Proarrhythmic consequences of a KCNQ1 AKAP-binding domain mutation: computational models of whole cells and heterogeneous tissue

Systems modeling of oncogenic G-protein and GPCR signaling reveals unexpected differences in downstream pathway activation

Mathematical models of biochemical reaction networks are an important and emerging tool for the study of cell signaling networks involved in disease processes. One promising potential application of such mathematical models is the study of how disease-causing mutations promote the signaling phenotype that contributes to the disease. It is commonly assumed that one must have a thorough characterization of the network readily available for mathematical modeling to be useful, but we hypothesized that mathematical modeling could be useful when there is incomplete knowledge and that it could be a tool for discovery that opens new areas for further exploration. In the present study, we first develop a mechanistic mathematical model of a G-protein coupled receptor signaling network that is mutated in almost all cases of uveal melanoma and use model-driven explorations to uncover and explore multiple new areas for investigating this disease. Modeling the two major, mutually-exclusive, oncogenic mutations (Gαq/11 and CysLT2R) revealed the potential for previously unknown qualitative differences between seemingly interchangeable disease-promoting mutations, and our experiments confirmed oncogenic CysLT2R was impaired at activating the FAK/YAP/TAZ pathway relative to Gαq/11. This led us to hypothesize that CYSLTR2 mutations in UM must co-occur with other mutations to activate FAK/YAP/TAZ signaling, and our bioinformatic analysis uncovers a role for co-occurring mutations involving the plexin/semaphorin pathway, which has been shown capable of activating this pathway. Overall, this work highlights the power of mechanism-based computational systems biology as a discovery tool that can leverage available information to open new research areas.

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Dissecting the roles of calcium cycling and its coupling with voltage in the genesis of early afterdepolarizations in cardiac myocyte models

Early afterdepolarizations (EADs) are abnormal depolarizations during the plateau phase of the action potential, which are known to be associated with lethal arrhythmias in the heart. There are two major hypotheses for EAD genesis based on experimental observations, i.e., the voltage (Vm)-driven and intracellular calcium (Ca)-driven mechanisms. In ventricular myocytes, Ca and Vm are bidirectionally coupled, which can affect each other's dynamics and result in new dynamics, however, the roles of Ca cycling and its coupling with Vm in the genesis of EADs have not been well understood. In this study, we use an action potential model that is capable of independent Vm and Ca oscillations to investigate the roles of Vm and Ca coupling in EAD genesis. Four different mechanisms of EADs are identified, which are either driven by Vm oscillations or Ca oscillations alone, or oscillations caused by their interactions. We also use 5 other ventricular action potential models to assess these EAD mechanisms and show that EADs in these models are mainly Vm-driven. These mechanistic insights from our simulations provide a theoretical base for understanding experimentally observed EADs and EAD-related arrhythmogenesis.

An ensemble of parameters from a robust Markov-based model reproduces L-type calcium currents from different human cardiac myocytes

The development of modeling structures at the channel level that can integrate subcellular and cell models and properly reproduce different experimental data is of utmost importance in cardiac electrophysiology. In contrast to gate-based models, Markov Chain models are well suited to promote the integration of the subcellular level of the cardiomyocyte to the whole cell. In this paper, we develop Markov Chain models for the L-type Calcium current that can reproduce the electrophysiology of two established human models for the ventricular and Purkinje cells. In addition, instead of presenting a single set of parameters, we present a collection of set of parameters employing Differential Evolution algorithms that can properly reproduce very different protocol data. We show the importance of using an ensemble of a set of parameter values to obtain proper results when considering a second protocol that suppresses calcium inactivation and mimics a pathological condition. We discuss how model discrepancy, data availability, and parameter identifiability can influence the choice of the size of the collection. In summary, we have modified two cardiac models by proposing new Markov Chain models for the L-type Calcium. We keep the original whole-cell dynamics by reproducing the same characteristic action potential and calcium dynamics, whereas the Markov chain-based description of the L-type Calcium channels allows novel small spatial scale simulations of subcellular processes. Finally, the use of collections of parameters was crucial for addressing model discrepancy, identifiability issues, and avoiding fitting parameters overly precisely, i.e., overfitting.

Artificial intelligence in the diagnosis and management of arrhythmias

The field of cardiac electrophysiology (EP) had adopted simple artificial intelligence (AI) methodologies for decades. Recent renewed interest in deep learning techniques has opened new frontiers in electrocardiography analysis including signature identification of diseased states. Artificial intelligence advances coupled with simultaneous rapid growth in computational power, sensor technology, and availability of web-based platforms have seen the rapid growth of AI-aided applications and big data research. Changing lifestyles with an expansion of the concept of internet of things and advancements in telecommunication technology have opened doors to population-based detection of atrial fibrillation in ways, which were previously unimaginable. Artificial intelligence-aided advances in 3D cardiac imaging heralded the concept of virtual hearts and the simulation of cardiac arrhythmias. Robotics, completely non-invasive ablation therapy, and the concept of extended realities show promise to revolutionize the future of EP. In this review, we discuss the impact of AI and recent technological advances in all aspects of arrhythmia care.

Molecular noise filtering in the β-adrenergic signaling network by phospholamban pentamers

Phospholamban (PLN) is an important regulator of cardiac calcium handling due to its ability to inhibit the calcium ATPase SERCA. β-Adrenergic stimulation reverses SERCA inhibition via PLN phosphorylation and facilitates fast calcium reuptake. PLN also forms pentamers whose physiological significance has remained elusive. Using mathematical modeling combined with biochemical and cell biological experiments, we show that pentamers regulate both the dynamics and steady-state levels of monomer phosphorylation. Substrate competition by pentamers and a feed-forward loop involving inhibitor-1 can delay monomer phosphorylation by protein kinase A (PKA), whereas cooperative pentamer dephosphorylation enables bistable PLN steady-state phosphorylation. Simulations show that phosphorylation delay and bistability act as complementary filters that reduce the effect of random fluctuations in PKA activity, thereby ensuring consistent monomer phosphorylation and SERCA activity despite noisy upstream signals. Preliminary analyses suggest that the PLN mutation R14del could impair noise filtering, offering a new perspective on how this mutation causes cardiac arrhythmias.

Dynamics of adrenergic signaling in cardiac myocytes and implications for pharmacological treatment

Dense innervation of the heart by the sympathetic nervous system (SNS) allows cardiac output to respond appropriately to the needs of the body under varying conditions, but occasionally the abrupt onset of SNS activity can trigger cardiac arrhythmias. Sympathetic activity leads to the release of norepinephrine (NE) onto cardiomyocytes, activating β₁-adrenergic receptors (β₁-ARs) and leading to the production of the second messenger cyclic AMP (cAMP). Upon sudden activation of β₁-ARs in experiments, intracellular cAMP can transiently rise to a high concentration before converging to a steady state level. Although changes to cellular cAMP concentration are important in modulating the overall cardiovascular response to sympathetic tone, the underlying mechanisms of the cAMP transients and the parameters that control their magnitude are unclear.

We reduce a detailed computational model of the β₁-adrenergic signaling cascade to a system of two differential equations by eliminating extraneous variables and applying quasi-steady state approximation. The structure of the reduced model reveals that the large cAMP transients associated with abrupt β₁-AR activation are generated by the interplay of production/degradation of cAMP and desensitization/resensitization of β₁-ARs. The reduced model is used to predict how the dynamics of intracellular cAMP depend on the concentrations of norepinephrine (NE), phosphodiesterases 3 and 4 (PDE3,4), G-protein coupled receptor kinase 2 (GRK2), and β₁-AR, in healthy conditions and a simple model of early stages of heart failure.

The key findings of the study are as follows: 1) Applying a reduced model of the dynamics of cardiac sympathetic signaling we show that the concentrations of two variables, cAMP and non-desensitized β₁-AR, capture the overall dynamics of sympathetic signaling; 2) The key factors influencing cAMP production are AC activity and PDE3,4 activity, while those that directly impact β₁-AR phosphorylation are GRK2 and PKA₁. Thus, disease states that affect sympathetic control of the heart can be thoroughly assessed by studying AC activity, PDE3,4, GRK2 and PKA activity, as these factors directly impact cAMP production/degradation and β₁-AR (de) phosphorylation and are therefore predicted to comprise the most effective pharmaceutical targets in diseases affecting cardiac β₁-adrenergic signaling.

Quantitative analysis of variability in an integrated model of human ventricular electrophysiology and β-adrenergic signaling

In ventricular myocytes, stimulation of β-adrenergic receptors activates critical cardiac signaling pathways, leading to shorter action potentials and increased contraction strength during the "fight-or-flight" response. These changes primarily result, at the cellular level, from the coordinated phosphorylation of multiple targets by protein kinase A. Although mathematical models of the intracellular signaling downstream of β-adrenergic receptor activation have previously been described, only a limited number of studies have explored quantitative interactions between intracellular signaling and electrophysiology in human ventricular myocytes. Accordingly, our objective was to develop an integrative mathematical model of β-adrenergic receptor signaling, electrophysiology, and intracellular calcium (Ca²⁺) handling in the healthy human ventricular myocyte. We combined published mathematical models of intracellular signaling and electrophysiology, then calibrated the model results against voltage clamp data and physiological changes occurring after stimulation of β-adrenergic receptors with isoproterenol. We subsequently: (1) explored how molecular variability in different categories of model parameters translated into phenotypic variability; (2) identified the most important parameters determining physiological cellular outputs in the model before and after β-adrenergic receptor stimulation; and (3) investigated which molecular level alterations can produce a phenotype indicative of heart failure with preserved ejection fraction (HFpEF). Major results included: (1) variability in parameters that controlled intracellular signaling caused qualitatively different behavior than variability in parameters controlling ion transport pathways; (2) the most important model parameters determining action potential duration and intracellular Ca²⁺ transient amplitude were generally consistent before and after β-adrenergic receptor stimulation, except for a shift in the importance of K⁺ currents in determining action potential duration; and (3) decreased Ca²⁺ uptake into the sarcoplasmic reticulum, increased Ca²⁺ extrusion through Na⁺/Ca²⁺ exchanger and decreased Ca²⁺ leak from the sarcoplasmic reticulum may contribute to HFpEF. Overall, this study provided novel insight into the phenotypic consequences of molecular variability, and our integrated model may be useful in the design and interpretation of future experimental studies of interactions between β-adrenergic signaling and cellular physiology in human ventricular myocytes.

Computational prediction of the effect of D172N KCNJ2 mutation on ventricular pumping during sinus rhythm and reentry

The understanding of cardiac arrhythmia under genetic mutations has grown in interest among researchers. Previous studies focused on the effect of the D172N mutation on electrophysiological behavior. In this study, we analyzed not only the electrophysiological activity but also the mechanical responses during normal sinus rhythm and reentry conditions by using computational modeling. We simulated four different ventricular conditions including normal case of ten Tusscher model 2006 (TTM), wild-type (WT), heterozygous (WT/D172N), and homozygous D172N mutation. The 2D simulation result (in wire-shaped mesh) showed the WT/D172N and D172N mutation shortened the action potential duration by 14%, and by 23%, respectively. The 3D electrophysiological simulation results showed that the electrical wavelength between TTM and WT conditions were identical. Under sinus rhythm condition, the WT/D172N and D172N reduced the pumping efficacy with a lower left ventricle (LV) and aortic pressures, stroke volume, ejection fraction, and cardiac output. Under the reentry conditions, the WT condition has a small probability of reentry. However, in the event of reentry, WT has shown the most severe condition. Furthermore, we found that the position of the rotor or the scroll wave substantially influenced the ventricular pumping efficacy during arrhythmia. If the rotor stays in the LV, it will cause very poor pumping performance. Graphical Abstract A model of a ventricular electromechanical system. This whole model was established to observe the effect of D172N KCNJ2 mutation on ventricular pumping behavior during sinus rhythm and reentry conditions. The model consists of two components; electrical component and mechanical component. The electrophysiological model based on ten Tusscher et al. with the IK1 D172N KCNJ2 mutation, and the myofilament dynamic (cross-bridge) model based on Rice et al. study. The 3D electrical component is a ventricular geometry based on MRI which composed of nodes representing single-cell with electrophysiological activation. The 3D ventricular mechanic is a finite element mesh composed of single-cells myofilament dynamic model. Both components were coupled with Ca2+ concentration. We used Gaussian points for the calcium interpolation from the electrical mesh to the mechanical mesh.

Slow Delayed Rectifier Current Protects Ventricular Myocytes From Arrhythmic Dynamics Across Multiple Species: A Computational Study

BACKGROUND

The slow and rapid delayed rectifier K⁺ currents (I_Ks and I_Kr, respectively) are responsible for repolarizing the ventricular action potential (AP) and preventing abnormally long APs that may lead to arrhythmias. Although differences in biophysical properties of the 2 currents have been carefully documented, the respective physiological roles of I_Kr and I_Ks are less established. In this study, we sought to understand the individual roles of these currents and quantify how effectively each stabilizes the AP and protects cells against arrhythmias across multiple species.

METHODS

We compared 10 mathematical models describing ventricular myocytes from human, rabbit, dog, and guinea pig. We examined variability within heterogeneous cell populations, tested the susceptibility of cells to proarrhythmic behavior, and studied how I_Ks and I_Kr responded to changes in the AP.

RESULTS

We found that (1) models with higher baseline I_Ks exhibited less cell-to-cell variability in AP duration; (2) models with higher baseline I_Ks were less susceptible to early afterdepolarizations induced by depolarizing perturbations; (3) as AP duration is lengthened, I_Ks increases more profoundly than I_Kr, thereby providing negative feedback that resists excessive AP prolongation; and (4) the increase in I_Ks that occurs during β-adrenergic stimulation is critical for protecting cardiac myocytes from early afterdepolarizations under these conditions.

CONCLUSIONS

Slow delayed rectifier current is uniformly protective across a variety of cell types. These results suggest that I_Ks enhancement could potentially be an effective antiarrhythmic strategy.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

Assessing Escherichia coli metabolism models and simulation approaches in phenotype predictions: Validation against experimental data

Over the last years, several genome-scale metabolic models (GEMs) and kinetic models of Escherichia coli were published. Their predictive performance varies according to the evaluation metric considered, the computational simulation methods used, and the type/quality of experimental data available. However, the GEM approach is often not compared with the kinetic modeling framework. Also, the different genome-scale reconstruction versions and simulation methods of mutant phenotypes are usually not validated to predict intracellular fluxes using large experimental datasets. Here, we intended to (i) systematically evaluate the prediction performance of three E. coli GEMs (iJR904, iAF1260, and iJO1366) available in the literature according to predictive growth metrics (intracellular flux distribution); (ii) assess the reliability of a E. coli GEM in the prediction of gene knockout phenotypes when different simulation methods (parsimonious flux balance analysis, Minimization of Metabolic Adjustment, linear version of MoMA, Regulatory on/off minimization, and Minimization of Metabolites Balance) are used; and finally (iii) investigate the flux distribution predictive power of the constrained-based modeling approach (selected stoichiometric GEM) and compare it with the kinetic modeling approach (two published kinetic models) for E. coli central metabolism, in order to assess their accuracy. Results show that the phenotype predictions were not significantly sensitive to the metabolic models, although the GEM iAF1260 was more accurate in the prediction of central carbon fluxes at low dilution rates. Furthermore, we observed that the choice of the appropriate simulation method of mutant phenotypes depends on the biological question to be addressed. In terms of the two modeling approaches, none outperformed the other for all the tested scenarios. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 34:1344-1354, 2018.

An engineering design approach to systems biology

Measuring and modeling the integrated behavior of biomolecular-cellular networks is central to systems biology. Over several decades, systems biology has been shaped by quantitative biologists, physicists, mathematicians, and engineers in different ways. However, the basic and applied versions of systems biology are not typically distinguished, which blurs the separate aspirations of the field and its potential for real-world impact. Here, we articulate an engineering approach to systems biology, which applies educational philosophy, engineering design, and predictive models to solve contemporary problems in an age of biomedical Big Data. A concerted effort to train systems bioengineers will provide a versatile workforce capable of tackling the diverse challenges faced by the biotechnological and pharmaceutical sectors in a modern, information-dense economy.

Distinct physiological effects of β1- and β2-adrenoceptors in mouse ventricular myocytes: insights from a compartmentalized mathematical model

The β1- and β2-adrenergic signaling systems play different roles in the functioning of cardiac cells. Experimental data show that the activation of the β1-adrenergic signaling system produces significant inotropic, lusitropic, and chronotropic effects in the heart, whereas the effects of the β2-adrenergic signaling system is less apparent. In this paper, a comprehensive compartmentalized experimentally based mathematical model of the combined β1- and β2-adrenergic signaling systems in mouse ventricular myocytes is developed to simulate the experimental findings and make testable predictions of the behavior of the cardiac cells under different physiological conditions. Simulations describe the dynamics of major signaling molecules in different subcellular compartments; kinetics and magnitudes of phosphorylation of ion channels, transporters, and Ca2+ handling proteins; modifications of action potential shape and duration; and [Ca2+]i and [Na+]i dynamics upon stimulation of β1- and β2-adrenergic receptors (β1- and β2-ARs). The model reveals physiological conditions when β2-ARs do not produce significant physiological effects and when their effects can be measured experimentally. Simulations demonstrated that stimulation of β2-ARs with isoproterenol caused a marked increase in the magnitude of the L-type Ca2+ current, [Ca2+]i transient, and phosphorylation of phospholamban only upon additional application of pertussis toxin or inhibition of phosphodiesterases of type 3 and 4. The model also made testable predictions of the changes in magnitudes of [Ca2+]i and [Na+]i fluxes, the rate of decay of [Na+]i concentration upon both combined and separate stimulation of β1- and β2-ARs, and the contribution of phosphorylation of PKA targets to the changes in the action potential and [Ca2+]i transient.

Species-Dependent Mechanisms of Cardiac Arrhythmia: A Cellular Focus

Although ventricular arrhythmia remains a leading cause of morbidity and mortality, available antiarrhythmic drugs have limited efficacy. Disappointing progress in the development of novel, clinically relevant antiarrhythmic agents may partly be attributed to discrepancies between humans and animal models used in preclinical testing. However, such differences are at present difficult to predict, requiring improved understanding of arrhythmia mechanisms across species. To this end, we presently review interspecies similarities and differences in fundamental cardiomyocyte electrophysiology and current understanding of the mechanisms underlying the generation of afterdepolarizations and reentry. We specifically highlight patent shortcomings in small rodents to reproduce cellular and tissue-level arrhythmia substrate believed to be critical in human ventricle. Despite greater ease of translation from larger animal models, discrepancies remain and interpretation can be complicated by incomplete knowledge of human ventricular physiology due to low availability of explanted tissue. We therefore point to the benefits of mathematical modeling as a translational bridge to understanding and treating human arrhythmia.

Rabbit-specific computational modelling of ventricular cell electrophysiology: Using populations of models to explore variability in the response to ischemia

Computational modelling, combined with experimental investigations, is a powerful method for investigating complex cardiac electrophysiological behaviour. The use of rabbit-specific models, due to the similarities of cardiac electrophysiology in this species with human, is especially prevalent. In this paper, we first briefly review rabbit-specific computational modelling of ventricular cell electrophysiology, multi-cellular simulations including cellular heterogeneity, and acute ischemia. This mini-review is followed by an original computational investigation of variability in the electrophysiological response of two experimentally-calibrated populations of rabbit-specific ventricular myocyte action potential models to acute ischemia. We performed a systematic exploration of the response of the model populations to varying degrees of ischemia and individual ischemic parameters, to investigate their individual and combined effects on action potential duration and refractoriness. This revealed complex interactions between model population variability and ischemic factors, which combined to enhance variability during ischemia. This represents an important step towards an improved understanding of the role that physiological variability may play in electrophysiological alterations during acute ischemia.

Simulation of the effects of moderate stimulation/inhibition of the β1-adrenergic signaling system and its components in mouse ventricular myocytes

The β1-adrenergic signaling system is one of the most important protein signaling systems in cardiac cells. It regulates cardiac action potential duration, intracellular Ca2+concentration ([Ca2+]i) transients, and contraction force. In this paper, a comprehensive experimentally based mathematical model of the β1-adrenergic signaling system for mouse ventricular myocytes is explored to simulate the effects of moderate stimulations of β1-adrenergic receptors (β1-ARs) on the action potential, Ca2+and Na+dynamics, as well as the effects of inhibition of protein kinase A (PKA) and phosphodiesterase of type 4 (PDE4). Simulation results show that the action potential prolongations reach saturating values at relatively small concentrations of isoproterenol (∼0.01 μM), while the [Ca2+]itransient amplitude saturates at significantly larger concentrations (∼0.1–1.0 μM). The differences in the response of Ca2+and Na+fluxes to moderate stimulation of β1-ARs are also observed. Sensitivity analysis of the mathematical model is performed and the model limitations are discussed. The investigated model reproduces most of the experimentally observed effects of moderate stimulation of β1-ARs, PKA, and PDE4 inhibition on the L-type Ca2+current, [Ca2+]itransients, and the sarcoplasmic reticulum Ca2+load and makes testable predictions for the action potential duration and [Ca2+]itransients as functions of isoproterenol concentration.

Interaction between phosphodiesterases in the regulation of the cardiac β-adrenergic pathway

In cardiac myocytes, the second messenger cAMP is synthesized within the β-adrenergic signaling pathway upon sympathetic activation. It activates Protein Kinase A (PKA) mediated phosphorylation of multiple target proteins that are functionally critical to cardiac contractility. The dynamics of cAMP are also controlled indirectly by cGMP-mediated regulation of phosphodiesterase isoenzymes (PDEs). The nature of the interactions between cGMP and the PDEs, as well as between PDE isoforms, and how these ultimately transduce the cGMP signal to regulate cAMP remains unclear. To better understand this, we have developed mechanistically detailed models of PDEs 1-4, the primary cAMP-hydrolyzing PDEs in cardiac myocytes, and integrated them into a model of the β-adrenergic signaling pathway. The PDE models are based on experimental studies performed on purified PDEs which have demonstrated that cAMP and cGMP bind competitively to the cyclic nucleotide (cN)-binding domains of PDEs 1, 2, and 3, while PDE4 regulation occurs via PKA-mediated phosphorylation. Individual PDE models reproduce experimentally measured cAMP hydrolysis rates with dose-dependent cGMP regulation. The fully integrated model replicates experimentally observed whole-cell cAMP activation-response relationships and temporal dynamics upon varying degrees of β-adrenergic stimulation in cardiac myocytes. Simulations reveal that as a result of network interactions, reduction in the level of one PDE is partially compensated for by increased activation of others. PDE2 and PDE4 exert the strongest compensatory roles among all PDEs. In addition, PDE2 competes with other PDEs to bind and hydrolyze cAMP and is a strong regulator of PDE interactions. Finally, an increasing level of cGMP gradually out-competes cAMP for the catalytic sites of PDEs 1, 2, and 3, suppresses their cAMP hydrolysis rates, and results in amplified cAMP signaling. These results provide insights into how PDEs transduce cGMP signals to regulate cAMP and how PDE interactions affect cardiac β-adrenergic response.

Lessons learned from multi-scale modeling of the failing heart

Heart failure constitutes a major public health problem worldwide. Affected patients experience a number of changes in the electrical function of the heart that predispose to potentially lethal cardiac arrhythmias. Due to the multitude of electrophysiological changes that may occur during heart failure, the scientific literature is complex and sometimes ambiguous, perhaps because these findings are highly dependent on the etiology, the stage of heart failure, and the experimental model used to study these changes. Nevertheless, a number of common features of failing hearts have been documented. Prolongation of the action potential (AP) involving ion channel remodeling and alterations in calcium handling have been established as the hallmark characteristics of myocytes isolated from failing hearts. Intercellular uncoupling and fibrosis are identified as major arrhythmogenic factors. Multi-scale computational simulations are a powerful tool that complements experimental and clinical research. The development of biophysically detailed computer models of single myocytes and cardiac tissues has contributed greatly to our understanding of processes underlying excitation and repolarization in the heart. The electrical, structural, and metabolic remodeling that arises in cardiac tissues during heart failure has been addressed from different computational perspectives to further understand the arrhythmogenic substrate. This review summarizes the contributions from computational modeling and simulation to predict the underlying mechanisms of heart failure phenotypes and their implications for arrhythmogenesis, ranging from the cellular level to whole-heart simulations. The main aspects of heart failure are presented in several related sections. An overview of the main electrophysiological and structural changes that have been observed experimentally in failing hearts is followed by the description and discussion of the simulation work in this field at the cellular level, and then in 2D and 3D cardiac structures. The implications for arrhythmogenesis in heart failure are also discussed including therapeutic measures, such as drug effects and cardiac resynchronization therapy. Finally, the future challenges in heart failure modeling and simulation will be discussed.

Arrhythmogenic transient dynamics in cardiac myocytes

Cardiac action potential alternans and early afterdepolarizations (EADs) are linked to cardiac arrhythmias. Periodic action potentials (period 1) in healthy conditions bifurcate to other states such as period 2 or chaos when alternans or EADs occur in pathological conditions. The mechanisms of alternans and EADs have been extensively studied under steady-state conditions, but lethal arrhythmias often occur during the transition between steady states. Why arrhythmias tend to develop during the transition is unclear. We used low-dimensional mathematical models to analyze dynamical mechanisms of transient alternans and EADs. We show that depending on the route from one state to another, action potential alternans and EADs may occur during the transition between two periodic steady states. The route taken depends on the time course of external perturbations or intrinsic signaling, such as β-adrenergic stimulation, which regulate cardiac calcium and potassium currents with differential kinetics.

Modeling the effects of β1-adrenergic receptor blockers and polymorphisms on cardiac myocyte Ca2+ handling

β-Adrenergic receptor blockers (β-blockers) are commonly used to treat heart failure, but the biologic mechanisms governing their efficacy are still poorly understood. The complexity of β-adrenergic signaling coupled with the influence of receptor polymorphisms makes it difficult to intuit the effect of β-blockers on cardiac physiology. While some studies indicate that β-blockers are efficacious by inhibiting β-adrenergic signaling, other studies suggest that they work by maintaining β-adrenergic responsiveness. Here, we use a systems pharmacology approach to test the hypothesis that in ventricular myocytes, these two apparently conflicting mechanisms for β-blocker efficacy can occur concurrently. We extended a computational model of the β(1)-adrenergic pathway and excitation-contraction coupling to include detailed receptor interactions for 19 ligands. Model predictions, validated with Ca(2+) and Förster resonance energy transfer imaging of adult rat ventricular myocytes, surprisingly suggest that β-blockers can both inhibit and maintain signaling depending on the magnitude of receptor stimulation. The balance of inhibition and maintenance of β(1)-adrenergic signaling is predicted to depend on the specific β-blocker (with greater responsiveness for metoprolol than carvedilol) and β(1)-adrenergic receptor Arg389Gly polymorphisms.

A590T mutation in KCNQ1 C-terminal helix D decreases IKs channel trafficking and function but not Yotiao interaction

KCNQ1 encodes the α subunit of the voltage-gated channel that mediates the cardiac slow delayed rectifier K(+) current (IKs). Here, we report a KCNQ1 allele encoding an A590T mutation [KCNQ1(A590T)] found in a 39-year-old female with a mild QT prolongation. A590 is located in the C-terminal α helical region of KCNQ1 that mediates subunit tetramerization, membrane trafficking, and interaction with Yotiao. This interaction is known to be required for the proper modulation of IKs by cAMP. Since previous studies reported that mutations in the vicinity of A590 impair IKs channel surface expression and function, we examined whether and how the A590T mutation affects the IKs channel. Electrophysiological measurements in HEK-293T cells showed that the A590T mutation caused a reduction in IKs density and a right-shift of the current-voltage relation of channel activation. Immunocytochemical and immunoblot analyses showed the reduced cell surface expression of KCNQ1(A590T) subunit and its rescue by coexpression of the wild-type KCNQ1 [KCNQ1(WT)] subunit. Moreover, KCNQ1(A590T) subunit interacted with Yotiao and had a cAMP-responsiveness comparable to that of KCNQ1(WT) subunit. These findings indicate that the A590 of KCNQ1 subunit plays important roles in the maintenance of channel surface expression and function via a novel mechanism independent of interaction with Yotiao.

Comprehensive analyses of ventricular myocyte models identify targets exhibiting favorable rate dependence

Reverse rate dependence is a problematic property of antiarrhythmic drugs that prolong the cardiac action potential (AP). The prolongation caused by reverse rate dependent agents is greater at slow heart rates, resulting in both reduced arrhythmia suppression at fast rates and increased arrhythmia risk at slow rates. The opposite property, forward rate dependence, would theoretically overcome these parallel problems, yet forward rate dependent (FRD) antiarrhythmics remain elusive. Moreover, there is evidence that reverse rate dependence is an intrinsic property of perturbations to the AP. We have addressed the possibility of forward rate dependence by performing a comprehensive analysis of 13 ventricular myocyte models. By simulating populations of myocytes with varying properties and analyzing population results statistically, we simultaneously predicted the rate-dependent effects of changes in multiple model parameters. An average of 40 parameters were tested in each model, and effects on AP duration were assessed at slow (0.2 Hz) and fast (2 Hz) rates. The analysis identified a variety of FRD ionic current perturbations and generated specific predictions regarding their mechanisms. For instance, an increase in L-type calcium current is FRD when this is accompanied by indirect, rate-dependent changes in slow delayed rectifier potassium current. A comparison of predictions across models identified inward rectifier potassium current and the sodium-potassium pump as the two targets most likely to produce FRD AP prolongation. Finally, a statistical analysis of results from the 13 models demonstrated that models displaying minimal rate-dependent changes in AP shape have little capacity for FRD perturbations, whereas models with large shape changes have considerable FRD potential. This can explain differences between species and between ventricular cell types. Overall, this study provides new insights, both specific and general, into the determinants of AP duration rate dependence, and illustrates a strategy for the design of potentially beneficial antiarrhythmic drugs.

Several drugs intended to treat cardiac arrhythmias have failed because of unfavorable rate-dependent properties. That is, the drugs fail to alter electrical activity at fast heart rates, where this would be beneficial, but they do affect electrical activity at slow rates, where this is unwanted. In targeted studies, several agents have been shown to exhibit these unfavorable properties, suggesting that these rate-dependent responses may be intrinsic to ventricular muscle. To determine whether drugs with desirable rate-dependent properties could be rationally designed, we performed comprehensive and systematic analyses of several heart cell models. These analyses calculated the rate-dependent properties of changes in any model parameter, thereby generating simultaneously a large number of model predictions. The analyses showed that targets with favorable rate-dependent properties could indeed be identified, and further simulations uncovered the mechanisms underlying these behaviors. Moreover, a quantitative comparison of results obtained in different models provided new insight in why a given drug applied to different species, or to different tissue types, might produce different rate-dependent behaviors. Overall this study shows how a comprehensive and systematic approach to heart cell models can both identify novel targets and produce more general insight into rate-dependent alterations to cardiac electrical activity.

A compartmentalized mathematical model of the β1-adrenergic signaling system in mouse ventricular myocytes

The β₁-adrenergic signaling system plays an important role in the functioning of cardiac cells. Experimental data shows that the activation of this system produces inotropy, lusitropy, and chronotropy in the heart, such as increased magnitude and relaxation rates of [Ca²⁺]_i transients and contraction force, and increased heart rhythm. However, excessive stimulation of β₁-adrenergic receptors leads to heart dysfunction and heart failure. In this paper, a comprehensive, experimentally based mathematical model of the β₁-adrenergic signaling system for mouse ventricular myocytes is developed, which includes major subcellular functional compartments (caveolae, extracaveolae, and cytosol). The model describes biochemical reactions that occur during stimulation of β₁-adrenoceptors, changes in ionic currents, and modifications of Ca²⁺ handling system. Simulations describe the dynamics of major signaling molecules, such as cyclic AMP and protein kinase A, in different subcellular compartments; the effects of inhibition of phosphodiesterases on cAMP production; kinetics and magnitudes of phosphorylation of ion channels, transporters, and Ca²⁺ handling proteins; modifications of action potential shape and duration; magnitudes and relaxation rates of [Ca²⁺]_i transients; changes in intracellular and transmembrane Ca²⁺ fluxes; and [Na⁺]_i fluxes and dynamics. The model elucidates complex interactions of ionic currents upon activation of β₁-adrenoceptors at different stimulation frequencies, which ultimately lead to a relatively modest increase in action potential duration and significant increase in [Ca²⁺]_i transients. In particular, the model includes two subpopulations of the L-type Ca²⁺ channels, in caveolae and extracaveolae compartments, and their effects on the action potential and [Ca²⁺]_i transients are investigated. The presented model can be used by researchers for the interpretation of experimental data and for the developments of mathematical models for other species or for pathological conditions.

Bifurcations, sustained oscillations and torus bursting involving ionic concentrations dynamics in a canine atrial cell model

Atrial fibrillation is a disorganization of the electrical propagation in the atria often initiated by ectopic beats. This spontaneous activity might be associated with the appearance of sustained oscillations in some portion of the tissue. Adrenergic stress and specific gene polymorphisms known to promote atrial fibrillation are notably related to calcium and potassium channel conductances. We performed codimension-one and two bifurcation analysis along these conductances in an ionic canine atrial myocyte model. Two Hopf bifurcations were found, related to two distinct mechanisms: (1) a fast calcium gating-driven oscillator, and (2) a slow concentration-driven oscillator. These two mechanisms interact through a double Hopf bifurcation (HH) in a neighborhood of which a torus (Neimark-Sacker) bifurcation leads to bursting. A complex codimension-two theoretical scenario was identified around HH, through systematic comparison with the attractors found numerically. The concentration oscillator was further decomposed to reveal the minimal oscillating subnetwork, in which the Na(+)/Ca(2+) exchanger plays a prominent role.

Biology of the KCNQ1 Potassium Channel

Ion channels are essential for basic cellular function and for processes including sensory perception and intercellular communication in multicellular organisms. Voltage-gated potassium (Kv) channels facilitate dynamic cellular repolarization during an action potential, opening in response to membrane depolarization to facilitate K+ efflux. In both excitable and nonexcitable cells other, constitutively active, K+ channels provide a relatively constant repolarizing force to control membrane potential, ion homeostasis, and secretory processes. Of the forty known human Kv channel pore-forming α subunits that coassemble in various combinations to form the fundamental tetrameric channel pore and voltage sensor module, KCNQ1 is unique. KCNQ1 stands alone in having the capacity to form either channels that are voltage-dependent and require membrane depolarization for activation, or constitutively active channels. In mammals, KCNQ1 regulates processes including gastric acid secretion, thyroid hormone biosynthesis, salt and glucose homeostasis, and cell volume and in some species is required for rhythmic beating of the heart. In this review, the author discusses the unique functional properties, regulation, cell biology, diverse physiological roles, and involvement in human disease states of this chameleonic K+ channel.

Scaffold state switching amplifies, accelerates, and insulates protein kinase C signaling

Scaffold proteins localize two or more signaling enzymes in close proximity to their downstream effectors. A-kinase-anchoring proteins (AKAPs) are a canonical family of scaffold proteins known to bind protein kinase A (PKA) and other enzymes. Several AKAPs have been shown to accelerate, amplify, and specify signal transduction to dynamically regulate numerous cellular processes. However, there is little theory available to mechanistically explain how signaling on protein scaffolds differs from solution biochemistry. In our present study, we propose a novel kinetic mechanism for enzymatic reactions on protein scaffolds to explain these phenomena, wherein the enzyme-substrate-scaffold complex undergoes stochastic state switching to reach an active state. This model predicted anchored enzymatic reactions to be accelerated, amplified, and insulated from inhibition compared with those occurring in solution. We exploited a direct interaction between protein kinase C (PKC) and AKAP7α as a model to validate these predictions experimentally. Using a genetically encoded PKC activity reporter, we found that both the strength and speed of substrate phosphorylation were enhanced by AKAP7α. PKC tethered to AKAP7α was less susceptible to inhibition from the ATP-competitive inhibitor Gö6976 and the substrate-competitive inhibitor PKC 20-28, but not the activation-competitive inhibitor calphostin C. Model predictions and experimental validation demonstrated that insulation is a general property of scaffold tethering. Sensitivity analysis indicated that these findings may be applicable to many other scaffolds as well. Collectively, our findings provide theoretical and experimental evidence that scaffold proteins can amplify, accelerate, and insulate signal transduction.

The promise of CaMKII inhibition for heart disease: preventing heart failure and arrhythmias

INTRODUCTION

Calcium-calmodulin-dependent protein kinase II (CaMKII) has emerged as a central mediator of cardiac stress responses which may serve several critical roles in the regulation of cardiac rhythm, cardiac contractility and growth. Sustained and excessive activation of CaMKII during cardiac disease has, however, been linked to arrhythmias, and maladaptive cardiac remodeling, eventually leading to heart failure (HF) and sudden cardiac death.

AREAS COVERED

In the current review, the authors describe the unique structural and biochemical properties of CaMKII and focus on its physiological effects in cardiomyocytes. Furthermore, they provide evidence for a role of CaMKII in cardiac pathologies, including arrhythmogenesis, myocardial ischemia and HF development. The authors conclude by discussing the potential for CaMKII as a target for inhibition in heart disease.

EXPERT OPINION

CaMKII provides a promising nodal point for intervention that may allow simultaneous prevention of HF progression and development of arrhythmias. For future studies and drug development there is a strong rationale for the development of more specific CaMKII inhibitors. In addition, an improved understanding of the differential roles of CaMKII subtypes is required.

Defective interactions of protein partner with ion channels and transporters as alternative mechanisms of membrane channelopathies

The past twenty years have revealed the existence of numerous ion channel mutations resulting in human pathology. Ion channels provide the basis of diverse cellular functions, ranging from hormone secretion, excitation-contraction coupling, cell signaling, immune response, and trans-epithelial transport. Therefore, the regulation of biophysical properties of channels is vital in human physiology. Only within the last decade has the role of non-ion channel components come to light in regard to ion channel spatial, temporal, and biophysical regulation in physiology. A growing number of auxiliary components have been determined to play elemental roles in excitable cell physiology, with dysfunction resulting in disorders and related manifestations. This review focuses on the broad implications of such dysfunction, focusing on disease-causing mutations that alter interactions between ion channels and auxiliary ion channel components in a diverse set of human excitable cell disease. This article is part of a Special Issue entitled: Reciprocal influences between cell cytoskeleton and membrane channels, receptors and transporters. Guest Editor: Jean Claude Hervé

The functional role of electrophysiological heterogeneity in the rabbit ventricle during rapid pacing and arrhythmias

Electrophysiological heterogeneity in action potential recordings from healthy intact hearts remains highly variable and, where present, is almost entirely abolished at fast pacing rates. Consequently, the functional importance of intrinsic action potential duration (APD) heterogeneity in healthy ventricles, and particularly its role during rapidly activating reentrant arrhythmias, remain poorly understood. By incorporating both transmural and apicobasal APD heterogeneity within a biventricular rabbit computational model and comparing with an equivalent homogeneous model, we directly investigated the functional importance of intrinsic APD heterogeneity under fast pacing and arrhythmogenic protocols. Although differences in APD were significantly modulated at the tissue level during pacing and further reduced as pacing frequency increased, small differences were still noticeable. Such differences were further marginally accentuated/attenuated via electrotonic effects relative to wavefront propagation directions. The remaining small levels of APD heterogeneity under the fastest pacing frequencies resulted in arrhythmia initiation via heterogeneous conduction block, in contrast to complete block in the homogeneous model. Such induction mechanisms were more evident during premature stimuli at slower paced rhythms where intrinsic heterogeneity remained to a greater degree. During sustained arrhythmias, however, intrinsic heterogeneity made little difference to overall reentrant behavior, either visually, or in terms of duration, metrics quantifying filament/phase singularity dynamics, and global electrocardiogram characteristics. These findings suggest that, despite being important during arrhythmia initiation, intrinsic electrophysiological heterogeneity plays little functional role during rapid pacing and sustained arrhythmia dynamics in the healthy ventricle and thus questions the need to incorporate such detail in computational models when simulating rapid arrhythmias.

Early afterdepolarizations in cardiac myocytes: beyond reduced repolarization reserve

Early afterdepolarizations (EADs) are secondary voltage depolarizations during the repolarizing phase of the action potential, which can cause lethal cardiac arrhythmias. The occurrence of EADs requires a reduction in outward current and/or an increase in inward current, a condition called reduced repolarization reserve. However, this generalized condition is not sufficient for EAD genesis and does not explain the voltage oscillations manifesting as EADs. Here, we summarize recent progress that uses dynamical theory to build on and advance our understanding of EADs beyond the concept of repolarization reserve, towards the goal of developing a holistic and integrative view of EADs and their role in arrhythmogenesis. We first introduce concepts from nonlinear dynamics that are relevant to EADs, namely, Hopf bifurcation leading to oscillations and basin of attraction of an equilibrium or oscillatory state. We then present a theory of phase-2 EADs in nonlinear dynamics, which includes the formation of quasi-equilibrium states at the plateau voltage, their stabilities, and the bifurcations leading to and terminating the oscillations. This theory shows that the L-type calcium channel plays a unique role in causing the nonlinear dynamical behaviours necessary for EADs. We also summarize different mechanisms of phase-3 EADs. Based on the dynamical theory, we discuss the roles of each of the major ionic currents in the genesis of EADs, and potential therapeutic targets.

Computational medicine: translating models to clinical care

Because of the inherent complexity of coupled nonlinear biological systems, the development of computational models is necessary for achieving a quantitative understanding of their structure and function in health and disease. Statistical learning is applied to high-dimensional biomolecular data to create models that describe relationships between molecules and networks. Multiscale modeling links networks to cells, organs, and organ systems. Computational approaches are used to characterize anatomic shape and its variations in health and disease. In each case, the purposes of modeling are to capture all that we know about disease and to develop improved therapies tailored to the needs of individuals. We discuss advances in computational medicine, with specific examples in the fields of cancer, diabetes, cardiology, and neurology. Advances in translating these computational methods to the clinic are described, as well as challenges in applying models for improving patient health.

β-adrenergic stimulation activates early afterdepolarizations transiently via kinetic mismatch of PKA targets

Sympathetic stimulation regulates cardiac excitation-contraction coupling in hearts but can also trigger ventricular arrhythmias caused by early afterdepolarizations (EADs) in pathological conditions. Isoproterenol (ISO) stimulation can transiently cause EADs which could result from differential kinetics of L-type Ca current (ICaL) vs. delayed rectifier potassium current (IKs) effects, but multiple PKA targets complicate mechanistic analysis. Utilizing a biophysically detailed model integrating Ca and β-adrenergic signaling, we investigate how different phosphorylation kinetics and targets influence β-adrenergic-induced transient EADs. We found that: 1) The faster time course of ICaL vs. IKs increases recapitulates experimentally observed ISO-induced transient EADs (which are due to ICaL reactivation). These EADs disappear at steady state ISO and do not occur during more gradual ISO application. 2) This ICaL vs. IKs kinetic mismatch with ISO can also induce transient EADs due to spontaneous sarcoplasmic reticulum (SR) Ca release and Na/Ca exchange current. The increased ICaL, SR Ca uptake and action potential duration (APD) raise SR Ca to cause spontaneous SR Ca release, but eventual IKs activation and APD shortening abolish these EADs. 3) Phospholemman (PLM) phosphorylation decreases both types of EADs by increasing outward Na/K-ATPase current (INaK) for ICaL-mediated EADs, and reducing intracellular Na and Ca loading for SR Ca-release-mediated EADs. Slowing PLM phosphorylation kinetics abolishes this protective effect. 4) Blocking phospholamban (PLB) phosphorylation has little effect on ICaL-mediated transient EADs, but abolishes SR Ca-release-mediated transient EADs by limiting SR Ca loading. 5) RyR phosphorylation has little effect on either transient EAD type. Our study emphasizes the importance of understanding non-steady state kinetics of several systems in mediating β-adrenergic-induced EADs and arrhythmias.

Network reconstruction and systems analysis of cardiac myocyte hypertrophy signaling

Cardiac hypertrophy is managed by a dense web of signaling pathways with many pathways influencing myocyte growth. A quantitative understanding of the contributions of individual pathways and their interactions is needed to better understand hypertrophy signaling and to develop more effective therapies for heart failure. We developed a computational model of the cardiac myocyte hypertrophy signaling network to determine how the components and network topology lead to differential regulation of transcription factors, gene expression, and myocyte size. Our computational model of the hypertrophy signaling network contains 106 species and 193 reactions, integrating 14 established pathways regulating cardiac myocyte growth. 109 of 114 model predictions were validated using published experimental data testing the effects of receptor activation on transcription factors and myocyte phenotypic outputs. Network motif analysis revealed an enrichment of bifan and biparallel cross-talk motifs. Sensitivity analysis was used to inform clustering of the network into modules and to identify species with the greatest effects on cell growth. Many species influenced hypertrophy, but only a few nodes had large positive or negative influences. Ras, a network hub, had the greatest effect on cell area and influenced more species than any other protein in the network. We validated this model prediction in cultured cardiac myocytes. With this integrative computational model, we identified the most influential species in the cardiac hypertrophy signaling network and demonstrate how different levels of network organization affect myocyte size, transcription factors, and gene expression.

Interpreting genetic effects through models of cardiac electromechanics

Multiscale models of cardiac electromechanics are being increasingly focused on understanding how genetic variation and environment underpin multiple disease states. In this paper we review the current state of the art in both the development of specific models and the physiological insights they have produced. This growing research body includes the development of models for capturing the effects of changes in function in both single and multiple proteins in both specific expression systems and in vivo contexts. Finally, the potential for using this approach for ultimately predicting phenotypes from genetic sequence information is discussed.

Mechanisms and determinants of ultralong action potential duration and slow rate-dependence in cardiac myocytes

In normal cardiac myocytes, the action potential duration (APD) is several hundred milliseconds. However, experimental studies showed that under certain conditions, APD could be excessively long (or ultralong), up to several seconds. Unlike the normal APD, the ultralong APD increases sensitively with pacing cycle length even when the pacing rate is very slow, exhibiting a sensitive slow rate-dependence. In addition, these long action potentials may or may not exhibit early afterdepolarizations (EADs). Although these phenomena are well known, the underlying mechanisms and ionic determinants remain incompletely understood. In this study, computer simulations were performed with a simplified action potential model. Modifications to the L-type calcium current (I_Ca,L) kinetics and the activation time constant of the delayed rectifier K current were used to investigate their effects on APD. We show that: 1) the ultralong APD and its sensitive slow rate-dependence are determined by the steady-state window and pedestal I_Ca,L currents and the activation speed and the recovery of the delayed rectifier K current; 2) whether an ultralong action potential exhibits EADs or not depends on the kinetics of I_Ca,L; 3) increasing inward currents elevates the plateau voltage, which in general prolongs APD, however, this can also shorten APD when the APD is already ultralong under certain conditions; and 4) APD alternans occurs at slow pacing rates due to the sensitive slow rate-dependence and the ionic determinants are different from the ones causing APD alternans at fast heart rates.

Computational approaches to understand cardiac electrophysiology and arrhythmias

Cardiac rhythms arise from electrical activity generated by precisely timed opening and closing of ion channels in individual cardiac myocytes. These impulses spread throughout the cardiac muscle to manifest as electrical waves in the whole heart. Regularity of electrical waves is critically important since they signal the heart muscle to contract, driving the primary function of the heart to act as a pump and deliver blood to the brain and vital organs. When electrical activity goes awry during a cardiac arrhythmia, the pump does not function, the brain does not receive oxygenated blood, and death ensues. For more than 50 years, mathematically based models of cardiac electrical activity have been used to improve understanding of basic mechanisms of normal and abnormal cardiac electrical function. Computer-based modeling approaches to understand cardiac activity are uniquely helpful because they allow for distillation of complex emergent behaviors into the key contributing components underlying them. Here we review the latest advances and novel concepts in the field as they relate to understanding the complex interplay between electrical, mechanical, structural, and genetic mechanisms during arrhythmia development at the level of ion channels, cells, and tissues. We also discuss the latest computational approaches to guiding arrhythmia therapy.

Modeling defibrillation of the heart: approaches and insights

Cardiac defibrillation, as accomplished nowadays by automatic, implantable devices (ICDs), constitutes the most important means of combating sudden cardiac death. While ICD therapy has proved to be efficient and reliable, defibrillation is a traumatic experience. Thus, research on defibrillation mechanisms, particularly aimed at lowering defibrillation voltage, remains an important topic. Advancing our understanding towards a full appreciation of the mechanisms by which a shock interacts with the heart is the most promising approach to achieve this goal. The aim of this paper is to assess the current state-of-the-art in ventricular defibrillation modeling, focusing on both numerical modeling approaches and major insights that have been obtained using defibrillation models, primarily those of realistic ventricular geometry. The paper showcases the contributions that modeling and simulation have made to our understanding of the defibrillation process. The review thus provides an example of biophysically based computational modeling of the heart (i.e., cardiac defibrillation) that has advanced the understanding of cardiac electrophysiological interaction at the organ level and has the potential to contribute to the betterment of the clinical practice of defibrillation.

AKAP phosphatase complexes in the heart

Directed protein phosphorylation is indisputably critical for a multitude of cellular processes. A growing body of research demonstrates A kinase anchoring proteins (AKAPs) to mediate a significant number of phosphorylation events in the heart. By acting as molecular tethers for the regulatory subunit of protein kinase A, AKAPs focus kinase activity onto specific substrate. In the time since their discovery, the AKAP model has evolved in appreciation of the broader role these scaffolds play in coordinating multiple signaling enzymes to efficiently regulate dynamic cellular processes. The focus of this review is on the emerging role of AKAPs in regulating the 3 main cardiac phosphatases: Protein Phosphatase 1 by AKAP18 and Yotiao, and Protein Phosphatases 2A and 2B by muscle specific A-kinase anchoring protein.

Synchronization of early afterdepolarizations and arrhythmogenesis in heterogeneous cardiac tissue models

Early afterdepolarizations (EADs) are linked to both triggered arrhythmias and reentrant arrhythmias by causing premature ventricular complexes (PVCs), focal excitations, or heterogeneous tissue substrates for reentry formation. However, a critical number of cells that synchronously exhibit EADs are needed to result in arrhythmia triggers and substrates in tissue. In this study, we use mathematical modeling and computer simulations to investigate EAD synchronization and arrhythmia induction in tissue models with random cell-to-cell variations. Our major observations are as follows. Random cell-to-cell variations in action potential duration without EAD presence do not cause large dispersion of refractoriness in well-coupled tissue. In the presence of phase-2 EADs, the cells may synchronously exhibit the same number of EADs or no EADs with a very small dispersion of refractoriness, or synchronize regionally to result in large dispersion of refractoriness. In the presence of phase-3 EADs, regional synchronization leads to propagating EADs, forming PVCs in tissue. Interestingly, even though the uncoupled cells exhibit either no EAD or only a single EAD, when these cells are coupled to form a tissue, more than one PVC can occur. When the PVCs occur at different locations and time, multifocal arrhythmias are triggered, with the foci shifting in space and time in an irregular manner. The focal arrhythmias either spontaneously terminate or degenerate into reentrant arrhythmias due to heterogeneities and spatiotemporal chaotic dynamics of the foci.

Modeling Ca2+ signaling in the microcirculation: intercellular communication and vasoreactivity

A network of intracellular signaling pathways and complex intercellular interactions regulate calcium mobilization in vascular cells, arteriolar tone, and blood flow. Different endothelium-derived vasoreactive factors have been identified and the importance of myoendothelial communication in vasoreactivity is now well appreciated. The ability of many vascular networks to conduct signals upstream also is established. This phenomenon is critical for both short-term changes in blood perfusion as well as long-term adaptations of a vascular network. In addition, in a phenomenon termed vasomotion, arterioles often exhibit spontaneous oscillations in diameter. This is thought to improve tissue oxygenation and enhance blood flow. Experimentation has begun to reveal important aspects of the regulatory machinery and the significance of these phenomena for the regulation of local perfusion and oxygenation. Mathematical modeling can assist in elucidating the complex signaling mechanisms that participate in these phenomena. This review highlights some of the important experimental studies and relevant mathematical models that provide the current understanding of these mechanisms in vasoreactivity.

Bigger, better, faster: principles and models of AKAP anchoring protein signaling

A kinase anchoring proteins (AKAPs) bind multiple signaling proteins and have subcellular targeting domains that allow them to greatly impact cellular signaling. AKAPs localize, specify, amplify, and accelerate signal transduction within the cell by bringing signaling proteins together in space and time. AKAPs also organize higher-order network motifs such as feed forward and feedback loops that may create complex network responses, including adaptation, oscillation, and ultrasensitivity. Computational models have begun to provide an insight into how AKAPs regulate signaling dynamics and cardiovascular pathophysiology. Models of mitogen-activated protein kinase and epidermal growth factor receptor scaffolds have revealed additional design principles and new methods for representing signaling scaffolds mathematically. Coupling computational modeling with quantitative experimental approaches will be increasingly necessary for dissecting the diverse information processing functions performed by AKAP signaling complexes.

Mathematical modeling and simulation of ventricular activation sequences: implications for cardiac resynchronization therapy

Next to clinical and experimental research, mathematical modeling plays a crucial role in medicine. Biomedical research takes place on many different levels, from molecules to the whole organism. Due to the complexity of biological systems, the interactions between components are often difficult or impossible to understand without the help of mathematical models. Mathematical models of cardiac electrophysiology have made a tremendous progress since the first numerical ECG simulations in the 1960s. This paper briefly reviews the development of this field and discusses some example cases where models have helped us forward, emphasizing applications that are relevant for the study of heart failure and cardiac resynchronization therapy.

A model of cellular cardiac-neural coupling that captures the sympathetic control of sinoatrial node excitability in normotensive and hypertensive rats

Hypertension is associated with sympathetic hyperactivity. To represent this neural-myocyte coupling, and to elucidate the mechanisms underlying sympathetic control of the cardiac pacemaker, we developed a new (to our knowledge) cellular mathematical model that incorporates signaling information from cell-to-cell communications between the sympathetic varicosity and sinoatrial node (SAN) in both normotensive (WKY) and hypertensive (SHR) rats. Features of the model include 1), a description of pacemaker activity with specific ion-channel functions and Ca(2+) handling elements; 2), dynamic β-adrenergic modulation of the excitation of the SAN; 3), representation of ionic activity of sympathetic varicosity with NE release dynamics; and 4), coupling of the varicosity model to the SAN model to simulate presynaptic transmitter release driving postsynaptic excitability. This framework captures neural-myocyte coupling and the modulation of pacemaking by nitric oxide and cyclic GMP. It also reproduces the chronotropic response to brief sympathetic stimulations. Finally, the SHR model quantitatively suggests that the impairment of cyclic GMP regulation at both sides of the sympathetic cleft is crucial for development of the autonomic phenotype observed in hypertension.

Robustness portraits of diverse biological networks conserved despite order-of-magnitude parameter uncertainty

MOTIVATION

Biological networks are robust to a wide variety of internal and external perturbations, yet fragile or sensitive to a small minority of perturbations. Due to this rare sensitivity of networks to certain perturbations, it is unclear how precisely biochemical parameters must be experimentally measured in order to accurately predict network function.

RESULTS

Here, we examined a model of cardiac β-adrenergic signaling and found that its robustness portrait, a global measure of steady-state network function, was well conserved even when all parameters were rounded to their nearest 1-2 orders of magnitude. In contrast, β-adrenergic network kinetics were more sensitive to parameter precision. This analysis was then extended to 10 additional networks, including Escherichia coli chemotaxis, stem cell differentiation and cytokine signaling, of which nine exhibited conserved robustness portraits despite the order-of-magnitude approximation of their biochemical parameters. Thus, both fragile and robust aspects of diverse biological networks are largely shaped by network topology and can be predicted despite order-of-magnitude uncertainty in biochemical parameters. These findings suggest an iterative strategy where order-of-magnitude models are used to prioritize experiments toward the fragile network elements that require precise measurements, efficiently driving model revision.

CONTACT

jsaucerman@virginia.edu

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Bi-stable wave propagation and early afterdepolarization-mediated cardiac arrhythmias

BACKGROUND

In normal atrial and ventricular tissue, the electrical wavefronts are mediated by the fast sodium current (I(Na)), whereas in sinoatrial and atrioventricular nodal tissue, conduction is mediated by the slow L-type calcium current (I(Ca,L)). However, it has not been shown whether the same tissue can exhibit both the I(Na)-mediated and the I(Ca,L)-mediated conduction.

OBJECTIVE

This study sought to test the hypothesis that bi-stable cardiac wave conduction, mediated by I(Na) and I(Ca,L), respectively, can occur in the same tissue under conditions promoting early afterdepolarizations (EADs), and to study how this novel wave dynamics is related to the mechanisms of EAD-mediated arrhythmias.

METHODS

Computer models of two-dimensional (2D) tissue with a physiologically detailed action potential model were used to study the bi-stable wave dynamics. Theoretical predictions were tested experimentally by optical mapping in neonatal rat ventricular myocyte monolayers.

RESULTS

In the same 2D homogeneous tissue, we could induce spiral waves that are mediated by either I(Na) or I(Ca,L) under conditions in which the action potential model exhibited EADs. This bi-stable wave propagation behavior was similar to bi-stability shown in many other nonlinear systems. Because the bi-stable states are also excitable, we call this novel behavior bi-excitability. In a 2D heterogeneous tissue, the I(Ca,L)-mediated spiral wave meanders, giving rise to a twisting electrocardiographic QRS axis, resembling torsades de pointes, whereas the coexistence and interplay between the I(Na)-mediated wavefronts and I(Ca,L)-mediated wavefronts give rise to polymorphic ventricular tachycardia. We also present experimental evidence for bi-excitability under EAD-promoting conditions in neonatal rat ventricular myocyte monolayers exposed to BayK8644 and isoproterenol.

CONCLUSION

Under EAD-prone conditions, both I(Na)-mediated conduction and I(Ca,L)-mediated conduction can occur in the same tissue. These novel wave dynamics may be responsible for certain EAD-mediated arrhythmias, such as torsades de pointes and polymorphic ventricular tachycardia.