1Department of Integrative Brain Science,
Isomura, Yoshikazu and
Nobuo Kato.
Action Potential-Induced Dendritic Calcium Dynamics Correlated
With Synaptic Plasticity in Developing Hippocampal Pyramidal Cells.
J. Neurophysiol. 82: 1993-1999, 1999.
In hippocampal CA1 pyramidal cells, intracellular calcium increases are
required for induction of long-term potentiation (LTP), an
activity-dependent synaptic plasticity. LTP is known to develop in
magnitude during the second and third postnatal weeks in the rats.
Little is known, however, about development of intracellular calcium
dynamics during the same postnatal weeks. We investigated postnatal
development of intracellular calcium dynamics in the proximal apical
dendrites of CA1 pyramidal cells by whole cell patch-clamp recordings
and calcium imaging with the Ca2+ indicator fura-2.
Dendritic calcium increases induced by intrasomatically evoked action
potentials were slight during the first postnatal week but gradually
became robust 3 to 6-fold during the second and third postnatal weeks.
These calcium increases were blocked by application of 250 µM
CdCl2, a nonspecific blocker for high-threshold voltage-dependent calcium channels (VDCCs). Under the voltage-clamp condition, both calcium currents and dendritic calcium accumulations induced by depolarization were larger at the late developmental stage
(P15-18) than the early stage (P4-7), indicating developmental enhancement of calcium influx mediated by high-threshold VDCCs. Moreover, theta-burst stimulation (TBS), a protocol for LTP induction, induced large intracellular calcium increases at the late developmental stage, in synchrony with maturation of TBS-induced LTP. These results
suggest that developmental enhancement of intracellular calcium
increases induced by action potentials may underlie maturation of
calcium-dependent functions such as synaptic plasticity in hippocampal neurons.
Intracellular free calcium plays crucial roles in
synaptic plasticity such as long-term potentiation (LTP; Bliss
and Collingridge 1993 Wistar rats (P4-20) anesthetized with ether were decapitated
and the brains were dissected in cold artificial cerebrospinal fluid
(ACSF) consisting of (in mM) 124 NaCl, 3.4 KCl, 1.3 KH2PO4, 26 NaHCO3, 2.0 MgSO4, 2.5 CaCl2, and 20-40 D-glucose saturated with 95% O2:5% CO2
(Kato 1993 Whole cell patch-clamp recordings were made from CA1 pyramidal cells
near the surface of slices. Patch electrodes (8-10 M Fura-2 in neurons was excited by single- (380 nm) or
dual- (360 and 380 nm) wavelength illumination, and
fluorescence images on the basis of emission lights passing a 520 nm
filter were captured with an intensified charge-coupled device (I-CCD)
camera. The intensity of excitation lights and the sensitivity of I-CCD
camera were controlled by the RatioArc and RatioVision systems
(Attofluor, MD). The settings of this optical system were never changed
through the entire course of experiments. Images were acquired in
"static ratio" imaging' mode; one image based on 360 nm excitation
was captured at the beginning of each trial, and consecutive images based on 380 nm excitation were captured at video-rate (30 Hz) during
the same trial. The images were stored with a rewritable optical disk
recorder (LQ-4100A; Panasonic, Osaka, Japan) and digitized for off-line
analysis. Regions of interest (ROIs), rectangles of 12 × 10 pixels (5 × 4 µm), were placed at 10 µm intervals along apical dendrite from soma-dendrite boundary, and the fluorescence intensities in each ROI were averaged over 4-5 trials except for Fig.
3, B and C. Background was routinely subtracted
and photobleaching of fura-2 was corrected. In the experiments by
single-wavelength excitation, we defined
- Subthreshold EPSPs, which were not summed up but isolated,
elicited only small calcium transients in the proximal dendrite of CA1
pyramidal cells from 3-wk-old rats (Fig.
1, A and B). Once action potentials were generated, dendritic calcium transients became
larger (Fig. 1C), in agreement with earlier studies
(Christie et al. 1996
ABSTRACT
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
INTRODUCTION
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
; Yuste and Tank 1996
).
Induction of LTP is known to be regulated age-dependently. LTP hardly
occurs in hippocampal CA1 pyramidal cells during the first postnatal
week, whereas robust LTP can be induced after the second week
(Baudry et al. 1981
; Dudek and Bear 1993
;
Figurov et al. 1996
; Harris and Teyler
1984
). Such age-dependent difference in susceptibility of LTP
might be based on developmental changes of postsynaptic calcium
dynamics. Recent studies by calcium imaging revealed that
N-methyl-D-aspartate (NMDA) receptors and
voltage-dependent calcium channels (VDCCs) contribute to synaptically
induced calcium accumulations in the dendrites of CA1 pyramidal cells
(Malinow et al. 1994
; Miyakawa et al.
1992
; Perkel et al. 1993
; Regehr and Tank
1990
, 1992
; Regehr et al. 1989
). In addition,
calcium imaging techniques were able to show that action potentials
cause large dendritic calcium influx through VDCCs (Christie et
al. 1995
; Jaffe et al. 1992
; Spruston et
al. 1995
) and play critical roles in induction of LTP
(Magee and Johnston 1997
). In the present report, we
made use of calcium imaging to investigate postnatal development of
intracellular calcium dynamics in proximal apical dendrites of the rat
CA1 pyramidal cells. Action potential-induced calcium increase was
adopted to compare calcium dynamics across different age groups for the
following reasons. First, individual action potentials are known to
cause a constant calcium increase under physiological conditions (e.g., Spruston et al. 1995
). Second, critical roles played by
action potentials in LTP have recently been supported (Magee and
Johnston 1997
). Third, action potentials may be potentially
useful for quantitative comparison because of their all or none nature.
To our knowledge, this paper provides the first direct evidence of developmental enhancement of dendritic calcium increases in hippocampal neurons in situ.
METHODS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
; Kato and Yoshimura 1993
).
Hippocampal slices (200 µm thick for whole cell recordings or 300 µm for field potential recordings) were prepared with a Microslicer
(DTK-1000; Dosaka EM, Kyoto, Japan) and allowed to recover in ACSF at
room temperature for
60 min. Each slice was transferred into a
submerged-type recording chamber continuously circulated with ACSF at
30°C. The glucose concentration in ACSF was raised up to 40 mM to
increase viability of neurons near the surface of slices during the
dissection and slicing. No noticeable differences in
electrophysiological properties were detected for recordings obtained
in ACSF containing either 10 or 40 mM glucose.
) were filled
with an internal solution containing (in mM) 122.5 K-glucuronate, 17.5 KCl, 5 NaCl, 1 MgCl2, 10 HEPES, 0.2 EGTA, 2 5'-ATP Na2, and 1 fura-2 (Dojindo, Kumamoto,
Japan) (pH 7.3). After whole cell recordings were established by visual
guidance under an upright microscope (Axioskop FS, Zeiss, Germany) with a ×63 water-immersion objective (Achroplan-63/0.90W, Zeiss), fura-2 was loaded for
15 min and membrane potentials were recorded in
the current-clamp mode (I = 0) with an amplifier
(Axopatch 200A, Axon Instruments, CA). The data were low-pass-filtered
at 2-5 kHz and digitized at 2-10 kHz with an A/D interface (Digidata 1200, Axon Instruments). Recordings were obtained from the neurons which had sufficiently negative resting membrane potentials (see RESULTS) without spontaneous action potentials. To evoke
excitatory postsynaptic potentials (EPSPs) or action potentials
synaptically, four consecutive pulses were given at 5 Hz to the
Schaffer collateral fibers by a bipolar tungsten stimulation electrode
placed in the stratum radiatum. To evoke action potentials
intrasomatically, four brief depolarizing currents were injected at 5 Hz through the patch electrode, except for experiments described in
Fig. 2G. The intensities of these stimulations were adjusted
to be just suprathreshold. Theta-burst stimulation (TBS; 10 bursts at 5 Hz, with each burst consisting of 4 pulses at 100 Hz) was delivered by
the stimulation electrode, where the intensities were adjusted to
elicit a single action potential by the initial burst. Before finishing
each experiment, a large and prolonged depolarization (+ 0.2 nA, 800 ms) was given to generate strong calcium increases and confirm that
calcium signals were within a measurable range during test sessions.
For blockade of VDCCs, CdCl2 (250 µM; Nacalai, Kyoto, Japan) was added to
KH2PO4-free ACSF. For
blockade of ryanodine receptors, ruthenium red (20 µM; Nacalai) was
added to the internal solution. For recording calcium currents,
tetrodotoxin (TTX; 1 µM, Alomone Labs, Jerusalem, Israel),
4-aminopyridine (4-AP; 0.5 mM, RBI, MA), and tetraethylammonium
chloride (TEA; 20 mM, RBI) were added to the ACSF, in which the
concentrations of NaCl and CaCl2 were reduced to
100 and 1 mM, respectively. Patch electrodes were filled with another
internal solution containing (in mM) 130 Cs-glucuronate, 5 CsCl, 5 NaCl, 2 MgCl2, 10 HEPES, 0.5 EGTA, 2 5'-ATP
Na2, and 1 fura-2 (pH 7.3). Calcium currents
induced by step-depolarizations from a holding potential of
50 mV to
50,
30,
10, and 10 mV for 200 ms were recorded in the
voltage-clamp mode. Pipette capacitance and whole cell capacitance were
compensated. Series resistance (15-36 M
) was also compensated
to
70%. For field potential recordings, recording electrodes
(2-5 M
) filled with 2.5 M NaCl were placed in the stratum radiatum.
Test pulses were delivered every 12 s with the intensity adjusted
to be 50-75% of threshold for population spikes and two trains of TBS
at the interval of 20 s were given to induce LTP. In simultaneous
recordings of calcium transients and field EPSPs, a patch electrode was
withdrawn from the whole cell-clamped neuron after fura-2 was
sufficiently loaded for
15 min. Before the electrode
withdrawal, the stimulation intensity was adjusted to elicit a single
action potential by the initial burst of TBS. Then another electrode
for field potential recording was placed within 50 µm from the apical
dendrite of the neuron, and the simultaneous recordings were started
when the field responses became stable.
F/F380 as the index to estimate relative changes of intracellular calcium concentration.
F380 is the averaged fluorescence intensity based
on 380 nm excitation, obtained for 1 s before the stimulation.
F is the difference from F380 to fluorescence
intensity excited at 380 nm at a given time. In the experiments by
dual-wavelength excitation, we defined
-
F380/F360 as the index
to estimate absolute changes of the calcium concentration. F360 is the fluorescence intensity based on 360 nm excitation at the beginning of each trial.
F380 is identical to
F as described above.
With calcium concentration increasing, the intensity of 380 nm-excited
fluorescence decreases, whereas that of 360 nm-excited fluorescence
remains unchanged (Grynkiewicz et al. 1985
). Therefore increases in calcium ions will be expressed as positive values in both
indexes. We did not determine the absolute concentration of
intracellular calcium, given the apparent difficulty of accurate calibration in slice preparations. Student's t-test or
analysis of variance (ANOVA) was applied for statistical comparison.
Data in text and figures were expressed as means ± SE, unless
otherwise stated.
RESULTS
TOP
ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES
; Magee et al.
1995
). Synaptically and intrasomatically evoked action
potentials induced dendritic calcium increases to much the same extents
(P15-18, n = 8; data not shown), and here we examined
proximal dendritic calcium increases induced by intrasomatically evoked
action potentials during the first few postnatal weeks (Fig. 1,
D-F). The calcium increases were measured at the proximal regions (0-50 µm from soma-dendrite boundary) of apical dendrites, but not at the more distal dendritic shaft and the branches. We presumed that the proximal regions are less prone to influences because
of the difference in morphological parameters such as dendritic length
and branching number from one developmental stage to another
(Pokorný and Yamamoto 1981
), and therefore are
more suitable for quantitative comparison across developmental stages than are the distal regions.
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Fig. 1.
Postnatal development of action potential-induced calcium transients in
the proximal apical dendrite of CA1 pyramidal cells. A:
fluorescence image of a fura-2-loaded neuron (P18) from which
recordings shown in B and C were
obtained. Scale bar: 20 µm. B: top, 4 subthreshold excitatory postsynaptic potentials (EPSPs) at 5 Hz were
evoked for 1 trial of calcium imaging. Traces of membrane potential
from 5 trials are superimposed. Scale bars: 100 ms and 10 mV.
Bottom, relative changes of intracellular calcium
concentration against time and distance from the soma. Calcium
transients were estimated by averaging fura-2 signals over the 5 trials. Stimulation started at 0 s. C: dendritic
calcium transients induced by 4 synaptically evoked action potentials
at 5 Hz. Top and bottom diagrams
described in B. D: dendritic calcium transients induced
by 4 intrasomatically evoked action potentials at 5 Hz, measured at 30 µm distant from the soma, for 4 age-groups: P4-6
(n = 8), P8-10 (n = 8),
P12-14 (n = 8), and P16-18 (n = 8). : time at which action potentials were evoked.
E: age-dependency of dendritic calcium increases. Peak
values of the calcium increase in all the neurons analyzed in
D (n = 32) are plotted against the
age, with each dot representing an individual neuron. A sigmoidal curve
is fitted tentatively by using Boltzman function. Calcium increases
were kept small during the first postnatal week and gradually developed
at the second and third postnatal weeks. F: development
of dendritic calcium increases at different distances from the soma.
Calcium increases became enhanced during development at roughly a
similar rate at all the distances. F:
inset, ratios (rest
F380/F360; means and SD) of 380 nm-excited
fluorescence intensity (F380) at the resting states to 360 nm-excited one (F360) acquired immediately before the
measurement of F380.
Proximal dendritic calcium increases were very small at the first
postnatal week (P4-6). At the second postnatal week they started to
develop and reached a plateau level by P16-18 (Fig. 1D).
The developmental enhancement was not simply linear but looked sigmoidal; almost no change was seen at the first postnatal week and
prominent augmentation followed during the second and third weeks (Fig.
1E). There were significant augmentations observed at all
the distances (one-way ANOVA, P < 0.001 at 0 µm,
P < 0.001 at 10 µm, P < 0.001 at 20 µm, P < 0.001 at 30 µm, P < 0.001 at 40 µm, P < 0.001 at 50 µm; Fig. 1F).
The baseline ratios
(restF380/F360), measured at the resting states before stimulation, showed no
significant difference among four age-groups from P4 to P18 (one-way
ANOVA, P > 0.4; Fig. 1F, inset). The
resting membrane potentials in these neurons (in mV, mean± SD) were
52.5 ± 2.6 for P4-6, 57.8 ± 2.1 for P8-10, 61.4 ± 3.4 for P12-14, and 61.9 ± 4.5 for P16-18. We used relatively
high concentration of fura-2 to improve the S/N ratio, which could have
critically blurred calcium transient owing to its buffering effects
(Helmchen et al. 1996) and might have possibly affected
the present results. To exclude this possibility, we examined the
developmental change of calcium increase with 200 µM fura-2. At this
concentration also, the proximal dendritic calcium increases were
larger at the late developmental stage than the early (0.038 ± 0.005 for the early (n = 4) and 0.116 ± 0.007 for
the late (n = 4), t-test, P < 0.001). This result was essentially consistent with the results
described above. The proximal dendritic calcium increases induced by
action potentials were greatly reduced by 250 µM
CdCl2 at both the early (P4-7) and the late
(p15-18) developmental stages (n = 7 in both groups; data not shown), suggesting that the calcium increases were mainly mediated by high-threshold VDCCs.
We attempted to explain underlying mechanisms involved in the
developmental enhancement of proximal dendritic calcium increases. First, to examine whether the amounts of calcium influx are
developmentally augmented, calcium currents and intracellular calcium
accumulations induced by step-depolarization were simultaneously
recorded under the voltage-clamp condition in situ. Both calcium
currents and calcium accumulations induced by depolarization were much
greater at the late developmental stage (P15-18) than the early
developmental stage (P4-7) (Fig. 2,
A and B). The maximal values of calcium currents
were significantly larger at the late developmental stage than the
early at 10 and 10 mV (t-test, n = 6 in
both, P < 0.001 at
10 mV, P < 0.005 at 10 mV; Fig. 2C). As expected from the developmental
increase in membrane area, whole cell capacitance increased during the
development (27.8 ± 5.2 for the early and 51.3 ± 2.7 for
the late (in pF), t-test, P < 0.005), and
current densities at
10 mV, obtained by normalizing to the
capacitance, were also significantly greater at the late stage than the
early (11.4 ± 4.5 for the early and 26.0 ± 3.4 for the late
(in pA/pF), t-test, P < 0.05). The
intracellular calcium accumulations were also significantly larger at
the late developmental stage than the early (t-test,
n = 6 in both, P < 0.05 at
30 mV,
P < 0.002 at
10 mV, P < 0.002 at 10 mV; Fig. 2D). The extents of calcium currents and
intracellular calcium accumulations were significantly correlated
(
=0.75, P < 0.01; Fig. 2E). The calcium
accumulations were larger at the late developmental stage than the
early at each of 0-50 µm distances (t-test,
n = 6 in both, P < 0.001 at 0 µm,
P < 0.001 at 10 µm, P < 0.005 at 20 µm, P < 0.005 at 30 µm, P < 0.005 at 40 µm, P < 0.005 at 50 µm; Fig. 2F).
These recordings of calcium currents in situ were consistent with the
previous studies in acutely dissociated neurons (Kortekaas and
Wadman 1997
; Thompson and Wong 1991
).
|
Second, we considered whether calcium-induced calcium release (CICR),
calcium buffering, and calcium sequestration contribute to
developmental change of the calcium dynamics (Blaustein
1988). The calcium transients were not changed by intracellular
application of 20 µM ruthenium red, a ryanodine receptor blocker, in
our experimental conditions (t-test, n = 8 in both,
P > 0.1), suggesting no major participation of CICR in developmental changes of the calcium dynamics.
The decay of calcium transients were significantly slower at the early
developmental stage than the late (t-test, n = 8 in both, P < 0.001; Fig. 2G). This
slower decay at the early stage may be due to stronger calcium
buffering or weaker calcium sequestration. It is unlikely that calcium
buffering is stronger at the early stage than the late, because
calcium-binding proteins including calbindin, acting as endogenous
calcium buffers, generally increase during development (e.g.,
Rami et al. 1987
) and that we routinely used the same
concentration of fura-2, which may work as exogenous calcium buffer.
Hence, calcium sequestration seems to be strengthened during
development. This alone, however, could not bring about a developmental
enhancement of action potential-induced calcium increases.
Third, somatic action potentials were compared at the early and late
developmental stages as shown in Fig. 2H. In agreement with
the previous reports (e.g., Costa et al. 1991), the
amplitude became larger during development (72.4 ± 2.5 mV for the
early (n = 3) and 88.9 ± 0.7 mV for the late
(n = 3), t-test, P < 0.005) and the width at half height shorter (2.5 ± 0.2 ms for the early (n = 3) and 1.7 ± 0.1 ms for the late
(n = 3), t-test, P < 0.02). Because the calcium increases were voltage-dependent, enlargement of
the amplitude is thought to enhance the calcium increase during the
development. However, dendritic rather than somatic action potentials
should have more relevance to dendritic calcium increases. It is yet to
be determined whether backpropagation of dendritic action potentials
could undergo developmental changes. In summary, increases in the
voltage-dependent calcium conductances have been shown to contribute to
the developmental enhancement of proximal dendritic calcium increases,
and moreover it is possible that developmental changes in other ion
channels such as dendritic sodium and potassium channels are involved.
In the hippocampal CA1 region, TBS-induced LTP does not appear
until the second postnatal week (Dudek and Bear 1993;
Figurov et al. 1996
). Indeed, in our own slice
preparations, TBS-induced LTP remarkably developed during the second
and third postnatal weeks (109.5 ± 7.7% for P8-10
(n = 10) and 173.6 ± 10.2% for P18-20 (n = 8), t-test, P < 0.001;
Fig. 3A). Given
calcium-dependence of LTP induction, postsynaptic calcium dynamics
induced by TBS may change during maturation. To examine this
possibility, proximal dendritic calcium transients and field EPSPs were
simultaneously recorded at the beginning of the second postnatal week
(P8-10, n = 6) and at the third postnatal week
(P16-18, n = 6) (Fig. 3, B and
C). The change of EPSPs in fura-2-loaded neurons themselves were not monitored because fura-2 was expected to buffer calcium increase required for LTP induction (see METHODS).
TBS-induced calcium increases in the proximal apical dendrite were
significantly larger at P16-18 than at P8-10 (0.051 ± 0.013 for
P8-10 and 0.123 ± 0.015 for P16-18, t-test,
P < 0.005). The baseline calcium levels (restF380/F360)
in all the recorded neurons were within the ranges illustrated in Fig.
1F, inset, suggesting that they were kept healthy. Only one
of the six slices at P8-10 exhibited TBS-induced LTP (defined as
>120% at 25 min), whereas TBS caused prominent LTP in all of the six
slices at P16-18. Thus in correlation with developmental enhancement
of proximal dendritic calcium increase, LTP was significantly augmented
during the second and third postnatal weeks (106.9 ± 5.9% for
P8-10 and 129.0 ± 3.1% for P16-18, t-test, P < 0.01). To analyze the role of action potentials
during TBS, the TBS-induced dendritic calcium increases and membrane
potentials were compared at the early (P4-7) and the late (P15-18)
developmental stages. Larger calcium increases were induced by TBS at
the late than the early stage (Fig. 3, D and E),
even with similar numbers of overshooting action potentials generated
during TBS. Greater calcium increases were induced by comparable
numbers of action potentials at the late than the early developmental
stage (Fig. 3F). At each of 0-50 µm distances, the
calcium increases were significantly larger at the late than the early
developmental stage (t-test, n = 7 in both,
P < 0.001 at 0 µm, P < 0.001 at 10 µm, P < 0.001 at 20 µm, P < 0.001 at 30 µm, P < 0.001 at 40 µm, P < 0.001 at 50 µm; Fig. 3G). Thus TBS-induced calcium
increases were developmentally enhanced in harmony with the maturation
of TBS-induced LTP.
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DISCUSSION |
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We showed developmental enhancement of action potential-induced
proximal dendritic calcium increases in CA1 pyramidal cells and focused
on its correlation to maturation of TBS-induced LTP. Hippocampal LTP is
known as a synaptic model for learning and memory (Bliss and
Collingridge 1993; Chen and Tonegawa 1997
). Induction of LTP requires increases in postsynaptic calcium
concentration (Lynch et al. 1983
; Malenka et al.
1988
) mediated by NMDA receptors (Collingridge et al.
1983
), VDCCs (Grover and Teyler 1990
) and/or metabotropic glutamate receptors (Bashir et al. 1993
).
Recently, TBS-induced LTP has been shown to depend on high- and
low-threshold VDCCs and on NMDA receptors (Magee and Johnston
1997
). They also demonstrated that dendritic action potentials
were required for the induction of LTP, suggesting that VDCC-mediated
dendritic calcium increases induced by action potentials may be
critical for induction of TBS-induced LTP. In developing rats, LTP in
CA1 pyramidal cells does not appear until 1 week of age and then
drastically develops to the mature level during the second and third
postnatal weeks (Baudry et al. 1981
; Harris and
Teyler 1984
; Dudek and Bear 1993
; Figurov
et al. 1996
). Interestingly, LTP can be induced even during the
first postnatal week if synaptically activated depolarization is
reinforced by pairing with a very strong postsynaptic depolarization up
to ~0 mV (Durand et al. 1996
). Because NMDA receptors
have already been functional only a few days after the birth
(Durand et al. 1996
), the amount of VDCC-mediated
calcium component may put restrictions on susceptibility to LTP
induction. We showed that the time course of developmental enhancement
of VDCC-mediated calcium increases in the proximal apical dendrite resembles that of TBS-induced LTP (Fig. 1E, and see also
Figurov et al. 1996
). Thus developmental
enhancement of action potential-induced proximal dendritic calcium
increases may play a crucial role for maturation of calcium-dependent
functions such as synaptic plasticity in hippocampal neurons.
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ACKNOWLEDGMENTS |
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The authors are grateful to Dr. S. Kawaguchi for encouragement and to Drs. K. Yamamoto and K. Hashimoto for help in experiments.
This work was supported by a project of the Japan Science and Technology Corporation and grants from the Ministry of Education, Science, Sports and Culture of Japan.
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FOOTNOTES |
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Address for reprint requests: N. Kato, Dept. of Integrative Brain Science, Graduate School of Medicine, Kyoto University, Kyoto 606-8501, Japan.
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 1 March 1999; accepted in final form 17 May 1999.
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REFERENCES |
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