Unidirectional block between isolated rabbit ventricular cells coupled by a variable resistance

Fibrosis and Conduction Abnormalities as Basis for Overlap of Brugada Syndrome and Early Repolarization Syndrome

Brugada syndrome and early repolarization syndrome are both classified as J-wave syndromes, with a similar mechanism of arrhythmogenesis and with the same basis for genesis of the characteristic electrocardiographic features. The Brugada syndrome is now considered a conduction disorder based on subtle structural abnormalities in the right ventricular outflow tract. Recent evidence suggests structural substrate in patients with the early repolarization syndrome as well. We propose a unifying mechanism based on these structural abnormalities explaining both arrhythmogenesis and the electrocardiographic changes. In addition, we speculate that, with increasing technical advances in imaging techniques and their spatial resolution, these syndromes will be reclassified as structural heart diseases or cardiomyopathies.

Stabilizer Cell Gene Therapy: A Less-Is-More Strategy to Prevent Cardiac Arrhythmias

BACKGROUND

In cardiac gene therapy to improve contractile function, achieving gene expression in the majority of cardiac myocytes is essential. In preventing cardiac arrhythmias, however, this goal may not be as important since transduction efficiencies as low as 40% suppressed ventricular arrhythmias in genetically modified mice with catecholaminergic polymorphic ventricular tachycardia.

METHODS

Using computational modeling, we simulated 1-, 2-, and 3-dimensional tissue under a variety of conditions to test the ability of genetically engineered nonarrhythmogenic stabilizer cells to suppress triggered activity due to delayed or early afterdepolarizations.

RESULTS

Due to source-sink relationships in cardiac tissue, a minority (20%-50%) of randomly distributed stabilizer cells engineered to be nonarrhythmogenic can suppress the ability of arrhythmogenic cells to generate delayed and early afterdepolarizations-related arrhythmias. Stabilizer cell gene therapy strategy can be designed to correct a specific arrhythmogenic mutation, as in the catecholaminergic polymorphic ventricular tachycardia mice studies, or more generally to suppress delayed or early afterdepolarizations from any cause by overexpressing the inward rectifier K channel Kir2.1 in stabilizer cells.

CONCLUSIONS

This promising antiarrhythmic strategy warrants further testing in experimental models to evaluate its clinical potential.

German Cardiac Society Working Group on Cellular Electrophysiology state-of-the-art paper: impact of molecular mechanisms on clinical arrhythmia management

Cardiac arrhythmias remain a common challenge and are associated with significant morbidity and mortality. Effective and safe rhythm control strategies are a primary, yet unmet need in everyday clinical practice. Despite significant pharmacological and technological advances, including catheter ablation and device-based therapies, the development of more effective alternatives is of significant interest to increase quality of life and to reduce symptom burden, hospitalizations and mortality. The mechanistic understanding of pathophysiological pathways underlying cardiac arrhythmias has advanced profoundly, opening up novel avenues for mechanism-based therapeutic approaches. Current management of arrhythmias, however, is primarily guided by clinical and demographic characteristics of patient groups as opposed to individual, patient-specific mechanisms and pheno-/genotyping. With this state-of-the-art paper, the Working Group on Cellular Electrophysiology of the German Cardiac Society aims to close the gap between advanced molecular understanding and clinical decision-making in cardiac electrophysiology. The significance of cellular electrophysiological findings for clinical arrhythmia management constitutes the main focus of this document. Clinically relevant knowledge of pathophysiological pathways of arrhythmias and cellular mechanisms of antiarrhythmic interventions are summarized. Furthermore, the specific molecular background for the initiation and perpetuation of atrial and ventricular arrhythmias and mechanism-based strategies for therapeutic interventions are highlighted. Current "hot topics" in atrial fibrillation are critically appraised. Finally, the establishment and support of cellular and translational electrophysiology programs in clinical rhythmology departments is called for to improve basic-science-guided patient management.

Applications of Dynamic Clamp to Cardiac Arrhythmia Research: Role in Drug Target Discovery and Safety Pharmacology Testing

Dynamic clamp, a hybrid-computational-experimental technique that has been used to elucidate ionic mechanisms underlying cardiac electrophysiology, is emerging as a promising tool in the discovery of potential anti-arrhythmic targets and in pharmacological safety testing. Through the injection of computationally simulated conductances into isolated cardiomyocytes in a real-time continuous loop, dynamic clamp has greatly expanded the capabilities of patch clamp outside traditional static voltage and current protocols. Recent applications include fine manipulation of injected artificial conductances to identify promising drug targets in the prevention of arrhythmia and the direct testing of model-based hypotheses. Furthermore, dynamic clamp has been used to enhance existing experimental models by addressing their intrinsic limitations, which increased predictive power in identifying pro-arrhythmic pharmacological compounds. Here, we review the recent advances of the dynamic clamp technique in cardiac electrophysiology with a focus on its future role in the development of safety testing and discovery of anti-arrhythmic drugs.

Restitution characteristics of His bundle and working myocardium in isolated rabbit hearts

The Purkinje system (PS) and the His bundle have been recently implicated as an important driver of the rapid activation rate after 1-2 minutes of ventricular fibrillation (VF). It is unknown whether activations during VF propagate through the His-Purkinje system to other portions of the the working myocardium (WM). Little is known about restitution characteristic differences between the His bundle and working myocardium at short cycle lengths. In this study, rabbit hearts (n = 9) were isolated, Langendorff-perfused, and electromechanically uncoupled with blebbistatin (10 μM). Pacing pulses were delivered directly to the His bundle. By using standard glass microelectrodes, action potentials duration (APD) from the His bundle and WM were obtained simultaneously over a wide range of stimulation cycle lengths (CL). The global F-test indicated that the two restitution curves of the His bundle and the WM are statistically significantly different (P<0.05). Also, the APD of the His bundle was significantly shorter than that of WM throughout the whole pacing course (P<0.001). The CL at which alternans developed in the His bundle vs. the WM were shorter for the His bundle (134.2±13.1ms vs. 148.3±13.3ms, P<0.01) and 2:1 block developed at a shorter CL in the His bundle than in WM (130.0±10.0 vs. 145.6±14.2ms, P<0.01). The His bundle APD was significantly shorter than that of WM under both slow and rapid pacing rates, which suggest that there may be an excitable gap during VF and that the His bundle may conduct wavefronts from one bundle branch to the other at short cycle lengths and during VF.

Electrophysiological properties of computational human ventricular cell action potential models under acute ischemic conditions

Acute myocardial ischemia is one of the main causes of sudden cardiac death. The mechanisms have been investigated primarily in experimental and computational studies using different animal species, but human studies remain scarce. In this study, we assess the ability of four human ventricular action potential models (ten Tusscher and Panfilov, 2006; Grandi et al., 2010; Carro et al., 2011; O'Hara et al., 2011) to simulate key electrophysiological consequences of acute myocardial ischemia in single cell and tissue simulations. We specifically focus on evaluating the effect of extracellular potassium concentration and activation of the ATP-sensitive inward-rectifying potassium current on action potential duration, post-repolarization refractoriness, and conduction velocity, as the most critical factors in determining reentry vulnerability during ischemia. Our results show that the Grandi and O'Hara models required modifications to reproduce expected ischemic changes, specifically modifying the intracellular potassium concentration in the Grandi model and the sodium current in the O'Hara model. With these modifications, the four human ventricular cell AP models analyzed in this study reproduce the electrophysiological alterations in repolarization, refractoriness, and conduction velocity caused by acute myocardial ischemia. However, quantitative differences are observed between the models and overall, the ten Tusscher and modified O'Hara models show closest agreement to experimental data.

Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking

We used the Dynamic Clamp technique for i) comparative validation of conflicting computational models of the hyperpolarization-activated funny current, If, and ii) quantification of the role of If in mediating autonomic modulation of heart rate. Experimental protocols based on the injection of a real-time recalculated synthetic If current in sinoatrial rabbit cells were developed. Preliminary results of experiments mimicking the autonomic modulation of If demonstrated the need for a customization procedure to compensate for cellular heterogeneity. For this reason, we used a cell-specific approach, scaling the maximal conductance of the injected current based on the cell's spontaneous firing rate. The pacemaking rate, which was significantly reduced after application of Ivabradine, was restored by the injection of synthetic current based on the Severi-DiFrancesco formulation, while the injection of synthetic current based on the Maltsev-Lakatta formulation did not produce any significant variation. A positive virtual shift of the If activation curve, mimicking the Isoprenaline effects, led to a significant increase in pacemaking rate (+17.3 ± 6.7%, p < 0.01), although of lower magnitude than that induced by real Isoprenaline (+45.0 ± 26.1%). Similarly, a negative virtual shift of the activation curve significantly lowered the pacemaking rate (-11.8 ± 1.9%, p < 0.001), as did the application of real Acetylcholine (-20.5 ± 5.1%). The Dynamic Clamp approach, applied to the If study in cardiomyocytes for the first time and rate-adapted to manage intercellular variability, indicated that: i) the quantitative description of the If current in the Severi-DiFrancesco model accurately reproduces the effects of the real current on rabbit sinoatrial cell pacemaking rate and ii) a significant portion (50-60%) of the physiological autonomic rate modulation is due to the shift of the If activation curve.

A proposed route to independent measurements of tight junction conductance at discrete cell junctions

Direct recording of tight junction permeability is of pivotal importance to many biologic fields. Previous approaches bear an intrinsic disadvantage due to the difficulty of separating tight junction conductance from nearby membrane conductance. Here, we propose the design of Double whole-cell Voltage Clamp - Ion Conductance Microscopy (DVC-ICM) based on previously demonstrated potentiometric scanning of local conductive pathways. As proposed, DVC-ICM utilizes two coordinated whole-cell patch-clamps to neutralize the apical membrane current during potentiometric scanning, which in models described here will profoundly enhance the specificity of tight junction recording. Several potential pitfalls are considered, evaluated and addressed with alternative countermeasures.

Stochastic spontaneous calcium release events trigger premature ventricular complexes by overcoming electrotonic load

AIMS

Premature ventricular complexes (PVCs) due to spontaneous calcium (Ca) release (SCR) events at the cell level can precipitate ventricular arrhythmias. However, the mechanistic link between SCRs and PVC formation remains incompletely understood. The aim of this study was to investigate the conditions under which delayed afterdepolarizations resulting from stochastic subcellular SCR events can overcome electrotonic source-sink mismatch, leading to PVC initiation.

METHODS AND RESULTS

A stochastic subcellular-scale mathematical model of SCR was incorporated in a realistic model of the rabbit ventricles and Purkinje system (PS). Elevated levels of diastolic sarcoplasmic reticulum Ca(2+) (CaSR) were imposed until triggered activity was observed, allowing us to compile statistics on probability, timing, and location of PVCs. At CaSR≥ 1500 µmol/L PVCs originated in the PS. When SCR was incapacitated in the PS, PVCs also emerged in the ventricles, but at a higher CaSR (≥1550 µmol/L) and with longer waiting times. For each model configuration tested, the probability of PVC occurrence increased from 0 to 100% within a well-defined critical CaSR range; this transition was much more abrupt in organ-scale models (∼50 µmol/L CaSR range) than in the tissue strand (∼100 µmol/L) or single-cell (∼450 µmol/L) models. Among PVCs originating in the PS, ∼68% were located near Purkinje-ventricular junctions (<1 mm).

CONCLUSION

SCR events overcome source-sink mismatch to trigger PVCs at a critical CaSR threshold. Above this threshold, PVCs emerge due to increased probability and reduced variability in timing of SCR events, leading to significant diastolic depolarization. Sites of lower electronic load, such as the PS, are preferential locations for triggering.

Role of sinoatrial node architecture in maintaining a balanced source-sink relationship and synchronous cardiac pacemaking

Normal heart rhythm (sinus rhythm) depends on regular activity of the sinoatrial node (SAN), a heterogeneous collection of specialized myocytes in the right atrium. SAN cells, in general, possess a unique electrophysiological profile that promotes spontaneous electrical activity (automaticity). However, while automaticity is required for normal pacemaking, it is not necessarily sufficient. Less appreciated is the importance of the elaborate structure of the SAN complex for proper pacemaker function. Here, we review the important structural features of the SAN with a focus on how these elements help manage a precarious balance between electrical charge generated by the SAN (“source”) and the charge needed to excite the surrounding atrial tissue (“sink”). We also discuss how compromised “source-sink” balance due, for example to fibrosis, may promote SAN dysfunction, characterized by slow and/or asynchronous pacemaker activity and even failure, in the setting of cardiovascular disease (e.g., heart failure, atrial fibrillation). Finally, we discuss implications of the “source-sink” balance in the SAN complex for cell and gene therapies aimed at creating a biological pacemaker as replacement or bridge to conventional electronic pacemakers.

Dynamic clamp as a tool to study the functional effects of individual membrane currents

Today, the patch-clamp technique is the main technique in electrophysiology to record action potentials or membrane current from isolated cells, using a patch pipette to gain electrical access to the cell. The common recording modes of the patch-clamp technique are current clamp and voltage clamp. In the current clamp mode, the current injected through the patch pipette is under control while the free-running membrane potential of the cell is recorded. Current clamp allows for measurements of action potentials that may either occur spontaneously or in response to an injected stimulus current. In voltage clamp mode, the membrane potential is held at a set level through a feedback circuit, which allows for the recording of the net membrane current at a given membrane potential.A less common configuration of the patch-clamp technique is the dynamic clamp. In this configuration, a specific non-predetermined membrane current can be added to or removed from the cell while it is in free-running current clamp mode. This current may be computed in real time, based on the recorded action potential of the cell, and injected into the cell. Instead of being computed, this current may also be recorded from a heterologous expression system such as a HEK-293 cell that is voltage-clamped by the free-running action potential of the cell ("dynamic action potential clamp"). Thus, one may directly test the effects of an additional or mutated membrane current, a synaptic current or a gap junctional current on the action potential of a patch-clamped cell. In the present chapter, we describe the dynamic clamp on the basis of its application in cardiac cellular electrophysiology.

MEMBRANE AND TISSUE LEVEL CONTRIBUTIONS TO PURKINJE-VENTRICULAR INTERACTIONS: A MODEL STUDY

Purkinje-to-ventricular (P-to-V) propagation and electrotonic modulation of repolarization at discrete Purkinje-ventricular junctions (PVJs) depend on differences in the ionic currents and tissue structure of the P network and the V myocardium. We used computer simulations to assess these membrane and tissue level contributions to P-V interactions. At the membrane level, we used the DiFrancesco-Noble membrane equations to model P ionic kinetics and the Luo-Rudy dynamic membrane equations to model V ionic kinetics. At the tissue level, we modeled the P network as a layer of branching cables, and we modeled a single myocardial sheet with an anisotropic layer of excitable cells. P-to-V propagation was enhanced at the tissue level when multiple wavefronts in the branching P network collided at the PVJ. At the membrane level, P-to-V propagation was enhanced by a reduced transient outward current (Ito) in the P layer. Repolarization at the PVJ was also modulated by both membrane and tissue level contributions. Under nominal conditions, action potential duration (APD) shortened in the P layer and prolonged in the V layer. However, when the V mass was reduced, both P and V cell APDs shortened during coupling with nominal Ito. Subsequent Ito inhibition restored coupling-induced prolongation of the V action potential in the reduced V mass. These results suggest that under physiologic conditions, both membrane and tissue level contributions to P-V interactions are important, while membrane level contributions become even more important under pathologies that reduce the difference in P and V tissue size, particularly in the setting of healed myocardial infarction.

So little source, so much sink: requirements for afterdepolarizations to propagate in tissue

How early (EADs) and delayed afterdepolarizations (DADs) overcome electrotonic source-sink mismatches in tissue to trigger premature ventricular complexes remains incompletely understood. To study this question, we used a rabbit ventricular action potential model to simulate tissues in which a central area of contiguous myocytes susceptible to EADs or DADs was surrounded by unsusceptible tissue. In 1D tissue with normal longitudinal conduction velocity (0.55 m/s), the numbers of contiguous susceptible myocytes required for an EAD and a barely suprathreshold DAD to trigger a propagating action potential were 70 and 80, respectively. In 2D tissue, these numbers increased to 6940 and 7854, and in 3D tissue to 696,910 and 817,280. These numbers were significantly decreased by reduced gap junction conductance, simulated fibrosis, reduced repolarization reserve and heart failure electrical remodeling. In conclusion, the source-sink mismatch in well-coupled cardiac tissue powerfully protects the heart from arrhythmias due to sporadic afterdepolarizations. Structural and electrophysiological remodeling decrease these numbers significantly but still require synchronization mechanisms for EADs and DADs to overcome the robust protective effects of source-sink mismatch.

How different two almost identical action potentials can be: a model study on cardiac repolarization

Spatial heterogeneity in the properties of ion channels generates spatial dispersion of ventricular repolarization, which is modulated by gap junctional coupling. However, it is possible to simulate conditions in which local differences in excitation properties are electrophysiologically silent and only play a role in pathological states. We use a numerical procedure on the Luo-Rudy phase 1 model of the ventricular action potential (AP1) in order to find a modified set of model parameters which generates an action potential profile (AP2) almost identical to AP1. We show that, although the two waveforms elicited from resting conditions as a single AP are very similar and belong to membranes sharing similar passive electrical properties, the modified membrane generating AP2 is a weaker current source than the one generating AP1, has different sensitivity to up/down-regulation of ion channels and to extracellular potassium, and a different electrical restitution profile. We study electrotonic interaction of AP1- and AP2- type membranes in cell pairs and in cable conduction, and find differences in source-sink properties which are masked in physiological conditions and become manifest during intercellular uncoupling or partial block of ion channels, leading to unidirectional block and spatial repolarization gradients. We provide contour plot representations that summarize differences and similarities. The present report characterizes an inverse problem in cardiac cells, and strengthen the recently emergent notion that a comprehensive characterization and validation of cell models and their components are necessary in order to correctly understand simulation results at higher levels of complexity.

Enhancement of ventricular gap-junction coupling by rotigaptide

AIMS

Rotigaptide is proposed to exert its anti-arrhythmic effects by improving myocardial gap-junction communication. To directly investigate the mechanisms of rotigaptide action, we treated cultured neonatal murine ventricular cardiomyocytes with clinical pharmacological doses of rotigaptide and directly determined its effects on gap-junctional currents.

METHODS AND RESULTS

Neonatal murine ventricular cardiomyocytes were enzymatically isolated and cultured for 1-4 days. Primary culture cell pairs were subjected to dual whole cell patch-clamp procedures to directly measure gap-junctional currents (I(j)) and voltage (V(j)). Rotigaptide (0-350 nM) was applied overnight or acutely perfused into 35 mm culture dishes. Rotigaptide (35-100 nM) acutely and chronically increased the resting gap-junction conductance (g(j)), and normalized steady-state minimum g(j) (G(min)) by 5-20%. Higher concentrations produced a diminishing response, which mimics the observed therapeutic efficacy of the drug. The inactivation kinetics was similarly slowed in a therapeutic concentration-dependent manner without affecting the V(j) dependence of inactivation or recovery. The effects of 0-100 nM rotigaptide on ventricular g(j) during cardiac action potential propagation were accurately modelled by computer simulations which demonstrate that clinically effective concentrations of rotigaptide can partially reverse conduction slowing due to decreases in g(j) and inactivation.

CONCLUSION

These results demonstrate that therapeutic concentrations of rotigaptide increase the resting gap-junction conductance and reduce the magnitude and kinetics of steady-state inactivation in a concentration-dependent manner. Rotigaptide may be effective in treating re-entrant forms of cardiac arrhythmias by improving conduction and preventing the formation of re-entrant circuits in partially uncoupled myocardium.

Dynamic clamp analyses of cardiac, endocrine, and neural function

The dynamic clamp introduces artificial conductances into cells to simulate electrical coupling, votage-dependent, leak, and synaptic conductances. This review describes how the dynamic clamp has been used to address various questions in the cardiac, endocrine, and nervous systems.

Dynamic clamp: a powerful tool in cardiac electrophysiology

Dynamic clamp is a collection of closely related techniques that have been employed in cardiac electrophysiology to provide direct answers to numerous research questions regarding basic cellular mechanisms of action potential formation, action potential transfer and action potential synchronization in health and disease. Building on traditional current clamp, dynamic clamp was initially used to create virtual gap junctions between isolated myocytes. More recent applications include the embedding of a real pacemaking myocyte in a simulated network of atrial or ventricular cells and the insertion of virtual ion channels, either simulated in real time or simultaneously recorded from an expression system, into the membrane of an isolated myocyte. These applications have proven that dynamic clamp, which is characterized by the real-time evaluation and injection of simulated membrane current, is a powerful tool in cardiac electrophysiology. Here, each of the three different experimental configurations used in cardiac electrophysiology is reviewed. Also, directions are given for the implementation of dynamic clamp in the cardiac electrophysiology laboratory. With the growing interest in the application of dynamic clamp in cardiac electrophysiology, it is anticipated that dynamic clamp will also prove to be a powerful tool in basic research on biological pacemakers and in identification of specific ion channels as targets for drug development.

Combined electric field and gap junctions on propagation of action potentials in cardiac muscle and smooth muscle in PSpice simulation

Propagation of action potentials in cardiac muscle and smooth muscle were simulated using the PSpice program. Excitation was transmitted from cell to cell along a strand of 6 cells (cardiac muscle) or 10 cells (smooth muscle) either not connected (control) or connected by low-resistance tunnels (gap-junction connexons). A significant negative cleft potential (V(jv) ) develops in the narrow junctional cleft when the pre-JM fires. V(jc) depolarizes the postjunctional membrane (post-JM) to threshold by a patch-clamp action. With few connecting tunnels, cell-to-cell transmission by the EF mechanism was facilitated. With many tunnels, propagation was dominated by the low-resistance mechanism, and propagation velocity (theta) became very fast and nonphysiological. In conclusion, when the 2 mechanisms for cell-to-cell transfer of excitation were combined, the two mechanisms facilitated each other in a synergistic manner. When there were many connecting tunnels, the tunnel mechanism was dominant.

Action potential modulation of connexin40 gap junctional conductance

Connexin40 (Cx40) is abundantly expressed in the atrial myocardium, ventricular conduction system, and vascular endothelial and smooth muscle cells of the mammalian cardiovascular system. Rapid conduction through cardiac tissues depends on electrotonic transfer of the action potential between neighboring cells. To determine whether transjunctional voltages (Vj) elicited by an action potential can modulate conductance of Cx40 gap junctions, simulated myocardial action potentials were applied as voltage-clamp waveforms to Cx40 gap junctions expressed in mouse neuro2A (N2A) cells. Junctional currents resembled the action potential morphology but declined by >50% from peak to near-constant plateau values. Kinetics of Cx40 voltage gating were examined at peak voltages > or =100 mV, and decay time constants changed e-fold per 17.6 mV for Vj > +/-40 mV. Junctional conductance recovered during phase 3 repolarization and early diastole to initial values. These phasic changes in junctional conductance were due to rapid decay kinetics, increasing to tens of milliseconds at peak Vj of 130 mV, and the increase in the steady-state conductance curve as Vj returned toward 0 mV. Time-dependent conductance curves for Cx40 were modeled with one inactivation and two recovery Vj-dependent components. There was a temporal correlation between development of conduction delay or block and the inactivation phase of junctional conductance. Likewise, recovery of junctional conductance was coincident with recovery from refractoriness, suggesting that gap junctions may play a role in the genesis and propagation of cardiac arrhythmias.

The dynamic clamp comes of age

The dynamic clamp uses computer simulation to introduce artificial membrane or synaptic conductances into biological neurons and to create hybrid circuits of real and model neurons. In the ten years since it was first developed, the dynamic clamp has become a widely used tool for the study of neural systems at the cellular and circuit levels. This review describes recent state-of-the-art implementations of the dynamic clamp and summarizes insights gained through its use, ranging from the role of voltage-dependent conductances in shaping neuronal activity to the effects of synaptic dynamics on network behavior and the impact of in vivo-like input on neuronal information processing.

Transverse propagation of action potentials between parallel chains of cardiac muscle and smooth muscle cells in PSpice simulations

BACKGROUND

We previously examined transverse propagation of action potentials between 2 and 3 parallel chain of cardiac muscle cells (CMC) simulated using the PSpice program. The present study was done to examine transverse propagation between 5 parallel chains in an expanded model of CMC and smooth muscle cells (SMC).

METHODS

Excitation was transmitted from cell to cell along a strand of 5 cells not connected by low-resistance tunnels (gap-junction connexons). The entire surface membrane of each cell fired nearly simultaneously, and nearly all the propagation time was spent at the cell junctions, the junctional delay time being about 0.3-0.5 ms (CMC) or 0.8-1.6 ms (SMC). A negative cleft potential (Vjc) develops in the narrow junctional clefts, whose magnitude depends on the radial cleft resistance (Rjc), which depolarizes the postjunctional membrane (post-JM) to threshold. Propagation velocity (theta) increased with amplitude of Vjc. Therefore, one mechanism for the transfer of excitation from one cell to the next is by the electric field (EF) that is generated in the junctional cleft when the pre-JM fires. In the present study, 5 parallel stands of 5 cells each (5 x 5 model) were used.

RESULTS

With electrical stimulation of the first cell of the first strand (cell A1), propagation rapidly spread down that chain and then jumped to the second strand (B chain), followed by jumping to the third, fourth, and fifth strands (C, D, E chains). The rapidity by which the parallel chains became activated depended on the longitudinal resistance of the narrow extracellular cleft between the parallel strands (Rol2); the higher the Rol2 resistance, the faster the theta. The transverse resistance of the cleft (Ror2) had almost no effect. Increasing Rjc decreases the total propagation time (TPT) over the 25-cell network. When the first cell of the third strand (cell C1) was stimulated, propagation spread down the C chain and jumped to the other two strands (B and D) nearly simultaneously.

CONCLUSIONS

Transverse propagation of excitation occurred at multiple points along the chain as longitudinal propagation was occurring, causing the APs in the contiguous chains to become bunched up. Transverse propagation was more erratic and labile in SMC compared to CMC. Transverse transmission of excitation did not require low-resistance connections between the chains, but instead depended on the value of Rol2. The tighter the packing of the chains facilitated transverse propagation.

Regulation of connexin43 gap junctional conductance by ventricular action potentials

Transjunctional voltage regulates cardiac gap junctional conductance, but the kinetics of inactivation were considered too slow to affect cardiac action potential propagation. Connexin43 (Cx43) is abundantly expressed in the atrial and ventricular myocardium and the rapid ventricular conduction tissues (ie, His-Purkinje system) of the mammalian heart and is important to conduction through these cardiac tissues. The kinetics of Cx43 voltage gating were examined at peak action potential voltages using simulated ventricular myocardial action potential waveforms or pulse protocols exceeding 100-mV transjunctional potentials. Junctional current responses approximate the action potential morphology but conductance calculations reveal a 50% to 60% decline from peak to near constant plateau values. Junctional conductance recovers during phase 3 repolarization and early diastole to initial values. The bases for these transient changes in junctional conductance are the rapid decay kinetics in tens of milliseconds at peak transjunctional voltages (Vj) of 130 mV and the gradual increase in junctional conductance as Vj returns toward 0 mV. The decay time constants change e-fold per 22.1 mV above the half-inactivation voltage for Cx43 gap junctions of +/-58 mV. A realistic dynamic model for changes in junctional resistance between excitable and nonexcitable cells during cardiac action potential propagation was developed based on these findings. This dynamic model of cardiac gap junctions will further our understanding of the role gap junctions play in the genesis and propagation of cardiac arrhythmias. The full text of this article is available online at http://www.circresaha.org.

A methodology for achieving high-speed rates for artificial conductance injection in electrically excitable biological cells

We present a novel approach to implementing the dynamic-clamp protocol (Sharp et al., 1993), commonly used in neurophysiology and cardiac electrophysiology experiments. Our approach is based on real-time extensions to the Linux operating system. Conventional PC-based approaches have typically utilized single-cycle computational rates of 10 kHz or slower. In thispaper, we demonstrate reliable cycle-to-cycle rates as fast as 50 kHz. Our system, which we call model reference current injection (MRCI); pronounced merci is also capable of episodic logging of internal state variables and interactive manipulation of model parameters. The limiting factor in achieving high speeds was not processor speed or model complexity, but cycle jitter inherent in the CPU/motherboard performance. We demonstrate these high speeds and flexibility with two examples: 1) adding action-potential ionic currents to a mammalian neuron under whole-cell patch-clamp and 2) altering a cell's intrinsic dynamics via MRCI while simultaneously coupling it via artificial synapses to an internal computational model cell. These higher rates greatly extend the applicability of this technique to the study of fast electrophysiological currents such fast a currents and fast excitatory/inhibitory synapses.

A spontaneously active focus drives a model atrial sheet more easily than a model ventricular sheet

Tachycardias can be produced when focal activity at ectopic locations in either the atria or the ventricles propagates into the surrounding quiescent myocardium. Isolated rabbit atrioventricular nodal cells were coupled by an electronic circuit to a real-time simulation of an array of cell models. We investigated the critical size of an automatic focus for the activation of two-dimensional arrays made up of either ventricular or atrial model cells. Over a range of coupling conductances for the arrays, the critical size of the focus cell group for successful propagation was smaller for activation of an atrial versus a ventricular array. Failure of activation of the arrays at smaller focus sizes was due to the inhibition of pacing of the nodal cells. At low levels of coupling conductance, the ventricular arrays required larger sizes of the focus due to failure of propagation even when the focus was spontaneously active. The major differences between activation of the atrial and ventricular arrays is due to the higher membrane resistance (lower inward rectifier current) of the atrial cells.

Measurements of calcium transients in ventricular cells during discontinuous action potential conduction

The L-type calcium current (I(Ca)) is important in sustaining propagation during discontinuous conduction. In addition, I(Ca) is altered during discontinuous conduction, which may result in changes in the intracellular calcium transient. To study this, we have combined the ability to monitor intracellular calcium concentration ([Ca(2+)](i)) in an isolated cardiac cell using confocal scanning laser fluorescence microscopy with our "coupling clamp" technique, which allows action potential propagation from the real cell to a real-time simulation of a model cell. Coupling a real cell to a model cell with a value of coupling conductance (G(C) = 8 nS) just above the critical value for action potential propagation results in both an increased amplitude and an increased rate of rise of the calcium transient. Similar but smaller changes in the calcium transient are caused by increasing G(C) to 20 nS. The increase of [Ca(2+)](i) by discontinuous conduction is less than the increase of I(Ca), which may indicate that much of [Ca(2+)](i) is the result of calcium released from the sarcoplasmic reticulum rather than the integration of I(Ca).

Mechanism of procainamide-induced prevention of spontaneous wave break during ventricular fibrillation. Insight into the maintenance of fibrillation wave fronts

BACKGROUND

Ventricular fibrillation (VF) is maintained by 2 mechanisms: first by reentry formation and second by spontaneous wave break or wave splitting. We hypothesized that spontaneous wave break results from a critical shortening of the action potential duration (APD) during VF and that its prevention by procainamide eliminates spontaneous wave break.

METHODS AND RESULTS

The endocardial surfaces of 7 isolated, perfused swine right ventricles were mapped with a 3.2x3.8 cm plaque with 477 bipolar electrodes. Activation pattern during VF was visualized dynamically while simultaneously recording epicardial action potentials with a glass microelectrode. APD restitution curves were constructed during VF (dynamic) and during S(1)S(2) protocols. At baseline, VF was maintained by 5.3+/-1 wavelets. Procainamide (PA) at 10 microgram/mL decreased the number of wavelets to 3.5+/-1 (P<0.05). At baseline VF was maintained by spontaneous wave break and by new reentrant wave front formation. PA eliminated spontaneous wave break during VF while having no effect on reentry formation. PA increased the cycle length of the VF (148.5+/-41.2 ms vs 81+/-10 ms, P<0.01) and the core area of the reentry from 5.8 to 14.5 mm(2) (P<0.05). Dynamic APD restitution curve during VF showed that PA eliminated the initiation of activation with APDs shorter than 30 ms. The effects of PA on cellular properties and wave front dynamics were reversed during 60 minutes of drug-free perfusion.

CONCLUSIONS

Critically short APDs during VF promote spontaneous wave break. Their elimination with PA, however, maintains VF by generating new reentrant wave front.

Electrical interactions among real cardiac cells and cell models in a linear strand

Previous work with model systems for action potential conduction have been restricted to conduction between two real cells or conduction between a model cell and a real cell. The inclusion of additional elements to make a linear strand has allowed us to investigate the interactions between cells at a higher level of complexity. When, in the simplest case of a linear strand of three elements, the conductance between elements 2 and 3 (GC2) is varied, this affects the success or failure of propagation between elements 1 and 2 (coupled by GC1) as well as the success or failure of propagation between elements 2 and 3. Several major features were illustrated. 1) When GC1 was only slightly greater than the coupling conductance required for successful propagation between a model cell and a real cell, addition of a third element of the strand either prevented conduction from element 1 to element 2 (when GC2 was high) or allowed conduction from element 1 to element 2 but not conduction from element 2 to element 3 (when GC2 was low). 2) For higher levels of GC1, there was an allowable "window" of values of GC2 for successful conduction from element 1 through to element 3. The size of this allowable window of GC2 values increased with increasing values of GC1, and this increase was produced by increases in the upper bound of GC2 values. 3) When the size of the central element of the strand was reduced, this facilitated conduction through the strand, increasing the range of the allowable window of GC2 values. The overall success or failure of conduction through a structure of cells that has a spatially inhomogeneous distribution of coupling conductances cannot be predicted simply by the average or the minimum value of coupling conductance but may depend on the actual spatial distribution of these conductances.

Modulation of repolarization in rabbit Purkinje and ventricular myocytes coupled by a variable resistance

Purkinje-ventricular junctions (PVJs) have been implicated as potential sites of arrhythmogenesis, in part because of the dispersion of action potential duration (APD) between Purkinje (P) and ventricular (V) myocytes. To characterize electrotonic modulation of APD as a function of junctional resistance (Rj), we coupled single isolated rabbit P and V myocytes with an electronic circuit. In seven of eight PV myocyte pairs, both APDs shortened on coupling at Rj = 50 MOmega. This was in contrast to modulation of APD in paired ventricular myocytes, which demonstrated APD shortening of the intrinsically longer action potential and APD prolongation of the intrinsically shorter action potential. Companion computer simulations, performed to suggest possible mechanisms for the paradoxical shortening of the V action potential in paired P and V myocytes, showed that the difference in intrinsic peak plateau potentials (Vpp) of the P and V myocytes determined whether the V action potential shortened or prolonged on coupling. This difference in Vpp caused a large, repolarizing coupling current to flow to the V myocyte, contributing to early inactivation of the L-type calcium current and early activation of the inward rectifier current. These results suggest that intrinsic differences in phase 1 repolarization could yield differing patterns of APD shortening or prolongation in the network of subendocardial PVJs, leaving some PVJs vulnerable to conduction of premature stimuli while other PVJs remain refractory.

Determinants of action potential initiation in isolated rabbit atrial and ventricular myocytes

Action potential conduction through the atrium and the ventricle of the heart depends on the membrane properties of the atrial and ventricular cells, particularly with respect to the determinants of the initiation of action potentials in each cell type. We have utilized both current- and voltage-clamp techniques on isolated cells to examine biophysical properties of the two cell types at physiological temperature. The resting membrane potential, action potential amplitude, current threshold, voltage threshold, and maximum rate of rise measured from atrial cells (-80 +/- 1 mV, 109 +/- 3 mV, 0.69 +/- 0.05 nA, -59 +/- 1 mV, and 206 +/- 17 V/s, respectively; means +/- SE) differed significantly (P < 0.05) from those values measured from ventricular cells (-82.7 +/- 0.4 mV, 127 +/- 1 mV, 2.45 +/- 0.13 nA, -46 +/- 2 mV, and 395 +/- 21 V/s, respectively). Input impedance, capacitance, time constant, and critical depolarization for activation also were significantly different between atrial (341 +/- 41 M omega, 70 +/- 4 pF, 23.8 +/- 2. 3 ms, and 19 +/- 1 mV, respectively) and ventricular (16.5 +/- 5.4 M omega, 99 +/- 4.3 pF, 1.56 +/- 0.32 ms, and 36 +/- 1 mV, respectively) cells. The major mechanism of these differences is the much greater magnitude of the inward rectifying potassium current in ventricular cells compared with that in atrial cells, with an additional difference of an apparently lower availability of inward Na current in atrial cells. These differences in the two cell types may be important in allowing the atrial cells to be driven successfully by normal regions of automaticity (e.g., the sinoatrial node), whereas ventricular cells would suppress action potential initiation from a region of automaticity (e.g., an ectopic focus).

Electrical interactions between a rabbit atrial cell and a nodal cell model

Atrial activation involves interactions between cells with automaticity and slow-response action potentials with cells that are intrinsically quiescent with fast-response action potentials. Understanding normal and abnormal atrial activity requires an understanding of this process. We studied interactions of a cell with spontaneous activity, represented by a "real-time" simulation of a model of the rabbit sinoatrial (SA) node cell, simultaneously being electrically coupled via our "coupling clamp" circuit to a real, isolated atrial myocyte with variations in coupling conductance (Gc) or stimulus frequency. The atrial cells were able to be driven at a regular rate by a single SA node model (SAN model) cell. Critical Gc for entrainment of the SAN model cell to a nonstimulated atrial cell was 0.55 +/- 0.05 nS (n = 7), and the critical Gc that allowed entrainment when the atrial cell was directly paced at a basic cycle length of 300 ms was 0.32 +/- 0.01 nS (n = 7). For each atrial cell we found periodic phenomena of synchronization other than 1:1 entrainment when Gc was between 0.1 and 0.3 nS, below the value required for frequency entrainment, when the atrial cell was directly driven at a basic cycle length of either 300 or 600 ms. In conclusion, the high input resistance of the atrial cells allows successful entrainment of nodal and atrial cells at low values of Gc, but further uncoupling produces arrhythmic interactions.

Conduction between isolated rabbit Purkinje and ventricular myocytes coupled by a variable resistance

Conduction at the Purkinje-ventricular junction (PVJ) demonstrates unidirectional block under both physiological and pathophysiological conditions. Although this block is typically attributed to multidimensional electrotonic interactions, we examined possible membrane-level contributions using single, isolated rabbit Purkinje (P) and ventricular (V) myocytes coupled by an electronic circuit. When we varied the junctional resistance (Rj) between paired V myocytes, conduction block occurred at lower Rj values during conduction from the smaller to larger myocyte (115 +/- 59 M omega) than from the larger to smaller myocyte (201 +/- 51 M omega). In Purkinje-ventricular myocyte pairs, however, block occurred at lower Rj values during P-to-V conduction (85 +/- 39 M omega) than during V-to-P conduction (912 +/- 175 M omega), although there was little difference in the mean cell size. Companion computer simulations, performed to examine how the early platea currents affected conduction, showed that P-to-V block occurred at lower Rj values when the transient outward current was increased or the calcium current was decreased in the model P cell. These results suggest that intrinsic differences in phase 1 repolarization can contribute to unidirectional block at the PVJ.

Modeling triggered cardiac activity: an analysis of the interactions between potassium blockade, rhythm pauses, and cellular coupling

It is known that under certain conditions, a combination of potassium channel blockade, sympathetic nervous activity, and pauses in sinus rhythm can increase the occurrence of cardiac arrhythmias. Although the arrhythmogenic interactions of these three factors are not completely understood, it is believed that the associated arrhythmias may be initiated by afterpotentials via a process that we refer to as propagated triggered activity. Using a two-cell computational model of ventricular action potential kinetics, we simulate nonuniform potassium blockade, sympathetic nervous activity, and pauses in sinus rhythm under conditions of hypokalemia. Under these conditions, the two-cell model suggests that (1) the arrhythmogenic interactions of potassium blockade and sympathetic nervous activity are highly dependent on heart rate; (2) triggered activity induced by potassium blockade would most likely occur during a pause in sinus rhythm; (3) during a sufficiently large pause in sinus rhythm, potassium blockade can induce triggered activity at normal levels of sympathetic activity; and (4) potassium blockade can increase the probability of triggered activity only if heart rate falls within a critical range. We also show that during pauses in sinus rhythm, two-cell triggering interactions between potassium blockade and sympathetic activity closely parallel the parametric displacement of the dynamic instability underlying the afterpotentials. Our results indicate that the behavior of the triggering mechanism studied here is consistent with that of pause-induced arrhythmias.

Modulating L-type calcium current affects discontinuous cardiac action potential conduction

We have used pairs of cardiac cells (i.e., one real guinea pig ventricular cell and a real-time simulation of a numerical model of a guinea pig ventricular cell) to evaluate the effects on action potential conduction of a variable coupling conductance in combination with agents that either increase or decrease the magnitude of the L-type calcium current. For the cell pairs studied, we applied a direct repetitive stimulation to the real cell, making it the "leader" cell of the cell pair. We have demonstrated that significant delays in action potential conduction for a cell pair can occur either with a decreased value of coupling conductance or with an asymmetry in size such that the follower cell is larger than the leader cell. In both conditions we have shown that isoproterenol, applied to the real cell at very low concentrations, can reversibly decrease the critical coupling conductance (below which action potential conduction fails) for a cell pair with fixed cell sizes, or, for a fixed value of coupling conductance, increase the maximum allowable asymmetry in cell size for successful conduction. For either of these effects, we were able to show that treatment of the real cell with BayK 8644, which more specifically increases the magnitude of the L-type calcium current, was able to mimic the actions of isoproterenol. Treatment of the leader cell of the cell pair (the real cell) with nifedipine, which selectively lowers the magnitude of the L-type calcium current, had effects opposite those of isoproterenol or BayK 8644. The actions of nifedipine, isoproterenol, and BayK 8644 are all limited to conditions in which the conduction delay is on the order of 5 ms or more, whether this delay is caused by limited coupling conductance or by asymmetry in size of the cells. This limitation is consistent with the time course of the L-type calcium current and suggests that the effects of calcium channel blockers or beta-adrenergic blocking drugs, in addition to being selective for regions of the heart that depend on the L-type calcium current for the upstroke of the action potential, would also be somewhat selective for regions of the heart that have discontinuous conduction, either normally or because of some pathological condition.

Action potential conduction between a ventricular cell model and an isolated ventricular cell

We used the Luo and Rudy (LR) mathematical model of the guinea pig ventricular cell coupled to experimentally recorded guinea pig ventricular cells to investigate the effects of geometrical asymmetry on action potential propagation. The overall correspondence of the LR cell model with the recorded real cell action potentials was quite good, and the strength-duration curves for the real cells and for the LR model cell were in general correspondence. The experimental protocol allowed us to modify the effective size of either the simulation model or the real cell. 1) When we normalized real cell size to LR model cell size, required conductance for propagation between model cell and real cell was greater than that found for conduction between two LR model cells (5.4 nS), with a greater disparity when we stimulated the LR model cell (8.3 +/- 0.6 nS) than when we stimulated the real cell (7.0 +/- 0.2 nS). 2) Electrical loading of the action potential waveform was greater for real cell than for LR model cell even when real cell size was normalized to be equal to that of LR model cell. 3) When the size of the follower cell was doubled, required conductance for propagation was dramatically increased; but this increase was greatest for conduction from real cell to LR model cell, less for conduction from LR model cell to real cell, and least for conduction from LR model cell to LR model cell. The introduction of this "model clamp" technique allows testing of proposed membrane models of cardiac cells in terms of their source-sink behavior under conditions of extreme coupling by examining the symmetry of conduction of a cell pair composed of a model cell and a real cardiac cell. We have focused our experimental work with this technique on situations of extreme uncoupling that can lead to conduction block. In addition, the analysis of the geometrical factors that determine success or failure of conduction is important in the understanding of the process of discontinuous conduction, which occurs in myocardial infarction.

Failure of impulse propagation in a mathematically simulated ischemic border zone: influence of direction of propagation and cell-to-cell electrical coupling

INTRODUCTION

It is suggested that heterogeneous extracellular potassium concentration, cell-to-cell coupling, and geometric nonuniformities of the ischemic border zone contribute to the incidence of unidirectional block and subsequent development of lethal ventricular arrhythmias.

METHOD AND RESULTS

A discrete electrical network was used to model a single cardiac fiber with a [K+]e gradient characteristic of an ischemic border zone. Directional differences in propagation were evaluated by creating discrete regions with increased gap junctional resistance within the [K+]e gradient. Furthermore, the effect of homogeneity/heterogeneity of call length on impulse propagation through the [K+]e gradient in the presence of increased gap junctional resistance was evaluated. The results indicate that failure of impulse propagation occurs at the junction between partially uncoupled and normally coupled cells. Furthermore, propagation failure was more likely to occur as the impulse propagated from a region of high [K+]e to low [K+]e. Heterogeneity in cell length contributes to the variability in the occurrence of unidirectional and bidirectional block.

CONCLUSIONS

The onset of cellular uncoupling in an ischemic border zone may interact with the inherent [K+]e gradient leading to unidirectional conduction block. This mechanism may be important for the generation of reentrant arrhythmias at the ischemic border zone.