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The Journal of Neuroscience, March 1, 2002, 22(5):1550-1561

Consequences of the Stoichiometry of Slo1  and Auxiliary  Subunits on Functional Properties of Large-Conductance Ca²⁺-Activated K⁺ Channels

Ying-Wei Wang, Jiu Ping Ding, Xiao-Ming Xia, and Christopher J. Lingle

Departments of Anesthesiology and Anatomy and Neurobiology, Washington University School of Medicine, St. Louis, Missouri 63110

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Auxiliary  subunits play a major role in defining the functional properties of large-conductance, Ca²⁺-dependent BK-type K⁺ channels. In particular, both the 1 and 2 subunits produce strong shifts in the voltage dependence of channel activation at a given Ca²⁺.  subunits are thought to coassemble with  subunits in a 1:1 stoichiometry, such that a full ion channel complex may contain up to four  subunits per channel. However, previous results raise the possibility that ion channels with less than a full complement of  subunits may also occur. The functional consequence of channels with differing stoichiometries remains unknown. Here, using expression of  and  subunits in Xenopus oocytes, we show explicitly that functional BK channels can arise with less than four  subunits. Furthermore, the results show that, for both the 1 and 2 subunits, each individual  subunit produces an essentially identical, incremental effect on the voltage dependence of gating. For channels arising from  + 2 subunits, the number of 2 subunits per channel also has a substantial impact on properties of steady-state inactivation and recovery from inactivation. Thus, the stoichiometry of : subunit assembly can play a major functional role in defining the apparent Ca²⁺ dependence of activation of BK channels and in influencing the availability of BK channels for activation.

Key words: auxiliary subunits; BK channels; Ca²⁺- and voltage-gated K⁺ channels; Slo1 channels; inactivation; ion channel stoichiometry; gating mechanisms

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Large-conductance, Ca²⁺-activated BK-type K⁺ channels exhibit substantial functional diversity (McManus, 1991; Vergara et al., 1998) contributed, in part, from coexpression of the pore-forming Slo  subunit (Adelman et al., 1992; Butler et al., 1993) with members of an auxiliary  subunit family. At present, four mammalian  subunits have been identified (Knaus et al., 1994b; Wallner et al., 1999; Xia et al., 1999, 2000; Brenner et al., 2000; Meera et al., 2000; Uebele et al., 2000; Weiger et al., 2000). Both the 1 and 2 subunits result in pronounced negative shifts in the voltage of half-activation at a given [Ca²⁺] (McManus et al., 1995; Wallner et al., 1995, 1999; Xia et al., 1999; Brenner et al., 2000). Both the 2 (Wallner et al., 1999; Xia et al., 1999) and 3b (Uebele et al., 2000; Xia et al., 2000) subunits result in kinetically distinct inactivating BK channels.

subunits can exist in a 1:1 stoichiometry with  subunits (Knaus et al., 1994a): four  subunits can coassemble with four  subunits into an intact BK channel. Previous work on inactivating BK (BK_i) channels in rat chromaffin cells (Ding et al., 1998) suggests that the variability in inactivation behavior might arise from differential stoichiometry of some inactivation-competent subunit in the channel population (Ding et al., 1998). Given the presence of 2 subunit message in rat chromaffin cells (Xia et al., 1999) and the similarity of  + 2 currents to BK_i currents (Wallner et al., 1999; Xia et al., 1999), one possibility is that, in rat chromaffin cells, channels occur with less than a 1:1 assembly of 2: subunits. The dependence of BK channel properties on : coassembly was also examined in Xenopus oocytes by varying the ratio of coinjected 1 and  subunits (Jones et al., 1999). This work proposed the view that 1 subunits produced an all-or-none shift in gating properties of the resulting BK channels (Jones et al., 1999).

These previous studies raise interesting questions concerning the functional consequences that result from less than a full 1:1 stoichiometric assembly of  and  subunits BK. First, it remains unclear whether BK channels can form with less than four  subunits. Second, if BK channels can contain less than four  subunits, what is the role that a single  subunit plays in influencing the various functional properties of the channel? To address these issues, we use the inactivation properties conferred on BK channels by the 2 subunit as an indicator of 2: subunit stoichiometry within a channel population that can then be related to other functional properties. The results demonstrate that BK channels that contain less than four  subunits can occur. Furthermore, channels with less than a full complement of  subunits show gating properties and inactivation behavior that scale with the average number of  subunits per channel.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Expression in Xenopus oocytes. The preparation of the 1 and 2 expression constructs used here has been described previously (Xia et al., 1999). Two other constructs used here were also described in previous work (Xia et al., 1999): first, the 2-33 construct in which 33 N-terminal amino acids were removed from the 2 subunit; and second, a construct in which the 33 initial amino acids from the 2 N terminus were appended to the N terminus of the 1 subunit. This latter construct is here termed 1-C2. The  subunit used here was the mouse Slo1 construct used previously (Xia et al., 1999), which corresponds to a zero amino acid insert at splice site 1 and a three amino acid insert at splice site 2. Methods of expression in Xenopus oocytes were as described previously (Xia et al., 1999).

After injection, oocytes were maintained in ND96 (in mM: 96 NaCl, 2.0 KCl, 1.8 CaCl₂, 1.0 MgCl₂, and 5.0 HEPES, pH 7.5) supplemented with sodium pyruvate (2.5 mM), penicillin (100 U/ml), streptomycin (100 mg/ml), and gentamycin (50 mg/ml). Oocytes were used for electrophysiological experiments 1-7 d after injection of cRNA.

Ratios of the injected : subunits are identified in specific experiments. These ratios reflect the ratio of weights of injected material. cRNA preparations typically result in ~1 ng/µl, regardless of RNA species. The molecular weight of Slo1  cRNA is approximately fivefold greater than that of 1 and 2 cRNA. Thus, at a 1:1 ratio by weight,  subunits are expected to be in an approximately fivefold molar excess over  subunits. In our experience, the same nominally identical ratio may not yield identical results over time or in different batches of oocytes, even when we are reasonably confident that RNA degradation has been minimized. To minimize degradation problems that might be associated with freezing and thawing, each preparation of RNA was separated into aliquots at the time of preparation, and a separate aliquot was used for each injection. Another potential problem is that, for distinct nonhomologous RNA species (i.e.,  and  cRNA), it is not clear how the injected ratio may relate to the stoichiometry of assembly. To circumvent this problem, we have therefore used the properties of inactivation as independent estimators of the stoichiometry of channel assembly.

Electrophysiology. Macroscopic and single-channel current measurement follow methods in standard use in this laboratory. For these experiments, currents were recorded in the inside-out patch mode (Hamill et al., 1981). Digitization for macroscopic currents was typically at 10-50 kHz with analog filtering during acquisition (5-20 kHz, Bessel low-pass filter, 3 dB). For single-channel experiments, digitization was at 100 kHz, with 5 kHz filtering. Preparation of the pipette solution and Ca²⁺ solutions has been described previously (Wei et al., 1994; Xia et al., 1999). The pipette extracellular solution was (in mM): 140 potassium methanesulfonate, 20 KOH, 10 HEPES, and 2 MgCl₂, pH 7.0. Test solutions bathing the cytoplasmic face of the patch membrane contained (in mM): 140 potassium methanesulfonate, 20 KOH, 10 HEPES, pH 7.0, and one of the following: 5 mM EGTA (for nominally zero Ca²⁺ and 0.5 and 1 µM Ca²⁺ solutions), 5 mM HEDTA (for 4 and 10 µM Ca²⁺ solutions), or no added Ca²⁺ buffer (for 60, 100, and 300 µM and 1 and 5 mM Ca²⁺ solutions). The methanesulfonate solutions were calibrated against a commercial set of Ca²⁺ standards (WPI, Sarasota, FL). which yielded values essentially identical to our own Cl-based standards. Local perfusion of membrane patches was as described previously (Solaro and Lingle, 1992; Solaro et al., 1997).

pClamp 7.0 or pClamp 8.0 for Windows (Axon Instruments, Foster City, CA) was used to generate voltage commands and to digitize currents. Current values were measured using ClampFit (Axon Instruments), converted to conductances, and then fit with a custom nonlinear least squares fitting program. Conductance-voltage (G-V) curves for activation were fit with a Boltzmann equation with the form:

(1)

where V_0.5 is the voltage of half-maximal activation of conductance, and k is the voltage dependence of the activation process (mV¹). Experiments were done at room temperature (21-24°C). All salts and chemicals were obtained from Sigma (St. Louis, MO).

Simulation of G-V curves based on partial occupancy of 2 subunit binding sites. The strategy for evaluation of the functional consequences of channel populations containing differing stoichiometries of : subunits follows that outlined in previous work (Ding et al., 1998). All channels were assumed to contain four possible  subunit binding sites. Fractional occupancy by  subunits of those sites was assumed in all cases to follow a binomial distribution. At a given fractional occupancy, the fraction of channels in any of the possible stoichiometries was then calculated, and the contribution of channels of a particular stoichiometry to the overall G-V curves was determined based on different assumptions (e.g., independence, positive cooperativity, or negative cooperativity) about  subunit effects (Ding et al., 1998). Time constants for inactivation of a channel population containing  + 2 subunits in differing stoichiometries would be expected to exhibit up to four exponential components (corresponding to the presence of one to four inactivation domains). However, empirically, the relative amplitudes and time constants of these components result in currents that decay with a time course that can be reasonably approximated by a single exponential (Ding et al., 1998). To generate predictions for the inactivation time constant for channel populations containing some average number of 2 subunits per channel, currents were simulated and fit with single exponentials.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION REFERENCES

Inactivation properties of  + 2 currents indicate that channels can contain less than four inactivation domains and that inactivation domains act in an independent manner

Previous work has suggested that the inactivation properties of native inactivating BK currents among different chromaffin cells can be used as indicators of the average stoichiometry of assembly of inactivating and noninactivating subunits (Ding et al., 1998). At least in regard to inactivation behavior, each inactivating subunit appears to behave in an independent manner. Thus, the average number of inactivating subunits per channel within a population of channels defines the average inactivation rate of channels in that population. With identification of the 2 auxiliary subunit in chromaffin cells (Xia et al., 1999), this raised the possibility that variability in the average number of 2 subunits (or other inactivating  subunit) per channel may account for the previous observations in chromaffin cells.

If, in fact, inactivation properties and _i provide a direct assay for the stoichiometry of 2: subunits in a channel population; it therefore becomes possible to examine the consequences of subunit stoichiometry on other channel functional properties without having specific information about the expression levels of subunits within the cell. This is particularly advantageous when it is unclear to what extent oocyte-to-oocyte variability or variability in RNA preparations may have an impact on the ability of subunits to be expressed. Using this strategy, we have therefore sought to address how channel stoichiometry may affect other functional properties of the resulting BK channels.

Specifically, the 2 subunit was coinjected with mSlo  subunits into Xenopus oocytes at different ratios, and the following aspects of BK channel function were determined: (1) the relationship between conductance and activation voltage at 10 and 300 µM Ca²⁺; (2) the rates of onset and recovery from inactivation; (3) the ratio of inactivating to noninactivating current; and (4) the voltage dependence of steady-state inactivation.

Figure 1 shows families of currents activated by depolarizing voltage steps at either 10 or 300 µM Ca²⁺ for four different injection ratios of 2 and  subunits. Qualitatively, as the relative amount of 2 subunit is reduced, there is less current activation at potentials negative to zero, _i is slowed, and there is a larger noninactivating component of current at the end of the most depolarized voltage step. All of these changes are those expected for a model in which various indicators of BK channel function scale in accordance with the average number of 2 subunits per channel. This is examined more explicitly below. Another feature of the currents shown in Figure 1 is that peak current activated at positive command potentials is smaller with 300 than with 10 µM Ca²⁺. This reflects the persistence of steady-state inactivation even after a 100 msec step to 180 mV.

View larger version (29K): [in this window] [in a new window]   Figure 1.   Decreasing the ratio of injected 2: subunits slows the inactivation time constant of  + 2 currents. A-E, Traces show currents obtained in inside-out patches, with each patch from an oocyte injected with the indicated ratio of 2:  subunits. From top to bottom, traces correspond to oocytes injected with 1:1 2: (A), 0.05 2: (B), 0.025 2: (C), 0.01 2: (D), and  alone (E). Left traces were obtained in 10 µM Ca2+, and right traces were obtained in 300 µM Ca2+. Traces show currents activated to potentials between 100 and +120 mV in steps of 20 mV, with tail currents at 120 mV with a prepulse to 180 mV. The reduction in peak current activation with 300 µM Ca2+ corresponds to the additional steady-state inactivation of channels at 180 mV.

The slowing of _i as a function of the injected ratio of 2: subunits is illustrated in Figure 2A for currents obtained with 300 µM Ca²⁺ at either +100 or +160 mV. _i reaches a limit of ~20 msec, at ratios of both 1:1 and 2:1 suggesting that maximal occupation of  subunits by 2 subunits has occurred. The slowest observed values of _i are ~90 msec. This value is a bit larger than the theoretical limit of 80 msec predicted for an inactivation model involving four independent inactivation domains, in which 20 msec is the minimal _i. However, measurement of the slowest _i values can be influenced by other factors. For example, at positive activation potentials, Slo1 currents, even in the absence of  subunits, can exhibit a slow reduction in current during depolarization (Fig. 1E). The presence of such additional slow blocking components at +100 and +160 mV would tend to slow the apparent inactivation time constant resulting from 2 subunit action, which might account for the slower than expected time constants observed at the 0.01 2: injection ratio.

View larger version (21K): [in this window] [in a new window]   Figure 2.   The inactivation properties of  + 2 currents exhibit behavior consistent with the idea that i provides a direct indication of the average stoichiometry of 2: subunits in the expressed channels. A, i measured with 10 µM Ca2+ at either +160 or +100 mV is plotted as a function of the ratio of injected 2:  subunits. Each point is the mean of four to six patches; error bars indicate SD. B, i is plotted as a function of command potential for 0.025 (4 patches) and 1.0 (6 patches) 2: injection ratios. At potentials of +80 mV and more positive, the change in i is small compared with the change produced by the different injection ratio. C, i, peak current (Ip), and steady-state current (Iss) were measured at various injection ratios from currents activated at +160 mV with 10 µM Ca2+. fss was determined from Iss/Ip and plotted as a function of the inactivation time constant observed in each patch. Each symbol corresponds to patches obtained from oocytes at a particular injection ratio (, 2.0; , 1.0; , 0.1; , 0.05; , 0.025; , 0.01). The curved lines are the predictions for the relationship between i and fss assuming various minimal i values (as indicated, 17.5, 20, 22.5, and 25 msec), based on the model in which inactivation can be mediated by up to four independently acting inactivation domains, with one domain sufficient to produce inactivation.

The voltage dependence of _i at both low (0.025) and high (1.0) ratios of 2: subunits is plotted in Figure 2B. Because it is known that  subunits shift the voltage dependence of activation at a given [Ca²⁺], a shift in _i might occur simply because of a shift resulting from coupling of inactivation to activation. However, over the range of +100 to +160 mV, there is little voltage dependence to _i at either injection ratio. This indicates that the large changes in _i at +160 mV that are observed as a consequence of different injection ratios must reflect the underlying stoichiometry of the inactivation process and not a consequence of a shift in activation potentials.

As mentioned in Materials and Methods, the injection ratio of 2: subunits does not provide any handle on the stoichiometry of assembly within the oocyte. Therefore, we have attempted to use the inactivation behavior to reveal something about channel stoichiometry. As above, we measured _i during activation steps to +160 mV at 10 µM Ca²⁺. For the same currents, we also measured the peak current activated by the voltage step to +160 mV and the steady-state current at the end of the voltage step (300 msec). For the simple model in which channel stoichiometries are defined by a binomial distribution and up to four 2 subunits independently contribute to the onset of inactivation (MacKinnon et al., 1993; Ding et al., 1998), the ratio of steady-state current to peak current (f_ss) should vary in accordance with _I: at the largest steady-state current, _i should reach a limiting value that is approximately fourfold slower than the fastest values of _i. The conditions for these experiments were chosen for the following reasons. At 10 µM Ca²⁺, there is minimal steady-state inactivation at a potential of 140 mV, so that a subsequent activation step should define the maximal current expected for the total population of expressed channels (Ding and Lingle, 2002); +160 mV was used as an activation step so that the kinetics of channel opening at 10 µM Ca²⁺ are relatively fast compared with the onset of inactivation. A drawback of the use of a step to +160 mV is that there are usually slow "inactivation" components, perhaps because of a divalent cation block that may contaminate the estimate of _i and steady-state current. This latter issue is most problematic for the smaller 2: ratios.

The relationship between changes in _i as a function of f_ss is plotted in Figure 2C for several 2: injection ratios. Over the range of injection ratios used, _i ranged from ~20 msec to time constants of >80 msec. The basic heteromultimeric model for Shaker K⁺ inactivation (MacKinnon et al., 1993) and BK channel inactivation (Ding et al., 1998) would predict that, at the limit of the lowest ratios of 2: subunits, _i should approach approximately four times that at the highest ratios. The values exhibit considerable scatter but follow the general trend required by an inactivation model in which up to four 2 subunits, each with an independently acting inactivation domain, can contribute to an intact channel containing  + 2 subunits. Lines are drawn over the data showing the predictions for this model for cases in which the minimal _i is 17.5-25 msec. At the lowest f_ss, the results appear to follow the expectations for the lines corresponding to minimal _i values of ~20 msec. As f_ss increases, values for _i deviate from the theoretical expectations. This was also observed in rat chromaffin cells during trypsin-mediated removal of inactivation (Ding et al., 1998). The values at high f_ss are likely to be in error for two reasons. The slow blocking processes mentioned above will result in slower values of _I, and any additional slow blocking processes will also reduce the value of f_ss. Both errors will contribute to the observed deviation at the lower injection ratios. However, the change in _i relative to f_ss argues strongly that channels can assemble with less than a full complement of 2 subunits and that each subunit acts in an independent manner to contribute to the onset of inactivation.

Each 2 subunit contributes incrementally to the shift in activation V_0.5

To examine the dependence of the activation of conductance on various injection ratios, G-V curves (for 10 µM, Fig. 3A; for 300 µM, Fig. 3B) were calculated from measurement of peak currents. As the 2: ratio is reduced, V_0.5 at either 10 or 300 µM Ca²⁺ is shifted to more positive potentials approaching the values for  alone at the lowest 2: ratios. For this set of patches, the full shift in G-V curves resulting from the 2 subunits was 77.8 mV at 10 µM and 66.3 mV at 300 µM.

View larger version (42K): [in this window] [in a new window]   Figure 3.   G-V curves shift in a parallel manner as a function of the injected ratio of 2 to  subunit message. Currents were generated as in Figure 1, and peak current amplitude during each activation step was used to generate G-V curves. Each point at a given injection ratio represents the mean value ± SD for a set of patches (,  alone, 5 patches; , 0.01 2:, 4 patches; , 0.025 2:, 4 patches; , 0.05 2:, 5 patches; , 0.1 2:, 6 patches; , 1.0 2:, 5 patches; , 2.0 2:, 4 patches). A, Curves were generated with 10 µM Ca2+. Solid lines are fits of Equation 1 with values for V0.5 of +49.6, +34.9, +21.3, +4.1, 8.2, 22.5, and 20.1 mV for 2: ratios of 0, 0.01, 0.025, 0.05, 0.1, 1, and 2, respectively. Values of k, for the same ratios, were +17.3, +19.6, +21.7, +23.5, +23.0, +18.8, and +22.4 mV. B, Curves were generated with 300 µM Ca2+. Values for V0.5 were 23.0, 37.7, 54.3, 64.2, 74.4, 87.1, and 85.3 mV for the same injection ratios as in A, with values for k of +22.6, +19.9, +21.8, +22.9, +24.6, +27.1, and +23.6 mV. C, G-V curves were calculated for a channel population containing some average number of 2 subunits per channel, distributed binomially in the channel population. The numbers correspond to the percentages of the total numbers of possible sites on  subunits that are occupied by 2 subunits. The V0.5 for activation of a channel was assumed to shift incrementally with the number of 2 subunits associated with the channel. Channels with zero 2 subunits were assumed to have a V0.5 of +35 mV, whereas those with four 2 subunits had a V0.5 of 35 mV; while k = +17 mV for all stoichiometries. Fits of Equation 1 yielded values for V0.5 of 35, 21.2, 7.1, +7.1, +21.2, and +35 mV, with values for k of +17, +19.1, +20.1, +20.1, +19.1, and +17 mV. D, G-V curves were calculated as in C, except that the V0.5 for a channel containing one to three 2 subunits was assumed to be identical to that of a channel containing four 2 subunits. Thus, V0.5 was defined in an all-or-none manner by the presence of a single 2 subunit. E, G-V curves were calculated assuming positive cooperativity in the activation process from association of each additional 2 subunit with a channel. For each stoichiometry, the V0.5 values were +35, +32.11, +26.63, +10.80, and 35 mV at average numbers of zero to four 2 subunits per channel. The increment of shift was defined from (maximal shift)1/4. F, G-V curves were calculating assuming negative cooperativity, which was indistinguishable from the case shown in D. As in E, changes in V0.5 were defined by the one-fourth root of the full shift, except that the largest shift results from a single 2 subunit.

There are two possible explanations for the action of  subunits that might affect the shift in G-V curves. In one case, as the mole fraction of 2 subunits is reduced, the fraction of channels containing less than four 2 subunits will be increased. The shift in V_0.5 could arise from channels with less than a full complement of 2 subunits having a smaller shift in V_0.5 than those with four 2 subunits. In this case, the G-V curves would represent a binomially weighted sum of five distinct Boltzmann functions corresponding to the five possible 2: stoichiometries (Fig. 3C). Alternatively, it is possible that the shift in the G-V curves arises from changes in the proportion of two functional populations of channels, each with a characteristic V_0.5. Channels containing one or more 2 subunits would all share a similar V_0.5, whereas those containing no 2 subunits would appear as  alone. If so, the G-V curves would represent a weighted sum of two Boltzmann functions (Fig. 3D). This is the mechanism implied by observations in one previous study (Jones et al., 1999). This latter model might also appear to arise when there is strong cooperativity in the channel assembly process, such that channels contain either four or zero 2 subunits.

Comparison of the expectations arising from each type of model with the actual G-V curves obtained at 10 µM Ca²⁺ (Fig. 3A) suggests that a model in which each 2 subunit exerts some incremental contribution to the processes involved in shifting the G-V curve better approximates the actual results. We also considered two other cases: first, a case of strong positive cooperativity in which each additional 2 subunit associated with a channel results in a stronger effect on the V_0.5 (Fig. 3E); and second, a case of strong negative cooperativity in which most of the shift in V_0.5 results from the action of a single 2 subunit, with smaller effects contributed by each additional 2 subunit (Fig. 3F). The latter case was essentially indistinguishable from the case in which a single 2 subunit accounted for all the shift in V_0.5.

The V_0.5 for activation of conductance shifts in accordance with the fraction of injected 2 subunit (Fig. 4A). Similar to the relationship between _i and 2: ratio, the V_0.5 reaches a limiting value at ratios of 1.0 and 2.0. Values for V_0.5 at a ratio of 0.01 approach those for Slo1  alone. Because there is no simple relationship between the injected ratio of 2: subunits and the resulting channel stoichiometry, we have used the relationship between _i and V_0.5 to examine the effect of stoichiometry on activation V_0.5. In Figure 4B, the activation V_0.5 measured at 10 µM Ca²⁺ is plotted as a function of _i. Making a specific assumption about the minimal _i, _i can then be used to make estimates of the average number of 2 subunits per channel. Vertical lines correspond to the expected time constants for a channel population with an average of four, three, two, and one 2 subunits per channel. It should be realized that, except in the case of four, these expected values for the time constants are not equivalent to those predicted when all channels contain a given number of 2 subunits. This analysis suggests that the values of _i obtained in these experiments probably reflect average stoichiometries that vary from approximately four 2 subunits per channel to less than one 2 subunit per channel. Figure 4B also shows the predicted relationship between V_0.5 and _i expected when each 2 subunit contributes an identical amount of shift in V_0.5. The two lines compare predictions for the cases in which _min is 20 and 25 msec.

View larger version (20K): [in this window] [in a new window]   Figure 4.   Dependence of V0.5 for activation on the stoichiometry of  + 2 channels. A, The V0.5 for activation is plotted as a function of 2: injection ratios for either 10 or 300 µM Ca2+. Each point shows the mean V0.5 ± SD for a set of four to six patches. B, the mean V0.5 ± SD is plotted as a function of i ± SD for values measured with 10 µM Ca2+. Vertical lines 4, 3, 2, and 1 correspond to i expected for a binomially distributed stoichiometry with an average of four, three, two, and one 2 subunits per channel, respectively, with the minimum i assumed to be 20 msec. Horizontal lines correspond to V0.5 ± SD recorded for currents resulting from  alone. Dashed lines correspond to an empirical relationship between V0.5 and i for the case in which each 2 subunit produces an incremental effect on V0.5 as shown in Figure 3C. The two lines correspond to cases in which the minimal i was assumed to be either 20 or 25 msec. C, Larger symbols plot the relationship between V0.5 and the average number of 2 subunits per channel calculated from the inactivation time constants. Large , Data values from B (obtained at 10 µM Ca2+) with the assumption that the minimum i for a channel with four 2 subunits is 20 msec. , Same calculation but with a minimum i of 25 msec. For this conversion, when i for a patch exceeded the minimal or maximal i, the average number of 2 subunits per channel was assumed to reflect either four or zero 2 subunits, respectively. For comparison, the V0.5 at different average numbers of 2 subunits are shown for the cases of positive cooperativity (Fig. 3E; ) and negative cooperativity (Fig. 3F; ) and for an additive, incremental effect of each 2 subunit (Fig. 3C; ).

Given the scatter in experimental estimates and the variation in V_0.5 that seems to naturally occur among different sets of experiments, caution must be taken in attempting to relate how much shift in V_0.5 may occur in accordance with which levels of occupancy of the channels by 2 subunits. However, on the basis of the model of inactivation in which the average _i in a patch reflects some average, binomially distributed occupancy of channels by 2 subunits, we can calculate a predicted average number of 2 subunits per channel, relating it to the observed values for activation V_0.5 (Fig. 4C). The estimate of 2 subunits per channel depends on the assumption of a particular value for _min, and the predicted relationship for _min values of either 20 or 25 msec is illustrated. This procedure suggests that V_0.5 appears to shift in an approximately linear manner with the number of 2 subunits per channel between the limits defined by  subunits alone and full occupancy by 2 subunits. For comparison, predictions based on models with either positive or negative cooperativity (from Fig. 3E,F) are also shown in Figure 4C, indicating that the actual results fit better with the model in which each subunit adds linearly to shift the gating equilibrium of the resulting  + 2 channels.

In sum, these results are most consistent with the view that each 2 subunit independently contributes a fixed amount to the shift in activation V_0.5.

Single  + 2 channels exist in four different channel stoichiometries, each with a different voltage dependence of activation at a given Ca²⁺

It might be argued that the failure to observe an all-or-none effect of a single 2 subunit reflects the possibility that in macropatch recordings the G-V curves from two functional types of channel (Fig. 3D) simply average to be indistinguishable from the curves predicted for five separate functional types (Fig. 3C). To address this possibility, we therefore turned to single-channel recordings. In Figure 5, example sweeps and ensemble averages from single-channel patches are illustrated, corresponding to channels that inactivated with _i of 21.8, 33.4, 56.4, and 99 msec. A total of 49 single-channel patches were examined. A frequency histogram of the number of occurrences of single-channel inactivation time constants of various values is plotted in Figure 6A. Although the observed values show considerable variability, a fit of a four-component Gaussian distribution indicates that the values cluster at peaks corresponding to 22.6, 33.0, 49.1, and 99.8 msec. Although the number of examples of more slowly inactivating channels is a bit limited, these values correspond quite well to those that would be predicted for four stoichiometries with fully independent inactivation by each inactivation domain (e.g., 22, 33, 44, and 88 msec). These results provide direct evidence that individual channels can contain zero to four 2 subunits per channel.

View larger version (33K): [in this window] [in a new window]   Figure 5.   Single channels resulting from  + 2 coexpression reveal that individual channels can contain less than four 2 subunits per channel. A-D, Traces from four different patches are illustrated. In each panel, the top three traces show records of single-channel openings, whereas the bottom trace shows the ensemble current average. Channel openings were activated by a voltage-step to +100 mV with 10 µM Ca2+. A, The resulting ensemble current average exhibited a i of 21.8 msec; B, i = 33.6 msec; C, i = 54.3 msec; D, i = 97.9 msec. Note the differences in the single-channel current amplitude in each case measured at +100 mV. The tendency toward a larger single-channel conductance with fewer numbers of  subunits was consistently observed. There is also a tendency for channels to exhibit more frequent brief closures per unit of open time as the number of 2 subunits per channel is reduced. For each single channel trace, the dashed lines indicate the open current level (top) and closed current level (bottom). For current averages, the dashed lines indicate P(0) levels of 1.0 (top) and 0.0, respectively.

View larger version (36K): [in this window] [in a new window]   Figure 6.   Channel stoichiometry revealed by inactivation correlates with an incremental shift in activation V0.5. A, A frequency distribution of i values determined from ensemble current averages for 49 single-channel patches is plotted. i values were distributed into 5 msec bins, and a four-component Gaussian function was fit to the binned data, resulting in peak values of 22.6, 33.0, 49.1, and 99.8 msec, as indicated. For an inactivation mechanism with four independently acting inactivation domains, if channels with only one domain inactivate with a time constant of 100 msec, channels with two to four inactivation domains are predicted to inactivate with i of 50, 33, and 25 msec, respectively. B, A set of the channels studied in A were briefly treated with trypsin to remove inactivation and the relationship between P(0) and activation potential was determined at 4 µM Ca2+. Each filled symbol corresponds to a different patch expressing a channel with some mixture of  + 2 subunits. Open symbols correspond to patches expressing  alone. C, The relationship between activation V0.5 and i is plotted for 15 patches studied as in A and B. Channels that exhibited a slower i exhibited a more positive activation V0.5. Values appear to cluster into four groups, which were chosen by eye and indicated by the different symbols. D, Values in C were grouped as indicated, and V0.5 was plotted as a function of 100/i; 100/i should reflect the number of 2 subunits per channel assuming that a channel with one 2 subunit inactivates with i = 100 msec. The value at 0 corresponds to V0.5 values for single-channel patches containing  subunits only.

An interesting aspect of the single-channel recordings was that single-channel current amplitude at +100 mV appeared to scale with the number of 2 subunits per channel, with smaller current amplitudes at higher numbers of 2 subunits (Fig. 5). To confirm that observation, single-channel current measurements were made at potentials from +20 to +100 mV. Single-channel conductances were 214 ± 28.1 pS (_i = 21.6 ± 1.42; three patches), 228 ± 22 pS (_i = 31.3 ± 2.4 msec; three patches), 234 ± 14 pS (_i = 48.2 ± 2.5 msec; three patches), and 278 ± 15 pS (_i = 98.8 ± 1.2 msec; two patches), with extrapolated zero current potentials of <2 mV. The estimate under these conditions for the conductance of  alone is ~270 pS. Thus, the differences in single-channel current amplitudes seen here reflect a true difference in single-channel conductance resulting from the presence of the 2 subunit.

We next addressed the issue of how 2: subunit stoichiometry affects activation when observed in single channels. To do this, after determination of single-channel _i, inactivation was then removed by brief application of trypsin (0.5 mg/ml) to the cytosolic face of patches. Ensemble averages were then generated at voltages from +20 to +140 mV using 4 µM Ca²⁺. Four micromolar Ca²⁺ was preferable to 10 µM Ca²⁺ for this experiment, because with 4 µM Ca²⁺, the voltage of half-activation is sufficiently positive to 0 mV both for purely  + 2 channels and for -alone channels to allow better estimation of activation V_0.5. Figure 6B shows the resulting estimates of normalized open probability P(0) for such trypsin-treated single-channel patches along with estimates from four patches containing  subunits alone. The P(0)-V curves span a range of ~60 mV, somewhat similar to that seen with macroscopic currents in Figure 3A. The fitted estimate of V_0.5 for each single-channel recording is plotted as a function of _i in Figure 6C. For this set of 15 single-channel patches, the values appear to cluster into four groups, with the inactivation time constant strongly correlated with the activation V_0.5. Coupled with other results presented above, this strongly argues that each 2 subunit independently produces an equivalent effect on the resulting V_0.5 at a given [Ca²⁺].

Steady-state inactivation is also dependent on the average number of 2 subunits per channel

Other physiologically important properties of  + 2 currents may also be dependent on the stoichiometry of channel composition. Therefore, the dependence of two other properties of inactivating BK channels on the ratios of 2: subunits was also determined: first, the voltage dependence of steady-state inactivation measured at 10 µM Ca²⁺; and second, the rate of recovery from inactivation at 140 mV also with 10 µM Ca²⁺.

To examine steady-state inactivation properties, patches were held for at least 500 msec at conditioning potentials between 190 and +10 mV (Fig. 7A) before steps to +160 mV. At higher mole fractions of the 2 subunit, steady-state inactivation measured with 10 µM cytosolic Ca²⁺ was essentially identical to that previously observed for inactivating BK channels in RIN cells (Li et al., 1999), and for BK_i channels in chromaffin cells (Ding and Lingle, 2002). The fractional availability of current as a function of the initial conditioning potential was determined. As the ratio of 2: was reduced, the fractional availability of the resulting BK current was shifted to more positive potentials, and at the lowest dilutions it is clear that there is a substantial amount of current that does not inactivate. Because the activation step was to +160 mV, any channel that contains even one inactivation domain will contribute little to the steady-state current. Thus, the steady-state current represents almost exclusively the fraction of channels that contain no 2 subunits. The currents were analyzed in two ways. First, we measured only the fractional availability of the inactivating portion of the current (Fig. 7B). This takes into account only those channels that contain at least one 2 subunit. We also plotted the total amount of current available from any conditioning potential (Fig. 7C). This provides a better indication of the entire channel population at each 2: dilution. Qualitatively, it is quite clear that reducing the ratio of injected 2: subunits results in two effects: first, a marked shift in the fractional availability of channels for activation; and second, an increase in the fraction of channels that do not inactivate. The dependence of the voltage of half-channel availability on injection ratio is shown in Figure 7D.

View larger version (38K): [in this window] [in a new window]   Figure 7.   Steady-state inactivation shifts with changes in the 2: subunit ratio. A1-A5, Currents were activated with the voltage protocol indicated on the top for five different 2: injection ratios with 10 µM Ca2+. At smaller ratios, the amount of noninactivating current increases, and the rate of inactivation slows. The duration of the conditioning step was 600 msec. The dashed lines indicate the 0-current level. B, The percent availability ± SD of only the inactivating portion of current is plotted as a function of conditioning potential for four to six patches at each of the indicated 2: injection ratios. For ratios of 0.01, 0.025, 0.05, 0.1, 1.0, and 2.0, V0.5 values were 17.2, 38.9, 60.1, 73.1, 88.5, and 97.6 mV, respectively. C, The maximal current activated from different conditioning potentials was determined, providing an indication of the percent availability of the total channel population at different potentials. For ratios from 0.01 to 2.0, the voltages at which half the channels in the total population were available for activation were 97.6, 88.5, 67.8, 29.7, 3.5, and +37 mV. D, The voltage of half-availability determined in B is plotted as a function of injection ratio.

Recovery from inactivation exhibits an anomalous dependence on 2: ratio

The time constant of recovery from inactivation (_r) was defined at 10 µM with a paired pulse protocol in which, after complete inactivation of the channels at +140 mV, a second test step to +140 mV followed a variable recovery interval at 140 mV (Fig. 8A). At high 2: ratios, _r was ~20-25 msec similar to values measured for inactivating BK channels in RIN cells (Ding et al., 1998; Li et al., 1999). As the ratio of 2: was reduced (Fig. 8B,C), _r became faster, appearing to reach a limiting value at ~5 msec at the smallest ratios of 2:.

View larger version (40K): [in this window] [in a new window]   Figure 8.   Recovery from inactivation shifts with changes in the 2: subunit ratio. A, Currents were activated with 10 µM with the paired pulse recovery protocol shown on the top. Each set of traces corresponds to a different 2: injection ratio as indicated. Note the much slower recovery from inactivation at 1.0 2: than at lower ratios. The dashed lines indicate the 0-current level. B, The percent recovery ± SD is displayed as a function of recovery interval for a set of four to six patches at each injection ratio. The recovery time points at a ratio of 1.0 are obscured by those at 2.0. The recovery time course was fit in each case with a single exponential. For ratios of 0.01, 0.25, 0.05, 0.1, 1.0, and 2.0, r was 3.9, 4.8, 6.5, 9.0, 19.3, and 19.0 msec, respectively. C, The dependence of r on the injection ratio is displayed.

This change of _r with the ratio of 2: would appear to contradict previous work in which progressive trypsin-mediated removal of inactivation of inactivating BK channels in chromaffin cells did not alter _r (Ding et al., 1998). For a model of a block in which occupancy of a blocking site by a single inactivation domain is sufficient to produce inactivation, if recovery is governed solely by dissociation of a single domain from its blocking site, no alteration in _r is expected as the number of inactivation domains per channel is altered. Thus, the present result would seem to conflict with previous results and may challenge one simple conception of the molecular steps involved in the inactivation process, namely that the recovery process should be governed by dissociation by a single inactivation domain from its blocking site.

Is there a possible explanation for the dependence of recovery from inactivation on channel stoichiometry that would not require us to discard the view that dissociation of a single inactivation determines recovery? One simple explanation of this result is that it does not reflect some unusual aspect of the inactivation mechanism per se but rather reflects the coupling of recovery from inactivation to Ca²⁺-dependent activation steps. In fact, for both BK_i currents in chromaffin cells and  + 2 currents, the time course of recovery from inactivation becomes faster both at more negative potentials and with reductions in cytosolic Ca²⁺ (Ding and Lingle, 2002). Thus, although dissociation of a single inactivation particle may be sufficient to remove inactivation, it seems likely that, dependent on Ca²⁺ and recovery potential, channels may reinactivate during the recovery process. As a consequence, the time course of recovery from inactivation most likely reflects multiple kinetic steps, including dissociation of an inactivation domain, but also other Ca²⁺-dependent transitions. Because reductions in the 2: injection ratio shift the V_0.5 for activation to more positive values, this would naturally then be expected to also produce effects on recovery from inactivation.

Two sets of experiments were done to test this idea. First, we examined the time course of recovery from inactivation after different amounts of removal of inactivation of  + 2 currents by trypsin. Similar to our previous results (Ding et al., 1998; Li et al., 1999), when the average number of inactivation domains per channel is altered by digestion with trypsin, the time course of recovery from inactivation remains virtually unchanged (results not shown). The difference between the experiment with trypsin and the results with 2: dilution is that, in the former case, channels with fewer inactivation domains still have a full set of  subunits per channel, thereby leaving the voltage dependence of activation unchanged. In a second type of experiment, the average number of inactivation domains per channel was altered not by dilution of 2 subunits but by coexpression of 2 and  subunits, along with a 2 subunit in which the N-terminal inactivation domain has been removed (construct 2-33; Xia et al., 1999). Thus, a full complement of 2 subunits will be available to associate with  subunits, but less than a full complement of inactivation domains will be present. We varied the ratio of 2:2-33 to change the number of inactivation domains per channel in the population. Regardless of the ratio of 2:2-33, the time course of recovery is indistinguishable whether channels inactivate with time constants of 20-30 or 60-70 msec.

The above results therefore support the view that the seemingly anomalous faster rate of recovery from inactivation with smaller 2: ratios is simply a consequence of the influence of current activation transitions on the recovery time course (Ding and Lingle, 2002). In essence, _r is not dependent on the number of inactivation domains per channel but rather on the number of  subunits per channel because of coupling of the recovery process to steps in the activation pathway. An interesting implication of this result is that variation in _r based on the stoichiometry of 2: subunit assembly suggests a novel mechanism by which key functional properties of BK_i current might be regulated.

To summarize how steady-state inactivation and _r vary in accordance with the stoichiometry of those channels, we have plotted V_0.5 for steady-state inactivation and _r as a function of _i (Fig. 9A,B). To evaluate the extent to which stoichiometry may