Correspondence to: Richard W. Aldrich, Department of Molecular and Cellular Physiology, Howard Hughes Medical Institute, Stanford University School of Medicine, Stanford, CA 94305., raldrich{at}leland.stanford.edu (E-mail), Fax: 650-725-4463; (fax)
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Abstract |
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Large-conductance Ca2+-activated K+ channels can be activated by membrane voltage in the absence of Ca2+ binding, indicating that these channels contain an intrinsic voltage sensor. The properties of this voltage sensor and its relationship to channel activation were examined by studying gating charge movement from mSlo Ca2+-activated K+ channels in the virtual absence of Ca2+ (<1 nM). Charge movement was measured in response to voltage steps or sinusoidal voltage commands. The chargevoltage relationship (QV) is shallower and shifted to more negative voltages than the voltage-dependent open probability (GV). Both ON and OFF gating currents evoked by brief (0.5-ms) voltage pulses appear to decay rapidly (ON = 60 µs at +200 mV,
OFF = 16 µs at -80 mV). However, QOFF increases slowly with pulse duration, indicating that a large fraction of ON charge develops with a time course comparable to that of IK activation. The slow onset of this gating charge prevents its detection as a component of IgON, although it represents ~40% of the total charge moved at +140 mV. The decay of IgOFF is slowed after depolarizations that open mSlo channels. Yet, the majority of open channel charge relaxation is too rapid to be limited by channel closing. These results can be understood in terms of the allosteric voltage-gating scheme developed in the preceding paper (Horrigan, F.T., J. Cui, and R.W. Aldrich. 1999. J. Gen. Physiol. 114:277304). The model contains five open (O) and five closed (C) states arranged in parallel, and the kinetic and steady-state properties of mSlo gating currents exhibit multiple components associated with CC, OO, and CO transitions.
Key Words: calcium, potassium channel, BK channel, ion channel gating, gating current
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Introduction |
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Large-conductance Ca2+-activated K+ channels (BK channels)1 are sensitive to membrane potential as well as intracellular calcium. Although the voltage dependence of these channels is weak compared with that of many purely voltage-gated K+ (Kv) channels (
In the preceding article ((IK)) and steady-state open probability (Po) both exhibit complex voltage dependencies that are inconsistent with many conventional sequential gating schemes. A particularly important finding is that
(IK) and Po become less voltage dependent at very negative voltages. To account for these results, we proposed a voltage-gating scheme based on an allosteric mechanism.
This diagram illustrates the idea that mSlo channels undergo a transition between a closed (C) and open (O) conformation, and that this transition is influenced allosterically by the state of four independent and identical voltage sensors (one for each subunit). We assume each voltage sensor can undergo a transition between a resting (R) and an activated (A) conformation, and the equilibrium constant for the CO transition (L) increases by a constant factor (D) for each voltage sensor that is activated. Similarly, the equilibrium constant for voltage sensor activation (J) increases D-fold in favor of the activated state, when the channel opens. Therefore, the factor D embodies the allosteric interaction between voltage-sensor activation and channel opening. This mechanism results in a gating scheme (Figure 144) that contains a parallel arrangement of open and closed states.
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The horizontal transitions (CC and OO) reflect the activation or movement of voltage sensors while vertical (CO) transitions represent channel opening. The closed and open conformations are each represented by five states, with subscripts (04) denoting the number of activated voltage sensors.
For this scheme to reproduce IK, it is necessary that voltage-sensor activation is fast and accounts for most of the channel's voltage dependence while CO transitions are slow and weakly voltage dependent ((IK) and Po at negative voltages implies that the charge associated with channel opening is small (zL = 0.4 e). Finally, the equilibrium constant L is small (~10-6) and the allosteric factor large (D = 17), equivalent to an interaction energy of 2.8 kT, to account for the shape of the PoV relationship in 0 Ca2+.
Such a model provides mechanistic insight and places constraints on the possible molecular events that link voltage-sensor movement and channel opening (
Although the properties of mSlo IK are consistent with the allosteric model, several aspects of the gating scheme are not tightly constrained by the ionic current data (
Our results are consistent with the assumption that mSlo voltage sensors move rapidly and independently while channels are open or closed. Measurements of the charge associated with voltage-sensor movement are in line with previous estimates based on the ionic current data. Our results also support the prediction that channel opening alters the kinetics of voltage-sensor movement. Finally, we show that some complex kinetic and steady-state properties of mSlo charge movement are reproduced by the proposed gating scheme. These include a large slow component of ON charge that is limited by the speed of channel opening, and three components of OFF charge reflecting CC, OO, and CO transitions. The relationships between these components are consistent with the allosteric model and rule out many alternative schemes.
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Materials and Methods |
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Channel Expression
Experiments were performed with the mbr5 clone of the mouse homologue of the Slo gene (mSlo), kindly provided by Dr. Larry Salkoff (Washington University School of Medicine, St. Louis, MO). The clone was modified to facilitate mutagenesis and was propagated and cRNA transcribed as described previously by ; kindly provided by Dr. A.P. Braun, University of Calgary, Calgary, Alberta, Canada) containing the SV40 promoter. HEK 293 cells expressing the large T-antigen of the SV40 virus were cotransfected with mSlo and green fluorescent protein (GFP, as a marker) using LipofectAMINE (GIBCO BRL) 3 d before recording.
Electrophysiology
Currents were recorded using the patch clamp technique in the inside-out configuration (
Measurement of rapid gating current in response to voltage pulses requires accurate subtraction of linear capacitive currents due to the electrode and cell membrane. Electrodes were pulled from thick-walled 1010 glass (World Precision Instruments) and coated with wax (sticky wax; Kerr) to minimize electrode capacitance (~1 pF). Pipette access resistance (Rs) ranged from 0.7 to 1.5 MV in K-free solutions. Membrane capacitance ranged from 0.25 to 1 pF as determined by the responses to a -10 mV voltage step from -80 mV before and after sealing the electrode tip onto Sylgard (Dow Corning). Data were acquired with an Axopatch 200B amplifier (Axon Instruments, Inc.) in patch mode at a relatively low gain (12 mV/pA) to avoid saturation of capacitive transients in response to voltage steps that often exceeded 300 mV. Both the voltage command and current output were filtered at 20 kHz with 8-pole bessel filters (Frequency Devices, Inc.) to limit the speed of fast capacitive transients so that they could be accurately sampled and subtracted. The Axopatch's internal filter was set at 100 kHz. Currents were sampled at 100 kHz with a 16 bit A/D converter (ITC-16; Instrutech). Ig records were typically signal-averaged in response to at least eight voltage pulses, and a P/-4 protocol was used for leak subtraction (
Simulations
Simulations were calculated at 1-µs intervals using a fifth order Runga-Kutta algorithm with adaptive step size (
Admittance Analysis
Admittance (Y) is defined by the expression Y = I/V where V and I represent the amplitude of the sinusoidal voltage command and resultant current at a specific frequency (
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(1) |
where Gm and Cm are membrane conductance and capacitance, respectively (j=,
= 2
The total admittance of the patch equivalent circuit is:
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(2) |
where Cs is the stray capacitance of the electrode and holder, and Rs is the series resistance. Combining (1) and (2):
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(3) |
where
Under typical experimental conditions [RS 106 , Cm
1 pF, Gm < 1 nS,
= 5,451 (
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(4) |
Therefore, Cg(V) can be determined directly as the voltage-dependent component of Yp/ appearing at a phase angle of 90° relative to the command voltage.
For admittance measurements, the membrane was clamped with a sinusoidal voltage command (60 mV peak to peak) generated by the D/A converter of the ITC-16 interface at 18-µs intervals (at least eight samples per cycle of the sinusoid). The voltage command and current signal were both filtered at 20 kHz. Admittance was determined for each cycle of the sinusoid at 0° and 90° after correcting for phase shifts () due to the filters and amplifier. These were determined at each frequency by measuring the admittance of an electrode in solution (Y = 1/RS), which should appear at an angle of
relative to the command voltage. DC current was determined as the mean current over each cycle of the sinusoid.
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Results |
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Gating charge movement was examined in excised macropatches from Xenopus oocytes and HEK 293 cells expressing the pore-forming subunit of mSlo Ca2+-activated K channels. Several factors combine to make gating currents more difficult to measure for mSlo than for Kv channels such as Shaker. First, mSlo is less voltage dependent than Shaker, and the gating charge is correspondingly smaller. The steady-state GKV relationships for mSlo in 0 Ca2+ and Shaker can be approximately fit by Boltzmann functions with equivalent charges of 1 e (
Two approaches were used to measure mSlo gating charge movement. The first involved clamping the membrane with a sinusoidal voltage command and measuring gating charge as a voltage-dependent component of membrane capacitance using admittance analysis (
Gating Capacitance Measurements and Admittance Analysis
Membrane capacitance (Cm) represents the ability of charge to redistribute across or within the cell membrane in response to a change in voltage. Therefore, Cm includes a nonlinear voltage-dependent contribution from gating charge movement (Cg) as well as a voltage-independent component due to the lipid bilayer. One of the most sensitive methods for measuring capacitance is admittance analysis. The membrane is driven with a sinusoidal voltage command, and the resulting current is analyzed with a phase-sensitive detector to determine Cm as well as other parameters in the membrane equivalent circuit (
Gating capacitance (Cg) represents the amount of gating charge that moves (Qg) in response to a small change in voltage (
V) and therefore reflects the slope of the QgV relationship (
Qg/
V). Cg is also dependent on the kinetics of charge movement and is therefore sensitive to the frequency (
Figure 1 A shows the CgV relationship for mSlo measured at 868 Hz in 0 Ca2+ (see Materials and Methods) from channels expressed in an excised macropatch. Cg exhibits a bell-shaped voltage dependence and is well fit by the derivative of a Boltzmann function (Figure 1 A, Fit). In nontransfected cells, the CV relationship is flat (Figure 1 A, Control), representing only the uncompensated linear capacitance of the lipid bilayer and electrode (Co = Cb + Cs; see Equation 4). These contributions to the record in Figure 1 A were effectively eliminated by setting the baseline equal to zero at negative voltages (less than -100 mV) where C is voltage independent and presumed equal to Co. The QgV relationship was obtained by integrating the CgV trace with respect to voltage, and is plotted in Figure 1 B together with the normalized conductancevoltage (GKV) relationship for mSlo in 0 Ca2+ (mean ± SEM, n = 23 [
The CgV relationship in Figure 1 A was measured during a 1-s voltage ramp from -160 to +200 mV. A sinusoidal command (
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(5) |
where the real and imaginary terms represent the components of Yp appearing at phase angles of 0° and 90°, respectively, relative to the command voltage, and = 2
Gating Capacitance Represents mSlo Charge Movement
Although a voltage-dependent component of Cm was not detected in uninjected oocytes, it is important to verify that Cg arises from mSlo channels. High levels of heterologous expression of many membrane proteins in Xenopus oocytes have been shown to upregulate expression of endogenous ion channels (
The Ca2+ sensitivity of Cg is examined in Figure 2 A. CgV traces obtained in 0 or 60 µM Ca2+ from the same patch were normalized to peak capacitance and superimposed. The CgV relationships are similar in shape but shift to more negative voltages with increasing [Ca2+]i. The GKV relationship for mSlo also exhibits a negative voltage shift upon application of Ca2+ in this concentration range (
The Ca2+ sensitivity of Cg suggests that this signal represents mSlo charge movement but does not rule out contributions from endogenous Ca2+-sensitive channels. To eliminate this possibility, we examined the properties of an mSlo mutant. Neutralization of a charged residue in the 17 domain of mSlo (R207Q) shifts the GKV relationship to more negative voltages and reduces its slope relative to that of the wild-type (
The Kinetics of mSlo Gating Charge Movement
To assess the speed of charge movement, we examined the frequency dependence of Cg. In the simplest case, where gating charge movement can be represented by a two-state process, such as voltage-sensor activation from R to A, gating admittance
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(6) |
can be represented by an equivalent circuit consisting of a capacitor Cg0 in series with a resistor Rg0 where g = Cg0Rg0 is the time constant of gating charge relaxation at a particular voltage (
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(7) |
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(8) |
When the frequency of the sinusoidal voltage command is low ( << 1/
), Yg reduces to a purely capacitive signal (Yg
j
Cg0), where Cg0 = dQss/dV. As
increases, Cg should be attenuated, since the gating charge effectively cannot move fast enough to keep up with the voltage command. Cg(
) is a Lorenzian function that describes the frequency dependence of Cg. At higher frequencies, the gating current should also change phase with respect to the voltage command such that a component of Yg, described by the function Gg(
), appears in phase with the membrane voltage.
The frequency dependence of mSlo charge movement is shown in Figure 2CF. Consistent with the above predictions, the CgV relationship is attenuated as the frequency of the sinusoidal voltage command is increased from 200 to 6,944 Hz (Figure 2 C). At the same time, a voltage-dependent signal appears in the orthogonal G trace and increases at higher frequencies (Figure 2 D). The DC current level during the voltage ramp is small and increases in a roughly linear manner with voltage, indicating a constant membrane resistance (Rm) of ~125 GV (Figure 2 E). Thus, the G signal in Figure 2 D represents a component of gating charge movement (Gg) and not a voltage-dependent change in membrane conductance. Gg is almost eliminated at 200 Hz, consistent with the prediction that Yg will reduce to a purely capacitive signal at low frequencies. Figure 2 F plots the amplitudes of Cg and Gg measured at +120 mV versus frequency for two experiments. Cg and Gg are well fit by Equation 7 and Equation 8, respectively, with a time constant () of 70 µs. The relative amplitudes of the admittance components are also consistent with a 70-µs time constant, since Cg and Gg were normalized by Cg0 and Cg0/
, respectively. Thus, a component of mSlo gating charge appears to move much faster than IK activation, which is described by a mean time constant of 1.63 ms at +120 mV (
Conclusions from Capacitance Measurements
Admittance analysis reveals several important properties of mSlo charge movement. Comparison of the QgV and GKV relationships (Figure 1 B) suggests that charge movement can occur at voltages where most channels are closed. The frequency dependence of Cg shows that charge relaxes with a time constant that is much faster than that of IK activation (Figure 2 F). Together, these results suggest that admittance analysis detects charge movement associated with rapid closed-state transitions that precede channel opening. In terms of the allosteric voltage-gating scheme, such transitions result from voltage-sensor movement. That the QgV relationship can be fit by a Boltzmann function is consistent with the movement of each voltage sensor being described by a two-state model with a single transition between a resting (R) and an activated state (A). The simple voltage dependence of Qg also supports the notion that the voltage sensors, in different subunits of the mSlo homotetramer, behave identically and act independently. The approximate 4th power relationship between QgV and GV is consistent with the assumption that channel opening is linked to the activation of four voltage sensors. However, as discussed below, this relationship may be affected by the different ionic conditions under which IK and Ig are measured.
Advantages and Limitations of Admittance Analysis
Our results show that admittance analysis provides a sensitive method for detecting and characterizing some aspects of mSlo gating charge movement. By using a large amplitude sinusoidal voltage command in combination with a voltage ramp, we were able to acquire the CgV relationship rapidly, and to determine Qg(V) at submillivolt intervals. The speed of mSlo charge movement is advantageous for admittance analysis because it allows measurements to be performed at hundreds or thousands of Hz where the signal to noise ratio is high (
The charge movement detected with capacitance measurements is much faster than IK activation. However, any scheme that assumes the CO conformational change is voltage dependent or that channel opening affects the ability of voltage sensors to move requires that a component of gating charge will relax with the kinetics of IK activation. The frequency dependence of Cg (Figure 2 F) can be adequately fit by a single Lorenzian function between 200 and 7,000 Hz and therefore provides no evidence for a slow component of gating charge, which should appear as an additional Lorenzian component at low frequencies. However, the frequency range of our measurements may limit our ability to detect such components. For example, charge that moves with a time constant of 2 ms would produce a Cg component that is attenuated by ~85% at frequencies >200 Hz.
Admittance analysis is also not an ideal method for dissecting a model as complex as the one we have proposed for mSlo. The allosteric scheme predicts that multiple kinetic components of charge movement will result from CC, CO, and OO transitions. Admittance analysis detects charge movement associated with perturbations about an equilibrium distribution of channel states, and will therefore contain contributions from all of these sources. Slow transitions associated with channel opening should contribute little to Cg at the frequencies used in our experiments. However, fast transitions among closed or open states (CC, OO) should be detected. At voltages less than +100 mV, most channels are closed in 0 Ca2+, and Cg will mainly reflect CC transitions. However, at more positive voltages, Cg should represent a combination of open- and closed-state charge movement. For this reason, gating currents measured in response to step depolarizations provide a better method for isolating the various transitions predicted by the model.
A Fast Component of Gating Current
Figure 3 A shows Ig evoked in response to a 0.5-ms pulse to +160 mV from a holding potential of -80 mV in 0 Ca2+. The ON current decays rapidly with a time course that is well fit by an exponential function (dashed line) with a time constant of 59 µs, similar to that determined with admittance analysis at +120 mV (70 µs). The OFF current measured at -80 mV decays more quickly, with a time constant of 17 µs. A family of Ig evoked at different voltages (0 to +160 mV) in response to 1-ms pulses is shown in Figure 3 B. The QONV and QOFFV relationships obtained by integrating IgON and IgOFF are plotted in Figure 3 C (open symbols) together with the QgV relationship obtained from capacitance measurements at 868 Hz in the same patch (solid line). At all voltages, QON and QOFF are equivalent, as expected for gating charge. The gating current and capacitance measurements superimpose from 0 to +120 mV but diverge at +160 mV.
Similar results were obtained with brief voltage pulses and capacitance measurements because both methods mainly detect fast charge movement. Figure 3 D compares the time course of Ig evoked at +160 mV to the initial activation of IK measured at the same voltage from a different experiment. Ig decays, to a large extent, before IK begins to increase. After 1 ms, IK increases to 31% of its steady-state amplitude, representing only 7% of maximum Po. Thus, the channel does not achieve a steady state during a 1-ms pulse, and Ig should reflect little if any slow charge movement that might be associated with channel opening. An important difference between the gating current and capacitance measurements is that the initial decay of IgON represents charge moved when most channels are closed, while Cg is measured after Po has reached a steady state and therefore reflects the behavior of both open and closed channels. Thus, Ig measurements allow better isolation of closed-state transitions owing to the large kinetic difference between IgON and IK.
Fast Ig: Isolation and Voltage Dependence
According to the allosteric model, the initial decay of Ig represents activation of voltage sensors from a resting (R) to an activated state (A) while channels are closed (i.e., CC transitions). The exponential decay of IgON is consistent with such a two-state model. Moreover, in Figure 3 D, IK achieves an exponential time course (dashed line) at a time (arrows) when the gating current has almost completely decayed. This correlation between Ig and the delay in IK activation is consistent with Ig reflecting closed-state transitions in the activation pathway. However, QON measured during a 1-ms pulse is not only an assay of closed-state charge movement, as some channels do open during this time (Figure 3 D). QON measurements can also be contaminated by outward leak currents that often are observed at voltages greater than +200 mV. To better characterize closed-state transitions, the fast component of ON charge was isolated by fitting an exponential function to the decay of Ig during the first 200 µs of the voltage pulse when most channels are closed. The area under the fit (Qfast), as indicated by the shaded region in Figure 3 D, was used as an estimate of closed-state charge movement (QC). The QfastV relation in Figure 3 C (filled symbols) is similar to the QgV relation. When data were acquired over a larger voltage range (Figure 3 E), Qg and Qfast diverge at more positive voltages (Figure 3 F). The QfastV relationship in Figure 3 F is well fit by a Boltzmann function (z = 0.57 e, Vh = 136 mV). The difference between Qg and Qfast is expected, as it occurs at voltages (>100 mV) where channels begin to open, and Qg therefore cannot be equivalent to QC.
Figure 4 A1 plots the normalized QfastV relationships for many experiments. The data were initially fit with Boltzmann functions where all parameters were allowed to vary, yielding a mean equivalent charge <z> = 0.59 ± 0.03 e (mean ± SEM, n = 10). The QVs were then refit with z = <z> and normalized as shown in Figure 4 A1. Although the individual plots are reasonably fit using identical values of z, they are scattered in their position along the voltage axis, similar to the mSlo GKV relationships (V =
Vh
-Vh where Vh is the half-activation voltage of an individual QV and
Vh
is the mean (155 ± 6.5 mV, n = 10) determined from Figure 4 A1. These voltage-shifted plots were then used to determine the average QV (Figure 4 A2, filled symbols). A Boltzmann function with z = 0.59 e and Vh = 155 is superimposed on the data (solid line).
Voltage Dependence of Fast Ig Kinetics
To further characterize the properties of closed-channel charge movement, we examined the voltage dependence of fast Ig kinetics. Time constants of fast Ig relaxation (gFast) were determined from exponential fits to ON and OFF currents for the experiments in Figure 4 A1 and are plotted in Figure 4 B1. OFF currents, measured at voltages less than +40 mV, were evoked after very brief pulses (0.050.25 ms) to +160 or +200 mV and therefore should represent the relaxation of closed channels.
gFast exhibits a bell-shaped voltage dependence, consistent with a two-state model of voltage-sensor activation where forward and backward rate constants are voltage dependent.
gFastV relationships from three experiments that covered a large voltage range are compared in Figure 4 C1. The individual plots are similar in shape but shifted relative to each other along both axes. The amplitude differences resemble those described previously for the delay in IK activation (
gFastVs, the plots were first shifted along the voltage axis based on the QV shifts determined in Figure 4 A. The data were then normalized to the mean
gFast determined over an interval around the peak of the
gFastV (59.0 ± 2.2 µs, n = 10, from +100 to +180 mV). The resulting records, corresponding to Figure 4, B1 and C1, are plotted in Figure 4, B2 and C2, respectively, and exhibit improved alignment of the
gFastV relationships.
The data in Figure 4 B2 were fit with a function gFast = 1/(
+ß), representing the predicted
gFastV relationship for a two-state process where the forward (
) and backward (ß) rate constants are exponential functions of voltage [
=
0e(
)]. Fits were constrained such that the equilibrium constant J =
/ß equals one at the half-activation voltage of the QfastV (Vh(J) = 155 mV). The solid line in Figure 4 B2 represents the best fit and is characterized by a total equivalent charge of zJ = 0.51e (z
= +0.30 e, zß = -0.21 e).
Estimates of the charge associated with voltage-sensor activation (zJ) based on fits to the QfastV and gFastV relationships (0.59 and 0.51 e, respectively) apparently differ. However, both relationships can be reasonably fit using the average of these two estimates (0.55 e) (Figure 4, A2, B2, and C2; dashed lines). This value of zJ was also used in the preceding article to reproduce the ionic current data using the allosteric voltage-gating scheme (
and zß used to fit the
gFastV relationship (z
= +0.33 e, zß = -0.22 e) indicate that the RA transition in the allosteric model is not symmetrically voltage dependent as previously assumed.
A Slow Component of ON Charge Movement
Although the ON currents in Figure 3 appear to decay with a single-exponential time course, there is a significant slow component of charge movement. Figure 5 A plots a family of Ig evoked at +140 mV in response to voltage pulses of different duration (see also Figure 6 A). The peak amplitude of IgOFF increases rapidly with pulse duration, paralleling the rapid decay of IgON, and then remains relatively constant for pulses longer than 0.5 ms. The total gating charge moved during the pulse (Qp) was determined by integrating IgOFF and is plotted versus pulse duration in Figure 5 B. Qp increases with a time course that can be fit by a double-exponential function (solid line) with a fast phase (QpFast) corresponding to the rapid decay of IgON, and an additional phase that is roughly 100-fold slower. The slow component (QpSlow) relaxes with a time constant (gSlow) of 4.22 ms and represents a significant fraction of the total gating charge movement at +140 mV (43%) but is too slow to be observed as a component of IgON. This point is illustrated in Figure 5 C, which compares IgON evoked at +140 mV to Qp'(t) (dashed line). Qp'(t) is the time derivative of the double-exponential fit to Qp(t) and should represent the time course of IgON (Qp'(t) = dQON/dt = IgON). These two relationships superimpose, demonstrating that observed IgON kinetics are consistent with the presence of a large slow component of ON charge movement.
The predicted amplitude of the slow component of IgON, determined from Qp'(t), is small (2.1 pA) because it decays slowly. For similar reasons, the slow component of ON charge could not be reliably measured from IgON. Small sustained outward currents on the order of a few pA were often observed at high voltages, presumably representing residual ionic or leak current. For example, the current trace in Figure 5 C decays to a steady-state level of 2.2 pA at the end of the pulse. While such small currents have little effect on measurement of Qfast they can contaminate estimates of slow charge determined by integrating IgON over a 20-ms pulse. The slow component of Qp from Figure 5 B is only 8 fC, equivalent to a 0.4 pA current for 20 ms. Measurements of OFF charge (Qp) provide a more reliable estimate of slow charge movement because leak is constant at the holding potential.
The voltage dependence of Qp(t) is examined in Figure 6. Families of Ig evoked at different voltages in response to pulses of 0.0620 ms duration are shown in Figure 6 A. At each voltage, Qp was plotted versus pulse duration (Figure 6 B) and fit with a double-exponential function as in Figure 5 B. The plots represent data from three experiments and were normalized to the total fast charge movement QTfast estimated from the amplitude of a Boltzmann fit to the QfastV relationship for each experiment. The indicated voltages were corrected for shifts in the QfastV relationship as determined in Figure 4 A.
A slow component of Qp is observed in Figure 6 B for V +100 mV. The time constant of QpSlow (
gSlow) is comparable to that for IK activation (
(IK)) measured from +140 to +240 mV (Figure 6 C). The similar magnitude and voltage dependence of
gSlow and
(IK) suggest that slow charge movement is limited by channel opening. These kinetics also show that gating charge and open probability equilibrate on a similar time scale. Therefore, QOFF determined with a 1-ms voltage pulse, as in Figure 3 C, can underestimate steady-state QOFF (Qss), determined with a 20-ms pulse, by as much as 40%. Despite this difference, the QssV and QfastV relationships are similar in shape. Figure 6 D compares normalized QssVs from four experiments to the normalized QfastV and GKV relationships. QssV almost superimposes with QfastV, and the steady-state data were fit with Boltzmann functions with an equivalent charge z = 0.65 ± 0.03 e (mean ± SEM, n = 4), indicating a slightly steeper voltage dependence than Qfast.
The Relationship between Slow Charge Movement and Channel Activation
The predominantly exponential time course of mSlo IK suggests that the kinetics of voltage-dependent activation are dominated by a rate-limiting transition (
We have previously concluded that the transition from a closed to open conformation represents the rate-limiting step in mSlo activation and is weakly voltage dependent (
The allosteric model predicts that the majority of charge movement can be attributed to voltage-sensor activation. Fast Ig is evoked in response to a voltage step as sensors initially equilibrate between resting (R) and activated (A) conformations while the channel is closed. Qfast is determined by the voltage-dependent equilibrium constant (J) that characterizes the RA transition. In addition, a slow component of charge movement should be produced as channels open, representing the CO transition. However, voltage-sensor movement can also contribute to QpSlow. When a channel opens, the equilibrium constant for voltage-sensor activation increases by the allosteric factor D, causing sensors to reequilibrate between R and A and produce additional charge movement. This charge movement will be slow because the voltage-sensor reequilibration is limited by the speed of channel opening.
The amplitude of QpSlow should depend upon the number of channels that open as well as the fraction of voltage sensors that are initially activated before channels open. For example, at very positive voltages (approximately +300 mV), the model predicts that voltage sensors can be completely activated with channels closed. In this case, channel opening cannot cause additional voltage sensors to be activated so QpSlow will represent only the charge associated with the CO transition (zL). At less positive voltages, however, QpSlow will represent a combination of channel opening and voltage-sensor reequilibration and may therefore be larger than zL. We will demonstrate later that the magnitude and voltage dependence of QpSlow are consistent with the allosteric gating scheme (Figure 14). The notion that the CO transition limits slow charge movement is also important in understanding the properties of IgOFF as discussed below.
Three Components of OFF Gating Charge Movement
The large slow component of Qp(t) observed at V +140 mV in Figure 6 B indicates that QOFF increases with pulse duration. In contrast, the peak amplitude of IgOFF remains roughly constant or decreases with pulse duration at the same voltages (Figure 6 A). That IgOFF can decrease or remain constant while its integral (QOFF) increases implies that the kinetics of OFF current change with pulse duration. This change is obvious in Figure 7 A, which compares OFF currents evoked at -100 mV after pulses to +140 mV of different duration (0.0620 ms). Two components of IgOFF are evident from these records. After brief pulses (0.06 or 0.11 ms), OFF current decays with a rapid exponential time course, but an additional slower component appears as pulse duration is increased. The decay of IgOFF at all pulse durations can be well fit by double-exponential functions with time constants of 15.5 and 59 µs (Figure 7 B). Both components decay within 300 µs and therefore appear to be fast relative to the time course of channel closing. Potassium tail currents decay with a time constant of 172 ± 15 µs at -80 mV (
(IK) = 900 µs to decay completely. However, a slower component of OFF charge movement can be detected by plotting the integral of IgOFF (QOFF(t); Figure 7 C). QOFF(t) measured after a brief (0.06 ms) voltage pulse achieves a steady state within 300 µs (Figure 7 C, arrow), consistent with the rapid decay of IgOFF. In contrast, QOFF(t) measured after a 20-ms pulse requires >1 ms to reach a steady state, indicating a slow component of charge relaxation. This component of QOFF is not evident in the corresponding IgOFF trace because it is slow and represents <20% of the total OFF charge.
The components of QOFF(t) relaxation were further analyzed by plotting the quantity (QOFF(t) - QOFFss) where QOFFss is the steady-state value of QOFF(t) measured 3 ms after the voltage pulse (Figure 7 D). The relaxation of (QOFF(t)- QOFFss) after a brief pulse (0.06 ms) can be fit by a single-exponential function as indicated by a linear relationship on this semilog plot (F = 15.5 µs). The relaxation of (QOFF(t) - QOFFss) after a prolonged pulse (average of 1020-ms records) is more complicated and was best fit by three exponential components (
F = 15.5 µs,
M = 59 µs,
S = 448 µs), indicated by dashed lines in Figure 7 D, where
F was constrained to that used to fit the 0.06-ms record. On average, time constants of 15.7 ± 1.3, 64.7 ± 10.6, and 580 ± 50 µs were measured at -80 mV (mean ± SEM, n = 6).
The time course of development of the OFF charge components were examined by fitting (QOFF(t)- QOFFss) with triple-exponential functions for all pulse durations (Figure 7 E). The time constants (termed Fast, Medium, and Slow) were determined from the 0.06- and 1020-ms traces as in Figure 7 D, and component amplitudes were varied to fit the other records. The QOFF component amplitudes (QOFFfast, QOFFmed, and QOFFslow) are plotted versus pulse duration in Figure 7 F. The Fast component develops rapidly and then slowly decreases in amplitude as pulse duration is increased. At the same time, a parallel increase in the Medium and Slow components is observed. The slow relaxations in the development of all three components were fit by exponential functions (solid lines) with a time constant of 4.2 ms. This time constant is identical to that used to fit QpSlow (Figure 5 B) and is therefore assumed to represent the time course of channel opening. As discussed below, the results in Figure 7 F suggest that the Fast component of OFF charge movement represents the relaxation of closed channels, while the Medium and Slow components represent the relaxation of open channels.
Factors Influencing OFF Component Characterization
Accurate separation of QOFF components depends on several factors, including the estimation of their time constants. F is most easily determined because the fast component is large and can be examined in isolation using brief voltage pulses. The Slow component can also be effectively isolated because
S is almost 10-fold larger than
M. However, the small amplitude of the Slow component and its sensitivity to baseline drift make
S more difficult to determine than
F. The relaxation of QOFF(t) to a steady state in Figure 7 C indicates that IgOFF decays to the baseline level after ~1 ms. A small offset or drift in baseline current can prevent QOFF(t) from achieving such a steady state and affects determination of
S and QOFFslow. To minimize such artifacts, the Ig baseline was typically set equal to the mean current measured during an interval 45 ms after the end of the pulse. Despite this precaution, drift in QOFFss was observed in some experiments (data not shown) and contributes to variability in the estimate of
S.
The medium time constant (M) was also difficult to determine because it is only fourfold slower than
F and cannot be studied under conditions where the Fast and Slow components are absent. Thus, estimates of
M from triple exponential fits to QOFF relaxation were sensitive to the estimates of
F and
S. Error bars in Figure 7 F indicate the effect of ±10% changes in
M on the estimated amplitudes of the different OFF components (with
F and
S held constant). Such variation still allows reasonable fits to QOFF(t) (data not shown); however, an increase in
M results in a decrease in the measured QOFFmed and a complimentary increase in QOFFfast. Larger changes in
M produce inadequate fits to QOFF(t), and the time course of the Medium component development becomes biphasic as the separation of Fast and Medium components is compromised.
Measurements of QOFFmed can be affected by baseline drift or variation in S. Therefore, the development of Fast and Medium components were also studied by fitting IgOFF with double-exponential functions (Figure 7 B), a procedure that is less sensitive to the slow component. Figure 7 G plots the amplitude of the IgOFF components versus pulse duration, indicating a time course of Fast and Medium component development similar to that determined from QOFF (Figure 7 F). Exponential fits in Figure 7F and Figure G, used identical values of
gSlow. However, in experiments where baseline drift was a problem, fits to IgOFF produced more consistent results and were used to determine
gSlow.
mSlo Charge Movement and Allosteric Voltage Gating
The presence of three components of OFF gating charge movement, their kinetics, and development with pulse duration can be understood in terms of the allosteric voltage-gating scheme (Figure 14). As indicated in Figure 7 H, the allosteric model predicts that OFF charge relaxation will be characterized by Fast, Medium, and Slow components that reflect CC, OO, and OC transitions, respectively. When mSlo channels are closed, OFF currents should represent the relaxation of voltage sensors from an activated to a resting state, corresponding to CC transitions in the gating scheme. Since brief voltage pulses allow few channels to open, the fast relaxation of IgOFF after such a pulse (F) mainly reflects the kinetics of this closed-state relaxation pathway. As pulse duration is increased, channels open and their deactivation after the pulse reflects a more complex relaxation pathway involving OO and OC transitions. The model predicts that voltage sensors can move even when channels are open. Therefore, the OFF current should exhibit a component that reflects relaxation of voltage sensors from an activated to a resting state, corresponding to OO transitions in the gating scheme. If these open-state transitions account for the Medium QOFF component, to account for the difference between
M and
F, we must assume that voltage-sensor relaxation is slower when the channel is open than when it is closed. This is a reasonable assumption because the allosteric mechanism requires that channel opening increase the equilibrium constant for voltage-sensor movement D-fold, stabilizing the activated state (A) relative to the resting state (R). Finally, the model predicts that there will be a slow component of OFF charge movement associated with the transition of open channels back to the closed state. Therefore, the slow component should have the same time course as channel deactivation. We will argue later that differences in the observed time course of IK deactivation and slow charge movement (
S) may reflect effects of ionic conditions on channel gating.
If the Fast component of OFF charge movement represents the relaxation of closed channels while Medium and Slow components represent the relaxation of open channels, the effect of pulse duration on the relative amplitude of these components can be understood in terms of the kinetics of channel activation. QOFFfast increases initially because voltage sensors can be activated rapidly during brief pulses while channels are closed. As pulse duration increases, the number of closed channels is reduced and QOFFfast decreases with the time course of channel activation. At the same time, both Medium and Slow components increase, reflecting an increase in the number of open channels.
Charge Movement Measurements Are Not Contaminated by Ionic Currents
An important conclusion from the above analysis is that the slow components of ON and OFF charge movement are limited by channel opening and closing. Since the kinetics of these components are similar to those of IK, it is critical to establish that they do not represent contamination of Ig by residual ionic currents. The slow component of ON charge movement was detected as an increase in QOFF measured after pulses of different duration, whereas the slow OFF charge was seen as a component of QOFF relaxation. Thus, the presence of an inward potassium tail current could potentially contribute to both measurements. This possibility appears unlikely because gating current records that give rise to large slow components of ON charge movement (e.g., Figure 5 and Figure 6) do not exhibit appreciable sustained (ionic) current during the voltage pulse. In addition, the slow increase in Qp with pulse duration involves simultaneous changes in the amplitudes of all three components of QOFF relaxation. The Fast component decreases while the Medium and Slow components increase (Figure 7 F). Although the Slow component relaxes with kinetics similar to that of ionic tail currents, it accounts for only a small fraction of QpSlow. Finally, as discussed below, the relative amplitudes and voltage dependence of the different QOFF components are consistent with previous estimates of the charge and equilibrium properties of CC, OO, and CO transitions in the allosteric scheme (Figure 14).
Testing the Allosteric Voltage-gating Scheme
The relationship between Po and QOFFfast.
The allosteric model predicts that the fast component of OFF charge movement should be eliminated after voltage pulses that open all channels. One way to increase Po is by stepping to more positive voltages. Figure 8 A plots the time course of QOFF component development at +240 mV. The decay of QOFFfast is more complete than at +140 mV (Figure 7 F), consistent with a voltage-dependent increase in Po. It is likely that the fast component was not eliminated because, in the absence of Ca2+, mSlo channels are maximally activated only at very positive voltages (greater than +300 mV) (F = 23.8 µs,
M = 150 µs,
S = 822 µs), with the Fast component representing the majority of OFF charge (91%). However, the 20-ms record is well fit by a double-exponential function using only
M and
S. This confirms that the Fast component can be eliminated and that the relaxation of open channels back to the closed state contributes only to the Medium and Slow components of QOFF.
Voltage dependence of QOFF component amplitudes.
To further test the allosteric model, we examined the effect of repolarization voltage on the relative amplitudes of QOFF components. Ig was evoked in response to pulses of different duration to +160 mV (0.120 ms). After each pulse, the membrane was repolarized to either -80 or 0 mV, and OFF currents were analyzed as in Figure 7. The amplitudes of the three QOFF components are plotted versus pulse duration in Figure 8C and Figure D, for -80 and 0 mV, respectively. The component amplitudes were normalized to Qfast measured in response to a pulse from -80 to +160 mV because a 20% increase in this quantity was observed during the course of the experiment. In the absence of Ca2+, steady-state open probability at 0 mV is expected to be small (<10-4) (
The effect of voltage on the relative amplitude of Slow and Medium components of QOFF can be understood in terms of the allosteric gating scheme (Figure 14). According to the model, the Medium component represents open state (OO) transitions while the Slow component is limited by channel closing (OC). Therefore, QOFFmed reflects the voltage-dependent reequilibration of channels among open states. If the membrane is repolarized to a sufficiently negative voltage, QOFFmed will be maximal because open channels will rapidly occupy the leftmost open state (O0) before closing. Under these conditions QOFFslow will be small, representing only the charge moved during the transition from O0 to C0 (zL). However, if the membrane is repolarized to a less negative voltage, the open-channel equilibrium may favor occupancy of intermediate open states (Oi) rather than O0, and QOFFmed will be reduced. At the same time, QOFFslow will increase to reflect relaxation from Oi to the resting closed state (C0).
To examine the quantitative predictions of the allosteric scheme (Figure 14), it is convenient to compare the charge distributions predicted for Closed and Open channels (Figure 8 E, QC(V) and QO(V)). QC can be expressed in terms of the voltage-sensor equilibrium constant J(V) and charge zJ.
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(9) |
Therefore, QC(V) has the same shape as the QfastV relation, with a maximum amplitude of 2.2 e (4 zJ) when zJ = 0.55 e. QO(V) is determined by the open-channel voltage-sensor equilibrium constant (DJ), the voltage-sensor charge zJ, and the charge for the CO transition (zL = 0.4 e):
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(10) |
When D is assigned a value of 17, as in the preceding paper, the half-activation voltage for QO(V) is shifted by -130 mV relative to that of QC(V), indicating that voltage sensors are easier to activate when channels are open (G2.83 kT). The relative amplitudes of QOFFmed and QOFFslow predicted by the model are indicated by arrows in Figure 8 E at repolarization voltages of -80 and 0 mV. If voltage sensors equilibrate before channels close, the Medium OFF component evoked from an open channel can be expressed in terms of QO:
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(11) |
where VP is the pulse voltage and VR is the repolarization voltage. The Slow OFF component is determined by the difference of QO and QC.
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(12) |
As illustrated in Figure 8 E, the model predicts that QOFFslow will increase 1.93-fold when OFF charge is measured at 0 mV rather than -80 mV, similar to the 2.38-fold change observed in Figure 8C and Figure D.
Simulations of the allosteric model.
The results discussed thus far are qualitatively consistent with the behavior of the allosteric gating scheme (Figure 14). Simulations based on the model as shown in Figure 9, Figure 10, and Figure 11 also reproduce the major features of the data. However, the parameters that were ultimately used to fit Ig differ from those used to describe ionic currents (
In the preceding article, parameters for the allosteric scheme (Figure 14) were estimated based on fits to the GKV relationship, and the voltage dependence of both IK relaxation kinetics ((IK)-V) and the delay in IK activation (
t(IK)-V). The charge assigned to voltage-sensor movement (zJ = 0.55 e) was identical to that used here to fit the QfastV (Figure 4 A2) and
gFastV (Figure 4 B2) relationships. However, the half-activation voltage of the QfastV (Vh(J) = 155 mV) determined from gating current measurements is 10 mV more positive than previously estimated. Although this discrepancy is small, it is useful to consider several factors that could potentially contribute to such a difference. First, patch to patch variability is observed for both ionic and gating current data in the position of relationships such as the GKV and QfastV along the voltage axis (Figure 4; see also
t(IK)V relationship. Parameters were assigned to the model with the simplifying assumption that the rate constants for voltage-sensor movement (
, ß) are symmetrically voltage dependent (z
= -zß). Under this condition, with Vh(J) = 145 mV, the model reproduces the observation that the maximum delay is observed at approximately +153 mV (Vmax(
t)). However, the
gFastV relationship (Figure 4 B2) indicates that z
(0.33 e) is greater than -zß (0.22 e). Under this condition the predicted relationship between QV and
t(IK)V changes such that Vh(J) > Vmax(
t). Thus, Vh(J) is not merely determined by the
t(IK)V relationship but is also influenced by z
and zß. Finally, experimental conditions were different for IK and Ig measurements and might contribute to a real difference in channel gating. For example,
t(IK) was measured at a lower temperature (5°C) than Ig (2022°C). In Shaker K+ channels, decreased temperature has been shown to shift the QV relationship to more negative voltages (
Initial Ig simulations (Figure 9) were generated using parameters determined from a combination of ionic and gating current measurements. The parameters describing the RA transition for closed channels (zJ = 0.55, Vh(J) = 155 mV, z = 0.33, zß = -0.22) were determined from QfastV and
gFastV relationships as described above. The RA equilibrium for open channels was assumed to differ from that for closed channels by the allosteric factor D = 17, estimated in the preceding article. The rate constants for this transition were assumed to be symmetrically affected by channel opening such that the forward rate is increased f-fold (f=
) and the backward rate is decreased by the same factor. Rate constants for the CO transitions were identical to those used to fit the IK data at 20°C (
Figure 9 A plots a family of IgON evoked at different voltages and compares them to simulations of the allosteric scheme (solid lines). The model reproduces the fast decay and relative amplitudes of these ON currents. The amplitudes of fast gating currents are sensitive to filtering; therefore, the voltage command used in the simulation and the resulting current were filtered at 20 kHz to reproduce experimental conditions (see Materials and Methods). Figure 9 B plots a family of gating currents evoked at +140 mV in response to pulses of different duration (from Figure 5 A). The model (solid lines) reproduces the time course and relative amplitudes of ON and OFF currents in response to brief pulses.
The time constants of Fast and Medium charge movement (F and
M), predicted by the model, are plotted in Figure 9 C (solid lines). The
FV relationship is defined (
F = [
+ ß]-1) by the parameters assigned to the RA transition when the channel is closed, and is identical to the fit of the
gFast data in Figure 4, B2 and C2 (dashed lines).
gFast measured from simulated currents (Figure 9 C, solid symbols) superimposes on
F, confirming that exponential fits to fast Ig can be used to estimate the properties of closed-channel voltage-sensor movement. Similarly, the QfastV relationship, determined from these fits, superimposes on the QCV relationship (Figure 9 D) defined by the model (Equation 9).
The MV relationship predicted by the model is the same shape as the
F V but is shifted to more negative voltages owing to the allosteric interaction between channel opening and voltage-sensor movement (
M = (
f + ßf/D)-1). Measurements of
M from several experiments (Figure 9 C, open symbols) are similar to those predicted by the model, consistent with the assumption that the forward and backward rate constants for voltage-sensor activation are symmetrically affected by channel opening (i.e., f=
=4.13). A better fit to the data is obtained if f is increased to 4.8 (dashed line) but, given the limited number and voltage range of
M measurements, we continue to assume f = 4.13 in the following simulations. The similar voltage dependence of the
M and
F data supports the conclusion that both Fast and Medium components of OFF charge represent voltage-sensor movement.
In addition to reproducing Ig in response to brief pulses, the model exhibits a slowing of IgOFF with increased pulse duration (Figure 9 B). However, this effect is more prominent in the data, suggesting that the model underestimates the amount of slow charge movement. To examine the time course and magnitude of slow charge predicted by the model, IgON was simulated in response to 20-ms pulses to different voltages and then integrated to obtain QON(t) (Figure 9 E, solid lines). The time course of QON is biphasic and the fast component matches the data (Qp(t); Figure 9 E, symbols), but the slow component is too small, especially at lower voltages. One possible explanation for this underestimate of QpSlow is that the model underestimates the number of channels that open at different voltages. In other words, the shape of the PoV relationship and/or its position along the voltage axis may not be accurately reproduced. Since the GKV relationship was well fit by the allosteric scheme in the preceding paper, this situation could occur if channel opening is enhanced under the ionic conditions where Ig is measured. To test this possibility, we further analyzed the voltage dependence and kinetics of the different charge movement components.
Estimating Po from charge movement.
The allosteric model predicts that slow changes in both ON and OFF charge movement components are related to channel opening and closing. Therefore, the amplitudes of these components are related to open probability as well the charge distribution for open (QO) and closed (QC) channels. For example, the fast component of OFF charge depends on QC and the number of closed channels at the end of a voltage pulse (1 - Po):
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(13) |
For a particular pulse voltage (VP) and holding potential (HP), the second term in this expression can be determined by measuring the fast component of ON charge:
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(14) |
Therefore, Po can be estimated by comparing fast components of ON and OFF charge:
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(15) |
Figure 10 A plots the steady-state PoV relationship estimated in this way for three experiments where QOFFfast(VP) was measured after a 20-ms pulse and QONfast(VP) was determined from an exponential fit to IgON (i.e., Qfast). Although measurements are scattered, reflecting, in part, the previously noted difficulties in separating QOFF components, the data generally follow the shape of the PoV relationship predicted by the original model parameters (Figure 10 A, Case A) but are shifted to more negative voltages. Two additional PoV relationships (Cases B and C) are superimposed on the data and will be used throughout this analysis. Case B indicates the prediction of the allosteric scheme (Figure 14) when the equilibrium constant L is increased 12-fold (equivalent to G = 2.5 kT) while leaving the other parameters unchanged. The PoV relationship indicated by Case C is roughly the same shape as Case A but is shifted along the voltage axis. Case C was not generated by a gating scheme but can be used in combination with the QC and QO relationships defined by the original model to make predictions about the voltage dependence of different charge movement components. As discussed below, various aspects of the data are consistent with these altered PoV relationships.
The predicted amplitude of the slow component of OFF charge is directly proportional to Po:
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(16) |
Figure 10 B plots normalized QOFFslow versus voltage for the same experiments as in Figure 10 A. Again, the data follow the general shape of the PoV relationship predicted by Case A but appear shifted to more negative voltages. The model relationships were generated from the above expression for QOFFslow where Po was specified by Case A, B, or C in Figure 10 A and QO and QC were determined from the parameters assigned to the original model as illustrated in Figure 8 E. The data and model traces were normalized to the total fast charge movement QTfast for each experiment. According to the model QTfast = 4zJ, therefore, the maximum amplitude of the normalized data should be [QO(HP) - QC(HP)]/4zJ. That the data fall within the amplitude range predicted by the model is therefore consistent with the relative amplitudes of QO(HP), QC(HP), and zJ specified in the model.
The Medium component of OFF charge is larger and therefore easier to measure than QOFFslow but its voltage dependence is determined by QO(V) as well as Po(V):
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(17) |
Figure 10 C compares the normalized QOFFmedV relationships to the model predictions. Again, the data plots are similar in shape and magnitude to the prediction of Case A but are shifted to more negative voltages. Both data and model predictions were normalized to QTfast as in Figure 10 B such that the maximum amplitude should be [QO(VP) - QO(HP)]/4zJ. Therefore, the magnitude of QOFFmed is consistent with QO(V) and zJ specified in the model.
The amplitude of the data and model predictions in Figure 10A, Figure B, and Figure C, as noted above, are influenced by several factors in addition to Po. These include model parameters (QO(V), QC(V), zJ, zL) as well as our ability to separate QOFF components and determine QTfast. To better examine the voltage dependence of the data, IgOFFmedV relationships from several experiments were normalized together with the model predictions to a maximum amplitude of one (Figure 10 D). IgOFFmed is proportional to QOFFmed, so the model relationships represent normalized versions of those used in Figure 10 C. IgOFFmed was normalized based on a Boltzmann fit to the IgOFFmedV relationship for each experiment (z = 0.98 e). When scaled in this way, the data from different experiments superimpose. Case C represents a Boltzmann fit to these normalized data (z = 0.98 e, Vh = 121 mV). The PoV relationship for Case C (Figure 10 A) was derived from this fit and the expression for QOFFmed (Equation 17).
The slow component of ON charge movement (QpSlow) should exhibit a complex voltage dependence that is determined by Po(V), QC(V), and QO(V):
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(18) |
The QpSlowV relationships plotted in Figure 10 E were normalized by QTfast and exhibit amplitudes that are larger than predicted by Case A, but are similar to those specified by Cases B and C. The model predicts that QpSlow will have a bell-shaped voltage dependence and that QpSlow/QTfast approaches a limiting value of zL/4zJ at positive voltages (Figure 10 E, dashed line). Our measurements do not extend to high enough voltages to test these predictions. However, the data fall close to the relationships determined by Cases B and C over the voltage range tested, and appear to trend downward at the highest voltages. Importantly, the comparison of QpSlowV relationships for Cases A, B, and C demonstrate that the amount of slow charge movement is highly sensitive to Po and that QpSlow can be considerably larger than the charge associated with the CO transition.
Finally, we examined the ability of the model to reproduce slow charge movement kinetics. Figure 10 F plots gSlow over a large voltage range. At positive voltages,
gSlow was measured from the time course of development of the Medium component of IgOFF as in Figure 7 G. At negative voltages,
gSlow was determined from the relaxation of Slow QOFF(t) (
S). The dashed line in Figure 10 F represents a fit of the allosteric scheme (Figure 14) to the time constants of IK relaxation (
(IK)), measured in the preceding paper (equivalent to Case A).
gSlow is faster than
(IK) for V > ~+100 mV and is slower than
(IK) at negative voltages. However, the voltage dependence of
gSlow can be fit (Figure 10 F, solid line) by adjusting the model parameters as specified for Case B where the equilibrium constant L is increased 12-fold. Both
gSlow and
(IK) are weakly voltage dependent from -80 to 0 mV, consistent with the idea that the slow relaxation of QOFF is limited by channel closing.
Taken together, the data in Figure 10 support the hypothesis that the properties of slow charge movement can be accounted for by the allosteric voltage-gating scheme (Figure 14), provided we assume that Po is increased under the conditions where gating currents are measured. Coordinated changes in all three components of QOFF are observed with pulse voltage, consistent with the assumption that their amplitudes depend upon the PoV relationship. The relative amplitudes of these components are also consistent with their proposed source in terms of the allosteric scheme and with the charges assigned to various transitions in the model. The voltage dependence of the Medium OFF component suggests that the PoV relationship may be similar in shape to that measured with ionic currents (Case A) but is shifted to more negative voltages (Case C). The Fast and Slow component data are consistent with this hypothesis but are inadequate to test the precise voltage dependence of Po. The data are also insufficient to specify how the model parameters should be altered to account for a change in Po. Case B, assuming a 12-fold increase in the equilibrium constant L, provides a reasonable first approximation that can account for both a shift in the PoV relationship as well as the observed kinetics of slow charge movement.
Simulations of the modified allosteric scheme.
When the CO transition rates in the allosteric scheme (Figure 14) are modified, as specified by Case B, improved fits to the gating currents are generated. Figure 11A and Figure B, compares simulated currents to Ig evoked at +140 and +224 mV in response to pulses of different duration. The model accurately reproduces the amplitudes of ON and OFF currents, including the decrease in IgOFF amplitude that occurs with increased pulse duration at +224 mV (Figure 11 B). The model also fits the time course of IgOFF and accounts for the slowing of decay kinetics that accompanies increased pulse duration (Figure 11A and Figure B). The time course of OFF charge relaxation (QOFFQOFFss) after +140 mV pulses are plotted on a semilog scale in Figure 11 C, and are well fit at all pulse durations. Thus, the model accurately reproduces the kinetics and amplitudes of the three OFF components. The model can account for the slow time constants of both ON and OFF charge movement at all voltages (Figure 10 F); however, the amplitude of QpSlow is underestimated at low voltages (Figure 10 E, Case B). This point is illustrated in Figure 11 D, which compares Qp(t) at different voltages to QON(t) generated by the model. Both the time course and amplitude of Qp are well fit at V +140 mV; however, the slow component predicted by the model at lower voltages is reduced in comparison to the data.
Simulation of gating admittance. To further test the above conclusions, gating currents were simulated in response to a sinusoidal voltage command and compared with admittance analysis results. The CgV relationship is compared with the simulations for Cases A and B (solid lines) in Figure 11 E. Dashed lines indicate the QO'V and QC'V relationships specified by the model. These relationships are the main determinants of CgV since they reflect fast voltage-sensor movement. At voltages below +100 mV where channels are closed, Cg approximates QC'. At higher voltages, Cg represents an average of QC' and QO' weighted by Po. Thus, Cg decreases at positive voltages (approaching QO') when Po is increased (compare Cases A and B). Case A overestimates Cg, suggesting that it underestimates Po. However, as the PoV relationship is shifted (Case B), the model better approximates the peak amplitude and peak voltage of Cg. The effect of Po on the shape of the CgV relationship explains why the mean peak voltage of Cg (+127 mV) is more negative than the half-activation voltage of the QfastV relationship (+155 mV).
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Discussion |
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Examination of gating currents evoked from mSlo Ca2+-activated K+ channels in the absence of Ca2+ has revealed several components of charge movement associated with voltage-dependent gating. We have shown that these results are consistent with an allosteric voltage-gating scheme (Figure 14) that was proposed in the preceding article to account for the kinetic and steady-state properties of mSlo IK in 0 Ca2+ (
Previous Models of BK Channel Gating
BK channel gating has been extensively studied at the single channel level (
A model of BK channel gating has been proposed by
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As in the McManus and Magleby model (1991), Figure 15 contains many states representing different Ca2+-bound versions of the closed and open conformation. However, in the absence of Ca2+, Figure 15 reduces to a two-state model with a single voltage-dependent transition between a unliganded closed and open state (highlighted above). By assuming that voltage-dependent activation can be described by a two-state mechanism, Figure 15 implies that channel opening, voltage-sensor movement, and changes in Ca2+ binding-site affinity all occur during a concerted allosteric transition. Our results demonstrate that a more complicated scheme is required to explain voltage-dependent gating and therefore imply that the interaction of Ca2+ with the channel may also be more complicated than proposed in Figure 15 (see
The preceding paper examines several properties of mSlo IK that are inconsistent with a two-state model of voltage gating (
Fast Ig: Evidence for a Two-state Model of Voltage-sensor Movement
Although the overall response of mSlo channels to voltage is complex, gating currents suggest that the movement of individual voltage sensors can be described by a simple two-state model when channels are closed.
Ig evoked during a voltage step exhibits a prominent fast component (IgFast) representing a majority of ON charge. This fast charge is also detected as a voltage-dependent component of membrane capacitance measured in response to a sinusoidal voltage command, thereby ruling out the possibility that leak subtraction or voltage clamp artifacts contribute to rapid current transients measured in response to large voltage steps. Both admittance analysis and the response to voltage steps indicate that fast gating charge can move at voltages where Po is normally low, and relaxes roughly 100-fold faster than the time constant of IK activation. IgFast decays with exponential kinetics during a time when few channels have opened. The relaxation of OFF current is also fast and single-exponential after brief pulses that open few channels. These results demonstrate that closed unliganded mSlo channels can undergo rapid voltage-dependent transitions.
Because the majority of ON charge moves rapidly, we assume that IgFast can be attributed to voltage-sensor movement. The exponential kinetics of IgFast and lack of a rising phase are consistent with a two-state model in which voltage sensors undergo a transition between a resting (R) and activated (A) conformation. The observation that the QfastV relationship is fit by a single Boltzmann function also supports a two-state model. In addition, the time constant of fast Ig relaxation (gFast) exhibits a bell-shaped voltage dependence that can be fit by the inverse sum of two exponential functions, as predicted for a two-state model in which forward and backward rate constants are voltage dependent.
mSlo channels assemble as homotetramers (
The Coupling of Voltage-sensor Movement to Channel Activation
Since the decay of IgFast is much faster than the activation of IK, we considered the possibility that fast charge movement might be unrelated to channel activation. An early component of charge movement has been described in Shaker K channels ( < 10 µs, Na channel:
< 25 µs) and represent <10% of the total gating charge. The speed and small magnitude of this early charge movement suggest it could represent transitions that are not important for channel activation. IgFast described for mSlo is only severalfold slower than these early components and exhibits a similar equivalent charge. However, in the case of mSlo, several lines of evidence support the idea that fast charge movement is coupled to channel activation.
In contrast to the "early" charge movement in Shaker and Na channels, IgFast represents a majority of ON charge (Figure 6 B). In addition, the estimated fast charge per channel Qfast = 4zJ = 2.36 e (assuming independent voltage sensors) is similar to the equivalent charge that characterizes the maximum voltage dependence of Po in 0 Ca (z(Po) = 2.0 e; Horrigan et al., 1999). Thus, the magnitude of IgFast is consistent with the idea that fast charge movement is important for mSlo channel activation.
The kinetic relationship between IgFast and IK also argues that fast charge movement reflects transitions in the activation pathway. Fast charge movement and the delay in IK activation occur on similar time scales. An example in Figure 3 D shows that IgON decays at the same time that IK achieves an exponential time course. Thus, the achievement of a maximal rate of IK activation appears correlated with equilibration of fast gating charge. IK also exhibits a multiexponential rate of increase during the delay (t) should be roughly proportional to
gFast (
gFast (Figure 4) and
t (
Finally, the QfastV and PoV relationships, defining the voltage dependence of fast charge movement and IK activation, respectively, activate over a similar voltage range, consistent with the idea that these two processes are coupled. We have also shown that the normalized GKV relationship can be approximated by raising the QgV relationship to the 4th power (Figure 1 B). As discussed below, an approximate 4th power relationship between QfastV and PoV is predicted by many schemes that assume Po is enhanced by the activation of four voltage sensors. The relationship between QV and GV is an important test of any voltage-dependent model, but experimental factors limit the interpretation of these data in the case of mSlo. The precise relationship because QV and GV is unclear, owing to the likelihood that gating is altered under the conditions where gating currents are measured.
Sequential Voltage-gating Schemes
Taken together, the above observations indicate that the conformational changes underlying fast charge movement are involved in mSlo channel activation. Therefore, any plausible gating scheme must include a pathway that allows rapid voltage-dependent transitions to occur before channels open. The properties of fast charge movement are consistent with these closed-state transitions, arising from the activation of four independent and identical voltage sensors. Two sequential gating schemes incorporating such a mechanism are considered below (Figure 14 and Figure 15) and can reproduce many features of fast charge movement, but can be ruled out based on their failure to account for slow charge movement. These arguments parallel those in the preceding paper based on IK measurements (
One of the simplest schemes that can account for the properties of IgFast is the Hodgkin-Huxley (HH) model (Figure 16).
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The HH scheme assumes channels are open when all four voltage sensors are activated and predicts a 4th power relationship between the QV and GV relationships:
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(19) |
where Q represents the normalized charge distribution defined by the equilibrium constant for voltage-sensor activation (Q = J/(1 + J)). As noted previously, the observed relationship between QgV and GKV appears consistent with this prediction. However, Figure 16 is inadequate because it cannot account for the presence of both fast and slow components of mSlo charge movement. Similarly, the HH scheme cannot reproduce both the brief delay and slow exponential relaxation that characterize IK activation kinetics (
Models that assume voltage-sensor activation is followed by a distinct opening transition have proven useful in describing the behavior of channels that deviate from the predictions of the HH scheme (
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Figure 17 predicts an approximate 4th power relationship between GV and QV described by the expression
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(20) |
where QC, the closed channel charge distribution, defines the voltage dependence of fast charge movement (QC = J/(1 + J)). As illustrated in Figure 12 A, this model can approximate the observed relationship between the QfastV and GKV for mSlo. Figure 17 can also account for a slow component of ON charge movement (Figure 12 B) but, as discussed below, cannot reproduce some important aspects of gating current behavior. Similarly, Figure 17 can approximate the time course of mSlo IK but does not account for the complex voltage dependence of IK relaxation kinetics and open probability (
The Slow Component of ON Charge Movement
A slow component of ON charge movement (QpSlow) is detected as an increase in QOFF after pulses of increasing duration. QpSlow develops with the exponential kinetics of IK activation at depolarized voltages, suggesting that activation and slow charge movement are limited by the same transitions. We have shown that the allosteric voltage-gating scheme (Figure 14) can reproduce both the kinetics and voltage dependence of QpSlow (Figure 10E and Figure F). An important conclusion of this analysis is that QpSlow represents not only charge moved during the CO conformational change but a reequilibration of voltage sensors that is limited by channel opening. The allosteric model predicts that transitions among open states (OO) can contribute to slow charge movement, since voltage sensors reequilibrate after channels have opened. However, a contribution of voltage-sensor activation to slow charge movement does not require a model with multiple open states.
Figure 17 provides an example of a mechanism by which closed-state transitions contribute to both fast and slow charge movement. Fast Ig is evoked as voltage sensors initially equilibrate between resting (R) and activated (A) while the channel is closed. As channels open, this equilibrium is perturbed because channels can only open when all four voltage sensors are activated. In other words, opening stabilizes the activated voltage sensor, as in the allosteric model. However, in the case of Figure 17, the establishment of a new voltage-sensor equilibrium can only involve transitions between R and A while the channel is closed.
Figure 17 can reproduce the time course of Qp measured at +140 mV, including a large slow component (Figure 12 B). In addition, Figure 17 predicts a QpSlowV relationship (Figure 12 C, solid lines) similar to that produced by the allosteric model (Figure 12 C, dashed lines). As with the allosteric scheme (Figure 14), a portion of QpSlow represents the charge assigned to the CO transition (z = 0.32 e). The bell-shaped voltage dependence of QpSlow predicted by Figure 17 demonstrates that closed-state transitions also contribute to slow charge movement.
In summary, the presence of fast and slow components of ON charge, and their relationship to the time course of IK activation, suggest that the activation pathway must, at minimum, contain a rate-limiting step that is preceded by one or more rapid voltage-dependent transitions. The kinetics and voltage dependence of IgFast and the delay in IK activation, the voltage dependence of Qfast and GK together with the tetrameric structure of the channel further suggest that the rapid transitions may be described by the movement of four independent and identical voltage sensors. Therefore, Figure 17 provides the simplest model that can account for these basic features of the ionic and ON gating current data. However, as discussed below, the properties of OFF charge movement are inconsistent with Figure 17 and indicate that the activation pathway must include multiple open states.
OFF Charge Movement: Evidence for Multiple Open States
OFF currents, recorded after brief voltage pulses, decay with a single-exponential time course. Such a response is predicted by Figure 17 and is consistent with activated voltage sensors relaxing rapidly back to a resting state when channels are closed. However, Figure 17 also predicts that, once channels open, the decay of IgOFF will be limited by the speed of channel closing (
Contrary to the prediction of Figure 17, we observed three components of OFF charge movement. The Fast and Slow components are analogous to those predicted by Figure 17. However, the Medium component, representing a majority of QOFF when channels are maximally activated, provides evidence that channels can undergo transitions among open states. In response to pulses of increasing duration, QOFFfast decreases with approximately the same time course as IK activation while the two slower components, QOFFmed and QOFFslow, increase in parallel. QOFFfast is essentially eliminated under conditions that maximally activate mSlo channels (20 ms at +160 mV in 60 µM Ca2+; Figure 8 B), implying that the Slow and Medium components reflect the relaxation of open channels back to the resting closed state.
We have proposed that the relaxation of the Slow OFF component is limited by the speed of channel closing and, at -80 mV, primarily represents charge moved during the OC conformational change. QOFFslow represents a minority of the total OFF charge (Figure 10 B), consistent with the notion that the OC transition is weakly voltage dependent. Similarly, the time constants of slow charge movement (gSlow) and IK deactivation (
(IK)) are weakly voltage dependent at negative voltages (Figure 10 F). However, the decay of the Slow component is approximately threefold slower than that of potassium tail currents. To account for this difference, we have suggested that channel closing is slowed under the ionic conditions that are used to measure gating currents. The
gSlowV relationship is similar in shape to the
(IK)V relationship and can be fit by the allosteric model if the forward rate constants from C to O are increased while the backward rates are decreased relative to those used to describe IK. Such a change requires a 12-fold increase in the CO equilibrium constant (
G = 2.48 kT), producing a change in the PoV relationship that appears consistent with the observed voltage dependence of QOFF components and QpSlow (Figure 10, Case B).
The Medium component of OFF charge relaxes ninefold faster than the Slow component and threefold faster than IK tail currents. Thus, regardless of the effect of ionic conditions on channel gating, the Medium component appears to relax faster than channel closing, implying that voltage sensors can move when channels are open. The similar voltage dependence of M and
F (Figure 4 B2 and 9 C) supports the idea that the Medium component represents voltage-sensor movement. Thus, any plausible gating scheme must include multiple open states with rapid voltage-dependent transitions between them. The voltage dependence of Po leads to the same conclusion (
A Sequential Scheme with Multiple Open States
A sequential scheme, represented in general form below (Figure 18), could account for Medium and Slow components of OFF charge relaxation, provided transitions among open states are fast compared with the transition from O to C.
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However, such a model is inconsistent with the voltage dependence of steady-state activation. Po is weakly voltage dependent at limiting negative voltages, consistent with a charge of 0.4e assigned the CoOo transition in the allosteric scheme (
Figure 18 also appears inconsistent with the relative amplitudes of various ON and OFF charge movement components. For example, we observe that the Medium component of OFF charge is two- to threefold larger than the Slow component measured at -80 mV (Figure 7 E and 8 A). Thus,
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(21) |
In addition, the fast component of ON charge is larger than the slow component at all voltages studied:
![]() |
(22) |
It can be shown (below) that Figure 18 cannot account for these observations if Equation 21 and Equation 22 are valid at voltages where Po 1/2. This last condition cannot be verified directly, but appears reasonable since Equation 21 and Equation 22 are true at +224 to +240 mV (Figure 6 B and 8 A), whereas the half-activation voltage of the GKV relationship is +190 mV (
The amplitudes of the different charge movement components for either the allosteric model or Figure 18 can be expressed in terms of QC, QO, and Po as specified by Equation 11Equation 12Equation 13Equation 14Equation 15Equation 16Equation 17Equation 18. Therefore, by substituting Equation 11 and Equation 12, Equation 21 can be rewritten:
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(23) |
where V is the pulse voltage and HP is the holding potential (-80 mV). Solving for QO(V), we obtain:
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(24) |
Equation 22 can also be rewritten by substituting Equation 14 and Equation 18.
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(25) |
Combining Equation 24 and Equation 25:
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(26) |
For a sequential model like Figure 18, we can further assume:
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(27) |
Finally, combining Equation 26 and Equation 27:
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(28) |
Equation 28 reduces to Po(V) < 1/2, indicating that Figure 18 cannot account for the relative amplitude of ON and OFF charge components while also assuming Po 1/2.
The Allosteric Voltage-gating Scheme
Figure 18 assumes that closed- and open-state transitions occur sequentially and must therefore represent distinct conformational events. An alternative, represented by the allosteric model, is that CC and OO transitions represent the same conformational events, i.e., voltage-sensor movement. The kinetics and voltage dependence of the Fast and Medium components of OFF charge movement (Figure 9 C) are consistent with both CC and OO transitions representing voltage-sensor movement, differing only in that the equilibrium constant for voltage-sensor activation is increased when channels open. As demonstrated in this study and in the preceding article, the allosteric model can account for many other properties of mSlo gating in 0 Ca2+.
The allosteric model is mechanistically similar to Figure 17 in that it assumes channels undergo only two types of conformational change: voltage-sensor activation and channel opening. Voltage sensors are assumed to move rapidly and independently in each subunit. Channel opening is relatively slow, weakly voltage dependent, and assumed to represent a concerted transition. Like Figure 17, the allosteric model assumes channel opening stabilizes the activated voltage sensor. Thus, opening results in a slow component of charge movement that is limited by the speed of channel opening but largely represents voltage-sensor charge movement. Unlike Figure 17, the coupling of voltage-sensor activation to channel opening is not an obligatory process but rather an allosteric interaction. Therefore, voltage sensors can move when channels are open, accounting for the Medium component of IgOFF, and channels can open when voltage sensors are not activated, accounting for the weak voltage dependence of Po measured at negative voltages (
Although the allosteric model allows channels to open when voltage sensors are in a resting state, it predicts that they are most likely to open when all four are activated. Consequently, channels pass through multiple closed states before opening, consistent with the presence of a delay in IK activation (
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(29) |
When L is small and D >> 1, as determined in the preceding article (L = 2 x 10-6, D = 17, 0 Ca2+), this expression can be approximated as:
![]() |
(30) |
Finally, the allosteric scheme can account for the presence of three components of OFF charge movement as well as the relative amplitudes of various ON and OFF components. In contrast to Figure 18, the allosteric model predicts that pathways traversed during channel activation and deactivation are different. Activation involves fast voltage-sensor movement as channels undergo closed-state transitions before opening. Deactivation involves movement of the same voltage sensors as channels undergo open-state transitions before closing. Because the same voltage sensors are moved during open- and closed-state transitions, the rapid components of ON (Qfast) and OFF charge (QOFFfast, QOFFmed) are of similar amplitude while the slow components are smaller. Furthermore, the relative amplitudes of QOFFmed and QOFFslow change with repolarization voltage in a manner specifically predicted by the allosteric scheme (Figure 8C and Figure D).
Comparison with Previous Studies of BK Channel Gating
mSlo ionic currents.
The gating current data support the conclusion from the preceding paper that mSlo channel voltage gating in the absence of Ca2+ can be described by an allosteric scheme. Indeed, many of the model parameters that were derived to fit IK data required little or no adjustment to describe the gating currents (e.g., zJ, Vh(J), zL, D). One feature of the model that could not be determined accurately from IK measurements was the speed of transitions among open states. The Medium component of IgOFF provides a direct assay of these transitions and demonstrates that channel opening slows the relaxation of voltage sensors from A to R. The magnitude of this effect is consistent with our previous estimate of the allosteric factor D = 17, provided we assume channel opening almost symmetrically affects the forward and backward rate constants for the RA transition (Figure 9 C). However the effect of channel opening on the forward rate was not measured; therefore, the value of D cannot be directly determined from the gating current data.
Single channel studies.
Many of the properties of IK that implicate a model with multiple open states are observed only at extreme voltages (
Gating currents.
BK channel gating currents have been described previously for hSlo by = 57 ± 10 µs, at +200 mV). A slow component of charge movement was also detected but not examined in detail. The QV curve determined with brief 1-ms depolarizations was well fit by a Boltzmann function (z = 0.6 e, Vh = 190 ± 15 mV). In addition, the GV curve was reported to be steeper than the QV, and charge movement was observed at voltages where most channels should be closed.
In addition to these similarities, there are important differences between our results and conclusions and those of
Some of the discrepancies between our results and those of
Cs+ permeates BK channels poorly, allowing Cs+ currents to be recorded in patches where IK would be immeasurably large (
hSlo gating currents were also measured in the presence of internal Cs+, using isotonic external TEA to block the channel. Therefore, the use of Cs+ has the apparent advantage of allowing gating and ionic currents to be recorded with the same internal solution. However, the presence of internal Cs+ does not guarantee that channels gate identically when blocked by TEA or conducting Cs+. Aside from the possibility that TEA directly affects gating (see below), TEA may inhibit the effect of Cs+.
As discussed previously, mSlo gating may also be affected by the presence of external TEA, internal NMDG, or the absence of K+ in experiments measuring gating currents. Several properties of slow charge movement summarized in Figure 10 suggest that mSlo channels open more readily under the conditions where gating currents were measured. A 10-fold reduction in internal and external K+ had no appreciable effect on the GKV (data not shown) but we cannot rule out the possibility that gating is altered by the complete removal of K+ or its replacement with NMDG.
Another factor that could contribute to an apparent cross-over between QV and GV is the duration of the voltage pulses used to measure gating currents. The QV for hSlo was determined using 1-ms pulses and is therefore similar to Qfast and not a steady-state measurement.
Despite uncertainties as to the precise relationship between the QV and GV, gating currents recorded for both mSlo and hSlo show that most charge movement in 0 Ca2+ is fast, indicating that most charge moves before channels open. The kinetics and voltage dependence of the delay in IK activation are also consistent with the idea the multiple voltage-dependent closed-state transitions, accounting for the bulk of charge movement, occur before channels open. Finally, the change in delay duration with prepulse voltage (Cole-Moore shift [
Detection of Allosteric Voltage Gating
In the preceding article (
Many of the gating current properties described here for mSlo can also be accounted for by sequential gating schemes containing a single open state such as Figure 17. However, deviations from the prediction of Figure 17 are more obvious for gating current than for ionic current. The Medium component of OFF charge movement, in particular, provides a direct indication of open-state transitions. Many voltage-gated K+ channels such as Shaker exhibit OFF currents that become slower as pulse duration is increased and channels open (
Two factors allow open-channel charge movement to be detected for mSlo. First, voltage-sensor movement is much faster than channel closing. This difference allows the Medium and Slow components of OFF charge movement to be distinguished and allows open-state transitions to occur before channels close. As discussed below, the relative speed of Ig and IK in channels such as Shaker might prevent detection of open-state transitions. Another factor that is important for detecting open-state transitions is the open-state charge distribution (QO). That is, the voltage dependence of open-state transitions must be such that repolarization to the holding potential causes a redistribution of channels among open states. The effect of repolarization voltage on QOFF components in Figure 8 shows that the Medium component is sensitive to the open-channel charge distribution. Therefore, a change in the voltage dependence of QO might alter the ability to detect open-state transitions. For example, if the allosteric factor D is increased, QO will be shifted to more negative voltages such that QOFFmed measured at -80 mV is reduced.
Figure 13 shows that a slowing of voltage-sensor kinetics reduces the ability to detect open-channel charge movement. IK and Ig were simulated in response to a 20-ms pulse to +240 mV as the forward and backward rates for voltage-sensor movement (, ß) were both slowed 10-fold (10x) or 30-fold (30x) relative to those describing mSlo (1x). CO transition rates and all equilibrium constants were unchanged (relative to Case B parameters). As voltage-sensor movement is slowed, the delay in IK activation increases (Figure 13 A) and gating currents are slowed (Figure 13 B). Under these conditions, IK and Ig resemble those evoked from a channel such as Shaker where IK activation kinetics are sigmoidal and ionic and gating currents relax on a similar time scale. Interestingly, a 30-fold slowing of voltage sensor movement also produces a "hook" in IgOFF, a feature that is also observed in Shaker Ig (
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Acknowledgements |
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This work was supported by a grant from the National Institutes of Health (N153294) and by a National Institute of Mental Health Silvio Conte Center for Neuroscience Research grant (MH48108). R.W. Aldrich is an investigator with the Howard Hughes Medical Institute.
Submitted: March 16, 1999; Revised: June 1, 1999; Accepted: June 7, 1999.
1used in this paper: BK channel, large-conductance Ca2+-activated K+ channel; NMDG, N-methyl-D-glucamine; TEA, tetraethylammonium
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