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Copyright © 1999 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 76, Issue 4, 1959-1971, 1 April 1999

doi:10.1016/S0006-3495(99)77355-8

Channels, Receptors, and Transporters

Blockade of HERG Channels Expressed in Xenopus laevis Oocytes by External Divalent Cations

Won-Kyung Ho^*, , Injune Kim^#, Chin O. Lee^#, Jae Boum Youm^*, Suk Ho Lee^* and Yung E. Earm^*

^* Department of Physiology, Seoul National University College of Medicine, Seoul 110-799, Republic of Korea
^# Department of Life Science, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea

Address reprint requests to Won-Kyung Ho, M.D., Ph.D., Department of Physiology, Seoul National University College of Medicine, Yonkeun-Dong, Chongno-Ku, Seoul 110-799, Republic of Korea. Tel.: 82-2-7408227; Fax: 82-2-7639667.

The human ether-a-go-go related gene (HERG), has recently been found to encode a voltage-gated K⁺ channel with properties nearly identical to a cardiac delayed rectifier K⁺ current, I_Kr (Sanguinetti et al,Trudeau et al). I_Kr plays a fundamental role in cardiac excitability by contributing to repolarization and thereby regulating action potential duration (Noble and Tsien, 1969,Sanguinetti and Jurkiewicz, 1991). In sinoatrial node cells of the heart, the decay of I_Kr also contributes to pacemaker depolarization (Brown et al,Brown and DiFrancesco, 1980,Irisawa et al). Tissue distribution study shows that the erg-related gene is abundant in a wide variety of tissues, suggesting that it plays an important role in other tissues (Wymore et al). The functional role of HERG channels in noncardiac tissues is not yet fully understood. Recently, it has been shown that HERG encodes an inward rectifying K⁺ channel (I_IR) in a variety of tumor cell lines, and a role of I_IR in neoplastic transformation and cell proliferation was suggested (Arcangeli et al,Bianchi et al). The same group had previously observed that in neuroblastoma cells resting membrane potential (V_REST) is much lower and varies widely (−40–10mV) compared to normal cells, and found that the scattering of V_REST correlates with the scattering of the voltage dependence of I_IR (Arcangeli et al). These results indicate that the biophysical property of I_IR is responsible for determining the characteristic feature of V_REST.

Although HERG belongs a family of voltage-dependent K⁺ channels, its electrophysiological characteristics are quite distinct from those of other voltage-dependent K⁺ channels. A fully activated current-voltage relationship shows strong inward rectification, and its mechanism has been investigated by many authors, showing that it is attributable to a rapid voltage-dependent inactivation mechanism (Shibasaki, 1987,Smith et al,Spector et al). However, the activation mechanism has not been investigated widely, but was considered in general not to be different from that of other voltage-dependent channels. Recent studies have shown that the voltage dependence of the HERG channel activation is affected sensitively by the concentration of external Ca²⁺ and Mg²⁺. The same observation had been made for I_Kr in sinoatrial cells (Ho et al), and for I_IR in neuronal cells (Faravelli et al). From these reports it can be proposed that the high sensitivity of the voltage dependence of activation to external Ca²⁺ and Mg²⁺ is one of characteristic features that distinguish the HERG channel from classical inward rectifier channels. Ho et al interpreted this effect by using a voltage-dependent block model originally proposed by Woodhull, 1973, and suggested that the voltage dependence of HERG in physiological conditions is mainly determined by the voltage dependence of the channel block by Ca²⁺, rather than by the intrinsic gating whose voltage dependence lies at very negative potentials (Zou et al). However, it has still not been determined whether this effect is specific to Ca²⁺ and Mg²⁺. In the present study we investigated the effect of various divalent cations (Ba²⁺, Sr²⁺, Mn²⁺, Co²⁺, Ni²⁺, Zn²⁺) on the activation of HERG, and found that all of them modify HERG channel activation, but with different characteristics. We have evaluated various possible mechanisms in the Discussion.

Complementary RNA of HERG was synthesized by in vitro transcription from 1μg of linearized cDNA using T7 mMessage mMachine kits (Ambion, Austin, TX) and stored in 10mM Tris-HCl (pH 7.4) at −80°C. Stage V–VI oocytes were surgically removed from female Xenopus laevis (Nasco, Modesto, CA) anesthetized with 0.17% tricaine methanesulfonate (Sigma). Following suture, frogs were allowed to recover in isolation in a tank. Theca and follicle layers were manually removed from the oocytes by using fine forceps. Oocytes were then injected with 40 nl cRNA (0.1–0.5μg/μl). After injection, oocytes were maintained in modified Barth's solution containing (in mM): 88 NaCl, 1 KCl, 0.4 CaCl₂, 0.33 Ca(NO₃)₂, 1 MgSO₄, 2.4 NaHCO₃, 10 HEPES (pH 7.4), supplemented with 50μg ml⁻¹ gentamicin sulfate. Currents were studied 2–7 days after injection.

Ringer's solution contained (in mM): 96 NaCl, 2 KCl, 0.5 CaCl₂, and 5 HEPES (pH adjusted to 7.4 with NaOH). The concentrations of BaCl₂, NiCl₂, SrCl₂, MnCl₂, CoCl₂, NiCl₂, and ZnCl₂ were varied as indicated in each experiment without changing the concentration of other chemicals. Currents were measured at room temperature (21–23°C) with a two-electrode voltage clamp amplifier (Warner Instrument, Hamden, CT). Electrodes were filled with 3M KCl and had a resistance of 2–4 MΩ for voltage-recording electrodes and 0.6–1 MΩ for current-passing electrodes. Stimulation and data acquisition were controlled with Digidata and pCLAMP software (Axon Instruments, Foster City, CA).

HERG currents (I_HERG) expressed in Xenopus oocytes were recorded in 2mM [K⁺]_o Ringer's solution. External Ca²⁺ concentration was kept at 0.5mM, since nonselective leak conductance of oocytes increases if divalent cations are totally absent. Throughout the experiments, the holding potential was adjusted between −60–80mV to obtain the minimum leak current, but the repolarization potential was made constant at −60mV. As shown in Figure 1A, depolarizing pulses from a holding potential of −70mV induced time-dependent increases of outward I_HERG. The amplitude of outward I_HERG was measured at the end of a 5-s pulse (I_ss) and plotted against test potentials in Figure 1B. I_ss grew larger as the membrane was depolarized, and then decreased progressively with further depolarization due to rapid inactivation of HERG current, resulting in a bell-shaped I-V relationship with its peak at −30mV. On repolarizing to −60mV, outward tail currents (I_tail) developed (Figure 1A). The amplitude of I_tail increased progressively as increasing the amplitude of depolarizing pulses. The amplitude of I_tail was normalized relative to the amplitude obtained at +20mV test pulse, and plotted against the test potential in Figure 1C (filled squares). Continuous curves were drawn by fitting the data with the Boltzmann equation, and half-activation voltages (V_1/2) were obtained. We considered that this plot can represent the voltage dependence of HERG channel activation, although a 5-s pulse was not enough to induce a steady state activation, especially at potentials near threshold where the time course of activation was very slow. When a longer pulse (10s) was applied, V_1/2 slightly shifted to the left, but the shift caused by prolonging the pulse duration was not >5mV. We considered this error as acceptable, and used 5-s pulses throughout the subsequent experiments.

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Figure 1

Effect of external Ba²⁺ concentration on HERG currents elicited by depolarizing voltage pulses. (A) Superimposed current traces elicited by depolarizing voltage pulses (5s) in 10-mV steps (top panel) from a holding potential of −70mV in 0mM (middle panel) and in 1mM [Ba²⁺]_o (bottom panel). [K⁺]_o is 2mM. (B) Plot of the steady-state current measured at the end of depolarizing pulses against the pulse potential in different external [Ba²⁺]_o (obtained from the same cell shown in A. (C) Plot of the normalized tail current measured at its peak just after repolarization. Similar observations from three more cells. Symbols in B and C: 0mM (■), 0.05mM (●), 0.5mM (▴), 1mM (▾), 2.0mM (♦), 5mM (+). Lines in C are the fits to the Boltzmann equation, y=1/{1+exp((−V+V_1/2)/dx)} (V_1/2 from left to right; −43.1mV, −41.8mV, −25.5mV, −21.9mV, −14.0mV, −8.1mV).

When Ba²⁺ was added to the bath solution, the amplitudes of HERG current decreased in a dose-dependent manner. The effect of various concentrations of [Ba²⁺]_o on I_ss is demonstrated in Figure 1B. As [Ba²⁺]_o was progressively increased, the I_ss-V relationship shifted to the right and the amplitude of I_ss decreased. The decrease of I_ss by Ba²⁺ was voltage-dependent: 0.5mM Ba²⁺ reduced I_ss by 80.5±4.3% at −40mV, 67.6±7.1% at −30mV, 51.6±8.6% at −20mV, and 31.4±9.6% at −10mV (n=5). I_ss at more positive potentials was not significantly affected by increasing Ba²⁺, but a slight increase was observed. Since HERG current was mostly inactivated at this potential (Fig. 2), we regarded this effect as not being due to the change of HERG current, but to a gradual increase of nonspecific leak current during the course of experiments.

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Figure 2

Effect of Ba²⁺ (A, B) and Mn²⁺ (C, D) on the fully activated current-voltage relationship and the inactivation curve. (A) Inset: Superimposed current traces (lower traces) elicited by various level of test pulses ranging from −110 to +20mV following the prepulse to +20mV for 5s (upper traces). Peak currents measured in the beginning of test pulses were plotted against the test pulse potential in various concentrations of Ba²⁺. Similar observations in three more cases for Ba²⁺. (B) Plot of the normalized chord conductance measured from the data shown in A. Inactivation curves were obtained by fitting data to the Boltzmann equation. V_1/2 and slope factor (in mV) were −49.2 and 18.9 in 0mM Ba²⁺ (left curve); −45.5 and 23.0 in 1mM Ba²⁺ (right curve). (C) Same protocol as in A with various [Mn²⁺]_o. (D) Same protocol as in B with various [Mn²⁺]_o. Continuous curves are for 0mM Mn²⁺ (left) and 2.5mM Mn²⁺ (right).

The I_tail-V curve, which is generally regarded as representing the voltage-dependent activation property of HERG current, was also significantly affected by [Ba²⁺]_o (Figure 1C). It shifted progressively to the right as [Ba²⁺]_o increased, and the maximum I_tail obtained after large depolarization was also reduced very significantly. These results indicate that as [Ba²⁺]_o is increased, larger depolarization is needed for the activation of HERG channel, and the fully activated conductance induced by a sufficient depolarization is also reduced.

To examine whether the change of maximum I_tail represents the change of maximum conductance of HERG currents, fully activated current-voltage relationships were obtained by using a double-pulse protocol: a varying level of test pulses following the prepulse to +20mV, which is given to induce a full activation (Fig. 2). The amplitude of the current at the beginning of test pulses was measured at its peak when inactivation was removed, but deactivation had not yet progressed. The fully activated current-voltage relationship showed a strong inward rectification with a negative slope conductance, which is a well-known characteristic of HERG channels caused by rapid inactivation (Smith et al,Spector et al). The increase of [Ba²⁺]_o decreased the fully activated conductance in a dose-dependent manner. There was no shift in fully activated I-V relationships and no change in reversal potentials.

For further analysis, the chord conductance was obtained from the fully activated current-voltage relationship. It was normalized to the maximum slope conductance at each concentration of [Ba²⁺]_o, and plotted in Figure 2B. This could be an estimation of inactivation, and V_1/2 in the absence of Ba²⁺ was −49.2mV. This value agrees well with previous reports (−49mV in Sanguinetti et al; −45mV in Wang et al). It was shifted slightly to the right by increasing [Ba²⁺]_o, and V_1/2 at 1mM [Ba²⁺]_o was −45.5mV. At higher concentrations of Ba²⁺, rapid block by Ba²⁺ prevented the accurate measurement of the fully activated current at high negative potential, and curve-fitting was not appropriate. However, it could be noticed that data points were not far from the curve for 1mM Ba²⁺, suggesting that the effect of Ba²⁺ on inactivation is not as prominent as that on activation.

In Fig. 3, the dose-response relationship of Ba²⁺ block was analyzed. The relative amplitude of I_tail in the presence of Ba²⁺ in respect to the maximum I_tail in the absence of Ba²⁺ was regarded as the fraction of unblocked channels (y) in the presence of Ba²⁺ at the steady state. The dose-response relationship for the effect of [Ba²⁺]_o on y was obtained at each test potential, and plotted in Figure 3A. It could be fitted by the Hill equation as follows:

(1)

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Figure 3

Dose-response relationship (A) and voltage dependence of K_i (B) for Ba²⁺. (A) Data obtained from four cases using the same protocol as shown in Fig. 1C were averaged and plotted against [Ba²⁺]_o for different potentials (−30mV (○), −20mV (●), −10mV (□), and 0mV (■)), and the curves were drawn by fitting with the Hill equation. Concentrations for half-maximum inhibition (K_i) from left to right: 0.06, 0.15, 0.34, and 0.59mM, respectively. (B) Semilogarithmic plot of the concentration of Ba²⁺ for half-inhibition (K_i) against the membrane potential. K_i was obtained from the dose response curve shown in A at different potentials. Lines drawn by a least-square fitting. K_i decreased e-fold for 15.1mV hyperpolarization.

The other important feature was observed in the effect of Ba²⁺ on current kinetics. In Figure 4A, current traces evoked by depolarization to −20mV from the holding potential of −80mV at various [Ba²⁺]_o are shown on a different scale to compare the time course easily by adjusting each trace to have the same amplitude. The effect of Ba²⁺ on current onset was strikingly prominent. Application of 0.05mM Ba²⁺ induced profound slowing of current activation. Furthermore, the current onset showed a significant delay, resulting in a sigmoid time course. Interestingly, further increase of [Ba²⁺]_o produced only a little more effect. This effect is demonstrated in the plot of the reciprocal of the time constant of current activation at various [Ba²⁺]_o and various potentials (Figure 4B). The time course did not fit well with a single exponential function, suggesting that several steps may be involved in channel opening in the presence of Ba²⁺, but the time constant was obtained using single exponential fitting in order to present the change of time course by [Ba²⁺]_o in a simple manner. However, the decay rate was generally well-fitted with a single exponential. It was proportionally increased by increasing [Ba²⁺]_o as shown in Figure 5A. The relationship between [Ba²⁺]_o and the decay rate (see Figure 10A) shows that the data are fitted with a straight line. The decay rate was plotted over wide potential range in Figure 5B, showing that it is exponentially increased by hyperpolarization.

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Figure 4

Effect of Ba²⁺ on kinetics of current onset. (A) Current traces evoked by depolarization to −20mV from the holding potential of −80mV at 0mM, 0.05mM, and 1mM [Ba²⁺]_o on a different scale. Note the prominent initial delay in the presence of Ba²⁺. (B) Current activation was fitted to a single exponential function, and the reciprocal of time constant was plotted against test potential. Mean±SE obtained from four cells. [Ba²⁺]_o: 0mM (■), 0.05mM (●), 1mM (○). Amplitude (μA) at −40, −30, −20, −10, 0, 10, and 20mV were 0.86±0.27, 1.21±0.51, 1.21±0.43, 0.9±0.34, 0.55±0.21, 0.29±0.11, and 0.08±0.03 for 0mM Ba²⁺; 2.89±1.48, 2.44±0.97, 1.65±0.59, 1.11±0.51, 0.67±0.33, 0.51±0.22, and 0.29±0.11 for 0.05mM Ba²⁺; 0.45±0.16, 0.88±0.44, 1.13±0.68, 1.22±0.79, 0.92±0.73, 0.63±0.54, and 0.4±0.33 for 1mM Ba²⁺.

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Figure 5

Effect of Ba²⁺ on kinetics of current decay. (A) Superimposed current traces recorded on repolarization to −60mV after 5-s depolarizing pulses to +40mV at different [Ba²⁺]_o. (B) Current decay was fitted with single exponential functions and the reciprocal of the time constant was plotted against voltage at various [Ba²⁺]_o. Symbols: 0mM (■), 0.05mM (●), 0.5mM (▴), 1mM (▾), and 2.0mM (♦).

We then tested the effect of another divalent cation belonging to the alkali metal, Sr²⁺, on I_HERG using the same experimental protocol. In Figure 6A, superimposed current traces activated by depolarization to −20mV from the holding potential, −60mV, were demonstrated. When [Sr²⁺]_o was increased progressively, the amplitudes of I_HERG decreased, but in contrast to the effect of Ba²⁺, the rate of current activation was hardly affected by increasing [Sr²⁺]_o. The amplitude of tail currents recorded upon repolarization was reduced by increasing [Sr²⁺]_o, but with little change in the time course of current decay. The plot of I_tail-V curves (Figure 6B) showed that V_1/2 shifted to the right and maximum I_tail was decreased by the increase of [Sr²⁺]_o. The decrease of maximum I_tail was more significant than the shift of V_1/2 when compared with the effect of [Ba²⁺]_o. This result may suggest that shift of the voltage dependence and decrease of maximum conductance are independent phenomena.

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Figure 6

Effect of external Sr²⁺ on current activation. (A) Superimposed current traces elicited by depolarizing voltage pulses (5s) to −20mV from the holding potential of −60mV in 0mM, 0.5mM, 1mM, and 5mM [Sr²⁺]_o. (B) Plot of the normalized tail current measured at its peak just after repolarization from various level of depolarizing pulses. Obtained by same protocol shown in Fig. 1. Similar observations from two more cells. Symbols: 0mM (■), 0.5mM (●), 1mM (▴), 2.5mM (▾), and 5mM (♦). Lines in B are the fits to the Boltzmann equation. V_1/2 from left to right; −38.6mV, −35.8mV, −33.9mV, −30.3mV, −28.4mV).

We then tested divalent cations that belong to transitional metals Mn²⁺, Ni²⁺, Co²⁺, and Zn²⁺. In Figure 7A, superimposed current traces evoked by depolarization to −20mV from the holding potential of −80mV at various [Mn²⁺]_o were demonstrated. Not only the amplitude of current, but also the speed of current activation decreased. However, contrary to the effect of Ba²⁺, initial delay of current onset was not observed. Alternatively, the tail current obtained at −60mV after 5-s depolarization to +20mV showed significant acceleration dose-dependently, but without a change in amplitude (Figure 7B). I_ss-V relationship obtained at various [Mn²⁺]_o is shown in Figure 7C. It shifted to the right and the amplitude of I_ss decreased as [Mn²⁺]_o was increased. The decrease of I_ss by Mn²⁺ was also voltage-dependent: 1mM Mn²⁺ reduced I_ss by 90.3±8.1% at −50mV, 66.7±5.0% at −40mV, 48.3±3.2% at −30mV, and 32.4±3.7% at −20mV (n=4). K_i of Mn²⁺ obtained using the same method shown in Figure 3A at 0mV was 2.36mM, indicating that Mn²⁺ is ∼4 times less potent than Ba²⁺. It decreased e-fold by 14.7mV hyperpolarization, showing that voltage dependence is similar. I_tail-V curve also shifted progressively to the right, indicating that larger depolarization is needed for the activation of HERG channel as [Mn²⁺]_o increases (Figure 7D). However, the amplitude of the tail current evoked by large depolarization was hardly affected. It was reduced a little only at high concentration. This result suggests that Mn²⁺ hardly affected the maximum conductance, and this was confirmed in the experiment obtaining the fully activated current shown in Figure 2C. Contrary to the effect of Ba²⁺, the effect of [Mn²⁺]_o on fully activated current was very small. The effect of Mn²⁺ on the inactivation was examined in the same way described for the Ba²⁺ effect, and the result is shown in Figure 2D. One mM Mn²⁺ caused a 3.2mV shift, and 2.5mM Mn²⁺ caused a 8.2mV shift in inactivation.

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Figure 7

Effect of Mn²⁺. (A) Superimposed current traces elicited by depolarizing voltage pulses (5s) to −20mV from the holding potential of −80mV in 0mM, 0.5mM, 1mM, and 5mM [Mn²⁺]_o. (B) Superimposed current traces recorded on repolarization to −60mV after the pulse at +20mV for 5s. (C) Plot of the steady-state current measured at the end of depolarizing pulses (same protocol shown in Fig. 1) against the pulse potential in different external [Mn²⁺]_o. (D) Plot of the normalized tail current measured at its peak just after repolarization. Similar observations from three more cells. Symbols in C and D: 0mM (■), 0.2mM (●), 1mM (▴), 2.5mM (▾), 5mM (♦), 10mM (+). Lines in C are the fits to the Boltzmann equation. V_1/2 from left to right; −39.4mV, −29.2mV, −22.2mV, −13.2mV, −6.4mV, 1.4mV.

In Fig. 8, the effect of Zn²⁺ is demonstrated. An increase of [Zn²⁺]_o decreased the current amplitude very significantly (Figure 8AC). Initial delay of current onset, which was the characteristic feature of the effect of Ba²⁺, was not significant in Zn²⁺. In the inset of Figure 8A, currents activated at −10mV at various [Zn²⁺]_o were normalized and superimposed to compare the time course, showing a small decrease of activation rate by increasing [Zn²⁺]_o. However, the effect on the rate of current decay was very significant, and the amplitude of maximum I_tail was also greatly reduced by Zn²⁺ (Figure 8B). Therefore, the increase of [Zn²⁺]_o resulted in a right shift of the activation curve along with a decrease of maximum conductance (Figure 8D). K_i of Zn²⁺ at 0mV was 0.19mM, indicating that Zn²⁺ is the most potent among all divalent cations tested in the present study.

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Figure 8

Effect of Zn²⁺. (A) Superimposed current traces elicited by depolarizing voltage pulses to −20mV from the holding potential of −80mV in 0mM, 0.02mM, 0.1mM, and 0.2mM [Zn²⁺]_o. (B) Superimposed current traces recorded on repolarization to −60mV after the pulse at +40mV for 5s. (C) Plot of the steady-state current measured at the end of depolarizing pulses (same protocol shown in Fig. 1) against the pulse potential in different external [Zn²⁺]_o. (D) Plot of the normalized tail current measured at its peak just after repolarization. Similar observations from three more cells. Symbols in B and C: 0mM (■), 0.02mM (●), 0.1mM (▴), 0.2mM (▾). Lines in C are the fits to the Boltzmann equation. V_1/2 from left to right; −38.2mV, −37.7mV, −28.2mV, −17.7mV.

Effects of Ni²⁺ and Co²⁺ were also examined using the same experimental protocols. The effects of Co²⁺ were similar to those of Mn²⁺: voltage-dependent block with a shift of activation, but with little effect on maximum conductance. K_i of Co²⁺ at 0mV was 0.5mM, which is about as potent as Ba²⁺. The effect of Ni²⁺ was similar to that of Zn²⁺: shift of activation along with a moderate decrease of maximum conductance. K_i of Ni²⁺ at 0mV was 0.36mM, which is more potent than Ba²⁺, but less than Zn²⁺.

To demonstrate the different effects of various cations on various parameters reflecting gating mechanisms of the HERG channel, we summarize the above results in the next two figures. For the parameter reflecting the effect on the voltage dependence of the channel, the shift of half-maximal activation voltage (ΔV_1/2) is presented (Figure 9A). The effects of Sr²⁺ was the weakest of all; Mn²⁺ and Ba²⁺ are next. Zn²⁺, Ni²⁺, and Co²⁺ are the most potent in their effect on shifting the voltage dependence of activation.

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Figure 9

Effect of various divalent cations on the shift of the current activation (A) and on the decrease of maximum conductance (B). (A) Concentrations of ions on the x axis in log scale. Shift of V_1/2 on the y axis. Symbols indicate the mean of V_1/2 shift: Sr²⁺ (●, n=2), Mn²⁺ (■, n=4), Ba²⁺ (144, n=6), Ni²⁺ (▾, n=2), Co²⁺ (▴, n=2), and Zn²⁺ (○, n=5). Solid straight line: simulation result obtained from Figure 11A, assuming k₁(0) of 0.068. Dotted line: simulation result assuming k₁(0) of 0.34. Broken curve: simulation result assuming surface charge effect when charge density is 1/1nm². (B) Inhibition of maximum conductance was obtained from the ratio of maximum tail current in the presence of test cations at varying concentrations to that in the absence of test cations. Continuous lines obtained by fitting with the Hill equation. K_i: 0.26mM for Zn²⁺ (○, n=4). 1.4mM for Ba²⁺ (□, n=4), 6.4mM for Sr²⁺ (●, n=2), 15.6mM for Co²⁺ (▴, n=2), and 72.8mM for Mn²⁺ (■, n=4).

Contrary to the effect on V_1/2, the potency of various ions for decreasing maximum conductance shows the difference in order. The relative magnitude of the maximum conductance (g_max in the presence of X²⁺/g_max in the absence of X²⁺) was obtained by dividing maximum tail currents (I_tail at +40mV) in the presence of testing divalent cations by those in the absence of testing ions. This parameter was plotted against the concentration of various divalent cations in Figure 9B. Concentrations for half-maximum inhibition of maximum conductance, K_i, were obtained by fitting the data with Eq. (1), and they were 0.26mM, 1.4mM, 6.4mM, 15.6mM, and 72.8mM for Zn²⁺, Ba²⁺, Sr²⁺, Co²⁺, and Mn²⁺, respectively. The discrepancy of potency order for decreasing maximum conductance and for shifting voltage dependence indicates that they are modulated via different mechanisms.

In Fig. 10 the rate of current decay (obtained at −60mV) and current activation (obtained at −20mV) are plotted against divalent concentration. For comparison, the data obtained from the same cell is demonstrated. The decay rate was proportionally increased by increasing the concentration of divalent cations, and the data were well-fitted with straight lines. The steepness was in the order Zn²⁺>Ba²⁺>Mn²⁺>Sr²⁺ (Figure 10A). However, the activation rate decreased with increasing concentration of divalent cations, but the effect on activation and deactivation was not equal: effects of Zn²⁺ and Mn²⁺ on current activation were similar, whereas Zn²⁺ induced a much greater effect on current deactivation than Mn²⁺.

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Figure 10

Effect of various divalent cations on the kinetics of current activation (A) and current decay (B). Obtained from one cell. (A) Current decay obtained at −60mV was fitted with a single exponential function. The reciprocal of the time constant was plotted against the concentration of test cations. Straight lines are the best fits for each ion. The slopes are 14.9, 4.8, 0.29, and 0.05mV for Zn²⁺, Ba²⁺, Mn²⁺, and Sr²⁺, respectively. (B) Current activation evoked by the depolarization to −20mV was fitted with a single exponential function. The reciprocal of the time constant was plotted against the concentration of test cations.

We have shown that all divalent cations tested in the present study inhibit HERG current in a dose-dependent manner. The effects are manifested as follows: 1) decrease of current amplitude, 2) shift of voltage dependence of activation, 3) acceleration of deactivation, 4) slowing of activation, and 5) decrease of maximum conductance. These effects had also been observed in our previous study investigating Ca²⁺ and Mg²⁺ (Ho et al,Ho et al). The present study, however, has revealed that each parameter is not affected by each cation to the same extent, implying that the underlying mechanism is not a single process, but that several different pathways are involved in inhibiting HERG channels by divalent cations. Fig. 9 clearly demonstrates that the effect on V_1/2 and that on g_max is not equal, suggesting that two parameters are controlled by different mechanisms. These results might suggest the existence of at least two different binding sites: one for modulating the maximum conductance and one for modulating voltage-dependent gating. Fig. 10 demonstrates that the effect on activation and that on deactivation are not equal, implying that effect of divalent cations on current kinetics does not result from a simple shift of voltage dependence of gating.

Divalent cations have been one of the classical tools used to investigate gating and permeation of K⁺ channels (Hille, 1992). Three mechanisms have been proposed to explain various aspects of actions of divalent cations: 1) surface charge theory, 2) voltage-dependent block theory, and 3) gating modifier theory. Although the results of the present study suggest that various mechanisms are involved in action of external divalent cations on the HERG channel, a simple scheme of the voltage-dependent block model, which has been used widely, especially to describe a voltage- and time-dependent block of various K⁺ channels (Armstrong, 1971,Hagiwara et al,Standen and Stanfield, 1978,French and Shoukimas, 1985), can still explain major important features of the actions of divalent cations on HERG channels. Since the effect of Ba²⁺ has the most complicated features, we examine whether Ba²⁺ effects can be reproduced using this model. Since the inactivation process was little affected by Ba²⁺ (Fig. 2), we did not consider the inactivation process in the following simulation. The effect of Ba²⁺ producing channel blockade is described as follows:

In this model, acceleration of current decay on repolarization is viewed as a manifestation of channel blockade by a blocking particle. Thus, the binding rate constant, k₁, can be obtained from the time constant of current decay from the following equation.

(2)

(3)

(4)

(5)

(6)

Zn²⁺ caused faster decay. According to the result shown in Figure 10B, k₁ is about five times larger than that of Ba²⁺ (Figure 10A). The effect of the increase of k₁ by five times on the shift of V_1/2 is tested using the above model. The result is illustrated as a dotted line in Figure 9A, showing that it agrees reasonably well with the experimental data. However, the effect of Mn²⁺ on V_1/2 is more profound than expected from the above model. k₁ for Mn²⁺ is about five times smaller than that for Ba²⁺, but V_1/2 shifts to a similar extent as Ba²⁺. The effect of Co²⁺ and Ni²⁺ on V_1/2 is also more profound than expected, since the decay rate was not faster than Ba²⁺, but produced larger effects on V_1/2 shift. Such discrepancy may suggest that other mechanisms are contributing to the effect of these ions on the voltage dependence of the HERG channel. In this respect, the surface charge effect should be considered in addition to the voltage-dependent blockade.

The surface charge theory was proposed to explain the channel blockade by divalent cations when it is accompanied by a shift of the voltage dependence of channel activation (Green and Andersen, 1991,Hille, 1992). The shift of gating of various ion channels has been described by the Gouy-Chapman-Stern theory (Gilbert and Ehrenstein, 1969,Hille et al,Campbell and Hille, 1976,Ohmori and Yoshii, 1977), and we used the same equation to predict the relationship between the external ionic concentration of species i (C_i) and the outer surface potential (ψ) in our experimental conditions. When the charge density remaining unneutralized in control conditions is assumed to be one negative charge per nm², we could obtain a theoretical curve (shown as a broken line in Figure 9A), which is reasonably close to the Sr²⁺ data. It is difficult to infer at present that this value is realistic for the HERG channel, but the previous studies for Na⁺ and Ca²⁺ channels reported similar values: surface charge densities calculated from the shift of sodium channel activation by external divalent cations were 1/nm² in frog nodes of Ranvier (Hille et al), and 1/0.9nm² in the tunicate egg cell (Ohmori and Yoshii, 1977). Therefore, the shift of voltage dependency (V_1/2) by Sr²⁺ may be explained by a nonspecific charge-screening effect. In general, binding affinity of transitional metals for surface negative charge is higher than that of alkali metals, in the order of Ba²⁺, Sr²⁺<Mg²⁺<Ca²⁺<Mn²⁺<Co²⁺, Ni²⁺<Zn²⁺. So, the surface charge effect is expected to be greater for transitional metal ions, causing a greater shift of V_1/2. The result showing that transitional metal ions produce the shift of V_1/2 larger than expected from the direct channel blocking effect may well be accountable by the additional surface charge effect.

The time course of current onset is also affected by external divalent cations (Figure 10B). The effect of Ba²⁺ is remarkable, and only a low concentration (0.05mM) causes marked slowing (Figure 4A), suggesting that the unblock rate is very slow for Ba²⁺. This finding may suggest that Ba²⁺ binds to a site somewhere on the channel protein to stabilize a conformational state of the pore so that unblock is delayed. A sigmoid onset of current with a significant initial delay is characteristic of Ba²⁺. To test whether such a characteristic time course is explained by the above model, we simulated the current traces in the same experimental condition shown in Fig. 4 using the simple Hodgkin-Huxley formulation. Activation at −20mV in the absence of Ba²⁺ was well-fitted by a double-exponential function, and the effect of Ba²⁺ was reproduced by multiplying the unblock process. The result is illustrated in Figure 11B, showing a good agreement with the experimental result shown in Figure 4A. A low concentration of Ba²⁺ (0.05mM) results in a sigmoid onset of current to a similar degree observed in the experiment. This result shows that current activation in the presence of Ba²⁺ is mainly determined by the unblock rate. On the contrary, the effect of other divalent cations on the activation kinetics differs from that of Ba²⁺. The increase of other divalent cations caused a gradual decrease of the rate of current onset, but the slowing is not as prominent as observed in Ba²⁺, suggesting that unblock rate is not very slow.

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Figure 11

Simulation of the effect of [Ba²⁺]_o on HERG channel activation based on the voltage-dependent block model. (A) Simulation result of the voltage dependence of channel opening (Po) obtained by assuming k₁(0) of 0.068. Inset: Rate constant of block at various [Ba²⁺]_o calculated by Eq. (3). (B) Superimposition of current traces and simulated results. Current traces are same as in Figure 4A. Simulated curves at 0mM Ba²⁺: z(t)=1.672−0.664 exp(−t/0.378)−0.859 exp(−t/2.101). Unblock rate (y(t)) at 0.05mM and 1mM Ba²⁺ was calculated from the time constant obtained from Eqs. (3): y(t)=0.952−0.924 exp(−t/4.315) at 0.05mM. y(t)=0.5−0.499 exp(−t/2.27) at 1mM. Curves are calculated as Po(t)=y(t) · z(t). Current magnitude is in an arbitrary scale.

Another advantage of the voltage-dependent block model is to give the information about the location of the binding site in the electrical field, the so-called fractional electrical distance (δ). According to the original Woodhull, 1973, it is represented by the voltage dependence of the dissociation constant, K_D, and can be expressed as follows:

(7)

A gating modifier theory should also be considered as a possible mechanism. This theory has been proposed to explain the effects of divalent cations when they are not sufficiently explained by surface charge theory, because activation and deactivation are not equally affected (Spires and Begenisich, 1992,Spires and Begenisich, 1994). This possibility cannot be excluded, but it is difficult to make a general model to test this possibility.

The three models described above mainly explain the voltage-dependent effect: shift of V_1/2 and change of kinetics. In this paper we could not propose a proper model for the decrease of maximum conductance. In the case of Ca²⁺ channel and Na⁺ channels, a decrease of conductance by divalent cations was explained by the surface charge theory, since neutralizing surface negative charge by external cations can cause a decrease of the effective concentration of permeating ions near the channel pore, and thus an apparent decrease of conductance (Ohmori and Yoshii, 1977). However, the decrease of maximum conductance of HERG current cannot be explained by this theory, since HERG current was recorded as an outward current, and outward currents would not be reduced by the decrease of the effective concentration of a permeating ion from the external side of the membrane. From the result shown in Fig. 9, it was only suggested that the conductance and the voltage dependence of the HERG channel are controlled by different sites by divalent cations.