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(Circulation Research. 2000;87:1026.)
© 2000 American Heart Association, Inc.

Cellular Biology

Role of the Calcium-Independent Transient Outward Current I_to1 in Shaping Action Potential Morphology and Duration

Joseph L. Greenstein, Richard Wu, Sunny Po, Gordon F. Tomaselli, Raimond L. Winslow

From the Department of Biomedical Engineering, Whitaker Biomedical Engineering Institute (J.L.G., R.L.W.), the Center for Computational Medicine & Biology (J.L.G., R.L.W.), the Section of Molecular and Cellular Cardiology, Division of Cardiology, Department of Medicine (R.W., S.P., G.F.T.), and the Institute for Molecular Cardiobiology (R.W., S.P., G.F.T., R.L.W.), Johns Hopkins University School of Medicine, Baltimore, Md.

Correspondence to Raimond L. Winslow, PhD, Room 411, Traylor Research Building, 720 Rutland Ave, Baltimore, MD 21205. E-mail rwinslow{at}bme.jhu.edu

	Abstract

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Abstract—The Kv4.3-encoded current (I_Kv4.3) has been identified as the major component of the voltage-dependent Ca²⁺-independent transient outward current (I_to1) in human and canine ventricular cells. Experimental evidence supports a correlation between I_to1 density and prominence of the phase 1 notch; however, the role of I_to1 in modulating action potential duration (APD) remains unclear. To help resolve this role, Markov state models of the human and canine Kv4.3- and Kv1.4-encoded currents at 35°C are developed on the basis of experimental measurements. A model of canine I_to1 is formulated as the combination of these Kv4.3 and Kv1.4 currents and is incorporated into an existing canine ventricular myocyte model. Simulations demonstrate strong coupling between L-type Ca²⁺ current and I_Kv4.3 and predict a bimodal relationship between I_Kv4.3 density and APD whereby perturbations in I_Kv4.3 density may produce either prolongation or shortening of APD, depending on baseline I_to1 current level.

Key Words: K⁺ channel • transient outward current • ventricular action potential • action potential duration

	Introduction

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The voltage-dependent calcium (Ca²⁺)-independent transient outward current I_to1 is a key contributor in shaping the early phase of the cardiac ventricular action potential (AP). Recordings obtained from single ventricular myocytes isolated from different depths within the ventricular wall have shown a correlation between I_to1 density and prominence of the phase 1 notch.^{1 2 3 4 5} I_to1 magnitude is also reduced substantially in ventricular myocytes isolated from failing human and canine hearts,^{6 7} and APs recorded from these cells exhibit a decreased phase 1 notch depth. In addition, blockers of I_to1, such as 4-aminopyridine (4-AP), reduce or eliminate the phase 1 notch.^{6 7 8 9}

Although the evidence linking I_to1 magnitude to characteristics of the phase 1 notch is strong, the role of I_to1 on AP duration (APD) remains unclear. Heart failure–induced reduction of I_to1 density in canine and human myocytes is accompanied by significant prolongation of APD.^{6 7} However, heart failure is also accompanied by altered expression of genes encoding the inward rectifier potassium (K⁺) current I_K1,⁶ the sarcoplasmic reticulum (SR)-Ca²⁺ ATPase,^{10 11} and the sodium-calcium exchanger.^{10 12} Recently, a model of the failing canine ventricular myocyte was developed and used to investigate mechanisms influencing APD in heart failure.¹³ Model predictions are that reduction of both I_to1 and I_K1 magnitude, on the basis of the average decrease in current densities measured in terminal heart failure,⁷ have only modest effects on APD and that AP prolongation occurs mainly because of altered expression of intracellular Ca²⁺-handling proteins and the accompanying reduction of both SR Ca²⁺ concentration and Ca²⁺-mediated inactivation of the L-type Ca²⁺ current (I_CaL).¹³

Experiments designed to reveal the role of I_to1 on APD have yielded conflicting results. In the absence of Ca²⁺ buffers, low concentrations of 4-AP (1 mmol/L) shorten APD in isolated canine midmyocardial⁹ and epicardial⁸ ventricular cells. Higher doses of 4-AP (3 to 5 mmol/L) prolong the AP in Ca²⁺-buffered canine⁷ and human⁶ ventricular midmyocardial cells. Interpretation of these findings is complicated by the lack of specificity of 4-AP for I_to1 and the use of Ca²⁺ buffers. AP prolongation may result from modest block of delayed rectifier K⁺ currents in response to higher concentrations of 4-AP. In guinea pig myocytes, the introduction of I_to1 by cell fusion techniques produces a reduction of APD that is correlated with increasing I_to1 density.¹⁴ However, the presence of sustained inward currents may have influenced APD in these studies. Functional knockout of a major component of I_to1 (I_to,f) in mouse also prolongs APD.^{15 16} However, I_to1 density is much larger in mouse than in canine or human myocytes and APD is significantly shorter.^{2 7 15}

These data highlight the uncertainty of the role of I_to1 in controlling APD. To help clarify this role, we have functionally expressed and characterized the human Kv4.3-encoded current (long splice variant, denoted as hKv4.3-2) at 35°C; developed a Markov state model of the hKv4.3-2 encoded current on the basis of these data; developed a Markov state model of the human Kv1.4-encoded current on the basis of data of Po et al^{17 18} and combined the hKv1.4 and hKv4.3-2 models to form a model of canine I_to1; incorporated the I_to1 model into a computational model of a canine midmyocardial ventricular cell¹³ ; and determined the mechanisms by which I_to1 influences AP shape and duration.

	Materials and Methods

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Composition of I_to1
Canine and human I_to1 is likely a combination of Kv4.3- and Kv1.4-encoded currents (I_Kv4.3 and I_Kv1.4, respectively). Each component has different kinetics of recovery from inactivation.^{2 5 19 20} The Kv4.3-encoded current^{21 22 23} has kinetics and pharmacological sensitivity similar to the I_to1 component with fast recovery.² Reduction in Kv4.3 mRNA transcript level is also correlated with reduction in I_to1 density in human and canine heart failure.^{7 24} The Kv1.4 current has kinetics similar to the slowly recovering component of I_to1^{2 17} In addition, Kv1.4 mRNA transcripts have been detected in canine²³ and human²⁴ myocytes at levels 16% and 72% as abundant, respectively, as those of Kv4.3.

On the basis of these data, the model of I_to1 is constructed as a combination of I_Kv4.3 and I_Kv1.4. The balance of I_Kv4.3 and I_Kv1.4 (77% and 23%, respectively) is based on the relative magnitudes of fast versus slow recovery time constants measured by Kääb et al⁷ (estimated from their Figure 7D) in canine midmyocardial cells. The strategy for modeling I_Kv4.3 and I_Kv1.4 is to express hKv4.3 in cell culture and characterize and model properties of human I_Kv4.3; adjust parameters of this human I_Kv4.3 model to better correspond to properties of the rapidly recovering component of I_to1 measured in isolated canine myocytes; formulate a human I_Kv1.4 model using published data on expressed hKv1.4 current; and adjust parameters of this human I_Kv1.4 model to better correspond to properties of the slowly recovering component of I_to1 measured in isolated canine myocytes.

View larger version (26K): [in this window] [in a new window]   Figure 7. Figure 7. Effect of IKv4.3 current density on simulated guinea pig APs (1 Hz steady state). APD90 as a function of GKv4.3 for the LRII32 (A) and JRW33 (B) models. Alternans in APD90 were present for the values of GKv4.3 enclosed by the dashed lines in (B). Maximum () and minimum () APDs observed in this region of alternans are shown. C, APs simulated by introducing IKv4.3 and an instantaneous background inward current (Ib, Gb=0.1GKv4.3 with reversal potential EK) into the JRW33 model with increasing values of GKv4.3 in 0.2 nS/pF increments.

Characterization of I_Kv4.3
The hKv4.3 gene has two splice variants with quantitatively similar biophysical properties in the basal state. In this study, only the long splice variant, denoted hKv4.3-2, is expressed. Full-length cDNA encoding hKv4.3-2²¹ was subcloned into the pIRES-GFP vector for bicistronic expression of the hKv4.3-2 channel and green fluorescence protein in mouse Ltk^- fibroblasts. Transient transfection was performed using the lipofectamine method (GIBCO-BRL), as previously described.²¹ Cells were transferred to the stage of an inverted microscope (Nikon Diaphot) and selected by epifluorescence for patch-clamp experiments using the whole-cell configuration.²⁵

All currents were recorded at 35°C using an Axopatch 200A amplifier (Axon Instruments). Glass pipettes had 1 to 2 M tip resistance when filled with an internal solution containing (in mmol/L) KCl 115, HEPES 10, EGTA 1, and MgATP 5, adjusted to pH 7.2 with KOH to yield a final K⁺ concentration of 130 mmol/L. Cells were perfused with Tyrode’s solution containing (in mmol/L) NaCl 140, KCl 5, MgCl₂ 1, CaCl₂ 2, HEPES 10, and glucose 10, adjusted to pH 7.4. Cell capacitance was estimated by integrating the area under an uncompensated 10-mV depolarizing voltage step from -80 mV. The cell capacitance was 15.9±0.9 pF (n=11). Currents were low-pass filtered at 2 kHz and digitized at 10 kHz through a Digidata 1200 analog-to-digital interface (Axon Instruments) for offline analysis. The measured hKv4.3-2 current was defined as the difference between the peak transient current and steady-state current at the end of a 500-ms clamp. Pooled data are presented as mean±SE.

Figure 1 shows the Markov state model structure for the hKv4.3-2 channel, which is assumed to be homotetrameric. Rightward transitions represent activation, whereas transitions into the lower row represent inactivation. Kv4.3 model parameters are optimized to accurately reproduce experimentally measured peak current, time-to-peak, time constant of inactivation, steady-state availability, and recovery from inactivation in response to standard voltage-clamp protocols. The I_Kv4.3 time constant of inactivation was reduced slightly to ensure behavior consistent with native currents^{1 2 3} (see online data supplement).

View larger version (18K): [in this window] [in a new window]   Figure 1. Figure 1. State diagram of the hKv4.3-2–encoded K+ channel Markov model. The model structure consists of 4 closed states (C0 to C3), 4 closed-inactivated states (CI0 to CI3), 1 open state (O), and 1 open-inactivated state (OI). Transition rates a, ßa, i, and ßi are voltage dependent, and scaling factors f1 to f4 and b1 to b4 allow for coupling of inactivation to activation.

Characterization of I_Kv1.4
The I_Kv1.4 model uses the same structure as shown in Figure 1 and is based on the data of Po et al.^{17 18} Inactivation is assumed to be voltage-independent.²⁶ The I_Kv1.4 recovery time constant was reduced to ensure behavior consistent with native currents.^{2 3 7 27} Parameters were determined at room temperature and then scaled to 35°C (see online data supplement).

Modeling I_to1 Effects on the AP
The canine I_to1 is incorporated into the Winslow-Rice-Jafri (WRJ)¹³ canine ventricular cell model to investigate its interaction with other membrane currents. Additional myocyte models are implemented to test robustness of simulation results (see Discussion). APs are simulated at 1 and 2 Hz periodic pacing to steady state. For brevity, only those at 1 Hz are shown.

An expanded Materials and Methods section can be found in an online data supplement available at http://www.circresaha.org.

	Results

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Functional Expression of hKv4.3 and I_Kv4.3 Model Validation
Representative normalized whole-cell currents elicited by a family of depolarizing voltage steps from 0 to 60 mV in 20-mV increments are shown in Figure 2A (solid lines) with corresponding model-simulated currents (dashed lines). Experimental currents are normalized by the peak current measured at 60 mV (2118 pA). Successive current traces are displaced vertically by 0.1 normalized units (212 pA) for clarity. The current activates and inactivates rapidly, decaying within 100 ms. Time to peak decreases monotonically from 6.5 ms at -10 mV to 2 ms at 60 mV (Figure 2B). The time constant of inactivation becomes nearly voltage-independent, with a time constant of 13.5 ms at potentials >10 mV (Figure 2C). The current activates in the range of -40 to -30 mV, and peak current increases nearly linearly over more positive potentials (Figure 2D). In all cases, experimental data (symbols) are well fit by the model (lines).

View larger version (26K): [in this window] [in a new window]   Figure 2. Figure 2. Electrophysiological characteristics of the expressed hKv4.3-2 current and model-simulated currents at 35°C. A, Representative normalized whole-cell currents (solid lines) and model simulated currents (dashed lines) elicited by voltage steps from -80 mV to 0, 20, 40, and 60 mV. Current traces at each test potential are displaced along the ordinate for clarity. Time-to-peak current (B), time constant of decay (C), and normalized peak current (D) are shown as functions of membrane potential (•, experiment; dashed line, model). E, Steady-state availability curves are obtained by stepping to a 50-mV test potential from various conditioning prepulse potentials (•, experiment; , model). A Boltzmann function fit to both data and model (dashed line) yields half-maximal availability voltage (V1/2) and slope factor (k) of -51.1±0.7 mV and 5.6±0.4 mV, respectively (±SE values and n=6 for experiments). F, For recovery curves obtained at -100 mV (•, experiment; , model) and -80 mV (, experiment; , model), respectively, recovery time constants are 20.23±1.72 ms (n=5) and 37.69±1.76 ms (n=6) for experiments and 20 ms (dashed line) and 38 ms (solid line) for the model.

The steady-state availability curve is shown in Figure 2E. Boltzmann function fits to experimental data (•, data; dashed line, fit) and to the model (, data; fit not shown) both yield half-maximal current at (V_1/2) -51.1±0.7 mV, with slope factor (k) of 5.6±0.4 mV (±SE values and n=6 for experiments), in agreement with previous measurements.^{14 21 22} The current inactivates fully at potentials more positive than -10 mV. Recovery kinetics were determined at -100 and -80 mV (Figure 2F). The currents recover monoexponentially with time constants of 20.23±1.72 ms (•, n=5) and 37.69±1.76 ms (, n=6) for experiments and 20 ms (, simulated current; dashed line, fit) and 38 ms (, simulated current; solid line, fit) for the model at -100 and -80 mV, respectively. These data demonstrate the ability of the model to reproduce properties measured experimentally.

Model Validation of I_Kv1.4 and Canine I_to1
Figure 3 shows features of the I_Kv1.4 model at 22°C. Figure 3A shows peak I_Kv1.4 model current (normalized to the +100-mV peak current) with the corresponding model current traces in the inset. The current activates at potentials greater than -50 mV, and the current-voltage relation shows slight outward rectification in agreement with experimental data.¹⁷ The time constant of inactivation is nearly voltage-independent at potentials >-10 mV, ranging from 52.4 ms at -10 mV to 49.1 ms at +100 mV. Time to peak is 10 to 17 ms, depending on clamp potential (not shown). Steady-state availability of I_Kv1.4 (Figure 3B; symbols, model; line, fit) exhibits V_1/2 of -66.3 mV and k of 4 mV, in close agreement with experiments.¹⁸

View larger version (22K): [in this window] [in a new window]   Figure 3. Figure 3. Voltage-dependence of peak current and steady-state availability for the IKv1.4 model at room temperature. A, Peak current-voltage relationship normalized to the peak current at +100 mV with corresponding model current traces in the inset. B, Steady-state availability curve (, model currents; line, Boltzmann fit) with V1/2 and k of -66.3 and 4 mV, respectively.

Peak I_to1 current in response to a family of depolarizing voltage steps is shown in Figure 4A, with corresponding current traces shown in the inset. Currents are normalized by peak I_to1 magnitude at 60 mV. Model I_to1 activates at -40 mV, and the peak current-voltage relation increases monotonically. The steady-state availability curve (Figure 4B; symbols, model; line, fit) exhibits a V_1/2 of -55.5 mV, with k of 6.8 mV. The features of Figures 4A and 4B agree well with native I_to1 measured in both canine^{1 7} and human^{3 27 28} myocytes. Currents in these experiments activate in the range of -20 to -10 mV^{1 3 7 27 28} and have V_1/2 in the range of -23 to -37 mV.^{1 3 7 28} The 20-mV difference in both the voltage where I_to1 first activates and in the half-inactivation voltage is accounted for by the presence of extracellular divalent cations (usually 0.1 to 0.3 mmol/L Cd²⁺), which produce a 15 to 25 mV positive shift in both the peak current-voltage relation and the steady-state inactivation curve of native I_to1^{28 29} and expressed Kv4.3 currents.³⁰

View larger version (19K): [in this window] [in a new window]   Figure 4. Figure 4. Canine Ito1 model electrophysiological characteristics at 35°C. A, Peak current-voltage relationship simulated from a holding potential of -80 mV and normalized to the peak current at +60 mV. Inset shows corresponding current traces. B, Steady-state availability curve (, model currents; line, Boltzmann fit) with V1/2 and k of -55.5 and 6.8 mV respectively. C, Recovery curve for Ito1 at -80 mV () using a protocol identical to that of Liu et al1 (see text). The best fit to a biexponential recovery function (line) yields time constants of 37 ms (77.9%) and 583.6 ms (22.1%). Inset depicts the same data () and fit (line), both subtracted from unity, on a logarithmic scale.

The time constant of inactivation for model I_to1 is nearly voltage-independent at potentials greater than -10 mV, ranging from 10.8 ms at -10 mV to 8.4 ms at +60 mV, and the current reaches its peak value in 2 to 5 ms, depending on test potential. The inactivation kinetics agree with values obtained at 35°C for human subendocardial and subepicardial myocytes (7 and 7.9 ms, respectively²⁷ ) and for canine midmyocardial cells (9.4 ms, estimated from Figure 8 of Liu et al¹ ). Figure 4C shows the time course of recovery from inactivation at -80 mV. Normalized peak currents () in response to a 2-pulse protocol with 200-ms steps to +40 mV are fit to the biexponential recovery function 1-a₁e^-t/₁-a₂e^-t/₂ (solid line). These data are replotted on a log scale to illustrate the clearly biexponential nature of the model recovery process (Figure 4C, inset). The fit yields values of 37 ms and 583.6 ms for ₁ and ₂, respectively, where the relative amplitude of ₁ (ie, a₁/[a₁+a₂]) is 0.779. These time constants and their relative weights have the values expected on the basis of the individual recovery properties and the combination ratio of the component currents I_Kv4.3 and I_Kv1.4 and are in agreement with those measured experimentally at or near 35°C in both canine^{1 7} and human^{3 27} ventricular midmyocardial cells.

Effect of I_to1 Density on Canine AP Shape and Duration
Downregulation of Kv4.3, without an associated reduction in Kv1.4 level, is believed to be the basis for the reduction of I_to1 observed in failing canine myocytes.²⁴ Therefore, the I_to1 model was incorporated into the WRJ canine ventricular cell model to study the impact of Kv4.3 downregulation on AP properties. The effect of varying the density of the Kv4.3 component of I_to1 on model AP shape (Figure 5A) and duration (Figure 5B, •) is multifaceted. With complete elimination of I_Kv4.3, APD at 90% repolarization (APD₉₀) is approximately 250 ms. As I_Kv4.3 current density is increased, phase 1 repolarization becomes more prominent, resulting in an AP with a spike and dome configuration. Hyperpolarization of phase 1 membrane potential attributable to an early repolarizing current is commonly observed in experiments; however, the model reveals an additional effect of I_Kv4.3 on APD. At relatively low densities of I_Kv4.3, incremental changes in current density produce progressive prolongation of APD. For example, an I_Kv4.3 with maximal conductance (G_Kv4.3) of 0.07 nS/pF (corresponds to 4.6 pA/pF peak current in response to a depolarization to +20 mV from -80 mV) results in an APD of 263 ms. Increasing G_Kv4.3 to 0.10 and 0.12 nS/pF produces APs with durations of 275 and 300 ms, respectively. Additional increases in the density of I_Kv4.3 reveal the presence of a threshold phenomenon, whereby the AP configuration switches from the spike and dome morphology with relatively long duration to a short triangular AP that lacks a plateau phase. The short APs resemble those measured in species normally expressing high levels of I_to1, such as mouse and rat.¹⁵ At these relatively high current densities, any additional increase in maximal conductance leads to shortening of APD. The same simulations were repeated with a 50% reduction in density of the fast inward sodium current I_Na (Figure 5B, ). This decrease in I_Na shifts the G_Kv4.3 versus APD relationship only slightly toward lower conductance values. The effects of G_Kv4.3 on APD are seen to depend on the baseline value of G_Kv4.3 against which perturbations in current density are made. At lower levels of I_Kv4.3 expression, increasing G_Kv4.3 prolongs APD, whereas at higher levels of expression, increasing G_Kv4.3 shortens APD. Qualitatively similar results were obtained at both 1 Hz (Figure 5) and 2 Hz (not shown) pacing rates.

View larger version (24K): [in this window] [in a new window]   Figure 5. Figure 5. Effect of IKv4.3 current density on canine action potential shape and duration (1 Hz steady state). A, APs simulated with the WRJ13 canine ventricular cell model with increasing values of GKv4.3. B, APD90 as a function of GKv4.3 from simulations described in panel A with normal INa (•) and INa reduced by 50% ().

Mechanism of I_Kv4.3 Influence on AP Shape
To understand mechanisms underlying the influence of I_Kv4.3 on AP shape, the effect of varying G_Kv4.3 on individual membrane currents and state variables was examined. I_CaL shape and magnitude is closely coupled to the density of I_Kv4.3. Figure 6A shows 3 simulated canine APs. In case 1, I_Kv4.3 is underexpressed by 70% (dashed line, G_Kv4.3=0.0358 nS/pF); in case 2, I_Kv4.3 is expressed at normal levels (solid line, G_Kv4.3=0.1194 nS/pF); and in case 3, I_Kv4.3 is overexpressed by 20% (dotted line, G_Kv4.3=0.1432 nS/pF). The normal current level of case 2 is set such that total I_to1 density (9.5 pA/pF peak current in response to a step to +20 mV) agrees with that measured in control canine left ventricular midmyocardial cells (5 to 11 pA/pF^{1 7} ) and consists of 77% I_Kv4.3.⁷ Figures 6B and 6C (inset) show corresponding L-type Ca²⁺ channel open probability (P_open-ICaL), I_CaL, and I_to1 for each of the 3 cases. An increase in the expression level of I_Kv4.3 leads to an increase in the phase 1 repolarization rate, which results in stronger hyperpolarization of the notch potential (Figure 5A). This decrease in phase 1 notch potential has 2 effects on I_CaL. The rate of decline of P_open-ICaL during phase 1 increases for case 2 versus case 1 due to a partial deactivation of the L-type channel. There is a concurrent increase in occupation probability of the closed states immediately preceding the open state of the L-type channel (not shown), brought about by activation of I_Kv4.3. In addition, the driving force for the L-type current is increased for case 2 versus case 1, increasing peak I_CaL by 70% (Figure 6C). Indeed, I_CaL for case 2 remains greater than that for case 1 throughout phase 1 even though P_open-ICaL is decreased (Figures 6B and 6C). This increased inward current prevents the relatively large I_Kv4.3 from truncating the AP and allows for the subsequent return to activation of the L-type channel after inactivation of I_Kv4.3 and progression to phase 2 of the AP. The delayed secondary activation of the L-type channel is shown by the increase in P_open-ICaL and I_CaL, which occurs between 30 and 50 ms after the upstroke of the AP for case 2 (Figure 6B, arrow). Subsequent to this secondary activation, P_open-ICaL and I_CaL for cases 1 and 2 are time-shifted versions of each other (Figure 6B, inset). Thus, the difference in APD in case 1 versus case 2 can be attributed to the difference in duration of phase 1. The case 3 AP exhibits an even more rapid early phase 1 rate of hyperpolarization compared with case 2. This results in a more complete deactivation of the L-type channel, thus eliminating the ability of I_CaL to overcome I_Kv4.3 regardless of the increase in L-type channel driving force. The resulting AP repolarizes rapidly and is therefore lacking a plateau phase.

View larger version (20K): [in this window] [in a new window]   Figure 6. Figure 6. Effect of IKv4.3 current density on canine action potential, Popen-ICaL, and ICaL magnitude. A, Membrane potential simulated with the WRJ13 canine ventricular cell model for case 1 (dashed line, underexpression of IKv4.3 by 70%), case 2 (solid line, normal expression level of IKv4.3), and case 3 (dotted line, overexpression of IKv4.3 by 20%). B, Popen-ICaL for the model parameters described in panel A. Inset of panel B depicts Popen-ICaL with case 1 shifted with respect to case 2. C, ICaL and Ito1 (inset) for the model parameters described in panel A.

	Discussion

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Recent experimental findings suggest that reductions in magnitude of I_to1, as a consequence of reduced Kv4.3 expression, may be important in modulating APD in normal versus failing canine and human cardiac myocytes.^{6 7} To investigate the role of I_to1 in AP profile and duration, a new model of canine I_to1, built on descriptions of I_Kv4.3 and I_Kv1.4, has been developed in this study. Incorporation of this I_to1 model into the WRJ canine ventricular cell model¹³ reveals a complex interaction between I_Kv4.3 density and I_CaL magnitude, which in turn modulates APD. At relatively low levels of I_Kv4.3, increasing I_Kv4.3 augments the driving force for I_CaL and produces a delay in activation of the late phase of I_CaL. Both effects contribute to the modest prolongation of APD. Additionally increasing I_Kv4.3 density reveals a threshold phenomenon, whereby the early outward current overcomes I_CaL, thus eliminating phase 2 producing a short AP with triangular shape. Loss of the AP dome resulting from imbalance of membrane currents during phase 1 has been observed previously both experimentally⁴ and in simulations.³¹ As a consequence of this bimodal phenomenon, increasing I_Kv4.3 density shortens APD at high baseline densities, whereas at lower levels, increasing I_Kv4.3 density produces modest prolongation of APD. Thus, the effect of perturbing I_Kv4.3 density is dependent on the underlying current level against which the changes are imposed (Figure 5).

This study indicates that the relationship between APD and I_to1 or I_Kv4.3 density is not a simple monotonic correlation. Rather, this relationship exhibits a bifurcation separating 2 distinct modes of behavior. In mouse ventricular myocytes, a 57% reduction in mean peak outward current density induced by overexpression of dominant-negative Kv4 subunits leads to prolongation of APD.¹⁵ Because I_to1 density is significantly greater in mouse than in human or canine cells,^{2 7 15} model predictions for the APD versus I_to1 relationship at high baseline levels of I_to1 are consistent with these data. However, the complex nature of the relationship between APD and I_to1 over a wider range of I_to1 density suggests that extrapolation of the consequences of altering expression levels of I_to1 in mouse to other species may not be valid. In fact, the WRJ canine model predicts that reduction of I_to1 from normal levels will lead to modest shortening of APD (Figure 6A). Via this mechanism, a rate-dependent decrease in the availability of I_to1 is expected to contribute to both a shallower phase 1 notch potential and a shorter APD. Such rate-dependent changes in AP morphology have been observed in canine epicardial^{1 4 8} and midmyocardial⁹ cells and human subepicardial cells^{2 3} and have led to the suggestion that the main impact of I_to1 on APD is secondary to its effects on I_CaL,^{8 9} consistent with the mechanism described in this study.

To show that the I_Kv4.3 versus APD behavior is not unique to the WRJ canine cell model, the hKv4.3-2 model was incorporated into the Luo-Rudy Phase II (LRII)³² and the Jafri-Rice-Winslow (JRW)³³ guinea pig ventricular cell models. Descriptions of Ca²⁺ handling and I_CaL differ greatly in the WRJ/JRW versus the LRII models. Simulations using the guinea pig models (Figures 7A and 7B) produced qualitatively similar results to those of the WRJ canine model (Figure 5). The similar effects of I_Kv4.3 density on AP morphology in all 3 models demonstrate that this behavior is not likely to be attributed to any particular mathematical formulation of Ca²⁺ cycling or detailed representation of ionic currents. Rather, this behavior emerges as a general consequence of interactions between a rapidly activating and inactivating outward current and a rapidly activating and partially inactivating inward current.

The finding that introduction of I_Kv4.3 to guinea pig ventricular cell models produces APD prolongation (at low I_Kv4.3 density) contrasts with experimental findings.¹⁴ In these experiments, expressed rat Kv4.3 current was introduced into isolated guinea pig myocytes via cell fusion techniques. Kv4.3 current density had a strong influence on AP plateau potential and was inversely correlated with APD over the entire range of I_Kv4.3 densities studied (see Figure 5 of Hoppe et al¹⁴ ). The presence of a maintained outward current complicates interpretation of these results. The I_to1-related maintained current magnitude (measured as the difference between the fully activated current and the current following an inactivating prepulse to 0 mV) was not correlated with Kv4.3 current density, consistent with complete inactivation of the Kv4.3 current. However, the possibility remains that a time-independent maintained outward current was correlated with APD. JRW model simulations show that concurrent increases in both I_Kv4.3 and an instantaneous leak current (I_b, with reversal potential E_K) produce monotonic decreases in both APD and plateau potential qualitatively similar to those observed experimentally¹⁴ (Figure 7C). For each AP, conductance of I_b is equal to 10% of G_Kv4.3, corresponding to a background current that is 16% of peak I_Kv4.3, which is in the lower range of those observed experimentally.¹⁴ Clearly, the G_Kv4.3 versus APD relationship described in Figures 7A and 7B may be obscured in the presence of background currents.

The properties of I_to1 and its relationship to AP shape may be modulated by additional factors. Recently, members of the KChIP family of proteins were found to modulate Kv4.3 currents in oocytes at room temperature.³⁴ Extrapolation of these data to myocytes at 35°C is difficult. At this time, there is insufficient data to explore this issue quantitatively. Moreover, the close similarity in kinetic properties of expressed Kv4.3 and Kv1.4 currents to the 2 major components of native I_to1 in human and canine myocytes suggests that the role of accessory proteins may be subtle. Since I_CaL (Figure 6) and, to a lesser extent, I_Na (Figure 5B) interact with I_to1, any factors that modulate these currents, in addition to direct modulators of I_to1, are likely to influence the impact of I_to1 on AP shape.

The influence of I_to1 on the trajectory of I_CaL and on the profile and duration of the AP demonstrates the complex interaction of currents that are active during phase 1. A reduction of I_to1 from normal levels tends to produce modest shortening of APD, contrary to the belief that loss of I_to1 may be responsible for the extreme APD prolongation observed in heart failure. Implicit in this finding is that I_to1 may not play a critical role in APD prolongation-induced arrhythmias, such as early after depolarizations.

	Interactive Model Available on the Internet

Top Abstract Introduction Materials and Methods Results Discussion Interactive Model Available on... References

 
An interactive version of the WRJ canine myocyte model as described in this article is available at the National Simulation Resource (NSR) via the Internet at http://nsr.bioeng.washington.edu/Software/DEMO/CANINE-AP. Please see the online data supplement at http://www.circresaha.org for more details.

	Acknowledgments

 

This study was supported by the National Institutes of Health (P50-HL-52307 to G.F.T. and R.L.W., RO1 HL60133-01 to R.L.W., and T32H207227 to S.P.), a Sarnoff Foundation Fellowship (to R.W.), and a Whitaker Foundation Fellowship (to J.L.G.). We would like to thank James Bassingthwaighte and Zheng Li for making the canine action potential model available to the scientific community via the NSR. We are grateful to Eduardo Marbán and the editors of Circulation Research for embracing Web-based interactive modeling technologies as a valued component of its online publication content.

	Footnotes

 
This manuscript was sent to Michael R. Rosen, Consulting Editor, for review by expert referees, editorial decision, and final disposition.

Received September 7, 2000; revision received September 29, 2000; accepted September 29, 2000.

	References

Top Abstract Introduction Materials and Methods Results Discussion Interactive Model Available on... References

 

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