Contribution of quantitative changes in individual ionic current systems to the embryonic development of ventricular myocytes: a simulation study
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Early embryonic rodent ventricular cells exhibit spontaneous action potential (AP), which disappears in later developmental stages. Here, we used 3 mathematical models—the Kyoto, Ten Tusscher–Panfilov, and Luo–Rudy models—to present an overview of the functional landscape of developmental changes in embryonic ventricular cells. We switched the relative current densities of 9 ionic components in the Kyoto model, and 160 of 512 representative combinations were predicted to result in regular spontaneous APs, in which the quantitative changes in Na+ current (INa) and funny current (If) made large contributions to a wide range of basic cycle lengths. In all three models, the increase in inward rectifier current (IK1) before the disappearance of If was predicted to result in abnormally high intracellular Ca2+ concentrations. Thus, we demonstrated that the developmental changes in APs were well represented, as INa increased before the disappearance of If, followed by a 10-fold increase in IK1.
KeywordsComputer simulation Ion channels Cardiac ventricular cells Development Electrophysiology Spontaneous activity
Several hundred types of cells develop from a single genome through accurate spatiotemporal regulation of gene expression. The vertebrate heart is a good example of this phenomenon, as it substantially changes its shape and function at the cellular, tissue, and organ levels throughout a lifetime. In early embryonic development, the heart becomes a functional organ, acting as a pump. The heart develops and gains new functions while continuously pumping blood, and heart abnormalities during the early developmental stages progress to congenital heart malformations; therefore, the developmental program of the heart, including the expression of the genes responsible for various ionic channels, is likely to be tightly regulated. Electrophysiological recordings of various ionic channels and quantification of the genes responsible for the channels have been reported primarily for 4 representative stages: early embryonic (EE), late embryonic (LE), neonatal, and adult. To provide a complete overview of developmental regulation, it is necessary to observe the developmental changes occurring in the heart across these representative stages.
In rodents, spontaneous action potentials (APs) have been reported for the EE stage in developing rodent ventricular myocytes, eventually disappearing in passive contracting cells in the LE stage . The electrophysiological properties of individual ion channels have been investigated in isolated ventricular myocytes at the 4 representative stages by means of patch-clamp methods [2, 3, 4]. In addition to cells that exhibit spontaneous APs, embryonic rodent ventricular tissues also contain quiescent cells with no spontaneous APs. In 12-day fetal hearts, for example, 9 of 14 ventricular cells were quiescent and exhibited a resting membrane potential (RMP) of −48.4 ± 1.8 mV ; similarly, in 18-day postcoitum (dpc) mice, 6 of 13 isolated ventricular cells were spontaneously active, whereas the remaining 7 cells were quiescent . Moreover, the beating rate of the spontaneous APs ranged from 35 ± 11 beats per minute (bpm)  to 232 bpm  in 12.5-dpc embryonic rat ventricles, and from 178 ± 12.7  to 124 ± 8.7 bpm  in 9.5-dpc embryonic mouse ventricles; the reported beating rates roughly correspond to a basic cycle length (BCL) of approximately 259–2,500 ms. In addition to regular spontaneous APs, irregular spontaneous APs have also been reported in the embryonic ventricular cells of both mice  and rats . Previously, we modeled the developmental changes in the APs of cardiac ventricular myocytes  by using the Kyoto model  and the Luo–Rudy dynamic (LRd) model . The measured APs at developmental stages were reproduced using common sets of these models by varying the relative densities of the ionic currents, pumps, exchangers, and sarcoplasmic reticulum (SR) Ca2+ kinetics. In addition, Jonsson et al.  combined molecular biology and computer simulations to demonstrate that human embryonic stem cell-derived cardiomyocytes (hESC-CMs) have an immature electrophysiological phenotype, based on insufficient function of inward rectifier K+ current (IK1) channels and a shift in the activation of sodium channels. Thus, computer simulation is a powerful approach for confirming experimental data and providing insights into the possible functional mechanisms involved in cardiac development. Although our simulations well reproduced the disappearance of the spontaneous APs between the EE and LE stages as well as the changes in AP durations during the transition from the LE to the neonatal and adult stages, we have not clarified the contribution of each ionic current system to the reported characteristics of rodent ventricular cells.
In the present study, we examined the functional changes in developing embryonic ventricular cells to identify the pivotal components in the model in order to describe the reported characteristics of embryonic rodent ventricular cells. We switched the relative densities of ionic components that differ between the EE and LE stages, and tested 512 combinations with the Kyoto model, 128 combinations with the Ten Tusscher–Panfilov (TP) human ventricular cell model , and 32 combinations with the LRd model. The 160 regular spontaneous APs predicted in the Kyoto model had a wide range of BCL values, all of which were within the reported range of the BCL in 9.5-dpc mice [6, 8, 9] and in 11.5-dpc rats [5, 7]. In all 3 models, the combinations in which IK1 was increased before the disappearance of If were predicted to result in high [Ca2+]i, and most of the combinations had quiescent membrane potentials slightly positive to −80 mV, as reported in 12.5-dpc fetal rat ventricular cells .
Previously, we simulated the APs of rodent ventricular cells at the EE, LE, and neonatal stages by using the Kyoto model—an electrophysiological model of guinea pig ventricular cells [10, 11]. Briefly, quantitative changes in various ionic components were represented as the densities of the components in the developmental stages relative to those in the adult stage. These relative densities were then multiplied by the corresponding conductance (nS/pF) or conversion factors (pA/pF·mM) to demonstrate that developmental changes in the APs can be reproduced using common sets of mathematical equations. We adopted the same procedure in the present study, and reconstructed EE and LE ventricular cell models by using the updated Kyoto model .
Ionic currents, exchangers, and SR Ca2+ kinetics
Estimated conversion factors for the funny current (If) and sustained inward current (Ist)
Relative ratios of ion fluxes in exchanger, pump, and sarcoplasmic reticulum (SR) Ca2+ kinetics
Volumes of cell compartments
In the Kyoto model, 80 % of the total cell volume (Vt, 16,000 μm3) is considered accessible for ion diffusion (Vi, 12,800 μm3) . The volumes of the cell compartments of the EE ventricular cell were computed as described previously ; the volumes of the SR uptake site (Vup) and the SR release site (Vrel) were set to 3.394 and 1.3576 μm3, respectively, based on the Vi in the EE ventricular cell model (Vi,EE, 1697 μm3). In addition, the updated Kyoto model included the mitochondrion as a cell compartment in addition to the SR, and the mitochondrial volume (Vmit) was set to 23 % of Vi . Because the mitochondria are marginally developed in rodent EE ventricular cells, we arbitrary set the Vmit for the EE ventricular cells to 2.3 % of Vi,EE (39.031 μm3), which is 1/10 the ratio in the adult stage.
Switching the relative densities of the ionic components
We selected the following nine components to be switched between the EE and LE stages: If, Ist, IK1, Na+ current (INa), L-type Ca2+ current (ICaL), Na+/Ca2+ exchange current (INaCa), transient outward current (Ito), ATP-sensitive K+ current (IKATP), and a set of 4 electrical components of the SR. The electrical components of the SR—which included the permeability of Ca2+ release from SR to the dyadic space through the RyR channel (IRyR), Ca2+ leak from the SR (ISR,leak), the SR Ca2+ pump, and Ca2+ transfer from the SR uptake site to the release site (ISR,transfer)—were treated as a set of components in the SR because all 4 components are located in the SR and develop along with the development of the SR. The other ionic components in the model were assumed to have constant current densities during embryonic development.
We applied the exact same procedure to simulations with the TP human ventricular cell model , in which the following 7 components were switched between the EE and LE stages: INa, If, IK1, ICaLIst, INaCa, and SR-related components. Although the original TP model does not contain If, we implemented a mathematical model for If . Similarly, we implemented the same mathematical model for If  in the LRd model  and switched the INa, If, IK1, ICaL, and SR-related components between the EE and LE stages for further confirmation of our simulation with the Kyoto and the TP models.
We assumed that the 9 components in the Kyoto model switched relative densities directly from EE to LE values without intermediate levels, independently from the other components; therefore, we first tested 512 (29) combinations of the model. We then classified the simulation results for the 512 combinations according to their electrical activities and also compared the simulated results in terms of contractile force. The Kyoto model adopted a 4-state contraction model  to simulate cardiac cell contraction; the authors of the Kyoto model also assumed that all transition steps from cross-bridge-formed states ([T*] and [TCa*]) to cross-bridge-released states ([T] and [TCa]) are ATP-dependent, because ATP binding to a myosin head disrupts the cross-bridge formation between myosin and actin [24, 25]. Although we adopted the value of half sarcomere length (hSL, μm)—computed using the model proposed by Negroni and Lascano —as a quantitative parameter for cell contraction, this value is not completely quantitatively accurate because we did not consider the developmental changes in contractile proteins.
The Kyoto model contains a β1-adrenergic signaling cascade in which binding of isoproterenol (Iso) to the β1-adrenergic receptor activates protein kinase A (PKA) through activation of adenylate cyclase, and the activated PKA modulates ICaL, IKs, phospholamban, SR Ca2+-ATPase (SERCA), and plasma membrane Ca2+-ATPase . The application of iso-enhanced ICaL density had a minimal effect on the EE ventricular myocytes but had strong effects on LE and adult ventricular myocytes, as observed in an experimental study . Differences in β1-adrenergic modulation between EE and LE ventricular myocytes were not considered in this study because we focused on membrane excitation and contraction to present an overview of the functional landscape of developmental changes in embryonic ventricular cells.
Computer simulation procedures
We switched the relative conductances of the 9 components between EE and LE values, and simulated the 512 combinations of the Kyoto model for 600 s with no external stimuli. For those combinations that showed no spontaneous activity for 600 s, we applied an external stimulation of −38 pA/pF, which is −8,000 pA divided by cell capacitance of the original Kyoto model (211.2 pF), at 2.5 Hz to determine whether the cells functioned as passive contracting cells. The exact same simulation procedures were applied to the TP and LRd models; we first simulated 128 combinations of the TP model and 32 combinations of the LRd model for 600 s, and provided additional 600-s simulations with external stimulation for those combinations without spontaneous activities. The external stimulation of −80 pA/pF was applied at a frequency of 2.5 Hz for the LRd model and that of −52 pA/pF at 1.0 Hz was applied for the TP model. The amplitudes of the external stimulation differed among the 3 models because we adopted the amplitudes that were used to evoke APs in the original models [12, 14, 15].
Classification of the 512 combinations simulated with the Kyoto model
Of the 512 combinations simulated using the Kyoto model, 248 combinations were predicted to result in quiescent cells with no spontaneous activity; the external stimulus was applied at a frequency of 2.5 Hz for 600 s to pace the 248 combinations; however, 32 of them failed to fire APs. The evoked activities are illustrated as blue hysteresis loops in Suppl. Figs. 1 and 2; the loops begin at the upper left representing their RMP, and the membrane is then depolarized, overshooting the potential, and gradually repolarized to the RMP. The sarcomere length shortens during the repolarization phase; thus, the height of the hysteresis loop represents the force of contraction. In 64 combinations in which the relative densities of INa, If, and IK1 were set to LE values, an increase in the relative activities of ICaL and SR-related components resulted in larger amplitudes of hSL and a decrease in INaCa resulted in smaller amplitudes of hSL. The exact same results were observed in the TP model; the amplitudes of Ca2+ transients were increased as the relative densities of ICaL and SR-related components were increased to the LE values, and the amplitudes were decreased as the relative INaCa density was decreased to the LE values (Suppl. Fig. 2).
The changes in If and IK1 in other models—the TP and LRd models—demonstrated similar results in terms of regular spontaneous APs (Suppl. Figs. 3 and 4); the shifts in relative densities of If and IK1 to LE values terminated the spontaneous APs, which were observed when the relative densities of both If and IK1 were set to the EE values. The APs were not evoked by the external stimulus, when the relative densities of IK1 and Ist were set to the LE values and those of If and ICaL were set to the EE values in the Kyoto model (Fig. 2, solid light boxes); similar results were observed in both the TP and LRd models, when the relative density of IK1 was set to the LE value and that of If was set to the EE value, regardless of the remaining components (Suppl. Figs. 3 and 4). The spontaneous oscillations with long AP duration were observed only in the Kyoto model (Fig. 2, solid black box). The burst-like behaviors were observed in 10 combinations simulated using the TP model; in the LRd model, however, all 16 combinations for which the relative density of IK1 was set to the EE value showed regular spontaneous APs, and the burst-like behaviors were not observed.
Burst-like membrane potentials in the Kyoto and TP models
The [Na+]i was increased during repetitive bursts and decreased during the quiescent state between bursts in both the Kyoto and the TP models. In the Kyoto model, the [Na+]i was 4.14 mM when the relative densities of all ionic components were set to EE values; the [Na+]i was 3.2 mM when the burst was terminated and decreased to 2.7 mM during the quiescent state. In the TP model, however, the [Na+]i was 4.01 mM when the burst was terminated and decreased to 3.65 mM, which are both higher than 1.56 mM—the [Na+]i when all relative densities were set to EE values. In both models, however, the amplitudes of INaK increased during repetitive bursts and gradually decreased during the quiescent state between bursts.
Increase in IK1 before the disappearance of If resulted in high intracellular Ca2+ concentrations in all 3 models
In the Kyoto model, increase in IK1 to the LE value before the disappearance of If resulted in either the spontaneous oscillation of the membrane potential with long APs or quiescent membrane potentials at approximately −50 mV. Of the 128 combinations in which IK1 was increased before the disappearance of If, 32 combinations in which the relative density of ICaL was set to the EE value and that of Ist was set to the LE value were predicted to result in quiescent membrane potentials at approximately −50 mV, and the APs were not evoked upon external stimulus application (Fig. 2, solid light boxes). Similarly, in the TP and LRd models, the APs were not evoked upon external stimulus application when IK1 was increased before the disappearance of If (Suppl. Figs. 3 and 4). The average RMPs were approximately −62.9 mV in the TP model and −69.1 mV in the LRd model.
In the Kyoto model, the increase in [Ca2+]i resulted in the spontaneous oscillations of the membrane potential with long APs (Fig. 4c); the membrane potential spontaneously oscillated approximately every 20 s between −35 and −80 mV. The [Na+]i oscillated between 24.2 and 24.9 mM, which is considerably higher than the original [Na+]i (4.14 mM) in the original EE model; the [Na+]i was also increased from 9.16 to 68.9 mM in the LRd model and from 1.56 to 60.9 mM in the TP model (data not shown). The [Ca2+]i also oscillated at high concentrations, from 0.46 to 3.9 μM. The membrane was depolarized to −35 mV when If began to apply an inward current, followed by activation of the Ca2+-activated background cation current (ILCCa), which is activated when the intracellular Ca2+ concentration ([Ca2+]i) is high. The membrane potential was maintained at −35 mV for approximately 20 s when the amount of the outward K+ current, i.e., the sum of IKr and IK1, was approximately the same as that of ILCCa. The rapid increase in IK1 followed by deactivation of ILCCa subsequently led to the repolarization of the membrane to −80 mV.
Contribution of INa and If to the BCL of regular spontaneous APs
Of the 512 combinations simulated using the Kyoto model, 160 combinations were predicted to result in regular spontaneous APs. The BCL of the 160 regular spontaneous APs ranged from 306 to 884 ms; the maximum diastolic potential (MDP) ranged only from −85.0 to −80.9 mV, and the overshoot potential ranged from 1.6 to 54.3 mV. Of the 9 components that were shifted between EE and LE values, the developmental changes in INa and If made large contributions to the variation in the BCL and the overshoot potential in the Kyoto model; therefore, we further tested the contribution of the developmental changes in INa and If to the BCL and the overshoot potential.
Representative developmental changes in APs as INa, If, and IK1 were sequentially switched
Characteristics of representative spontaneous action potentials
Overshoot potential (mV)
INa set to LE
INa and If set to LE
In the EE model, ICaL was responsible for rapid depolarization of the membrane to overshoot the potential. As we sequentially switched INa, If, and IK1 to the LE values, the peak amplitude of ICaL decreased from approximately −3.57 to −0.38 pA/pF and that of INa increased from 0 to −178.57 pA/pF, and INa became responsible for rapid depolarization rather than ICaL. Although we observed variations in the inward currents responsible for rapid depolarization, there were only slight differences in the outward currents (IKr, IK1, and INaK) responsible for membrane repolarization.
We predicted membrane excitation patterns from among computer simulations of 512 combinations with the Kyoto model (Suppl. Fig. 1) and confirmed the simulated results with 2 other models, the TP model (Suppl. Figs. 2 and 3) and the LRd model (Suppl. Fig. 4). In all 3 models, [Ca2+]i was increased to nonphysiological levels when IK1 was increased to the LE value before the disappearance of If.
Burst-like membrane potentials in the Kyoto and TP models
Burst-like APs were observed in 8 combinations when the relative densities of Ist and ICaL were set to the LE values and those of INa, If, IK1, and INaCa were set to the EE values (Suppl. Fig. 1); the burst-like APs disappeared as one of INa, If, IK1, and INaCa densities was shifted to LE value. In the TP model, on the other hand, burst-like APs were observed in 8 combinations in which the relative densities of If and INaCa were set to LE values and those of IK1 and Ist were set to EE values, and 2 combinations in which the relative densities of INa, If, ICaL, INaCa, and Ist were set to LE values, and that of IK1 was set to the EE value (Suppl. Fig. 3). Although the combinations in which burst-like APs were observed were completely different between the Kyoto and the TP model, we observed similar dynamic changes in [Na+]i, which was increased during the repetitive bursts and decreased during the quiescent state between bursts (Fig. 3). During repetitive bursts, the amplitude of INaK was increased, which then decreased the amplitude of APs. As the bursts were terminated, INaK gradually decreased and contributed to the gradual increase in membrane potential during the quiescent state between bursts.
A similar pattern exhibiting burst-like APs (Fig. 3) has been reported in the pulmonary vein of rodents , and such APs in the pulmonary vein are known to cause atrial fibrillation [28, 29]. In our simulations, burst-like membrane potentials were observed when the relative densities of Ist and ICaL were set to the LE values and those of INa, If, and IK1 were set to the EE values in the Kyoto model. Ist has been reported as ionic currents of Na+ and K+ and has been observed only in SAN cells ; however, there is no evidence for the presence of Ist in embryonic ventricular cells. Furthermore, we have no evidence for burst-like activities in ventricular cells at any stages of development. Although it may be interesting to note that such burst-like APs were predicted using both the Kyoto and TP models, we cannot draw notable conclusions from the simulated results because the combinations in which burst-like APs were observed were completely different between the Kyoto and TP models.
If should disappear before the increase in IK1 to avoid high intracellular Na+ and Ca2+ concentrations
We observed abnormally high [Ca2+]i values in all three models when IK1 was increased before the disappearance of If; the simulated [Ca2+]i was 12.1 μM in the LRd model, 6.27 μM in the TP model, and oscillated between 0.46 and 3.9 μM in the Kyoto model, when the relative IK1 density was set to LE and all the other densities were set to EE. In the TP model, the outward K+ current was increased as the relative IK1 density was increased from 0.11 to 1.0. Although the increase in outward K+ current polarized the membrane, the net inward current through If depolarized the membrane; therefore, the RMP was approximately −62.9 mV when the relative IK1 density was increased before the disappearance of If. The increase in the inward Na+ current through If subsequently increased [Na+]i, which decreased the amount of Ca2+ excluded from the cytoplasm through INaCa. Therefore, the high [Ca2+]i in our simulation is mostly attributed to the decrease in INaCa.
In the Kyoto model, the high [Ca2+]i further led to the activation of ILCCa (Fig. 4c), a current whose open probability increases at high [Ca2+]i and contributes to transient inward current . The activated ILCCa contributed to the depolarization of the membrane to −35 mV; subsequent activation of IK1 resulted in repolarization of the membrane to −80 mV. Although abnormally high [Na+]i and [Ca2+]i were observed in all three models, the spontaneous oscillation with long AP duration between −35 and −80 mV was observed only in the Kyoto model; therefore, we should note that such spontaneous oscillations are unlikely to be observed in actual embryonic ventricular cells.
In addition to the abnormally high [Ca2+]i, we observed that the RMP was slightly positive to −80 mV when IK1 increased before the disappearance of If; the average RMP of 8 combinations in the LRd model was −69.1 mV and that of 32 combinations in the TP model was −62.9 mV. Of the 128 combinations in which IK1 was increased before the disappearance of If in the Kyoto model, the membrane potentials did not oscillate but were quiescent at approximately −50 mV in 32 combinations for which the relative ICaL density was set to the EE value and the relative Ist density was set to the LE value. None of the combinations could fire APs even after the application of a large external stimulus in all 3 models because the depolarized membrane caused voltage-dependent inactivation of INa, whereas abnormally high [Ca2+]i caused Ca2+-dependent inactivation of ICaL. Although there is no evidence to suggest that quiescent cells from 12-day fetal rat hearts failed to evoke APs upon the application of external stimulus, it is worth noting that the predicted RMPs were roughly consistent with the experimental observations obtained from 12-day fetal rat hearts; Nagashima et al.  obtained both cells with spontaneous APs and quiescent cells from 12-day fetal hearts wherein the quiescent cells exhibited an RMP of −48.4 ± 1.8 mV, which is more positive than the RMP of quiescent cells from 18-day fetal hearts (−80.9 ± 1.8 mV) .
Relative densities of INa and If determine the BCLs and the overshoot potentials of the regular spontaneous APs
Of the 9 components shifted between EE and LE values, the developmental changes in INa and If had large contributions to the variation in the BCL and the overshoot potential in the Kyoto model; the BCLs of the 160 regular spontaneous APs ranged from 306 to 884 ms and the overshoot potential ranged from 1.6 to 54.3 mV. We further shifted the relative densities of INa and If independently by a 10 % increment from EE to LE values and showed that the increase in INa shortened the BCL, whereas the decrease in If prolonged the BCL; the BCLs of the regular spontaneous APs were prolonged up to 1,550 ms when the relative INa density was set to 0.07 (EE value) and the relative If density was set to 0.1 (90 % shift to LE).
EE ventricles have a large range of BCLs—337–542 ms in 9.5-dpc mice [6, 8, 9] and 273–2,500 ms in 12.5-dpc rats [5, 7]—and the beating rhythms of embryonic ventricular cells are irregular as reported in both 11.5-dpc rat ventricular cells  and 18.5-dpc mouse ventricular cells with spontaneous APs . Although our simulations could not reproduce the irregular spontaneous APs reported in both mouse and rat embryonic ventricular cells, our predicted BCLs were all within the range of BCLs reported in experimental studies. We also showed that the wide range of the BCLs reported in vitro can be described by shifting the relative densities of INa and If.
INa becomes responsible for membrane depolarization as INa, If, and IK1 are sequentially switched from EE to LE levels
The simulated results imply that the increase in the relative IK1 density before the disappearance of If results in high [Ca2+]i in all three models. In addition, we showed that the relative densities of both INa and If determine the BCL and overshoot potential of the regular spontaneous APs. On the basis of all the observations, we illustrated the representative changes in APs in which INa was increased before the disappearance of If, followed by an increase in IK1 (Fig. 6). Following the sequence with representative models, we observed that INa took over the role of ICaL, which was originally the current responsible for the depolarization of the membrane in the EE model. This change in the dependence of depolarization from the Ca2+ current to the Na+ current is consistent with experimental observations in rodent ventricular myocytes  in which the MDP shifted to a negative direction, also consistent with our simulation (Table 4). The changes in BCL were roughly consistent with experimental observations on rat embryonic hearts; the BCL of the proximal ventricle in the 11.5-dpc embryonic rat heart was shorter than that of the ventricle in the 10.5-dpc rat; however, the BCL was prolonged again in the 12.5-dpc rat .
Our hypothesis that an increase in INa density and disappearance of If should be observed in the early stage of embryonic development is supported by experimental observations that the densities of INa and If change earlier than those of other components [3, 6], including ICaL, IK1, INaCa, and SR-related components [2, 20]. We demonstrate here that switching all the components in the mathematical model enabled us to simulate all possible combinations and identify pivotal component switches to describe the reported characteristics of embryonic ventricular cells. Our simulation procedure, together with experimental observations in the literature, will likely be useful in identifying the sequential regulation of gene or protein expression during development, which is difficult to determine through experimental data alone.
Our study has several limitations. The densities of ionic components were obtained from various rodents, including rats, mice, rabbits, and guinea pigs (Tables 1, 2, 3), and implemented in the Kyoto and LRd models, both of which represent guinea pig ventricular cells. Therefore, simulations with the Kyoto and LRd models represent electrical activities of rodent ventricular cells in general. Although the TP model represents human ventricular cells, we implemented the densities listed in Tables 1, 2, and 3 in order to confirm our simulations with the Kyoto model; thus, the simulation with the TP model is not intended to represent developmental changes in human embryonic ventricular cells. In addition, changes in mRNA subtypes of the genes encoding the If and IK1 currents were not considered; the gene responsible for If is known to switch from HCN4 to HCN2 , whereas that for IK1 switches from Kir 2.2 to Kir 2.1  during embryonic development. Although the length of the sarcomere was adopted as an index for the force of contraction, we did not consider developmental changes in contractile proteins; α- and β-myosin heavy chains (MHC), for example, are coexpressed and equally abundant in early embryonic ventricular cells, but α-MHC becomes predominant in adult ventricular cells . Therefore, the simulated changes in the length of the sarcomere may not be quantitatively accurate.
The relative densities of ionic components in mathematical models were switched independently between the EE and LE stages to identify pivotal components to describe reported characteristics of embryonic ventricular cells; all simulations were conducted using three models, the Kyoto, TP, and LRd models. In all three models, our simulations suggested that the tenfold increase in IK1 before the disappearance of If results in abnormally high [Ca2+]i. The developmental changes in relative densities of INa and If had large contributions to the wide range of BCL values in the regular spontaneous APs. Of the remaining six components in the Kyoto model, increases in ICaL and SR-related components were involved in the enhancement of cell contraction.
This research was supported by funds from the Yamagata Prefectural Government and Tsuruoka City, Japan. We would like to thank the members of WGSP at the Institute for Advanced Bioscience, Keio University, for critical suggestions.
Conflict of interest
The authors declare that they have no conflicts of interest.
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