Repolarization Reserve Evolves Dynamically During the Cardiac Action Potential: Effects of Transient Outward Currents on Early Afterdepolarizations

Abstract

Background

Transient outward K currents (I_to) have been reported both to suppress and facilitate early afterdepolarizations (EADs) when repolarization reserve is reduced. Here we used the dynamic clamp technique to analyze how I_to accounts for these paradoxical effects on EADs by influencing the dynamic evolution of repolarization reserve during the action potential.

Methods and Results

Isolated patch-clamped rabbit ventricular myocytes were exposed to either oxidative stress (H₂O₂) or hypokalemia to induce bradycardia-dependent EADs at a long pacing cycle length (PCL) of 6 s, when native rabbit I_to is substantial. EADs disappeared when the PCL was shortened to 1 s, when I_to becomes negligible due to incomplete recovery from inactivation. During 6-s PCL, EADs were blocked by the I_to blocker 4-aminopyridine, but reappeared when a virtual current with appropriate I_to-like properties was reintroduced using the dynamic clamp (n=141 trials). During 1-s PCL in the absence of 4-aminopyridine, adding a virtual I_to-like current (n=1,113 trials) caused EADs to reappear over a wide range of I_to conductance (0.005–0.15 nS/pF), particularly when inactivation kinetics were slow (τ_inact≥20 ms) and the pedestal (non-inactivating component) was small (<25% of peak I_to). Faster inactivation or larger pedestals tended to suppress EADs.

Conclusions

Repolarization reserve evolves dynamically during the cardiac action potential. Whereas sufficiently large I_to can suppress EADs, a wide range of intermediate I_to properties can promote EADs by influencing the temporal evolution of other currents affecting late repolarization reserve. These findings raise caution in targeting I_to as an antiarrhythmic strategy.

Introduction

Normal cardiac repolarization relies on a critical balance between depolarizing inward currents and repolarizing outward currents during the action potential (AP) plateau. Repolarization has built-in redundancy, or ‘reserve’, to protect against excessive AP duration (APD) lengthening and consequent QT interval prolongation. Repolarization reserve protects the heart against early afterdepolarizations (EADs) and triggered activities—both of which can promote ventricular arrhythmias such as torsade de pointes, polymorphic ventricular tachycardia and ventricular fibrillation. The concept of ‘reduced repolarization reserve’, originally formulated by Roden,¹ summarizes conditions in which vulnerability to EAD-related arrhythmias increases due to a net decrease in repolarizing current—whether related to increased inward currents, decreased outward currents, or both. An intuitive commonly-held assumption is that all outward currents during the plateau phase increase repolarization reserve and thereby suppress EAD formation. However, recent experimental studies have shown that this is not always true for transient outward K currents (I_to). Although I_to suppressed EADs in atrial myocytes,² I_to exacerbated EADs in ventricular myocytes with repolarization reserve reduced by oxidative stress.³ This seemingly paradoxical effect that an outward K current, which increases repolarization reserve, can exacerbate EADs has been explained theoretically^3,4 as follows. By lowering the plateau voltage during the early phase 1 of the AP plateau, I_to delays the subsequent activation of other, slower time- and voltage-dependent outward currents (such as I_Ks), thus diminishing their contribution to repolarization reserve during phases 2 and 3 of the AP, and thereby facilitating EADs. The specific biophysical properties of I_to that determine whether it suppresses or promotes EADs, however, have not been systematically defined. This is an important concern given that drug therapy targeting I_to has been proposed as an antiarrhythmic and anti-heart failure therapy.

In this study, we used the dynamic clamp technique to experimentally define the arrhythmogenic ranges of three I_to properties—maximum conductance, inactivation kinetics, and pedestal (here defined as the I_to non-inactivating component). The dynamic clamp technique allows an I_to-like current with programmable properties to be introduced into a patch-clamped myocyte after the endogenous I_to is blocked. In this fashion, we could systematically analyze how each specific biophysical characteristic of I_to-like currents promotes or suppresses EAD formation. This systematic analysis is an important advantage of the dynamic clamp because the properties of I_to currents are quite diverse, both within and across species, with fast and slow voltage-dependent subtypes (I_to1,f and I_to1,s) and a Ca-dependent current (I_to2), all with differing kinetics. The dynamic clamp affords the opportunity to create virtual I_to currents with properties covering this full spectrum, including human I_to characteristics.

Our findings indicate that when overall repolarization reserve is reduced, I_to-like currents can promote EADs in rabbit ventricular myocytes over a wide range of conductances, particularly when the time constant of inactivation of I_to is relatively slow (>20 ms) and its pedestal is small. Large I_to conductances or large pedestals can also shorten APD and suppress EAD formation. These findings indicate that the repolarization reserve is not pre-determined at the onset of the action potential, but is a process that evolves dynamically during the entire AP plateau. This factor must be taken into account when designing antiarrhythmic strategies targeting I_to or preventing EAD-mediated arrhythmias, particularly because we find that human I_to properties fall within the range that can promote EADs.

Methods

An expanded methods section is available in the Supplemental Material.

Experimental animals and patch clamping

This study was approved by the UCLA Chancellor’s Animal Research Committee (ARC 2003-063-23C) and performed in accordance with the Guide for the Care and Use of Laboratory Animals published by the United States National Institutes of Health (NIH Publication No. 85-23, revised 1996) and with UCLA Policy 990 on the Use of Laboratory Animal Subjects in Research (revised 2010). From young adult (3- to 4-month-old) New Zealand white male rabbits (1.7–2.0 kg), single ventricular myocytes were freshly isolated for whole-cell patch clamp with unbuffered intracellular Ca and dynamic clamp studies as described previously.⁵ To induce EADs, H₂O₂ (0.2 or 1 mmol/L) was added to the superperfusate or the extracellular [K] was reduced from 5.4 to 2.7 mmol/L. To inhibit I_to, 4-aminopyridine (4-AP; 2 mmol/L) was added to the perfusate.

Dynamic clamp technique and virtual I_to formulation

Patch-clamped rabbit ventricular myocytes were injected with a programmable virtual I_to using the dynamic clamp^5,6 (10-kHz sampling frequency; real-time Linux-based software; www.rtxi.org). The virtual I_to, with instantaneous recovery from inactivation at −80 mV, was formulated as follows:

$$I_{to}=G_{to}{x}_{\mathit{tof}}(\alpha +(1-\alpha )y_{\mathit{tof}})(V-E_k)$$ (Eq.1)

$${\tau }_{\mathit{ytof}}={\tau }_{\mathit{inact}}\ast \left(1.0/\left(1.0+e^{\frac{v+33.5}{10.0}}\right)+1.0\right)$$ (Eq.2)

Three parameters in the virtual I_to—the maximum conductance Ḡ_to, the inactivation time constant τ_inact, and the pedestal α—were varied to simulate a wide range of features encompassing various I_to subtypes. Pedestal is the non-inactivating I_to component controlled by parameter α (Eq.1).

Data and statistical analysis

Electrophysiological data were analyzed using Clampfit 10.4 (Axon instruments, Inc.) and OriginPro 9.0 SR2 (Microcal software, Inc.). In the statistical analysis of the contingency table, measures of association (odds ratio) and accuracy (sensitivity, specificity, positive and negative predictive values, positive and negative likelihood ratios) were obtained under a logistic regression model using generalized estimating equation (GEE) methods. GEE allows for non-independent (correlated) binary observations due to multiple observations from the same myocyte and rabbit (hierarchical structure). The 95% confidence intervals ([95% CI]) were computed using resampling (bootstrap) methods under this model. A P value of <0.05 was considered significant.

Results

To investigate the biophysical properties that determine whether I_to suppresses or promotes EADs, we formulated a virtual I_to current to introduce into isolated patch-clamped rabbit ventricular myocytes using the dynamic clamp technique. The virtual I_to has three independently-adjustable parameters (Supplemental Figure 1): maximal conductance Ḡ_to, a single inactivation time constant τ_inact, and a pedestal (a very slowly-inactivating or non-inactivating component defined here as % of peak I_to that remains after 300 ms). Table 1 provides a literature review of experimentally-measured ranges of these I_to parameters in normal and failing hearts from different species, including humans. These data include both the fast subtype I_to1,f encoded by Kv4.3/Kv4.2/KCHiP2 and the slow subtype I_to1,s encoded by Kv1.4. To cover the spectrum of the three parameter ranges in Table 1, as well as to approximate aggregate currents composed of multiple I_to subtypes in the same cell or additional time-independent K currents that confer the equivalent of a pedestal, we varied the virtual I_to over a wide range, as follows: Ḡ_to from 0.0005 to 5.0 nS/pF, τ_inact from 5 to 1200 ms, and the pedestal from 0 to 100% of peak I_to. The parameter ranges of the virtual I_to also cover the reported features of both the human and rabbit I_to currents.

Table 1.

Literature review of ventricular I_to1 parameters measured from different species. I_to1 density was reported either as peak or as difference between peak and pedestal. Inactivation kinetics were reported as a mono- (τ₁) or bi-exponential (τ₁, τ₂) decay time course.

Species	Ito1 Subtype	Temp (°C)	Density (pA/pF)	Gto (nS/pF)	τinact (ms)	Pedestal (% of peak)	References
Human
Normal	Ito1,f	35	-	-	8	-	7
	Ito1,f	21–24	8–14	0.06–0.11	46–75	16–22	7–10
Heart failure	Ito1,f	21–24	↓ ↔	↓ ↔	-	-	8–12
	Ito1,s	21–24	5–10	0.04–0.08	59–73	0–17	8–12
Rabbit
Normal	Ito1,s	34–37	10–18	0.08–0.14	10–20	4–25	3,13–17
	Ito1,s	25	33–38	0.25–0.29	30–35	15	17
Heart failure	Ito1,s	34–37	6–27	0.05–0.21	τ1: 7–8, τ2: 70–118	5–21	13–17
	Ito1,s	25	8	0.06	38–50	24	17
H2O2	Ito1,s	37	13	0.10	τ1: 65–80, τ2: 350	35	3
Canine
Normal	Ito1	36–37	17–46	0.13–0.35	18–36	-	3,9,18–23
	Ito1	24	20–22	0.15–0.17	34–49	0–16	9
Heart failure	Ito1	36–37	5–13	0.04–0.10	22–43	0–69	18–20,23
Rat
Normal	Ito1,f	37	20–22	0.15–0.17	45–97	-	24
	Ito1,f	20–25	9–39	0.07–0.30	16–55	7–40	21,25–28
LVH	Ito1,f	20–25	2–40	0.02–0.31	35–81	11–36	25–27,29,30
Chronic MI	Ito1,f	37	11–12	0.08–0.09	45–97	-	24

Temp: recording temperature; LVH: left ventricular hypertrophy; MI: myocardial infarction

Blockade of endogenous I_to suppresses EADs

To induce EADs, patch-clamped rabbit ventricular myocytes were exposed to either oxidative stress with H₂O₂ (1 mmol/L) or ionic stress with moderate hypokalemia (2.7 mmol/L). With either stress, bradycardia-dependent EADs were consistently observed at a slow pacing cycle length (PCL) of 6 s (Figure 1B–C row 1).

Figure 1.

I_to blockade by rapid pacing at PCL 1 s or by 4-AP suppresses H₂O₂-induced and hypokalemia-induced EADs in rabbit ventricular myocytes. A. No EADs arose under control conditions at PCL 6 s, 1 s, or 6 s in the presence of 4-AP (2 mmol/L). B–C. Following exposure to H₂O₂ (1 mmol/L; B) or hypokalemia (2.7 mmol/L; C), EADs (*) occurred at PCL 6 s (row 1), but were suppressed by rapid pacing at PCL 1 s (row 2) or by adding 4-AP (row 3). Superimposed action potentials under the 3 conditions are shown below.

EADs disappeared when I_to was blocked, either by shortening the PCL to 1 s (Figure 1B–C row 2) or by application of the I_to blocker 4-AP (2 mmol/L) during pacing at 6 s (Figure 1B–C row 3 & Figure 2). Suppression of EADs by I_to blockade suggests that I_to contributes to EAD formation under both stressed conditions. However, the evidence of EAD suppression by 4-AP is not definitive because 4-AP is not completely selective for I_to³¹ such that 4-AP off-target effects could have also been responsible.

Figure 2.

Virtual I_to reconstitutes H₂O₂-induced (A) and hypokalemia-induced (B) EADs blocked by 4-AP. Row 1: Action potentials were elicited during pacing at PCL 6 s under control conditions. Row 2: H₂O₂ (1 mmol/L) or hypokalemia (2.7 mmol/L) induced EADs (*) during slow pacing at 6 s. Row 3: I_to blockade with 4-AP (2 mmol/L) suppressed EADs. Row 4: Representative parameter combinations of the virtual I_to that caused EADs to reappear. Rows 5–6: Representative parameter combinations of the virtual I_to that shortened APD and suppressed EAD reappearance by increasing the pedestal or I_to conductance.

I_to reconstitution reverses EAD suppression by 4-AP

To determine whether EAD suppression by 4-AP was related primarily to its blockade of I_to rather than its off-target effects, we injected a virtual dynamic-clamp I_to resembling the native rabbit I_to. In myocytes superfused with control Tyrode’s solution and paced at PCL 6 s or 1 s, EADs were never observed in the absence or presence of an injected virtual I_to for any parameter combinations tested (46 trials, 6 myocytes, 5 rabbits). Thus, when repolarization reserve was normal, I_to reconstitution did not promote EADs de novo.

However, after EADs had already been induced by either H₂O₂ or hypokalemia and subsequently suppressed by 4-AP, injection of a virtual I_to with properties approximating the native rabbit I_to1,s (Table 1) caused EADs to reappear (representative illustration in Figure 2, row 4). For the same value of Ḡ_to, increasing the pedestal current from 0 to 50–55% of peak I_to caused EADs to disappear and APD to shorten markedly (Figure 2 row 5). Likewise, increasing Ḡ_to without increasing the pedestal had the same effect (Figure 2 row 6).

I_to reconstitution reverses EAD suppression by rapid pacing

To eliminate possible confounding off-target effects of 4-AP unequivocally, we took advantage of the fact that the native rabbit ventricular I_to1 (chiefly I_to1,s) has an unusually long time constant of recovery from inactivation, averaging 6 s at −80 mV.³ Thus, whereas I_to1 amplitude is substantial at a PCL of 6 s due to the long diastolic recovery interval between beats, I_to1 is almost completely inactivated and makes a negligible contribution to the AP at a PCL of 1 s. Coincidentally, EADs induced by either oxidative stress or hypokalemia at PCL 6 s disappeared at PCL 1 s (Figure 1). These features allowed us to introduce a dynamic-clamp I_to programmed with instantaneous recovery from inactivation kinetics at −80 mV during PCL 1 s to determine if EADs reappear, and, if so, to evaluate what properties of I_to are required.

To assess the independent contribution of each of the three I_to parameters to EAD formation, we introduced a virtual I_to, varying only one parameter at a time (Figs 3–5), into myocytes in which stress-induced EADs at PCL 6 s had been suppressed by decreasing the PCL to 1 s.

Figure 3.

Effects of Ḡ_to on reappearance of pacing-suppressed EADs. Row 1: EADs induced by hypokalemia (2.7 mmol/L) at PCL 6 s (not shown) were suppressed by shortening PCL to 1 s. Rows 2–4: A virtual I_to with τ_inact = 25 ms and no pedestal reconstituted EADs (*) at an intermediate I_to conductance (Ḡ_to = 0.05 nS/pF, row 3), whereas smaller (0.01 nS/pF, row 2) or larger conductances (0.15 nS/pF, row 4) caused APD shortening.

Figure 5.

Effects of the pedestal component on the reappearance of pacing-suppressed EADs. Row 1: EADs induced by H₂O₂ (1 mmol/L) at PCL 6 s (not shown) were suppressed by shortening PCL to 1 s. Rows 2–6: A virtual I_to with Ḡ_to = 0.025 nS/pF and τ_inact = 80 ms reconstituted EADs (*) for pedestals up to 50% (rows 2–5), but not for a pedestal of 75% (row 6).

Figure 3 illustrates the contribution of Ḡ_to, assessed by altering Ḡ_to while holding τ_inact and the pedestal constant. In this representative myocyte, after hypokalemia-induced EADs were suppressed by pacing at 1 s (row 1), introducing a small virtual I_to (Ḡ_to = 0.01 nS/pF, τ_inact = 20 ms, 0% pedestal) caused APD to shorten (row 2). When Ḡ_to was increased to 0.05 nS/pF, EADs reappeared (row 3). Further increasing Ḡ_to to 0.15 nS/pF caused EADs to disappear and the APD to shorten markedly (row 4). These findings demonstrate that for a given τ_inact and pedestal, I_to promotes EADs over a critical range of Ḡ_to and shortens APD at smaller or larger Ḡ_to values beyond that critical range.

Figure 4 illustrates the contribution of τ_inact, assessed by altering τ_inact while holding Ḡ_to and the pedestal constant. In another myocyte, after H₂O₂-induced EADs were suppressed by pacing at 1 s (row 1), I_to was reconstituted using the dynamic clamp (Ḡ_to = 0.05 nS/pF, τ_inact = 20 ms, 0% pedestal). In this myocyte, τ_inact of 20 ms did not cause EADs to reappear, but shortened APD (row 2). Prolonging τ_inact to 80 or 100 ms, however, caused EADs to reappear (rows 3–4).

Figure 4.

Effects of τ_inact on reappearance of pacing-suppressed EADs. Row 1: EADs induced by H₂O₂ (1 mmol/L) at PCL 6 s (not shown) were suppressed by shortening PCL to 1 s. Rows 2–4: A virtual I_to with Ḡ_to = 0.05 nS/pF and no pedestal did not reconstitute EADs (*) for τ_inact =20 ms (row 2), but did when τ_inact was prolonged to 80 (row 3) or 100 ms (row 4).

Figure 5 illustrates the contribution of the pedestal, assessed by altering the pedestal while holding Ḡ_to and τ_inact constant. In this myocyte, after H₂O₂-induced EADs were suppressed by pacing at 1 s (row 1), introducing a virtual I_to (Ḡ_to 0.025 nS/pF, τ_inact = 80 ms) with no pedestal caused EADs to re-emerge (row 2). EADs persisted (albeit with decreased frequency) when the pedestal was increased to 10, 25, and then 50% (rows 3–5). However, EADs disappeared when the pedestal was further increased to 75% (row 6).

I_to properties that reverse EAD suppression by rapid pacing

Figure 6 summarizes results from 772 parameter combinations of Ḡ_to, τ_inact, and pedestal values obtained in 1,113 trials using 131 rabbit ventricular myocytes isolated from a total of 46 rabbits. Using the protocols illustrated in Figures 3–5, we exposed myocytes to either H₂O₂ or hypokalemia at PCL 6 s to induce EADs, then suppressed EADs by shortening the PCL to 1 s, prior to injecting a virtual I_to. In the plots of Ḡ_to vs. τ_inact, parameter combinations of the virtual I_to that caused EADs to reappear at PCL 1 s are indicated by solid symbols, while those that did not are indicated by open symbols. The four plots, labeled A–D, correspond to the size of the pedestal, which was 0% in A, 10–24% in B, 25–49% in C, and 50–75% in D.

Figure 6.

Virtual I_to parameter combinations causing pacing-suppressed H₂O₂-induced or hypokalemia-induced EADs to reappear. Graphs show (Ḡ_to, τ_inact) combinations that did (solid circles) or did not (open circles) cause EADs to reappear at PCL 1 s, using the protocols shown in Figures 3–5, for the different ranges of I_to pedestal components as indicated in A–D. A. Dashed black line outlines the border of the experimental region in parameter space causing EADs to reappear, compared to the predictions from a computer model (gray shaded area), adapted from Zhao et al.³ B–D. Solid colored regions outline the experimental region in parameter space causing EADs to reappear for pedestals ranging from 10–24% (B), 25–49% (C), and 50–75% (D), compared to the no-pedestal case (black line reproduced from A). In B, the red box indicates the typical parameter values for human ventricular I_to1,f in normal and failing hearts (see Table 1). No EADs re-emerged with pedestals>75%.

Figure 6A shows that a wide range of (Ḡ_to, τ_inact) parameter combinations (outlined by the dashed black line) caused EADs to reappear when the virtual I_to had no pedestal component. The distribution of these parameter combinations agrees well with theoretical predictions from computer modeling simulating the effects of an I_to with 0% pedestal on EAD formation.³ The gray-shaded area indicates the region in (Ḡ_to, τ_inact) parameter space that caused EADs in the computer model. Note that the parameter combinations that caused EADs to reappear at PCL 1 s (the solid symbols) are mostly clustered inside the gray region, whereas those that did not (the open symbols) are mostly outside this gray area. This preferential clustering was statistically significant (P<0.0001, Table 2). The mismatches, indicated by the fraction of open symbols falling within the gray area or solid symbols outside the gray area, most likely reflect biological variability that does not exist in the deterministic computer AP model, as different patch-clamped myocytes came from different hearts and different ventricular regions in the same heart.

Table 2.

Statistical analysis of predicted vs. observed (G_to, τ_inact) parameter combinations causing EADs to reappear. A total of 480 observed (G_to, τ_inact) combinations of a virtual I_to with no pedestal (787 trials in 79 ventricular myocytes from 25 rabbit hearts) that did (EAD⁺) or did not (EAD⁻) cause H₂O₂-induced or hypokalemia-induced EADs to reappear at PCL 1 s are compared to theoretical predictions from a computer model.

No. of Gto-τinact Combinations		Observed
		EAD+	EAD−	Total
Predicted	EAD+	186	49	235
	EAD−	22	223	245
	Total	208	272	480
Positive Predictive Value [95% CI]		0.77 [0.67, 0.87]
Negative Predictive Value [95% CI]		0.93 [0.86, 0.99]
Sensitivity [95% CI]		0.92 [0.82, 0.99]
Specificity [95% CI]		0.72 [0.55, 0.89]
Positive Likelihood Ratio		3.3 [1.21, 5.41]
Negative Likelihood Ratio		0.11 [0.01, 0.26]
Odds Ratio [95% CI]		41.5 [1.8, 84.9]
P		<0.0001

Figure 6B–D reveal the EAD-suppressing effects of pedestal current. As the pedestal component became larger, the region in the (Ḡ_to, τ_inact) parameter space causing EADs to reappear (outlined by the colored regions) became progressively smaller, consistent with previously reported theoretical predictions.³ No EADs reemerged with pedestal current>75% (data not shown).

Finally, the red box in Figure 6B encloses parameter combinations representative of the human ventricular I_to (predominantly I_to1) reported in the literature for both normal and failing human hearts (Table 1). Note that the human I_to range falls within the virtual I_to parameter region causing EADs to re-emerge.

In summary, the data in Figure 6 demonstrate that virtual I_to-like currents can promote EADs over a wide range of peak conductances (Ḡ_to over a 30-fold range from 0.005–0.15 nS/pF), especially when inactivation kinetics are slow (τ_inact>20 ms) and the pedestal is small (<25% of peak I_to), in good overall agreement with theoretical predictions.³

Discussion

I_to as friend and foe in EAD genesis

Transient outward currents have been reported to both suppress and promote EADs.^2,3 Because of the wide diversity of I_to properties between different subtypes (I_to1,s, I_to1,f, and I_to2), marked differences in regional expression profiles within atrial and ventricular tissue in the same species, as well as marked interspecies differences (Table 1), the dynamic clamp technique offers a powerful tool to analyze how variations in I_to properties affect EAD formation in diverse experimental settings. Moreover, the previous experimental evidence that I_to promotes EADs has relied solely on the disappearance of EADs after applying 4-AP to block I_to. However, 4-AP is not completely selective for I_to and has significant off-target effects on other ionic currents.^31,32 The dynamic clamp allows the effects of I_to on EADs to be tested directly without this complication.

The role of I_to in EAD formation is a critical issue to understand because derangements in I_to physiology have been linked to increased susceptibility to malignant arrhythmias and pharmacological strategies targeting this current are under development. In this context, both selective I_to blockade and activation have been suggested as potential antiarrhythmic strategies.^2,18 Downregulation of I_to1 contributes to reduced repolarization reserve in heart failure,³³ which has been linked to higher risk of triggered ventricular arrhythmias.³⁴ Genetic ablation of I_to1 in transgenic mice by Kv1.4^−/− and Kv4.2W362F crossbreeding³⁵ or KChIP2 knockout³⁶ significantly prolonged APD, promoting EADs in single ventricular myocytes³⁵ and markedly prolonged QT interval, promoting spontaneous ventricular tachycardia in intact tissue in the absence of ventricular hypertrophy or heart failure.^35,36 Potentiation of I_to to increase repolarization reserve has therefore been suggested as a potential antiarrhythmic strategy in heart failure, with the caveat that excessive I_to can cause arrhythmias by a different mechanism, namely phase 2 reentry as in Brugada syndrome ^37,38 and acute ischemia.³⁹

Our findings indicate that additional caution is warranted, since in addition to these potential pro-arrhythmic effects of excessive I_to, even mild to moderate augmentation of I_to may be proarrhythmic by promoting EADs when repolarization reserve is already compromised. However, we emphasize that when repolarization reserve was normal, adding a virtual I_to to the normal rabbit ventricular AP never induced EADs. Hence, for I_to to promote EADs, overall repolarization reserve must be reduced by additional factors, such as oxidative stress or hypokalemia. Also, we do not mean to imply that I_to is an absolute requirement for EADs. Rather I_to is a current whose properties can enable EADs that otherwise would not occur depending on specific (but common) electrophysiological conditions in multiple species.

Our systematic analysis of the I_to properties promoting EADs in this study also provides novel insights into the apparent discrepancy between Zhao et al’s study,³ which concluded that I_to promotes EADs in ventricular and Purkinje myocytes from multiple species, and Workman et al’s dynamic clamp study,² which concluded that I_to suppresses EADs in rabbit and human atrial myocytes. Atrial tissue has a very large endogenous I_to that accounts for the triangular shape of its action potential. This large I_to is in the range that typically suppresses EADs (>0.10 to 0.15 nS/pF in Figure 6), such that reducing I_to by dynamic clamp subtraction brought Ḡ_to into the range that frequently promotes EADs (<0.10 nS/pF). Indeed, in Workman et al study,² Ḡ_to averaged 0.34 nS/pF in rabbit atrial myocytes and 0.12 nS/pF in human atrial myocytes. In contrast, ventricular myocytes from most non-rodent mammals have a smaller I_to density (Table 1) that may place them in the range of Ḡ_to that facilitates EAD formation such that I_to block with 4-AP or other agents will suppress EADs. Rat and mouse ventricular myocytes, on the other hand, have higher I_to densities than larger mammals, but may also develop EADs that are suppressed by 4-AP,³ suggesting that other differences between ventricular and atrial electrophysiology may also be important.

Applicability to human I_to

Our study is the first systematic analysis demonstrating that the range of I_to properties capable of promoting EADs is wide and inclusive of I_to from other species than just rabbit. We show that EADs were promoted over a 30-fold range of I_to conductance, favored by an inactivation time constant τ_inact≥20 ms and a pedestal component <25% of peak I_to. This range includes the typical I_to1 characteristics of both healthy and failing human ventricles, which exhibited a single inactivation time constant τ_inact averaging 8–75 ms and a pedestal of 16–22% in normal and failing epicardial ventricular myocytes.^10,12,40 As shown in Figure 6B (red box), these characteristics fall clearly within the parameter range promoting EADs.

In addition, our findings also establish that the EAD-promoting effect of I_to occurs not just when EADs are induced by oxidative stress with H₂O₂ (which significantly modified I_to properties³), but also when EADs are induced by the clinically relevant condition of moderate hypokalemia, a common complication of diuretic therapy in patients with heart failure. Hypokalemia induces EADs primarily by reducing outward K currents, whereas H₂O₂ augments the late Na current and Ca currents primarily through oxidative CaMKII activation (reflected in the more common appearance of DADs in association with H₂O₂-induced EADs, rather than with hypokalemia-induced EADs, as in Figure 2).^41,42 Thus, the specific mechanism by which overall repolarization reserve is reduced does not appear to be critical to the ability of I_to to promote EADs. The overall implication is that I_to may play an important role in facilitating EAD formation in multiple settings and in multiple species, including humans.

Mechanism of EAD potentiation by I_to

The mechanism by which I_to potentiates EADs is consistent with the dynamic theory of EAD formation by a Hopf-homoclinic bifurcation mechanism.^4,43 In this theory, EADs are generated by the opposing effects of inward I_CaL, which is activated as the plateau voltage dips below 0 mV and outward K currents, particularly I_Ks, which is reactivated during the I_CaL-mediated EAD upstroke. The activation-deactivation kinetics of I_Ks must be matched appropriately to I_CaL recovery kinetics to achieve membrane potential oscillations,^4,43 the defining feature of EADs. If I_Ks activates too rapidly, then repolarization rate is too fast for I_CaL to reactivate and prevent repolarization. I_to can promote EADs by lowering the voltage during the early plateau, thereby slowing I_Ks activation (since I_Ks activation rate and its open probability are highly voltage-dependent) while giving I_CaL enough time to reactivate and oppose full repolarization. Thus, although I_to always increases early repolarization reserve, the indirect effect of I_to on the temporal evolution of other voltage-dependent currents such as I_Ks and I_CaL can paradoxically reduce late repolarization reserve, which is the critical phase during which EADs develop. This also explains why a larger I_to pedestal current tends to suppress EADs, since the outward pedestal current directly increases late repolarization reserve, compensating for the reduction in I_Ks.

The agreement in Figure 6A between the computer model and the experimental findings lends further support to the dynamic theory of EAD formation via I_CaL reactivation, even though other factors such as Ca cycling dynamics may also contribute importantly to EAD formation in many settings.⁴⁴ The effects of Ca cycling might also account for the lack of an exact overlap between the computer model predictions (gray-shaded area) and the observed I_to properties causing EADs to reappear in Figure 6A.

Finally, the findings in this study are also consistent with a previous study⁵ showing that fibroblast-myocyte coupling can promote EADs as a result of the I_to-like outward capacitive current introduced by the fibroblast into the myocyte through gap junctions during the early AP plateau phase. However, that myocyte-fibroblast gap junctional current also has a late sustained component that can become inward during the later phases of the action potential plateau, thus can further directly reduce late repolarization reserve.

Study limitations

To keep the number of parameters manageable, we simplified the virtual I_to formulation to include only a single inactivation time constant τinact, whereas two time constants have been reported in some studies, although not in humans (Table 1). A pedestal component was used to approximate long time constants of inactivation (>200 ms) as well as truly non-inactivating components. In addition, under some conditions, time-independent K currents, such as the plateau K current (I_Kp) or the ATP-sensitive K current (I_KATP), can potentially contribute a sustained outward current during the plateau phase that may summate with the I_to pedestal current.

We did not explicitly test scenarios in which multiple virtual I_to currents with different parameter combinations were added together into the same myocyte, even though multiple I_to subtypes (I_to1f, I_to1s, and I_to2) can coexist in the same myocyte. However, the wide range of parameter combinations that we tested, which exceeded the experimentally measured range in Table 1, would approximate many of these potential cases. Unlike I_to1, I_to2 is not a K current, but a Ca-activated Cl current with time course that parallels the intracellular Ca transient.^45,46 Nevertheless, since I_to2 activates rapidly and inactivates within 20–50 ms,^45,46 its kinetics as an outward current fall within the range of virtual I_to parameter combinations that we tested. Similarly, recent evidence indicates that small Ca-activated K (SK) channels are present in normal atrium and failing ventricles.^47,48 These SK currents track the Ca transient, similar to I_to2, and likewise are expected to fall within the parameter ranges that we tested. Given these limitations, however, our virtual I_to model with three independently adjustable parameters should be viewed as a rough guideline for identifying the key EAD-promoting characteristics of I_to–like currents.

Although the ranges of virtual I_to parameters in this study encompasses the endogenous I_to parameter ranges from multiple species, the caveat is that we injected the virtual I_to only into rabbit ventricular myocytes. Therefore, we cannot exclude the possibility that myocytes from other species, including humans, or myocytes remodeled by heart diseases, would behave differently. However, we believe that the differences would likely be quantitative rather than qualitative given that Zhao et al ³ found that I_to block with 4-AP suppressed H₂O₂-induced EADs in multiple species exhibiting markedly different action potential properties.