The Journal of Neurophysiology Vol. 78 No. 5 November 1997, pp. 2321-2335
Copyright ©1997 by the American Physiological Society

Role of Voltage-Gated K⁺ Currents in Mediating the Regular-Spiking Phenotype of Callosal-Projecting Rat Visual Cortical Neurons

Rachel E. Locke and Jeanne M. Nerbonne

Department of Molecular Biology and Pharmacology, Washington University School of Medicine, St. Louis, Missouri 63110

	ABSTRACT

Abstract Introduction Methods Results Discussion References

Locke, Rachel E. and Jeanne M. Nerbonne. Role of voltage-gated K⁺ currents in mediating the regular-spiking phenotype of callosal-projecting rat visual cortical neurons. J. Neurophysiol. 78: 2321-2335, 1997. Whole cell current- and voltage-clamp recordings were combined to examine action potential waveforms, repetitive firing patterns, and the functional roles of voltage-gated K⁺ currents (I_A, I_D, and I_K) in identified callosal-projecting (CP) neurons from postnatal (day 7-13) rat primary visual cortex. Brief (1 ms) depolarizing current injections evoke single action potentials in CP neurons with mean ± SD (n = 60) durations at 50 and 90% repolarization of 1.9 ± 0.5 and 5.5 ± 2.0 ms, respectively; action potential durations in individual cells are correlated inversely with peak outward current density. During prolonged threshold depolarizing current injections, CP neurons fire repetitively, and two distinct, noninterconverting "regular-spiking" firing patterns are evident: weakly adapting CP cells fire continuously, whereas strongly adapting CP cells cease firing during maintained depolarizing current injections. Action potential repolarization is faster and afterhyperpolarizations are more pronounced in strongly than in weakly adapting CP cells. In addition, input resistances are lower and plateau K⁺ current densities are higher in strongly than in weakly adapting CP cells. Functional studies reveal that blockade of I_D reduces the latency to firing an action potential, and increases action potential durations at 50 and 90% repolarization. Blockade of I_D also increases firing rates in weakly adapting cells and results in continuous firing of strongly adapting cells. After applications of millimolar concentrations of 4-aminopyridine to suppress I_A (as well as block I_D), action potential durations at 50 and 90% repolarization are further increased, and firing rates are accelerated over those observed when only I_D is blocked. Using VClamp/CClamp and the voltage-clamp data in the preceding paper, mathematical descriptions of I_A, I_D, and I_K are generated and a model of the electrophysiological properties of rat visual cortical CP neurons is developed. The model is used to simulate the firing properties of strongly adapting and weakly adapting CP cells and to explore the functional roles of I_A, I_D, and I_K in shaping the waveforms of individual action potentials and controlling the repetitive firing properties of these cells.

	INTRODUCTION

Abstract Introduction Methods Results Discussion References

Although the functional roles of Ca²⁺-independent, depolarization-activated K⁺ currents have been explored in a number of mammalian central neurons (Bargas et al. 1989; Budde et al. 1992; Gean and Shinnick-Gallagher 1989; Halliwell et al. 1986; Hammond and Crepel 1992; McCormick 1991; Nisenbaum et al. 1994; Schwindt et al. 1988a,b; Segal 1984; Spain et al. 1991; Storm 1987, 1988; Wu and Barish 1992; Zhang and McBain 1995), few studies have been completed on cortical neurons (but see Hammond and Crepel 1992; Schwindt et al. 1988a,b; Spain et al. 1991), and none have investigated the functional roles of K⁺ currents in identified cells. In the experiments described here and in the preceding paper (Locke and Nerbonne 1997), we employed in vivo retrograde labeling to permit the in vitro identification of callosal-projecting (CP) neurons from rat primary visual cortex (Giffin et al. 1991; Katz 1984; Katz and Iarovici 1990; Solomon et al. 1993). As discussed previously (Giffin et al. 1991; Locke and Nerbonne 1997; Solomon et al. 1993), CP cells were selected to correspond to the "regular-spiking" phenotype described previously in recordings from cortical neurons in vivo and in the in vitro slice preparation (Connors and Gutnick 1990; McCormick et al. 1985). In response to brief depolarizing current injections, regular-spiking cells fire single action potentials that are followed by prolonged, and often complex, afterhyperpolarizations (Connors and Gutnick 1990). In response to prolonged current injections, regular-spiking cells fire action potentials repetitively at a frequency that depends on the amplitude of the injected current and, over time, these cells adapt (Chagnac-Amitai et al. 1990; Connors and Gutnick 1990; Mason and Larkman 1990). In vivo and in vitro, therefore, regular-spiking cells are readily distinguished from "fast-spiking" and "intrinsically bursting" cortical neurons (Connors and Gutnick 1990).

In the preceding paper, three distinct, Ca²⁺-independent, voltage-gated K⁺ currents, termed I_D, I_A, and I_K, were identified in CP neurons from rat primary visual cortex, and the detailed time- and voltage-dependent properties of these currents were delineated (Locke and Nerbonne 1997). Importantly, although the voltage-dependent properties of I_D, I_A, and I_K were found to be similar, these currents were distinguished readily based on differing kinetic properties and pharmacological sensitivities (Locke and Nerbonne 1997). Although the relative densities of the currents varied among cells, I_D, I_A, and I_K were found to be expressed in all CP cells (Locke and Nerbonne 1997). The differences in the kinetic properties and the densities of the currents suggested that I_D, I_A, and I_K likely make distinct functional contributions to determining the firing properties of CP neurons. The experiments here were designed to test this hypothesis directly. The waveforms of single action potentials and the repetitive firing behavior of isolated, identified CP neurons were examined using the whole cell version of the patch-clamp technique. The pharmacological properties of I_D, I_A, and I_K (Locke and Nerbonne 1997) were exploited to examine the functional roles of these currents in determining the latency of firing, shaping the waveforms of single action potentials, and controlling the repetitive firing properties of CP neurons. In addition, the CClamp/VClamp neuronal simulation program, developed by Huguenard and McCormick (Huguenard and McCormick 1992; McCormick and Huguenard 1992) to describe the firing properties of thalamocortical relay neurons, was used to develop a model of the electrophysiological properties of rat visual cortical CP neurons. I_A, I_D, and I_K were simulated using the detailed time- and voltage-dependent properties determined in the preceding paper (Locke and Nerbonne 1997) and incorporated into the model; the relative conductances of I_A, I_D, and I_K in the model were matched to the experimental data (Locke and Nerbonne 1997). The model then is used to simulate the firing properties of strongly adapting and weakly adapting CP cells and to examine the functional effects of reducing or eliminating I_D, I_A, and I_K on the waveforms of individual action potentials and the repetitive firing properties of CP neurons.

	METHODS

Abstract Introduction Methods Results Discussion References

Isolation and identification of CP neurons

Whole cell voltage- and current-clamp recordings were obtained from identified CP visual cortical neurons isolated from postnatal day 7-13 (P7-P13) Long Evans rat pups. Methods for CP cell labeling, isolation, and identification were as previously described (Giffin et al. 1991; Locke and Nerbonne 1997; Solomon et al. 1993).

Electrophysiological recordings

Whole cell patch-clamp recordings were obtained at room temperature (23-25°C) from identified CP neurons within 48 h of cell isolation (Locke and Nerbonne 1997). Current- and voltage-clamp experiments were completed using a Dagan 3900 patch-clamp amplifier. Experiments were controlled and data were acquired using an IBM-compatible 486 computer with TL-1 interface to the physiological equipment and the PClamp (Axon Instruments) software package. Series resistance compensation and pipette fabrication and resistances were essentially as described in the preceding paper (Locke and Nerbonne 1997). Both current- and voltage-clamp recordings were obtained from all cells examined. Single action potentials and action potential trains were evoked routinely by 1-ms, 1,000- to 1,500-pA current injections and by 1.5- to 2.0-s, 10- to 120-pA current injections, respectively. Whole cell currents were evoked during 160-ms voltage steps to potentials between 60 and +60 mV from a holding potential of 70 mV.

Solutions

The procurement, handling and perfusion of the K⁺ channel blockers 4-aminopyridine (4-AP), dendrotoxin (DTX), and tetraethylammonium chloride (TEACl) were as described in Locke and Nerbonne (1997). For recordings, the bath solution routinely contained (in mM) 140 NaCl, 4 KCl, 2 CaCl₂, 2 MgCl₂, 10 N-2-hydroxyethylpiperazine-N-2-ethanesulfonic acid (HEPES), and 5 glucose (pH 7.4; 305 mOsm). Importantly, because current-clamp and voltage-gated recordings were obtained from the same cells and, in several experiments, switching repeatedly between voltage- and current-clamp modes was required, all voltage-clamp recordings were obtained in the absence of tetrodotoxin and Co²⁺ or Cd²⁺ (blockers of voltage-gated Na⁺ and Ca²⁺ channels, respectively). Voltage-clamp records, therefore, reflect the sum of voltage-gated, as well as any Na⁺- and Ca²⁺-dependent, inward and outward K⁺ currents. The pipette solution contained (in mM) 135 KCl, 10 HEPES, 5 glucose, 3 MgATP, 0.5 NaGTP, 2 ethylene glycol-bis(-aminoethyl ether)-N,N,N,N-tetraacetic acid, and 1.2 CaCl₂ (pH 7.4; 305 mOsm); the intracellular free Ca²⁺ concentration was 10⁷ M.

Data analysis

Data were compiled and analyzed using Clampfit (Axon Instruments), Excel (Microsoft) and CSS Statistica (Stat Soft). All data are means ± SD. Resting membrane potentials were determined immediately on achieving the whole cell configuration, and only those cells that had resting membrane potentials up to 55 mV and overshooting action potentials were selected for experiments. Leak currents were always <100 pA at 70 mV and were not corrected. Input resistances and the amplitudes of the total outward (Ca²⁺ independent and Ca²⁺ dependent) and inward (Na⁺ and voltage gated Ca²⁺) currents were monitored during all recordings, and only cells in which these parameters remained constant were selected for analysis. The mean input resistance of analyzed CP cells was 1.3 ± 0.6 G (n = 60), and the mean whole cell membrane capacitance of these cells was 31 ± 10 pF (n = 60). Note that the membrane capacitances of the cells examined here were, on average, larger than those reported in the previous paper. This reflects the fact that the cells studied here were in culture longer, and, as a result, in many cases, had elaborated processes. Action potential durations at 50% (and 90%) repolarization were determined by measuring the widths of the action potentials when the membrane voltage had returned halfway (or 90% of the way) back to the resting potential; values are reported in milliseconds. The peak outward current was defined as the maximum value the current attained during 160-ms voltage steps; the plateau current was defined as the current remaining 150 ms after the onset of the depolarizations. I_D amplitudes were determined by subtraction of currents recorded in the presence of 50 µM 4-AP (or 50 nM -DTX) from controls, as previously described (Locke and Nerbonne 1997). I_A amplitudes were estimated from the peak currents remaining in the presence of 50 µM 4-AP, and I_K amplitudes were estimated from the plateau currents (measured 150 ms after the onset of the depolarizations) remaining in the presence of 50 µM 4-AP.

Increases in action potential durations at 50 and 90% repolarization in the presence of 50 µM 4-AP or 10 mM TEA were measured in individual cells, and percentage increases with respect to control durations are presented; increases in action potential durations in the presence of 2-5 mM 4-AP were measured, and percentage increases over the durations measured in 50 µM 4-AP are presented. Decreases in latency in the presence of 50 µM 4-AP were determined as percentage latencies for the same stimulus amplitude in the same cell. For all experiments, statistical significance of observed differences among different populations was examined using Student's t-test for paired and for unpaired data; P values are presented in the text.

Modeling of voltage-gated K⁺ currents and simulations of the firing properties of CP cells

The VClamp/CClamp software package, generously provided to us by Drs. David McCormick and John Huguenard, was used to model the voltage-gated K⁺ currents in CP neurons and to simulate the firing properties of these cells. The development and application of the model to simulate the properties of thalamocortical relay neurons has been described in detail (Huguenard and McCormick 1992; McCormick and Huguenard 1992). The model assumes a single compartment, and includes the following currents: the fast Na⁺ current, I_Na; a persistent Na⁺ current, I_Na,p; the rapidly activating, rapidly inactivating (transient) K⁺ current, I_A; a delayed rectifier K⁺ current, I_K; a rapidly activating, slowly inactivating K⁺ current, I_K2; the low-threshold Ca²⁺ current, I_T; the high-threshold Ca²⁺ current, I_L; a fast, voltage- and Ca²⁺-dependent K⁺ current, I_C; a slow, voltage-independent, Ca²⁺-dependent K⁺ current, I_AHP; the hyperpolarization-activated cationic conductance, I_H; a muscarine-sensitive, depolarization-activated K⁺ current, I_M; a Na⁺ leak current, I_Na,leak; and a K⁺ leak current, I_K,leak. The currents (with the exception of I_Na,leak and I_K,leak) are described by Hodgkin-Huxley-like formulations; each current reflects the activity of a population of channels with identical microscopic properties, and the activity of each channel type is controlled by gates that are opened, closed, and inactivated by membrane voltage. Using data obtained from previous voltage-clamp studies, I_T, I_H, I_A, and I_K2 were simulated, and hypotheses about the specific roles of these currents in controlling rhythmic firing in thalamic relay neurons were advanced (Huguenard and McCormick 1992). To simulate the firing properties of thalamocortical relay neurons, the mathematical descriptions of I_T, I_H, I_A, and I_K2 were incorporated, I_Na,leak and I_K,leak were determined from the passive properties and input resistances of thalamic relay neurons, and mathematical descriptions of the other currents in the model, i.e., I_Na, I_Nap, I_K, I_C, etc., were developed using the time- and voltage-dependent properties of similar currents in other cells (McCormick and Huguenard 1992). The model was shown to reproduce both the rhythmic and the tonic firing behavior of thalamic relay neurons (McCormick and Huguenard 1992).

To develop a model of the electrophysiological properties of CP neurons, we used a similar approach. The Ca²⁺-independent, depolarization-activated K⁺ currents, I_A, I_D, and I_K in CP neurons were modeled (see: RESULTS) using the parameters obtained in the voltage-clamp experiments described in detail in the preceding paper (Locke and Nerbonne 1997); mean values of all parameters were used. The time-and voltage-dependent properties of the remaining currents in the model, I_Na, I_Nap, I_T, I_L, I_H, I_C, I_AHP, and I_M, were not altered; only the relative densities of these currents were varied. In previous studies, we have shown that I_T is expressed only in a subset (18%) of CP neurons, and that, when expressed, the amplitudes/densities of I_T are small, even when compared with I_L amplitudes/densities in the same cell (Giffin et al. 1991). Similarly, I_H amplitudes/densities in CP neurons are small (Solomon et al. 1993). In preliminary attempts to model CP neurons, therefore, we set the conductances of I_H and I_T equal to zero. Subsequent testing with the model confirmed that including low-density I_T and I_H currents (such as recorded in CP neurons) had little effect on simulated action potential waveforms or repetitive firing properties. For simplicity, therefore, the amplitudes of these conductances were set to zero for all of the simulations presented here. I_Na and I_L amplitudes were estimated from analyses of voltage-clamp data from CP neurons (Giffin et al. 1991) and were not changed throughout the simulations. The densities of the remaining currents in the model, I_Nap, I_C, and I_AHP, then were varied. The goal was to make the minimum number of changes necessary to produce simulated action potential waveforms and repetitive firing properties that resembled those in strongly adapting and weakly adapting CP neurons (see RESULTS). For all simulations, numerical solutions to the differential equations describing each of the currents used a one-step Euler integration method. Although the time step could be varied, in general, the increment was set at 0.01 ms, such that the individual gates changed by <1% during each step.

	RESULTS

Abstract Introduction Methods Results Discussion References

Action potential waveforms and repetitive firing properties of CP neurons

Single action potentials are evoked routinely in identified CP visual cortical neurons by 1-ms, 1,000- to 1,500-pA depolarizing current injections (Fig. 1). In all cells (n = 60), action potentials rise rapidly to a maximal potential of +50 mV, and repolarization is complete in 5-20 ms. Action potential durations, measured at 50% repolarization, ranged from 1.1 to 3.2 ms (Fig. 1A) with a mean of 1.9 ± 0.5 ms (n = 60); action potential durations at 90% repolarization ranged from 2.9 to 12.4 ms, with a mean of 5.5 ± 2.0 ms. During prolonged threshold depolarizing current injections (1.5 s; 10-120 pA), CP neurons fire repetitively at a rate that increases with stimulus strength, and, over time, the firing rate adapts (Fig. 1B). The repetitive firing properties of CP cells are therefore consistent with our working hypothesis (Giffin et al. 1991; Locke and Nerbonne 1997; Solomon et al. 1993) that CP cells are regular-spiking neurons (see DISCUSSION).

View larger version (34K): [in this window] [in a new window]   FIG. 1. Callosal-projecting (CP) visual cortical neurons are regular spiking. A: action potential waveforms evoked by 1-ms, 1,000- to 1,500-pA depolarizing current injections in 3 different CP cells are displayed. Resting membrane potentials are noted beside the voltage traces, and action potential durations at 50% (APD50) and 90% (APD90) repolarization are indicated. B: during prolonged (1.5 s) depolarizing current injections, CP neurons fire repetitively at a rate that increases with increasing stimulus strength. Amplitudes of the current injections are noted beside the traces; the resting membrane potential of this cell was 66 mV.

To determine whether the differences in action potential durations at 50 and 90% repolarization (Fig. 1A) reflect differences in outward current densities among CP neurons, voltage-clamp recordings were obtained from each cell on which current-clamp experiments were performed. Peak outward currents, evoked from a holding potential of 70 mV by 160-ms voltage steps to potentials between 60 and +60 mV, were measured and subsequently normalized to cell capacitance to obtain peak outward current densities. It is important to note here that voltage-clamp recordings in these (and in all subsequent) experiments were, by necessity, performed in the absence of Na⁺ and Ca²⁺ channel blockers. The voltage-clamp records obtained and analyzed here, therefore, reflect the sum of voltage-gated and Ca²⁺-dependent inward and outward currents. Plotting action potential duration at 50% repolarization (APD₅₀) versus the peak outward current density revealed a correlation (R² = 0.38; Fig. 2A): broad action potentials are recorded from cells with low outward current densities and brief action potentials are recorded from cells with high outward current densities. Data from two cells, representing the extremes of the data set in Fig. 2A, are presented in Fig. 2, B and C. As suggested above, owing to the conditions employed in these experiments, inward and outward currents are evident in these records. Importantly, the action potential is broad (2.5 ms at 50% repolarization) in the cell with a low outward K⁺ current density (86 pA/pF), whereas in the cell with a high K⁺ current density (258 pA/pF), the action potential is brief (1.6 ms at 50% repolarization). Action potential durations in CP cells, therefore, are correlated outward K⁺ currents amplitudes/densities (Fig. 2A).

View larger version (20K): [in this window] [in a new window]   FIG. 2. Action potential durations at 50% repolarization (APD50) vary as a function of peak outward current density. Single action potentials were evoked as described in Fig. 1, and voltage-dependent K+ currents (in the same cells) were evoked during 160-ms voltage steps to potentials between 60 and +60 mV from a holding potential of 70 mV. It is important to note that, because of the recording conditions employed (i.e., without Ca2+ and Na+ channel blockers), the voltage-clamp records reflect both inward Ca2+ and Na+ currents as well as outward K+ currents. Peak outward current amplitudes at +60 mV were measured, normalized to cell capacitance, and plotted (A) with respect to the APD50 determined in the same cell (n = 60). B and C: current- and voltage-clamp recordings from 2 representative cells from the extremes of the data set in A. For the cell with low peak outward current density (B), the action potential is broad, whereas for the cell with the high peak outward current density (C), the action potential is relatively brief.

Interestingly, two distinct repetitive firing patterns, differing in the extent of spike-frequency adaptation, were observed in CP cells. Of the 49 cells in which repetitive firing patterns were examined, 12 cells (24%) exhibited a strongly adapting firing pattern (Fig. 3A). The most striking characteristics of the strongly adapting firing pattern are the clustering of action potentials at the stimulus onset, the pronounced afterhyperpolarizations at the termination of each spike, and the cessation of repetitive firing in spite of maintained depolarizing current injections. Importantly, strongly adapting cells never were observed to resume firing during maintained depolarizing current injections (see DISCUSSION). In 37 of 49 cells examined (76%), a distinct firing pattern, which we refer to as weakly adapting, was observed (Fig. 3B). In weakly adapting cells, firing was maintained throughout the duration of the current injection and afterhyperpolarizations are not pronounced. In addition, the interval between spikes in weakly adapting cells increased as a function of time after the onset of the current injection (Fig. 3B), whereas the interspike interval varies only slightly in strongly adapting CP cells (Fig. 3A). During recordings, cells never switched between displaying the weakly and strongly adapting repetitive firing patterns. In addition, firing patterns were not affected by variations of ±5 mV in the membrane potential around rest. Thus strongly and weakly adapting cells are distinct, nonoverlapping populations of regular-spiking CP cells (see DISCUSSION). In addition, it is of interest to note that the strongly adapting firing pattern was observed only in CP cells isolated from animals P11; 12 of the 30 (40%) P11 CP cells were classified as strongly adapting, whereas all of 19 P10 CP cells were weakly adapting. Taken together, these results suggest that strongly adapting cells likely are not immature CP neurons (see DISCUSSION).

View larger version (26K): [in this window] [in a new window]   FIG. 3. Two distinct firing patterns are evident in CP neurons. A and B: action potentials trains were evoked by 1.5-s depolarizing current injections of increasing amplitude. A: action potentials in strongly adapting cells occurred at the onset of the stimuli, and despite maintained current injections, these cells stop firing. B: continuous firing is observed at most stimulus intensities for weakly adapting cells. Examination of the waveforms of individual action potentials revealed that afterhyperpolarizations are more pronounced in strongly (C) than in weakly (D) adapting cells. The records in A and C and in B and D were from the same cells; the resting membrane potentials of these cells were 64 mV (A and C) and 60 mV (B and D).

Analysis of the interspike-interval voltage trajectories in strongly and weakly adapting cells revealed that action potentials in strongly adapting cells have more prominent afterhyperpolarizations (Fig. 3C) than do action potentials in weakly adapting cells (Fig. 3D). The pronounced afterhyperpolarizations result in a marked shortening of the action potential duration in strongly adapting as compared with weakly adapting cells. Mean action potential durations at 90% repolarization were 4.4 ± 0.6 ms (n = 12) and 6.3 ± 2.1 ms (n = 37) for strongly and weakly adapting cells, respectively (P < 0.001). At 50% repolarization, however, action potential durations were indistinguishable in the two cell types: mean durations were 1.9 ± 0.2 and 2.0 ± 0.5 ms, in strongly and weakly adapting cells, respectively.

Comparison of the membrane properties of weakly adapting and strongly adapting CP cells revealed two important differences (Table 1): input resistances are significantly lower and plateau outward K⁺ current densities are significantly higher in strongly adapting, than in weakly adapting, CP cells. Because plateau current densities are higher and peak current densities are similar, peak-to-plateau current ratios are significantly lower in strongly adapting, than in weakly adapting, CP cells (Table 1). As demonstrated in the companion paper (Locke and Nerbonne 1997), detailed analysis of voltage-clamp records revealed the expression of three Ca²⁺-independent, voltage-gated K⁺ currents (I_D, I_A, and I_K) in CP visual cortical neurons. I_D activates rapidly, inactivates slowly, and is blocked by micromolar concentrations of 4-AP and nanomolar concentrations of DTX; I_A activates and inactivates rapidly and is sensitive to millimolar, but not micromolar, concentrations of 4-AP; and I_K activates and inactivates slowly, is 4-AP insensitive, and is blocked by millimolar concentrations of TEA. As also demonstrated, the peak outward currents in CP cells reflect primarily I_A and I_D, whereas only I_D and I_K contribute to the plateau currents (Locke and Nerbonne 1997). The finding that the peak-to-plateau current ratios are lower in strongly adapting cells, therefore, suggests that the relative densities of I_D and/or I_K are larger in strongly than in weakly adapting cells and, further, that I_D and I_K likely play important roles in producing the strongly adapting phenotype. Subsequent experiments, therefore, were focused on assessing the functional roles of I_A, I_D, and I_K in shaping the waveforms of action potentials and in controlling repetitive firing in (strongly and weakly adapting) regular-spiking CP neurons.

Functional roles of I_D in regular-spiking CP neurons

One role attributed to I_D (or I_D-like currents) in other preparations is to control the latency to firing an action potential in response to a threshold depolarizing current stimulus (Hammond and Crepel 1992; McCormick 1991; Nisenbaum et al. 1994; Storm 1988). To determine whether I_D in CP neurons plays a similar role, action potentials (evoked by 400 ms, 20- to 70-pA depolarizing current injections) were recorded in control bath solution and after superfusion of 50 µM 4-AP (Locke and Nerbonne 1997). As illustrated in Fig. 4A, the latency to firing an action potential was reduced when I_D was blocked. Similar decreases in latency were observed in eight of nine cells examined (in 1 cell no change was observed), and the mean decrease in latency resulting from block of I_D by 50 µM 4-AP was 37 ± 11%. Voltage-clamp experiments completed in parallel revealed that the decrease in latency is correlated (R² = 0.68) with the amplitude of I_D (Fig. 4B), i.e., the greater the amplitude of I_D, the more the latency was affected when I_D was blocked. Similar results were obtained with 50 nM -DTX (n = 3).

View larger version (27K): [in this window] [in a new window]   FIG. 4. ID contributes to the latency to firing and to action potential repolarization. A: action potentials were evoked by 400-ms threshold current injections under control conditions and after superfusion of 50 µM 4-aminopyridine (4-AP). In the presence of 50 µM 4-AP, the latency to firing the 1st action potential is reduced relative to the control. Similar results were obtained on 7 other cells. Percent decrease in latency in the presence of 50 µM 4-AP is plotted for each cell with respect to ID amplitude (in the same cell) in B; the increase in latency to firing when ID is blocked is correlated (R2 = 0.68) with the amplitude of ID. For these analyses, latencies were measured from the stimulus onset to the inflection of the voltage trajectory at the base of the action potential ( in A), and ID amplitudes were obtained by subtraction of the voltage-clamp records obtained in the presence of 50 µM 4-AP from control records. C: single action potentials, evoked by brief current injections, were recorded under control conditions and after superfusion of 50 µM 4-AP. After blockade of ID, repolarization is slowed and action potential durations are prolonged. For the 3 cells shown, ID contributes 39, 24, and 12%, respectively, to the peak outward currents. Percent increase in action potential duration at 50% repolarization (APD50) after blockade of ID is plotted vs. ID amplitude (n = 30) in D; the increase in APD50 when ID is blocked is correlated (R2 = 0.76) with ID amplitude (D) and to the percentage contribution of ID to the peak outward current (not shown). E: mean ± SD (n = 30) action potential durations at 50% () and 90% () repolarization under control conditions and in the presence of 50 µM 4-AP.

The fact that activation of I_D is rapid (Locke and Nerbonne 1997) suggested that I_D also should play a role in action potential repolarization in CP neurons. To test this hypothesis directly, action potential durations recorded in control bath solution were compared with those evoked in the same cell after superfusion of 50 µM 4-AP or 50 nM -DTX. As illustrated in Fig. 4C, action potentials are prolonged markedly when I_D is blocked, and the peaks of the action potentials are increased slightly. Although qualitatively similar results were obtained in all cells examined (n = 30), the effect of blocking I_D is quantitatively distinct in individual cells. In some cells, the action potential duration at 50% repolarization increased by >50% (Fig. 4C, top), whereas in other cells, action potential durations at 50% repolarization increased only slightly (Fig. 4C, bottom). For the cells in Fig. 4C, voltage-clamp experiments revealed that I_D contributes 39, 24, and 12%, respectively, to the peak outward currents. Similar to the effect on latency, therefore, the magnitude of the effect of blocking I_D on action potential duration is correlated (R² = 0.76) with the amplitude of I_D (Fig. 4D). A similar relation was observed when I_D amplitudes and action potential durations at 90% repolarization were compared (not shown). No significant differences were observed, however, in the effects of 50 µM 4-AP on action potential durations in strongly and weakly adapting cells. When data from all cells are pooled (Fig. 4E), it is clear that blockade of I_D increases mean action potential durations at 50% repolarization significantly (n = 30, paired t-testP < 0.001) from 1.9 ± 0.5 ms to 2.5 ± 0.6 ms; mean action potential durations at 90% repolarization also increased significantly (n = 30, paired t-test P < 0.001), from 6.6 ± 5.2 ms to 9.6 ± 6.2 ms (Fig. 4E).

Subsequent experiments revealed that repetitive firing patterns in CP cells are altered when I_D is blocked (Fig. 5) and, in addition, that the effects of blockade of I_D in strongly and weakly adapting cells are distinct. In weakly adapting cells, blockade of I_D increases the firing frequency in response to the same current injection (Fig. 5B). In strongly adapting cells, however, blockade of I_D results in continuous firing throughout the duration of depolarizing current injections (Fig. 5A). In all cells, blockade of I_D permitted current stimuli too weak to evoke action potentials in control conditions to produce repetitive firing (Fig. 5B1). Taken together, these results demonstrate that I_D plays an important role in damping excitability in both strongly and weakly adapting cells and suggest that I_D contributes importantly to the strongly adapting firing pattern (see DISCUSSION).

View larger version (35K): [in this window] [in a new window]   FIG. 5. Blockade of ID increases excitability in both strongly (A) and weakly (B) adapting CP cells. Action potential trains were evoked under control conditions (left) and in the presence of 50 µM 4-AP (right); the amplitudes of the currents injections are indicated. In strongly adapting cells (A), blockade of ID results in continuous firing. In weakly adapting cells (B), blocking ID increases the firing rate. For the cells in A and B, voltage-clamp experiments revealed that ID contributes 17 and 15%, respectively, to the peak outward currents; the resting membrane potentials of these cells were 68 mV (A) and 65 mV (B). Similar results were obtained on 2 other strongly adapting and 10 other weakly adapting cells.

Functional roles of I_A in regular-spiking CP neurons

The facts that activation of I_A is rapid and that I_A is expressed at high-density in CP neurons (Locke and Nerbonne 1997) suggested that this conductance pathway likely also plays an important role in action potential repolarization in these cells. Because there is no selective blocker of I_A, however, assessing the functional role of I_A is more complicated than was the case for I_D: i.e., the role of I_A could only be examined after first blocking I_D. As illustrated in Fig. 6A, exposure to 2 or 5 mM 4-AP markedly slows repolarization and increases the duration of evoked action potentials in CP neurons. Parallel voltage-clamp experiments allowed direct determination of the amplitude of I_A blocked in each cell. These experiments revealed that the percentage increase in the action potential duration at 50% repolarization is correlated (R² = 0.66) with the amplitude of I_A (in the same cell) that was blocked by 4-AP (Fig. 6B). A similar correlation was observed when the percentage increase in action potential duration at 90% repolarization and the amplitude of I_A that was blocked by 2 mM or 5 mM 4-AP were compared (not shown). When data from all cells (n = 18) are pooled (Fig. 6C), it is clear that applications of 2-5 mM 4-AP increased the mean action potential duration at 50% repolarization significantly (paired t-test P < 0.001) from 2.3 ± 0.6 ms (in 50 µM 4-AP) to 4.0 ± 0.9 ms. Mean action potential duration at 90% repolarization also increased significantly (paired t-test P < 0.001) from 8.4 ± 3.8 ms (in 50 µM 4-AP) to 15.9 ± 5.9 ms (in 2-5 mM 4-AP) (Fig. 6C).

View larger version (27K): [in this window] [in a new window]   FIG. 6. IA contributes importantly to action potential repolarization in CP cells. Single action potentials were evoked under control conditions, after application of 50 µM 4-AP, and again after superfusion of 2 mM (or 5 mM) 4-AP. Results obtained in experiments completed on 3 different cells are presented in A; the amplitude of IA that was blocked in each cell and the resting membrane potential of each cell are noted. B: percent increase in APD50 (beyond that observed with 50 µM 4-AP) in the presence of 2 or 5 mM 4-AP is plotted with respect to the amplitude of IA that was blocked in the same cell (n = 18). Similar to the findings for ID (Fig. 4D), the prolongation of the APD50 in each cell is correlated (R2 = 0.66) with the amplitude of the current (in this case IA) that was blocked. C: mean ± SD action potential durations at 50% () and 90% () repolarization under control conditions, in the presence of 50 µM 4-AP, and in the presence of 5 mM 4-AP are displayed.

Subsequent experiments were aimed at determining the role of I_A in controlling repetitive firing behavior of CP neurons. Similar to the experiments described above, it was only possible to explore the functional role of I_A with I_D also blocked. Nevertheless, these experiments did reveal that suppression of I_A results in further increases (i.e., beyond those seen when only I_D is blocked) in firing rates in both strongly (Fig. 7A) and weakly (Fig. 7B) adapting cells. These results support the hypothesis that I_A functions to slow the rate of repetitive firing in CP neurons (see below and DISCUSSION).

View larger version (33K): [in this window] [in a new window]   FIG. 7. Attenuation of IA increases excitability in strongly (A) and weakly (B) adapting CP cells. Action potential trains were evoked under control conditions (insets in A and B), after application of 50 µM 4-AP (A and B, left) and again after superfusion of 5 mM 4-AP (A and B, right). Injected current amplitudes are indicated; the resting membrane potentials of these cells were 68 mV (A) and 65 mV (B). Parallel voltage-clamp recordings revealed that 42 and 29% of IA was blocked in A and B, respectively.

Functional roles of I_K in regular-spiking CP neurons

The fact that I_K activates more slowly than I_D or I_A suggested that this conductance pathway should play a more prominent role during the later (rather than the earlier) phases of action potential repolarization. To test this hypothesis, single action potentials and action potential trains were recorded from isolated CP neurons before and after superfusion of 10 mM TEA. In the presence of TEA, action potential durations at 50 and 90% repolarization increased, although the effect on the APD₉₀ was more pronounced (Fig. 8). Importantly, afterhyperpolarizations were eliminated in both strongly (Fig. 8A) and weakly (Fig. 8B) adapting CP cells in the presence of 10 mM TEA. Exposure to 10 mM TEA also has profound effects on the repetitive firing properties of CP cells. At low stimulus strengths, 10 mM TEA increased firing rates in both strongly (Fig. 8C) and weakly adapting (Fig. 8D) cells. When the amplitudes of the injected currents were increased, however, action potential amplitudes decreased and firing rates actually slowed (Fig. 8C). Although suggesting a prominent role for I_K in mediating the firing properties of CP neurons, these results (Figs. 7 and 8) were somewhat surprising in light of the facts that, on average, I_K amplitudes are approximately four times I_D amplitudes and that 10 mM TEA only blocks ~45% of I_K (Locke and Nerbonne 1997). In other preparations, TEA has been shown to be a potent blocker of Ca²⁺-dependent K⁺ currents (IC₅₀ = 0.1-1 mM) (Blatz and Magleby 1987). It is quite possible, therefore, that the results obtained here with TEA (Fig. 8) are confounded by blockade of Ca²⁺-dependent K⁺ currents as well as I_K (see below and DISCUSSION). Unfortunately, more selective blockers of I_K are not yet available.

View larger version (30K): [in this window] [in a new window]   FIG. 8. tetraethylammonium (TEA) has dramatic effects on action potential repolarization and repetitive firing in both strongly and weakly adapting CP cells. A and B: single action potentials were recorded under control conditions and after superfusion of 10 mM TEA. C and D: at low stimulus strengths (top), TEA increased firing rates in both strongly (C) and weakly (D) adapting cells. During larger amplitude current injections (bottom), however, action potential amplitudes decreased and repetitive firing slowed (D) or stopped (C). Amplitudes of the injected currents are indicated beside the records; the resting membrane potentials of these cells were 65 mV (A and C) and 66 mV (B and D), respectively.

Modeling of strongly adapting and weakly adapting regular-spiking CP neurons

As discussed above, the lack of specific blockers for I_A and I_K complicated experiments aimed at investigating the functional roles of these currents. In an alternative approach, we sought to develop a model of CP neurons using the VClamp/CClamp software package and to use this model to probe the functional roles of the Ca²⁺-independent, voltage-gated K⁺ currents, particularly I_A and I_K, in shaping the waveforms of individual action potentials and in mediating the repetitive firing properties of CP cells. The development and application of the model to simulate the properties of thalamocortical relay neurons has been described in detail (Huguenard and McCormick 1992; McCormick and Huguenard 1992) (see METHODS). The strategy employed here was similar to that of Huguenard and McCormick in that the currents of interest, i.e., I_A, I_D, and I_K, were first modeled with VClamp using the detailed time- and voltage-dependent properties (Table 2) determined experimentally (Locke and Nerbonne 1997). The CClamp program then was modified to reflect the properties and relative densities of I_A, I_D, and I_K, and the other conductances in the model were adjusted as described below.

To simulate voltage-gated K⁺ current waveforms, mean values of the time- and voltage-dependent parameters describing I_A, I_D, and I_K in CP neurons (Table 2) were used. As illustrated in Fig. 9, the simulated I_A, I_D, and I_K waveforms are indistinguishable from the currents recorded in isolated, identified CP neurons. Simulations also were completed, however, in which the time- and voltage-dependent properties of I_A, I_D, and I_K were varied over ranges encompassed by ±1 SD from the means (Table 2). Although the waveforms of the currents varied slightly, changing the time- and voltage-dependent properties of I_A, I_D, and I_K over ranges encompassed by ±1 SD from the means did not appreciably change the waveforms of simulated action potentials or repetitive firing patterns. Mean values for the time- and voltage-dependent properties of I_A, I_D, and I_K (Table 2), therefore, were used in subsequent simulations of action potentials and repetitive firing in CP neurons.

View larger version (27K): [in this window] [in a new window]   FIG. 9. Simulated Ca2+-independent, depolarization-activated K+ currents reliably reflect the properties of the currents expressed in isolated, identified CP neurons. A: simulated IA, ID, and IK waveforms generated with VClamp using mean values for all of the time- and voltage-dependent properties of the currents (Table 2). B: representative IA, ID, and IK waveforms recorded in CP neurons are displayed. Depolarization-activated outward K+ currents were recorded under voltage-clamp conditions with tetrodotoxin and Cd2+ in the bath to block voltage-gated Na+ and Ca2+ currents, as well as Ca2+-dependent K+ currents. Individual current components were separated based on differential sensitivity to 4-AP, dendrotoxin, and TEA (see text and Locke and Nerbonne 1997 for details). Recorded and simulated currents were obtained at room temperature (22-23°C).

After modifying CClamp to reflect the properties of I_A, I_D, and I_K, the densities of the currents were adjusted consistent with the experimental data (Locke and Nerbonne 1997). I_A amplitudes, for example, were set equal to four times I_D amplitudes (in the same cell) and were equal in strongly and weakly adapting CP cells (Locke and Nerbonne 1997). I_K amplitudes, however, were set 30% larger in strongly than in weakly adapting cells to reflect the fact that plateau current densities are higher in strongly adapting CP cells (Table 1). The time- and voltage-dependent properties of the other currents, I_Na, I_Nap, I_T, I_L, I_H, I_C, and I_AHP (see METHODS) were not altered; only the relative densities of the currents were varied. In previous studies, for example, we have shown that I_T is expressed only in a subset (18%) of CP neurons and that, when expressed, the amplitudes/densities of I_T are small (Giffin et al. 1991). Similarly, I_H amplitudes/densities in CP neurons are small (Solomon et al. 1993). In preliminary simulations, therefore, I_H and I_T amplitudes were set equal to zero. After the models were developed fully, however, it was clear that including I_T and/or I_H at densities comparable with those recorded in CP neurons (Giffin et al. 1991; Solomon et al. 1993) had little effect on simulated action potential waveforms or repetitive firing properties. For simplicity, therefore, I_T and I_H amplitudes/densities were zero for all of the simulations presented here. I_Na and I_L amplitudes were estimated from analyses of voltage-clamp data from CP neurons (Giffin et al. 1991) and were not changed throughout the simulations.

The remaining currents in the model, I_Nap, I_C, and I_AHP, to date have not been characterized in CP neurons, and the densities of these currents were varied somewhat randomly. Clearly, the goal was to produce simulated action potential waveforms and repetitive firing properties that resembled those in strongly adapting and weakly adapting CP neurons as simply as possible. Preliminary simulations with the model constrained by the known properties of CP neurons revealed that I_C was required to produce the brief action potentials and prominent afterhyperpolarizations evident in strongly adapting CP neurons (Fig. 3). Because, to our knowledge, there have been no previous reports documenting the presence of functional I_C-like currents in cortical neurons, it will be of great interest to test the predictions of this model that I_C is expressed in rat visual cortical CP neurons (see DISCUSSION). In all simulations here, I_C densities were equal in strongly and weakly adapting CP cells. The simulations also revealed that varying the densities of I_AHP and I_Nap allowed the generation of the strongly and weakly adapting firing patterns observed experimentally in CP neurons. Specifically, I_AHP density in weakly adapting cells was twice that in strongly adapting cells; this difference was necessary to simulate the marked increase in the interval between spikes as a function of time during prolonged current injections that is observed in weakly (but not in strongly) adapting CP cells (Fig. 3). A low density I_Nap (equal to 0.005-0.05% of the fast inactivating I_Na) was also necessary to reproduce the weakly adapting phenotype (see DISCUSSION).

Simulated action potential waveforms and repetitive firing patterns generated by the model are presented in Fig. 10. As is evident, the simulations closely resemble the experimental data (Fig. 3) for both strongly (Fig. 10A) and weakly (Fig. 10B) adapting CP cells. In particular, strongly adapting cells cease firing in spite of maintained depolarizing current injections, and the interval between successive spikes in a train is greater in weakly than in strongly adapting cells. In addition, single action potentials in strongly adapting cells have pronounced afterhyperpolarizations (Fig. 10C), whereas action potentials in weakly adapting cells do not (Fig. 10D).

View larger version (24K): [in this window] [in a new window]   FIG. 10. Action potential waveforms and repetitive firing properties of modeled strongly and weakly adapting regular spiking CP neurons (see text for details of the models and the simulations). Repetitive firing patterns generated in response to different depolarizing current injections in strongly (A) and weakly (B) adapting modeled CP cells are displayed; the resting membrane potential of each modeled cell was 70 mV. Consistent with the experimental data, action potentials in strongly adapting cells have pronounced afterhyperpolarizations (C), whereas those in weakly adapting cells do not (D).

Simulations provide insights into the functional roles of I_D, I_A, and I_K in CP neurons

Similar to results obtained experimentally (see Fig. 4) when I_D is "blocked" (i.e., the conductance is reduced to zero) in modeled CP neurons, the latency to firing an action potential is reduced (Fig. 11Aa). Because removal of I_D produced similar effects in strongly and weakly adapting modeled CP neurons, results are illustrated only for strongly adapting cells. Removing I_D also increased action potential durations at both 50 and 90% repolarization and slightly increased action potential amplitudes (Fig. 11Ab). The simulations also revealed that reductions in I_A after removal of I_D leads to further increases in action potential durations at both 50 and 90% repolarization (Fig. 11Ac), and the magnitudes of these increases are similar to those observed experimentally on application of 2-5 mM 4-AP to CP cells (see Fig. 6A).

View larger version (30K): [in this window] [in a new window]   FIG. 11. Removal of ID in modeled CP neurons decreases the latency to firing, slows the time course of action potential repolarization, and alters repetitive firing. In both strongly and weakly adapting modeled CP cells, removal of ID decreases the latency to firing (Aa) and increases both the APD50 and the APD90 (Ab). When 50% of IA also is removed, action potential repolarization is slowed further (Ac). Note that the results are illustrated for strongly adapting cell. Elimination of ID results in continuous firing throughout the stimulus duration in strongly adapting modeled cells (Be) and accelerates firing frequency in weakly adapting modeled cells (Bb). In both cell types, removal of 30% of IA in addition to 100% of ID further increases the firing rate in response to a stimulus of the same amplitude (Bc and Bf).

The effects of removing I_D on repetitive firing in modeled CP cells were also similar to those observed experimentally (see Fig. 5). In strongly adapting modeled cells, for example, elimination of I_D results in continuous firing throughout the stimulus duration (Fig. 11Be). In weakly adapting modeled cells, however, the firing rate (relative to the rate observed for the same current stimulus under control conditions) is increased when I_D is removed (Fig. 11Bb). When I_A is attenuated after removal of I_D, firing rates are increased (relative to the firing rates observed when only I_D was eliminated) in both strongly and weakly adapting modeled CP cells (Figs. 11B, c and f). Interestingly, in weakly adapting modeled cells, removal of more than ~30% of I_A (after removal of I_D) prevents repetitive firing. In strongly adapting modeled cells, however, repetitive firing continues even when >50% of I_A (and all of I_D) are eliminated. Presumably, the difference in the responses of the modeled strongly and weakly adapting CP cells to the removal of I_A reflects the facts that I_K density is higher in strongly than in weakly adapting CP cells, whereas I_Nap density is higher in weakly adapting cells (see DISCUSSION).

Although insights into the functional roles of I_A and I_K were obtained by examining the effects of millimolar 4-AP and TEA on the firing properties of CP cells, the lack of specific blockers for these currents clearly compromised interpretation of these experiments. As a result, it was of interest to use the newly generated models of CP neurons to examine the effects of "blocking" I_A and I_K on action potential waveforms and repetitive firing patterns. These simulations revealed that, in both strongly and weakly adapting modeled CP cells, removal of I_A slows action potential repolarization (Fig. 12Aa). In contrast, removal of I_K has no significant effect on the waveforms of individual action potentials in either strongly or weakly modeled adapting cells (Fig. 12Ab). The latter result is in marked contrast to what was observed experimentally using 10 mM TEA (see Fig. 8, A and B) and suggests that application of TEA to CP neurons indeed blocks Ca²⁺-activated K⁺ currents as well as I_K and, further, that Ca²⁺-dependent K⁺ currents are also important for action potential repolarization in CP cells (see DISCUSSION). The simulations also revealed that attenuation or removal of either I_A or I_K from modeled cells decreases the latency to firing (Fig. 11A, c and d).

View larger version (34K): [in this window] [in a new window]   FIG. 12. Removal of IA from modeled strongly and weakly adapting CP cells substantially increases the APD50 and APD90; the waveforms of action potentials before and after removal of IK, in contrast, are virtually indistinguishable (Ab). Eliminating either IA or IK from modeled weakly adapting and strongly adapting (not shown) CP cells decreases the latency to firing in response to threshold current injections (Ac and Ad). Removing either IA or IK results in continuous firing in strongly adapting modeled cells (Be and Bf) and dramatically increases the firing rate in weakly adapting modeled cells (Bb and Bc).

In weakly adapting modeled CP neurons, removal of I_A accelerates the rate of repetitive firing in response to the same current stimulus and substantially depolarizes the interspike membrane potential (Fig. 12Bb). When I_A is removed from strongly adapting modeled CP cells, repetitive firing throughout the duration of the depolarizing stimulus is observed routinely (Fig. 12Bf). Interestingly, the simulations also suggest that I_K makes no significant contribution to the waveforms of single action potentials, but that this conductance pathway does markedly influence the repetitive firing behavior of modeled CP cells. When I_K is removed from weakly adapting modeled CP cells, for example, a dramatic increase in the rate of repetitive firing is observed (Fig. 12Bc). In strongly adapting modeled CP cells, removing I_K results in continuous firing throughout the duration of the depolarizing stimulus (Fig. 12Bf).

	DISCUSSION

Abstract Introduction Methods Results Discussion References

CP visual cortical neurons are regular spiking

The experiments here were undertaken to examine the firing properties of isolated, identified CP rat visual cortical neurons and to explore directly the functional roles of the Ca²⁺-independent, voltage-gated K⁺ currents I_A, I_D, and I_K (Locke and Nerbonne 1997) in mediating the firing properties of the cells. As discussed previously (Giffin et al. 1991; Locke and Nerbonne 1997; Solomon et al. 1993), CP neurons were selected to correspond to prototypical regular-spiking cortical neurons (Connors and Gutnick 1990; McCormick et al. 1985). The results presented here reveal that, similar to regular-spiking cells characterized previously by others (Connors and Gutnick 1990; Huettner and Baughman 1988; Huguenard et al. 1988), isolated CP neurons fire single action potentials in response to brief current injections. During prolonged depolarizing current injections, CP neurons fire repetitively at rates that depend on the stimulus intensity, and these cells display varying degrees of spike-frequency adaptation (see also below). Taken together, these results confirm that CP neurons indeed can be classified as regular-spiking cortical cells.

Action potential durations at 50 and 90% repolarization are variable among CP cells, although there was no correlation between spike width either at 50 or 90% repolarization and the age of the animal from which the cells were isolated (P7-P13) or the time the cells were in culture before recording. Importantly, however, combined voltage- and current-clamp recordings revealed that the differences in action potential durations among CP cells are correlated with peak outward K⁺ current densities, i.e., the higher the peak outward current density, the briefer the action potential.

Strongly and weakly adapting regular-spiking CP neurons

Interestingly, two distinct regular-spiking patterns, which we have termed strongly adapting and weakly adapting, were evident among isolated CP neurons. Strongly adapting cells fire repetitively at the onset of depolarizing current injections but cease firing despite maintained depolarization. Weakly adapting cells, in contrast, fire continuously throughout the duration of depolarizing current injections. Examination of the waveforms of single action potentials revealed that action potential repolarization is faster and afterhyperpolarizations are more pronounced in strongly than in weakly adapting cells (see Fig. 3 and Table 1). In addition, analyses of combined voltage- and current-clamp recordings revealed that plateau current densities, corresponding to the slowly inactivating K⁺ currents (i.e., I_D and I_K) are significantly higher in strongly than in weakly adapting CP cells (Table 1).

Previous studies have demonstrated that the waveforms of individual action potentials and the repetitive firing properties of early postnatal cortical neurons are distinct from those of mature cortical neurons (Kriegstein et al. 1987; Lorenzon and Foehring 1993; McCormick and Prince 1987). Maximum firing rates, for example, are higher in mature than in immature neurons, and immature neurons are observed to stop firing in spite of maintained depolarizing current injections (Kriegstein et al. 1987; Lorenzon and Foehring 1993; McCormick and Prince 1987). The observation of strongly adapting CP cells, therefore, might be interpreted as suggesting that these (strongly adapting) cells are simply immature CP neurons rather than a distinct phenotype. Several lines of evidence, however, suggest that strongly adapting CP cells likely do not reflect an immature phenotype of regular-spiking CP cells particularly when compared with weakly adapting CP cells. The input resistances, for example, of strongly adapting cells are significantly lower (rather than higher as would be expected for less mature neurons) than those of weakly adapting CP cells (Table 1). In addition, action potential durations at 90% repolarization are significantly shorter (rather than longer as would be expected for less mature neurons) in strongly adapting than in weakly adapting CP cells (Table 1). Finally, repolarization is faster and fast afterhyperpolarizations are more prominent in strongly than in weakly adapting CP cells.

In addition, we note that distinct types of regular-spiking firing patterns have been described previously in mature neocortical neurons. In cat association cortex, for example, regular-spiking (RS) cells were subdivided into fast- and slow-adapting subtypes similar to those observed in CP neurons. Fast-adapting cells (16% of all RS cells) fired trains of spikes only at the beginning of depolarizing current pulses, whereas slow-adapting cells (84% of RS cells) fired continuously during a maintained stimulus (Nunez et al. 1993). Chagnac-Amitai and Connors (1989) subdivided regular-spiking cells in (4-6 wk) postnatal rat primary somatosensory cortex into three distinct subgroups (RS₁, RS₂, and RS₃) based on characteristic differences in fast afterhyperpolarizations, depolarizing afterpotentials and the extent of spike-frequency adaptation observed during maintained depolarizing current injections. In addition, it was demonstrated that RS₁, RS₂, and RS₃ cells have distinct laminar distributions: RS₁ and RS₃ cells, for example, were found in all cortical layers, whereas RS₂ cells were found only in lower layers (IV-VI). Two distinct regular-spiking phenotypes, termed RS₁ and RS₂, also have been described in postnatal mouse somatosensory cortex (Agmon and Connors 1992). Strongly adapting CP cells resemble RS₂ cells, whereas weakly adapting CP cells more closely resemble the RS₁ phenotype described by Chagnac-Amitai and Connors (1989) and Agmon and Connors (1992). During prolonged depolarizing current injections, for example, RS₂ cells often stop firing, i.e., RS₂ cells are "strongly adapting." In addition, the waveforms of individual action potentials in RS₂ and strongly adapting CP cells are remarkably similar, both being characterized by large, fast afterhyperpolarizations. Weakly adapting CP cells, in contrast, resemble RS₁ cells in that, although the interval between successive spikes increases initially, the intervals between spikes later in a train do not, i.e., the cells are "weakly adapting"; in both RS₁ and weakly adapting CP cells, a spike doublet is sometimes observed at the onset of the stimulus. In addition, the waveforms of individual action potentials in weakly adapting CP cells and RS₁ cells are similar; afterhyperpolarizations are not prominent in either cell type. Because CP neurons are found throughout cortical layers II-VI (Olavarria and Van Sluyters 1985) and are morphologically heterogeneous (Peters et al. 1990; Voigt et al. 1988), it may not be surprising that more than one regular-spiking phenotype is seen.

Finally, we note that the strongly adapting cells have only been observed in recordings from P11 CP cells: 12 of the 30 (40%) P11 CP cells studied were classified as strongly adapting. The strongly adapting phenotype was not seen in P10 (n = 0/19) CP neurons. Although it is possible that the strongly adapting phenotype is transient, the fact that strongly adapting CP cells are only seen at P11, whereas weakly adapting cells are seen at all ages (P8-P13), suggests that strongly adapting CP cells are not immature CP neurons particularly when compared with weakly adapting CP cells.

The expression of the strongly or weakly adapting phenotype is expected to have important functional consequences in that weakly adapting cells will track prolonged depolarizing inputs more reliably than will strongly adapting cells. Indeed, strongly adapting cells would be expected to actually attenuate prolonged excitation. As noted, RS₁ cells in mouse somatosensory cortex display an initial phase of rapid adaptation followed by firing at a fairly constant rate, whereas RS₂ cells continue to adapt throughout the stimulus duration (Agmon and Connors 1992). Interestingly, RS₁ cells were found in cortical layers II-VI, whereas RS₂ cells were encountered only in cortical layers V and VI, suggesting the participation of RS₁ and RS₂ cells in different cortical circuits.

Simulated voltage-clamp currents and firing properties of CP neurons

VClamp/CClamp, developed to simulate the properties of thalamocortical relay neurons (Huguenard and McCormick 1992; McCormick and Huguenard 1992), was used here to develop models of the firing properties of strongly and weakly adapting CP neurons. The voltage-gated K⁺ currents I_A, I_D, and I_K, were modeled first with VClamp using the detailed time- and voltage-dependent properties determined experimentally in isolated, identified CP cells (Locke and Nerbonne 1997). As illustrated in Fig. 9, the simulated and the experimental current waveforms are indistinguishable. The CClamp program then was modified to reflect the properties and relative densities of I_A, I_D, and I_K in CP cells, and the densities of the other conductances in the model were adjusted. I_Na and I_L amplitudes, for example, were estimated from analyses of voltage-clamp data from CP neurons (Giffin et al. 1991), and, for the reasons outlined previously (see RESULTS), I_H and I_T amplitudes were set equal to zero (Giffin et al. 1991; Solomon et al. 1993). The other three conductances in the model, I_Nap, I_C, and I_AHP, however, have not been characterized in CP neurons. As a result, the densities of these currents were, by necessity, varied arbitrarily in our effort to reproduce the observed firing properties of CP cells. Importantly, the goal was to make the minimum number of adjustments in the models necessary to allow the generation of the firing patterns observed in strongly and weakly adapting CP cells.

Subsequent simulations revealed that an additional, rapidly activating outward current (i.e., in addition to I_A, I_D, and I_K) was required to produce action potential durations and afterhyperpolarizations similar to those observed experimentally in CP neurons, particularly in strongly adapting CP neurons. Specifically, inclusion of the fast, Ca²⁺- and voltage-dependent K⁺ current I_C at a density equal to the density of I_D in the same cell resulted in shortened action potentials and prominent afterhyperpolarizations (Fig. 10) similar to those observed experimentally in (strongly adapting) CP neurons (Fig. 3). These findings were initially somewhat surprising primarily because there have been no published reports documenting the presence of functional I_C-like currents in cortical neurons. In preliminary experiments, however, we have found that exposure to 100 µM Cd²⁺ [which blocks voltage-gated Ca²⁺ channels (Giffin et al. 1991) and, therefore, any Ca²⁺-dependent K⁺ channels present], markedly prolongs action potentials and reduces the amplitudes of afterhyperpolarizations in CP neurons (n = 10) (unpublished observations). In addition, in voltage-clamp experiments, 100 µM Cd²⁺ suppresses the amplitudes of outward currents recorded in response to membrane depolarizations (n = 10) (unpublished data). Taken together, these results clearly demonstrate that Ca²⁺-dependent K⁺ currents contribute to determining action potential durations and afterhyperpolarizations in CP neurons. In addition, these observations, together with the results of the simulations, suggest the presence of an I_C-like current in CP cells, and that at least part of the effect of Cd²⁺ on CP neurons is due to effects on I_C. Clearly, further experiments aimed at characterizing the detailed properties and the functional roles of the Ca²⁺-dependent K⁺ currents in CP neurons are warranted.

After including I_C in the model, adjustments were made to the remaining two conductances, I_Nap and I_AHP, in an effort to produce the weakly adapting phenotype. These simulations revealed that small variations in I_AHP and I_Nap densities were sufficient to allow the generation of firing patterns (Fig. 10) indistinguishable from those observed experimentally in CP neurons (Fig. 3). The presence of a low density (0.005-0.05% of the fast I_Na) of the I_Nap conductance in the model of weakly adapting CP cells allows these cells to continuous firing during maintained depolarizing current injections. I_AHP, on the other hand, underlies the more pronounced spike-frequency adaptation seen in weakly (but not strongly) adapting CP cells. Interestingly, Nunez and colleagues (1993) hypothesized that differences in outward K⁺ current, I_Nap and/or I_AHP, densities underlie the fast- and slow-adapting firing patterns seen in RS cells in cat association cortex. It will be of interest to test the predictions of these models and, in particular, to determine if I_Nap and I_AHP expression levels are indeed higher in weakly than in strongly adapting CP cells.

Functional roles of I_D, I_A, and I_K in regular-spiking CP neurons

The fact that I_D is blocked selectively and completely by 50 µM 4-AP and by nanomolar concentrations of -dendrotoxin allowed direct evaluation of the role of I_D in shaping the waveforms of action potentials and in controlling the repetitive firing properties of CP neurons. These experiments revealed that action potentials are prolonged when I_D is blocked. In addition, combined voltage- and current-clamp recordings demonstrated that the magnitude of the prolongation of the action potential is correlated directly with the relative amplitude (density) of I_D. Thus in all CP neurons, I_D plays an important role in action potential repolarization. The experiments here also revealed that I_D contributes to controlling first spike latency. Although the effect of I_D on latency in CP neurons is significantly smaller than observed in CA1 hippocampal neurons (Storm 1988), these differences are quantitative, rather than qualitative, and likely reflect differences in the detailed properties and/or densities of I_D in hippocampal and cortical neurons. In hippocampal neurons, for example, I_D begins to activate at approximately equal to 75 mV, whereas the threshold for I_D activation in CP neurons is approximately equal to 40 mV. In both strongly and weakly adapting CP neurons, I_D also functions to control repetitive firing. Changes in firing rates after low concentrations of 4-AP have been observed in rat CA1 hippocampal (Storm 1988), prefrontal cortical (Hammond and Crepel 1992), nodose ganglion (Stansfeld et al. 1986), and neostriatal (Nisenbaum et al. 1994) neurons and in mouse hippocampal (Wu and Barish 1992) and guinea pig lateral geniculate relay (McCormick 1991) neurons. Importantly, the functional roles of I_D revealed in experiments with low concentrations of 4-AP or DTX (Figs. 4 and 5) were reproduced in the models of strongly and weakly adapting CP cells (Fig. 11).

In the studies here, hypotheses regarding the functional roles of I_A were tested experimentally using 4-AP (see Figs. 6 and 7). The results suggested that I_A contributes importantly to shaping the waveforms of individual action potentials and to controlling the rate of repetitive firing in CP neurons. Although similar functional roles have been suggested for I_A in rat lateral geniculate (Budde et al. 1992) and amygdala neurons (Gean and Shinnick-Gallagher 1989) and in rat CA1 hippocampal pyramidal (Storm 1987) and nonpyramidal (Zhang and McBain 1995) neurons, the lack of a selective blocker for I_A clearly compromised the interpretation of these experiments and our ability to draw conclusions about the role(s) of I_A in controlling the firing properties of CP neurons. After generating and validating the models of strongly and weakly adapting CP cells (Figs. 10 and 11), therefore, simulations were completed to explore the functional roles of I_A. The simulations (see Fig. 12) clearly suggest that I_A plays an important role in action potential repolarization and in determining first spike latencies. In addition, the simulations reveal that I_A functions to slow the frequency of repetitive firing in weakly adapting cells and that suppression of I_A in strongly adapting cells results in continuous firing. Taken together, therefore, the results of the simulations suggest that the functional roles of I_A and I_D in strongly and in weakly adapting CP cells are qualitatively very similar. It is interesting also to note that the results here indicate that neurotransmitter modulation of I_D or I_A will have similar functional effects and that these effects will be distinct in strongly and weakly adapting cells.

Exposure of isolated CP neurons to TEA has a greater effect on the APD₉₀ than on the APD₅₀ and profoundly influences repetitive firing in both strongly and weakly adapting cells. It is known, however, that TEA blocks other K⁺ currents, specifically Ca²⁺-dependent K⁺ currents (Blatz and Magleby 1987), and preliminary experiments indeed suggest that Ca²⁺-dependent K⁺ currents contribute importantly to action potential repolarization and to afterhyperpolarizations in rat visual cortical CP neurons (unpublished observations). Although it certainly would be possible to examine the effects of TEA on action potentials and firing patterns in the absence of Ca²⁺ (and therefore of Ca²⁺-dependent currents), such experiments would not allow one to assess directly the normal, i.e., the physiological, role(s) of I_K because action potential waveforms and firing properties are affected profoundly by the removal of Ca²⁺ alone (unpublished observations). Studies aimed at examining the functional role(s) of I_K certainly would be aided greatly by the identification of a specific blocker(s) of I_K. In lieu of a specific blocker of I_K, simulations of modeled CP neurons were completed to explore the likely role(s) of I_K.

In marked contrast to the results obtained with TEA, the waveforms of single action potentials essentially were unaltered when I_K was removed from both strongly and weakly adapting modeled CP neurons (Fig. 12). The simulations also demonstrated that I_K contributes to setting first spike latencies and to regulating repetitive firing patterns: removal of I_K dramatically increased the firing rate in weakly adapting modeled cells and produced continuous firing in the strongly adapting modeled CP neurons. The functional roles of I_K, therefore, are partially overlapping with those of I_A and I_D. An importance difference is the lack of contribution of I_K to single action potentials. Transmitter mediated modulation of I_K, therefore, unlike modulation of I_A and I_D, would be expected to selectively regulate repetitive firing in strongly and weakly adapting regular-spiking cells, without affecting the responses of these cells to brief depolarizing inputs. In addition, and similar to I_A, modulation of I_K will have more dramatic effects on repetitive firing than will modulation of I_D due to the fact that I_K is expressed at fourfold higher density (than I_D). Indeed, the simulations demonstrated that removing I_K (Fig. 12B, c and f) or I_A (Fig. 12B, b and e) resulted in firing at a more rapid rate than did removal of I_D (Fig. 11B, b and e). It will be most interesting to test these hypotheses directly should a specific blocker of I_K become available.

	ACKNOWLEDGEMENTS

  We thank R. J. Martinez and J. M. Coates for expert technical assistance with the in vivo retrograde labeling and with the preparation and the maintenance of cortical glial cultures. In addition, we thank Drs. John Huguenard and David McCormick for providing us with the VClamp/CClamp simulation package and Dr. Andreas Burkhalter for many helpful discussions.

  Finally, we acknowledge the financial support provided by the National Institute of Neurological Disorders and Stroke Grant NS-30676.

	FOOTNOTES

  Address reprint requests to J. M. Nerbonne.

  Received 3 September 1996; accepted in final form 30 June 1997.

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