A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes

The functional role of cardiac T-tubules explored in a model of rat ventricular myocytes

The morphology of the cardiac transverse-axial tubular system (TATS) has been known for decades, but its function has received little attention. To explore the possible role of this system in the physiological modulation of electrical and contractile activity, we have developed a mathematical model of rat ventricular cardiomyocytes in which the TATS is described as a single compartment. The geometrical characteristics of the TATS, the biophysical characteristics of ion transporters and their distribution between surface and tubular membranes were based on available experimental data. Biophysically realistic values of mean access resistance to the tubular lumen and time constants for ion exchange with the bulk extracellular solution were included. The fraction of membrane in the TATS was set to 56%. The action potentials initiated in current-clamp mode are accompanied by transient K+ accumulation and transient Ca2+ depletion in the TATS lumen. The amplitude of these changes relative to external ion concentrations was studied at steady-state stimulation frequencies of 1-5 Hz. Ca2+ depletion increased from 7 to 13.1% with stimulation frequency, while K+ accumulation decreased from 4.1 to 2.7%. These ionic changes (particularly Ca2+ depletion) implicated significant decrease of intracellular Ca2+ load at frequencies natural for rat heart.

ATX-II Effects on the Apparent Location of M Cells in a Computational Model of a Human Left Ventricular Wedge

INTRODUCTION

The apparent location of the myocytes (M cells) with the longest action potential duration (APD) in a canine left ventricular (LV) wedge have been reported to shift after application of a sea anemone toxin, ATX-II. This toxin slows inactivation of I(Na) and thus prolongs APD. Thus, M cells may exhibit dynamic functional states, rather than being a static, anatomically discrete, myocyte population. In this study, we attempted to further define and understand this phenomenon using a mathematical model of the human ventricular myocyte action potential incorporated into an in silico "wedge" preparation. Our simulations demonstrate that even under conditions of a fixed population and ratio of epicardial, M, and endocardial myocytes, the apparent anatomical position (transmural location) of the myocytes with the longest APD can shift following ATX-II treatment. This arises because the ATX-II effect, modeled as a small increase in the late or persistent Na(+) current, and consequent prolongation of APD significantly changes the electrotonic interactions between ventricular myocytes in this LV wedge preparation.

METHODS AND RESULTS

This LV wedge model is based on bidomain equations. It corresponds to a rectangular tissue immersed in a passive and isotropic medium that represents the superfusion bath. In this theoretical work, the three known different and discrete populations of myocytes in the human left ventricle have been included: the epicardial, M, and endocardial cells. The effects of ATX-II on I(Na) were simulated by altering the voltage-dependent steady-state inactivation of the parameters h (fast gate) and j (slow gate). As a result, in these ATX-II simulations a persistent late Na(+) current was generated in all three types of ventricular myocytes. However, the APDs were prolonged in a heterogeneous pattern. Our simulations demonstrate that after the ATX-II effects develop, alterations in transmural electrotonic interactions can produce changes in the transmural location of myocytes with the longest APD.

CONCLUSIONS

The combination of intercellular electrotonic interactions, which tend to reduce and smooth out the discrete transmural APD variations, and the heterogeneous effects of ATX-II, which preferentially prolong the APD of M cells, can shift the location of the ventricular myocytes. This shift results in significantly altered transmural patterns of action potential durations, which would be expected to change localized refractory period and excitability. These cellular changes give rise to alterations in the corresponding surface electrograms and may change the overall substrates for conduction and rhythm disturbances.

Autonomic Regulation of Voltage-Gated Cardiac Ion Channels

Altering voltage-gated ion channel currents, by changing channel number or voltage-dependent kinetics, regulates the propagation of action potentials along the plasma membrane of individual cells and from one cell to its neighbors. Functional increases in the number of cardiac sodium channels (Na(V)1.5) at the myocardial sarcolemma are accomplished by the regulation of caveolae by beta adrenergically stimulated G-proteins. We demonstrate that Na(V)1.5, Ca(V)1.2a, and K(V)1.5 channels specifically localize to isolated caveolar membranes, and to punctate regions of the sarcolemma labeled with caveolin-3. In addition, we show that Na(V)1.5, Ca(V)1.2a, and K(V)1.5 channel antibodies label the same subpopulation of isolated caveolae. Plasma membrane sheet assays demonstrate that Na(V)1.5, Ca(V)1.2a, and K(V)1.5 cluster with caveolin-3. This may have interesting implications for the way in which adrenergic pathways alter the cardiac action potential morphology and the velocity of the excitatory wave.

Measurements of Electrophysiological Effects of Components of Acute Ischemia in Langendorff-Perfused Rat Hearts Using Voltage-Sensitive Dye Mapping

INTRODUCTION

This study was carried out to evaluate optical mapping in the presence of cytochalasin-D as a method for measuring electrophysiological responses in general, and in particular the responses to acute ischemia in the Langendorff-perfused rat heart. Cytochalasin-D is commonly used to reduce contraction for the purpose of suppressing motion artifacts in voltage-sensitive dye recordings of cardiac membrane potential.

METHODS AND RESULTS

Observations using optical mapping were complemented by recordings of the surface electrogram to provide information independent of the optical measurements. Perfusion of Langendorff-perfused rat hearts with 3 microM cytochalasin-D resulted in a 24% prolongation of the QT interval of surface electrograms indicating that cytochalasin-D prolongs the rat ventricular action potential. Individual components of the electrophysiological response to acute ischemia were globally induced as follows: (1) opening of K(ATP) channels was induced by perfusion of 2 micro M P-1,075, (2) accumulation of extracellular K(+) was simulated by increasing perfusate [K(+)] to 12 mM, and (3) acidosis was simulated by reducing perfusate pH to 6.5. The responses to these interventions could be reliably documented using optical recordings, as well as from surface electrograms. Whole-cell patch clamp measurements on isolated rat ventricular myocytes indicate that cytochalasin-D produces an approximately 2.5-fold increase in P-1,075-induced I(K,ATP).

CONCLUSION

These results provide the necessary background information for interpreting electrophysiological measurements during acute ischemia in the presence of cytochalasin-D.

Mathematical Simulations of the Effects of Altered AMP-Kinase Activity on INa and the Action Potential in Rat Ventricle

INTRODUCTION

Alterations in the activity of a so-called "metabolic switch" enzyme, adenosine monophosphate-activated protein kinase (AMP kinase), in mammalian heart contribute to the conduction abnormalities and rhythm disturbances in the settings of Wolff-Parkinson-White syndrome and ventricular pre-excitation. A recent study by Light et al. has shown that augmented AMP kinase activity can alter the biophysical properties of mammalian cardiac sodium currents. These experiments involved an electrophysiological analysis following heterologous expression of human Na(v)1.5 in tsA201 cells. Constitutive activation of AMP kinase followed by co-transfection caused: (i) a hyperpolarizing shift in the activation curve for I(Na), (ii) a small change in the voltage dependence of steady-state inactivation, and (iii) a significant slowing in the rate of inactivation of I(Na).

METHODS AND RESULTS

We have attempted to simulate these results using our mathematical model of the membrane action potential of the adult rat ventricular myocyte. The changes in I(Na) produced by AMP kinase activation and/or overexpression can be reconstructed mathematically by altering two rate constants in a Markovian model that governs the I(Na) kinetics. Simulated macroscopic I(Na) records in which a fraction (10-100%) of the Na(+) channels had the appropriate rate constants for two state-dependent transitions increased by a factor of 100-fold exhibited: (i) slowed inactivation, (ii) a shift in steady-state activation to more hyperpolarized membrane potentials, and (iii) a very small change in the voltage dependence of steady-state inactivation.

SUMMARY

Thus, straightforward modifications of a previously published kinetic scheme for the time and voltage dependence of mammalian heart I(Na), when incorporated into a mathematical model for the rat ventricular action potential can reproduce the main features of these AMP kinase-induced modifications in I(Na) in mammalian ventricle. Ongoing mathematical simulations are directed toward developing formulations that mimic the molecular mechanisms for the AMP kinase effects, e.g., changes in the kinetics of I(Na) resulting from selective phosphorylation/dephosphorylation of sites on the alpha or beta subunits which comprise human Na(v)1.5. Thereafter, incorporation of these changes into a mathematical model for the action potential of the human ventricular myocyte is planned.

Effects of the ??2-Adrenergic/DA2-Dopaminergic Agonist CHF-1024 in Preventing Ventricular Arrhythmogenesis and Myocyte Electrical Remodeling, in a Rat Model of Pressure-Overload Cardiac Hypertrophy

Cardiac hypertrophy induces morpho-functional myocardial alterations favoring arrhythmogenesis, especially under specific conditions such as sympathetic stimulation. We analyzed whether the dopaminergic agent CHF-1024, given its effect in decreasing adrenergic drive and collagen deposition in hypertrophied hearts, can also reduce arrhythmia vulnerability. Eighty-one male Wistar rats with intrarenal aortic coarctation and 18 control animals were studied. Fifty-eight banded animals were treated with CHF-1024 at four different doses (6, 2, 0.67, or 0.067 mg/Kg/die). One month after aortic ligature, spontaneous and sympathetic-induced ventricular arrhythmic events (VAEs) were telemetrically recorded in conscious animals. After sacrifice, membrane capacitance (Cm) and action potential duration (APD) were measured in isolated left ventricular myocytes (patch-clamp). In all groups, spontaneous VAEs were negligible whereas they significantly increased during sympathetic activation (stress exposure). Banded untreated animals showed a higher number of stress-induced VAEs, longer action potentials, and larger values of Cm and cell width as compared with control group. The treatment with CHF-1024 exhibited an antiarrhythmic effect, abolished APD prolongation, and reduced cell width at all doses. The lowest dose also prevented Cm increase. In conclusion, we demonstrated that in this model of pressure-overload hypertrophy CHF-1024 reduces arrhythmogenesis and causes a recovery of cell excitable properties toward a normal phenotype.

Cardiac microimpedance measurement in two-dimensional models using multisite interstitial stimulation

We analyzed central interstitial potential differences during multisite stimulation to assess the feasibility of using those recordings to measure cardiac microimpedances in multidimensional preparations. Because interstitial current injected and removed using electrodes with different proximities allows modulation of the portion of current crossing the membrane, we hypothesized that multisite interstitial stimulation would give rise to central interstitial potential differences that depend on intracellular and interstitial microimpedances, allowing measurement of those microimpedances. Simulations of multisite stimulation with fine and wide spacing in two-dimensional models that included dynamic membrane equations for guinea pig ventricular myocytes were performed to generate test data ( partial differentialphio). Isotropic interstitial and intracellular microimpedances were prescribed for one set of simulations, and anisotropic microimpedances with unequal ratios (intracellular to interstitial) along and across fibers were prescribed for another set of simulations. Microimpedance measurements were then obtained by making statistical comparisons between partial differentialphio values and interstitial potential differences from passive bidomain simulations (Deltaphio) in which a wide range of possible microimpedances were considered. Possible microimpedances were selected at 25% increments. After demonstrating the effectiveness of the overall method with microimpedance measurements using one-dimensional test data, we showed microimpedance measurements within 25% of prescribed values in isotropic and anisotropic models. Our findings suggest that development of microfabricated devices to implement the procedure would facilitate routine measurement as a component of cardiac electrophysiological study.

An integrative model of mouse cardiac electrophysiology from cell to torso

AIMS

Although the transgenic mouse has become an important new tool in the study of human diseases and the design of new therapies, a complete picture of cardiac electrophysiology in the mouse, from genome to body surface, is lacking. A computational model of the mouse heart is presented, which is used to study the impact of ion-channel and structural manipulations on the distributions of extracellular potentials on the heart and body surface.

METHODS

A model of the mouse heart anatomy, fibre organization and torso geometry was constructed from DTMRI images. An anisotropic bidomain model, with a modified Pandit et al. model for the ionic currents, was used to represent the electrical properties of the tissue. Spatial heterogeneity in the ion currents was introduced by modulating the transient outward current. A sinus beat was simulated in hearts with different tissue and membrane properties and the extracellular potentials were computed at both the heart and body surface.

RESULTS

The simulated transmembrane patterns in the heart, and the timing and morphology of the simulated ECG waveforms were consistent with experimental measurements. In addition, the patterns of activation and recovery and the waveforms of the corresponding ECG were found to be relatively insensitive to changes in cell type distribution and tissue anisotropy.

CONCLUSION

Because of the small size of the heart, an integrative model of mouse electrophysiology can be simulated from cell to torso, enabling a new tool to study how extracellular signals might be used to detect molecular changes underlying an arrhythmogenic substrate.

Hybrid duplex: a novel method to study the contractile function of heterogeneous myocardium

In an earlier study, we experimentally mimicked the effects of mechanical interaction between different regions of the ventricular wall by allowing pairs of independently maintained cardiac muscle fibers to interact mechanically in series or in parallel. This simple physiological model of heterogeneous myocardium, which has been termed “duplex,” has provided new insight into basic effects of cardiac electromechanical heterogeneity. Here, we present a novel “hybrid duplex,” where one of the elements is an isolated cardiac muscle and the other a “virtual cardiac muscle.” The virtual muscle is represented by a computational model of cardiomyocyte electromechanical activity. We present in detail the computer-based digital control system that governs the mechanical interaction between virtual and biological muscle, the software used for data analysis, and working implementations of the model. Advantages of the hybrid duplex method are discussed, and experimental recordings are presented for illustration and as proof of the principle.

Mechanisms of excitation-contraction coupling in an integrative model of the cardiac ventricular myocyte

It is now well established that characteristic properties of excitation-contraction (EC) coupling in cardiac myocytes, such as high gain and graded Ca(2+) release, arise from the interactions that occur between L-type Ca(2+) channels (LCCs) and nearby ryanodine-sensitive Ca(2+) release channels (RyRs) in localized microdomains. Descriptions of Ca(2+)-induced Ca(2+) release (CICR) that account for these local mechanisms are lacking from many previous models of the cardiac action potential, and those that do include local control of CICR are able to reconstruct properties of EC coupling, but require computationally demanding stochastic simulations of approximately 10(5) individual ion channels. In this study, we generalize a recently developed analytical approach for deriving simplified mechanistic models of CICR to formulate an integrative model of the canine cardiac myocyte which is computationally efficient. The resulting model faithfully reproduces experimentally measured properties of EC coupling and whole cell phenomena. The model is used to study the role of local redundancy in L-type Ca(2+) channel gating and the role of dyad configuration on EC coupling. Simulations suggest that the characteristic steep rise in EC coupling gain observed at hyperpolarized potentials is a result of increased functional coupling between LCCs and RyRs. We also demonstrate mechanisms by which alterations in the early repolarization phase of the action potential, resulting from reduction of the transient outward potassium current, alters properties of EC coupling.

Computational modeling of cardiac ventricular action potentials in rat and mouse: review

Little is known about the ionic mechanisms underlying the action potential heterogeneity in ventricle-associated healthy and disease conditions, even though five decades of histological, electrophysiological, pharmacological, and biochemical investigations exist. The computational modeling in murine ventricular myocytes can complement our knowledge of the experimental data and provide us with more quantitative descriptions in understanding different conditions related to normal and disease conditions. This paper initially reviews the theoretical modeling for cardiac ventricular action potentials of various species and the related experimental work. It then presents the progress of the computational modeling of cardiac ventricular cells for normal, diabetic, and spontaneously hypertensive rats. The paper also introduces recent modeling efforts for the action potential heterogeneity in mouse ventricular cells. The computational insights gained into the ionic mechanisms in rodents will continue to enhance our understanding of the heart and provide us with new knowledge for future studies to treat cardiac diseases in children and adults. Because the dissemination of computational models is very important, we continue to disseminate these models by iCell, the interactive cell modeling resource. iCell (http://ssd1.bme.memphis.edu/icell/) has been developed as a simulation-based teaching and learning tool for electrophysiology and contains JAVA applets that present models of various cardiac cells and neurons and simulation data of their bioelectric activities at cellular level.

Effect of input resistance voltage-dependency on DC estimate of membrane capacitance in cardiac myocytes

The measure of membrane capacitance (C(m)) in cardiac myocytes is of primary importance as an index of their size in physiological and pathological conditions, and for the understanding of their excitability. Although a plethora of very accurate methods has been developed to access C(m) value in single cells, cardiac electrophysiologists still use, in the majority of laboratories, classical direct current techniques as they have been established in the early days of cardiac cellular electrophysiology. These techniques are based on the assumption that cardiac membrane resistance (R(m)) is constant, or changes negligibly, in a narrow potential range around resting potential. Using patch-clamp whole-cell recordings, both in current-clamp and voltage-clamp conditions, and numerical simulations, we document here the voltage-dependency of R(m), up to -45% of its resting value for 10-mV hyperpolarization, in resting rat ventricular myocytes. We show how this dependency makes classical protocols to misestimate C(m) in a voltage-dependent manner (up to 20% errors), which can dramatically affect C(m)-based calculations on cell size and on intracellular ion dynamics. We develop a simple mechanistic model to fit experimental data and obtain voltage-independent estimates of C(m), and we show that accurate estimates can also be extrapolated from the classical approach.

Selenium-induced alterations in ionic currents of rat cardiomyocytes

In the present study, rats were treated with sodium selenite (5 micromol/kg body weight/day, ip) for 4 weeks and the parameters of contractile activity, action potential, L-type Ca2+-current (ICaL), as well as transient outward (Ito), inward rectifier (IK1), and steady state (Iss) K+-currents were investigated. Sodium selenite treatment increased rat blood glucose level and lowered plasma insulin level, significantly. This treatment also caused slightly prolongation in action potential with no significant effects on spontaneous contraction parameters and intracellular Ca2+ transients of the heart preparations. These effects were associated with marked alterations in the kinetics of both ICaL and Ito including a significant slowing in both inactivation time constants of ICaL and a significant shift to negative potential at half-inactivation of these channels without any change in the current density. Also, there was a significantly faster inactivation of Ito and no shift in half-inactivation of this channel without any change in its current density. Consequently, there was a approximately 50% increase in total charges carried by Ca2+ current and approximately 50% decrease in total charges carried by K+ currents of the treated rat cardiomyocytes. Additionally we observed a significant inhibition in IK1 density in treated rat cardiomyocytes. Oxidized glutathione level was significantly increased (70%) while the observed decrease in reduced glutathione was much less. Since a shift in redox state of regulatory proteins is related with cell dysfunction, selenium-induced increase in blood glucose and decrease in plasma insulin may correlate these alterations. These alterations, in the kinetics of the channels and in IK1 density, might lead to proarrhythmic effect of chronic selenium supplementation.

Electrotonic influences on action potential duration dispersion in small hearts: a simulation study

Intrinsic spatial variations in repolarization currents in the heart can produce spatial gradients in action potential duration (APD) that serve as possible sites for conduction block and the initiation of reentrant activity. In well-coupled myocardium, however, electrotonic influences at the stimulus site and wavefront collision sites act to modulate any intrinsic heterogeneity in APD. These effects alter APD gradients over an extent larger than that suggested by the length constant associated with propagation and, thus, are hypothesized to play a greater role in smaller hearts used as experimental models of human disease. This study uses computer simulation to investigate how heart size, tissue properties, and the spatial assignment of cell types affect functional APD dispersion. Simulations were carried out using the murine ventricular myocyte model of Pandit et al. or the Luo-Rudy mammalian model in three-dimensional models of mouse and rabbit ventricular geometries. Results show that the spatial extent of the APD dispersion is related to the dynamic changes in transmembrane resistance during recovery. Also, because of the small dimensions of the mouse heart, electrotonic effects on APD primarily determine the functional dispersion of refractoriness, even in the presence of large intrinsic cellular heterogeneity and reduced coupling. APD dispersion, however, is found to increase significantly when the heart size increases to the size of a rabbit heart, unmasking intrinsic cell types.

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

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

Frequency-dependent and proarrhythmogenic effects of FK-506 in rat ventricular cells

FK-506, a widely used immunosuppressant, has caused a few clinical cases with QT prolongation and torsades de pointe at high blood concentration. The proarrhytmogenic potential of FK-506 was investigated in single rat ventricular cells using the whole cell clamp method to record action potentials (APs) and ionic currents. Fluorescence measurements of Ca2+ transients were performed with indo-1 AM using a multiphotonic microscope. FK-506 (25 μmol/l) hyperpolarized the resting membrane potential (RMP; −3 mV) and prolonged APs (AP duration at 90% repolarization increased by 21%) at 0.1 Hz. Prolongation was enhanced by threefold at 3.3 Hz, and early afterdepolarizations (EADs) occurred in 59% of cells. EADs were prevented by stronger intracellular Ca2+ buffering (EGTA: 10 vs. 0.5 mmol/l in the patch pipette) or replacement of extracellular Na+ by Li+, which abolishes Na+/Ca2+ exchange [Na+/Ca2+ exchanger current ( INaCa)]. In indo-1-loaded cells, FK-506 generated doublets of Ca2+ transients associated with increased diastolic Ca2+ in one-half of the cells. FK-506 reversibly decreased the L-type Ca2+ current ( ICaL) by 25%, although high-frequency-dependent facilitation of ICaL persisted, and decreased three distinct K+ currents: delayed rectifier K+ current ( IK; >80%), transient outward K+ current (<20%), and inward rectifier K+ current ( IK1; >40%). A shift in the reversal potential of IK1 (−5 mV) accounted for RMP hyperpolarization. Numerical simulations, reproducing all experimental effects of FK-506, and the use of nifedipine showed that frequency-dependent facilitation of ICaL plays a role in the occurrence of EADs. In conclusion, the effects of FK-506 on the cardiac AP are more complex than previously reported and include inhibitions of IK1 and ICaL. Alterations in Ca2+ release and INaCa may contribute to FK-506-induced AP prolongation and EADs in addition to the permissive role of ICaL facilitation at high rates of stimulation.

Interpretation of relevance of sodium?calcium exchange in action potential of diabetic rat heart by mathematical model

Sarcolemmal Na+-Ca2+ exchange plays a central role in ion transport of the myocardium and the current carried with it contributes to the late phase of the action potential (AP) besides the contribution of outward K+-currents. In this study, the mathematical model for AP of the diabetic rat ventricular myocytes [34] was modified and used for the diabetic rat papillary muscle. We used our experimentally measured values of two K+-currents; transient outward current, Ito and steady-state outward current, Iss, as well as L-type Ca2+-current, I(CaL), then compared with the simulated values. We have demonstrated that the prolongation in the AP of the papillary muscle of the diabetic rats are not due to the alteration of I(CaL) but mainly due to the inhibition of the K+-currents and also the Na+-Ca2+ exchanger current, I(Na-Ca). In combination with our experimental data on sodium-selenite-treated diabetic rats, our simulation results provide new information concerning plausible ionic mechanisms, and second a possible positive effect of selenium treatment on the altered I(Na-Ca) for the observed changes in the AP duration of streptozotocin-induced diabetic rat heart.

Ascending aortic stenosis selectively increases action potential-induced Ca2+ influx in epicardial myocytes of the rat left ventricle

A decrease of the transient outward potassium current (Ito) has been observed in cardiac hypertrophy and contributes to the altered shape of the action potential (AP) of hypertrophied ventricular myocytes. Since the shape and duration of the ventricular AP are important determinants of the Ca2+ influx during the AP (QCa), we investigated the effect of ascending aortic stenosis (AS) on QCa in endo- and epicardial myocytes of the left ventricular free wall using the AP voltage-clamp technique. In sham-operated animals, QCa was significantly larger in endocardial compared to epicardial myocytes (803 +/- 65 fC pF(-1), n = 27 vs. 167 +/- 32 fC pF(-1), n = 38, P < 0.001). Ascending aortic stenosis significantly increased QCa in epicardial myocytes (368 +/- 54 fC pF(-1), n = 42, P < 0.05), but did not alter QCa in endocardial myocytes (696 +/- 65 fC pF(-1), n = 26). Peak and current-voltage relation of the AP-induced Ca2+ current were unaffected by AS. However, the time course of the current-voltage relation was significantly prolonged in epicardial myocytes of AS animals. Model calculations revealed that the increase in QCa can be ascribed to a prolonged opening of the activation gate, whereas an increase in inactivation prevents an excessive increase in QCa. In conclusion, AS significantly increased AP-induced Ca2+ influx in epicardial but not in endocardial myocytes of the rat left ventricle.

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.

Genetic manipulation of calcium-handling proteins in cardiac myocytes. II. Mathematical modeling studies

We developed a mathematical model specific to rat ventricular myocytes that includes electrophysiological representation, ionic homeostasis, force production, and sarcomere movement. We used this model to interpret, analyze, and compare two genetic manipulations that have been shown to increase myocyte relaxation rates, parvalbumin (Parv) de novo expression, and sarco(endo)plasmic reticulum Ca(2+)-ATPase (SERCA2a) overexpression. The model was used to seek mechanistic insights into 1) the relative contribution of two mechanisms by which SERCA2a overexpression modifies Ca2+ sequestration, i.e., more pumps and an increase in the SERCA2a-to-phospholamban ratio, 2) the mechanisms behind postrest potentiation and how Parv and SERCA2a influence this response, and 3) why Parv myocytes retain their fast kinetics when endogenous SERCA2a is partially impaired by thapsigargin (a condition used to mimic diastolic dysfunction). The model was also utilized to predict whether Parv metal-binding characteristics might be modified to improve diastolic and systolic functions and whether Parv or SERCA2a might affect diastolic Ca2+ levels and myocyte energetics. One outcome of the model was to demonstrate a higher peak and total ATP consumption in SERCA2a myocytes and more even distribution of ATP throughout the cardiac cycle in Parv myocytes. This may have implications for failing hearts that are energetically compromised.

Modeling the isolated cardiac myocyte

Computer modeling of cardiac myocytes has flourished in recent years. Models have evolved from mathematical descriptions of ionic channels alone to more sophisticated formulations that include calcium transport mechanisms, ATP production and metabolic pathways. The increased complexity is fueled by the new data available in the field. The continuous production of experimental data has led to the evolution of increasingly refined descriptions of the phenomena by modelers. Integrating the numerous systems involved in cardiac myocyte homeostasis makes the use of computer models necessary due to the unreliability of intuitive approaches. However the complexity of the model should not imply a cumbersome operation of the program. As with any tool, computer models have to be easy to operate or their strength will be diminished and potential users will not benefit fully from them. The contribution of the computer modeler to their respective biological fields will be more successful and enduring if modelers devote sufficient time to implement their equations into a model with user-friendly characteristics.

Effects of Electrical Shocks on Ca i 2+ and V m in Myocyte Cultures

Changes in intracellular calcium concentration (ΔCa i 2+ ) induced by electrical shocks may play an important role in defibrillation, but high-resolution ΔCa i 2+ measurements in a multicellular cardiac tissue and their relationship to corresponding V m changes (ΔV m ) are lacking. Here, we measured shock-induced ΔCa i 2+ and ΔV m in geometrically defined myocyte cultures. Cell strands (width=0.8 mm) were double-stained with V m -sensitive dye RH-237 and a low-affinity Ca i 2+ -sensitive dye Fluo-4FF. Shocks (E≈5 to 40 V/cm) were applied during the action potential plateau. Shocks caused transient Ca i 2+ decrease at sites of both negative and positive ΔV m . Similar Ca i 2+ changes were observed in an ionic model of adult rat myocytes. Simulations showed that the Ca i 2+ decrease at sites of ΔV + m was caused by the outward flow of I CaL and troponin binding; at sites of ΔV − m it was caused by inactivation of I CaL combined with extrusion by Na–Ca exchanger and troponin binding. The important role of I CaL was supported by experiments in which application of nifedipine eliminated Ca i 2+ decrease at ΔV + m sites. Largest ΔCa i 2+ were observed during shocks of ≈10 V/cm causing simple monophasic ΔV m . Shocks stronger than ≈20 V/cm caused smaller ΔCa i 2+ and postshock elevation of diastolic Ca i 2+ . This was paralleled with occurrence of biphasic negative ΔV m that indicated membrane electroporation. Thus, these data indicate that shocks transiently decrease Ca i 2+ at sites of both ΔV − m and ΔV + m . Outward flow of I CaL plays an important role in Ca i 2+ decrease in the ΔV + m areas. Very strong shocks caused smaller negative ΔCa i 2+ and postshock elevation of diastolic Ca i 2+ , likely caused by membrane electroporation.

Computer model of action potential of mouse ventricular myocytes

We have developed a mathematical model of the mouse ventricular myocyte action potential (AP) from voltage-clamp data of the underlying currents and Ca2+ transients. Wherever possible, we used Markov models to represent the molecular structure and function of ion channels. The model includes detailed intracellular Ca2+ dynamics, with simulations of localized events such as sarcoplasmic Ca2+ release into a small intracellular volume bounded by the sarcolemma and sarcoplasmic reticulum. Transporter-mediated Ca2+ fluxes from the bulk cytosol are closely matched to the experimentally reported values and predict stimulation rate-dependent changes in Ca2+ transients. Our model reproduces the properties of cardiac myocytes from two different regions of the heart: the apex and the septum. The septum has a relatively prolonged AP, which reflects a relatively small contribution from the rapid transient outward K+ current in the septum. The attribution of putative molecular bases for several of the component currents enables our mouse model to be used to simulate the behavior of genetically modified transgenic mice.

Regulation of Ion Channel Expression

A potentially important mechanism controlling ion channel expression is homeostatic regulation, which can act to maintain a stable electrophysiological phenotype in cardiac myocytes as well as to provide plasticity in response to genetic, pathological, or pharmacological insults. The capabilities and limitations of the homeostatic regulatory mechanisms that contribute to the control of cardiac ion channel expression are the primary topic of this review.

Pharmacological activation of plasma-membrane KATP channels reduces reoxygenation-induced Ca(2+) overload in cardiac myocytes via modulation of the diastolic membrane potential

1. The opening of cardiac plasma-membrane ATP-sensitive K(+) channels (pmK(ATP)) can protect the heart against ischaemia/reperfusion injury. We recently demonstrated that the resting membrane potential (E(m)) of ventricular myocytes strongly modulates reoxygenation-induced Ca(2+) overload. This led to the hypothesis that activation of pmK(ATP) can influence the extent of chemically induced hypoxia (CIH)/reoxygenation Ca(2+) overload via hyperpolarization of the diastolic membrane potential of ventricular myocytes. 2. The membrane potential (E(m)) of isolated rat myocytes was determined using the perforated patch-clamp technique and DiBac(4)(3) imaging. Intracellular Ca(2+) ([Ca(2+)](i)) was monitored using FURA-2 imaging. 3. CIH/reoxygenation caused a significant depolarization of E(m) and a substantial increase in [Ca(2+)](i). The K(ATP) opener pinacidil (100 microm) and the pmK(ATP) opener P-1075 (100 microm) hyperpolarized the E(m) of normoxic myocytes. Pinacidil (100 microm) and P-1075 (10 and 100 microm), applied during reoxygenation, hyperpolarized E(m) and prevented reoxygenation-induced increases in [Ca(2+)](i). 4. Myocyte hypercontracture and death increased in parallel with an E(m) depolarization of 10-15 mV and increases in [Ca(2+)](i). Under these conditions, the selective pmK(ATP) channel inhibitor HMR 1098 further depolarized myocyte membrane potential and increased hypercontracture. 5. In conclusion, activation of pmK(ATP) channels can prevent CIH/reoxygenation-induced Ca(2+) overload via a mechanism that is dependent on hyperpolarization of diastolic membrane potential. Hyperpolarization toward normal resting membrane potential favours the Ca(2+) extrusion mode of Na(+)/Ca(2+) exchange.

Prenatal Exposure to Carbon Monoxide Affects Postnatal Cellular Electrophysiological Maturation of the Rat Heart

Background— Maternal smoking is an independent risk factor for sudden infant death syndrome (SIDS). Carbon monoxide (CO) is a major component of smoke. No information is available about the effect of CO and/or smoking on postnatal maturation of the heart. The aim of this study was to investigate the effect of prenatal exposure to CO on cellular electrophysiological maturation in male Wistar rats.

Methods and Results— The patch-clamp technique was used to measure action potential (AP) and ionic currents ( I to and I Ca,L ) from rat ventricular myocytes. During growth, AP duration measured at −20 and −50 mV (APD − 20 and APD − 50 ) decreased progressively in both groups; the process was significantly delayed in rats exposed prenatally to 150 ppm CO: At 4 weeks, APD − 20 and APD − 50 were 89.5±18.2 and 147.7±24.5 ms in CO (n=13) and 35.6±4.5 and 77.8±8.3 ms in control rats (Ctr; n=14; P <0.01 and P <0.05, respectively) and normalized at 8 weeks. At 4 weeks, the density of I Ca,L was significantly higher (21.3±1.6 pA/pF, n=17, versus 15.9±1.6 pA/pF, n=22; P <0.05) and the density of I to significantly lower (9.6±1.5, n=22, versus 15.2±2.2 pA/pF, n=19; P <0.01) in CO than in Ctr and normalized thereafter.

Conclusions— Prenatal CO exposure affects the physiological shortening of APD in neonatal rats. We speculate that a prolonged myocyte repolarization induced by prenatal exposure to smoke may establish a period of vulnerability for life-threatening arrhythmias in infancy.

Genesis of the monophasic action potential: role of interstitial resistance and boundary gradients

The extracellular potential at the site of a mechanical deformation has been shown to resemble the underlying transmembrane action potential, providing a minimally invasive way to access membrane dynamics. The biophysical factors underlying the genesis of this signal, however, are still poorly understood. With the use of data from a recent experimental study in a murine heart, a three-dimensional anisotropic bidomain model of the mouse ventricular free wall was developed to study the currents and potentials resulting from the application of a point mechanical load on cardiac tissue. The applied pressure is assumed to open nonspecific pressure-sensitive channels depolarizing the membrane, leading to monophasic currents at the electrode edge that give rise to the monophasic action potential (MAP). The results show that the magnitude and the time course of the MAP are reproduced only for certain combinations of local or global intracellular and interstitial resistances that form a resting tissue length constant that, if applied over the entire domain, is smaller than that required to match the wave speed. The results suggest that the application of pressure not only causes local depolarization but also changes local tissue properties, both of which appear to play a critical role in the genesis of the MAP.

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.

Modeling beta-adrenergic control of cardiac myocyte contractility in silico

The beta-adrenergic signaling pathway regulates cardiac myocyte contractility through a combination of feedforward and feedback mechanisms. We used systems analysis to investigate how the components and topology of this signaling network permit neurohormonal control of excitation-contraction coupling in the rat ventricular myocyte. A kinetic model integrating beta-adrenergic signaling with excitation-contraction coupling was formulated, and each subsystem was validated with independent biochemical and physiological measurements. Model analysis was used to investigate quantitatively the effects of specific molecular perturbations. 3-Fold overexpression of adenylyl cyclase in the model allowed an 85% higher rate of cyclic AMP synthesis than an equivalent overexpression of beta 1-adrenergic receptor, and manipulating the affinity of Gs alpha for adenylyl cyclase was a more potent regulator of cyclic AMP production. The model predicted that less than 40% of adenylyl cyclase molecules may be stimulated under maximal receptor activation, and an experimental protocol is suggested for validating this prediction. The model also predicted that the endogenous heat-stable protein kinase inhibitor may enhance basal cyclic AMP buffering by 68% and increasing the apparent Hill coefficient of protein kinase A activation from 1.0 to 2.0. Finally, phosphorylation of the L-type calcium channel and phospholamban were found sufficient to predict the dominant changes in myocyte contractility, including a 2.6x increase in systolic calcium (inotropy) and a 28% decrease in calcium half-relaxation time (lusitropy). By performing systems analysis, the consequences of molecular perturbations in the beta-adrenergic signaling network may be understood within the context of integrative cellular physiology.

A model of graded calcium release and L-type Ca2+ channel inactivation in cardiac muscle

We have developed a model of Ca(2+) handling in ferret ventricular myocytes. This model includes a novel L-type Ca(2+) channel, detailed intracellular Ca(2+) movements, and graded Ca(2+)-induced Ca(2+) release (CICR). The model successfully reproduces data from voltage-clamp experiments, including voltage- and time-dependent changes in intracellular Ca(2+) concentration ([Ca(2+)](i)), L-type Ca(2+) channel current (I(CaL)) inactivation and recovery kinetics, and Ca(2+) sparks. The development of graded CICR is critically dependent on spatial heterogeneity and the physical arrangement of calcium channels in opposition to ryanodine-sensitive release channels. The model contains spatially distinct subsystems representing the subsarcolemmal regions where the junctional sarcoplasmic reticulum (SR) abuts the T-tubular membrane and where the L-type Ca(2+) channels and SR ryanodine receptors (RyRs) are localized. There are eight different types of subsystems in our model, with between one and eight L-type Ca(2+) channels distributed binomially. This model exhibits graded CICR and provides a quantitative description of Ca(2+) dynamics not requiring Monte-Carlo simulations. Activation of RyRs and release of Ca(2+) from the SR depend critically on Ca(2+) entry through L-type Ca(2+) channels. In turn, Ca(2+) channel inactivation is critically dependent on the release of stored intracellular Ca(2+). Inactivation of I(CaL) depends on both transmembrane voltage and local [Ca(2+)](i) near the channel, which results in distinctive inactivation properties. The molecular mechanisms underlying many I(CaL) gating properties are unclear, but [Ca(2+)](i) dynamics clearly play a fundamental role.

Computational model of the ventricular action potential in adult spontaneously hypertensive rats

INTRODUCTION

Cardiac hypertrophy has substantial clinical significance because many hypertrophic cells have markedly prolonged repolarization behavior, which may lead to increased risk for cardiac arrhythmias. Spontaneously hypertensive rat (SHR) is one model of hypertension that is studied extensively and is considered to be the best laboratory model of human hypertension. We extended our previously published model of the rat ventricular myocyte to simulate the effects of hypertrophy in SHR.

METHODS AND RESULTS

In SHR it has been shown that the membrane capacitance is increased, the density of transient outward K+ current is decreased, the sarcoplasmic reticulum Ca2+ ATPase activity is reduced, and the cell volumes are increased compared to those of the normal rat. We introduced these changes into our previous model of the rat ventricular myocyte and simulated the ventricular action potential of SHR. Our results demonstrated increased action potential duration (APD) and increased peak systolic value of the intracellular calcium transient in SHR. Simulations with reduced extracellular K+ concentration ([K+]o) have shown that there is increased APD shortening in SHR compared to that of the normal rat.

CONCLUSIONS

Our computational model qualitatively simulated the electrophysiologic changes observed in SHR and provided the plausible mechanistic linkage between the prolonged APD and increased inotropy. Our model results also demonstrated the electrophysiologic changes observed with reduced [K+]o in SHR, a finding that is clinically significant in hypertensive patients with left ventricular hypertrophy undergoing diuretic treatment.

Resting membrane potential regulates Na(+)-Ca2+ exchange-mediated Ca2+ overload during hypoxia-reoxygenation in rat ventricular myocytes

In the heart, reperfusion following an ischaemic episode can result in a marked increase in [Ca2+]i and cause myocyte dysfunction and death. Although the Na(+)-Ca2+ exchanger has been implicated in this response, the ionic mechanisms that are responsible have not been identified. In this study, the hypothesis that the diastolic membrane potential can influence Na(+)-Ca2+ exchange and Ca2+ homeostasis during chemically induced hypoxia-reoxygenation has been tested using right ventricular myocytes isolated from adult rat hearts. Superfusion with selected [K+]o of 0.5, 2.5, 5, 7, 10 and 15 mM yielded the following resting membrane potentials: -27.6+/-1.63 mV, -102.2+/-1.89, -86.5+/-1.03, -80.1+/-1.25, -73.6+/-1.02 and -66.4+/-1.03, respectively. In a second set of experiments myocytes were subjected to chemically induced hypoxia-reoxygenation at these different [K+]o, while [Ca2+]i was monitored using fura-2. These results demonstrated that after chemically induced hypoxia-reoxygenation had caused a marked increase in [Ca2+]i, hyperpolarization of myocytes with 2.5 mM [K+]o significantly reduced [Ca2+]i (7.5+/-0.32 vs. 16.9+/-0.55%); while depolarization (with either 0.5 or 15 mM [K+]o) significantly increased [Ca2+]i (31.8+/-3.21 and 20.8+/-0.36 vs. 16.9+/-0.55%, respectively). As expected, at depolarized membrane potentials myocyte hypercontracture and death increased in parallel with Ca2+ overload. The involvement of the Na(+)-Ca2+ exchanger in Ca2+ homeostasis was evaluated using the Na(+)-Ca2+ exchanger inhibitor KB-R7943. During reoxygenation KB-R7943 (5 microM) almost completely prevented the increase in [Ca2+]i both in control conditions (in 5 mM [K+]o: 2.2+/-0.40 vs. 10.8+/-0.14%) and in depolarized myocytes (in 15 mM [K+]o: -2.1+/-0.51 vs. 11.3+/-0.05%). These findings demonstrate that the resting membrane potential of ventricular myocytes is a critical determinant of [Ca2+]i during hypoxia-reoxygenation. This appears to be due mainly to an effect of diastolic membrane potential on the Na(+)-Ca2+ exchanger, since at depolarized potentials this exchanger mechanism operates in the reverse mode, causing a significant Ca2+ influx.

Dihydropyridine Ca2+ channel antagonists and agonists block Kv4.2, Kv4.3 and Kv1.4 K+ channels expressed in HEK293 cells

(1) We have determined the molecular basis of nicardipine-induced block of cardiac transient outward K(+) currents (I(to)). Inhibition of I(to) was studied using cloned voltage-dependent K(+) channels (Kv) channels, rat Kv4.3L, Kv4.2, and Kv1.4, expressed in human embryonic kidney cell line 293 (HEK293) cells. (2) Application of the dihydropyridine Ca(2+) channel antagonist, nicardipine, accelerated the inactivation rate and reduced the peak amplitude of Kv4.3L currents in a concentration-dependent manner (IC(50): 0.42 micro M). The dihydropyridine (DHP) Ca(2+) channel agonist, Bay K 8644, also blocked this K(+) current (IC(50): 1.74 micro M). (3) Nicardipine (1 micro M) slightly, but significantly, shifted the voltage dependence of activation and steady-state inactivation to more negative potentials, and also slowed markedly the recovery from inactivation of Kv4.3L currents. (4) Coexpression of K(+) channel-interacting protein 2 (KChIP2) significantly slowed the inactivation of Kv4.3L currents as expected. However, the features of DHP-induced block of K(+) current were not substantially altered. (5) Nicardipine exhibited similar block of Kv1.4 and Kv4.2 channels stably expressed in HEK293 cells; IC(50)'s were 0.80 and 0.62 micro M, respectively. (6) Thus, at submicromolar concentrations, DHP Ca(2+) antagonist and agonist inhibit Kv4.3L and have similar inhibiting effects on other components of cardiac I(to), Kv4.2 and Kv1.4.

A mathematical model of the electrophysiological alterations in rat ventricular myocytes in type-I diabetes

Our mathematical model of the rat ventricular myocyte (Pandit et al., 2001) was utilized to explore the ionic mechanism(s) that underlie the altered electrophysiological characteristics associated with the short-term model of streptozotocin-induced, type-I diabetes. The simulations show that the observed reductions in the Ca(2+)-independent transient outward K(+) current (I(t)) and the steady-state outward K(+) current (I(ss)), along with slowed inactivation of the L-type Ca(2+) current (I(CaL)), can result in the prolongation of the action potential duration, a well-known experimental finding. In addition, the model demonstrates that the slowed reactivation kinetics of I(t) in diabetic myocytes can account for the more pronounced rate-dependent action potential duration prolongation in diabetes, and that a decrease in the electrogenic Na(+)-K(+) pump current (I(NaK)) results in a small depolarization in the resting membrane potential (V(rest)). This depolarization reduces the availability of the Na(+) channels (I(Na)), thereby resulting in a slower upstroke (dV/dt(max)) of the diabetic action potential. Additional simulations suggest that a reduction in the magnitude of I(CaL), in combination with impaired sarcoplasmic reticulum uptake can lead to a decreased sarcoplasmic reticulum Ca(2+) load. These factors contribute to characteristic abnormal [Ca(2+)](i) homeostasis (reduced peak systolic value and rate of decay) in myocytes from diabetic animals. In combination, these simulation results provide novel information and integrative insights concerning plausible ionic mechanisms for the observed changes in cardiac repolarization and excitation-contraction coupling in rat ventricular myocytes in the setting of streptozotocin-induced, type-I diabetes.

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.