Mechanism of pacemaking in I(K1)-downregulated myocytes

R-on-T and the initiation of reentry revisited: Integrating old and new concepts

Initiation of reentry requires 2 factors: (1) a triggering event, most commonly focal excitations such as premature ventricular complexes (PVCs); and (2) a vulnerable substrate with regional dispersion of refractoriness and/or excitability, such as occurs during the T wave of the electrocardiogram when some areas of the ventricle have repolarized and recovered excitability but others have not. When the R wave of a PVC coincides in time with the T wave of the previous beat, this timing can lead to unidirectional block and initiation of reentry, known as the R-on-T phenomenon. Classically, the PVC triggering reentry has been viewed as arising focally from 1 region and propagating into another region whose recovery is delayed, resulting in unidirectional conduction block and reentry initiation. However, more recent evidence indicates that PVCs also can arise from the T wave itself. In the latter case, the PVC initiating reentry is not a separate event from the T wave but rather is causally generated from the repolarization gradient that manifests as the T wave. We call the former an "R-to-T" mechanism and the latter an "R-from-T" mechanism, which are initiation mechanisms distinct from each other. Both are important components of the R-on-T phenomenon and need to be taken into account when designing antiarrhythmic strategies. Strategies targeting suppression of triggers alone or vulnerable substrate alone may be appropriate in some instances but not in others. Preventing R-from-T arrhythmias requires suppressing the underlying dynamic tissue instabilities responsible for producing both triggers and substrate vulnerability simultaneously. The same principles are likely to apply to supraventricular arrhythmias.

A Carvedilol Analogue, VK-II-86, Prevents Hypokalaemia-induced Ventricular Arrhythmia through Novel multi-Channel Effects

BACKGROUND AND PURPOSE

QT prolongation and intracellular Ca²⁺ loading with diastolic Ca²⁺ release via ryanodine receptors (RyR2) are the predominant mechanisms underlying hypokalaemia-induced ventricular arrhythmia. We investigated the antiarrhythmic actions of two RyR2 inhibitors: dantrolene and VK-II-86, a carvedilol analogue with no β-blocking activity, in hypokalaemia.

EXPERIMENTAL APPROACH

Surface ECG and ventricular action potentials (APs) were recorded from whole-heart murine Langendorff preparations. Ventricular arrhythmia incidence was compared in hearts perfused with low [K⁺ ], and those pre-treated with dantrolene or VK-II-86. Whole-cell patch clamping was used in murine and canine ventricular cardiomyocytes to study the effects of dantrolene and VK-II-86 on AP parameters in low [K⁺ ] and the effects of VK-II-86 on the inward rectifier current (I_K1 ), late sodium current (I_{Na_L} ) and the L-type Ca²⁺ current (I_Ca ). Effects of VK-II-86 on I_Kr were investigated in transfected HEK-293 cells. A fluorogenic probe quantified the effects of VK-II-86 on oxidative stress in hypokalaemia.

KEY RESULTS

Dantrolene reduced the incidence of ventricular arrhythmias induced by low [K⁺ ] in explanted murine hearts by 94%, whereas VK-II-86 prevented all arrhythmias. VK-II-86 prevented hypokalaemia-induced AP prolongation and depolarization, but did not alter AP parameters in normokalaemia. Hypokalaemia was associated with a significant reduction of I_K1 and I_Kr , and increase in I_Na-L , and I_Ca . VK-II-86 prevented all hypokalaemia-induced changes in ion channel activity and oxidative stress.

CONCLUSIONS AND IMPLICATIONS

VK-II-86 prevents hypokalaemia-induced arrhythmogenesis by normalising calcium homeostasis and repolarization reserve. VK-II-86 may provide an exciting treatment in hypokalaemia and other arrhythmias caused by delayed repolarization or Ca²⁺ overload.

Patch-Clamp Recordings of Action Potentials From Human Atrial Myocytes: Optimization Through Dynamic Clamp

Introduction: Atrial fibrillation (AF) is the most common cardiac arrhythmia. Consequently, novel therapies are being developed. Ultimately, the impact of compounds on the action potential (AP) needs to be tested in freshly isolated human atrial myocytes. However, the frequent depolarized state of these cells upon isolation seriously hampers reliable AP recordings.

Purpose: We assessed whether AP recordings from single human atrial myocytes could be improved by providing these cells with a proper inward rectifier K⁺ current (I_K1), and consequently with a regular, non-depolarized resting membrane potential (RMP), through “dynamic clamp”.

Methods: Single myocytes were enzymatically isolated from left atrial appendage tissue obtained from patients with paroxysmal AF undergoing minimally invasive surgical ablation. APs were elicited at 1 Hz and measured using perforated patch-clamp methodology, injecting a synthetic I_K1 to generate a regular RMP. The injected I_K1 had strong or moderate rectification. For comparison, a regular RMP was forced through injection of a constant outward current. A wide variety of ion channel blockers was tested to assess their modulatory effects on AP characteristics.

Results: Without any current injection, RMPs ranged from −9.6 to −86.2 mV in 58 cells. In depolarized cells (RMP positive to −60 mV), RMP could be set at −80 mV using I_K1 or constant current injection and APs could be evoked upon stimulation. AP duration differed significantly between current injection methods (p < 0.05) and was shortest with constant current injection and longest with injection of I_K1 with strong rectification. With moderate rectification, AP duration at 90% repolarization (APD₉₀) was similar to myocytes with regular non-depolarized RMP, suggesting that a synthetic I_K1 with moderate rectification is the most appropriate for human atrial myocytes. Importantly, APs evoked using each injection method were still sensitive to all drugs tested (lidocaine, nifedipine, E-4031, low dose 4-aminopyridine, barium, and apamin), suggesting that the major ionic currents of the atrial cells remained functional. However, certain drug effects were quantitatively dependent on the current injection approach used.

Conclusion: Injection of a synthetic I_K1 with moderate rectification facilitates detailed AP measurements in human atrial myocytes. Therefore, dynamic clamp represents a promising tool for testing novel antiarrhythmic drugs.

Reciprocal interaction between IK1 and If in biological pacemakers: A simulation study

Pacemaking dysfunction (PD) may result in heart rhythm disorders, syncope or even death. Current treatment of PD using implanted electronic pacemakers has some limitations, such as finite battery life and the risk of repeated surgery. As such, the biological pacemaker has been proposed as a potential alternative to the electronic pacemaker for PD treatment. Experimentally and computationally, it has been shown that bio-engineered pacemaker cells can be generated from non-rhythmic ventricular myocytes (VMs) by knocking out genes related to the inward rectifier potassium channel current (IK1) or by overexpressing hyperpolarization-activated cyclic nucleotide gated channel genes responsible for the "funny" current (If). However, it is unclear if a bio-engineered pacemaker based on the modification of IK1- and If-related channels simultaneously would enhance the ability and stability of bio-engineered pacemaking action potentials. In this study, the possible mechanism(s) responsible for VMs to generate spontaneous pacemaking activity by regulating IK1 and If density were investigated by a computational approach. Our results showed that there was a reciprocal interaction between IK1 and If in ventricular pacemaker model. The effect of IK1 depression on generating ventricular pacemaker was mono-phasic while that of If augmentation was bi-phasic. A moderate increase of If promoted pacemaking activity but excessive increase of If resulted in a slowdown in the pacemaking rate and even an unstable pacemaking state. The dedicated interplay between IK1 and If in generating stable pacemaking and dysrhythmias was evaluated. Finally, a theoretical analysis in the IK1/If parameter space for generating pacemaking action potentials in different states was provided. In conclusion, to the best of our knowledge, this study provides a wide theoretical insight into understandings for generating stable and robust pacemaker cells from non-pacemaking VMs by the interplay of IK1 and If, which may be helpful in designing engineered biological pacemakers for application purposes.

Biological pacemaker: from biological experiments to computational simulation

Pacemaking dysfunction has become a significant disease that may contribute to heart rhythm disorders, syncope, and even death. Up to now, the best way to treat it is to implant electronic pacemakers. However, these have many disadvantages such as limited battery life, infection, and fixed pacing rate. There is an urgent need for a biological pacemaker (bio-pacemaker). This is expected to replace electronic devices because of its low risk of complications and the ability to respond to emotion. Here we survey the contemporary development of the bio-pacemaker by both experimental and computational approaches. The former mainly includes gene therapy and cell therapy, whilst the latter involves the use of multi-scale computer models of the heart, ranging from the single cell to the tissue slice. Up to now, a bio-pacemaker has been successfully applied in big mammals, but it still has a long way from clinical uses for the treatment of human heart diseases. It is hoped that the use of the computational model of a bio-pacemaker may accelerate this process. Finally, we propose potential research directions for generating a bio-pacemaker based on cardiac computational modeling.

A Simulation Study on the Pacing and Driving of the Biological Pacemaker

The research on the biological pacemaker has been very active in recent years. And turning nonautomatic ventricular cells into pacemaking cells is believed to hold the key to making a biological pacemaker. In the study, the inward-rectifier K⁺ current (I_K1) is depressed to induce the automaticity of the ventricular myocyte, and then, the effects of the other membrane ion currents on the automaticity are analyzed. It is discovered that the L-type calcium current (I_CaL) plays a major part in the rapid depolarization of the action potential (AP). A small enough I_CaL would lead to the failure of the automaticity of the ventricular myocyte. Meanwhile, the background sodium current (I_bNa), the background calcium current (I_bCa), and the Na⁺/Ca²⁺ exchanger current (I_NaCa) contribute significantly to the slow depolarization, indicating that these currents are the main supplementary power of the pacing induced by depressing I_K1, while in the 2D simulation, we find that the weak electrical coupling plays a more important role in the driving of a biological pacemaker.

The Cardiac Pacemaker Story-Fundamental Role of the Na+/Ca2+ Exchanger in Spontaneous Automaticity

The electrophysiological mechanism of the sinus node automaticity was previously considered exclusively regulated by the so-called "funny current". However, parallel investigations increasingly emphasized the importance of the Ca²⁺-homeostasis and Na⁺/Ca²⁺ exchanger (NCX). Recently, increasing experimental evidence, as well as insight through mechanistic in silico modeling demonstrates the crucial role of the exchanger in sinus node pacemaking. NCX had a key role in the exciting story of discovery of sinus node pacemaking mechanisms, which recently settled with a consensus on the coupled-clock mechanism after decades of debate. This review focuses on the role of the Na⁺/Ca²⁺ exchanger from the early results and concepts to recent advances and attempts to give a balanced summary of the characteristics of the local, spontaneous, and rhythmic Ca²⁺ releases, the molecular control of the NCX and its role in the fight-or-flight response. Transgenic animal models and pharmacological manipulation of intracellular Ca²⁺ concentration and/or NCX demonstrate the pivotal function of the exchanger in sinus node automaticity. We also highlight where specific hypotheses regarding NCX function have been derived from computational modeling and require experimental validation. Nonselectivity of NCX inhibitors and the complex interplay of processes involved in Ca²⁺ handling render the design and interpretation of these experiments challenging.

Contribution of potassium channels to action potential repolarization of human embryonic stem cell-derived cardiomyocytes

BACKGROUND AND PURPOSE

The electrophysiological properties of human pluripotent stem cell-derived cardiomyocytes (CMs) have not yet been characterized in a syncytial context. This study systematically characterized the contributions of different repolarizing potassium currents in human embryonic stem cell-derived CMs (hESC-CMs) during long-term culture as cell monolayers.

EXPERIMENTAL APPROACH

The H9 hESC line was differentiated to CMs and plated to form confluent cell monolayers. Optical mapping was used to record the action potentials (APs) and conduction velocity (CV) during electrophysiological and pharmacological experiments. RT-PCR and Western blot were used to detect the presence and expression levels of ion channel subunits.

KEY RESULTS

Long-term culture of hESC-CMs led to shortened AP duration (APD), faster repolarization rate, and increased CV. Selective block of I_Kr , I_Ks , I_K1 , and I_Kur significantly affected AP repolarization and APD in a concentration- and culture time-dependent manner. Baseline variations in APD led to either positive or negative APD dependence of drug response. Chromanol 293B produced greater relative AP prolongation in mid- and late-stage cultures, while DPO-1 had more effect in early-stage cultures. CV in cell monolayers in early- and late-stage cultures was most susceptible to slowing by E-4031 and BaCl₂ respectively.

CONCLUSIONS AND IMPLICATIONS

I_Kr , I_Ks , I_K1 , and I_Kur all play an essential role in the regulation of APD and CV in hESC-CMs. During time in culture, increased expression of I_Kr and I_K1 helps to accelerate repolarization, shorten APD, and increase CV. We identified a new pro-arrhythmic parameter, positive APD dependence of ion channel block, which can increase APD and repolarization gradients.

Ionic and cellular mechanisms underlying TBX5/PITX2 insufficiency-induced atrial fibrillation: Insights from mathematical models of human atrial cells

Transcription factors TBX5 and PITX2 involve in the regulation of gene expression of ion channels and are closely associated with atrial fibrillation (AF), the most common cardiac arrhythmia in developed countries. The exact cellular and molecular mechanisms underlying the increased susceptibility to AF in patients with TBX5/PITX2 insufficiency remain unclear. In this study, we have developed and validated a novel human left atrial cellular model (TPA) based on the ten Tusscher-Panfilov ventricular cell model to systematically investigate how electrical remodeling induced by TBX5/PITX2 insufficiency leads to AF. Using our TPA model, we have demonstrated that spontaneous diastolic depolarization observed in atrial myocytes with TBX5-deletion can be explained by altered intracellular calcium handling and suppression of inward-rectifier potassium current (IK1). Additionally, our computer simulation results shed new light on the novel cellular mechanism underlying AF by indicating that the imbalance between suppressed outward current IK1 and increased inward sodium-calcium exchanger current (INCX) resulted from SR calcium leak leads to spontaneous depolarizations. Furthermore, our simulation results suggest that these arrhythmogenic triggers can be potentially suppressed by inhibiting sarcoplasmic reticulum (SR) calcium leak and reversing remodeled IK1. More importantly, this study has clinically significant implications on the drugs used for maintaining SR calcium homeostasis, whereby drugs such as dantrolene may confer significant improvement for the treatment of AF patients with TBX5/PITX2 insufficiency.

Potassium currents in the heart: functional roles in repolarization, arrhythmia and therapeutics

This is the second of the two White Papers from the fourth UC Davis Cardiovascular Symposium Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias (3-4 March 2016), a biennial event that brings together leading experts in different fields of cardiovascular research. The theme of the 2016 symposium was 'K⁺ channels and regulation', and the objectives of the conference were severalfold: (1) to identify current knowledge gaps; (2) to understand what may go wrong in the diseased heart and why; (3) to identify possible novel therapeutic targets; and (4) to further the development of systems biology approaches to decipher the molecular mechanisms and treatment of cardiac arrhythmias. The sessions of the Symposium focusing on the functional roles of the cardiac K⁺ channel in health and disease, as well as K⁺ channels as therapeutic targets, were contributed by Ye Chen-Izu, Gideon Koren, James Weiss, David Paterson, David Christini, Dobromir Dobrev, Jordi Heijman, Thomas O'Hara, Crystal Ripplinger, Zhilin Qu, Jamie Vandenberg, Colleen Clancy, Isabelle Deschenes, Leighton Izu, Tamas Banyasz, Andras Varro, Heike Wulff, Eleonora Grandi, Michael Sanguinetti, Donald Bers, Jeanne Nerbonne and Nipavan Chiamvimonvat as speakers and panel discussants. This article summarizes state-of-the-art knowledge and controversies on the functional roles of cardiac K⁺ channels in normal and diseased heart. We endeavour to integrate current knowledge at multiple scales, from the single cell to the whole organ levels, and from both experimental and computational studies.

A Dynamical Threshold for Cardiac Delayed Afterdepolarization-Mediated Triggered Activity

Ventricular myocytes are excitable cells whose voltage threshold for action potential (AP) excitation is ∼-60 mV at which INa is activated to give rise to a fast upstroke. Therefore, for a short stimulus pulse to elicit an AP, a stronger stimulus is needed if the resting potential lies further away from the INa threshold, such as in hypokalemia. However, for an AP elicited by a long duration stimulus or a diastolic spontaneous calcium release, we observed that the stimulus needed was lower in hypokalemia than in normokalemia in both computer simulations and experiments of rabbit ventricular myocytes. This observation provides insight into why hypokalemia promotes calcium-mediated triggered activity, despite the resting potential lying further away from the INa threshold. To understand the underlying mechanisms, we performed bifurcation analyses and demonstrated that there is a dynamical threshold, resulting from a saddle-node bifurcation mainly determined by IK1 and INCX. This threshold is close to the voltage at which IK1 is maximum, and lower than the INa threshold. After exceeding this dynamical threshold, the membrane voltage will automatically depolarize above the INa threshold due to the large negative slope of the IK1-V curve. This dynamical threshold becomes much lower in hypokalemia, especially with respect to calcium, as predicted by our theory. Because of the saddle-node bifurcation, the system can automatically depolarize even in the absence of INa to voltages higher than the ICa,L threshold, allowing for triggered APs in single myocytes with complete INa block. However, because INa is important for AP propagation in tissue, blocking INa can still suppress premature ventricular excitations in cardiac tissue caused by calcium-mediated triggered activity. This suppression is more effective in normokalemia than in hypokalemia due to the difference in dynamical thresholds.

Pacemaker Created in Human Ventricle by Depressing Inward-Rectifier K⁺ Current: A Simulation Study

Cardiac conduction disorders are common diseases which cause slow heart rate and syncope. The best way to treat these diseases by now is to implant electronic pacemakers, which, yet, have many disadvantages, such as the limited battery life and infection. Biopacemaker has been expected to replace the electronic devices. Automatic ventricular myocytes (VMs) could show pacemaker activity, which was induced by depressing inward-rectifier K⁺ current (I_K1). In this study, a 2D model of human biopacemaker was created from the ventricular endocardial myocytes. We examined the stability of the created biopacemaker and investigated its driving capability by finding the suitable size and spatial distribution of the pacemaker for robust pacing and driving the surrounding quiescent cardiomyocytes. Our results suggest that the rhythm of the pacemaker is similar to that of the single cell at final stable state. The driving force of the biopacemaker is closely related to the pattern of spatial distribution of the pacemaker.

Maturing human pluripotent stem cell-derived cardiomyocytes in human engineered cardiac tissues

Engineering functional human cardiac tissue that mimics the native adult morphological and functional phenotype has been a long held objective. In the last 5 years, the field of cardiac tissue engineering has transitioned from cardiac tissues derived from various animal species to the production of the first generation of human engineered cardiac tissues (hECTs), due to recent advances in human stem cell biology. Despite this progress, the hECTs generated to date remain immature relative to the native adult myocardium. In this review, we focus on the maturation challenge in the context of hECTs, the present state of the art, and future perspectives in terms of regenerative medicine, drug discovery, preclinical safety testing and pathophysiological studies.

Mechanisms of ventricular arrhythmias: from molecular fluctuations to electrical turbulence

Ventricular arrhythmias have complex causes and mechanisms. Despite extensive investigation involving many clinical, experimental, and computational studies, effective biological therapeutics are still very limited. In this article, we review our current understanding of the mechanisms of ventricular arrhythmias by summarizing the state of knowledge spanning from the molecular scale to electrical wave behavior at the tissue and organ scales and how the complex nonlinear interactions integrate into the dynamics of arrhythmias in the heart. We discuss the challenges that we face in synthesizing these dynamics to develop safe and effective novel therapeutic approaches.

Size and ionic currents of unexcitable cells coupled to cardiomyocytes distinctly modulate cardiac action potential shape and pacemaking activity in micropatterned cell pairs

BACKGROUND

Cardiac cell therapies can yield electric coupling of unexcitable donor cells to host cardiomyocytes with functional consequences that remain unexplored.

METHODS AND RESULTS

We micropatterned cell pairs consisting of a neonatal rat ventricular myocyte (NRVM) coupled to an engineered human embryonic kidney 293 (HEK293) cell expressing either connexin-43 (Cx43 HEK) or inward rectifier potassium channel 2.1 (Kir2.1) and Cx43 (Kir2.1+Cx43 HEK). The NRVM-HEK contact length was fixed yielding a coupling strength of 68.9±9.7 nS, whereas HEK size was systematically varied. With increase in Cx43 HEK size, NRVM maximal diastolic potential was reduced from -71.7±0.6 mV in single NRVMs to -35.1±1.3 mV in pairs with an HEK:NRVM cell surface area ratio of 1.7±0.1, whereas the action potential upstroke ([dV(m)/dt](max)) and duration decreased to 1.6±0.7% and increased to 177±32% in single NRVM values, respectively (n=21 cell pairs). Pacemaking occurred in all NRVM-Cx43 HEK pairs with cell surface area ratios of 1.1 to 1.9. In contrast, NRVMs, coupled with Kir2.1+Cx43 HEKs of increasing size, had similar maximal diastolic potentials, exhibited no spontaneous activity, and showed a gradual decrease in action potential duration (n=23). Furthermore, coupling single NRVMs to a dynamic clamp model of HEK cell ionic current reproduced the cardiac maximal diastolic potentials and pacemaking rates recorded in cell pairs, whereas reproducing changes in (dV(m)/dt)(max) and action potential duration required coupling to an HEK model that also included cell membrane capacitance.

CONCLUSIONS

Size and ionic currents of unexcitable cells electrically coupled to cardiomyocytes distinctly affect cardiac action potential shape and initiation with important implications for the safety of cardiac cell and gene therapies.

Nonlinear dynamics in cardiology

The dynamics of many cardiac arrhythmias, as well as the nature of transitions between different heart rhythms, have long been considered evidence of nonlinear phenomena playing a direct role in cardiac arrhythmogenesis. In most types of cardiac disease, the pathology develops slowly and gradually, often over many years. In contrast, arrhythmias often occur suddenly. In nonlinear systems, sudden changes in qualitative dynamics can, counterintuitively, result from a gradual change in a system parameter-this is known as a bifurcation. Here, we review how nonlinearities in cardiac electrophysiology influence normal and abnormal rhythms and how bifurcations change the dynamics. In particular, we focus on the many recent developments in computational modeling at the cellular level that are focused on intracellular calcium dynamics. We discuss two areas where recent experimental and modeling work has suggested the importance of nonlinearities in calcium dynamics: repolarization alternans and pacemaker cell automaticity.

Evolution of spiral and scroll waves of excitation in a mathematical model of ischaemic border zone

Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity that can rise on the boundary of cardiac cell network upon its recovery from ischaemia-like conditions. The main factors included in our analysis are macroscopic gradients of the cell-to-cell coupling and cell excitability and microscopic heterogeneity of individual cells. The interplay between these factors allows one to explain how spirals form, drift together with the moving boundary, get transiently pinned to local inhomogeneities, and finally penetrate into the bulk of the well-coupled tissue where they reach macroscopic scale. The asymptotic theory of the drift of spiral and scroll waves based on response functions provides explanation of the drifts involved in this mechanism, with the exception of effects due to the discreteness of cardiac tissue. In particular, this asymptotic theory allows an extrapolation of 2D events into 3D, which has shown that cells within the border zone can give rise to 3D analogues of spirals, the scroll waves. When and if such scroll waves escape into a better coupled tissue, they are likely to collapse due to the positive filament tension. However, our simulations have shown that such collapse of newly generated scrolls is not inevitable and that under certain conditions filament tension becomes negative, leading to scroll filaments to expand and multiply leading to a fibrillation-like state within small areas of cardiac tissue.

Cytosolic calcium accumulation and delayed repolarization associated with ventricular arrhythmias in a guinea pig model of Andersen-Tawil syndrome

BACKGROUND

Andersen-Tawil syndrome (ATS1)-associated ventricular arrhythmias are initiated by frequent, hypokalemia-exacerbated, triggered activity. Previous ex vivo studies in drug-induced Andersen-Tawil syndrome (DI-ATS1) models have proposed that arrhythmia propensity in DI-ATS1 derives from cytosolic Ca(2+) ([Ca(2+)](i)) accumulation leading to increased triggered activity.

OBJECTIVE

The purpose of this study was to test the hypothesis that elevated [Ca(2+)](i) with concomitant APD prolongation, rather than APD dispersion, underlies arrhythmia propensity during DI-ATS1.

METHODS

DI-ATS1 was induced in isolated guinea pig ventricles by perfusion of 2 mM KCl Tyrode solution containing 10 μM BaCl(2). APD and [Ca(2+)](i) from the anterior epicardium were quantified by ratiometric optical voltage (di-4-ANEPPS) or Ca(2+) (Indo-1) mapping during right ventricular pacing with or without the ATP-sensitive potassium channel opener pinacidil (15 μM).

RESULTS

APD gradients under all conditions were insufficient for arrhythmia induction by programmed stimulation. However, 38% of DI-ATS1 preparations experienced ventricular tachycardias (VTs), and all preparations experienced a high incidence of premature ventricular complexes (PVCs). Pinacidil decreased APD and APD dispersion and reduced VTs (to 6%), and PVC frequency (by 79.5%). However, PVC frequency remained significantly greater relative to control (0.5% ± 0.3% of DI-ATS1). Importantly, increased arrhythmia propensity during DI-ATS1 was associated with diastolic [Ca(2+)](i) accumulation and increased [Ca(2+)](i) transient amplitudes. Pinacidil partially attenuated the former but did not alter the latter.

CONCLUSION

The study data suggest that arrhythmias during DI-ATS1 may be a result of triggered activity secondary to prolonged APD and altered [Ca(2+)](i) cycling and less likely dependent on large epicardial APD gradients forming the substrate for reentry. Therefore, therapies aimed at reducing [Ca(2+)](i) rather than APD gradients may prove effective in treatment of ATS1.

Kir 2.1 channelopathies: the Andersen-Tawil syndrome

As a multisystem disorder, Andersen-Tawil syndrome (ATS) is rather unique in the family of channelopathies. The full spectrum of the disease is characterized by ventricular arrhythmias, dysmorphic features, and periodic paralysis. Most ATS patients have a mutation in the ion channel gene, KCNJ2, which encodes the inward rectifier K+ channel Kir2.1, a component of the inward rectifier IK1.IK1 provides repolarizing current during the most terminal phase of repolarization and is the primary conductance controlling the diastolic membrane potential. Thus, ATS is a disorder of cardiac repolarization. The chapter will discuss the most recent data concerning the genetic, cellular, and clinical data underlying this unique disorder.

Electrotonic loading of anisotropic cardiac monolayers by unexcitable cells depends on connexin type and expression level

Understanding how electrotonic loading of cardiomyocytes by unexcitable cells alters cardiac impulse conduction may be highly relevant to fibrotic heart disease. In this study, we optically mapped electrical propagation in confluent, aligned neonatal rat cardiac monolayers electrotonically loaded with cardiac fibroblasts, control human embryonic kidney (HEK-293) cells, or HEK-293 cells genetically engineered to overexpress the gap junction proteins connexin-43 or connexin-45. Gap junction expression and function were assessed by immunostaining, immunoblotting, and fluorescence recovery after photobleaching and were correlated with the optically mapped propagation of action potentials. We found that neonatal rat ventricular fibroblasts negative for the myofibroblast marker smooth muscle alpha-actin expressed connexin-45 rather than connexin-43 or connexin-40, weakly coupled to cardiomyocytes, and, without significant depolarization of cardiac resting potential, slowed cardiac conduction to 75% of control only at high (>60%) coverage densities, similar to loading effects found from HEK-293 cells expressing similar levels of connexin-45. In contrast, HEK-293 cells with connexin-43 expression similar to that of cardiomyocytes significantly decreased cardiac conduction velocity and maximum capture rate to as low as 22% and 25% of control values, respectively, while increasing cardiac action potential duration to 212% of control and cardiac resting potential from -71.6 +/- 4.9 mV in controls to -65.0 +/- 3.8 mV. For all unexcitable cell types and coverage densities, velocity anisotropy ratio remained unchanged. Despite the induced conduction slowing, none of the loading cell types increased the proportion of spontaneously active monolayers. These results signify connexin isoform and expression level as important contributors to potential electrical interactions between unexcitable cells and myocytes in cardiac tissue.

Genesis and regulation of the heart automaticity

The heart automaticity is a fundamental physiological function in higher organisms. The spontaneous activity is initiated by specialized populations of cardiac cells generating periodical electrical oscillations. The exact cascade of steps initiating the pacemaker cycle in automatic cells has not yet been entirely elucidated. Nevertheless, ion channels and intracellular Ca(2+) signaling are necessary for the proper setting of the pacemaker mechanism. Here, we review the current knowledge on the cellular mechanisms underlying the generation and regulation of cardiac automaticity. We discuss evidence on the functional role of different families of ion channels in cardiac pacemaking and review recent results obtained on genetically engineered mouse strains displaying dysfunction in heart automaticity. Beside ion channels, intracellular Ca(2+) release has been indicated as an important mechanism for promoting automaticity at rest as well as for acceleration of the heart rate under sympathetic nerve input. The potential links between the activity of ion channels and Ca(2+) release will be discussed with the aim to propose an integrated framework of the mechanism of automaticity.

Development of functional I f channels in mMSCs after transfection with mHCN4: effects on cell morphology and mechanical activity in vitro

OBJECTIVE

To study the functional properties of I(f) channels and the changes in mechanical activity of mouse mesenchymal stem cells (mMSCs) transfected with mHCN4.

METHODS

mMSCs were purified by using CD11b-immunomagnetic microbeads and transfected with pMSCV-mHCN4-EGFP or pMSCV-EGFP. We examined the kinetic characteristics of the mHCN4 channel. The morphological changes of positively transfected mMSCs were investigated at the same time.

RESULTS

The I(f) current recorded from the experimental group was sensitive to extracellular Cs(+) (-44.5 +/- 4.2 vs. -5.5 +/- 1.0 pA/pF, p < 0.001). The half-maximal activation was -99.0 +/- 5.8 mV. The time constant of activation was 451 +/- 61 ms under -140 mV. The control cells did not show the current under the same conditions. The absolute values of half-maximal activation decreased in the presence of cAMP or cGMP in the experimental group (-78.6 +/- 10.4 and -85.7 +/- 8.6 vs. -99.0 +/- 5.8 mV, respectively, p < 0.05). mMSCs transfected with pMSCV-mHCN4-EGFP could form spontaneous beating cells. Extracellular Cs(+) decreased the beating rate significantly (196 +/- 50 vs. 66 +/- 23 bmp, p < 0.01).

CONCLUSIONS

Functional I(f) channels can be reconstructed in mMSCs infected with mHCN4. mMSCs modified by successful transfection with mHCN4 can differentiate so as to develop spontaneous mechanical activity.

Generation and escape of local waves from the boundary of uncoupled cardiac tissue

We aim to understand the formation of abnormal waves of activity from myocardial regions with diminished cell-to-cell coupling. En route to this goal, we studied the behavior of a heterogeneous myocyte network in which a sharp coupling gradient was placed under conditions of increasing network automaticity. Experiments were conducted in monolayers of neonatal rat cardiomyocytes using heptanol and isoproterenol as means of altering cell-to-cell coupling and automaticity, respectively. Experimental findings were explained and expanded using a modified Beeler-Reuter numerical model. The data suggest that the combination of a heterogeneous substrate, a gradient of coupling, and an increase in oscillatory activity of individual cells creates a rich set of behaviors associated with self-generated spiral waves and ectopic sources. Spiral waves feature a flattened shape and a pin-unpin drift type of tip motion. These intercellular waves are action-potential based and can be visualized with either voltage or calcium transient measurements. A source/load mismatch on the interface between the boundary and well-coupled layers can lock wavefronts emanating from both ectopic sources and rotating waves within the inner layers of the coupling gradient. A numerical approach allowed us to explore how 1), the spatial distribution of cells, 2), the amplitude and dispersion of cell automaticity, and 3), the speed at which the coupling gradient moves in space affect wave behavior, including its escape into well-coupled tissue.

Computer modelling of the sinoatrial node

Over the past decades patch-clamp experiments have provided us with detailed information on the different types of ion channels that are present in the cardiac cell membrane. Sophisticated cardiac cell models based on these data can help us understand how the different types of ion channels act together to produce the cardiac action potential. In the field of biological pacemaker engineering, such models provide important instruments for the assessment of the functional implications of changes in density of specific ion channels aimed at producing stable pacemaker activity. In this review, an overview is given of the progress made in cardiac cell modelling, with particular emphasis on the development of sinoatrial (SA) nodal cell models. Also, attention is given to the increasing number of publicly available tools for non-experts in computer modelling to run cardiac cell models.

Mechanisms of intrinsic beating variability in cardiac cell cultures and model pacemaker networks

Heart rate variability (HRV) exhibits fluctuations characterized by a power law behavior of its power spectrum. The interpretation of this nonlinear HRV behavior, resulting from interactions between extracardiac regulatory mechanisms, could be clinically useful. However, the involvement of intrinsic variations of pacemaker rate in HRV has scarcely been investigated. We examined beating variability in spontaneously active incubating cultures of neonatal rat ventricular myocytes using microelectrode arrays. In networks of mathematical model pacemaker cells, we evaluated the variability induced by the stochastic gating of transmembrane currents and of calcium release channels and by the dynamic turnover of ion channels. In the cultures, spontaneous activity originated from a mobile focus. Both the beat-to-beat movement of the focus and beat rate variability exhibited a power law behavior. In the model networks, stochastic fluctuations in transmembrane currents and stochastic gating of calcium release channels did not reproduce the spatiotemporal patterns observed in vitro. In contrast, long-term correlations produced by the turnover of ion channels induced variability patterns with a power law behavior similar to those observed experimentally. Therefore, phenomena leading to long-term correlated variations in pacemaker cellular function may, in conjunction with extracardiac regulatory mechanisms, contribute to the nonlinear characteristics of HRV.

Sudden cardiac death in Andersen-Tawil syndrome

Andersen-Tawil syndrome (ATS) is an autosomal dominant or sporadic disorder characterized by periodic paralysis, dysmorphic features, and ventricular arrhythmias. Although ventricular tachycardia burden is quite high sudden cardiac death in ATS is rare. We describe a case with sudden cardiac death due to electrical storm a few days after ICD implantation in KCNJ2 mutation-negative ATS.

Developmental changes in cardiomyocytes differentiated from human embryonic stem cells: a molecular and electrophysiological approach

Cardiomyocytes derived from human embryonic stem cells constitute a promising cell source for the regeneration of damaged hearts. The assessment of their in vitro functional properties is mandatory to envisage appropriate cardiac cell-based therapies. In this study, we characterized human embryonic stem cell-derived cardiomyocytes over a 3-month period, using patch-clamp or intracellular recordings to assess their functional maturation and reverse transcriptase-polymerase chain reaction to evaluate the expression of ion channel-encoding subunits. I(to1) and I(K1), the transient outward and inward rectifier potassium currents, were present in cardiomyocytes only, whereas the rapid delayed rectifier potassium current (I(Kr)), pacemaker current (I(f)), and L-type calcium current (I(Ca,L)) could be recorded both in undifferentiated human embryonic stem cells and in cardiomyocytes. Most of the currents underwent developmental maturation in cardiomyocytes, as assessed by modifications in current density (I(to1), I(K1), and I(Ca,L)) and properties (I(f)). Ion-channel mRNAs were always present when the current was recorded. Intracellular recordings in spontaneously beating clusters of cardiomyocytes revealed changes in action potential parameters and in response to pharmacological tools according to time of differentiation. In summary, human embryonic stem cell-derived cardiomyocytes mature over time during in vitro differentiation, approaching an adult phenotype. Disclosure of potential conflicts of interest is found at the end of this article.

Chronotropic response of cultured neonatal rat ventricular myocytes to short-term fluid shear

Ventricular myocytes are continuously exposed to fluid shear in vivo by relative movement of laminar sheets and adjacent cells. Preliminary observations have shown that neonatal myocytes respond to fluid shear by increasing their beating rate, which could have an arrhythmogenic effect under elevated shear conditions. The objective of this study is to investigate the characteristics of the fluid shear response in cultured myocytes and to study selected potential mechanisms. Cultured neonatal rat ventricular myocytes that were spontaneously beating were subjected to low shear rates (5-50/s) in a fluid flow chamber using standard culture medium. The beating rate was measured from digital microscopic recordings. The myocytes reacted to low shear rates by a graded and reversible increase in their spontaneous beating rate of up to 500%. The response to shear was substantially attenuated in the presence of the beta-adrenergic agonist isoproterenol (by 86+/-8%), as well as after incubation with integrin-blocking RGD peptides (by 92+/-8%). The results suggest that the beta-adrenergic signaling pathway and integrin activation, which are known to interact, may play an important role in the response mechanism.

Effects of pacemaker currents on creation and modulation of human ventricular pacemaker: theoretical study with application to biological pacemaker engineering

A cardiac biological pacemaker (BP) has been created by suppression of the inward rectifier K+ current ( IK1) or overexpression of the hyperpolarization-activated current ( Ih). We theoretically investigated the effects of incorporating Ih, T-type Ca2+ current ( ICa,T), sustained inward current ( Ist), and/or low-voltage-activated L-type Ca2+ channel current ( ICa,LD) on 1) creation of BP cells, 2) robustness of BP activity to electrotonic loads of nonpacemaking (NP) cells, and 3) BP cell ability to drive NP cells. We used a single-cell model for human ventricular myocytes (HVMs) and also coupled-cell models composed of BP and NP cells. Bifurcation structures of the model cells were explored during changes in conductance of the currents and gap junction. Incorporating the pacemaker currents did not yield BP activity in HVM with normal IK1 but increased the critical IK1 conductance for BP activity to emerge. Expressing Ih appeared to be most helpful in facilitating creation of BP cells via IK1 suppression. In the coupled-cell model, Ist significantly enlarged the gap conductance ( GC) region where stable BP cell pacemaking and NP cell driving occur, reducing the number of BP cells required for robust pacemaking and driving. In contrast, Ih enlarged the GC region of pacemaking and driving only when IK1 of the NP cell was relatively low. ICa,T or ICa,LD exerted effects similar to those of Ist but caused shrinkage or irregularity of BP oscillations. These findings suggest that expressing Ist most effectively improves the structural stability of BPs to electrotonic loads and the BP ability to drive the ventricle.

Modeling of IK1 mutations in human left ventricular myocytes and tissue

Elucidation of the cellular basis of arrhythmias in ion channelopathy disorders is complicated by the inherent difficulties in studying human cardiac tissue. Thus we used a computer modeling approach to study the mechanisms of cellular dysfunction induced by mutations in inward rectifier potassium channel (Kir)2.1 that cause Andersen-Tawil syndrome (ATS). ATS is an autosomal dominant disorder associated with ventricular arrhythmias that uncommonly degenerate into the lethal arrhythmia torsade de pointes. We simulated the cellular and tissue effects of a potent disease-causing mutation D71V Kir2.1 with mathematical models of human ventricular myocytes and a bidomain model of transmural conduction. The D71V Kir2.1 mutation caused significant action potential duration prolongation in subendocardial, midmyocardial, and subepicardial myocytes but did not significantly increase transmural dispersion of repolarization. Simulations of the D71V mutation at shorter cycle lengths induced stable action potential alternans in midmyocardial, but not subendocardial or subepicardial cells. The action potential alternans was manifested as an abbreviated QRS complex in the transmural ECG, the result of action potential propagation failure in the midmyocardial tissue. In addition, our simulations of D71V mutation recapitulate several key ECG features of ATS, including QT prolongation, T-wave flattening, and QRS widening. Thus our modeling approach faithfully recapitulates several features of ATS and provides a mechanistic explanation for the low frequency of torsade de pointes arrhythmia in ATS.

Creating a cardiac pacemaker by gene therapy

While electronic cardiac pacing in its various modalities represents standard of care for treatment of symptomatic bradyarrhythmias and heart failure, it has limitations ranging from absent or rudimentary autonomic modulation to severe complications. This has prompted experimental studies to design and validate a biological pacemaker that could supplement or replace electronic pacemakers. Advances in cardiac gene therapy have resulted in a number of strategies focused on beta-adrenergic receptors as well as specific ion currents that contribute to pacemaker function. This article reviews basic pacemaker physiology, as well as studies in which gene transfer approaches to develop a biological pacemaker have been designed and validated in vivo. Additional requirements and refinements necessary for successful biopacemaker function by gene transfer are discussed.

Bioartificial sinus node constructed via in vivo gene transfer of an engineered pacemaker HCN Channel reduces the dependence on electronic pacemaker in a sick-sinus syndrome model

BACKGROUND

The normal cardiac rhythm originates in the sinoatrial (SA) node that anatomically resides in the right atrium. Malfunction of the SA node leads to various forms of arrhythmias that necessitate the implantation of electronic pacemakers. We hypothesized that overexpression of an engineered HCN construct via somatic gene transfer offers a flexible approach for fine-tuning cardiac pacing in vivo.

METHODS AND RESULTS

Using various electrophysiological and mapping techniques, we examined the effects of in situ focal expression of HCN1-DeltaDeltaDelta, the S3-S4 linker of which has been shortened to favor channel opening, on impulse generation and conduction. Single left ventricular cardiomyocytes isolated from guinea pig hearts preinjected with the recombinant adenovirus Ad-CMV-GFP-IRES-HCN1-DeltaDeltaDelta in vivo uniquely exhibited automaticity with a normal firing rate (237+/-12 bpm). High-resolution ex vivo optical mapping of Ad-CGI-HCN1-DeltaDeltaDelta-injected Langendorff-perfused hearts revealed the generation of spontaneous action potentials from the transduced region in the left ventricle. To evaluate the efficacy of our approach for reliable atrial pacing, we generated a porcine model of sick-sinus syndrome by guided radiofrequency ablation of the native SA node, followed by implantation of a dual-chamber electronic pacemaker to prevent bradycardia-induced hemodynamic collapse. Interestingly, focal transduction of Ad-CGI-HCN1-DeltaDeltaDelta in the left atrium of animals with sick-sinus syndrome reproducibly induced a stable, catecholamine-responsive in vivo "bioartificial node" that exhibited a physiological heart rate and was capable of reliably pacing the myocardium, substantially reducing electronic pacing.

CONCLUSIONS

The results of the present study provide important functional and mechanistic insights into cardiac automaticity and have further refined an HCN gene-based therapy for correcting defects in cardiac impulse generation.

Recreating an artificial biological pacemaker: Insights from a theoretical model

BACKGROUND

Normal cardiac rhythm is critically dependent on the sinoatrial (SA) node, the natural biological pacemaker. Although recent studies have focused on the development of "artificial" biological pacemakers using gene transfer, less is known about the functional consequences of such interventions.

OBJECTIVE

The purpose of this study was to investigate the electrophysiological consequences of two approaches used to create a biological pacemaker: overexpression of the hyperpolarization-activated cyclic nucleotide gated channel (HCN "pacemaker" channels) and suppression of the inward-rectifier potassium current, I(K1).

METHODS

We used a linear multicellular Luo-Rudy (LRd) AP model consisting of 130 ventricular cells connected by resistive gap junctions. To induce automaticity, I(K1) current was reduced or I(f) (HCN) current was introduced in endocardial and midmyocardial (M) cells.

RESULTS

Similar to the previously published results for a single LRd model, myocyte I(K1) suppression induced automaticity in the fiber. While introduction of I(f) also resulted in automaticity, the main differences between I(K1) suppression and I(f) expression were (1) a relatively more gradual phase 4 depolarization with HCN expression, (2) stabilization of cycle lengths during I(K1) suppression, but not during HCN expression, and (3) responsiveness to beta-adrenergic stimulation during HCN expression, but not during I(K1) suppression. Upon further investigation, we found that cycle length instability during HCN expression was primarily due to a gradual reduction of intracellular potassium ([K(+)](i)) from its baseline value of 142 mM to 120 mM in 600 beats and subsequent alteration of potassium-dependent ionic currents. A twofold increase in HCN expression also led to a similar behavior. We attribute this decrease in [K(+)](i) to a large I(K1) during phase 4 depolarization. When intracellular [K(+)](i) loss was minimized, cycle lengths stabilized during HCN expression.

CONCLUSIONS

Our results help to further understand the electrophysiologic consequences as well as some of the challenges associated with the creation of biological pacemakers using HCN and I(K1) gene transfer strategies.

Endogenous driving and synchronization in cardiac and uterine virtual tissues: bifurcations and local coupling

Cardiac and uterine muscle cells and tissue can be either autorhythmic or excitable. These behaviours exchange stability at bifurcations produced by changes in parameters, which if spatially localized can produce an ectopic pacemaking focus. The effects of these parameters on cell dynamics have been identified and quantified using continuation algorithms and by numerical solutions of virtual cells. The ability of a compact pacemaker to drive the surrounding excitable tissues depends on both the size of the pacemaker and the strength of electrotonic coupling between cells within, between, and outside the pacemaking region. We investigate an ectopic pacemaker surrounded by normal excitable tissue. Cell-cell coupling is simulated by the diffusion coefficient for voltage. For uniformly coupled tissues, the behaviour of the hybrid tissue can take one of the three forms: (i) the surrounding tissue electrotonically suppresses the pacemaker; (ii) depressed rate oscillatory activity in the pacemaker but no propagation; and (iii) pacemaker driving propagations into the excitable region. However, real tissues are heterogeneous with spatial changes in cell-cell coupling. In the gravid uterus during early pregnancy, cells are weakly coupled, with the cell-cell coupling increasing during late pregnancy, allowing synchronous contractions during labour. These effects are investigated for a caricature uterine tissue by allowing both excitability and diffusion coefficient to vary stochastically with space, and for cardiac tissues by spatial gradients in the diffusion coefficient.

Dynamical mechanisms of pacemaker generation in IK1-downregulated human ventricular myocytes: insights from bifurcation analyses of a mathematical model

Dynamical mechanisms of the biological pacemaker (BP) generation in human ventricular myocytes were investigated by bifurcation analyses of a mathematical model. Equilibrium points (EPs), periodic orbits, stability of EPs, and bifurcation points were determined as functions of bifurcation parameters, such as the maximum conductance of inward-rectifier K+ current (I(K1)), for constructing bifurcation diagrams. Stable limit cycles (BP activity) abruptly appeared around an unstable EP via a saddle-node bifurcation when I(K1) was suppressed by 84.6%. After the bifurcation at which a stable EP disappears, the I(K1)-reduced system has an unstable EP only, which is essentially important for stable pacemaking. To elucidate how individual sarcolemmal currents contribute to EP instability and BP generation, we further explored the bifurcation structures of the system during changes in L-type Ca2+ channel current (I(Ca,L)), delayed-rectifier K+ currents (I(K)), or Na(+)/Ca2+ exchanger current (I(NaCa)). Our results suggest that 1), I(Ca,L) is, but I(K) or I(NaCa) is not, responsible for EP instability as a requisite to stable BP generation; 2), I(K) is indispensable for robust pacemaking with large amplitude, high upstroke velocity, and stable frequency; and 3), I(NaCa) is the dominant pacemaker current but is not necessarily required for the generation of spontaneous oscillations.

Genesis of ectopic waves: role of coupling, automaticity, and heterogeneity

Many arrhythmias are believed to be triggered by ectopic sources arising from the border of the ischemic tissue. However, the development of ectopic activity from individual sources to a larger mass of cardiac tissue remains poorly understood. To address this critical issue, we used monolayers of neonatal rat cardiomyocytes to create conditions that promoted progression of ectopic activity from single cells to the network that consisted of hundreds of cells. To explain complex spatiotemporal patterns observed in these experiments we introduced a new theoretical framework. The framework's main feature is a parameter space diagram, which uses cell automaticity and coupling as two coordinates. The diagram allows one to depict network behavior, quantitatively address the heterogeneity factor, and evaluate transitions between different regimes. The well-organized wave trains were observed at moderate and high cell coupling values and network heterogeneity was found to be qualitatively unimportant for these regimes. In contrast, at lower values of coupling, spontaneous ectopic activity led to the appearance of fragmented ectopic waves. For these regimes, network heterogeneity played an essential role. The ectopic waves occasionally gave rise to spiral activity in two different regions within the parameter space via two distinct mechanisms. Together, our results suggest that localized ectopic waves represent an essential step in the progression of ectopic activity. These studies add to the understanding of initiation and progression of arrhythmias and can be applied to other phenomena that deal with assemblies of coupled oscillators.

An ionic model for rhythmic activity in small clusters of embryonic chick ventricular cells

We recorded transmembrane potential in whole cell recording mode from small clusters (2-4 cells) of spontaneously beating 7-day embryonic chick ventricular cells after 1-3 days in culture and investigated effects of the blockers D-600, diltiazem, almokalant, and Ba2+. Electrical activity in small clusters is very different from that in reaggregates of several hundred embryonic chick ventricular cells, e.g., TTX-sensitive fast upstrokes in reaggregates vs. TTX-insensitive slow upstrokes in small clusters (maximum upstroke velocity approximately 100 V/s vs. approximately 10 V/s). On the basis of our voltage- and current-clamp results and data from the literature, we formulated a Hodgkin-Huxley-type ionic model for the electrical activity in these small clusters. The model contains a Ca2+ current (ICa), three K+ currents (IKs, IKr, and IK1), a background current, and a seal-leak current. ICa generates the slow upstroke, whereas IKs, IKr, and IK1 contribute to repolarization. All the currents contribute to spontaneous diastolic depolarization, e.g., removal of the seal-leak current increases the interbeat interval from 392 to 535 ms. The model replicates the spontaneous activity in the clusters as well as the experimental results of application of blockers. Bifurcation analysis and simulations with the model predict that annihilation and single-pulse triggering should occur with partial block of ICa. Embryonic chick ventricular cells have been used as an experimental model to investigate various aspects of spontaneous beating of cardiac cells, e.g., mutual synchronization, regularity of beating, and spontaneous initiation and termination of reentrant rhythms; our model allows investigation of these topics through numerical simulation.