Molecular determinants of Ca2+-dependent K+ channel function in rat dorsal vagal neurones


  • Paola Pedarzani,

    Corresponding author
    1. Max-Planck-Institut für experimentelle Medizin, Department of Molecular Biology of Neuronal Signals, Hermann-Rein-Strasse 3
    • Corresponding author
      P. Pedarzani: Max-Planck-Institut für experimentelle Medizin, Department of Molecular Biology of Neuronal Signals, Hermann-Rein-Strasse 3, 37075 Göttingen, Germany. Email:

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  • Anna Kulik,

    1. II. Physiologisches Institut, Universität Göttingen, Humboldtallee 23, 37075 Göttingen, Germany
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  • Michael Müller,

    1. II. Physiologisches Institut, Universität Göttingen, Humboldtallee 23, 37075 Göttingen, Germany
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  • Klaus Ballanyi,

    1. II. Physiologisches Institut, Universität Göttingen, Humboldtallee 23, 37075 Göttingen, Germany
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  • Martin Stocker

    1. Max-Planck-Institut für experimentelle Medizin, Department of Molecular Biology of Neuronal Signals, Hermann-Rein-Strasse 3
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  • 1Using in situ hybridisation histochemistry in combination with patch-clamp recordings and specific pharmacological tools, the molecular nature of the channels underlying Ca2+-dependent K+ currents was determined in dorsal vagal neurones (DVNs) of rat brainstem slices.
  • 2In situ hybridisation analysis at cellular resolution revealed the presence of ‘big’-conductance Ca2+- and voltage-activated K+ (BK) channel α-subunit mRNA, and of only one ‘small’-conductance Ca2+-activated K+ (SK) channel subunit transcript, SK3, at very high levels in DVNs. By contrast, SK1 and SK2 mRNAs were below the threshold limit of detection.
  • 3The SK channel-mediated after-hyperpolarising current (IAHP) was blocked by apamin with a half-maximal inhibitory concentration of ∼2.2 nm. This is consistent with homomultimeric SK3 channels mediating IAHP in DVNs. IAHP was also blocked by scyllatoxin (20–30 nm) and curare (100–200 μm).
  • 4Application of apamin (100 nm) or scyllatoxin (20 nm) invariably caused a substantial increase to 146.1 ± 10.4 and 181.8 ± 12.9 % of control, respectively, in the spontaneous firing rate of DVNs. Action potential duration was not affected by these SK channel blockers.
  • 5The selective BK channel blocker iberiotoxin (50 nm) increased action potential duration by 22.5 ± 7.3 %, as did low concentrations of tetraethylammonium (0.5 mm; 99.3 ± 16.4 %) and the Ca2+ channel blocker Cd2+ (100 μm; 49.5 ± 20.9 %). BK channel blockade did not significantly affect the firing rate of DVNs.
  • 6These results allow us to establish a tight correlation between the properties of cloned and native BK and SK channels, and to achieve an understanding, at the molecular level, of their role in regulating the spontaneous firing frequency and in shaping single action potentials of central neurones.

Ca2+-dependent K+ channels play a crucial role in neuronal function by shaping single action potentials and modifying firing patterns (Sah, 1996). They can be subdivided into three main groups. (i) ‘Big’-conductance, Ca2+- and voltage-activated K+ (BK) channels activate during the repolarising phase of action potentials, and generate the ‘fast’ after-hyperpolarisation (fAHP) that is due to the so-called ‘C’ current (IC; Adams et al. 1982; Lancaster & Nicoll, 1987; Storm, 1987). (ii) ‘Small’-conductance Ca2+-activated K+ (SK) channels open after single spikes or trains of action potentials and contribute to the ‘medium’-duration after-hyperpolarisation (mAHP) underlain by IAHP (Pennefather et al. 1985; Schwindt et al. 1988; Sah, 1996; Stocker et al. 1999). (iii) A third group of neuronal low-conductance Ca2+-activated K+ channels generates a ‘slow’ after-hyperpolarisation

(sAHP) due to the sIAHP following trains of action potentials (Lancaster & Adams, 1986; Sah, 1996). In contrast to sIAHP, IC and IAHP can be pharmacologically dissected with specific K+ channel blockers. BK channels are blocked by charybdotoxin and iberiotoxin, whereas SK channels are sensitive to apamin and scyllatoxin (for reviews see Kaczorowski et al. 1996; Sah, 1996; Wallner et al. 1999).

Molecular cloning has recently led to the identification of genes that code for a BK channel α-subunit (Tseng-Crank et al. 1994) and a family of SK channel subunits (SK1-3; Kohler et al. 1996; Joiner et al. 1997). Pharmacological and biophysical analysis in expression systems has greatly improved the understanding of the operation of Ca2+-activated K+ channels (cf. Kaczorowski et al. 1996; Wallner et al. 1999). However, at present there is little information on the correlation between expression pattern and functional relevance of BK and SK channel subunits in neurones in situ. Such information would be of particular importance for dorsal vagal neurones (DVNs), as a substantial body of data on the contribution of native SK and BK channels to neuronal excitability is derived from studies on these medullary cells (Sah, 1996), which are involved in the nervous control of several autonomic functions (Loewy & Spyer, 1990). In addition, no studies have yet been undertaken on the extent to which specific blockers of these K+ channels modify the spontaneous spike activity that is characteristic for DVNs (Raggenbass et al. 1987; Loewy & Spyer, 1990; Travagli et al. 1991; Wang et al. 1995).

The primary aim of the present study was to determine the expression pattern of BK and SK channel subunits in DVNs and to analyse whether the pharmacological profile of electrophysiological responses correlates with the sensitivity to toxin blockers of Ca2+-activated K+ channels in expression systems. We combined in situ hybridisation histochemistry and whole-cell patch-clamp recording in DVNs of brainstem slices, and found that the native BK α-subunit and the SK3 subunit tightly correlate with the concentration dependence of the blocking effects of iberiotoxin on IC and of apamin on IAHP. The rate of spontaneous spiking was considerably increased by apamin and scyllatoxin, whereas iberiotoxin prolonged spike duration. Our results establish a tight correlation between the properties of cloned and native BK and SK channels, leading to an understanding, at the molecular level, of the regulation of neuronal activity in situ by Ca2+-dependent conductances.


Preparation and solutions

The experiments were performed on 12- to 20-day-old Wistar rats anaesthetised with ether and decapitated. After removal of the brain, the brainstem was isolated and kept in ice-cold artificial cerebrospinal fluid (ACSF) with a reduced Ca2+ concentration (0.5 mm) for less than 5 min. The brainstem was then glued to the stage of a vibratome (FTB Vibracut, Weinheim, Germany), and 8–10 transverse 300 μm-thick slices were cut around the obex level. Prior to transfer to the recording chamber, the slices were stored at 30°C in standard ACSF. For the recordings, slices were transferred to a submersion-type recording chamber (volume 3 ml), immobilised with a net, and superfused at a rate of 5 ml min−1 with ACSF (30°C) of the following composition (mm): 118 NaCl; 3 KCl; 1 MgCl2; 1.5 CaCl2; 25 NaHCO3; 1.2 NaH2PO4; 10 D-glucose; pH adjusted to 7.4 by gassing with 95 % O2 and 5 % CO2. In most voltage-clamp experiments tetrodotoxin (TTX; 0.5 μm) and tetraethylammonium (TEA; 1 mm) were added to the ACSF. Drugs were purchased from Sigma (Munich, Germany), except for the scorpion toxins scyllatoxin and iberiotoxin and the bee venom apamin, which were obtained from Latoxan (Rosans, France). Toxins were prepared as stock solutions in toxin buffer (100 mm NaCl; 20 mm Hepes; pH = 7.4) and kept at −20°C until use. For applications, toxins and other agents were added to ACSF and, in the case of iberiotoxin, 0.1 mg ml−1 cytochrome c was added to minimise unspecific binding.

Intracellular recordings

Patch pipettes were pulled from thin-walled borosilicate glass capillaries (Clark Instruments, Pangbourne, UK). The standard pipette solution contained (mm): 140 potassium gluconate; 1 MgCl2; 10 Hepes (osmolarity 270–290 mosmol l−1, pH adjusted to 7.3–7.4 with KOH). Whole-cell recordings were performed on 85 superficial DVNs under visual control (Trapp & Ballanyi, 1995), using an EPC-9 amplifier (HEKA, Lambrecht, Germany). Patch electrodes had a resistance of 4–7 MΩ, series resistance was 12–20 MΩ, and cell capacitance (determined by the automatic C-slow procedure of the EPC-9 amplifier) ranged from 30 to 65 pF. The holding potential of −50 mV was close to the resting potential (Trapp & Ballanyi, 1995). IAHP could be measured as a tail current following short depolarising pulses (200 ms to 0 mV every 30 s) to activate Ca2+ influx, and it remained stable for the duration of the recordings. We performed some tests with a pipette solution containing 140 mm potassium methylsulphate instead of potassium gluconate, but did not observe any major change in the mean IAHP amplitude or in the stability of our recordings. Electrophysiological signals (low-pass-filtered at 10 kHz) were sampled via the ITC-16 interface of the EPC-9 amplifier into a Macintosh PowerPC 7200/90 using Pulse-Pulsefit and X-chart software from HEKA. Data analysis was done with IgorPro (Wavemetrics, Lake Oswego, USA). Values are reported as means ±s.e.m., with error bars in figures corresponding to the s.e.m. Student's two-tailed t test was used for statistical comparisons between groups (α= 0.05), with * indicating P < 0.05 and ** indicating P < 0.01.

In situ hybridisation

In situ hybridisation was performed as previously described (Stocker et al. 1999). Briefly, brain sections (10–16 μm) from adult male rats were hybridised with 35S-labelled antisense and sense oligonucleotide probes. For each SK and BK channel subunit, at least two antisense oligonucleotides corresponding to the 5′ and 3′ regions, with no significant similarity to other known K+ channel subunits, were chosen (SK1: 5′-GGCCTGCAGCTCCGACACCACCTCATATGCGATGCTCTGTGCCTT-3′ and 5′-CAGTGGCTTTGTGGGCTCTGGGCGGCTGTGGTCAGGTGACTGGGC-3′; SK2: 5′-AGCGCCAGGTTGTTAGAATTGTTGTGCTCCGGCTTAGACACCACG-3′ and 5′-CTTCTTTTTGCTGGACTTAGTGCCGCTGCTGCTGCCATGCCCGCT-3′; SK3: 5′-CGATGAGCAGGGGCAGGGAATTGAAGCTGGCTGTGAGGTGCTCCA-3′ and 5′-TAGCGTTGGGGTGATGGAGCAGAGTCTGGTGGGCATGGTTATCCT-3′; BK: 5′-GGCAGCAAACGGTCCACAGGTACTTGAGAGTCCGCCAGAGCAAGATGATG-3′ and 5′-CCCGAGGATGAAGAAGACCATGAAGAGGCGTCCAAGCGTGGTTTTTGC-3′). The sense oligonucleotides had complementary sequences which allowed us to control for general background. Specificity of the oligonucleotides was confirmed in two ways: (i) identical hybridisation patterns were obtained with each pair of antisense oligonucleotides; (ii) hybridisation with a mixture of the same labelled and non-labelled oligonucleotide in 100- to 500-fold excess did not produce detectable signals (Fig. 1G). Slides were dipped in photographic emulsion Kodak NTB2 and developed after 12–20 weeks. Brain structures were identified according to Paxinos & Watson (1986).

Figure 1.

Expression of SK and BK channel subunit transcripts in rat DVNs and hypoglossal neurones

Dark-field photomicrographs of coronal sections through the medulla hybridised with oligonucleotides specific for SK1 (A), SK2 (B), SK3 (C) and BK (D) subunit mRNAs; G, control. The dorsal vagal nuclei are encircled by dashed lines in A-D. The white arrows indicate high expression of SK3 (C) and BK (D) in DVNs. Below the dorsal vagal nuclei, hypoglossal neurones present very high signals with the SK2 (B) and the BK (D) probes. SK1 (A) and SK3 (C) labelling of hypoglossal neurones is less pronounced and limited to a subset of cells. E and F, bright-field high power photomicrographs showing the high expression level of BK (E) and SK3 (F) subunit mRNAs in single DVN (arrowheads). Scale bars: G, 150 μm (also applies to panels A-D);F, 25 μm (also applies to panel E).


To identify Ca2+-dependent K+ channels in DVNs at the molecular level, we studied the expression of SK and BK channel subunit mRNAs by in situ hybridisation with oligonucleotide probes. Analysis at cellular resolution revealed the presence of only one SK transcript, namely SK3, at very high levels in somata of DVNs (Fig. 1C and F), whereas SK1 and SK2 mRNAs were below the threshold limit of detection (Fig. 1A and B). This expression pattern was cell-type specific, as in the motoneurones of the adjacent hypoglossal nucleus SK2 was the most abundant transcript (Fig. 1B), while SK1 and SK3 mRNAs were expressed at lower levels in subsets of these cells (Fig. 1A and C). The BK channel subunit was expressed at very high levels in both DVNs and hypoglossal motoneurones (Fig. 1D); this is further illustrated in the high power photomicrograph showing clusters of silver grains on single DVNs (Fig. 1E).

SK channels have different sensitivities to apamin according to their subunit compositions in heterologous expression systems (Kohler et al. 1996; Ishii et al. 1997; Shah & Haylett, 2000; Strobaek et al. 2000). Therefore we tested under voltage clamp the concentration dependence of apamin suppression of the DVN after-hyperpolarising current (IAHP). In 13 neurones, 100 nm apamin abolished IAHP in an irreversible manner (Fig. 2A). The dose-response curve in Fig. 2B shows that a half-maximal blockade of IAHP was achieved at an apamin concentration of ∼2.2 nm, consistent with the half-inhibitory concentration obtained for apamin on cloned homomultimeric SK3 channels (Kohler et al. 1996; Hosseini et al. 1999). In rat hippocampal pyramidal neurones, both scyllatoxin and the nicotinic acetylcholine receptor blocker d-tubocurarine (curare) have been shown to selectively block the apamin-sensitive IAHP, which in those neurones is most probably mediated by channels formed by SK2 and/or SK1 subunits (Stocker et al. 1999). Both blockers also effectively suppressed IAHP in DVNs, with scyllatoxin blocking irreversibly approximately 51.2 ± 4.3 % of the current at a concentration of 5 nm ( n= 3; not shown), and > 90 % at 20–30 nm (Fig. 2C–E). The effect of curare was, in contrast, partially reversible. The K+ channel blocker tetraethylammonium (TEA) preferentially blocks BK channels at low concentrations (Wallner et al. 1999). In four DVNs, TEA (0.5 mm) had no effect on IAHP (not shown).

Figure 2.

Effects of SK channel blockers on IAHP measured in the whole-cell configuration from DVNs in acute medulla slices in the presence of tetrodotoxin and tetraethylammonium

A, apamin (100 nm) fully suppressed IAHP. IAHP was elicited in response to 200 ms pulses to 0 mV (see Methods), and measured as a tail current. B, dose-response curve for the block of IAHP by apamin. Data points (each n= 3–7) were fitted with the function: I/Imax= (1 + ([toxin]/IC50)n)−1, giving an IC50 value of 2.2 nm and a Hill coefficient of 1. C and D, similarly to apamin, scyllatoxin (ScyTx; 20 nm) and d-tubocurarine (curare; 200 μm) completely blocked IAHP in DVNs. E, bar graph summarising the effects of ScyTx (20–30 nm) and curare (100–200 μm) at saturating concentrations on IAHP. The number of cells tested is reported above each bar.

The involvement of SK3 and BK channels in regulating the spontaneous activity of DVNs was assessed by pharmacological tools and whole-cell recordings of membrane potential. Bath application of the SK channel blocker apamin (100 nm) resulted in a consistent increase in the rate of spontaneous firing of these neurones by 46.1 ± 10.4 % ( n= 6; Fig. 3A and D), together with a reduction in the mAHP following every single action potential (Fig. 4E). Similarly, scyllatoxin (20–30 nm, n= 3; 100 nm, n= 5) increased the firing rate by 81.8 ± 12.9 % (Fig. 3B and D), and substantially reduced the mAHP following each spike (Fig. 4CE). The effect of both toxins was irreversible upon wash-out for 10–15 min (not shown). Neither apamin nor scyllatoxin significantly affected the resting membrane potential of DVNs.

Figure 3.

The apamin-sensitive conductance plays a role in controlling the spontaneous firing frequency of DVNs

A and B, the SK channel toxins apamin (100 nm) and scyllatoxin (20 nm) increased the spontaneous firing frequency of DVNs. C, low concentrations of tetraethylammonium (TEA; 0.5 mm) did not affect the spontaneous firing rate. D, bar graph summarising the effects of apamin (100 nm), scyllatoxin (ScyTx; 100 nm), TEA (0.5 mm) and iberiotoxin (IbTx; 20–50 nm) on DVN spontaneous firing frequency. Initial resting membrane potential was −47 to −50 mV. The number of cells tested is indicated above each bar.

Figure 4.

Involvement of BK and SK channels in the repolarisation and after-hyperpolarisation of single spontaneous action potentials

A, tetraethylammonium (TEA; 0.5 mm) produced spike broadening and suppressed the fast AHP (fAHP). Spike width was measured 20 mV above the resting potential (see arrow). B, application of the selective BK channel blocker iberiotoxin (IbTx; 50 nm) led to a significant increase in action potential duration, affecting mostly the last third of the spike repolarisation, and reduced the fAHP, although the effects were less pronounced than those of TEA. C and D, the selective SK channel blocker scyllatoxin (ScyTx; 100 nm) did not affect spike repolarisation or the fast AHP, but significantly reduced the medium-duration AHP (mAHP) following a single action potential. E, bar diagrams summarising the effects of BK (TEA, 0.5 mm; IbTx, 20–50 nm) and SK (apamin, Apa, 100 nm; ScyTx, 100 nm) channel blockers on spike duration (left panel) and on the amplitude of the mAHP following single action potentials (right panel). The number of cells tested is displayed above each bar.

Furthermore, the involvement of BK-type K+ channels in the spontaneous activity of DVNs was tested. In eight DVNs, the application of 0.5 mm TEA had no effect on spike frequency (Fig. 3C and D). In contrast, the drug inhibited the fAHP and slowed spike repolarisation (Fig. 4A and E). Thus TEA substantially increased spike duration, as measured 20 mV positive to resting potential, by 99.3 ± 16.4 % (Fig. 4A and E). The effects of TEA on spike repolarisation and fAHP were reversible upon wash-out (∼10 min; not shown). Similar results were obtained with the Ca2+ channel blocker Cd2+ (100 μm; 49.5 ± 20.9 % increase in spike duration), which additionally reduced the peak amplitude of the action potential (not shown). Following administration for 30–45 min (recirculation), iberiotoxin (20–50 nm), the most selective BK channel blocker (Wallner et al. 1999), produced action potential broadening in five of six DVNs (Fig. 4B and E). The effect of iberiotoxin on spike broadening was not as pronounced as that of TEA (22.5 ± 7.3 % increase in spike duration; Fig. 4A, B and E), and was not reversible. This toxin had no effect on the rate of spontaneous firing (Fig. 3D) or on the resting membrane potential. By contrast, application of apamin (100 nm) or scyllatoxin (100 nm) did not affect action potential duration (Fig. 4C and E).


The interplay between different ionic conductances has been shown to play an important role in producing the intrinsic rhythmic activity of a number of central neurones (see, for example, Steriade et al. 1993). In this study we have elucidated for the first time the molecular nature of Ca2+-dependent K+ currents that have been previously described in DVNs (Sah & McLachlan, 1992; Sah, 1996). We have also shown their involvement in the regulation of the spontaneous firing in DVNs that mediates an essential component of the central vagal drive regulating oesophageal, gastric and pancreatic functions (Raggenbass et al. 1987; Loewy & Spyer, 1990; Travagli et al. 1991; Wang et al. 1995).

The exclusive high expression of SK3 mRNA detected by in situ hybridisation indicates that in DVNs homomultimeric SK3 channels mediate IAHP. This view is supported by the sensitivity of the DVN IAHP to apamin. In expression systems, the channels with the highest sensitivity to apamin have been shown to be SK2 homomultimers (IC50∼63 pM; Kohler et al. 1996; Ishii et al. 1997). The apamin sensitivity of SK1 channels is controversial, with the half-inhibitory concentration reported initially to be > 100 nm (Kohler et al. 1996; Ishii et al. 1997), and more recently to be in the range 3.3–12 nm (Shah & Haylett, 2000; Strobaek et al. 2000). Additionally, SK1 and SK2 subunits form heteromultimeric channels with an intermediate sensitivity to apamin, compared to the corresponding homomultimers (Ishii et al. 1997). The IC50 value we obtained for IAHP in DVNs is in agreement with the IC50 for apamin of cloned homomultimeric SK3 channels (∼2 nm; Ishii et al. 1997; Hosseini et al. 1999). This result corroborates the finding of high levels of SK3 transcript in DVNs, demonstrating that SK3 homomultimeric channels underlie IAHP and are important determinants in setting the spontaneous level of activity of these neurones. From our data we cannot strictly exclude the possibility that SK1 or SK2 subunits might be expressed at very low levels (below our detection limit) and might take part in the formation of a small fraction of SK channels or co-assemble with a majority of SK3 subunits (in a 1:3 stoichiometry, for example), thus having a negligible impact on the observed sensitivity of the DVN SK channels to apamin. However, there is so far no experimental evidence for the formation of heteromultimeric SK channels containing both SK3 and SK1 or SK2 subunits in either expression systems or native tissues. Another possible scenario we cannot exclude is that SK3 subunits might coassemble with as yet unidentified α- or accessory subunits. We think that the availability of an increasing number of selective toxins tested on cloned and native K+ channels (Strong, 1990), together with detailed analysis of the expression of specific K+ channel subunits at the cellular level, will allow the exploitation of the approach used in this study to identify the molecular nature of K+ channels in other central neurones.

Another interesting point emerging from our study concerns the specificity of the scorpion toxin scyllatoxin for SK channels. Scyllatoxin has been shown to bind to receptors that colocalise with the apamin-binding sites in the central nervous system (Auguste et al. 1992). It was also found to block IAHP in hippocampal neurones, where this current is highly sensitive to apamin and most probably mediated by channels formed by SK2 and/or SK1 subunits (Stocker et al. 1999). The results obtained here, testing the effect of scyllatoxin on IAHP in DVNs, show for the first time that scyllatoxin can also exert its effect by blocking presumably homomultimeric SK3 channels. We can therefore conclude that scyllatoxin, like apamin and curare, is a valuable tool as blocker of all known neuronal apamin-sensitive SK channels.

In rat DVN neurones, IAHP has been shown to be a target of the actions of neuromodulatory agents such as thyrotropin-releasing hormone (Travagli et al. 1992) and adenosine (Marks et al. 1993). Our results raise the possibility of testing whether the target of such modulation is directly the SK3 channel and of dissecting the molecular mechanism of modulation, for example by reconstituting the signal transduction cascade in expression systems.

Low concentrations of iberiotoxin and TEA inhibited the fast AHP and slowed spike repolarisation in DVNs (Fig. 4), an effect also observed in hippocampal neurones and attributed to BK-mediated currents (Storm, 1987; Shao et al. 1999). The stronger effect of TEA, compared to iberiotoxin, might be due either to a concomitant action of TEA on voltage-gated K+ channels involved in spike repolarisation, or to limited diffusion and access of iberiotoxin to the neurones. Consistent with our results, charybdotoxin has been shown to slow action potential repolarisation in DVNs, but the effect of this toxin was also weaker than that of TEA at low concentrations (Sah & McLachlan, 1992). In general, our results are in agreement with previous data based exclusively on pharmacological evidence (Sah & McLachlan, 1992), and, together with the BK expression pattern detected by in situ hybridisation, they suggest that the expression of BK α-subunit mRNA leads to the formation of BK channels involved in setting the duration of action potentials in DVNs. Based on our data, BK channels do not seem to be involved in regulating the spontaneous firing rate of DVNs.

In conclusion, the main message emerging from this study is that Ca2+-dependent K+ channels of the SK and BK type, identified at the molecular level, fulfil distinct functions in DVNs neurones. The SK channels are important regulators of the firing frequency, whereas the BK channels are mainly involved in setting the duration of single action potentials.

Finally, future studies where the expression of Ca2+-dependent K+ channel genes is genetically suppressed or enhanced will potentially provide useful information on the functional role of these channels at the systemic level. In particular, based on the present results, we predict that suppression or overexpression of SK3 channels will affect the spontaneous firing of DVNs neurones in vivo, thereby potentially perturbating the parasympathetic regulation of important cardiac and visceral functions.


This work was supported by the DFG and the Hermann-and-Lilly-Schilling-Stiftung (K.B.), the Sonderforschungsbereich 406 (P.P., K.B. and M.S.), and a Human Frontier Science Program grant to P.P. The authors are grateful to Walter Stühmer for generous support, and to A. A. Grützner for expert technical assistance.