Correspondence to Daniel H. Cox: dan.cox{at}tufts.edu
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INTRODUCTION |
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The ß2 subunit, for example, confers rapid inactivation upon the BKCa channels of adrenal chromaffin cells (Wallner et al., 1999; Xia et al., 1999
), and ß4 renders many of the BKCa channels of the brain insensitive to the scorpion toxin charybdotoxin (Meera et al., 2000
). Perhaps most profound, however, the BKCa ß1 subunit, which is predominately expressed in smooth muscle, slows the BKCa channel's kinetic behavior and dramatically increases its Ca2+ sensitivity (McManus et al., 1995
; Wallner et al., 1995
; Meera et al., 1996
; Cox and Aldrich, 2000
; Nimigean and Magleby, 2000
). In fact, mice that lack ß1 have hypertension, because the BKCa channels of their vascular smooth muscle lack the Ca2+ sensitivity required for BKCa-mediated feedback regulation of smooth muscle contraction (Brenner et al., 2000b
). Thus, ß1 is important in the vascular system and indeed in many other smooth muscledependent systems as well (Nelson and Quayle, 1995
; Snetkov and Ward, 1999
; Bayguinov et al., 2001
; Niu and Magleby, 2002
; Meredith et al., 2004
; Morales et al., 2004
). Four ß1 subunits associate with a single BKCa channel (Wang et al., 2002
).
How ß1 enhances the BKCa channel's Ca2+ sensitivity is not well understood. Perhaps the simplest mechanism would be for it to increase the affinities of the channel's Ca2+-binding sites, but this does not appear to be the case. Nimigean and Magleby (1999)(2000
) found that ß1 increases the length of time that the BKCa channel spends in bursting states and that this effect persists in the absence of Ca2+. They suggested that it is this Ca2+-independent effect that underlies most of the channel's increased Ca2+ sensitivity. Furthermore, we found previously that as the Ca2+ concentration is raised, the concentration at which the BKCa channel's conductancevoltage relation begins to shift leftward is essentially unaffected by ß1 (Cox and Aldrich, 2000
), a result that suggests that, at least when it is open, the channel's affinity for Ca2+ is not greatly altered by ß1. In fact, this study leads us to suggest that, rather than greatly altering the channel's Ca2+-binding properties, ß1 may be enhancing its voltage-sensing properties by shifting the equilibrium for voltage sensor activation, and therefore the channel's gating charge vs. voltage relation (QV relation)
100 mV toward more negative voltages. This would be expected to decrease the work that Ca2+ binding must do to open the channel at most voltages and thereby bring about an apparent increase in Ca2+ affinity at most voltages as well. Contrary to this hypothesis, however, Orio and Latorre (2005)
have recently proposed that it is a decrease in effective gating charge, rather that a shift in the channel's QV relation, that accounts for the effects of ß1.
Here, to distinguish between these possibilities, we have measured gating currents from heterologously expressed BKCa channels with and without ß1 coexpression. Our results indicate that the channel's QV relation does shift dramatically leftward upon ß1 coexpression, with no change in gating charge. Thus, ß1 stabilizes the active conformation of the channel's voltage sensors, and this has a large effect on the Ca2+ sensitivity of the channel. In addition, however, in order to fully account for the increase in apparent Ca2+ affinity brought about by ß1, we have also found it necessary to suppose that ß1 decreases the true affinity of the closed channel for Ca2+.
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MATERIALS AND METHODS |
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Electrophysiology
All recording were done in the inside-out patch clamp configuration (Hamill et al., 1981). Patch pipettes were made of borosilicate glass (VWR micropipettes) with 0.54 M
resistances that were varied for different recording purposes. The tips of the patch pipettes were coated with sticky wax (Sticky Wax) and fire polished. Data were acquired using an Axopatch 200B patch-clamp amplifier and a Macintosh-based computer system equipped with an ITC-16 hardware interface (Instrutech) and Pulse acquisition software (HEKA Electronik). For macroscopic current recording, data were sampled at 50 kHz and filtered at 10 kHz.
In most macroscopic current experiments, capacity and leak currents were subtracted using a P/5 subtraction protocol with a holding potential of 120 mV and leak pulses opposite in polarity to the test pulse, but with BK+ß1 currents recorded at 10 and 100 µM Ca2+ no leak subtraction was performed.
Unitary currents were sampled at 100 kHz and filtered at 10 kHz. For gating current recordings, voltage commands were filtered at 7.5 kHz to limit the size of fast capacity transients, and the data were sampled at 100 kHz and filtered at 510 kHz. Capacity and leak currents were subtracted using a P/5 protocol with a holding potential of 120 mV and leak pulses opposite in polarity to the test pulse. All experiments were performed at room temperature, 2224°C.
Solutions
Gating current solutions were made according to Horrigan and Aldrich (1999). Pipette solutions contained (in mM) 127 TEA-OH, 125 HMeSO3, 2 HCl, 2 MgCl2, 20 HEPES, pH 7.2 (adjusted with HMeSO3 or TEA-OH). The 0.5 nM Ca2+ internal solution contained (in mM) 141 NMDG, 135 HMeSO3, 6 HCl, 20 HEPES, 40 µM (+)-18-crown-6-tetracarboxylic acid (18C6TA), 5 EGTA, pH 7.2 (adjusted with NMDG and HMeSO3).
K+ current recording solutions were composed of the following (in mM): pipette solution, 80 KOH, 60 NMDG, 140 HMeSO3, 20 HEPES, 2 KCl, 2 MgCl2 (pH 7.20); internal solution, 80 KOH, 60 NMDG, 140 HMeSO3, 20 HEPES, 2 KCl, 1 HEDTA or 1 EGTA, and CaCl2 sufficient to give the appropriate free Ca2+ concentration (pH 7.20). EGTA (Sigma-Aldrich) was used as the Ca2+ buffer for solutions containing <1 µM free [Ca2+]. HEDTA (Sigma-Aldrich) was used as the Ca2+ buffer for solutions containing between 1 and 10 µM free Ca2+, and no Ca2+ chelator was used in solutions containing 100 µM free Ca2+. 50 µM (+)-18-crown-6-tetracarboxylic acid (18C6TA) was added to all internal solutions to prevent Ba2+ block at high voltages (Cox et al., 1997b).
The appropriate amount of total Ca2+ (100 mM CaCl2 standard solution; Orion Research Inc.) to add to the base internal solution containing 1 mM HEDTA to yield the desired free Ca2+ concentration was calculated using the program Max Chelator (http://www.stanford.edu/~cpatton/maxc.html), and the solutions were prepared as previously described (Bao et al., 2004). To change Ca2+ concentration, the solution bathing the cytoplasmic face of the patch was exchanged using a sewer pipe flow system (DAD 12) purchased from Adams and List Assoc. Ltd.
Data Analysis
All data analysis was performed with Igor Pro graphing and curve fitting software (WaveMetrics Inc.), and the Levenberg-Marquardt algorithm was used to perform nonlinear least-squares curve fitting. Values in the text are given ± SEM.
GV Curves
Conductancevoltage (GV) relations were determined from the amplitude of tail currents measured 200 µs after repolarizations to 80 mV following voltage steps to the test voltage. Each GV relation was fitted with a Boltzmann function
![]() | (1) |
QV Curves
The amount of activated gating charge (Q) at a given voltage was determined from the area under the gating current trace between 0 and 300 µs after the initiation of the voltage step. Repolarizations were to 80 mV. Each QV relation was fitted with a Boltzmann function and normalized to the maximum of the fit. The voltage sensor's half-activation voltage Vhc and the gating charge zJ were determined from the fitting.
Limiting Popen Analysis
Popen measurements <103 were made in 3 nM Ca2+ with patches that contained hundreds of channels. The number of channels in a given patch (N) was determined by switching the patch into a solution that contained either 100 µM Ca2+ () or 10 µM Ca2+ (
+ß1) and recording macroscopic currents at moderate to high voltages. N was than calculated as N = I/(iPO), where i represents the single channel current at a given voltage and PO represents the open probability at that same voltage. Both i and PO were determined previously in separate experiments. In some experiments PO was estimated from the GV relation determined from the same patch. After determining the number of channels in a given patch, the membrane voltage was moved to lower voltages, the patch was superfused with a 3 nM Ca2+ solution, and unitary currents were recorded for 530 s at progressively more negative voltages. All-points histograms were then used to determine the probability of observing 0, 1, 2, 3, ... open channels at a given time, and true channel Popen was then determined as
![]() | (2) |
Fitting V Curves Based on the Model of Horrigan et al. (1999)
Relaxation time constants as a function of voltage were calculated for Scheme I (see Fig. 5) assuming its horizontal steps equilibrate much more rapidly than its vertical steps, such that they are always at equilibrium (Cox et al., 1997a; Cui et al., 1997
; Horrigan et al., 1999
; Horrigan and Aldrich, 2002
). Under this assumption,
(V) can be calculated as a weighted average of all the vertical rate constant in Scheme I as follows:
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For the open channel, fO0fO4 were calculated in the same way but using Jo rather than Jc. Each vertical rate constant was also assigned a voltage dependence as follows
![]() | (5) |
![]() | (6) |
Thus, to fit the V curves in Fig. 7, 11 independent parameters were required: L, Vhc, D, zJ, zL, z
,
0(0),
1(0),
2(0),
3(0), and
4(0). For definitions of L, Vhc, D, zJ, and zL see RESULTS.
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RESULTS |
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ß1's Effects on BKCa Gating Currents
What does the ß1 subunit do to the normal process of BKCa channel gating that creates these large and physiologically important effects? Previously, we addressed this question by comparing the effects of ß1 to what happens to simulated currents when various parameters in models of BKCa channel gating were altered (Cox and Aldrich, 2000). From this work we concluded that multiple aspects of gating are likely altered by ß1, including small changes in Ca2+ binding, gating charge, and the intrinsic energetics of channel opening. One large change we predicted, however, was a large ß1-induced leftward shift in the channel's chargevoltage (QV) relation. This, we supposed, would lower the free energy difference between open and closed states at most voltages, and thus lower as well the work Ca2+ binding must do to open the channel (Cox and Aldrich, 2000
).
Here, to directly test this prediction we have examined BKCa gating currents in the absence and presence of ß1. A family of gating currents for the BK channel is shown in Fig. 3 A. These currents were recorded in the essential absence of Ca2+ (0.5 nM) with 1-ms voltage steps. Most notable, they are small and fast, 5001,000 times smaller than the ionic currents we typically observe under the same conditions of channel expression (Fig. 1 A), and at +160 mV (Fig. 3 A, fourth trace down) the ON gating current decays with a time constant of 57.2 ± 4.0 µs (n = 16), and the OFF gating current at 80 mV is similarly fast (
(off) = 31.2 ± 3.3 µs, n = 20). Thus, care had to be taken to ensure that what we were observing was in fact gating current and not the result of capacity current subtraction errors. We are confident, however, that these currents are indeed gating currents, as they are not seen in uninjected oocytes (second trace down). They are not seen in response to voltage pulses of equal magnitude but opposite polarity (third trace down), and they have characteristics very similar to those reported previously for the BK
channel (Horrigan and Aldrich, 1999
, 2002
) (Table II).
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The gating currents we have recorded from both BK and BK
+ß1 channels have relaxation time constants close to the theoretical time resolution of our recording system
40 µs, and so we have not analyzed the kinetics of these currents further, as they may be distorted by our hardware. What is clear, however, is that both with and without ß1, BKCa gating currents are very fast.
An important consequence of the speed of the BK and BK
+ß1 channels' gating charge movement is illustrated in Fig. 3 (C and D). In response to a strong depolarization, both channels' voltage sensors move almost completely (Ig) before the channels begin to open (IK). The time constants of channel opening are 18 (BK
) and 177 (BK
+ß1) times larger than those of gating charge movement. Thus, for both channels, rapid ON gating currents reflect voltage sensor movement in the channel's closed conformation (Stefani et al., 1997
; Horrigan and Aldrich, 1999
).
To determine QV relations we integrated both ON and OFF gating currents and plotted these integrals separately as a function of test potential. These integrals report the amount of gating charge that moves rapidly during each voltage pulse. Examples of QV curves from individual BK and BK
+ß1 patches are shown in Fig. 4 (A and B), and as is evident, both with and without ß1, there is very little difference between the BKCa channels' rapid ON and OFF QV curves. Thus, charge is not immobilized by depolarization in either case.
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![]() | (7) |
![]() | (8) |
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![]() | (9) |
As is the case for other voltage-gated K+ channels, it is fairly clear that the S4 region, and probably part of S3, forms the BKCa channel's voltage sensor, whose gating charge is designated here zJ (Stefani et al., 1997; Diaz et al., 1998
; Horrigan and Aldrich, 1999
; Hu et al., 2003
). The physical basis for zL, however, has yet to be determined, but without assigning some voltage dependence to the closed-to-open conformational change, it is not possible to fit the BK
ionic current data at all well (Horrigan and Aldrich, 1999
, 2002
; Horrigan et al., 1999
; Cox and Aldrich, 2000
; Cui and Aldrich, 2000
; Rothberg and Magleby, 2000
). Thus, the equilibrium voltage dependence of BK
gating in the absence of Ca2+ is well described by five parameters, Vhc, Vho, zJ, L, and zL, and to this point our data allows us to specify two of them Vhc and zJ. To fully determine the effects of ß1 on the voltage-dependent aspects of BKCa channel gating at equilibrium, however, requires that we specify Vho, L, and zL for both channels as well. To do this we have performed the experiments described below.
Estimating ß1's Effects on the Closed-to-Open Conformational Change
At far negative voltages, where no voltage sensors are active, Eq. 9 reduces to Eq. 10 (Horrigan et al., 1999)
![]() | (10) |
![]() | (11) |
Eq. 11 states that as we make the membrane voltage more and more hyperpolarized, a plot of log(Popen) vs. voltage will begin to turn away from the voltage axis, and it will reach a limiting slope that is less than the maximum slope and reflects the voltage dependence of just the closed-to-open conformational change (Horrigan and Aldrich, 1999, 2002
; Horrigan et al., 1999
). That is, in this voltage range, the slope of the log(Popen)V relation will be determined only by zL, and the position of the curve on the vertical axis will be determined only by L. Thus, as has been discussed previously (Horrigan and Aldrich, 1999
, 2002
), by determining the BKCa channel's Popen vs. voltage relation at far negative potentials we can estimate zL and L directly.
To do this, we recorded BK and BK
+ß1 macroscopic currents at depolarized voltages (+10 to +80 mV) and 10 or 100 µM Ca2+. From these currents we could determine the number of channels in a given patch (N) (see MATERIALS AND METHODS). Then, we lowered the Ca2+ concentration to 3 nM and the membrane voltage to negative values where the channels are rarely open, and recorded unitary currents. Such currents are shown in Fig. 6 (A and B). Notice, the BK
channels appear to open more frequently than the BK
+ß1 channels, but the burst times of the BK
+ß1 channels appear on average longer (expanded traces). From data like that in A and B, the probabilities of observing 1, 2, 3 ... open channels at a given time were determined with all-points histograms, and these probabilities and N were then used to determine the true mean open probability of the channels in each patch (see MATERIALS AND METHODS). In this way, we could measure open probabilities as low as 106.
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-Relaxation vs. Voltage Relations Suggest No Change in zL
But for a brief delay, the onset and offset of BK ionic currents can be well fitted with a simple exponential function over a very wide voltage range. ß1 does not change this; however, at 0 Ca2+ it does slow both activation and deactivation. On a plot of log(
-relaxation) vs. voltage this is seen as an upward shift in the channel's log(
)V curve (Fig. 7 C). The general shapes of the BK
and the BK
+ß1 curves, however, remain similar. At far negative voltages there is a shallow region of positive slope. This transitions into a steeper region that persists until the plots reach a peak, and after the peak,
-relaxation falls often steadily at high voltages. According to the Horrigan, Cui, and Aldrich model (Fig. 5, bottom), the phases of these plots are understood as follows. At far negative voltages, no voltage sensors are active, and
-relaxation is determined by the rate constant of the O0 to C0 transition and its voltage dependence (z
). At far positive voltages a similar situation obtains, and
-relaxation is determined by the C4 to O4 rate constant and its voltage dependence (z
); where z
+ z
= zL. In the middle, no single transition determines the time constant of relaxation; but rather, as voltage sensors become active, a weighted average of all the vertical rate constants in Scheme I prevails. Thus, just as with the log(Popen)V relation, the model predicts that there will be a transition or inflection point in the channel's log(
)V relation at the voltage where voltage sensors start to become activated, and at voltages more negative than this the plot will reach a limiting slope that reflects now the portion of zL associated with the closing transition (z
) (Horrigan and Aldrich, 2002
).
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Estimating L and Vho With and Without ß1
To this point then we have specified Vhc, zJ, and zL for both channels, and left to specify are Vho for the BK channel, and Vho and L for the BK
+ß1 channel. One way we have attempted to estimate these parameters is to fit the two curves in Fig. 7 C with Eq. 12 below, which approximates Scheme I's
V relation in the limit that voltage sensor movement is much faster than channel opening and closing (Cox et al., 1997a
; Horrigan and Aldrich, 2002
; for details of the approximation see MATERIALS AND METHODS). As this condition applies for both channels over much of the voltage range, such an approximation is likely to be reasonably good. Indeed, Eq. 12 fits both curves quite well (Fig. 7 C, solid lines).
![]() | (12) |
Here i and
i are the forward and backward rate constants enumerated in Fig. 7 (bottom) and fOi and fCi represent the fraction of open channels or closed that occupy state Oi or Ci respectively. In fitting the BK
log(
)V curve we held Vhc, zJ, L, and zL to the values we estimated from gating current and limiting Popen measurements, leaving only Vho to vary along with z
and five rate constants, one for each vertical step in Scheme I. The resulting fit yielded z
= 0.11 and Vho = +39 mV. For the BK
+ß1 fit we adjusted Vhc to the value we obtained from our BK
+ß1 gating current measurements, +80 mV, zJ was again fixed, and L was now allowed to vary freely along with zL, Vho, z
, and again five rate constants. The resulting fit yielded Vho = 25 mV, z
= 0.15, and L = 3.3 x 106, zL = 0.46 (for standard deviations of fit parameters see figure legend). Thus, this analysis suggests, as we surmised above, that zL and z
change little, if any, with ß1 coexpression, but that Vho moves
64 mV leftward, while L perhaps increases slightly (2.2 x 106
3.3 x 106) but remains on the order of 106.
A more direct way to measure Vho for either channel would be to measure gating charge movement exclusively when the channel is open. This, however, requires large prolonged depolarizations that we have found technically unfeasible. Another way we can estimate Vho, however, and indeed also L for the BK+ß1 channel, is to simply fit each channel's PopenV relation with Eq. 9, while holding the parameters we have already determined constant. Since for the BK
channel we have specified four of five parameters, and for the BK
+ß1 channel three of five, we expect such fits to be very well constrained.
To do this we combined our limiting Popen data (Fig. 6) with macroscopic current data (Fig. 2 G) to obtain PopenV curves that are well determined over large ranges of both voltage and Popen. Fig. 8 shows these curves fitted with Eq. 9. For the BK fit in A, Vhc, zJ, L, and zL were set to the following values: zJ = 0.58 e, Vhc = 151 mV, zL = 0.41 e, L = 2.2 x 106, and D was allowed to vary freely. This yielded D = 16.8, which indicates a Vho value of +27 mV, similar to a previous report (Horrigan and Aldrich, 1999
) (Table II). Similarly, for the BK
+ß1 fit (Fig. 8 B, solid line), Vhc, zJ, and zL were set as follows: zJ = 0.57 e, Vhc = 80 mV, zL = 0.41 e, and the fit yielded a D value of 12.8 that equates to Vho = 34 mV, and L = 2.5 x 106. Thus ß1 is estimated here to shift Vho leftward 61 mV (see simulations in Fig. 8 C) but it has almost no effect on L.
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ß1 Affects Ca2+ Binding
The question still remains, however, as to whether these changes are enough to explain the changes in Ca2+ sensitivity described in Figs. 1 and 2. To address this issue we have incorporated our findings into a model of BKCa channel gating that takes into account both Ca2+ and voltage sensing.
Our recent work suggests that the BKCa channel has two sets of four high-affinity Ca2+ binding sites, which are structurally distinct but have similar binding properties (Bao et al., 2002, 2004
; Xia et al., 2002
). Assuming one site does not affect another, and the channel's voltage sensors and Ca2+ binding sites also act independently, this information can be combined with Scheme I to produce a model of BKCa channel gating that considers both Ca2+ binding and voltage sensing (Cox and Aldrich, 2000
; Cui and Aldrich, 2000
; Rothberg and Magleby, 2000
; Zhang et al., 2001
; Horrigan and Aldrich, 2002
). The open probability of such a model is given by Eq. 13:
![]() | (13) |
![]() | (14) |
To see, then, if the changes in Vhc and Vho that we have observed upon ß1 coexpression are sufficient to account for the BK channel's enhanced Ca2+ response, for each channel type, we fitted a series of GV relations with Eq. 14 (Fig. 9). For the BK
fit (Fig. 9 A), Vhc, Vho, zJ, L, and zL were held at the values we determined from our experiments in the absence of Ca2+ (Table II), and only KC and KO were allowed to vary. Still a reasonably good fit was obtained that captured well the shifting nature of the BK
channel's GV relation as a function of Ca2+ concentration. This fit yielded KC = 3.71 µM and KO = 0.88 µM, similar to our previous estimates (Bao et al., 2002
).
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To determine then what is required to fully account for the BK+ß1 GV relation as a function of Ca2+, we fit the BK
+ß1 G-V relations with Eq. 14, now fixing the voltage-sensing parameters to their BK
+ß1 values (Vhc = 80 mV and Vho = 34 mV, L = 2.5 x 106, zL = 0.41) and allowing KC and KO to vary. The resulting fit is shown in Fig. 9 D. To account for the additional leftward shifting KC increases from 3.71 to 4.72 µM, while KO declines slightly from 0.88 to 0.82 µM. This causes the ratio KC/KO to increase from 4.2 to 5.7.
Thus, our analysis suggests that ß1 has a very small effect (<10%) or perhaps no affect on Ca2+ binding when the channel is open, consistent with our earlier study (Cox and Aldrich, 2000), and it reduces the affinity of each binding site for Ca2+ when the channel is closed, increasing KC
27%. It is perhaps surprising that such small changes in affinity can have such a dramatic effect on the position of the channel's GV relation at high Ca2+ concentrations, but in fact this should be expected, as at saturating Ca2+ the equilibrium constant between open and closed depends on the eighth power of (KC/KO).
Perhaps only Half of the Channel's Binding Sites Are Affected by ß1
The estimates of ß1's effects on KC and KO just offered suppose that ß1 affects all binding sites equally. However, the BKCa channel is thought to have two types of high-affinity binding sites (Schreiber and Salkoff, 1997; Bao et al., 2002
; Xia et al., 2002
), and it could reasonably be that ß1 affects only one type of site. In this case, to account for the effects of ß1, the ratio KC/KO for the site that is affected would have to increase more. To determine how much more we fitted the BK
+ß1 GV data with Eq. 13, which supposes two types of Ca2+ binding sites, referred to as 1 and 2 (Fig. 9 E). For the fit we again used the BK
+ß1 voltage-sensing parameters, but now we set one set of Ca2+-binding constants to the values we determined for the BK
channel (KC1 = 3.71 µM and KO1 = 0.88 µM), and we let the second set vary. This yielded a fit similar to the one that was obtained when all sites were assumed to be affected equally (see Fig. 11 D), but now, with only half the sites affected, KC2 increased to 5.78 µM and KO2 decreased to 0.73 µM. Thus, KC increased an additional 22%, and now a larger change in KO was also produced (0.88 µM
0.73 µM, 17% decline). To determine, however, whether this change in KO2 was in fact needed, we reran the fit, now also holding KO2 to 0.88 µM. The result is shown in Fig. 9 F. A similar fit is obtained, now with KC2 increased to 7.14 µM.
Thus, whether we allow all eight or only four of the model channel's Ca2+-binding sites to be modified by ß1, we can account for the general effects of ß1 on the position of the BKCa channel's GV relation as a function of Ca2+ concentration without supposing any change in KO, and whether KO does in fact decrease as ß1 binds, we are as yet uncertain. What is clear, however, is that in order to account for the GV shift produced by ß1 at 100 µM Ca2+, the closed affinity of at least one type of high-affinity Ca2+-binding site must be lowered such that KC increases between 27% and 92%.
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DISCUSSION |
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The Horrigan, Cui, and Aldrich model may be summarized as follows. The BK channel opens and closes via a single conformational change that is weakly voltage dependent. This central conformational change is indirectly, or allosterically, affected by four voltage sensors, each of which can be either active or inactive. When a voltage sensor becomes active, it promotes opening by lowering the energy of the open conformation of the channel relative to the closed. For this to occur each voltage sensor's half-activation voltage must become more negative as the channel opens.
With this model as a guide, our task then became twofold, to determine if the Horrigan and Aldrich model still describes the gating of the BKCa channel when the ß1 subunit is part of the channel, and if so, to then determine how the five parameters, Vhc, Vho, zJ, L, and zL that govern the model' s behavior at equilibrium change upon ß1 coexpression. Calculations indicate that changes in any or all of these parameters could lead to changes in the apparent affinity of the channel for Ca2+ at many voltages (Cox and Aldrich, 2000). To determine, however, which were actually changing, following the lead of Horrigan and Aldrich (1999)
, we used both gating and ionic currents to constrain the parameters of the model so that each could be well determined. Our results may be summarized as follows.
With ß1 coexpression, the Horrigan, Cui, and Aldrich model (Fig. 5, Scheme I) is still applicable. ß1 does not slow voltage sensor movement, which remains fast relative to opening and closing. It has very little or no effect on the parameters that govern the central conformational change at equilibrium (L and zL), and it has no effect on the gating charge carried by each voltage sensor (zJ). It does, however, have an important effect on the energy required for voltage sensor activation, both when the channel is open and when it is closed. That is, ß1 affects Vhc and Vho, both of which are shifted tens of millivolts leftward on the voltage axis. Interestingly, however, ß1 shifts Vhc 10 mV further than it shifts Vho, and this reduces by 24% the factor D by which voltage sensor movement influences opening. As will be discussed below, this reduction in D has consequences for the shape and position of the BKCa channel's GV relation in the absence of Ca2+.
We have also found, however, that, although changes in Vhc and Vho can account for much of the effects of ß1 on Ca2+ sensing at low Ca2+ concentrations (1 µM and below), at higher Ca2+ concentrations, some effect of ß1 on Ca2+ binding must also be supposed. In particular, our data suggest that ß1 either has no effect or a very small effect on the affinity of the channel's Ca2+ binding sites when the channel is open (a decrease in KO from 0.9 µM to no less than 0.7 µM), but it increases the Ca2+ dissociation constant of the closed channel by
27% (3.7 to 4.7 µM), if all eight binding sites are affected, or by
5792% (3.7 to 5.8 µM or 7.1 µM), if only four sites are affected. These numbers correspond to a change in the factor C by which Ca2+ binding influences opening by 5793%. Thus, paradoxically, BK
+ß1 channels are more sensitive to Ca2+ throughout the physiological voltage range, because they bind Ca2+ worse when they are closed and because their voltage sensors activate at lower voltages.
ß1's Effects in Energetic Terms
To gain an intuitive understanding of these results as they relate to the BKCa channel's GV and Ca2+ doseresponse curves (Fig. 2, AG), we have found it useful to consider the influence of Ca2+ and voltage on channel gating in energetic terms. For this purpose, we may write for the eightCa2+ binding site fourvoltage sensor model the following equation, which relates the free energy difference between open and closed (GOC) to Ca2+ concentration [Ca2+] and membrane voltage.
![]() | (15) |
Eq. 15 has four terms. Term 1 represents the change in GOC that occurs as Ca2+ is varied (
GOC Ca2+), term 2 the change in
GOC that occurs as voltage sensors become active (
GOC VS), term 3 the influence of voltage on the central conformational change, and term 4 the intrinsic energy difference between open and closed when no Ca2+ ions are bound and no voltage sensors are active (Cui and Aldrich, 2000
).
In Fig. 10 A, the sum of terms 3 and 4 is plotted as a function of voltage, and, as is evident, the direct influence of the membrane's electric field on the central conformational change contributes linearly to GOC. Because ß1 does not change L appreciably, or zL, the same curve describes this influence for both channels, and only one curve has been drawn.
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![]() | (16) |
Also worth noting, at the bottoms of these curves, where nearly all four voltage sensors are active, the relationship between a change in membrane voltage and a change in GOC becomes quite shallow, while in the middle of these curves, it is much steeper.
Combining now terms 2, 3, and 4 yields the plot in Fig. 10 C, which describes the energetics of gating in the absence of Ca2+. Superimposed on the plot is a box that indicates the range of GOC over which the channel's open probability is between 5% (upper edge) and 95% (lower edge, for the complete relation; Fig. 10 D). Outside the box, changes in
GOC have little effect on Popen, while the progress of each curve through the box describes channel activation with voltage. At the dashed centerline
GOC = 0 and thus Popen = 0.5, so the voltage at which each curve intersects this line indicates each channel's V1/2.
ß1 and the GV at 0 Ca2+?
With these plots in mind, then, we may consider such questions as why is the BK+ß1 GV relation at 0 Ca2+ less steep than that of the BK
channel? And what determines the size of the ß1-induced GV shift? And why does it increase as Ca2+ is raised?
Beginning with the first question, we see in Fig. 10 C that in the absence of Ca2+, the BK+ß1 curve (blue) traverses the gating box at a shallower angle than does the BK
curve (red). This makes the BK
+ß1 channel's PopenV relation shallower than that of the BK
channel, and it creates a crossover between the two channels'
GOCV and PopenV curves (see inset). Thus, the models recapitulate the data. This type of plot, however, makes it readily apparent why. The BK
+ß1 channel's GV relation is shallower primarily because ß1 reduces D, and this brings the shallow part of the BK
+ß1 channel's
GOCV relation (Fig. 10 B), now combined with L(V) to yield its
GOCV relation (Fig. 10 C), into the gating box, while in the BK
channel the larger influence of voltage sensor movement on channel opening places less of this shallow region in the box. Or to put it another way, when ß1 is present, the effect of voltage sensor movement on
GOC is reduced, and this causes the channel's PopenV relation in the absence of Ca2+ to reflect in larger part the shallow voltage dependence of the central conformational change. Thus, in the absence of Ca2+, ß1 reduces the BKCa channel's PopenV slope (or equivalently its GV slope) because it shifts Vhc further leftward than it shifts Vho. Indeed as shown in Fig. 10 E, if this were not the case, if ß1 shifted both Vhc and Vho equally such that D was unchanged, no crossover would occur, and the two PopenV relations would have similar slopes with the BK
+ß1 curve now standing to the left of the BK
curve (see inset).
Differences between Mouse and Bovine ß1 at 0 Ca2+
The converse case it also of interest. Suppose ß1 shifted Vho less than we have found it does, say 47 mV rather than 61 mV, while still shifting Vhc 71 mV. In this instance (Fig. 10 F) D would be lowered further by ß1, and the crossover point would now occur outside the gating box, such that the progress of the hypothetical BK+ß1 channel's
GOCV curve through the box would be determined almost solely by L(V). That is, in such an instance voltage sensor movement would no longer lower
GOC enough to be observed as a change in Popen, and the channel's
GOCV relation and its PopenV relation would reflect predominately zL. This would cause a large rightward GV shift upon ß1 coexpression (Fig. 10 F, inset), which is interesting, because this is what we think occurs with mouse ß1.
Here we have studied the effects of the bovine ß1 subunit, which under most conditions are very similar to those of the mouse ß1. In the absence of Ca2+, however, the GV curve of the BK+ß1mouse channel is much further right shifted than that of the BK
+ß1bovine channel, and it has a much shallower slope (unpublished data). We suggest therefore that perhaps mouse ß1 reduces D more than does bovine ß1, and this gives rise to their different effects at 0 Ca2+. Indeed, the BKCa ß4 subunit also produces a large rightward GV shift in 0 Ca2+, perhaps for the same reason (Ha et al., 2004
).
More generally, however, our data suggest that in the absence of Ca2+, the energy imparted to BKCa channel opening by its voltage sensors (when combined with the effect of voltage on the central conformational change) is just enough to influence opening, but small changes in either the amount of energy required to open the channel (changes in L, or the addition of Ca2+), or how much energy each voltage sensor's movement contributes to channel opening (changes in D), are expected to have a profound effect on the shape and position of the BKCa channel's PopenV relation.
ß1's Effect on the BKCa GV curve as a Function of Ca2+
Looking again at Fig. 10 C, what is also evident is that if the two GOCV curves were shifted downward, steeper parts of each curve would traverse the gating box, and the BK
+ß1 curve would lie significantly to the left of the BK
curve. Indeed, this is what occurs with Ca2+ binding. Term 1 of Eq. 15 is plotted in Fig. 11 A as a function of Ca2+. Here we see that as the Ca2+ concentration increases, Ca2+ binding lowers
GOC for the BK
channel
6.7 kcal/mol, similar to what voltage sensor movement does (Fig. 10 B), while, owing to its larger KC value, it lowers
GOC for the BK
+ß1
8.2 kcal/mol, 22% more. On a plot of
GOC vs. voltage, Ca2+ binding is seen as a downward shift along the energy axis, with a larger shift for higher Ca2+. 1 µM Ca2+, for example, shifts both channel's
GOCV curves downward 2.4 to 2.8 kcal/mol, such that they each now pass through the gating box at a steeper angle (Fig. 11 C). Thus, for both channels, the increase in GV steepness observed between 0 and 1 µM Ca2+ (Fig. 2, C and D) is seen here to be due to Ca2+ lowering the energy that the voltage sensors must supply to open the channel that brings a steeper region of the
GOCV relation (Fig. 10 B) into the gating box. The BK
+ß1
GOCV curve, however, now lies to the left of the BK
curve, because the BK
+ß1 channel's voltage sensors are activated at lower voltages.
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ß1's Effects on BKCa Ca2+ DoseResponse Curves
By picking a single voltage on these plots, we can also see why at negative voltages Ca2+ more effectively opens the channel when ß1 is present (as shown in Fig. 2, AC). Examining 40 mV for example, the membrane potential of typical smooth muscle myocyte, 100 µM Ca2+ shifts the BK
GOCV curve downward such that
GOC (40 mV) = 0.96 kcal/mol, which corresponds to a Popen of 0.164 (Fig. 11 E, gray line). With ß1 present, the downward shift with 100 µM Ca2+ makes
GOC (40 mV) = 1.34 kcal/mol, which corresponds to a Popen of 0.907. Thus, Ca2+ more effectively opens the channel at low voltages because it shifts the BK
+ß1 channel's
GOCV curve deeper into the gating box when ß1 is present. Part of this is due to ß1's effects on voltage sensing, in this case 41%, as if ß1 only affecting voltage sensing, Popen at 40 mV and 100 µM Ca2+ would be 0.467, and part is due to its effects on Ca2+ binding, here 59%. At higher voltages, however, +100 mV for example, 100 µM Ca2+ is able to lower both
GOCV curves enough to fully activate both channels, and thus no difference in maximum Popen is expected. But because at all voltages on average fewer bound Ca2+ are required to maximally activate the channel when ß1 is present, at this voltage, as well as almost all others (between
200 and +200 mV), the ß1 subunit is expected to increase the apparent affinity of the channel for Ca2+.
Our Results Relative to Previous Work
Studies by Nimigean and Magleby (1999)(2000
) at the single channel level have indicated that the ß1 subunit shifts the BKCa channel's Ca2+ doseresponse curve leftward at +30 mV from an apparent affinity of 9.2 to 2.6 µM (Nimigean and Magleby, 1999 [Fig. 2 A], 2000 [Fig. 2 B]). The models of the BK
and BK
+ß1 channels we have produced predict almost an identical shift (9.3 to 2.3 µM). Furthermore, Nimigean and Magleby estimated that 80% of the shift was due to ß1's effects on aspects of gating separate from Ca2+ binding, while 20% were due to a Ca2+-dependent effect. Our models suggest a similar ratio (87% voltage sensing, 13% Ca2+ binding). Also they found that at +30 mV, in the absence of Ca2+, ß1 increases Popen approximately sevenfold (Nimigean and Magleby, 2000
). Our models predict a 12-fold increase. Thus, on the whole, our results are remarkably consistent with those of Nimigean and Magleby. Furthermore, they found that ß1 increases Popen by increasing the occupancy of bursting states, which, when interpreted in terms of our results, suggests that voltage sensor activation gives rise to longer bursts of openings.
In a previous study (Cox and Aldrich, 2000) we concluded, based on macroscopic ionic current recordings, that ß1 shifted Vhc and Vho leftward, qualitatively, as we have observed, but as well probably increased L from 3.4 x 106 to 17.9 x 106 and decreased zJ from 0.51 to 0.4. Having now directly measured the movement of the channel's gating charge, however, we no longer think that zJ changes upon ß1 coexpression, and if there are changes in L they are smaller than we first supposed. We also concluded in this study that ß1 reduces the affinity of the channel for Ca2+ when it is closed, but has little or no effect on the affinity of the channel when it is open. As we have discussed, we still think this is correct.
Recently, Orio and Latorre (2005) concluded that the effects of ß1 on Ca2+ sensing can be explained entirely by a reduction in zJ from
0.5e to
0.3e, with no effect on Ca2+ binding and no change in Vhc. Clearly, this idea is not consistent with our results, as with gating currents, we have directly determined the value of zJ to be 0.57e to 0.58e and unchanged by ß1 coexpression, and we have found Vhc to be shifted 71 mV leftward by ß1. Why their conclusions differ from ours is not clear, and it could be due in part to species differences between ß1 subunits, as we have used bovine and they used human ß1. Perhaps more important, however, in the absence of gating currents they relied in their analysis on the notion that the peak of the BKCa channel's
relaxationV relation could not remain at or near the same voltage, if Vhc were changing appreciably. But, as can be seen by our fits in Fig. 7 C, this statement is not correct. While it is true that changes in Vhc will tend to alter the position of the peak of this curve, it is also true that changes in Vho can, and apparently do, counteract this effect. Also, as evidence that zJ is changing with ß1 coexpression, Orio and Latorre (2005)
sited a change in the maximum slope of the channel's ln(Popen) vs. voltage relation upon ß1 coexpression; however, as can be seen in Fig. 8 B (compare solid line to dashed line), we do not observe a clear change in the maximum slope of this relation upon ß1 coexpression. Where our two studies agree, however, is in the finding, based in both studies on limiting-Popen measurements, that the voltage dependence of the central conformational changed (zL) is unaltered by ß1.
A Structural Hypothesis
While our data do not bear directly on the issue of what physical interactions between and ß1 are required for ß1 to stabilize the activated voltage sensor, considerable evidence indicates that the extracellular loop common to all BKCa ßs can extend over the
subunit as far as the channel's pore. The extracellular loop of ß3 enters and blocks the pore in a voltage-dependent manner (Zeng et al., 2003
), and the extracellular loop of ß4 prevents charybdotoxin, a pore-blocking peptide, from interacting with the channel (Meera et al., 2000
). Thus, it seems reasonable to suppose that the extracellular loop of ß1 may interact with the external face of the
subunit as well. Indeed, perhaps it interacts with the voltage sensor at or near the top of S4. If this interaction were specific for the activated voltage sensor, than it would stabilize this position of the voltage sensor and create leftward QV shifts as we have observed. How much energy would it take to create such an effect? As it turns out, not very much. The 71-mV leftward Vhc shift we have observed with ß1 coexpression corresponds to a stabilization of the active voltage sensor by only 0.9 kcal/mol, the energy of a very weak hydrogen bond or a hydrophobic interaction. Thus from an energetic point of view this idea is plausible.
Of course this hypothesis doesn't explain the effects of ß1 on Ca2+ binding, and at this point we have none but the most general hypothesis to offer. As the physical nature of the BK channel's Ca2+ binding sites becomes more clear, however, perhaps how ß1 influences one or more of the channel's Ca2+-binding sites will become more clear as well.
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ACKNOWLEDGMENTS |
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Olaf S. Andersen served as editor.
Submitted: 15 June 2005
Accepted: 26 August 2005
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REFERENCES |
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