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¹ Institute of Basal Medicine, Department of Physiology, and Centre of Molecular Biology and Neuroscience, University of Oslo, PB 1103 Blindern, N-0317 Oslo, Norway

	Abstract

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In hippocampal pyramidal cells, a single action potential (AP) or a burst of APs is followed by a medium afterhyperpolarization (mAHP, lasting 0.1 s). The currents underlying the mAHP are considered to regulate excitability and cause early spike frequency adaptation, thus dampening the response to sustained excitatory input relative to responses to abrupt excitation. The mAHP was originally suggested to be primarily caused by M-channels (at depolarized potentials) and h-channels (at more negative potentials), but not SK channels. In recent reports, however, the mAHP was suggested to be generated mainly by SK channels or only by h-channels. We have now re-examined the mechanisms underlying the mAHP and early spike frequency adaptation in CA1 pyramidal cells by using sharp electrode and whole-cell recording in rat hippocampal slices. The specific M-channel blocker XE991 (10 µM) suppressed the mAHP following 1–5 APs evoked by current injection at –60 mV. XE991 also enhanced the excitability of the cell, i.e. increased the number of APs evoked by a constant depolarizing current pulse, reduced their rate of adaptation, enhanced the afterdepolarization and promoted bursting. Conversely, the M-channel opener retigabine reduced excitability. The h-channel blocker ZD7288 (4-ethylphenylamino-1,2-dimethyl-6-methylaminopyrimidinium chloride; 10 µM) fully suppressed the mAHP at –80 mV, but had little effect at –60 mV, whereas XE991 did not measurably affect the mAHP at –80 mV. Likewise, ZD7288 had little or no effect on excitability or adaptation during current pulses injected from –60 mV, but changed the initial discharge during depolarizing pulses injected from –80 mV. In contrast to previous reports, we found that blockade of Ca²⁺-activated K⁺ channels of the SK/K_Ca type by apamin (100–400 nM) failed to affect the mAHP or adaptation. A computational model of a CA1 pyramidal cell predicted that M- and h-channels will generate mAHPs in a voltage-dependent manner, as indicated by the experiments. We conclude that M- and h-channels generate the somatic mAHP in hippocampal pyramidal cells, with little or no net contribution from SK channels.

(Received 18 March 2005; accepted after revision 5 May 2005; first published online 12 May 2005)
Corresponding author J. F. Storm: Department of Physiology at IMB and Centre for Molecular Biology and Neuroscience (CMBN), University of Oslo, PB 1103 Blindern, N-0317 Oslo, Norway. Email: jstorm{at}medisin.uio.no

	Introduction

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In many excitable cells, action potentials are followed by afterpotentials that regulate the excitability of the cell for periods ranging from a few milliseconds up to several seconds. Afterpotentials that follow a single spike or a spike train can mediate different forms of feedback regulation of excitability.

Potassium (K⁺) channels are particularly important for negative feedback regulation. Once activated by the action potentials (APs) – i.e. by the ensuing depolarization, Ca²⁺ influx, or both – K⁺ channels mediate outward currents that outlast the APs and tend to hyperpolarize the cell, thus generating afterhyperpolarizations (AHPs). These AHP-generating K⁺ currents are essential determinants of refractoriness, interspike interval durations and trajectories and, hence, spike timing, discharge patterns and discharge frequencies. In addition, inward currents evoked by spikes can generate afterdepolarizations (ADPs) that mediate positive feedback, thus facilitating extra spikes and bursts.

Neurones in the vertebrate CNS are equipped with a variety of AHP-generating K⁺ currents and AHPs. A common pattern first described in hippocampal pyramidal cells (Storm, 1987a, 1990) is a sequence of three AHPs: (1) a fast one (fAHP, lasting 1–5 ms) that is a continuation of the spike repolarization; (2) a medium one (mAHP, typically lasting 50–200 ms), that mediates early spike frequency adaptation during a train of APs; and (3) a slow one (sAHP, lasting from about 0.5 s to several seconds) that mediates late spike frequency adaptation (Madison & Nicoll, 1984, Storm, 1990). In addition, a prominent ADP often occurs between the fAHP and mAHP (Kandel & Spencer, 1961; Storm, 1987a, 1990; Jensen et al. 1996; Yue & Yaari, 2004). In addition to mammalian hippocampal pyramidal cells (Lancaster & Nicoll, 1987; Storm, 1987a, 1990), a similar pattern is found in many other central neurones, e.g. pyramidal neurones in various layers of the mammalian neocortex (Schwindt et al. 1988) and amygdala (Pape & Driesang, 1998), in bulbar and spinal motoneurones (Takahashi, 1990; Viana et al. 1993) and in neurones of the striatum (Pineda et al. 1992).

Although this afterpotential pattern was first described almost two decades ago (Storm, 1987a), important issues remain partly unresolved or controversial, in particular regarding the mAHP mechanism. In contrast to the hippocampal sAHP, which has been studied in considerable detail (Madison & Nicoll, 1986; Madison et al. 1987; Lancaster & Nicoll, 1987; Pedarzani & Storm, 1993; Sah, 1996; Pedarzani et al. 1998), the mAHP has received relatively little attention, and seemingly conflicting interpretations persist. In particular, it is a widespread perception that the hippocampal mAHP is mediated largely by SK-type Ca²⁺-activated K⁺ channels (see reviews: Sah, 1996; Bond et al. 1999). For example, two recent studies support this notion (Stocker et al. 1999; Stackman et al. 2002), and apparently contradict previous studies that found no SK channel contribution to the mAHP (Storm, 1989; Williamson & Alger, 1990).

A second reason for re-examining the mAHP is that the molecular identity of the M-current (I_M) (Halliwell & Adams, 1982), which was originally proposed to be the main generator of the mAHP (Storm, 1989), has now been determined. The M-channels are made of subunits encoded by members of the Kv7 (KCNQ) family of K⁺ channel genes (Wang et al. 1996). Hence, we use the term Kv7/KCNQ/M-channels. The M-channels of CA1 pyramidal cells are probably composed of Kv7.2 (KCNQ2), Kv7.3 (KCNQ3) and Kv7.5 (KCNQ5), subunits (Selyanko et al. 1999; Lerche et al. 2000; Shah et al. 2002). Furthermore, the importance of these channels for brain function and human disease has been elucidated (Jentsch et al. 2000; Jentsch, 2000). Mutations in the KCNQ2 and KCNQ3 genes cause hereditary forms of human epilepsy (benign familial neonatal convulsions; Biervert et al. 1998), and possibly also mental retardation (Borgatti et al. 2004). In vitro data also suggest that I_M is important for preventing bursting and epileptiform activity (Williamson & Alger, 1990; Yue & Yaari, 2004; Peters et al. 2005). Furthermore, I_M in CA1 pyramidal cells was recently shown to be an important mechanism for subthreshold electrical resonance in the theta frequency range – a likely mechanism of hippocampal theta oscillations (Hu et al. 2002b; Peters et al. 2005), which are strongly implicated in hippocampal memory formation and spatial navigation, and can enhance long-term synaptic plasticity (O'Keefe & Recce, 1993; Holscher et al. 1997; Jensen & Lisman, 2000; Dragoi et al. 2003). Kv7/KCNQ/M-channel genes are expressed in many parts of the brain that engage in slow oscillations (Cooper et al. 2001). Moreover, drugs developed as cognitive enhancers for treatment of Alzheimer disease and other memory disorders have turned out to be potent and rather selective blockers of Kv7/KCNQ/M-channels (Aiken et al. 1996). Recently, such channels have also been found in axons and presynaptic terminals, and implicated in axonal function and transmitter release (Martire et al. 2004; Devaux et al. 2004).

A third reason for re-examining the mAHP mechanism is that several new specific pharmacological tools for blocking or enhancing the currents putatively underlying the mAHP have become available. These include more selective and reliable M-channel blockers (Wang et al. 1998; Schnee & Brown, 1998) and openers (Main et al. 2000), SK-channel blockers (Johnson & Seutin, 1997) and h-channel blockers (Pape, 1994).

For these reasons, we have re-examined the mAHP mechanisms. We find that the mAHP of rat CA1 pyramidal cells is generated by Kv7/KCNQ/M-channels at depolarized membrane potentials and by HCN/h-channels at more negative potentials, with no detectable contribution from Ca²⁺-activated K⁺ channels. Some of these results have been presented in abstract form (Gu et al. 2003, 2004).

	Methods

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Slice electrophysiology

Transverse hippocampal slices (400 µm thick) were prepared from young adult male Wistar rats (3–8 weeks of age). The experimental procedures were approved by the responsible veterinarian of the Institute, in accordance with the statute regulating animal experimentation given by the Norwegian Ministry of Agriculture 1996. Briefly, the rats were deeply anaesthetized with Suprane before decapitation. Hippocampal slices (400 µm) were cut with a vibratome (Campden Instruments, UK) and maintained in an interface chamber filled with artificial cerebral spinal fluid (ACSF) containing (mM): 125 NaCl, 25 NaHCO₃, 1.25 KCl, 1.25 KH₂PO₄, 1.5 MgCl₂, 1.0 CaCl₂, 16 glucose and saturated with 95% O₂–5% CO₂. In experiments with Ca²⁺-free medium, KH₂PO₄ was replaced by 1.25 mM KCl. During the recordings, the slices were kept submerged in a chamber perfused with ACSF of the composition described above, except that the CaCl₂ concentration was 2.0 mM. In a minority of the current-clamp experiments, 10 µM DNQX (6,7-dinitroquinoxaline-2,3-dione) was added to the extracellular medium to block spontaneous excitatory synaptic transmission. The ACSF was saturated with 95% O₂/5% CO₂ and heated to 30°C. The temperature was kept constant within ±0.5°C during recording.

Intracellular recordings were obtained from CA1 pyramidal neurones with sharp electrodes filled with 2 mM potassium acetate (resistance 80–140 M, pH 7.35). Whole-cell recordings from CA1 pyramidal neurones were established with the ‘blind’ method. The patch pipettes were filled with a solution containing (mM): 140 KMeSO₄ or potassium gluconate, 10 Hepes, 10 phosphocreatine sodium salt, 2 ATP sodium salt, 0.4 GTP sodium salt, and 2 MgCl₂, giving a pipette resistance of 4–7 M. For current-clamp recordings, an Axoclamp 2A amplifier (Molecular Devices Corporation, Union City, USA) was used in bridge mode. The series resistance was 10–40 M in whole-cell current-clamp recording. All potentials were corrected for the junction potential.

Only cells with a stable resting membrane potential more negative than –60 mV and stable AP amplitudes (>80 mV) were used for recording.

Data acquisition, storage and analysis

The data were acquired using pCLAMP 7.0 or 9.0 (Axon Instruments) at a sampling rate of 5–20 kHz, analysed and plotted with pCLAMP 9.0 and Origin 7.0 (OriginLab Corp.). Values are expressed as means ± S.E.M. Two-tailed Student's t test was used for statistical analysis ( = 0.05). The P values are given in the figure legends.

The mAHP and sAHP amplitudes were measured by averaging the values within the time window (20 and 50 ms, respectively) around the peak of each AHP (20–100 ms and 0.1–3 s after a spike train, respectively). The cell input resistance was measured by injecting small (0.1–0.2 nA) hyperpolarizing current pulses (200 ms) and calculated by dividing the steady-state voltage response by the current pulse amplitude (R_input = V/I).

Chemicals and drugs

The M-channel blocker XE991 was obtained from DuPont pharmaceutical company. DNQX and ZD7288 (4-ethylphenylamino-1,2-dimethyl-6-methylaminopyri-midinium chloride) were purchased from Tocris Cookson (UK). Apamin was purchased from Latoxan (France). Retigabine was generously provided by Dr J. B. Jensen, Neurosearch, Copenhagen, Denmark. The remaining drugs were from Sigma-Aldrich, Norway AS (Oslo). Substances were bath-applied by adding them to the perfusion medium.

Computational methods

In the supplemental data (online address) we describe and motivate the CA1 pyramidal cell model in detail. Briefly, computer simulations were performed with the Surf-Hippo simulator, version 3.5a (Graham, 2004). The model is derived from the Borg-Graham CA1 pyramidal neurone model (Borg-Graham, 1999) that has been refined through collaborative studies by using our experimental data on discharge patterns, AHPs, subthreshold resonance and oscillations (Shao et al. 1999; Hu et al. 2002b, Gu et al. 2003). The cell was represented as a ball-and-stick type of model with five compartments: an isopotential soma (diameter 20 µm) and a dendritic cable (total length 800 µm and diameter 5 µm) consisting of four segments of equal length. This model combines intracellular Ca²⁺ dynamics with 11 active currents including persistent and transient Na⁺ currents (I_NaP, I_NaT) (Borg-Graham, 1999), four voltage-gated K⁺ currents (I_A, I_D, I_DR, I_M), a fast inactivating BK-type Ca²⁺- and voltage-dependent K⁺ current (I_BK) (Shao et al. 1999), two voltage-gated Ca²⁺ currents (I_CaN and I_CaL), a hyperpolarization-activated nonspecific cation current (I_h), and a Ca²⁺-activated sAHP current (I_sAHP) (Borg-Graham, 1999).

	Results

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Current-clamp recordings were obtained from 117 CA1 pyramidal cells in strata pyramidale of rat hippocampal slices. In order to control for possible effects of different recording methods, both sharp electrode intracellular recordings (n = 76) and whole-cell patch-clamp recordings (n = 41) were used (see Methods). Except for a limited number of examples from other conditions, which are explicitly indicated in each case, the results presented are all from cells from young adult male rats (3–6 weeks), recorded with sharp electrodes or whole-cell patch-clamp (as indicated in the figure legends) in normal ACSF (with [K⁺]_o = 2.5 mM and [Ca²⁺]_o = 2.0 mM) at 30 ± 0.5°C.

The resting membrane potential (V_rest) and input resistance (R_input) were –65.0 ± 0.9 mV and 45.9 ± 2.3 M for sharp electrode recordings, and –73.3 ± 1.1 mV and 51.4 ± 2.9 M for whole-cell recordings, respectively.

Elimination of Ca²⁺ ions failed to affect the isolated mAHP

Figure 1 shows data from a typical intracellular recording from a rat CA1 pyramidal cell. The membrane potential was maintained at a slightly depolarized level, –60 mV, to enhance the amplitude of the mAHP. In order to test whether Ca²⁺-activated K⁺ channels contribute to the mAHP, we first eliminated the slow AHP (sAHP) by adding the adenylyl cyclase activator forskolin to the extracellular medium (Madison & Nicoll, 1986; Pedarzani & Storm, 1993) before exposing the slice to Ca²⁺-free medium in which the Ca²⁺ was replaced by 2.0 mM Mn²⁺) (see Methods for details). As shown in Fig. 1A and B, the isolated mAHP amplitude was not significantly affected by the Ca²⁺-free medium. Similar results were obtained in all five cells tested (summarized in Fig. 1C). In contrast, the decay time and waveform of the AP, monitored in parallel with the mAHP in the same cell, were clearly altered by the Ca²⁺-free medium (Fig. 1D and E). The latter effect was expected as a consequence of suppression of currents through voltage-gated Ca²⁺ channels and Ca²⁺-activated BK channels (Storm, 1987a). This confirmed that our application of Ca²⁺-free medium with Mn²⁺ efficiently eliminated the activation of Ca²⁺-activated channels in the same cell. The prior elimination of the sAHP by forskolin ensured that blockade of the sAHP by Ca²⁺-free medium did not interfere with our measurements of the mAHP.

View larger version (23K): [in this window] [in a new window]   Figure 1.  The mAHP in CA1 pyramidal neurones is not dependent on extracellular Ca2+ A, intracellular sharp-electrode recording showing typical example of the medium afterhyperpolarization (mAHP) in a rat CA1 pyramidal cell recorded after inhibition of the slow AHP (sAHP) with bath-applied forskolin (50 µM). Subsequent application of Ca2+-free extracellular medium with 2 mM Mn2+ caused no apparent change of the mAHP (overlay). The background membrane potential of the cell was kept at –60 mV by injecting steady depolarizing current. To evoke the mAHP and sAHP, a depolarizing current pulse was injected into the cell. The intensity of the current pulse was adjusted to evoke a constant number of action potentials (APs) per pulse (five). B, time course of the mAHP amplitude during the experiment shown in A. C, summary data showing the amplitude of mAHP before and after the application of Ca2+-free medium in the presence of forskolin in five cells. D, typical example of an AP, before and after applying Ca2+-free medium. Note that Ca2+-free medium caused a dual effect on the spike repolarization, reflected as a narrowing of the upper two-thirds and broadening of the lower one-third of the spike. E, time course of AP 90–10% decay time, showing the effect of Ca2+-free medium on spike repolarization during the experiment shown in D. A, B, D and E are records obtained from the same cell.

The isolated mAHP is suppressed by M-channel blockade, but not by SK-channel blockade, at –60 mV

Figure 2A shows the effect of forskolin and the M-channel blocker XE991 on the AHPs in a CA1 pyramidal neurone, activated from a background membrane potential of –60 mV (maintained by steady current injection). In normal ACSF (Fig. 2A1), a train of five APs, evoked by injection of a 50-ms-long current pulse, was followed by a mAHP lasting 80 ms, and a sAHP lasting more than 2 s. Bath application of forskolin (50 µM) fully suppressed the sAHP, thus leaving the mAHP in isolation (Fig. 2A2). Although forskolin often appeared to reduce the total AHP amplitude measured at the peak of the mAHP (Fig. 2B1, open triangle), this effect was most likely to be due to suppression of the overlapping early part of the sAHP. Thus, there appeared to be no obvious effect of forskolin on the mAHP per se.

View larger version (35K): [in this window] [in a new window]   Figure 2.  Effect of forskolin, apamin and XE991 on the mAHP and the sAHP A, intracellular sharp electrode recording showing typical examples of the medium (mAHP, ) and slow (sAHP, ) afterhyperpolarizations in a CA1 pyramidal cell before (1) and after (2) bath-application of 50 µM forskolin, followed by 100 nM apamin (3), and then 10 µM XE991 (4). Inserts in A2 and 3 show the mAHP on an expanded scale. The background membrane potential of the cell was kept at –60 mV by injecting steady depolarizing current. XE991 caused the cell to depolarize, but this was compensated by decreasing the positive steady current (open arrow), thus keeping the membrane potential at –60 mV. To evoke the mAHP and sAHP, a depolarizing current pulse was injected into the cell. The intensity of the current pulse was adjusted to always evoke five APs per pulse. B, mAHP and sAHP traces from A are shown superimposed on an expanded scale: before and after forskolin (1), before and after apamin (2), before and after XE991 (3). Note that forskolin completely suppressed the sAHP, thereby also affecting the peak amplitude measurement of the mAHP (1, vertical dashed line). The latter effect is probably due to overlap of the mAHP and sAHP. In the presence of forskolin, the mAHP was unaffected by apamin (2), but was completely blocked and converted to an after-depolarization potential (ADP) by subsequent application of XE991 (3) (see also insert in A4). C, time course showing the effects of forskolin, apamin and XE991 on the amplitude of the mAHP (•) and sAHP () from the same cell as in A and B. D, summary graph showing the effect of forskolin, apamin and XE991 on the amplitude of the mAHP (filled columns) and sAHP (open columns) in all cells tested with these drugs (n = 4, *P < 0.05, **P < 0.01, NS P > 0.05).

Essentially identical results to those presented in Fig. 2A–C were obtained in all CA1 pyramidal cells tested with this stimulation protocol in the presence of forskolin, followed by apamin (n = 4) and XE991 (n = 4). Figure 2D shows the summary data from all cells tested.

These results indicate that the mAHP is largely due to activation of I_M, with little or no contribution from SK channels (Storm, 1989). This hypothesis is consistent with the apparent lack of effect of forskolin on the mAHP (Fig. 2A1 and 2), since I_M is reported to be largely resistant to protein kinase A activation in CA1 pyramidal cells (Madison & Nicoll, 1986; Madison et al. 1987).

Robust SK currents in CA1 pyramidal cells

In view of the lack of effect of apamin described above, one might suspect that the SK channels for some reason might be downregulated (including ‘run down’) and thus unavailable for activation under our experimental conditions, or that our apamin or application procedure was ineffective. In order to test for these possibilities, we used an experimental protocol that is known to strongly activate SK channels (Sailer et al. 2002; Fig. 3A).

View larger version (22K): [in this window] [in a new window]   Figure 3.  Apamin-sensitive AHP (SK) current can be evoked in the presence of TTX and TEA, but does not contribute to the mAHP in normal extracellular medium A, typical example of afterhyperpolarization (AHP) current recorded with whole-cell voltage-clamp in CA1 pyramidal neurones. The cell was voltage clamped at –50 to –55 mV with 1 µM TTX and 5 mM TEA in the bath. A 100 ms voltage step of sufficient amplitude (usually to 0 mV) to trigger a Ca2+ spike was applied to the cell to evoke AHP currents. Note that the outward tail current following the voltage step contains two components with different kinetics: a fast component (IAHP) of medium duration (200 ms) and a slow component (IsAHP) lasting several seconds. Apamin (100 nM) selectively inhibited IAHP, sparing IsAHP. The insets show IAHP before and after apamin on expanded scales. B, summary data showing time course of the normalized IAHP amplitude before and after apamin (n = 7). C, current-clamp recording obtained with a sharp intracellular electrode, showing that without the presence of TTX and TEA, the mAHP () following a 400 ms train of 10 APs can not be blocked by 100 nM apamin. The recording temperature was 23°C. D, averaged time course showing the application of the selective SK-channel blocker apamin (100 nM) had no apparent effect on mAHP amplitude. (n = 6, P > 0.05)

Apamin had similar effects, with a convincing time course (Fig. 3B), in all cells tested in this manner (n = 7). Specifically, clear effects of apamin on the early tail current were seen also when the whole-cell recording prior to apamin application lasted longer (10 min; n = 5) than in the whole-cell current clamp experiments (without TTX or TEA) where apamin failed to affect the mAHP (6–8 min, n = 9, data not shown). These results indicate that the SK channels of CA1 pyramidal cells are available for activation, i.e. they are not lost or downregulated, under our recording conditions, and that our apamin applications effectively block these channels. Nevertheless, apamin consistently failed to affect the mAHPs, even following long-duration high-frequency spike trains as shown in Fig. 3C and D (n = 6, P > 0.05). Taken together, these results seem to indicate that SK channels, although available for activation, are not normally activated by spike trains in CA1 pyramidal cells.

M-channel blockade suppresses the mAHP, but not the sAHP

The experiments presented in Figs 1 and 2 have the advantage that they permit analysis of the mAHP in isolation, after suppression of the sAHP. However, they leave open the possibility that forskolin might alter the mAHP mechanism, e.g. by suppressing an otherwise important component of the mAHP while perhaps enhancing another. Although previous experiments indicate that SK channel activity is not affected (Varnum et al. 1993) or possibly even somewhat enhanced (Stocker et al. 1999) by protein kinase A activation, it is important to examine the mAHP also in the absence of artificial kinase activation.

Figure 4A and C shows the effect of XE991 on the mAHP and sAHP following a train of five APs in normal ACSF. XE991 (10 µM) fully suppressed the mAHP. In contrast, the sAHP was enhanced, most likely because the cell's R_input was increased, thus increasing the voltage deflection produced by the sAHP current. Similar results were obtained in all cells tested (Fig. 4E, **P < 0.01, n = 5). Other experiments showed that muscarine (10 µM), which is known to suppress both I_M (Halliwell & Adams, 1982) and I_sAHP (Madison et al. 1987) through cholinergic receptor activation, abolished both the mAHP and sAHP. As the AHPs were blocked, an ADP appeared (Yue & Yaari, 2004). Similar results were obtained in all cells tested with muscarine (n = 5; data not shown), in close agreement with previous findings (Storm, 1989), thus further supporting the hypothesis that the mAHP, at membrane potentials close to –60 mV, is largely due to I_M.

View larger version (28K): [in this window] [in a new window]   Figure 4.  Blockade of IM suppressed the mAHP at depolarized membrane potentials A, whole-cell recording showing that blockade of M-current (IM) by 10 µM XE991 selectively suppressed the mAHP () at a depolarized background membrane potential, –60 mV. Similar effects were seen in all five cells tested in this way. Note that the sAHP () was enhanced by blocking IM with XE991. The insets show the mAHP (from the dashed box) on an expanded scale. B, sharp electrode intracellular recording showing that blockade of IM with XE991 had no apparent effect on the mAHP following a train of spikes evoked at a hyperpolarized background membrane potential –80 mV. The insets show the mAHP (dashed box) on expanded scales. The dashed lines in A and B indicate the membrane potential at which the neurones were maintained by constant current injection (–60 mV in A, and –80 mV in B). C and D, time courses from the experiments A and B, showing the XE911 effect on the mAHP amplitude while holding the membrane potential at –60 and –80 mV, respectively. E, summary data showing the voltage-dependent effect of XE991 on mAHP (at –60 mV, n = 5, **P < 0.01; at –80 mV, n = 5, NS P > 0.05).

M-channel blockade failed to suppress the mAHP at –80 mV

So far, the mAHP mechanisms were tested in cells whose background membrane potential was kept close to –60 mV by steady current injection (Figs 2, 4A and C). This was done to mimic an activated depolarized state, which is likely to occur often in pyramidal cells in vivo (Steriade et al. 1993; Buzsaki, 2002), and in which AHPs are likely to have their greatest impact. This condition also facilitates analysis of K⁺ current contributions to the AHPs, since they are enhanced by the increased driving force for K⁺. However, since the putative mAHP mechanisms are voltage dependent (Storm, 1989; Maccaferri et al. 1993; Hu et al. 2002b), we also studied the mAHP at different potentials. Figure 4B shows the effect of XE991 on the mAHP following a five-spike train at a background membrane potential (V_m) of –80 mV, maintained by steady current injection. At this potential, there was little or no apparent sAHP, presumably because V_m was close to the reversal potential for K⁺ (E_K, calculated to be –105 mV under our whole-cell recording conditions). We found that XE991 had no effect on the mAHP at this potential (Fig. 4B and D), in striking contrast to its effect at –60 mV (Fig. 4A and C), indicating that the mAHP at –80 mV is not due to I_M. Similar results were obtained in all cells tested (Fig. 4E, P > 0.05 (NS), n = 5).

HCN/h-channel blockade suppressed the mAHP at –80 mV, but not at –60 mV

The observation that M-channel blockade failed to suppress the mAHP at highly negative potentials (Fig. 4B and D) is consistent with the hypothesis (Storm, 1989) that it is I_h, rather than I_M that generates the mAHP at these potentials. However, this hypothesis was largely based on the use of Cs⁺ – a blocker that is not selective for I_h, but which also blocks inward-rectifier K⁺ channels (Lesage et al. 1995; Mermelstein et al. 1998).

We therefore re-examined this issue by using the more selective h-channel blocker ZD7288. As shown in Fig. 5, ZD7288 (10 µM) had no consistent effect on the mAHP at –60 mV (Fig. 5A and B), but fully blocked the mAHP evoked at –80 mV (Fig. 5C and D). It also abolished the I_h-induced depolarizing ‘sag’ in response to hyperpolarizing current pulses (Fig. 5E and F). Similar results were obtained in all cells tested with ZD7288 at –60 (n = 5) and –80 mV (n = 5), as illustrated by the summary graphs (Fig. 5G and H). These results strongly support the idea that the mAHP at highly negative membrane potentials is caused by I_h deactivation (Storm, 1989; Williamson & Alger, 1990; Maccaferri et al. 1993).

View larger version (30K): [in this window] [in a new window]   Figure 5.  Blockade of h-current (Ih) suppressed the mAHP at hyperpolarized membrane potentials A–D, the h-channel blocker ZD7288 (10 µM) suppressed the mAHP () at –80 mV (C) but not at –60 mV (A). B and D, time courses of the ZD7288 effect on the mAHP amplitude from the experiments shown in A and C, respectively. The example illustrated in A and B was from a sharp electrode intracellular recording; the one shown in C and D was obtained with whole-cell patch-clamp recording. Note that ZD7288 enhanced the sAHP () (A), and caused the cell to hyperpolarize, which was compensated by increasing the positive steady current to keep the membrane potential at –80 mV (open arrow). E, ZD7288 (10 µM) inhibited the Ih-dependent ‘sag’ evoked by a hyperpolarizing current pulse and increased the input resistance at –80 mV. F, time course of the ZD7288 effect on the cell input resistance, measured at the end of each current pulse. C and D, and E and F, are from the same cell. G, summary data (n = 10) showing the voltage-dependent effect of ZD7288 on ADP and mAHP (NS P > 0.05, **P < 0.01). H, normalized time course showing the average effect of ZD7288 on the mAHP and ADP at –60 mV () and at –80 mV (•).

It may appear dubious that such a slow current as I_M, which has activation time constants of up to several hundred milliseconds, can be activated appreciably by a single spike that last only about 1 ms (Goh & Pennefather, 1987; Storm, 1987a, 1989; Yue & Yaari, 2004). Nevertheless, each AP during slow repetitive firing in CA1 pyramidal cells is usually followed by a mAHP, and a similar mAHP is also evident after a single-pulse-evoked spike (Lanthorn et al. 1984; Storm, 1989). Such single-spike mAHPs are likely to play an important role in determining the relative refractory period, ISIs and, hence, the discharge frequency (Lanthorn et al. 1984; Madison & Nicoll, 1984; Storm, 1989, 1990).

To test whether the single-spike mAHP is caused by I_M, XE991 was applied to CA1 pyramidal cells that fired repetitively at a moderate rate (1–3 Hz) in response to injection of long-lasting (1–2 s) depolarizing current pulses. Figure 6A and B shows that 10 µM XE991 suppressed the mAHP following each single AP in the train: the mAHP following the first AP, evoked soon after the onset of the current pulse (Fig. 6A), as well as the later mAHP during steady-state repetitive firing (data not shown).

View larger version (26K): [in this window] [in a new window]   Figure 6.  Effects of XE991 on the afterpotentials following a single AP Sharp-intracellular-electrode recordings showing the ADP (*) and mAHP () following a single AP. Each AP was evoked by injecting a long lasting (2 s, A) or brief (2 ms, C) depolarizing current pulse into the neurone, starting from a membrane potential of –60 mV (maintained by steady depolarizing current injection). A, application of 10 µM XE991 first inhibited the mAHP and enhanced the ADP (10 min after onset of XE991 application), and subsequently caused discharge of a second AP (spike doublet; 13 min). C, XE991 application caused blockade of the mAHP and enhancement of the ADP (after 5 min), leading to an all-or-none burst discharge (after 10 min). Note that XE991 also caused the membrane potential to depolarize. Therefore, less positive holding current was needed to maintain the same potential compared to the control situation (lower traces in A; n = 10, P < 0.01). The insets in C show the mAHP and the ADP on expanded scales. B and D, time courses of the XE991 effect on the mAHP amplitude from the experiments shown in A and C, respectively. E and F, summary graphs of the XE991 effects from two different groups of experiments shown in A and C (each group: n = 5, P < 0.01).

Excitability control by I_M and I_h

In order to test how I_M affects excitability, we bath-applied 10 µM XE991 while injecting long current pulses (Fig. 7). XE991 caused a depolarization of V_rest and increased R_input, as indicated by increased voltage deflections to depolarizing and hyperpolarizing pulses of subthreshold intensities (Fig. 7A). These changes in V_rest and R_input will both tend to increase excitability, and such an increase was clearly observed in response to pulses of suprathreshold intensities. Thus, a current pulse that under normal conditions evoked only three spikes at low frequency, triggered a high-frequency burst of six spikes, followed by an enhanced sAHP (Fig. 7B, right, filled triangle) after application of XE991. To test how much of the excitability increase was due to the XE991-induced depolarization, we used direct current (DC) to readjust the background membrane potential back to the control level after applying XE991 (Fig. 7C). Also in this case, a current pulse that previously caused only a few APs at low frequency, evoked a high-frequency burst in the presence of XE991. Similar effects of XE991 as illustrated in Fig. 7A–C were observed in all 16 cells tested in these ways (n = 5, 5 and 6, respectively).

View larger version (36K): [in this window] [in a new window]   Figure 7.  XE991, but not apamin, increased neuronal excitability and bursting A, the M-channel blocker XE991 caused a depolarization of the resting membrane potential (Vrest), accompanied by an increase in the input resistance. Typical example from a whole-cell recording. The cell was at Vrest (–70 mV); current pulses (1 s duration) of opposite polarity were injected. B and C, sharp electrode intracellular recording showing that XE991 increased excitability and promoted burst firing. The background membrane potential was maintained at –70 mV by injecting steady current, and a depolarizing current pulse (0.3 nA, 400 ms duration) was injected every 20 s. Application of XE991 depolarized the cell, and transformed its response to a high-frequency burst followed by a sAHP ( in B). A similar burst response was also observed when the background depolarization caused by XE991 was reversed by adjusting the steady current injection (C). Similar results were obtained in all cells tested in these ways (A, n = 5; B, n = 6). D, XE991, but not apamin, increased the excitability of CA1 pyramidal cells; typical example from a sharp electrode intracellular recording. Responses to injection of 400-ms-long depolarization and hyperpolarizing current pulses of ±0.2 nA are shown superimposed. E, time course of changes in average AP frequency from the cell illustrated in D, before and after application of apamin followed by XE991. The AP frequency was calculated by averaging the instantaneous frequencies (i.e. 1/interspike interval) for all APs during each current pulse. F and G, summary time courses for all cells tested with apamin (F, n = 5) and XE991 (G, n = 5), showing the effects of these blockers on the average AP frequency. H, summary data, average AP frequencies resulting from application of apamin (n = 5) and XE991 (n = 5) versus normal medium prior to drug application (control) for all cells tested (**P < 0.01; NS P > 0.05).

We next tested whether I_h affects excitability. As illustrated in Fig. 8A, application of ZD7288 (10 µM) caused a hyperpolarization of the cell, and increased its R_input, presumably because a standing I_h and h-conductance were blocked. In the presence of ZD7288, the normal I_h-dependent over-/undershoot and sag pattern (Fig. 8A, left) was replaced by a more linear response to hyperpolarizing current pulses, and a slow ramp in response to subthreshold depolarizing current pulses (Fig. 8A, right). Stronger depolarizing currents evoked, in normal saline, a short-latency spike train with clear frequency adaptation (Fig. 8B, left). In contrast, after addition of ZD7288, the same stimulus elicited long-latency discharge, during which the spike frequency tended to increase toward the end of the pulse (Fig. 8B, right). Similar effects of ZD7288 as illustrated in Fig. 8A and B were observed in all five cells tested in this way. Such a slow ramp (Fig. 8A and B, right) and the much delayed discharge with ‘inverse adaptation’ or ‘warming-up’ (Fig. 8B, right) is typical of responses dominated by the slowly inactivating D-current (I_D) (Storm, 1988, 1990). Presumably, the effect of I_D (and also A-current, I_A) was unmasked by blockade of the opposing I_h by ZD7288 (for a discussion of this issue, see Storm, 1990, p. 179). I_D and I_A would also be strengthened by de-inactivation caused by the hyperpolarization following blockade of I_h. Accordingly, such ramp-and-delay response pattern was found to be eliminated by low concentrations of 4-aminopyridine (4-AP) or –dendrotoxin, which block I_D (Storm, 1988, 1990; N. Gu & J. F. Storm, unpublished data).

View larger version (21K): [in this window] [in a new window]   Figure 8.  Complex changes in excitability resulting from Ih blockade by ZD7288 A, typical example from whole-cell recording: ZD7288 caused a hyperpolarization of Vrest, accompanied by an increase in the input resistance. The cell was at Vrest (–76 mV); current pulses (1 s duration) of opposite polarity were injected. Application of ZD7288 (10 µM) hyperpolarized the cell (in this case by 8 mV, from –76 to –84 mV), eliminated the Ih-dependent ‘overshoots’, ‘sags’ and ‘rebounds’ in the voltage responses; instead a slowly depolarizing ramp appeared in response to depolarizing pulses. B and C, sharp electrode recording; the cell was at Vrest (in this case –65 mV). Application of ZD7288 again caused a hyperpolarization, thereby reducing the excitability of the neurone, manifested as fewer APs and longer discharge latency (related to the slow depolarizing ramp shown in A) in response to identical current pulses (B). However, when the hyperpolarizing effect of ZD7288 was compensated by steady depolarizing current injection, the same cell fired more APs in response to same current pulse, indicating increased excitability (C), presumably due to increased input resistance, as shown in A. Thus, ZD7288 caused both an apparent ‘increase’ and an apparent ‘decrease’ in excitability in the same cell, depending on how it was tested. Similar effects were observed in all cells tested in this way (n = 4).

These results illustrate the mixed effects of I_h on neuronal excitability, and can be explained in the following manner. On one hand, h-channels that are open already before stimulation provide a steady inward current and depolarization that tends to increase excitability. Therefore, h-channel blockade by ZD7288 hyperpolarizes the cell and, thus, reduces its excitability (Fig. 8B). This inhibitory effect is further strengthened by the hyperpolarization-induced enhancement (de-inactivation) of the K⁺ currents I_D and I_A, which also reduce excitability and induce a delay in the onset of firing (Fig. 8B, right). On the other hand, the open h-channels provide a shunt that reduces the cell input resistance. Therefore, when ZD7288 blocks these channels, the injected depolarizing current will have greater impact and produce more spikes, provided the background hyperpolarization has been compensated by DC (Fig. 8C, right), thus giving ‘increased excitability’.

In addition, it is likely that the delayed closure of h-channels in response to depolarization, which produces the initial overshoot and sag following the onset of a subthreshold depolarization (Fig. 8A, left), will have a similar impact on the discharge frequency during a suprathreshold depolarization: the transient inward I_h (‘overshoot’) increases the frequency of the initial discharge, and the subsequent decay in I_h (‘sag’) contributes to the early spike frequency adaptation (Storm, 1990). This explains why the adaptation was reduced by ZD7288 (Fig. 8C, right). However, this effect of I_h can best be studied when the number of APs is kept constant (Fig. 9F–I).

View larger version (34K): [in this window] [in a new window]   Figure 9.  IM and Ih regulate early spike frequency adaptation in a voltage-dependent manner A–D, XE991 (10 µM) reduced the early spike frequency adaptation, at background membrane potentials of –60 mV (A and B) and –80 mV (C and D). The cell was kept either at –60 mV (A) or at –80 mV (C) by steady current injection. A depolarizing current pulse lasting 50 (A) or 100 ms (C) was injected every 20 s to evoke constant number (5) of APs. At –80 mV (C), 100 ms pulse duration was used, because 50 ms was often insufficient for evoking five APs. The first to the fourth interspike intervals (ISIs) were compared before and after each drug application. B and D, summary data of spike frequency adaptation before and after XE991 at –60 mV (B) and at –80 mV (D). Note that XE991 inhibited early spike frequency adaptation at –60 mV, manifested as reduction of the second to fourth ISIs. However, at –80 mV, XE991 only significantly reduced the second and third ISIs. E, typical responses to subthreshold depolarizing current pulse injection (1 s duration) before and after XE991 application. The overshoot () and sag in the control condition was inhibited by XE991. In order to obtain responses of comparable, subthreshold amplitudes, the current pulse amplitude was reduced to compensate for the increased input resistance induced by XE991, and the XE991-induced depolarization was compensated by reducing the positive holding current (open arrow). F–I, typical examples showing the effect of ZD7288 on early spike frequency adaptation at –60 mV (F–G) and –80 mV (H–I). Note that ZD7288 reduced early spike frequency adaptation only when spikes were evoked from –80 mV, reflected as changes in the second to fourth ISIs (summary data in G and I). A, whole-cell recording; C, E, F and H, sharp electrode intracellular recordings.

Whereas excitability reflects the overall tendency to generate APs, spike frequency adaptation specifically refers to time-dependent decline in AP frequency during a spike train. To determine the roles of I_h and I_M in early spike frequency adaptation, we evoked repetitive firing by injecting depolarizing pulses of 50–100 ms, while applying blockers of I_h and I_M (Fig. 9). In order to isolate the effect on spike frequency adaptation from effects on excitability, we kept the spike number during each pulse constant (five APs) by varying the pulse intensity. XE991 (10 µM) caused the duration of the late interspike intervals (ISIs) to be reduced relative to the first ISI, indicating a reduced adaptation (Fig 9A and D). This effect was observed in all cells tested by using both sharp electrode and whole-cell recording methods (n = 10) when the background V_m was –60 mV (summary data, Fig. 9B). At –80 mV (Fig. 9C), however, the effect of XE991 on the frequency towards the end of the pulse was relatively weak (Fig. 9D, ISIs nos 3–4), probably because of opposing effects of I_A and I_D (see above).

Since I_M activates already below the spike threshold, it may also shape subthreshold responses. To study such effects, we injected weak depolarizing current pulses and applied XE991. The pulse intensity was adjusted to be just subthreshold (Fig. 9E). The control response showed an initial overshoot and sag, and a small undershoot after the end of the pulse, resembling a weak mAHP (Fig. 9E, left, arrows), but these features disappeared after XE991 application (Fig 9E, right; n = 5). This indicates that M-channels that activate below the spike threshold can slowly shunt excitatory current, thus repolarizing the cell and reducing excitability during a maintained stimulus (Brown, 1988). When tested from a holding potential of –65 mV, XE991 application caused an increase in the cell R_input from 49.6 ± 6.2 to 67.1 ± 6.4 M, i.e. by 38 ± 10%. (in five sharp-electrode recordings, P = 0.009).

To assess the role of I_h during repetitive firing, ZD7288 was applied (Fig. 9F–I). When the background V_m was –80 mV, ZD7288 slightly prolonged the mean duration of the first ISI (Fig. 9H and I; not statistically significant; n = 5, P = 0.17), whereas the second to fourth ISIs were significantly shortened (P = 0.008, 0.002, 0.002, respectively). No effect was observed when the background V_m was –60 mV (Fig. 9F and G), where h-channels are largely closed (n = 5, P > 0.05; Fig. 9G).

These results indicate that the inward I_h that still flows at the onset of an abrupt depolarization from a highly negative membrane potential can affect the initial excitability and spike frequency adaptation in CA1 pyramidal cells, in agreement with the data shown in Fig. 8.

The M-channel opener retigabine reduces excitability and the sAHP

In order to elucidate the functional roles of I_M, we also used the M-channel opener retigabine. Bath application of 10 µM retigabine caused a slight hyperpolarization of the cell (routinely compensated by injecting depolarizing DC: box arrows in Fig 10A, C and E). It also caused a clear reduction in R_input and increased the depolarizing overshoot and sag following a hyperpolarizing pulse (Fig. 10C and D). As expected from the hyperpolarization and reduced R_input, retigabine also caused a concomitant reduction in excitability, with fewer spikes evoked by a constant depolarizing current pulse (Fig. 10E). Furthermore, we observed a clear reduction in the amplitude of the sAHP (Fig. 10A and B, filled triangle). However, retigabine caused no significant change in the mAHP amplitude following a five-spike train at –60 mV (Fig. 10A, B and F; n = 4, P > 0.05). All effects of retigabine were reversed by XE991, as expected (Fig. 10A–E).

View larger version (32K): [in this window] [in a new window]   Figure 10.  The effect of the Kv7/KCNQ/M-channel opener retigabine on the mAHP, early spike frequency adaptation and input resistance A and B, mAHP () and sAHP () following a train of five spikes, recorded under normal conditions, followed by application of 10 µM retigabine and subsequently 10 µM XE991. Retigabine caused the cell to hyperpolarize, but this was reversed by increasing the positive steady current to keep the membrane potential at –60 mV (open arrow). However, retigabine had no apparent effect on the mAHP, whereas the sAHP was reduced by 50%. XE991 blocked the mAHP and fully reversed the effect of retigabine on the sAHP and membrane potential. B, time courses of the mAHP (•) and sAHP () amplitudes during the experiment illustrated in A. C and D, retigabine reduced the input resistance at –60 mV by 38.9 ± 3.1% (mean ± S.E.M.), and increased the rebound; both effects were blocked by XE991 (same cell as in A and B). E, retigabine reduced the excitability of the cell, reflected as fewer APs evoked by a current pulse of constant amplitude. The open arrows in A, C and E indicate that less positive steady current was injected into the neurone after retigabine to keep it at –60 mV, reflecting that retigabine had a hyperpolarizing effect. F, summary data showing the effect of retigabine and XE991 on the mAHP amplitude (n = 4, NS P > 0.05, **P < 0.01). All cells were obtained with sharp electrode recording.

View larger version (27K): [in this window] [in a new window]   Figure 11.  Modelling study of the mAHP following a single AP A, a single AP evoked by a current pulse (1 ms) while holding the membrane potential at –60 mV by steady-state current. Simulations were repeated with and without sAHP current. The left- and right-hand panels show the same simulations at different time scales. B1, same protocol as A while holding the membrane potential at different levels, as indicated. Superimposed voltage responses of simulations are shown of ‘control’ or with either ‘no IM’ or ‘no Ih’. B1, inset, (at a different scale) the AHPs following a single spike evoked at –60 mV, in normal conditions (control, continuous line), without IM (‘no IM’, dashed line) and with a –7 mV negative shift of the IM steady-state activation curve, i.e. resembling the retigabine effect (thin dotted line). Note that blocking IM or shifting its activation curve towards more negative potentials, increases and decreases the sAHP, respectively. B2 and B3, IM and Ih responses, respectively, during the protocol shown in B1. Insets show the open probability (Po) of IM (B2) or Ih (B3) during the AP. C, left panel, summary data of the mAHP amplitude at various holding potentials with or without sAHP current. Right panel, voltage dependence of the amplitude of the isolated mAHP (i.e. without sAHP current) with either IM or Ih blocked. D, voltage dependence of the Po (left) and time constant (right) of IM and Ih. Scale bar of insets in B1: 100 ms, 2 mV; B2 and B3: 0.5 ms, 20 mV.

View larger version (29K): [in this window] [in a new window]   Figure 12.  Modelling study of the mAHP following a train of APs A, train of APs evoked by a current pulse (50 ms) while holding the membrane potential at –60 mV by steady-state current. Simulations were repeated with and without sAHP current. The left- and right-hand panels show the same simulations at different time scales. B1, same protocol as A while holding the membrane potential at different levels as indicated. Voltage responses of simulations of normal conditions or with either ‘no IM’ or ‘no Ih’ are shown superimposed. The inset in B1 shows the AHPs following a five-spike train evoked at –60 mV, in normal conditions (control, continuous line), without IM (‘no IM’, dashed line) and with a –7 mV negative shift of the IM steady-state activation curve, i.e. resembling the retigabine effect (thin dotted line). Note that blocking IM, or shifting its activation curve, increases and decreases the sAHP, respectively. B2 and B3, IM and Ih response, respectively, during the protocol shown in B1. C, left panel, summary data of the mAHP amplitude at various holding potentials with or without sAHP current. Right panel, voltage dependence of the amplitude of the isolated mAHP (i.e. without sAHP current) with either IM or Ih blocked. D, to determine whether IM and Ih are activated and deactivated, respectively, by the APs or by the interspike depolarized plateau during a spike train (as in B), we compared IM and Ih during voltage responses with and without spikes. The voltage responses from the simulations in B1 at –60 and –80 mV, with or without spikes, were used as voltage-clamp commands (lower panels, dashed traces and continuous lines, respectively). The APs were clipped at the threshold. Upper panels, IM (left) and Ih (right) during the voltage-clamp command, before (dashed traces) and after (continuous lines) clipping the APs. Note that IM was strongly reduced by eliminating the spikes, indicating that it was mainly activated during the APs. In contrast, Ih was little affected by clipping the spikes, showing that it was mainly activated by the depolarized plateau. Inset scale bar of B1: 100 ms, 2 mV.

Computational analysis of the mAHP mechanisms following a single AP

Although the above experiments with selective channel blockers can elucidate qualitative questions about which ion channels contribute to the mAHP, they do not answer a number of important quantitative questions that may be hard to handle intuitively. For example: how can I_M, in spite of its overall very slow kinetics, activate sufficiently during a single AP to account for the observed mAHP (Fig. 6)?

In order to examine issues like these, we performed a computational analysis of the mAHP mechanisms, using a similar mathematical model of a CA1 pyramidal cell that was used previously in our laboratory (Hu et al. 2002b; Shao et al. 1999; for details, see Methods, and Supplemental material for computer modelling).

Figure 11A shows (at two different time scales) that a simulated single AP evoked by a brief (1 ms) current pulse, gave rise to a fAHP (largely due to BK current), mAHP (largely due to I_M) and sAHP (largely due to I_sAHP). A constant current injection was used to keep the background V_m at –60 mV, as in the slice experiments. When the sAHP current was omitted, the mAHP peak amplitude decreased slightly (dash-dot-dot traces; open triangle), resembling the effect of forskolin-induced suppression of I_sAHP (Fig. 2B1). This illustrates that the early I_sAHP, due to overlap, can contribute to the early AHP amplitude at the peak of the mAHP.

In Fig. 11B1, single APs were evoked while changing the background V_m from –60 to –80 mV, with no currents blocked (continuous line). The results show how hyperpolarization reduced the fAHP and mAHP due to a reduced driving force. Subsequently, the simulations were repeated after eliminating some of the ionic currents. When I_M was omitted (dashed line), the mAHP was virtually abolished at –60 mV, while there was no effect at –80 mV, thus resembling the results with XE991 (cf. Figs 2 and 4). In contrast, when I_h was omitted (dash-dot line), the mAHP was abolished at –80 mV (Fig. 11B1, right) but not affected at –60 mV, thus mimicking the effects of ZD7288 (cf. Fig. 5A–D).

The inset of Fig. 11B1 compares the sAHP under normal conditions (continuous line) and when I_M was blocked (dashed line) or enhanced by shifting its voltage-dependence (thin dotted line). The increased sAHP amplitude following elimination of I_M (dashed line) was simply due to the increased R_input, caused by lack of M-conductance. This largely explains the experimentally observed effects of XE991 (increased sAHP; in Fig. 4A) and retigabine (reduced sAHP due to increased M-conductance that reduces R_input; in Fig. 10A). Blocking I_M also caused a slight depolarization of the membrane potential as in the experiments at –60 mV. Also, we simulated the retigabine effect by shifting the I_M steady-state activation curve by –7 mV (Tatulian et al. 2001) (inset of Fig. 11B1, thin dotted line). This caused a strong reduction in the sAHP (through a decrease in R_input) and a slight decrease of the mAHP, thus resembling qualitatively the experimental observations of Fig. 10A and B. The simulated retigabine effect also caused a hyperpolarization of V_m at –60 mV. These simulations show that the observed effects of XE991 and retigabine can be explained in terms of their specific actions on I_M, thus not implying any side effects.

The lower two panels (Fig. 11B2–3) show the currents underlying the mAHP: I_M and I_h. The insets show the open probabilities (P_o) of the M-channels (Fig. 11B2) and h-channels (Fig. 11B3) during the AP, at a fast time scale. Due to their slow kinetics, the M-channels open late during the AP (Fig. 11B2). Thus, only about 30% of the full M-conductance (g_M = 7 pS µM^–2) is activated by a single spike in the model. I_M increases from 10% (P_o 0.10) to 40% (P_o 0.40) activation (inset of panel Fig. 11B2, left). However, this is sufficient to account for the observed single-AP mAHP amplitude of 2–5 mV at –60 mV (compare Figs 6A and 11A) (Storm, 1989). In contrast to I_M, I_h showed little change during the AP, partly because of the slowness of I_h. When starting from –80 mV, where I_h is moderately activated, I_h is very small during the AP itself because of its reduced driving force at depolarized potentials (Fig. 11B3, right). Nevertheless, starting from –80 mV, I_h is sufficiently deactivated by a single AP and ADP (70% of the deactivation was due to the AP and 30% due to the ADP) to generate a very small mAHP at that potential (Fig. 11B1 and 3). This is in agreement with the slice experiments (Fig. 5; see also Storm, 1989).

Figure 11C (left panel) summarizes the voltage dependence of the mAHP after a single AP, with or without the sAHP current included in the model. The right panel shows the changes in mAHP amplitude when various currents are blocked: (filled squares, no I_sAHP; open squares, no I_sAHP and no I_M; open triangles, no I_sAHP and no I_h). Figure 11D shows the voltage dependence of the open probabilities and time constants of the M- and h-channels used in the model. In accordance with the consistently negative experimental results with Ca²⁺-free medium or SK-channel blockers (Figs 1A, 2, 3C and D, and 7D–F), no SK conductance was included in the model.

Computational analysis of the mAHP following a train of APs

Figure 12A (upper traces) shows a simulated train of five spikes at two different time scales. The train was evoked by a 50 ms current pulse, while the background V_m was maintained at –60 mV with constant current injection (i.e. similar to the wet experiments shown in Fig. 4A). Elimination of I_sAHP (dash-dot-dot traces) caused a small reduction in the mAHP amplitude, similar to the forskolin effect in Fig. 2B (open triangle).

Figure 12B shows the effects of changing the background V_m in the normal model (i.e. with all currents included) and after omitting I_M or I_h. Again, the mAHP is shown to be due to I_M at –60 mV, but is caused by I_h at –80 mV (Storm, 1989).

The lower panels (Fig. 12B2 and 3) show ionic currents during the spike trains at –60 and –80 mV. Again (cf. Figure 11B2 and 3), I_M is activated during each AP, but also during the ISIs, and is the main current during the postburst mAHP at –60 mV. It participates appreciably to the mAHP also at –70 mV (data not shown). In contrast, I_h was small during each AP (Fig. 12B3), but deactivates substantially during the 50 ms depolarization, thus generating the mAHP at –80 mV, in agreement with our experimental results (Fig. 5). Figure 12C shows the voltage dependence of the mAHP after five APs, with and without I_sAHP, I_M and/or I_h. These plots illustrate the graded transition from an I_M-dependent mAHP at depolarized potentials to an I_h-dependent mAHP at hyperpolarized potentials, resulting in an overall U-shaped voltage dependence of the mAHP amplitude (Figs 11C and 12C) (Williamson & Alger, 1990).

Given the very slow kinetics of I_M and I_h, it may seem surprising that