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Address correspondence to Dr. Frank T. Horrigan, Department of Physiology, University of Pennsylvania School of Medicine, A401 Richards, 3700 Hamilton Walk, Philadelphia, PA 19104. Fax: (215) 573-5851; E-mail: horrigan{at}mail.med.upenn.edu
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Key Words: calcium • potassium channel • BK channel • gating current • ion channel gating
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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).
Large conductance BK channels possess many advantages as a system for studying interactions between sensors and gates. First, voltage- and ligand-dependent gating mechanisms can be studied in the same channel. Second, the mechanisms of voltage sensor activation, Ca2+-binding, and channel opening appear simple and reasonably represented as two-state processes. The homotetrameric nature of the channel and the absence of inactivation also help to limit the potential complexity of interactions between sensors and gates. Third, closed to open state transition kinetics in Slo1 channels are slow relative to voltage sensor activation and Ca2+-binding (Cox et al., 1997a; Horrigan and Aldrich, 1999; Horrigan et al., 1999). This simplifies the analysis of macroscopic IK kinetics and allows sensor function to be examined while channels are maintained in either an open or closed conformation. Fourth, voltage sensors and Ca2+ sensors appear to interact with channel opening through allosteric mechanisms such that no combination of sensor and gate conformation is prohibited. Finally, the sensitivity of BK channels to both Ca2+ and voltage allows the manipulation of channel function in ways that facilitate analysis of sensor–gate interaction.
In the present study, we address several features of BK channel gating that are readily explained by allosteric models. Our ability to test this mechanism and to characterize sensor–gate interaction in BK channels depends on isolating subsets of transitions under extreme conditions and measuring both ionic and gating currents. For example, we show that the effect of Ca2+-binding on channel opening is best characterized when the C-O equilibrium constant is reduced by forcing voltage sensors into a resting state at extreme negative voltages. Conversely, some effects of channel opening on voltage sensor activation are best detected when the open conformation is stabilized by high [Ca2+]. The observed properties of Ca2+- and voltage-dependent transitions and their relationship to each other define how Ca2+ and voltage interact to determine mSlo1 channel activity.
The BK Channel Gating Mechanism
Because the response of BK channels to Ca2+ and voltage is complex, it is useful to present our results in the framework of a plausible general model. BK channel gating involves voltage sensor activation, Ca2+ binding, channel opening, and some interaction among these three processes. Previous analysis of ionic and gating currents from mSlo1 in 0 Ca2+ ([Ca2+] < 1 nM) showed that voltage sensor activation promotes channel opening through an allosteric mechanism, illustrated in Fig. 1
A, Scheme I (Horrigan and Aldrich, 1999; Horrigan et al., 1999). In Scheme I, voltage sensors in each of the four identical subunits can undergo transitions between resting (R) and activated (A) conformations. In addition, the channel can undergo a transition between closed (C) and open (O) conformations. Voltage sensor activation and channel opening interact through an allosteric mechanism, represented by a factor D, such that the C-O equilibrium constant increases D-fold for each voltage sensor activated, and the R-A equilibrium constant increases D-fold when the channel opens.
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; Rios et al., 1993; McCormack et al., 1994), and the basic finding that channels undergo both independent and concerted (or cooperative) transitions is well established (Sigworth, 1994; Zagotta et al., 1994). The kinetic and equilibrium properties of mSlo1 channels allow us to study these transitions in isolation (Horrigan and Aldrich, 1999; Horrigan et al., 1999), an advantage that will be exploited here to determine the mechanism of Ca2+ action.
Several lines of evidence indicate that Ca2+-binding also influences channel opening through an allosteric mechanism. The voltage-dependent activation of unliganded channels shows that Ca2+-binding is not obligatory for channel opening or for voltage sensor activation (Cui et al., 1997; Nimigean and Magleby, 2000; Talukder and Aldrich, 2000). Similarly, macroscopic IK relaxation kinetics are altered by Ca2+ in a saturable manner, indicating that Ca2+ binding is not a rate-limiting step in channel activation. The kinetic and steady-state properties of mSlo1 activation in the presence and absence of Ca2+ exhibit similar voltage dependencies (Cox et al., 1997a; Cui et al., 1997; Rothberg and Magleby, 2000), suggesting that a similar gating scheme with altered rate constants might account for the activation of unliganded and Ca2+-bound channels. In line with this prediction, single channel data from native BK channels in high Ca2+ are consistent with a two-tiered gating scheme for Ca2+-bound channels similar to Scheme I* (Rothberg and Magleby, 1999). Moreover, an allosteric model of Ca2+ action reproduces many features of macroscopic mSlo1 IK over a wide range of Ca2+ despite the use of a simplified voltage-gating mechanism (Cox et al., 1997a; Cui et al., 1997).
A General Allosteric Model of BK Channel Gating
Any BK channel gating scheme that incorporates four identical subunits and accounts for the effects of both Ca2+ and voltage must necessarily contain a large number of states (Cox et al., 1997a). In addition to the four voltage sensors, each channel presumably contains at least four high affinity Ca2+ binding sites, since dose-response relationships describing the effect of micro molar Ca2+ on steady-state open probability require Hill coefficients greater than three (Cox et al., 1997a; Rothberg and Magleby, 2000). To describe a channel that can be open or closed with any number (0–4) of Ca2+-bound and voltage sensors activated requires a minimum of 50 states, divided into two interconnected tiers of open and closed states (Horrigan et al., 1999; Rothberg and Magleby, 1999; Cox and Aldrich, 2000; Cui and Aldrich, 2000; Rothberg and Magleby, 2000).
Despite the apparent complexity of a large gating scheme, the mechanism underlying such a model and the parameters required to describe it may be relatively simple as illustrated by Fig. 1 C, Scheme II. The homotetrameric nature of the mSlo1 channel implies that high affinity binding sites are identical. Thus, in Scheme II, Ca2+ binds to these subunits with identical equilibrium constants K. The independence of the binding sites is an initial simplifying assumption. As in Scheme I, the gating of unliganded channels is specified by an allosteric interaction between voltage sensor activation (R-A) and channel opening (C-O). Similarly, Ca2+ is coupled to channel gating through allosteric interactions represented by the factors C and E that connect the Ca2+-binding transitions to the C-O and R-A voltage sensor transitions respectively. The steady-state properties of this model are fully described by three allosteric factors (C, D, E) and three equilibrium constants (J, K, L):
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Scheme II highlights an important strategy used in our analysis: to define the simplest mechanism—rather than the gating scheme with the fewest kinetic states—that can account for the data. The simplest or most physically plausible mechanism often does not produce the fewest states. The number of states specified by Scheme II is determined by the nature of interactions between C-O, R-A, and X-XCa2+ transitions. Interactions of channel opening with voltage sensors and Ca2+ binding sites are the most easily defined. If the C-O transition is concerted, channel opening should affect individual subunits equally. Therefore, by energy conservation, each bound Ca2+ or activated voltage sensor must have an additive effect on the energy of the C-O transition, increasing the C-O equilibrium constant C- or D-fold, respectively. By contrast, interactions between the X-XCa2+ and R-A transitions in Scheme II do not involve a concerted transition and several mechanisms can be postulated, each resulting in a different number of functionally distinct states.
In cases where no interaction between Ca2+ binding sites and voltage sensors exist, Scheme II will define a gating scheme with the minimum 50 states and PO can be described by Eq. 1 with E = 1 (Cox and Aldrich, 2000; Shi and Cui, 2001; Zhang et al., 2001). A 50-state scheme is also generated if Ca2+ binding to one subunit affects voltage sensors in all subunits equally and the activation of a voltage sensor affects all Ca2+-binding sites equally (Fig. 2
A1). However, this would require a complex mechanism for coordinated communication among subunits independent of their relative positions in the tetramer. The equation describing such a mechanism is more complex than Eq. 1 (Cui and Aldrich, 2000). We will instead make the simplifying assumption that Ca2+ binding sites and voltage sensors can only interact within the same subunit (Fig. 2 A2). This assumption, although mechanistically and mathematically simpler, increases the number of states to 70 because interactions between voltage sensors and Ca2+ binding sites now depend on their relative location within the tetramer, and some combinations of i-activated voltage sensors and j-occupied binding sites are no longer energetically equivalent. For example, a channel with two activated voltage sensors and two Ca2+ bound can exist in three distinct states depending on whether Ca2+ and activated voltage sensors are in the same or different subunits (Fig. 2 B). More general gating schemes that distinguish the relative Ca2+ occupancy and/or voltage sensor conformation in adjacent and diagonally opposed subunits result in even more than 70 states (Cox et al., 1997a) but, like the 50-state model, require additional mechanisms to account for interactions between or among voltage sensors and Ca2+ binding sites in different subunits.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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) expressed in Xenopus oocytes or HEK 293 cells. The clone was modified to facilitate mutagenesis and was propagated and cRNA transcribed as described previously (Cox et al., 1997b). Xenopus oocytes were injected 3–7 d before recording with 
0.5–5 ng or 50 ng of cRNA for ionic current or gating current experiments respectively (50 nl, 0.01–1 ng/nl). mSlo1 was also subcloned into a mammalian expression vector (SR
, provided by Dr. A.P. Braun, University of Calgary, Calgary, Canada) containing the SV-40 promoter. HEK 293 cells expressing the large T-antigen of the SV-40 virus were cotransfected with mSlo1 and green fluorescent protein (GFP, as a marker) using LipofectAMINE (GIBCO BRL/Life Technologies, Inc.) 3 d before recording.
Electrophysiology
Currents were recorded using the patch clamp technique in the inside out configuration (Hamill et al., 1981). Upon excision, patches were transferred to a separate chamber and washed with at least 20x volumes of internal solution. K+ currents were recorded with internal solutions containing (in mM) 110 KMeSO3, 20 HEPES, and an external (pipette) solution containing 104 KMeSO3, 6 KCl, 2 MgCl2, 20 HEPES. Gating currents were recorded with internal solutions containing 135 N-methyl-d-glucamine(NMDG)-MeSO3, 20 HEPES, and an external solution containing 125 tetraethylammonium(TEA)-MeSO3, 6 TEA-Cl, 2 MgCl2, 20 HEPES. Internal solutions contained 40 µM (+)-18-crown-6-tetracarboxylic acid (18C6TA) to chelate contaminant Ba2+ (Diaz et al., 1996; Neyton, 1996; Cox et al., 1997b). "0 Ca2+" solutions contained 2 mM EGTA reducing free Ca2+ to an estimated 0.8 nM based on the presence of 10 µM contaminant Ca2+ (Cox et al., 1997b). Ca2+ solutions were buffered with 2 or 5 mM HEDTA and CaCl2, and free Ca2+ was measured with a Ca2+-electrode (Orion Research, Inc.). Total Cl- was adjusted to 10 mM with HCl. The pH of all solutions was adjusted to 7.2. Solutions were prepared and experiments performed at 20°C (approximately ±1°C).
Electrodes were pulled from thick walled 1010 glass (World Precision Instruments), coated with wax (KERR sticky wax) to minimize electrode capacitance (1 pF), and fire-polished before use. Pipette access resistance measured in the bath solution (0.5–1.5 M
) was used as an estimate of series resistance (Rs) to correct the pipette voltage (Vp) at which IK was recorded. The corrected pipette voltage, Vm, was used in determining membrane conductance (GK) from tail current measurements and in plotting the voltage dependence of GK or the time constant of IK relaxation (
[IK]). Series resistance error was <15 mV for all data presented and <10 mV for (IK) measurements.
Data were acquired with an Axopatch 200B amplifier (Axon Instruments, Inc.) set in patch mode with the Axopatch's internal 4-pole Bessel filter set at 100 kHz. Currents were subsequently filtered by an 8-pole Bessel filter (Frequency Devices, Inc.) at 20 kHz (Ig) or 50 kHz (IK) and sampled at 100 kHz with a 16 bit A/D converter (Instrutech ITC-16). Macroscopic currents were recorded at a relatively low gain (1–2 mV/pA) to avoid saturation of capacitive transients in response to voltage steps that often exceeded 300 mV. In addition, for gating currents, the voltage command was filtered at 20 kHz to limit the speed of fast capacitive transients so that they could be sampled accurately and subtracted. Gating current records were typically signal averaged in response to at least eight voltage pulses. A P/4 protocol was used for leak subtraction (Armstrong and Bezanilla, 1974) except at voltages less than the holding potential where a P/8 protocol was used to avoid channel activation during the leak pulses. The holding potential was adjusted from -80 mV in 0 Ca2+ to -120 mV in 1,000 µM Ca2+.
A Macintosh-based computer system was used in combination with Pulse Control acquisition software (Herrington and Bookman, 1995) and Igor Pro for graphing and data analysis (WaveMetrics, Inc.). A Levenberg-Marquardt algorithm was used to perform nonlinear least-squared fits. Error estimates for fit parameters are given as ± SD.
Single Channel Analysis
Under conditions where the open probability (PO) is small (<10-3), single channel opening events were observed in patches containing hundreds of channels and NPO was determined from steady-state recordings of 5–45 s duration. Currents were filtered at 20 kHz, yielding a dead-time of 10 µs, and were sampled at 100 kHz. NPO was then determined from all-points amplitude histograms by measuring the fraction of time spent (Pk) at each open level (k) using a half-amplitude criteria and summing their contributions 
. NPO was also determined by fitting Pk with a Poisson distribution 
. The values of NPO obtained by these two methods differ by <5%, consistent with the assumption that the observed currents represent the activity of a large uniform population of channels opening with very low probability (Horrigan et al., 1999).
Normalized open probability (PO/POMAX = NPO/NPOMAX) was determined by combining NPO measurements with an estimate of NPOMAX obtained from the macroscopic GK-V relationship in the same patch (NPOMAX = GKMAX/gK, where gK is the single channel conductance). Patches that were used to measure single channel activity at negative voltages often produced currents that were too large to measure (>20 nA) at voltages that activate mSlo1 channels maximally. In these cases, Gmax was estimated by fitting the macroscopic GK-V with a Boltzmann function {1 + exp[-z(V - Vh)/kT]} raised to a power n (e.g., Fig. 4 C1), where z and n were determined at each [Ca2+] from other patches where the entire GK-V relationship was measured.
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30%) were observed at the most negative voltages in 0 Ca2+ and little change was observed for [Ca2+] > 1 µM. Thus, PO in low Ca2+ may be underestimated. To minimize this effect, dose-response relationships used to quantify the effect of Ca2+ on channel activation (Fig. 9) were determined from NPO at V < -80 mV using 20 kHz filtering.
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; Horrigan et al., 1999) and hSlo1 (Stefani et al., 1997), possibly due to differences in the redox state of channels (DiChiara and Reinhart, 1997; Tang et al., 2001). Such shifts do not appreciably alter the shape of voltage-dependent relationships but make comparison of data between different experiments difficult and cause broadening in averaged voltage-dependent relationships. To compensate for this effect, Vh was determined for each patch and compared with the mean for all experiments (<Vh>) at the same [Ca2+]. Data from individual experiments were then shifted along the voltage-axis by 
Vh = (<Vh> - Vh) before averaging. This procedure yields average relationships that accurately represent the shape of individual GK-V and Q-V relationships.
Admittance Analysis
Admittance analysis was performed as described previously (Horrigan and Aldrich, 1999). Briefly, in gating current solutions, the membrane was clamped with a sinusoidal voltage command (868 Hz, 60 mV peak to peak) superimposed on a 1 s voltage-ramp. The voltage command and current signal were both filtered at 20 kHz and current was sampled at 18-µs intervals (64 samples/period). Admittance was determined for each cycle of the sinusoid. Gating capacitance (Cg[V]) was determined as the voltage-dependent component of patch admittance appearing at a phase angle of 90° relative to the command voltage (after correction for instrumentation phase delays).
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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). However, concentrations of Ca2+ or other divalent cations in the 100 µM to 100 mM range produce distinct effects on channel gating that have been attributed to nonselective, low-affinity (millimolar) binding sites (Shi and Cui, 2001; Zhang et al., 2001). As a compromise, 70–100 µM Ca2+ was used throughout this study to approximate the Ca2+-saturated condition for high affinity binding sites while minimizing possible contributions from low affinity sites.
Fig. 4 A compares IK evoked at different voltages in 0 or 70 µM Ca2+. Ca2+ increases the steady-state open probability (PO) such that conductance-voltage (GK-V) relationships shift to more negative voltages (Fig. 4 C1). The records in Fig. 4 A indicate that Ca2+ speeds IK activation during the pulse and slows deactivation at -80 mV after the pulse. This effect is illustrated in Fig. 4 B, where currents evoked by pulses to 160 mV in 0 and 100 µM Ca2+ from the same patch have been superimposed and normalized. Activation and deactivation kinetics are well fit by exponential functions following a brief delay (dashed lines) (Horrigan et al., 1999). The time constants ([IK]) of such fits over a wide range of voltages in 0 and 70 µM Ca2+ are plotted in Fig. 4 D1.
Figs. 4, C1 and D1, show that Ca2+ shifts the GK-V and (IK)-V relationships along the voltage axis with little change in shape, suggesting that unliganded and ligand-bound channels gate by similar mechanisms. Indeed, Scheme II reduces, in saturating Ca2+ (Fig. 3, sub-Scheme IIb), to a 10-state gating scheme (Fig. 4 E, sub-Scheme IIb*) analogous to the unliganded scheme (Fig. 1, Scheme I*)(Horrigan and Aldrich, 1999; Horrigan et al., 1999). Despite this general similarity, significant changes in the shape of GK-V and (IK)-V relationships are observed when the plots obtained in 70 µM Ca2+ are shifted by 135 mV to align them with the 0 Ca2+ data (Fig. 4, C2 and D2). Such differences are expected if mSlo1 gating is governed by multiple voltage-dependent processes (e.g., C-O and R-A transitions).
In general, Ca2+ will shift the GK-V and (IK)-V relationships without changing their shape only if the rate constants in the unliganded scheme (Fig. 1, Scheme I*) at any voltage V are identical to those for the Ca2+-saturated scheme (Fig. 4 E, sub-Scheme IIb*) at V-V. Since the horizontal (R-A) transitions are more voltage dependent than the vertical (C-O) transitions, this condition can only be satisfied if voltage sensor activation is more Ca2+ dependent than channel opening. In fact we will show that the opposite is true. Therefore, the relationship between the horizontal and vertical transitions in Schemes I* and IIb* is altered by Ca2+ in a manner that cannot be compensated for by voltage, producing a change in the shape of the GK-V and (IK)-V relations.
Effects of Ca2+ on Gating Current
The data in Fig. 4 are insufficient to determine if Ca2+ effects channel opening (C-O) or voltage sensor activation (R-A) because IK kinetics and steady-state activation are generally dependent on both processes (Horrigan et al., 1999). To help address this question mSlo1 gating currents (Ig) were compared in 0 Ca2+ and 70 µM Ca2+. As the following analysis indicates (Figs. 5– 7)
, the Ca2+ sensitivity of Ig can be attributed mainly to an effect on channel opening and the interaction between Ca2+ binding and voltage sensor activation is weak.
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), whereas the 70 µM Ca2+ trace has an obvious slow component (see also Fig. 5 D). In addition, OFF gating currents (IgOFF) recorded at -80 mV after the pulse are slowed substantially in the presence of Ca2+.
Since Ca2+ affects gating current and shifts the voltage dependence of GK and (IK), it might appear reasonable to conclude that Ca2+ acts by promoting voltage sensor activation (Diaz et al., 1998). However, a closer examination of gating charge movement reveals that this is not the case. Although gating currents provide a direct assay of voltage sensor activation, they are also influenced by channel opening. Indeed, we have shown previously that mSlo1 Ig exhibits multiple kinetic components reflecting C-C, O-O, and C-O transitions in Scheme I* (Horrigan and Aldrich, 1999). These components must be isolated before conclusions can be drawn about the mechanism of Ca2+ action.
The Ca2+ Dependence of Slow Gating Charge Movement
IgON evoked during a pulse to 160 mV in 0 Ca2+ (Fig. 5 A) consists of a prominent fast component, representing voltage sensor activation while channels are closed, and an additional component that is 100-fold slower. The relaxation of the slow component, like IK activation, is limited by the speed of channel opening (Horrigan and Aldrich, 1999) and therefore should exhibit a Ca2+ and voltage dependence similar to that of (IK) (Fig. 4 B). To examine the slow component in detail, Ig was measured in response to pulses of different duration to 160 mV in 0 Ca2+ and 70 µM Ca2+ (Fig. 5 B). The total charge moved during each pulse (QP) was determined by integrating IgOFF and is plotted versus pulse duration in Fig. 5 C. These QP time courses, which indicate the kinetics of ON charge movement, are fit with double exponential functions (solid lines). Prominent slow components are observed in both 0 and 70 µM Ca2+ representing 43% and 47% of the steady-state charge movement, respectively. Time-derivatives of the fits to Qp superimpose with IgON (Fig. 5 D) demonstrating that Ig kinetics reflect large slow components of ON charge movement.
Slow charge movement is evident as a distinct component of IgON in 70 µM Ca2+ (dashed line – Fig. 5 D) but not in 0 Ca2+ because its time constant (gSLOW) is decreased from 4.2 ms in 0 Ca2+ to 0.85 ms in 70 µM Ca2+ (Fig. 5 C). This fivefold change in kinetics produces a fivefold increase in slow gating current amplitude in 70 µM Ca2+. The marked Ca2+-sensitivity of gSLOW is consistent with the ability of Ca2+ to speed IK activation (Fig. 4 A).
The Voltage Dependence of Slow Gating Charge Movement in 70 µM Ca2+
The properties of slow charge movement in 70 µM Ca2+ are examined in more detail in Fig. 6. Families of Ig evoked after pulses of different duration to various voltages are shown in Fig. 6 A. Time courses of ON charge movement (Qp) determined from these data are plotted in Fig. 6 B and fit with double exponential functions. The time constant of the slow component is plotted against voltage in Fig. 6 C together with gSLOW at negative voltages, determined from the slow component of OFF charge movement (Horrigan and Aldrich, 1999) (see also Fig. 13 C). Also shown are the mean time constants of IK relaxation ([IK]) in 70 µM Ca2+. At both positive and negative voltages the voltage dependencies of gSLOW and (IK) are identical (Fig. 6 C, compare solid and dashed lines), supporting the idea that slow charge movement is limited by channel opening. However, gSLOW is approximately fourfold slower than (IK) at positive voltages and twofold slower at negative voltages. Differences between (IK) and gSLOW were also reported previously in 0 Ca2+ and may reflect the different ionic conditions used to measure IK and Ig (Horrigan and Aldrich, 1999).
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). The steady-state QSS-V relationship determined with a 20 ms pulse (Qp(20), Fig. 6 D) is steeper and shifted to more negative voltages than Qfast-V. This difference reflects the voltage dependence of slow charge movement and contrasts with results in 0 Ca2+ where QSS-V and Qfast-V curves are similar in shape (Horrigan and Aldrich, 1999).
The steady-state Q-V and G-V relationships in 0 and 70 µM Ca2+ are compared in Fig. 6 E and indicate that Ca2+-binding changes the relationship between charge movement and open probability. In 0 Ca2+ the Q-V is shallower and activates at more negative voltages than the G-V, exhibiting an approximate fourth-power relationship between the two, as in many voltage-dependent channels (Horrigan and Aldrich, 1999). In 70 µM Ca2+, however, the Q-V and G-V almost superimpose. Calcium has changed the coupling between charge movement and channel opening so that less charge moves, on average, at voltages where most channels are closed. That is, Ca2+ allows channels to open when fewer voltage sensors have been activated.
The Effects of Ca2+ on Voltage Sensor Activation
To determine whether Ca2+ affects voltage sensor activation directly, we compared the fast components of gating charge movement in the presence and absence of Ca2+ (Fig. 7). This analysis shows that the interaction between Ca2+ binding and voltage sensor activation is weak.
Because voltage sensor movement in BK channels is rapid compared with channel opening and closing, the fast component of ON or OFF gating current (Igfast) assays voltage sensor movement while channels remain in either a closed or open conformation (Horrigan and Aldrich, 1999) corresponding to sub-Schemes IIe and IIf, respectively (Fig. 3). For example, IK activates with a delay of 100 µs after a voltage step (0 Ca2+, 20°C) (Horrigan et al., 1999). During this period, Ig reflects voltage sensor activation while channels are closed. If voltage sensor activation is a two state process as in Scheme II, then the initial decay of Ig should be exponential, reflecting the R to A transition (Horrigan and Aldrich, 1999). Therefore, Igfast at positive voltages was isolated by fitting the first 100 µs of IgON with an exponential function (Fig. 7, A and B, dashed lines). Because channels are closed, the Ca2+ dependence of Igfast must reflect a direct interaction between Ca2+ binding and voltage sensor movement that is independent of the ability of Ca2+ to alter channel opening.
Ca2+Increases the Equilibrium Constant for Voltage Sensor Activation
The amount of fast charge movement (Qfast) was estimated by integrating the area under the exponential fit to Igfast, corresponding to the shaded regions in Fig. 7, A and B. Normalized Qfast (mean ± SEM) is plotted against voltage on linear and log scales in Fig. 7, C and D, respectively for 0 Ca2+ and 70 µM Ca2+. The mean half-activation voltage (<Vh(Qfast)>) determined by fitting Boltzmann functions to individual Q-V records was shifted by -20 mV from 155 ± 7 mV in 0 Ca2+ (n = 10) to 135 ± 8 mV in 70 µM Ca2+ (n = 8), whereas the shape of the curves represented by the voltage sensor charge zJ was not appreciably altered (0 Ca2+: zJ = 0.59 ± 0.03 e; 70 µM Ca2+: zJ = 0.57 ± 0.03 e).
Because of the considerable patch-to-patch variation in Vh(Qfast), individual Qfast-V curves were aligned to the mean half-activation voltage in 0 or 70 µM Ca2+ before averaging (Horrigan and Aldrich, 1999)(see MATERIALS AND METHODS). The resulting plots (Fig. 7, C and D) are well fit by Boltzmann functions (solid lines) with identical valence (0.58 e) but different half-activation voltages, implying a small increase in the equilibrium constant for voltage sensor activation upon Ca2+ binding, as predicted by Scheme II when E > 1. The good fit by Boltzmann functions is also consistent with the assumption that voltage sensor activation can be described by a single R-A transition and that voltage sensors act independently when channels are closed.
Ca2+ Slows Voltage Sensor Deactivation
The kinetics of fast charge movement are altered slightly by Ca2+, consistent with a small increase in the equilibrium constant for voltage sensor activation. The mean Igfast time constants (gfast) from Fig. 7, A and B, and similar experiments are plotted versus voltage in Fig. 7 E. At negative voltages, gfast was determined by fitting the fast component of IgOFF evoked after brief pulses (0.06–0.25 ms) that activate voltage sensors while most channels remain closed. The gfast-V relationships were fit (Fig. 7 E, solid lines) with bell-shaped functions gfast = ( + ß)-1 as predicted for a two-state model of voltage sensor activation where = 0exp(-z/kT) and ß = ß0exp(-zß/kT) represent the forward and backward rate constants for voltage sensor activation when channels are closed. The partial charges associated with these rate constants (z, zß) were determined from the best fit to the 0 Ca2+data when zL = |z| + |zß| was constrained to 0.55 e (Horrigan and Aldrich, 1999). Attempts to constrain zL = 0.58 e as for the Qfast-V fits produced gfast-V fits that were too steep (unpublished data). Ca2+ shifts the peak of the gfast-V fit by -20 mV, consistent with the shift in Qfast-V. Ca2+ mainly reduces the backward rate for voltage sensor activation, and therefore increases gfast at negative voltages, but has little effect on gfast at positive voltages where the forward rate predominates (e.g., Fig. 7, A and B, at 160 mV).
Quantifying the Interaction between Ca2+-binding and Voltage Sensor Activation
Fig. 7, A–E, show that Ca2+ has a small direct effect on voltage sensor movement. However, Qfast-V relationships in 0 and 70 µM Ca2+ were rarely obtained from the same patch because Ig is small and extensive signal averaging was required. Thus, the change in mean Vh(Qfast) (<Vh(Qfast)> = (<Vh(Qfast)[0 Ca]> - <Vh(Qfast)[70 Ca]>) = 20 mV) may not represent accurately the Qfast-V shift in individual experiments.
A more accurate estimate of the Qfast-V shift (-33 mV) was obtained using admittance analysis. Admittance analysis provides an alternative method for selectively measuring fast gating charge movement (Fernandez et al., 1982). When the membrane is clamped with a sinusoidal voltage command, a nonlinear gating capacitance (Cg) proportional to dQfast/dV can be determined (Horrigan and Aldrich, 1999) (see MATERIALS AND METHODS). This technique provides a rapid assay of Qfast(V) such that the effects of 0 Ca2+ and 70 µM Ca2+ can be compared in the same patch. Fig. 7 F shows the Cg-V relationship is altered by Ca2+. To estimate the Qfast-V relationships for closed channels, the Cg-V traces were fit by the derivative of Boltzmann functions with respect to voltage over a voltage range where PO is small (Horrigan and Aldrich, 1999). The 0 Ca2+ fit determined for V < 100 mV (solid line) was shifted along the voltage-axis by -32 mV to fit the 70 µM Ca2+ data from the same patch for V < -10 mV. Similar analysis in several different experiments indicate a mean Qfast-V shift of -33 ± 4 mV (mean ± SEM, n = 6).
The Energetic Relationship between Ca2+-binding and Voltage Sensor Activation
A -33 mV shift in Qfast(V) upon Ca2+ binding can be accounted for by Scheme II if the allosteric factor E is assigned a value of 2.1 (zJ = 0.58 e). Thus, Ca2+-binding increases the R-A equilibrium constant 2.1-fold, altering the energetics of voltage sensor activation by 0.45 kcal mole. This represents a lower limit for the interaction energy because 70 µM Ca2+ may not be sufficient to completely saturate Ca2+ binding sites and the saturating shift in Qfast(V) may therefore be underestimated.
Effects of Ca2+ on Voltage Sensor Activation Cannot Account for the Shift in PO-V
To determine whether the Ca2+-dependent shift in the half-activation voltage of the PO-V relationship (Vh[PO]) can be accounted for by an effect of Ca2+ on voltage sensor activation, we examined the behavior of Scheme II when there is no direct interaction between Ca2+ binding and channel opening (i.e., C = 1). If we set E = 2.1 to account for the -33 mV shift in the Qfast-V relationship produced by 70 µM Ca2+ then the model predicts Vh(PO) = -19 mV, only 11% of the observed value (Vh[PO] = -166 mV, Fig. 4 C). Even if E is infinite, Scheme II cannot reproduce a -166 mV shift when C = 1. If E is large then Ca2+ binding will effectively lock voltage sensors in the activated conformation (i.e., JE >> 1) such that in saturating [Ca2+] the channel can only occupy a single closed and open state with a C-O equilibrium constant of LC4D4, hence:
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 | (2) |
VhE
(PO) represents, for any zL, L0,D, and C in saturating Ca2+, the lower limit of Vh(PO) as E becomes large. Given the parameters (zL, L0,D) used previously (0.4 e, 2 x 10-6, 17) (Horrigan et al., 1999) or in the present study (0.3 e, 0.98 x 10-6, 25), Eq. 2 predicts VhE (PO) = 81 or 113 mV, respectively, when C = 1 as compared with the observed Vh(PO) = 20 ± 8 mV in 70 µM Ca2+. Thus, interaction of Ca2+ binding with voltage sensor activation is insufficient to account for the observed Vh(PO), even if E is large. We conclude that Ca2+ binding must affect the C-O transition directly (i.e., C > 1).
Effects of Ca2+ on the C-O Transition
The weak Ca2+-sensitivity of fast charge movement and data presented in Figs. 8 and 9
show that the primary mechanism of Ca2+ action involves direct interaction between Ca2+-binding and the C-O transition.
|
Ca2+ Increases PO when Voltage Sensors Are Not Activated
At sufficiently negative voltages, voltage sensors should remain in the resting (R) state even when Ca2+ is bound. The Qfast-V relationships in Fig. 7, C and D, show that the fraction of activated voltage sensors is small (<10-2) for V < 0 mV in 0 or 70 µM Ca2+. With voltage sensors effectively locked in the R conformation, Scheme II reduces to sub-Scheme IIc (Fig. 3), which specifies a 10 state Monod-Wyman-Changeux (MWC)-type gating scheme (Fig. 8 B, sub-Scheme IIc*). Under this extreme condition, channels can open in a Ca2+-dependent manner only through direct interaction between Ca2+ binding and the C-O transition. At negative voltages PO is highly Ca2+ sensitive (Figs. 8 and 9), confirming that a strong interaction exists between Ca2+ binding and channel opening and providing a direct estimate of the allosteric factor C that embodies this interaction.
Fig. 8 C compares IK recorded at -120 mV from a single patch in various [Ca2+]. The corresponding amplitude histograms are superimposed in Fig. 8 D. Although the patch contains hundreds of mSlo1 channels, PO is low in the absence of Ca2+ and activity is observed as the infrequent and brief opening of single channels. Application of Ca2+ causes a large increase in open probability, resulting in multichannel openings. NPO increases 2,130-fold, from 6.1 x 10-4 in 0 Ca2+ to 1.3 in 100 µM Ca2+. Histograms in Fig. 8 E demons
), 0.13 (
), 0.27 (
), 0.58 (
), 0.79 (
), 3.8 (
), 19 (
), 68 (
), 102 (
), 313 (
), 1030 (
)). Dashed lines are exponential fits with z = 0.3 e. (B) PO-V relationships determined from normalized G-Vs at different [Ca2+](in µM: 0 (
), 3.8 (
), 19 (
120 mV in 70 µM Ca2+ (see E). (C) 
