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Logo of nihpaAbout Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;
 
Am J Physiol Heart Circ Physiol. Author manuscript; available in PMC 2011 February 3.
Published in final edited form as:
PMCID: PMC3032983
NIHMSID: NIHMS48353

Mathematical model of the neonatal mouse ventricular action potential

Abstract

Therapies for heart disease are based largely on our understanding of the adult myocardium. The dramatic differences in action potential (AP) shape between neonatal and adult cardiac myocytes, however, indicate that a different set of molecular interactions in neonatal myocytes necessitates different treatment for newborns. Computational modeling is useful for synthesizing data to determine how interactions between components lead to systems-level behavior, but this technique has not been used extensively to study neonatal heart cell function. We created a mathematical model of the neonatal (day 1) mouse myocyte by modifying, based on experimental data, the densities and/or formulations of ion transport mechanisms in an adult cell model. The new model reproduces the characteristic AP shape of neonatal cells, with a brief plateau phase and longer duration than the adult (APD80=60.1 vs. 12.6 ms). The simulation results are consistent with experimental data, including: 1) decreased density, and altered inactivation, of transient outward K+ currents, 2) increased delayed rectifier K+ currents, 3) Ca2+ entry through T-type as well as L-type Ca2+ channels, 4) increased Ca2+ influx through Na+-Ca2+ exchange, and 5) Ca2+ transients resulting from transmembrane Ca2+ entry rather than release from the sarcoplasmic reticulum (SR). Simulations performed with the model generated novel predictions, including increased SR Ca2+ leak and elevated intracellular [Na+] in neonatal compared with adult myocytes. This new model can therefore be used for testing hypotheses and obtaining a better quantitative understanding of differences between neonatal and adult physiology.

Keywords: ionic currents, excitation-contraction coupling, cardiac development, cardiac myocyte

INTRODUCTION

Developmental changes in heart morphology and function occur in all species. A number of studies performed in recent years have shed light on the changes in electrophysiology and ion transport that take place in myocytes as hearts develop. These studies have generally found that cells from immature ventricles, compared with adult myocytes, display: 1) a reduction in the density of outward K+ currents (28; 51); 2) greater activity and expression of Na+-Ca2+ exchange (NCX) (2); and 3) intracellular Ca2+ transients that depend less on sarcoplasmic reticulum (SR) Ca2+ release and more on transmembrane Ca2+ influx (21; 32). In addition, action potentials (APs) recorded in myocytes from neonatal mouse and rat hearts have a brief plateau phase and are longer in duration than the extremely short spike-like APs seen in adult cells from these species (30; 42; 50).

It is important to understand these developmental changes in heart cell function for a number of reasons. First, therapies developed to treat electrophysiological or contractile abnormalities in adult hearts may be inappropriate for treating heart disease in children due to the differing physiology of the immature heart cells. Second, cultured neonatal rat and mouse myocytes are a popular experimental model and have been used in many studies examining electrical propagation and reentrant arrhythmias (17; 34). The specific physiological characteristics of these cells may influence whether results obtained in these studies are applicable to phenomena seen in adult hearts. Finally, the development of heart failure in mature myocardium is associated with the induction of a “fetal gene program,” suggesting that the complement of genes expressed in heart failure resembles the set expressed earlier in development (12; 19). All of these reasons illustrate the potential benefits of a greater understanding of the behavior of the neonatal heart cell.

Though much has been learned about differences in electrophysiology and ion transport between immature and mature heart cells, many of the observed changes can be understood only qualitatively. To synthesize data from diverse sources and develop quantitative predictions, computer modeling can be used; however, this technique has been used only infrequently in studies of neonatal myocytes, and a complete model of the neonatal action potential has not yet been developed. To address this gap, we created a computer model that describes the ionic currents and Ca2+ transport mechanisms in the neonatal (1 day old) mouse ventricular myocyte. To build this model, we began with a recently published description of the adult mouse AP (7), then altered the density and/or function of ion transport mechanisms in accordance with experimental data obtained in neonatal cells. The model recapitulates the AP shape seen in neonatal cells and is broadly consistent with results on how experimental interventions affect electrical behavior and intracellular Ca2+ transients. This new model can be used to understand, in quantitative terms, how altered expression and function of channels, pumps, and transporters contributes to changes observed during development.

METHODS

Bondarenko et al. (7) have presented a computer model of the AP of the adult mouse ventricular myocyte. The model includes ionic currents, transmembrane pumps, ion exchangers, and a system for intracellular Ca2+ cycling. Beginning with the adult mouse model, we modified the densities of ionic currents and/or their formulations on the basis of experimental data obtained in immature cells. We used data obtained in day 1 neonatal mouse ventricular myocytes wherever possible; when these were not available we used results from embryonic mouse or neonatal rat cells, as noted. The main changes made to the model are summarized here; the complete set of model equations and parameters is provided in the online Supplementary Material.

Geometry

In a variety of species, including the mouse, neonatal cells are significantly smaller than adult myocytes (21; 42; 49). We assumed that the neonatal cell was a cylinder of length 50 μm and diameter 9 μm. The 3.2 pL volume is divided into four compartments: network sarcoplasmic reticulum (NSR; 6.6% of total cellular volume), junctional SR (JSR; <1 %), subsarcolemmal space (1.0%), and the bulk cytosolic space (71.8%). The remainder (20.6%) is assumed to consist of mitochondria and nuclei. Because of a lack of quantitative data, Ca2+ cycling into and out of these latter organelles was not explicitly considered in the simulations. Any effects of mitochondria or nuclei on intracellular Ca2+ homeostasis can only occur indirectly through the overall cytosolic Ca2+ buffering. We assumed that a larger relative proportion of the total cell volume was occupied by cytosol because of structural studies showing a decreased density of mitochondria in immature myocardium (31). Compartment volumes are listed in Table S1 in the online Supplementary Material.

Electron micrographs of adult mouse myocytes reveal invaginations of the cell membrane, known as transverse or T-tubules, that greatly increase the cell's surface area. In many species, including the mouse, T-tubules are not yet present in day-1 neonatal cells (45). For this reason, we assumed that the capacitive surface area of the cell was equal to the physical surface area of the cylindrical cell (1541 μm2). In addition, because neonatal cells lack the close couplings between T-tubule and JSR membranes seen in adult cells, we assumed that the model “subspace,” which is important for Ca2+ signaling (see below), included the entire region directly underneath the cell membrane, with a depth of 20 nm.

To achieve consistency with experiments performed on homogenates prepared from developing rat ventricles (6), we reduced the cytosolic buffering capacity in the neonatal cell by a factor of 2 compared with the adult myocyte. The resulting total cytosolic buffering is very similar to that measured in the experiments: an increase in free [Ca2+] from 0.1 to 0.5 μM requires an increase in total [Ca2+] of 25 μM in the model, compared with a 27 μM as estimated by Bassani et al. (6). We kept the formulation of Bondarenko et al. (7) in which buffering results from binding of Ca2+ to calmodulin and two sites on tropinin; however, we should note that concentrations of these proteins have not been determined in neonatal cells. Since changes in SR buffering in neonatal cells have not been reported, the SR buffering capacity of the adult cell (15 mM) was maintained.

Na+ current

In the adult mouse model, Na+ current (INa) is described by the Markov scheme originally developed by Clancy and Rudy (10), with some parameters modified. This model consists of three closed states, an open state, a fast inactivated state, two intermediate inactivated states, and two closed inactivated states. When we reduced the density of outward K+ currents in the adult model to reproduce data from neonatal cells (see below), we found that a persistent, non-inactivating Na+ current (2−3 pA/pF) greatly extended the AP duration (> 250 ms). This resulted from the relatively large “window current” seen in this model compared with other models of the cardiac Na+ current (see Supplementary Figure S1). Since experimental data on mouse INa are relatively sparse, and an important role for late Na+ current in neonatal myocytes has not been established, we described INa using the more conventional Hodgkin-Huxley type equation given in Luo and Rudy (26):

INa=GNam3hj(VENa)

With this model, sustained INa was not present, and this current had little effect on the AP duration. The maximum conductance GNa was adjusted to fit the maximum overshoot and dV/dtmax values measured in neonatal mouse myocytes.

K+ currents

The neonatal model contains all of the K+ currents that are present in the Bondarenko model of the adult AP, but maximal conductances and, in some cases, gating variables have been altered in accordance with experimental data, as described below.

Inward rectifier (IK1) density increases with age in both rabbit (23) and rat (27), consistent with the more negative resting membrane potential observed in adult compared with neonatal cells (51). We therefore reduced the maximum IK1 conductance (GK1) by 20% compared with the adult value.

The Bondarenko model includes both rapid and slow delayed rectifier currents (IKr and IKs, respectively), even though each current is small and plays little role in repolarization of the adult AP. These currents, however, have been shown to be relatively larger in day 1 mouse myocytes compared with adult cells (50). We increased GKr and GKs, the maximum conductances for IKr and IKs, by factors of 15 and 8, respectively.

Wang and Duff (49) showed that transient outward current (Ito) density increases greatly during development in the mouse, suggesting that these currents play a smaller role in repolarization in neonatal hearts than in adult hearts. Ito was also shown to inactivate faster, and with simpler kinetics, in day 1 neonatal compared with adult cells. To reproduce both the smaller amplitude and altered kinetics (see Figure 2), we decreased GKtof, GKur, and GKss, the maximal conductances, respectively, for fast transient outward current (IKtof), ultrarapid delayed rectifier current (IKur) and steady-steady K+ current (IKss) by 75%, 97%, and 70 %. Slow transient outward current, IKtos, has a maximum conductance of zero in simulations of cells from the ventricular apex in the Bondarenko et al. model (7). Since inactivation kinetics of transient outward current in neonatal mouse cells are more consistent with IKtof than IKtos, the latter current was not included in the neonatal model.

Figure 2
Differences in ionic currents in adult versus neonatal models. A and B: Simulated voltage-clamp recordings of outward K+ currents. Currents were evoked by 1 s pulses from a holding potential of −80 mV to test potentials ranging from −70 ...

In addition to a change in current density, Wang and Duff (49) observed a shift in the steady-state inactivation of transient outward current in neonatal cells. To reproduce this behavior (see Supplementary Figure S2), the equations governing the state variable itof were modified as follows:

ditofdt=itof,itofτitofαi=0.000152e(V3.81)/15.750.067083e(V+132.05)/15.75+1βi=0.00095e(V+132.05)/15.750.051335e(V+132.05)/15.75+1itof,=αi/(αi+βi)τitof=(0.000152e(V+13.5)/7.00.067083e(V+33.5)/7.0+1+0.00095e(V+33.5)/7.00.051335e(V+33.5)/7.0+1)1

Sarcolemmal Ca2+ fluxes

In the developing myocardium, sarcolemmal Ca2+ channels are essential for supporting myocyte contraction. Several studies have demonstrated an increase in L-type Ca2+ current (ICaL) density with increasing age in the rabbit (51), but results in rodent myocytes are more mixed. Cohen and Lederer (11) measured increased ICaL in neonatal rat myocytes that had been cultured for two days whereas Vornanen (48) observed relatively constant current ICaL density at different developmental stages in freshly dissociated rat myocytes. Consistent with the latter study, we choose to increase GCaL, the maximum conductance of ICaL, by 10%.

T-type current Ca2+ (ICaT) is generally not detected in adult mouse ventricular cells but has been observed in cells from neonatal rats (18) and fetal mice (13). We therefore incorporated ICaT, computing this current using the equations of Puglisi and Bers (33):

ICaT=GCaTbg(VECaT)dbdt=(bb)τbdgdt=(gg)τgb=11+e(V+48)/6.1τb=0.1+5.41+e(V+100)/33g=11+e(V+66)/6.6τg=8+321+e(V+65)/5

The maximal conductance GCaT was selected so that the peak of the ICaT current-voltage (IV) relation is approximately 3 pA/pF. This is consistent with several studies performed on either neonatal rat (18; 24) and embryonic mouse (13; 29) myocytes.

Na+-Ca2+ exchange (NCX) has been shown to be upregulated in neonatal heart cells from a number of species and is thought to play a much greater role excitation-contraction coupling in the neonate than in the adult (1). Accordingly, we increased the maximal NCX current density by a factor of 3.1 in the neonatal model. The maximum sarcolemmal Ca2+ pump current was decreased by 80% so that the model more closely matched the relative contribution of each Ca2+ transport system to relaxation (see Figure 6). To maintain diastolic Ca2+ balance across the cell membrane, we also decreased the background Ca2+ conductance, GCab, by 32% compared with the value in the adult model.

Figure 6
Integrated Ca2+ fluxes simulated using the adult (A) and neonatal (B) models. Each trace shows running integrals of the fluxes responsible for the decay of the Ca2+ transient, beginning from its peak. Total (bold, solid line) and individual fluxes are ...

Ca2+-activated Cl current (ICaCl) is included in the Bondarenko model of the adult myocyte. However, the IV plots produced by the model equations do not match those recorded in neonatal rabbit ventricular myocytes (51). We therefore chose to describe this current using a modified form of the equations presented by Verkerk et al. (47). The equation describing ICaCl and IV plots at different levels of intracellular [Ca2+] are displayed in Supplementary Figure S3.

Sarcoplasmic Reticulum Ca2+ handling

We preserved the SR Ca2+ handling system used in the adult model, but modified model variables dramatically to reproduce the much smaller contribution of SR Ca2+ release to excitation-contraction coupling in neonatal cells. The rate constant (ν3) controlling Ca2+ uptake from the cytosol via SR Ca2+ ATPase (SERCA) was reduced by 80% to match the slower decay of Ca2+ transients seen in neonatal rat cells (5; 42). The volume of the JSR was decreased by a factor of 100 to simulate a dearth of close couplings between the T-tubule and JSR membranes in the neonatal cell. Since neonatal myocytes largely lack T-tubules, a much smaller percentage of the SR volume can be considered junctional compared with the adult cell. The SR Ca2+ release rate constant (ν1) was reduced by 90%. Together these two changes ensured that, consistent with experiments, release amplifies the Ca2+ transient amplitude only slightly (see Figure 5). In addition, recent immunocytochemical studies in rabbit suggest that the close couplings between L-type Ca2+ channels and SR Ca2+ release channels (ryanodine receptors, RyRs) seen in adult cells may be less pronounced in neonatal myocytes (14; 38). We therefore assumed that all transmembrane Ca2+ fluxes, rather than only ICaL, enter the model subspace, and Ca2+ flux through any pathway can trigger SR Ca2+ release. Finally, to prevent diastolic SR Ca2+ content from becoming unrealistically large, the rate constant controlling Ca2+ leak from NSR to cytosol (ν2) was increased by 20%.

Figure 5
Cellular Ca2+ transients, kinetics, and effects of SR block. APs were evoked at a pacing frequency of 0.5 Hz for 200 seconds. A: Ca2+ transients produced in the neonatal (dashed line) and adult (solid line) models. B: Sub-cellular differences in neonatal ...

Summary

Schematics of the Bondarenko et al. (7) adult mouse model and the model of the neonatal cell are shown in Figures 1A and 1B, respectively. Where the flux through a particular channel, pump, or transporter is increased compared with the adult model, the corresponding symbol is larger in Fig. 1B, and vice-versa. Model parameters that are unchanged compared with the adult are shown the same size in the two panels.

Figure 1
Schematic diagrams of the adult and neonatal models. Arrows point in the predominant direction of each ionic flux (J) or transmembrane current (I). A: Adult cell. Only L-type Ca2+ current and Ca2+ released from the junctional SR (JSR) enter into the subspace, ...

Overall, our formulation contains 15 ionic currents, 6 intracellular Ca2+ fluxes, and 37 state variables. The model was implemented in MATLAB r2006a (The MathWorks, Natick, MA) and solved using the program's variable order stiff differential equation solver (ode15s).

RESULTS

We begin by presenting simulation results that illustrate important differences between neonatal and adult electrophysiology as predicted by the new model. We then show simulations that can be compared directly with experiments previously performed on hearts or myocytes from newborn animals. We conclude with novel predictions generated by the model that can be tested in subsequent experiments in neonatal heart cells. These predictions illustrate the potential strengths of the computational approach and suggest avenues for further research.

Simulated ionic currents under conditions of whole-cell voltage-clamp are shown in Figure 2. Figs. 2A and 2B display, for the adult and neonatal models respectively, fast-activating outward K+ currents (sum of Itof, IKur, and IKss) produced by steps from −80 mV to more positive potentials (see figure legend for details). The plots illustrate two important characteristics of this composite K+ current in neonatal cells, compared with adult cells: 1) transient outward currents are much smaller in magnitude (note scale bars), and 2) currents inactivate more quickly and with a simpler time course. This model behavior is consistent with the experimental results obtained by Wang and Duff (49), who measured transient outward K+ currents in day-1 mouse myocytes (see e.g. their Figure 2). These authors reported increases in peak and steady-state current densities of ~4 and ~2.5 times, respectively, in adult compared with newborn myocytes. The complex inactivation time course (two time constants) measured by Wang and Duff in adult cells is consistent with the idea that multiple K+ currents contribute to the overall “transient outward” current that is measured, as subsequent studies have demonstrated (8; 52). The simple and fast decay seen in neonatal cells suggests that this inactivating current consists primarily of fast transient outward current Itof. In addition, Wang and Duff (49) reported slower recovery from inactivation of transient outward current in adult cells compared with neonatal cells (see their Figure 5). This behavior is also reproduced by our model simulations (see Supplementary Figure S4). These observations on K+ current in day 1 mouse cells dictated the percentages by which we reduced the maximum conductances GKtof, GKur, and GKss when formulating the neonatal model.

Current-voltage (IV) relations of inward Ca2+ currents in the adult and neonatal models, respectively, are displayed in Figs. 2C and 2D. In each model inward currents were simulated under voltage-clamp conditions with holding potentials of −90 mV (closed symbols) and −40 mV (open symbols). Since T-type Ca2+ current is present in the neonatal but not the adult model, IV plots produced by the former show significantly more current at potentials negative to −20 mV, as well as a greater dependence of peak current on holding potential. These model results are qualitatively consistent with experiments recently performed in cells isolated from neonatal rat (42) and embryonic mouse (37) hearts.

The AP produced by the model of the neonatal myocyte, and the underlying currents upon steady-state pacing at 0.5 Hz, are shown in Figure 3. Compared with the adult, early repolarization is slowed significantly in the neonatal model, leading to a much longer AP. AP duration, measured from the maximum upstroke velocity to 80% repolarization, is 60.1 ms, which compares favorably with measurements made in day 1 mouse ventricular myocytes (63.2 ms; (50)). The main inward and outward ionic currents responsible for the neonatal AP are displayed in Figs. 3B and 3C, on different scales so that their time courses can be more easily compared. As in most cardiac cell types, INa is an order of magnitude larger than most other currents and is responsible for the rapid AP upstroke. The primary inward currents that sustain depolarization are ICaL and ICaT, with the magnitude of the former roughly 5 times greater than the latter. The model predicts that the slower repolarization in neonatal cells is mainly due to reduced outward K+ currents. The primary outward current early in the AP is fast transient outward current, IKtof, but its magnitude (~7 pA/pF) is considerably reduced compared with the contribution it can make in the adult model (> 20 pA/pF; compare with Figure 16 in (7)). The peak current supplied by IKss is not great (~1.5 pA/pF), but since this current activates quickly and does not inactivate, its cumulative repolarizing effect is significant. Ionic currents that play a lesser role in shaping the simulated AP are shown in Fig. 3C. The model predicts that “reverse mode” Na+-Ca2+ exchange, whereby Ca2+ is imported and Na+ is exported, will supply repolarizing current during most of the AP. IK1 and IKr are small in magnitude but become important during phase 3 repolarization after IKtof has largely inactivated.

Figure 3
Simulated action potential (AP) and membrane currents. The simulated neonatal cell was paced at 0.5 Hz for >500 seconds to reach steady state. A: Membrane potential versus time. Electrical stimulus delivered at t=20 ms. B and C: Currents corresponding ...

Figure 4 displays simulations that mimic effects of drugs on APs. In addition to illustrating differences between the adult and neonatal responses to pharmacological perturbations, these results demonstrate the consistency of the neonatal model with published experimental data. Figs. 4A and 4B show the effects of a moderate dose (0.5 mM) of 4-aminopyridine (4-AP) on adult and neonatal APs, respectively. According to Xu et al. (52), this dose blocks Itof and IKur by 54% and 78% respectively; the maximal conductance of each current was therefore reduced by the appropriate amount to perform these simulations. The results show that this dose of 4-AP causes modest prolongation of the AP in either model. However, the percentage increase in APD was much greater in the adult than in the neonatal cell due to the much shorter baseline APD in the adult. The effects of dofetilide, which was assumed to block IKr completely, are shown in Figs. 4C and 4D. The model results predict that dofetilide has virtually no effect on APD in adult cells but can cause slower phase 3 repolarization and significant lengthening of APD in the neonate. Both sets of simulations are consistent with the experimental results presented by Wang et al. (50).

Figure 4
Effects of K+ current block on action potential morphology. A and B: Effect of 4-aminopyridine (4-AP) on action potentials simulated using the adult (A) and neonatal (B) models. Application of 0.5 mM 4-AP was assumed to reduce IKto,f and IKur by 54% and ...

As numerous studies have investigated excitation-contraction coupling in neonatal cells (3; 21; 32; 40; 42), we also examined factors influencing Ca2+ cycling in the neonatal model. Results are shown in Figures 5 and and6.6. Intracellular Ca2+ transients produced under conditions of steady-state pacing (0.5 Hz) in the adult and neonatal models are shown in Figure 5A. In the neonatal model diastolic [Ca2+] is considerably higher than in the adult model (205 versus 100 nM), consistent with experimental results obtained in rabbit myocytes (21). The amplitude of the Ca2+ transient, measured as peak [Ca2+] minus diastolic [Ca2+], is similar in the neonatal model. Fig. 5B shows that [Ca2+] reaches a higher peak, and displays much faster kinetics, in the region directly underneath the cell membrane, corresponding to the model “sub-space,” than in the cell interior. This is consistent with measurements made using confocal microscopy in newborn rat (40) and rabbit myocytes (21).Figs. 5C and 5D show the effects of disabling SR Ca2+ release on Ca2+ transients in the adult and neonatal models, respectively. In the adult mouse, most of the Ca2+ that activates contraction is released from the SR, and inhibiting this process decreases the Ca2+ transient amplitude profoundly. In contrast, inhibition of SR Ca2+ release in the neonatal model causes only a modest (12.4%) reduction, consistent with the 19% decrease recently observed in acutely dissociated day 1 rat myocytes upon application of 10 μM ryanodine (42). Inhibition of SR function in the model also slows the rate of decay of the Ca2+ transient, consistent with experimental results (5).

The contributions to relaxation are examined quantitatively in Figure 6. Similar to the analyses presented by Bassani and Bassani (4; 5), these plots display the amounts of Ca2+ carried by various transport pathways, computed by integrating each flux beginning at the peak of the Ca2+ transient. The percentage of the total [Ca2+] transported by each pathway is indicated to the right of the plots. In the adult model (Fig. 6A), SR uptake via SERCA pumps is responsible for over 90% of the Ca2+ decay, consistent with the dominant role played by SR Ca2+ release in EC coupling. Surprisingly, the model predicts that the integrated flux through the sarcolemmal Ca2+ pump is roughly twice the Ca2+ efflux via NCX, contrary to what has been observed in experiments (25). Because of this, we reduced the transport rate of the SL Ca2+ pump when constructing the neonatal myocyte model. The flux analysis in the neonatal model (Fig. 6B) shows the following notable features: 1) the total quantity of Ca2+ cycled through the cytoplasm with each beat is less than in the adult cell; 2) the percentage taken up into the SR (70%) is less than in the adult but still greater than any other pathway; 3) the percentage transported by the Na+-Ca2+ exchanger (24%) is considerably greater than in the adult. These characteristics are consistent with results obtained in day 1 neonatal rat myocytes by Bassani and Bassani (5), who calculated contributions of 72%, 24%, and 4%, respectively, for SERCA, Na+-Ca2+ exchange, and slow pathways. We should note, however, that our model predicts reduced flux through the sarcolemmal Ca2+ pump in neonatal compared with adult myocytes, in contrast to the increased role of slow pathways that has been seen in experiments (5). Based on the good quantitative match shown in Figure 6B, however, we feel that this difference results from a maximum pump rate that is quite high in the original model of the adult myocyte (7).

To gain insight into the behavior of the neonatal myocyte and generate novel predictions, we implemented “action potential clamp” versions of the adult and neonatal models. Simulated APs obtained during steady-state pacing at 0.5 Hz were recorded in both models, and these were used as input waveforms to the voltage-clamp versions of either model. These simulations can illustrate which neonatal model behaviors are due solely to the changes in ionic fluxes, and which depend specifically on the neonatal AP morphology. Figures 7A and 7B show Ca2+ transients obtained, respectively, in the adult and neonatal AP clamp models, using either AP as a command waveform. For these simulations, the initial conditions of all state variables besides voltage were set to the values obtained upon steady-state pacing at 0.5 Hz. Fig. 7A shows that, in the adult model, replacing the adult AP with the neonatal AP causes a large increase in the Ca2+ transient amplitude. Conversely, the Ca2+ transient in the neonatal model using the adult AP is much smaller than the one that results when the neonatal AP is the clamp waveform (Fig. 7B). Thus, the longer AP in neonatal cells appears critical for maintaining a significant Ca2+ transient.

Figure 7
Effects of AP shape on Ca2+ transients. Simulations were performed with AP clamp versions of the adult and neonatal models. A. In the adult model, the Ca2+ transient amplitude is considerably larger when the neonatal AP (dashed line), rather than the ...

We observed in our simulations that, after steady-state pacing, intracellular [Na+] ([Na+]i) was greater in the neonatal than in the adult model. We used AP clamp simulations to gain insight into the mechanisms underlying this difference, as shown in Figure 8. When the adult model was paced in current clamp mode at 0.5 Hz, or when a long train of adult APs was used as an input waveform, [Na+]i increased from 14 to 15.6 mM over the course of 2000 s (Fig. 8A, lower solid line). When a train of neonatal APs was used instead as the clamp waveform, the resulting steady-state value of [Na+]i was slightly less (15.5 mM; lower dashed line). In contrast, [Na+]i in the neonatal model increased to over 20.2 mM when the model was clamped with a train of either neonatal (upper dashed line) or adult (upper solid line) APs. The increased [Na+]i during pacing in the neonatal model is therefore primarily a consequence of altered ion transport pathways rather than the AP shape. To determine the mechanisms underlying this predicted altered [Na+] homeostasis, we systematically changed parameters affecting [Na+] and [Ca2+] balance back to their values in the adult model, then repeated the simulations. The results (Fig. 8B) show that the factor most responsible for increased [Na+]i is the decreased sarcolemmal Ca2+ pump in the neonatal model (blue line). The changes in NCX (red), SR Ca2+ release (green), and Ca2+ currents (magenta), and all contribute to the increase in [Na+]i, but to a somewhat lesser extent. Changing the characteristics of all four pathways back to their values in the adult model (cyan line) eliminates the increase in [Na+]i compared with the adult model, indicating that other changes in the neonatal model do not influence [Na+] balance substantially.

Figure 8
Changes in [Na+]i observed during steady-state pacing. Simulations were performed with AP clamp versions of the adult and neonatal models, using a train of action potentials delivered at 0.5 Hz as the clamp waveform. A. In the neonatal cell (upper plots), ...

DISCUSSION

We have presented a new mathematical model of ionic currents and intracellular Ca2+ handling in the neonatal mouse ventricular myocyte. Simulations performed with this model successfully reproduce both the AP morphology and important characteristics of the Ca2+ transient in the immature cell. The model predicts that the longer AP seen in neonatal compared with adult cells is primarily due to reduced outward K+ currents, specifically the fast-activating outward currents IKtof, IKur, and IKss (Fig. 3). Ca2+ transients in the neonatal model are similar in amplitude to those in the adult model, but diastolic [Ca2+]i is higher and Ca2+ transients result primarily from Ca2+ influx through the cell membrane rather than SR Ca2+ release (Fig. 5). In addition to reproducing these experimentally-observed features of normal neonatal cellular physiology, the model can recapitulate the effects of pharmacological interventions, such as block of transient outward currents (Fig. 4B), block of rapid delayed rectifier currents (Fig. 4D), and inhibition of SR Ca2+ release (Fig. 5D). These validations suggest that the model assumptions are reasonable, although, as mentioned below, several specific issues remain somewhat unresolved.

In addition to reproducing previously obtained experimental results, this new model can generate novel predictions (Figs. 7 and and8).8). The model predicts that the longer AP in neonatal compared with adult myocytes is necessary to maintain an adequate Ca2+ transient amplitude in these cells. Because the Ca2+ transient in neonatal cells relies on Ca2+ transport across the cell membrane, the short plateau phase of the neonatal AP is critical, as it allows additional time for Ca2+ influx through both Ca2+ channels and the Na+-Ca2+ exchanger. This idea can now be explored quantitatively using computer simulations. An additional factor favoring Ca2+ entry via reverse-mode NCX in the neonatal model is the increased [Na+]i seen upon steady-state pacing. The model predicts that this result depends on altered ion transport pathways rather than the difference in the neonatal AP shape per se (Fig. 8). To our knowledge this is a novel prediction that has not been examined experimentally in developing rodent myocytes. The model also predicts that during steady-state pacing, neonatal cells will exhibit elevated diastolic [Ca2+] compared with adult myocytes. While this has indeed been seen in cells isolated from newborn rabbits (21), we should note that a study on isolated rat myocytes (5) did not observe differences in diastolic [Ca2+]. This may therefore represent a model prediction that warrants additional experimental scrutiny.

Although many studies have examined electrophysiology and excitation-contraction coupling in neonatal cells and hearts (see (1; 51) for review), few attempts have been made to synthesize results using computational modeling. For instance, an important investigation by Haddock et al. (21) simulated diffusion of [Ca2+] within the newborn rabbit myocyte, but these computations did not consider the ionic currents responsible for the neonatal action potential. Our study therefore represents an initial attempt to apply the techniques that have proven successful for understanding normal and pathological adult cellular physiology (36). These types of studies may, by leading to a greater understanding of the unique characteristics of immature hearts, suggest therapies that are especially effective in the treatment of pediatric heart disease. It is also important to investigate developing hearts because heart failure (HF) is associated with the induction of a “fetal gene program,” meaning that many of the genes expressed in HF are similar to those seen during development (12; 19). Indeed, the neonatal cell shares some characteristics with the failing myocyte, including a longer AP, reduced K+ currents, increased Na+-Ca2+ exchange, and reduced SR Ca2+ release compared with healthy adult myocytes (22). A better quantitative understanding of neonatal heart function may therefore provide insight into changes observed in HF, particularly as the signaling pathways activated during normal development and in disease states continue to become better understood.

Studies of neonatal cardiac physiology have been performed in a number of different species, including rat (42), mouse (50), and rabbit (21). We chose to develop a model of the neonatal mouse AP for a number of reasons. One is the popularity of this species for transgenic studies. Several genetic modifications that should conceivably produce interesting cardiac phenotypes also lead to embryonic or neonatal lethality (15; 35; 39). Understanding heart function in these mouse strains will therefore require a comparison with the appropriate age-matched control. In addition, neonatal mouse and rat myocytes are frequently cultured to form confluent monolayers. These cell networks are a popular experimental model for examining tissue-level aspects of cardiac electrophysiology and ion transport (17; 34). However, translating results obtained in these systems to adult hearts requires a detailed, quantitative understanding of the unique cellular physiology of the cultured cells. We anticipate that our new model can provide a general framework for such efforts, although modifications will have to be made to account for physiological differences between neonatal mice and rats, and for changes that occur to cells after several days in culture (42).

One of the benefits of constructing computer models is that the process clarifies assumptions and reveals the limits of one's understanding, and this is true in the present case. For instance, we altered the conductances of the ionic currents IKtof, IKur, and IKss to match the data of Wang and Duff (49), who observed a smaller and more rapidly inactivating “transient outward” K+ current in day 1 neonatal mouse myocytes. However, these experiments were performed before the molecular entities responsible for the different current components had been identified, and the ionic current whose characteristics we attempted to reproduce (e.g. Figs. 2 and S4) was therefore a composite. It was reassuring to discover a paper published very recently, after our model had been constructed, that measured separately IKtof, IKur, and IKss in developing mouse myocytes (20). The observed differences in the currents between adult and day 1 cells were very similar to the conductance scaling factors we chose on the basis of different data, with extremely large reductions in IKur and smaller, but still substantial, changes in IKtof and IKss. This gives us confidence that the K+ current parameters chosen for our neonatal AP model are reasonable.

On the other hand, with respect to differences in inward currents between neonatal and adult myocytes, several issues remain unresolved. For instance, we reverted to a simple Hodgkin-Huxley type formulation of INa because the more complex scheme in the Bondarenko model (7) produced considerable late, non-inactivating Na+ current at negative potentials. This “window current” is not apparent in simulations of the adult AP because strong outward K+ currents rapidly repolarize the membrane, but it lengthened the AP considerably when we reduced K+ conductances to construct the neonatal model (Fig. S1). Since a prominent late INa in neonatal mouse myocytes has not been observed, it seemed reasonable to change this formulation. It is possible, however, that such a current is present in neonatal cells, but it is counterbalanced by additional changes in outward currents not considered in our model. Additional experiments will be required to resolve this issue.

Questions also exist regarding the Ca2+ currents in the neonatal mouse myocyte model. Many studies have shown that T-type Ca2+ currents are more prominent in developing than in mature ventricles (see (46; 53)for review), but we were unable to find quantitative data obtained in day 1 mouse myocytes. The voltage-dependence and peak magnitude (~3 pA/pF) of ICaT in our model are consistent with currents measured in developing rats and mice in several studies (13; 18; 24; 29), but our formulation should not be considered unique, and parameters may change as more data become available. Similarly, for L-type Ca2+ currents we could not find a direct comparison between day 1 mouse and adult ventricular myocytes. We increased L-type Ca2+ current by a mere 10% based on a study by Vornanen (48) that observed little change in ICaL density with development in freshly-dissociated rat myocytes. Some recent studies have suggested that L-type Ca2+ current in developing rodent hearts may have a different voltage dependence (42), and perhaps result from a different gene product (37; 44), than in adult myocytes. Because these observations are still preliminary, we maintained the ICaL gating parameters of the Bondarenko model, but it is possible that this formulation will be modified as additional studies are published.

Perhaps the cellular process about which the most uncertainty exists is the system for intracellular Ca2+ handling. Several studies in a number of species have shown that the SR in immature heart cells can store Ca2+ (3; 32; 40). However, inhibiting SR Ca2+ release pharmacologically tends to cause only slight reductions in Ca2+ transient amplitude in cells from neonatal rabbits (21) and rats (32; 42). In addition, the elementary units of SR Ca2+ release, Ca2+ sparks (9), are infrequently observed in myocytes from immature rat hearts (40; 42), tending to not be seen until transverse tubules develop several days after birth. In our new model of the neonatal mouse myocyte, we kept the adult formulation for SR Ca2+ release but changed the relevant rate constants and reduced the JSR volume to diminish the contribution of SR release to the Ca2+ transient. In addition, since it is not clear whether L-type Ca2+ channels have privileged access to RyRs in neonatal cells (38; 45), we altered the model so that all transmembrane Ca2+ fluxes can contribute equally to SR Ca2+ release. It should be emphasized, however, that the formulation for release is phenomenological rather than mechanistic, and the equations may change as SR Ca2+ release in neonatal cells becomes better understood.

Looking at the role of SR function more quantitatively, it appears at first glance difficult to reconcile two set of results recently obtained in day 1 neonatal rat myocytes. Snopko et al. (42) observed a roughly 20% reduction in Ca2+ transient amplitude upon inhibition of release, whereas Bassani and Bassani (5) estimated that SR uptake accounts for approximately 75% of the decline in [Ca2+] during relaxation. One would expect that, unless the cell is accumulating or losing Ca2+ with each beat, the SR contributions to Ca2+ transient amplitude and to relaxation should be equivalent. Our computational results, which are consistent with both studies, provide a possible resolution to this paradox. When we initially decreased the maximal Ca2+ release rate (ν1) to reduce the quantity of Ca2+ released with each beat, we observed a dramatic increase in the SR Ca2+ load, similar to the results of experiments in which this is accomplished pharmacologically (16). To make the steady-state SR Ca2+ load in the model more consistent with experimental measurements (3; 32; 40), we then increased the rate of passive Ca2+ leak from SR to cytosol (ν2). Thus, the SR contribution to Ca2+ transient decay calculated by integrating the SERCA flux (Fig. 6B) is an overestimate because some of the Ca2+ pumped into the SR leaks back into the cytosol later. As a direct consequence of these parameter choices, the model predicts that diastolic SR Ca2+ leak will be higher in neonatal than in adult myocytes. This represents another novel prediction that can be tested in future studies using experimental protocols to measure Ca2+ leak as a function of SR load (41). What makes this prediction especially interesting is the fact that Ca2+ sparks are rarely seen in newborn cells. Thus, if increased leak is indeed present, it must occur in an “invisible” mode (43).

In conclusion, we have presented a novel computational model of the action potential and Ca2+ transient in the day 1 mouse ventricular myocyte. The model, which is generally consistent with experimental data obtained in a number of studies, can be used to generate novel predictions regarding differences between adult and neonatal cellular physiology. This model should prove to be a useful tool for understanding changes in heart function that occur during development.

ACKNOWLEDGEMENTS

Supported by the National Institutes of Health grant HL076230. The authors thank Mr. Frank Fabris for assistance in preparing the figures, and Dr. W.A. Coetzee of New York University School of Medicine for helpful discussions. We would also like to thank the anonymous reviewers for useful suggestions.

Footnotes

Conflicts of interest: none

Supplementary Material

supplement

REFERENCES

1. Artman M, Henry G, Coetzee WA. Cellular basis for age-related differences in cardiac excitation-contraction coupling. Prog Pediatr Cardiol. 2000;11:185–194. [PubMed]
2. Artman M, Ichikawa H, Avkiran M, Coetzee WA. Na+/Ca2+ exchange current density in cardiac myocytes from rabbits and guinea pigs during postnatal development. Am J Physiol. 1995;268:H1714–H1722. [PubMed]
3. Balaguru D, Haddock PS, Puglisi JL, Bers DM, Coetzee WA, Artman M. Role of the sarcoplasmic reticulum in contraction and relaxation of immature rabbit ventricular myocytes. J Mol Cell Cardiol. 1997;29:2747–2757. [PubMed]
4. Bassani JW, Bassani RA, Bers DM. Relaxation in rabbit and rat cardiac cells: species-dependent differences in cellular mechanisms. J Physiol. 1994;476:279–293. [PubMed]
5. Bassani RA, Bassani JW. Contribution of Ca2+ transporters to relaxation in intact ventricular myocytes from developing rats. Am J Physiol Heart Circ Physiol. 2002;282:H2406–H2413. [PubMed]
6. Bassani RA, Shannon TR, Bers DM. Passive Ca2+ binding in ventricular myocardium of neonatal and adult rats. Cell Calcium. 1998;23:433–442. [PubMed]
7. Bondarenko VE, Szigeti GP, Bett GC, Kim SJ, Rasmusson RL. Computer model of action potential of mouse ventricular myocytes. Am J Physiol Heart Circ Physiol. 2004;287:H1378–H1403. [PubMed]
8. Brouillette J, Clark RB, Giles WR, Fiset C. Functional properties of K+ currents in adult mouse ventricular myocytes. J Physiol. 2004;559:777–798. [PubMed]
9. Cheng H, Lederer WJ, Cannell MB. Calcium sparks: elementary events underlying excitation-contraction coupling in heart muscle. Science. 1993;262:740–744. [PubMed]
10. Clancy CE, Rudy Y. Na+ channel mutation that causes both Brugada and long-QT syndrome phenotypes: a simulation study of mechanism. Circulation. 2002;105:1208–1213. [PMC free article] [PubMed]
11. Cohen NM, Lederer WJ. Changes in the calcium current of rat heart ventricular myocytes during development. J Physiol. 1988;406:115–46. 115–146. [PubMed]
12. Colucci WS. Molecular and cellular mechanisms of myocardial failure. American Journal of Cardiology. 1997;80:L15–L25. [PubMed]
13. Cribbs LL, Martin BL, Schroder EA, Keller BB, Delisle BP, Satin J. Identification of the t-type calcium channel (Cav3.1d) in developing mouse heart. Circ Res. 2001;88:403–407. [PubMed]
14. Dan P, Lin E, Huang J, Biln P, Tibbits GF. Three-dimensional distribution of cardiac Na+-Ca2+ exchanger and ryanodine receptor during development. Biophysical Journal. 2007;93:2504–2518. [PubMed]
15. de la Pompa JL, Timmerman LA, Takimoto H, Yoshida H, Elia AJ, Samper E, Potter J, Wakeham A, Marengere L, Langille BL, Crabtree GR, Mak TW. Role of the NF-ATc transcription factor in morphogenesis of cardiac valves and septum. Nature. 1998;392:182–186. [PubMed]
16. Eisner DA, Choi HS, Diaz ME, O'Neill SC, Trafford AW. Integrative analysis of calcium cycling in cardiac muscle. Circ Res. 2000;87:1087–1094. [PubMed]
17. Entcheva E, Bien H. Macroscopic optical mapping of excitation in cardiac cell networks with ultra-high spatiotemporal resolution. Progress in Biophysics & Molecular Biology. 2006;92:232–257. [PubMed]
18. Ferron L, Capuano V, Deroubaix E, Coulombe A, Renaud JF. Functional and molecular characterization of a T-type Ca2+ channel during fetal and postnatal rat heart development. J Mol Cell Cardiol. 2002;34:533–546. [PubMed]
19. Frey N, Olson EN. Cardiac hypertrophy: The good, the bad and the ugly. Annual Review of Physiology. 2003;65:45–79. [PubMed]
20. Grandy SA, Trepanier-Boulay V, Fiset C. Postnatal development has a marked effect on ventricular repolarization in mice. Am J Physiol Heart Circ Physiol. 2007;293:H2168–H2177. [PubMed]
21. Haddock PS, Coetzee WA, Cho E, Porter L, Katoh H, Bers DM, Jafri MS, Artman M. Subcellular [Ca2+]i gradients during excitation-contraction coupling in newborn rabbit ventricular myocytes. Circ Res. 1999;85:415–427. [PubMed]
22. Houser SR, Piacentino V, Weisser J. Abnormalities of calcium cycling in the hypertrophied and failing heart. J Mol Cell Cardiol. 2000;32:1595–1607. [PubMed]
23. Huynh TV, Chen F, Wetzel GT, Friedman WF, Klitzner TS. Developmental changes in membrane Ca2+ and K+ currents in fetal, neonatal, and adult rabbit ventricular myocytes. Circ Res. 1992;70:508–515. [PubMed]
24. Leuranguer V, Monteil A, Bourinet E, Dayanithi G, Nargeot J. T-type calcium currents in rat cardiomyocytes during postnatal development: contribution to hormone secretion. American Journal of Physiology-Heart and Circulatory Physiology. 2000;279:H2540–H2548. [PubMed]
25. Li L, Chu G, Kranias EG, Bers DM. Cardiac myocyte calcium transport in phospholamban knockout mouse: relaxation and endogenous CaMKII effects. Am J Physiol Heart Circ Physiol. 1998;274:H1335–H1347. [PubMed]
26. Luo CH, Rudy Y. A model of the ventricular cardiac action potential. Depolarization, repolarization, and their interaction. Circ Res. 1991;68:1501–1526. [PubMed]
27. Masuda H, Sperelakis N. Inwardly rectifying potassium current in rat fetal and neonatal ventricular cardiomyocytes. Am J Physiol. 1993;265:H1107–H1111. [PubMed]
28. Nerbonne JM. Regulation of voltage-gated K+ channel expression in the developing mammalian myocardium. J Neurobiol. 1998;37:37–59. [PubMed]
29. Niwa N, Yasui K, Opthof T, Takemura H, Shimizu A, Horiba M, Lee JK, Honjo H, Kamiya K, Kodama I. Cav3.2 subunit underlies the functional T-type Ca2+ channel in murine hearts during the embryonic period. Am J Physiol Heart Circ Physiol. 2004;286:H2257–H2263. [PubMed]
30. Nuss HB, Marban E. Electrophysiological properties of neonatal mouse cardiac myocytes in primary culture. J Physiol. 1994;479:265–279. [PubMed]
31. Olivetti G, Anversa P, Loud AV. Morphometric study of early postnatal development in the left and right ventricular myocardium of the rat. II. Tissue composition, capillary growth, and sarcoplasmic alterations. Circ Res. 1980;46:503–512. [PubMed]
32. Perez CG, Copello JA, Li Y, Karko KL, Gomez L, Ramos-Franco J, Fill M, Escobar AL, Mejia-Alvarez R. Ryanodine receptor function in newborn rat heart. Am J Physiol Heart Circ Physiol. 2005;288:H2527–H2540. [PubMed]
33. Puglisi JL, Bers DM. LabHEART: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport. Am J Physiol Cell Physiol. 2001;281:C2049–C2060. [PubMed]
34. Rohr S, Kucera JP, Kleber AG. Slow conduction in cardiac tissue, I - Effects of a reduction of excitability versus a reduction of electrical coupling on microconduction. Circ Res. 1998;83:781–794. [PubMed]
35. Rossant J. Mouse Mutants and Cardiac Development : New Molecular Insights Into Cardiogenesis. Circ Res. 1996;78:349–353. [PubMed]
36. Rudy Y, Silva JR. Computational biology in the study of cardiac ion channels and cell electrophysiology. Quarterly Reviews of Biophysics. 2006;39:57–116. [PMC free article] [PubMed]
37. Schroder EA, Wei YD, Satin J. The developing cardiac myocyte - maturation of excitability and excitation-contraction coupling. Ann N Y Acad Sci. 2006;1080:63–75. [PubMed]
38. Sedarat F, Xu LQ, Moore EDW, Tibbits GF. Colocalization of dihydropyridine and ryanodine receptors in neonate rabbit heart using confocal microscopy. American Journal of Physiology-Heart and Circulatory Physiology. 2000;279:H202–H209. [PubMed]
39. Seisenberger C, Specht V, Welling A, Platzer J, Pfeifer A, Kuhbandner S, Striessnig J, Klugbauer N, Feil R, Hofmann F. Functional embryonic cardiomyocytes after disruption of the L-type alpha(1C) (Cav1.2) calcium channel gene in the mouse. Journal of Biological Chemistry. 2000;275:39193–39199. [PubMed]
40. Seki S, Nagashima M, Yamada Y, Tsutsuura M, Kobayashi T, Namiki A, Tohse N. Fetal and postnatal development of Ca2+ transients and Ca2+ sparks in rat cardiomyocytes. Cardiovasc Res. 2003;58:535–548. [PubMed]
41. Shannon TR, Ginsburg KS, Bers DM. Quantitative assessment of the SR Ca2+ leak-load relationship. Circ Res. 2002;91:594–600. [PubMed]
42. Snopko RM, Aromolaran AS, Karko KL, Ramos-Franco J, Blatter LA, Mejia-Alvarez R. Cell culture modifies Ca2+ signaling during excitation-contraction coupling in neonate cardiac myocytes. Cell Calcium. 2007;41:13–25. [PubMed]
43. Sobie EA, Guatimosim S, Gomez-Viquez L, Song LS, Hartmann H, Saleet JM, Lederer WJ. The Ca2+ leak paradox and rogue ryanodine receptors: SR Ca2+ efflux theory and practice. Prog Biophys Mol Biol. 2006;90:172–185. [PMC free article] [PubMed]
44. Takemura H, Yasui K, Opthof T, Niwa N, Horiba M, Shimizu A, Lee JK, Honjo H, Kamiya K, Ueda Y, Kodama I. Subtype switching of L-Type Ca2+ channel from Cav1.3 to Cav1.2 in embryonic murine ventricle. Circ J. 2005;69:1405–1411. [PubMed]
45. Tibbits GF, Xu LQ, Sedarat F. Ontogeny of excitation-contraction coupling in the mammalian heart. Comparative Biochemistry and Physiology A-Molecular and Integrative Physiology. 2002;132:691–698. [PubMed]
46. Vassort G, Talavera K, Alvarez JL. Role of T-type Ca2+ channels in the heart. Cell Calcium. 2006;40:205–220. [PubMed]
47. Verkerk AO, Wilders R, Zegers JG, van Borren MMGJ, Ravesloot JH, Verheijck EE. Ca2+-activated Cl- current in rabbit sinoatrial node cells. Journal of Physiology-London. 2002;540:105–117. [PubMed]
48. Vornanen M. Contribution of sarcolemmal calcium current to total cellular calcium in postnatally developing rat heart. Cardiovasc Res. 1996;32:400–410. [PubMed]
49. Wang L, Duff HJ. Developmental changes in transient outward current in mouse ventricle. Circ Res. 1997;81:120–127. [PubMed]
50. Wang L, Feng ZP, Kondo CS, Sheldon RS, Duff HJ. Developmental changes in the delayed rectifier K+ channels in mouse heart. Circ Res. 1996;79:79–85. [PubMed]
51. Wetzel GT, Klitzner TS. Developmental cardiac electrophysiology recent advances in cellular physiology. Cardiovasc Res. 1996;31:E52–E60. [PubMed]
52. Xu H, Guo W, Nerbonne JM. Four kinetically distinct depolarization-activated K+ currents in adult mouse ventricular myocytes. J Gen Physiol. 1999;113:661–678. [PMC free article] [PubMed]
53. Yasui K, Niwa N, Takemura H, Opthof T, Muto T, Horiba M, Shimizu A, Lee JK, Honjo H, Kamiya K, Kodama I. Pathophysiological significance of T-type Ca2+ channels: expression of T-type Ca2+ channels in fetal and diseased heart. J Pharmacol Sci. 2005;99:205–210. [PubMed]