INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

In cells expressing voltage-gated Ca²⁺ channels (VGCCs), action potential (AP) firing promotes Ca²⁺ entry, which triggers a variety of biochemical events involved in the control of cell function. The frequency, amplitude, duration, and rate of rise and fall of AP-driven Ca²⁺ signals determine the magnitude and/or specificity of the cellular response (Spencer et al., 1989; Hsu et al., 1996; Dolmetsch et al., 1997; De Konninck and Schulman, 1998; Charles et al., 1999). In general, the profile of the AP waveform and the gating properties of the VGCCs determine the peak and duration of the voltage-gated Ca²⁺ current (I_Ca), which in turn dictate the pattern of Ca²⁺ influx. Consequently, changes in the AP profile and/or VGCC gating properties can alter AP-driven Ca²⁺ signaling. This is of potential physiological relevance for many cell types, in which receptor activation is frequently accompanied by changes in the pattern of AP firing. For example, in immortalized gonadotropin-releasing hormone (GnRH)-secreting neurons (GT1 cells), activation of endogenous phospholipase C-coupled GnRH receptors stimulates a voltage-independent Ca²⁺ current that depolarizes the baseline potential reached during the interpulse interval. This increases the frequency of firing and shifts the profile of the AP waveform from sharp, high-amplitude spikes (hereafter sharp spikes) to broad, low-amplitude spikes (hereafter broad spikes) (Van Goor et al., 1999a,b). Activation of thyropropin-releasing hormone or corticotropin-releasing hormone receptors also depolarizes the baseline potential, which leads to a similar shift in the pattern of firing in pituitary lactotrophs and corticotrophs, respectively (Sankaranarayanan and Simasko, 1996; Kuryshev et al., 1997).

However, the relationship between the profile of the AP waveform and voltage-gated Ca²⁺ influx and the ionic mechanisms mediating agonist-induced spike broadening in neuroendocrine cells have been incompletely characterized. For example, experimental (McCobb and Beam, 1991; Toth and Miller, 1995) and theoretical (Augustine, 1990) findings indicate that spike broadening increases peak I_Ca because of an increase in the probability of the channels being in the open state. In contrast, spike broadening has been found to decrease the peak I_Ca in some neurons (Park and Dunlap, 1998). A reduction in spike amplitude has also been demonstrated to decrease the peak I_Ca (Toth and Miller, 1995) and associated Ca²⁺ entry (Callaway and Ross, 1995; Spruston et al., 1995), reflecting the activation of fewer channels. In addition, several potential mechanisms could mediate agonist-induced spike broadening. One possibility is that agonist-induced activation of intracellular signaling pathways may inhibit voltage-gated K⁺ currents (I_K) to stimulate spike broadening (Goldsmith and Abrams, 1992). Alternatively, membrane depolarization and the ensuing increase in spike frequency may inactivate I_K and slow AP repolarization (Jackson et al., 1991). Finally, the decrease in spike amplitude in response to agonist-induced membrane depolarization may activate less I_K and thus cause spike broadening and change the pattern of AP-driven Ca²⁺ entry and the associated increase in intracellular Ca²⁺ concentration ([Ca²⁺]_i).

In this study, we first examined the ionic mechanism mediating depolarization-induced spike broadening in GT1 neurons, using prerecorded sharp and agonist-induced broad AP waveforms as the voltage command. The use of prerecorded AP waveforms allows for the physiological characterization of the ionic currents underlying the generation of different AP waveform subtypes. The validity of our experimental findings was tested by comparing them with a computational model that was based exclusively on the properties of the individual ionic currents characterized in GT1 neurons. We next examined the impact of the shift in the AP profile on I_Ca to determine why Ca²⁺ influx is enhanced despite the decrease in spike amplitude during sustained membrane depolarization. Finally, we used the GT1 cell model to examine the influence of VGCC gating properties on the ability of AP broadening to enhance the I_Ca.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

GT1 cell culture

All experiments were performed on the GT1-7 subtype of immortalized GnRH neurons (Mellon et al., 1990), which were originally provided by Richard I. Weiner (University of California, San Francisco). The cells were grown in 75-ml culture flasks containing culture medium composed of Dulbecco's minimum essential medium/F-12 (1:1) with L-glutamate, pyridoxine hydrochloride, 2.5 g/liter sodium bicarbonate, 10% heat-inactivated fetal bovine serum, and 100 µg/ml gentamicin (GIBCO, Grand Island, NY). At confluence, the cells were dispersed by trypsinization (0.05% trypsin) for 10 min, resuspended in culture medium, and plated on poly-L-lysine-coated (0.01%) coverslips (50,000 cells/ml) in 35-mm tissue culture dishes (Corning, Corning, NY). After incubation for 48 h, the culture medium was replaced with medium containing B-27 serum-free supplement (GIBCO) to induce morphological differentiation of the cells. All experiments were performed 3-5 days after serum removal.

Electrophysiological recordings

With the exception of I_Ca recordings, all ionic currents and membrane potentials (V_m) were measured with the perforated-patch recording technique (Rae et al., 1991). For the recording of I_Ca, regular whole-cell recording techniques were used (Van Goor et al., 1999b). Current-clamp and voltage-clamp recordings were performed at room temperature with an Axopatch 200 B patch-clamp amplifier (Axon Instruments, Foster City, CA) and were low-pass filtered at 2 kHz. For perforated-patch recordings, the patch pipette tips (3-5 M) were briefly immersed in amphotericin B-free solution and then back-filled with amphotericin B (240 µg/ml)-containing solution. Before seal formation, liquid junction potentials were canceled. An average series resistance of 17 ± 1 M was reached 10 min after the formation of a gigaohm seal (seal resistance > 5 G) and remained stable for up to 1 h. When necessary, series resistance compensation was optimized. Capacitive current was reduced by coating the pipette tips with Sylgard (Dow Corning Corporation, Midland, MI) and by maintaining low bath solution levels. The remaining capacitive current was removed by using the capacity compensation circuitry of the patch-clamp amplifier. An average membrane capacitance (C_m) of 10 ± 1 pF (n = 41) was determined using the membrane test function in Clampex 8 (Axon Instruments). Pulse generation, data acquisition, and analysis were done with a PC equipped with a Digidata 1200 A/D interface in conjunction with Clampex 8 (Axon Instruments). All values in the text are reported as means ± SEM. In some cases, the current-voltage relations were fit with a single Boltzmann relation: I/I_max = 1/(1 + exp((E  E_1/2)/k)), where I_max is the maximum inward current, E is the prepulse potential, E_1/2 is the V_m at which there is 50% of the maximum current, and k is the slope factor. Differences between groups were considered to be significant when p < 0.05 with the paired t test.

Measurement of [Ca²⁺]_i

GT1 neurons were incubated for 15 min at 37°C in phenol red-free medium 199 containing Hanks' salts, 20 mM sodium bicarbonate, 20 mM HEPES, and 0.5 µM indo-1 AM (Molecular Probes, Eugene, OR). The coverslips with cells attached were then washed twice with modified Krebs-Ringer's solution containing (in mM) 120 NaCl, 4.7 KCl, 2.6 CaCl₂, 2 MgCl₂, 0.7 MgSO₄, 10 HEPES, and 10 glucose (pH adjusted to 7.4 with NaOH) and mounted on the stage of an inverted epifluorescence microscope (Nikon). A Nikon photon counter system was used to simultaneously measure the intensity of light emitted at 405 nm and at 480 nm after excitation at 340 nm. Background intensity at each emission wavelength was corrected. Perforated patch recording techniques (see above) were used to control the V_m and to inject the different AP waveforms to measure AP-driven Ca²⁺ entry. The data were digitized at 4 kHz, using a PC equipped with the Clampex 8 software package in conjunction with a Digidata 1200 A/D converter (Axon Instruments). The [Ca²⁺]_i was calibrated in vivo according to the method of Kao (1994). Briefly, R_min was determined by exposing the cells to 10 µM Br-A23187 in the presence of Krebs-Ringer's solution with 2 mM EGTA and 0 Ca²⁺ for 60 min; 15 mM Ca²⁺ was then added to determine R_max. The values used for R_min, R_max, S_f,480/S_b,480, and K_d were 0.472, 3.634, 3.187, and 230 nM, respectively.

Chemicals and solutions

Stock solutions of tetrodotoxin (TTX) citrate (Research Biochemicals International, Natick, MA) were prepared in double-distilled, deionized water. Stock solutions of nifedipine and S()-Bay K 8644 (Research Biochemicals International) were prepared in dimethylsulfoxide and ethanol, respectively. The maximum final concentrations of dimethylsulfoxide and ethanol were 0.1% and 0.01%, respectively, neither of which altered the electrical membrane activity of ionic currents.

For the recording of electrical activity and total inward and outward currents, the extracellular medium contained modified Krebs-Ringer salts, and the pipette solution contained (in mM) 70 KCl, 70 K-aspartate, 1 MgCl₂, and 10 HEPES (pH adjusted to 7.2 with KOH). To isolate voltage-dependent Na⁺ currents (I_Na), the extracellular medium contained Krebs-Ringer's solution without CaCl₂ and with 20 mM tetraethylammonium (TEA), 5 mM 4-AP, and 50 µM CdCl₂, and the pipette contained (in mM) 70 CsCl, 70 Cs-methanesulfonate, 2 MgCl₂, and 10 HEPES (pH adjusted to 7.2 with CsOH). To isolated I_Ca, conventional whole-cell recording techniques were used as previously described (Van Goor et al., 1999b). The extracellular medium contained Krebs-Ringer's solution with 20 mM TEA, 2.6 mM or 10 mM CaCl₂, and 1 µM TTX (pH adjusted to 7.4 with NaOH). The pipette solution contained (in mM) 120 CsCl, 20 TEA-Cl, 4 MgCl₂, 10 EGTA, 9 glucose, 20 HEPES, 0.3 Tris-GTP, 4 Mg-ATP, 14 CrPO₄, and 50 U/ml creatine phosphokinase (pH adjusted to 7.2 with Tris base). Under these recording conditions, the I_Ca was further isolated by subtracting the current evoked in the presence of 100 µM NiCl₂ and 200 µM CdCl₂ from the total current. All I_Ca recordings shown and analyzed were of the Ni²⁺- and Cd²⁺-sensitive current. To isolate I_K, the extracellular medium contained Krebs-Ringer's solution without CaCl₂ and with 1 µM TTX, and the pipette contained (in mM) 70 KCl, 70 K-aspartate, 1 MgCl₂, and 10 HEPES (pH adjusted to 7.2 with KOH). All reported V_m measurements made under total current and I_K recording conditions were corrected for a liquid junction potential of +10 mV between the pipette and bath solution (Barry, 1994). The V_m under I_Na recording conditions was corrected for a liquid junction potential of +7 mV. No correction was required under isolated I_Ca recording conditions. The bath contained <500 µl of saline that was continuously replaced at a rate of 2 ml/min with a gravity-driven perfusion system. The inflow was placed adjacent to the cell, resulting in complete solution exchange around the cell within 2 s. A solid Ag/AgCl reference electrode was connected to the bath via a 3 M KCl agar bridge.

Model description

To provide a rigorous quantitative test of the experimental data, we developed a mathematical model in which the properties of the ionic currents used were determined directly from square-wave pulse voltage-clamp data. The ionic currents used included a TTX-sensitive I_Na, L- and T-type I_Ca, a voltage-sensitive (delayed-rectifier-type) I_K, an M-like I_K (I_M), and an inward rectifier I_K (I_ir). Furthermore, there is a Ca²⁺-permeable, voltage-insensitive inward leak current that offsets the I_ir (the major I_K active during the interspike period) to maintain repetitive firing. Although GT1 cells express large- and small-conductance Ca²⁺-activated K⁺ currents (Spergel et al., 1996; Van Goor et al., 1999a), the [Ca²⁺]_i levels reached during spontaneous AP firing are not sufficient to activate them and were therefore omitted. All of the currents, except I_Na, are described by typical Hodgkin-Huxley equations (Hodgkin and Huxley, 1952), including voltage-regulated activation and inactivation gating variables, macroscopic ionic conductances, and linear driving forces. The parameters and precise forms of the equations, as well as other model parameters, were obtained directly from our experimental recordings in GT1 cells (Van Goor et al., 1999b, and unpublished observations). Full model equations and parameter values are given in the Appendix.

In the development of a model system describing the electrical membrane activity in GT1 neurons, a Hodgkin-Huxley-like description of the TTX-sensitive I_Na was initially used. In this description, I_Na exhibited a large surge of activation during the spike repolarization (data not shown), which was never observed experimentally. Simulated V_m depolarization also did not induce spike broadening (data not shown), suggesting that the gating kinetics for the I_Na in this description do not accurately reflect those in GT1 neurons. In the Hodgkin-Huxley-like description, it is assumed that activation and inactivation are independent processes and that both are voltage dependent (Hodgkin and Huxley, 1952). However, it has long been known that this is not the case for TTX-sensitive Na⁺ channels (Bezanilla and Armstrong, 1977; Aldrich et al., 1983; Kuo and Bean, 1994). Instead, inactivation is linked to activation and may not be intrinsically voltage dependent, deriving its apparent voltage dependence from the linkage with activation. In addition, Kuo and Bean (1994) showed that Na⁺ channels must deactivate fully before they can recover from inactivation.

Consequently, we adapted Kuo and Bean's (1994) model of I_Na in rat hippocampal CA1 neurons for the GT1 neuronal I_Na to fit the experimental data. In particular, the slow recovery from inactivation of the I_Na (>500 ms; Van Goor et al., 1999b) was incorporated into the description of the I_Na in the GT1 cell model. In this description, the Na⁺ channel is composed of subunits with four possible states: deactivated (D), activated (A), deactivated-inhibited (D*), and activated-inhibited (A*) (see the reaction scheme in the Appendix for further details). A channel consists of three such subunits, meaning that there are 64 possible states overall. As a whole, however, the channel can be considered to be in one of three states. The conducting (open) state is denoted O and is given solely by A³; the channel is inactivated (I) if any of the three subunits is in either inhibited state. All other modes represent the closed (C) state.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Depolarization-induced shift in AP firing patterns

It has been shown that activation of endogenous Ca²⁺-mobilizing receptors in GT1 neurons induces sustained depolarization in the baseline V_m, which shifts the pattern of AP firing from sharp to broad spikes (Fig. 1 A; Van Goor et al., 1999a,b). In this study, both experimental and theoretical approaches were used to determine if depolarization of the baseline V_m in the absence of receptor activation could also shift the profile of the AP waveform. To do this, GT1 cells were depolarized by the application of positive current injections. This should mimic the effects of agonist-induced V_m depolarization, but not those resulting from the activation of intracellular messengers other than Ca²⁺. In nine separate cells, 15-pA current injection (Fig. 1 B) depolarized the V_m by 9 ± 1 mV, which is similar to that observed in GnRH-stimulated cells (9 ± 1 mV, n = 15; Van Goor et al., 1999a,b). Depolarization of the V_m by current injection also mimicked the action of GnRH on firing frequency and the profile of the AP waveform (Fig. 1 A versus Fig. 1 B). In particular, depolarization of the baseline potential by 15-pA current injections increased the firing frequency from 0.6 ± 0.2 Hz to 1.3 ± 0.2 Hz (n = 9, p < 0.05). In addition, the peak AP amplitude decreased from 0.4 ± 1.6 mV to 14.5 ± 1.0 mV, and the AP duration at one-half amplitude increased from 6.7 ± 0.3 ms to 18.8 ± 2.5 ms (mean ± SEM; p < 0.05; n = 9). In the GT1 cell model, simulation of depolarizing current injections also shifted the firing pattern from sharp to broad spikes (Fig. 1 C). These results indicate that sustained depolarization of the baseline V_m is sufficient to mimic the agonist-induced shift in the profile of the AP waveform from sharp to broad spikes.

View larger version (30K): [in this window] [in a new window]   FIGURE 1   Depolarization-induced shift from sharp to broad spikes in GT1 neurons. (A and B) Representative Vm traces of the response to application of 100 nM GnRH (A, bar) or +15 pA current injection (B, bar). (C) Simulation of depolarizing current injection (bar) in the GT1 cell model. Expanded time scales for the APs identified by a and b in A-C (left) are shown in the right panels. The dotted lines represent the baseline Vm.

Voltage-gated ionic currents contributing to sharp and broad firing patterns

The ionic currents underlying the generation of the different AP waveforms in GT1 neurons were analyzed using the AP clamp technique. Prerecorded spike trains from before (sharp spike train) and after (broad spike train) non-receptor-mediated membrane depolarization were used as the command potential in the voltage-clamp recording mode (Fig. 2). The interspike interval of the sharp spike train was characterized by a pacemaker depolarization that initiated at a baseline V_m of 66.7 ± 0.3 mV and culminated in spike initiation at a threshold of 50.7 ± 0.7 mV (Fig. 2 A, left). The rapid upstroke of the AP had a rise rate of 19.3 ± 2.4 mV/ms and reached a peak potential of 13.0 ± 1.5 mV. Repolarization was also rapid (16.0 ± 2.0 mV/ms), limiting spike duration measured at half-amplitude to 4.2 ± 0.2 ms. For the broad spike train, the pacemaker depolarization was initiated at 56.3 ± 0.7 mV and culminated in spike initiation at a threshold of 46.3 ± 0.9 mV. Compared to the sharp AP, the upstroke had a slower rise rate (3.7 ± 0.3 mV/ms) and a lower peak potential (8.0 ± 1.0 mV; Fig. 2 A, right). Repolarization was also slower (5.3 ± 0.3 mV/ms), resulting in a longer duration of AP (19.3 ± 1.1 ms). Under total current recording conditions in the voltage-clamp mode, both the sharp and broad spike trains activated an inward current followed by an outward current (Fig. 2 B). The net inward current increased rapidly during the spike upstroke, whereas the net outward current predominated during the repolarization phase (Fig. 2 C).

View larger version (20K): [in this window] [in a new window]   FIGURE 2   Total ionic current evoked by prerecorded sharp and broad spike train command potentials in GT1 neurons. (A) Typical example of the AP firing patterns before (sharp spike train) and after (broad spike train) agonist-induced Vm depolarization. (B) Total ionic current evoked by the sharp and broad spike trains in the voltage-clamp mode from the same cell. (C) Expanded time scale of spikes (-----) and the evoked currents () identified by the asterisks in B. The Vm recordings shown in A were used as the broad and sharp spike train command potentials under all subsequent experimental conditions.

The ionic currents underlying the generation of the sharp and broad AP waveforms in GT1 neurons were also analyzed using the GT1 cell model (Fig. 3 A). As observed under experimental conditions, a net inward current generated the upstroke of both the sharp and broad AP waveforms. This was followed by the development of a net outward current that repolarized the cells (Fig. 3, B and C). These experimental and theoretical results indicate that the depolarization-induced shift in the AP waveform is due to the inherent properties of the individual ionic currents expressed in GT1 neurons.

View larger version (20K): [in this window] [in a new window]   FIGURE 3   Simulations of the total ionic current evoked by sharp and broad spike train command potentials in the GT1 cell model. (A) The AP firing patterns before (sharp spike train) and after (broad spike train) the simulation of agonist-induced Vm depolarization. (B) Total ionic current underlying the generation of sharp and broad spike trains. (C) Expanded time scale of spikes (-----) and the underlying currents () identified by the asterisks in B.

Dependence of spiking pattern on voltage-gated I_Na

The physiological roles of I_Na in the generation of sharp and broad AP waveforms were analyzed under isolated I_Na recording conditions as described in Materials and Methods. Under these conditions, both the sharp and broad spike trains evoked an inward current that was abolished by TTX, a specific blocker of voltage-gated I_Na (Fig. 4, A and B). The sharp spike train evoked a transient inward current at V_m more depolarized than 50 ± 1 mV (n = 12), which was near the spike initiation threshold in these cells (Fig. 4 A, left). The I_Na reached a peak amplitude of 213 ± 17 pA, then decreased rapidly because of inactivation and deactivation (Fig. 4 C, left). Most of the I_Na was observed during the sharp upstroke of the AP, but a small amount was observed during the repolarization phase (Fig. 4 C, left) and may correspond to the resurgent I_Na in other neurons (Raman and Bean, 1997, 1999). The broad spike train also activated a transient I_Na at V_m more depolarized than 47 ± 1 mV (n = 12). The mean amplitude of this current (25 ± 3 pA, n = 12; Fig. 4 A, right) was much smaller than that evoked by the sharp spike train (Fig. 4, A and C). Although a majority of the I_Na was activated during the upstroke of the broad spikes, small amounts of current were also observed during the sustained pacemaker depolarization and the repolarization phase (Fig. 4 C, right). The GT1 cell model mimicked these experimental observations when Kuo and Bean's (1994) description of I_Na was used (Fig. 4 D).

View larger version (24K): [in this window] [in a new window]   FIGURE 4   The contribution of TTX-sensitive INa to the generation of sharp and broad spike trains in GT1 neurons. (A) Representative current trace of the isolated INa (bottom) evoked by the sharp (holding potential = 67 mV) and broad (holding potential = 51 mV) spike trains (top) in the same cell. (B) (Left) Representative INa traces evoked by sharp () and broad () spike trains in the absence and presence (arrows) of 1 µM TTX in the same cell. For clarity, only the currents evoked during the middle spikes were shown. (Right) Effects of 1 µM TTX on the INa evoked by the spike train command potentials (mean ± SEM, n = 5). Asterisks denote significant differences compared with control values: p < 0.01, paired t-test. (C) Expanded time scales of the spike trains (-----) and the evoked INa () identified by the asterisks in A. (D) Simulation of the INa () underlying the generation of sharp and broad AP waveforms (-----) in the GT1 cell model.

Based on the conventional square waveform voltage-step protocols, we previously suggested that the reduction in AP amplitude during agonist-induced V_m depolarization reflected the steady-state inactivation of the I_Na. To test this hypothesis more directly, the steady-state inactivation of the spike-induced I_Na was examined using a modified two-pulse protocol. Cells held at 67 mV were subjected to 1.5-s conditioning prepulses from 87 mV to 37 mV before the application of a single sharp spike (Fig. 5 A, left). The peak I_Na evoked during the spike was then plotted against the conditioning prepulse and fitted with a Boltzmann relation, where E_1/2 and k (see Materials and Methods) were 61.3 mV and 5.6 mV, respectively (Fig. 5 A, right). The sharp decline in peak I_Na between 80 mV and 50 mV indicates that small degrees of depolarization of the baseline potential are sufficient to limit I_Na participation during spike generation. This is consistent with the smaller peak I_Na amplitude activated by the broad spike train than that activated by the sharp spike train.

View larger version (20K): [in this window] [in a new window]   FIGURE 5   Depolarization-induced inactivation leads to the reduction in INa amplitude during the broad spike train. (A) Steady-state inactivation of the INa evoked by a single sharp spike in GT1 neurons. The steady-state inactivation curves for the INa were generated from prepulse experiments in which the Vm was stepped from 87 mV to 37 mV for 1.5 s before the application of the AP waveform (holding potential = 87 mV). (Left) Representative traces of the INa evoked by the spike train after prepulse potentials between 87 and 37 mV. (Right) Steady-state inactivation curve of the INa (mean ± SEM; n = 5). The current was normalized to the maximum inward current and fitted with a single Boltzmann relation. The dashed lines indicate the range of baseline Vm observed in spontaneously active GT1 neurons. (B) The time course of the open (O), inactivated (I), and closed (C) states of the INa during the firing of sharp and broad AP waveforms.

The reason for the decrease in I_Na amplitude in response to sustained V_m depolarization is illustrated by the relative proportions of the Na⁺ channel states during AP activity derived from the GT1 cell model (Fig. 5 B). For sharp spikes (Fig. 5 B, left), ~60% of the channels are available to be activated before spike initiation, the remainder being in the inactivated state. During the spike, less than 10% of the sodium channels are in the conducting state, as most become inactivated and recover slowly to the closed state. In depolarized cells firing broad spikes (Fig. 5 B, right), more than 90% of the channels are in the inactivated state before spike initiation. Consequently, the fraction of available sodium channels is small, which is reflected by the small I_Na evoked during the spike upstroke (Fig. 4 D). Together with the experimental data, these results demonstrate that sustained V_m depolarization inactivates I_Na to reduce spike amplitude in GT1 neurons.

Dependence of spiking pattern on voltage-gated I_K

We next examined the possibility that the decrease in spike amplitude caused by inactivation of I_Na during sustained baseline V_m depolarization limits I_K activation to promote spike broadening. Under isolated I_K recording conditions (see Materials and Methods), both the sharp and broad spike trains evoked an outward current that was reduced by the application of 2 mM tetraethylammonium (TEA) (Fig. 6 A and B). However, the peak TEA-sensitive I_K evoked by the broad spike train was much lower than that evoked by the sharp spike train (Fig. 6 C). The peak I_K amplitudes during the sharp and broad spike trains were 300 ± 28 pA and 107 ± 17 pA, respectively (n = 12; p < 0.01). In the GT1 cell model, the behavior of the I_K was similar to that observed experimentally. In particular, the I_K underlying the generation of sharp spikes was of much greater amplitude than that observed during broad spikes (Fig. 6 D).

View larger version (24K): [in this window] [in a new window]   FIGURE 6   Voltage-gated IK evoked by sharp and broad spike trains in GT1 neurons. (A) Isolated IK (bottom) evoked by the sharp and broad spike train command potentials (top) in the same cell. (B) (Left) Representative IK traces evoked by sharp () and broad () spike trains in the absence () and presence (-----) of 2 mM TEA in the same cell. For clarity, only the currents evoked during the middle spikes were shown. (Right) Effects of 2 mM TEA on the IK evoked by the spike train command potentials (mean ± SEM, n = 5). Asterisks in B indicate significant differences compared with control values: p < 0.01, paired t-test. (C) Expanded time scale of the spike trains (-----) and the evoked IK () identified by the asterisks in A. (D) Simulation of the IK () underlying the generation of sharp and broad AP waveforms (-----) in the GT1 cell model.

Under both experimental and theoretical conditions, the I_K began to activate during the latter part of the spike upstroke. Most of the I_K, however, was observed during the falling phase of both waveform subtypes (Fig. 6, C and D). The impact of I_K on the rate of V_m repolarization (dV_m/dt) at a given time point was calculated by dividing the I_K by the C_m. Using a mean C_p of 10 ± 1 pF (n = 41) and the peak I_K evoked by sharp or broad spike trains, the maximum calculated rates of V_m repolarization due to I_K activation for each waveform were 30 mV/ms and 10.7 mV/ms, respectively. These results demonstrate that TEA-sensitive I_K mediates the rate of V_m repolarization during both sharp and broad AP firing patterns in GT1 neurons. They also indicate that spike amplitude, which is determined by the availability of I_Na before spike initiation, controls the rate of V_m repolarization by determining the amount of I_K activation.

Dependence of voltage-gated Ca²⁺ entry on the pattern of firing

To examine the impact of spike broadening on voltage-gated Ca²⁺ entry, we monitored the I_Ca evoked by the sharp and broad AP waveforms under isolated I_Ca recording conditions as described in Materials and Methods. In 15 individual cells, application of both sharp and broad spike trains evoked rapid increases in inward I_Ca that peaked during the initial phases of spike repolarization (Fig. 7, A and B). The occurrence of the peak I_Ca during the repolarization phase is presumably due to the increase in driving force and time required for the voltage-dependent deactivation of the Ca²⁺ channel. Consistent with the role of spike amplitude in mediating voltage-gated Ca²⁺ influx, the peak I_Ca amplitude evoked by the broad spike train was lower than that evoked by the sharp spike train. However, despite the lower peak I_Ca amplitude, the integrated I_Ca was greater (Fig. 7, B and C). In the GT1 cell model, the behavior of the I_Ca was similar to that observed experimentally. In particular, despite the decrease in peak I_Ca amplitude, the integrated I_Ca was greater during the broad spike train compared to the sharp spike train (Fig. 7 D).

View larger version (29K): [in this window] [in a new window]   FIGURE 7   Voltage-gated ICa evoked by sharp and broad spike trains in GT1 neurons. (A) Isolated ICa (bottom) evoked by the sharp and broad spike train command potentials (top) in the same cell. (B) Expanded time scale of the spike trains (-----) and the evoked ICa () identified by the asterisks in A. (C) Peak ICa amplitude (left) and integrated ICa (right) evoked by the sharp () and broad () (mean ± SEM, n = 15) AP waveforms. Asterisks in C indicate significant differences compared with control values: p < 0.01, paired t-test. (D) Simulation of the ICa () underlying the generation of sharp and broad AP waveforms (-----) in the GT1 cell model.

In further studies, we characterized the ionic and pharmacological characteristics of the I_Ca evoked by the prerecorded spike trains. In 15 individual cells, increasing the extracellular Ca²⁺ concentration from 2.6 to 10 mM augmented the peak I_Ca evoked by both sharp (from 135 ± 15 pA to 256 ± 37 pA) and broad (from 103 ± 11 pA to 161 ± 29 pA) AP waveforms. Moreover, the ability of the broad AP waveform to drive more Ca²⁺ per spike into the cell was maintained in the presence of 10 mM extracellular Ca²⁺ (Fig. 8 A). Application of the VGCC antagonist nifedipine reduced the integrated I_Ca evoked by both AP waveform subtypes (Fig. 8 B). In contrast, the VGCC activator Bay K 8644 increased the integrated I_Ca evoked by both the sharp and broad AP waveforms (Fig. 8 B). Thus, depolarization-induced spike broadening increases the integrated I_Ca through L-type Ca²⁺ channels.

View larger version (38K): [in this window] [in a new window]   FIGURE 8   Extracellular Ca2+ dependence and dihydropyridine sensitivity of the ICa evoked by the sharp and broad spike trains in GT1 neurons. (A) (Left) Representative ICa traces evoked by the sharp and broad spike trains (top) in the presence of 2.6 mM and 10 mM extracellular Ca2+ in the same cell. (Right) Integrated ICa evoked during the sharp and broad AP waveforms in the presence of 2.6 mM and 10 mM extracellular Ca2+ (mean ± SEM, n = 15). (B) (Left) Representative ICa traces evoked by sharp and broad spike trains in the absence and presence of 1 µM nifedipine or 1 µM Bay K 8644 in the same cell. (Right) Effects of 1 µM nifedipine or 1 µM Bay K 8644 on the integrated ICa amplitude evoked by the sharp and broad AP waveforms (mean ± SEM, n = 6). For clarity, only the currents evoked during the middle spikes were shown. Asterisks indicate significant differences compared with control values: p < 0.01, paired t-test.

To examine the dependence of voltage-gated Ca²⁺ entry on the profile of the AP waveform, we measured the increase in [Ca²⁺]_i in response to sequential application of 60 prerecorded sharp or broad APs given at a frequency of 2 Hz. Under total current recording conditions, the broad spike train increased the [Ca²⁺]_i more than the sharp spike train (Fig. 9). This increase in [Ca²⁺]_i evoked by both the sharp and broad spike trains was attenuated by application of 1 µM nifedipine and enhanced by the application of 1 µM Bay K 8644 (Fig. 9). These results are consistent with the ability of broad spike trains to drive more Ca²⁺ entry via L-type Ca²⁺ channels than the sharp spike trains.

View larger version (26K): [in this window] [in a new window]   FIGURE 9   Dependence of calcium signaling on the profile of the AP waveform in GT1 neurons. A train of 60 sharp or broad AP waveforms was given at a frequency of 2 Hz under total current recording conditions. (A) Representative [Ca2+]i traces (bottom) evoked by the sharp and broad AP train before (Con) and after application of 1 µM nifedipine (Nif) or 1 µM Bay K 8644 (Bay K). All [Ca2+]i tracings are from the same cell. (B) Net change in peak [Ca2+]i (mean ± SEM, n = 6) during the sharp () and broad () AP trains before (Con) and after the application of 1 µM nifedipine or Bay K 8644. Double asterisks denote a significant difference between controls in the sharp and broad treatment groups, and single asterisks denote significant difference compared with control values in the same group (p < 0.01, paired t-test).

Relationship between I-V characteristics and the size of I_Ca in firing cells

In contrast to other cell types, spike broadening in GT1 cells increases the integrated I_Ca despite a decrease in spike amplitude. Experimental studies indicate that both the activation threshold and peak amplitude of the dihydropyridine-sensitive I_Ca in GT1 neurons occur at relatively hyperpolarized membrane potentials compared to those of other cell types. We utilized the mathematical model to estimate the impact of their different I-V characteristics on I_Ca during the firing of sharp and broad APs. To do this, we shifted the half-maximum activation of the L-type Ca²⁺ channels in the hyperpolarizing or depolarizing direction (Fig. 10 A; see the Appendix for details). The modified I-V profiles were within the range observed experimentally in cells expressing different isoforms of the L-type Ca²⁺ channel; they are represented by the dashed lines in Fig. 10 A. The experimentally derived I-V relationship for the L-type Ca²⁺ channel in GT1 neurons and the corresponding I_Ca underlying the generation of both the sharp and broad AP waveforms are represented by the solid lines in Fig. 10, A and B. Shifting the half-maximum activation by 10 mV in the hyperpolarizing direction increased the integrated I_Ca evoked by both AP waveforms (Fig. 10 B). However, the capacity of the broad spikes to drive more Ca²⁺ entry than the sharp spikes was reduced (Fig. 10 C). Incremental shifts in the half-maximum activation of the L-type Ca²⁺ channels by 10 mV in the depolarizing direction decreased the integrated I_Ca evoked by both AP waveforms (Fig. 10 B). In addition, the capacity of the broad spikes to drive more Ca²⁺ entry than the sharp spikes was reduced. Moreover, when the half-maximum activation of the I_Ca was depolarized beyond 20 mV, the integrated I_Ca underlying the generation of the sharp spike was greater than that underlying the broad spike (Fig. 10 C). These results indicate that the activation properties of the L-type Ca²⁺ channel isoform expressed in a particular cell type can determine the impact of spike broadening on voltage-gated Ca²⁺ entry.

View larger version (24K): [in this window] [in a new window]   FIGURE 10   Effect of voltage sensitivity of L-type Ca2+ current on Ca2+ influx. (A) Steady-state current-voltage (I-V) curves. The solid line is the I-V curve for the standard model (half-maximum activation = 40 mV). By shifting the activation properties of the current, we obtained the alternate I-V curves (long, medium, and short dashed, and dotted = 50, 30, 20, and 10 mV, respectively; see the Appendix for further details). (B) Sharp (left) and broad (right) APs (upper traces) were injected into the model with varying L-type Ca2+ current-voltage sensitivities. Lower traces show resultant Ca2+ currents. Line types correspond to those in A. (C) Total Ca2+, for sharp () and broad () AP trains, from integrating curves in B. The curve shows the ratio of integrated Ca2+ for broad to sharp spikes. Note that the curve peaks at 40 mV, the standard model value.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION APPENDIX REFERENCES

Changes in the AP waveform, as observed in our studies using GT1 neurons, can occur by a number of physiological processes, and alterations in the I_Na and/or I_K can account for the observed effects. For example, developmental changes in Na⁺ or K⁺ channel density alter the profile of the AP waveform in some cell types (Gao and Ziskind-Conhaim, 1998). Similarly, the heterogeneous properties of the AP waveform in pacemaker cells from the sinoatrial node are partially due to differences in Na⁺ channel density (Nathan, 1986; Irisawa et al., 1993). Regional differences in Na⁺ or K⁺ channel density or subtype (Westenbroek et al., 1989; Magee et al., 1998; Poolos and Johnston, 1999) also alter the AP waveform in discrete regions of the cell. In hippocampal neurons, activity-dependent I_Na inactivation mediates the decrease in dendritic spike amplitude and [Ca²⁺]_i during AP trains (Callaway and Ross, 1995; Spruston et al., 1995; Jung et al., 1997; Colbert et al., 1997). Activity-dependent inactivation of K⁺ channels also alters spike duration and AP-driven Ca²⁺ entry in pituitary nerve terminals (Jackson et al., 1991). Finally, activation of intracellular messengers can modulate the activation and inactivation properties of I_Na and I_K to influence the pattern of AP firing (Cantrell et al., 1999; Johnston et al., 1999).

In GT1 neurons, however, the ability of non-receptor-mediated depolarization to mimic agonist application in GT1 neurons argues against the involvement of intracellular messengers in the development of spike broadening. In addition, because of the low firing frequencies observed in spontaneously active and depolarized GT1 neurons (<5 Hz), activity-dependent inactivation of I_Na or I_K contributes little to spike broadening (Van Goor, unpublished data). Rather, our data indicate that the inactivation properties of the TTX-sensitive I_Na provide a very narrow range of interpulse V_m in which the current is available for activation before spike initiation. Consequently, small degrees of depolarization of the baseline V_m by receptor-mediated or non-receptor-mediated pathways decrease the magnitude of I_Na, which in turn reduces the rate of rise and amplitude of the AP upstroke. This decrease in spike amplitude reduces the peak amplitude of the TEA-sensitive I_K to slow membrane repolarization, which increases spike duration and augments Ca²⁺ influx through L-type Ca²⁺ channels. Thus amplitude-dependent spike broadening facilitates AP-driven Ca²⁺ entry, which leads to the increase in [Ca²⁺]_i.

Among the voltage-gated K⁺ channels that may participate in AP repolarization in GT1 neurons, delayed rectifier and A-type K⁺ channels have been identified in GT1 neurons (Bosma, 1993) and embryonic GnRH neurons (Kusano et al., 1995). Although we made no specific attempts to separate these currents, the delay in K⁺ channel activation and the sensitivity of the spike-induced I_K to TEA suggest that the delayed-rectifying I_K is critical for spike repolarization in GT1 neurons. This is consistent with the ability of TEA to facilitate AP-driven Ca²⁺ signals in GT1 neurons (Charles and Hales, 1995). The role of other voltage-gated K⁺ channels in the control of spike duration and baseline potential in GT1 neurons requires further investigation.

In addition to voltage-gated K⁺ channels, Ca²⁺-activated K⁺ channels participate in the control of AP duration and the associated Ca²⁺ signal. In GT1 neurons, it has been demonstrated that small-conductance, apamin-sensitive K⁺ channels (SK channels) contribute to spike repolarization during broad but not sharp AP firing (Van Goor et al., 1999a). In the present study, however, we did not observe a significant Ca²⁺-sensitive outward current during the application of sharp or broad spike trains (data not shown). Similarly, apamin has no effect on the current-voltage relation in GT1 neurons (Spergel et al., 1996). This is most likely due to the requirement for sustained firing of broad APs to elevate [Ca²⁺]_i to the levels required for activation of the SK channels. During the intermittent application of the AP waveforms used in this study, it is unlikely that such levels would be attained. In addition to SK channels, large-conductance, Ca²⁺-activated K⁺ channels (BK channel) have been identified in GT1 neurons (Spergel et al., 1996), but they do not participate in spontaneous or agonist-induced AP firing (Van Goor et al., 1999a).

In general, the pattern of AP-driven Ca²⁺ signaling in excitable cells is determined by the AP profile and gating properties of the underlying VGCCs. Using the AP clamp technique in combination with the GT1 cell model, we have shown that spike broadening increases the integrated I_Ca to facilitate voltage-gated Ca²⁺ entry. Based on the biophysical and pharmacological properties of I_Ca in these cells, it has been concluded that only L- and T-type Ca²⁺ channels are expressed in the plasma membrane (Bosma, 1993; Hales et al., 1994; Van Goor et al., 1999b; Costantin and Charles, 1999). The fraction of available T-type Ca²⁺ channels decreases sharply within the range of baseline potentials observed in GT1 neurons, and their participation in AP firing is probably similar to that of I_Na. Therefore, in addition to the reduction in peak spike amplitude, the inactivation of T-type Ca²⁺ channels in response to receptor-mediated and non-receptor-mediated V_m depolarization may also partially explain the decrease in peak I_Ca. In contrast, the L-type Ca²⁺ channel inactivates very slowly and exhibits little or no steady-state inactivation between the baseline potentials reached during unstimulated or agonist-stimulated AP firing (Van Goor et al., 1999b). Consequently, voltage-gated Ca²⁺ entry during the sharp spike is probably due to activation of both T- and L-type Ca²⁺ channels, whereas the L-type I_Ca is the primary current contributing to Ca²⁺ entry during broad spikes.

The influence of AP broadening on the duration and amplitude of the underlying I_Ca varies among the different cell types examined. This may be due to differences in the activation properties of the voltage-gated Ca²⁺ channel subtype(s) or isoforms expressed in a particular cell type. For example, several L-type Ca²⁺ channel isoforms have been identified, all of which exhibit different activation and inactivation properties and sensitivities to dihydropyridine agonists and antagonists (Wheeler et al., 1995; Catterall, 1998). In GT1 cells, the activation threshold and peak amplitude of the L-type I_Ca is shifted in the hyperpolarizing direction compared to that in other cell types (Van Goor et al., 1999b). In our GT1 cell model, incremental shifts in the half-maximum activation of the L-type Ca²⁺ channels in the depolarizing direction caused a progressive reduction in the ability of AP broadening to enhance voltage-gated Ca²⁺ entry. When the current-voltage relation more closely resembled that of classical L-type Ca²⁺ channels, the sharp AP spike drove more Ca²⁺ entry than the broad waveform. These results suggest that the activation properties of the L-type Ca²⁺ channel isoform expressed in a particular cell type can determine the impact of AP broadening on voltage-gated Ca²⁺ entry.