C. Note that control and ZD7288 current traces to 45 mV overlap perfectly at steady-state, thus indicating that in the voltage range examined the actions of ZD7288 were selective for Ih. Voltage-clamp recordings were performed in the presence of 1 µM TTX and 2 mM Co2+.

Finally, it also might be argued that the disappearance of sustained subthreshold oscillations with ZD7288 resulted from the membrane conductance decrease due to the I_h block and not by the I_h block per se. This possibility was tested with the use of Ba²⁺ (1-2 mM; n = 7), which, in contrast to ZD7288, does not affect I_h (cf. Fig. 3) but which, similarly to ZD7288, also produces a major decrease in membrane conductance. Importantly, and in sharp contrast to the ZD7288 results, bath superfusion with Ba²⁺ resulted in both a significant increase in the amplitude [1.2 ± 0.5 mV; t(4) = 2.7; P < 0.05] and a significant decrease in the frequency [1.3 ± 0.1 Hz; t(6) = 8.8; P < 0.01] of the subthreshold oscillations (Fig. 9, D-F). In consequence, the above indicates that I_h plays an essential role in the generation of rhythmic subthreshold oscillations by the SCs and that leak conductances can modulate their amplitude and frequency through their effects on passive membrane properties.

Role of I_h and I_NaP in the generation of subthreshold oscillations

Although the preceding experimental data indicate that I_h is necessary for the genesis of subthreshold oscillations by the SCs, previous studies have shown that these oscillations are also dependent on the activation of a subthreshold persistent Na⁺ current (I_NaP) (Alonso and Llinás 1989). To generate an oscillatory phenomenon, a process is needed the action of which feeds-back to slow down the rate of the process itself and, most critically, a delay in the execution of the feedback. In SCs, the slow kinetics of activation and deactivation of I_h potentially can implement such a feedback process. To further clarify the role of I_h in the generation of subthreshold oscillations by the SCs and to complement the preceding experimental data, we next implemented a simplified biophysical simulation of the subthreshold membrane voltage behavior of these neurons. Using classical Hodgkin-Huxley formalism, a theoretical reconstruction of the biophysical properties of I_h first was carried out. To be consistent with our experimental data indicating both a fast and a slow kinetic component of I_h (see preceding text; Fig. 5), we constructed activation plots of the corresponding fast and slow conductance components (G_h1 and G_h2, respectively; Fig. 11A, 1 and 2) from which the m_i curves were derived directly by using a standard Boltzmann fitting (see METHODS and legend of Fig. 11). The voltage dependence of the fast and slow rate constants (_i and _i; Fig. 11C, 1 and 2) was estimated from the corresponding time constants of activation and deactivation (_i; Fig. 11B, 1 and 2) and the m_i curves, as explained in detail in METHODS.

View larger version (30K): [in this window] [in a new window]   Fig. 11. Modeling of the biophysical properties of Ih. A: voltage dependence of the normalized conductances derived from amplitude coefficients returned by double-exponential fittings of average Ih traces. Amplitude coefficients relating to the fast and slow time constants (A, 1 and 2, respectively) were used to calculate the values of the underlying conductances (GA1 and GA2, respectively) as explained in METHODS. Boltzmann fittings to the experimental data points also are shown. Fitting parameters are: V1/21 = 67.4 mV, k1 = 12.66 mV (A1); V1/22 = 57.92 mV, k2 = 9.26 mV (A2). B: voltage dependence of fast (1) and slow (2) time constants (1 and 2, respectively) returned by double-exponential fittings of average Ih traces. , theoretical functions describing the behavior of the experimental plots, as obtained from the theoretical functions derived from fittings of rate-constant plots (see following text; see also METHODS for details). C: voltage dependence of fast and slow rate constants (1, 1, and 2, 2, respectively) calculated from normalized conductance values and time-constant values as explained in METHODS. , "on" reaction rate constants (); , "off"-reaction rate constants (). , fittings obtained using the theoretical function described in METHODS. Fitting parameters are: a = 2.89 · 103 mV1 · ms1, b = 0.445 ms1, k = 24.02 mV (1); a = 2.71 · 102 mV1 · ms1, b = 1.024 ms1, k = 17.4 mV (1); a = 3.18 · 103 mV1 · ms1, b = 0.695 ms1, k = 26.72 mV (2); a = 2.16 · 102 mV1 · ms1, b = 1.065 ms1, k = 14.25 mV (2).

The derived parameters for the kinetics and voltage dependence of I_h and those for I_NaP as described previously (Magistretti and Alonso 1999) then were incorporated in a single compartment model of the SC (see METHODS). The model then was explored to test whether it could reproduce characteristic current-clamp phenomena such as the sag in membrane potential during hyperpolarizing current steps and the generation of subthreshold membrane potential oscillations.

Voltage responses to hyperpolarizing current steps in the model SC are illustrated in Fig. 12A. Note that the model cell did display the typical delayed large-amplitude depolarizing sags in response to membrane hyperpolarization as well as robust rebound potentials at the break of the hyperpolarizing current pulses. More importantly, as shown in Fig. 12B, the model SC also developed sustained rhythmic membrane potential oscillations in response to DC membrane depolarization from its resting level to about 53 mV. The combined experimental and model work thus demonstrates that in the SCs the interplay between I_h and I_NaP is essential for the generation of sustained rhythmic subthreshold membrane potential oscillations.

View larger version (13K): [in this window] [in a new window]   Fig. 12. Modeling of the current-clamp behavior of SCs. A: current-clamp V-I simulation in a simplified model of a SC. In this simulation, 600-ms hyperpolarizing current pulses of