Rationale: Variability in delivery of oxygen can lead to electric instability in the myocardium and the generation of
arrhythmias. In addition ischemic heart disease and angina are associated with an increase in circulating
catecholamines that further increases the risk of developing ventricular tachyarrhythmias.
Objective: We investigated the net effects of acute hypoxia and catecholamines on the cardiac action potential.
Methods and Results: We incorporated all published data on the effects of hypoxia on the late Na current (INa-L),
the fast Na urrent (INa), the basal L-type Ca2 hannel current (ICa-L), and the slow (IKs) and rapid
components of the delayed rectifier K-current (IKr) in the absence and presence of beta-adrenergic receptor
(BAR) stimulation into the Luo–Rudy model of the action potential. Hypoxia alone had little effect on the action
potential configuration or action potential duration. However in the presence of BAR stimulation, hypoxia
caused a prolongation of the action potential and early afterdepolarizations (EADs) and spontaneous tachycardia
were induced. Experiments performed in guinea pig ventricular myocytes confirmed the modeling results.
Conclusions: EADs occur predominantly because of the increased sensitivity of ICa-L to BAR stimulation during
hypoxia. BAR stimulation is necessary to induce EADs as EADs are never observed during hypoxia in the
absence of BAR stimulation.

Development and application of physiologically detailed dynamic models of the action potential (AP) and Ca 2+ cycling in cardiac cells is a rapidly growing aspect of computational cardiac electrophysiology. Given the large scale of the nonlinear system involved, questions were recently raised regarding reproducibility, numerical stability, and uniqueness of model solutions, as well as ability of the model to simulate AP propagation in multicellular configurations. To address these issues, we reexamined ventricular models of myocyte AP developed in our laboratory with the following results. 1), Recognizing that the model involves a system of differential-algebraic equations, a procedure is developed for estimating consistent initial conditions that insure uniqueness and stability of the solution. 2), Model parameters that can be used to modify these initial conditions according to experimental values are identified. 3), A convergence criterion for steady-state solution is defined based on tracking the incremental contribution of each ion species to the membrane voltage. 4), Singularities in state variable formulations are removed analytically. 5), A biphasic current stimulus is implemented to completely eliminate stimulus artifact during long-term pacing over a broad range of frequencies. 6), Using the AP computed based on 1–5 above, an efficient scheme is developed for computing propagation in multicellular models.

Ion-channel function is determined by its gating movement. Yet, molecular dynamics and electrophysiological simulations were never combined to link molecular structure to function. We performed multiscale molecular dynamics and continuum electrostatics calculations to simulate a cardiac K⁺ channel (I_Ks) gating and its alteration by mutations that cause arrhythmias and sudden death. An all-atom model of the I_Ks a-subunit KCNQ1, based on the recent Kv1.2 structure, is used to calculate electrostatic energies during gating. Simulations are compared with experiments where varying degrees of positive charge—added via point mutation—progressively reduce current. Whole-cell simulations show that mutations cause action potential and ECG QT interval prolongation, consistent with clinical phenotypes. This framework allows integration of multiscale observations to study the molecular basis of excitation and its alteration by disease.

Computational models of cardiac myocytes are important tools for understanding ionic mechanisms of arrhythmia. This work presents a new model of the canine epicardial myocyte that reproduces a wide range of experimentally observed rate dependent behaviors in cardiac cell and tissue, including action potential duration (APD) adaptation, restitution and accommodation. Model behavior depends on updated formulations for the 4-AP sensitive transient outward current (I_to1), the slow component of the delayed rectifier potassium current (I_Ks), the L-type Ca²⁺ channel (I_Ca,L) and the sodium-potassium pump (I_NaK) fit to data from canine ventricular myocytes. We find that Ito1 plays a limited role in potentiating peak ICa,L and sarcoplasmic reticulum Ca²⁺ release for propagated APs, but modulates the time course of APD restitution. I_Ks plays an important role in APD shortening at short diastolic intervals, despite a limited role in AP repolarization at longer cycle lengths. In addition, we find that I_Ca,L plays a critical role in APD accommodation and rate dependence of APD restitution through its indirect role in intracellular Na+ accumulation and increased outward I_NaK at rapid heart rates. Our simulation results provide valuable insight into the mechanistic basis of rate-dependent phenomena important for determining the heart's response to rapid and irregular pacing rates (e.g. arrhythmia). Accurate simulation of rate dependent phenomena and increased understanding of their mechanistic basis will lead to more realistic multicellular simulations of arrhythmia and identification of molecular therapeutic targets.

The National Heart, Lung, and Blood Institute (NHLBI) convened a workshop of cardiologists, cardiac electrophysiologists, cell biophysicists, and computational modelers on August 20 and 21, 2007, in Washington, DC, to advise the NHLBI on new research directions needed to develop integrative approaches to elucidate human cardiac function. The workshop strove to identify limitations in the use of data from nonhuman animal species for elucidation of human electromechanical function/activity and to identify what specific information on ion channel kinetics, calcium handling, and dynamic changes in the intracellular/extracellular milieu is needed from human cardiac tissues to develop more robust computational models of human cardiac electromechanical activity. This article summarizes the workshop discussions and recommendations on the following topics: (1) limitations of animal models and differences from human electrophysiology, (2) modeling ion channel structure/function in the context of whole-cell electrophysiology, (3) excitation-contraction coupling and regulatory pathways, (4) whole-heart simulations of human electromechanical activity, and (5) what human data are currently needed and how to obtain them. The recommendations can be found on the NHLBI Web site at http://www.nhlbi.nih.gov/meetings/workshops/electro.htm.

Cardiac I_Kr is a critical repolarizing current in the heart and a target for inherited and acquired long-QT syndrome (LQTS). Biochemical and functional studies have demonstrated that I_Kr channels are heteromers composed of both hERG 1a and 1b subunits, yet our current understanding of I_Kr functional properties derives primarily from studies of homooligomers of the original hERG 1a isolate. Here, we examine currents produced by hERG 1a and 1a/1b channels expressed in HEK-293 cells at near-physiological temperatures. We find that heteromeric hERG 1a/1b currents are much larger than hERG 1a currents and conduct 80% more charge during an action potential. This surprising difference corresponds to a 2-fold increase in the apparent rates of activation and recovery from inactivation, thus reducing rectification and facilitating current rebound during repolarization. Kinetic modeling shows these gating differences account quantitatively for the differences in current amplitude between the 2 channel types. Drug sensitivity was also different. Compared to homomeric 1a channels, heteromeric 1a/1b channels were inhibited by E-4031 with a slower time course and a corresponding 4-fold shift in the IC50. The importance of hERG 1b in vivo is supported by the identification of a 1b-specific A8V missense mutation in 1/269 unrelated genotype-negative LQTS patients that was absent in 400 control alleles. Mutant 1bA8V expressed alone or with hERG 1a in HEK-293 cells dramatically reduced 1b protein levels. Thus, mutations specifically disrupting hERG 1b function are expected to reduce cardiac I_Kr and enhance drug sensitivity, and represent a potential mechanism underlying inherited or acquired LQTS.

Ca²⁺/calmodulin-dependent protein kinase II is a multifunctional serine/threonine kinase with diverse cardiac roles including regulation of excitation contraction, transcription, and apoptosis. Dynamic regulation of CaMKII activity occurs in cardiac disease and is linked to specific disease phenotypes through its effects on ion channels, transporters, transcription and cell death pathways. Recent mathematical models of the cardiomyocyte have incorporated limited elements of CaMKII signaling to advance our understanding of how CaMKII regulates cardiac contractility and excitability. Given the importance of CaMKII in cardiac disease, it is imperative that computer models evolve to capture the dynamic range of CaMKII activity. In this study, using mathematical modeling combined with biochemical and imaging techniques, we test the hypothesis that CaMKII signaling in the canine infarct border zone (BZ) contributes to impaired calcium homeostasis and electrical remodeling. We report that the level of CaMKII autophosphorylation is significantly increased in the BZ region. Computer simulations using an updated mathematical model of CaMKII signaling reproduce abnormal Ca²⁺ transients and action potentials characteristic of the BZ. Our simulations show that CaMKII hyperactivity contributes to abnormal Ca²⁺ homeostasis and reduced action potential upstroke velocity due to effects on I(Na) gating kinetics. In conclusion, we present a new mathematical tool for studying effects of CaMKII signaling on cardiac excitability and contractility over a dynamic range of kinase activities. Our experimental and theoretical findings establish abnormal CaMKII signaling as an important component of remodeling in the canine BZ.

Two mechanisms are generally proposed to explain right precordial ST-segment elevation in Brugada syndrome: 1) right ventricular (RV) subepicardial action potential shortening and/or loss of dome causing transmural dispersion of repolarization; and 2) RV conduction delay. Here we report novel mechanistic insights into ST-segment elevation associated with a Na⁺ current (I_Na) loss-of-function mutation from studies in a Dutch kindred with the COOH-terminal SCN5A variant p.Phe2004Leu. The proband, a man, experienced syncope at age 22 yr and had coved-type ST-segment elevations in ECG leads V1 and V2 and negative T waves in V2. Peak and persistent mutant I(Na) were significantly decreased. I_Na closed-state inactivation was increased, slow inactivation accelerated, and recovery from inactivation delayed. Computer-simulated I_Na-dependent excitation was decremental from endo- to epicardium at cycle length 1,000 ms, not at cycle length 300 ms. Propagation was discontinuous across the midmyocardial to epicardial transition region, exhibiting a long local delay due to phase 0 block. Beyond this region, axial excitatory current was provided by phase 2 (dome) of the M-cell action potentials and depended on L-type Ca²⁺ current ("phase 2 conduction"). These results explain right precordial ST-segment elevation on the basis of RV transmural gradients of membrane potentials during early repolarization caused by discontinuous conduction. The late slow-upstroke action potentials at the subepicardium produce T-wave inversion in the computed ECG waveform, in line with the clinical ECG.

OBJECTIVES: Patients with a missense mutation of the calsequestrin 2 gene (CASQ2) are at risk for catecholaminergic polymorphic ventricular tachycardia. In this theoretical study, we investigate a potential mechanism by which CASQ2(D307H) manifests its pro-arrhythmic consequences in patients. METHODS: Using simulations in a model of the guinea pig ventricular myocyte, we investigate the mutation's effect on SR Ca²⁺ storage, the Ca²⁺ transient (CaT), and its indirect effect on ionic currents and membrane potential. We model the effects of isoproterenol (ISO) on Ca(V)1.2 (the L-type Ca²⁺ current, I(Ca(L))) and other targets of beta-adrenergic stimulation. RESULTS: CASQ2(D307H) reduces SR storage capacity, thereby reducing the magnitude of CaT (Control: 0.79 muM, CASQ2(D307H): 0.52 muM, at cycle length of 1500 ms). The combined effect of CASQ2(D307H) and ISO elevates SR free Ca²⁺ at a rapid rate, leading to store-overload-induced Ca²⁺ release and delayed afterdepolarization (DAD). If resting membrane potential is sufficiently elevated, the Na⁺-Ca²⁺ exchange-driven DAD can trigger I_Na and I_Ca(L) activation, generating a triggered arrhythmogenic AP. CONCLUSIONS: The CASQ2(D307H) mutation manifests its pro-arrhythmic consequences due to store-overload-induced Ca(2+) release and DAD formation due to excess free SR Ca²⁺ following rapid pacing and beta-adrenergic stimulation.

Macroscopic ion channel current is the summation of the stochastic records of individual channel currents and therefore relates to their statistical properties. As a consequence of this relationship, it may be possible to derive certain statistical properties of single channel records or even generate some estimates of the records themselves from the macroscopic current when the direct measurement of single channel currents is not applicable. We present a procedure for generating the single channel records of an ion channel from its macroscopic current when the stochastic process of channel gating has the following two properties: (I) the open duration is independent of the time of opening event and has a single exponential probability density function (pdf), (II) all the channels have the same probability to open at time t. The application of this procedure is considered for cases where direct measurement of single channel records is difficult or impossible. First, the probability density function (pdf) of opening events, a statistical property of single channel records, is derived from the normalized macroscopic current and mean channel open duration. Second, it is shown that under the conditions (I) and (II), a non-stationary Markov model can represent the stochastic process of channel gating. Third, the non-stationary Markov model is calibrated using the results of the first step. The non-stationary formulation increases the model ability to generate a variety of different single channel records compared to common stationary Markov models. The model is then used to generate single channel records and to obtain other statistical properties of the records. Experimental single channel records of inactivating BK potassium channels are used to evaluate how accurately this procedure reconstructs measured single channel sweeps.

Macroscopic ion channel current can be derived by summation of the stochastic records of individual channel currents. In this paper, we present two probability density functions of single channel records that can uniquely determine the macroscopic current regardless of other statistical properties of records or the stochastic model of channel gating (presented often with stationary Markov models). We show that H(t), probability density function of channel opening events (introduced explicitly in this paper), and D(t), probability density function of the open duration (sometimes has named dwell time distribution as well), determine the normalized macroscopic current, G(t), throughwhere P(t) is the cumulative density function of H(t), Q(t) is the cumulative density function of D(t), * is the symbol of convolution integral and G(t) is the macroscopic current divided by the amplitude of single channel current and the number of single channel sweeps. Compared to other equations for the macroscopic current, here the macroscopic current is expressed only in terms of the statistical properties of single channel current and not the stochastic model of ion channel gating or a conditioned form of macroscopic current. Single channel currents of an inactivating BK channel were used to validate this relationship experimentally too. In this paper, we used median filters as they can remove the unwanted noise without smoothing the transitions between open and closed states (compare to low pass filters). This filtering leads to more accurate measurement of transition times and less amount of missed events.

We present a theoretical approach for investigating effects of drug-channel interaction. We use as an example open-channel or inactivated-channel block by the local anesthetics mexiletine and lidocaine, respectively, of normal and DKPQ mutant Na⁺ channels associated with the long-QT syndrome type 3. Results show how kinetic properties of channel gating, which are affected by mutations, are important determinants of drug efficacy. Investigations of Na⁺ channel blockade are conducted at multiple scales: single channel, macroscopic current and, importantly, during the cardiac action potential (AP). Our findings suggest that channel mean open time is a primary determinant of open state blocker efficacy. The simulations also suggest that inactivation state block by lidocaine is less effective in restoring normal repolarization and adversely suppresses peak Na⁺ current.

Ion channels are typically studied in isolation (in expression systems or isolated membrane patches), away from the physiological environment of the cell where they interact to generate the AP. A major challenge remains the integration of ion-channel properties into the functioning, complex and highly interactive cell system, with the objective to relate molecular-level processes and their modification by disease to whole-cell function and clinical phenotype. In this article we describe how computational biology can be used to achieve such integration. We explain how mathematical (Markov) models of ion-channel kinetics are incorporated into integrated models of cardiac cells to compute the AP. We provide examples of mathematical (computer) simulations of physiological and pathological phenomena, including AP adaptation to changes in heart rate, genetic mutations in SCN5A and HERG genes that are associated with fatal cardiac arrhythmias, and effects of the CaMKII regulatory pathway and β-adrenergic cascade on the cell electrophysiological function.

More than 20 years have passed since the discovery that a collection of specific calcium/calmodulin-dependent phosphorylation events is the result of a single multifunctional kinase. Since that time, we have learned a great deal about this multifunctional and ubiquitous kinase, known today as calcium/calmodulin-dependent protein kinase II (CaMKII). CaMKII is interesting not only for its widespread distribution and broad specificity but also for its biophysical properties, most notably its activation by the critical second messenger complex calcium/calmodulin and its autophosphorylating capability. A central role for CaMKII has been identified in regulating a diverse array of fundamental cellular activities. Furthermore, altered CaMKII activity profoundly impacts function in the brain and heart. Recent findings that CaMKII expression in the heart changes during hypertrophy, heart failure, myocardial ischemia, and infarction suggest that CaMKII may be a viable therapeutic target for patients suffering from common forms of heart disease.

The role of I_Ks, the slow delayed rectifier K⁺ current, in cardiac ventricular repolarization has been a subject of debate. We develop a detailed Markov model of I_Ks and its ß-subunit KCNQ1 and examine their kinetic properties during the cardiac ventricular action potential at different rates. We observe that interaction between KCNQ1 and KCNE1 (the ß-subunit) confers kinetic properties on I_Ks that make it suitable for participation in action potential repolarization and its adaptation to rate changes; in particular, the channel develops an available reserve of closed states near the open state that can open rapidly on demand. Because of its ability to form an available reserve, I_Ks can function as a repolarization reserve when I_Kr, the rapid delayed rectifier, is reduced by disease or drug and can prevent excessive action potential prolongation and development of arrhythmogenic early afterdepolarizations.

BACKGROUND: Computational biology is a powerful tool for elucidating arrhythmogenic mechanisms at the cellular level, where complex interactions between ionic processes determine behavior. A novel theoretical model of the canine ventricular epicardial action potential and calcium cycling was developed and used to investigate ionic mechanisms underlying Ca2+ transient (CaT) and action potential duration (APD) rate dependence. METHODS AND RESULTS: The Ca2+/calmodulin-dependent protein kinase (CaMKII) regulatory pathway was integrated into the model, which included a novel Ca2+-release formulation, Ca2+ subspace, dynamic chloride handling, and formulations for major ion currents based on canine ventricular data. Decreasing pacing cycle length from 8000 to 300 ms shortened APD primarily because of I(Ca(L)) reduction, with additional contributions from I(to1), I(NaK), and late I(Na). CaT amplitude increased as cycle length decreased from 8000 to 500 ms. This positive rate-dependent property depended on CaMKII activity. CONCLUSIONS: CaMKII is an important determinant of the rate dependence of CaT but not of APD, which depends on ion-channel kinetics. The model of CaMKII regulation may serve as a paradigm for modeling effects of other regulatory pathways on cell function.

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.

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.

Our phase-2 cardiac ventricular action potential model is presented in this paper. The article focuses on processes that regulate intracellular calcium and depend on its concentration. This model for the mammalian ventricular action potential is based mostly on the guinea pig ventricular cell. However, it provides the framework for modeling other types of ventricular cells with appropriate modifications made to account for species differences. The model provides the basis for the study of arrhythmogenic activity of the single myocyte including afterdepolarizations and triggered activity. It can simulate cellular responses under different degrees of calcium overload.

A computer model of a ring-shaped one-dimensional cardiac fiber was used to examine responses of reentrant propagation to premature stimuli applied under different degrees of head-tail interaction. Two different types (type I and type II) of termination window (TW) were identified. It was demonstrated that electrical alternans were most significant in medium degree head-tail interaction. For stronger or weaker head-tail interaction, the electrical alternans tended to decrease.

A mathematical model of the membrane action potential of the mammalian ventricular cell is introduced. The model is based, whenever possible, on recent single-cell and single-channel data and incorporates the possibility of changing extracellular potassium concentration [K]_o. Physiological simulations focus on the interaction between depolarization and repolarization (i.e., premature stimulation).