Misaki Marine Biological Station, Graduate School of Science, University of Tokyo, Misaki, Miura, Kanagawa 238-0225, Japan
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ABSTRACT |
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Abe, Hideki and
Yoshitaka Oka.
Characterization of K+ currents underlying pacemaker
potentials of fish gonadotropin-releasing hormone cells.
Endogenous pacemaker activities are important for the putative
neuromodulator functions of the gonadotropin-releasing hormone
(GnRH)-immunoreactive terminal nerve (TN) cells. We analyzed several
types of voltage-dependent K+ currents to investigate the
ionic mechanisms underlying the repolarizing phase of pacemaker
potentials of TN-GnRH cells by using the whole brain in vitro
preparation of fish (dwarf gourami, Colisa lalia). TN-GnRH
cells have at least four types of voltage-dependent K+
currents: 1) 4-aminopyridine (4AP)-sensitive K+
current, 2) tetraethylammonium (TEA)-sensitive
K+ current, and 3) and 4) two types
of TEA- and 4AP-resistant K+ currents. A transient,
low-threshold K+ current, which was 4AP sensitive and
showed significant steady-state inactivation in the physiological
membrane potential range (40 to
60 mV), was evoked from a holding
potential of
100 mV. This current thus cannot contribute to the
repolarizing phase of pacemaker potentials. TEA-sensitive
K+ current evoked from a holding potential of
100 mV was
slowly activating, long lasting, and showed comparatively low threshold of activation. This current was only partially inactivated at steady
state of
60 to
40 mV, which is equivalent to the resting membrane
potential. TEA- and 4AP-resistant sustained K+ currents
were evoked from a holding potential of
100 mV and were suggested to
consist of two types, based on the analysis of activation curves. From
the inactivation and activation curves, it was suggested that one of
them with low threshold of activation may be partly involved in the
repolarizing phase of pacemaker potentials. Bath application of TEA
together with tetrodotoxin reversibly blocked the pacemaker potentials
in current-clamp recordings. We conclude that the TEA-sensitive
K+ current is the most likely candidate that contributes to
the repolarizing phase of the pacemaker potentials of TN-GnRH
cells.
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INTRODUCTION |
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The terminal nerve (TN)-gonadotropin releasing
hormone (GnRH) cells show endogenous pacemaker activities and project
widely in the brain (Oka and Matsushima 1993). Such
characteristics of TN-GnRH cells may be relevant for simultaneous
regulation of the target neuron's excitability in a wide variety of
brain regions, depending on the animal's physiological conditions. We
consider that TN-GnRH system may function as a neuromodulator that is
involved in the regulation of many long-lasting changes in animal
behaviors, such as changes in motivational or arousal states
(Oka 1992a
,b
, 1997
; Oka and Matsushima
1993
). Because TN-GnRH cells of the dwarf gourami (Colisa
lalia, a freshwater tropical fish) form morphologically distinctive clusters immediately beneath the ventral meningeal membrane
(Oka and Ichikawa 1990
, 1991
), they can be easily
identified in the whole brain in vitro preparations (Oka 1995
,
1996
; Oka and Matsushima 1993
). This gives an
obvious experimental advantages over peptidergic neurons of other
vertebrates because they are small and scattered, so that it was
extremely difficult to study the physiology of single peptidergic
neurons. Interestingly, recent studies suggest that the monoamine
neurons, which were also suggested to be involved in neuromodulation,
share some anatomic and physiological characteristics in common with
TN-GnRH cells (e.g., dopaminergic neurons in the substantia nigra and
ventral tegmental area) (Grace 1988
, 1991
). Thus the
study of TN-GnRH cells may give insight to the cellular mechanisms of
neuromodulation in general.
As for the mechanisms of the generation of pacemaker potentials, we
have already shown by voltage- and current-clamp analyses that a
tetrodotoxin (TTX)-resistant persistent Na+ current,
INa(slow), plays an important role in the
generation of pacemaker potentials of TN-GnRH cells (Oka 1995,
1996
). We investigated the voltage-dependent outward currents
[K+ current(s)] that should be involved in the
repolarizing phase of pacemaker potentials by using the whole cell
patch-clamp technique in in vitro whole brain preparations. We did not
study the calcium-dependent potassium currents because we have
previously shown that calcium currents may not be the primary
component(s) that generate the depolarizing phase of pacemaker
potentials of TN-GnRH cells (Oka 1995
).
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METHODS |
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Adult male and female dwarf gourami (Colisa lalia), ~4 cm in standard length, were purchased from a local dealer and kept at 25-27°C until used. The fish were decapitated, and the whole brain was dissected out and pinned ventral side up to the silicone elastomer (Shin-Etsu Silicone No. KE-106, Shin-Etsu Chemical, Japan) base of a small recording chamber. This whole brain preparation was continuously superfused with an oxygenated Ringer solution until the whole cell recording was established. The Ringer solution contained (in mM) 124 NaCl, 5 KCl, 1.2 KH2PO4, 2.4 CaCl2, 1.3 MgSO4, 26 NaHCO3, and 10 glucose (pH 7.4 adjusted with NaOH).
The ventral meningeal membrane was carefully removed with fine forceps.
The cluster of TN-GnRH cells could be visually identified under the
dissecting microscope. Patch pipettes contained (in mM) 110 KCl, 3 MgCl2, 40 N-2-hydroxyethylpiperazine-N'-2-ethanesulfonic acid (HEPES), 5 ethylene
glycol-bis(-aminoethylether)-N,N,N'N'- tetraacetic acid (EGTA), and 2 Na2ATP (pH 7.4 adjusted with
NaOH). Pipette resistance was ~8 M
, and seal resistance was >10
G
. Series resistances as measured from the amplitude of capacitative transients in response to 10-mV pulses were 23 ± 9 (SE) M
(n = 27). They were compensated as much as possible.
After gigaohm seal formation and "break in" for the whole cell
recording mode, characteristic spontaneous pacemaker activities were
confirmed in the current-clamp mode (see Oka and Matsushima
1993
).
Next the solution was changed to the experimental solutions. The standard solution superfusing the cells contained (in mM) 135 choline Cl, 5 KCl, 5 MgCl2, 5 glucose, 10 HEPES (pH adjusted 7.4 with NaOH). In some experiments, 0.01 mM CaCl2 was added in the saline, and MnCl2 was substituted for MgCl2 in equivalent amount or 5 µM La3+ was added in the saline. The experimental solutions were made by modifying the standard solution. 4-aminopyridine (4AP; 5 mM), and TTX (0.75 µM) were added directly in the saline. Tetraethylammonium chloride (TEA; 20 mM)-containing solution was made by adding TEA to the normal saline in equimolar replacement of choline Cl. The temperature of perfusing solutions was maintained at room temperature.
Whole cell voltage- and current-clamp recordings were carried out with the use of CEZ-2300 amplifier (Nihon Kohden, Japan) and pCLAMP software (Axon instruments). The linear leakage currents were digitally subtracted, either automatically with the use of the P/4 protocol, or manually, after measuring ohmic resistance in response to hyperpolarizing command pulses. The data were not corrected for the liquid junction potentials. All data in this report represent means ± SE.
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RESULTS |
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Morphological and basic electrophysiological characteristics of
TN-GnRH cells were reported in detail elsewhere (Oka 1992a,b
, 1995
; Oka and Ichikawa 1990
, 1991
; Oka
and Matsushima 1993
; Yamamoto et al. 1995
).
TN-GnRH cells can be identified easily by their characteristic anatomy
(location, soma size, and morphology) and regular pacemaker activities.
Moreover, the cluster of TN-GnRH cells was visually identified under a
dissecting microscope after removing the meningeal membrane.
Spontaneous activities of the cells were recorded in the current-clamp
mode before the whole cell voltage-clamp experiments, and all recorded
cells were identified as TN-GnRH cells (i.e., by the presence of
regular pacemaker activities) (see Oka 1995
, 1997
; Oka and Matsushima
1993
).
Total outward currents in TN-GnRH cells
In agreement with our previous study (Oka 1996),
the whole cell currents in the Ringer solution evoked by depolarizing
voltage steps between
100 and +50 mV (10-mV increments, duration 200 ms) from a holding potential of
100 mV were composed of a mixture of
inward and outward currents (Fig.
1A). Large and transient inward currents were activated above
40 mV (Fig. 1A,
INa(fast)). They are the conventional fast
sodium currents because they can be blocked by 0.75 µM TTX (Fig. 1,
B and C). In contrast, at
50 mV, small but
persistent inward currents were observed (Fig. 1A, INa(slow)). They are the TTX-resistant
persistent Na+ current, INa(slow)
(Oka 1996
). The INa(slow)
currents were masked by large fast sodium currents and outward currents
in response to larger depolarizing command pulses. To block the inward
currents (INa(fast),
INa(slow), and Ca2+ currents),
Na+- and Ca2+-free solution was used that was
made by equimolar substitution of NaCl and CaCl2 by choline
Cl and MgCl2, respectively. In addition, 5 µM
La3+ was added in this Na+- and
Ca2+-free solution. When the current responses were
measured in a Na+- and Ca2+-free solution
containing 0.75 µM TTX, only outward currents were recorded (Fig. 1,
B and C).
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The isolated outward current responses to depolarizing command pulses
from holding potential of 100 mV are shown in Fig. 1B. The
outward currents consisted of transient and persistent current
components. When the holding potential was changed from
100 to
60
mV, the total outward current amplitudes were decreased (Fig.
1C). We could not find hyperpolarization-activated (inward rectifier) currents nor M-like potassium currents in our cells.
To define the permeant ion, the reversal potential of the outward
current was evaluated by a tail current analysis with three different
concentrations of extracellular K+
([K+]o) in Na+- and
Ca2+-free experimental solution containing 0.75 µM TTX
(Fig. 2, A and B).
After a 200-ms conditioning pulse to +50 mV from a holding potential of
100-mV, tail currents were evoked by a series of subsequent
hyperpolarizing voltage steps in 5, 10, and 20 mM
[K+]o, which reversed at
78.22 ± 2.21 mV (n = 3),
62.69 ± 3.79 mV
(n = 3), and
41.05 ± 0.83 mV (n = 3), respectively (Fig. 2C). When these reversal potentials
were plotted as a function of [K+]o (Fig.
2D), it could be well fitted by a line predicted from Nernst
equation (58 mV per log unit changes in
[K+]o). Therefore it follows that the
channels underlying these outward currents are highly selective for
K+ ions. We then isolated the individual K+
currents from the total outward current and investigated the voltage
dependence and kinetics of these currents.
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Isolation of K+ current components
4AP-SENSITIVE TRANSIENT K+ CURRENT.
First, we examined the 4AP-sensitive transient current, which was
briefly described in our previous study (Oka 1996). When the current responses were measured in Na+- and
Ca2+-free experimental solution containing 0.75 µM TTX
and 20 mM TEA, almost all the inward currents and some portions of the
persistent outward currents were eliminated, but large transient
currents and smaller persistent outward currents could be recorded in
response to a series of 200 ms depolarizing pulses (in 10-mV
increments) from a holding potential of
100 mV (Fig.
3A1). When 5 mM 4AP was
further added to this solution, the transient outward currents were
eliminated, but some outward currents could be still elicited by the
same depolarizing pulses (Fig. 3A2). This residual outward currents and the dose response of TEA blockade will be described in the
next section. The subtracted current (4AP-sensitive current, Fig.
3B) are transient K+ currents and appeared to be
similar to the potassium-A current (Rudy 1988
). The peak
amplitude of the 4AP-sensitive transient current was dependent on the
test potential (Fig. 3, B and C), increasing as
the test potential was made more positive. The 4AP-sensitive transient
current could be elicited by voltage steps to test potentials more
positive than
50 mV (Fig. 3C).
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TEA-SENSITIVE CURRENT.
Next we examined the TEA-sensitive current. To define TEA-sensitive
current or TEA- and 4AP-resistant current (Fig. 3A2, see next section), we examined the dose dependence of TEA blockade of the
persistent K+ current component, which was recorded in
Na+- and Ca2+-free solution containing 0.75 µM TTX and 5 mM 4AP. The current amplitudes were measured at the end
of 200-ms test pulses to +50 mV from a holding potential of 100 mV
before and after the application of various concentrations of TEA (in
the range of 1-60 mM). Application of TEA reduced the current
amplitudes in a dose-dependent manner. The persistent K+
current was reduced 11 ± 5.2% by 1 mM TEA (n = 3) and 61.6 ± 4.8% by 60 mM TEA (n = 6). The
current amplitudes were normalized to the value in the absence of TEA
and were plotted as a function of TEA concentration (Fig.
4A). The
concentration-response curve was best fitted with the form
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TEA- AND 4AP-RESISTANT CURRENTS.
Finally, we examined another outward current component that is
resistant to both TEA and 4AP. As already described in the previous
section, when the current responses were measured in a solution
containing 0.75 µM TTX, 20 mM TEA, and 5 mM 4AP, persistent outward
current responses remained (Fig. 3A2). Figure
6 shows the properties of TEA- and
4AP-resistant currents. In response to voltage steps from a holding
potential of 100 mV, persistent current was activated more positive
than
30 mV (Fig. 6A). However, when the holding potential
was changed to
60 mV, which is closer to the resting membrane
potential of TN-GnRH cells, the amplitude of the persistent current was
decreased, and the activation threshold was shifted to a more positive
potential (
10 mV, Fig. 6B). Figure 6D shows the
I/V relationships with these two different holding potentials.
Steady-state inactivation of TEA- and 4AP-resistant current was also
investigated by measuring the change evoked by a voltage step to +50 mV
when the holding potential was varied from
120 to +50 mV (Fig.
6C).
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Effects of TEA on the pacemaker potentials of TN-GnRH cells
From the voltage-clamp experiments, we identified at least four types of K+ currents in TN-GnRH cells. Among these currents, TEA-sensitive K+ current was suggested to be the most likely candidate that contributes to the repolarizing phase of the pacemaker potentials. To confirm this possibility, current-clamp experiments were performed. The left column of Fig. 7 shows the effects of TTX alone. TN-GnRH cells show regular beating discharges in a Ringer solution (Fig. 7A1). Bath application of TTX (3 µM, 9 min) blocked action potentials, but subthreshold pacemaker potentials remained intact (Fig. 7A2).
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The right column of Fig. 7 shows the effect of TTX and TEA. The action potentials were blocked by TTX to check whether TEA affects the subthreshold pacemaker potentials. When 20 mM TEA was added to the Ringer solution together with 0.75 µM TTX, the pacemaker potentials were blocked, and the base membrane potential was shifted to a level more depolarized (10-30 mV) than that of the control (n = 27; Fig. 7B3). These effects are more clearly shown in a trace on a slower time scale (Fig. 7B2). In the experiments where the pacemaker potentials were completely blocked by TTX and TEA, hyperpolarizing DC current injection did not reinstate the pacemaker potentials (n = 8, data not shown). Thus the blockade of pacemaker potentials is not simply caused by the depolarizing shift of the membrane potentials. The pacemaker potentials recovered after washout in normal Ringer (n = 7; Fig. 7B4).
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DISCUSSION |
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Several components of the voltage-dependent K+ current recorded from TN-GnRH cells of the dwarf gourami were identified on the basis of their voltage dependence, kinetics, and pharmacology. The identified voltage-dependent K+ currents are 1) 4AP-sensitive K+ current, 2) TEA-sensitive K+ current, and 3) and 4) two types of TEA- and 4AP-resistant K+ current.
4AP-sensitive transient K+ current
A low-threshold transient K+ current was evoked from a
holding potential of 100 mV. The current activated at test potentials more positive than
50 mV and was fully inactivated at holding potentials more positive than
40 mV. Also, the transient current was
preferentially blocked by 4AP. This transient current therefore resembles the A-current identified in embryonic LHRH (mammalian GnRH)
neurons (Kusano et al. 1995
) and GT1 cells (Bosma
1993
).
However, at the holding potential of 60 to
40 mV, which is near the
resting membrane potentials of TN-GnRH cells, 4AP-sensitive transient
K+ current is almost inactivated, and the membrane
potential of TN-GnRH cell usually does not hyperpolarize beyond
60 mV
under physiological conditions. In addition, the pacemaker activity was
not affected by 5 mM 4AP in current-clamp experiments (Oka 1996
). Therefore we suggest that 4AP-sensitive K+
current contributes very little to the pacemaker activity of the
TN-GnRH cells.
TEA-sensitive K+ current
TEA-sensitive K+ current was activated during voltage
steps to potentials more positive than 30 mV from a holding potential of
100 mV. This current activated slowly and did not inactivate during the test pulse, and the activation curve obtained from current
responses was well fitted by a single Boltzmann function. Furthermore,
this current showed little voltage-dependent steady-state inactivation
at
60 mV, which is closer to the base of the pacemaker potentials of
TN-GnRH cells. On the basis of these characteristics, we concluded that
the TEA-sensitive K+ current consists of a single current
and is the most likely candidate that contributes to the repolarizing
phase of the pacemaker potentials of TN-GnRH cells. The results of
current-clamp experiments in which bath application of 0.75 µM TTX
and 20 mM TEA blocked the subthreshold pacemaker potentials strongly
support this conclusion.
The characteristics of TEA-sensitive K+ current of this
study may be similar to the delayed rectifier K+ current
described in LHRH secretory GT1 cell line (Bosma 1993), embryonic LHRH neuron (Kusano et al. 1995
), cultured
dorsal root ganglion (IKlt) (Gold et al.
1996
), and many excitable cells (see review by Rudy
1988
). These currents activate slowly, do not inactivate during
the test pulse, are sensitive to extracellular TEA, and are insensitive
to 4AP in concentrations as high as 2 mM (GT1 cell line) or 5 mM
(IKlt). Especially, the steady-state
inactivation of these currents occur at relatively positive potential
range. However, the voltage dependence of activation of these currents are different; Iklt of the dorsal root ganglion
and TEA-sensitive K+ current of the TN-GnRH cell have
relatively low activation threshold (approximately
40 mV), but
delayed rectifier K+ currents of the GT1 cell and embryonic
LHRH neuron have relatively high activation threshold (approximately
20 mV).
It may be possible that a kind of Ca2+-dependent
K+ current(s) contribute in part to the sustained outward
current because the total sustained outward current was reduced by
Ca2+-free Ringer solution (Fig. 1).
Ca2+-dependent K+ currents were described in
cultured embryonic LHRH neuron (Kusano et al. 1995) and
LHRH secretory GT1-7 cell line (Spergel et al. 1996
).
However, our previous current-clamp study has shown that Ca2+-free Ringer solution and Ca2+ channel
blockers do not affect regular beating pacemaker activities of TN-GnRH
cells (Oka 1995
). From these data, it is suggested that
neither Ca2+ nor Ca2+-dependent K+
current(s) are the primary component(s) that generate regular pacemaker
potentials. On the other hand, it was also reported that TN-GnRH cells
show different firing modes according to the physiological condition of
the fish (regular beating, irregular, and burst firing mode)
(Oka and Matsushima 1993
). Therefore it may be possible
that these Ca2+ and Ca2+-dependent
K+ current(s) may be involved in the switching among
different firing modes. Thus it may be another very important problem
to examine the nature and functional significance of these currents.
TEA- and 4AP-resistant K+ currents
Persistent outward K+ current was still evoked from a
holding potential of 100 mV in Na+- and
Ca2+-free Ringer solution containing 0.75 µM TTX, 20 mM
TEA, and 5 mM 4AP. The current activated at test potentials more
positive than
30 mV. However, when the holding potential was changed
to
60 mV, which is closer to the base membrane potential of TN-GnRH cells, the amplitude of these persistent currents was reduced, and the
activation threshold of these currents were shifted to around
10 mV.
Furthermore, the activation curve obtained from the current responses
was fitted with a linear summation of two Boltzmann functions when a
holding potential was
100 mV while it was fitted with a single
Boltzmann function when the holding potential was changed to
60 mV.
From these data, we conclude that at least two kinds of outward
K+ currents that is resistant to 20 mM TEA and 5 mM 4AP are
present in TN-GnRH cells. The activation threshold of one of them is
relatively low (
40 mV), and that of the other one is relatively high
(
20 mV). The voltage dependence of activation/steady-state
inactivation and pharmacology of these currents are comparable with
that of IKi and IKn in
cultured dorsal root ganglion, respectively (Gold et al.
1996
). Considering the membrane potential range during the
pacemaker activities, we suggest that these currents should contribute
very little, if any, to the repolarizing phase of subthreshold pacemaker potentials.
On the other hand, one might argue that these outward currents may
belong to a kind of nonselective cation current that was reported in
hippocampal pyramidal neurons (Oyama et al. 1991) and
mitral cells of rat olfactory bulb (Wang et al. 1996
).
Alzheimer (1994)
reported a similar nonselective cation current from
rat neocortical neurons. The channel responsible for this current was
not Ca2+ dependent, was resistant to block by 4AP and TEA
(<35 mM), and was permeable to monovalent cations but not to anions,
such as Cl
. If the TEA- and 4AP-resistant currents of
TN-GnRH cells belonged to a kind of nonselective cation currents,
deactivating tail current should be inward, when the membrane
potentials are repolarized from depolarizing test potentials to
60
mV. However, in some experiments with the P/4 leak subtraction
protocol, TEA- and 4AP-resistant currents showed outward deactivating
tail current on membrane repolarization to
60 mV (data not shown).
Thus TN-GnRH cells may not have such nonselective cation current.
Another possibility that may not be completely excluded is that some,
if not all, TEA- and 4AP-resitant currents can be regarded as residual
K+ outward currents that failed to be blocked by 20 mM or
higher concentrations of TEA. This is because of the fact that the
activation threshold of TEA- and 4AP-resistant current evoked from a
holding potential of
100 mV is similar to the activation threshold of TEA-sensitive current. However, this current should be negligible because higher concentration of TEA (
60 mM) did not cause further blockade of TEA- and 4AP-resistant currents (Fig. 4A).
Functional significance of K+ currents
We previously proposed a hypothesis that may be relevant to the
peptidergic neuromodulatory system of vertebrate brains in general; the
modulator neurons have endogenous rhythmic activities that vary
according to the animal's physiological (hormonal or environmental)
conditions, and they regulate the excitability of target neurons in a
wide variety of brain regions simultaneously (Oka 1992b,
1997
; Oka and Matsushima 1993
). TN-GnRH cells
mainly exhibit regular beating discharge activities (pacemaker
activities), and a TTX-resistant persistent Na+ current,
INa(slow), supplies the persistent depolarizing
drive. Therefore INa(slow) contributes to the
depolarizing phase of the pacemaker potentials (Oka 1995
,
1996
). We assumed that an interplay between the persistent
inward current and counteracting outward current should generate basic
rhythmic pacemaker activities. Therefore we studied the outward
K+ currents and examined which type of K+
currents are involved in the generation of pacemaker potentials.
We identified four types of voltage-dependent K+ currents
and concluded that the TEA-sensitive K+ current is the most
likely candidate that contributes to the repolarizing phase of
pacemaker potentials, based on the voltage- and current-clamp studies.
It is suggested that INa(slow) and TEA-sensitive
K+ current interact in the following manner to generate the
subthreshold pacemaker potentials. When the TN-GnRH cells are at a
negative potential the INa(slow) is
deinactivated and supplies the persistent depolarizing drive, and the
membrane potentials gradually depolarizes. When the membrane potential
reaches the activation threshold for the TEA-sensitive K+
current, outward current gradually develops and the net flux of current
reverses. Then the membrane potential becomes hyperpolarized and
deactivates the K+ current, and the next cycle begins. Thus
the pacemaker mechanism in TN-GnRH cells is different from those
reported in other pacemaker cells where interaction between the
Ca2+ current and Ca2+-dependent K+
current was suggested (see review by Connor 1985).
In our hypothetical model on the peptidergic and monoaminergic
modulatory neurons, it was suggested that the frequency of intrinsic
pacemaker activities or the firing mode may change according to the
physiological or environmental conditions, and the change may be the
neural basis for long-lasting changes in animal behavior (Oka
1992a,b
, 1997
; Oka and Matsushima 1993
). Here it
was further suggested that ionic channels underlying the pacemaker
activities may be the target for modulation by hormones or
transmitters. In fact, we recently found that certain transmitters or
hormones modify the frequency of pacemaker activities in TN-GnRH cells (unpublished observations). For example, in the bag-cell neurons of
Aplysia, a set of command neurons that trigger egg laying, an elevation of cyclic AMP by exogenous application of an analog induces a period of high-frequency burst discharges lasting up to
one-half hour in normally quiescent cells of the intact ganglion (Kaczmarek et al. 1978
). Voltage-clamp studies on the
bag-cell neurons in culture demonstrated a modulation (significant
diminution) by cAMP analogs of TEA-sensitive "delayed rectifier"
K+ currents (Connor 1985
; Strong and
Kaczmarek 1985
). Thus it would be an interesting future problem
to study possible modulation of TEA-sensitive K+ currents
(or other current) by various hormones or transmitters.
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FOOTNOTES |
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Address reprint requests to Y. Oka.
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.
Received 3 August 1998; accepted in final form 14 October 1998.
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REFERENCES |
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