Effects of IKr and IKs Heterogeneity on Action Potential Duration and Its Rate Dependence
A Simulation Study
Background—A growing body of evidence suggests that heterogeneity of ion channel expression and electrophysiological characteristics is an important property of the ventricular myocardium. The 2 components of the delayed rectifier potassium current, IKr (rapid) and IKs (slow), play a dominant role in the repolarization of the action potential and are important determinants of its duration.
Methods and Results—In this report, the effects of heterogeneities of IKr and IKs on action potential duration (APD) and its rate dependence (adaptation) are studied with the use of the LRd model of a mammalian ventricular cell. Results demonstrate the importance of IKs density variations in heterogeneity of repolarization. Cells with reduced IKs (eg, mid-myocardial M cells) display long APD and steep dependence of APD on rate. Mechanistically, accumulation of IKs activation and increased sodium calcium exchange current, INaCa, secondary to Na+ accumulation at a fast rate underlie the steep APD-rate relation of these cells. When cells are electrotonically coupled in a multicellular fiber through resistive gap junction, APD differences are reduced. The results demonstrate strong dependence of APD heterogeneity on the degree of intercellular coupling even in the normal physiological range. Highly reduced coupling maximizes APD heterogeneity.
Conclusions—Heterogeneity of IKs:IKr density strongly influences APD and its rate dependence. However, in the intact myocardium, the degree of gap-junction coupling may be an important factor that determines the manifestation of APD heterogeneity and dispersion of repolarization. The clinical significance of this study is in the context of repolarization abnormalities and associated arrhythmias (eg, long QT syndrome and torsade de pointes).
A growing body of evidence suggests that electrophysiological heterogeneity is an important property of ventricular myocardium. Variability of protein expression and/or electrophysiological function has been reported for the transient outward current,1 the late sodium current,2 and the slow3 and rapid4 components of the delayed rectifier current. Importantly, a subpopulation of cells (mid-myocardial M cells) has been described in the ventricular wall of the guinea pig,5 canine,6 and human.7 The M cells display a longer action potential (AP) duration (APD) and a steeper dependence of APD on rate than the other (epicardial or endocardial) ventricular cell types. These cells also show greater responsiveness to interventions that prolong APD (eg, class III antiarrhythmic drugs)8 and higher susceptibility to the development of arrhythmogenic early afterdepolarizations (EADs).
The 2 components of the delayed rectifier potassium current, IKr (rapid) and IKs (slow), play a dominant role in AP repolarization.9 10 The physiological heterogeneity of repolarization and of APD across the ventricular wall has been associated with heterogeneity in the relative densities of IKr and IKs.3 In particular, IKs density in M cells is lower than in other cell types. The relative densities of functional IKr and IKs channels can be altered by disease (eg, LQT1, LQT5, and LQT2, forms of the long QT syndrome11 12 ) or by class III agents that preferentially block one of these currents.
It is important, therefore, to answer the following question: What are the electrophysiological consequences, in terms of APD and its rate dependence, of heterogeneities in the relative densities of IKr and IKs? In this report, we use theoretical simulations to investigate this phenomenon and its ionic mechanism in isolated cells and in the multicellular tissue.
The theoretical dynamic model of a mammalian ventricular AP (Figure 1A⇓), the LRd model, provides the basis for the simulations in this study.13 14 In this model, the AP is numerically constructed from ionic processes that are formulated on the basis of experimental data obtained mostly from the guinea pig. The model also accounts for processes that regulate ionic concentration changes. IKs was recently shown to display 2 (fast and slow) activation processes.15 The slow time constant is larger than the fast time constant by a factor of 3 to 5. We incorporated this property into the formulation of IKs by introducing an activation Xs2 gate, whose time constant is 4 times that of Xs1 (which corresponds to Xs in Reference 1010 ). The calcium dependence of IKs was modified on the basis of the recent study by Nitta et al.16 Formulation of IKs is provided in the Appendix. Heterogeneities of IKr and IKs densities were introduced by altering their maximum conductances, ḠKr and ḠKs. In view of recent findings regarding continuous Ca2+ release from the sarcoplasmic reticulum (SR), we have also modified the formulation of Ca2+ handling (Appendix). The modified formulation prevents nonphysiological discontinuities and oscillation(s) of [Ca2+]i under extreme conditions. A detailed description of the cell model and its equations is provided in References 10, 13, and 1410 13 14 .
Adaptation curves (the steady-state dependence of APD on rate) were obtained by pacing the cell at a constant cycle length (CL) for 5 minutes to achieve steady state, followed by a step increase to the next CL. APDs were obtained for CL of 300, 500, 800, 1000, 1500, 2000, and 5000 ms. APD was measured between the time of stimulus onset and 90% repolarization (APD90). All computations were performed at a simulated temperature of 37°C.
Multicellular Fiber Model
The theoretical fiber17 (Figure 1B⇑) used in this study is composed of 190 ventricular cells, each of LRd formulation. The fiber contains an endocardial region (cells 1 to 80), M-cell region (cells 81 to 110), and an epicardial region (cells 111 to 190). Gap junction conductance (gj) is homogeneous throughout the fiber and for different simulations varies from 2.5 μS (normal coupling18 ) to 0.025 μS (poor coupling). The fiber is stimulated or paced from cell 1.
Relative Density of IKs and IKr Has a Major Effect on APD and Its Rate Dependence
We have previously shown10 that modulation of IKr or IKs results in dramatic changes in the APD. Figure 2⇓ shows the effect of different IKs:IKr density ratios on APD and its rate dependence. In panel A, IKs density is varied, whereas IKr density is held constant. In panel B, IKs density is maintained, whereas IKr density is varied. Cell type 1 (CT1) serves as control. In panel A, IKs is decreased by 40% and 80% in CT2 and CT3 cells, respectively. In panel B, IKr is similarly decreased in CT4 and CT5 cells. At a basic cycle length (BCL) of 5000 ms, the increase of APD between CT3 and CT1 (IKs variations) is 70%, whereas between CT5 and CT1 (IKr variations) it is only 16%. This dominant effect of IKs is consistent with the experimental findings3 that transmural heterogeneity of IKs density (it is greatly reduced in the M cells) plays a major role in the transmural heterogeneity of APD (IKr density was found to be relatively uniform across the ventricular wall).
Guided by these findings, the following simulations of APD heterogeneity will focus on the role of IKs. It should be mentioned, however, that the simulated variations of IKr in Figure 2B⇑ are likely to have greater effects on APD if they occurred on the background of a significantly smaller IKs. Such a situation can arise when IKr in M cells is suppressed by mutation (eg, LQT2) or by a specific blocking agent.
Figure 3⇓ shows the effect of pacing frequency on APD for 3 different IKs:IKr density ratios (IKr was kept constant). Figure 3A⇓ shows computed steady-state APs at fast and slow pacing frequencies (BCL of 300 and 5000 ms, respectively) in comparison to experimentally recorded APs (Figure 3B⇓) from the 3 regions of the guinea pig ventricular wall.5 The model accurately simulates the APD at the fast and slow rates for the different cell types on the basis of IKs heterogeneity. At a BCL of 300 ms, experimentally measured APDs5 are 102±21, 136±9, and 95±15 ms in epicardial cells, M cells, and endocardial cells, respectively; the corresponding simulated APDs computed from the model are 95, 129, and 96 ms. At a BCL of 5000 ms, measured APDs are 133±14, 185±24, and 135±13 ms in epicardial cells, M cells, and endocardial cells; corresponding simulated APDs are 138, 188, and 139 ms. These values indicate a much longer APD and a slightly more accentuated dependence of APD on stimulation frequency in the M cells compared with either epicardial or endocardial cells.
The presence of transitional cells and heterogeneous APD even within the same cell type (see Figure 1B⇑ of Reference 33 ) indicates that there is no unique value of IKs:IKr density ratio that is associated with each cell type. Instead, there is wide range of density ratios in the myocardium that result in a distribution of APDs and their rate dependence. Figure 4⇓ compiles the effects of different IKs:IKr density ratios on the adaptation of APD to rate changes (adaptation: ΔAPD=APD(slow)−APD(fast)). A decrease in ḠKs:ḠKr (introduced by decreasing ḠKs) increases ΔAPD. The slope of the curve is steep for ḠKs:ḠKr in the range from 5 to 35 (shaded region), indicating a strong effect of IKs:IKr heterogeneity on APD adaptation in this range. It is to be noted that these studies were conducted assuming uniform IKr density, consistent with the experimental findings.3 We choose to focus on this range in the mechanistic investigation of APD adaptation because in this range the effect of changing IKs density is most significant. Interestingly, Figure 5⇓ shows that for ḠKs:ḠKr ratio in this range, the adaptation curves are in very good agreement with experimentally recorded adaptation curves from the human left ventricle.7 Figure 5A⇓ also extends the simulated adaptation curves (dotted) to BCLs ranging from 300 to 1000 ms (a range of human basal heart rates). Experimental data from human myocytes for this range are currently unavailable.
Figure 6⇓ shows simulated APs of the 3 cell types at a BCL of 2000 ms (A), together with the associated IKr (B) and IKs (C). We label the simulated cell types with density ratios ḠKs:ḠKr=23:1, 15:1, and 7:1 as epicardial cells, endocardial cells, and M cells, respectively. It is important to emphasize that this classification is based only on IKs:IKr density differences and the resulting heterogeneity of APD and its rate dependence (the focus of this report). Other differences between these cell types (eg, the presence of a large Ito in epicardial cells of certain species and the associated “spike and dome” morphology of their AP) are not considered here. It is observed from the figure that the APD of the M cell is longer than that of the epicardial cell. IKs is significantly smaller in the M cell (Figure 6C⇓), starting from the early phase of the AP, and attains a much smaller peak magnitude during the course of the AP. IKr (Figure 6B⇓) appears to be smaller during the plateau phase of the AP in the M cell. However, it should be noted that the smaller IKr during this phase merely reflects the different time course of the AP.
Figure 7⇓ shows simulated APs of the 3 cell types for a wide range of BCLs, superimposed to facilitate comparison. At a BCL of 300 ms, all 3 cell types display relatively short APs of similar APD (105, 113, and 135 ms for epicardial cells, endocardial cells, and M cells, respectively). With the slowing of pacing rate, the APD of the M cell is prolonged much more than that of the epicardial or endocardial cells, demonstrating a steeper dependence of APD on rate (greater adaptation). At a BCL of 2000 ms the APD of epicardial cells, endocardial cells, and M cells are 168, 188, and 240 ms, respectively. An important observation is that the effect of IKs heterogeneity (reduced IKs in M cells) is to prolong phase 3 repolarization without significantly affecting the plateau.
IKs and INaCa Play an Important Role in APD Adaptation and in Greater Adaptability of M Cells
The ability of cardiac myocytes to adjust their APD to changes in pacing frequency is termed adaptation. The most prominent effect of decreasing BCL is shortening of APD (Figures 2⇑, 3⇑, and 7⇑). To investigate the mechanism of APD adaptation we examined selected transmembrane currents (IKr, IKs, ICa(L), and INaCa) that play a role during the plateau and repolarization phases of the AP. Figure 8⇓ shows simulated APs (panels A and E); corresponding ionic currents: IKs (D), IKr (F), ICa(L) (G), and INaCa (H); maximal conductance of IKs, ḠKs (B); and IKs activation, Xs1 · Xs2 (C). All parameters are shown for 2 different BCLs (300 ms and 2000 ms). The upstroke of the APs are aligned to facilitate comparison.
IKr is similar at the 2 frequencies (panel F, differences secondary to APD differences should not be considered and currents should be compared at the same Vm). Due to the slow kinetics of IKs, there is residual activation at the onset of the upstroke (arrow in Figure 8C⇑). ḠKs, which depends on intracellular calcium, is not significantly altered (Figure 8B⇑) at the fast rate. For [Ca2+]i=0.12 μmol/L (resting level), ḠKs is 0.6495 ms/μF. At a steady-state BCL of 300 ms, peak [Ca2+]i is 1.5 μmol/L. For this concentration, the value of ḠKs is 0.6912 ms/μF, which is not significantly different from the resting value (an increase by only 6.5%). Therefore elevation of [Ca2+]i at rapid rates has only a minor augmenting effect on IKs. The accumulation of IKs activation caused by incomplete deactivation is therefore the main cause of the larger IKs, which (together with increased outward INaCa; see below) acts to shorten the APD at a shorter BCL (arrow in Figure 8D⇑). The greater cumulative activation of IKs at the time of stimulation for the short BCL is reflected in the instantaneous jump (Figure 8D⇑) in the current at the onset of depolarization. The greater peak IKs at a longer BCL should not be considered in the comparison, as it is merely a consequence of the longer AP (because the membrane is depolarized for a longer duration, IKs is activated for a longer time and, in the absence of inactivation, reaches a greater peak current).
ICa(L) (Figure 8G⇑) has a larger plateau magnitude at the short BCL because of a larger driving force arising from a more negative plateau potential. Because ICa(L) is an inward current, this would act to prolong the AP rather than shorten it. Therefore this current cannot contribute to APD shortening. However, at the short BCL, INaCa (Figure 8H⇑), is predominantly outward (“reverse-mode”) during the plateau phase. INaCa is regulated by [Ca2+]i and [Na+]i. Elevation of [Ca2+]i increases inward INaCa, whereas elevation of [Na+]i increases outward INaCa. Fast pacing results in accumulation of [Ca2+]i and [Na+]i. Our simulations show that the net effect of ion accumulation is a larger outward INaCa than control conditions (no accumulation). The increased outward INaCa (arrow in Figure 8H⇑) acts to shorten the APD at the shorter BCL. Initially, the magnitude of this current appears to be greater than that of IKs (Figure 8D⇑) at the fast rate. However, this current diminishes relatively quickly, reverses direction, and becomes a relatively large depolarizing current. This direction reversal limits the role of INaCa in APD shortening. However, this current still remains a participant in the APD adaptation process.
The results of Figure 8⇑ provide insight into the processes that underlie adaptation. In Figure 9⇓, we attempt to explain the greater adaptability of cells with lower IKs density (eg, M cells). Transmembrane currents computed from epicardial and M cells are compared at 2 different frequencies, fast (BCL=300 ms) and slow (BCL=2000 ms). Figure 9⇓ shows plots of the APs (Figure 9A⇓), the activation kinetics of IKs (Figure 9B⇓), and IKs current (Figure 9C⇓). It is seen from Figure 9B⇓ that at a shorter BCL, Xs1 · Xs2 is greater in the M cell than in the epicardial cell, reflecting a greater degree of activation and of channel availability. Activation is greater because of the longer APD and shorter time (diastolic interval) between complete repolarization and the next stimulus, which results in less deactivation and greater residual activation (Xs1 · Xs2) at the time of the next stimulus. This results in a greater relative increase of IKs at smaller BCL in the M cell (128%) than in the epicardial cell (33%). The greater increase of channel availability on BCL shortening in the M cell is not evident from the plot of IKs itself (Figure 9C⇓), because IKs appears to be smaller in the M cell than in the epicardial cell. This simply reflects the smaller density of IKs in the M cell. The important observation is the greater percentage increase of IKs in the M cell (128% compared with 33% in the epicardial cell) on BCL shortening, which accounts for the greater adaptability. Due to a smaller total repolarizing current in the M cell (reflecting the smaller IKs density), any change in outward current magnitude, albeit small, will have a significant effect on the APD.
INaCa (not shown in Figure 9⇑) also plays a role in the greater adaptability of M cells. The Na+-Ca2+ exchanger is transiently outward during the initial phase of the AP because of a transient increase in [Na+] influx through INa. However, at fast stimulation rates, accumulation of [Na+]i increases the magnitude and duration of the transient outward component of INaCa (as seen in Figure 8H⇑), thereby increasing the total repolarizing current. As stated previously, because of a smaller total repolarizing current in the M cell, any change in this current (in this case due to an increased outward INaCa resulting from an elevated [Na+]i) causes a significant change in APD.
Effect of Gap-Junction Coupling on APD
In the preceding sections we focused on understanding the mechanisms underlying the differences in APD and its rate dependence between isolated cells of the different types. However, in the intact heart, the cells are coupled through gap junctions and are subject to electrotonic interactions that affect their behavior. In this section we study the effects of intercellular coupling on APD and its rate dependence in the context of myocardial heterogeneity.
Figure 10A⇓ shows APDs along a multicellular fiber containing endocardial, M, and epicardial regions for different degrees of gap-junction coupling. The horizontal bold lines indicate APDs obtained from each cell type in isolation, in the absence of gap-junction coupling effects. For normal coupling of gj=2.5 μS (velocity=56 cm/s, typical for propagation along fibers), APD differences (dispersion) between the 3 cell types are greatly reduced compared with the isolated cell case. For this value of gap-junction coupling, the APD difference between M cells and epicardial cells is only 18 ms (differences are computed between middle cells of the respective regions). This is reflected in the figure by the relatively flat APD curve (bold line) along the fiber. However, with reduced coupling, APD differences increase sharply. At gj=0.25 μS (velocity=18 cm/s, typical for propagation transverse to fibers), the APD difference between M cells and epicardial cells increases to 44 ms. When cells are very poorly coupled, APDs approach isolated cell values, resulting in a marked dispersion of APD along the fiber. At gj=0.025 μS (velocity=3.5 cm/s, observed under pathological conditions such as infarction), APD difference between M cells and epicardial cells in the fiber increases to 71 ms (90 ms in the isolated cells).
The importance of intercellular coupling is better illustrated in Figure 10B⇑, which compiles the effects of different gap-junction conductances on APD differences between M cells and epicardial cells in a fiber (ΔAPD between middle cells of each region). A 10-fold decrease in coupling (2.5 to 0.25 μS) increases dispersion of APD (ΔAPD) from 18 to 44 ms, demonstrating a steep dependence of ΔAPD on gap-junction coupling conductance in the physiological range. The simulations of Figure 10⇑ were limited to an action potential elicited by a single stimulus, a protocol that tends to maximize APD differences. This protocol approximates certain pathological conditions such as extreme bradycardia or a postpause AP. Under such circumstances, APD differences would indeed be maximized. In the normal beating heart, the myocardium is subject to periodic stimulation. The following section addresses the issue of APD dispersion during periodic beating by characterizing the rate dependence of APD heterogeneity in the multicellular fiber.
Figure 11⇓ shows the dispersion of APD along the fiber for 3 degrees of gap-junction coupling (top to bottom panels) during fast (BCL=300 ms, bold line) and slow (BCL=2000 ms, dotted line) pacing. It is observed that an increase in rate results in shortening of APD in all the 3 cell types. It is also observed that at the faster rate, APD differences along the fiber (dispersion) are reduced. The reduced dispersion is reflected in the flattening of the APD curve along the fiber at the fast rate compared with the slow rate. This behavior is similar to that of the isolated cells, in which at fast rates APDs of the 3 cell types converge (Figures 2⇑ and 7⇑). The mechanism of rate-dependent shortening of APD in the multicellular fiber is the same as in the isolated cells, that is, accumulation of IKs and a greater outward INaCa at fast rates.
This study examines the effects of IKr and IKs heterogeneities on APD and its rate dependence and investigates the ionic mechanisms that underlie these phenomena. There is growing evidence that heterogeneities of these currents exist not only transmurally across the ventricular wall6 but also in different regions of the ventricle.4 The significance of this study lies in this broad context of heterogeneities in channel density, although special emphasis is on transmural heterogeneity (the presence of M cells in the mid-myocardium), a case that has been extensively studied and very well characterized experimentally.
Our results demonstrate that changes in IKs:IKr density ratios result in heterogeneity of the repolarization properties of cells. A smaller density of IKs lengthens APD and results in greater prolongation of APD with slowing of stimulation rate, a behavior typical of the recently characterized M cells in the deep subepicardium. This study provides mechanistic insights into the rate-dependent shortening of APD (adaptation) and the greater adaptability of cells with reduced IKs density (eg, M cells) to changes in rate. Important findings include: (1) The relative density of IKr and IKs plays an important role in determining APD and its rate dependence. A smaller density of IKs can account for the distinct APD characteristics of M cells. (2) IKs and INaCa play an important role in APD adaptation to rate changes and in the greater adaptability of cells with reduced IKs density. (3) APD shortening at fast rates involves accumulation of IKs activation and augmentation of INaCa. Increase in IKs conductance secondary to intracellular Ca2+ accumulation has a negligible effect. (4) When cells are electrotonically coupled, the degree of intercellular (gap-junction) coupling plays a major role in determining APD heterogeneity and its rate dependence in the multicellular tissue. APD dispersion increases sharply with reduced coupling, approaching the isolated cells’ APD differences when coupling is poor. (5) For normal coupling (typical to propagation along fibers), APD dispersion can reach a maximum value of 18 ms. With a 10-fold decrease in coupling (as observed transverse to fibers in the anisotropic myocardium), APD dispersion increases to a maximum value of 44 ms. These values decrease with increasing rate of stimulation.
Small IKs Density Can Account for Distinct APD Characteristics of M Cells: IKs and INaCa Underlie APD Adaptation and Greater Adaptability of M Cells
Rate-dependent shortening of APD is an important property of cardiac myocytes. Abrupt shortening of APD caused by a premature stimulus (APD restitution) has been shown to result from incomplete deactivation of IKr and IKs.10 Steady-state shortening (APD adaptation) is also thought to be mainly due to incomplete deactivation and accumulation of ionic currents, in particular the slow delayed rectifier potassium current, IKs. Jurkiewicz et al19 have measured an increased IKs at fast heart rates, lending support to this hypothesis.
From simulations conducted in this study we have determined that IKs accumulation at fast rates can explain the shortening of APD during adaptation. Because of the slow deactivation kinetics of IKs, there is residual activation at the onset of the succeeding AP that accumulates at fast rates, increasing the probability of the channel being in an open state. This is reflected in an instantaneous jump in IKs, as observed in Figure 8D⇑ (arrows). The resulting greater IKs acts to shorten the APD at fast rates.
An increase in heart rate results in a progressive rise in [Na+]i,20 accompanied by an increase in the strength of contraction and shortening of the AP.21 The INaCa has been implicated in the sodium-induced changes in contraction as well as the rate-dependent shortening of AP.21 As seen in Figure 8H⇑, outward INaCa increases at fast rates during the initial plateau phase of the AP and contributes to the observed rate-dependent shortening of the AP. Other plateau currents (ICa(L) and IKr) do not play an important role in APD adaptation.
M cells have a steeper APD-rate relation than epicardial or endocardial cells. Investigation into this behavior has highlighted the importance of a reduced total repolarizing current in the M cells. As seen in the simulations, rapid pacing causes abbreviation of the APD as the result of increase in the repolarizing currents IKs and INaCa. This is true for all cell types, but the effect on APD is much greater in the M cells because it occurs on the background of a much smaller total repolarizing current.
Importance of Gap-Junction Coupling in Determining APD Heterogeneity in Multicellular Tissue
The unique repolarization properties of isolated M cells are widely accepted; however, controversy still exists over the extent to which heterogeneity in repolarization is expressed across the normal ventricular wall.22 23 This is an important issue with major implications to the mechanism of arrhythmias associated with delayed and presumably nonuniform ventricular repolarization (eg, torsade de pointes). The simulations conducted in this theoretical study, in which gap-junction coupling and ion channels could be simultaneously controlled and systematically varied, provide valuable insights into APD heterogeneity. Our study highlights the important influence of gap-junction coupling on the manifestation of APD heterogeneity in the multicellular tissue. Small changes in intercellular coupling have a profound effect on APD dispersion (Figure 10B⇑). This theoretical finding is consistent with a recent experimental observation made with optically recorded APs.24 Small changes within the physiological range of gap-junction coupling (eg, directional differences caused by anisotropy, or presence of connective tissue septae) result in significant dispersions that are similar to values reported in the literature.23 25 In this regard, experiments designed to investigate the effects of gap-junction coupling (through application of uncouplers or coupling enhancers) could provide important information regarding APD heterogeneity in the intact tissue.
The results reported in this study were obtained mainly from a multicellular fiber consisting of equal segments of cell types. We have also conducted studies with a smaller/larger number of M cells. Results indicate that the smaller the M-cell region, the smaller the APD dispersion. However, increasing the M region beyond 30 cells did not enhance APD dispersion any further.
Significance of IKs:IKr Heterogeneity to Arrhythmogenesis
APD is an important factor in arrhythmogenesis. Heterogeneity of APD and the resulting dispersion of refractoriness across the ventricular wall could provide the substrate for unidirectional block and reentrant arrhythmias.26 In addition, adaptation of APD can influence the degree of head-tail interaction during reentry and the stability of the reentrant circuit.27 As seen in Figures 2⇑, 3⇑, and 7⇑, changes in the density of IKs could result in dramatic changes in APD and its rate dependence. For example, cells with decreased IKs increase APD disproportionately as stimulation rate is decreased. In more general terms, cells with smaller density of IKs are more responsive to pathologies or interventions (eg, the hereditary or acquired long QT syndrome) that cause APD prolongation. The results obtained from the multicellular fiber suggest that a baseline level of APD differences exists even in the normal myocardium. These differences can increase substantially in the presence of reduced intercellular coupling, even if the cellular repolarization properties remain normal. Conversely, the higher susceptibility of M cells to pathologies and interventions that prolong APD suggests that large dispersion can arise in the normally coupled myocardium. Of course, a combination of enhanced cellular heterogeneity and reduced coupling (eg, class III effects in an infarcted heart) can result in extreme levels of APD dispersion.
In the present study, we focus on intrinsic cellular heterogeneities and their interplay with gap-junction coupling in the context of dispersion of repolarization. In the presence of pathologies or interventions that slow repolarization, sufficient APD prolongation can generate EADs,8 28 preferentially in the M cells. Consequently, M cells could become a source of triggered activity and focal arrhythmias.8 The focal mechanism and the enhanced APD heterogeneity introduced by the M cells could act synergistically, with an EAD providing the trigger (a premature stimulus) to a substrate that is predisposed to the development of unidirectional block and reentry caused by large APD dispersion.23 Although the study addresses the issue of IKs/IKr heterogeneity in ventricular myocardium and M cells, it is to be noted that Purkinje cells are also very prone to EAD generation.
Limitations of the Study
Of particular importance to myocardial electrophysiological heterogeneity is the variability in the density of Ito, IKr, and IKs, which are major players in determining the shape and duration of the AP. This study focuses on heterogeneities in IKr and IKs and their effects on APD and its rate dependence. Such heterogeneities have been observed in guinea pig ventricular myocardium, in which Ito is absent.5 The use of a guinea pig–type myocyte model in this study permitted us to investigate the effects of IKr and IKs variations without the complicating influences of Ito. Clearly, the role of Ito in influencing APD and its rate dependence also needs to be investigated, especially in the context of transmural heterogeneity of action potential morphology (“spike and dome” configuration1 ).
It is well established that IKs decays more slowly than IKr in the guinea pig but decays more rapidly than IKr in canine ventricular myocytes. Therefore the conclusions of this study do not necessarily apply to canine myocytes. However, this study shows that rate-dependent shortening of APD results not only from IKs accumulation but also from a greater outward INaCa at rapid rates. It is likely that in the absence of IKs accumulation (eg, in the canine) the main mechanism of rate-dependent APD shortening is a larger outward INaCa at fast rates.
The role of gap-junction coupling in APD heterogeneity was studied in a 1-dimensional fiber. This is a simplified model that allowed us to investigate this phenomenon at the cellular and ionic channel levels and to establish the principle that APD dispersion is highly sensitive to the degree of intercellular coupling. Moreover, 1-dimensional propagation that can be simulated in a 1-dimensional model occurs frequently in the 3-dimensional heart when broad-plane waves are generated. Importantly, this is the situation during normal sinus rhythm in which planar waves created by the Purkinje network propagate from endocardium to epicardium. A similar situation occurs in the wedge preparation used extensively25 to study myocardial heterogeneity. It is possible that the higher degree of connectivity in the 3-dimensional myocardium acts to reduce APD dispersion under conditions of tight coupling. However, the principle of strong dependence of APD dispersion on gap junction coupling should carry over to the 3-dimensional myocardium. It should also be emphasized that local dispersion on a cellular scale is involved in the generation of unidirectional block and possibly reentry. Even in the presence of complex 3-dimensional global wave fronts, local excitation can be 1-dimensional in nature. This is particularly true in the presence of structural complexities and pathologies, such as a narrow fiber connecting islands of surviving tissue in an infarct.
Formulation of IKs
CICR From Junctional SR (JSR)
Recent experimental evidence29 has suggested that the apparent “threshold” for calcium release from the SR is due to the degree of recruitment of local SR release channels. It follows that there is always calcium release triggered by calcium entry, and the release becomes significant as calcium entry increases. In light of these findings we have modified the release criterion such that there is always a small release, which increases with the increase in calcium entry. This is achieved by adding a “tail” to the calcium entry–dependent term of the SR calcium release conductance, Grel (see Reference 13). The modified formulation of the SR release current, Irel, is given below. If Δ[Ca2+]i,2>Δ[Ca2+]i, th 2 ms after the time of Vmax, If 0<Δ[Ca2+]i,2<Δ[Ca2+]i, 2 ms after the time of Vmax, If Δ[Ca2+]i,2≤0 2 ms after the time of Vmax,
Grel=0.0 Δ[Ca2+]i,th=0.242 μmol/L; Km,rel=0.8 μmol/L; τon=τoff=2 ms; Ḡrel=18 ms−1 for voltage clamp simulations; and Ḡrel=60 ms−1 for action potential simulations.
This study was supported by National Institutes of Health grants ROI-49054 and R37-33343 (National Heart, Lung, and Blood Institute) to Y.R.
Presented in part at the 69th Scientific Sessions of the American Heart Association, New Orleans, La, November 10–13, 1996, and published in abstract form (Circulation. 1996;94[suppl I]:I-712 and Biophys J. 1997;72:MP131–MP131).
- Received September 18, 1998.
- Revision received December 7, 1998.
- Accepted January 11, 1999.
- Copyright © 1999 by American Heart Association
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