Department of Anesthesiology, Washington University School of Medicine, St. Louis, Missouri 63110
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ABSTRACT |
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Prakriya, Murali and Christopher J. Lingle. Activation of BK Channels in Rat Chromaffin Cells Requires Summation of Ca2+ Influx From Multiple Ca2+ Channels. J. Neurophysiol. 84: 1123-1135, 2000. Large-conductance Ca2+ and voltage-dependent K+ channels (BK channels) in many tissues require high Ca2+ concentrations for activation and therefore might be expected to be tightly coupled to Ca2+ channels. However, in most cases, little is known about the relative organization of the BK channels and the Ca2+ channels involved in their activation. We probed the nature of the organization of BK and Ca2+ channels in rat chromaffin cells by manipulating Ca2+ influx through Ca2+ channels and by altering cellular Ca2+ buffering using EGTA and bis-(o-aminophenoxy)-N,N,N',N'-tetraacetic acid (BAPTA). The results were analyzed to determine the distance between Ca2+ and BK channels that would be most consistent with the experimental data. Most BK channels are close enough to Ca2+ channels to be resistant to the buffering action of millimolar of EGTA, but are far enough to be inhibited by BAPTA. Analysis of the EGTA/BAPTA results suggests that BK channels are at a distance of 50 to 160 nm from Ca2+ channels. A model that assumes random distribution of Ca2+ and BK channels fails to account for the observed [Ca2+]i detected by BK channels, suggesting that a specific mechanism may exist to mediate the functional coupling between these channels. Importantly, the effects of EGTA and BAPTA cannot be explained by assuming a one-to-one coupling between Ca2+ and BK channels. Rather, Ca2+ influx through a number of Ca2+ channels appears to act in concert to regulate the behavior of any individual BK channel. Thus differences in BK channel open probabilities may be explained by differences in the extent of Ca2+ domain overlap at the sites of individual BK channels.
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INTRODUCTION |
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Ca2+ is
involved in a wide range of signaling events ranging from activation of
ion channels to gene expression. It is clear that some
Ca2+-dependent processes such as transmitter
release and activation of certain Ca2+-dependent
K+ channels require very high
Ca2+ concentrations for activation
(Heidelberger et al. 1994; Roberts et al.
1990
). Because large and localized Ca2+
elevations are thought to only occur in the immediate vicinity of
Ca2+ channels (Augustine and Neher
1992
; Neher 1986
), this has prompted the
suggestion that these Ca2+-dependent processes
must be tightly coupled to Ca2+ channels
(Adler et al. 1991
; Roberts et al. 1990
).
Additional evidence for this conclusion has come from the use of
Ca2+ buffers with different kinetic properties
(Adler et al. 1991
; Mennerick and Matthews
1996
; Roberts et al. 1990
). However, in most
cases, it is unknown whether these Ca2+-dependent
processes are coupled to Ca2+ channels tightly
enough that single open Ca2+ channels may trigger
activation, or whether their distance from Ca2+
channels is sufficiently large that the simultaneous opening of
multiple Ca2+ channels is necessary for activation.
In rat chromaffin cells, voltage-dependent K+
channels (BK channels) are selectively activated by
Ca2+ influx through L- and Q-type
Ca2+ channels (Prakriya and Lingle
1999) and contribute significantly to the rapid termination of
action potentials (Solaro et al. 1995
). In a previous
study (Prakriya et al. 1996
), we examined the properties of Ca2+ signals activating BK channels in
chromaffin cells and proposed that BK channels occur in either of two
populations. One population is activated to high open probabilities
during brief Ca2+ influx steps, whereas the
second population is only revealed following longer influx steps.
Intracellular EGTA is ineffective in preventing the activation of the
first population, whereas it completely blocks the activation of the
second population. Based on these initial observations, we proposed
that BK channels in the first population are closely associated with
Ca2+ channels, whereas BK channels in the second
population are activated by Ca2+ that diffuses
some distance from open Ca2+ channels. However,
analysis of the precise distances between Ca2+
and BK channels that would account for the experimental data was not
performed in that study.
In this paper, we revisit the issue of the nature of the relative organization of Ca2+ and BK channels and address the following questions: 1) Does a two-populations-of-BK-channels model best account for all the key experimental observations? 2) What are the approximate distances between Ca2+ channels and the BK channels activated by brief Ca2+ influx steps, and those activated by long Ca2+ influx steps? 3) Can a model that assumes random distribution of Ca2+ and BK channels account for the physiological effects, or is some specific spatial coupling between the Ca2+ and BK channels required? 4) Does the Ca2+ signal activating individual BK channels arise from single Ca2+ channels or does it arise from multiple Ca2+ channels?
We manipulated the Ca2+ signals presented to BK channels by altering Ca2+ influx and cellular Ca2+ buffering. From these results, we estimated the approximate distance between Ca2+ and BK channels that would be consistent with the data. Our current results are incompatible with the hypothesis that there are two distinct populations of BK channels at differing distances from Ca2+ channels. Instead, the new data suggest that all BK channels are located at roughly the same distance, between 50 and 160 nm from Ca2+ channels. We find that random distribution of BK and Ca2+ channels is insufficient to account for the [Ca2+]i detected by BK channels, suggesting that some specific mechanism may be involved in mediating the functional coupling between BK and the L- and Q-type Ca2+ channels. Moreover, analysis of the effects of intracellular EGTA and bis-(o-aminophenoxy)-N,N,N',N'-tetraacetic acid (BAPTA) suggest that this association cannot result from one-to-one coupling between single BK channels and single Ca2+ channels. Rather, Ca2+ influx through a number of Ca2+ channels appears to act in concert to regulate the [Ca2+]i that governs the behavior of any individual BK channel. In this scheme, differences in the extent of BK channel activation arise not because of significant differences in distances of BK channels from Ca2+ channels, but because of differences in the extent of Ca2+ domain overlap at the sites of the individual BK channels.
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METHODS |
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About 75% of rat chromaffin cells express an inactivating
variant of a BK current, with the rest expressing either
noninactivating BK current or a mixture of inactivating and
noninactivating BK current (Ding et al. 1998;
Solaro et al. 1995
). All the data shown in this paper
are from cells with inactivating BK currents, although we observed no
difference between the two cell types in the nature of
BK/Ca2+ channel coupling.
Chromaffin cell culture
Adrenal glands were removed from Sprague-Dawley rats and
enzymatically digested with an enzyme cocktail containing 3%
collagenase, 2.4% hyaluronidase, 0.2% DNAse as described earlier
(Neely and Lingle 1992). Chromaffin cells were
plated on collagen-coated dishes and maintained at 37°C and 5%
CO2 in a medium composed of Dulbecco's modified
Eagle's medium (DMEM) supplemented with 10% fetal bovine serum (FBS)
and 25 µl/ml ascorbic acid.
Electrophysiological methods
Recordings were performed on cells 2-14 days after plating. In perforated patch-clamped cells, amphotericin was employed as the permeabilizing agent. Currents were recorded with an Axopatch-1C amplifier (Axon Instruments, Foster City, CA) and voltage clamp was controlled with the Clampex program in the pClamp software package (Axon Instruments, Foster City, CA).
Solutions
The standard extracellular solution contained (in mM) 140 NaCl, 5.4 KCl, 10 HEPES, 1.8 CaCl2, and 2 MgCl2 (pH 7.4, 290-310 mosm). Apamin (200 nM) was included in all experiments to block SK channels. To isolate ICa, the following extracellular solution was used (in mM): 40 tetraethylammonium chloride, 10 HEPES, 90 NaCl, and 2 MgCl2 (pH 7.4) with added CaCl2 as required. The standard pipette saline contained the following (in mM): 120 K-aspartate, 30 KCl, 10 HEPES(H+), and 2 MgCl2 (pH 7.4, 290-310 mosm). In some cells, whole cell BK current was activated by dialyzing via the patch pipette, a solution containing 10 µM [Ca2+]i buffered with 5 mM HEDTA. Voltages for perforated-patch whole cell recordings have been corrected for a +9-mV junction potential resulting from the use of aspartate-based pipette salines. Extracellular solution changes and drug applications were accomplished via a multi-barrel perfusion system.
Drugs
Stock solution of Bay K 8644 (Sigma, St. Louis, MO) was prepared
in ethanol at a concentration 5 mM. -Conotoxin GVIA (CgTx GVIA, RBI,
Natick, MA) and
-agatoxin TK (Aga TK, Peptide Institute, Osaka,
Japan) were dissolved in dH2O at stock
solutions of 500 and 100 µM, respectively. Final concentrations are
given in the figure legends. BAPTA and EGTA (both from Molecular
Probes, Eugene, OR) were introduced by incubating the cells in 20 µM
of the AM-ester form of the drug dissolved in the normal external
solution. In some cells, BAPTA and EGTA were introduced directly via
the patch pipette by including magnesium salts at the indicated
concentrations in the standard pipette solution.
Simulations of [Ca2+]i detected by BK channels due to Ca2+ influx
Simulation programs were written in C and C++ and implemented on
a Linux platform. The cell surface was modeled as a square of length
L, over which a specified number of BK and
Ca2+ channels were distributed. The surface area
of the model chromaffin cell was assumed to be 800 µm2. This was inferred from the measured cell
capacitance (~8 pF). To eliminate edge effects, a larger square, of
length f * L was used (along with f
times the number of channels). Only the BK channels falling in the
smaller square (length L) were taken into consideration,
although each BK channel could detect the effects of all
Ca2+ channels placed over the larger square. The
steady-state Ca2+ concentration,
[Ca(r)]ss, at each BK
channel was determined using a derivation for the buffered diffusion of
Ca2+ away from the pore of an open
Ca2+ channel (Stern 1992)
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(1) |
The effects of multiple Ca2+ channels were
determined by linearly summing the effects of individual
Ca2+ channels (Neher
1998). The diffusion rate constants of
Ca2+, buffer, and
Ca2+-bound buffer
(DCa,
Dbuffer,
DCa-buffer) were assumed to be 2 × 10
10
m2s
1
(Naraghi 1997
). The Ca2+-binding
rate constants of EGTA and BAPTA were assumed to be: KD(EGTA) = 250 nM;
KD(BAPTA) = 400 nM;
Kf(EGTA) = 1.5 × 106M
1s
1;
Kf(BAPTA) = 2.5 × 108M
1s
1
(Naraghi 1997
). The space constant (
) was calculated
from the relationship
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(2) |
The total number of L- and Q-type Ca2+ channels
in rat chromaffin cells was assumed to be around 10,000. This was
estimated as follows. Noise analysis predicts the number of L-type
channels to be around 5,000 (Prakriya and Lingle 1999).
Measurements of the number of Q-type Ca2+
channels are unavailable. However, the whole cell Q-type current is
about 72% of the amplitude of the L-type current (Prakriya and
Lingle 1999
). Accounting for the fact that the conductance of
L-type Ca2+ channels may be greater than that of
other Ca2+ channels (De Waard et al.
1996
), we estimated that the number of Q-type
Ca2+ channels may be ~5,000. As a comparison,
estimates for the total number of Ca2+
channels in chromaffin cells vary from ~10,000 (Fenwick et al. 1982
) to over 20,000 channels (Artalejo et al.
1992
).
The relaxation of [Ca2+]i
after closure of a Ca2+ channel was determined
from the relation (Pape et al. 1995,
1998
)
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(3) |
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RESULTS |
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Effects of EGTA and BAPTA on BK current activation
For analysis of the BK current activated by
Ca2+ influx, the membrane voltage was first
stepped to 0 mV to activate Ca2+ influx for a
variable length of time. This was then followed by a test step to +81
mV (Fig. 1). In
perforated patch-clamped cells where cellular
Ca2+ buffering is retained, BK current at +81 mV
exhibits two components. The first is an instantaneous current, which
is simply the ohmic increase in the K+ current
because of the increased driving force on K+ ions
(arrow, Fig. 1A). The second is a more slowly developing current that results from activation of additional BK channels due to
increased open probability of BK channels at +81 mV (Prakriya et
al. 1996).
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Our previous study (Prakriya et al. 1996) proposed that
two populations of BK channels, each distributed at different average distances from Ca2+ channels, might account for
these results. One population is selectively activated during brief
(5-10 ms) and the other during long (>50 ms) duration
Ca2+ influx steps. This hypothesis was supported
by the effects of EGTA: at concentrations up to 5 mM, EGTA has no
affect on the instantaneous BK current activated by brief
Ca2+ influx steps, whereas the increase in the
slowly activating component with long influx steps is completely
abolished (Prakriya et al. 1996
). Further, BK channels
in this putative first population rapidly inactivate as the influx step
duration is increased due to high
[Ca2+]i in their
vicinity. These effects are shown in Fig. 1, B and C. The differential effects of EGTA on the two components of
BK current were interpreted in the context of EGTA's slow calcium binding on-rate, which produces a region of relatively unbuffered [Ca2+]i around individual
Ca2+ channels (Neher 1986
;
Stern 1992
). BK channels located in this unbuffered
region may be unaffected by the presence of EGTA, whereas those located
outside this region may be subject to the buffering action of EGTA.
Hence, the instantaneous current was proposed to reflect BK channels in
close association with Ca2+ channels and exposed
to high [Ca2+]i, and the
more slowly activating BK current was thought to reflect channels at
greater distances from sites of Ca2+ influx and
exposed to a much lower bulk
[Ca2+]i (Prakriya
et al. 1996
). We will refer to this hypothesis as the
two-population model.
In contrast to EGTA, BAPTA at concentrations of 1-5 mM was found to
prevent BK current activation completely (e.g., Fig. 1D) (Prakriya et al. 1996). BAPTA has a
Ca2+ affinity similar to EGTA (Naraghi
1997
), but its 150-fold faster calcium-binding
rate is predicted to cause
[Ca2+]i to drop very
steeply to resting levels tens of nanometers from a
Ca2+ channel (Stern 1992
). This
suggests that the distance between Ca2+ and BK
channels must be sufficiently large that, at millimolar concentrations,
BAPTA is effective in abolishing activation of all BK current.
The effectiveness of Ca2+ buffering in the
vicinity of an open Ca2+ channel increases with
distance from the Ca2+ channel and depends on the
kinetic properties and concentration of the buffer (Neher
1986). The spatial effectiveness of a buffer can be
approximated by a space constant (
), which is the characteristic distance that a Ca2+ ion travels before it is
captured by the buffer. At
for a given buffer,
[Ca2+]i is reduced to
about 36.8% of that in the absence of buffer. For EGTA and BAPTA at
concentrations of 5 and 1 mM, respectively,
EGTA and
BAPTA are
~160 and ~40 nm. Although the consequences of a buffer on
activation of BK channels will depend not only on the buffer effects on
[Ca2+]i but also on the
Ca2+ dependence of BK channel activation, for
purposes of focusing this analysis, these distances are useful as lower
and upper approximations of the range over which BK channels may be
separated from Ca2+ channels.
The ability of 1 mM BAPTA to completely block activation of BK current
suggests that very few single BK channels are likely to be nearer to a
Ca2+ channel than 40 nm. Similar considerations
regarding EGTA would suggest that those BK channels whose activation is
unaffected by EGTA would be within 160 nm of a
Ca2+ channel. However, BK channels whose
activation is blocked by EGTA would be expected to be located at
distances >160 nm from Ca2+ channels. In fact,
since 80-90% of the total BK current is sensitive to EGTA
(Prakriya et al. 1996), this suggests that the majority of BK channels are located at distances >160 nm from
Ca2+ channels.
BK current activation promoted by Bay K is unaffected by intracellular EGTA
We next examined whether the two-population model could explain
experimental observations involving Bay K and elevated
[Ca2+]ext. Bay K
increases the fraction of BK channels activated by brief influx steps
two-fold, from ~17 to 36% (Prakriya and Lingle 1999).
Although the basis for this effect is unknown, noise analysis indicates
that Bay K increases the average Popen of L-type
Ca2+ channels without altering the number of
active L-type Ca2+ channels (Prakriya and
Lingle 1999
). In this manner, Bay K shifts the balance of BK
current activated by brief and long duration steps such that some
proportion of the BK current that is usually activated only by long
duration Ca2+ influx steps can now be activated
by brief influx steps. Because the slow BK current activated by long
duration Ca2+ influx steps is blocked by EGTA, it
might be expected that the additional current activated by brief
Ca2+ influx steps in Bay K arises from BK
channels located at distances >160 nm from Ca2+
channels. Therefore this effect of Bay K should be inhibited by EGTA.
We sought to directly test this idea.
Rat chromaffin cells were loaded with EGTA by incubating in 20 µM EGTA-AM for 45 min to 1 h. EGTA loading eliminated the slow increases in BK current that are normally seen by increasing the duration of the Ca2+ influx step (Fig. 2A). Moreover, the peak BK current at +81 mV rapidly decreased as the duration of the Ca2+ influx step is increased, similar to current observed after direct dialysis of 5 mM EGTA (Fig. 1C).
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Surprisingly, when Bay K was applied to these cells, the dramatic
increases in BK current activated by Ca2+ influx
persisted (7 of 7 cells; Fig. 2B). BK current activated by
5-ms steps increased by 116 ± 17% in Bay K, which is essentially identical to the 120% increase in BK current activation induced by Bay
K in cells with native buffering (Prakriya and Lingle
1999). Further, as the influx step duration was increased, the
activated BK current displayed very prominent inactivation (Fig.
2C), suggesting that the underlying BK channels are
experiencing a [Ca2+]i
sufficiently high to promote their rapid inactivation. The time
constant of BK current inactivation at 0 mV in the traces in which the
duration of the Ca2+ influx step was larger than
100 ms was 44 ± 2 ms (n = 8 cells) in the
presence of Bay K. A comparison of this inactivation time constant to
the [Ca2+] dependence of the time constant of
BK current inactivation (Prakriya et al. 1996
) suggested
that the underlying BK channels are probably exposed to
[Ca2+]i of at least 20 µM.
In contrast to EGTA, when the cells were loaded with BAPTA, no BK current activation could be elicited either in the control solution or in the presence of Bay K (Fig. 2, D and E). This suggests that the additional BK channels activated in the presence of Bay K are still sensitive to the strong buffering action of BAPTA.
These results suggest that the BK channels underlying the Bay K-sensitive BK current are located at a distance that lies between the space constants for EGTA and BAPTA. However, because determination of the space constant depends on knowledge of the precise EGTA and BAPTA concentrations, which was unavailable here, we also repeated these experiments in cells in which defined concentrations of EGTA or BAPTA were introduced via the patch pipette (see below). Nevertheless, this result hinted that the two-population model has limitations in explaining the effect of Bay K.
BK current activation promoted by high [Ca2+]ext is unaffected by intracellular EGTA
Similar to the effect of Bay K, BK current activated by brief
Ca2+ influx steps increases when
[Ca2+]ext is increased
(Prakriya and Lingle 1999). Because the total available
BK current is not altered by high
[Ca2+]ext (data not
shown), the two-population hypothesis predicts that the additional
increase in BK current activation should arise from activation of those
BK channels that are normally inhibited by EGTA. This predicts that the
increase in BK current activation during brief influx steps by high
[Ca2+]ext should be
inhibited by EGTA. We tested this prediction by raising
[Ca2+]ext and evaluating
the effects of EGTA on the additional BK current.
We observed a significant increase in BK current activation by brief influx steps in intact cells when [Ca2+]ext was raised from 2 to 5 mM (Fig. 3A). A subsequent increase in [Ca2+]ext from 5 to 10 mM, however, failed to increase BK current despite a significant increase in the amplitude of the Ca2+ current (Fig. 3A). We did not investigate the flattening of the BK current-Ca2+ current relationship, but rather focused on the effects of EGTA and BAPTA on the increase in BK current caused by elevating [Ca2+]ext. Also, in separate experiments, we did not find any change in the open probability of whole cell BK current in 10 µM [Ca2+]i when [Ca2+]ext was altered from 2 to 10 mM (not shown). Thus changes in BK current activation seen by changes in [Ca2+]ext are not due to direct effects on BK channels of varying the external divalent concentration.
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Surprisingly, in cells loaded with EGTA, the increase in BK current activation by elevated [Ca2+]ext was essentially identical to that seen in perforated patch-clamped cells (Fig. 3B). BK current amplitude increased by 47 ± 3% (n = 4) by increasing [Ca2+]ext from 2 to 10 mM in EGTA-loaded cells and by 40 ± 3% (n = 5) in perforated-patch clamped cells. Thus this result suggests that the additionally active BK channels are within the 160-nm space constant for EGTA. Moreover, the effect of increasing [Ca2+]ext was additive to that of Bay K (Fig. 4A). Whereas Bay K roughly doubled the BK current activated by 5-ms influx steps, there was an additional 95 ± 20% (n = 5) increase when [Ca2+]ext was subsequently raised to 10 mM. This effect also persisted in EGTA-AM loaded cells (82 ± 24% increase, n = 5, when [Ca2+]ext was increased from 1.8 to 10 mM). The lack of an appreciable EGTA effect on the additionally active BK current in all these conditions implies that the additionally active BK channels must be located within a region in which EGTA is ineffective in buffering [Ca2+]i.
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Finally, elevation of
[Ca2+]ext did not cause
BK current activation to lose its selective dependence on influx
through L-, but not N- or P-type Ca2+ channels
(Prakriya and Lingle 1999). When a cocktail of 1 µM CgTx-GVIA and 100 nM Aga TK was applied, BK current activation was
unaffected (4/4 cells). This suggests that, even under these conditions
of altered Ca2+ influx, N- and P-type
Ca2+ channels do not play a role in the BK
current activation.
The lack of effect of EGTA on both the Bay K and the high [Ca2+]ext-mediated increases in BK current suggests that the underlying BK channels must be located sufficiently close to Ca2+ channels so as to be in the region of unbuffered [Ca2+]i. Any estimate of the spatial extent of this unbuffered region requires knowledge of the exact concentration of EGTA in the cell, which was not determined in experiments with EGTA-AM. Therefore experiments with Bay K and high [Ca2+]ext were also repeated in cells directly dialyzed with 5 mM EGTA using the standard whole cell method. A disadvantage in these experiments was that rundown of the BK current activated by Ca2+ influx often occurred after the first few minutes of recording, irrespective of whether EGTA was present or not in the recording pipette. However, in three cells in which stable BK currents could be recorded for >5 min with a 5-mM intracellular EGTA solution, the effects of Bay K and elevation of the [Ca2+]ext were similar to those evoked in the EGTA-AM-loaded cells. The average increase in BK current evoked by Bay K was 86 ± 17% over control, and the increase in BK current activation by the combination of Bay K and 10 mM [Ca2+]ext was 71 ± 12% over that seen in the presence of Bay K alone. Figure 4B illustrates these effects in one cell. Collectively, these experiments suggest that EGTA cannot be used to distinguish the BK-Ca2+ channel distance between currents activated by brief and long duration Ca2+ influx steps and point to serious limitations in the two-population model.
In contrast to EGTA, when chromaffin cells were loaded with 1 mM BAPTA
via the patch pipette, all BK current activation was blocked, and this
effect could not be overcome even by elevating [Ca2+]ext to 10 mM in Bay
K (Fig. 4C). This suggests that most BK channels in
chromaffin cells must be located beyond the
BAPTA from Ca2+ channels
(approximately 40 nm at 1 mM BAPTA).
A 20-ms step can activate all available BK current in Bay K and high [Ca2+]ext
The data presented above indicate that the balance of current
activated by brief and long Ca2+ influx steps is
not a fixed property of the cell but can be dramatically varied by
varying Ca2+ influx. What fraction of BK current
can be activated by brief steps when Ca2+ influx
is enhanced by Bay K and high
[Ca2+]ext? BK current
activated by 5-ms steps to 0 mV in the presence of Bay K comprises
~36% of the total available current (Prakriya and Lingle
1999). BK current activation roughly doubles by
subsequently increasing
[Ca2+]ext from 1.8 to 10 mM (Fig. 4A). This implies that over 70% of the BK current
is activated by 5-ms influx steps in Bay K and high
[Ca2+]ext in an
EGTA-resistant manner. Even this could be an underestimate as BK
current activation time constants at 0 mV are
3 ms (Cui et al.
1997
). Thus 5-ms Ca2+ influx steps would
almost certainly be insufficient to produce steady-state activation of
BK current. This suggests that if the duration of the
Ca2+ influx step is increased by 5-10 ms to
allow BK current to reach steady state, possibly all of the BK current
in the cell might be activated.
We examined this by increasing the duration of the
Ca2+ influx step in 10-ms increments to determine
the duration of the influx step that results in full activation of
BK current. The condition of maximal activation was tested by stepping
the membrane potential from +81 to +111 mV to see whether the
voltage step produced additional activation of BK current
(Prakriya et al. 1996). In the presence of normal
[Ca2+]ext, steps from +81
to +111 mV always produced additional BK current activation when brief
Ca2+ influx steps were used, and maximal
activation occurred only after the duration of
Ca2+ influx steps reached 100 ms or greater (Fig.
5A). The addition of Bay K
reduced this duration to about 50 ms (Fig. 5B). However, when both Bay K and 10 mM
[Ca2+]ext were present, a
20-ms influx step was sufficient to produce activation of all available
BK current (Fig. 5C). Thus this result shows that the large
numbers of BK channels that normally remain silent during brief
Ca2+ influx steps can be activated in conditions
of elevated Ca2+ influx.
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Collectively, these results show that the fraction of BK channels
activated by brief influx steps can be increased by either of two
manipulations: 1) an increase in the
Popen of L-type
Ca2+ channels by Bay K or 2) an
increase in the single-channel Ca2+ current by
elevating the [Ca2+]ext.
BK channels that remain silent or that are activated with low open
probabilities during brief influx steps under control conditions can be
robustly activated in Bay K and high
[Ca2+]ext. EGTA has no
effect on the activation of these BK channels (Fig. 4A),
implying that their average distance from Ca2+
channels is less than EGTA. Thus rather than
representing two distinct populations of BK channels at differing
distances from Ca2+ channels, BK current
activated by brief and long duration Ca2+ influx
steps might represent BK channels that are activated with a continuum
of open probabilities, and exposed to a continuum of
[Ca2+]i, but that are all
located within 40-160 nm from Ca2+ channels.
Can randomly distributed Ca2+ and BK channels account for the observed coupling?
The precise distribution of Ca2+ channels in
chromaffin cells remains largely unknown. Some studies have suggested
that Ca2+ channels may be organized in clusters
so that "hotspots" of elevated [Ca2+]i result from their
activation (Robinson et al. 1995). However, a
more recent study has taken the view that Ca2+
channels are uniformly distributed over most of the cell surface (Carabelli et al. 1998
). Whatever the precise
Ca2+ channel distribution, the
relative distribution of Ca2+ and BK
channels must result in the following: 1) selective
activation of BK current by L- and Q-type Ca2+
channels and 2) the constraint imposed by the ability of
BAPTA but not EGTA to inhibit BK current activation. As a first step in
exploring this issue, we asked whether a particular arrangement of
Ca2+ and BK channels is required to account for
these results.
We asked whether an apparent "coupling" between Ca2+ and BK channels could simply arise from random positioning of enough channels in the membrane. For this, we calculated the theoretical fraction of BK channels that would be exposed to a given [Ca2+]i if BK and Ca2+ channels were assumed to be randomly distributed. Our experimental data suggest that, in the presence of Bay K and in 5 mM intracellular EGTA, about 30-40% of the BK channels in the cell are activated by brief Ca2+ steps. In addition, the rate of BK current inactivation at 0 mV with 5 mM intracellular EGTA suggested that the channels are exposed to an average [Ca2+]i of 20 µM or higher (Fig. 2C). Therefore we compared this to the theoretical fraction of BK channels that would be exposed to [Ca2+]i of at least 20 µM with 5 mM EGTA in the cell, when BK and Ca2+ channels are randomly distributed. To calculate the steady-state [Ca2+]i detected by individual BK channels, we used a buffered diffusion model of Ca2+ migration (see METHODS). An important parameter in this simulation is the number of Ca2+ channels, which was estimated to be 5,000-10,000 (see METHODS).
We found that when Ca2+ and BK channels are
distributed randomly, the fraction of BK channels exposed to 20 µM
[Ca2+]i is less than the
experimentally observed number. With 5,000-10,000 Ca2+ channels, only 1-2% of all the BK channels
were close enough to Ca2+ channels to be exposed
to [Ca2+]i of 20 µM or
higher. Even when 15,000 Ca2+ channels were
assumed, the fraction of BK channels exposed to 20 µM or higher
increased only to 2.5%. This is dramatically lower than the 30-40%
fraction suggested by experimental observations. In fact, the random
distribution model predicted that only about 10% of available BK
channels are exposed to [Ca2+] of 10 µM or
higher (Fig. 6). In contrast, the
experimental observation that 30-40% of all BK channels are activated
by 5-ms steps to 9 mV in the presence of Bay K implies a minimum
average [Ca2+]i of ~10
µM for all BK channels (Fig. 4 of Prakriya et al.
1996
). Note that in these simulations, we assumed a
Ca2+ channel open probability of 1.0. A lower Ca
channel open probability would have reduced the above calculated
estimates even lower. Thus these simulations strongly suggest that
random localization of Ca2+ and BK channels
cannot lead to the functional coupling between them seen
experimentally.
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Note that changes in the estimate of the single-channel Ca2+ current do not alter these conclusions. An assumption of a single channel current of 0.08 pA and 5,000-10,000 Ca2+ channels predicts a maximum possible whole cell Ca2+ current of 400-800 pA, which is actually an overestimate of the current observed with physiological Ca2+ (1.8 mM). If the single-channel current amplitude is 10-fold higher, this would require a 10-fold reduction in the assumed number of Ca2+ channels to maintain consistency with whole cell current values. Thus, although the local [Ca2+]i in the immediate vicinity of open Ca2+ channels would be higher with an increased single-channel current, the reduced number of Ca2+ channels would increase the distance between Ca2+ channels and BK channels, such that a random distribution of Ca2+ and BK channels is still unable to account for the results.
Multiple Ca2+ channels may be involved in driving the activation of single BK channels
The results with BAPTA and EGTA suggest that there are both lower
and upper bounds for the distances between single
Ca2+ and BK channels in rat chromaffin cells, and
we have used the space constants of 40 and 160 nm for BAPTA and EGTA,
respectively, to focus this discussion. However, this analysis has not
taken into account whether BK channels at such distances are exposed to
sufficient Ca2+ to produce the amounts of current
activation observed in the experimental results. Here, using
information about the Ca2+ sensitivity of BK
channel activation in chromaffin cells (Prakriya et al.
1996), we reconsider this issue. Because experimental data on
the effects of EGTA and BAPTA are available at concentrations of 400 µM, 1 mM, and 5 mM (Prakriya et al. 1996
), we first
examined the predicted steady-state profiles of
[Ca2+]i at various
distances at these buffer concentrations (Fig.
7). From this information, we asked
whether we could determine the separation between individual BK and
Ca2+ channels that would be compatible with the
effects of EGTA and BAPTA.
|
Figure 7, A and B, shows the expected
[Ca2+]i profiles at
various EGTA and BAPTA concentrations. Because BAPTA is effective in
preventing BK current activation under all influx conditions (Fig.
4C), we computed the distance where 1 mM BAPTA lowers the [Ca2+]i to below the
threshold for BK channel activation (4 µM at 0 mV) (Prakriya
et al. 1996). This distance should also satisfy the requirement
that, in 5 mM EGTA, BK channels detect [Ca2+]
of at least 20 µM. We find that, for 1 mM BAPTA to effectively lower
[Ca2+]i below 4 µM, the
BK channel-Ca channel separation has to be at least 40 nm (Fig.
7B). In fact, when
[Ca2+]ext is raised to 10 mM, the single-channel Ca2+ current might be
expected to be doubled (Fig. 3A), predicting that
[Ca2+]i at all distances
would be increased. With this condition, the separation between BK and
Ca2+ channels necessary for 1 mM BAPTA to
maintain [Ca2+]i below 4 µM becomes 50 nm (not shown).
However, this result leads to a paradox. If BK channels are located at
least 50 nm from a Ca2+ channel (which is
required to account for the total effectiveness of BAPTA), Fig.
7A indicates that
[Ca2+]i in the presence
of 5 mM EGTA will be only ~5 µM. The Ca2+
dependence for activation (and inactivation) of BK channels
(Prakriya et al. 1996) predicts that this
[Ca2+]i will be grossly
insufficient to elicit the rapid activation (and inactivation) of BK
channels that is seen in EGTA. Conversely, for a BK channel to be
exposed to [Ca2+]i of 20 µM or higher in the presence of 5 mM EGTA, Fig. 7A
predicts that it would have to be within 15 nm from an individual
Ca2+ channel. However, at this distance,
[Ca2+]i is predicted to
be >10 µM in the presence of BAPTA (Fig. 7B). This
[Ca2+]i would be
sufficient to elicit substantial BK current activation. In fact, a
close examination of Fig. 7, A and B, indicates
that there is no distance where single BK channels can be exposed to [Ca2+]i of 20 µM or
higher in 5 mM EGTA, but where the
[Ca2+]i is below 4 µM
in 1 mM BAPTA. Increasing or decreasing the assumed value of the single
Ca2+ channel current did not satisfy this paradox.
How can this paradox be resolved? One assumption in the above analysis
has been that each BK channel is influenced by
[Ca2+]i arising only from
a single Ca2+ channel. In reality, the
Ca2+ signal driving BK channel activation may
arise from multiple neighboring Ca2+ channels.
[Ca2+]i at the location
of each BK channel will then be significantly higher for a given
Ca2+-BK channel separation because contributions
from all the nearby Ca2+ channels will summate
(Naraghi and Neher 1997; Pape et al.
1998
). A consequence of this summation is that, to be exposed
to a given value of
[Ca2+]i, the average
separation distance between Ca2+ and BK channels
can be larger than if each Ca2+ channel were
acting alone. In fact, because the
s for BAPTA and EGTA are so
different (40 vs. 160 nm), the possibility arises that at a particular
Ca2+-BK channel separation (d) such
that
BAPTA
d
EGTA,
[Ca2+]i in BAPTA may be
quite small, but yet in EGTA, it could add up to substantial
concentration. As an example, consider a hypothetical case in which BK
channels are located at an average distance of 75 nm from
Ca2+ channels and are exposed to a cumulative
[Ca2+]i arising from,
say, 10 Ca2+ channels. In the presence of 1-5 mM
BAPTA, Fig. 7B predicts that the contribution to
[Ca2+]i from each
Ca2+ will be ~0.38-0.11 µM, and the
cumulative [Ca2+]i will
therefore be <4 µM. This
[Ca2+]i would produce
little, if any, BK activation at 0 mV. However, in the presence of 5 mM
EGTA, each Ca2+ channel would contribute ~4
µM of [Ca2+]i at the
site of the BK channel (Fig. 7A). These
Ca2+ signals would summate to produce a
[Ca2+]i of ~40 µM at
the location of the BK channel, which should be sufficient to almost
maximally activate BK channels (Prakriya et al. 1996
).
Thus the distance criteria imposed by the EGTA-BAPTA results would be
satisfied if the high
[Ca2+]i around BK
channels in chromaffin cells arose not from the micro-domains of single
Ca2+ channels, but from overlapping domains from
multiple Ca2+ channels.
We next examined the effects of distributing 10,000 Ca2+ and 2,000 BK channels in a hypothetical membrane and determined [Ca2+]i detected by BK channels when each BK channel was associated either with only one, or with several Ca2+ channels. Because experimental observations suggested that, in Bay K, roughly 40% of BK channels are activated in an EGTA-resistant fashion with [Ca2+]i of at least 20 µM, we attempted to define the distance between BK and Ca2+ channels at which 40% of BK channels would be exposed to [Ca2+]i of 20 µM or higher in EGTA, but where all BK channels would be exposed to [Ca2+]i below their threshold for activation (~4 µM at 0 mV) in BAPTA.
As before, when only one Ca2+ channel was associated with a BK channel, no distance could be found that accommodated the constraints imposed by the EGTA-BAPTA results (Fig. 7, C and D). A BK channel had to be located closer than 10 nm from Ca2+ channel to be exposed to [Ca2+]i in the range of 20 µM in 5 mM EGTA (Fig. 7C). Yet, at these distances, the simulations predicted that a significant fraction of BK channels also detected [Ca2+]i in the range of 10-20 µM in BAPTA (Fig. 7D). In contrast, when each BK channel was placed within a cluster of Ca2+ channels containing, on average, 5 Ca2+ channels, and when the BK-Ca2+ channel distance was at least 50 nm, ~40% of BK channels detected [Ca2+]i larger than 20 µM in the presence of EGTA, while in BAPTA, virtually no BK channels were exposed to [Ca2+]i above 4 µM (Fig. 7, E and F). Note that because the number of open Ca2+ channels in the cluster is variable, this arrangement also produces heterogeneity in the [Ca2+] detected by the individual BK channels (Fig. 7E). Collectively, this is consistent with our experimental observations and suggests that the high [Ca2+]i around BK channels during Ca2+ influx arise from clusters of open Ca2+ channels and not from the micro-domains of single Ca2+ channels.
Concentration of residual Ca2+ after termination of influx may determine the extent of slow BK current activation
The above analysis suggests that the heterogeneity in [Ca2+] detected by individual BK channels during influx might arise because of differences in the extent of Ca2+ domain overlap at the sites of the individual BK channels. However, one issue that is unexplained by this model is what produces the slow secondary phase of BK current activation at +81 mV with long Ca2+ influx steps (Fig. 1B). This is addressed next.
We hypothesized that the slow component could arise if the decay of
[Ca2+]i after termination
of influx is slow enough such that residual [Ca2+]i is sufficient to
support additional BK channel activation. Decay of
[Ca2+]i immediately
following the termination of Ca2+ influx is
influenced by the nature of buffers in the cell: fixed buffers slow the
fall of [Ca2+]i, whereas
mobile buffers speed them up (Naraghi and Neher 1997; Roberts 1994
). Chromaffin cells are known to possess
significant amounts of fixed buffers (Xu et al.
1997
), but only minor quantities of mobile buffers
(Zhou and Neher 1993
). Hence, it is likely that the slow
secondary activation of BK current could arise from the slow fall of
[Ca2+]i subsequent to the
termination of the influx step.
To quantitatively evaluate this possibility, we simulated the transient
relaxation of [Ca2+]i at
a given distance (100 nm) from a Ca2+ channel and
examined the time course of relaxation subsequent to the termination of
influx under various buffer conditions (Fig. 8). We then compared the time course
predicted from these simulations to the experimental observations. The
presence of a mobile buffer, such as EGTA, dramatically speeds up the
fall in [Ca2+]i,
consistent with previous predictions (Naraghi and Neher
1997). Thus in 1 mM EGTA,
[Ca2+]i reaches 99% of
its steady-state value 1 ms after the closure of the
Ca2+ channel. This implies that when the membrane
potential is stepped from 0 to +81 mV,
[Ca2+]i may fall below 1 µM from 20 µM within a millisecond. This is consistent with the
virtual lack of slow activation of BK current at +81 mV in EGTA-loaded
cells. By contrast, in the presence of 1 mM of a fixed, low-affinity
buffer, [Ca2+]i
transients are sufficiently delayed that even 4 ms after the termination of influx,
[Ca2+]i has relaxed to
only 80% of its steady-state value. Hence, a [Ca2+]i of 10 µM, which
is the average [Ca2+]i
detected by BK channels after influx steps of 100 ms or longer (Prakriya et al. 1996
), will fall to only ~2 µM
after 4 ms into the +81-mV step. Ten micromolar
[Ca2+]i will activate
only ~30% of the available BK current activation at 0 mV, but, at
+81 mV, a significant amount of BK current activation can occur at 2 µM [Ca2+]i
(Solaro and Lingle 1992
). Thus the additional BK current
activation at +81 mV after the termination of long duration
Ca2+ influx steps may simply reflect the presence
of residual [Ca2+]i
sufficient to activate BK channels not opened at 0 mV.
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DISCUSSION |
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Using manipulations of extracellular Ca2+,
Bay K, and cytosolic Ca2+ buffers, we have
defined properties of the coupling between Ca2+
channels and BK channels with the aim of placing constraints on the
possible arrangement of Ca2+ channels and BK
channels. Our analysis suggests that random localization of
Ca2+ and BK channels underestimates the fraction
of BK channels that are activated by brief influx steps. Specifically,
an insufficient number of BK channels are exposed to sufficiently high
[Ca2+]i to be activated.
This suggests that a specific mechanism must exist in chromaffin cells
to mediate the functional coupling between Ca2+
and BK channels. Moreover, analysis of the EGTA/BAPTA effects suggests
that the Ca2+ signals that drive individual BK
channels are probably obtained from overlapping domains from a set of
Ca2+ channels in the vicinity of the BK channel,
not from the microdomains of single Ca2+
channels. Thus in chromaffin cells, the distance between
Ca2+ and BK channels appears to be sufficiently
large that efficient activation of BK current requires summation of
Ca2+ signals. A recent study similarly reports
that, at the synapses between the calyces of Held and the medial
nucleus of the trapezoid body, most synaptic vesicles may be released
by the combined action of multiple Ca2+ channels
(Borst and Sakmann 1999).
Effects of manipulations of Ca2+ channel behavior on BK channel activation
Both Bay K and increases in [Ca2+]ext increased the fractional activation of BK current elicited by 5-ms steps to 0 mV. Each of these manipulations is expected to increase net Ca2+ influx in different ways: Bay K by increasing the open probability of L-type Ca2+ channels and high [Ca2+]ext by increasing the single Ca2+ channel current. What, if anything, do these results reveal about the details of BK and Ca2+ channel organization in the membrane?
Bay K, by increasing the average number of Ca2+ channels open at any time, might increase the overlap of Ca2+ arising from distinct Ca2+ channels without affecting the submembrane profile of Ca2+ resulting from any individual Ca2+ channel. This will increase the open probability of BK channels detecting sub-maximal [Ca2+]i, and therefore increase BK current activation. In contrast, a change in single channel current resulting from increased [Ca2+]ext will change the Ca2+ concentration profile in the vicinity of each open Ca2+ channel without altering the number of open Ca2+ channels. The increased spread of Ca2+ could promote overlap of Ca2+ from adjacent Ca2+ channels, and hence, also increase the open probability of BK channels. Thus the ability of these two independent manipulations to increase the fractional activation of BK current is consistent with activation of BK channels by Ca2+ signals originating from multiple Ca2+ channels.
The possibility that activation of each BK channel arises from
Ca2+ arising from multiple
Ca2+ channels is also supported by the
observation that block of BK current activation by various selective
Ca2+ channel antagonists sums to more than 100%.
Blockade of L-, Q-, P-, and N-type Ca2+ currents
reduces BK current activation during 5-ms Ca2+
influx steps by 77, 42, 14, and 11%, respectively, which sums to
144%. By contrast, the corresponding Ca2+
current amplitudes are reduced by only 33, 24, 12, and 21%,
respectively, which sums to 90% (Prakriya and Lingle
1999). This is inconsistent with the idea that single
Ca2+ channels activate single BK channels, but
would be expected if the Ca2+ signal activating
BK channels arose from overlapping domains from different
Ca2+ channel subtypes.
These results, coupled with the effects of EGTA and BAPTA, support a
view that BK and Ca2+ channels (primarily L-type)
are associated in such a way that multiple Ca2+
channels contribute to the Ca2+ elevation
required for activation of each BK channel. Moreover, the observation
that BK current is preferentially activated by Ca2+ influx only through the L- and, when
present, Q-type Ca2+ channels but not the N- and
P-type Ca2+ channels (Prakriya and Lingle
1999) supports the view that specific association of BK and
Ca2+ channels also occurs. Thus in chromaffin
cells, BK and Ca2+ channels are associated in
such a way that specificity in Ca2+ signaling is
provided without the two channel types being in tight physical
association. In fact, considering that the cross-sectional diameter of
channel proteins may be only 8-10 nm (Unwin
1995
), our conclusion that the distance between
Ca2+ and BK channels is at least several tens of
nanometers implies that the coupling between these two proteins is
unlikely to involve direct physical contact. Instead, the selective
association of BK channels with L- and Q-type
Ca2+ channels may require a family of
intermediate proteins (Sheng and Wyszynski 1997
).
Reconciling the current results with earlier work
In previous work (Prakriya et al. 1996), we
proposed that BK channels occur in either of two populations: one
closely associated with Ca2+ channels and one
activated by Ca2+ that diffuses some distance
from Ca2+ channels. A key point in this work was
the idea that BK channels opened during brief influx steps are
maximally activated. This was suggested by the rapid inactivation of BK
current in EGTA, indicating that these channels are exposed to a high
Ca2+, most likely in excess of 20 µM. At
[Ca2+]i above 20 µM, BK
channels are near maximally activated (Prakriya et al.
1996
). Hence, to test whether those channels activated during
brief influx steps were maximally activated, we simultaneously elevated
bulk cytosolic Ca2+ by activation of muscarinic
acetylcholine receptors. This was expected to produce an overall
additional [Ca2+]i
elevation of 3-4 µM (Prakriya et al. 1996
). If BK
channels activated during brief influx steps were only partially
activated by sub-saturating amounts of
[Ca2+]i, the additional
Ca2+ elevation should increase the fractional
activation of BK current. This was not observed, arguing that the BK
channels activated by brief influx steps were already maximally
activated. Muscarine did enhance BK current activated by longer
duration steps, indicating that for channels activated at lower open
probability the additional increment of
[Ca2+]i contributed by
muscarinic receptor activation does have an effect.
The present results, on the other hand, suggest that BK channels are activated by a continuum of Ca2+ arising from overlapping Ca2+ domains. Further, the fact that Bay K and elevations in [Ca2+]ext increase BK current during brief influx steps in a BAPTA-sensitive, but EGTA-resistant fashion support a view in which most BK channels are within an approximately 50- to 160-nm disk of influence of a set of Ca2+ channels. Some BK channels may, in fact, be maximally activated during the brief influx steps. However, variation in the fractional activation of BK channels could arise based on variation in the average Popen of Ca2+ channels, the specific local density of Ca2+ channels, and the single-channel Ca2+ current. Note that this view does not preclude the possibility that, under normal conditions, the augmentation of BK current by long influx steps (e.g., in Fig. 1B) could arise from activation of some BK channels by diffuse Ca2+. Instead, the data simply indicate that most BK channels are positioned sufficiently close to Ca2+ channels that if those Ca2+ channels are opened, BK channels are activated in an EGTA-resistant fashion. This view raises two questions. First, why did muscarine-induced Ca2+ elevations fail to produce an additional increase in the fractional activation of BK channels during brief influx steps? Second, what accounts for the apparently slow secondary activation of BK channels with longer influx steps?
At present, we cannot fully answer the first question. One possibility
is that the muscarine-induced
[Ca2+]i elevations are
less than the 2-4 µM suggested in our earlier work (Prakriya
et al. 1996). A second possibility is that muscarinic receptor-mediated inhibition of Ca2+ influx
resulted in a decrease in BK current activation that exactly balanced
any increase in BK current activation resulting from the muscarinic
induced elevation of Ca2+. We consider the latter
possibility unlikely. Although the former possibility cannot be
entirely excluded, the inactivation behavior of BK current activated in
the presence of muscarine, the fractional activation of BK current
during muscarine action, and the effects on inactivation of cytosolic
addition of various
[Ca2+]i argue for a
concentration of 2-4 µM. Thus this earlier result remains
incompletely explained. The slow secondary activation of BK channels
during longer influx steps is addressed in the next section.
Residual Ca2+ and the slow secondary phase of BK current activation
Analysis of the kinetics of [Ca2+] decay
after the closure of a Ca2+ channel suggests that
the secondary activation of BK current at +81 mV during long influx
steps arises from residual Ca2+ that is
sufficiently high to support additional BK current activation. The
decay of residual Ca2+ after termination of
influx is influenced by the properties of intracellular
Ca2+ buffers: Ca2+ decay is
slow in the presence of immobile buffers but fast in mobile buffers
(Naraghi and Neher 1997; Roberts 1994
).
Our conclusion that residual Ca2+ influences the
extent of slow BK current activation is consistent with the report that
chromaffin cells contain large quantities of immobile buffers but
little or no mobile buffers (Zhou and Neher 1993
). It is
also supported by the observation that introduction of a mobile buffer
like EGTA largely eliminates the slow component. Thus in chromaffin
cells, activation of BK current during brief Ca2+
influx steps is triggered by large and brief rises in
[Ca2+]i, whereas the
augmentation of the slow BK current during long Ca2+ loads appears to arise from smaller and
slower rises in residual Ca2+. This is
reminiscent of Ca2+ effects on transmitter
release and potentiation of release in synapses (Swandulla et
al. 1991
).
Interestingly, the slow component of BK current is largely absent after
brief (<10 ms) Ca2+ influx steps
(Prakriya et al. 1996), implying that
[Ca2+]i falls very
rapidly below the threshold for BK activation after brief
Ca2+ influx steps. As the influx step duration is
progressively increased, the slow component also increases, suggesting
that the rate of decay of [Ca2+] is
progressively slowing down. What leads to the slowing in the rate of
decay of [Ca2+]i is
unknown, but in principle, it could happen because of the progressive
saturation of a limited quantity of mobile buffer, which contributes
significantly in rapidly clearing Ca2+ for small
Ca2+ loads, but is saturated by large
Ca2+ loads. After saturation of the mobile
buffer, the time course of the
[Ca2+]i relaxation may be
governed by the effects of fixed Ca2+ buffers and
Ca2+ sequestration agents such as mitochondria,
Na+-Ca2+ exchangers, and
Ca2+-ATPases.
In summary, our results lead us to propose that the average BK-Ca2+ channel distance in chromaffin cells is several tens of nanometers. Activation of individual BK channels must result from Ca2+ arising from groups of Ca2+ channels, and random distributions of BK and Ca2+ channels are unable to account for the coupling observed. With this type of arrangement, some variation in the average open probability of BK channels during Ca2+ influx would therefore be expected to result from variations in single Ca2+ channel activation probability, the exact local density and distribution of Ca2+ channels, or spatial differences in the extent of endogenous Ca2+ buffering. The contribution of these various factors to the observed Ca2+ channel-BK channel coupling will have to await future studies.
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ACKNOWLEDGMENTS |
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The authors thank Drs. Steven Mennerick, Jiu Ping Ding, Joe Henry Steinbach (Washington University), and Jack Waters (Stanford University) for helpful discussions and comments, and S. Swanson for cell culture.
This work was supported by National Institute of Neurological Disorders and Stroke Grant NS-37671 to C. Lingle.
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FOOTNOTES |
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Present address and address for reprint requests: M. Prakriya, B-100, Beckman Center, Dept. of Molecular and Cellular Physiology, Stanford University, Stanford, CA 94305 (E-mail: prakriya{at}leland.stanford.edu).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 26 January 2000; accepted in final form 9 May 2000.
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REFERENCES |
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