Drug-induced block of the cardiac rapid delayed rectifying potassium current (IKr), carried by the human ether-a-go-go-related gene (hERG) channel, is the most common cause of acquired long QT syndrome. Indeed, some, but not all, drugs that block hERG channels cause fatal cardiac arrhythmias. However, there is no clear method to distinguish between drugs that cause deadly arrhythmias and those that are clinically safe. Here we propose a mechanism that could explain why certain clinically used hERG blockers are less proarrhythmic than others. We demonstrate that several drugs that block hERG channels, but have favorable cardiac safety profiles, also evoke another effect; they facilitate the hERG current amplitude in response to low-voltage depolarization. To investigate how hERG facilitation impacts cardiac safety, we develop computational models of IKr block with and without this facilitation. We constrain the models using data from voltage clamp recordings of hERG block and facilitation by nifekalant, a safe class III antiarrhythmic agent. Human ventricular action potential simulations demonstrate the ability of nifekalant to suppress ectopic excitations, with or without facilitation. Without facilitation, excessive IKr block evokes early afterdepolarizations, which cause lethal arrhythmias. When facilitation is introduced, early afterdepolarizations are prevented at the same degree of block. Facilitation appears to prevent early afterdepolarizations by increasing IKr during the repolarization phase of action potentials. We empirically test this prediction in isolated rabbit ventricular myocytes and find that action potential prolongation with nifekalant is less likely to induce early afterdepolarization than action potential prolongation with dofetilide, a hERG channel blocker that does not induce facilitation. Our data suggest that hERG channel blockers that induce facilitation increase the repolarization reserve of cardiac myocytes, rendering them less likely to trigger lethal ventricular arrhythmias.

## Introduction

A rapid component of the delayed-rectifier potassium current (IKr) plays an important role in the repolarization of the cardiac action potential (AP). IKr is especially important in ventricular muscle of the hearts of large mammals. Certain blockers of IKr are class III antiarrhythmic agents, used to treat ventricular tachyarrhythmias (Sanguinetti and Jurkiewicz, 1990; Vaughan Williams, 1992; Zeng et al., 1995; Clancy et al., 2003). Blockers of IKr prolong the AP duration (APD) and effective refractory period to suppress premature ventricular contraction. Blockade of IKr also is a side effect of many drugs. Blockers of IKr can cause acquired long QT syndrome and the life-threatening ventricular tachyarrhythmia called “torsades de pointes” (Surawicz, 1989; Sanguinetti et al., 1995; Roden, 2000, 2008; Sanguinetti and Tristani-Firouzi, 2006). At the myocardial cellular level, the development of abnormal transient depolarization during AP repolarization phase called early afterdepolarization (EAD) has been considered as a trigger of lethal arrhythmias related to the usage of IKr blockers (Roden, 2000, 2008; Thomsen et al., 2003; Nattel et al., 2007; Weiss et al., 2010). Emphasis on detecting IKr blockade early in drug discovery (ICH, 2005) has contributed to the successful removal of torsades de pointes risk for new chemical entities. However, there is concern that promising new drug candidates are being unnecessarily discarded because they benignly block IKr (Sager et al., 2014; Gintant et al., 2016). Indeed, numerous examples exist of drugs that block IKr and prolong the QT interval but have little proarrhythmic risk (De Ponti et al., 2001; Redfern et al., 2003).

The human ether-a-go-go-related gene (hERG) encodes the ion channel through which IKr current passes (Sanguinetti et al., 1995; Trudeau et al., 1995). We have found that some hERG blockers also increase hERG currents at potentials close to the threshold for channel activation. We refer to this electrical phenomenon as “facilitation” (Hosaka et al., 2007; Furutani et al., 2011; Yamakawa et al., 2012). A series of hERG blockers with lower proarrhythmic risk were found to evoke facilitation of hERG (Hosaka et al., 2007; Furutani et al., 2011; Yamakawa et al., 2012). The correlation between clinical safety and facilitation led to our current hypothesis: facilitation by hERG blockers increases IKr during cardiac AP repolarization and thereby decreases their proarrhythmic risk. Stringently testing this hypothesis requires a system in which facilitation can be selectively removed from an hERG blocker’s mechanism. In the present study, we test the aforementioned facilitation hypothesis by developing a mathematical model of the actions of nifekalant, a hERG channel blocker that induces facilitation and has been used safely in the treatment of life-threatening ventricular tachyarrhythmias (Nakaya et al., 1993; Takenaka et al., 2001; Igawa et al., 2002; Sato et al., 2017), and calculating the impact of facilitation on the APs of human ventricular myocytes.

## Materials and methods

### Cell preparation and hERG channel current recording

Frogs (Xenopus laevis) were treated in accordance with the guidelines for the use of laboratory animals of Osaka University Graduate School of Medicine. Isolation and maintenance of the oocytes and injection with complementary RNA (cRNA) were performed as previously described (Hosaka et al., 2007; Furutani et al., 2011; Yamakawa et al., 2012). The hERG expression plasmid (provided by Drs. M.T. Keating and M.C. Sanguinetti, University of Utah, Salt Lake City, UT; Sanguinetti et al., 1995) was verified by sequencing, linearized, and transcribed in vitro using the mMESSAGE mMACHINE Transcription kit (Thermo Fisher Scientific). The oocytes were injected with 5 ng hERG cRNA and incubated at 18°C in ND96 solution (96 mM NaCl, 2 mM KCl, 1.8 mM CaCl2, 1 mM MgCl2, and 5 mM HEPES, pH 7.6 with NaOH) supplemented with 50 µg/ml gentamicin. Membrane currents were recorded with the two-electrode voltage-clamp technique with a GeneClamp 500 amplifier (Axon Instruments) 4–7 d after cRNA injection. The glass electrodes had resistances of 0.4–1.5 MΩ when filled with 3 M KCl. Oocytes were bathed in a low-Cl solution (96 mM Na-2-(N-morpholino) ethanesulfonic acid [NaMes], 2 mM KMes, 2 mM CaCl2, 1 mM MgCl2, and 5 mM HEPES, pH 7.6 with methane sulfonic acid) to minimize interference from endogenous Cl currents. Oocyte experiments were conducted at room temperature (22–25°C).

A human embryonic kidney (HEK) 293 cell line stably expressing hERG was provided by Dr. C.T. January (University of Wisconsin–Madison, Madison, WI) and maintained in minimum essential medium supplemented with 10% FBS and 400 µg/ml G418 (Axenia Biologix) as previously described (Zhou et al., 1998). Ventricular myocytes were enzymatically isolated from the rabbit ventricles on the day of electrophysiological experiments as previously described (Wood et al., 2018). HEK cells or cardiac myocytes used for electrophysiological study were adhered to the poly-l-lysine–coated (MW 30,000–70,000; Sigma-Aldrich; 0.1 mg/ml for 2 h at 37°C) coverslips in 12-well plates and transferred to a small recording chamber mounted on the stage of an inverted microscope (Axiovert S100; Carl Zeiss) and were continuously superfused with HEPES-buffered Tyrode’s solution containing (in mM) 137 NaCl, 4 KCl, 1.8 CaCl2, 1 MgCl2, 10 glucose, and 10 HEPES, pH 7.4 with NaOH. Membrane currents were recorded in a whole-cell configuration established using pipette suction (Hamill et al., 1981). Leak compensation was not used. The borosilicate micropipette had a resistance of 2–4 MΩ when filled with the internal pipette solution containing (in mM) 120 KCl, 5.374 CaCl2, 1.75 MgCl2, 10 EGTA, and 10 HEPES, pH 7.2 with KOH. Liquid junction potential with this internal solution was less than −4 mV, and the offset was not corrected. Series resistance was typically 5 MΩ. Series resistance compensation was used when needed to constrain voltage error to 10 mV. Whole-cell recordings were performed using an Axopatch 200B patch-clamp amplifier (Molecular Devices), ITC-18 interface, and PatchMaster software (HEKA Elektronik). The data were stored on a computer hard disk and analyzed using PatchMaster and Igor Pro 7 (WaveMetrics). In AP clamp experiments, we used the human ventricular AP waveform simulated with our AP model as voltage-clamp commands. In AP recordings, ventricular myocytes were stimulated with minimal suprathreshold current pulses (2 ms) at a cycle length of 2,000 ms in whole-cell current clamp mode. Beat-to-beat instability of AP was assessed by calculating the standard deviation of APD measured at 90% repolarization, APD90, based on 30 consecutive beats. EAD was defined as a transient depolarization during AP phases 2 and 3. Experiments to characterize hERG facilitation (Fig. 1; Fig. 2, A–G; Figs. S1, S2, and S3) were performed at room temperature (22–25°C), and experiments to test the prediction from simulation studies (Figs. 2 H and 11) were performed at 37.0°C, which was maintained with a CL-200A temperature controller (Warner Instruments).

Nifekalant was obtained from Nihon Schering and Cayman Chemical. Dofetilide was obtained from Alomone Labs. For comparisons of dofetilide and nifekalant effects on APs in ventricular myocyte, stock solutions were prepared, and then the researcher was blinded to their identity during experiments and analysis.

MiRP1 (KCNE2) is a β-subunit of IKr (Abbott et al., 1999). We examined whether nifekalant caused distinct effects on currents mediated by hERG alone and by hERG and KCNE2. Rat KCNE2 was provided by Dr. K. Nakajo (Jichi Medical University, Shimotsuke City, Japan), subcloned into a mammalian expression vector, pcDNA3 (Thermo Fisher Scientific), and verified by sequencing. Rat KCNE2 was cotransfected with a hERG expression plasmid and a GFP marker plasmid (pCA-GFP) into HEK293 cells by using Lipofectamine 2000 reagent (Thermo Fisher Scientific), following the manufacturer’s instructions (typically 0.5 µg of total DNA/1.5 µl of Lipofectamine 2000 per well in 12-well plates). Transfected cells were identified by GFP fluorescence and modified hERG gating by KCNE (rightward shift in half-activation voltage, V1/2; −10.4 ± 1.5 mV for hERG alone vs. −4.2 ± 2.8 mV for hERG with KCNE2; Abbott et al., 1999). We found that the drugs caused similar effects on currents from hERG + KCNE2 and hERG alone (currents not depicted) and that the V1/2 shift due to nifekalant facilitation was similar (Table 1). As KCNE2 did not appear to impact the mechanism of facilitation, we used HEK cells and oocytes expressing hERG channels alone for further experiments.

### Formulations of kinetic properties for hERG current

To model the macroscopic current of hERG channels expressed in HEK293 cells, we first estimated the kinetics of the channels. The voltage-dependent activation kinetics (time constant of activation) was determined from current activation experiments (Fig. 2 A). The activation time constant was measured by fitting IKr activation at each depolarized voltage pulse, Vdepo (typically Vdepo greater than −40 mV), with a single exponential function:

$I act ( t )=K[ 1−exp(−t/τ xr ( V depo ) ],$
(1)

where K is the asymptote and τxr(Vdepo) is the activation time constant. Fig. 2 A and Fig. S3 A show the activation time constants as a function of Vdepo. Furthermore, the voltage-dependent deactivation kinetics were divided into two processes (i.e., fast and slow processes) in accordance with the O’Hara–Rudy formalism (O’Hara et al., 2011). From current deactivation experiments (Fig. S3 B), the deactivation time constants were measured by fitting IKr deactivation at each repolarized voltage pulse, Vrepo (typically Vrepo less than −30 mV), to a double exponential function:

$I deact ( t )=K+A 1 ⋅exp[ −t/τ xr,fast ( V repo ) ]+ A 2 ⋅exp[ −t/τ xr,slow ( V repo ) ],$
(2)

where K is the asymptote, and A1 and A2 are the relative components of the fast and slow processes; and τxr,fast and τxr,slow are the fast and slow deactivation time constants, respectively. Fig. S3 (C and D) shows the fast and slow deactivation time constants as a function of Vrepo, respectively. Each time constant value in Eqs. 1 and 2 was determined by nonlinear least-squares fitting. From these experimental data and comparison with kinetics parameters of hERG channel in other experiments (Table S1), the activation and deactivation time constants were expressed as continuous functions of membrane potential, Vm, as follows (Fig. S3, E and F).

For τxr,fast,

$τ xr,fast =1,400 1+exp( V m +10.0 13.8 ) +1,300⋅ [ 1 1+exp( −V m +55.0 12.3 ) −1 ].$
(3)

For τxr,slow, if Vm ≥ −80 mV,

$τ xr,slow =5,000 1+exp( V m +22.8 11.5 ) +2,000 1+exp( V m +25 2.5 ) + 4,000 1+exp( −V m +61.5 5.0 ) +3,000 1+exp( −V m +54 2.5 ) −7,000,$
(4)

and if Vm −80 mV,

$τ xr,slow =2,000+8,000 1+exp( −V m +74.9 10.2 ) .$
(5)

### Modeling of IKr

The IKr current was defined as

$IKr=GKr⋅Op⋅RKr⋅(Vm−EK),$
(6)

where GKr is IKr conductance (mS/μF) under the drug action, Vm is the membrane potential (mV), EK is the reversal potential, Op is the open state variable in the activation of IKr channel, and RKr is a time-independent function related to the inactivation property for IKr. The voltage dependence of the Op in Eq. 6 was defined as

$O p =f⋅x r1 +( 1−f )⋅x r2 ,$
(7)

where xr1 and xr2 are voltage-dependent activation variables for unfacilitated and facilitated components in the IKr, respectively, and f is a fraction of unfacilitated component in IKr current. The dose–fraction relationship of f for nifekalant with an EC50 of 92.84 nM and a Hill coefficient (he) of 1.50 was represented as follows:

$f=11+([D]EC50)he.$
(8)

In O’Hara–Rudy dynamic (ORd) model (O’Hara et al., 2011), the voltage-dependent activation variable was comprised of two variables as follows:

$xri=Axr,fast⋅xri,fast+Axr,slow⋅xri,slow,$
(9)

where i represents the voltage-dependent type, where the voltage-dependent type can be unfacilitated (xr1) or facilitated (xr2) activation variables, and Axr,fast and Axr,slow (≡ 1−Axr,fast) are the fraction of channels with IKr activation gate undergoing fast and slow processes, respectively. The fraction Axr,fast was obtained as the following function that best reproduces voltage clamp experimental data (Fig. 2):

$A xr,fast =0.05+0.95 1+exp( V m +73.4 16.0 ) .$
(10)

The unfacilitated (xr1) and facilitated (xr2) activation variables were calculated with the following first-order differential equation:

$dxri,j/dt=Φ⋅(xri,∞−xri,j)/τxr,j,$
(11)

where xri,, for i = 1, 2, is the steady-state value of xri,j, i.e., the voltage-dependent activation curve in the hERG channel; τxr,j for j = fast, slow, is the time constant for xri,j; and Φ is a temperature coefficient as expressed at 3[(T−25)/10], where T is temperature. The voltage-dependent activation curve in the hERG channel (xri,, for i = 1, 2) is well represented by a single Boltzmann function. Based on our experimental data (Fig. 2, A and C), we set the Boltzmann function’s half-activation voltage (V1/2) and the slope factor to –10.7 mV and 7.4, respectively, as the voltage dependence of the unfacilitated component (xr1,) in IKr activation, and shifted the voltage dependence of facilitated components (xr2,) in IKr activation by 26.5 mV in the negative direction (Fig. 2 G), i.e.,

$x r1,∞ =1 1+exp( −V m +10.7 7.4 ) ,$
(12)

$x r2,∞ =1 1+exp( −V m +37.2 7.7 ) .$
(13)

Furthermore, the RKr was reconstructed as the following function that best reproduces voltage clamp experimental data (Fig. 2 A):

$R Kr =[ 0.12+0.88 1+exp( V m +60.3 27 ) ]⋅ [ 0.32+0.68 1+exp( V m −7 20 ) ].$
(14)

Based on our experimental measurement (Figs. 2 and S4), the GKr of when the IKr was blocked by nifekalant in a concentration-dependent manner with an IC50 of 145 nM and a Hill coefficient (hi) of 1.15 was represented as follows:

$G Kr =g Kr ⋅1 1+( [D] IC 50 ) h i$
(15)

where [D] is the drug concentration (nM) and gKr is the IKr channel conductance absent drug. The gKr was set to 0.058 mS/μF to recapitulate the APD of endocardial myocyte represented in the ORd model (O’Hara et al., 2011).

In addition, we constructed a conventional block model modified only in IKr conductance (block without facilitation model) for comparison with the block model with facilitation.

### Electrophysiological models for AP simulations

Replacing the IKr model in the original ORd model (O’Hara et al., 2011) into our aforementioned experimental based IKr model, we modified the ORd model and constructed three AP models (endocardial [ENDO], midmyocardial [MID], and epicardial [EPI]) describing cells from ENDO, MID, and EPI layers of the ventricular wall according to O’Hara et al. (2011). Scaling factors for heterogeneous model implementation are summarized in Table S2. To evaluate the impact of the IKr facilitation effect on the vulnerability for EAD development in patients with heart failure, we also constructed a heart failure model. The electrical remodeling of cardiomyocytes in failing hearts is characterized by decreases in outward ionic currents, including IKr, the slow component of the delayed-rectifier potassium current (IKs), and Na+-K+ pump current (INaK), as well as an increase in Na+/Ca2+ exchanger current (INCX). Based on a previous study (Elshrif et al., 2015), we made several modifications of the ORd endocardial myocyte model (see details in Elshrif et al. [2015] and Table S3). These modified ORd models (non–heart failure and heart failure models) that were constructed in the present study were also implemented in an XML-based Physiological Hierarchy Markup Language (PHML), which is available as an open-access resource (http://physiodesigner.org/; Asai et al., 2013). Details on the modified ORd models as non–heart failing (and failing) endocardial myocytes with and without facilitation effect can referred from PHML models in PH database (https://phdb.unit.oist.jp/modeldb/; ID931 to 936).

For examining effects of facilitation on AP morphology, we further used two mathematical models published by ten Tusscher and colleagues (ten Tusscher et al., 2004; ten Tusscher and Panfilov, 2006; referred to as the TNNP model) representing human ventricular myocytes and by Faber and Rudy (2000) (referred to as the FRd model) representing guinea pig ventricular myocytes. The TNNP model was modified based on a previous theoretical study (Vandersickel et al., 2014) for enhancing EAD development. Furthermore, for the FRd guinea pig model, we made a few modifications based on the EPI myocyte model and constructed MID and ENDO myocyte models. Parameter modifications in both TNNP and FRd models are provided in Table S3. In both TNNP and FRd models, the facilitated component that the voltage-dependence of IKr activation shifted by 26.5 mV in the negative direction was added to each AP model.

### Simulation protocol and computation

Voltage-clamping simulations for calculating IhERG for each clamped voltage pulse with 4-s duration (Fig. 2) were performed using a homemade C language program, simulating by the forward Euler method with a 0.01-ms time step. The activation variables (xri, for i = 1, 2) was set equal to zero as an initial condition.

The simulated AP was calculated by the fourth-order Runge–Kutta method with double precision numbers. To minimize transient responses in each simulation, pacing stimuli of threefold diastolic threshold and the stimuli were applied repeatedly until the AP response observed in all the models reached the stationary state. To evaluate the effects of hERG channel blockade on the vulnerability of a cardiomyocyte to premature ventricular contractions, additional simulations were performed using the S1–S2 stimulation protocol: S1 stimuli until the AP converged to a steady state were applied at the stimulating frequency of 1 Hz followed by an S2 stimulus with various coupling intervals. When the effects of the hERG channel blocker on APs were examined, the stimulating frequency was set to 0.5 Hz for the ORd and TNNP models to avoid the stimulus being applied before the complete repolarization of the AP. In the FRd model, the stimulating frequency was set to 1 Hz. All simulations were encoded in C/C++ and run on an IBM-compatible computer with the Intel ICC compiler version 15.0.1. In addition, major AP simulations presented in this study can be reproduced by performing their PHML model simulations using Flint software (http://www.physiodesigner.org/simulation/flint/).

### Online supplemental material

Fig. S1 shows the concentration dependence of hERG block by nifekalant and dofetilide in Xenopus oocytes and HEK293 cells. Fig. S2 shows the voltage dependence of induction of hERG facilitation. Fig. S3 shows the voltage dependence of activation and inactivation time constants of hERG channel. Fig. S4 shows the agreement of the concentration dependence of nifekalant-induced hERG block and facilitation in the experiments and simulations. Fig. S5 shows the impact of facilitation on the APD in normal heart. Table S1 shows the time constants of hERG/IKr activation and deactivation. Table S2 shows the scaling factors for heterogeneous model implementation in ORd models. Table S3 shows the modification parameters of the relevant models.

## Results

### AP voltage stimuli induce facilitation by nifekalant

The degree of facilitation of IKr depends on the dose of hERG blocker and the membrane’s history of voltage changes. Facilitation by blockers, with the exception of amiodarone derivative KB130015 (Gessner et al., 2010), requires a preceding strong depolarization as a conditioning stimulus (Carmeliet, 1993; Jiang et al., 1999; Hosaka et al., 2007; Furutani et al., 2011; Yamakawa et al., 2012). To test whether cardiac APs are sufficient to stimulate facilitation, we applied an AP clamp protocol to hERG channels. This experiment assessed hERG current at −50 mV, a potential near its activation threshold which leaves the majority of channels closed. To achieve an adequate signal-to-noise ratio, we used Xenopus oocytes to express a high density of hERG channels in a membrane with minimal endogenous currents. Based on our pilot studies in Xenopus oocyte expression system (Figs. S1 and S2), we chose 30 µM nifekalant, the concentration close to the IC50 (16.6 ± 2.4 µM, n = 5), as the drug concentration to ensure that the assessment of the stimulus-dependent increases respond to preceding pulses. Xenopus oocytes were kept at ∼18°C until the recordings, and in our experience hERG currents, become unstable after heating to 37°C. For this reason, we recorded from oocytes at room temperature. We first confirmed that a step depolarization (+60 mV for 4 s) as a preceding conditioning pulse could induce the facilitation effect of nifekalant (Fig. 1). Similar to the strong step depolarization, repeated stimulation with a human ventricular myocyte waveform at 1 Hz induced facilitation of nifekalant-treated hERG channels (Fig. 1). The facilitation effect on hERG current saturated as the number of APs increased, indicating that facilitation reached 90% of its steady-state level within 20 heartbeats (Fig. 1 C). Without nifekalant, this voltage protocol induced little, if any, increase in hERG current (Fig. 1 D). The induction of facilitation by cardiac AP stimuli suggests that facilitation is potentially physiologically relevant.

### Facilitation can be incorporated into cardiac electrophysiology modeling

To understand how facilitation could impact cellular electrophysiology mechanisms specific to human ventricular myocytes, we performed calculations with the ORd human ventricular AP model (O’Hara et al., 2011). First, we modified the IKr formula in the ORd model to reproduce hERG channel block by nifekalant, with or without facilitation. The modified IKr formula was first constrained by currents recorded from HEK cells expressing hERG (Fig. 2, A–C; and Fig. S3). These voltage clamp recordings typically required 40–60 min, and our experience conducting experiments at 37°C suggested the whole-cell recording configuration would be more stable at room temperature over these long durations. Consequently, electrophysiology on HEK cells was conducted at room temperature, and kinetics were corrected post hoc for AP modeling at 37°C. Fig. 2 shows the agreement of our IKr model with hERG current from HEK cells and its modulation by nifekalant. Left panels of Fig. 2 (D and E) show experimental hERG currents blocked with 100 nM nifekalant, before (magenta traces) and after (green traces) the induction of facilitation effect by a conditioning pulse. After the induction of the facilitation effect, nifekalant enhanced the current induced by a −30-mV pulse (Fig. 2 D), but it still suppressed the current induced by a +30-mV pulse (Fig. 2 E). The current enhancement is due to a modification of channel activation gating that shifts the voltage dependence to more hyperpolarized membrane potentials (Hosaka et al., 2007; Furutani et al., 2011). The voltage dependence of the hERG current in the facilitation condition could be described as the sum of two Boltzmann functions reflecting two populations of hERG currents having different activation voltage dependences (Furutani et al., 2011). The high-V1/2 fraction of the channel population has biophysical characteristics typical for the hERG channel, while the low-V1/2 fraction is facilitated. The facilitated V1/2 was shifted negative by −26.5 mV (Table 1). This shift was consistent with that of hERG channels expressed in Xenopus oocytes (Furutani et al., 2011). Thus, the facilitation effect could be explained by a fraction of channels opening with a negatively shifted activation curve (Fig. 2, F and G). Inclusion of the facilitation effect in the IKr model reproduced measurements of hERG currents from voltage-step experiments (Fig. 2, D–G), and over a range of concentrations (Fig. S4). Thus, modeling facilitation as a negative shift in the voltage-dependence of a component of IKr predicted the drug-dependent facilitation of IKr.

We corrected the effect of temperature on channel gating by the equation QΔT = (Q10)ΔT/10, where Q10 is 10° temperature coefficient of 3. This method is imperfect because hERG kinetics are differentially sensitive to temperature: activation has a Q10 of ∼7.5, deactivation has a Q10 of 1.5, and inactivation and recovery from inactivation each have a Q10 of ∼4 (Zhou et al., 1998). However, the simple assumption of a universal Q10 = 3 appeared adequate: in AP clamp experiments and simulations at 37°C, our corrected IKr model predicted the effects of nifekalant on hERG currents during AP (Fig. 2 H), indicating that the model describes the block and facilitation effects of nifekalant sufficiently to allow assessment of the impact of facilitation in simulations of human ventricular myocyte electrophysiology.

### Facilitation selectively increases IKr during late phase-2 and phase-3 repolarization of cardiac APs

To understand the role of facilitation in the cardiac AP, we investigated the influence of facilitation on AP morphology. When endocardial APs are evoked with 1-Hz pacing, 100 nM nifekalant prolonged the APD measured at 90% repolarization, APD90 (334.4 ms, vs. 257.4 ms in the control condition, see Fig. 3 A), in agreement with experimental results in human ventricular myocytes (Jost et al., 2005). The AP was slightly further prolonged in simulations with IKr block without facilitation (342.0 ms APD90, compare green and magenta traces in Fig. 3 A). In the model, 100 nM nifekalant blocks 40% of total IKr at voltages 0 mV with or without facilitation (Fig. 2 G). When facilitation is implemented in the model, 32% of the hERG channels enter a facilitated state such that they produce substantially more IKr than control conditions when the potential is between −20 and −50 mV (Fig. 2 G). There was little difference between the voltage-dependent activation variables in the IKr model during phase 1 and early phase 2 of the AP (xr1 and xr2 for the unfacilitated channels and facilitated channels, respectively), indicating that IKr behaved similarly (Fig. 3, B and C). This result is consistent with Fig. 2 H and expected, because facilitation has little impact on hERG current amplitudes at positive voltages (Fig. 2, E–G). During late phase-2 and phase-3 repolarization, an increase can be seen in IKr (asterisks in Fig. 3, A–C). However, in block conditions with or without facilitation, the APs were terminated by an increase in the inward-rectifier potassium current (IK1)-mediated repolarization current (Fig. 3 D) before much prolongation of the AP by facilitation. Thus, in this model of a healthy heart under unstressed conditions, only very minimal IKr facilitation is seen in simulations of facilitated IKr during late phase-2 and phase-3 repolarization of the AP (Fig. 3 B) because the facilitation effect of a negative shift in the voltage dependence of IKr activation primarily manifests in a narrow voltage range (−50 to −30 mV; see Fig. 2 G), and the AP only briefly traverses that voltage range.

### Facilitation relieves reverse frequency dependence of APD prolongation

Class III antiarrhythmic agents are hERG blockers that are used clinically to suppress ventricular tachyarrhythmias (Sanguinetti and Jurkiewicz, 1990; Vaughan Williams, 1992; Sanguinetti and Tristani-Firouzi, 2006). To suppress tachyarrhythmias without provoking torsades de pointes, IKr block would ideally be use dependent and prolong APD only in response to high-frequency stimulation (Surawicz, 1989; Hondeghem and Snyders, 1990). Previous studies reported that actions of sotalol (Hafner et al., 1988; Hondeghem and Snyders, 1990) and dofetilide (Tande et al., 1990) trend against this antiarrhythmic ideal by prolonging APDs more at low than high frequencies, showing reverse frequency dependence. Notably, sotalol and dofetilide are hERG blockers that do not induce facilitation (Furutani et al., 2011; Yamakawa et al., 2012). Nifekalant also showed reverse frequency dependence, but it was not as marked (Nakaya et al., 1993; Cheng et al., 1996; Igawa et al., 2002). To determine why, we used our model to test the frequency-dependent effects of nifekalant on APD. The left panel of Fig. 4 shows changes in the APD90 with 100 nM nifekalant at stimulation frequencies from 0.2 to 2 Hz. Without facilitation (magenta trace in Fig. 4 A), the prolongation of APD was more effective at lower stimulation frequencies, resulting in a reverse frequency dependence. When facilitation was included in the model, the reverse frequency dependence became slightly weaker at low frequencies (green trace in Fig. 4 B). APD90 with facilitation was 5.5 ms shorter than without at 2.0 Hz, 7.7 ms shorter at 1.0 Hz, and 10.7 ms shorter at 0.2 Hz (Fig. 4 B). This suggests facilitation can partially relieve the reverse frequency dependence that is a risk factor for torsades de pointes.

### IKr facilitation has greater impacts on repolarization in a failing heart model

Heart failure patients are at risk for malignant ventricular arrhythmias. Clinical and theoretical data have shown that the APs in heart failure patients at slow and modest heart rates are destabilized compared with healthy subjects (Bayer et al., 2010). A more recent study indicated that the APs of the heart failure models exhibit stronger rate dependence compared with the APs of the normal model and can generate EADs and alternans at modest pacing rates (Elshrif et al., 2015). These features are thought to trigger ventricular arrhythmias (Roden, 2000, 2008; Thomsen et al., 2003; Nattel et al., 2007; Weiss et al., 2010). To determine whether facilitation might have a more critical impact on failing hearts, we investigated the frequency-dependent effects of IKr facilitation on the simulated AP in a heart failure model (see Materials and methods; Fig. 5; Elshrif et al., 2015). APs in the heart failure model were prolonged from the control (non–heart failure) model (compare black traces in Fig. 4 B and Fig. 5 B) and were further prolonged by IKr blockade. The effect of facilitation was more prominent with low frequency pacing of the heart failure model, and the reverse frequency dependence of APD prolongation was more dramatically attenuated (compare Fig. 4 A and Fig. 5 A) because the delayed repolarization at low frequency pacing prolongs the latency before facilitation increases the IKr current. APD90 during block with facilitation was 16.5 ms shorter than without facilitation at 2.0 Hz, 36.3 ms shorter at 1.0 Hz, and 53.0 ms shorter at 0.2 Hz (Fig. 5 B), suggesting that the electrical remodeling in failing myocytes makes cellular responses more sensitive to IKr modulation.

Excessive AP prolongation by a hERG blocker showing strong reverse frequency dependence creates an electrophysiological environment that favors the development of EAD at low stimulating frequencies. Increasing IKr block from 40% to 50% caused further APD prolongation (Fig. 5, C and D). Without facilitation, the APD was dramatically prolonged with low-frequency pacing (magenta trace in Fig. 5 C). We found that in the heart failure model paced at 0.2 Hz, EAD appeared at 50% IKr block without facilitation (magenta traces in Fig. 5 D), and facilitation suppressed these EADs (green traces in Fig. 5 D). Although this pacing is unphysiologically slow, these findings suggest hERG facilitation could have a more significant impact on arrhythmogenesis in a failing heart.

APs are heterogeneous between different regions of the ventricles (Drouin et al., 1995,; Konarzewska et al., 1995; Näbauer et al., 1996; Szabó et al., 2005). To test whether the facilitation effects are generalizable to models of myocardial cells from other layers of the ventricular wall or just an oddity of one model of an endocardial cell, we similarly constructed two other AP models (MID, EPI) describing cells from midmyocardial and epicardial layers (O’Hara et al., 2011). We found that IKr facilitation can prevent EAD development not only in the endocardial cell but also in the MID and EPI models (Fig. 7). In addition to the ORd models, we tested if IKr facilitation prevents EAD development in the TNNP human ventricular AP models (ten Tusscher et al., 2004; ten Tusscher and Panfilov, 2006) and in the FRd guinea pig ventricular AP model (Faber and Rudy, 2000). These models differ in the AP configuration/duration and the vulnerability of the regular AP termination to the decrease in IKr. Kinetic parameters of the IKr formula of TNNP models and FRd models are different from those of our modified ORd models. The differences in the ventricular AP models affect the impact of IKr facilitation on AP, but IKr facilitation has a similar preventive effect on EAD development in each model (Fig. 7). This suggests that prevention of EAD development is not an oddity exclusive to any one model and may be a general cardiac electrical phenomenon resulting from facilitation of IKr by blockers. Next, we studied the ionic mechanism by which IKr facilitation prevents EAD development in a cardiac myocyte model.

IKr facilitation suppresses reactivation of L-type Ca2+ channels. In the heart failure model at 55% inhibition of IKr without facilitation (magenta lines in Fig. 8, left), the repolarization delay caused by IKr reduction augmented the window current in L-type Ca2+ channel current (ICaL) during late AP phase 2 with each stimulation (Fig. 8 C, left). As a result, the evoked APs were gradually prolonged with each stimulation, leading to further augmentation of the ICaL window current (Fig. 8 C, left) and AP prolongation (Fig. 8 B, left). Then, the stagnated repolarization caused more reactivation of L-type Ca2+ channels (arrowhead in Fig. 8 C, left), enhancing an inward current component of the net ionic current (Inet) during late AP phase 2 (Fig. 8 D, left). This caused the inward-outward balance of Inet (asterisks in Fig. 8 D, left) that temporally interrupted AP repolarization, followed by a second rising phase of the AP that led to EAD. This IKr block-induced dysfunction eventually converged to a periodic EAD response (Fig. 6 C; Fig. 8 A, right column). In contrast, an increase in IKr due to facilitation (blue arrow in Fig. 8 E, right) enhanced an outward current component in Inet during late AP phase 2 and phase 3 (Fig. 8 D, right). This accelerated the membrane repolarization and completed the AP repolarization (Fig. 8 B, right). Thus, facilitation suppresses EADs by selectively amplifying IKr during late phase 2 and phase 3 of APs when the repolarization is in danger of stagnating. The facilitated IKr overwhelms the reactivating ICaL, preventing EAD.

### Modeling suggests that IKr facilitation could improve patient safety

Class III antiarrhythmic agents are powerful antiarrhythmics used to treat patients with serious ventricular tachycardias in spite of their narrow therapeutic index (Tamargo et al., 2015). The maximal therapeutic dose of class III antiarrhythmics is generally limited by proarrhythmic risk of IKr block. At low doses with minimal proarrhythmic risk, nifekalant suppresses malignant ventricular tachyarrhythmia (Takenaka et al., 2001) and improves short-term and long-term survival of adult patients with ventricular fibrillation/pulseless ventricular tachycardia (Sato et al., 2017). In animal models, a torsades de pointes response was not detected with the therapeutic dose of nifekalant (Satoh et al., 2004), and nifekalant has a broader safety window than IKr blockers without facilitation (Sugiyama, 2008; Yamakawa et al., 2012). To determine whether nifekalant’s favorable safety profile could be related to the facilitation mechanism, we conducted simulations of nifekalant’s predicted safety window with and without facilitation.

We calculated the “therapeutic” dose of nifekalant that prolongs APD90 by 500 ms, an established clinical standard (Igawa et al., 2002; Drew et al., 2010). With facilitation, the simulated therapeutic dose was 278.9 nM (68.0% IKr block); without facilitation, 14% less drug was required, 240.2 nM (64.1% IKr block; Fig. 9). To confirm the antiarrhythmic effect of nifekalant at those therapeutic doses, we assessed the vulnerability of cardiomyocytes to premature excitation. We measured the refractory period of APs in the normal, non–heart failure model by calculating the shortest timing sufficient to produce secondary voltage overshoot by a second stimuli (S2 stimuli) after regular pacing (S1-S2 stimulation protocol). The effective refractory periods with nifekalant were 216 or 215 ms longer than control, with or without facilitation, respectively (Fig. 9), suggesting that facilitation has little impact on effectiveness as a class III antiarrhythmic. We simulated the safety window for nifekalant as the ratio of the dose that produces toxicity (EAD) to the therapeutic dose. Without facilitation, EADs occurred at 657.5 nM, 2.74× the calculated therapeutic dose (Fig. 10). With facilitation, EADs did not occur until 894.5 nM, 3.21× the therapeutic dose. Thus, facilitation widens the simulated safety window for EADs, suggesting that with facilitation an IKr blocker can remain an efficacious class III antiarrhythmic agent, with an improved safety profile.

## Discussion

The objective of this study was to examine the influence of the facilitation mechanism on electrical activity in cardiomyocytes. This mathematical model represents a general view of the role that facilitation may play with IKr blockers. We found that IKr facilitation effects on simulated cardiac APs depended on the AP morphology and APD. Facilitation enhances IKr during prolonged APs. The repolarizing effect of facilitated IKr is augmented at low frequencies and as APD prolongs, thus avoiding repolarization reserve impairment and suppressing EAD development. Therefore, hERG channel blockers with facilitation may offer a safety advantage for arrhythmia treatment.

In a previous article (Furutani et al., 2011), we proposed that the increase in hERG current by facilitation could result from blockers binding to a second site on the channel. In this “two-site” model, increased current arises from a population of channels with blocker bound to a facilitation site causing a shift of voltage-dependent activation gating to more negative potentials. Herein, we used an analytic Hodgkin–Huxley formulation of the two-site model to recapitulate nifekalant’s actions on IKr current as the sum of facilitated and unfacilitated fractions (see Materials and methods). This empirical kinetic description enabled practical calculations of macroscopic electrical responses (Fig. 2), to model how facilitation could impact cellular electrophysiology mechanisms specific to human ventricular myocytes.

We do not yet understand how nifekalant increases the activity of hERG channels in terms of statistical thermodynamics. Facilitation and blockade appear to be inextricably intertwined, as all drugs that cause hERG facilitation are pore blockers of the channel (Carmeliet, 1993; Jiang et al., 1999; Hosaka et al., 2007; Gessner et al., 2010; Furutani et al., 2011; Yamakawa et al., 2012). However, certain mutations in hERG’s S6 helix that lines the K+ conduction path affect facilitation without affecting block, suggesting that drug–channel interactions within the pore are involved in facilitation (Hosaka et al., 2007). This suggests that the coupling between block and facilitation can be altered. Another important characteristic of hERG facilitation is that it requires a preceding depolarization. The voltage dependence of the development of facilitation in the presence of nifekalant was fitted by single Boltzmann function with V1/2 of −19.3 ± 0.9 mV and k of 7.4 ± 0.8 (Fig. S2). Such voltage dependence is similar to the voltage dependence of hERG activation (Table 1, in Xenopus oocytes at room temperature), suggesting the hERG channel opening has a role in developing facilitation effect. In the future, we hope to develop a more satisfying Markov-chain type model based on Eyring rate theory that captures the microscopic kinetics of binding and conformational changes that underlie nifekalant’s actions.

Our conclusions are based on modeling, yet suggest a general cardioprotective mechanism. To exert cardioprotective effects in vivo, certain conditions are required. First, the concentration of the hERG blocker needs to be in a range conducive to facilitation. Second, the membrane potential must depolarize sufficiently to induce the IKr facilitation effect. We have previously reported the concentration- and voltage-dependence relationships between block and facilitation for several drugs in hERG channels expressed in Xenopus oocytes (Furutani et al., 2011; Yamakawa et al., 2012). In the present study, we evaluated the concentration dependence of nifekalant on hERG channels expressed in HEK293 cells (Fig. S1 and Table 2). As in oocytes, the IC50/EC50 for block and facilitation by nifekalant were similar (92.84 ± 7.71 nM for facilitation; 142.6 ± 13.1 nM for block; Table 2). However, for other class III antiarrhythmic agents, the concentration dependences of block and facilitation are distinct. For example, the EC50 for IKr facilitation by amiodarone is lower than that for IC50 block (Furutani et al., 2011). These data indicate that when these agents are administered in the treatment of arrhythmias at concentrations effective for block, they certainly also reach the effective concentration for facilitation. Our experimental data show that facilitation by nifekalant could be induced by cardiac APs (Fig. 1). An important finding of this work is that facilitation had a negligible impact on APs under normal conditions (Fig. 3 and Fig. 4), suggesting that facilitation would not greatly affect normal ECGs. Our simulation study suggests that facilitation may have a selective impact during severe repolarization impairment and heart failure conditions, leading to a lower risk of arrhythmias.

It is widely accepted that IKr plays an important role in the repolarization of the AP (Surawicz, 1989; Sanguinetti and Jurkiewicz, 1990; Zeng et al., 1995; Clancy et al., 2003; Sanguinetti and Tristani-Firouzi, 2006). The decrease in IKr is believed to be associated with EADs, an important cause of lethal ventricular arrhythmias in long QT syndrome and heart failure. Experiments by Guo et al. (2011) in isolated nonfailing human endocardial ventricular myocytes showed EADs in the presence of the IKr blocker dofetilide (0.1 µM, corresponding to ∼85% IKr block; Thomsen et al., 2003), which induces torsades de pointes arrhythmias (Thomsen et al., 2003). In the present study using the modified ORd model, we successfully reproduced the experimental results of Guo et al. (2011), as did the original ORd model (O’Hara et al., 2011). In rabbit ventricular myocytes, we observed EADs with low incidence (26%) in the presence of 1 µM dofetilide. Our result is qualitatively consistent with a previous study that found 1 µM dofetilide induced EADs in a subset (65%) of rabbit ventricular myocytes (Nalos et al., 2012). 10 µM nifekalant did not induce EAD under these same conditions, consistent with models predicting that facilitation prevents EADs. In HEK293 cells either 1 µM dofetilide or 10 µM nifekalant blocks 99% of hERG current (Figs. 11 and S1), which suggests only a small fraction of IKr might be available to be facilitated. However, these hERG blockers act by partitioning into the cell membrane to access cells, and can have dramatically different IC50 values in different cell types (e.g., IC50 for HEK293 cell vs. Xenopus oocytes were 142.6 ± 13.1 vs. 16.6 ± 2.4 µM for nifekalant, respectively; 27.7 ± 5.5 vs. 441.6 ± 24.8 nM for dofetilide, respectively; Fig. S1 and Furutani et al., 2011). hERG blockers have been found to be less effective inhibitors of IKr from isolated myocytes than hERG block in HEK293 cells. For example, E-4031 blocks hERG current in HEK293 cells with an IC50 of 7.7 nM (Zhou et al., 1998) and blocks IKr from rabbit ventricular myocytes with an IC50 of ∼20 nM (Zhou et al., 1995, 1998).

Reverse frequency–dependent action on APs is a property common to class III antiarrhythmic agents (Hafner et al., 1988; Hondeghem and Snyders, 1990; Tande et al., 1990; Carmeliet, 1993; Jurkiewicz and Sanguinetti, 1993; Nakaya et al., 1993; Jiang et al., 1999), and the associated proarrhythmic risk limits their clinical usefulness (Hondeghem and Snyders, 1990; Okada et al., 1996). Reverse frequency dependence of IKr block was first explained by an increase in the slowly activated delayed-rectifier K+ current with rapid heart rates (Jurkiewicz and Sanguinetti, 1993). Drug mechanisms can prolong APD at higher stimulation frequencies to attenuate reverse frequency dependence (Hondeghem and Snyders, 1990). For example, some IKr blockers, such as vesnarinone, have high affinities to opened and/or inactivated hERG channels and exhibit an accumulation of inhibition at higher stimulation frequencies (use-dependent block), reducing proarrhythmic risk (Toyama et al., 1997). In our model, IKr block is not altered by stimulation frequency. Therefore, the reverse frequency dependence may be even less than predicted. Facilitation attenuates reverse frequency dependence by enhancing IKr during late phase 2 and phase 3. The effect on reverse frequency dependence becomes more prominent at higher concentrations of drug. Fig. 4 and Fig. 5 (A and B) show the effects of the modest IKr block by 100 nM nifekalant (∼40% IKr block and ∼32% IKr facilitation). When the drug concentration increased, the effect of facilitation was more prominent (Fig. 5, C and D) because of the concentration-dependent increase in the facilitated fraction and the prolonged phase 2–3 of AP. Under the higher concentrations of blocker, EADs and alternans emerged at low frequencies that dramatically affect APD (Fig. 5, C and D). These EADs were effectively suppressed by IKr facilitation (Figs. 6, 7, 8, and S5).

Previous studies showed that ICaL reactivation is crucial for the development of EADs (Zeng and Rudy, 1995; O’Hara et al., 2011; Tsumoto et al., 2017). Prolongation of the time at plateau voltages caused by IKr block allows ICaL reactivation (O’Hara et al., 2011). The EAD initiation mechanism in the present study is consistent with an ICaL reactivation mechanism (Fig. 8). IKr facilitation accelerates the repolarization just before ICaL reactivation (Fig. 8). Therefore, the inward-outward balance of Inet during the plateau and AP phase 3 is one determinant for the development of EADs. Such inward-outward balance of Inet results from the interaction of ionic mechanisms underlying the cardiac AP. In addition to an increase in IKr by facilitation, these secondary changes may contribute to preventing ICaL reactivation and development of EADs.

Our modeling and experiments indicate that IKr facilitation prevents EAD development, which may decrease proarrhythmic risk. In considering the clinical and physiological relevance of facilitation to class III antiarrhythmic agents, it is important to be aware of the limitations of our study. The models only approximate currents from isolated myocytes. The absolute voltage and concentration dependence of facilitation has not yet been determined with native IKr currents at physiological temperature. Our model of IKr facilitation was constrained by hERG currents from HEK cells recorded at room temperature, and the effect of temperature was imperfectly corrected. We have not yet examined the facilitation effect on native tissues. Additionally, off-target effects of blocker may cause further changes, although appreciable cardiac off-target effects of nifekalant have not yet been found. The experiments conducted with rabbit myocytes here are limited, and are just the beginnings of an in-depth study into induction of EADs by drugs with and without facilitation. These types of experiments serve as an important empirical test of our hypothesis, but ultimately will lack the precision of modeling results, as we are unlikely to find hERG blockers with and without facilitation that otherwise have identical binding and dissociation properties. Therefore, a combination of cardiac AP modeling and experiment are expected to provide greater insights than either alone.

These limitations notwithstanding, this study sheds light on the potential impact of facilitation on cardiac safety. As EAD is considered to be a trigger of drug-induced ventricular tachycardia and torsades de pointes arrhythmia (Roden, 2000, 2008; Thomsen et al., 2003; Nattel et al., 2007; Weiss et al., 2010), facilitation defines a novel mechanism that could suppress proarrhythmic risk and broaden the safety window of hERG blocking agents. The facilitation effect may explain the reason many clinically useful drugs, especially class III antiarrhythmic agents, are surprisingly safe, despite hERG block and QT interval prolongation. Meanwhile, a lack of a facilitation effect may explain why dofetilide, d-sotalol, atenolol, and terfenadine have a high risk for lethal arrhythmia (Furutani et al., 2011; Yamakawa et al., 2012). Recent studies have described the general utility of the in silico integration of drug effects on multiple cardiac currents to reduce false-positive and false-negative classifications based on hERG block alone (Mirams et al., 2011; Kramer et al., 2013). More elaborate models incorporating detailed descriptions of ion channel modulation and experimental tests will improve future investigations of the mechanisms underlying the proarrhythmic risk of class III antiarrhythmic agents.

In conclusion, we propose that hERG blockers with facilitation effects have a lower risk for inducing EADs and other triggered activities and thus are more suitable to treat arrhythmias. If this hypothesis is correct, it suggests that the early assessment of cardiotoxicity risk could be improved by using in vitro ion channel assays that assess facilitation. Such an improvement could reduce the likelihood of mistakenly discarding viable drug candidates and speed the progression of safer drugs into clinical trials and clinical use.

## Acknowledgments

We are grateful to Dr. Mark T. Keating and Dr. Michael C. Sanguinetti (University of Utah) for providing us with hERG clone; Dr. Craig T. January (University of Wisconsin) for providing us with HEK293 cell lines stably expressing hERG; Dr. Koichi Nakajo (Jichi Medical University) for providing us with rat KCNE2 clone; Benjamin Van, Dr. Julie Bossuyt, and Dr. Donald Bers (University of California, Davis) for providing rabbit ventricular myocytes; and Dr. Parashar Thapa (University of California, Davis) for help with blinding. We also thank Dr. Colleen Clancy and Dr. Eleonora Grandi (University of California, Davis) for discussion.

This study was supported by the Hiroshi and Aya Irisawa Memorial Promotion Award for Young Physiologists (K. Furutani and K. Tsumoto) from the Physiological Society of Japan; a Dean’s Award from Department of Physiology and Membrane Biology, University of California, Davis (K. Furutani and J.T. Sack); Grants-in-Aid for the Scientific Research on Innovative Areas 22136002 (Y. Kurachi)15H01404 (K. Furutani) from the Ministry of Education, Science, Sports and Culture of Japan; Grants-in-Aid for the Scientific Research (C) 15K08231 (K. Furutani) and 16KT0194 (K. Tsumoto) from the Japan Society for the Promotion of Science; and National Institutes of Health grants U01HL126273 and R01HL128537 (K. Furutani and J.T. Sack).

The authors declare no competing financial interests.

Author contributions: K. Furutani and K. Tsumoto designed the experiments, conducted the experiments, analyzed the data, made figures, and wrote the manuscript. I-S. Chen conducted the experiments and wrote the manuscript. K. Handa and Y. Yamakawa conducted the experiments and revised the manuscript. J.T. Sack and Y. Kurachi supervised the project and wrote the manuscript.

Richard W. Aldrich served as editor.

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## Author notes

*

K. Furutani and K. Tsumoto contributed equally to this work.

I-S. Chen's present address is Division of Biophysics and Neurobiology, Department of Molecular and Cellular Physiology, National Institute for Physiological Sciences, Aichi, Japan.