Activation of BK Channels in Rat Chromaffin Cells Requires Summation of Ca2+ Influx From Multiple Ca2+ Channels

Murali Prakriya and Christopher J. Lingle

Department of Anesthesiology, Washington University School of Medicine, St. Louis, Missouri 63110


    ABSTRACT
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    INTRODUCTION
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    METHODS
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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. omega -Conotoxin GVIA (CgTx GVIA, RBI, Natick, MA) and omega -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)
[<IT>Ca</IT>(<IT>r</IT>)]<SUB><IT>ss</IT></SUB><IT>=</IT><FR><NU>(<IT>Q</IT><IT>1−</IT><IT>Q</IT><IT>0</IT>)<IT>∗</IT><IT>e<SUP>−r·W</SUP></IT><IT>+</IT><IT>Q</IT><IT>0</IT></NU><DE><IT>r</IT></DE></FR><IT>+</IT>[<IT>Ca</IT>]<SUB><IT>0</IT></SUB> (1)
where Q1, Q0, and W are constants (Stern 1992) calculated from the influx and buffer parameters, r is the distance from a Ca2+ channel, and [Ca]0 is the basal [Ca2+]i.

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 (lambda ) was calculated from the relationship
&lgr;=<RAD><RCD><IT>D<SUB>Ca</SUB></IT><IT>/</IT><IT>K<SUB>f</SUB></IT><IT>·</IT>[<IT>buf</IT>]</RCD></RAD> (2)
The single-channel Ca2+ current (ICa) was assumed to be 0.08 pA. This was derived from the observation that ICa in 10 mM [Ba2+]ext is ~0.4 pA (Prakriya and Lingle 1999), and the observation that whole cell Ca2+ current amplitudes in 2 mM [Ca2+]ext are roughly 20-25% of the current amplitudes in 10 mM [Ba2+]ext (Prakriya and Lingle 1999). Note that this agrees well with the 2.4-pS conductance reported for L-type Ca2+ channels in 2 mM [Ca2+]ext (Church and Stanley 1996). Two thousand BK channels were assumed for all simulations. This estimate was determined from estimates of the total BK current in the cell and the single-channel BK conductance.

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)
[<IT>Ca</IT>(<IT>r</IT><IT>, </IT><IT>t</IT>)]<IT>=</IT>[<IT>Ca</IT>(<IT>r</IT>)]<SUB><IT>ss</IT></SUB><IT>∗</IT><IT>f</IT>(<IT>t</IT><IT>, </IT><IT>r</IT>) (3)
where [Ca(r)]ss is the steady-state [Ca2+]i at time t = infinity , and f(t,r) is a function given by
<IT>f</IT>(<IT>t</IT><IT>, </IT><IT>r</IT>)<IT>=erf </IT><IT>c</IT><FENCE><FR><NU><IT>r</IT></NU><DE><RAD><RCD><IT>4</IT><IT>D<SUB>Ca</SUB>t</IT></RCD></RAD></DE></FR></FENCE> (<IT>for no buffer</IT>)

<IT>f</IT>(<IT>t</IT><IT>, </IT><IT>r</IT>)<IT>=</IT><FR><NU><IT>1</IT></NU><DE><IT>2</IT></DE></FR> <FENCE><IT>erf </IT><IT>c</IT><FENCE><FR><NU><IT>r</IT></NU><DE><RAD><RCD><IT>4</IT><IT>D<SUB>Ca</SUB>t</IT></RCD></RAD></DE></FR><IT>−</IT><RAD><RCD><FR><NU><IT>t</IT></NU><DE><IT>&tgr;</IT><SUB><IT>Ca</IT></SUB></DE></FR></RCD></RAD></FENCE><IT>+</IT><IT>e</IT><SUP>(<IT>2</IT><IT>r</IT><IT>/&lgr;</IT><SUB><IT>Ca</IT></SUB>)</SUP></FENCE>

×erf <IT>c</IT><FENCE><FENCE><FR><NU><IT>r</IT></NU><DE><RAD><RCD><IT>4</IT><IT>D<SUB>Ca</SUB>t</IT></RCD></RAD></DE></FR><IT>+</IT><RAD><RCD><FR><NU><IT>t</IT></NU><DE><IT>&tgr;</IT><SUB><IT>Ca</IT></SUB></DE></FR></RCD></RAD></FENCE></FENCE> (<IT>for one mobile buffer</IT>)
and
<IT>f</IT>(<IT>t</IT><IT>, </IT><IT>r</IT>)<IT>=erf </IT><IT>c</IT><FENCE><FR><NU><IT>r</IT></NU><DE><RAD><RCD><IT>4</IT><IT>D</IT><SUB><IT>app</IT></SUB><IT>t</IT></RCD></RAD></DE></FR></FENCE> (<IT>for one immobile buffer</IT>)
where
<IT>D</IT><SUB><IT>app</IT></SUB><IT>=</IT><FR><NU><IT>D<SUB>Ca</SUB></IT></NU><DE><IT>1+</IT>[<IT>buf</IT>]<IT>/</IT><IT>K</IT><SUB><IT>d</IT></SUB></DE></FR>
and
&tgr;<SUB><IT>Ca</IT></SUB><IT>=</IT>(<IT>k</IT><SUB><IT>f</IT></SUB>[<IT>buf</IT>])<SUP><IT>−1</IT></SUP>
f(t,r) starts with a value of 0 at t = 0 and approaches 1 as t approaches infinity. We calculated the value of f(t,r), which gives the normalized [Ca2+] at a given time t.


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INTRODUCTION
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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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Fig. 1. Voltage-dependent K+ (BK) current activation is abolished by bis-(o-aminophenoxy)-N,N,N',N'-tetraacetic acid (BAPTA), but not by EGTA. A: the membrane voltage was stepped to +81 mV either with, or without a 20-ms conditioning step to 0 mV. In the absence of the conditioning step, no Ca2+-dependent current is activated, and all the outward current arises from a small purely voltage-dependent K+ current. By contrast, a conditioning step to 0 mV produces Ca2+ influx and activates a large amount of BK current at +81 mV. The arrow indicates the instantaneous BK current that is activated at +81 mV following the Ca2+ influx step. The instantaneous BK current is followed by a slowly activating BK current component. Perforated patch method. Rs = 12 MOmega ; Cm= 7 pF; 80% compensated. B: incremental increases in the Ca2+ influx step produce progressive increases in the amplitude of the peak current activated at +81 mV. The Ca2+ influx step duration was increased in steps of 20 ms. Most of the increase in the peak current at +81 mV arises from an increase in the slowly activating BK current component. Perforated patch method. Rs = 14 MOmega ; Cm = 6 pF; 80% compensated. C: BK channels exposed to high [Ca2+] can be unmasked by EGTA. Five millimolor EGTA was introduced into a chromaffin cell via the patch pipette. BK current activation was examined using the voltage protocol used in B. Virtually all the BK current at +81 is due to the instantaneous BK current, and the slow secondary component of BK current seen in perforated patch-clamped cells is eliminated. As the duration of the influx step is increased, BK current progressively declines due to inactivation during the influx step. Standard whole cell method. Rs = 4 MOmega ; Cm = 6 pF; 80% compensated. D: BAPTA inhibits activation of all BK current. One millimolar BAPTA was introduced into a chromaffin cell via the patch pipette. BK current activation was examined using the voltage protocol used in Fig. 1B. Rs = 7 MOmega ; Cm = 7 pF; 80% compensated.

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 (lambda ), which is the characteristic distance that a Ca2+ ion travels before it is captured by the buffer. At lambda  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, lambda EGTA and lambda 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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Fig. 2. The Bay K-induced enhancement of BK current persists in the presence of intracellular EGTA. A: a chromaffin cell was incubated with EGTA-AM for 45 min prior to electrophysiological recordings. The voltage of the cell was stepped to 0 mV to produce Ca2+ influx, and then stepped to +81 mV. The duration of the influx step was increased in steps of 20 ms (voltage protocol shown in Fig. 1). EGTA loading abolishes the slow secondary activation of BK current activation at +81 mV and produces progressive inactivation of BK current as the influx step duration is increased. B: 2 µM Bay K was applied on the cell shown in A. BK current activation was elicited by a single 5-ms influx step. C: same cell and voltage protocol as in A in the presence of 2 µM Bay K. D and E: Ca2+ influx fails to elicit BK current activation in a cell loaded with BAPTA, and this cannot be overcome by Bay K. Cell was incubated in 10 mM BAPTA-AM for 30 min. Perforated patch method. EGTA loaded cell: Rs = 12 MOmega ; Cm = 6 pF; 80% compensated. BAPTA loaded cell: Rs = 13 MOmega ; Cm = 6 pF; 80% compensated.

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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Fig. 3. The BK current activation enhanced by high [Ca2+]ext is resistant to EGTA. A: titration of BK and Ca2+ current amplitudes plotted at [Ca2+]ext of 2, 5, and 10 mM. BK current activation was measured as the instantaneous current activated at +81 mV following a 5-ms influx step to 0 mV. Peak Ca2+ current was measured during 10-ms steps to 0 mV. All currents are normalized to the amplitudes measured in 2 mM [Ca2+]ext. B: intracellular EGTA does not inhibit the high [Ca2+]ext effects. This cell was loaded with EGTA-AM for 1 h, and BK current activation was examined by 5-ms Ca2+ influx steps to 0 mV followed by test pulses to +81 mV.

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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Fig. 4. The effects of Bay K and high [Ca2+]ext on BK current activation are additive. A: the lower plot shows the effects of Bay K and high [Ca2+]ext on the amplitude of the instantaneous BK current. The increase in BK current activation seen by elevating the [Ca2+]ext is also observed after Bay K was applied. Moreover, the toxins CgTx GVIA (1 µM) and AgTx TK (100 nM) have no effects on the BK current, indicating that the N- and P-type Ca2+ channels are not involved in mediating activation of BK current, even under these conditions of altered Ca2+ influx. This chromaffin cell was loaded with EGTA-AM for 1 h, and BK current activation was examined by 5-ms Ca2+ influx steps to 0 mV followed by test pulses to +81 mV. B: the effects of Bay K and high [Ca2+]ext persist in cells directly loaded with 5 mM EGTA. EGTA was loaded via the patch pipette using the standard whole cell method. Recording was started 3-5 min after break-in. C: BK current activation is abolished by BAPTA, even in Bay K and high [Ca2+]ext. This cell was loaded with 1 mM BAPTA via the patch-pipette using the standard whole cell method.

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 lambda 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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Fig. 5. In the presence of Bay K and high [Ca2+]ext, a 20-ms Ca2+ influx step is sufficient to elicit maximal activation of all available BK current. The cell was stepped to 0 mV for varying durations, and then stepped to +81 mV. After 20 ms at +81 mV, the membrane voltage was again stepped to +111 mV to evaluate whether the BK current at +81 mV was maximally activated. A: in control solutions, brief influx steps always produce additional BK current activation when the potential is stepped from +81 to +111 mV, and maximal activation of BK current at +81 mV is achieved only after influx steps of 100 ms or longer. B: the addition of Bay K reduces the duration of the influx step when maximal activation of BK current occurs to ~50 ms. C: in the presence of Bay K and 10 µM [Ca2+]ext, a 20-ms Ca2+ influx step is sufficient to elicit maximal activation of the BK current at +81 mV. In this experiment, external Na+ was replaced with N-methyl-D-glucamine (NMG) to avoid blockade of BK channels by Na+ at positive voltages (Yellen 1984).

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 lambda 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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Fig. 6. Random arrangement of Ca2+ and BK channels grossly underestimates the fraction of BK channels exposed to high [Ca2+]i. The y-axis denotes the percentage of BK channels exposed to a [Ca2+]i greater than or equal to the corresponding numbers on the x-axis. The model assumes the presence of 5 mM EGTA with properties as described in METHODS. Only 0.5-2% of BK channels are exposed to [Ca2+]i of 20 µM or higher when channels are randomly distributed.

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.



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Fig. 7. Multiple Ca2+ channels may be required to account for the high [Ca2+]i detected by individual BK channels. A and B: the steady-state [Ca2+]i as a function of distance was calculated for EGTA and BAPTA as described in METHODS. In 5 mM EGTA, Ca2+ concentrations >= 20 µM occur only within ~15 nm from the Ca2+ channel. However, at these distances, [Ca2+]i in the presence of 1 mM BAPTA is also sufficiently large (>= 10 µM) so as to be above the threshold for BK current activation. Conversely, at distances where 1 mM BAPTA lowers the [Ca2+]i to below 4 µM (>40 nm from the Ca2+ channel), [Ca2+]i in the presence of EGTA is too low (<4 µM) to account for the robust activation of BK current observed physiologically. C and D: simulations of large numbers of Ca2+ and BK channels in the membrane indicate that the constraints imposed by the EGTA-BAPTA results cannot be accounted by assuming that each BK channel is associated with only 1 Ca2+ channel. Ten thousand Ca2+ channels and 2,000 BK channels were assumed. Each plot shows the effect of coupling 40% of BK channels (800 channels) in the cell to Ca2+ channels, at a ratio of one BK to one Ca2+ channel. The distance between the Ca2+ and BK channels in this group was varied and is indicated in the plot. Each BK-Ca2+ channel pair was localized randomly. The remaining BK and Ca2+ channels were placed at random. E and F: the EGTA-BAPTA results can be explained by assuming that each BK channel is influenced by Ca2+ arising from multiple Ca2+ channels. When 40% of BK channels are associated with multiple Ca2+ channels at a sufficiently large distance from the Ca2+ channels, a large fraction of BK channels are exposed to [Ca2+]i above 20 µM in 5 mM EGTA, whereas virtually no BK channels are exposed to [Ca2+]i above 4 µM in 1 mM BAPTA. Four thousand Ca2+ channels were randomly placed in rings around 800 BK channels. Thus each of these BK channels has an average of 5 Ca2+ channels around it. Because BK channels in this group were picked at random and assigned a Ca2+ channel, some BK channels will have more than five and others less than five Ca2+ channels. The remaining BK and Ca2+ channels were localized randomly. The diameter of the ring was varied and is indicated in the plot.

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 lambda 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 lambda BAPTA d lambda 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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Fig. 8. The slow BK current component and its abolishment by EGTA can be explained by the time course of relaxation of [Ca2+]i subsequent to the termination of influx. The plot shows the theoretical time course of the fall of [Ca2+] subsequent to the closure of a Ca2+ channel 100 nm away. In the presence of a mobile buffer (EGTA), [Ca2+]i approaches its steady-state value extremely rapidly so that within 1 ms after the termination of Ca2+ influx, [Ca2+] drops to <99% of its initial value. By contrast, in the presence of a fixed buffer, Ca2+ transients are slowed substantially to the point where even 4 ms after the termination of influx, at least 20% of the initial [Ca2+] is still present. EGTA (1 mM) was assumed for the mobile buffer. In the case of the fixed buffer, a concentration of 1 mM was assumed with the following properties: KD = 100 µM; Kf = 2 × 108 M-1s-1 (see Xu et al. 1997).


    DISCUSSION
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ABSTRACT
INTRODUCTION
METHODS
RESULTS
DISCUSSION
REFERENCES

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.


    ACKNOWLEDGMENTS

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.


    FOOTNOTES

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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ABSTRACT
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