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Frequency-dependent effects of various I_Kr blockers on cardiac action potential duration in a human atrial model

¹Division of Molecular and Cellular Pharmacology, Department of Pharmacology, Graduate School of Medicine, and ²Center for Advanced Medical Engineering and Informatics, Osaka University, Osaka, Japan

Submitted 4 October 2006 ; accepted in final form 6 January 2007

	ABSTRACT

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Rapidly activating K⁺ current (I_Kr) blockers prolong action potential (AP) duration (APD) in a reverse-frequency-dependent manner and may induce arrhythmias, including torsade de pointes in the ventricle. The I_Kr blocker dofetilide has been approved for treatment of atrial arrhythmias, including fibrillation. There are, however, a limited number of studies on the action of I_Kr blockers on atrial AP. When we tested a mathematical model of the human atrial AP (M Courtemanche, RJ Ramirez, S Nattel. Am J Physiol Heart Circ Physiol 275: H301–H321, 1998) to examine the effects of dofetilide-type I_Kr blockade, this model could not reproduce the reverse-frequency-dependent nature of I_Kr blockade on atrial APD. We modified the model by introducing a slowly activating K⁺ current activation parameter. As the slow time constant was increased, dofetilide-type blockade induced more prominent reverse-frequency-dependent APD prolongation. Using the modified model, we also examined the effects of two more types of I_Kr blockade similar to those of quinidine and vesnarinone. Voltage- and time-dependent block of I_Kr through the onset of inhibition by quinidine is much faster than by vesnarinone. When we incorporated the kinetics of the effects of these drugs on I_Kr into the model, we found that quinidine-type blockade caused a reverse-frequency-dependent prolongation of APD that was similar to the effect of dofetilide-type blockade, whereas vesnarinone-type blockade did not. This finding coincides with experimental observations. The lack of the reverse frequency dependence in vesnarinone-type blockade was accounted for by the slow development of I_Kr blockade at depolarized potentials. These results suggest that the voltage- and time-dependent nature of I_Kr blockade by drugs may be critical for the phenotype of the drug effect on atrial AP.

rapidly activating potassium current; slowly activating potassium current; atrial action potential; reverse frequency dependence; computer simulation

Drugs such as dofetilide and E-4031 block I_Kr in a voltage- and time-independent manner (32, 33). On the other hand, we showed that the positive inotropic agent vesnarinone and the widely used class Ia antiarrhythmic drug quinidine inhibit current flowing through the pore-forming subunit of I_Kr, HERG (human ether-a-go-go-related gene), in a voltage- and time-dependent manner (13, 33). Although both drugs inhibit the current more potently and rapidly as the membrane potential is depolarized, the development of blockade at the same potential is much faster with quinidine than with vesnarinone (13, 33). Accordingly, I_Kr blockade by drugs can be classified into at least three representative groups: voltage- and time-independent blockade (e.g., by dofetilide and E-4031), fast voltage- and time-dependent blockade (e.g., by quinidine), and slow voltage- and time-dependent blockade (e.g., by vesnarinone). Previous studies have shown that although dofetilide and quinidine cause reverse-frequency-dependent prolongation of APD, vesnarinone does not (10, 12, 32) and that, clinically, dofetilide and quinidine often cause torsades de pointes, but vesnarinone does not (7, 30). These different effects among the drugs may be due to the differences in their kinetics of HERG blockade (13, 33), but the underlying mechanism has not been fully clarified.

I_Kr and I_Ks were also found in human atrial myocytes (37), and, recently, the I_Kr-specific blocker dofetilide was approved for treatment of atrial fibrillation (AF) (6). Therefore, the action of I_Kr blockers on atrial, as well as ventricular, APs is of interest. The aims of this study were 1) to establish a human atrial AP model that can differentiate the effects of drugs with the three distinct I_Kr blockade kinetics, 2) to elucidate the underlying mechanism of the different effect of I_Kr blockade on APD prolongation, and 3) to predict the requirement for non-reverse-frequency-dependent prolongation of APD in I_Kr blockade. To examine the effects of pure I_Kr blockade on APD, other possible effects by the I_Kr blockers [e.g., blockade of ultrarapid delayed rectifier K⁺ current (I_Kur) and inactivating transient outward K⁺ current (I_to) by quinidine] needed to be excluded. This is very difficult, if not impossible, in vitro. However, in silico approaches can realize such hypothetical experimental conditions. Therefore, we have developed an applicable human atrial AP model.

We first examined the effect of I_Kr blockade caused by dofetilide on the model of human atrial AP that was developed by Courtemanche et al. (2). We found that this model could not reproduce dofetilide's reverse-frequency-dependent prolongation of atrial APD. To correct this defect, we incorporated the slow component of I_Ks (27, 31) into the model. The modified model reproduced and accounted for the different frequency-dependent responses of APD due to three kinetically distinctive I_Kr blockade types. These results suggest that the voltage and time dependence of I_Kr blockade by drugs may be critical for the phenotype of drug effect on atrial AP.

	MATERIALS AND METHODS

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AP simulation. To simulate the human atrial AP, we used the mathematical model developed by Courtemanche et al. (2). Briefly, this model has passive properties (e.g., membrane capacitance and membrane resistance) and 12 voltage-dependent and carrier-mediated ionic currents as follows: fast Na⁺ current (I_Na), inward rectifier K⁺ current (I_K1), I_to, I_Kur, I_Kr, I_Ks, L-type Ca²⁺ current (I_Ca,L), sarcolemmal Ca²⁺ pump current (I_p,Ca), Na⁺-K⁺ pump current (I_NaK), Na⁺/Ca²⁺ exchanger current (I_NaCa), background Na⁺ current (I_b,Na), and background Ca²⁺ current (I_b,Ca). Hodgkin-Huxley-type equations are used to calculate the forward and backward kinetics of the activation and inactivation processes of each voltage-gated ion channel. The program was coded in C/C++, and simulations were run on an IBM-compatible computer with a C++ compiler.

I_Ks in the original atrial AP model of Courtemanche et al. (2) is expressed as follows

(1)

where g_Ks is the maximum conductance for I_Ks,x_s is the activation gate variable for I_Ks, V is the membrane potential, and E_K is the equilibrium potential for K⁺. The activation of I_Ks in the original model of Courtemanche et al. is assumed to have one gate represented by squared variables (x). It has been experimentally shown, however, that I_Ks possesses at least two (fast and slow) activation processes (27, 31). The time constant in the original model of Courtemanche et al. represents only the fast process. An additional slow activation process was introduced into the formulation of I_Ks in our model in a manner similar to that in the Luo-Rudy (LRd) model, the de facto standard guinea pig ventricle cell model (35). We modified this to incorporate two activation processes as follows

(2)

where x_s1 and x_s2 are the fast and slow activation gate variables, respectively. Although the time constant of x_s1 [_x(s1)] was set to be the same as the value of the time constant of x_s in the original model of Courtemanche et al., that of x_s2 [_x(s2)] was two, four, or six times _x(s1). The maximum I_Ks conductance was adjusted in each case so that the APD in the control at 1,000-ms cycle length (CL) did not change from that of the original model: it was 0.129, 0.187, 0.251, and 0.277 mS/µF for the original and the two-, four-, and sixfold increases, respectively.

Thirty AP simulations were run at each CL. The last AP in each run was used for analysis. The APD was measured at –70 mV, which closely approximates APD at 90% repolarization (APD₉₀).

Formulation of kinetic properties of I_Kr blockade types. To incorporate the effects of the three blockade groups, we modified the formulation of I_Kr given by Courtemanche et al. (2) as follows

(3)

where i represents the blockade type where dofetilide type is the voltage- and time-independent blockade, quinidine type is the voltage-dependent blockade with fast development, and vesnarinone type is the voltage-dependent blockade with slow development, y_i is the fraction of I_Kr that is not blocked by drug type i, g_Kr is the maximum conductance of I_Kr, and x_r is the activation gate variable,.

Dofetilide blocks I_Kr in a voltage- and time-independent manner (33). Therefore, dofetilide represents the voltage- and time-independent blockade and y_{dofetilide type} was set to 0.1.

On the other hand, the effects of the two types of voltage- and time-dependent blockade were calculated with the following first-order differential equation

(4)

where i represents the blockade type where quinidine or vesnarinone, y_i is the state variable of the unblocked fraction of I_Kr in the presence of drug type i, y_,i, is the steady-state value of y_i, and _i is the time constant for y_i. Simulations of y_,i and _i derived from our experimental data for quinidine and dofetilide (33) and vesnarinone (13) are shown in Fig. 1.

View larger version (17K): [in this window] [in a new window]   Fig. 1. Modeling of voltage-dependent (A–C)- and time-dependent (D-E) blockade of IKr by quinidine (A and D), vesnarinone (B and E), and dofetilide (C). Traces represent results obtained from formulations of blockade described in MATERIALS AND METHODS. Symbols represent experimental data from Tsujimae et al. (33) for dofetilide and quinidine and from Katayama et al. (13) for vesnarinone. Vm represents membrane potential. Values for ydeporalization were 0.159, 0.412, and 0.756 for 30, 100, and 300 nM dofetilide, respectively; 0.491, 0.225, and 0.088 for 3, 10, and 30 µM quinidine, respectively; and 0.550, 0.289, and 0.109 for 1, 3, and 10 µM vesnarinone, respectively.

,i

(5)

(6)

where i represents quinidine type or vesnarinone type

(7)

(8)

(9)

(10)

y_{depolarization,i} is the limit set for the minimum of unblocked I_Kr (y_,i), which was set to 0.1 for both drug types and corresponds to 90% block, _i is the unbinding rate constant for drug type i, and _i is the binding rate constant for drug type i. The values in the formulas for y_{,quinidine type} and _{quinidine type} were determined from the experimental data of Tsujimae et al. (33) by nonlinear least-squares fitting. In the same way, the values in the formulas for y_{,vesnarinone type} and _{vesnarinone type} were derived from Katayama et al. (13). The experimental data for the temperature sensitivity of I_Kr blockade by these drugs are not available. However, because it was reported that the temperature dependence of I_Kr blockade is usually not prominent in various drugs (14), we assumed that the temperature difference among these experiments would not largely affect the present model results. Furthermore, in this study, we adopted the kinetics of dofetilide, quinidine, and vesnarinone from our previous experimental results only to represent the three representative types of I_Kr blockade by various drugs, and we did not intend to reproduce precisely the experimental results of the effects of these drugs on atrial AP. These formulations are used to simulate the development and recovery from blockade for dofetilide, quinidine, and vesnarinone (Fig. 2). For simulation of development of blockade, voltage steps (1-s duration) from a holding potential of –80 mV to between –20 and +40 mV with a 20-mV increment (Fig. 2, A–C) were used. For simulation of recovery from blockade, voltage steps (10-s duration) from a holding potential of +40 mV to between –40 and –100 mV with a 20-mV increment were used (Fig. 2, D–F). Although the kinetics of quinidine blockade are complex and consist of at least two exponential components (33), we treated this as a single-exponential process (Fig. 2, A and D) (33). Block and recovery due to vesnarinone could be represented by single exponentials (Fig. 2, B and E) (13). Blockade by dofetilide was constant (Fig. 2, C and F) (33).

View larger version (14K): [in this window] [in a new window]   Fig. 2. Simulation of onset and recovery from blockade of IKr by each drug type. A–C: simulation of onset of quinidine-, vesnarinone-, and dofetilide-type IKr blockade during 1,000-ms voltage steps from –80 to –20, 0, +20, and +40 mV. D–F: simulation of recovery from quinidine-, vesnarinone-, and dofetilide-type IKr blockade during 10,000-ms voltage steps from +40 to –40, –60, –80, and –100 mV. Value for ydepolarization was set to 0.1 for each drug type.

	RESULTS

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View larger version (24K): [in this window] [in a new window]   Fig. 3. Frequency-dependent effects of 90% reduction in rapidly activating K+ current (IKr) density on prolongation of action potential (AP) duration (APD) in models of human atrial AP. A: simulated APs with the original model of Courtemanche et al. (2) at 500-, 1,000-, and 1,500-ms cycle length (CL). Simulations correspond to control conditions and 90% reduction of maximum IKr conductance (filled square). B: same as A, with a modified model, where a slow component (xs2) is added to the activation gate of IKs (Eq. 2). Time constant of xs2 was 6 times that of xs1. Ca: APD–70 mV-CL relation with the original model of Courtemanche et al. under control conditions and after 90% reduction of maximum IKr conductance. Cb: effects of alteration of time constant of slow component of activation of slowly activating K+ current (IKs, xs2) in the modified model on CL-APD relation under control conditions and after 90% reduction of IKr. Slow time constants 2, 4, and 6 times the time constant of the fast component of IKs (xs1) were tested. Cc: effect of CL on APD–70 mV prolongation after 90% reduction of maximum IKr conductance in original and modified models. Values were normalized to 500-ms CL. Modified model involved inclusion of a slow phase of activation of IKs (xs2) with time constants of activation 2, 4, and 6 times the time constant of xs1.

Activation of I_Ks contains fast and slow processes (27, 31). I_Ks in the model of Courtemanche et al. (2) has one fast activation process. Therefore, we incorporated a second variable for slow kinetics (x_s2) into the activation gate of I_Ks (Eq. 2). The time constant of slow activation of I_Ks has been reported to be three to five times larger than that of fast activation (31). Therefore, we set the slow time constant [_x(s2)] to two, four, or six times _x(s1) (Fig. 4). For each value of _x(s2), the maximum conductance of I_Ks was adjusted to maintain the AP configuration at 1,000-ms CL.

View larger version (13K): [in this window] [in a new window]   Fig. 4. Comparison of voltage dependence of time constants of activation gate of IKs described by Courtemanche et al. (2) and the two gates of IKs (LRd fast and LRd slow) used in the Luo-Rudy ventricular AP model (35). Equivalent of the time constant of the model of Courtemanche et al. (2) multiplied by 2, 4, and 6, which we used as time constants for the slow gating component (xs2) of IKs, is also shown.

The effect of varying _x(s2) on CL-dependent prolongation of APD_{–70 mV} in the presence of the voltage- and time-independent blocker is shown in Fig. 3Cb. In control conditions, as _x(s2) increased, APD_{–70 mV} at 500-ms CL decreased, but _x(s2) had less effect at 1,000-ms CL. When I_Kr was reduced as _x(s2) was increased, CL-dependent prolongation of APD_{–70 mV} was more apparent, and the slope of the CL-APD_{–70 mV} relation became steeper. When _x(s2) was set to four or six times _x(s1), APD_{–70 mV} did not reach a plateau until 1,500-ms CL. In addition, normalization of APD_{–70 mV} prolongation caused by reduced I_Kr density (Fig. 3Cc) clearly demonstrated that the prolongation of APD_{–70 mV} caused by I_Kr reduction depends on _x(s2). Clearly, these results more closely resemble experimental results (12, 18) than those obtained with the original model of Courtemanche et al. (2) (Fig. 3Ca). Therefore, in the following studies, we used the modified model with _x(s2) set to six times _x(s1).

Comparison of delayed rectifier currents in original and modified models. Figure 5 shows I_Kr and I_Ks during APs at various CLs in the original and modified models. Since the formulation of I_Kr was not modified, the form and amplitude of I_Kr during each AP at each CL in the original (Fig. 5A) and modified (Fig. 5B) models were very similar. The peak of I_Kr during an AP increased as APD was prolonged, because the activation process of I_Kr progressed during an AP, even in the presence of very rapid C-type inactivation (36). As CL increased, I_Kr increased by the same amount in both models, although at 500-ms CL, the peak of I_Kr was slightly smaller during an AP in the modified than in the original model.

View larger version (16K): [in this window] [in a new window]   Fig. 5. Contributions of IKr and IKs to AP simulated by different models and at different CLs. A and B: simulations with original model of Courtemanche et al. (2) and modified model at 500-, 1,000-, and 1,500-ms CL. AP: representative APs. Arrowheads, 0 mV. IKr and IKs: time course of simulations of IKr and IKs currents during APs. Dashed horizontal lines (IKr and IKs) indicate 0 pA/pF; dotted horizontal lines (IKs) indicate maximum current through IKs during AP at 500-ms CL. Gate: time course of gating variables (xs in A and xs1 and xs2 in B) of IKs. To facilitate comparison between gating of IKs in A and B, dashed lines represent the product of the gating variables: x in A and xs1 and xs2 in B. Data have been multiplied by 10 to appear on this scale. IK/(IKr + IKs): contribution of IKr to total IK during each AP.

As a result of these differences, deactivation of the product of x_s1 and x_s2 in Eq. 2 for the modified model is slower than deactivation of x in Eq. 1 in the original model. Consequently, at short CL in the modified model, I_Ks showed little deactivation at the end of repolarization, and its initial jump at the onset of the next AP was large; with increasing CL, deactivation could develop further, and the amplitude of the initial jump decreased markedly. After the initial jump, I_Ks increased during an AP, but the combination of a slower activation and the decline of the initial current meant that the peak of I_Ks during an AP decreased as CL was prolonged. On the other hand, in the original model, deactivation was more rapid, and the initial jump of I_Ks was less at 500-ms CL and was influenced less by increasing CL. I_Ks increased rapidly during an AP because of its fast activation kinetics, and peak I_Ks increased with CL. Finally, in the original model, the relative proportions of I_Kr and I_Ks showed little change with CL [Fig. 5A; I_Kr/(I_Kr + I_Ks)]. In the modified model, the contribution of I_Kr to the total repolarizing current increased with CL (Fig. 5B). Thus it is the modified model that can reproduce the experimental data for the frequency-dependent behavior of I_Ks and APD.

Effects of I_Kr blockers on APD prolongation. Experimentally, it is also recognized that excessive AP prolongation is quite divergent among dofetilide, quinidine, and vesnarinone (10, 12, 32). We next examined how voltage- and time-dependent kinetics in I_Kr blockade affect the reverse frequency dependence of APD prolongation in the model. Although dofetilide and E-4031 block I_Kr in a voltage-independent manner, quinidine and vesnarinone do so in a voltage- and time-dependent manner (13, 33). Both drugs inhibit the current more potently and rapidly as the membrane potential is more depolarized. However, at the same depolarized potential, the development of block is much faster with quinidine than with vesnarinone. To isolate the effects of these three typical kinetic properties of I_Kr blockade, we fixed their maximal effect to correspond to 90% block of I_Kr. Thus we calibrated the blockades with different kinetics by assuming the same possible maximal block effect, so that the effects of the kinetics of I_Kr blockade on APD can be compared selectively. This is represented in the calculations as a steady-state unblocked fraction of 0.1 (see MATERIALS AND METHODS).

Figure 6 illustrates the effects of these drug types on APD at different CLs in absolute and relative terms. Dofetilide-type blockade exhibited the strongest and the most prominent reverse-frequency-dependent increase in APD_{–70 mV} (Fig. 6A). Quinidine-type blockade was less effective than dofetilide-type blockade but showed a similar reverse frequency dependence. Vesnarinone-type blockade was weaker than quinidine- or dofetilide-type blockade, and it showed no frequency dependence at >800-ms CL. The result in relative terms also more clearly demonstrates no frequency dependence of vesnarinone-type blockade at >800-ms CL; thus frequency dependence is similar for vesnarinone-type blockade and control (Fig. 6B). These results are consistent with experimental findings (10, 12, 32). We conclude that the modified model can reproduce the characteristic frequency-dependent prolongation of atrial APD by the I_Kr blockers with the three representative kinetics.

View larger version (10K): [in this window] [in a new window]   Fig. 6. AP elongation by blockade of IKr from modified model. A: effect of CL on APD (measured at –70 mV) under control conditions and in the presence of dofetilide, quinidine, or vesnarinone. B: data from A normalized as drug-induced increase in APD relative to APD under control conditions.

View larger version (16K): [in this window] [in a new window]   Fig. 7. Effects of IKr blockade on AP and IKr and IKs at 500-, 1,000-, and 1,500-ms CL. AP: simulations of APs at 500-, 1,000-, and 1,500-ms CL under control conditions and in the presence of dofetilide, quinidine, and vesnarinone. Arrowheads, 0 mV. Unblocked fraction: yi for IKr for each drug type (see Eq. 4). Traces show degree and time course of blockade of IKr by each drug. IKr + IKs: total IK. Traces show time course of these currents during AP at 500-, 1,000-, and 1,5000-ms CL and effects of dofetilide, quinidine, and vesnarinone on IKr blockade. IKr/(IKr + IKs): contribution of IKr to total IK.

The total delayed rectifier current increases with increasing CL under control conditions (Fig. 7, I_Kr + I_Ks) because of the increase in I_Kr [Fig. 7, I_Kr/(I_Kr + I_Ks); see also Fig. 5B, I_Kr]. In the presence of a vesnarinone-type drug, total I_K also increased with increasing CL, because the relative proportion of I_Kr also increased. As a result, vesnarinone-type blockade did not induce reverse-frequency-dependent prolongation of APD. In contrast, in the presence of dofetilide- and quinidine-type drugs, total I_K decreased as CL was prolonged. This is due to their constant maximum blockade of I_Kr over a wide range of CL and the reduction of I_Ks with longer CL. As a result, APD prolongation with CL was enhanced by dofetilide- and quinidine-type blockade.

	DISCUSSION

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The major findings in this study are as follows. 1) Incorporation of a slow process of activation into I_Ks enabled a human atrial AP model to reproduce the reverse-frequency-dependent elongation of APD that is associated with the reduction of I_Kr. 2) This model could account for the mechanisms underlying the difference between the frequency-dependent effects of the three kinetically distinctive types (dofetilide, quinidine, and vesnarinone) of I_Kr blockade on APD. 3) The analysis with the models predicted that the drugs with the voltage- and time-dependent I_Kr blockade with slow kinetics may be good candidates without the adverse effect of arrhythmias.

There are many mathematical models for cardiac APs, e.g., models for Purkinje fibers (19, 20), rabbit sinoatrial node (4), and ventricular cells of rat (22, 23), guinea pig (35, 40), dog (9, 38), and human (24) and models for atrial cells of dog (15, 25) and human (2, 21). No model is perfect, but each has its use for examination of different properties of cardiac AP behavior, with their respective limitations taken into account. In practical terms, it is important to adjust models according to the purposes for which they will be used.

A problem in pharmacology is the proarrhythmic action of many drugs. A number of compounds inhibit I_Kr in cardiac myocytes and, therefore, have the potential to prolong the AP in a reverse-frequency-dependent manner, which could induce torsades de pointes in the ventricle. Because of this side effect, drugs such as terfenadine, astemizole, grepafloxacin, droperidol, and cisapride have been withdrawn or restricted in their clinical application (26). Also, the development of a number of new pharmacological agents was stopped when they were shown to block I_Kr. A mathematical model of the cardiac AP that can reproduce reverse-frequency-dependent APD prolongation on I_Kr blockade could be used to assess the risk of such side effects.

Inasmuch as dofetilide has been approved by the US Food and Drug Administration for treatment of AF (6), the importance of elucidating the action of I_Kr blockade on atrial APD prolongation is increasing. The model of the human atrial AP of Courtemanche et al. (2) could not reproduce reverse-frequency-dependent elongation of APD with blockade of I_Kr. To reproduce this property, we introduced a slow process of activation and deactivation of I_Ks, which has been identified experimentally (27, 31). The modified human atrial AP model reproduced reverse-frequency-dependent prolongation of atrial APD, which results from the reduction of maximum conductance of I_Kr by voltage- and time-independent I_Kr blockers such as dofetilide and E-4031. It also differentiates between the effects of the voltage- and time-dependent blockade caused by quinidine- and vesnarinone-type I_Kr blockers. Therefore, the model can be used to assess the frequency-dependent action of different types of pure I_Kr blockade on the human atrial AP. Because the simulation results with pure I_Kr blockade are very close to the experimental results of the effects of dofetilide, quinidine, and vesnarinone on atrial APD (10, 18, 32), it was also suggested that the effects of these drugs on I_Kr are the major determinants for atrial APD, although quinidine is known to affect a number of ion currents, including I_Na and I_to, and vesnarinone is known to increase I_Ca,L (16, 39). Indeed, our preliminary model study showed that additional blockade of I_Kur and I_to only marginally enhanced the reverse frequency dependence of APD prolongation induced purely by the quinidine-type blockade of I_Kr (not shown).

This study showed that the slow activation/deactivation of I_Ks plays an important role in reproducing the reverse-frequency-dependent APD prolongation by I_Kr blockers in an atrial model. The Luo-Rudy model (35, 40), which is the de facto standard for the guinea pig ventricular cell, also has fast and slow components of I_Ks activation; in this example, the slow time constant is four times the fast (35) (Fig. 4). Reconstitution of I_Ks with KvLQT1/minK exhibited three activation processes: fast, slow, and very slow (27). The time constants for fast and slow were 0.68 and 1.48 s, respectively, at +40 mV, which approximate the fast and slow activation processes of I_Ks that we use. We have not incorporated the very slow time constant (8.0 s at +40 mV) into I_Ks. If this slower activation process were incorporated into our model, the reverse-frequency-dependent APD prolongation associated with the dofetilide-type of blockade of I_Kr would become more prominent. Further experimental studies are needed to identify the gating processes of I_Ks for further improvement of the model.

APD is shorter in atrial cells from AF patients than from normal subjects; this is due to electrical remodeling of atrial myocytes, where expression of ion channel currents, including I_Ca,L, I_to, I_Kur, and I_K1, is altered (5). Courtemanche and colleagues (3) incorporated such changes into their original model and examined the effects of modification of the different outward currents on atrial AP configuration. The modified human atrial AP model that we present here could also be extended to an AF-atrial AP model that will be suitable for assessing the effects of drugs with the potential to treat AF.

In conclusion, this simulation showed that slow activation and deactivation of I_Ks underlie the reverse-frequency-dependent atrial APD prolongation induced by I_Kr blockers. It also demonstrated that the effects of these compound types on APD prolongation depended on the kinetics of their interactions with I_Kr. Further studies may provide useful information for understanding the underlying mechanisms of cardiac arrhythmias and estimating the balance between antiarrhythmic effect and proarrhythmic risk of I_Kr blocking agents. This approach may also be useful for the in silico design of antiarrhythmic agents.

	GRANTS

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This work was supported by the Leading Project for Biosimulation "Development of Heart and Lung Models for In Silico Prediction of Drug Action and Clinical Treatment" from the Ministry of Education, Culture, Sports, Science, and Technology (Japan) to Y. Kurachi.

	ACKNOWLEDGMENTS

 
We thank Dr. I. Findlay and A. O'Meara for comments about the manuscript.

	FOOTNOTES

 

Address for reprint requests and other correspondence: Y. Kurachi, Div. of Molecular and Cellular Pharmacology, Dept. of Pharmacology, Graduate School of Medicine, Osaka Univ., 2-2 Yamada-oka, Suita, Osaka 565-0871, Japan (e-mail: ykurachi{at}pharma2.med.osaka-u.ac.jp)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

	REFERENCES

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