§
From the * Department of Anesthesiology, and Department of Physiology, School of Medicine, University of California, Los Angeles,
Los Angeles, California 90095-1778; and § Conicet, Buenos Aires, Argentina 1033
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ABSTRACT |
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Ca2+ currents recorded from Xenopus oocytes expressing only the 1C pore-forming subunit of the cardiac
Ca2+ channel show Ca2+-dependent inactivation with a single exponential decay. This current-dependent inactivation is
not detected for inward Ba2+ currents in external Ba2+. Facilitation of pore opening speeds up the Ca2+-dependent inactivation process and makes evident an initial fast rate of decay. Facilitation can be achieved by (a) coexpression of the
2a
subunit with the
1C subunit, or (b) addition of saturating Bay K 8644 (
) concentration to
1C channels. The addition of Bay K 8644 (
) to
1C
2a channels makes both rates of inactivation faster. All these maneuvers do not induce inactivation
in Ba2+ currents in our expression system. These results support the hypothesis of a mechanism for the Ca2+-dependent
inactivation process that is sensitive to both Ca2+ flux (single channel amplitude) and open probability. We conclude that
the Ca2+ site for inactivation is in the
1C pore-forming subunit and we propose a kinetic model to account for the main
features of
1C
2a Ca2+ currents.
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INTRODUCTION |
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Regulation of Ca2+ currents by Ca2+ influx includes a
negative feedback mechanism that inactivates the current itself when Ca2+ is the charge carrier. Currents
elicited by depolarizing steps show a fast activating
phase followed by a Ca2+-dependent inactivating phase.
This feature has been extensively studied in native
channels (Eckert and Chad, 1984; Chad, 1989
; Gutnick
et al., 1989
; Kostyuk, 1992
; Shirokov at el., 1993) and has been recently demonstrated in cloned channels
(Neely et al., 1994
; Zong et al., 1996; de Leon et al.,
1995
). It has been shown that Ca2+ chelators can reduce the efficiency of the inactivation process (Imredy
and Yue, 1992
; Haack and Rosenberg, 1994
) and that
the Ca2+ influx through a channel can contribute to
the inactivation of adjacent channels (cross talk) (Mazzanti et al., 1991
; Imredy and Yue, 1992
; Galli et al.,
1994
). These results suggested the presence of a specific Ca2+ site on the intracellular face of the channel
protein (Huang et al., 1989
). Two questions emerge:
(a) Is the
1C pore-forming subunit alone capable of
Ca2+-dependent inactivation, or, on the contrary, is the
accessory
2a subunit required (Neely et al., 1994
; Zong
et al., 1996)? (b) Is this inactivating process related to
intracellular Ca2+ build-up (Chad et al., 1984
; Mazzanti
et al., 1991
), or does Ca2+ entry through a single channel inactivate the same channel by a Ca2+ regulatory
site located deep inside the pore (Yue et al., 1990
)?
To address these questions, we performed whole cell
experiments with the cut-open oocyte Vaseline gap
technique (Stefani et al., 1994) on Xenopus oocytes expressing the cloned
1C subunit of the rabbit cardiac
Ca2+ channel, with and without the accessory
2a subunit (Neely et al., 1994
). Ca2+ and Ba2+ currents were
recorded in oocytes after the intracellular injection of
the fast Ca2+ chelating agent Na4-BAPTA (1,2-bis(o-aminophenoxy)-ethane-N,N,N',N'-tetraacetate, Kon = 6 × 108 M
1 s
1) to prevent contaminant Ca2+-activated Cl
currents (Neely et al., 1994
). The action of the dihydropyridine (DHP)1 agonist Bay K 8644 (
) on the inactivation rates was also investigated, since this agent increases the size of the macroscopic current by changing
the channel open probability without significantly changing the single channel amplitude (Hess et al.,
1984
). In this respect, the effect of Bay K 8644 (
)
would mimic the effect of the
2a subunit.
We found that Ca2+ currents from the 1C subunit expressed alone can inactivate in a Ca2+-dependent manner. The single exponential fits to these currents have
time constants that decrease when the Ca2+ concentration is increased. The coexpression of the
2a subunit makes evident a double exponential decay with a faster
time course and with rates that are Ca2+ dependent.
Similarly, the addition of saturating concentrations of
Bay K 8644 (
) to
1C channels induces the appearance of the fast rate of Ca2+-dependent inactivation.
These results confirm the view that the Ca2+ binding
site for the inactivation is part of the pore-forming
1C
subunit (Neely et al., 1994
; de Leon et al., 1995
; Zhou
et al., 1997
) and is located in a region very close to the
inner mouth pore, within a microdomain where the local Ca2+ concentration can reach its steady state in a
few microseconds. Based on the fact that the rates of
Ca2+-dependent inactivation are sensitive to both Ca2+
flux through the channel (single channel current) and
open probability, we propose a kinetic model for the
Ca2+-dependent inactivation process in
1C
2a channels.
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MATERIALS AND METHODS |
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RNA Synthesis and Oocyte Injection
The plasmids containing cDNA fragments encoding the cardiac
1C and
2a subunits were digested with HindIII (Wei et al.,
1991
). The linearized templates were treated with 2 µg proteinase K and 0.5% SDS at 37°C for 30 min, and then twice extracted
with phenol/chloroform, precipitated with ethanol, and resuspended in distilled water to a final concentration of 0.5 µg/µl.
The cRNAs were transcribed from 0.5 µg of linearized DNA template at 37°C with 10 U of T7 RNA polymerase (Boehringer Mannheim Biochemicals, Indianapolis, IN), in a volume of 25 µl containing 40 mM Tris-HCl (pH 7.2), 6 mM MgCl2, 10 mM dithiothreitol, 0.4 mM each of ATP, GTP, CTP, and UTP, 0.8 mM
7-methyl-GTP. The transcription products were extracted with
phenol and chloroform, twice precipitated with ethanol and resuspended in double distilled water to a final concentration of
0.2 µg/µl, and 50 nl were injected per oocyte. Before injection, oocytes were defolliculated by collagenase treatment (type I, 2 mg/ml for 40 min at room temperature; Sigma Chemical Co., St. Louis, MO). Oocytes were maintained at 19.0°C in Barth solution. Recordings were done 4-12 d after RNA injection.
Recording Technique and Solutions
Recording of macroscopic current was performed using the cut-open oocyte Vaseline gap technique (Stefani et al., 1994) on Xenopus laevis oocytes. The oocyte was placed in a triple compartment perspex chamber; voltage clamped currents were recorded
from the top chamber, while the middle chamber (set at the
same voltage as the recording chamber) isolated the top from
the bottom chamber. The oocyte membrane exposed to the bottom chamber was permeabilized with 0.1% saponin in the internal saline (see bottom chamber solution). Microelectrodes probing voltage across the membrane (top chamber) had a resistance
of ~0.5-1 M
, and they were filled with (M): 2.7 NaMES (Na-methanesulfonic acid), 0.01 Na2-EGTA, 0.01 NaCl. Holding potential was
90 mV. All experiments were performed at room
temperature. Subtraction of linear components was digitally obtained by scaled currents elicited by small control pulses of one-fourth the amplitude of the stimulating pulse (P/
4). Acquisition and data analysis were done on a personal computer. Signals
were filtered at one-fifth the sampling frequency.
External solutions, used in the top and guard compartments
were: NaMESBa-10 (10 mM BaOH; 96 mM NaMES; 10 mM HEPES,
titrated to pH 7.0 with CH3SO3H), NaMESCa-2, -5, or -10 (2, 5, or
10 mM CaOH, 102 mM NaMES, 10 mM HEPES, titrated to pH
7.0 with CH3SO3H), or NMGMESCa-10 (10 mM Ca2+, 96 mM
N-methyl-D-glucamine [NMG+], 10 mM HEPES, titrated to pH 7.0 with CH3SO3H). The solution in the bottom chamber in contact
with the oocyte cytoplasm was 110 mM K-glutamate (10 mM HEPES,
titrated to pH 7.0 with KOH). Na4-BAPTA (tetrasodium-1,2-bis
(o-aminophenoxy)-ethane-N,N,N ',N '-tetraacetate) was loaded into
a glass micropipette of ~20-µm tip diameter, and ~100 nl were
injected with an automatic microinjector immediately before
mounting the oocyte in the recording chamber. Na4-BAPTA stock
solutions of 50 mM were made in distilled water and titrated at
pH 7.0 with CH3SO3H. The BAPTA injections were performed
before the experiments to prevent contamination of Ca2+ currents with Ca2+- and Ba2+-activated Cl currents (Miledi, 1982
;
Barish, 1983
; Neely et al., 1994
). This BAPTA concentration selectively eliminated Cl
currents without any significant action
on Ca2+-dependent current decay (Neely et al., 1994
). To probe
the accessibility of the internal Ca2+ site, we had to dramatically
increase the internal BAPTA concentration (500 mM BAPTA and
10 mM NaCl) and to continuously perfuse the oocytes (1 ml/h)
via a glass pipette inserted into the bottom side of the oocyte.
Values for the rates of Ca2+-dependent inactivation were obtained by fitting to a double exponential (1C
2a;
1C in the presence of 500 nM Bay K 8644 (
)) or to a single exponential (
1C)
the decay of the Ca2+ current (from the peak of the current up to
800 ms). The exponential functions were
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with n = 1 and 2. P was the offset factor, and Ai the amplitude of each exponential component.
The model-fitting procedure was implemented with SCoP
(Simulation Resources, Inc., Barren Springs, MI). The rates in
the transitions were exponential functions of the voltage, as predicted by the Eyring theory. Simultaneous fitting of current traces
at different potentials was performed to evaluate the kinetic parameters in a non-steady state model. The source file, containing
a system of differential equations, was compiled and the resulting
executable file was fed with ensembles of current recordings under different conditions, such as subunit expression, Ca2+ concentration, and presence of the DHP agonist Bay K 8644 ().
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RESULTS |
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Ca2+-dependent Inactivation in 1C-expressing Oocytes
Fig. 1 shows Ba2+ and Ca2+ currents (left and right, respectively) recorded from an oocyte expressing the 1C
subunit alone. The currents were elicited by depolarizing pulses from a holding potential of
90 mV. The figure shows that, during large depolarizing pulses, Ba2+
currents had a very slow decay, while Ca2+ currents
showed a much faster decay that could be attributed to
the Ca2+-dependent inactivation process. The decay
phase of the currents was fitted to a single exponential
function of the form Ae
tr + C, where A is the amplitude factor, t the time, r the rate, and C the offset. The
fit was for Ba2+ (Fig. 1 A): A =
4.1 nA, r = 0.001 ms
1
and C =
17.9 nA at 0 mV and for Ca2+ (Fig. 1 B): A =
4.5 nA, r = 0.003 ms
1, and C =
4.8 nA at 0 mV.
The relative amplitude factor, A/(A + C), was larger
and the rate of decay was much faster in external Ca2+.
This difference in the decay phase between Ca2+ and
Ba2+ currents became more evident after potentiating
the Ca2+ current by adding a submaximal concentration (50 nM) of the DHP agonist Bay K 8644 (
). The
potentiated Ba2+ currents had a similar time course to
the control (compare Fig. 1, C and A). Thus, Ba2+ does
not substitute Ca2+ for the inactivation in the time scale
used (0.5-1 s). During the time course of our experiments, the main effect of Bay K 8644 was to potentiate
Ba2+ currents. On the other hand, in external Ca2+,
Bay K 8644 induced an increase in the size of the peak
current as well as an increase in the decay (Fig. 1, B and
D). Thus, facilitation of pore opening by Bay K 8644 (
) makes more evident Ca2+-dependent inactivation,
which is already present in the absence of the agonist.
|
Effect of the 2a Subunit on
1C Currents
Fig. 2 shows the effect of coexpression of the 2a subunit with the
1C subunit on the rates of Ca2+-dependent inactivation. Ba2+ and Ca2+ currents (Fig. 2, left
and right, respectively) in oocytes coexpressing the
pore-forming
1C subunit together with the regulatory
2a subunit had faster activation rates and larger amplitudes than in oocytes expressing the
1C subunit alone.
This is expected from the facilitation of the pore opening by the coexpression of the
2a subunit. By comparing the recordings in external Ca2+ (Figs. 1 and 2,
right), it becomes evident that the
2a subunit speeds up
the Ca2+-dependent inactivation process (Fig. 2, B and
D). As was the case for
1C currents, in
1C
2a, the addition of a submaximal concentration of Bay K 8644 (
)
(50 nM) increased both Ba2+ and Ca2+ current amplitudes. From these results we can conclude that maneuvers that increase the open probability of the Ca2+
channel without affecting the single channel amplitude
(addition of Bay K 8644 (
) and the coexpression of
the
2a subunit; Costantin et al., 1995
) speed up the
Ca2+-dependent inactivation process.
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In addition to the Ca2+-dependent inactivation phase,
both 1C and
1C
2a currents show a slow smaller component of inactivation that is weakly voltage dependent. This slow inactivation is more clearly detected in
Ba2+ currents (Figs. 1, A and C, and 2, A and C) since,
in external Ca2+, the Ca2+ inactivation process predominates. This slower component can be attributed to a
slow voltage-dependent inactivation (Lee et al., 1985
;
Hadley and Hume, 1987
; Campbell et al., 1988
; Gutnick et al., 1989
; Hadley and Lederer, 1991
; Giannattasio et al., 1991
), or to a less efficient Ba2+-dependent inactivation process (Ferreira et al., 1997
). This voltage-dependent component has not been analyzed here;
since its time course is much slower than Ca2+-dependent inactivation, it should not interfere with the main conclusions of this paper.
Voltage and Ca2+ dependence of the Inactivation Rates in 1C
and
1C
2a Currents
The currents in Fig. 3 were recorded in an oocyte expressing the 1C
2a Ca2+ channel at three different external Ca2+ concentrations: 2 (A), 5 (B), and 10 (C)
mM Ca2+. Each panel shows currents elicited by three
different voltages (holding potential
90 mV), together with superimposed fits to the decay phase of the
currents. The inactivating currents were fitted with a
double exponential function, yielding to a slow and a
fast rate of inactivation. The fast rate depended on external Ca2+ concentration, while the slow rate was
much less affected by external Ca2+ (see also Fig. 6).
The peak of the ionic current occurred at +10 mV in
2 mM Ca2+, at +20 mV in 5 mM Ca2+, and at +25 mV
in 10 mM Ca2+. The fast rate of inactivation, compared
at equivalent voltages corrected for surface charge effect, increased from rf= 0.0126 ms
1 (0 mV, 2 mM
Ca2+) to rf = 0.0224 ms
1 (+20 mV, 10 mM Ca2+).
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The voltage dependencies of current (I-V) and fast
rate of inactivation (r-V) for the experiment in Fig. 3
are shown in Fig. 4 A (normalized rates and peak current values). The graph shows a negative voltage shift
between the peak of the r-V (open symbols) and the peak
of the I-V (filled symbols). The fact that the peak of the
r-V always occurred at more negative voltages than the peak of the I-V suggests a complex dependence of
the Ca2+ inactivation mechanism on the parameters of
channel activation. Possibly, open probability, single
channel amplitude, Ca2+ influx and accumulation, buffer
capacity, and diffusion could be involved. A similar voltage shift between the peak of the r-V and I-V curves was
observed in 1C alone (Fig. 4 B).
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Effect of DHP Agonist Bay K 8644 () on
1C and
1C
2a
Ca2+ Currents
The ability of the DHP agonist Bay K 8644 () to increase the size of the current by enhancing the open
probability, without affecting the single channel amplitude, was used to further investigate the role of the
open probability in the Ca2+-dependent inactivation
mechanism. We compared the effect of Bay K 8644 (
)
on
1C and
1C
2a Ca2+ currents at three different Ca2+
concentrations. Fig. 5 shows
1C
2a Ca2+ currents elicited by three different voltages, both in the absence (A,
2 mM Ca2+) and presence (2, 5, and 10 mM Ca2+, B-D,
respectively) of Bay K 8644 (
) 500 nM, with the corresponding superimposed fits. The addition of saturating
concentration of Bay K 8644 (
) (500 nM) produced a
small negative shift of the activation-voltage curve (~5
mV), an approximately twofold increase in the size of
the ionic current and a twofold increase in both rates.
|
Fig. 6 summarizes the effect of external Ca2+ and Bay
K 8644 () on
1C
2a Ca2+-dependent rates of inactivation. The maximum value of the fast rates of inactivation in 2 mM Ca2+ and in the absence of the DHP agonist was 0.017 ms
1 (diamonds), and it became 0.038 ms
1 in 10 mM Ca2+ and in the presence of 500 nM Bay
K 8644 (
), thus undergoing a more than threefold
overall increase. An equivalent pattern as in Fig. 6 was
observed in
1C channels. The slow time constant of the
double-exponential inactivation in
1C
2a is of the same order of magnitude of the single exponential time constant in
1C alone, and it is Ca2+ dependent, as it can be
seen in Fig. 6 A. Fig. 7 shows the relative position in the
voltage axis of the r-V and I-V curves for
1C
2a in 5 mM
Ca2+ and in the presence of 500 nM Bay K 8644 (
).
|
The same protocol as shown in Fig. 5 for 1C
2a currents was applied to
1C alone. In
1C channels, the
Ca2+ current decay in 2 mM external Ca2+ (Fig. 8 A)
could be fitted to a single exponential function. In
1C
alone, the Ca2+-dependent inactivation might be contaminated by the presence of a voltage-dependent inactivation rate recorded in external Ba2+ (Fig. 1). However, the addition of Bay K 8644 (
) 500 nM produced the expected negative shift of the activation-voltage
curve of ~5 mV together with a significant increase in
the size of the current. This current potentiation was
associated with a double exponential time course of decay. As expected for a Ca2+-dependent process, the fast
component became faster as the Ca2+ concentration increased. Taking altogether the results in
1C and
1C
2a
channels and the action of Bay K 8644 (
) on both
channels, we can conclude that both single channel
amplitude and open probability participate in the process of Ca2+-dependent inactivation. The effect of the
single channel amplitude is reflected by the Ca2+ dependence of the inactivation rates and the left shift of
the r-V vs. I-V curves, while the role of the open probability is manifested by the faster inactivation rates after
facilitating pore opening by the addition of Bay K 8644 (
) and the coexpression of the
2a subunit.
|
The Effect of BAPTA on Ca2+-dependent Inactivation in
1C
2a Currents
To test the accessibility of the site to internal Ca2+
buffer, we investigated the effect of perfusing high
BAPTA concentration on the Ca2+-dependent inactivation rates (Fig. 9). The six traces in Fig. 9 A have been
recorded at different times after the oocyte was mounted and the internal perfusion started (BAPTA
500 mM at the speed of 1 ml/h). Ca2+ currents (5 mM
Ca2+) were initially contaminated by outward Ca2+-activated Cl currents shown as inward slow component
and slow tail currents (trace a, t = 1 min 15 s). As the
perfusion progressed, the Cl
currents were removed
showing the Ca2+-dependent inactivation process. The
initial phase of decay in trace c (t = 4 min 26 s) could
be fitted with a single exponential function (r = 0.0099 ms
1). After 20 min 5 s (trace f), the rate of inactivation
had become much slower (r = 0.0025 ms
1). The time
course of the inactivation rates for the whole experiment is shown in Fig. 9 B. During the perfusion, peak
current amplitude decreased due to run down. In equivalent prolonged recordings (20 min), when BAPTA was
not perfused in the oocyte, the decrease in the size of
the current due to run down did not slow down the inactivation rate (Fig. 9, right). Fig. 9 C shows the progressive run down of the current, while there were no
changes in their time course. Fig. 9 D shows that the
voltage dependence of the fast rate of inactivation at the
beginning and after 23 min remained unmodified. Fig.
9 E shows small changes in the rates of inactivation during the whole experiment. These results confirm that
the internal Ca2+ site is accessible to fast Ca2+ chelators
(Imredy and Yue, 1992
; Haack and Rosenberg, 1994
), thus ruling out the possibility that this site is located
within the conduction pathway.
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DISCUSSION |
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We have shown that raising the external Ca2+ concentration increased the Ca2+-dependent inactivation rates
and left-shifted their voltage dependence: enhancing
the Ca2+ influx through the channels determined
faster decaying currents under conditions in which the
open probability should remain unaffected. We also
have shown that the rates of Ca2+-dependent inactivation are open probability dependent. Thus, both the
single channel amplitude and the open probability
contribute to the Ca2+-dependent inactivation mechanism. One hypothesis that would explain the dependence of the rates on external Ca2+ concentration would
be a Ca2+ binding site facing the external medium. This
possibility is ruled out by the role of internal Ca2+ buffers
(Lee et al., 1985; Imredy and Yue, 1992
; Haack and
Rosenberg, 1994
) and by recent molecular biology experiments. de Leon et al. (1995)
and Zhou et al. (1997)
showed that the required region for Ca2+-dependent
inactivation in
1C Ca2+ channels is located within the
COOH terminus of the protein, facing the cytoplasm.
The Ca2+ binding site could be sensitive to the internal
accumulation of Ca2+ in a shell underneath the plasma
membrane. In this case, the build up of Ca2+ would depend on the time integral of the current, the open
probability, and the efflux from the shell into the cytoplasm. This mechanism has been proposed and extensively studied for native Ca2+ channels (Chad et al.,
1984
; Lee et al., 1985
); it was supported by the dependence of the rates of inactivation on the internal buffer
concentration (Lee et al., 1985
; Imredy and Yue, 1992
; Haack and Rosenberg, 1994
) and by observed cross talk
among channels (Yue et al., 1990
; Mazzanti et al., 1991
;
Imredy and Yue, 1992
). In our case, the shell mechanism becomes unlikely for two reasons: (a) only extreme conditions of Ca2+ buffering capacity were able
to slow down the inactivation process, and (b) the lack
of observed cross talk among channels. In the oocyte expression, the rates of Ca2+ inactivation are independent
of the level of expression as shown before by our group
(Neely et al., 1994
). We have confirmed this finding. In
this new set of experiments in
1C
2a, changes of expression level measured as the peak currents in the I-V
curve (from 100-1,200 nA; 2 mM Ca2+) did not affect
the predominant fast rate of inactivation, which remained between 0.015 and 0.02 ms
1 (data not shown).
Our results favor a domain mechanism in which the local Ca2+ concentration equilibrates in microseconds
(Sherman et al., 1990
; Shirokov et al., 1993
). However,
we cannot rule out the possibility that the absence of
cross talk was due to the expression level. Under our
experimental conditions, it is possible that the expression level was not high enough to reach the critical
channel density necessary to the interaction among adjacent channels.
A concern that must be addressed refers to the accessibility of BAPTA to the Ca2+ binding site. It is unlikely
that the lack of effect on the inactivation rates by the injected BAPTA is due to a slow diffusion in the oocyte cytoplasm. In fact, injections of small quantities of BAPTA or EGTA (Neely et al., 1994) was effective to eliminate
the activation of the Ca2+-activated Cl
channels.
A Minimum Model for Ca2+-dependent Inactivation: Role of the Single Channel Amplitude and Open Probability
Several models have been proposed for Ca2+-dependent inactivation. All these models agree on identifying the Ca2+ dependence of the inactivation in one (or more) state-to-state transitions where the rate is dependent on the internal Ca2+ concentration. Two main conditions are considered: the "shell" model and the "local domain" model.
In the shell model, the Ca2+ flowing through the
channels accumulates into a shell underneath the
plasma membrane (Standen and Stanfield, 1982; Chad
et al., 1984
) or it is thought of as charge accumulating
on a leaky capacitor (Mazzanti et al., 1991
). This assumption leads to second order rates of Ca2+-dependent inactivation where the parameters of channel
opening (i.e., single channel conductance and open
probability) usually have to be integrated over the variable time.
In the local domain model, the Ca2+-sensing site is located very close to the channel mouth, making it less accessible to chelators, as well as to Ca2+ ions coming from
adjacent channels. The calculation would thus be restricted to a very small domain surrounding the mouth
of the channel, where the Ca2+ concentration would
reach its steady state value in a few microseconds. This
assumption justifies the use of the steady state diffusion equation and results in a linear dependence of the second order rates of inactivation on the single channel
amplitude (Sherman et al., 1990; Shirokov et al., 1993
).
Both classes of models can account for the main features of the Ca2+-dependent inactivation in L-type Ca2+
channels. The domain models also include the possibility of an "extended local domain" in which the volume
where the Ca2+ concentration is calculated is larger,
and a channel can sense the flux of ions that is entering
a neighboring channel (cross talk). The fact that Yue et
al. (1990) reported that Ca2+ entry inactivates the channel it goes through, together with our finding that high
concentrations of fast chelators are necessary to reduce
the inactivation rates, leads us to test the local domain hypothesis proposed by Sherman et al. (1990)
. The local domain model has been used with an expanded kinetic scheme to account for the voltage shift between
the r-V and I-V curves.
The steady state equation for diffusion in a sphere is, when the diffusion happens only on the radial dimension:
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(1) |
where C is the ion concentration, B is the boundary
concentration (in our case, B is the cytoplasmic Ca2+
concentration), is the influx, and r is the radius. Eq. 1
means that, if [Ca2+]i is the internal Ca2+ concentration at rest, then the concentration near the pore will be
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(2) |
where i is the single channel amplitude and A is a constant. The constant A takes into account the diffusion
coefficient for Ca2+ and the effect of chelators. In a
voltage-independent transition from an open state to a
Ca2+-inactivated state, the rate will be linearly dependent on the internal Ca2+ concentration: =
0[Ca2+].
Thus, with the assumptions that Ca2+ binds instantaneously to a single site and at a fixed distance from the
site, the rate of Ca2+-dependent inactivation depends
linearly on the flux; i.e., on the single channel amplitude i. The inactivation process will also be open probability dependent since the inactivated state is sequentially connected to the open state.
Then we assumed that the transition rates between all the states in the kinetic model follow the Eyring rate theory; i.e., they are exponential functions of the form:
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where i are the forward rates and
i are the backward
rates.
0i and
0i are the voltage-independent rates:
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![]() |
where k is the Boltzmann constant (1.38 × 1023 J/°K, T
is the absolute temperature (K), h is the Planck constant
(6.63 × 10
34 J s), e
is the electronic charge (1.602 × 10
19 C), and
Wif and
Wib are the energies required
for the transition to occur in the two directions (forward
and backward). zi is the gating charge (e
),
i is the fraction of the electric field sensed by zi, and V is the membrane voltage. The rates to the Ca2+-inactivated states
are voltage independent:
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Within the above theoretical premises, we started
building a kinetic scheme of closed, open, and inactivated states. The computer routine (SCoP) numerically
solves the system of differential equations that describes the kinetic scheme, and assigns numbers to the parameters 0i,
0i, zi,
i,
0Ca2+,
0Ca2+. The internal Ca2+ concentration, [Ca2+], is calculated as a linear
function of the single channel amplitude at each potential.
The kinetic scheme has to satisfy our experimental
results, which are summarized as: (a) The inactivation
is Ca2+ dependent: increasing the external Ca2+ concentration produces an increase in the absolute values
of the rates of inactivation. (b) The process is open
probability dependent: increasing the open probability
with DHP agonist Bay K 8644 () or by coexpressing
the
2a subunit together with the
1C subunit produces
an increase in the rates of inactivation. (c) The time
course of the decay can be fitted with a double exponential function. The initial fast rate of inactivation is
not present (or not detectable) if the
1C subunit is expressed alone and when
1C currents are measured in
the absence of Bay K 8644 (
). (d) The r-V curve peaks
at more negative voltages than the I-V curve.
A sequential model of the form
cannot predict all of these features, specifically it cannot reproduce the observed shift between I-V and r-V.
This model predicts that the r-V and the I-V peak at the
same potentials under conditions of a fast activation
and a slow inactivation (Sherman et al., 1990). If we
were to relax these constraints, the decay phase of the
current would be less evident due to the slow activation, and the peak of the r-V would tend to be more positive than the peak of the I-V curve.
We know from single channel data that the 1C and
1C
2a Ca2+ channels undergo "silent" transitions (i.e.,
they gate without opening), and they are able to open
with different open probability patterns (Costantin et
al., 1995
). Thus, we have tested the model proposed by
Bean (1989)
with the modifications shown in Fig. 10. The kinetic scheme has three parallel lines of states
that develop as branches from an initial closed state.
The parallel transitions carry the same amount of
charge. In the top line, the channel never opens, although it displaces all the charge of the voltage sensor.
The middle (unwilling) and bottom (willing) lines
have final open states connected to final inactivated
states. The vertical transitions between the lines are
voltage independent and can be Bay K 8644 (
) and
subunit sensitive.
|
|
Fig. 11 shows experimental data from an oocyte injected with the 1C
2a Ca2+ channel together with superimposed fitted traces to the model of Fig. 10. In this
model, the rates connecting the open states to the
Ca2+-inactivated states consist of a constant coefficient
times the local Ca2+ concentration, according to Eq. 2
(Table I). The simulated traces in Fig. 11 B are shown
together with their I-V and r-V curves (fast rate, Fig. 11
C). This model predicts the shift between the peaks of
the two curves.
|
Thus, we can conclude that the kinetic scheme in
Fig. 10 reproduces well the experimental data for
1C
2a channels. In the case of
1C alone, though it is
possible to reproduce the main kinetic features of the
data, such as the slower activation phase of the currents
and the u-shaped voltage dependence of the inactivation rates, the possible presence of a contaminating
voltage-dependent inactivation does not allow a clear
analysis of the time course of decay. This intrinsic limitation in the modeling of
1C currents would not produce a reliable set of parameters for the kinetic scheme
in the case of
1C alone.
In testing the effect of the 2a subunit on
1C Ca2+-
dependent inactivation, a possible concern is whether
the endogenous
3xo subunit changed the properties of
the
1 subunits when injected alone. The coexpression
3xo with the
1E and
1C (data not published for
1C)
clones produced the generic effect of
subunit of shifting to more negative potential G-V curves (Tareilus et
al., 1997
). We concluded that the endogenous
3xo has
a role in channel expression, but the quantities present
are not sufficient to induce kinetic changes.
A further question concerns the molecular mechanism for the Ca2+-dependent inactivation process. Since
the Ca2+-sensitive region has been identified within the
COOH terminus of the subunit (de Leon et al., 1995
;
Zhou et al., 1997
), we can speculate that the Ca2+ binding to the COOH terminus produces an allosteric
change in the conformation of the protein, such as a
collapse of the pore. Another possibility is that the
COOH terminus, once Ca2+ has bound, folds backward
and blocks the pore, with a mechanism analogous to
the N-type inactivation in Shaker K+ channels (Hoshi et
al., 1990
). However, if the Ca2+ binding site is located
in the COOH terminus of the
1C subunit, the COOH
terminus could be folded in order for the Ca2+ site to
be in close proximity to the pore. Differences in the tertiary structure between native and cloned channels that
could arise from differences in the folding of the
COOH terminus may modify the accessibility of the
Ca2+ binding site to intracellular Ca2+ buffers.
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FOOTNOTES |
---|
Address correspondence to Dr. Enrico Stefani, UCLA, Dept. of Anesthesiology, BH-612 CHS, Box 951778, Los Angeles, CA 90095-1778. Fax: 310-825-6649; E-mail: estefani{at}ucla.edu
Received for publication 28 April 1997 and accepted in revised form 14 January 1998.
1 Abbreviations used in this paper: DHP, dihydropyridine; HP, holding potential; I-V, voltage dependencies of current; r-V, voltage dependencies of rate of inactivation; SHP, subtracting holding potential.We thank Dr. Ramon Latorre and Dr. Ligia Toro for kindly reading the manuscript and Ms. Jin for injection of Xenopus laevis oocytes.
This work was supported by National Institutes of Health (NIH) grant AR-38970 to E. Stefani. N. Qin is the recipient of NIH National Research Service Award GM17120-02 and of the American Heart Association (AHA) Scientist Development Grant 9630053N. This work was done during the tenure of a Grant-in-Aid 113-GI1 award to R. Olcese from the American Heart Association, Greater Los Angeles Affiliate (Los Angeles, CA).
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