Intrinsic Voltage Dependence and Ca²⁺ Regulation of mslo Large Conductance Ca-activated K⁺ Channels

Large conductance Ca-activated potassium channels (BK channels)¹ comprise a large group of membrane proteins found in a wide variety of cells (Latorre et al., 1989). These channels are identified by their potassium selectivity and large single channel conductance, as well as by their ability to sense changes in both membrane voltage and intracellular Ca²⁺ concentration (Lux et al., 1981; Marty, 1981; Pallotta et al., 1981; Barrett et al., 1982; Latorre et al., 1982; Latorre et al., 1989; Marty, 1989; McManus, 1991). When activated by an increase in intracellular Ca²⁺, BK channels respond with increased open probability and concomitantly increased K⁺ flux. These channels therefore can serve as a link between cellular processes which involve intracellular Ca²⁺ elevation and those which involve membrane excitability.

The proper functioning of BK channels depends not only on their ability to sense changes in membrane potential or intracellular Ca²⁺ concentration but also on the time course of their response. This is perhaps best exemplified in the inner hair cells of the turtle cochlea. Here, it has been demonstrated that there is a correlation between the frequency to which a particular hair cell is tuned and the kinetic properties of the BK channels native to that cell, suggesting that the kinetic behavior of these channels is critical for determining the frequency of the electrical oscillations in the hair cell during auditory stimulation (Hudspeth and Lewis, 1988a, b  ; Art et al., 1995; Wu et al., 1995).

Because the kinetic behavior of ion channels in general, and BK channels in particular, is critical for their proper function, and this behavior necessarily reflects the number and sequence of conformational states that a channel assumes as it gates, researchers have been interested in relating channel kinetics to the protein's underlying conformations. For BK channels this effort has been most successful at the single channel level where BK currents can be unambiguously identified and the internal Ca²⁺ concentration easily controlled. Extensive single channel studies on native BK channels have led to a kinetic picture in which there are at least five closed states and three open states with many paths between closed and open (McManus and Magleby, 1988; 1991). Hill analysis indicates that from two to perhaps as many as six Ca²⁺ ions can bind to the channel simultaneously, and it is likely that the different open states differ in the number of Ca²⁺ molecules bound (Barrett et al., 1982; Methfessel and Boheim, 1982; Moczydlowski and Latorre, 1983; McManus et al., 1985; Golowasch et al., 1986; Oberhauser et al., 1988; McManus, 1991; McManus and Magleby, 1991; Art et al., 1995).

The voltage sensitivity of BK channel gating has been less extensively studied than its Ca²⁺ sensitivity. Single channel studies suggest, however, that the mechanism by which BK channels sense the membrane voltage may not be the same as that used by purely voltage-gated K⁺ channels. In an extensive kinetic study, Moczydlowski and Latorre (1983) suggested that the voltage dependence of the gating properties of single skeletal muscle BK channels can be explained if it is supposed that the binding of Ca²⁺ to the channel is influenced by the transmembrane electric field, and it is this voltage sensitivity in Ca²⁺ binding that confers voltage-dependent gating properties on the channel rather than the action of voltage sensing elements intrinsic to the channel's primary sequence (see also Salomao et al., 1992). However, other studies have suggested, often on the basis of less extensive data and analysis, separate voltage-dependent and Ca-dependent steps in activation (Methfessel and Boheim, 1982; Blair and Dionne, 1985; Pallotta, 1985b; Cornejo et al., 1987; Singer and Walsh, 1987; Wei et al., 1994; DiChiara and Reinhart, 1995; Meera et al., 1996). Despite this previous work, the nature of the voltage-sensitive gating remains an open question.

The cloning of the pore forming subunits of several BK channels (Atkinson et al., 1991; Adelman et al., 1992; Butler et al., 1993; Tseng-Crank et al., 1994; McCobb et al., 1995; Wallner et al., 1995) has revealed some structural similarity between slo channels and shaker  -type, purely voltage-gated K⁺ channels. Although slo channels contain approximately twice as many amino acids as does a shaker channel, over the first ∼330 amino acids of slo their predicted topologies are quite similar. slo channels contain a sequence homologous to the P region which forms a portion of the ion conducting pore and the selectivity filter of the shaker channel (MacKinnon and Yellen, 1990; Yellen et al., 1991; Yool and Schwarz, 1991; Heginbotham et al., 1992; 1994), as well as six (or seven, see Wallner et al., 1996) putative membrane spanning regions. The fourth such region (S4) contains several positively charged residues spaced in a similar manner as those found in the corresponding S4 region of voltage-gated ion channels. The S4 regions form, at least in part, the voltage sensing elements of these channels (Liman et al., 1991; Lopez et al., 1991; Papazian et al., 1991; Logothetis et al., 1993; Sigworth, 1994; Yang and Horn, 1995; Aggarwal and MacKinnon, 1996; Larsson et al., 1996; Mannuzzu et al., 1996; Seoh et al., 1996; Yang et al., 1996). The sequence of the remaining ∼840 amino acids of slo channels appear to be unique to this channel family and is likely to contain Ca²⁺ binding domains (Lagrutta et al., 1994; Tseng-Crank et al., 1994; Wei et al., 1994).

The structural homology between cloned BK channels and voltage-gated K⁺ channels is perhaps surprising given the lack of intrinsic voltage sensitivity suggested by previous single channel experiments (Moczydlowski and Latorre, 1983). It again raises the question as to whether the voltage-dependence of BK channel gating may be due at least in part to an intrinsic voltage sensing domain. Indeed the recent work of Wei et al. (1994) in which the COOH-terminal domain of dslo was combined with the NH₂-terminal domain of mslo suggests that this may be the case. Reports of voltage-dependent activation of BK channel currents at very low Ca²⁺ concentrations and after treatment to remove Ca²⁺ sensitivity suggest the possibility of an intrinsic voltage dependence as well (Barrett et al., 1982; Methfessel and Boheim, 1982; Wong et al., 1982; Findlay et al., 1985; Pallotta, 1985b; Meera et al., 1996).

To address this question, and to understand further the gating mechanisms of BK channels, we have taken advantage of the ability to express cloned channels at high density in Xenopus oocyte membranes to study the kinetic and steady-state properties of mslo macroscopic currents over a wide range of internal Ca²⁺ concentrations and membrane voltages. In this paper we present the basic steady-state and kinetic properties of these currents and discuss constraints these data place on any system designed to model the gating behavior of the mslo channel. A result of particular importance is that our data are not consistent with a model of mslo gating which ascribes the majority of the voltage dependence of activation to voltage-dependent Ca²⁺ binding; but rather, it is necessary to suppose that charges intrinsic to the channel protein are involved in voltage sensing. In fact, we find that with strong depolarizations it is possible to nearly maximally activate mslo channels at very low Ca²⁺ concentrations, so low as to not allow time for Ca²⁺ to bind to the channel before opening. Based on our analysis, a general scheme SIs proposed to account for the relationship between Ca-dependent and voltage-dependent activation of the mslo channel.

Unless otherwise indicated, experiments were done using the conditions defined in the preceding paper (Cox et al., 1997). These conditions together with the appropriate analysis techniques allow for the discrimination between current properties arising from gating and those which are due to changes in channel permeation or block (Cox et al., 1997).

One of the goals of this study is an extensive characterization of the macroscopic gating kinetics of mslo channels. Shown in Fig. 1,A is an experiment designed to examine the voltage dependence of mslo activation at a constant [Ca]_i. [Ca]_i was buffered to 10.2 μM, and at 2-s intervals an excised membrane patch containing ∼60 mslo channels was stepped from −100 mV to a series of increasingly more positive potentials. Several features of these currents are worth noting. First, at −100 mV the mslo channels were very seldom open as is indicated by the very low level of steady-state current. This was the case despite the presence of 10.2 μM Ca²⁺ in the solution exposed to the intracellular face of the patch, and thus demonstrates that, at this concentration, a negative membrane voltage can overcome any activating effects of Ca²⁺. Second, upon depolarization, outward currents were observed which relaxed to their new steady-state level with a nearly single exponential time course. This can be seen most clearly in the middle panel in which a subset of traces have been expanded and fitted with exponential functions. There is some evidence, however, for a brief delay in the activation process. That is, when exponential fits such as those in Fig. 1,A are extrapolated backward in time to the point of zero current, they typically cross the time axis 75–175 μs after the beginning of the voltage step. After taking into account the appropriate filter delay (∼33 μs, 4 pole bessel filter at 10 kHz), this result suggests an actual delay of 50–150 μs. Due to complications in directly observing the time course of ionic currents during the first ∼100 μs after the voltage step, it is difficult to assess whether this apparent delay is an inherent property of the gating of mslo channels, or rather, at least in part an artifact produced by the subtraction of capacity and leak currents from the raw data before analysis. For this reason we have not emphasized this delay in our analysis and, in order to avoid errors, have fitted the time course of both activation and deactivation starting usually 200 μs after the beginning of the voltage step. Preliminary experiments specifically designed to examine very early times in the activation process, however, suggest that this brief delay may truly reflect an aspect of the mslo gating process (see also Ottalia et al., 1996), and therefore further investigation is certainly warranted. And third, over the voltage range examined the time constant of mslo channel activation decreases with increasing voltage (Fig. 1 A, right).

The primarily exponential time course of activation suggests that, at 10.2 μM [Ca]_i, a single conformational change limits the rate at which mslo channels move from closed to open. The increasing rate of activation with increasing voltage could be explained if this conformational change were voltage dependent. To estimate the charge associated with this forward rate limiting transition we fitted the relationship between the time constant of activation and membrane voltage (Tau-V) with an exponential function. We limited the fit to depolarized voltages where reverse rates are likely to contribute less to the time course of activation. The fit superimposed on the data in Fig. 1,A (right) yielded a gating charge of 0.71 e. We found this estimate to be sensitive to the exact voltage range used and to whether or not the minimum of the exponential was allowed to vary. This estimate therefore is likely to represent only a rough approximation of the charge associated with this transition. From patch to patch, allowing the minimum to vary, this method yielded charge estimates ranging from 0.55 to 0.76 e (for mean see Table II). To obtain a lower limit for this number we fit the Tau-V curve over a wider voltage range, and fixed the minimum of the exponential to 0. Considering a single voltage-dependent rate limiting step in activation, at intermediate voltages where forward and backward rates become comparable, the contribution of the backward rate constant will be to decrease the observed activation time constant. This method is therefore likely to lead to an under estimate of the true charge. For the data in Fig. 1,A, fitting in this way produced an estimate of 0.47 charges (for mean see Table II).

Standard tail current protocols were used to study the voltage dependence of mslo deactivation. At 10.2 μM [Ca]_i (Fig. 1,B), depolarizing voltage steps were applied to near maximally activate the channels, followed by hyperpolarizing steps to various potentials. Upon hyperpolarization, the channels closed, and the extent of tail current decay was voltage dependent. The time course of deactivation could be well approximated by a single exponential function over the entire voltage range examined (Fig. 1,B, middle), again suggesting a rate limiting conformational change between open and closed. The deactivation time constant was appreciably voltage dependent, increasing with depolarization. In Fig. 1,B (right), the time constant of deactivation, determined from exponential fits, is plotted as a function of membrane voltage. The charge associated with the apparent rate limiting backward transition in deactivation was estimated in a similar manner to that of activation. Exponential fits to the most hyperpolarized region of the Tau-V data (Fig. 1,B, right) yielded charge estimates ranging from 0.54 to 0.80 e (for mean see Table II). Fitting these Tau-V curves over a wider voltage range provided lower limit estimates of between 0.42 and 0.57 e.

Shown in Fig. 1,C is the conductance vs. voltage (G  -V) relationship derived from the current traces in Fig. 1,A. The maximum slope of this relation, which is an indication of the voltage sensitivity of the channel, is less steep for mslo than for most purely voltage-gated K⁺ channels suggesting that there may be comparatively less charge movement accompanying mslo gating. G-V curves for mouse Kv1.1(Grissmer et al., 1994) and Kv2.1(Pak et al., 1991) channels have been placed on Fig. 1 C for comparison. The mslo G-V curve has been fitted (solid line) with a Boltzmann function with an associated equivalent gating charge of 1.54 e, and a half activation voltage (V_1/2) of +34.6 mV. Notice that the equivalent gating charge associated with this fit (which represents a lower limit for the true gating charge of the channel) is approximately equal to the sum of the equivalent charges associated with forward and backward rate limiting kinetic transitions. Taking into account as well the monoexponential nature of current relaxations, these data point to a channel which, at 10.2 μM [Ca]_i, can be well approximated by a two-state system with similar voltage dependence in forward and backward transition rates:

Fits assuming such a model have been included in the Tau-V and G-V graphs of Fig. 1 .

To examine the Ca²⁺ dependence of mslo gating, we recorded macroscopic currents with protocols similar to that of Fig. 1 at a variety of [Ca]_i, from 0.84 to 1,000 μM (Figs. 2 and 3). In each experiment, as [Ca]_i was increased it was necessary to hyperpolarize the holding voltage to maintain a low level of basal activity, as well as to adjust the range of the test voltages to accommodate the shifting activation range of the channels. What is perhaps most interesting in these data is that the essential characteristics of the mslo current traces recorded with 10.2 μM [Ca]_i (Fig. 1) were maintained over the entire [Ca]_i range tested. At each [Ca]_i over the voltage range in which the time course of current relaxation could be accurately determined, the rate of activation increased with depolarization, and the rate of deactivation generally decreased. Also, the kinetics of both activation and deactivation could be well fitted with single exponential functions (Figs. 2 and 3, middle panels), suggesting that the kinetics of activation and deactivation are dominated by a single conformational change. As was the case at 10.2 μM [Ca]_i, however, at each [Ca]_i when exponential fits to the time course of activation were extrapolated to the point of zero current, they typically crossed the time axis between 50 and 150 μs after the onset of the voltage pulse, again suggesting the presence of a brief delay in the activation process.

Shown in the right panels of Figs. 2 and 3 are plots of the time constants of activation (Fig. 2) and deactivation (Fig. 3) as a function of voltage. The charges associated with the rate limiting transitions at each [Ca]_i were estimated in the same manner as was done for the data in Fig. 1. As [Ca]_i was varied the charge estimates associated with both forward and backward rate limiting transitions remained similar to that observed at 10.2 μM [Ca]_i. Although for activation there was a trend toward somewhat smaller charge estimates as [Ca]_i was increased (see Table II), the predominant effect of raising [Ca]_i was simply to translate the Tau-V curves of both activation and deactivation leftward along the voltage axis with little change in the voltage dependence of the kinetics (Fig. 4).

In addition to shifting the kinetics of mslo gating, raising [Ca]_i caused a similar leftward shift in the G-V relationship. In Fig. 5,A is displayed a set of G-V curves recorded from a single membrane patch, and in Fig. 5,B are shown average G-V relations from several experiments. Curves corresponding to 0.84, 1.7, 4.5, 10.2, 65, 124, 490, and 1,000 μM [Ca]_i are displayed. With both Tau-V curves (Fig 4) and G-V curves, for a given fold increase in [Ca]_i, we see a larger shift at low [Ca]_i (e.g., between 0.84 and 10.2 μM) than at higher [Ca]_i (e.g., between 124 and 1,000 μM). As will be discussed later, this property with regard to the Ca²⁺ dependence of the G-V relation is in agreement with previously published data (Wei et al., 1994) and has important implications for the physical relationship between Ca²⁺ binding and voltage sensing. As [Ca]_i was varied, the G-V relation maintained a shape which could be approximated by a single Boltzmann function, and the slope of this relation was similar at each [Ca]_i (Table I). That is, as with the kinetics of activation and deactivation, the predominant effect of an increase in [Ca]_i was to simply translate the G-V curve leftward along the voltage axis. Similar data have been published for both native (Barrett et al., 1982; Latorre et al., 1982; Methfessel and Boheim, 1982; Moczydlowski and Latorre, 1983; Markwardt and Isenberg, 1992; Art et al., 1995; Giangiacomo et al., 1995) and cloned (Butler et al., 1993; Tseng-Crank et al., 1994; Wei et al., 1994; DiChiara and Reinhart, 1995; McCobb et al., 1995; McManus et al., 1995; Wallner et al., 1995; Meera et al., 1996) BK channels.

We did, however, see some change in the slope factor of fits to the mslo G-V relation as [Ca]_i was varied. In particular there was a trend toward shallower slopes as [Ca]_i was increased above 1.7 μM. In Fig. 5,A, for example, equivalent gating charge estimates as determined from Boltzmann fits varied between extremes of 1.88, at 1.7 μM [Ca]_i, to 1.18 at 1,000 μM [Ca]_i. This is representative of the behavior observed in several experiments (see Table I and Fig. 5 B) and is therefore not due to random variability in the data. As discussed in the preceding paper (Cox et al., 1997), contaminant Ba²⁺ block at high voltages might cause a small increase in the steepness of the G-V curve measured at 0.84 μM [Ca]_i. At 1.7 μM [Ca]_i and above, however, the G-V curve spans less depolarized voltages, and Ba²⁺ block is not likely to have a significant effect (Cox et al. 1997). Therefore, this trend may reflect a genuine change in the voltage dependence of mslo gating as [Ca]_i is increased.

The effects of varying [Ca]_i are more easily seen when a single voltage is considered (Fig. 6). In Fig. 6,A are shown several traces recorded in response to voltage steps to +70 mV. Traces labeled a through f were recorded at increasing [Ca]_i (see legend). Several features of these currents are apparent. First, as expected for a Ca-activated channel, peak current amplitude increased with [Ca]_i. This point is only strictly true for the traces recorded in the [Ca]_i range 0.84–124 μM. At higher [Ca]_i, peak current actually declined. This decline, however, became more pronounced as [Ca]_i was increased and was not associated with a decline in tail current amplitude at −80 mV. It can therefore be attributed to voltage-dependent Ca²⁺ block (see preceding paper in this issue, Cox et al., 1997) and as such is not indicative of an actual reduction in channel activity. Second, as can be seen when the currents in A are normalized to their maxima (Fig. 6,B), the rate of current activation increased with increasing [Ca]_i, while the rate of deactivation decreased (Fig. 6 C). And third, as emphasized by the exponential fits superimposed on the traces in B and C, the primarily monoexponential nature of both activation and deactivation was maintained as [Ca]_i was varied.

Plotted in Fig. 6,D is the relationship between relative conductance and [Ca]_i at +70 mV. This relation was determined from the G-V curves of Fig. 5, amounting essentially to a transformation of these data to [Ca]_i dose response form. As was the case for the G-V relations, G/G_max plotted on the ordinate is proportional to open probability. The smooth curve through the data represents a fit to the Hill equation below (Hill, 1910).

Here K_D represents the apparent Ca²⁺ dissociation constant, n the Hill coefficient, and A the maximum value of G/G_max. The Hill coefficient (n = 3.08) from this fit is within the range of values reported in studies of single BK channel gating (Barrett et al., 1982; Moczydlowski and Latorre, 1983; Golowasch et al., 1986; Oberhauser et al., 1988; McManus and Magleby, 1991). The fact that this value is greater than 1 indicates that more than one Ca²⁺ molecule binds to the mslo channel, and that Ca²⁺ binds in a cooperative manner (Adair, 1925). The apparent K_D determined from the fit is 1.44 μM.

Plotted in Fig. 6 E is the relationship between the macroscopic rate constant of mslo current activation (the reciprocal of the time constant) and [Ca]_i also at +70 mV. There is not a linear relationship between these variables as would be expected from a system whose macroscopic rate constant was limited by a Ca²⁺ binding transition. The data are better described by a hyperbolic function which approaches a saturating value at high [Ca]_i. This result indicates that changes in the rate constants of kinetic transitions which involve Ca²⁺ binding no longer affect the kinetic behavior of the system at high [Ca]_i. This saturating behavior cannot be explained by kinetic schemes which involve only Ca²⁺ binding steps. Considering, for example, a scheme composed of a string of n Ca²⁺ binding steps:

the activation time course for scheme SII will contain (n − 1) exponential components. As [Ca]_i is increased, the forward rates become much larger than the backward rates, and each of the macroscopic rate constants of the system approaches one of the first order forward rate constants. Thus, at high [Ca]_i, each of the macroscopic rate constants (r_i) becomes a linear function of [Ca]_i.

To account for the saturating behavior in Fig. 6 E then, there must be at least one elementary step in the gating of the mslo channel which does not involve Ca²⁺ binding and serves to limit the rate of activation at high [Ca]_i. The minimum scheme contains one Ca²⁺ binding step and one Ca-independent step (scheme SIII below).

In general, a three-state kinetic scheme like scheme SIII will have a relaxation time course described by the sum of two exponential functions. This is contrary to the monoexponential nature of the mslo currents. The kinetic behavior of scheme SIII, however, will be dominated by a single exponential component if the rate constants for one step are fast relative to those for the other step. For mslo it would have to be the Ca²⁺ binding step which equilibrates most rapidly; otherwise, the activation rate could not become Ca-independent at high [Ca]_i. Making this designation then, the dominant macroscopic rate constant r for scheme SIII becomes:

This function is the rectangular hyperbola used to fit the data in Fig. 6 E (solid line), thus demonstrating that by including a Ca-independent step a very simple system can account for the saturating behavior of the macroscopic rate constant of activation at high [Ca]_i.

Scheme SIII, however, is not sufficient to account simultaneously for the Ca²⁺ dependence of the macroscopic rate constant of activation at +70 mV and the macroscopic rate constant of deactivation at −80 mV (Fig. 6 F). As with activation, the kinetics of deactivation become much less Ca²⁺ sensitive at high [Ca]_i. At lower concentrations, however, deactivation kinetics are slowed rather than accelerated as [Ca]_i is increased. This behavior cannot be explained by scheme SIII because, according to Eq. 3, under no condition will the relaxation rate of this system decrease as [Ca]_i is increased. To account for the Ca²⁺ dependence of both activation and deactivation kinetics it is necessary to add another Ca-dependent step to scheme SIII.

If a Ca²⁺ binding step is added after opening (scheme SIV), again assigning rapid Ca²⁺ binding on and off rates to maintain exponential kinetics, the macroscopic rate constant for scheme SIV is approximated by:

This equation contains two terms, one containing α weighted by the fraction of closed channels in C₁ which increases with increasing [Ca]_i and the other containing β weighted by the fraction of open channels in O₂ which decreases with increasing [Ca]_i. Whether the macroscopic rate constant of this system increases or decreases as [Ca]_i is increased will depend upon which term is changing more rapidly. In general, depending on the specific binding and unbinding rates, when α is greater than β, the first term will increase more rapidly than the second term decreases, and the macroscopic relaxation rate constant of the system will increase with increasing [Ca]_i. Conversely, when β is greater than α, the second term will change more rapidly than the first, and the macroscopic relaxation rate constant will decrease as [Ca]_i is increased. In either case, at high [Ca]_i, saturation is expected with r_sat equal to α. Therefore, if the rate constants α and β were to change with voltage, scheme SIV could qualitatively explain both the increasing rate of mslo current activation as a function of [Ca]_i at +70 mV and the decreasing rate of deactivation as a function of [Ca]_i at −80 mV. The data in Fig. 6 E and F have been fitted with Eq. 4 (dashed lines) simply by changing the values of α and β.

Another observation we might make with regard to the data in Fig. 6 is that at +70 mV it takes less Ca²⁺ to saturate the channel's steady-state conductance G/G_max (which is proportional to open probability) than it does to saturate the macroscopic rate constant of activation. Can we understand this behavior in terms of scheme SIV as well? To answer this question it is useful to write the open probability of scheme SIV as:

and compare it to the expression for the relaxation rate constant, Eq. 4. The differences between these expressions are that the terms involving α and β in Eq. 4 are now in the denominator of Eq. 5, and the term containing α is in the numerator. This term represents α weighted by the fraction of channels occupying state C₁ at equilibrium. Supposing that α and β are voltage- dependent and that α is several fold larger than β at +70 mV, it will then not be necessary for the closed state Ca²⁺ binding step to be saturated for the channel to be very nearly maximally activated. It is necessary only that α{1/(1 + k₋₁/k₁[Ca])}, which increases with [Ca]_i, be much larger than β(1 − {1/(1 + k₋₃/k₃[Ca])}), which decreases with [Ca]_i. As is evident from Eq. 4, however, in order for the kinetic behavior of the system to be saturated, the closed state binding step must be fully saturated, and therefore [Ca]_i must be severalfold greater than K_D1 (k₋₁/k₁). Thus it is clear that, given a wide rage of parameters, scheme SIV predicts another aspect of the data: the apparent K_D estimated from steady-state conductance measurements might be considerably smaller than that estimated from kinetic measurements.

The preceding analysis illustrates that many aspects of mslo gating can be understood, at least qualitatively, in terms of a central closed to open, voltage-dependent, conformational change flanked by rapid Ca²⁺ binding steps. In fact, Methfessel and Boheim (1982) have proposed a model which takes the form of scheme SIV to account for the Ca-dependent and voltage-dependent gating properties of single skeletal muscle BK channels. Moczydlowski and Latorre (1983), however, were able to account for many properties of those same channels by considering a scheme SIdentical to scheme SIV excepting that all of the voltage dependence of the system resided in the voltage dependence of Ca²⁺ binding. Models based on their idea can successfully predict several features of our data: (1) approximately exponential kinetic behavior, (b) a G-V relation which can be approximated by a Boltzmann function at any [Ca]_i, (c) channels which can be both maximally activated and deactivated at any nonzero [Ca]_i, and (d) a leftward shift in the G-V curve when [Ca]_i is increased. However, as also shown by Wei et al. (1994) such a gating mechanism can be tentatively excluded for mslo based on the observation that for each 10-fold increase in [Ca]_i the channel's G-V curves are not evenly spaced (Fig. 5, see also DiChiara and Reinhart, 1995).

To see that this is the case, it is useful to first consider the simplest form of a voltage-dependent binding mechanism in which there is a single Ca²⁺ binding site some distance into the plasma membrane such that in binding, Ca²⁺ traverses a fraction of the membrane voltage δ (the electrical distance). In this case the probability of the binding site being occupied by Ca²⁺, and thus the channel being open (P_o), depends on [Ca]_i as follows (Woodhull, 1973).

where F represents Faraday's constant, R the universal gas constant, T temperature, and K_D(0) the Ca²⁺ dissociation constant at 0 mV. Analyzing Eq. 6 in terms of the voltage required to reach half maximal activation (V_1/2), we see that for P_o equal to 0.5, we must have

This equation can be rewritten as

(Wong et al., 1982) which predicts a logarithmic relationship between V_1/2 and [Ca]_i.

Plotted in Fig. 5 C is the relationship between V_1/2 and [Ca]_i for the data in Fig. 5 A (closed circles). Also shown are the average V_1/2 values from several experiments (open squares). The curvature in these plots is indicative of the closer spacing of the G-V curves at higher [Ca]_i. This behavior was seen in every experiment in which G-V curves where determined at 3 or more [Ca]_i (n = 13). In the experiment of Fig. 5,A Ca²⁺ was presented to the patch in the following order: 1.7, 4.5, 65, 490, 124, 10.2, 0.84, and 1,000 μM, thus ruling out the possibility that the tendency toward closer G-V spacing at high [Ca]_i was due to a slow, time-dependent change in mslo current properties. From the curvature in the plot of Fig. 5,C then, we can rule out the single voltage-dependent Ca²⁺ binding site model. However, mslo is thought to be a tetramer (Shen et al., 1994), and is likely to have more than one Ca²⁺ binding site (Fig. 6 D). Nevertheless, it turns out that for a large class of models with multiple binding sites a logarithmic relationship between V_1/2 and [Ca]_i is predicted. The following statement holds true: For models of channel gating in which the voltage dependence of gating resides solely in the voltage dependence of Ca²⁺ binding, regardless of the number of Ca²⁺ binding sites or their affinities for Ca²⁺, there will be a logarithmic relationship between V_1/2 and [Ca]_i so long as the electrical distances of all the binding sites are equivalent. A conclusion very similar to this was arrived at by Wei et al. (1994) through simulations of various possible gating schemes. Below we provide a mathematical argument which extends their analysis.

In a channel with multiple binding sites, whose occupancy somehow relates to channel opening, the probability of a given site being occupied by Ca²⁺ at any given time will depend on the Ca²⁺ concentration and the affinity of each site, such that the overall probability of the channel being open is a function of all of the dissociation constants:

where K₁ through K_n represent the Ca²⁺ dissociation constants of binding sites 1 through n, and C represents the combined effects of all elementary steps not involving Ca²⁺ binding. If Ca²⁺ binding is voltage dependent, then each dissociation constant can be written as

where j ranges from 1 to n, K_j(0) represents the Ca²⁺ dissociation constant of the jth site at 0 mV, and δ_j represents the electrical distance of the jth site. From Eq. 10 we may write for each binding site in Eq. 9:

with

where

or conversely,

From Eqs. 11, 12, and 13, we see that X_j varies logarithmically with [Ca]_i, and that in order to maintain (V − X_j) constant in Eq. 11, and therefore [Ca]/K_j constant as well, the necessary change in membrane voltage will be equal to the change in X_j. That is,

If we suppose, as stipulated above, that all Ca²⁺ binding sites have the same voltage dependence,

then as [Ca] is varied the change in voltage necessary to maintain [Ca]/K_j constant is the same at each binding site and given as

Because we are considering cases in which all of the channel's voltage dependence resides in Ca²⁺ binding steps, the change in P_o in response to a change in voltage is determined solely by the effects of voltage on the Ca²⁺ binding equilibria (i.e., C in Eq. 9 is independent of voltage), and therefore the change in voltage necessary to maintain P_o constant as [Ca]_i is varied is also given by Eq. 16. A logarithmic relationship is therefore expected between a change in [Ca]_i and the change in voltage necessary to maintain any specific P_o. Choosing P_o equal to 0.5 as a convenient reference, the voltage necessary to maintain P_o = 0.5 is explicitly given as the following function of [Ca]:

Here [Ca]_1/2 is defined as the concentration of Ca²⁺ necessary to half maximally activate the channels at 0 mV.

Thus, we can say that the data in Fig. 5 are inconsistent with gating models in which the voltage dependence lies solely in Ca²⁺ binding to binding sites having equivalent electrical distances. When the electrical distances are not the same, the effect of voltage is different at each site and the situation is more complex. Two aspects of our data, however, suggest that if the voltage dependence of mslo gating were to arise solely from voltage-dependent Ca²⁺ binding, then the electrical distances for the mslo Ca²⁺ binding sites would have to be similar. The first is that computer simulations of models involving multiple voltage-dependent Ca²⁺ binding sites indicate that as the δ values for the sites diverge, the predicted G-V relation deviates markedly from Boltzmann behavior at either low or high [Ca]_i. No such effect is seen in the mslo data. The second aspect has to do with the minimum slope of the V_1/2 vs. log[Ca]_i relation. From Eq. 17 we see that for the simple system discussed above in which all electrical distances are equal the minimum possible slope is reached when δ is equal to 1. In this situation voltage is exerting its maximum possible effect on Ca²⁺ binding, and therefore, it takes a minimum change in voltage to compensate for a change in [Ca]_i. Substituting δ = 1 into Eq. 17 the minimum slope is found to be −29.4 mV per 10-fold change in [Ca]_i. If we assume that each Ca²⁺ binding contributes positively towards channel activation, then this minimum slope applies to systems in which the δs are not all identical as well. This is because if at some binding sites δ values were <1, these binding steps would become less sensitive to voltage. It would take a larger change in voltage to compensate for the effect of changing [Ca]_i at these sites, leading to a V_1/2 vs. log[Ca]_i relation which could only be more steep. Between 124 and 1,000 μM the slope of the mean V_1/2 vs. log[Ca]_i plot in Fig. 5 C is −28.9 mV per 10-fold change in [Ca]_i. This result indicates that if the channel's voltage dependence lies solely in Ca²⁺ binding, all sites which contribute to channel activation must have a δ value close to 1.² If this is the case, however, a logarithmic relationship between V_1/2 and [Ca]_i is predicted over the entire [Ca]_i range, a prediction which is not born out in the data. So, a wide variety of models of activation by voltage-dependent Ca²⁺ binding are incompatible with our data and that of Wei et al. (1994). We can tentatively conclude, therefore, that there must be an intrinsic voltage sensor in the mslo protein that is distinct from Ca²⁺ binding.

Kinetic observations strengthen this conclusion. As was shown in Fig. 6,E, the macroscopic rate constant of mslo activation at +70 mV increases with increasing [Ca]_i until a plateau is reached at high [Ca]_i indicating a Ca-independent step is rate limiting. Plotted in Fig. 7 A are similar data for a series of voltages. Clearly, the effect of an increase in membrane voltage is to increase the maximum rate of activation, while otherwise having little effect on the shapes of these curves. This change in the maximum macroscopic activation rate constant (r_max) with voltage indicates that a Ca-independent step (or steps), most likely that which is limiting the mslo kinetic behavior at high [Ca]_i, is voltage dependent.

Considering scheme SIV and Eq. 4 for example, if all of the channel's voltage dependence resided in either one or both Ca²⁺ binding steps, then at high [Ca]_i, regardless of the membrane voltage, r_sat would be simply equal to α. Depolarizing the membrane voltage would have no effect on r_sat but would reduce the amount of [Ca]_i necessary to reach saturation. Conversely, if the channel's voltage dependence resided in the central Ca-independent conformational change, then, r_sat would increase with depolarization as α(V) increased, while less effect would be expected on the [Ca]_i necessary to achieve saturation. For mslo, the apparent affinity, as defined by the [Ca]_i necessary to half saturate the macroscopic activation rate constant, changes only to a small degree with changing voltage (Fig. 7,C), whereas r_max is voltage dependent (Fig. 7 B). These results are therefore most consistent with the voltage dependence of mslo gating residing in large part in Ca-independent steps.

To estimate the charge associated with Ca-independent steps, we might examine the voltage dependence of the macroscopic activation rate constant at saturating [Ca]_i (Fig. 7,B). This is essentially what was done when a charge estimate was made from the voltage dependence of the time constant of activation at 1,000 μM (Fig. 2, bottom). Fitting the most depolarized region of this curve yielded a charge estimate of 0.58 ± 0.03 (SEM) e with a lower limit 0.39 ± 0.03 (SEM) e (Table II). We can conclude therefore that in the gating of the mslo channel there is at least this much charge associated with Ca-independent steps. If the reverse rate constants associated with these steps are also voltage dependent, this number would be an underestimate.

If there are both Ca²⁺ and voltage sensing elements in the mslo protein, it is important to know whether the activation of either or both types of elements is necessary for the channel to open. To address the question of whether [Ca]_i binding is necessary, we have looked for mslo currents at very low [Ca]_i. When Ca²⁺ is omitted from our standard internal solution, and no Ca²⁺ chelator is added, we have measured the free Ca²⁺ concentration to be between 10 and 20 μM. Adding 5 mM EGTA to this solution should then bring [Ca]_i to ∼0.5 nM (pH = 7.20, apparent Ca²⁺ K_D 160 nM calculated from the stability constants of Fabiato and Fabiato [1979]). Fig. 8,A shows mslo currents recorded using such a low [Ca]_i solution. The membrane voltage was held at −50 mV and then stepped to increasingly more positive voltages (+50 to +200 mV). Up until +90 mV, no significant current was observed. At more positive potentials, however, a large time-dependent outward current developed. The size of this current increased with depolarization, and at +200 mV was typically equal to 69 ± 7% (SEM) (n = 5) of the mslo current recorded from the same patch with 124 μM [Ca]_i (Fig. 8,B). Several lines of evidence indicate that this current is passing through mslo channels: It is not present in uninjected oocytes (Fig. 9,A). From patch to patch its size correlates well with the amplitude of Ca-dependent currents recorded with 124 μM [Ca]_i (Fig. 9,B). It is almost completely and reversibly blocked by 3 mM external TEA as is expected for the mslo channel (Butler et al., 1993) (Fig. 9,C), and, its single channel conductance is large, and identical to that of mslo (Fig. 9 D). In addition to these observations Palotta (1985b) and Meera et al. (1996) have reported low probability BK channel opening at very low [Ca].

It appears, then, that the mslo channel can open without binding Ca²⁺. However, it could be that there are voltage-dependent Ca²⁺ binding sites on the mslo channel, and at the extreme voltages necessary to activate the channel with ∼0.5 nM [Ca]_i, the affinity of these sites for Ca²⁺ increases to such an extent that a significant fraction of channels have Ca²⁺ bound. Considering for example a Ca²⁺ binding site with an electrical distance of 0.8, at +180 mV the dissociation constant for this site would decrease by a factor of 1.25 × 10⁵ as compared to its value at 0 mV, moving perhaps from 10 μM to 0.125 nM. Such a site would be 80% occupied at 0.5 nM [Ca]_i. The question then remains open as to whether Ca²⁺ must bind to the channel before it will open.

More can be learned about this question when the rate of activation at very low [Ca]_i is considered. Fig. 10 shows two current traces recorded from the same membrane patch, one at 10.2 μM [Ca]_i after a voltage step to +170 mV, and the other at ∼0.5 nM [Ca]_i (5 mM EGTA) after a voltage step to +250 mV. At 10.2 μM [Ca]_i the voltage step to +170 mV fully activates the channels as can be seen by examining the G-V relation determined at 10.2 μM in Fig. 5. Judging by the similar amplitudes of the traces recorded at 10.2 μM and ∼0.5 nM [Ca]_i in Fig. 10, the voltage step to +250 mV with ∼0.5 nM [Ca]_i must have brought the mslo channels near to their maximum open probability as well (differences in driving force here are not an issue as the mslo single channel current saturates at potentials above ∼+120 mV, see Cox et al., 1997, in this issue). The trace recorded with ∼0.5 nM [Ca]_i has been fitted with an exponential function (dashed curve) whose time constant is 1.15 ms. In six similar experiments the mean time constant of activation under these conditions was 1.4 ms ± 0.36 (SD). In these experiments the Ba²⁺ chelator (+)-18-crown-6-tetracarboxylic acid was added to the internal solution to reduce the possibility of Ba²⁺ block altering current kinetics (Diaz et al., 1996; Neyton, 1996) (although such effects are likely to be small, Cox et al., 1997). At high open probability, such as is the case here (see Figs. 5 and 8 in Cox et al., 1997), the above time constant (1.4 ms) represents the mean time it takes for an mslo channel to move from closed to open after the voltage step. This can be made more explicit by considering that at high open probability rates entering open states are necessarily much larger than rates leaving open states so that the rate of change of the current (d[I/I_max]dt) becomes very close to the rate of arrival of channels into open states. The mean transit time (m_t) from closed to open is given by

In the present case, where the timecourse of current activation is described by an exponential function with time constant τ, we have

whose solution is

demonstrating that the mean time for a channel to move from closed to open after the voltage step under these conditions will closely correspond to the time constant of current activation. Inverting the mslo activation time constant at ∼0.5 nM [Ca]_i and +250 mV (1.4 ms) yields a first order rate constant of 714 s⁻¹. All the elementary transitions that the channel undergoes on its way to opening, therefore, must have rate constants at least this rapid, and if Ca²⁺ must bind to the channel after the voltage step and before opening, then Ca²⁺ must bind at least this fast as well. The rate of Ca²⁺ binding, however, depends on its concentration. At 0.5 nM in order for Ca²⁺ to bind to the channel with a first order rate constant of 714 s⁻¹, the second order rate constant for Ca²⁺ binding must be at least 1.4 × 10¹² M⁻¹s⁻¹. Is this a reasonable on rate? We might use the expression of Smoluchowski (1916) below to calculate the diffusion limited on rate constant for the Ca²⁺ binding reaction.

Here N_A represents Avogadro's number, D_Ca the diffusion coefficient of Ca²⁺, and r_o the reaction radius (the distance between reacting particles at the point of collision). Considering that D_Ca equals 0.79 × 10⁻⁵ cm²s⁻¹, at 25°C (Hille, 1992), and r_o is on the order of a few angstroms (Pauling radius of Ca²⁺ = 0.99 Å, Pauling radius of oxygen = 1.40 Å), the diffusion limited k_on is on the order of 10⁹ M⁻¹s⁻¹. This value is three orders of magnitude smaller than the value experimentally determined above to be necessary to allow time for Ca²⁺ to bind to its site after the voltage step and activate the channel. This result therefore suggests that the mslo channel can be activated by a change in membrane voltage without binding Ca²⁺. This rate limiting value, however, is calculated based on simple diffusion alone. No electrical driving force is taken into the consideration. If the Ca²⁺ binding site is in the electric field, the diffusion-limited rate at which Ca²⁺ approaches its binding site may be increased due to the electrical driving force the field imparts on the ion with a factor of about z F   Ψ/RT, where z = 2 is the valence of Ca²⁺, Ψ is the potential near the binding site, and F, R, and T have their usual meanings (Getzoff et al., 1992; Pilling and Seakins, 1995). The negative surface potential near the Ca²⁺ binding site on the intracellular face of the membrane (Frankenhaeuser and Hodgkin, 1957; Chandler et al., 1965) may contribute to this driving force. The contribution of the surface potential should be <−90 mV (Hille et al., 1975). This would enhance the Ca²⁺ binding rate to a value of 7 × 10⁹ M⁻¹s⁻¹. This limit is still ∼200 times smaller than the value necessary to account for the rapid activation kinetics observed (1.4 × 10¹² M⁻¹s⁻¹).

Other evidence that indicates that at very low [Ca]_i the mslo channel can be activated by voltage without first binding Ca²⁺ comes from experiments in which [Ca]_i was varied in the low nanomolar range. Several internal solutions were prepared with the following calculated free [Ca]_i: 0.5 nM (no added Ca²⁺, 5 mM EGTA), 2 nM (no added Ca²⁺, 1 mM EGTA,), 10 nM (0.28 mM added CaCl_2, 5 mM EGTA), and 50 nM (1.18 mM added CaCl₂, 5 mM EGTA). mslo currents were then recorded from a single membrane patch using each of these solutions. The rationale behind this experiment was that if at very low [Ca]_i (∼0.5 nM) and high voltage, it is Ca²⁺ binding that is activating the mslo channel, then we would expect to see changes in the amplitude and time course of mslo currents as [Ca]_i is varied in the low nanomolar range. I-V curves from one such experiment are shown in Fig. 11,A. The clear result is that there was no significant increase in the amplitudes of currents recorded with internal solutions containing 2 or 10 nM [Ca]_i over those recorded with ∼0.5 nM [Ca]_i. Nor was there a clear increase in activation rate. (Fig. 11 B). The same result was obtained in five additional experiments, all supporting the conclusion that at very low [Ca]_i the channel is opening without binding Ca²⁺. These results also indicate that if surface charges are concentrating Ca²⁺ near its binding sites, then the channels are not sensitive to changes in the surface charge enhanced Ca²⁺ concentration as well. This is because the relationship between [Ca]_bulk and that which is concentrated by surface charge is expected to be linear. At 50 nM [Ca]_i a small increase in current amplitude relative to that at 0.5, 2, or 10 nM was observed suggesting that at this [Ca]_i the mslo channels may be just starting to bind Ca²⁺ appreciably.

To guard against errors in solution making, we measured the Ca²⁺ concentrations in the solutions employed in the experiment of Fig. 11 using the Ca²⁺ indicator fura II (100 μM) with the following results: calculated 0.5 nM, measured 0 nM; calculated 2 nM, measured 0 nM; calculated 10 nM, measured 1 nM; calculated 50 nM, measured 63 nM. The precision of these measurements, ± 20 nM, was limited by the sensitivity of the indicator. Nevertheless, they do confirm that the free Ca²⁺ concentrations in these solutions are in the high picomolar to low nanomolar range.

The experiments described above strongly support the conclusion that the mslo channel has intrinsic voltage sensing elements and that the action of these elements is sufficient to activate the channel substantially. In fact the similar amplitudes of the traces in Fig.10 argue that with strong depolarizations the mslo channel can be maximally activated without binding [Ca]_i. More evidence to support this conclusion is shown in Fig. 12,B. Here G-V relations determined from patches exposed to both 10.2 μM (squares) and ∼0.5 nM [Ca]_i (circles) are displayed. To maximally activate mslo channels at ∼0.5 nM [Ca]_i, it was necessary to depolarize to potentials greater than +200 mV. In 6 of 17 experiments, voltages as high as +250 mV were attained (closed circles). In 3 experiments it was possible to depolarize to +280 mV (open circles). At this potential the maximum current observed with ∼0.5 nM [Ca]_i was on average 101 ± 6% (SD) of that measured with 10.2 μM [Ca]_i at +150 mV (Fig. 12 A). Because the mslo channel's single channel current saturates ∼+120 mV (see Cox et al., 1997, in this issue), current amplitude and open probability at these high voltages become directly comparable. These results therefore indicate that, in contrast to the low probability openings reported previously in extremely low [Ca]_i and lower voltages (Pallotta, 1985a; Meera et al., 1996), by +280 mV the mslo channels were very close to being fully activated.

The data in Fig. 12,B also allow a comparison to be made between the shape of the mslo G-V relation under conditions in which the channel is activating without binding Ca²⁺ (∼0.5 nM [Ca]_i) to that observed with [Ca]_i sufficient to regulate channel gating (10.2 μM [Ca]_i). In this experiment (+)-18-crown-6-tetracarboxylic acid was included in the internal solution to ensure that the shape of the G-V relation was not distorted by Ba²⁺ block. Also, to control for time-dependent changes unrelated to changes in [Ca]_i, in each experiment current families were recorded at 10.2 μM [Ca]_i before (filled squares) and after (open squares) families with ∼0.5 nM [Ca]_i (filled circles). Each set of data in Fig. 12 B is fitted with a Boltzmann function of the form G/G_max = 1/(1+e ^{zF(V1/2 − V)/RT}). The equivalent gating charge estimates determined from these fits were 1.18 e (before) and 1.19 e (after) for the G-V relations determined with 10.2 [Ca]_i, and 0.87 e (voltages to +250 mV) and 0.83 e (voltages to +280 mV) for those measured with ∼0.5 nM [Ca]_i. These numbers suggest that the mslo channel is less sensitive to changes in membrane voltage when gating without Ca²⁺ binding than it is in the presence of 10.2 μM [Ca]_i. There is an apparent 26 to 31% decrease in equivalent gating charge at low [Ca]_i.

We have considered three possible explanations for this observation. The first is that while most of the gating charge of the channel derives from intrinsic voltage sensing elements, Ca²⁺, as it binds to the channel, may bind a short distance into the electric field (δ < 0.2) and therefore contribute approximately a quarter to a third of the total gating charge. Second, as pointed out by Zagotta et al. (1994a), the steepness of a channel's G-V relation depends not only on the amount of charge moved through the membrane's electric field during opening but also on the cooperativity of gating conformational changes. The decrease in maximum G-V slope observed at low [Ca]_i therefore might be attributed to Ca-dependent changes in the cooperative interactions between subunits, rather than to a change in gating charge. And third, the more shallow maximum G-V slope at ∼0.5 nM [Ca]_i as compared to 10.2 μM [Ca]_i may be not so much a consequence of the change in [Ca]_i, as it is a consequence of the fact that when gating in a Ca-  independent way, the mslo G-V relation spans extreme positive potentials. It may be that the equivalent gating charge of the channel changes as a function of the voltage range examined. A physical interpretation of such a phenomenon might be that there is a change in polarizability of the channel between open and closed states such as might come about if dipoles can be induced by the electric field in one state and not the other (Stevens, 1978; Sigworth, 1994). Such a change in polarizability would make the work done when the channel moves from closed to open a nonlinear function of voltage (Stevens, 1978) and could result in a more shallow G-V relation at extreme potentials. Unfortunately, at present we are unable to distinguish between these possibilities. In the future, however, experiments involving gating current measurements and the study of mutant channels whose G-V relations at low [Ca]_i are shifted to more hyperpolarized potentials may help make such a distinction possible. At present, however, the most we can say is that the mslo channel retains ∼70% of its apparent voltage sensitivity at very low [Ca]_i as estimated by simple Boltzmann fitting.

The results of experiments with very low [Ca]_i demonstrate that a lack of [Ca]_i does not limit the extent to which mslo channels can be activated by voltage provided sufficiently large depolarizations are used. It is important to ask whether the converse is true. Can a high enough [Ca]_i maximally active mslo channels regardless of the membrane voltage? We can see from the G-V curves of Fig. 5 that the answer to this question is likely to be no. Even with 1,000 μM [Ca]_i, applying a membrane voltage of −180 mV essentially completely prevented the mslo channels from opening.

The ability of membrane voltage to limit the extent to which mslo channels can be activated by [Ca]_i can be better seen when steady-state open probability (P_o) is plotted as a series of Ca²⁺ dose response curves (Fig. 13,A). Here, the curves from top to bottom correspond to data taken at successively more negative voltages in increments of 20 mV. Each curve has been fitted with the Hill equation (Eq. 1). At +90 mV (top curve) the channels are essentially fully activated by 10.2 μM [Ca]_i and the fitted curve approaches 1 on the ordinate. Near full activation is also reached at +50 mV (third from top), although here it takes more Ca²⁺ to bring the channels to full open. By −10 mV (third from bottom), however, the fitted curve reaches a maximum below 1 on the ordinate, and when the maximum of each fit is plotted as a function of voltage (Fig. 13 B), the fraction of channels which can be activated decreases with decreasing voltage. These data therefore suggest that negative potentials can limit the ability of [Ca]_i to activate mslo. Some studies, however, indicate that the BK channel G-V relation moves further leftward along the voltage axis with increases in [Ca]_i above the maximum [Ca]_i we have used (1,000 μM) (Moczydlowski and Latorre, 1983; Meera et al., 1996). That we have reached saturation of the mslo channel's Ca²⁺ binding sites by 1,000 μM [Ca]_i is therefore not clear. Wei et al.(1994) have suggested that leftward G-V curve shifts above ∼100 μM [Ca]_i are due to a nonspecific divalent cation binding site rather than the channel's primary Ca²⁺ sensors, and that saturation of the primary site is reached by ∼100 μM [Ca]_i. Because of these complications, we can only tentatively conclude that membrane voltage limits the ability of [Ca]_i to activate the mslo channel at negative potentials.

To gain further insight into the Ca²⁺-dependent activation of mslo it would be useful to know how many Ca²⁺ binding sites there are on the channel. We can determine a lower limit for this number by considering the Hill coefficients determined from fitting the Ca²⁺ dose response curves in Fig. 13,A. In general for a system with N binding sites, this coefficient will be less than or equal to N (Adair, 1925). In Fig. 13,C are plotted Hill coefficients as a function of voltage for both the data in Fig. 13 A (filled circles) and the mean of five similar experiments (open circles). The trend in these data is toward larger Hill coefficients at more depolarized voltages. Over the majority of the voltage range the Hill coefficient varied between 1 and 3 clearly indicating that at least three Ca²⁺ binding sites are associated with channel activation.

In Fig. 13 D the apparent K_D of the channel for Ca²⁺ as determined from fits to the Hill equation is plotted as a function of membrane voltage. As expected from the shifting behavior of the mslo G-V relation in response to changes in [Ca]_i, the apparent K_D declines sharply with increasing voltage. The mean data (open circles) have been fitted with an exponential function which changes e -fold per 21.6 mV.

In this study we have examined macroscopic mslo currents over a wide range of membrane voltages and Ca²⁺ concentrations to address some fundamental questions about the channel's gating mechanism. One important question related to BK channel gating is whether the channel's voltage dependence derives from intrinsic gating charges which are part of the protein sequence or instead from voltage-dependent Ca²⁺ binding? A leading model from single channel studies of skeletal muscle BK channels has suggested that the channel's voltage dependence resides in Ca²⁺ binding (Moczydlowski and Latorre, 1983). With the cloning of slo channels (Atkinson et al., 1991; Adelman et al., 1992; Butler et al., 1993), however, it became apparent that BK channels contain an S4 region which in purely voltage-gated channels is thought to span the membrane and form at least a part of an intrinsic voltage sensor (Stuhmer et al., 1989; Liman et al., 1991; Papazian et al., 1991; Perozo et al., 1994; Sigworth, 1994; Smith-Maxwell et al., 1994; Yang and Horn, 1995; Aggarwal and MacKinnon, 1996; Larsson et al., 1996; Mannuzzu et al., 1996; Seoh et al., 1996; Yang et al., 1996). These results suggested that slo channels may contain intrinsic voltage-sensing elements like those of the shaker channel. The shaker channel, however, contains seven basic residues in this region, whereas slo channels have only four. The reduced number of basic residues, therefore, might reasonably have rendered the slo channels' S4 regions no longer able to sense changes in membrane potential. Furthermore, the presence of an S4 region does not ensure that a channel will exhibit voltage- dependent gating. For example, the cyclic-nucleotide– gated channel of rod outer segment also has structural similarity to shaker channels including S4 and pore regions; this channel contains 5 positive charges in its S4 region (Kaupp et al., 1989), yet shows very little voltage dependence (Karpen et al., 1988).

In this study we provide three lines of evidence which indicate that the mslo channel does indeed have intrinsic voltage sensing elements which are distinct from Ca²⁺ binding. The first is that the position of the mslo G-V relation does not vary logarithmically with [Ca]_i. This observation is in support of the work of Wei et al. (1994), who also observed smaller shifts in the position of the mslo G-V relation per 10-fold change in [Ca]_i at high [Ca]_i than at low [Ca]_i. As they pointed out, it is difficult to find markovian models whose V_1/2 vs. log[Ca]_i relation is not linear if voltage dependence is assigned only to Ca²⁺ binding steps and these Ca²⁺ binding steps have approximately equal voltage dependence. Extending their analysis, we have shown that for all systems whose voltage dependence resides solely in Ca²⁺ binding, a logarithmic relationship between V_1/2 and [Ca]_i is expected so long as the electrical distances of all binding sites are the same (this was shown for a sequential binding model by Wong et al. [1982]). Given that we and others have observed Hill coefficients as high as 3, and evidence suggests that slo α subunits expressed alone form homotetrameric channels (Shen et al., 1994), it is reasonable to suppose that slo channels contain four identical Ca²⁺ binding sites, one per subunit. In such systems all binding sites naturally have equivalent electrical distances unless cooperative interactions between subunits serially alter the position of Ca²⁺ binding sites as each new Ca²⁺ molecule binds to the protein. Even without relying on simple symmetry, however, between 124 and 1,000 μM [Ca]_i the slope of the V_1/2 vs. log[Ca]_i relation is so shallow as to require that, if the channel's voltage dependence were to reside solely in Ca²⁺ binding steps, the electrical distance of each binding site would have to be close to 1. If this were the case, however, the V_1/2 vs. log[Ca]_i relation would necessarily be linear. This contradiction indicates that there must be some gating charge associated with conformational changes which do not involve Ca²⁺ binding.

Further supporting this conclusion, we have found that the macroscopic rate constant of mslo activation approaches saturation at high [Ca]_i. This saturating behavior indicates that gating transitions which do not involve Ca²⁺ binding are limiting the kinetic behavior of the mslo channel at high [Ca]_i. The fact that the maximum value of this limiting rate is voltage dependent, as was shown in Fig. 7, indicates that transitions that are separate from Ca²⁺ binding are necessarily voltage dependent, and thus, there must be gating charges intrinsic to the channel.

The third line of evidence in support of intrinsic voltage sensing is the observation that mslo channels can be substantially activated with [Ca]_i as low as ∼0.5 nM. This observation agrees with several reports of low probability BK channel activity at very low [Ca]_i (Barrett et al., 1982; Methfessel and Boheim, 1982; Wong et al., 1982; Findlay et al., 1985; Pallotta, 1985b; Meera et al., 1996). In fact, we have found that with depolarizations to +280 mV the mslo channels can be nearly maximally activated at ∼0.5 nM [Ca]_i, indicating that a lack of Ca²⁺ binding does not limit the ability of the channel to be activated by voltage. It is clear that this activation is truly Ca²⁺ independent, rather than due to very high affinity Ca²⁺ binding, because the time constant of current activation at ∼0.5 nM [Ca]_i is three orders of magnitude faster than the mean diffusion-limited time it would take Ca²⁺ to find its binding site after a depolarizing voltage step.

From the above analysis it is clear that, at very low [Ca], Ca²⁺ is not binding to and activating the mslo channels after the voltage step. We considered the possibility, however, that in the essential absence of Ca²⁺, some other ion in our internal solution was binding to Ca²⁺ binding sites and activating the channels. Oberhauser et al.(1988) have reported the following rank order of activating ions for skeletal muscle BK channels: Ca²⁺ (K_D = 8.98 × 10⁻⁴ mM) >> Cd²⁺(K_D = 0.27 mM) > Sr²⁺(K_D = 0.73 mM) > Mn²⁺(K_D = 0.96 mM) > Fe²⁺(K_D = 2.7 mM) > Co²⁺(K_D = 3.81 mM). K_D here indicates half-saturating ion concentration at +80 mV. Excepting Ca²⁺, none of these ions were added to our internal solutions. Some of them, however, may have entered into these solutions as a contaminant. To check this point the total concentrations of the most potent of these ions were measured by atomic absorption spectroscopy (AA). Cd²⁺, Sr²⁺, and Mn²⁺ were not detected indicating that if present their concentrations were lower than the resolution of the assay (∼0.3 μM). Iron was present at 4.56 μM. Given these results one might still suppose that Cd²⁺, Sr²⁺, or Mn²⁺ present at just below the AA detection limit, or perhaps Fe²⁺, is able to rapidly activate mslo channels at high voltages. EGTA however has high affinity for all of these ions, and calculations of the maximum possible free concentrations of these ions in our internal solution containing 5 mM EGTA indicates that only Sr²⁺ could be present at a free concentration higher than Ca²⁺, and then only at ∼1.3 nM. This concentration is still too small to account for the rapid activation of mslo currents in the presence of 5 mM internal EGTA. Based on these results we do not believe that in our low [Ca]_i experiments the mslo channels are being activated by a contaminant ion.

Our conclusion that the mslo channel has intrinsic voltage sensors differs from the mechanism proposed by Moczydlowski and Latorre (1983) for the voltage- dependent gating of a skeletal muscle BK channel. They concluded that this channel's voltage dependence comes from the voltage dependence of Ca²⁺ binding. There are several differences between the two studies including: native skeletal muscle channels vs. cloned α subunits expressed alone in oocytes, and single channel vs. macroscopic currents. However, the manner by which Moczydlowski and Latorre plotted their data may have made the intrinsic voltage dependence of the channel they studied less apparent. Their conclusion was based primarily on the observations that the channel's mean open time (τ_open) and mean closed time (τ_closed) were not clearly voltage dependent when extrapolated to [Ca]_i = 0 and 1/[Ca]_i = 0, respectively. However, at these extremes the mean open and closed times are at their minimum. Voltage-dependent changes in these values will appear small. Rather than plotting the τ_closed vs. 1/[Ca]_i as was done by Moczydlowski and Latorre (1983, Fig. 7), in Fig. 7,A we have plotted the macroscopic activation rate constant, r (1/ τ_activation) vs. [Ca]_i. At high [Ca]_i and moderate to high voltages this parameter approximates 1/τ_closed. Plotted in this way voltage-dependent changes in the channel's opening rate constant at saturating [Ca]_i are more easily seen. Between +20 and +120 mV, r_max varied between 1,000 and 5,000 s⁻¹. This corresponds to a variation in τ_closed of from 1 to 0.2 ms. In the plot of Moczydlowski and Latorre (1983, Fig. 7), this variation would be very hard to discern from random variability in the data, and the minimum τ_closed might easily be considered to be the same for each voltage. However, upon closer inspection of this plot it appears that each curve does not intersect the τ_closed axis at exactly the same point. In fact, there is an increase in the τ_closed intercept as the membrane voltage is made more negative. This is expected for a kinetic system whose closed to open rate constant increases with depolarization. It seems unlikely therefore that there is a fundamental difference between the voltage-dependent gating mechanisms of the channels in the two studies, and more likely that methodological differences allowed for intrinsic voltage dependence to be more clearly seen in our study.

A striking feature of macroscopic mslo currents is that the time course of both activation and deactivation can be well described by a single exponential function after the first ∼100 μs. This was found to be the case under all conditions in which the relaxation time course was accurately determined despite the fact that Ca²⁺ and voltage had strong effects on the time course of mslo current relaxation. These results are perhaps surprising given that at least eight kinetic states are necessary to describe the stationary gating behavior of single skeletal muscle BK channels (McManus and Magleby, 1988; 1991), and they suggest that in the gating of the mslo channel there is a single conformational change which is rate limiting over a wide range of stimuli. The observation that the time course of mslo current activation is still voltage dependent at saturating [Ca]_i argues that the rate limiting conformational change is voltage dependent. Further supporting this idea the mslo G-V relation can be fairly well described by a Boltzmann function over a wide range of [Ca]_i as is expected for a system which contains a single voltage dependent step between closed and open, and when estimates of the charge associated with forward and backward rate limiting steps at each [Ca]_i are summed, they are similar to equivalent gating charge estimates obtained by fitting the G-V relation with a Boltzmann function (see Tables I and II). Taken together these results suggest that it may be reasonable to model the gating of the mslo channel as a single voltage-dependent conformational change between closed and open states with Ca²⁺ binding shifting this equilibrium towards open.

Several observations, however, suggest that this view may be too simple. Single channel records from both native and cloned channels display complex kinetic behavior (Moczydlowski and Latorre, 1983; Pallotta, 1983; McManus and Magleby, 1988; 1991; DiChiara and Reinhart, 1995; Giangiacomo et al., 1995). Gating current studies indicate that there is a component of gating charge which moves very rapidly before slo channels open (Horrigan et al., 1996; Ottalia et al., 1996). Also, we and others (Ottalia et al., 1996) have observed a brief delay before the exponentially rising phase of mslo current activation. Although this delay lasted typically only ∼100 μs and was not studied in depth, it did appear to persist over a wide range of [Ca]_i and membrane potentials. The delay was evident even at ∼0.5 nM [Ca]_i where the channels were activating without binding Ca²⁺. Ca²⁺ binding kinetics therefore cannot explain the delay. To account for this delay we must suppose that there are at least two kinetic steps between closed and open. The presence of more than one step between closed and open is also suggested by the observation that while the mslo G-V relation appears fairly well fitted by a simple Boltzmann function, it is often as well or better fitted with a Boltzmann function raised to a power between 1 and 3 (Fig. 14). A sequential scheme with a single voltage-dependent transition along the path from closed to open predicts a G-V relation which takes the form of a Boltzmann function. If there are multiple voltage-dependent steps along this path, the exact shape of the G-V relation will depend on the equilibrium constants of all transitions and the magnitude of the associated gating charges. In general, multiple appreciably voltage-dependent elementary steps lead to G-V relations that deviate from simple Boltzmann behavior, producing a curve whose maximum slope is more shallow than would be observed if all of the gating charge was associated with a single conformational change. For many schemes, the G-V relation can be better approximated by a Boltzmann function raised to a power greater than 1 (Zagotta et al., 1994b). That the mslo G-V relation can often be better fitted by a Boltzmann function raised to a power greater than 1 suggests that more than one voltage-dependent step exists between closed and open states. Nevertheless, the essentially exponential kinetic behavior of the mslo channel coupled with fairly good single Boltzmann fits to its G-V relation suggests that even if there are multiple conformational changes involved in activation, there must be a high degree of cooperativity between them such that the probability of the channel existing in an intermediate closed state at equilibrium is low. Putting this discussion in more physical terms, if each subunit of the tetramer has a voltage-sensing element, then the observations discussed above suggest that these voltage-sensing elements are not acting independently, but rather the movement of one voltage sensor facilitates the movements of others such that together these elements move in a highly concerted manner. This mechanism differs from that of the shaker K⁺ channel whose voltage sensing elements appear to move independently (Zagotta et al., 1994a). Based on our results a high degree of cooperativity between subunits in mslo channel opening seems inescapable.

It should be noted that while we have expressed a single species of mslo RNA, through some process, such as posttranslational modification, the mslo channel populations we have studied may not have been completely homogeneous. This could also give rise to deviation from exponential kinetic behavior, as well as simple Boltzmann steady-state behavior.

Boltzmann fits to mslo G-V curves over a range of [Ca]_i yielded equivalent gating charge estimates of between 1.1 and 1.9 e. At very low [Ca]_i, this estimate was somewhat reduced (∼0.8 e). Other studies on both native (Barrett et al., 1982; Latorre et al., 1982; Methfessel and Boheim, 1982; Oberhauser et al., 1988) and cloned (Wei and Salkoff, 1986; Butler et al., 1993; Perez et al., 1994; Tseng-Crank et al., 1994; DiChiara and Reinhart, 1995; McCobb et al., 1995; Wallner et al., 1995) channels report values ranging between ∼1 and 2 as well. These values suggest that the equivalent gating charge of BK channels may be as much as 12 e less than that of the shaker channel (Schoppa et al., 1992; Zagotta et al., 1994b; Aggarwal and MacKinnon, 1996; Seoh et al., 1996) or DRK1(Kv2.1) (Islas and Sigworth, 1996). However, the fact that the G-V relation for a sequential gating scheme comprised of multiple voltage-dependent steps will be more shallow than it would be if all the gating charge moved in a single step means that fitting a channel's G-V relation with a Boltzmann function will often lead to an underestimate of the true gating charge of the channel. The severity of the underestimate will depend on the number of voltage-dependent steps between closed and open, the extent to which the total gating charge is spread throughout these steps, and the degree of cooperativity of the system. As pointed out by Zagotta et al. (1994b), as a gating scheme becomes more concerted such that the equilibrium constant for the last step before opening becomes large relative to early steps, the deviation from simple Boltzmann behavior decreases. In the limit that the relative magnitude of the last step becomes very large, a Boltzmann function which would describe the G-V relation for a two-state system containing all of the gating charge is predicted. This suggests then that for a channel like mslo, which appears to have a concerted conformational change between closed and open, Boltzmann fits to the G-V relation may not seriously underestimate the true gating charge of the channel, at least not to the same extent as is seen for the shaker channel whose G-V relation deviates more strongly from Boltzmann behavior and whose activation kinetics are much more sigmoid (Zagotta et al., 1994b). In the shaker channel Boltzmann fitting underestimates the gating charge by a factor of ∼3 (Schoppa et al., 1992; Zagotta et al., 1994b). Equivalent gating charge estimates of between ∼1 and 2 from Boltzmann fits to the mslo G-V relation are therefore likely to be no less accurate. Even if these estimates are off by as much as a factor of 3, however, they still indicate that the total gating charge of the mslo channel is likely to be no more than 6 e, at least ∼2-fold less than the best studied purely voltage-gated K⁺ channels. Whether the smaller amount of gating charge in the mslo channel is due to the fewer basic residues in its S4 region will be important to determine.

Despite the arguments above which suggest that it may be better to think of the mslo channel as having a highly concerted rather than a single step between closed and open, in considering scheme SIV we have seen that several properties of mslo macroscopic currents can be understood in terms of a kinetic scheme SIn which there is a central voltage-dependent conformational change both preceded and proceeded by rapid Ca²⁺ binding steps. These properties include: exponential activation and deactivation kinetics, relaxation rates which increase with [Ca]_i at depolarized voltages and decrease with [Ca]_i at hyperpolarized voltages, saturating kinetic behavior at high [Ca]_i, and an apparent affinity for Ca²⁺, as judged by half saturation of the macroscopic activation rate constant, which is much less sensitive to voltage than is the apparent affinity as judged by half saturation of the channels normalized conductance. Scheme SIV, however, cannot account for all aspects of our data as (a) it does not allow for channel opening with strong depolarizations in the absence of Ca²⁺ binding, (b) it does not predict that membrane voltage can limit the extent to which Ca²⁺ can activate mslo channels, and (c) it supposes that only two Ca²⁺ molecules bind to the channel. Still, its qualitative success with many aspects of mslo gating suggests that its general premise may be worth further consideration.

We can expand scheme SIV to a form which can qualitatively account for all the properties listed above and yet maintain its essential nature by considering scheme SV  below (the portion of scheme SV which corresponds to scheme SIV has been boxed).

Like scheme SIV, scheme SV describes a channel which must undergo a central voltage-dependent conformational change in order to open. Here, however, the channel can open with 0 to n Ca²⁺ molecules bound. In order for this system to be activated by Ca²⁺, on average, Ca²⁺ must bind more tightly to the open conformation than to the closed. When this is the case the leftward shifting nature of the mslo G-V relation with increasing [Ca]_i (Fig. 5) can be understood, because as more Ca²⁺ molecules bind to the channel, the central equilibrium will progressively shift toward opening. It therefore will take less voltage to bring the channel to its maximum open probability. The observation that the [Ca]_i required to half maximally activate mslo currents decreases as the membrane voltage is depolarized (Fig. 13 D) can also be explained in terms of scheme SV, as, according to this scheme, it would take fewer bound Ca²⁺ to maximally activate the channel as the membrane voltage is depolarized. In fact, at extremely positive voltages none are required, leading to Ca-independent opening as we have described.

As was the case for scheme SIV, scheme SV requires that Ca²⁺ binding is not rate limiting to reproduce the single exponential kinetics observed over a wide range of conditions, and the saturation of the macroscopic activation rate constant at high [Ca]_i. It is interesting to consider the possibility more closely, however, that it is the Ca²⁺ binding steps which are rate limiting. If the horizontal rates in scheme SV were very slow relative to the vertical rates, the channels would move predominately vertically before horizontally, and the activation time course of the population would have many exponential components, at least one for each vertical step in the scheme. If on the other hand the vertical rates were much slower than the horizontal rates, then the channels would redistribute laterally while moving to open, producing relaxation kinetics which would be much more simple. In fact, it can be shown that, in the limit that the Ca²⁺ binding and unbinding rates become very fast relative to the vertical rates such that each horizontal step can be considered to be in a steady state at all times, the kinetics of scheme SV are described by a single exponential function. The time constant of this exponential will depend on [Ca]_i, and on the values of all the vertical rates and horizontal equilibrium constants in the system. Due to the exponential nature of the mslo currents, therefore, we favor the idea that it is a Ca²⁺ independent conformational change which is limiting the kinetic behavior of the mslo channel over a wide range of conditions.

DiChiara et al. (1995) concluded that it was Ca²⁺ binding which was limiting the activation time course of dslo currents in part based on the observation that at high open probabilities the time course of dslo macroscopic current activation parallels the cumulative time to first opening of dslo single channels and that this time course changes as a function of [Ca]_i. This observation, in fact, is not at odds with the above conclusion as, at high open probability and in the rapid Ca²⁺ binding limit, both the time to first opening and the macroscopic activation rate constant of scheme SV will be determined by the same weighted average of all of the forward rate constants in the system, and the contribution of each rate constant to this average will change as a function of [Ca]_i. Their observation that the time course of dslo and hslo activation is best described by two exponential components, however, may indicate that in these channels Ca²⁺ binding rates are contributing in a more direct way to the kinetics of relaxation than they do for mslo.

Wei et al.(1994) have studied the G-V relations of chimeric channels comprised of core (the NH₂ terminus through S8) and tail (after S8 to the COOH terminus) regions from either mslo or dslo channels. mslo has a higher apparent affinity for Ca²⁺ than does dslo. Interestingly, they found that when a dslo tail was expressed together with a mslo core, the dslo tail had little effect on the chimeric channel's G-V relation at high [Ca]_i (300 μM). That is, the chimeric channel's G-V relation was very similar to the parent mslo channel. At lower [Ca]_i however, much stronger depolarizations were required to activate the chimeric channel as compared to mslo. They also found that the reverse chimera's (dslo- mslo) G-V relation at high [Ca]_i was in a similar position on the voltage axis to that of the dslo channel but was shifted to more hyperpolarized voltages than that of dslo at lower [Ca]_i. They interpreted these results to indicate that the slo channel's Ca²⁺ binding affinity is determined by its tail region, and that the dslo tail binds Ca²⁺ with lower affinity than does the mslo tail, whereas the channel's closed to open equilibrium at saturating [Ca]_i is determined by its core region.

Some aspects of scheme SV support this hypothesis. If the dslo tail region confers lower Ca²⁺ affinity on the channel than does the mslo tail, then, according to scheme SV, at low [Ca] the chimeric channel's G-V relation would likely lie to the right of the mslo G-V relation due to the fact that fewer Ca²⁺ would be bound to the mslo-dslo channel. At saturating [Ca]_i, however, the two G-V curves would not necessarily be expected to converge. This is because, according to scheme SV, and indeed for any gating system activated by Ca²⁺, the position of the G-V relation on the voltage axis at saturating [Ca]_i will not be determined solely by the intrinsic conformational free energy difference between closed and open (in scheme SV this free energy difference determines the equilibrium constant between C₀ and O₀), but it will also depend on the difference in Ca²⁺ binding energy between closed and open. For scheme SV the equilibrium constant between closed and open at saturating [Ca]_i is given by

The term in square brackets represents the ratio of the product of the Ca²⁺ dissociation constants for Ca²⁺ binding to closed states, to the product of the Ca²⁺ dissociation constants for Ca²⁺ binding to open states. Therefore, changes in Ca²⁺ binding affinities can affect the closed to open equilibrium even at saturating [Ca]_i, and changing from mslo tail to dslo tail might be expected to affect the position of the mslo-dslo G-V relation at saturating [Ca]_i. Such an effect would not be observed, however, if in changing from mslo tail to dslo tail, the ratio of Ca²⁺ binding energies between closed and open states remained constant. The observations of Wei et al. therefore suggest that this may be the case. Our results, however, suggest that a more direct way to examine the effects of the core region on the intrinsic conformational energy of the channel would be to examine the G-V relations of the chimeric channels at very low [Ca]_i where the channels are gating without bound Ca²⁺. If it is the core region that determines the intrinsic energy difference between closed and open, then one would predict that in the zero [Ca]_i limit the mslo and mslo-dslo G-V relations would again converge. Whether this is actually the case will be interesting to determine.

McManus and Magleby (1991) have considered schemes which take the form of scheme SV to account for the Ca-dependent, stationary gating properties of skeletal muscle BK channels at +30 mV and have proposed as the simplest model to account for their data a subset of this system shown below.

One obvious difference between scheme SVI and scheme SV is the absence of direct opening pathways from C₀ and C₁. However, we do not believe this to be an important discrepancy, because in scheme SV these transitions would not be favored with [Ca]_i between 1 and 25 μM, and at the moderately depolarized voltage they used. Although it was derived from data on different channels, the general form of their model is clearly quite similar to, and a subset of, scheme SV . McManus and Magleby, however, did not study the voltage dependence of gating. As an exercise, we wondered whether if by supplying voltage dependence to the vertical transitions of scheme SVI and using the kinetic parameters defined for +30 mV by McManus and Magleby (cell #1), we could account for the kinetics of macroscopic mslo currents. We found that if we let the channels distribute among the closed states at negative potentials and then jumped the voltage to +30 mV, the kinetics of this system were similar to mslo at low (0.84 μM) [Ca]_i and high (124 μM) [Ca]_i. At intermediate [Ca]_i, however, the model was either significantly slower (1.7, 4.5 μM [Ca]_i) or faster (10.2 μM [Ca]_i) than the mslo currents, and more than one kinetic component was usually evident. If we assigned to the McManus and Magleby model an amount of gating charge similar to that estimated for mslo (qf = 0.7, qb = −0.7), over a range of voltages, the modified McManus and Magleby model in general showed much slower activation kinetics than mslo at [Ca]_i below 124 μM and much faster deactivation kinetics at negative potentials. This result is not surprising as we have studied the α subunit of a cloned channel in a heterologous expression system, while their experiments were done with native skeletal muscle BK channels which may have been composed of α and β subunits. It does indicate, however, that we can not co-opt this system as it stands to account quantitatively for the macroscopic kinetics of the mslo channel. The type of detailed studies done by McManus and Magleby certainly must be applied to mslo channels. In the broader sense, however, that both detailed single channel analysis and macroscopic current measurements are pointing to a channel with a concerted closed to open conformational changed regulated by multiple Ca²⁺ binding sites lends further credence to the idea that this general view is correct.

We gratefully acknowledge Larry Salkoff for providing the mslo clone, Marcus Hoth and Richard Lewis for performing Ca²⁺ concentration measurements by fluorescence microscopy, Victor Corvalan for algorithms for Ca²⁺ concentration calculations, and Frank Horrigan for helpful comments on the manuscript.

This work was supported by a National Institute of Mental Health Silvio Conte Center for Neuroscience Research grant (MH 48108). J. Cui was supported by a postdoctoral fellowship from the Muscular Dystrophy Association. R.W. Aldrich is an investigator with the Howard Hughes Medical Institute.

BK channels

large conductance Ca-activated potassium channels