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J Neurophysiol (February 1, 2003). 10.1152/jn.00324.2002
Submitted on Submitted 2 May 2002; accepted in final form 21 October, 2002
McGill Centre for Research in Neuroscience and Departments of Biology and Neurology and Neurosurgery, McGill University, Montreal, H3G 1A4 Quebec, Canada
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ABSTRACT |
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Buss, Robert R., Charles W. Bourque, and Pierre Drapeau. Membrane Properties Related to the Firing Behavior of Zebrafish Motoneurons. J. Neurophysiol. 89: 657-664, 2003. The physiological and pharmacological properties of the motoneuron membrane and action potential were investigated in larval zebrafish using whole cell patch current-clamp recording techniques. Action potentials were eliminated in tetrodotoxin, repolarized by tetraethylammonium (TEA) and 3,4-diaminopyridine (3,4-AP)-sensitive potassium conductances, and had a cobalt-sensitive, high-threshold calcium component. Depolarizing current injection evoked a brief (approximately 10-30 ms) burst of action potentials that was terminated by strong, outwardly rectifying voltage-activated potassium and calcium-dependent conductances. In the presence of intracellular cesium ions, a prolonged plateau potential often followed brief depolarizations. During larval development (hatching to free-swimming), the resting membrane conductance increased in a population of motoneurons, which tended to reduce the apparent outward rectification of the membrane. The conductances contributing to action potential burst termination are hypothesized to play a role in patterning the synaptically driven motoneuron output in these rapidly swimming fish.
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INTRODUCTION |
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Larval zebrafish swim with rapid
undulating body movements (Budick and O'Malley 2000
;
Buss and Drapeau 2001
; Fuiman and Webb 1988
; Saint-Amant and Drapeau 1998
) powered by
the contraction of embryonic red and white myotomal muscle (Buss
and Drapeau 2000
). Myotomal muscle is driven by a
motoneuron-evoked synaptic drive that alternates between ipsilateral
and contralateral myotomes and propagates in a rostral to caudal
direction (Buss and Drapeau 2002
). The coordinated
neural output generated during swimming is maintained in paralyzed
preparations (Buss and Drapeau 2001
, 2002
), thus
allowing an electrophysiological analysis of motoneuron activation.
During fictive swimming, motoneurons receive a glutamatergic and
glycinergic synaptic drive (Buss and Drapeau 2001
). The
glutamatergic drive is highly rhythmic, driving motoneurons to spike
threshold and patterning the motor output to myotomal muscle. There has been considerable investigation of the activity of motoneurons during
zebrafish motor behaviors (Fetcho and O'Malley 1995
;
Saint-Amant and Drapeau 2000
, 2001
), the synaptic inputs
to (Ali et al. 2000
) and from motoneurons (Buss
and Drapeau 2000
; Drapeau and Legendre 2001
;
Drapeau et al. 2001
; Legendre et al.
2000
; Nguyen et al. 1999
), and their growth and
development (Eisen 1999
; Eisen and Melancon
2001
; Lewis and Eisen 2001
; Westerfield
and Eisen 1988
). However, there is a paucity of information on
the physiological properties of motoneurons.
In this study, the physiological and pharmacological properties of the motoneuron action potential and membrane were investigated in larval zebrafish using whole cell patch current-clamp recording techniques. Fast sodium-dependent action potentials, a high-threshold calcium conductance, and repolarizing potassium conductances were observed, and their features were related to the motoneuron firing pattern during swimming.
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METHODS |
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Experiments were performed on zebrafish (Danio rerio)
larvae of the Longfin strain raised at approximately 28.5°C and
obtained from a breeding colony maintained according to
Westerfield (1995)
. All procedures were carried out in
compliance with the guidelines stipulated by the Canadian Council for
Animal Care and McGill University. The experimental methodology has
been described (Buss and Drapeau 2001
; Drapeau et
al. 1999
). Results are taken from 84 morphologically identified
(dye-filled) motoneurons (located dorsal or lateral to the central
canal) of zebrafish aged 1.9-2.5 (day 2), 3.0-3.5 (day 3), and
4.1-4.4 (day 4) days postfertilization, encompassing the period from
hatching to free-swimming.
Experiments were performed at room temperature (approximately 22°C).
Evan's fish saline recording solution (Buss and Drapeau 2001
; Drapeau et al. 1999
) contained (in mM) 134 NaCl, 2.9 KCl, 2.1 CaCl2, 1.2 MgCl2, 10 HEPES, and 0-10 glucose, and
osmolarity was adjusted (with glucose) to 290 mOsm and pH 7.8. Larvae
were paralyzed by immersion in
-bungarotoxin (10 µM;
n = 16) for 10-20 min or
D-tubocurarine (15 µM; n = 68)
for the duration of the experiment. Similar observations were made
using
-bungarotoxin or D-tubocurarine.
Patch-clamp electrodes (4-7 M
) were pulled from thin-walled
Kimax-51 borosilicate glass and were filled with either a potassium
gluconate (n = 70) or cesium gluconate solution (n = 14). The potassium gluconate solution was composed
of (in mM) 116 D-gluconic acid potassium salt, 16 KCl, 2 MgCl2, 10 HEPES, 10 EGTA, 4 Na2ATP, and 0.2% sulforhodamine B (osmolarity
280-290 mOsm, pH adjusted to 7.2). In the cesium gluconate solution,
potassium gluconate and KCl were replaced with cesium gluconate and
CsCl. Tetrodotoxin (TTX; 1 µM), tetraethylammonium chloride (TEA; 5 mM), 3,4-diaminopyridine (3,4-AP; 1 mM), or cobalt chloride (1 mM) were
dissolved in fish saline (constant osmolarity was maintained by
replacing glucose with equivalent amounts of TEA, 3,4-AP, or cobalt)
and applied by bath perfusion. The actions of TTX, TEA, 3,4-AP, cobalt,
and cesium intracellular solution on the action potential and membrane
properties were investigated in day 2 (newly hatched) larvae. A liquid
junction potential of -10 mV was experimentally determined according
to (Barry and Lynch 1991
; Neher 1992
) and records were corrected for this potential.
Current-clamp recordings were performed with an Axoclamp-2A patch clamp
amplifier (0.01 headstage; 10-kHz low-pass filter) and digitized at
20-40 kHz. All chemicals were purchased from Sigma Chemical (St.
Louis, MO). Voltage-clamp recordings were not obtained because the goal
of this first study was to relate the firing behavior of larval motor
neurons to their membrane properties, which is only directly revealed
in current-clamp recordings. Analyses were performed using pClamp 8 or
Axograph 4.4 software (Axon Instruments). Motoneurons were held at -75
mV by current injection and all measurements were made from this
potential. Short (2 ms) or long (300 ms) depolarizing current pulses
were used to evoke single spikes or bursts of action potentials,
respectively. The steady-state membrane potential at the end of long
current pulses (when firing had stopped) was used to construct
I-V curves. Input resistances
(RI) were calculated from the slopes
of the I-V relation for the following voltages:
105 to
75 mV,
75 to -45 mV, and > -45 mV. The ratio of
RI(>-45 mV) to
RI(
75 to -45 mV) was used as an index of
outward rectification (rectification ratio), and the ratio of
RI(
75 to
45 mV) to
RI(
105 to -75 mV) as an index of
inward rectification of the membrane; a ratio of 1 indicates a linear
relationship. Membrane time constants (
fast and
slow) were determined by fitting the
voltage response to long current pulses (resulting in
hyperpolarizations of 15-25 mV) with a sum of exponential curves.
Capacitance was calculated by dividing
fast by
RI(
105 to -75 mV).
fast was assumed to represent the time to
charge the motoneuron soma, whereas the smaller but longer lasting
slow was assumed to represent the charging of
a small dendritic tree (consistent with anatomical descriptions) and
possibly an active conductance. Rheobase was the smallest current that
could initiate an action potential during long (300 ms) current pulses.
Spike afterhyperpolarization measurements were performed on the single
action potential evoked at rheobase; the steady-state potential
following the spike was used as baseline. Instantaneous firing
frequency was determined by taking the inverse of the time between the
first and second, second and third, and third and fourth action
potentials in a burst. Because of the wide range of motoneuron input
resistances, injected current was normalized to rheobase current and
firing frequencies are presented for current pulses 1.5 and 2.0 times
rheobase current. Spike threshold, amplitude, rise time, and half-width
measurements were made on single action potentials evoked during
threshold short current pulses. Action potentials initiated on the
decay of the short pulse; spike threshold was measured as the most
negative potential reached during the decay prior to spike initiation.
Rise time was defined as the time between the action potential upstroke and peak, and half-width as the time from peak amplitude to when the
action potential had decayed to 50% of its amplitude. Results are
presented as mean ± SE throughout the text. The term significant denotes a relationship with P < 0.01 determined using
the Student's and paired t-test on normally distributed
data, the Mann-Whitney rank sum test and Wilcoxon signed-rank test for
nonparametric comparisons, and the Spearman rank order test for correlations.
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RESULTS |
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Active and passive properties
The resting membrane potential of motoneurons ranged from
63 to
79 mV (mean =
74 ± 0.4 mV) and did not change during
development (Table 1). Nearly all (93%)
motoneurons responded to sustained depolarization by firing a short
(approximately 10-30 ms) burst of action potentials followed by a
period of silence or erratic firing (Figs.
1, 5, 6, 7, and 8). However, five
motoneurons (7%) responded by firing throughout the current injection.
Four of these were day 2 motoneurons having a high-input resistance
(640 ± 78 M
;
75 to -45 mV range) and small- to medium-sized
amplitude action potentials (53 ± 9.3 mV), and one was a day 4 motoneuron with an average spike amplitude (79 mV) and a low input
resistance (84 M
). During the burst, instantaneous firing
frequencies of
800 Hz were observed. Instantaneous firing frequencies
accommodated rapidly during the first four spikes and significantly
higher (P < 0.001) frequencies were observed when
stimulation strength was increased from 1.5 to 2.0 times rheobase
(Table 2). Instantaneous firing
frequencies were significantly higher (P < 0.001) in
day 3-4 versus day 2 motoneurons (Table 2). During the sustained depolarization, when the membrane is more positive to
EK, a hyperpolarization following the
action potential was observed in 90% of motoneurons. Measured at
rheobase, the afterhyperpolarization can reach
13 mV and last
40 ms
(Table 1).
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Membrane potentials used for constructing I-V relationships
were measured at the end of 300-ms current steps, when the initial burst of action potentials had terminated and a steady-state potential had been reached. Three distinct components were observed in the I-V relationship (Fig. 1C; Table 1), which
included an inward rectification at potentials negative to
Vm and an outward rectification at
potentials positive to spike threshold. Input resistances were calculated from the slopes of the I-V relation over these
three voltage ranges, i.e., negative to
Vm (
75 to
105 mV), positive to
Vm (
75 to -45 mV), and near spike
threshold (>
45 mV). From day 2 to day 3-4, there was a significant
decrease in the input resistance of the membrane measured during
subthreshold steps negative and positive to the resting potential,
while there was no significant change in the input resistance at
potentials near spike threshold (Table 1). Consistent with the decrease
in input resistance negative to spike threshold, rheobase current
increased significantly from day 2 to day 3-4 (Table 1).
Interestingly, while there was no significant change in the input
resistance of the outwardly rectifying portion of the I-V
relationship, there was a change in the apparent outward rectification,
as quantified by the rectification ratio
(RI(>-45
mV)/RI(
75 to -45 mV)), which increased 73% from day 2 to day 3-4 (Table 1). Together, these
findings indicate that the decrease in outward rectification was due to
a conductance increase at membrane potentials around Vm.
In addition to the parallel developmental changes in input
resistance and rheobase, there was also a strong negative
relationship (r =
0.96; P < 0.001) between input resistance and rheobase (Fig. 2A). Figure 2A also
shows that although mean input resistance (RI(
105 to -75 mV) and
RI (
75 to -45 mV)), and rheobase
values changed significantly from day 2 to day 3-4 (Table 1), their
values overlap in many motoneurons at all ages. However, a population
of motoneurons (n = 11) with input resistances <125
M
, and rheobase values >250 pA (values never observed in day 2 motoneurons), appeared at day 3-4. Motoneurons within this population
had larger rectification ratios (means of 0.59 ± 0.06 vs.
0.27 ± 0.01; P < 0.001) and contained the
neurons with the most linear I-V relationships (Fig. 1)
observed in this study (3 motoneurons with rectification ratios ranging
from 0.79 to 0.86).
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The developmental changes in input resistance and rheobase could be due
to an increase in conductance per unit area of membrane (e.g., ion
channel insertion) or because of a developmental increase in motoneuron
size. However, capacitance (a measure of membrane area and motoneuron
size) values overlapped considerably at all ages (Fig. 2B)
and did not change significantly from day 2 to day 3-4 (Table 1),
ruling out motoneuron size as the only changing variable. A decrease in
the fast component of the membrane time constant
(
fast), which accounted for approximately 85%
of the membrane charging, compensated for the decrease in input
resistance (Table 1). We assumed that the fast time constant represents the charging of the motoneuron soma as larval neurons lack extensive dendrites and chose to use it to calculate cell capacitance.
Conductance was strongly and positively correlated to capacitance (Fig.
2B; r = 0.75; P < 0.001),
indicating that the largest neurons had the highest conductance. A
closer examination of individual age classes revealed an additional
trend in this relationship. The relationship of day 3 and day 4 motoneurons is shifted to the left and steeper, indicating that there
is an increase in specific membrane conductance during development.
Thus the decrease in outward rectification observed in this study is
due to an additional "leak" conductance that is active at the
resting membrane potential (although small changes in motoneuron
capacitance, obscured by the large overlap in motoneuron capacitances
and sizes, cannot be ruled out).
Interestingly, the duration of the action potential burst was
approximately the length of a swim cycle (Buss and Drapeau 2001
, 2002
). The conductances active during the outwardly rectifying portion of the I-V curve were thus likely to be responsible
for the termination of the action potential burst and so these
conductances were investigated pharmacologically. Because there was no
change observed in the action potential bursting from day 2 to day 4, a
pharmacological investigation of motoneuron membrane and bursting properties were only performed in day 2 larvae, an age where stable, high resolution, motoneuron recordings were made with the greatest success.
Pharmacology
Action potentials were initiated during the decay of voltage
transients generated following short 2-ms current injections (Fig.
3), indicating a remote spike initiation
site. Mean spike threshold was -37 ± 0.6 mV, ranged from
49 to
24 mV, and was correlated with input resistance (r =
0.407; P < 0.001;
75 to -45 mV range), and spike
rise time (r =
0.51; P < 0.001). Spikes were generally slightly overshooting or slightly undershooting (mean
amplitude = 75 ± 1.4 mV; range, 30 to 95 mV). These findings are also consistent with an axonal spike initiation site. Spikes elicited by short 2-ms current injections were not followed by a
noticeable hyperpolarization (Fig. 3). However,
EK (approximately
97 mV) is close to
the resting potential, and closer examination revealed that the decay
time-course of voltage transients following action potentials were
faster in 68% of motoneurons than the decay of subthreshold voltage
transients.
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Action potentials were generated by a voltage-activated sodium conductance because they were abolished by TTX (Fig. 3A; n = 6) and not cobalt (Fig. 3B; n = 5), although cobalt increased spike threshold by 11 ± 2 mV (P = 0.004). Addition of the potassium channel blockers TEA (Fig. 3C; n = 6) or 3,4-AP (Fig. 3D; n = 5) prolonged the duration of the action potential (Table 3), revealing that it is terminated by potassium conductances. Rise times increased in TEA and 3,4-AP, whereas there was no large change in spike threshold (Table 3).
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TTX unmasked an outward conductance (Fig. 5C) that appeared as a transient depolarization (Fig. 5B), possibly of a regenerative nature, which lasted approximately as long as an action potential burst (Fig. 5A). In the presence of TEA and 3,4-AP, the outward rectification is reduced, and addition of cobalt reduces it further (Fig. 6). When applied alone, cobalt reduced the outward rectification, decreased the firing frequency of the action potential burst (33 ± 12% decrease; determined from the first inter-spike interval normalized to 1.5 or 2.0 times rheobase), and blocked the erratically occurring or delayed clusters of action potentials that can follow the bursts (Fig. 6). Cobalt also reduced the level of membrane noise. Although TEA, 3,4-AP, and cobalt had the greatest effect on the outwardly rectifying portion of the I-V relationship, they also had minor effects at more negative potentials. Rheobase current decreased 26 ± 3% in TEA and 3,4-AP, while it increased 35 ± 14% in cobalt. The action of cobalt was surprising as cobalt reduced outward rectification and thus would be expected to decrease rheobase. This finding suggests that cobalt is either blocking a low threshold calcium conductance or is producing a charge screening effect.
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A high-threshold transient potential was observed in the presence of TTX, TEA, and 3,4-AP (Fig. 4) at membrane potentials between -10 and -25 mV. This depolarizing potential was blocked by cobalt and is thus defined as a calcium-dependent action potential. The calcium spike activated slowly, and 2-ms current pulses were ineffective, whereas 10-ms pulses activated a spike. At higher membrane potentials (>0 mV), a sustained train of cobalt-sensitive, calcium-dependent action potentials (occurring at 60-80 Hz) followed the initial calcium spike in 3 of 4 motoneurons (Fig. 6B).
It was anticipated that TEA and 3,4-AP would facilitate repetitive
action potential firing if the outward rectification they reduce
contributed to burst termination. Application of TEA or 3,4-AP led to
repetitive firing, at 20-70 Hz, following the initial prolonged action
potential burst (Fig.
8). However, these potassium channel
blockers do not block all potassium channels (e.g., the calcium-dependent potassium conductance observed in this study), and to
further reduce potassium conductances, intracellular potassium ion was
replaced with the less permeant ion cesium. With a cesium ion-based
intracellular solution, short 2-ms current pulses initiated a prolonged
after discharge (lasting 170-1,000 ms), resembling a plateau potential
(5/14 motoneurons) that was not observed in cobalt solutions (Fig.
9). In motoneurons that did not initiate a plateau, the action potential was broadened similarly to action potentials observed in TEA or 3,4-AP (Fig. 9B). Motoneurons
examined using cesium ion-based intracellular solutions had
significantly larger mean half-widths (27 ± 3 ms), rise times
(0.61 ± 0.05 ms), and a lower spike threshold (
43 ± 0.8 vs. -37 ± 0.6 mV), than those recorded with potassium
gluconate-based intracellular solutions. The prolonged action
potential was attenuated in cobalt (Fig. 9B; 57 ± 0.1% as long; n = 5) and completely blocked in TTX
(data not shown). Together, these findings show that the conductances active during the outwardly rectifying portion of the I-V
relationship are important for burst termination.
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DISCUSSION |
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The action potential recorded from motoneurons of larval zebrafish
is initiated distal to the soma, is generated by a TTX sensitive sodium
ion conductance, and is terminated by a potassium ion conductance
sensitive to TEA and 3,4-AP. I-V curves revealed an inwardly
rectifying conductance at voltages negative to resting potential and an
outwardly rectifying conductance at voltages near spike threshold. From
hatching to the free-swimming stage, average membrane input resistance
at potentials negative to spike threshold decreased, and I-V
relationships became more linear even though the input resistance of
the suprathreshold outwardly rectifying segment of the I-V
curves did not change significantly. The decrease in input resistance
was not accounted for simply by increases in motoneuron size, as
reflected by less variable membrane capacitance estimates, but rather
by an increase in specific membrane conductance. The population of
motoneurons examined had a wide range of input resistances,
capacitative values (sizes), and rheobase current thresholds,
supporting the presence of graded motoneuron recruitment during
swimming at these larval stages (Buss and Drapeau 2002
).
Over 90% of motoneurons responded to long depolarizing current pulses by firing a brief (approximately 10-30 ms) burst of action potentials at all ages. A strong outward rectification, antagonized by voltage-activated potassium channel antagonists (TEA and 3,4-AP), intracellular cesium, and cobalt, contributes strongly to burst termination. The role of potassium conductances in burst termination is most clearly demonstrated in Fig. 9, where a sustained plateau potential appears when intracellular potassium ions are replaced with impermeant cesium ions. Although not tested directly, cobalt is likely preventing the activation of a calcium-dependent potassium ion (and/or chloride ion) conductance by blocking a voltage-activated calcium influx. A high-threshold, cobalt sensitive calcium conductance was also observed when sodium and potassium conductances were decreased in TEA, 3,4-AP, and TTX (Fig. 6). At positive potentials, the calcium spike could become repetitive with a long current pulse. Furthermore, the plateau potentials observed using cesium ion-based intracellular solutions were not observed and action potential half-widths were reduced in the presence of cobalt. Based on these observations, we hypothesize that the high-threshold calcium spike, activated by the overshooting depolarizing sodium-dependent action potentials, may provide an electrogenic contribution to action potential bursting.
This is the first study to examine the electrophysiological properties
of motoneurons in a larval fish. With the exception of the lamprey,
there have been few physiological investigations of fish locomotor
motoneurons. Fish motoneurons generally have low resting membrane
potentials: mean = -75 mV in goldfish (Fetcho 1992
); mean =
75 mV in a Japanese teleost (Bando
1975
); mean = <
80 mV in 25% of stingray motoneurons
(Williams et al. 1984
); mean =
75 mV in lamprey
(Buchanan 1993
). These are similar to that observed in
larval zebrafish with a mean =
74 mV. Depolarizing after
potentials have been observed in goldfish, a Japanese teleost, and
stingray motoneurons, while an afterhyperpolarization was observed in
stingray motoneurons (Bando 1975
; Fetcho
1992
; Williams et al. 1984
) and lamprey (see
following text). In larval zebrafish, an afterhyperpolarization
was not observed when action potentials were evoked by short pulses
from the negative resting membrane potential but were observed when the
membrane was held at more depolarized levels. The
afterhyperpolarization of larval zebrafish motoneurons could be
obscured by the fast membrane time constant, the proximity to
EK, or to calcium chelation by the
intracellular solution. However, examination of the I-V
relationship after the calcium conductance was blocked with cobalt did
reveal the presence of a calcium-activated conductance, which was
likely mediated by potassium ions.
Interestingly, Buss and Drapeau (2001)
reported a mean
spike threshold of -46 ± 0.8 mV (corrected for the different
junction potentials used in these papers) determined by measuring the
amplitude at which rhythmic locomotor drive potentials initiated action potentials during fictive swimming. This value is approximately 9 mV
closer to the resting potential than the spike threshold determined by
using somatic current injections in this study (
37 ± 0.6 mV).
The more negative spike threshold observed during fictive swimming
could be because excitatory locomotor synapses are located electrically
closer to the axonal spike initiation zone than the somatic patch
electrode point current source. In addition, there could be a
locomotor-related reduction in spike threshold, as reported in the cat
(Krawitz et al. 2001
).
Fin (Rovainen and Birnberger 1971
) and myotomal
(Teravainen and Rovainen 1971
) motoneurons have been
examined in detail in lamprey, where motoneurons to twitch fibers have
lower input resistances than those to slow fibers (Teravainen
and Rovainen 1971
). The I-V relation determined at
potentials 20 mV positive and negative to the resting membrane
potential is linear, and input resistances, action potential
thresholds, and instantaneous firing frequencies are considerably lower
in the lamprey (Buchanan 1993
). Similar to larval
zebrafish, the action potential is prolonged in TEA or 4-AP and blocked
by TTX (Hess and El Manira 2001
; Kemnitz
1997
; Matsushima et al. 1993
; Wallen et
al. 1989
). A calcium-activated potassium conductance, transient
A-type current, and high-threshold calcium current has also been
described in lamprey motoneurons (El Manira and Bussieres
1997
; Grillner and Wallen 1985
; Grillner et al. 2001
; Hess and El Manira 2001
;
Hill et al. 1992
; Matsushima et al. 1993
;
Wallen et al. 1989
).
The duration of the action potential bursts observed during long
depolarizing current pulses closely approximates the duration of the
active period of a swim cycle (Buss and Drapeau 2001
,
2002
). The factors contributing to burst termination may
include a high-threshold inactivating calcium spike and voltage- and
calcium-dependent potassium conductances. Together these conductances
help sculpt the period of action potential firing so that it is
consistent with the period of rhythmic excitatory drive to the
motoneurons. If the same conductances are present in interneurons of
the central pattern generator for swimming, they could also underlie
the generation of rhythmic locomotor network activity.
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ACKNOWLEDGMENTS |
|---|
This work was funded by the Canadian Institutes of Health Research (CIHR) and the Natural Sciences and Engineering Research Council of Canada (NSERC). R. R. Buss holds a CIHR Doctoral Research Award and C. W. Bourque is a CIHR Senior Scientist.
Present address of R. R. Buss: Department of Physiology, University of Manitoba, 730 William Avenue, Winnipeg, R3E 3J7 Manitoba, Canada.
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FOOTNOTES |
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Address for reprint requests: P. Drapeau, McGill Centre for Research in Neuroscience, 1650 Cedar Ave., Montreal, Quebec H3G 1A4, Canada (E-mail: pierre.drapeau{at}mcgill.ca).
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