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The Journal of Neuroscience, February 15, 2003, 23(4):1133
Modulation of the Kv3.1b Potassium Channel Isoform Adjusts
the Fidelity of the Firing Pattern of Auditory Neurons
Carolyn M.
Macica1,
Christian A. A.
von Hehn1,
Lu-Yang
Wang2,
Chi-Shun
Ho3,
Shigeru
Yokoyama4,
Rolf H.
Joho5, and
Leonard K.
Kaczmarek1
1 Department of Pharmacology, Yale University, New
Haven, Connecticut 06520, 2 Division of Neurology, Hospital
for Sick Children Research Institute, Toronto, Canada,
3 Department of Physiology, University of Michigan Medical
Center, Ann Arbor, Michigan 48109, 4 Department of
Biophysical Genetics, Kanazawa University Graduate School of Medicine,
Kanazawa, Ishikawa, 920-8640, Japan, and 5 Center for Basic
Neuroscience, University of Texas Southwestern Medical Center, Dallas,
Texas 75390
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ABSTRACT |
Neurons of the medial nucleus of the trapezoid body, which transmit
auditory information that is used to compute the location of sounds in
space, are capable of firing at high frequencies with great temporal
precision. We found that elimination of the Kv3.1
gene in mice results in the loss of a high-threshold component of
potassium current and failure of the neurons to follow high-frequency stimulation. A partial decrease in Kv3.1 current can be produced in
wild-type neurons of the medial nucleus of the trapezoid body by
activation of protein kinase C. Paradoxically, activation of protein
kinase C increases temporal fidelity and the number of action
potentials that are evoked by intermediate frequencies of stimulation.
Computer simulations confirm that a partial decrease in Kv3.1 current
is sufficient to increase the accuracy of response at intermediate
frequencies while impairing responses at high frequencies. We further
establish that, of the two isoforms of the Kv3.1 potassium channel that
are expressed in these neurons, Kv3.1a and Kv3.1b, the decrease in
Kv3.1 current is mediated by selective phosphorylation of the Kv3.1b
isoform. Using site-directed mutagenesis, we identify a specific
C-terminal phosphorylation site responsible for the observed difference
in response of the two isoforms to protein kinase C activation. Our
results suggest that modulation of Kv3.1 by phosphorylation allows
auditory neurons to tune their responses to different patterns of
sensory stimulation.
Key words:
Kv3.1; potassium channel; MNTB neurons; protein
kinase C; phosphorylation; auditory timing; channel isoforms
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Introduction |
The Kv3.1 potassium channel is
expressed at high levels in neurons that characteristically fire rapid
trains of action potentials (Perney et al., 1992
; Weiser et al., 1995;
Rudy, 1999). Particularly high levels of this channel are found in
neurons of the auditory brainstem, such as bushy cells of the cochlear
nucleus and neurons of the medial nucleus of the trapezoid body (MNTB).
These neurons participate in neural circuits that determine the
intensity and timing of auditory stimuli and use this information to
determine the location of sounds in space (Joris, 1996). To perform
their function, these neurons are endowed with a number of cellular specializations that allow them to fire at rates of many hundreds of
Hertz both in vivo and in vitro (Spirou et
al., 1990; Banks and Smith, 1992; Wu and Kelly, 1993; Trussell, 1999;
Taschenberger and von Gersdorff, 2000). Such cells lock their action
potentials precisely to the phase of auditory stimuli at frequencies of
up to 2000-4000 Hz or to rapid fluctuations in the amplitude of
higher-frequencies sounds (Joris and Yin, 1995; Joris, 1996). At those
frequencies at which an action potential cannot be generated to every
single stimulus, their firing pattern is characterized by alternating action potentials and failures of action potential generation (Banks
and Smith, 1992; Brew and Forsythe, 1995; Wang et al., 1998). For
example, in response to a 600 Hz stimulus, an MNTB neuron may fire at
300 Hz, locking its action potentials to every other stimulus (Wang et
al., 1998). The synaptic and electrophysiological specializations of
bushy cells and MNTB neurons ensure that the delay from a
suprathreshold stimulus to the occurrence of an action potential varies
by no more than a few tens of microseconds throughout a stimulus train
(Borst et al., 1995; Oertel, 1999; Trussel, 1999).
A major component of potassium current in MNTB neurons is a
high-threshold voltage-dependent potassium current
(IHT) that is selectively blocked by
low concentrations of tetraethylammonium (TEA) and whose properties
match those of the Kv3.1 potassium channel in heterologous expression
systems (Perney and Kaczmarek, 1991; Brew and Forsythe, 1995; Wang et
al., 1998; Grigg et al., 2000). Blockade of this current in MNTB
neurons significantly impairs their ability to fire high-frequency
trains of action potentials (Wang et al., 1998).
The Kv3.1 gene has retained a high degree of similarity
between human and rodents throughout evolution. Alternate splicing at
the 3' end of the Kv3.1 gene results in two channel isoforms that differ exclusively at their C termini (Luneau et al.,
1991). Previous work has shown that these two variants, termed Kv3.1a and Kv3.1b, share a similar expression pattern in the rat brain (Perney
et al., 1992; Weiser et al., 1995). Although both variants are present
in the same neurons, including MNTB neurons, levels of the Kv3.1b
variant increase markedly at the time of synapse formation, and this
isoform predominates in adult neurons (Perney et al., 1992; Liu and
Kaczmarek, 1998). The functional significance of such alternately
spliced channels that produce similar currents is unknown, although
there is evidence that divergent C termini may be involved in targeting
channels to different regions of the neuronal membrane (Pounce et al.,
1997; Rudy, 1999).
Previous work has shown that, in heterologous expression systems, the
Kv3.1 channel can be modulated by activation of protein kinase C, which
produces a decrease in current amplitude (Critz at al., 1993; Kanemasa
et al., 1995). We now found that regulation by this enzyme is specific
to the Kv3.1b isoform and results from phosphorylation of a single site
in the C terminus. We also compared the effects of the protein kinase
C-induced reduction of Kv3.1 current in MNTB neurons with those of
total elimination of the IHT current
through homologous recombination, using both native neurons and a
computer simulation of their firing patterns. We demonstrate that,
whereas total elimination of the Kv3.1 current in MNTB neurons severely
impairs high-frequency firing, a partial reduction of current
significantly increases both the number of action potentials generated
and their temporal fidelity at those intermediate frequencies at which
failures to generate action potentials are first detected. Our results
suggest that the transition from the Kv3.1a to the Kv3.1b isoform
during development allows MNTB neurons to modulate their firing pattern
to improve temporal fidelity at intermediate stimulus frequencies.
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Materials and Methods |
Generation of Kv3.1 mutant mice. The Kv3.1
gene was mutated by homologous recombination by a replacement vector as
previously described in 129/Sv mice (Ho et al., 1997). Briefly,
the coding region between EcoRI and MscI (35 bp
in the S2-S3 linker) was replaced with a neomycin-resistant cassette.
Identification of mutant animals was confirmed by PCR using
oligonucleotides directed against the 5' coding region (primer 5' GAA
ATC GAG AAC GTT CGA AAC GG 3') and the 35 bp recombinant sequence
(primer 5' CTA CTT CCA TTT GTC ACG TCC TG 3').
Stable expression of Kv3.1a in a Chinese hamster ovary cell
line. Chinese hamster ovary (CHO) cells with dihydrofolate
reductase thymidylate (DHFR) deficiency [CHO/DHFR(
)] were
maintained in Iscove's modified Dulbecco's medium
(Invitrogen, San Diego, CA) supplemented with 10% fetal
bovine serum, 0.1 mM hypoxanthine, and 0.01 mM thymidine and maintained in a 5%
CO2 incubator at 37°C. Cells were seeded 1 d before transfection at ~5 × 105
cells/60 mm plate. Kv3.1a expression vector (pcDNA3/Kv3.1a) was added
24 hr later to transfect CHO/DHFR() using Lipofectamine (Invitrogen). The cells were then grown in normal medium
for 48 hr to develop antibiotic resistance and subsequently exposed to geneticin (0.5 mg/ml; Invitrogen) for another 10-14 d.
The geneticin-resistant cells were subjected to single-cell sorting
using FACSIV (Becton Dickinson, Mountain View, CA) to generate
individual stable cell lines. The stable transfection of Kv3.1b into
CHO cells has been described previously (Wang et al., 1998).
Electrophysiological recordings from CHO cells. CHO/DHFR()
cells were maintained in Iscove's modified Dulbecco's medium
(Invitrogen) supplemented with 10% fetal bovine serum,
0.1 mM hypoxanthine, and 0.05 mg/ml geneticin
(Invitrogen) and maintained in a 5%
CO2 incubator at 37°C. CHO cells were grown on
coverslips 24-48 hr preceding recordings and transferred to
extracellular solution (in mM: 140 NaCl, 1.3 CaCl2, 5.4 KCl, 25 HEPES, and 33 glucose, pH 7.4)
1 hr before voltage clamping. Recordings were made as specified either
with the perforated-patch technique using nystatin or in the whole-cell
configuration using an Axopatch 1D amplifier (Axon
Instruments, Foster City, CA). The patch electrodes had a
resistance of 3-5 M
when filled with intracellular solution (in
mM: 32.5 KCl, 97.5 K-gluconate, 5 EGTA, and 10 HEPES, pH 7.2). All data were low-pass filtered at 2 kHz and digitized
using a modified digital data recorder (Instrutech, Great
Neck, NY). Data were analyzed using pClamp 6.0 software. Average data
are expressed as means ± SE. Conductance values were obtained by
dividing current by the electrochemical driving force
[IK/(Vm Ek)]. Normalized conductance-voltage
plots were obtained by normalizing conductance (G) to
maximal conductance (Gmax) and fit
using the Boltzmann isoform G = Gmax/[1 + exp ((V V1/2)/k)], where
V1/2 is the voltage at half-maximal
activation, and k is the slope factor.
Preparation of brainstem slices. Brains were rapidly removed
from postnatal 9-14 d old mice (control 129/Sv or Kv3.1 mutant mice)
or rats after decapitation and placed into ice-cold
bicarbonate-buffered artificial CSF (ACSF) (in
mM: 125 NaCl, 2.5 KCl, 26 NaHCO3, 1.25 NaH2PO4, 2 Na pyruvate, 3 myo-inositol, 10 glucose, 2 CaCl2, and 1 MgCl2,
pH 7.4) solution gassed with 95% O2-5%
CO2. The area of the brainstem containing MNTB
nuclei were cut into four to six transverse slices using a vibrotome.
The slices were incubated at 37°C for 1 hr and thereafter kept at
room temperature (22-25°C).
Electrophysiological recordings from MNTB. Recordings were
conducted on MNTB neurons as described previously (Macica and
Kaczmarek, 2001). Briefly, a slice was transferred to a recording
chamber that was continually perfused (1 ml/min) with gassed ACSF.
Whole-cell patch-clamp recordings were made from visually identified
MNTB neurons using an Axopatch 2D amplifier (Axon
Instruments). The patch electrodes had a resistance of 3-5
M when filled with intracellular solution (in
mM: 32.5 KCl, 97.5 K-gluconate, 5 EGTA, 10 HEPES, and 1 MgCl2, pH 7.2). For voltage-clamp
recordings, the extracellular calcium concentration was lowered to 0.5 mM to minimize the contribution of
calcium-activated K channels. TTX (0.5 µM) was
also included in ACSF to block sodium currents. The mean cell
capacitance was 12.0 ± 0.4 pF, with a mean series resistance of
5.3 ± 0.4 M. The compensation for series resistance was set at
least 85%, with a lag of 10 µsec. Data were low-pass filtered at 5 kHz, digitized, and acquired on-line with pClamp 6.0 software
(Axon Instruments). Total current was compared before and
after addition of activators of PKC in the presence and absence of PKC
inhibitors, and averaged data are expressed as means ± SE.
Conductance and normalized conductance values were obtained as above.
Immunoprecipitation and chemiluminescence. Stably
transfected CHO cells expressing Kv3.1a or Kv3.1b or untransfected
cells were grown to 80% confluence. Medium was removed, and cells were washed three times with ice-cold PBS. Cells were lysed with
radioimmunoprecipitation assay buffer (150 mM NaCl, 1.0% Nonidet P-40, 0.5% deoxycholate, 0.1% SDS, and 50 mM Tris, pH 8.0) containing a
protease inhibitor cocktail (Boehringer Mannheim,
Indianapolis, IN) and phosphatase inhibitors (100 µM NaF and 0.2 mM
NaVO3) and allowed to incubate on a rocking
platform for 30 min at 4°C. Lysates were spun in a microfuge for 15 min, and the supernatant was transferred to a new tube. Rat brain
membranes were prepared from whole brain homogenized in 320 mM sucrose-PBS, pH 7.4, containing a protease cocktail inhibitor and centrifuged at 1000 × g for 10 min at 4°C. The supernatant was then centrifuged at 15,000 × g for 30 min at 4°C, followed by centrifugation of the
supernatant at 105,000 × g for 1 hr at 4°C. Pellets
were reconstituted in sucrose-PBS. Lysates and membranes (brought up
to volume with PBS) were precleared with a 50% slurry aliquot of
protein A Sepharose beads, followed by incubation with the indicated
anti-Kv3.1 antibody (1:1000 dilution) at 4°C overnight. Lysates and
membranes were immunoprecipitated with protein A Sepharose beads for 2 hr at 4°C, spun, and washed three times in Triton X-100 buffer (0.1%
Triton X-100, 0.1% SDS, 300 mM NaCl, and 50 mM Tris, pH 7.5). Samples were eluted by boiling in 1× SDS-PAGE sample buffer (62.5 mM Tris, pH
6.8, 4% SDS, 10% glycerol, 0.02% bromophenol blue, and 4%
-mercaptoethanol) for 5 min. Samples were subjected to SDS-PAGE on a
7.0% gel and transferred to a polyvinylidene difluoride (PVDF)
membrane (Millipore, Bedford, MA). Peptides were visualized by
chemiluminescence. Briefly, the membrane was incubated with the Kv3.1
antibody against the C terminus at a 1:4000 dilution in antibody
diluent (1% casein and 0.04% Tween 20 in PBS, pH 7.4) for 1 hr,
washed three times, incubated with secondary antibody (1:10,000 in
diluent buffer), and washed three times. The blot was incubated with
substrate (5.5 mg of luminol, 0.28 mg of p-coumaric acid,
and 1% H2O2
-25 ml of PBS) for 1 min and briefly exposed to film.
Metabolic labeling, immunoprecipitation, and phosphoamino acid
analysis. Phosphorylation of Kv3.1 was analyzed in stably
transfected CHO cells expressing either Kv3.1a or Kv3.1b that was
metabolically labeled to equilibrium with
[32P]orthophosphate as described
previously (Macica and Kaczmarek, 2001). Cells were lysed,
immunoprecipitated, and subjected to SDS-PAGE as described above. This
gel was fixed as above and dried, and bands were visualized by
autoradiography. Phosphoamino acid analysis was also performed on
samples prepared as above and analyzed by two-dimensional
electrophoresis, as described previously (Macica and Kaczmarek,
2001).
Numerical simulations. Computer modeling was performed using
equations that have been used previously to model MNTB neurons (Wang et
al., 1998) and other auditory neurons (Perney and Kaczmarek, 1997;
Richardson and Kaczmarek, 2000). The model comprised a sodium current
INa, the Kv3.1 current
IKv3.1, a low-threshold potassium current ILT, and a leakage conductance
IL.
INa and
IL were given by the equations
INa = gNam3h(50 V) and IL = gL(63 V),
respectively. ILT and
IKv3.1 were simulated by the equations
ILT = gLT lr(80 V) and IKv3.1 = gKv3.1n3
(0.8 + 0.2p)(80 V). Evolution of
the variables m, h, l, r, n, and p were determined by Hodgkin-Huxley-like
equations as described previously (Perney and Kaczmarek, 1997).
Parameters for the sodium current were as follows:
gNa = 0.5 µS,
k
m = 76.4 msec
1,
m = 0.037 mV1,
k
m = 6.93 msec1,
m = 0.043
mV1, and
kh = 0.000533 msec1,
h = 0.0909
mV1,
kh = 7.87 msec1, and
h = 0.0691 mV1 . The leakage conductance
gL was 0.002 µS. Parameters for potassium current were obtained from direct fits to traces recorded from MNTB
neurons and Kv3.1-transfected CHO cells (Wang et al., 1998). Parameters
for the low-threshold potassium current were as follows: gLT = 0.02 µS , k1 = 1.2 msec1, 1 = 0.03512 mV1,
k1 = 0.2248 msec1, 1 = 0.0319 mV1,
kr = 0.0438 msec1,
r = 0.0053
mV1,
kr = 0.0562 msec1, and
r = 0.0047
mV1. Parameters for the Kv3.1 channel
were as follows: gHT = 0.15 µS
(control) or 0.10 µS [phorbol 12-myristate 13-acetate (PMA) treated], kn = 0.2719 msec1,
n = 0.04 mV1,
kn = 0.1974 msec1,
n = 0 mV1,
kp = 0.00713 msec1,
p = 0.1942
mV1,
kp = 0.0935 msec1, and
p = 0.0058 mV1. Numerical simulations of the
responses of the cells to external stimulation was performed using the
equation C dV/dt = INa + IKv3.1 + ILT + Iext(t), where C
is the cell capacitance (0.01 nF), and external currents
Iext(t) were presented as repeated current steps (1.4 nA, 0.25 msec) applied at frequencies from
100 to 600 Hz.
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Results |
Contribution of Kv3.1 to the firing pattern of MNTB neurons
We first tested the role of the Kv3.1 channel in MNTB neurons by
comparing the properties of MNTB neurons in 9- to 14-d-old brainstem
slices from wild-type mice with those in which the Kv3.1 gene had been deleted by homologous recombination (Ho et al., 1997). As
described previously, wild-type mice express a high-threshold potassium
current IHT whose properties closely
match those of Kv3.1 in transfected cell lines (Wang et al., 1998).
This current can be isolated by stepping to positive potentials from a
holding potential of 40 mV, at which potential the low-threshold
component of total outward current in these neurons is inactivated
(Brew and Forsythe, 1995; Wang et al., 1998). This current can be
substantially inhibited by extracellular application of 1 mM TEA ions, consistent with the
IC50 of 250 µM for the
Kv3.1 channel (Kanemasa et al., 1995; Wang et al., 1998; Rudy,
1999) (Fig.
1a,b).
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Figure 1.
Representative traces comparing native
high-threshold current from a 14 d wild-type MNTB neuron with the
high-threshold current from a 14 d Kv3.1 mutant MNTB neuron.
a, b, Outward currents evoked by stepping
from a holding potential of 40 mV for 2 min (to ensure complete
inactivation of low-threshold current) to test potentials from 80 to
+40 mV in 20 mV increments in wild-type mice before and after treatment
with 1 mM TEA or in Kv3.1 mutant mice
(c). d, e,
Representative recording from an MNTB neuron in response to brief
current injections (2 nA, 0.3 msec) at three different test frequencies
(100-300 Hz) in wild-type mice before and after treatment with 1 mM TEA or in Kv3.1 mutant mice
(f). Bars denote failure
to evoke an action potential in response to a stimulus. Failure was
defined as a membrane depolarization to less than 10 mV in response
to a current injection. Expanded traces below compare a
successful action potential with failures, which showed little
regenerative response.
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When recordings were made in MNTB neurons from Kv3.1/ mice, the
current evoked by depolarizing commands from 40 mV current was
reduced by >90%, indicating that the
IHT current had been eliminated (Fig.
1c). The remaining ~10% high-threshold current was
blocked by 1 mM TEA. In contrast, the
low-threshold currents evoked by stepping from a holding potential of
80 mV could still readily be recorded in the Kv3.1/ mice (data
not shown). The low-threshold current, which is TEA insensitive in
wild-type mouse, however, displays sensitivity to 1 mM TEA, suggesting a compensatory increase in a
TEA-sensitive low-threshold current in these mice (data not shown). It
is possible that the afterhyperpolarization in the Kv3.1/ mice
reflects a compensatory increase in low-threshold current in these
animals. Combined with previous work demonstrating the loss of Kv3.1
mRNA and protein in the Kv3.1/ mice (Ho et al., 1997), our findings
strongly support the identification of the
IHT current recorded at the somata of
MNTB neurons with the Kv3.1 channel.
To test the impact of knock-out of the Kv3.1 gene on the
firing properties of MNTB neurons, neurons were stimulated with trains of brief current pulses (0.3 msec, 2 nA) at frequencies ranging from
100 to 300 Hz (Fig. 1d). As described previously,
wild-type MNTB neurons faithfully follow stimulus frequencies up to 300 Hz (Wang et al., 1998). In the presence of extracellular TEA (1 mM) a normal pattern of action potentials is
evoked at the lower frequencies (100-200 Hz), but a progressive loss
of full action potentials occurs during a train at 300 Hz and at higher
frequencies (Fig. 1e). A similar, but more severe, deficit
occurs in MNTB neurons from Kv3.1/ mice. These can follow
stimulation at 100 Hz, but attenuation of action potentials is already
evident even at 200 Hz. At 300 Hz and at all higher frequencies, only a
single action potential is evoked at the start of the train (Fig.
1f). This complete loss of response at higher
frequencies exactly matches that predicted in numerical simulations for
elimination of the IHT current (Wang
et al., 1998).
The Kv3.1 isoforms differ in their response to activation of
protein kinase C
In transfected cells, the amplitude of Kv3.1 current is known to
be regulated by activators of protein kinase C, attributed to a
decrease in single-channel open probability (Critz et al., 1993;
Kanemasa et al., 1995). There exist two isoforms of the Kv3.1 channel,
Kv3.1a and Kv3.1b, which arise by alternate splicing of the
Kv3.1 gene. These differ in the number of consensus sites for phosphorylation by protein kinase C. The longer Kv3.1b isoform has
two additional consensus sites in the C terminus that are absent in
Kv3.1a. Both isoforms are coexpressed in the same neurons, with Kv3.1b
predominating in the mature nervous system (Perney et al., 1992; Weiser
et al., 1995; Rudy, 1999). To determine the physiological consequences
of modulation by protein kinase C, we compared the electrophysiological
properties of the two isoforms in transfected cells and of the native
IHT current in MNTB neurons.
We first compared the basal electrophysiological properties of the two
isoforms. Currents were evoked in CHO cells stably transfected with
either Kv3.1a or Kv3.1b by depolarizations to test potentials between
80 and 60 mV (Fig. 2a). In
some but not all experiments, a transient peak that decreased slightly
to a steady-state value was seen at positive potentials at the
beginning of the pulse for both Kv3.1a and Kv3.1b, a finding reported
previously for Kv3.1b (Rettig et al., 1992; Critz et al., 1993;
Kanemasa et al., 1995; Rudy, 1999). The conductance-voltage
relationships were fit by Boltzmann isotherms with a midpoint of
activation of 17.3 ± 1.26 mV (n = 9) versus
20.8 ± 1.60 mV (n = 9) for Kv3.1a and Kv3.1b,
respectively (Fig. 2b). The 10-90% rise times for maximal
activation at 60 mV were 1.25 ± 0.16 msec (n = 9)
versus 1.22 ± 0.09 msec, (n = 9) respectively.
Deactivation kinetics were obtained from tail currents recorded after a
100 msec depolarizing pulse to +40 mV, followed by membrane potential
repolarization to 40mV. These were fit by a single exponential and
yielded time constants of 2.38 ± 0.14 msec (n = 18) and 2.20 ± 0.12 msec (n = 10), respectively.
In addition, both Kv3.1a and Kv3.1b were inhibited to a similar degree
by 1 mM TEA (87 ± 1.5%, n = 3 vs 82 ± 5.1%, n = 12) (Fig.
2c).
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Figure 2.
Comparison of Kv3.1 current recorded from CHO
cells stably transfected with Kv3.1a or Kv3.1b. a,
Whole-cell current was evoked by depolarizing the membrane from a
holding potential of 80 to +60 mV in 20 mV increments.
b, Normalized conductance-voltage relationship for
Kv3.1a versus Kv3.1b. Conductance values
(G) were obtained as described in
Materials and Methods. c, Sensitivity of Kv3.1a or
Kv3.1b to 1 mM TEA. Currents were evoked as described in
a.
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Although the biophysical properties of Kv3.1a and Kv3.1b appear
indistinguishable under basal conditions, their response to 100 nM PMA, an activator of protein kinase C, was very
different. Kv3.1a or Kv3.1b currents were recorded from
nystatin-perforated patches before and after exposure to 100 nM PMA (n = 9) (Fig. 3a,b). PMA produced
a significant reduction of Kv3.1b current (32.4 ± 4.3%
inhibition), which was maximal by 10-15 min (Fig. 4). 4
-PMA, an analog of PMA that does
not activate protein kinase C, did not significantly affect Kv3.1b
current (Fig. 4). In contrast, Kv3.1a current amplitude was not
significantly affected by PMA (2.26 ± 1.7% inhibition) (Figs.
3a, 4). No effect of PMA was detected on the kinetics (data
not shown) or the voltage dependence of activation of either isoform
(midpoint of activation, 20.3 ± 1.3 mV during control period vs
19.1 ± 1.6 mV after PMA treatment in nystatin-perforated
patches).
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Figure 3.
Effect of 100 nM PMA on Kv3.1 current.
a, Whole-cell currents evoked from CHO cells stably
expressing Kv3.1a from a holding potential of 70 mV to test
potentials of 80 to +60 mV in 20 mV increments (left)
and corresponding current-voltage relationship of evoked currents
(right) before and after PMA treatment.
b, Whole-cell currents evoked from CHO cells stably
expressing Kv3.1b (left) and current-voltage
relationship of evoked currents. c, Whole-cell currents
evoked from CHO cells stably expressing Kv3.1b mutant S503A
(left) and current-voltage relationship of evoked
currents.
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Figure 4.
Time course of the effect of 100 nM
PMA on Kv3.1 current amplitude. Outward current evoked from a holding
potential of 70 mV in Kv3.1-transfected cells or from a holding
potential of 40 mV in MNTB neurons to a test potential of +40 mV was
monitored in perforated patches every 1 min in response to treatment
with exogenous PMA in Kv3.1a-transfected cells (filled
circles), in Kv3.1b-transfected cells (filled
squares), or in MNTB neurons (filled
triangles). The effect of the inactive phorbol ester 4-PMA
was also tested on Kv3.1b-transfected cells (open
squares) and MNTB neurons (open
triangles).
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Phosphorylation of Kv3.1 channel proteins
To determine whether the actions of activators of protein kinase C
on Kv3.1b currents result from the direct phosphorylation of the Kv3.1b
protein, CHO cells stably expressing either Kv3.1a or Kv3.1b were
radiolabeled to equilibrium with
[32P]orthophosphate and were then
stimulated for 15 min with 100 nM PMA. Immunoprecipitation
revealed substantial basal incorporation of
32P into both channel proteins, as well as
stimulated incorporation in the presence of PMA (Fig.
5a). Incorporation could be
eliminated by treatment of the immunoprecipitated phosphoprotein with
alkaline phosphatase. To determine the identity of the amino acids into which 32P was incorporated, the
immunoprecipitates were then subjected to phosphoamino acid analysis.
Radioactivity comigrating with unlabeled phosphoserine, but not
phosphothreonine or phosphotyrosine, was detected after acid hydrolysis
of 32P-labeled Kv3.1 (Fig. 5b).
These results indicate that, of the putative consensus sites for
phosphorylation, only those containing serine residues are
phosphorylated.
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Figure 5.
In vivo phosphorylation and
phosphoamino acid analysis of Kv3.1 in CHO cells. a, CHO
cells expressing Kv3.1a or Kv3.1b were radiolabeled with
[32P]orthophosphate to equilibrium, stimulated
with or without 100 nM PMA for 15 min, and lysed. Lysates
were immunoprecipitated with Kv3.1 antibody (Kv3.1a, lanes
1 and 2, with and without PMA, respectively or
Kv3.1b, lanes 4 and 5, with and without
PMA, respectively) and resolved as outlined in Materials and Methods.
An additional 32P-labeled Kv3.1a or Kv3.1b
immunoprecipitate was treated with calf intestinal alkaline phosphatase
for 1 hr at 37°C (lanes 3 and 6,
respectively). b, Phosphoamino acid analysis of the
Kv3.1a or Kv3.1b channel protein obtained from lysates and
immunoprecipitated and electrophoresed as above. The gel was
transferred to a PVDF membrane, and the Kv3.1 band was visualized by
autoradiography. The excised protein was subjected to phosphoamino acid
analysis as outlined in Materials and Methods and visualized by
ninhydrin staining (top), and standard phosphoamino
acids were visualized by autoradiography (bottom).
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Protein kinase C acts at serine 503 of Kv3.1b
Kv3.1b has 11 consensus sites for PKC-mediated phosphorylation,
two of which are absent from Kv3.1a as a result of the divergent C
terminus. Only one of these (S503), however, is a serine site. The
phosphoamino acid analysis suggests, therefore, that this is the only
consensus protein kinase C site that differs between the two isoforms.
To test the hypothesis that this unique site is responsible for
response of Kv3.1b to activation of protein kinase C, a mutant Kv3.1b
channel was constructed in which this serine was mutated to alanine.
When this mutation (S503A) was stably expressed in CHO cells, the
currents appeared identical to those of wild-type Kv3.1 but were
completely insensitive to PMA treatment (n = 6) (Fig.
3c).
The Kv3.1b channel subunit predominates in mature neurons
To identify native Kv3.1 protein isoforms, membranes were prepared
from adult rat brain homogenates or from CHO cells stably transfected
with either isoform. These were immunoprecipitated with antibodies
against either the N terminus, which recognizes both isoforms, or the
Kv3.1b C terminus, which recognizes only Kv3.1b (Perney and Kaczmarek,
1991) (Fig. 6a).
Immunoprecipitated Kv3.1a and Kv3.1b in CHO cells had mobilities
corresponding to ~98 and 110 kDa, respectively (Fig. 6a,
lanes 1-3). Immunoprecipitation in both cell lines also
yielded additional bands corresponding to the predicted molecular
weights of the unglycosylated forms of the channel proteins (85 and 80 kDa, respectively). In support of this interpretation, the size of the
in vitro translated product of the Kv3.1 channels in the
absence of membranes corresponded precisely to the
Mr of the lower bands (data not shown). The
predominant isoform in brain homogenates is Kv3.1b (Fig. 6a,
lane 4), consistent with the dominant expression
pattern of Kv3.1 mRNA transcripts in adult animals (Perney et al.,
1992). Although the expression of both isoforms in the same cells
(Perney et al., 1992; Weiser et al., 1995) suggests that they could
form heteromultimers in vivo, Kv3.1a protein could not be
detected in immunoprecipitates from rat brain membranes using the
C-terminus antibody, which recognizes only the Kv3.1 b channel protein
(Fig. 6a, lane 5).
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Figure 6.
Molecular identity and effect of 100 nM PMA on native Kv3.1 current. a,
Coimmunoprecipitation of Kv3.1a and Kv3.1b in brain homogenates or in
stably transfected CHO cells. Lane 1, Kv3.1a/CHO
with N-terminal antibody; lane 2, Kv3.1b/CHO with
N-terminal antibody; lane 3, Kv3.1b/CHO with C-terminal
antibody; lane 4, rat brain membranes with N-terminal
antibody; lane 5, rat brain membranes with C-terminal
antibody. b, Whole-cell currents evoked from a 13 d
MNTB neuron from a holding potential of 40 mV to test potentials of
80 to +60 mV (left) and current-voltage relationship
of evoked currents before and after PMA treatment.
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Effect of phorbol ester treatment on high-threshold current in
MNTB neurons
Having confirmed the molecular identity of the native
high-threshold current as Kv3.1, we next tested the effect of PMA on potassium currents and the firing pattern of MNTB neurons. In 9 of 12 experiments, the amplitude of the high-threshold component of current
evoked from a holding potential of 40 mV was reduced by 44.8 ± 2.17% in response to 100 nM PMA (Fig. 6b). The
time course of inhibition closely matched that for the inhibition of Kv3.1b by PMA in transfected cells. Moreover, the inactive phorbol ester 4-PMA had no effect on MNTB current amplitude (Fig. 4). In 3 of the 12 experiments conducted, however, there was very little effect
of PMA on IHT current (4.50 ± 0.76%). Finally, PMA had little or no effect on the low-threshold
component of current, obtained by subtracting the high-threshold
component of current from the total outward current at a test potential
of 20 mV, in which a majority of the total outward current is of the
low-threshold type (Fig. 7a).
Consistent with this finding was the observation that the spike
threshold is unaltered and that MNTB neurons fire a single action
potential in response to a sustained current injection both before and
after PMA treatment (Fig. 7b). This limited depolarization has been shown to be mediated by the activation of the low-threshold current, which results in the lowering of the input resistance and a
shortening of membrane time constants in the depolarizing voltage
range, thus preventing repetitive firing in response to a sustained
current injection (Wu and Kelly, 1993; Brew and Forsythe, 1995; Wang et
al., 1998).
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Figure 7.
Effect of 100 nM PMA on low-threshold
current from an MNTB neuron. a, Low-threshold current
was obtained by subtracting the high-threshold component of outward
current evoked from a holding potential of 40 mV to a test potential
of 20 mV from total outward current evoked from a holding potential
of 70 mV to a test potential of 20 mV
(ILT = ITOT IHT) before and after PMA treatment
(n = 8). b, Current-clamp recording
from an MNTB neuron in response to a series of 100 msec current
injections ranging from 50 to 150 pA before and after PMA treatment
(n = 4).
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Additional analysis of the action of PMA on the
IHT current also showed that its
effects closely matched those for Kv3.1 in CHO cells and that PMA
produced no change in the activation or deactivation kinetics in any
experiment. Native IHT currents had 10-90% rise times for maximal activation at 60 mV of 1.41 ± 0.18 msec (n = 8) during the control period versus
1.12 ± 0.15 msec (n = 8) after 15 min PMA
treatment. Deactivation kinetics of macroscopic currents were obtained
by tail currents generated by a 100 msec depolarizing pulse to +40 mV,
followed by membrane potential repolarization to test potentials
between 100 and 20 mV. Deactivation kinetics were fit by a single
exponential and yielded time constants of 2.35 ± 0.25 (n = 9) during the control period and 2.24 ± 0.28 (n = 8) at 40 mV after treatment of 15 min PMA. Like
the cloned Kv3.1b channel, there was also no effect on the voltage
dependence of activation of IHT
(midpoint of activation, 16.6 ± 1.5 mV during control period vs
17.8 ± 1.0 mV after PMA).
Other parameters that were measured before and after PMA treatment
included the mean slope of the rising phase of action potentials, which
remained unchanged (before PMA, 171.8 ± 16.6 mV/msec; after PMA,
189.3 ± 13.8 mV/msec). In addition, the peak voltage reached by
action potentials remained unchanged (before PMA, +28.8 ± 0.4 mV;
after PMA, +30.6 ± 0.8 mV), and the mean resting potential remained unchanged (before PMA, 64.2 ± 1.12 mV; after PMA,
65.2 ± 0.87 mV). The findings argue that a change in sodium
currents is unlikely to contribute to the observed effects.
Effect of phorbol ester on firing properties of MNTB neurons
In contrast to the complete loss of Kv3.1 current produced by
knock-out of the Kv3.1 gene, the partial suppression of Kv3.1b current
by protein kinase C might be expected to produce smaller changes in
firing characteristics and contribute to the fine-tuning of auditory
information processing. We therefore examined the effect of 100 nM PMA on the response of MNTB neurons to different frequencies of stimulation. To avoid the presynaptic effects of PMA at
the MNTB synapse (Hori et al., 1999), we used direct current stimulation of MNTB neurons. At frequencies up to 300 Hz, at which MNTB
neurons fire action potentials in response to every stimulus pulse,
there was no effect of PMA on the ability of the cells to follow
stimulation. At slightly higher frequencies, however, action potentials
are not generated in response to every stimulus, and the firing pattern
is characterized by intermittent failures separated by brief trains of
action potentials. For example, in the cell shown in Figure
8a, the control response at
400 Hz consists of groups of two or three consecutive action potentials
separated by failures to reach threshold for spike initiation. At these intermediate frequencies at which failures are first detected, exposure
of MNTB neurons to PMA reduced the number of failures. For example, in
the cell shown in Figure 8a, PMA produced a small reduction
in the number of failures in response to stimulation.
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Figure 8.
Effect of PMA treatment on firing properties of an
MNTB neuron (13 d old) in response to different frequencies of
stimulation (n = 6). a, Plots of the
delay from the onset of the stimulus pulse to the peak of the action
potential before (Control) and 15 min after
(PMA) treatment with 100 nM PMA.
Arrows denote failure to evoke an action potential in
response to a stimulus. Failure was defined as a membrane
depolarization to less than 10 mV in response to a current injection
(one that has no detectable regenerative component). b,
Superimposed action potentials in response to 100, 300, and 400 Hz
stimulation. Failures were omitted from the superimposed
traces.
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More striking than the effect of PMA on the number of failures was its
effect on the timing of action potentials. To examine differences in
the timing of the evoked action potentials, we superimposed successive
action potentials locked to the stimulus (Fig. 8b). In
addition, we plotted the change in the delay from the onset of the
stimulus to the peak of the action potential during the stimulus
trains. At frequencies up to 300 Hz at which all stimuli evoked action
potentials, the latency from the onset of the stimulus pulse to the
peak of the action potential was invariant, as seen by the
superposition of the response to consecutive current pulses. The
occurrence of failures, which occurs at higher frequencies, however,
substantially disrupts the timing of the action potentials. The latency
from onset of the current pulse to the peak of the action potential was
found to vary by 500 µsec or more in the burst of action potentials
separated by failures. Exposure of MNTB neurons to PMA, however, was
found to reduce significantly the variance of the latency at 400 Hz
[at 400 Hz, control delay of 0.99 ± 0.17 (SD) msec; after PMA,
delay of 0.85 ± 0.11 msec;
p(delay) < 0.0001;
p(variance) < 0.015;
n = 46 action potentials] (Fig. 8b).
Because it is certain that, in addition to their effects on Kv3.1
currents, activators of protein kinase C have a variety of other
actions on MNTB neurons, we performed numerical simulations to compare
the effects of a partial reduction of Kv3.1 current with those of PMA.
We used a model that had been used previously to predict the firing
pattern of MNTB neurons and that incorporates the amplitudes and
kinetics of currents measured directly in these cells (Wang et al.,
1998). The response of the model neurons to current pulses at different
frequencies were tested with control conditions (150 nS Kv3.1
conductance) and in response to altering the level of Kv3.1 current to
a similar degree as in PMA-treated MNTB neurons (100 nS Kv3.1
conductance) (Fig. 9). As with the native
neurons, the model neuron was able to respond to each stimulus pulse up
to 300 Hz, and the timing of action potentials was uniform throughout a
maintained stimulus train, with either level of Kv3.1 current. However,
as the stimulus frequency was increased, a critical frequency was
reached at which failures began to occur (350 Hz with 150 nS Kv3.1 in
Fig. 9a). At this point, the timing of the action potentials
was also disrupted, with a progressive increase in the latency of the
response with consecutive action potentials. At "intermediate"
stimulus frequencies above this critical frequency, the latency during
a train of action potentials could vary by >1 msec. When the level of
Kv3.1 current was reduced by 33% at these frequencies, the failures
were reduced or eliminated, and the timing of the action potentials was
restored (Fig. 9b). As the stimulus frequency was increased,
however, the effects of the reduction of Kv3.1 were less apparent (410 Hz in Fig. 9), and, at higher frequencies, the ability of the model
neurons to respond was attenuated by the reduction in Kv3.1 current
(data not shown). The simulation studies show that a reduction in Kv3.1 current alone is predicted to decrease the number of failures and to
significantly reduce the variance of the timing of action potentials at
intermediate frequencies of stimulation.
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Figure 9.
Model of an MNTB neuron in response to different
frequencies of stimulation. a, Plots of the delay from
the onset of the stimulus pulse to the peak of the action potential
under control conditions (150 nS Kv3.1 conductance) and under
conditions in which the level of Kv3.1 current amplitude is reduced to
a similar degree as in PMA-treated neurons (100 nS Kv3.1 conductance).
Arrows denote failure to evoke an action potential in
response to a stimulus. Failure was defined as a membrane
depolarization to less than 10 mV in response to a current injection.
b, Superimposed action potentials in response to 100, 350, 360, or 410 Hz stimulation. Failures were omitted from the
superimposed traces.
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Discussion |
Kv3.1 is critical for the preservation of timing information
Within the auditory brainstem, the Kv3.1 channel is expressed at
high levels in spherical and globular bushy cells of the cochlear
nucleus (Perney and Kaczmarek, 1997) and in principal neurons of the
MNTB (Li et al., 2001), which receive a secure synaptic input from the
globular bushy cells (Smith et al., 1991). The large calyx of Held
synaptic ending from globular bushy cells onto the somata of MNTB
neurons is specialized for temporally invariant transmission of
excitatory inputs (Morest, 1968; Borst et al., 1995; Joris, 1996;
Trussell, 1999), and evidence suggests that MNTB neurons faithfully
transmit temporal information from globular bushy cells (Smith et al.,
1998). Many globular bushy cells have spontaneous firing rates of over
100 Hz and, when driven by sounds, attain firing frequencies of
500-600 Hz (Rhode and Smith, 1986; Spirou et al., 1990). Our findings
suggest that the Kv3.1 potassium channel is required for the normal
ability of these cells to follow such high-frequency stimulation.
MNTB neurons provide an inhibitory input to the lateral superior olive
and participate in a pathway that detects interaural intensity
differences in high-frequency sounds (Joris and Yin, 1995, 1998; Tollin
and Yin, 2002). They also project to other auditory nuclei, including
the medial superior olive, which detects interaural timing differences
in lower-frequency sounds. The characteristic frequencies of a
population of globular bushy cells, which provide the excitatory input
to the MNTB, lie within the range at which phase-locking occurs (<4000
Hz), and experiments with cats have shown that these cells have the
ability to lock their action potentials very precisely to the phase of
auditory stimuli at these frequencies (Smith et al., 1991).
Nevertheless, the majority of these neurons, as well as their MNTB
targets, have characteristic frequencies >4000 Hz (Guinan et al.,
1972; Smith et al., 1991, 1998), and neurons are incapable of phase
locking to such higher frequencies. Neurons with high characteristic
frequencies, however, also respond to lower sound frequencies, and
their ability to phase lock at these lower frequencies is even enhanced
over that of cells with lower characteristic frequencies (Joris et al.,
1994). Our present results suggest that direct phosphorylation of the
Kv3.1 channel by protein kinase C provides a potential mechanism that
can adjust the accuracy of timing of the response of MNTB neurons. Such
adjustments of timing could occur either at frequencies close to the
characteristic frequency or when a neuron is driven at quite different
frequencies. Indeed, it has been proposed that the pathway from the
globular bushy cells to the lateral superior olive via the MNTB
comprises a circuit that can determine timing differences in
high-frequency sounds that are amplitude modulated at lower frequencies
(Joris and Yin, 1995; Joris, 1996).
Because the effects of PKC activation on the amplitude of Kv3.1 current
occur over a period of several minutes, such modulation could reflect a
slow adaptation to the auditory environment. Nevertheless, although the
pathways that lead to the regulation of protein kinase C in MNTB
neurons remains to be defined, it is likely that receptor-mediated activation is more rapid than pharmacological activation and that modulation could occur on a faster time scale.
The Kv3.1b isoform predominates in the principal neurons of
the MNTB
The simplest interpretation of the finding that deletion of the
Kv3.1 gene results in the near total elimination of the high-threshold IHT current is that the
IHT channel represents a homomultimer of Kv3.1 subunits. In addition to Kv3.1, MNTB neurons express mRNA for
Kv3.3, another Shaw subfamily channel. In contrast to Kv3.1,
Kv3.3 produces potassium currents with variable inactivation rates
dependent on the heterologous expression system in which the gene is
expressed (Rudy, 1999). The IHT
current is, however, noninactivating, and its kinetics very closely
match those of Kv3.1 (Brew and Forsythe, 1995; Wang et al., 1998).
Nevertheless, the small amount of residual high-threshold TEA-sensitive
current remaining in Kv3.1/ mice may also represent Kv3.3 current
or some other unidentified potassium channel.
We found that Kv3.1a and Kv3.1b, the two channel subunits that are
generated by the Kv3.1 gene, produce indistinguishable basal currents
and that both channel proteins are substrates for phosphorylation, but
that the two isoforms are differentially modulated by protein kinase C. In particular, phosphorylation of the consensus protein kinase site at
serine 503 of Kv3.1b produces a decrease in current for this isoform.
This is consistent with previous observations that activators of
protein kinase C produce a decrease in channel open probability in
Kv3.1b-transfected cells (Kanemasa et al., 1995).
Nevertheless, because activation of this enzyme produces little or
no change in the voltage dependence or kinetic behavior of the
macroscopic currents, we cannot eliminate the possibility that a
proportion of channels becomes silent during phosphorylation, as would
occur if phosphorylation at serine 503 allowed them to interact with an
endogenous inhibitor.
In situ hybridization and RNase protection assays indicate
that the regional expression of both Kv3.1 isoforms overlaps in all
brain areas (Perney et al., 1992). The Kv3.1a transcript predominates early in development and can be detected as early as embryonic day 17. There is a pronounced increase in the level of the Kv3.1b transcript
from postnatal day 8 to postnatal day 14, the major period of
synaptogenesis, and Kv3.1b becomes the major isoform in the mature
brain, although the Kv3.1a transcript also persist into adulthood
(Perney et al., 1992; Liu and Kaczmarek, 1998). In the cerebellum, in
which both splice variants are expressed, it has been shown that the
levels of the two variants are regulated by distinct mechanisms during
development (Weiser et al., 1995; Liu and Kaczmarek, 1998).
It has been suggested that the C terminus of Kv3.1a, which diverges
from Kv3.1b in the last 10 amino acids, plays a role in targeting
heteromultimers of Kv3.1a and Kv3.1b to axons and terminals. Although
we did not find evidence of heteromultimerization between Kv3.1a and
Kv3.1b by coimmunoprecipitation from whole-brain homogenates, we cannot
eliminate the possibility that Kv3.1b heteromultimerizes with Kv3.1a in
certain neuronal populations (Rudy, 1999).
PKC-mediated phosphorylation of Kv3.1 improves timing at
intermediate frequencies
A high level of basal phosphorylation of Kv3.1 has been
demonstrated previously and can be attributed primarily to the
actions of casein kinase 2 (Macica and Kaczmarek, 2001). Our present
data suggest that the switch from to Kv3.1a to Kv3.1b during
development permits the IHT current of
MNTB neurons to be modulated by protein kinase C, after synaptic
transmission has been established. Activation of this enzyme influences
the amplitude of the IHT current with no apparent change in voltage dependence or kinetics. Genetic knock-out, pharmacological, and computer modeling studies all indicate
that a decrease in IHT current impairs
the ability of the neurons to follow very-high-frequency stimulation.
Nevertheless, a partial decrease in
IHT current significantly improves the
fidelity of firing and the timing of action potentials at those
intermediate frequencies at which stimulation produces bursts of two or
more action potentials interrupted by failures. Under these conditions, there is a progressive build up of inhibitory potassium conductance (both IHT and
ILT) during the burst, resulting in a
progressive delay in the occurrence of action potentials. This delay
can reach hundreds of microseconds, a condition that would preclude
computation of small timing differences by the auditory brainstem
circuits. A decrease in IHT current
decreases the inhibitory conductance, generating additional action
potentials and restoring more uniform spike latencies. At high-stimulus
frequencies at which single action potentials are separated by
failures, however, a decrease in IHT
does not improve responses.
The biophysical characteristics of Kv3.1, particularly its activation
only at positive potentials, make it particularly suitable for
modulation of fidelity of propagation through the MNTB. In addition to
simulating the effects of small changes in Kv3.1 current, we modeled
the actions of decreases in the low-threshold potassium current or of
increases in sodium current. Although both of these manipulations can
restore one-to-one firing at intermediate frequencies of stimulation,
they render the cells more likely to fire spontaneous action potentials
and to generate more than one action potential in response to
depolarizing currents, changes that would degrade auditory information.
Nevertheless, although we did not find any modulation of
ILT by PKC, it is probable that
channels other than Kv3.1 are also subject to modulation in MNTB neurons.
Each individual auditory nerve fiber, neuron of the cochlear nucleus,
or principal neuron of the MNTB can be assigned a characteristic frequency, which represents that frequency of sound for which the
neuron has the lowest threshold. Neurons with different characteristic frequencies are organized tonotopically within their nuclei, reflecting their innervation by fibers originating in different regions of the
cochlea. At higher sound intensities, however, MNTB neurons respond
over a wider range of frequencies (Joris et al., 1994). Modulation of
potassium conductances may provide one mechanism for adjusting the
firing pattern of a neuron so that it can accurately follow a specific
pattern of auditory stimulation. Although the pathways that lead to the
regulation of protein kinase C in MNTB neurons remains to be defined,
modulation of Kv3.1 by PKC may provide one mechanism for fine-tuning
the frequency-dependent responses of MNTB neurons to auditory stimuli.
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FOOTNOTES |
Received May 13, 2002; revised Nov. 25, 2002; accepted Nov. 26, 2002.
This work was supported by National Institutes of Health Grant DC-01919
(L.K.K.) and National Research Service Award Fellowship MH12257-02
(C.M.M.). We thank Donata Oertel for valuable comments on this manuscript.
Correspondence should be addressed to Leonard K. Kaczmarek, Department
of Pharmacology, Yale University School of Medicine, 333 Cedar Street,
New Haven, CT 06520. E-mail: leonard.kaczmarek{at}yale.edu.
| |
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TOP
ABSTRACT
Introduction
