These findings suggest that I_Ks is important for AP repolarization and APD adaptation to changes in rate, as demonstrated in guinea pig.^5–7 However, I_Ks density has been reported to be much lower in larger mammals, specifically in canine and human ventricle.⁸ In canine myocytes, L-type calcium current, an inward depolarizing current, has been shown to mediate APD rate adaptation under control conditions without β-adrenergic effects.⁷ However, AP repolarization requires a sufficient outward repolarizing current during phases 2 and 3 of the AP. Such current is carried by I_Kr (the rapid delayed rectifier) and I_Ks, with I_Kr playing a primary role in large mammals under normal physiological conditions and in the absence of β-adrenergic stimulation. Because phases 2 and 3 depend on a delicate balance between inward and outward currents, one cannot rule out a priori an important role for I_Ks. Moreover, the arrhythmic consequences of LQT1 and LQT5² mutations, the existence of only 2 repolarizing currents (I_Kr and I_Ks) that constitute the delayed rectifier, and incorporation of the β-adrenergic signaling molecules into the I_Ks channel complex⁴ strongly suggest an important role for I_Ks in human heart electrophysiology under various conditions. It has been hypothesized that in large mammals I_Ks constitutes a “repolarization reserve” (RR) that compensates for reductions in other repolarizing currents, in particular I_Kr, caused by mutations (hereditary LQT2) or drugs (acquired LQT syndrome).^9,10 There is growing consensus that in the absence of RR, certain drugs such as sotalol (antiarrhythmic), erythromycin (anti-infective), chlorpromazine (antipsychotic), and methadone can trigger a life-threatening arrhythmia.⁹ The possibility of I_Ks generating this reserve and the dependence of I_Ks participation on its kinetics remain to be elucidated.

The Markov schemes we developed for KCNQ1 and I_Ks are shown in Figure 1A and 1B. Two closed-state zones are shown; green represents states in which at least 1 voltage sensor must still make a first transition, and blue represents states in which only faster second transitions are necessary for opening. Model derivation is described in the online-only Data Supplement. Criteria for fitting parameters are described below.

The KCNQ1 model is based on frog oocyte recordings¹³ (Figure 2). Simulated activation to various potentials (Figure 2A), inactivation measured by a triple-pulse protocol (Figure 2C), and dependence of deactivation time constant on prepulse duration (Figure 2E) were included in the fitting procedure (details are in the online-only Data Supplement). The reversal potential was −90 mV and temperature 23°C, as dictated by experimental conditions. (Sufficient KCNQ1 data are not available at 37°C). Model comparisons with experimental data are shown in Figure 2B, 2D, and 2F.

Lu et al¹⁵ have recorded E-4031 insensitive current (I_Ks) in guinea pig ventricular myocytes at 37°C for [K⁺]_o=5.4 mmol/L and [Na⁺]_o=143 mmol/L (Figure 3A). Data were digitized from the published experimental figure, and ion concentrations were set as reported. Channels were assumed to be closed at −50 mV on the basis of the current-voltage relationship that shows no activation below −10 mV (Figure 3B). Therefore, instantaneous current (possibly due to leakage) was subtracted. Current tracings were normalized according to the current-voltage relationship curve so that the steady state value for each tracing would match the experimental average. Deactivation at −50 mV was fit directly to published data.¹⁵ Rate of deactivation at resting V_m and current accumulation at fast pacing rates were simulated with I_Ks inserted in the whole-cell model (see below); comparison with experimental data¹⁵ is shown in Figure 3B. Additionally, mean current increase at fast rates and dynamic conductance (corresponding to APs and I_Ks simulated in Figure 4) were compared with recordings from AP clamp¹⁶ (Figure 5). A previously developed formulation of the reversal potential that accounts for sodium conductance through I_Ks channels was used (ratio of Na⁺:K⁺ permeability of 0.01833).⁶

Human I_Ks activation kinetics (Figure 3C) were fit to data from Kupershmidt et al,¹⁷ who recorded expressed human I_Ks in HEK cells at 37°C. [Na⁺]_o was 145 mmol/L, and [K⁺]_o was 4 mmol/L. Expressed currents were fit because they display activation kinetics more clearly than currents recorded from native cells while still displaying activation at ≈−10 mV and a delay before slow activation, as in native cells.⁸ Deactivation was constrained by time constants measured in human ventricular myocytes at 37°C for [Na⁺]_o=144 mmol/L and [K⁺]_o=4 mmol/L to ensure that open-state accumulation was not overestimated.⁸ Reversal potential was calculated as for guinea pig I_Ks. Comparisons with experimental data are shown in Figure 3D.

The AR concept can be examined experimentally. For example, a gapped double-pulse protocol with variation in the gap width could be used to characterize the AR in both guinea pig and human ventricular myocytes. In this protocol, a depolarizing pulse to 40 mV for 2 seconds would activate the channel. This step would then be followed by a repolarizing step of variable duration (from 10 ms to 1 second) to −80 mV so that the channel could partially deactivate. A second depolarizing pulse to 40 mV would be used to measure the rate of activation, providing a measure of the AR.

Our simulations also predict that I_Ks will increase more at fast rates when I_Kr is blocked (Figure 7), a manifestation of AR. This prediction could be experimentally tested by blocking I_Kr and measuring the increase in I_Ks during an AP clamp at slow and fast rates. Another protocol to test interaction between I_Kr and I_Ks would be to reduce I_Ks and measure the change in APD from control during pacing, and then to apply I_Kr reduction to control and block I_Ks to the same degree as in the previous protocol. Our simulations predict that the same I_Ks reduction will have a much greater effect on APD when I_Kr is also reduced.

At fast rates, the ability of guinea pig I_Ks to accumulate between APs allows it to participate in APD shortening. However, in human myocytes I_Ks deactivates rapidly, bringing into question its ability to accumulate and mediate APD adaptation. Our simulations show that open-state accumulation is not necessary for I_Ks to increase at fast rates. Because of the complex nature of potassium channel activation, channels can accumulate in closed states near the open states (zone 1) to form an AR that opens rapidly and generates large I_Ks current during AP repolarization. This effect is confirmed by AP clamp experiments¹⁶ that show little accumulation in the open state but rapid activation at fast rates (Figure 5) that leads to greater I_Ks during the AP. In canine myocytes, I_Ks accumulation is also observed in the presence of β-agonist.¹⁸ Here the mechanism of I_Ks accumulation is identical for both human and guinea pig I_Ks, indicating a common mechanism for I_Ks increase across species.

This novel mechanism of adaptation contrasts with the behavior of homomeric KCNQ1 channels that accumulate in the open states because of slow deactivation but show no significant AR. Consequently, the KCNQ1 AP does not adapt as much as the I_Ks AP (Figure 6). The fundamental difference between I_Ks and KCNQ1 channels is the degree of participation of the first voltage sensor transition in channel activation. Because of the stabilization of the voltage sensor first position by KCNE1, only a small fraction of I_Ks channels activate at slow rates, creating a reserve of channels that can activate at fast rates to accelerate repolarization. In contrast, a large percentage of KCNQ1 channels activate even at slow rates, preventing buildup of such a reserve. As shown in Figure 6C, the initial jump (arrow) of I_Ks current that reflects open-state accumulation at fast rates is small and is followed by a steady increase to a peak of 3.4 μA/μF late during the AP. At this phase of the AP, I_Ks has a maximal effect on repolarization and APD. In contrast (Figure 6D), KCNQ1 current displays a large initial jump (arrow) due to large open-state accumulation but does not increase during the AP in the absence of an AR; its magnitude stays at ≈2 μA/μF and lacks the late peak that is important for repolarization. Thus, interaction with the KCNE1 subunit strongly influences the I_Ks profile during the AP; it augments AP shortening and is essential to normal I_Ks function and its participation in APD adaptation. Other differences between KCNQ1 and I_Ks, such as open-state behavior and flickery block, are discussed in the online-only Data Supplement.

As stated earlier in this report, I_Ks is not likely to participate in rate adaptation in large mammals under control conditions.⁷ However, when I_Kr is reduced, I_Ks is the only remaining major repolarizing current. The guinea pig myocyte provides a natural electrophysiological environment in which I_Kr is reduced. Under these conditions, we show that human I_Ks can mediate rate adaptation when the maximum conductance of the current is increased (Figure 6). β-Agonists, which are present in the normal physiological environment even at basal heart rates, can readily confer such an increase in I_Ks conductance.

In the case of pathologically reduced I_Kr (by a mutation or a drug), outward currents carried by other channels (RR) can prevent excessive APD prolongation, EADs, and triggered activity. It is hypothesized that I_Kr reduction in conjunction with a compromised RR is a precursor to arrhythmia, especially after a pause.⁹ To test the ability of I_Ks to participate in the RR, we compared I_Ks with KCNQ1 accumulation under control conditions and with I_Kr block. During pacing, I_Ks displays greater accumulation than KCNQ1 and increases further when I_Kr is reduced (Figure 7A). When the pause protocol is simulated with blocked I_Kr, increased I_Ks results in normal repolarization, whereas the postpause AP with KCNQ1 develops an EAD (Figure 7B). These simulations indicate that the ability of I_Ks to form an AR, which leads to accumulation at fast rates, makes it an ideal candidate to play a critical role in RR. The accepted RR concept involves compensation for one repolarizing current by another. This study demonstrates the existence of a reserve (AR) within a single channel (I_Ks), thereby extending the RR concept to include single-current reserve.

We describe I_Ks with 2 transitions, a slow transition (to zone 1) followed by a fast transition (to open), which implies that a 2-closed-state model (rather than 15 states) representing lumped voltage sensor transitions could adequately describe I_Ks activation. However, this model would not reproduce the experimentally observed delay before activation,^14,19 which has important consequences during the AP. To reproduce these kinetics, a semi-Markov 2-closed-state model could be used that would introduce a memory property to the channel via time-dependent transition rates. Such models have been proposed²⁰ but introduce another level of complexity with the addition of memory. The present model was chosen because of its correlation to the tetrameric symmetry of K⁺ channels and the simplicity of 4 transitions without memory that describe I_Ks activation. This detailed description of activation, in particular the delay before activation, is a channel feature that has not previously been incorporated into an I_Ks model.

Model parameters were determined with the use of nonlinear optimization. Although we incorporated a large set of experiments, there may be different parameters that also reproduce channel properties. Our conclusions depend on the participation of numerous closed states in I_Ks activation. The necessity of these states for generating a delay before activation has been rigorously documented.¹⁹ Thus, any model of this topology (Figure 1) that fits I_Ks activation, regardless of the parameter set, would generate an AR and cause more adaptation at fast rates (see online-only Data Supplement).

Not all data were obtained from native myocytes. For KCNQ1, we used frog oocyte experiments¹³ conducted at room temperature, in which transition rates differ from body temperature. Still, KCNQ1 activation in mammalian cells (37°C)¹ and in oocytes (25°C) is quite similar, with 2 time constants of activation and similar current-voltage relationships.

Appendix