The roles of sustained components of INa and IKv43 in shaping the action potentials (AP) of myocytes isolated from the canine left ventricle (LV) have not been studied in detail. Here we investigate the hypothesis that these two currents can contribute substantially to heterogeneity of early repolarization and arrhythmic risk. Quantitative data from voltage-clamp and expression profiling experiments were used to complete meaningful modifications to an existing “local control” model of canine midmyocardial myocyte excitation-contraction coupling for epicardial and endocardial cells. We include 1) heterogeneous IKv43, IKs, and ISERCA density; 2) modulation of IKv43 by Kv channel interacting protein type 2 (KChIP2) channel subunits; 3) a possible Ca2+-dependent open-state inactivation of IKv43; and 4) a sustained component of the inward Na+ current, INaL. The resulting simulations illustrate ways in which KChIP2- and Ca2+-dependent control of IKv43 can result in a sustained outward current that can neutralize INaL in a rate- and myocyte subtype-dependent manner. Both these currents appear to play significant roles in modulating AP duration and rate dependence in midmyocardial myocytes. Furthermore, an increased ratio of IKv43 to INaL is capable of protecting epicardial myocytes from the early afterdepolarizations resulting from the SCN5A-I1768V mutation-induced increase in INaL. Experimentally observed transmural differences in Ca2+ handling, including greater sarcoplasmic reticulum Ca2+ content and faster Ca2+ transient decay rates on the epicardium, were recapitulated in our simulations. By design, these models allow upward integration into organ models or may be used as a basis for further investigations into cellular heterogeneities.
- sustained sodium ion current
- Kv4 channel regulation
significant differences in the expression patterns of a number of ion channels are an important functional distinction among cells isolated from the left ventricular (LV) endocardium, epicardium, and midmyocardium of many species, including human (12, 27), dog (3, 54), guinea pig (3), rabbit (33), and mouse (6). The major consequence of this systematic variation in ionic currents is a corresponding heterogeneity of action potential duration (APD), waveform, and rate dependence (27). It is hypothesized that these so-called intrinsic electrophysiological differences are responsible for a normal sequence of activation and repolarization in healthy hearts. Moreover, either exaggeration or significant reductions of repolarization heterogeneities, due to drug actions, inherited mutations, or acquired disease, may be proarrhythmic. Experimental studies in ventricular myocytes have begun to define the molecular and ionic mechanisms underlying the transmural heterogeneities of ion channel and calcium (Ca2+)-handling proteins. A relatively extensive data set is now available for the canine ventricular myocardium. The ionic currents that are known to exhibit transmural heterogeneities include the transient outward potassium (K+) current, IKv43(30); the slowly activating delayed rectifier K+ current, IKs (29); the late sodium (Na+) current, INaL (68); the Na+/Ca2+ exchanger, INaCa (62, 69); and the sarcoplasmic reticulum (SR) Ca2+-ATPase uptake rate, ISERCA (25). Important unresolved questions concerning the functional importance of these transmural heterogeneities remain.
This study was motivated by the possibility that we could integrate data concerning 1) known heterogeneities, to determine whether they are sufficient to explain the distinct AP waveforms; and 2) information regarding known interactions between the subunits comprising an ion channel, to reproduce channel function within intact myocytes and explore the functional roles of these interactions. Computational modeling provides a useful framework with which to integrate extensive experimental data and develop specific working hypotheses to guide quantitative investigations into these unresolved questions.
The ionic mechanisms responsible for the intrinsically long APDs and pronounced rate dependence of midmyocardial myocytes in the LV have been the focus of many experimental investigations (2). Most previous hypotheses have been centered on the relatively large K+ outward currents that are responsible for late repolarization (phase 3). However, evidence is emerging that some currents previously measured and defined as being transient (such as both INa and IKv43) modulate APD as a consequence of their smaller slowly inactivating or sustained components. The relatively high resistance of the ventricular AP plateau provides a substrate in which these small net currents can modulate the AP waveform (56). In this study, we have investigated the hypothesis that these two currents can contribute substantially to early repolarization. As such, transmural differences in these currents may lead to increased APD and arrhythmogenic risk of midmyocardial myocytes.
Intracellular Ca2+ cycling is an important regulator of normal and abnormal excitation-contraction coupling (ECC) (4). In the myoplasm, Ca2+ binds to regulatory molecules, such as calmodulin, and thereby can modify ion channel function on a beat-to-beat basis or over longer time periods (43). Furthermore, Ca2+-mediated early afterdepolarizations (EADs) can facilitate the development of potentially life-threatening reentrant arrhythmias by increasing transmural dispersion of repolarization. In an effort to create a mechanistic yet computationally efficient model of Ca2+ cycling in the cardiac ventricular myocyte, Hinch et al. (19) used a method based on time scale decomposition to simplify continuous-time Markov chain descriptions of L-type Ca2+ channel (LCC) and ryanodine receptor (RyR) gating. This resulted in a low-order system of ordinary differential equations (ODEs) representing the ensemble behavior of the so-called Ca2+ release units (comprising 1 LCC and 5 RyRs) while also retaining many key biophysical properties (19). Greenstein et al. (15) generalized this approach to allow LCC and RyR models of arbitrary complexity and combined this model with their equations for ionic currents in canine midmyocardial myocytes. The resulting whole-cell model was shown to faithfully reproduce features of LCC voltage and Ca2+ sensitivity, ECC, and AP and Ca2+ cycling properties of a canine midmyocardial myocyte (15).
The time- and voltage-dependent properties of the Kv4.3 channel current are now known to be much more complex than previous models accounted for. This is, at least in part, due to accessory β-subunits, such as the K+ channel interacting proteins (KChIPs). Specifically, KChIP isoforms both promote cell surface expression and modify gating kinetics (42). Furthermore, it has been suggested that the steep transmural gradient of KChIP expression may contribute to the heterogeneous measurements of IKv43 across the canine LV wall (48, 66). Patel et al. (42) propose that once Kv4.3 channels transition to the open state, inactivation can occur via two distinct mechanistic pathways: a Ca2+-independent closed-state mechanism or a Ca2+-dependent open-state mechanism. However, at present it is unknown whether these results, obtained in heterologous systems, are relevant to the cardiac myocyte AP waveform or ECC.
In this study, we completed meaningful modifications to the Greenstein model (15) of canine midmyocardial myocyte ECC for epicardial and endocardial cells. We accomplished this by utilizing recent experimental data describing the molecular basis of transmural cellular heterogeneity and existing Markov models of INaL and IKv43. We first demonstrate the ability of the models to simulate quantitative features of regionally varying ion channel function or expression levels. Next, we explore the consequences of a possible Ca2+-dependent inactivation of IKv43 on the canine LV AP waveforms. Finally, we investigate the contributions of sustained components of INaL and IKv43 to early repolarization and transmural heterogeneities of APD in canine LV myocytes. We also explore how an increase in INaL, e.g., due to the SCN5A-I1768V mutation, may contribute to regional increases in APD and arrhythmic risk, examine potential additional heterogeneities, and suggest targets for further experimental investigation. This particular mutation was selected because it modifies the sustained component of INa and, as such, may differentially alter AP values measured in myocytes isolated from different regions across the LV wall. These models are biophysically detailed, yet computationally tractable, allowing for upward integration into tissue- and organ-scale models.
The Greenstein model of ECC in a canine midmyocardial myocyte (15) was used as a basis for the three canine ventricular myocyte models in this study. Briefly, the original model consists of 76 ODEs, of which 40 represent intracellular Ca2+ cycling states. The other 36 ODEs represent gating kinetics and ion transfer relationships of the known ion channels and corresponding Na+, Ca2+, K+, and Cl− currents. We added an extra state variable representing open-state inactivation of IKv43 (42) and replaced the existing Hodgkin-Huxley equations (3 state variables) with a 13-state Markov model of INa (7). Thus our modified models comprised 87 ODEs. The ionic currents we have included as contributors to transmurally heterogeneous AP values are outlined below. A summary of the original and modified parameters is provided in Table S1 of the Supplemental Data.1 Experimental data used for model validation were converted to a digital format and digitized using MATLAB.
The transient outward K+ current, IKv43.
This K+ conductance is an important regulator of the early repolarization phase of the AP. Furthermore, changes in IKv43 can modify ECC in ventricular myocytes (51). To investigate the consequences of a Ca2+-dependent open-state inactivation of IKv43, as proposed by Patel et al. (42), we incorporated an additional state into the existing homotetrameric Markov model of Greenstein et al. (17) (see Fig. S1 in the Supplemental Data). Specifically, the scaling factor for Kv4.3 (controlling current amplitude), the recovery from inactivation transition rate αi, and the closed-state inactivation transition rate βi were modified so that they agreed with recent experimental data (Supplemental Table S1). The Ca2+-dependent inactivation from the open state was simulated by the inclusion of an additional state variable Io, and two transition rates, αo,i and βo,i. Since KChiP2 modifies only the Kv4.3 current (not Kv1.4 current), we altered only the biophysical parameters corresponding to Kv4.3. In the absence of any data to the contrary, we assumed that Kv1.4 is homogeneously expressed across the wall of the adult canine LV.
Voltage-clamp data from Rosati et al. (48) suggests that the current density of the transient outward current (Ito1) from the epicardium of the canine LV is 36% larger and that Ito1 from the endocardium is 80% smaller than in the midmyocardium. We used these data to estimate Kv4.3 scaling factors for epicardial and endocardial myocytes relative to the original value in the midmyocardial model (15). All three values were adjusted to closely match the voltage-clamp data of Liu et al. (30) (although they found no statistical significant difference between epicardial and midmyocardial IKv43). The KChIP2-dependent transition rates (αi, βi) were altered to match data from Patel et al. (42). Their data and this adjustment are based on an abundance of KChIP2 subunits on the epicardium and virtually no KChIP2 subunits on the endocardium. The corresponding midmyocardial transition rates were estimated by interpolating between epicardial and endocardial values using the measured gradient of KChIP2 mRNA expression of Rosati et al. (48). Since the kinetic measurements of IKv43 were performed at 22°C, all transition rates were scaled up to account for temperature dependence of this current.
The fourth EF-hand moiety of the KChIP β-subunit displays the highest Ca2+ affinity and underlies most of the Ca2+ sensitivity. We have assumed that the Ca2+-dependent transition rate αo,i is linearly dependent on cytosolic Ca2+ concentration ([Ca2+]i). The formulation of the transition rate controlling recovery from open-state inactivation (βo,i) was based on the voltage-dependent deactivation transition rate, βa, but scaled to result in an appropriate rate of current inactivation. The relative contribution of the K+ channel α-subunit transcripts Kv4.3 to Kv1.4 was adjusted slightly from 77%/23% to 85%/15% to match the data of Dixon et al. (11). After all transition rate modifications were made, Kv4.3 scaling factors were readjusted to yield appropriate peak currents.
The slowly inactivating or late Na+ current, INaL.
To account for this important biophysical property of INa, we replaced the existing Hodgkin-Huxley formulation with the Markov model of Clancy et al. (7). This version includes both a background mode, contributing predominantly to the large transient component of INa, and a burst mode, which is activated during the plateau phase of the AP and results in a sustained inward current of roughly 0.07% of the peak current density. The background mode also contributes to a second, albeit much smaller (0.2%), current density peak during phase 3 repolarization or a ramped voltage-clamp protocol (7). The magnitude of the channel conductance was reduced to 4.6 mS/μF to yield a similar peak current density (∼300 pA/pF) in both the Hodgkin-Huxley and Markov formulations.
Experimental evidence suggests that not all SCN5A channels exhibit this bursting behavior. Furthermore, the data of Zygmunt et al. (68) indicate that INaL is approximately twice as great in the midmyocardium as in the other regions. To reflect this heterogeneity, we reduced the bursting state conductance to one-fourth of the background conductance in endocardial and epicardial myocytes and one-half of the background conductance in midmyocardial myocytes. To model the I1768V mutation, we increased the recovery kinetics as described by Clancy et al. (7), although to a lesser extent (50% increase instead of 100%). This resulted in an equivalent increase in INaL in response in a ramped voltage protocol.
The slowly activating delayed rectifier current, IKs.
Our IKs current formulation is the same as that of Winslow et al. (60). However, we modified the maximal conductance in the three types of canine ventricular myocyte in order to yield tail current densities that match the experimental values of Liu and Antzelevitch (29). Specifically, the statistically significant difference in midmyocardial tail currents was accounted for in our model.
Transmural variation in Ca2+-handling proteins.
To model heterogeneity of the SERCA uptake rate, we included a scaling term for both the forward and reverse rate of the existing SERCA pump model, as has been done by Iyer et al. (21). SR uptake in epicardial myocytes was increased by a factor of 2.0, as suggested by the data of Laurita et al. (25).
Computational methods and analysis.
All simulations were implemented and executed in MATLAB using the built-in ode23t integrator with a maximum step size of 0.1 ms. APD was computed at 30% and 90% repolarization (APD30 and APD90). We fitted exponential functions to the inactivation and recovery curves of IKv43 in a manner similar to Patel et al. (42). Briefly, for τclosed,inact and τf, the time constants were obtained by fitting exponentials of the form I = A1exp(−t/τ). For τrec, the time constants were obtained by fitting exponentials of the form I = Ipeak[1 − exp(−t/τrec)].
The transient outward K+ current, IKv43.
Families of simulated current tracings corresponding to IKv43 in epicardial, midmyocardial, and endocardial myocytes are shown in Fig. 1A. The voltage clamp protocol is illustrated in the inset. The peak currents are plotted in Fig. 1B along with experimental results of Liu et al. (30) for comparison. These predicted IKv43 amplitudes for each canine ventricular myocyte subtype are also consistent with published current amplitudes in a number of previous papers (35, 48, 66). Note that Liu et al. (30) did not detect significant differences between epicardial and midmyocardial myocytes. We chose to use the more complete data of Rosati et al. (48) as a basis for the IKv43 scaling parameters. Hence, our model predicts a slightly larger difference in peak IKv43 between epicardial and midmyocardial cells, although this is still within the range of experimental variation.
The simulations in Fig. 2 demonstrate the ability of our model to account for differences in the gating kinetics of Kv4.3 that have been reported in the presence and absence of KChIP2 accessory subunits. Since the experimental results for different KChIP2 isoforms (KChIP2b and KChIP2d) were in general very similar, these data have been averaged. In our simulations, closed-stated inactivation kinetics (Fig. 2A) were measured using a P2 pulse to +50 mV preceded by a P1 pulse of progressively increasing duration applied at a number of selected membrane potentials (see inset to Fig. 2A for protocol). The time course of this family of peak currents was well approximated by a single exponential with associated time constant, τclosed,inact. Note that the model predictions closely match the experimentally measured voltage dependence of closed-state inactivation. The effect of KChIP2 on steady-state inactivation is also reproduced very well. The experimentally measured mean value of τclosed,inact at −60 mV for Kv4.3 with KChIP2 diverges from the exponential function that depicts the voltage dependence of closed-state inactivation kinetics at more depolarized potentials. Although the model fails to account for this deviation, it is unlikely to play a significant role in simulations of AP waveform, which are the main focus of this investigation.
The voltage dependence of Kv4.3 recovery kinetics was evaluated over the range −100 to −60 mV (Fig. 2B). A conventional double-pulse protocol (Fig. 2B, inset) was used in which interpulse intervals were varied at four selected holding potentials. Faster recovery kinetics for epicardial compared with endocardial cells were obtained at all holding potentials. Both plots are in agreement with experimental results. Midmyocardial myocyte transition rates for αi, βi, αo,i, and βo,i (not shown) were interpolated based on reported KChIP2 expression levels. Once again, all model predictions are within the bounds of reported experimental variation.
Macroscopic inactivation kinetics were examined over the voltage range from minimal to nearly maximal current activation (−30 to +50 mV). To test the ability of our models to yield inactivation rates, we fitted the time course of activated current decay to a single exponential function with associated time constant τf and compared this with the experimentally measured values of Patel et al. (42) (Fig. 2C).
We then explored the consequences of a proposed Ca2+-dependent inactivation of IKv43 on the canine LV AP waveforms. Our simulations predict that Ca2+-independent inactivation of IKv43 alone results in a pronounced unphysiological delay of the AP plateau (i.e., prolongation of phase 1 of the AP) in epicardial and midmyocardial myocyte models (Fig. 3). This is not consistent with experimental data. In contrast, simulations in which inactivation proceeded via both Ca2+-dependent and -independent mechanisms resulted in more realistic AP waveforms. These results suggest that KChIPs may modify IKv43 in both a Ca2+-dependent and -independent fashion.
The slowly inactivating or late Na+ current, INaL.
Figure 4A consists of computed records of INaL activated in response to a series of depolarizing steps (duration 700 ms) from −140 mV (to relieve inactivation) to voltages ranging from −60 mV to 0 mV. The resulting current-voltage relationship (Fig. 4B) closely matches the experimental measurements of Valdivia et al. (59) over much of the examined range of membrane potentials.
The slowly activating delayed rectifier current, IKs.
These models predict a heterogeneous distribution of IKs tail currents (Fig. 5A) resulting from repolarization to −20 mV following a 5-s depolarizing stimulus (inset for Fig. 5A shows magnified view of the tail currents). The predicted current-voltage relationship (Fig. 5B) appears to reproduce the corresponding experimental findings by Liu and Antzelevitch (29) (inset for Fig. 5B) accurately.
The Ca2+-activated chloride current, ICl(Ca).
These models of epicardial and midmyocardial myocytes include a small contribution of ICl(Ca) to total transient outward current (Fig. 6). Note that the net effect of this was appropriate AP morphology and duration for these two myocyte subtypes. However, the lack of any significant outward current generated an abnormal phase 2 “hump” that delayed repolarization and prolonged APD90 in endocardial cells. Selectively increasing ICl(Ca) in endocardial cells prevented this and resulted in an APD90 typical of these myocytes at this pacing rate (see discussion).
Ca2+ homeostasis and AP morphology in normal canine ventricular myocytes.
A major requirement of mathematical models of cardiac myocyte electrophysiology and ECC is the ability to accurately simulate qualitative and quantitative changes in the AP and Ca2+ transient, as a function of pacing frequency and LV location. In Fig. 7, we demonstrate the ability of our model to predict Ca2+ cycling kinetics that are consistent with the experimental results of Cordeiro et al. (8). Specifically, an enhanced greater SR Ca2+ content and faster Ca2+ transient decay rates are observed in myocytes from the LV epicardium.
Figure 8 shows the resulting APs at cycle lengths of 500, 1,000, and 2,000 ms in the three canine ventricular myocytes subtypes. Table 1 compares the predicted APD90 with the experimentally measured values of Liu and Antzelevitch (29). In all cases the model predictions are within one standard deviation of the experimentally reported means.
We also explored the extent to which early repolarization currents play a role in determining the differences in APD between epicardial, midmyocardial, and endocardial myocytes at varying pacing rates. APD30 was measured and compared with APD90. In all cases, the most significant difference was observed at APD30. The difference times (APD90 − APD30) showed very little dependence on pacing rate and myocyte subtype.
Our models can be used to investigate the relative contribution of each known heterogeneity to prolongation of the midmyocardial AP (Table 2). We systematically switched midmyocardial parameters relating to each heterogeneous current to epicardial parameters. Specifically, the perturbations were as follows: GNaL = 1.15 mS/uF, GKs = 0.02 mS/uF, kSR = 2.0, and all epicardial IKv43 parameters. Using the model, we found that modifying INaL and IKv43 parameters resulted in the most significant rate-dependent impact on APD30. Substituting midmyocardial for epicardial IKv43 parameters 1) decreased IKv43 conductance and 2) altered the KChIP-dependent effects on IKv43 inactivation. The KChIP modulation of IKv43 played the major role in shortening APD30 (a mere decrease in IKv43 conductance without modulation of KChIP-dependent kinetic parameters made little difference to APD measurements). IKs did not appear to contribute significantly to midmyocardial rate-dependent APD prolongation under physiological conditions. No perturbations resulted in large changes to the difference between APD90 and APD30, suggesting that early repolarization currents dominate transmural heterogeneities in AP morphology.
Proarrhythmia due to the SCN5A-I1768V mutation.
An enhancement of INaL, as in the case of the I1768V mutation (47), did not appear to alter early repolarization in any of the three myocyte subtypes. However, we observed EADs in both midmyocardial and endocardial myocytes that occurred at all examined stimulation cycle lengths (Fig. 9). This pattern of results may suggest that the sustained component of IKv43 cannot only produce rapid early repolarization in epicardial myocytes but may also protect against the late increase in INa and subsequent EAD formation.
Current and voltage-clamp studies of isolated canine ventricular myocytes have provided a wealth of quantitative data concerning the electrophysiological properties of the Na+, Ca2+, and K+ and Cl− currents that underlie the AP and contribute to AP heterogeneity. Information regarding the way in which individual subunits of ion channels can contribute to the electrical functioning of the ion channels has also been obtained. Evidence is emerging that in many instances, ion channels are components of macromolecular complexes, containing both pore-forming (α) and accessory (β or δ) subunits, and their function may be modified by a variety of regulatory proteins (38).
The transient outward K+ current, IKv43.
It has been suggested by many investigators that KChIPs can regulate the transmural heterogeneity of IKv43 in canine ventricular myocytes (41). In addition to altering expression levels and accelerating recovery from inactivation, KChIP2 isoforms can modify Kv4.3 gating kinetics by 1) a Ca2+-independent slowing of closed-state inactivation and 2) a [Ca2+]i-dependent open-state inactivation. This current was previously thought to be insensitive to [Ca2+]i, and previous models do not account for this.
The experimental data and proposed model of Patel et al. (42) predict that channels that inactivate by the open-state mechanism must reopen upon hyperpolarization before reentering the closed state (see Fig. S1 in the Supplemental Data). Such reopening events can generate an outward current. This current has been measured experimentally (9, 42, 50) and is maximal under conditions of elevated [Ca2+]i. In the model we have developed, IKv43 is most prominent in phase 1 but can also contribute to early repolarization since it fails to inactivate completely and can neutralize the sustained component of INa. This slow inactivation occurs as a consequence of KChIP2- and [Ca2+]i-dependent modifications to IKv43 gating kinetics. This effect may become important in conditions such as congestive heart failure, when IKv43 is significantly downregulated and APD90 is prolonged.
The hydrophobic interactions of KChIPs and Kv4 channels bear a striking resemblance to the modes of interaction between calmodulin and its target proteins (65). KChIPs and calmodulin moieties share the structural feature of a 4 EF-hand scaffold that undergoes Ca2+-mediated conformational changes. Furthermore, elution profiles from size-exclusion chromatography have indicated that chelating Ca2+ destabilizes the KChIP2-Kv4 interactions (65), consistent with similar results on calmodulin ion channel interaction. These and other studies suggest a common mechanism of Ca2+ regulation among ion channel proteins.
The slowly inactivating or late Na+ current, INaL.
In heart, the SCN5A-encoded Nav1.5 is the predominant carrier of INa. Accessory subunits also modulate INa current density and voltage-dependent gating (38). Recent evidence suggests that Na+ channels contribute not only to the AP upstroke but also to the plateau phase and repolarization. Sustained activity can result from channels that fail to inactivate or channels that recover from inactivation during repolarization. A recent report by Maltsev and Undrovinas (32) delineates the behavior into three separate mechanisms: channel bursting, window current, and recovery from inactivation. Here we demonstrate that the sustained component of INa can be a potent regulator of early repolarization and underlies to a large extent the increase in the measured APDs and rate dependency of midmyocardial myocytes.
The I1768V mutation-induced increase in INaL is a potent instigator of Ca2+-mediated EADs originating during phase 3 repolarization in our model. Specifically, this mutant has been demonstrated to result in long QT-syndrome type-3 (LQT3). Previous modeling studies of this mutation have suggested that the alteration in gating kinetics accounts for AP prolongation and susceptibility to Ca2+-mediated EADs (7). Our simulations demonstrate that these phenotypes are most pronounced in midmyocardial and endocardial myocytes. These effects are also more marked in our canine models than previous modeling studies (in guinea pig) have suggested.
The slowly activating delayed rectifier current, IKs.
Some previous models of the ionic currents that underlie the mammalian ventricular APs have tended to overestimate the magnitude of IKs. This may have been a practical adjustment made in order to exceed inward currents and hence generate the appropriate APD90. It may also have contributed to the role of IKs in AP heterogeneity being overstated. Increasing the conductance of IKs in the midmyocardium to be equal to that in the other two regions decreased APD90 only slightly. Our results suggest that, under normal physiological conditions, other currents such as INaL and IKv43 may have a greater influence on transmural heterogeneities of APD.
The Ca2+-activated chloride current, ICl(Ca).
The extent to which anionic currents contribute to transmural electrical heterogeneity has been investigated less thoroughly than their cationic counterparts (20). No difference in ICl(Ca) current density was measured in canine epicardial and midmyocardial myocytes (67), but endocardial myocytes were not included in this study. We could find no subsequent or prior report in the literature of an investigation into transmural heterogeneity of ICl(Ca) in canines that included endocardial cells. Hence our decision to assign a heterogeneous transmural conductance of this current is not based on quantitative experimental results. Its inclusion in the model can be justified by the both the absence of conflicting data and clear evidence that without it, endocardial cells display unphysiological features of AP morphology.
Heterogeneities in Ca2+ fluxes and homeostasis.
In canine LV myocytes, time to peak and the duration of the Ca2+ transient have been reported to be longer in endocardial cells (8). In addition, SR Ca2+ content, as measured by rapid application of caffeine, is largest in epicardial cells (8). A variety of experimental findings suggests that a combination of electrical heterogeneity and intrinsic differences in ECC may underlie these differences in the SR Ca2+ concentration and kinetics of the Ca2+ transients. Greater SERCA expression on the epicardium may contribute to a higher SR Ca2+ content and faster decay (25), while the spike and dome morphology of the epicardial AP waveform permits a greater LCC current (ICaL) (15). It is presumed that these differences result in a more coordinated contraction of the ventricular myocardium, i.e., the faster kinetics of epicardial myocyte Ca2+ transients compensate for the delay in activation.
It is known that intracellular Ca2+ handling can have significant effects on cellular electrical behavior. Hence, it is very important to include mechanistic detail of intracellular Ca2+ dynamics in studies of the AP waveform. Many previous ionic models of ventricular myocyte ECC have dealt with intracellular Ca2+ cycling in only a qualitative manner. These approaches therefore lack a mechanistic representation of local Ca2+-induced Ca2+ release control. For instance, common pool models, as their name suggests, direct Ca2+ influx and SR release into a single cytosolic domain, which simultaneously controls RyR current (22, 39, 40, 60). A consequence of this is that once the RyR current is triggered, the resulting increase in “subspace” Ca2+ ensures an all-or-none SR release. As such, these models fail to reproduce one of the most important features of Ca2+ handling in cardiac myocytes, that of the graded Ca2+ release, in which SR Ca2+ release is proportional to LCC influx (57). A further limitation of many previous models is their very strong reliance on voltage-dependent inactivation of ICaL for stability (57). This conflicts with experimental evidence that consistently points to Ca2+-dependent inactivation as the dominant mechanism (28). Other model formulations that base SR Ca2+ release on LCC influx do so in a phenomenological manner and have less predictive capability (13, 31, 44). In contrast, local control models (16, 46, 53, 55) have successfully reproduced experimental observations. However, in general, these are too computationally intensive for upward integration into tissue or whole organ models. Our model effectively addresses these limitations.
Our model, in its present form, has several limitations. The existence of apparent discrepancies between the measured INaCa data of Zygmunt et al. (69), that of Xiong et al. (62), and the existing model formulation of INaCa prevented the inclusion of transmural heterogeneity of this current in this study. The disparities may have arisen from differences in experimental protocols and/or the difficulties associated with isolating this current using the required pharmacological approaches. To reconcile the differences in predicted INaCa heterogeneities, further experimental investigation is required. Thereafter, a thorough analysis of this antiporter mechanism can be carried out.
Our model recapitulates many of the observed differences between Kv4.3 currents expressed alone and with KChiPs in heterologous systems. However, it fails to predict τclosed,inact at membrane potentials more negative than −50 mV. Furthermore, despite the evidence favoring two distinct mechanisms of inactivation, the current records were in most cases well-characterized with a single exponential with kinetics corresponding to the fast component (τf) of the results of Patel et al. (42). There may be several reasons for these discrepancies. First, it is difficult to predict intracellular Ca2+ concentrations (which are thought to regulate the slow component of inactivation) within the heterologous system. Second, as in the case of INa, multiple open states may underlie the different components of inactivation rate. Finally, many other mechanisms of Kv4 channel regulation have been demonstrated (see below).
Kuo et al. (24) have demonstrated the importance of KChIPs in the regulation of Kv4 channels by analyzing currents in right ventricular myocytes isolated from KChIP−/− mice. Their studies reveal a complete loss of Ito1 in the RV of KChIP−/− mice. The majority of experimental reports confirms the importance of KChIPs in the regulation of IKv43. However, Deschenes et al. (10) failed to detect a transmural gradient of KChIP across the canine LV wall. It has been suggested that nonspecific binding of the polyclonal antibody used in this study may have masked the KChIP expression profile (41).
Many other mechanisms of Kv4 channel regulation have been demonstrated, and we do not account for these in our model (for a review see Patel and Campbell, Ref. 41). Briefly, these other regulatory subunits include frequenin (37), MinK-related peptide 1 (MiRP1) (64), NFAT/calcineurin (49), and DPPXs (36). All of these may contribute to IKv43 regulation in vivo. Of these, frequenin is thought to be the most likely candidate (41), possibly due to the structural similarity to KChIPs (both are neuronal Ca2+ sensors containing multiple EF hands). Indeed, frequenin has been reported to coimmunoprecipitate with Kv4.3 α-subunits in mouse ventricle extracts (18). However, others were unable to detect this association (45). Furthermore, it has been demonstrated that the interactions of KChIPs with Kv4 channels are substantially stronger and/or more efficient than those of frequenin (45).
We have replicated and normalized model simulations as closely as possible to experimental data acquisition conditions and protocols. However, in some articles, a narrow temperature range was given instead of an exact value. The reaction rate measurement Q10 is ∼3 for gating kinetics and ∼1.3 for ion transfer, which may introduce small errors into our predictions. Nevertheless, these errors are well within the bounds of normal experimental variation. Furthermore, the results from extrapolating kinetic data to 37°C are in close agreement with independent data.
Some of the results used in the validation process were obtained in heterologous cell culture systems. Additional modulating proteins, such as caveolins (63), present in the native environment of the cardiac myocyte sarcolemma, may affect channel function. We also failed to account for any interactions between ion channels and the actin cytoskeleton and/or the extracellular matrix, which have been suggested to play a role in whole-cell functioning (38).
Recent results also draw attention to a transmural gradient of the α-subunit of the Na+-K+ pump, INaK, in which ion channel expression decreases from epicardium to endocardium (14). However, it is thought that under physiological conditions, transmural gradients of intracellular Na+ result in nearly homogeneous whole-cell INaK. The paucity of quantitative data regarding these results prohibited the inclusion of this electrochemical gradient in our investigation. There also appears to be a gradient of ICl(cAMP), increasing from endocardium to epicardium (23, 58, 61). However, under normal conditions, cAMP levels are low and constant, and thus this current is unlikely to significantly contribute to cellular electrical response.
The Greenstein model (15) is based on dynamic changes in intracellular ion concentrations and as such displays some degree of time-dependent “drift.” However, it is stable (in terms of both APD and intracellular ion concentrations to within 1.5%) over a period of greater than 50 heartbeats. This degree of stability is comparable, or better, than previous models of this type (34, 60).
Dixon et al. (11) report that Kv1.4 mRNA is present at 16% of the level of Kv4.3 mRNA in the canine LV. However, there appears to be no electrophysiological evidence for a Kv1.4-mediated slowly recovering cumulatively inactivating transient outward current phenotype in canine (41). With respect to the original Greenstein model (15), we have attempted to make only those changes that confer the molecular bases of transmural electrophysiological heterogeneities. Therefore, we have modified the original model of Greenstein et al. (15) to reflect the data of Dixon et al. (11) by decreasing the contribution of the Kv1.4 current but chose not to remove it completely. There is very strong evidence that Kv1.4 encodes the slow component of the transient outward current (41). Transmural heterogeneity of this current has been measured in the ferret and human LV (5, 35). We did not account for this heterogeneity in our model.
Recent experimental investigations suggest that calmodulin binding to KCNQ1, the pore-forming subunit of the IKs channel, is required for protein assembly and conferral of Ca2+ sensitivity to the IKs current (52). The role of calmodulin in the folding and assembly of KCNQ1 is likely to be accounted for indirectly in existing formulations of IKs. However, we do not model a Ca2+ sensitive component of IKs. Although we do not account for this potentially important mechanism of functional regulation of IKs, we demonstrate only a minimal contribution of IKs to repolarization in canine ventricular myocytes under our simulation conditions. Further investigations into AP regulation during elevated adrenergic tone may require these interactions to be incorporated into the model.
One of the consequences of detailed model development and testing is that it reveals where the published experimental results in single myocytes fail to fully account for physiological phenomena. Our results suggest a number of potential opportunities for further investigation, including additional examination of transient outward currents in canine endocardial myocytes and the detailed nature of the transmural heterogeneity of INaCa.
Our model may also be a useful tool to aid in the understanding of arrhythmia mechanisms in patients with Brugada syndrome. This condition is characterized by ST segment elevation, prominent J-waves, and sudden cardiac death (1). Brugada syndrome appears to be linked to SCN5A mutations that result in a reduction of Na+ influx across the right ventricular epicardium (26). It is hypothesized that premature repolarization in this region contributes to electrical heterogeneity of repolarization and creates an electrical substrate conducive to reentrant arrhythmias (1).
We have completed meaningful modifications to the Greenstein model (15) of canine midmyocardial myocyte ECC for epicardial and endocardial cells. Expression levels (current densities) and gating kinetics parameters for IKv43, IKs, INaL, and SERCA were constrained by experimental data from a number of different laboratories, using myocytes isolated from the three transmural locations within the canine LV. Our results suggest that early repolarization currents such as IKv43 and INaL play a major role in shaping the cardiac AP. The model predicted that KChIP2- and Ca2+-dependent control of IKv43 permits a sustained outward current that neutralizes INaL in a rate- and subtype-dependent manner. Both these currents appear to play major roles in the increased AP duration and rate dependence in midmyocardial myocytes. Furthermore, the increased ratio of IKv43 to INaL appears to protect epicardial myocytes, since the incidence of EADs resulting from the SCN5A-I1768V mutation-induced increase in INaL is much reduced.
This work was supported by an American Heart Association Predoctoral Fellowship (to S. N. Flaim), National Biomedical Computation Resource Grant P41RR-08605 (to A. D. McCulloch), and National Science Foundation Grant BES-0506252 (to A. D. McCulloch).
We gratefully acknowledge the generosity of Drs. Joseph Greenstein and Colleen Clancy in providing code for the original midmyocardial myocyte model and INa Markov model, respectively.
↵1 The online version of this article contains supplemental data.
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- Copyright © 2006 by the American Physiological Society