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(Circulation Research. 1997;80:782-789.)
© 1997 American Heart Association, Inc.

Articles

Rapid Inactivation Determines the Rectification and [K⁺]_o Dependence of the Rapid Component of the Delayed Rectifier K⁺ Current in Cardiac Cells

Tao Yang, Dirk J. Snyders, , Dan M. Roden

From the Vanderbilt University School of Medicine, Departments of Medicine and Pharmacology, Nashville, Tenn.

Correspondence to Dan M. Roden, MD, Director, Division of Clinical Pharmacology, Vanderbilt University School of Medicine, 532C Medical Research Building I, Nashville, TN 37232-6602.

	Abstract

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Abstract Two characteristic features of the rapid component of the cardiac delayed rectifier current (I_Kr) are prominent inward rectification and an unexpected reduction in activating current with decreased [K⁺]_o. Similar features are observed with heterologous expression of HERG, the gene thought to encode the channel carrying I_Kr; moreover, recent studies indicate that the mechanism underlying rectification of HERG current is the inactivation that channels rapidly undergo during depolarizing pulses. The present studies were designed to determine the mechanism of I_Kr rectification and [K⁺]_o sensitivity in the mouse atrial myocyte cell line, AT-1 cells. Reducing [Mg²⁺]_i to 0, which reverses inward rectification of some K⁺ channels, did not alter I_Kr current-voltage relationships, although it did decrease sensitivity to the I_Kr blockers dofetilide and quinidine 2- to 5-fold. To determine the presence and extent of fast inactivation of I_Kr in AT-1 cells, a brief hyperpolarizing pulse (20 ms to -120 mV) was applied during long depolarizations. Immediately after this pulse, a very large outward current that decayed rapidly to the previous activating current baseline was observed. This outward current component was blocked by the I_Kr-specific inhibitor dofetilide, indicating that it represented recovery from fast inactivation during the hyperpolarizing step, with fast reinactivation during the return to depolarized potential. With removal of inactivation using this approach, current-voltage relationships for I_Kr ([K⁺]_o, 1 to 20 mmol/L) were linear and reversed close to the predicted Nernst potential for K⁺. In addition, decreased [K⁺]_o decreased the time constants for openinactivated and inactivatedopen transitions. Thus, in these cardiac myocytes, as with heterologously expressed HERG, I_Kr undergoes fast inactivation that determines its characteristic inward rectification. These studies demonstrate that the mechanism underlying decreased activating current observed at low [K⁺]_o is more extensive fast inactivation.

Key Words: K⁺ current • delayed rectifier • extracellular K⁺ • fast inactivation • heart

	Introduction

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The delayed rectifier I_K is an important contributor to the time course of terminal repolarization in cardiac cells. In guinea pig myocytes, multiple components of I_K have been identified, and I_Kr was designated as the component sensitive to block by the methanesulfonanilides E4031 and D-sotalol.¹ The physiological and pharmacological features of I_Kr include inward rectification,^{1 2} an anomalous decrease in outward current when [K⁺]_o is lowered,^{3 4} [K⁺]_o sensitivity of I_Kr block by quinidine and the methanesulfonanilide dofetilide,⁴ and large deactivating tail currents often preceded by a rapid outward "hook."² Two general mechanisms underlying inward rectification have been proposed for voltage-gated K⁺ currents. The first mechanism, internal block by divalent cations such as Mg²⁺, was demonstrated in studies of I_K1^{5 6} ; changes in intracellular spermine or spermidine are thought to act through a similar internal blocking mechanism.^{7 8 9 10} In a recent study of guinea pig myocyte I_K, which represents both I_Kr and I_Ks, reduction of pipette Mg²⁺ was found to exert no effect on I_Kr rectification.¹¹ The authors also described a blocking effect of the methanesulfonanilide I_Kr blocker E4031 on I_Ks when [Mg²⁺]_i was eliminated; however, because guinea pig myocytes have both I_Kr and I_Ks, it was not possible in that study to assess any direct effect of changing [Mg²⁺]_i on drug block of I_Kr.

A second mechanism, proposed in 1987 by Shibasaki² during studies of a current strongly resembling I_Kr in rabbit AV nodal cells, is that rectification is determined by very fast inactivation from the open state. In the simplest model, closedopeninactivated, it was suggested that more channels entered the inactivated state with stronger depolarizations, thus producing apparent rectification. With repolarizing pulses, inactivated channels would rapidly enter the open state, from which channels would close slowly, thereby accounting for the experimentally observed hooks. Recent studies of currents resulting from expression of the human ether-à-go-go (HERG) gene, thought to be a major I_Kr subunit, have provided strong evidence in support of this mechanism.^{12 13 14 15 16}

In AT-1 cells, derived from the atrial tumors arising in mice carrying a transgene in which expression of the simian virus 40 large-T antigen is driven by the atrial natriuretic factor promoter,¹⁷ I_Kr is the sole delayed rectifier observed.^{18 19} We have shown that I_Kr in these cells is very similar to that recorded in other mammalian cardiac myocytes, making AT-1 cells a convenient system in which to study the physiology and pharmacology of this current.¹⁸ The goals of the present study were to determine if lowering intracellular Mg²⁺ influenced I_Kr rectification or drug block and to determine the role of rapid inactivation in I_Kr rectification and in the anomalous response of I_Kr to changes in [K⁺]_o. Portions of this study have been reported previously.^{20 21}

	Materials and Methods

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The methods used to culture AT-1 cells, kindly supplied by Loren Field (Krannert Institute, Indianapolis, Ind), and to record I_Kr have been described in detail previously.¹⁸ In brief, cells were injected subcutaneously into new syngeneic hosts ([C57BL/6JxDBA/2J]F₁ female mice, Jackson Laboratories, Bar Harbor, Maine) to propagate tumors, from which AT-1 cells were then isolated as previously described. The media (PC1 [Ventrex Laboratories], which included pen-strep, 10% fetal bovine serum, and 10 nmol/L dexamethasone) were changed every other day until used. The findings described in the present study were obtained from cells that had been in culture for 7 to 14 days. Cells were removed from the culture dish by a 2-minute exposure to a trypsin-containing solution (0.125% in Ca²⁺- and Mg²⁺-free Hanks'), decanted into sterile culture tubes, and kept at room temperature until study the same day.

Electrophysiological Recording
Recordings were performed using an Axopatch-1A or 200A patch-clamp amplifier (Axon Instruments, Inc) in the whole-cell configuration of patch-clamp technique.²² Experiments were conducted at room temperature (20°C to 22°C). After the whole-cell configuration was established, the capacitive transients elicited by symmetrical 10-mV voltage-clamp steps from -80 mV were recorded at 50 kHz (filtered at a bandwidth of 10 kHz, -3 dB) for calculation of capacitive surface area. Thereafter, capacitance and series resistance compensation were optimized; 80% compensation was usually obtained. The extracellular solution was normal Tyrode's that contained (in mmol/L) CaCl₂ 1.8, MgCl₂ 1, HEPES 10, and glucose 10; for the experiments studying changes in [Mg²⁺]_i, 4 mmol/L KCl and 130 mmol/L NaCl were used, whereas for experiments studying changes in [K⁺]_o, equimolar NaCl was substituted or added for KCl. The pH of the solution was adjusted to 7.35 with NaOH. The intracellular pipette filling solution contained (mmol/L) KCl 110, K₄BAPTA 5, K₂ATP 5, MgCl₂ 1, and HEPES 10, and the solution was adjusted to pH 7.2 with KOH, yielding a final [K⁺ ]_i of 145 mmol/L. In all experiments, L-type Ca²⁺ current, Na⁺ current, and T-type Ca²⁺ current were eliminated by adding 1 µmol/L nisoldipine, 30 µmol/L tetrodotoxin, and 200 µmol/L NiCl₂ to the extracellular solution. To study the effect of nominal [Mg²⁺]_o ([Mg²⁺]_o=0), MgCl₂ was omitted from the filling solution. To assess drug block as a function of [Mg²⁺]_o, tail current after a 1-second test pulse to 20 mV was monitored during drug washin; once steady state was established (usually within 10 to 15 minutes), tail currents were measured at a range of test potentials. A higher drug concentration was then washed in; a maximum of baseline and three sequentially increasing drug concentrations were assessed in this fashion. To study the inactivating behavior of I_Kr as a function of [K⁺]_o, currents were recorded before and during exposure to a high concentration (1 µmol/L) of the I_Kr-specific blocker dofetilide. Analysis of current amplitudes and calculation of time constants was then performed on dofetilide difference currents, obtained by digital subtraction. Salts and quinidine were purchased from Sigma Chemical Co. Nisoldipine was obtained from Miles Pharmaceutical, Inc, and dofetilide was provided by Pfizer Central Research. Stock solutions were stored at 4°C, and the final concentrations in the bath were obtained by diluting the stock solutions in the external solution during experiments.

Voltage-Clamp Protocols and Data Analysis
The specific protocols used are described in "Results." To compare current densities among cells, currents are reported as current per unit capacitance (pA/pF) after linear leak subtraction and normalization relative to cell surface area, determined by measurement of capacitance, as described above. The drug concentration blocking 50% of current, IC₅₀, was determined using a Hill function, ie, block=1/{1+(IC₅₀/[D])ⁿ}, where [D] is the drug concentration. Results are expressed as mean±1 SE.

	Results

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Fig 1A shows that lowering [Mg²⁺]_i produced no change in either I_Kr amplitude or rectification and a minimal (<5-mV) voltage shift. In addition, I_Kr rectification was not altered by adding a high concentration of ATP (15 mmol/L), which chelates intracellular polyamines,⁹ to the pipette filling solution (data not shown). We have previously shown that lowering [K⁺]_o increased the sensitivity of I_Kr to inhibition by the nonspecific blocker quinidine or the specific blocker dofetilide.⁴ Conversely, lowering [Mg²⁺]_i decreased the sensitivity of I_Kr to drug block. For example, the IC₅₀ for dofetilide block was 10.4±1.8 nmol/L with [Mg²⁺]_i=1 mmol/L, whereas the IC₅₀ for block with [Mg²⁺]_i=0 was 52.2±5.3 nmol/L (Fig 1B). As in our previous studies with [K⁺]_o, changes seen with quinidine were similar to those with dofetilide (Fig 1C): the IC₅₀ values were 1.0±0.1 µmol/L ([Mg²⁺]_i=1 mmol/L) versus 2.6±0.3 µmol/L ([Mg²⁺]_i=0).

View larger version (28K): [in this window] [in a new window]   Figure 1. A, Effect of altering [Mg2+]i on activating IKr. Current activated during a 1-s test pulse (ie, current at 1 s minus instantaneous current at time 0) is plotted as a function of test potential. B and C, Modulation by changes in [Mg2+]i of IKr block by dofetilide (B) and by quinidine (C). Fits to the Hill equation are indicated by the continuous lines. For both drugs, lowering [Mg2+]i increased the IC50 for drug block. *P<.05 for paired comparisons.

The lack of effect of altering intracellular constituents on I_Kr rectification suggests that fast inactivation may play a role. Fig 2 shows voltage dependence of deactivation and preceding hooks after a depolarizing pulse to +40 mV. Deactivation (transitions from open to closed states) proceeded relatively slowly (eg, =165 ms at -30 mV). In contrast, the time course of the hooks (transitions from inactivated to open states) was much faster and accelerated (as shown in Fig 2B) at hyperpolarized potentials. For example, at -120 mV, the time constant of the hook was 2.4 ms; summary data are presented below.

View larger version (18K): [in this window] [in a new window]   Figure 2. Voltage dependence of recovery from fast inactivation. In this experiment, currents were recorded after a depolarizing pulse to +40 mV (A). On an expanded time scale (B), the rapid hook before slow deactivation is more apparent and is fastest at hyperpolarized potentials (sampling rate, 5 kHz). The time constant of the hook was 2.4 ms at -120 mV in this experiment ([K+]o=4 mmol/L here and in Figs 3 through 6).

This difference in time courses was exploited to dissect inactivatedopen from openclosed transitions, as shown in Fig 3. Both tracings presented in Fig 3 represent different currents after exposure to the I_Kr blocker dofetilide. Fig 3A shows activating I_Kr and deactivating tail current (with a preceding hook) elicited by a 1520-ms pulse to +40 mV, with repolarization back to -40 mV. At the end of the depolarizing pulse, channels would be in the open (activating current) and inactivated states. Fig 3B shows the identical 600-pA current elicited in the same cell by a pulse to +40 mV. Instead of a 1520-ms pulse, however, the pulse was interrupted after 1 s by a brief (20-ms) hyperpolarizing step to -120 mV. Upon return to +40 mV, a very large (3900 pA) current that then decayed rapidly (=18 ms) back to the 600-pA baseline was observed. Repolarization back to -40 mV then elicited the same hook, followed by a slowly (=219 ms) deactivating tail current, as in the left panel. This provides direct evidence that I_Kr in these cells behaves in a fashion similar to that reported for expressed HERG: during strong depolarizations, the channel undergoes rapid and extensive inactivation that can be relieved by a short hyperpolarizing pulse.

View larger version (9K): [in this window] [in a new window]   Figure 3. A brief hyperpolarization reveals rapid inactivation. Currents were recorded in the same cell. In panel A, a depolarizing pulse to +40 mV results in a small activating current, followed by a prominent tail current at -40 mV. The protocol in panel B was identical, with the exception of a brief 20-ms hyperpolarizing pulse to -120 mV after 1 s at +40 mV. After the hyperpolarizing pulse, a large outward current that inactivated very rapidly (=18 ms) was observed. As discussed further in the text, this result indicates reinduction of rapid inactivation that had been relieved by the hyperpolarizing pulse.

Further evidence in support of this concept is shown in Fig 4. Here, the duration of the hyperpolarizing pulse from +40 to -120 mV was varied. The effect of 20- and 200-ms hyperpolarizing pulses is shown in Fig 4A. With the short hyperpolarizing pulse, a large current was observed with the pulse back to +40 mV (dotted line), as in Fig 3B. With the longer 200-ms hyperpolarizing pulse, channel deactivation was observed at -120 mV. Thus, just before the pulse back to +40 mV, fewer channels remain in the inactivated state, and most of the open channels had closed. Indeed, with the pulse back to +40 mV, the large rapidly inactivating current was not observed; rather, channel reopening occurred. Fig 4B shows the effect of varying the hyperpolarizing pulse from 20 to 200 ms. The amplitude of the currents elicited immediately after the subsequent steps back to +40 mV is shown, along with the time course of the current recorded during a long step (200 ms) to -120 mV. Fig 4C shows that the two time courses are similar, with time constants of 32 to 33 ms. Moreover, the ratio of tail current at -120 mV to instantaneous current at +40 mV was 0.33 and was independent of the duration of the hyperpolarizing pulse (Fig 4D); ie, an envelope test was satisfied. These data demonstrate that with longer hyperpolarizing pulses, not only do inactivated channels open, but open channels begin to close. The fact that the envelope test is satisfied indicates that both recovery from inactivation (with short pulses) and channel closing (with longer pulses) at -120 mV determine the availability of channels to open during a subsequent pulse to +40 mV. If a K⁺ reversal potential of -80 mV is assumed, the ratio of tail current at -120 mV to instantaneous current at +40 mV should be [-80-(-120)]/[40-(-80)], or 0.33. Thus, the result of the experiment also indicates that contamination by other conductances is minimal.

View larger version (26K): [in this window] [in a new window]   Figure 4. Effect of varying hyperpolarizing pulse duration on posthyperpolarization current. A, A brief hyperpolarizing pulse results in a large augmentation of activating current, which then inactivates rapidly, as in Fig 3B (dotted trace). With a longer hyperpolarization, channels not only recover from inactivation but also deactivate. Thus, with subsequent repolarization, a large augmentation inactivating current is not observed. B through D, Envelope test. Panel B shows peak outward currents after hyperpolarizations of variable duration (20 to 200 ms). In panel C, summary data from six experiments show a similar time course of peak outward current and deactivating current at -120 mV. In panel D, the ratio of the data from panel C is independent of the time interval, indicating that the envelope test is satisfied. All currents are those sensitive to 1 µmol/L dofetilide, as described in "Materials and Methods."

The experiment shown in Fig 3 was repeated at a range of depolarizing potentials in two different ways. In the first, a 1-s pulse to a range of activating potentials was followed by a 20-ms hyperpolarizing pulse to -120 mV and a third 500-ms pulse to the same potential as the first (Fig 5). In the second, a 1-s pulse to +50 mV and a subsequent 20-ms pulse to -120 mV were followed by pulses to a range of potentials (Fig 6). In both approaches, dofetilide difference currents were used, as described in "Materials and Methods." Fig 5 demonstrates that relief of inactivation by a hyperpolarizing pulse augmented the outward current to a small extent at negative test potentials (eg, -10 mV); the augmentation was considerably greater at more positive potentials (eg, +40 mV), indicating greater inactivation at positive potentials. I-V curves for activating current and for total current immediately after the hyperpolarizing pulse are presented in Fig 5B. It is apparent that the brief hyperpolarizing pulse completely relieved the inward rectification shown with the activating current.

View larger version (20K): [in this window] [in a new window]   Figure 5. Recovery from fast inactivation as a function of voltage. Currents were recorded before and after exposure to 1 µmol/L dofetilide. A, Dofetilide-sensitive currents, as a function of test potential. Activating current was smaller with strong depolarizations (inward rectification), but total current immediately following the test pulse (instantaneous current) was larger, with stronger depolarizations. B, Summary data from eight experiments. Activating current () displayed inward rectification typical of IKr. Instantaneous current showed quasiohmic, or slight, apparent outward rectification ().

View larger version (25K): [in this window] [in a new window]   Figure 6. Effect of varying amplitude of the posthyperpolarization pulse. A indicates control currents; B, currents recorded during 1 µm dofetilide; C, dofetilide difference current; D, I-V curve. As in Fig 5, the I-V curve (D) for instantaneous (immediately after hyperpolarization) current showed slight outward rectification.

When I_Kr was first fully activated and the effect of brief hyperpolarization was studied (Fig 6), a similar result was observed: the I-V curve for total current just after the hyperpolarizing pulse (instantaneous current, Fig 6D) displayed slight apparent outward rectification. This approach was then used to test the hypothesis that the decrease in activating I_Kr observed with low [K⁺]_o is due to [K⁺]_o enhancement of fast inactivation. The results of one such experiment are shown in Fig 7. As previously reported,^{3 4} activating current was smaller at low [K⁺]_o: activating current in this experiment after 1 s at +40 mV was 2.2 pA/pF with 1 mmol/L [K⁺]_o, 3.3 pA/pF with 4 mmol/L [K⁺]_o, and 4.9 pA/pF with 20 mmol/L [K⁺]_o. However, with relief of inactivation by a short hyperpolarizing pulse, it is evident that total (instantaneous) current was largest at 1 mmol/L [K⁺]_o and smallest at 20 mmol/L (arrows).

View larger version (10K): [in this window] [in a new window]   Figure 7. Effect of changing [K+]o (1 mmol/L [A], 4 mmol/L [B], and 20 mmol/L [C]) on IKr, measured as dofetilide-sensitive current as in Fig 6. Activating current was smallest with 1 mmol/L [K+]o and largest with 20 mmol/L [K+]o. However, after relief of inactivation by a brief hyperpolarizing pulse, instantaneous current was largest on 1 mmol/L [K+]o and smallest at 20 mmol/L [K+]o (arrows). In addition, the time constant of inactivation (9 ms in [K+]o=1 mmol/L, 33 ms in [K+]o=20 mmol/L) and the time constants of deactivation were longer at the higher [K+]o values. Summary data for these time constants are presented in Fig 9.

Fig 8 shows I-V curves for activating I_Kr at [K⁺]_o at 1, 4, and 20 mmol/L. With step depolarizations, prominent inward rectification was evident, and the currents were larger at 20 than at 1 mmol/L. In contrast, using the approach shown in Figs 6 and 7 to remove I_Kr inactivation, near-ohmic I-V curves are apparent. Furthermore, the curves were parallel, differing only in their x intercepts (reversal potentials), indicating that the rectification of I_Kr can be attributed virtually exclusively to rapid inactivation. The reversal potentials were consistently slightly positive to those predicted by the Nernst equation: -109±3 (observed) versus -127 mV (predicted) at 1 mmol/L, -80±1 versus -91 mV at 4 mmol/L, and -49±2 versus -50 mV at 20 mmol/L.

View larger version (23K): [in this window] [in a new window]   Figure 8. IKr rectification is determined by fast inactivation. IKr was measured as dofetilide-sensitive current as in Figs 5 and 6. A, With a "standard" protocol to assess activation at a range of depolarizing potentials, activating IKr displays prominent inward rectification and is greatest at high [K+]o. B, With a protocol designed to relieve rapid inactivation (that shown in Fig 6), the I-V curve for instantaneous IKr, measured immediately after the hyperpolarizing pulse to -120 mV, was virtually ohmic and at any given depolarizing potential was greatest at 1 mmol/L [K+]o. Note the different ordinate scales used: total instantaneous current at +40 mV was up to 10 times greater than activating current.

The experiment shown in Fig 7 indicates not only that the distribution of channel states during depolarizing pulses is [K⁺]_o dependent but also suggests that the transition rates between the states, reflected by the time constants indicated, are similarly [K⁺]_o dependent. Fig 9 shows that with elevated [K⁺]_o, both the inactivatedopen (Fig 2) and openinactivated (Figs 6 and 7) state transitions were markedly slower. However, even at 20 mmol/L [K⁺]_o, the rate of recovery from fast inactivation at -120 mV was still rapid enough that the process was still essentially complete within the 20-ms hyperpolarizing pulse. At potentials <0 mV, inactivation may be contaminated by deactivation (eg, see Fig 6A and 6C), making measured inactivation rate slower than the actual rate. For this reason, points negative to 0 mV are indicated by open symbols in Fig 9B.

View larger version (23K): [in this window] [in a new window]   Figure 9. [K+]o and voltage dependence of time constants for state transitions of IKr. A, Recovery from fast inactivation, measured using dofetilide difference currents and the protocol shown in Fig 2. With [K+]o at 1 mmol/L, time constants were too rapid to be measured at potentials <-90 mV. B, Time constant of fast inactivation of open channels (reinactivation), measured immediately after a brief hyperpolarizing pulse (eg, 18 ms; Fig 3). Open symbols represent possible overlap with deactivation (see text).

	Discussion

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Expression of the human ether-à-go-go–related gene (HERG) results in a current that recapitulates most of the physiological and pharmacological characteristics of I_Kr. These include inward rectification, [K⁺]_o sensitivity, and drug block.^{23 24 25} Importantly, block of I_Kr can produce marked prolongation of the QT interval and the distinctive polymorphic ventricular tachycardia, torsades de pointes²⁶ ; mutations in HERG cause the congenital long-QT syndrome, which has many of the same characteristics.^{27 28} Further studies comparing the behavior of heterologously expressed HERG with that of I_Kr recorded in cardiac myocytes are important not so much to demonstrate that HERG expression results in an I_Kr-like channel (that seems well established) but to define the extent to which the current observed with heterologous expression might differ from that in the myocyte. For example, activation of HERG currents in oocytes²³ or in transfected noncardiac mammalian cells¹³ is much slower than that reported in human cardiac myocytes,^{29 30} although temperature might help explain this difference. We have found drug block of I_Kr to be [K⁺]_o dependent⁴ in AT-1 cells, whereas drug block of HERG currents in oocytes has been reported to be [K⁺]_o insensitive.²⁵ Further definition of the mechanisms underlying differences between I_Kr and current observed with HERG expression should provide important insights into the function of HERG-mediated currents in myocytes.

A number of groups have reported that when HERG is expressed in oocytes^{10 14 15 16} or in noncardiac mammalian cells,^{12 13} the observed current displays I_Kr-like rectification that can be relieved using brief hyperpolarizations. Thus, the present experiments indicate that the mechanism underlying rectification of I_Kr in cardiac myocytes is very similar to that found with heterologous expression of HERG. Liu et al³¹ have reported that the delayed rectifier in ferret atrial myocytes also displays this behavior. Moreover, the present data, as well as previous studies involving guinea pig myocytes (where a prominent I_Ks is present)¹⁰ and, more recently, expressed HERG confirm the suggestion that intracellular Mg²⁺ does not mediate I_Kr rectification.¹¹ An important new finding in the present studies (previously suggested in studies of HERG expressed in Xenopus oocytes¹⁴ ) is that rapid inactivation is also the mechanism that determines another important physiological characteristic of I_Kr, its unusual sensitivity to changes in [K⁺]_o.

The approach we and others have used assumes that recovery of inactivated channels to the open state takes place much faster than open-channel deactivation, thereby allowing separation of the two processes. Indeed, if the duration of the hyperpolarizing pulse is prolonged, we did observe a decrease in the subsequent activated current (Fig 4). The finding that the time course of the outward peak currents following the hyperpolarizing pulse paralleled that of the current observed during a long hyperpolarization (ie, an envelope test is satisfied) indicates that channel recovery from inactivation during a hyperpolarizing pulse does determine the availability of open channels during the subsequent repolarizing pulse. We also make the simplifying assumption of a three-state model to provide a framework within which to conceptualize the relationship between inactivation and rectification. The sigmoid nature of activation with some depolarizing pulses speaks to the fact that this must be a simplification. Similarly, this model does not explain the very slow inactivation we and others have observed both in AT-1 cells¹⁸ and in human myocytes.^{29 30} When HERG was expressed in Xenopus oocytes, the voltage dependence of the time constants for inactivation and for recovery from fast inactivation was similar to that observed here.¹⁰ However, the actual rates were somewhat faster, raising the possibility of a species difference or of a difference between HERG (expressed in Xenopus oocytes) and I_Kr (in cardiac myocytes). Such a difference is further suggested by the recent cloning of a "cardiac-specific" ERG isoform from mouse³² and the report of altered I_Kr deactivation kinetics with coexpression of the cardiac and other ERG isoforms.³³ As discussed above, it is also possible that at negative potentials, the measured inactivation rate is contaminated by channel deactivation. Liu et al³¹ have presented evidence that modeling I_Kr in ferret cells requires at least four states. In their studies, fast inactivation was relatively insensitive to voltage (as in our Fig 9B), and activation was dependent on at least two processes, one voltage dependent and one voltage independent. The same group has more recently reported that when HERG is expressed in Xenopus oocytes, the rate of recovery from fast inactivation was decreased when [K⁺]_o was increased from 2 to 98 mmol/L.³⁴ However, the rates of recovery from fast inactivation that would occur over the lower range of [K⁺]_o used in the present study have not been studied.

Multiple mechanisms are thought to underlie inactivation in voltage-gated ion channels.³⁵ With N-type inactivation, a "ball-and-chain" mechanism has been proposed.^{36 37} With C-type inactivation, on the other hand, a direct effect of channel protein conformational transitions on the conducting pore is envisioned.³⁷ Smith et al¹² have now shown that inactivation is entirely removed by mutations on the extracellular face near the pore-S6 junction, indicating similarity to a C-type inactivation mechanism. Presumably, K⁺ ions interact with this site to affect C-type inactivation. Indeed, slowing of inactivation by elevation of [K⁺]_o has been reported for expressed HERG,¹⁴ for rapidly inactivating members of the Shaker family,^{38 39} and now for I_Kr (Figs 7 and 9); as discussed below, this slowing may contribute to the greater amplitude of activating I_Kr at elevated [K⁺]_o. Interestingly, preliminary studies indicate that the methanesulfonanilide E4031 (a compound with structural and pharmacological features similar to dofetilide) probably blocks the channel from the intracellular side.⁴⁰ Thus, the effect of changing [K⁺]_o to modulate drug block may not be determined at a single-channel protein domain. For example, conformational changes induced by [K⁺]_o effects at extracellular sites may make intracellular binding drug domain(s) more or less accessible. Another possibility is that competition between drug block and fast inactivation may change the apparent time course of block and possibly the apparent affinity, as suggested previously.¹³ The observed [K⁺]_o-induced changes in the rate constants for fast inactivation could then indirectly modulate observable block. The mechanism(s) underlying modulation of drug block by changing [Mg²⁺]_i remains to be determined, but in this case, a direct interaction between [Mg²⁺]_i and drug at a distinct binding site in the channel protein is one possibility.

The magnitude of macroscopic current during a depolarizing pulse will be determined by partitioning between open and inactivated channel states and by the time courses of the closedopen and openinactivated transitions. Even though faithful recapitulation of I_Kr may require models with multiple closed, open, or inactivated states, the smaller activating current in low [K⁺]_o suggests decreased open-channel probability at steady state. Shibasaki² demonstrated that single-channel conductance was dependent on [K⁺]_o, which was studied at values of >50 mmol/L; for example, increasing [K⁺]_o from 100 to 300 mmol/L increased conductance from 8 to 15 pS. However, it is not known whether such an effect contributes at all at the lower more physiological [K⁺]_o values we studied. For "conventional" inactivating channels, channel opening is much faster than inactivation, and a characteristic transient current signature results. For I_Kr, it is now apparent that the reverse is the case: the openinactivated transition occurs much more rapidly than does the closedopen one.² It has been suggested that hyperpolarization-mediated fast recovery from inactivation might result in a dramatic increase in I_Kr during repolarization, in analogy to the experiment shown in Fig 3B, and that this increase in I_Kr might thus be antiarrhythmic by inhibiting early afterdepolarizations.⁴¹ However, our data indicate that entry and exit from inactivated state(s) is very rapid, even at room temperature. Given the slow time course of repolarization in cardiac cells, it becomes difficult to conceive of the conditions under which the relief of inactivation by brief hyperpolarization (an entirely unphysiological event) might play such a direct antiarrhythmic role. However, mutations in HERG or the use of I_Kr-blocking drugs are both associated with torsade de pointes, which is thought to arise from early afterdepolarizations. If the mechanisms underlying reduced I_Kr under these circumstances were to involve sequestration of channels in the inactivated, rather than open, states during depolarization, a direct role of fast inactivation in arrhythmogenesis (and of normal inactivation in arrhythmia suppression) might be inferred. Generically, any augmentation of outward current during repolarization would shift the balance between inward and outward current during repolarization and might therefore inhibit the development of the inward current(s), such as L-type Ca²⁺ current reactivating through a window mechanism, responsible for early afterdepolarizations.⁴² Thus, a major role for I_Kr in normal physiology may be to repolarize cells sufficiently rapidly to avoid such arrhythmogenic mechanisms.

We have previously pointed out that the greater sensitivity of I_Kr to drug block at low [K⁺]_o may explain the well-recognized effect that hypokalemia promotes torsades de pointes.⁴ Moreover, this finding suggested that interventions (such as administration of K⁺) to increase [K⁺]_o should prove antiarrhythmic in torsade de pointes related to decreased I_Kr; indeed, clinical studies lend some support to this concept.^{43 44} The present data further suggest that drugs whose major effect is to prevent or delay I_Kr inactivation might also reverse torsades de pointes. In addition, the decreased sensitivity at high [K⁺]_o may provide an explanation for the "reverse use-dependent" effect of blocking drugs on action potential duration⁴ and raises the possibility of diminished drug effect during ischemia, which is frequently accompanied by elevations in [K⁺]_o. Our findings demonstrating inhibition of block by low intracellular [Mg²⁺]_i have similar implications: we speculate that with chronic hypomagnesemia (that may decrease [Mg²⁺]_i), drug block will be diminished. Moreover, since these changes are frequently inhomogeneous, they would be expected to exaggerate dispersion of action potential durations, a potentially arrhythmogenic effect. Thus, the further elucidation of the mechanisms underlying modulation of drug block by changes in intracellular and extracellular cations may provide clues to the development of safer ion channel blocking drugs.

	Selected Abbreviations and Acronyms

 

= time constant I-V = current-voltage IK = delayed rectifier K+ current IK1 = inward rectifier current IKr = rapid component of IK

	Acknowledgments

 
This study was supported in part by grants from the US Public Health Service (HL-49989, HL-46681, and HL-47599). Dr Roden is the holder of the William Stokes Chair in Experimental Therapeutics, a gift from the Daiichi Corp.

	Footnotes

 
Previously presented in part in abstract form (Biophys J. 1995;68:A110; Biophys J. 1996;70:A276).

Received December 19, 1996; accepted March 4, 1997.

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