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1Department of Electronic Engineering, Graduate School of Engineering, and 2Neuroscience Laboratories, Graduate School of Frontier Bioscience, Osaka University, Suita 565-0871, Japan
Submitted 31 October 2002; accepted in final form 4 February 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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). The contribution of A-type channels and other channels to
the firing behavior of a cell depends on the density of the channel in the
membrane. Channel density is expected to be primarily regulated during
development via transcription and translation
(Orphanides and Reinberg 2002;
Ramakrishnan 2002), although
the precise mechanism has not been made clear. There is a wealth of literature
on the development of A-type channels and other potassium channels
(Nerbonne 1998;
Ribera 1999;
Spitzer et al. 2002). On one
hand, voltage-clamp studies using cultured neurons or neurons in brain slices
have revealed that A-type currents are either up- or transiently regulated
during development (Cingolani et al.
2002; Nerbonne
1998; O'Dowd et al.
1988; Raucher and Dryer
1994; Shibata et al.
2000; Wu et al.
1998). On the other hand, the expression of genes coding for
potassium channels during development has also been studied in the CNS
(Cingolani et al. 2002;
Drewe et al. 1992;
Gan et al. 1998;
Levitan and Takimoto 1998;
Nerbonne 1998;
Perney et al. 1992;
Xu et al. 1996). Recent
studies using techniques combining patch clamp recording with
single-cell/reverse transcription/polymerase chain reaction (scRT-PCR) or
overexpression of antisense/dominant-negative constructs have begun to
identify genes responsible for A-type as well as other types of native
potassium currents in identified neurons and non-neuronal cells
(Baro et al. 1997;
Fiset et al. 1997;
Johns et al. 1997;
Liss et al. 2001;
Malin and Nerbonne 2000;
Martina et al. 1998;
Shibata et al. 2000;
Song et al. 1998;
Tkatch et al. 2000).
Somatodendritic A-type currents have often been found to be related to genes
of the Kv4 subfamily in adult neurons (Baro
et al. 1997; Malin and
Nerbonne 2000; Martina et al.
1998; Song et al.
1998; Tkatch et al.
2000). Thus A-type channel density in somatodendritic compartment
of neurons is likely to be regulated during development, through
transcriptional and translational regulation of Kv4 genes, together with
subcellular channel localization mechanisms.
Striatal cholinergic interneurons in adult rats have a prominent A-type
current and co-express Kv4.1 and Kv4.2 mRNAs
(Song et al. 1998).
Semi-quantitative examination of the message level in different types of
mature neurons, has revealed that Kv4.2, but not Kv4.1, mRNA is linearly
related to the amount of A-type current, suggesting the primary role of Kv4.2
in producing the current in adult cholinergic interneurons
(Tkatch et al. 2000). The
contribution of Kv4.2 and Kv4.1 to the A-type current in cholinergic
interneurons during development, however, is not known. The expression of both
genes can be dynamically regulated during development. In the present study,
we examined the postnatal development of A-type current and the expression of
Kv4.2 and Kv4.1 mRNAs, using patch-clamp recording and semi-quantitative
scRT-PCR techniques. Our results showed that during postnatal development,
A-type current and A-type current density were up-regulated together with the
expression level of Kv4.2 mRNA but not with Kv4.1 mRNA, suggesting that
up-regulation of Kv4.2 mRNA is a major factor in postnatal regulation of
A-type current density in striatal cholinergic interneurons.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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Sprague-Dawley rats aged from postnatal day 0 (P0) to P57 were used in this
study. All experiments were conducted in compliance with the Guidelines for
Use of Laboratory Animals of Osaka University. Neostriatal neurons were
acutely dissociated using procedures similar to those we previously described
(Song et al. 1998,
2000). In brief, rats were
anesthetized with ethyle-ether and decapitated; brains were quickly removed,
iced, and blocked for slicing. The blocked forebrain region was cut in
400-µm slices in the frontal plane with a Microslicer (Dosaka, Kyoto,
Japan) while bathed in a low Ca2+ (100 µM), HEPES buffered salt
solution (in mM: 140 Na isethionate, 2 KCl, 4 MgCl2, 0.1
CaCl2, 10 glucose, and 10 HEPES, pH = 7.4, 300–305 mOsm/l).
Slices were then incubated for 1–6 h at room temperature in a
NaHCO3 buffered Earle's balanced salt solution bubbled with 95%
O2-5% CO2. All reagents were obtained from Sigma
Chemical Co. (St. Louis, MO). Slices were then removed into the low
Ca2+ buffer and, with the aid of a dissecting microscope, regions
of the dorsal striatum were dissected with a pair of thin tungsten needles and
placed in an oxygenated beaker containing pronase (1–3 mg/ml) in
HEPES-buffered Hank's balanced salt solution (HBSS, Sigma Chemical) at
35°C. After 30–35 min of enzyme digestion, tissue was rinsed three
times in the low Ca2+, HEPES-buffered saline and mechanically
dissociated with a graded series of fire-polished Pasteur pipettes. The cell
suspension was then plated into a 35-mm Lux petri dish mounted on the stage of
an inverted microscope containing HEPES-buffered saline (in mM: 140 NaCl, 2
KCl, 1 CaCl2, 2 MgCl2, 10 glucose, and 15 HEPES, pH =
7.4 with NaOH, 300–305 mOsm/l).
Whole cell recordings
Whole cell recordings used standard techniques
(Hamill et al. 1981;
Song et al. 1998). Recordings
were obtained with an Axon Instruments 200 patch clamp amplifier and
controlled and monitored with a Pentium PC running pCLAMP (v. 7.0) with a 125
kHz interface (Axon Instruments, Foster City, CA). Signals were low-pass
filtered at 10 kHz and sampled at 50 kHz. After G
seal formation,
electrode capacitance was first compensated. Whole cell capacitance was
compensated using the whole cell compensation function of the amplifier after
membrane break. Whole cell capacitance values were recorded for calculation of
current density. For the results to be directly useful in future simulation
studies, we recorded K+ current with physiological concentrations
of K+. The internal solution consisted of (in mM) 120 potassium
gluconate, 3 MgCl2, 10 HEPES, 10 EGTA, 0.1 leu-peptin, 2 ATP, 0.2
GTP, and 12 phosphocreatine; pH was adjusted to 7.2 with NaOH, and osmolarity
was adjusted to 265–275 mOsm/l with N-methyl-glucamine. The
external solution consisted of (in mM) 130 Na isethionate, 5 KCl, 2
MgCl2, 10 HEPES, 28 glucose, and 0.0005 TTX; pH adjusted to 7.4
with 1 N NaOH (approximately 2 ml); osmolarity adjusted to 300 ± 5
mOsm/l. Using physiological concentrations of K+ resulted in large
current in adult neurons and thus may create error in voltage clamp. To
minimize this error, only recordings with series resistance <10 M
(typically approximately 8 M) were used for analysis, and series
resistance was compensated for 85–90%. Potentials were not corrected for
the liquid junction potential. Recordings were made only from large-sized
neurons that had only a few short proximal dendrites.
With our recording solutions, Na+ currents were blocked by TTX
and Ca2+ currents were eliminated by excluding Ca2+ in
the bathing medium. Ca2+ currents can also be effectively
eliminated using inorganic Ca2+ channel blockers, such as
Cd2+, but such blockers drastically alter channel voltage
dependence (Mayer and Sugiyama
1988; Song et al.
1998), and are thus not used in this study. Excluding
Ca2+ in the bathing solution, however, may also cause some shift of
channel voltage dependence (Mayer and
Sugiyama 1988). Thus the voltage-dependence of the A-type current
estimated here may be lower than normal.
Single cell RT-PCR analysis
Large cells were aspirated into electrodes filled with 5 µl diethyl
pyrocarbonate (DEPC)-treated water. After aspiration, the pipette tip was
broken and contents ejected into a 0.5 ml nylon-coated tube containing 5 µl
DEPC-treated water, 0.5 µl RNase inhibitor (RNAsin, 40,000 U/ml), and 0.5
µl dithiothreitol (DTT; 0.1 M). RT was done using the SuperScript
Preamplification System from GIBCO BRL (Grand Island, NY)
(Song and Surmeier 1996;
Yan and Surmeier 1996).
Oligo(dT) (0.5 µg/µl) primer (1 µl) were added and the mixture heated
to 70°C for 10 min and then incubated on ice for more than 1 min.
Single-strand cDNA was synthesized from the cellular mRNA by adding
SuperScript II RT (1 µl, 50 U/µl) and buffer (2 µl, 10x First
Strand Buffer: 200 mM Tris-HCl, 500 mM KCl), MgCl2 (2 µl, 25
mM), RNAsin (0.5 µl, 40,000 U/ml), DTT (1.5 µl, 0.1 M), and mixed dNTPs
(1 µl, 10 mM). The reaction mixture (20 µl) was incubated at 42°C
for 60 min. The reaction was terminated by heating the mixture to 70°C for
15 min and then icing. The RNA strand in the RNA-DNA hybrid was then removed
by adding 1 µl RNAse H (2 U/µl) and incubating for 20 min at 37°C.
The cDNA from the RT of RNA in single large neurons was subjected to PCR to
detect the expression of Kv4.1 and Kv4.2 mRNAs and the mRNA coding for choline
acetyltransferase (ChAT).
PCR was carried out with a thermal cycler (Perkin Elmer, Norwalk, CT). Thin-walled plastic tubes (Perkin Elmer, Norwalk, CT) were used. The reaction mixture contained 2.5 mM MgCl2, 0.5 mM of each of the dNTPs, 1 µM primers, 2.5 U Taq DNA polymerase (Promega), 5 µl 10x Buffer (Promega), and varying amount of the cellular cDNA (see RESULTS). Following denaturing at 94°C (10 min), the reaction mixture was cycled at 94°C for 1 min, 58°C (56°C for Kv4.1) for 1 min, and 72°C for 1 min. This was repeated 45 times and followed by a 10-min extension at 72°C for 10 min.
The ChAT mRNA was identified using a pair of primers flanking a splicing
site near to the 3' terminus of the coding region
(Yan and Surmeier 1996). The
upper primer was 5'-ATG GCC ATT GAC AAC CAT CTT CTG and the lower primer
was 5'-CCT TGA ACT GCA GAG GTC TCT CAT. The size of the amplified ChAT
cDNA was 324 base pairs (bp). The primers for K+ channel subunits
have been reported previously (Song et al.
1998). The upper primer for Kv4.1 was 5'-CGG ACA AAT GCT GTG
CGT TAG and the lower primer was 5'-TAG GGG AGG AAG GTT GAC TTT CAT. The
size of the amplified Kv4.1 cDNA was 467 bp. The upper primer for Kv4.2 was
5'-CCG AAT CCC AAA TGC CAA TGT G and the lower primer was 5'-CCT
GAC GAT GTT TCC TCC CGA ATA. The size of the amplified Kv4.2 cDNA was 265 bp.
PCR products were separated by electrophoresis in 2% agarose gel and
visualized by staining with ethidium bromide. In representative cases,
amplicons were purified from the gel (QIAquick Gel Extraction Kit, QIAGEN),
sequenced with a dye termination procedure, and found to match published
sequences.
Negative controls for contamination from extraneous and genomic DNA were run for every batch of neurons. This was done by omitting the reverse transcriptase in one neuron from each batch; the rest of the reactions for the neuron were done in the normal manner as in other cells. Results from such controls were consistently negative.
Quantification of mRNA expression level
All cells were first verified to be ChAT-positive. The expression level of
Kv4.1 and Kv4.2 relative to the maximum level was then estimated using a
serial dilution analysis (Song et al.
1998). cDNA of a single cell was diluted by one-half by adding an
equal volume of water at each step of serial dilution, until no PCR product
could be detected. The last step of dilution at which a PCR product could be
detected is called threshold dilution (2–x). The
amount of mRNA can then be estimated as
2x
–1, where is the
threshold of PCR detection (Surmeier et
al. 1996) and is the efficacy of RT reaction. The relative
amount of expression level in different cells can be calculated, assuming
constant values for and . This assumption should be reasonable
for a single kind of mRNA. Thus our method does not provide values of absolute
expression level, but values relative to a standard. In this sense, we call
our method semi-quantitative.
Statistical methods
Sample statistics are given as means with SE. Boltzmann functions were fitted to normalized conductance or current plots with a least squares fitting routine. Student's t-test was used to compare data sets.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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Cells were acutely dissociated from rat dorsal neostriatum. In animals
older than 1 wk, cholinergic interneurons were readily recognizable as cells
of large somata and few dendritic processes
(Song et al. 1998)
(Fig. 1A). The
difference in soma size among cells appeared smaller in younger animals but
was large enough for the interneurons to be distinguished. In a set of large
cells for scRT-PCR analyses (see next section), the identity of large cells
was further verified by detecting the expression of ChAT mRNA
(Fig. 1A,
inset; n = 105). Cells in younger animals required a larger
fraction of cellular cDNA to detect ChAT mRNA, but all cells tested were
ChAT-positive, suggesting that most, if not all, of the neurons studied here
are cholinergic interneurons.
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As shown previously, adult cholinergic interneurons expressed a prominent
component of A-type current, as well as a noninactivating current
(Fig. 1B)
(Song et al. 1998). In the
present study, we focus on the postnatal development of the A-type current. To
isolate the A-type current, currents were evoked with a test pulse to +20 mV
preceeded by a prepulse either to –100 or –50 mV
(Fig. 1B). A-type
current was obtained by subtraction of the two currents. The prepulse was set
to have a duration of 500 ms to fully remove A-type channel inactivation at
–100 mV and for inactivation of the channel to fully develop at
–50 mV (Song et al.
1998). We used this protocol for all ages (P0-P57) of animals to
study the development of A-type current.
The validity of the protocol, however, also depends on the voltage dependence of the channel. We thus studied the voltage-dependent activation and inactivation of the channel at each age. As shown in Fig. 2, A-type channels at all ages showed similar voltage dependence. From the activation curves (Fig. 2A), the test pulse to +20 mV is expected to activate the quasi-maximum number of channels at all ages. From the inactivation curves (Fig. 2B), the prepulse to –50 mV is expected to fully inactivate A-type channels at all ages; the prepulse to –100 mV is expected to remove most inactivation of the channel. We noticed a minor difference between the inactivation curves in animals younger than 1 wk and those in older ones. This difference would cause only an approximate 10% difference in inactivation among the age groups at –100 mV and was not further considered. Our protocol for isolation of A-type current, as shown in Fig. 1B, is thus expected to activate the quasi-maximum A-type conductance in all age groups.
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Representative A-type currents isolated at each age are shown in Fig. 3. As shown in Fig. 3, A and B, the current was detectable at birth, increased during postnatal development, and reached a plateau at about 3 wk postnatal. The largest increase occurred between P5 and P13. No significant difference was found among P23, P35, and P57 animals (P > 0.05). The average current at P0/P1 was 0.67 nA and that at P57 was 5.05 nA. The current thus increased about 7.5-fold during postnatal development. The size of cholinergic interneurons also increased during postnatal development, as evidenced by the increase of whole cell capacitance (data not shown). The increase in current, however, overwhelmed the increase in cell size, resulting in an increase in current density (Fig. 3C). The average current density at P35 and P57 appeared smaller than that at P23, but no significant difference was found among data from these ages (P > 0.05).
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Like Kv4 channels expressed in heterologous cells
(Baldwin et al. 1991;
Coetzee et al. 1999), the decay
of the current could be best fitted with more-than-one exponentials. We fitted
the current with two exponentials (Fig.
3A, bottom), a fast component and a slow one.
The fast component appeared to be the major component for all ages, accounting
for approximately 83% of the total current
(Fig. 4, A and
B). The developmental time course for the two components
appeared to be different. The magnitude of the fast component reached a
plateau at about 2 wk postnatal (Fig.
4A; no significant difference among data from
P13–P57; P > 0.05), while that of the slow one reached a
plateau by 3 wk after birth (Fig.
4B; no significant difference among P23-P57 data;
P > 0.05). The time constant of the fast component was 15.2
± 1.1, 17.2 ± 1.3, 20.5 ± 1.0, 27.4 ± 2.2, 22.7
± 1.6, and 24.9 ± 1.9 ms at P0/P1, P5, P13, P23, P35, and P57,
respectively. This time constant thus appeared to increase slightly with age
(Fig. 4C). The time
constant of the slow component was 125.2 ± 34.9, 122.6 ± 15.4,
122.4 ± 13.9, 119.4 ± 9.0, 98.8 ± 9.2, and 142.7 ±
23.7 ms, at P0/P1, P5, P13, P23, P35, and P57, respectively. The slow time
constant thus remained stable with age
(Fig. 4D). Because
there are five free parameters in the equation for fitting
(Fig. 3A,
bottom), the validity of these changes needs to be further
tested.
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Postnatal development of the expression level of Kv4.1 and Kv4.2 mRNA
The increase in current during postnatal development is attributable to
transcriptional and/or translational regulation. Kv4.1 and Kv4.2, known to
encode the principal subunit of the A-type channels, have been shown to be
co-expressed in cholinergic interneurons
(Song et al. 1998;
Tkatch et al. 2000). To study
the contribution of transcription during development, we quantified the
expression level of Kv4.1 and Kv4.2 mRNAs in individual cholinergic
interneurons by serial dilution (Song et
al. 1998; see METHODS). A total of 105 neurons were
used for serial dilution analysis (48 for Kv4.1 and 57 for Kv4.2), and all
these neurons had been verified as ChAT-positive before the analysis. Because
A-type current amplitude reached a plateau at 3 wk after birth
(Fig. 3), the analysis of mRNA
expression was done for animals at P35 or younger. The results of Kv4.2 are
shown in Fig. 5.
Figure 5, A and
B, shows examples of serial dilution in single cells at
P1 and P13, respectively. The threshold dilution, the last dilution at which a
PCR amplicon can be detected, can be clearly determined from such an analysis.
The threshold dilution is inversely related to the amount of Kv4.2 cDNA (see
METHODS). In Fig.
5C, the distribution of threshold dilution for cells at each age
is shown as histograms. There is a clear shift of the distribution toward
right with age. The results of a similar serial dilution analysis for Kv4.1
are shown in Fig. 6. Unlike
Kv4.2 mRNA, Kv4.1 mRNA was less detectable in cholinergic interneurons at all
ages. No Kv4.1 mRNA was detected during the first week. The expression level
of Kv4.1 mRNA after 1 wk did not show a clear tendency with development
(Fig. 6).
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The expression level of mRNA in each cell was calculated from its threshold dilution (see METHODS) and normalized to the largest average expression level (P35). Because of the lack of a tendency for Kv4.1 mRNA with age, this analysis was limited to Kv4.2. The relative amount of Kv4.2 mRNA at each age was calculated and plotted as a function of age. As shown in Fig. 7, the expression level rapidly increased after birth in an exponential manner and reached a plateau by 3 wk. For comparison, the developmental increase of A-type current was normalized to the maximum average current and also plotted in Fig. 7. It can be seen from the figure that the increase of the current is slower than that of the expression level of Kv4.2 mRNA. Kv4.2 mRNA level reached one-half of the peak value at about P4, while the current reached one-half value at about P9.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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Postnatal development of A-type channels
In other cells, A-type currents are either up- or transiently regulated
during postnatal development (Nerbonne
1998; Raucher and Dryer
1994; Ribera 1999;
Wu et al. 1998). The
functional significance of transiently expressing A-type channels during
development is not known, but up-regulation of the channel would allow adult
neurons to exploit the properties of A-type channels for regulation of firing
behavior and synaptic integration.
Although A-type current amplitude increased by more than seven-fold in
striatal cholinergic interneurons during postnatal development, the decay
phase of the current at all ages could be well fitted with two exponentials.
The time constants of both the fast component and the slow one agree well with
those found for Kv4 channels expressed in heterologous systems
(Coetzee et al. 1999),
suggesting the possibility that A-type current in cholinergic interneurons is
encoded by Kv4 genes during development. While the time constant of the slow
component remained stable during development, that of the fast one appeared to
slightly increase with age. This is in contrast with previous findings in
chick peripheral neurons that the inactivation time constant of A-type current
decreases with development (Raucher and
Dryer 1994). The reason for such developmental changes is not
clear at this time. Because time-dependent properties of channels are
important in determining cell's firing behavior, the mechanism regulating
channel kinetics should be an important subject for future studies.
Relationship between A-type current and Kv4 mRNAs during development
Evidence has been accumulating that Kv4 genes encode the principal subunits
of A-type K+ channels in neuronal and nonneuronal cells in adult
animals (Baro et al. 1997;
Fiset et al. 1997;
Johns et al. 1997;
Malin and Nerbonne 2000;
Martina et al. 1998;
Shibata et al. 2000;
Song et al. 1998;
Tkatch et al. 2000). Liss et
al. (2001) have also shown
that Kv4.3L encode A-type current in dopaminergic neurons at one stage of
development (P14). Although striatal cholinergic interneurons co-express Kv4.1
and Kv4.2 mRNAs, our results showed that during postnatal development the
expression level of Kv4.2 mRNA, but not Kv4.1 mRNA, was up-regulated with
A-type current, suggesting that Kv4.2 is primarily responsible for the current
during the entire course of postnatal development.
The more rapid increase of Kv4.2 mRNA compared with the current results in
a supra-linear relationship between the mRNA and the current
(Fig. 8C). This is the
first demonstration of a quantitative relationship between a current and the
expression level of its candidate gene during development. Previous studies
have quantified K+ channel mRNAs or proteins during development
(Perney et al. 1992;
Tansey et al. 2002;
Xu et al. 1996), but the
quantification was done either at the tissue level or at the whole-brain
level, making it difficult to compare with the development of K+
current in individual neurons. Gurantz et al.
(1996) have recorded
K+ currents and detected K+ channel messages during
development of single Xenopus spinal neurons; while interesting
relationships between properties of K+ currents and the expression
of Kv2 genes were found, no quantitative relationship between the current and
the messages was established.
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A linear relationship between shal transcripts and A-type channel
conductance has been found in stomatogastric neurons of an anthropod
(Baro et al. 1997). Similarly,
the expression level of Kv4.2 mRNA has been found to be linearly related to
the magnitude of A-type currents in several types of adult neurons in rats
(Tkatch et al. 2000).
Furthermore, at a fixed stage of development (P14), the A-type currents in
individual dopaminergic neurons were also found to be linearly related to
Kv4.3L transcripts (Liss et al.
2001). The supra-linear relationship between Kv4.2 mRNA and A-type
current demonstrated here may appear at odds with previous studies. This
discrepancy occurs because previous studies were done either with adult
neurons or with neurons at a single developmental stage, while our study
addressed developmental changes in A-type current and Kv4 mRNAs. The
supra-linear relationship between Kv4.2 mRNA and A-type current, resulting
from the more rapid increase of Kv4.2 mRNA compared with the current, is most
likely attributable to the fact that transcription occurs prior to
translation. Actually, the developmental time courses of the current and Kv4.2
mRNA, as well as the supra-linear relationship between the two, could be well
described with a model including transcription, translation, and mRNA/protein
degradation, with constant rates (Fig.
8). The supra-linear relationship between Kv4.2 mRNA and the
A-type current demonstrated here thus strongly suggests that Kv4.2 produces
the A-type current during development. The precise mechanism regulating the
level of Kv4.2 mRNA and A-type current, however, can be complicated
(Ma and Jan 2002;
Orphanides and Reinberg 2002;
Ramakrishnan 2002) and remains
to be clarified in future studies.
The increase in the level of mRNA and current during development highlights
the role of transcription and translation. The developmental time course of
changes in Kv4.2 mRNA and A-type current demonstrated here, however, indicates
that degradation is equally important as transcription and translation in
regulating the development of mRNA and channel protein quantity. Without
degradation, mRNA or current level will not reach a plateau unless
transcription or translation is turned off. Degradation of mRNA and proteins
has been found in the nervous system, and some of the mechanisms are beginning
to be elucidated (Beelman and Parker
1995; Glickman and Ciechanover
2002). To further understand the developmental regulation of
A-type channel density in striatal cholinergic interneurons, it is important
in future studies to determine the rates for transcription, translation, and
degradation of Kv4.2 mRNA/protein, and to identify the molecular substrates of
the rates. Each rate may represent the overall effect of multiple processes
(Ma and Jan 2002), and may be
time-dependent as well. Some factors affecting the rates, such as cell
contact, intracellular Ca2+, and kinases have been identified for
other genes (Barish 1998).
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ACKNOWLEDGMENTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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FOOTNOTES |
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Address for reprint requests: W.-J. Song, Dept. of Electronic Engineering, Graduate School of Engineering, Osaka Univ., 2-1 Yamadaoka, Suita 565-0871, Japan (E-mail: song{at}ele.eng.osaka-u.ac.jp).
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1). The time constant increased gradually with development.
D: development of the time constant of the slow component
(
1)[1 –
exp(–