Action potential and contractility changes in [Na(+)](i) overloaded cardiac myocytes: a simulation study

A computational model of the human left-ventricular epicardial myocyte

A computational model of the human left-ventricular epicardial myocyte is presented. Models of each of the major ionic currents present in these cells are formulated and validated using experimental data obtained from studies of recombinant human ion channels and/or whole-cell recording from single myocytes isolated from human left-ventricular subepicardium. Continuous-time Markov chain models for the gating of the fast Na(+) current, transient outward current, rapid component of the delayed rectifier current, and the L-type calcium current are modified to represent human data at physiological temperature. A new model for the gating of the slow component of the delayed rectifier current is formulated and validated against experimental data. Properties of calcium handling and exchanger currents are altered to appropriately represent the dynamics of intracellular ion concentrations. The model is able to both reproduce and predict a wide range of behaviors observed experimentally including action potential morphology, ionic currents, intracellular calcium transients, frequency dependence of action-potential duration, Ca(2+)-frequency relations, and extrasystolic restitution/post-extrasystolic potentiation. The model therefore serves as a useful tool for investigating mechanisms of arrhythmia and consequences of drug-channel interactions in the human left-ventricular myocyte.

From genetics to cellular function using computational biology

This article illustrates how computational biology (computer modeling) can be used to link genetic mutations to their cellular phenotypes. Examples are provided from ion channel defects that are associated with hereditary cardiac arrhythmias--that is, the long QT and Brugada syndromes. State-specific Markov models of wild-type and mutant channels are formulated and introduced into a computer model of the ventricular cardiac cell. Simulations are conducted to study the rate-dependent alterations in action potential properties caused by the mutations. Results provide insights into the cellular mechanisms of QT-interval prolongation on the ECG in the long QT syndrome and of ST-segment elevation in the right precordial leads in the Brugada syndrome.

Model of intracellular calcium cycling in ventricular myocytes

We present a mathematical model of calcium cycling that takes into account the spatially localized nature of release events that correspond to experimentally observed calcium sparks. This model naturally incorporates graded release by making the rate at which calcium sparks are recruited proportional to the whole cell L-type calcium current, with the total release of calcium from the sarcoplasmic reticulum (SR) being just the sum of local releases. The dynamics of calcium cycling is studied by pacing the model with a clamped action potential waveform. Experimentally observed calcium alternans are obtained at high pacing rates. The results show that the underlying mechanism for this phenomenon is a steep nonlinear dependence of the calcium released from the SR on the diastolic SR calcium concentration (SR load) and/or the diastolic calcium level in the cytosol, where the dependence on diastolic calcium is due to calcium-induced inactivation of the L-type calcium current. In addition, the results reveal that the calcium dynamics can become chaotic even though the voltage pacing is periodic. We reduce the equations of the model to a two-dimensional discrete map that relates the SR and cytosolic concentrations at one beat and the previous beat. From this map, we obtain a condition for the onset of calcium alternans in terms of the slopes of the release-versus-SR load and release-versus-diastolic-calcium curves. From an analysis of this map, we also obtain an understanding of the origin of chaotic dynamics.

Analysing cardiac excitation–contraction coupling with mathematical models of local control

Cardiac excitation-contraction (E-C) coupling describes the process that links sarcolemmal Ca2+ influx via L-type Ca2+ channels to Ca2+ release from the sarcoplasmic reticulum via ryanodine receptors (RyRs). This process has proven difficult to study experimentally, and complete descriptions of how the cell couples surface membrane and intracellular signal transduction proteins to achieve both stable and sensitive intracellular calcium release are still lacking. Mathematical models provide a framework to test our understanding of how this is achieved. While no single model is yet capable of describing all features of cardiac E-C coupling, models of increasing complexity are revealing unexpected subtlety in the process. In particular, modelling has established a general failure of 'common-pool' models and has emphasized the requirement for 'local control' so that microscopic sub-cellular domains can separate local behaviour from the whole-cell average (common-pool) behaviour. The micro-architecture of the narrow diadic cleft in which the local control takes place is a key factor in determining local Ca2+ dynamics. There is still considerable uncertainty about the number of Ca2+ ions required to open RyRs within the cleft and various gating models have been proposed, many of which are in reasonable agreement with available experimental data. However, not all models exhibit a realistic voltage dependence of E-C coupling gain. Furthermore, it is unclear which model features are essential to producing reasonable gain properties. Thus, despite the success of local-control models in explaining many features of cardiac E-C coupling, more work will be needed to provide a sound theoretical basis of cardiac E-C coupling.

Basic mechanisms of cardiac impulse propagation and associated arrhythmias

Propagation of excitation in the heart involves action potential (AP) generation by cardiac cells and its propagation in the multicellular tissue. AP conduction is the outcome of complex interactions between cellular electrical activity, electrical cell-to-cell communication, and the cardiac tissue structure. As shown in this review, strong interactions occur among these determinants of electrical impulse propagation. A special form of conduction that underlies many cardiac arrhythmias involves circulating excitation. In this situation, the curvature of the propagating excitation wavefront and the interaction of the wavefront with the repolarization tail of the preceding wave are additional important determinants of impulse propagation. This review attempts to synthesize results from computer simulations and experimental preparations to define mechanisms and biophysical principles that govern normal and abnormal conduction in the heart.

Computational tools for modeling electrical activity in cardiac tissue

Computer models offer many attractive benefits. However, the modeling of cardiac tissue is computationally expensive due to several physical constraints which result in fine spatiotemporal discretization over large spatiotemporal regions. Our laboratory has been actively trying to develop new techniques to make large scale cardiac simulations tractable over the past 15 years. This paper describes the latest modeling software that our group has developed, called Carp (Cardiac arrhythmias research package). It is designed to run in both shared memory and clustered computing environments. Carp aims to be modular and flexible by following a plug-in framework. This allows the latest models and most efficient solvers to be incorporated as well as enabling run-time selection of techniques. Performance results are given for a large-scale simulation which utilized a comprehensive membrane ionic current description.

Block of recombinant KCNQ1/KCNE1 K+ channels (IKs) by intracellular Na+ and its implications on action potential repolarization

I(Ks), the slow component of delayed rectifier K+ current, plays an important role for the repolarization of ventricular action potential. We investigated the block of I(Ks) by intracellular Na+ ([Na+](i)), using a heterologous expression system (KCNQ1/KCNE1 expressed in COS7 cells), since this well-known blocking action on various K+ channels has not been fully or quantitatively characterized in I(Ks) current. The Na+ block of I(Ks) was concentration- and voltage-dependent and was described by a conventional binding-site model (Woodhull AM: J Gen Physiol 61: 687-708, 1973). In physiological ionic conditions, the blocking action was operating noticeably with Delta ("electrical" distance of the block site) approximately 0.6 and K(d)(0) (apparent dissociation constant at 0 mV) approximately 300 mM. Because K(d)(0) was a function of intra- and extracellular K+ concentrations, changes in ionic environments not only of [Na+](i), but also of [K+](o), affected the amplitude of I(Ks) through the modulation of the Na+ block. Based on these experimental data, we analyzed the effects of Na+ block on action potentials by a computer simulation study, using the Luo-Rudy model. In a physiological ionic environment, the Na+ block of I(Ks) contributed little to modifying action potentials. However, when action potential duration (APD) was marginally prolonged because of decreased I(Ks), as observed in M cells under the conditions of bradycardia and low [K+](o), the Na+ block of I(Ks) may contribute to arrhythmogenesis through the facilitation of early afterdepolarizations (EADs).

The role of M cells and the long QT syndrome in cardiac arrhythmias: simulation studies of reentrant excitations using a detailed electrophysiological model

In this numerical study, we investigate the role of intrinsic heterogeneities of cardiac tissue due to M cells in the generation and maintenance of reentrant excitations using the detailed Luo-Rudy dynamic model. This model has been extended to include a description of the long QT 3 syndrome, and is studied in both one dimension, corresponding to a cable traversing the ventricular wall, and two dimensions, representing a transmural slice. We focus on two possible mechanisms for the generation of reentrant events. We first investigate if early-after-depolarizations occurring in M cells can initiate reentry. We find that, even for large values of the long QT strength, the electrotonic coupling between neighboring cells prevents early-after-depolarizations from creating a reentry. We then study whether M cell domains, with their slow repolarization, can function as wave blocks for premature stimuli. We find that the inclusion of an M cell domain can result in some cases in reentrant excitations and we determine the lifetime of the reentry as a function of the size and geometry of the domain and of the strength of the long QT syndrome.

Genetic defects, ionic currents and electrocardiographic alterations

Most experimental data on the kinetic properties of cardiac ion channels and their modification by genetic defects have been obtained in expression systems (e.g., Xenopus oocyte), away from the cellular environment where these channels function to generate the cardiac action potential. In this article, we describe the use of computational biology (computer simulations) in integrating such information on single ion channels into models of the functioning cardiac cell. We use this approach to mechanistically relate molecular processes to whole-cell electrophysiological function and its manifestation in electrocardiographic waveforms. Examples are provided from the congenital long QT syndrome and the Brugada syndrome.

From myocardial cell models to action potential propagation

Membrane equations that describe sarcolemmal currents and ion transfer processes are important building blocks for theoretical studies of action potential propagation in cardiac tissue. Introduction of such ionic models into cellular and tissue networks allows analyses of passive contributions associated with tissue structure to be considered alongside active contributions from myocytes themselves in studies involving arrhythmia initiation, maintenance and termination. Maturation of contemporary membrane equations that attempt to replicate voltage clamp experiments from different species and tissue types with specific examples of modifications to extend those equations for simulations under conditions of rapid pacing, myocardial ischemia and remodeling following myocardial infarction are considered. Additionally, the integrating of membrane equations into models where coupling to represent current flow paths associated with the anisotropic tissue structure is described.

K+ channel structure-activity relationships and mechanisms of drug-induced QT prolongation

Pharmacological intervention, often for the purpose of treating syndromes unrelated to cardiac disease, can increase the vulnerability of some patients to life-threatening rhythm disturbances. This may be due to an underlying propensity stemming from genetic defects or polymorphisms, or structural abnormalities that provide a substrate allowing for the initiation of arrhythmic triggers. A number of pharmacological agents that have proven useful in the treatment of allergic reactions, gastrointestinal disorders, and psychotic disorders, among others, have been shown to reduce repolarizing K(+) currents and prolong the QT interval on the electrocardiogram. Understanding the structural determinants of K(+) channel blockade may provide new insights into the mechanism and rate-dependent effects of drugs on cellular physiology. Drug-induced disruption of cellular repolarization underlies electrocardiographic abnormalities that are diagnostic indicators of arrhythmia susceptibility.

Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh refinement method

A recently developed space-time adaptive mesh refinement algorithm (AMRA) for simulating isotropic one- and two-dimensional excitable media is generalized to simulate three-dimensional anisotropic media. The accuracy and efficiency of the algorithm is investigated for anisotropic and inhomogeneous 2D and 3D domains using the Luo-Rudy 1 (LR1) and FitzHugh-Nagumo models. For a propagating wave in a 3D slab of tissue with LR1 membrane kinetics and rotational anisotropy comparable to that found in the human heart, factors of 50 and 30 are found, respectively, for the speedup and for the savings in memory compared to an algorithm using a uniform space-time mesh at the finest resolution of the AMRA method. For anisotropic 2D and 3D media, we find no reduction in accuracy compared to a uniform space-time mesh. These results suggest that the AMRA will be able to simulate the 3D electrical dynamics of canine ventricles quantitatively for 1 s using 32 1-GHz Alpha processors in approximately 9 h.

Osmosensitive properties of rapid and slow delayed rectifier K+ currents in guinea-pig heart cells

1. Changes in cell volume affect a variety of sarcolemmal transport processes in the heart. To study whether osmotically induced cell volume shrinkage has functional consequences for K+ channel activity, guinea-pig cardiac preparations were superfused with hyperosmotic Tyrode's solution (1.2-2-fold normal osmolality). Membrane currents and cell surface dimensions were measured from whole-cell patch-clamped ventricular myocytes and membrane potentials were recorded from isolated ventricular muscles and non-patched myocytes. 2. Hyperosmotic treatment of myocytes quickly (< 3 min to steady state) shrank cell volume (approximately 20% reduction in 1.5-fold hyperosmotic solution) and depressed the delayed rectifier K+ current (IK). Analysis using different activation protocols and a selective inhibitor (5 micro mol/L E4031) indicated that the IK inhibition was due to osmolality and cell volume-dependent changes in the two subtypes of the classical cardiac IK (rapidly activating IKr and slowly activating IKs); 1.5-fold hyperosmotic treatment depressed the amplitudes of IKr and IKs by approximately 30 and 50%, respectively. 3. Superfusion of muscles and myocytes with 1.5-fold hyperosmotic solution lengthened the action potentials by 14-17%. Hyperosmotic treatment also caused 6-7 mV hyperpolarization that is most likely due to a concentrating of intracellular K+. 4. The inhibition of IK helps explain the lengthening of action potentials observed in osmotically stressed heart cells. These results, together with the reported IK stimulation by hyposmotic cell swelling, provide further support for cell volume-sensitive properties of cardiac electrical activity.

Impulse propagation in synthetic strands of neonatal cardiac myocytes with genetically reduced levels of connexin43

Connexin43 (Cx43) is a major determinant of the electrical properties of the myocardium. Closure of gap junctions causes rapid slowing of propagation velocity (theta), but the precise effect of a reduction in Cx43 levels due to genetic manipulation has only partially been clarified. In this study, morphological and electrical properties of synthetic strands of cultured neonatal ventricular myocytes from Cx43+/+ (wild type, WT) and Cx+/- (heterozygote, HZ) mice were compared. Quantitative immunofluorescence analysis of Cx43 demonstrated a 43% reduction of Cx43 expression in the HZ versus WT mice. Cell dimensions, connectivity, and alignment were independent of genotype. Measurement of electrical properties by microelectrodes and optical mapping showed no differences in action potential amplitude or minimum diastolic potential between WT and HZ. However, maximal upstroke velocity of the transmembrane action potential, dV/dtmax, was increased and action potential duration was reduced in HZ versus WT. theta was similar in the two genotypes. Computer simulation of propagation and dV/dtmax showed a relatively small dependence of theta on gap junction coupling, thus explaining the lack of observed differences in theta between WT and HZ. Importantly, the simulations suggested that the difference in dV/dtmax is due to an upregulation of INa in HZ versus WT. Thus, heterozygote-null mutation of Cx43 produces a complex electrical phenotype in synthetic strands that is characterized by both changes in ion channel function and cell-to-cell coupling. The lack of changes in theta in this tissue is explained by the dominating role of myoplasmic resistance and the compensatory increase of dV/dtmax.

Ca2+ uptake by the sarcoplasmic reticulum in ventricular myocytes of the SERCA2b/b mouse is impaired at higher Ca2+ loads only

SERCA2a is the cardiac-specific isoform of Ca2+-ATPase of the sarcoplasmic reticulum (SR). A reduction of SERCA2a has been implicated in the contractile dysfunction of heart failure, and partial knockout of the SERCA2 gene (Atp2a2+/- mice) reiterated many of the features of heart failure. Yet, mice with a mutation of Atp2a2, resulting in full suppression of the SERCA2a isoform and expression of the SERCA2b isoform only (SERCA2b/b), showed only moderate functional impairment, despite a reduction by 40% of the SERCA2 protein levels. We examined in more detail the Ca2+ handling in isolated cardiac myocytes from SERCA2b/b. At 0.25 Hz stimulation, the amplitude of the [Ca2+]i transients, SR Ca2+ content, diastolic [Ca2+]i, and density of ICaL were comparable between WT and SERCA2b/b. However, the decline of [Ca2+]i was slower (t1/2 154+/-7 versus 131+/-5 ms; P<0.05). Reducing the amplitude of the [Ca2+]i transient (eg, SR depletion), removed the differences in [Ca2+]i decline. In contrast, increasing the Ca2+ load revealed pronounced reduction of SR Ca2+ uptake at high [Ca2+]i. There was no increase in Na+-Ca2+ exchange protein or function. Theoretical modeling indicated that in the SERCA2b/b mouse, the higher Ca2+ affinity of SERCA2b partially compensates for the 40% reduction of SERCA expression. The lack of SR depletion in the SERCA2b/b may also be related to the absence of upregulation of Na+-Ca2+ exchange. We conclude that for SERCA isoforms with increased affinity for Ca2+, a reduced expression level is better tolerated as Ca2+ uptake and storage are impaired only at higher Ca2+ loads.

Ca2+ entry-dependent inactivation of L-type Ca current: a novel formulation for cardiac action potential models

Cardiac L-type Ca current (I(Ca,L)) is controlled not only by voltage but also by Ca(2+)-dependent mechanisms. Precise implementation of I(Ca,L) in cardiac action potential models therefore requires thorough understanding of intracellular Ca(2+) dynamics, which is not yet available. Here, we present a novel formulation of I(Ca,L) for action potential models that does not explicitly require the knowledge of local intracellular Ca(2+) concentration ([Ca(2+)](i)). In this model, whereas I(Ca,L) is obtained as the product of voltage-dependent gating parameters (d and f), Ca(2+)-dependent inactivation parameters (f(Ca): f(Ca-entry) and f(Ca-SR)), and Goldman-Hodgkin-Katz current equation as in previous studies, f(Ca) is not a instantaneous function of [Ca(2+)](i) but is determined by two terms: onset of inactivation proportional to the influx of Ca(2+) and time-dependent recovery (dissociation). We evaluated the new I(Ca,L) subsystem in the framework of the standard cardiac action potential model. The new formulation produced a similar temporal profile of I(Ca,L) as the standard, but with different gating mechanisms. Ca(2+)-dependent inactivation gradually proceeded throughout the plateau phase, replacing the voltage-dependent inactivation parameter in the LRd model. In typical computations, f declined to approximately 0.7 and f(Ca-entry) to approximately 0.1, whereas deactivation caused fading of I(Ca,L) during final repolarization. These results support experimental findings that Ca(2+) entering through I(Ca,L) is essential for inactivation. After responses to standard voltage-clamp protocols were examined, the new model was applied to analyze the behavior of I(Ca,L) when action potential was prolonged by several maneuvers. Our study provides a basis for theoretical analysis of I(Ca,L) during action potentials, including the cases encountered in long QT syndromes.

Localization of sodium channels in intercalated disks modulates cardiac conduction

It is well known that the sodium current (I(Na)) and the degree of gap-junctional electrical coupling are the key determinants of action potential (AP) conduction in cardiac tissue. Immunohistochemical studies have shown that sodium channels (NaChs) are preferentially located in intercalated disks (IDs). Using dual immunocytochemical staining, we confirmed the colocalization of NaChs with connexin43 in cultures of neonatal rat ventricular myocytes. In mathematical simulations of conduction using the Luo-Rudy dynamic model of the ventricular AP, we assessed the hypothesis that conduction could be modulated by the preferential localization of NaChs in IDs. Localization of I(Na) at the ID caused a large negative potential in the intercellular cleft, which influenced conduction in two opposing ways, depending on the degree of electrical coupling: (1) for normal and moderately reduced coupling, the negative cleft potential led to a large overshoot of the transmembrane potential resulting in a decreased driving force for I(Na) itself (self-attenuation), which slowed conduction; (2) for greatly reduced coupling (<10%), the negative cleft potential induced by I(Na) in the prejunctional membrane led to suprathreshold depolarization of the postjunctional membrane, which facilitated and accelerated conduction. When cleft potential effects were not incorporated, conduction was not significantly affected by the ID localization of I(Na). By enhancing conduction through the establishment of cleft potentials, the localization of NaChs in IDs might protect the myocardium from conduction block, very slow conduction, and microreentry under conditions of greatly reduced coupling. Conversely, by supporting moderately slow conduction, this mechanism could also promote arrhythmias.

An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release

The local control theory of excitation-contraction (EC) coupling in cardiac muscle asserts that L-type Ca(2+) current tightly controls Ca(2+) release from the sarcoplasmic reticulum (SR) via local interaction of closely apposed L-type Ca(2+) channels (LCCs) and ryanodine receptors (RyRs). These local interactions give rise to smoothly graded Ca(2+)-induced Ca(2+) release (CICR), which exhibits high gain. In this study we present a biophysically detailed model of the normal canine ventricular myocyte that conforms to local control theory. The model formulation incorporates details of microscopic EC coupling properties in the form of Ca(2+) release units (CaRUs) in which individual sarcolemmal LCCs interact in a stochastic manner with nearby RyRs in localized regions where junctional SR membrane and transverse-tubular membrane are in close proximity. The CaRUs are embedded within and interact with the global systems of the myocyte describing ionic and membrane pump/exchanger currents, SR Ca(2+) uptake, and time-varying cytosolic ion concentrations to form a model of the cardiac action potential (AP). The model can reproduce both the detailed properties of EC coupling, such as variable gain and graded SR Ca(2+) release, and whole-cell phenomena, such as modulation of AP duration by SR Ca(2+) release. Simulations indicate that the local control paradigm predicts stable APs when the L-type Ca(2+) current is adjusted in accord with the balance between voltage- and Ca(2+)-dependent inactivation processes as measured experimentally, a scenario where common pool models become unstable. The local control myocyte model provides a means for studying the interrelationship between microscopic and macroscopic behaviors in a manner that would not be possible in experiments.

Insights into the molecular mechanisms of bradycardia-triggered arrhythmias in long QT-3 syndrome

Congenital long QT syndrome is a rare disease in which the electrocardiogram QT interval is prolonged due to dysfunctional ventricular repolarization. Variant 3 (LQT-3) is associated with mutations in SCN5A, the gene coding for the heart Na(+) channel alpha subunit. Arrhythmias in LQT-3 mutation carriers are more likely to occur at rest, when heart rate is slow. Several LQT-3 Na(+) channel mutations exert their deleterious effects by promoting a mode of Na(+) channel gating wherein a fraction of channels fails to inactivate. This gating mode, termed "bursting, " results in sustained macroscopic inward Na(+) channel current (I(sus)), which can delay repolarization and prolong the QT interval. However, the mechanism of heart-rate dependence of I(sus) has been unresolved at the single-channel level. We investigate an LQT-3 mutant (Y1795C) using experimental and theoretical frameworks to elucidate the molecular mechanism of I(sus) rate dependence. Our results indicate that mutation-induced changes in the length of time mutant channels spend bursting, rather than how readily they burst, determines I(sus) inverse heart-rate dependence. Our results indicate that mutation-induced changes in the length of time mutant channels spend bursting, rather than how readily they burst, determines I(sus) inverse heart-rate dependence. These results link mutation-induced changes in Na+ channel gating mode transitions to heart rate-dependent changes in cellular electrical activity underlying a key LQT-3 clinical phenotype.

Kb-R7943 prevents acute, atrial fibrillation-induced shortening of atrial refractoriness in anesthetized dogs

BACKGROUND

To test the hypothesis that Ca2+ influx via Na+/Ca2+ exchange (NCX) underlies atrial fibrillation (AF)-induced shortening of atrial effective refractory period (AERP), we examined the potential of KB-R7943 (KB), a selective inhibitor of Ca2+-influx mode NCX, to attenuate this effect.

METHODS AND RESULTS

Studies were performed in 41 isoflurane-anesthetized dogs. In sinus rhythm dogs, peak AERP changes resulting from intravenous KB infusion ranged from (mean+/-SEM) 4.4+/-0.4% (1 mg/kg) to 14.8+/-2.6% (5 mg/kg; ED50=1.9 mg/kg). AERP was maximally prolonged between 5 and 10 minutes after beginning of KB infusion and returned to baseline values within 30 minutes thereafter. Rapid atrial pacing-induced AF reversibly shortened AERP (P<0.001) in 5 dogs, averaging 14.9+/-2.1% after 90 minutes of AF. Both the time course and magnitude of mean AERP changes in 5 AF dogs receiving 5 mg/kg KB were indistinguishable from those in 5 sinus rhythm dogs receiving an equivalent KB dose (P>0.05). We measured cardiac tissue and arterial plasma KB concentrations produced by intravenous infusion (1 mg x kg(-1) x min(-1)) of 5 mg/kg KB. Plasma drug concentration peaked at the end of KB infusions (30.86+/-3.26 nmol/L; n=4 dogs) and declined to 0.56+/-0.19 nmol/L after 100 minutes. The cardiac tissue-to-plasma drug concentration gradient averaged approximately 40 at 100 minutes after start of KB infusion. KB at concentrations achieved in vivo irreversibly blocked NCX-mediated Ca2+ influx in isolated canine right atrial myocytes by approximately 60%, but had no significant effect on NCX-dependent Ca2+ extrusion.

CONCLUSION

NCX-mediated Ca2+ influx plays an important role in acute, AF-induced AERP shortening.

Ionic current basis of electrocardiographic waveforms: a model study

Body surface electrocardiograms and electrograms recorded from the surfaces of the heart are the basis for diagnosis and treatment of cardiac electrophysiological disorders and arrhythmias. Given recent advances in understanding the molecular mechanisms of arrhythmia, it is important to relate these electrocardiographic waveforms to cellular electrophysiological processes. This modeling study establishes the following principles: (1) voltage gradients created by heterogeneities of the slow-delayed rectifier (I(Ks)) and transient outward (I(to)) potassium current inscribe the T wave and J wave, respectively; T-wave polarity and width are strongly influenced by the degree of intercellular coupling through gap-junctions. (2) Changes in [K+]o modulate the T wave through their effect on the rapid-delayed rectifier, I(Kr). (3) Alterations of I(Ks), I(Kr), and I(Na) (fast sodium current) in long-QT syndrome (LQT1, LQT2, and LQT3, respectively) are reflected in characteristic QT-interval and T-wave changes; LQT1 prolongs QT without widening the T wave. (4) Accelerated inactivation of I(Na) on the background of large epicardial I(to) results in ST elevation (Brugada phenotype) that reflects the degree of severity. (5) Activation of the ATP-sensitive potassium current, I(K(ATP)), is sufficient to cause ST elevation during acute ischemia. These principles provide a mechanistic cellular basis for interpretation of electrocardiographic waveforms.

Inward rectifier K(+) current under physiological cytoplasmic conditions in guinea-pig cardiac ventricular cells

The outward current that flows through the strong inward rectifier K(+) (K(IR)) channel generates I(K1), one of the major repolarizing currents of the cardiac action potential. The amplitude and the time dependence of the outward current that flows through K(IR) channels is determined by its blockage by cytoplasmic cations such as polyamines and Mg(2+). Using the conventional whole-cell recording technique, we recently showed that the outward I(K1) can show a time dependence during repolarization due to competition of cytoplasmic particles for blocking K(IR) channels. We used the amphotericin B perforated patch-clamp technique to measure the physiological amplitude and time dependence of I(K1) during the membrane repolarization of guinea-pig cardiac ventricular myocytes. In 5.4 mM K(+) Tyrode solution, the density of the current consisting mostly of the sustained component of the outward I(K1) was about 3.1 A F(-1) at around -60 mV. The outward I(K1) showed an instantaneous increase followed by a time-dependent decay (outward I(K1) transient) on repolarization to -60 to -20 mV subsequent to a 200 ms depolarizing pulse at +37 mV (a double-pulse protocol). The amplitudes of the transients were large when a hyperpolarizing pre-pulse was applied before the double-pulse protocol, whereas they were small when a depolarizing pre-pulse was applied. The peak amplitudes of the transients elicited using a hyperpolarizing pre-pulse were 0.36, 0.63 and 1.01 A F(-1), and the decay time constants were 44, 14 and 6 ms, at -24, -35 and -45 mV, respectively. In the current-clamp experiments, a phase-plane analysis revealed that application of pre-pulses changed the current density at the repolarization phase to the extents expected from the changes of the I(K1) transient. Our study provides the first evidence that an outward I(K1) transient flows during cardiac action potentials.

Ca(2+)-activated Cl(-) current in rabbit sinoatrial node cells

The Ca(2+)-activated Cl(-) current (I(Cl(Ca))) has been identified in atrial, Purkinje and ventricular cells, where it plays a substantial role in phase-1 repolarization and delayed after-depolarizations. In sinoatrial (SA) node cells, however, the presence and functional role of I(Cl(Ca)) is unknown. In the present study we address this issue using perforated patch-clamp methodology and computer simulations. Single SA node cells were enzymatically isolated from rabbit hearts. I(Cl(Ca)) was measured, using the perforated patch-clamp technique, as the current sensitive to the anion blocker 4,4'-diisothiocyanostilbene-2,2'-disulphonic acid (DIDS). Voltage clamp experiments demonstrate the presence of I(Cl(Ca)) in one third of the spontaneously active SA node cells. The current was transient outward with a bell-shaped current-voltage relationship. Adrenoceptor stimulation with 1 microM noradrenaline doubled the I(Cl(Ca)) density. Action potential clamp measurements demonstrate that I(Cl(Ca)) is activate late during the action potential upstroke. Current clamp experiments show, both in the absence and presence of 1 microM noradrenaline, that blockade of I(Cl(Ca)) increases the action potential overshoot and duration, measured at 20 % repolarization. However, intrinsic interbeat interval, upstroke velocity, diastolic depolarization rate and the action potential duration measured at 50 and 90 % repolarization were not affected. Our experimental data are supported by computer simulations, which additionally demonstrate that I(Cl(Ca)) has a limited role in pacemaker synchronization or action potential conduction. In conclusion, I(Cl(Ca)) is present in one third of SA node cells and is activated during the pacemaker cycle. However, I(Cl(Ca)) does not modulate intrinsic interbeat interval, pacemaker synchronization or action potential conduction.

Ionic charge conservation and long-term steady state in the Luo-Rudy dynamic cell model

It has been postulated that cardiac cell models accounting for changes in intracellular ion concentrations violate a conservation principle, and, as a result, computed parameters (e.g., ion concentrations and transmembrane potential, V(m)) drift in time, never attaining steady state. To address this issue, models have been proposed that invoke the charge conservation principle to calculate V(m) from ion concentrations ("algebraic" method), rather than from transmembrane current ("differential" method). The aims of this study are to compare model behavior during prolonged periods of pacing using the algebraic and differential methods, and to address the issue of model drift. We pace the Luo-Rudy dynamic model of a cardiac ventricular cell and compare the time-dependent behavior of computed parameters using the algebraic and differential methods. When ions carried by the stimulus current are taken into account, the algebraic and differential methods yield identical results and neither shows drift in computed parameters. The present study establishes the proper pacing protocol for simulation studies of cellular behavior during long periods of rapid pacing. Such studies are essential for mechanistic understanding of arrhythmogenesis, since cells are subjected to rapid periodic stimulation during many arrhythmias.

Mechanistic insights into very slow conduction in branching cardiac tissue: a model study

It is known that branching strands of cardiac tissue can form a substrate for very slow conduction. The branches slow conduction by acting as current loads drawing depolarizing current from the main strand ("pull" effect). It has been suggested that, upon depolarization of the branches, they become current sources reinjecting current back into the strand, thus enhancing propagation safety ("push" effect). It was the aim of this study to verify this hypothesis and to assess the contribution of the push effect to propagation velocity and safety. Conduction was investigated in strands of Luo-Rudy dynamic model cells that branch from either a single branch point or from multiple successive branch points. In single-branching strands, blocking the push effect by not allowing current to flow retrogradely from the branches into the strand did not significantly increase the branching-induced local propagation delay. However, in multiple branching strands, blocking the push effect resulted in a significant slowing of overall conduction velocity or even in conduction failure. Furthermore, for certain slow velocities, the safety factor for propagation was higher when slow conduction was caused by branching tissue geometry than by reduced excitability without branching. Therefore, these results confirm the proposed "pull and push" mechanism of slow, but nevertheless robust, conduction in branching structures. Slow conduction based on this mechanism could occur in the atrioventricular node, where multiple branching is structurally present. It could also support reentrant excitation in diseased myocardium where the substrate is structurally complex.

Computational models of normal and abnormal action potential propagation in cardiac tissue: linking experimental and clinical cardiology

Computational models have the potential to make a huge impact on our understanding of normal and abnormal cardiac function. The aim of this article is to review tools that have been developed to simulate the electrophysiology of cardiac cells and tissue, and to show how computational models have been used to gain insight into normal and abnormal action potential propagation. Some of the practical problems experienced in the development and application of these models are described, and examples are given.

Model study of ATP and ADP buffering, transport of Ca(2+) and Mg(2+), and regulation of ion pumps in ventricular myocyte

We extended the model of the ventricular myocyte by Winslow et al. (Circ. Res 1999, 84:571-586) by incorporating equations for Ca(2+) and Mg(2+) buffering and transport by ATP and ADP and equations for MgATP regulation of ion transporters (Na(+)-K(+) pump, sarcolemmal and sarcoplasmic Ca(2+) pumps). The results indicate that, under normal conditions, Ca(2+) binding by low-affinity ATP and diffusion of CaATP may affect the amplitude and time course of intracellular Ca(2+) signals. The model also suggests that a fall in ATP/ADP ratio significantly reduces sarcoplasmic Ca(2+) content, increases diastolic Ca(2+), lowers systolic Ca(2+), increases Ca(2+) influx through L-type channels, and decreases the efficiency of the Na(+)/Ca(2+) exchanger in extruding Ca(2+) during periodic voltage-clamp stimulation. The analysis suggests that the most important reason for these changes during metabolic inhibition is the down-regulation of the sarcoplasmic Ca(2+)-ATPase pump by reduced diastolic MgATP levels. High Ca(2+) concentrations developed near the membrane might have a greater influence on Mg(2+), ATP, and ADP concentrations than that of the lower Ca(2+) concentrations in the bulk myoplasm. The model predictions are in general agreement with experimental observations measured under normal and pathological conditions.

Determinants of excitability in cardiac myocytes: mechanistic investigation of memory effect

The excitability of a cardiac cell depends upon many factors, including the rate and duration of pacing. Furthermore, cell excitability and its variability underlie many electrophysiological phenomena in the heart. In this study, we used a detailed mathematical model of the ventricular myocyte to investigate the determinants of excitability and gain insight into the mechanism by which excitability depends on the rate and duration of pacing (the memory effect).

RESULTS

i) The primary determinant of excitability depends upon the duration (T) of the stimulus. ii) For a short T, excitability is determined by the difference between the threshold membrane potential and the resting membrane potential. iii) For a long T, excitability is determined by the resting membrane resistance, R(m). iv) In the case of long T, pacing induced changes in [Na(+)](i) and [Ca(2+)](i) over time affect R(m) and excitability by shifting the current-voltage (IV) curve in the vertical direction and are responsible for the memory effect.

CONCLUSIONS

The results have important implications during an arrhythmia, where a cardiac cell may be subjected to rapid repetitive excitation for an extended period of time. Effective anti-arrhythmic strategies may be developed to exploit the R(m) dependence of excitability for a long T.

Dynamics of action potential head-tail interaction during reentry in cardiac tissue: ionic mechanisms

In a sufficiently short reentry pathway, the excitation wave front (head) propagates into tissue that is partially refractory (tail) from the previous action potential (AP). We incorporate a detailed mathematical model of the ventricular myocyte into a one-dimensional closed pathway to investigate the effects of head-tail interaction and ion accumulation on the dynamics of reentry. The results were the following: 1) a high degree of head-tail interaction produces oscillations in several AP properties; 2) Ca(2+)-transient oscillations are in phase with AP duration oscillations and are often of greater magnitude; 3) as the wave front propagates around the pathway, AP properties undergo periodic spatial oscillations that produce complicated temporal oscillations at a single site; 4) depending on the degree of head-tail interaction, intracellular [Na(+)] accumulation during reentry either stabilizes or destabilizes reentry; and 5) elevated extracellular [K(+)] destabilizes reentry by prolonging the tail of postrepolarization refractoriness.