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J Neurophysiol 95: 196-204, 2006. First published September 14, 2005; doi:10.1152/jn.00630.2005
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Origin of the Slow Afterhyperpolarization and Slow Rhythmic Bursting in Striatal Cholinergic Interneurons

Charles J. Wilson and Joshua A. Goldberg

Department of Biology, University of Texas, San Antonio, Texas

Submitted 16 June 2005; accepted in final form 12 September 2005


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Striatal cholinergic interneurons recorded in slices exhibit three different firing patterns: rhythmic single spiking, irregular bursting, and rhythmic bursting. The rhythmic single-spiking pattern is governed mainly by a prominent brief afterhyperpolarization (mAHP) that follows single spikes. The mAHP arises from an apamin-sensitive calcium-dependent potassium current. A slower AHP (sAHP), also present in these neurons, becomes prominent during rhythmic bursting or driven firing. Although not apamin sensitive, the sAHP is caused by a calcium-dependent potassium conductance. It is not present after blockade of calcium current with cadmium or after calcium is removed from the media or when intracellular calcium is buffered with bis-(o-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid. It reverses at the potassium equilibrium potential. It can be generated by subthreshold depolarizations and persists after blockade of sodium currents by tetrodotoxin. It is slow, being maximal ~1 s after depolarization onset, and takes several seconds to decay. It requires >300-ms depolarizations to become maximally activated. Its voltage sensitivity is sigmoidal, with a half activation voltage of –40 mV. We conclude the sAHP is a high-affinity apamin-insensitive calcium-dependent potassium conductance, triggered by calcium currents partly activated at subthreshold levels. In combination with those calcium currents, it accounts for the slow oscillations seen in a subset of cholinergic interneurons exhibiting rhythmic bursting. In all cholinergic interneurons, it contributes to the slowdown or pause in firing that follows driven activity or prolonged subthreshold depolarizations and is therefore a candidate mechanism for the pause response observed in cholinergic neurons in vivo.


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Although representing <1% of all striatal neurons (Oorschot 1998Go), cholinergic interneurons are the source of the dense cholinergic innervation of the striatum, and ACh released by these neurons is responsible for a host of important modulatory effects on neuronal excitability and synaptic transmission in the striatum (Akins et al. 1990Go; Calabresi et al. 1998Go; Centonze et al. 2003Go; Gabel and Nisenbaum 1999Go; Shen et al. 2005Go; Zhou et al. 2001Go). Studies of cholinergic interneurons in vivo (Reynolds et al. 2004Go; Wilson et al. 1990Go) and in vitro (Bennett and Wilson 1999Go; Jiang and North 1991Go; Kawaguchi 1992Go; Plenz and Aertsen 1996Go) have shown that these cells have a characteristic long-duration action potential and fire tonically at a low rate (2–10 Hz). In these ways, they correspond to the tonically active neurons (TANs) reported in extracellular recording studies of striatal neurons in awake, behaving animals (e.g., Aosaki et al. 1995Go; Kimura et al. 1984Go). The TANs observed in behaving animals also exhibit prominent pauses in their ongoing activity on presentation of stimuli of high salience either because of their novelty or because they have acquired signal significance as a result of learned associations (e.g., Apicella 2002Go; Morris et al. 2004Go). The mechanism of these pauses is unknown. Because of their relation to sensory stimuli, there is little doubt that they are triggered by synaptic input to the striatum. However, the cholinergic interneuron has very complex dynamics that can reshape and amplify synaptic inputs, so the input responsible for the pause may not have an amplitude or time course comparable to the pause (Wilson 2005Go). It may not even be an inhibitory input. Several studies have shown that experimental depolarization of striatal cholinergic interneurons by a current pulse is sometimes followed by a powerful and long-lasting afterhyperpolarization (AHP) (Bennett and Wilson 1998Go; Jiang and North 1991Go; Kawaguchi 1992Go; Reynolds et al. 2004Go). Reynolds et al. (2004)Go showed that in vivo this hyperpolarization can occur after application of a depolarizing pulse that is subthreshold for action potential generation. They propose that subthreshold excitatory inputs to the cholinergic cell may trigger a slow AHP, which would be seen in extracellular recording simply as a pause in ongoing activity.

Cholinergic interneurons are autonomously active, firing in the absence of synaptic input, and can exhibit at least three distinct firing patterns without the intercession of external signals (Bennett and Wilson 1998Go, 1999Go; Bennett et al. 2000Go; Wilson 2005Go). The rhythmic single-spiking pattern is the most prominent one, and it is caused primarily by the depolarizing influence of a persistent sodium current that brings the cell to action-potential threshold, and the subsequent fast- and medium-duration AHP that follow action-potential generation. The second pattern is an irregular single-spiking pattern with intermittent spontaneous bursts and pauses, and the third is a rhythmic bursting pattern in which high-frequency firing is terminated periodically by large hyperpolarizations that resemble those seen after firing driven by experimental current pulses. In both of these last patterns, there are spontaneous hyperpolarizations and pauses in firing that may be related to those seen in vivo and that also resemble the slow AHP that follows driven firing. The complexity of autonomous firing patterns is enhanced by the presence of another mechanism of subthreshold oscillation that operates in a range of membrane potentials just negative to (and overlapping with) that responsible for single spiking (Wilson 2005Go). This mechanism acts to amplify hyperpolarizations, and is often triggered during the slow afterhyperpolarization that follows firing driven by experimental current pulses (Wilson 2005Go). After blockade of the ion channels responsible for the amplification, a smaller and slower afterhyperpolarization was observed to follow depolarizing currents that triggered a sequence of action potentials. This smaller AHP is likely to more accurately reflect the time course of current that underlies the slow AHP. This slow AHP is presumed to be essential for the generation of the rhythmic bursting pattern. It acts both to terminate bursts and to generate the long periods of hyperpolarization that separate bursts.

The mechanism of the slow AHP in cholinergic interneurons is not known. Like many other neurons (Sah and Davies 2000; Vogalis et al. 2003Go), the cholinergic cells have spike AHPs that span three time scales (Bennett et al. 2000Go). A fast AHP (fAHP) results from the spike after-currents that are responsible for repolarization of the membrane potential after an action potential. One component of the fAHP is a calcium-dependent potassium current of the BK type. A medium AHP (mAHP), arises from an apamin-sensitive calcium-dependent potassium current. This mechanism is primarily responsible for the AHP that follows individual action potentials in the single spiking firing pattern (Bennett et al. 2000Go). In this report, we show that the sAHP is caused by an apamin-insensitive calcium dependent potassium current that can be triggered from calcium influx generated by driven firing or long duration (≥100 ms) subthreshold depolarizations.


    METHODS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Slices

Sprague-Dawley rats of both sexes, aged 16–24 days, were killed with ketamine/xylazine and perfused transcardially with ice-cold modified artificial cerebrospinal fluid (ACSF) containing (in mM) 230 sucrose, 2.5 KCl, 1.25 NaH2PO4, 26 NaHCO3, 0.5 CaCl2, 10 MgSO4, and 10 glucose. The brain was removed, blocked, glued to the stage of a vibrating microtome, and immersed in ice-cold modified ACSF. Sections through the neostriatum were cut at a thickness of 300 µm in the coronal or parasaggital plane and then transferred to a holding chamber where they were completely submerged in ACSF containing (in mM) 125 NaCl, 2.5 KCl, 26 NaHCO3, 1.25 NaH2PO4, 2 CaCl2, 1.5 MgCl2, and 10 glucose. This solution was continuously bubbled with 95% O2-5% CO2 and was maintained at room temperature (24–26°C). Slices were kept in the holding chamber for ≥1 h prior to recording. For experiments requiring reduced extracellular calcium, the solution contained (in mM) 123 NaCl, 2.5 KCl, 26 NaHCO3, 1.25 NaH2PO4, 3.0 MgCl2, 2 EGTA, and 10 glucose. For experiments requiring cadmium application, 400 µM cadmium was added to a reduced-phosphate solution containing (in mM) 125 NaCl, 3.0 KCl, 26 NaHCO3, 0.3 NaH2PO4, 1.5 MgCl2, 2.0 CaCl2, and 10 glucose.

Recording

Slices were examined using a x40 water-immersion objective (Axioskop, Zeiss, Germany) and standard infrared differential interference contrast (IR-DIC). Recordings were made with patch pipettes prepared from thin-wall borosilicate glass (Warner Instrument, Hamden, CT) on a P-87 Flaming/Brown electrode puller (Sutter Instrumemt, Novato, CA) and filled with a solution containing (in mM) 120 K-MeSO4, 10 KCl, 7.5 NaCl, 10 HEPES, 0.2 EGTA, 0.2 Mg-GTP, 2 Mg-ATP, 0.01 phosphocreatine, and 5 biocytin; pH 7.3, 280–300 mOsm, yielding tip resistances of 5–10 M{Omega}. Series resistance (15–30 M{Omega}) was monitored throughout the recording and neurons exhibiting >25% change during the period of data collection were rejected. Voltage errors due to series resistance were always <10% and were not corrected. The liquid junction potential was measured to be 7 mV and was corrected off-line. Recordings were made in the whole cell configuration using an Axopatch 200B amplifier and pClamp 8.0 (Axon Instrument, Foster City, CA). Signals were filtered at 5 kHz and digitized at >20 kHz. Experiments were performed at 32–35°C.

Measurements were made from the acquisition system’s binary files using custom software. Descriptive statistics for samples and hypothesis tests were calculated using Mathematica (Wolfram Research, Champaign, IL) and R (R Development Core Team 2005). Sample data were first examined using the Kolmogorov-Smirnov statistic for intrinsic hypotheses to confirm that they did not differ significantly from normal distributions, and differences in sample means were calculated using Student’s t-test. All other values are given as means ± SD throughout.


    RESULTS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
One hundred fifteen neurons were recorded in slices prepared from 49 animals. Cholinergic interneurons were identified by their unique appearance in IR-DIC visualization and by their characteristic spontaneous activity and response to current pulses (Bennett 1998; Kawaguchi 1992Go). During spontaneous single spiking, neurons exhibited fAHPs and mAHPs that regulated the rate and regularity of firing (as in Bennett et al. 2000Go). With constant current injection, the firing rate of the cells could be increased moderately, and sustained at an enhanced but still low rate (Fig. 1A). At higher rates, the cells exhibited a pronounced spike frequency adaptation associated with a hyperpolarizing sag of the membrane potential. After a period of driven firing (1 s in Fig. 1), a long and deep slow AHP (sAHP) could be evoked. The amplitude of the sAHP was enhanced when the depolarizing current pulse drove the generation of action potentials, but this was not required as blockade of action potentials with TTX reduced but did not abolish the sAHP (Fig. 1A). The sAHP was also not abolished by application of apamin (100 nM) or by combinations of apamin and TTX (1 µM, Fig. 1B), although the single-spike mAHP was clearly reduced by this treatment. This rules out the possibility that the sAHP is due simply to enhanced activation of SK channels by accumulation of intracellular calcium during repetitive firing. Because the amplitude and duration of the sAHP as seen in voltage recordings is largely shaped by the activation of hyperpolarization-activated currents (Wilson 2005Go), it was desirable to measure the sAHP as a postactivation current in voltage clamp. This method minimizes the change in membrane potential during the measurement and thus reduces the amplifying effect of hyperpolarization-activated currents. To measure the sAHP current (IsAHP) in voltage clamp, we held the membrane potential at –57 mV (near the voltage of minimal holding current for these cells) and then applied a depolarizing current pulse of varying amplitude and duration, followed by a return to –57 mV. The measurement of current in voltage clamp at potentials of –60 mV and above was intended to minimize activation of the hyperpolarization-activated potassium (IRK) and nonspecific cation (HCN) currents, which are active mostly below –60 mV (Wilson 2005Go).



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FIG. 1. Medium and slow afterhyperpolarization (AHP) in striatal cholinergic interneurons, and the medium and slow IsAHP that underlie them. A: 1-s current pulses are superimposed on a constant hyperpolarization to produce rhythmic single spiking from a silent background. Individual spikes during rhythmic single spiking are separated by a medium duration AHP (mAHP). On termination of the depolarizing pulse, a large long-lasting AHP (sAHP) ensues. Action potentials are not required for the sAHP, as it continues to be seen after blockade of sodium channels by TTX. B: in another cell treated with apamin, the mAHP is mostly blocked, rhythmic single spiking is disrupted, but the sAHP is still seen and is likewise not blocked by subsequent treatment with TTX. Note the hyperpolarizing sag that develops during the depolarizing pulse. This was present in many control cells, as well as those treated with apamin, and was especially prominent with large or prolonged depolarizations. AHP time course is shortened in this cell by the action of nonspecific cation (HCN) currents because the cell was hyperpolarized. C: long-lasting outward current seen in the presence of TTX in voltage-clamp in cholinergic neurons after depolarizing pulses appears to underlie the sAHP. The current has an early and late phase; the early phase is largely blocked by apamin, but the late phase is not. The apamin-insensitive slow afterhyperpolarization current (IsAHP) is maximal at ~1 s after the termination of the pulse.

 
After the current transient that followed termination of the positive voltage pulse, an outward current was observed that gradually decayed over a period of 2–4 s (Fig. 1C). Like the sAHP measured in voltage recordings, the IsAHP continued to be observed after blockade of sodium current by treatment with TTX. Usually, two components of the current could be observed, a faster component lasting <1 s, followed by a slower component, as shown in Fig. 1C. Application of apamin blocked the early component of current, leaving an apamin-insensitive component with a very slow onset and offset. To measure the sAHP component specifically, the tail current evoked by an 800-ms voltage pulse (to –2 mV) was measured 1 s after the termination of the pulse. This measurement was insensitive to apamin in 12 neurons studied. The mean IsAHP in this sample was 155 ± 63 (SD) pA compared with 148 ± 76 pA in the same cells after apamin treatment (t = 0.5).

Because somatic voltage clamp cannot be expected to adequately control voltage in all parts of the cell and because we do not know the cellular localization of IsAHP, it was possible that the slow AHP current could arise partly from the activation of hyperpolarization-activated currents in distal regions of the cell in which voltage control was inadequate. To test for this, both IRK and HCN currents were blocked by application of 3 mM cesium. This treatment greatly reduced the amplitude of the sAHP as seen in voltage recordings (not shown), but it had no effect on the amplitude of the IsAHP.

Tail current measured after the termination of a 800-ms depolarizing pulse (–2 mV) was unaffected by 3 mM cesium when tested in 10 neurons (control mean = 185 ± 107 pA; cesium mean = 188 ± 139 pA, t = –0.21). Thus the tail current measured here is a more accurate reflection of the ionic conductance primarily responsible for the sAHP, whereas the sAHP is much more complex, being subject to amplification and modification by hyperpolarization-activated voltage-sensitive conductances.

Activation of IsAHP

Individual action potentials trigger an mAHP, but usually not an sAHP, despite the fact that action potentials achieve very depolarized levels, and the sAHP can be seen after modest, even subthreshold, depolarizations. This suggests that the sAHP may be highly dependent on the duration as well as the amplitude of the depolarization. The sensitivity of the current to the amplitude of the voltage pulse was measured by the application of long (5 s) voltage pulses of various sizes, starting at a holding potential of –57 mV. IsAHP was apparent even for voltage pulses in the subthreshold range, was half-maximal at about –40 mV, and saturated for voltage pulses above about –20 mV. For a sample of 14 neurons tested, the average maximal current was 297 ± 201 pA, the half-activation voltage for the slow component of the tail current was –43 ± 6 mV, and the slope factor was 7 ± 2 mV. An example and normalized activation data from a group of 14 cells are shown in Fig. 2A. Because of a concern that activation of HCN currents may contribute to the tail current, the experiment was repeated for seven cells treated with a combination of TTX (1 µm), apamin (100 nM), and cesium (3 mM). For this sample of cells, the half activation voltage averaged 42 ± 4 mV, which did not differ significantly from that of the same cells measured before application of any blockers (–45 ± 9 mV) or after cesium was washed out of the bath, leaving TTX and apamin (–41 ± 10 mV). The sensitivity of IsAHP to the duration of the triggering voltage was determined by application of large voltage pulses (to –2 mV) and measuring the amplitude of the tail current with variation of pulse duration (10–1,000 ms). IsAHP showed a sigmoidal dependence on pulse duration. With pulse durations of ≤20 ms, very little sAHP current was generated, even by very large voltage pulses. The amplitude of IsAHP current increased dramatically between 20 and 100 ms and then increased approximately exponentially to an asymptotic maximum value. Disregarding the data from pulse durations <50 ms, IsAHP amplitudes were well-fit by an exponential approach to maximal amplitude (after a 50-ms delay), with a time constant of 52–231 ms (mean = 97 ± 52 ms, n = 12). An example showing the sigmoidal dependence on pulse duration and the exponential fit is shown in Fig. 2B. The requirement for a sustained depolarization, the accumulation of conductance with prolonged depolarization, and the slow onset after the offset of the current pulse all distinguish the IsAHP from the apamin-sensitive mAHP component of the tail current.



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FIG. 2. Voltage (A) and duration (B) sensitivity of IsAHP. These experiments were performed in the presence of apamin to avoid contamination by SK current and TTX to avoid uncontrollable action potential generation during the current pulses that evoke the tail current. A: normalized IsAHP for control data for a sample of 14 cells. The tail current increased smoothly with the amplitude of long voltage steps betwen –57 and –12 mV. Error bars are SE. Half-activation and slopes measured in TTX and apamin, or TTX and apamin and cesium did not differ from controls (not shown) B: short voltage pulses (<20 ms) failed to produce significant slow afterhyperpolarizing currents even when the pulse was very large. The amplitude of the tail current increased with pulse duration in a sigmodal fashion, requiring >300 ms to achieve its maximum.

 
IsAHP was also insensitive to application of tetraethylammonium (TEA; 1 mM), which is a potent blocker of BK calcium-dependent potassium currents. For six cells tested, the tail current measured at 1 s after pulse termination was not measurably altered by administration of TEA, measuring 154.8 ± 92.5 pA before and 137.2 ± 85.1 pA after the treatment. TEA was effective at blocking BK channels contributing to spike repolarization in these cells, significantly increasing spike duration (measured as a half-width) from 2.0 ± 0.3 to 2.8 ± 0.5 ms in six cells tested (t = 5.5, P < 0.01).

Reversal potential of IsAHP

To determine whether IsAHP was a potassium current, we measured its reversal potential by applying a strong, long-duration positive voltage pulse to maximally activate the current, followed by a long period of constant voltage at a variety of negative potentials. Because hyperpolarization-activated currents (both IRK and HCN currents) were strongly evoked at potentials below –60 mV, it was necessary to conduct these experiments in the presence of 3 mM cesium and/or 100 nM ZD-7288. In some cells, both treatments (either of which might be expected to be adequate) were required to get a complete block of HCN current at potentials of –90 mV or below, at which even a small HCN current could interfere with the measurement of the tail current. An example showing the results of this test are shown in Fig. 3. In standard media ([K+]o = 2.5 mM), the slow component of the tail current reversed between –100 and –112 mV for six cells tested (mean = –107.4 ± 3.6 mV). This corresponds closely to the Nernst potential for potassium, calculated from the extracellular K+ concentration and the concentration of K+ in the electrode filling solution (–107 mV). Variation of [K+]o produced a change in the reversal potential of IsAHP corresponding closely to that expected if the current were carried entirely by potassium (Fig. 3, bottom right).



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FIG. 3. IsAHP is a potassium current. The reversal potential of the tail current corresponded to the Nernst potential for potassium, for external potasssium concentrations ranging from 2.5 to 7.5 mM. IsAHP was measured 1 s after the termination of the depolarizing pulse, and relative to the final value of current at the end of the testing period (7 s after the depolarizing pulse).

 
The insensitivity of IsAHP to blockers of known calcium-dependent potassium channels suggests that although it is a potassium current, it may be calcium-independent. However, in other neurons, a similar slow tail current has been observed to be dependent on calcium concentration, although insensitive to blockade of SK2-3 or BK channels (Vogalis et al. 2003Go). To determine whether IsAHP in striatal cholinergic interneurons is calcium-dependent, we measured the effect of reducing extracellular calcium, blockade of calcium currents nonspecifically with cadmium, and reduction of intracellular calcium transients using intracellular perfusion with the high-affinity calcium buffer BAPTA (2–5 mM). The results of these experiments are shown in Fig. 4. In all 22 neurons tested, application of ACSF containing zero calcium (10 mM EGTA and Mg2+ increased to 3 mM) greatly reduced the amplitude of IsAHP (257 ± 151 pA in 2.5 mM Ca2+, 49 ± 47 pA in 0 mM Ca2+, t = 6.4, P < 0.01) in a reversible way (Fig. 4A). Likewise, blockade of calcium currents with 400 nM Cd2+ reduced or abolished the outward tail current (Fig. 4B) in six neurons tested (153 ± 123 pA in control solution, 17 ± 9 pA in Cd2+, t = 2.73, P < 0.05).



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FIG. 4. Calcium-dependence of IsAHP. A: slow component of the tail current was reversibly blocked by treatment in 0-calcium solution. B: it was reversibly blocked by application of 400 nM cadmium. C: current was slowed, and eventually blocked by intracellular dialysis with bis-(o-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid (BAPTA) through the patch pipette. The example shown at left is from a cell recorded using 5 mM BAPTA in the recording electrode. In 4 cells treated in this way (red lines at right in C), IsAHP rapidly decreased in amplitude and became nearly unmeasurable in <20 min. In the earliest recordings from these cells, made ~2 min after the start of dialysis, IsAHP was already reduced relative to controls. IsAHP from cells recorded using electrodes filled with 2 mM BAPTA were less reliably reduced (blue lines). Pooled data from both groups of cells showed a statistically significant reduction in the amplitude of IsAHP (black dots). Error bars are SE. *P < 0.05.

 
IsAHP was measured in 14 cells recorded using electrodes filled with BAPTA at a concentration of 2 mM (10 cells) or 5 mM (4 cells). In these experiments, IsAHP was measured from the tail current 1 s after a 1-s duration voltage pulse (Fig. 4C). Initially after breaking in, IsAHP measured in cells recorded with 2 mM BAPTA-containing electrodes was not different from that in control recordings, but the cells recorded with 5 mM BAPTA-containing electrodes had reduced tail currents at the time of the first measurement. Pooled results from both concentrations of BAPTA showed no significant difference between these cells initially and the control data from Fig. 4A (control = 257 ± 151 vs. 319 ± 123 pA in BAPTA). After 18 min of dialysis with BAPTA-containing electrode solution, the amplitude of the slow tail current in pooled data from BAPTA was reduced (mean = 190 ± 120 pA, t = 3.4, P < 0.01). The reduction IsAHP was clearly dose dependent, with a much larger decrease being seen in cells treated with the higher BAPTA concentration (mean: 56 ± 17 pA, Fig. 4C).

These results indicated that although not mediated by apamin- or TEA-sensitive calcium-dependent K+ currents, IsAHP is mediated by a calcium-dependent mechanism.

Model for slow oscillations

Because the biochemical mechanism of the slow AHP conductance is not known, a biophysically accurate model of the influence of this current cannot be constructed. There are a number of proposals for mechanisms responsible for the delayed activation of the current, including ones built on diffusion of calcium to a distal site of action, slow activation kinetics for the calcium-dependent channel, and enzymatic intermediate processes (Abel et al. 2004Go; Lancaster and Zucker 1994Go; Lasser-Ross et al. 1997Go; Sah and Clements 1999Go; Schwindt et al. 1992Go). Without attempting to distinguish between these alternative mechanisms, we constructed a phenomenological model based on slow kinetics of calcium activation. Both the slow activation and the requirement for prolonged depolarization to achieve a measurable current could be obtained using the fiction of a calcium-dependent potassium current similar to the SK current (requiring binding of 4 calcium ions to open the channel) but with very slow forward and backward rate constants to slow activation and deactivation. The time constant of the binding of calcium to the channel was made to be intermediate between that of calcium current activation and that of calcium disposition. For computational simplicity, the only voltage-sensitive currents that were included were a voltage-sensitive calcium current resembling the L-type calcium channel (Yan and Surmeier 1996Go) in cholinergic interneurons, a leak current that reversed at –50 mV, and a high-voltage activated voltage-sensitive potassium current that limited the membrane potential during large depolarizations. All voltage-sensitive currents were treated as instantaneous because they are so much faster than calcium disposition and the sAHP conductance. The equations governing this simple representation of the current were







in which [Ca] is the concentration of free calcium, CaB is the proportion of sAHP-channel-related calcium binding sites that have bound calcium, and v is membrane potential. IsAHP, ICa, IKv, and ILeak are currents through the sAHP, the voltage-sensitive calcium conductance, the voltage-sensitive potassium conductance, and the leak conductance, respectively, and C is membrane capacitance (1 µF/cm2). The parameter buf is the proportion of free to total intracellular calcium, d is the diameter of the spherical cell (d/6 is the surface area to volume ratio), z is the valence of calcium, F is Faraday’s constant, {tau}Ca is the time constant of calcium removal (reciprocal of the pump rate), vK, vCa, and vL are the reversal potentials for potassium, calcium, and the leak currents, respectively, gsAHP, gCa, gKv, and gLeak are the maximal conductances for the corresponding currents, vHCa and vHKv are the half-activation voltages for voltage-sensitive calcium and potassium currents, and vSKv and vSCa are the slope constants for activation of the voltage-sensitive calcium currents. Values used for these parameters in Fig. 5 are: d = 10 µm, {tau}Ca = 0.03 s/µm, buf = 0.1, gsAHP = 0.3 mS/cm2, gCa = 0.025 mS/cm2, gKv = 0.04 mS/cm2, gLeak = 0.001 mS/cm2, vCa = 100 mV, vK = –90 mV, vL = –50 mV, vHCa = –20 mV, vSCa = 6 mV, vHKv = –14 mV, vSKv = 6 mV. The key values for purposes of matching the kinetic properties of the sAHP are the forward and backward rate constants of binding of calcium to the sAHP conductance activation variable ({alpha} and {beta}). These were adjusted to 0.005/(nM/s) and 0.25/s, respectively, to match the delay in activation of the sAHP conductance as obtained in Fig. 2. The equations were integrated using XPPAUT (Ermentrout 2002Go) using the backward Euler method and a time step of 10 ms. The result of this is shown in Fig. 5. Despite its simplicity, this model of the sAHP conductance reproduced the fundamental features of the sAHP current seen in cholinergic interneurons and other cells. Activation of the sAHP current was delayed relative to the time course of the calcium current by ~1 s when using short large depolarizing steps (Fig. 5A). The peak current increased sigmoidally with pulse duration, requiring depolarizations of ≥20 ms to obtain a significant IsAHP even with very large depolarizations. Ignoring these short pulses, the curve relating peak IsAHP to pulse duration approached its saturation level exponentially, with a time constant of ~100 ms. The peak IsAHP occurred with pulse durations considerably less than that required for obtaining maximal calcium concentration. In the model, this was because of saturation of the high-affinity binding of calcium to the calcium sensor on the potassium channel. Similarly, the activation of IsAHP by long voltage steps of varying size produced a sigmoidal activation of the current but did not reflect the activation curve for the underlying calcium current. The calcium current was half-activated at –20 mV, but IsAHP activation was shifted ~15 mV to the left because of saturation of the calcium-dependent potassium current at calcium concentrations well below those obtained at the highest voltages.



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FIG. 5. Simple model for the sAHP current and the slow oscillation in cholinergic interneurons. The conductance was simulated using a simple high-affinity calcium-dependent potassium current model but with very slow kinetics. Calcium diffusion kinetics were ignored because of the slow time course of the processes of interest. A: activation using 2-s voltage pulses of various amplitudes showed similar activation to that seen in Fig. 2. Maximal activation of IsAHP occurred at considerably more hyperpolarized levels than that of the underlying calcium current because of saturation of the calcium-dependent potassium current. B: activation of the sAHP current by current pulses of various durations reproduced the results seen in cholinergic interneurons. C: simulated current-clamp recording using the same equations used in A and B. Note slow oscillations with period ~6 s. D: current-clamp recording of a spontaneously bursting cholinergic interneuron, after treatment with TTX and apamin, showing membrane potential oscilations with about the same amplitude and frequency. The difference in waveform is attributable to the action of HCN current in the cholinergic cell, but absent in the model. Data from Bennett and Wilson (1999)Go.

 
The same equations used in the voltage-clamp simulations in Fig. 5, A and B, were integrated with voltage unclamped and produced slow oscillations (Fig. 5C) when the reversal potential of the leak current was adjusted to –50 mV at which voltage there was calcium current activation exceeding the leak. Oscillations arose from activation of calcium current, depolarization, and delayed activation of the sAHP. The delay inherent in the sAHP and the slow disposition of calcium determined the period of oscillation. When the activation kinetics of the sAHP were adjusted to match the activation kinetics measured in cholinergic cells, the resulting oscillation matched that observed in spontaneously bursting cholinergic interneurons (Fig. 5D).


    DISCUSSION
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
Mechanism of the sAHP

The sAHP in cholinergic interneurons is complex in origin and not the result of any one ion channel. Any hyperpolarization in these neurons may trigger amplifying currents that will govern the depth and duration of the voltage response (Wilson 2005Go). The experiments described here show that the immediate cause of the hyperpolarizations that specifically follow prolonged driven firing in these neurons is a calcium-dependent potassium current insensitive to blockade of SK and BK channels. A similar current has been identified in a number of other neurons, especially cortical and hippocampal pyramidal cells (Abel et al. 2004Go; Lancaster and Zucker 1994Go; Lasser-Ross et al. 1997Go; Sah and Clements 1999Go; Schwindt et al. 1992Go), although the molecular identity of the channel responsible for this current is not yet known (Vogalis et al. 2003Go). Unlike cortical and hippocampal pyramidal cells, in which trains of action potentials are required to evoke a large sAHP, the underlying current in striatal cholinergic interneurons can be evoked by relatively small, even subthreshold, depolarizations. Thus the current can contribute to the generation of subthreshold oscillations that underlie rhythmic bursting. A key and puzzling feature of this current in all cells is its slow onset. Although calcium concentration is highest in all parts of the cell immediately after cessation of a depolarizing current pulse or train of action potentials, the sAHP requires additional time to develop. In the experiments here, it often did not attain its maximal value for as much as a second after the termination of a 1-s current pulse. This delay in the onset of the current has led to speculation that the potassium conductance may not be directly triggered by calcium concentration at the site of the conductance but rather require some intervening process with a long time constant (Lancaster and Zucker 1994Go; Lasser-Ross et al. 1997Go; Lee et al. 2005Go; Sah and Clements 1999Go; Schwindt et al. 1992Go).

In addition to the slow time course of its development, IsAHP requires the accumulation of intracellular calcium over a time course much longer than a single action potential. In the experiments described here, even very large depolarizations did not evoke a measurable sAHP current (at any latency) unless they were sustained for ≥20 ms, and maximal currents were obtained only with depolarizations lasting several hundred milliseconds. On the other hand, the calcium responsible for the IsAHP was carried by a calcium conductance that was activated at relatively low voltages, and the IsAHP could be evoked even at subthreshold voltages if the cell was held at those voltages for a sufficiently long time. This accounts for the observation of Reynolds et al. (2004)Go that the sAHP can be evoked by subthreshold depolarizations if they are prolonged. These properties insure that the sAHP will not be effectively evoked by single action potentials but will occur only after prolonged depolarizations or by bursts of firing.

Mechanism of rhythmic bursting in striatal cholinergic interneurons

In slices of the striatum, about half of cholinergic interneurons fire in the rhythmic single-spiking mode in which the apamin-sensitive mAHP is sufficiently strong to limit firing (Bennett et al. 2000Go; Wilson 2005Go). In this firing pattern, the sAHP is not evoked because the membrane potential and firing rate (and presumably the intracellular calcium concentration) are controlled by the AHP that follows single action potentials. The other half of cells fire bursts of varying intensity and regularity. Some of these cells exhibit powerful rhythmic bursting (Bennett 1999), associated with high firing rates for brief periods of time, separated by long intervals of hyperpolarization.

During rhythmic bursting, mAHPs arising from individual action potentials are not sufficient to counter large depolarizing currents that trigger high-frequency firing. Possibly, rhythmically bursting cells have exaggerated inward currents that overcome the mAHP. Strong applied current pulses can produce rapid firing followed by membrane potential sag similar to that seen in bursting neurons. Alternatively or additionally, cells exhibiting bursting may have weakened single spike AHPs. This is certainly the case for the rhythmic bursting seen in all cells after apamin-induced reduction of the mAHP (Bennett et al. 2000Go; Wilson 2005Go). In either case, the differences in firing pattern among striatal cholinergic interneurons is apparently attributable to variations in the strengths of these two calcium-dependent potassium currents relative to the inward current that sustains spontaneous firing. Cholinergic interneurons firing in the rhythmic bursting mode exhibit large slow subthreshold oscillations at about the same frequency after blockade of sodium currents with TTX (Fig. 5D). In these cells, at least, the relatively low-threshold calcium current responsible for the sAHP that phases the oscillation must be capable of providing the inward current necessary to sustain the depolarizing phase of the oscillations. Thus in bursting neurons, the inward current responsible for maintaining spontaneous firing may arise from calcium as well as sodium channels. The sAHP that separates bursts during the rhythmic bursting pattern is caused by the IsAHP, but its shape and duration are largely determined by other currents. Prominent among them are hyperpolarization-activated currents IRK and HCN, which are triggered by IsAHP and which can themselves support subthreshold oscillations in some cholinergic interneurons (Wilson 2005Go).

Three oscillatory mechanisms in striatal cholinergic interneurons

Cholinergic interneurons have three different oscillatory mechanisms, operating over three different time scales. The fastest is the oscillation responsible for the single-spiking firing pattern. In this mode, persistent sodium current activated at subthreshold potentials is responsible for the ramp-like depolarization of the cell that leads to action potential generation. Calcium entering the neuron through channels activated during the action potential produce a fast iberiotoxin-sensitive fAHP and an apamin-sensitive mAHP, which decay as calcium is removed from the cell after the action potential. When the mAHP current decays sufficiently, the cell is again depolarized by sodium current. This mechanism depends critically on action potential-generated AHP currents and so cannot be sustained after treatment of the cell with TTX (Bennett et al. 2000Go).

The second oscillatory mechanism occurs over a more hyperpolarized range of membrane potentials and does not require action potential generation. It relies on the interplay between the rapidly activating and deactivating hyperpolarization-activated outward current, IRK, and the slowly activating and deactivating hyperpolarization-activated inward current, HCN (Wilson 2005Go). This mechanism produces an intermediate-frequency oscillation in a subset of cholinergic interneurons, but it shapes and amplifies hyperpolarizations in all of them.

The third mechanism of oscillation seen in cholinergic interneurons is the one described here, which relies on sustained activation of low-voltage-activated calcium current and subsequent activation of the IsAHP. The slow build-up of the outward current in response to calcium accumulation functions as a delayed negative feedback that can give rise to slow oscillations. Cells firing under the influence of this current exhibit slow rhythmic bursting in which prolonged depolarizations produce high-frequency firing followed by very long duration hyperpolarizations. Of the three mechanisms, this one has the longest oscillatory period. In cells dominated by this mechanism, bursts occur every 1–10 s.

Although some cholinergic interneurons’ firing is clearly dominated by only one of these three mechanisms, many cholinergic interneurons fire in an irregular firing pattern consisting of periods of rhythmic single spiking, pauses, and bursts. Probably this pattern reflects a complex interaction between the three oscillatory mechanisms present in the cholinergic interneuron in which each mechanism dominates for brief periods of time. In addition to this apparent alternation in dominance of oscillatory mechanism within neurons, cells have been reported to change their firing patterns over slower time course, changing from a rhythmic single spiking to a rhythmic bursting pattern or the reverse over a period of minutes during a single recording session (Bennett et al. 2000Go; Reynolds et al. 2004Go). This suggests that the ion channels responsible for the three oscillatory mechanisms may change in relative strength under the influence of endogenous mechanisms. Perhaps these mechanisms are targets of modulation by spontaneously released modulators. In other cells, the sAHP is famous as a modulation target, being powerfully affected by activation of adrenergic, serotoninergic, and muscarinic receptors (Vogalis et al. 2003Go). It is also likely that the spike-triggered calcium currents responsible for the mAHP and the low-voltage-activated but slower calcium current responsible for the sAHP are subject to differential control that could shift the balance between bursting and single spiking in the cholinergic interneuron.


    GRANTS
 TOP
 ABSTRACT
 INTRODUCTION
 METHODS
 RESULTS
 DISCUSSION
 GRANTS
 REFERENCES
 
This work was supported by National Institute of Neurological Disorders and Stroke Grants NS-37760 and F32 NS-050900


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

Address for reprint requests and other correspondence: C. J. Wilson, Dept. of Biology, University of Texas at San Antonio, 6900 N. Loop 1604 W, San Antonio, TX 78249 (E-mail: Charles.Wilson{at}utsa.edu)


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