INTRODUCTION

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Rat adrenal chromaffin cells maintained in primary cell culture express either of two phenotypic forms of large-conductance, Ca²⁺-dependent, voltage-dependent K⁺ channel (BK-type). One form, termed BK_i, exhibits rapid and essentially complete inactivation after activation, whereas the other, termed BK_s, exhibits the more usual sustained activation (Solaro and Lingle, 1992; Solaro et al., 1995). In those cells and patches that express BK_i channels (~80%), there appears to be little or no Ca²⁺-dependent and voltage-dependent current that is noninactivating.

Despite the segregation of inactivating and noninactivating BK current phenotypes among chromaffin cells, some aspects of the behavior of BK_i current have suggested that BK_i channels may not be homogeneous. First, among cells and patches exhibiting complete BK current inactivation, there is some variability in limiting inactivation rates (Solaro et al., 1995, 1997). Second, we have noted that BK_i currents exhibit unexplained variability in sensitivity to charybdotoxin (CTX), whereas BK_s currents have the more usual CTX sensitivity (Solaro et al., 1995). Third, trypsin results in a gradual slowing of the BK_i inactivation rate, but in initial experiments the magnitude of this slowing was often less than would be expected from the hypothesis that BK channels contain four independent inactivation domains (Lingle et al., 1996). In addition, although the structural component of BK_i channels that confers inactivating behavior has not been identified, at least two alternative splice variants of Slo are found in chromaffin cells (Saito et al., 1997). Because of the known ability of members of the voltage-dependent K⁺ channel superfamily to form heteromultimeric tetramers within their immediate subfamily (Covarrubias et al., 1991; Li et al., 1992), it would not be surprising to learn that different naturally occurring Slo splice variants have the ability to form heteromultimers.

Here we test the possibility that BK_i currents and channels arise from heteromultimeric expression of two subunits, one necessary to confer inactivation and the other responsible for CTX sensitivity. First, we examine the peptidase dependence of the onset and recovery from inactivation. These results support the idea that BK_i channels contain up to four independently acting inactivation domains, but that, on average, most channels contain less than four such domains. Second, the resistance of BK_i current to blockade by CTX is examined and found to correlate with the inactivation behavior of the current. Third, the frequency of occurrence of BK_s channels in patches with BK_i channels, although rare, is found to be consistent with the idea that, on average, BK channels contain two to three inactivation-competent subunits. The results support the hypothesis that phenotypic diversity in BK channels in rat chromaffin cells may arise in part from the heteromultimeric assembly of two distinct BK subunits.

	MATERIALS AND METHODS

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Chromaffin cell culture

Methods of rat chromaffin cell isolation and maintenance of cultures were as described in previous work (Neely and Lingle, 1992a; Herrington et al., 1995; Solaro et al., 1995) based on the procedures of others (Fenwick et al., 1978; Kilpatrick et al., 1980; Role and Perlman, 1980; Livett, 1984).

Electrophysiological methods

Whole-cell and single-channel currents were recorded with standard techniques (Hamill et al., 1981) as reported previously (Solaro and Lingle, 1992; Solaro et al., 1995; Neely and Lingle, 1992a,b; Herrington et al., 1995). In whole-cell experiments, uncompensated series resistance (R_s) was typically 1.5-5 M, of which 80-95% was electronically compensated. Values for R_s and the percentage compensation for specific experiments are provided in the figure legends.

Solutions

The usual extracellular solution contained the following (in mM): 140 NaCl, 5.4 KCl, 10 HEPES, 1.8 CaCl₂, and 2.0 MgCl₂ (pH 7.4), adjusted with N-methylglucamine (NMG). When BK current was recorded with elevated pipette Ca²⁺, the extracellular solution bathing the cell contained (in mM): 150 NaCl, 5.4 KCl, 4 MgCl₂, 10 HEPES, adjusted to pH 7.4 with NaOH. For whole-cell recording, the pipette solution contained the following (in mM): 160 KCl, 10 HEPES, 10 mM HEDTA with added Ca²⁺ to make 10 µM free Ca²⁺, as defined by the EGTAETC program (E. McCleskey, Vollum Institute), with pH adjusted to 7.0. In some cases, KCl was partially removed by equimolar substitution of NaCl and/or CsCl to reduce the magnitude of the BK current. Trypsin (porcine pancreatic type IX; Sigma) was used in the pipette solution at 0.5 mg/ml. For experiments with trypsin, the tip of the pipette was first filled with the normal 10 µM Ca²⁺ solution, and then backfilled with the pipette solution containing trypsin. After formation of a gigaohm seal, whole-cell recording was not initiated for at least 7 min. At this time, the concentration of trypsin in the tip is at least 90% of that backfilled into the pipette (Pusch and Neher, 1988).

Osmolarity was measured by dew point (Wescor Osmometer) and adjusted to within 3% (internal saline, 290; external saline: 305). Apamin (200 nM) and 4-aminopyridine (4-AP) (1 mM) were routinely added to extracellular solutions to minimize contamination by SK currents (Neely and Lingle, 1992a) and voltage-dependent K⁺ current, respectively. Tetrodotoxin (200 nM) was used to reduce voltage-dependent Na⁺ current. For whole-cell recordings, no correction was made for the less than +3 mV liquid junction potential that arose when chloride-based salines were used for introducing high [Ca²⁺] into cells.

For recordings of channel activity in patches, cells were bathed in the extracellular saline used for whole-cell recordings. Just before patch excision, the solution bathing the cell was changed to the 0 Ca²⁺ saline described below. For inside-out single-channel recordings, the pipette saline contained (in mM) 140 KCl, 20 KOH, 2 MgCl₂, 10 HEPES (pH 7.0), adjusted with 1 N HCl. Apamin (200 nM) was also included in the pipette solution. The cytosolic saline used during excised inside-out patch recordings was the following (in mM): 140 KCl, 20 KOH, 10 HEPES, 5 N-hydroxyethylethylene-diaminetriacetic acid (HEDTA), with added CaCl₂ to make 10 µM free [Ca²⁺], with pH 7.0, adjusted with 1 N HCl. Estimates of free [Ca²⁺] were determined as described previously (Solaro and Lingle, 1992; Herrington et al., 1995).

Solution exchange and drug applications were accomplished as described previously (Herrington et al., 1995). Chemicals were from Aldrich or Sigma.

Data analysis

Whole-cell and single-channel currents were analyzed either with Clampfit or with our own software. Currents or extracted data were fitted with a Levenberg-Marquardt search algorithm to obtain nonlinear least-squares estimates of function parameters. Modeling of current waveforms based on different subunit compositions was carried out with our software or, in some cases, with Mathcad (MathSoft, Cambridge, MA).

Estimates of drug dissociation constants were made by fitting the complete time course of blockade at one or more drug concentrations to a first-order blocking reaction as described (Saito et al., 1997). If a reasonable period of recovery from drug application was achieved, blocking rate constants and the resulting K_d were tightly constrained, even by single applications of drug. In cases where different concentrations of toxin were applied sequentially with no period of washout, the entire time course of block was fit as above, while making allowance for changes in the toxin concentration at appropriate times.

Estimates of _i versus f_ss and fitting of current waveforms

Current waveforms based on different binomial distributions of channel subunits were calculated with a Hodgkin-Huxley (1952) activation/inactivation model, assuming that channels of each stoichiometry activated with similar kinetics, but inactivated in accordance with the number of inactivation domains. Thus total current arose from the sum of currents through five different channel stoichiometries, with the fraction of channels of each type defined by a single parameter, the percentage bk_i subunits. For simulated currents, the activation time constant, _a, was 2.5 ms, with a cooperativity factor of 1.0, which is similar to values obtained directly from fitting whole-cell current waveforms in these cells (e.g., Fig. 14). The minimum time constant of inactivation (_min) for a channel with four inactivation domains was assumed to be 25 ms. The inactivation rate for a particular channel stoichiometry was directly proportional to the number of inactivation domains (the number of bk_i subunits). The CTX sensitivity of a particular channel stoichiometry was determined by the number of bk_s subunits, assuming a simple block model. The CTX dissociation rate was assumed to be independent of the number of bk_s subunits, and the association rate was assumed to scale with the number of bk_s subunits. A channel with four bk_s subunits was assumed to have a K_d for CTX block of 2 nM and a channel with four bk_i subunits to usually have a K_d of 100 nM. The simulated current waveform derived from particular binomial distributions was then fit with a standard Hodgkin-Huxley activation/inactivation model to define empirically the inactivation time constant and the amount of noninactivating current present at 300 ms in the waveform. Similarly, currents in the presence of CTX were calculated with the assumptions for toxin block given above. Although such simulated currents contain multiple exponential components in the current decay, a single exponential fit provides a reasonable approximation of the decay time course.

Fitting of actual current waveforms during the trypsin digestion process (Fig. 7) or before and after CTX application (Fig. 14) followed a similar strategy based on a binomial distribution of channels among five possible channel stoichiometries. A term for contaminating voltage-dependent current was also included (I_KV). In this procedure, if both I_KV and the percentage bk_i subunits are free parameters, resulting fits are not well defined. However, given particular assumptions as described in the Results, well-defined estimates of _min and percentage bk_i subunits under a given set of assumptions can be obtained.

Fitting of currents with either a standard Hodgkin-Huxley model or with an H-H model modified to include channels of differing stoichiometries used the entire current time course (e.g., Figs. 2, 6, 7, 14). Single exponential fits to inactivation time courses (e.g., Figs. 3, 5, 9) typically covered a range encompassing 80% to less than 2% of the peak amplitude of the decaying current. Estimates of _i with either method typically agreed within 1-2%.

	RESULTS

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A hypothesis to account for the diversity of BK current in rat chromaffin cells

Based on our preliminary results, we hypothesize that BK channels in chromaffin cells arise from two distinct BK subunits (Fig. 1):

View larger version (28K): [in this window] [in a new window]   FIGURE 1   A model of BK channel assembly in chromaffin cells. (A) BK channels in chromaffin cells are proposed to arise from the random, independent assembly of two distinct BK subunits: an inactivation-competent, CTX-resistant bki subunit and an inactivation-null, CTX-sensitive bks subunit. Random assembly of subunits results in one BKs single-channel phenotype and four BKi phenotypes. Traces labeled Single Channel Ensemble reflect the average behavior of a single channel containing only the indicated ratios of bks:bki subunits. Traces labeled Population Ensemble reflect the behavior of a population of channels with the indicated average ratios of bks:bki subunits distributed binomially within the population. Macroscopic currents were generated assuming a 2.5-ms activation time constant with an exponent of 1.0 and a maximum current of 100 pA. The inactivation rate for a single inactivation domain was assumed to be 10/s, with no recovery during the waveform. Time constants are those obtained for single exponential fits to the ensemble behavior, although multiple exponential components actually contribute to each trace. The predicted currents in the presence of 100 nM CTX are shown along the bottom, assuming the Kd values for CTX block shown across the top (Kd1, 2.0 nM; Kd2, 100 nM). Time constants show that the residual current in the presence of CTX decays more rapidly than the control BKi current. The percentages of channels of each combination predicted from the binomial distribution for each average ratio of bks:bki subunits are listed at the bottom. (B) The simulated ensemble currents for the 3:1, 2:2, and 1:3 stoichiometries (points with dotted lines) shown in A are replotted along with the single exponential fits (thin lines) to the decay phase of the currents. The vertical line indicates the first fitted point. Although each simulated current contains multiple exponential components, as defined by the stoichiometries shown along the bottom in A, a single-exponential function provides a reasonable fit to the decay time course in each case. Time constants are given in A.

1. an inactivation competent, CTX-resistant bk_i subunit

2. an inactivation-null, CTX-sensitive bk_s subunit

We assume that BK channels are tetramers (Shen et al., 1994), analogous to voltage-dependent K⁺ channels (MacKinnon, 1991). CTX-resistant bk_i subunits are not insensitive to CTX, but exhibit a reduced sensitivity relative to bk_s subunits. Random assembly of subunits results in one BK_s single-channel phenotype and four BK_i phenotypes. Fig. 1 illustrates predicted average behavior both for a single channel comprising a particular ratio of bk_s:bk_i subunits and for a binomially distributed population of channels with a particular average ratio of bk_s:bk_i subunits. Predicted currents in the presence of 100 nM CTX are also shown along the bottom, given one assumption about CTX affinity, along with the predicted fraction of channels of particular stoichiometry. This model is a recapitulation of the experiment of MacKinnon et al. (1993), which defined the stoichiometry of Shaker K⁺ channel inactivation. Functionally, this model is also essentially equivalent to one in which inactivation is conferred by differing numbers of an inactivation-competent accessory subunit that may associate specifically with a particular variant of core bk_s subunit.

This model predicts the following.

1. BK_i channels should contain multiple inactivation domains, but the average number of inactivation domains per channel may be less than four in many cases.

2. Cells with fewer inactivation domains per channel should have, on average, slower initial inactivation rates.

3. Cells with BK_i current should have variable CTX sensitivity, depending on the average number of bk_i subunits.

4. BK_i current in cells that are more resistant to CTX blockade should, on average, inactivate more rapidly.

5. During blockade by CTX, residual unblocked BK_i current should inactivate more rapidly than BK_i current before CTX application.

6. The frequency of occurrence of BK_s channels in patches with predominantly BK_i channels should be consistent with macrosopic estimates of the number of inactivation domains per channel.

All six of the above predictions are essentially independent, despite the fact that three pertain to the effect of CTX. Below, each of these predictions is evaluated experimentally. We caution that alternative models may account equally well for specific predictions, but that it is difficult to imagine alternative models that would account for the full set of predictions. We also caution that, although many of the properties of BK_i inactivation, including trypsin sensitivity and properties of recovery from inactivation, exhibit similarities to Shaker-type inactivation, the specific physical mechanism of block to permeation during the inactivation process remains unknown (e.g., Solaro et al., 1997).

It should be noted that, despite the fact that the heteromultimer model predicts that there should be up to four exponential components in the current inactivation time course, the decay process can generally be described by a single exponential time course that represents some weighted sum of all of the different components (e.g., MacKinnon et al., 1993). Even in the absence of stochastic noise or slow decay processes that have an impact on real experimental data, it would be difficult to discern the predicted four components, because they are not well separated in time, e.g., 25, 33, 50, and 100 ms. Even when the binomial distribution is dominated by only two components, those components will not be sufficiently well separated to allow careful estimation of their relative amplitude and time constants. Examples of the adequacy of single exponential fits to idealized currents based on stoichiometries of 3:1, 2:2, and 1:3, each predicted to have four exponential decay components, are shown in Fig. 1 B. Thus a single exponential adequately describes the hypothesized four component decays shown here and will have a predictable relationship to the stoichiometry of the channel population.

Inactivation of BK_i channels involves multiple, trypsin-sensitive, cytosolic domains

Inactivation of many voltage-dependent channels is trypsin-sensitive. The changes in current waveform during progressive trypsin digestion can provide information about the inactivation mechanism. For inactivation mechanisms involving a single trypsin-sensitive structure or the concerted action of multiple domains, all of which must be functional, all inactivating channels will inactivate with the same time course (e.g., Gonoi and Hille, 1987). In contrast, if inactivation results from multiple, largely independent domains, during trypsin digestion a progressive slowing in the time constant of inactivation (_i) is predicted, depending on the mean number of inactivation domains per channel within the population. For the simple case analogous to that examined for ShakerB K⁺ channels (MacKinnon et al., 1993; Gomez-Lagunas and Armstrong, 1995), if normal channels inactivate because of the action of four independently acting inactivation domains and recovery from inactivation is slow, at most a fourfold slowing of _i would be expected as blocking domains were removed by trypsin.

BK_i channels in inside-out patches (1-10 channels) were activated by depolarizing voltage steps to +60 mV with 2 or 10 µM Ca²⁺. In some cases a conditioning step to a negative potential (120 or 140 mV) was used to remove partially resting inactivation (Fig. 2 A). Depending on the number of channels in the patch, 20-100 sweeps were used to generate each ensemble current. Trypsin (0.3 or 0.5 mg/ml) was then applied for 2-10 s to the cytosolic face of the patch. A second ensemble current was then generated, and this cycle was repeated through as many trypsin applications as was possible, or until inactivation was completely removed.

View larger version (50K): [in this window] [in a new window]   FIGURE 2   Slowing of the inactivation rate by trypsin suggests that BKi inactivation involves multiple, cytosolic trypsin-sensitive inactivation domains. (A) Example sweeps from a patch with two BKi channels are shown before and after the 6th, 14th, and 16th brief trypsin applications, respectively. The voltage protocol is indicated above the current traces. From a holding potential of 40, the patch was stepped to 140 mV for 100 ms before a 260-ms step to +60 mV. Three seconds separated the onset of each pulse sequence. After the 14th trypsin application, one channel becomes completely noninactivating, and after the 16th application, both channels become noninactivating. (B) The ensemble current averages, which included the traces in A, are plotted along with a fit of a Hodgkin-Huxley-type model to the activation and inactivation time course (Solaro et al., 1995). The inactivation time constants were 20.1 ms (30 sweeps), 56.0 ms (56 sweeps), and 62.8 ms (48 sweeps) for the inactivating currents. The noninactivating current was generated from 35 sweeps with a fitted maximum probability of being open of 0.89. Because the 100-ms step to 140 was insufficient to completely remove all resting inactivation, the change in peak ensemble current amplitude during the course of trypsin digestion largely reflects a trypsin-induced change in BKi channel availability. Examination of all single sweeps for the four cases (control and 6th, 14th, and 16th trypsin applications) showed that the probability of opening was 0.53, 0.78, 0.91, and 1.0, respectively. The estimates for the first three cases would be in error by the fraction of sweeps in which both channels open sequentially but fail to overlap. This fraction is expected to be quite small, given mean burst durations of at least 20 ms and fast activation rates. (C) The stationarity of the inactivation time constant for BKi channels is shown for three inside-out patches. Currents were activated with a protocol similar to that used in A. Ensemble current averages were generated from the idealized openings during the depolarizing step. Each point corresponds to the time constant of inactivation for an ensemble generated from ~20 voltage steps. These patches contained 7 BKi (bottom), 15 BKi (middle), and 15 BKi with 1 BKs channel (top). The thin, horizontal solid line in each case corresponds to the mean of all determinations for the given patch, and the thicker lines indicate the limits of the standard deviation. (D) The time course of removal of inactivation by trypsin is shown for a patch that contained 10 BKi channels. Closed symbols correspond to time constants of inactivation before trypsin application, and open symbols correspond to time constants after trypsin application. The mean and standard deviation of estimates before trypsin application are indicated by the horizontal lines, as in A.

Brief trypsin applications result in a gradual slowing of the channel inactivation rate and a gradual increase in the number of channels that fail to inactivate at all (Fig. 2, A and B). The patch in Fig. 2 A contained two BK_i channels; _i for six separate current averages generated over ~20 min of recording before trypsin application was 29.4 ± 4.9 ms (mean ± SD of six ensemble averages). After the third 2-s application of trypsin, some slowing in _i of the ensemble average was observed. After trypsin, single sweeps show increased cases of bursts persisting later in the voltage step, even though all channels remain inactivating. For example, the second column of current traces in Fig. 2 A followed the sixth application of trypsin; the _i of the resulting ensemble current (Fig. 2 B) was 56 ms. After the 14th application of trypsin, one channel became noninactivating, whereas after the 16th application, both channels were totally noninactivating. In some cases, particularly with patches with fewer than five channels, during the progressive removal of inactivation produced by trypsin, although a single exponential could be fit to the current decay, two exponentials provided a better description of the inactivation time course.

Intrinsic lack of stationarity or stochastic fluctuations might complicate the interpretation of any trypsin-induced effects. Therefore, the stability of the BK_i inactivation rate was examined by repeated activation of single-channel currents over 30-40 min (Fig. 2 C). _i was determined from the average of currents activated by each sequential set of 20-30 voltage steps. For three patches shown in Fig. 2 C, there is some fluctuation in _i, presumably reflecting stochastic fluctuations in channel behavior. Despite these fluctuations, both _i (Fig. 2 C) and the ensemble current amplitude (not shown) are reasonably stable about the mean over this 30-40-min time period. In contrast, in those patches where trypsin was applied, trypsin rapidly and irreversibly results in a slowing of _i, which clearly falls outside the range of variability observed before the onset of trypsin action (Fig. 2 D).

Slowing of _i was observed in 15 of 15 patches in which some removal of inactivation was observed. In patches in which almost complete removal of inactivation was achieved, prolongations exhibited considerable variability, ranging from 1.6-fold to a little over 4-fold. Qualitatively, the simplest interpretation of the slowing of inactivation by trypsin is that, like voltage-dependent K⁺ channels but unlike voltage-dependent Na⁺ channels, inactivation of BK_i channels results from multiple (perhaps up to four) independent cytosolic domains. However, in contrast to voltage-dependent K⁺ channel inactivation, the results suggest that there may be some variability in the average number of inactivation domains per channel in a population. We remain cautious about the interpretation of the magnitude of the slowing of _i, because the slower time constants were difficult to fit, thus compromising estimates of the limiting _i. We therefore turned to the use of peptidase removal of inactivation in whole-cell recordings to address this issue in more detail.

Peptidase removal of inactivation in whole-cell recordings argues for fewer than four inactivation domains per channel

Because whole-cell recordings reflect the behavior of perhaps 100-500 BK channels, we assume that trypsin-induced alterations in macroscopic current should better follow expectations based on a changing, but binomial, distribution of inactivation domains among channels, than would channels in excised patch experiments. Experiments described in Fig. 3 establish the utility of the method. Cells were voltage-clamped with pipettes containing 10 µM Ca²⁺. Voltage steps to +60 mV result in a robust activation of an inactivating outward current, which is strictly dependent on cytosolic Ca²⁺ (Solaro et al., 1995). This BK_i current was relatively stable, in terms of _i (Fig. 3, B and C) and amplitude (Fig. 3 D), for over 15 min of recording. Because these whole-cell currents also contain some noninactivating voltage-dependent K⁺ current, it is not possible to determine how much of the sustained current reflects BK current, although in the absence of cytosolic Ca²⁺ sustained voltage-dependent K⁺ current is typically less than 1 nA (Fig. 3 E; also Prakriya et al., 1996). In the presence of 1 mM external 4-AP, we have never observed inactivating current with 0 pipette Ca²⁺. Because experiments described below examined the effects of cytosolic peptidase on BK_i inactivation, the effect of trypsin on whole-cell voltage-dependent outward current was also examined in the absence of pipette Ca²⁺. The lack of effect of trypsin on voltage-dependent outward current is shown in Fig. 3, E and F. Trypsin does not unmask any noninactivating voltage-dependent K⁺ current that might complicate the interpretation of results described below.

View larger version (28K): [in this window] [in a new window]   FIGURE 3   BK current can be reliably elicited in whole-cell recordings with defined pipette Ca2+. (A) Currents elicited at +60 mV after a 200-ms step to 140 mV with 10 µM pipette [Ca2+] are shown at 100 and 940 s after breaking into the cell. The holding potential was 60 mV. Virtually all current used in this procedure is BK current (Solaro et al., 1995). The extracellular saline contained 1 mM 4-AP. In the absence of pipette Ca2+, no inactivating current is elicited in these cells. (B) Stability of i measured over 16 min for the cell in A. (C and D) Plots of the stability of i (C) and peak current (D) for four different cells. (E) Whole-cell current was elicited as in A, but with a pipette containing 0.5 mg/ml trypsin with 0 extracellular Ca2+. (F) Peak current amplitude for four separate cells in which the pipette contained trypsin, but 0 Ca2+, is plotted as a function of recording time.

As exploited in a study of mixtures of inactivating and noninactivating ShakerB K⁺ channel subunits (MacKinnon et al., 1993), for a population of channels with a particular average number of inactivation domains per channel, _i should display a predictable relationship to the fraction of channels that are completely noninactivating. Here we have taken a similar approach, using enzyme-mediated digestion of inactivation to examine the relationship between _i and the fraction of maximum BK current (BK_max) that is noninactivating current (f_ss). In Fig. 4, we show several types of predictions. First, the relationship between _i and f_ss is defined, given the assumption that each channel has a maximum of N inactivation domains and that each channel starts with N inactivation domains (Fig. 4 A). As digestion occurs, the number of inactivation domains per channel is assumed to follow a binomial distribution. This is identical to the case examined for ShakerB K⁺ channels (MacKinnon et al., 1993). Second, the relationship between _i and f_ss is provided, given the assumption that each channel can have a maximum of four inactivation domains, but the channel stoichiometries are binomially distributed around some value less than 4 before the onset of enzyme digestion (Fig. 4 B). In such a case, there will be some number of channels with no inactivation domains that would produce a steady-state BK current before the onset of the action of trypsin. Because experimentally we are unable to determine the resting amount of noninactivating BK current (e.g., Figs. 5 and 6), the predictions shown here calculate the change in apparent f_ss, ignoring the initial small steady-state current expected in all cases with an average number of inactivation domains of two or more. Third, the relationship between _i and f_ss is given for situations in which all channels have four inactivation domains, but there are either positive or negative interactions that affect the rate of inactivation (Fig. 4 C). Negative interactions between inactivation domains slow the rate at which any individual inactivation domain may reach a blocking position. Positive interactions might arise, for example, if adjacent domains, by reducing the effective degrees of freedom available to a given subunit, increase the likelihood that a given domain can move to a blocking position. It should be noted that, if there is steric hindrance between inactivation domains (Fig. 4 C), a prolongation of less than fourfold may result, even with four inactivation domains. Finally, we consider the case in which there is an additional slow component of inactivation that becomes revealed as fast inactivation is removed (Fig. 4 D). The consequence of such an additional, trypsin-resistant inactivation process is to increase the initial apparent change in _i as a function of f_ss, while resulting in a limiting asymptote of f_ss.

View larger version (34K): [in this window] [in a new window]   FIGURE 4   Predictions for the relationship between prolongation of i versus fss during the action of trypsin. For all cases, currents were simulated as decribed in Materials and Methods, assuming a Hodgkin-Huxley activation scheme with five channel stoichiometries. Simulated currents were then fit to obtain a single time constant of inactivation and a value for the steady-state current. From these, the prolongation in i and the change in fss were determined. (A) Standard predictions for the relationship between i and fss are given for the case where the population of channels is initially homogeneous, all beginning with either four, three, or two inactivation domains per channel. This is identical to the case considered by MacKinnon (1991). (B) The channel population begins with a binomially distributed population with some particular fraction of bki subunits (numbers on the right). Thus, in this case, fss represents an apparent fss in which the initial steady-state current level is set to 0. For 50% bki subunits, there will be a steady-state current of ~6.25% of the peak current. The thickened lines correspond to the standard predictions shown in A, with all channels beginning with either three or two inactivation domains. (C) Consequences of the lack of independence among inactivation domains. Currents were simulated as above, with the addition that the inactivation rate depended on the number of inactivation domains. The inactivation rate of any inactivation domain was either increased or reduced by some factor dependent on the number of other inactivation domains in the channel. Thus, if the intrinsic rate of inactivation of one ball is kf, then i for channels containing N inactivation domains is given by  = 1/(N*xN1*kf) where x is the fraction by which the inactivation rate is affected by each additional inactivation domain. (D) fss and i were calculated based an inactivation model in which, in addition to fast inactivation involving one to four inactivation domains, there was a slow inactivation process unaffected by trypsin. Amplitudes and time constants were calculated based on where the rate of fast inactivation (m * kf) for a particular channel stoichiometry was determined by m (the number of inactivation domains), and the rate of recovery from fast inactivation, kfr, was set to 0. For all curves, ks = 1/s and kf = 10/s. ksr varied from 3.3/s to 8/s. Note that even at early times in the digestion process, a slow inactivation process will result in a prolongation of i, suggestive of m > 4.

View larger version (33K): [in this window] [in a new window]   FIGURE 5   The slowing of inactivation by trypsin suggests that BKi channels have, on average, fewer than four inactivation domains. (A) Outward currents were elicited every 20 s by the indicated voltage protocol. The cell was held at 60 mV before the 100-ms step to 140 mV. The experimental conditions were identical to those described in Fig. 3, except that the recording pipette contained 0.5 mg/ml trypsin. Each trace shows primarily BK current at different times after initiation of whole-cell recording. Trypsin gradually slows inactivation. (B) The current decay time courses at two time points (250 and 850 s) are fit to a single exponential. (C) The changes in peak and noninactivating current during the digestion process are shown. (D) The relationship between prolongation of i and the fractional noninactivating current as a function of peak current is plotted. Peak current was defined from the maximum current elicited during the trypsin digestion process. The solid curve is the prediction based on the assumption that, at t = 0, channels contained an average of 3.2 trypsin-sensitive inactivation domains binomially distributed within the channel population.

View larger version (38K): [in this window] [in a new window]   FIGURE 6   Changes in BKi current during digestion by trypsin. A-D correspond to four different cells in which trypsin was used to remove BKi inactivation. The voltage protocol was as in Fig. 5, except that in B and C a 200-ms step to 140 mV preceded the step to +60 mV. In A1-D1, example traces of BKi current at different times during the digestion process are shown, along with measured time constants of inactivation. Cells are shown in order of smaller to large changes in i during the initial stages of trypsin digestion. In A2-D2, the change in i is plotted as a function of fss for each cell. For cells in A-C, BKmax was determined from the largest BK current amplitude late in the digestion process. For the cell in D, the BKmax was taken from the largest current in the set of traces. Because complete digestion was not achieved, values of fss in this case are overestimates. The solid curves in A2-D2 come from the predictions shown in Fig. 3 B, for assumptions of two to four inactivation domains per channel (mole fractions of bki subunits of 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0). The pipette saline used for these experiments included 35 mM Cs+ to minimize total BK current. Cm and Rs for each cell, respectively, were 5.0 pF and 2.2 M, 8.6 pF and 5.0 M, 11.4 pF and 4.4 M, and 7.8 pF and 4.0 M for A-D, respectively. Rs compensation was at least 80% in each case.

Cells were studied with whole-cell recording procedures in which trypsin or papain was backfilled into the recording pipette. After seal formation, enzyme was allowed to equilibrate into the pipette tip before initiation of whole-cell recording (see Materials and Methods). With this procedure, upon initiation of whole-cell recording, the delay until the onset of removal of inactivation was substantially reduced. Results for one cell are shown in Fig. 5. Currents activated by voltage steps to +60 mV at the indicated times after initiation of whole-cell recording are displayed (Fig. 5 A), along with examples of the decay time course at two time points after the introduction of trypsin (Fig. 5 B). Both the amplitude of peak outward current and the residual noninactivating current increase during the trypsin digestion process (Fig. 5 C). A large portion of the increase in peak current is likely to result from a change in the amount of residual inactivation persisting at the time of the voltage step to +60 mV, as suggested in Fig. 2 A. From the peak current measured at the end of the trypsin digestion process and the residual noninactivating current at each point in time, f_ss was determined. The amount of prolongation of _i is plotted as a function of f_ss, along with the predicted relationship for a population of channels beginning with an average number of inactivation domains of 3 (Fig. 5 D). The slowing of the inactivation process by trypsin supports the view that inactivation of BK_i channels involves multiple, inactivation domains. Furthermore, the change in _i as a function of residual noninactivating current suggests that inactivation involves fewer than four inactivation domains.

Considerable variability was observed in the relationship between the changes in _i and the changes in apparent f_ss. Examples of changes in current waveform during the action of trypsin are shown for four cells in Fig. 6, A-D, along with the measured changes in _i and f_ss. One key feature of the results can be inferred simply by inspection of the current traces. Specifically, there is substantial variability in the amount of change in _i with even small changes in steady-state current. For example, with changes in steady-state current that correspond to less than 20% of the initial peak current, the changes in _i illustrated in Fig. 6 range from 1.3 to 2.4. For a population of cells with a homogeneous set of channels among all cells, we could expect that, given a particular fractional increase in steady-state current, there should be a particular increase in _i. Qualitatively, the changes seen in the current traces appear contradictory to this expectation.

The right-hand panels of Fig. 6 plot the observed changes in _i versus the apparent f_ss for four cells. Although complete removal of inactivation was not obtained for the cell shown in Fig. 6 D, this cell was included to illustrate the large changes in _i that were observed, in this case, with only small changes in steady-state current. The values for f_ss were determined based on the peak of the largest recorded current. We expect this value to be an underestimate, and thus the apparent f_ss values would be even smaller than calculated in this case. The primary point of these plots is that there is substantial variability in the magnitude of the changes in _i with changes in apparent f_ss. When the experimental points are compared to the theoretical relationship between changes in _i and apparent f_ss, the results are consistent with the hypothesis that BK channels in chromaffin cells may exhibit substantial variability in the average number of inactivation domains per channel.

A number of factors may complicate the reliability of the estimates of the number of inactivation domains acquired in the above experiments. The most precarious parameter in defining the relationship between changes in _i and f_ss is the measurement of the maximum amount of BK current or BK_max. In stable cells, BK_max can presumably be determined directly from the peak current at the end of the trypsin digestion period, as shown for the cells in Fig. 6, A-C. For each of the cases illustrated, the initial transient BK current is a similar fraction of the final peak BK current observed after the removal of inactivation. Furthermore, this increase in current amplitude is similar to that observed in Fig. 2 A from an excised inside-out patch studied with a similar voltage protocol with identical submembrane [Ca²⁺]. This consistency suggests that such direct measurements of BK_max are probably fairly reliable. If this method were substantially underestimating the true peak BK current, this would shift f_ss values leftward for a given prolongation in _i. Assuming that BK_max was underestimated by 50%, a corrected f_ss would be shifted 33%. Although it unlikely that our estimates of peak BK current are in error by this amount, this amount of shift would be insufficient to account for the estimated values of less than 4 for the number of inactivation domains per channel.

Two other considerations were also used to ensure our confidence in any particular estimate. First, results from a cell were considered more reliable if the peak current amplitude exhibited a continuous, monotonic increase during the trypsin digestion process. In some cells, transient reduction of the access resistance could result in anomalous decrements in the peak current increase, which would also be associated with anomalous changes in _i, presumably as a result of changes in the cytosolic [Ca²⁺]. Second, cells in which there was little or no detectable change in current resulting from the step to 140 mV during the trypsin digestion process were considered more reliable. The example shown in Fig. 6 D in which large changes in _i were observed fails to meet either of these two criteria, but this cell has been included for illustrative purposes because, of all cells studied, it comes closest to the behavior expected for a population of channels containing four inactivation domains per channel.

To summarize these experiments, trypsin produced a slowing of inactivation in all 21 of the cells examined. On average, _i was prolonged by about two- to threefold by the action of trypsin (or papain). Furthermore, the initial change in _i versus f_ss followed a relationship consistent with an initial average of about two to three inactivation domains per channel. At late times during the action of trypsin, there was a slow component of inactivation, which in some cases even exceeded four times the original _i. Unexpectedly slow components of inactivation have been observed during both papain-induced removal of Shaker inactivation (Gomez-Lagunas and Armstrong, 1995) and papain-induced removal of Na⁺ current inactivation (Gonoi and Hille, 1987). As shown in Fig. 4 D, a second, slower, independent inactivation process unaffected by trypsin can result in upward curvature in the relationship between f_ss and prolongation of _i. Although this residual inactivation may arise from other intrinsic inactivation processes, from exogenous blocking molecules, or from trypsin-released blocking particles, we have no information that would allow us to discern among these possibilities. In any case, it is clear that caution must be used in interpreting _i values at late digestion times. Because at longer times of digestion trypsin may begin to exert other effects on BK channel function, the shorter periods of enzyme action are likely to be more reliable. Fortunately, the largest predicted changes in _i are expected over changes in f_ss of up to 0.5. Because this region of greatest predictive power is associated with the shorter periods of trypsin application, we consider the shape of the relationship between _i/_min versus f_ss during the initial stages of digestion (i.e., f_ss values up to ~0.4-0.5) to be the most useful predictor of the initial number of inactivation domains. The assumption of two to three inactivation domains per channel appears to best account for the cells illustrated in Fig. 5 and Fig. 6, A-C.

The change in fraction of noninactivating current as a function of digestion time was also used to provide an independent estimate of the number of inactivation domains per channel (Gomez-Lagunas and Armstrong, 1995), in conjunction with the predicted time course of increase in the enzyme concentration in the cell (based on the pipette access resistance; Pusch and Neher, 1988). Similar to the results with ShakerB channels (Gomez-Lagunas and Armstrong, 1995), the shape of the curve of I_ss/I_peak as a function of time deviated from all simple predictions. However, in contrast to the results from Shaker channels in which channels were expected to start with a defined stoichiometry of four inactivation domains per channel, the observed changes qualitatively fell in a range of values that were more consistent with an average of perhaps two to three (results not shown) inactivation domains per channel.

Changes in current waveform during trypsin digestion are consistent with a heteromultimeric model

The above results provide initial qualitative support for the idea that BK_i channels in chromaffin cells may contain zero to four inactivation domains and that the average number of such inactivation domains per channel is generally less than four. To provide an additional test of this idea, we tested whether the heteromultimeric model could account for the changes in current waveform during the peptidase digestion process by evaluating two distinct cases. In one case, we assumed that the initial inactivation rate reflected a homomultimeric population of channels, each containing four inactivation domains, and in the second case we assumed that the population of channels was heteromultimeric, with less than a full complement of inactivation domains per channel.

To describe the current waveform at any point in time, we used a Hodgkin-Huxley activation model as described in Materials and Methods. We used this model to fit 52 current waveforms obtained every 20 s over ~900 s of recording. Trypsin-induced changes in current waveform were first observed after ~180 s. Given that removal of inactivation results in changes in the amount of resting inactivation after 100-ms or 200-ms periods at 140 mV (e.g., Fig. 2 A), the changes in peak current amplitude during the removal of inactivation are not entirely predictable in the absence of a complete model of inactivation. However, the changes in observed time course and amount of residual noninactivating current are still of use in evaluation of the proposed heteromultimer model.

The steady-state level of current in these macroscopic recordings (Fig. 6) is determined by two factors: current arising from sources other than BK channels (which we call I_KV) and the amount of BK current that is noninactivating. In accordance with the model, the noninactivating BK current is defined by the mole fraction of bk_i subunits in the cell. If we knew explicitly how much of the steady-state current was BK current, this would define explicitly the mole fraction of bk_i subunits. However, experimentally, there is no convenient way of independently identifying the amount of steady-state current arising from BK channels (however, see Fig. 14). Therefore, for this analysis we examined two cases, each with a different assumption that constrains the amount of steady-state current that must be BK current. In the first case, we assume that, before the action of trypsin, all channels in a chromaffin cell contain a full complement of four inactivation domains. With this assumption, all steady-state current before the removal of inactivation by trypsin arises from I_KV. In the second case, we assume that the minimum _i is ~25 ms. This value constrains the fraction of BK current that is noninactivating and, therefore, defines the contaminating I_KV before the onset of trypsin digestion.

For the first case, using the initial set of current waveforms before the onset of digestion and assuming that the percentage of bk_i subunits is 100, estimates of I_KV and the minimum time constant (_min) resulting from channels with four inactivation domains were defined. For the cell shown in Fig. 7 A, the resulting _min was 39 ms with ~220 pA of contaminating current. We then assumed that these parameters are unaffected by the action of trypsin, allowing us to constrain these values in subsequent fits to currents obtained after the trypsin digestion process has begun. With these values, fits to the current waveforms at different times in the digestion process failed to adequately account for the changes in shape in the current waveforms (Fig. 7 A). The changes in peak current, current activation time constant, percentage of bk_i subunits, and _i are plotted in Fig. 7 D and compared to parameter values derived from other assumptions (Fig. 7, C, E, F). As a measure of the adequacy of the fits, a normalized measure of the sum of squares (SSQ) of the fit is plotted in the bottom row of Fig. 7 D. To obtain this measure, the raw currents were fit by the model with all parameters unconstrained (Fig. 7 C). Although correlations among parameters meant that no parameters are sharply defined in this case, the fit with unconstrained parameters provides an optimal estimate of the SSQ that can be used for evaluation of fits obtained with other assumptions. Thus, for each fitting procedure, the resulting SSQ was normalized to that obtained with all parameters unconstrained (Fig. 7, C-F, bottom row). The deviation from one of the ratios of the SSQ seen in Fig. 7 D provides a qualitative indication of the failure of the homomultimer model to account for the changes in time course during the trypsin digestion process. Clearly, the assumption that all channels initially contain four inactivation domains results in changes in current waveform that are inconsistent with the expectations of this assumption.

View larger version (27K): [in this window] [in a new window]   FIGURE 7   Changes in current waveform during trypsin digestion are consistent with a heteromultimer model. A chromaffin cell was held at 60 mV and, every 20 s, was stepped to 140 mV for 100 ms before a 500-ms step to +60 mV. The pipette saline contained 10 µM Ca2+ and was backfilled with trypsin. Traces are the 6th, 12th, 18th, 24th, 30th, 36th, and 43rd after onset of whole-cell recording. (A) Traces 4-7 were fit with a Hodgkin-Huxley model, as described in Materials and Methods, in which the percentage of bki subunits in the cell was constrained to 100%. This defined min as 39 ms, with 220 pA of contaminating voltage-dependent outward current. For subsequent fits of the currents, min was then constrained to 39 ms and IKV to 220 pA. Note the poor fit resulting from this assumption for traces obtained during partial digestion. (B) For sweeps 4-7, min was constrained to 25 ms, based on other estimates of min described below. This resulted in an estimate of IKV of 188 pA, with an initial percentage of bki subunits of 74%. Constraining tmin to 25 ms and IKV to 188 pA for all subsequent traces resulted in the best fits shown by the solid lines. (C-F) Values for the peak current amplitude (Imax), activation time constant (a), and percentage bki subunits are plotted for four fitting procedures. In C, all parameters were unconstrained. Because some parameters are strongly dependent on others (e.g., IKV and % bki subunits), the values are not well determined, but the best fit provides a measure of the optimal sum of squares (SSQ) for the generalized model. The bottom panel in each column therefore plots the SSQ of a fit divided by the SSQ obtained with all parameters unconstrained (ratio of SSQ). An SSQ ratio near 1 implies that the constraints of a particular set of assumptions result in a reasonable fit to the currents. In D, fits were generated as described in A, with open circles indicative of traces shown in A. At intermediate times during the digestion process, the ratio of SSQ deviated considerably from 1. In E, fits were generated as described in B, with open circles indicative of traces shown in B. Despite the fact that two parameters were constrained over all sweeps, the resulting ratio of SSQ was quite stable, being near 1 over the entire digestion time course. In F, the fit procedure was similar to that in E, except that min was unconstrained, and IKV was 188 pA. With this procedure, all min values providing the best fit were between 18 and 30 ms, consistent with the idea that min is ~25 ms.

The results of fitting the same set of current waveforms with the second set of assumptions is shown in Fig. 7 B. Based on other results that suggest that the limiting _min for channels containing four inactivation domains is ~20-30 ms, we constrained _min to 25 ms. From sweeps 4 through 7, this results in an estimate of the initial contaminating I_KV of 188 pA. Making the same assumption as above, i.e., that _min and the contaminating current will be unaffected by the action of trypsin, we then constrained these values during subsequent fits of all other traces. These assumptions result in rather reasonable approximations of the actual data traces over the entire time course of trypsin digestion (Fig. 7 B). The resulting values and normalized SSQ are plotted in Fig. 7 E. For comparison, Fig. 7 F shows resulting values from a fit in which I_KV, but no other parameter, was constrained to 188 pA. In this case, all resulting estimates of _min cluster around 25 ms, providing additional support for the idea that, in a cell with an initial inactivation time constant of ~39 ms, current waveforms are best accounted for by a model in which channels are heteromultimers with a limiting _min of ~25 ms.

Given the success of the heteromultimer model in accounting for the current waveform at all times in the digestion process, this analysis suggests that in this cell BK_i channels initially contained, on average, about three inactivation domains per channel, decreasing to ~0.06 inactivation domains per channel. Furthermore, the changes in the peak current amplitude seen during the trypsin digestion process are qualitatively consistent with those expected for the amount of removal of resting inactivation observed in Fig. 2. Finally, at later times in the digestion process, there is some change in _a, the rate of current activation, consistent with earlier observations that trypsin may have some effect on BK current activation rates (Solaro et al., 1995; Lingle et al., 1996).

This analysis allows the following conclusion. Not only does the slowing of inactivation by trypsin suggest that BK_i channels contain multiple inactivation domains, but, if the maximum number of inactivation domains is four, the changes in current waveform can only be well described by a model in which channels contain, on average, fewer than four inactivation domains. This analysis does not consider homomultimer models in which the maximum number of inactivation domains per channels is something other than four. However, the observation that the number of inactivation domains per channel exhibits substantial variability among cells argues against a simple homomultimer model involving something other than four inactivation domains.

Larger estimates of the average number of inactivation domains correlate with faster initial _i

Using the relationship between changes in _i and f_ss, we determined that values for the number of inactivation domains per channel ranged from ~1.7 up to ~4 for a set of 22 cells, with a mean value of 2.9 ± 0.4. The extent to which the trypsin-induced prolongation of _i shows less than a fourfold increase is consistent with the idea that the average number of inactivation domains is less than four in most cells. If this were the case, we would also expect there to be a correlation between the estimate of average number of inactivation domains per channel with the initial _i in a cell. Cells with faster initial inactivation rates would be expected, on average, to have a higher average number of inactivation domains per channel. This relationship is plotted in Fig. 8. Although there is considerable scatter, there is a strong tendency for slower initial inactivation rates to be associated with a smaller estimate of average number of inactivation domains. Assuming that any cell can have at most an average of four inactivation domains per channel, the limiting _i appears to approach ~25 ms. As noted above, a less than fourfold slowing during the action of trypsin might also result from lack of independence among inactivation domains during the inactivation process. However, in such a case, we would not expect there to be a correlation between faster _i with a larger average number of inactivation domains per channel. Similarly, the variability in the fractional prolongation of _i produced by trypsin would seem to be more consistent with true variability in the number of inactivation domains rather than the result of a lack of independence in the inactivation process.

View larger version (16K): [in this window] [in a new window]   FIGURE 8   Cells with a larger estimated average number of inactivation domains per channel tend to inactivate more rapidly. The average number of inactivation domains per channel estimated from the relationship shown in Fig. 5 is plotted against the initial i for each cell. More slowly inactivating cells have a smaller estimated average number of inactivation domains per channel. The solid line has no theoretical significance, but suggests that, with four inactivation domains per channel, the limiting i  25-30 ms.

Removal of inactivation by trypsin does not affect rates of recovery from inactivation

Examination of the time course of recovery from inactivation may also be informative about the number and independence of inactivation domains. To address this issue, the effect of trypsin on the time course of recovery from inactivation was examined in inside-out patches bathed with 10 µM Ca²⁺. Current averages were generated from BK channel openings activated with a sequence of paired pulses (Fig. 9 A) with interpulse recovery intervals at 140 mV from 1.5 to 800 ms. Trypsin was briefly applied, and then the recovery protocol was repeated. Both the inactivation time course (Fig. 9 B) and the fractional recovery as a function of recovery time were determined (Fig. 9 C). At [Ca²⁺] from 4 to 60 µM, recovery at potentials from 40 to 100 mV is described by two exponential components (Ding et al., 1996). However, at 140 mV and 10 µM, recovery can be adequately described by a single exponential function with a time constant of 16.3 ± 5.1 ms (mean ± SD; n = 7). For Shaker inactivation (MacKinnon et al., 1993), irrespective of the number of inactivation domains, once inactivation has occurred, recovery is thought to be controlled solely by the rate of dissociation of a single inactivation domain. On the other hand, if a single domain is necessary to produce inactivation, but multiple domains can move into independent positions, each sufficient to maintain inactivation, recovery from inactivation would be expected to exhibit a dependence on the number of residual trypsin-sensitive domains.

View larger version (35K): [in this window] [in a new window]   FIGURE 9   Trypsin removal of inactivation does not influence the rate of recovery from inactivation. Recovery from inactivation was defined with the paired pulse protocol shown in A. Pairs of 200-ms depolarizing steps to +60 mV were separated by 1.5-ms to 800-ms steps to 140 mV. A 100 ms step to 140 mV preceded the first step to +60 mV to remove resting inactivation at the holding potential (60 mV). The patch was bathed with 10 µM Ca2+, and patches with large, undefined numbers of channels were selected so that minimal averaging would be required in the recovery protocols. For the examples shown, 20 sweeps were used for each pulse-pair average. From top to bottom, traces show currents before and after each of three brief applications of trypsin to the patch. (B) The normalized inactivation time course for each of the currents in A is plotted, along with the best fit of a single exponential function (35, 45, 67, and 83 ms for control and subsequent trypsin applications, respectively). Current values for the last 100 ms of the second step to +60 mV after the 1.5-ms recovery interval were used to better define the exponential decay time course. (C) The fractional recovery as a function of recovery time is plotted for the set of traces in A. Single exponential functions are fit through the recovery points: 17.3 ms (control, ); 17.8 ms (first trypsin, ); 18.0 ms (second trypsin, ); 21.3 ms (third trypsin, ). Fractional recovery was defined as (P2max  P1min)/(P1max  P1min), where P1min refers to the final current level at the end of the first depolarizing step to +60, and P1max and P2max refer to maximum current amplitudes during the first and second depolarizing steps, respectively. Fits to the control recovery time course of the following function: N(t) = N*max(1  exp(t/r))n where Nmax and r were free parameters, and n  t/r was constrained to either two or four inactivation domains, are plotted as dotted lines. (D) The fractional recovery for the control and after the second trypsin application is shown. The solid line represents the best fit of Eq. 1 with a sigmoidicity term of 2.5. This fit yields a time constant of recovery of 7.65 ms and fails to describe the recovery time course. Assuming that the action of trypsin is to reduce the average number of inactivation particles in the population of channels, the predicted recovery time course when the average number of particles reaches 1, but assuming the same microscopic recovery rate, is shown for the dotted line. As inactivation is removed by trypsin, there is no indication of either changes in time constant or in sigmoidicity that would suggest that multiple domains must each dissociate during the recovery process. (E) The apparent sigmoidicity in the recovery from inactivation is plotted as a function of fractional prolongation of i during trypsin-induced removal of inactivation for a set of seven cells. The recovery time courses, as in C, were fit with the equation above, but with n as an additional free parameter.

For the patch shown in Fig. 9, irrespective of the trypsin-induced slowing of the inactivation rate (Fig. 9 B), no change in the recovery time constant (_r) was observed (Fig. 9 C). Thus, whatever the trypsin-induced alteration in channel structure that results in a prolongation of _i, neither an increase nor a decrease in _r is observed. In four cells from a set of seven, there was no significant change in _r as inactivation was removed. In the other three, there was an immediate increase in recovery rate after the first trypsin application. However, subsequent trypsin applications produced no additional change in recovery, although the rate of inactivation continued to slow with trypsin in these three cells. Thus the rapid, trypsin-induced change in recovery in some cells does not have the features expected for gradual digestion of inactivation domains. We therefore conclude that gradual removal of inactivation by trypsin is not associated with a change in the rate of recovery from inactivation.

We have evaluated the expected time course of recovery for a mechanism in which each of N inactivation domains must independently dissociate to produce recovery. Such a mechanism is functionally comparable to a Hodgkin-Huxley gating scheme in which two to four particles must each undergo some transition before channels are recovered from inactivation. For such a mechanism, recovery will exhibit an appreciable lag. The best fit predictions for recovery involving two or four inactivation particles are displayed over the data in Fig. 9 C. The actual recovery from inactivation proceeds in a fashion most consistent with the involvement of a single inactivation domain/particle. In Fig. 9 D, data points before trypsin and after the second trypsin application are plotted. The solid line provides the fitted recovery time course, assuming that the population of channels start with an average of 2.5 particles per channel, all of which participate in the recovery process. The dotted line provides the expected shift in the recovery time course, if the only effect of trypsin is to change the average number of inactivation particles per channel from 2.5 to 1. This shows that a trypsin-induced change in the number of inactivation particles participating in the recovery process would result in both a shift in apparent recovery time course and a change in apparent sigmoidicity. Such a change in sigmoidicity is not observed (Fig. 9 E).

This analysis suggests that changes in apparent sigmoidicity in the recovery process may perhaps be the strongest diagnostic parameter for assessing whether multiple particles may independently participate in a recovery process (see also Kuo and Bean, 1994). The single inactivation particle model predicts that neither recovery rate nor sigmoidicity will change as trypsin removes inactivation domains, as is observed. We conclude that the lack of sigmoidicity in the recovery process and lack of effect of trypsin on that recovery process argue that only a single inactivation particle must dissociate to remove inactivation.

BK_i current in chromaffin cells is relatively resistant to blockade by CTX

The CTX sensitivity of whole-cell BK current was examined in two types of experiments. In one set of experiments, Ca²⁺ influx was used to activate BK current during perforated-patch recordings (Horn and Marty, 1988). In the second set of experiments, depolarizing voltage steps with 10 µM pipette Ca²⁺ were used to activate BK current. The former method offered the advantage that the Ca²⁺-dependent component of outward current could be explicitly determined. The latter method offered the advantage that submembrane Ca²⁺ was better defined.

In Fig. 10, currents activated with and without extracellular 1.8 mM Ca²⁺ and with and without CTX are shown for a cell with BK_s current (Fig. 10 A) and a cell with BK_i current (Fig. 10 B). In both cases, a depolarizing command step to 9 mV was used to activate Ca²⁺ current and produce robust elevations of cytosolic Ca²⁺. A subsequent step to +81 mV was then used to activate BK current relatively free of contamination by other currents. The middle pair of traces in each case show the outward current activated before, during, and after the removal of Ca²⁺. The bottom traces show current before, during, and after the application of 100 nM CTX. For the cell with BK_s current, CTX blocks virtually all of the Ca²⁺-dependent outward current. For the cell with BK_i current, 100 nM CTX blocks ~50% of the Ca²⁺-dependent current. In Fig. 10, C and D, the time course of onset of block and recovery during CTX applications is plotted for the two cells shown in Fig. 10, A and B. The time cou