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

Phenotypic Manifestations of Mutations in Genes Encoding Subunits of Cardiac Potassium Channels

Since 1995, when a potassium channel gene, hERG (human ether-à-go-go-related gene), now referred to as KCNH2 , encoding the rapid component of cardiac delayed rectifier potassium channels was identified as being responsible for type 2 congenital long-QT syndrome, a number of potassium channel genes have been shown to cause different types of inherited cardiac arrhythmia syndromes. These include congenital long-QT syndrome, short-QT syndrome, Brugada syndrome, early repolarization syndrome, and familial atrial fibrillation. Genotype-phenotype correlations have been investigated in some inherited arrhythmia syndromes, and as a result, gene-specific risk stratification and gene-specific therapy and management have become available, particularly for patients with congenital long-QT syndrome. In this review article, the molecular structure and function of potassium channels, the clinical phenotype due to potassium channel gene mutations, including genotype-phenotype correlations, and the diverse mechanisms underlying the potassium channel gene–related diseases will be discussed.

Reorganized PKA-AKAP associations in the failing human heart

Here we reveal that the characterization of large-scale re-arrangements of signaling scaffolds induced by heart failure can serve as a novel concept to identify more specific therapeutic targets. In the mammalian heart, the cAMP pathway, with the cAMP-dependent protein kinase (PKA) in a central role, acts directly downstream of adrenergic receptors to mediate cardiac contractility and rhythm. Heart failure, characterized by severe alterations in adrenergic stimulation is, amongst other interventions, often treated with β-blockers. Contrasting results, however, have shown both beneficial and detrimental effects of decreased cAMP levels in failing hearts. We hypothesize that the origin of this behavior lies in the complex spatiotemporal organization of the regulatory subunit of PKA (PKA-R), which associates tightly with various A-kinase anchoring proteins (AKAPs) to specifically localize PKA's activity. Using chemical proteomics directly applied to human patient and control heart tissue we demonstrate that the association profile of PKA-R with several AKAPs is severely altered in the failing heart, for instance effecting the interaction between PKA and the novel AKAP SPHKAP was 6-fold upregulated upon failing heart conditions. Also a significant increase in captured cGMP-dependent protein kinase (PKG) and phosphodiesterase 2 (PDE2) was observed. The observed altered profiles can already explain many aspects of the aberrant cAMP-response in the failing human heart, validating that this dataset may provide a resource for several novel, more specific, treatment options. This article is part of a Special Issue entitled "Local Signaling in Myocytes".

Simulation of the undiseased human cardiac ventricular action potential: model formulation and experimental validation

Cellular electrophysiology experiments, important for understanding cardiac arrhythmia mechanisms, are usually performed with channels expressed in non myocytes, or with non-human myocytes. Differences between cell types and species affect results. Thus, an accurate model for the undiseased human ventricular action potential (AP) which reproduces a broad range of physiological behaviors is needed. Such a model requires extensive experimental data, but essential elements have been unavailable. Here, we develop a human ventricular AP model using new undiseased human ventricular data: Ca(2+) versus voltage dependent inactivation of L-type Ca(2+) current (I(CaL)); kinetics for the transient outward, rapid delayed rectifier (I(Kr)), Na(+)/Ca(2+) exchange (I(NaCa)), and inward rectifier currents; AP recordings at all physiological cycle lengths; and rate dependence and restitution of AP duration (APD) with and without a variety of specific channel blockers. Simulated APs reproduced the experimental AP morphology, APD rate dependence, and restitution. Using undiseased human mRNA and protein data, models for different transmural cell types were developed. Experiments for rate dependence of Ca(2+) (including peak and decay) and intracellular sodium ([Na(+)](i)) in undiseased human myocytes were quantitatively reproduced by the model. Early afterdepolarizations were induced by I(Kr) block during slow pacing, and AP and Ca(2+) alternans appeared at rates >200 bpm, as observed in the nonfailing human ventricle. Ca(2+)/calmodulin-dependent protein kinase II (CaMK) modulated rate dependence of Ca(2+) cycling. I(NaCa) linked Ca(2+) alternation to AP alternans. CaMK suppression or SERCA upregulation eliminated alternans. Steady state APD rate dependence was caused primarily by changes in [Na(+)](i), via its modulation of the electrogenic Na(+)/K(+) ATPase current. At fast pacing rates, late Na(+) current and I(CaL) were also contributors. APD shortening during restitution was primarily dependent on reduced late Na(+) and I(CaL) currents due to inactivation at short diastolic intervals, with additional contribution from elevated I(Kr) due to incomplete deactivation.

Calcium dynamics and signaling in vascular regulation: computational models

Calcium is a universal signaling molecule with a central role in a number of vascular functions including in the regulation of tone and blood flow. Experimentation has provided insights into signaling pathways that lead to or affected by Ca(2+) mobilization in the vasculature. Mathematical modeling offers a systematic approach to the analysis of these mechanisms and can serve as a tool for data interpretation and for guiding new experimental studies. Comprehensive models of calcium dynamics are well advanced for some systems such as the heart. This review summarizes the progress that has been made in modeling Ca(2+) dynamics and signaling in vascular cells. Model simulations show how Ca(2+) signaling emerges as a result of complex, nonlinear interactions that cannot be properly analyzed using only a reductionist's approach. A strategy of integrative modeling in the vasculature is outlined that will allow linking macroscale pathophysiological responses to the underlying cellular mechanisms.

A new ECG biomarker for drug toxicity: a combined signal processing and computational modeling study

QT prolongation is the only clinically proven, yet insufficient, electrocardiogram (ECG) biomarker for drug-induced cardiac toxicity. The goal of this study is to evaluate whether JT area, i.e., total area of the T-wave, can serve as an ECG biomarker for drug-induced cardiac toxicity using both signal processing and computational modeling approaches. An ECG dataset that contained recordings from patients under control and sotalol condition was analyzed. In order to relate sotalol-induced ECG changes to its effect on ion channel level, i.e., blockade of the rapid component of the delayed rectifier potassium channel (I(Kr)), varied degrees of I(Kr) blockade were simulated in a slab of ventricular tissue. The mean JT area increased by 36.5% following the administration of sotalol in patients. Simulations in the slab tissue showed that sotalol increased action potential duration preferentially in the midmyocardium, which led to increased transmural dispersion of repolarization and JT area. In conclusion, JT area reflects the transmural dispersion of repolarization and may be a potentially useful surrogate/supplemental ECG biomarker to assess drug safety.

Ionic mechanisms of electrophysiological properties and repolarization abnormalities in rabbit Purkinje fibers

Purkinje cells play an important role in drug-induced arrhythmogenesis and are widely used in preclinical drug safety assessments. Repolarization abnormalities such as action potential (AP) prolongation and early afterdeploarizations (EAD) are often observed in vitro upon pharmacological interventions. However, because drugs do not act on only one defined target, it is often difficult to fully explain the mechanisms of action and their potential arrhythmogenicity. Computational models, when appropriately detailed and validated, can be used to gain mechanistic insights into the mechanisms of action of certain drugs. Nevertheless, no model of Purkinje electrophysiology that is able to reproduce characteristic Purkinje responses to drug-induced changes in ionic current conductances such as AP prolongation and EAD generation currently exists. In this study, a novel biophysically detailed model of rabbit Purkinje electrophysiology was developed by integration of data from voltage-clamp and AP experimental recordings. Upon validation, we demonstrate that the model reproduces many key electrophysiological properties of rabbit Purkinje cells. These include: AP morphology and duration, both input resistance and rate dependence properties as well as response to hyperkalemia. Pharmacological interventions such as inward rectifier K(+) current and rapid delayed rectifier K(+) current block as well as late Na(+) current increase result in significant AP changes. However, enhanced L-type Ca(2+) current (i(CaL)) dominates in EAD genesis in Purkinje fibers. In addition, i(CaL) inactivation dynamics and intercellular coupling in tissue strongly modulate EAD formation. We conclude that EAD generation in Purkinje cells is mediated by an increase in i(CaL) and modulated by its inactivation kinetics.

Computational models reduce complexity and accelerate insight into cardiac signaling networks

Cardiac signaling networks exhibit considerable complexity in size and connectivity. The intrinsic complexity of these networks complicates the interpretation of experimental findings. This motivates new methods for investigating the mechanisms regulating cardiac signaling networks and the consequences these networks have on cardiac physiology and disease. Next-generation experimental techniques are also generating a wealth of genomic and proteomic data that can be difficult to analyze or interpret. Computational models are poised to play a key role in addressing these challenges. Computational models have a long history in contributing to the understanding of cardiac physiology and are useful for identifying biological mechanisms, inferring multiscale consequences to cell signaling activities and reducing the complexity of large data sets. Models also integrate well with experimental studies to explain experimental observations and generate new hypotheses. Here, we review the contributions computational modeling approaches have made to the analysis of cardiac signaling networks and forecast opportunities for computational models to accelerate cardiac signaling research.

Synergy between CaMKII substrates and β-adrenergic signaling in regulation of cardiac myocyte Ca(2+) handling

Cardiac excitation-contraction coupling is a highly coordinated process that is controlled by protein kinase signaling pathways, including Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) and protein kinase A (PKA). Increased CaMKII expression and activity (as occurs during heart failure) destabilizes EC coupling and may lead to sudden cardiac death. To better understand mechanisms of cardiac CaMKII function, we integrated dynamic CaMKII-dependent regulation of key Ca(2+) handling targets with previously validated models of cardiac EC coupling, Ca(2+)/calmodulin-dependent activation of CaMKII, and β-adrenergic activation of PKA. Model predictions are validated against CaMKII-overexpression data from rabbit ventricular myocytes. The model demonstrates how overall changes to Ca(2+) handling during CaMKII overexpression are explained by interactions between individual CaMKII substrates. CaMKII and PKA activities during β-adrenergic stimulation may synergistically facilitate inotropic responses and contribute to a CaMKII-Ca(2+)-CaMKII feedback loop. CaMKII regulated early frequency-dependent acceleration of relaxation and EC coupling gain (which was highly sarcoplasmic reticulum Ca(2+) load-dependent). Additionally, the model identifies CaMKII-dependent ryanodine receptor hyperphosphorylation as a proarrhythmogenic trigger. In summary, we developed a detailed computational model of CaMKII and PKA signaling in cardiac myocytes that provides unique insights into their regulation of normal and pathological Ca(2+) handling.

Modeling cardiac β-adrenergic signaling with normalized-Hill differential equations: comparison with a biochemical model

Background

New approaches are needed for large-scale predictive modeling of cellular signaling networks. While mass action and enzyme kinetic approaches require extensive biochemical data, current logic-based approaches are used primarily for qualitative predictions and have lacked direct quantitative comparison with biochemical models.

Results

We developed a logic-based differential equation modeling approach for cell signaling networks based on normalized Hill activation/inhibition functions controlled by logical AND and OR operators to characterize signaling crosstalk. Using this approach, we modeled the cardiac β₁-adrenergic signaling network, including 36 reactions and 25 species. Direct comparison of this model to an extensively characterized and validated biochemical model of the same network revealed that the new model gave reasonably accurate predictions of key network properties, even with default parameters. Normalized Hill functions improved quantitative predictions of global functional relationships compared with prior logic-based approaches. Comprehensive sensitivity analysis revealed the significant role of PKA negative feedback on upstream signaling and the importance of phosphodiesterases as key negative regulators of the network. The model was then extended to incorporate recently identified protein interaction data involving integrin-mediated mechanotransduction.

Conclusions

The normalized-Hill differential equation modeling approach allows quantitative prediction of network functional relationships and dynamics, even in systems with limited biochemical data.

Irregularly appearing early afterdepolarizations in cardiac myocytes: random fluctuations or dynamical chaos?

Irregularly occurring early afterdepolarizations (EADs) in cardiac myocytes are traditionally hypothesized to be caused by random ion channel fluctuations. In this study, we combined 1), patch-clamp experiments in which action potentials were recorded at different pacing cycle lengths from isolated rabbit ventricular myocytes under several experimental conditions inducing EADs, including oxidative stress with hydrogen peroxide, calcium overload with BayK8644, and ionic stress with hypokalemia; 2), computer simulations using a physiologically detailed rabbit ventricular action potential model, in which repolarization reserve was reduced to generate EADs and random ion channel or path cycle length fluctuations were implemented; and 3), iterated maps with or without noise. By comparing experimental, modeling, and bifurcation analyses, we present evidence that noise-induced transitions between bistable states (i.e., between an action potential with and without an EAD) is not sufficient to account for the large variation in action potential duration fluctuations observed in experimental studies. We conclude that the irregular dynamics of EADs is intrinsically chaotic, with random fluctuations playing a nonessential, auxiliary role potentiating the complex dynamics.

A macro finite-element formulation for cardiac electrophysiology simulations using hybrid unstructured grids

Electrical activity in cardiac tissue can be described by the bidomain equations whose solution for large-scale simulations still remains a computational challenge. Therefore, improvements in the discrete formulation of the problem, which decrease computational and/or memory demands are highly desirable. In this study, we propose a novel technique for computing shape functions of finite elements (FEs). The technique generates macro FEs (MFEs) based on the local decomposition of elements into tetrahedral subelements with linear shape functions. Such an approach necessitates the direct use of hybrid meshes (HMs) composed of different types of elements. MFEs are compared to classic standard FEs with respect to accuracy and RAM memory usage under different scenarios of cardiac modeling, including bidomain and monodomain simulations in 2-D and 3-D for simple and complex tissue geometries. In problems with analytical solutions, MFEs displayed the same numerical accuracy of standard linear triangular and tetrahedral elements. In propagation simulations, conduction velocity and activation times agreed very well with those computed with standard FEs. However, MFEs offer a significant decrease in memory requirements. We conclude that HMs composed of MFEs are well suited for solving problems in cardiac computational electrophysiology.

Arrhythmic risk biomarkers for the assessment of drug cardiotoxicity: from experiments to computer simulations

In this paper, we illustrate how advanced computational modelling and simulation can be used to investigate drug-induced effects on cardiac electrophysiology and on specific biomarkers of pro-arrhythmic risk. To do so, we first perform a thorough literature review of proposed arrhythmic risk biomarkers from the ionic to the electrocardiogram levels. The review highlights the variety of proposed biomarkers, the complexity of the mechanisms of drug-induced pro-arrhythmia and the existence of significant animal species differences in drug-induced effects on cardiac electrophysiology. Predicting drug-induced pro-arrhythmic risk solely using experiments is challenging both preclinically and clinically, as attested by the rise in the cost of releasing new compounds to the market. Computational modelling and simulation has significantly contributed to the understanding of cardiac electrophysiology and arrhythmias over the last 40 years. In the second part of this paper, we illustrate how state-of-the-art open source computational modelling and simulation tools can be used to simulate multi-scale effects of drug-induced ion channel block in ventricular electrophysiology at the cellular, tissue and whole ventricular levels for different animal species. We believe that the use of computational modelling and simulation in combination with experimental techniques could be a powerful tool for the assessment of drug safety pharmacology.

Multi-scale modeling of excitation-contraction coupling in the normal and failing heart

Here we describe new computational models of cardiac electromechanics starting from the cellular scale and building to the tissue, organ and system scales. We summarize application to human genetic diseases (LQT1 and LQT3) and to modeling of congestive heart failure.

Mechanisms of protein kinase A anchoring

The second messenger cyclic adenosine monophosphate (cAMP), which is produced by adenylyl cyclases following stimulation of G-protein-coupled receptors, exerts its effect mainly through the cAMP-dependent serine/threonine protein kinase A (PKA). Due to the ubiquitous nature of the cAMP/PKA system, PKA signaling pathways underlie strict spatial and temporal control to achieve specificity. A-kinase anchoring proteins (AKAPs) bind to the regulatory subunit dimer of the tetrameric PKA holoenzyme and thereby target PKA to defined cellular compartments in the vicinity of its substrates. AKAPs promote the termination of cAMP signals by recruiting phosphodiesterases and protein phosphatases, and the integration of signaling pathways by binding additional signaling proteins. AKAPs are a heterogeneous family of proteins that only display similarity within their PKA-binding domains, amphipathic helixes docking into a hydrophobic groove formed by the PKA regulatory subunit dimer. This review summarizes the current state of information on compartmentalized cAMP/PKA signaling with a major focus on structural aspects, evolution, diversity, and (patho)physiological functions of AKAPs and intends to outline newly emerging directions of the field, such as the elucidation of AKAP mutations and alterations of AKAP expression in human diseases, and the validation of AKAP-dependent protein-protein interactions as new drug targets. In addition, alternative PKA anchoring mechanisms employed by noncanonical AKAPs and PKA catalytic subunit-interacting proteins are illustrated.

Integrative computational models of cardiac arrhythmias -- simulating the structurally realistic heart

Simulation of cardiac electrical function, and specifically, simulation aimed at understanding the mechanisms of cardiac rhythm disorders, represents an example of a successful integrative multiscale modeling approach, uncovering emergent behavior at the successive scales in the hierarchy of structural complexity. The goal of this article is to present a review of the integrative multiscale models of realistic ventricular structure used in the quest to understand and treat ventricular arrhythmias. It concludes with the new advances in image-based modeling of the heart and the promise it holds for the development of individualized models of ventricular function in health and disease.

From Fifth Business to Protagonist: the complex roles of ion channel anchors in cardiac arrhythmia

Proper regulation of cardiac ion channel activity is critical for cellular ion homeostasis and myocyte electrical activity. Recent work has demonstrated that cardiac ion channels are not isolated pores in plasmid membranes, but rather exist within macromolecular signaling complexes. Moreover, within these macro-complexes resides the machinery to finely tune ion channel expression, activity, and signaling. While it is widely-accepted that mutations in ion channel pore-forming genes underlie a number of cardiac arrhythmias, current research is now focusing on the roles of auxiliary subunits in the development of arrhythmia syndromes.

Using computational modeling to predict arrhythmogenesis and antiarrhythmic therapy

The use of computational modeling to predict arrhythmia and arrhythmogensis is a relatively new field, but has nonetheless dramatically enhanced our understanding of the physiological and pathophysiological mechanisms that lead to arrhythmia. This review summarizes recent advances in the field of computational modeling approaches with a brief review of the evolution of cellular action potential models, and the incorporation of genetic mutations to understand fundamental arrhythmia mechanisms, including how simulations have revealed situation specific mechanisms leading to multiple phenotypes for the same genotype. The review then focuses on modeling drug blockade to understand how the less-than-intuitive effects some drugs have to either ameliorate or paradoxically exacerbate arrhythmia. Quantification of specific arrhythmia indicies are discussed at each spatial scale, from channel to tissue. The utility of hERG modeling to assess altered repolarization in response to drug blockade is also briefly discussed. Finally, insights gained from Ca(2+) dynamical modeling and EC coupling, neurohumoral regulation of cardiac dynamics, and cell signaling pathways are also reviewed.

Mechanisms of beta-adrenergic modulation of I(Ks) in the guinea-pig ventricle: insights from experimental and model-based analysis

Detailed understanding of I(Ks) gating complexity may provide clues regarding the mechanisms of repolarization instability and the resulting arrhythmias. We developed and tested a kinetic model to interpret physiologically relevant I(Ks) properties, including pause-dependence and modulation by beta-adrenergic receptors (beta-AR). I(Ks) gating was evaluated in guinea-pig ventricular myocytes at 36 degrees C in control and during beta-AR stimulation (0.1 micromol/L isoprenaline (ISO)). We tested voltage dependence of steady-state conductance (Gss), voltage dependence of activation and deactivation time constants (tau(act), tau(deact)), and pause-dependence of tau(act) during repetitive activations (tau(react)). The I(Ks) model was developed from the Silva and Rudy formulation. Parameters were optimized on control and ISO experimental data, respectively. ISO strongly increased Gss and its voltage dependence, changed the voltage dependence of tau(act) and tau(deact), and modified the pause-dependence of tau(react). A single set of model parameters reproduced all experimental data in control. Modification of only three transition rates led to a second set of parameters suitable to fit all ISO data. Channel unitary conductance and density were unchanged in the model, thus implying increased open probability as the mechanism of ISO-induced Gss enhancement. The new I(Ks) model was applied to analyze ISO effect on repolarization rate-dependence. I(Ks) kinetics and its beta-AR modulation were entirely reproduced by a single Markov chain of transitions (for each channel monomer). Model-based analysis suggests that complete opening of I(Ks) channels within a physiological range of potentials requires concomitant beta-AR stimulation. Transient redistribution of state occupancy, in addition to direct modulation of transition rates, may underlie beta-AR modulation of I(Ks) time dependence.

Bifurcation and chaos in a model of cardiac early afterdepolarizations

Excitable cells can exhibit complex patterns of oscillations, such as spiking and bursting. In cardiac cells, pathological voltage oscillations, called early afterdepolarizations (EADs), have been widely observed under disease conditions, yet their dynamical mechanisms remain unknown. Here, we show that EADs are caused by Hopf and homoclinic bifurcations. During period pacing, chaos always occurs at the transition from no EAD to EADs as the stimulation frequency decreases, providing a distinct explanation for the irregular EAD behavior frequently observed in experiments.

AKAP-scaffolding proteins and regulation of cardiac physiology

A kinase anchoring proteins (AKAPs) compose a growing list of diverse but functionally related proteins defined by their ability to bind to the regulatory subunit of protein kinase A. AKAPs perform an integral role in the spatiotemporal modulation of a multitude of cellular signaling pathways. This review highlights the extensive role of AKAPs in cardiac excitation/contraction coupling and cardiac physiology. The literature shows that particular AKAPs are involved in cardiac Ca(2+) influx, release, reuptake, and myocyte repolarization. Studies have also suggested roles for AKAPs in cardiac remodeling. Transgenic studies show functional effects of AKAPs, not only in the cardiovascular system but in other organ systems as well.

Mechanisms of transmurally varying myocyte electromechanics in an integrated computational model

The mechanical properties of myocardium vary across the transmural aspect of the left ventricular wall. Some of these functional heterogeneities may be related to differences in excitation-contraction coupling characteristics that have been observed in cells isolated from the epicardial, mid-myocardial and endocardial regions of the left ventricle of many species, including canine. Integrative models of coupled myocyte electromechanics are reviewed and used here to investigate sources of heterogeneous electromechanical behaviour in these cells. The simulations (i) illustrate a previously unrecognized role of the transient outward potassium current in mechanical function and (ii) suggest that there may also exist additional heterogeneities affecting crossbridge cycling rates in cells from different transmural regions.

From mitochondrial ion channels to arrhythmias in the heart: computational techniques to bridge the spatio-temporal scales

Computer simulations of electrical behaviour in the whole ventricles have become commonplace during the last few years. The goals of this article are (i) to review the techniques that are currently employed to model cardiac electrical activity in the heart, discussing the strengths and weaknesses of the various approaches, and (ii) to implement a novel modelling approach, based on physiological reasoning, that lifts some of the restrictions imposed by current state-of-the-art ionic models. To illustrate the latter approach, the present study uses a recently developed ionic model of the ventricular myocyte that incorporates an excitation-contraction coupling and mitochondrial energetics model. A paradigm to bridge the vastly disparate spatial and temporal scales, from subcellular processes to the entire organ, and from sub-microseconds to minutes, is presented. Achieving sufficient computational efficiency is the key to success in the quest to develop multiscale realistic models that are expected to lead to better understanding of the mechanisms of arrhythmia induction following failure at the organelle level, and ultimately to the development of novel therapeutic applications.

Mechanisms of human arrhythmia syndromes: abnormal cardiac macromolecular interactions

Many cardiac ion channels exist within macromolecular signaling complexes, comprised of pore-forming subunits that associate with auxiliary subunits, regulatory enzymes, and targeting proteins. This complex protein assembly ensures proper modulation of channel activity and ion homeostasis. The association of genetic defects in regulatory and targeting proteins to inherited arrhythmia syndromes has led to a better understanding of the critical role these proteins play in ion channel modulation.

Acetylcholine-induced shortening of the epicardial action potential duration may increase repolarization gradients and LQT3 arrhythmic risk

Unlike other variants of long QT syndrome, LQT3 patients are particularly susceptible to cardiac events during sleep. Changes in heart rate alone fail to fully account for this phenomenon. We hypothesize that the parasympathetic nervous system may play a role in increasing arrhythmic risk in the mammalian ventricular myocardium via acetylcholine (ACh)-mediated effects on repolarisation gradients and, furthermore, that the effects of ACh exhibit rate dependency. Here, we investigate this hypothesis in a mathematical model of action potential generation and excitation-contraction coupling in a canine left ventricular epicardial myocyte, using a previously developed formulation for the muscarinic K(+) current I(K,ACh). Our model was able to reproduce an experimentally observed dose-dependent reduction in canine epicardial action potential duration(90) at 90% repolarization in response to application of ACh. Moreover, our model also predicts a rate-dependent reduction of epicardial APD(90) with the greatest effects occurring at slower rates. This is likely to be due to decreased repolarisation reserve at these rates. Our results suggest that ACh-mediated effects on epicardial myocytes may amplify already steep repolarisation gradients in the mammalian left ventricular wall of LQT3 patients and consequently increase the risk of arrhythmia formation.

The role of transmural ventricular heterogeneities in cardiac vulnerability to electric shocks

Transmural electrophysiological heterogeneities have been shown to contribute to arrhythmia induction in the heart; however, their role in defibrillation failure has never been examined. The goal of this study is to investigate how transmural heterogeneities in ionic currents and gap-junctional coupling contribute to arrhythmia generation following defibrillation strength shocks. This study used a 3D anatomically realistic bidomain model of the rabbit ventricles. Transmural heterogeneity in ionic currents and reduced sub-epicardial intercellular coupling were incorporated based on experimental data. The ventricles were paced apically, and truncated-exponential monophasic shocks of varying strength and timing were applied via large external electrodes. Simulations demonstrate that inclusion of transmural heterogeneity in ionic currents results in an increase in vulnerability to shocks, reflected in the increased upper limit of vulnerability, ULV, and the enlarged vulnerable window, VW. These changes in vulnerability stem from increased post-shock dispersion in repolarisation as it increases the likelihood of establishment of re-entrant circuits. In contrast, reduced sub-epicardial coupling results in decrease in both ULV and VW. This decrease is caused by altered virtual electrode polarisation around the region of sub-epicardal uncoupling, and specifically, by the increase in (1) the amount of positively polarised myocardium at shock-end and (2) the spatial extent of post-shock wavefronts.

Simulation analysis of intracellular Na+ and Cl− homeostasis during β1-adrenergic stimulation of cardiac myocyte

To quantitatively understand intracellular Na+ and Cl- homeostasis as well as roles of Na+/K+ pump and cystic fibrosis transmembrane conductance regulator Cl- channel (ICFTR) during the beta1-adrenergic stimulation in cardiac myocyte, we constructed a computer model of beta1-adrenergic signaling and implemented it into an excitation-contraction coupling model of the guinea-pig ventricular cell, which can reproduce membrane excitation, intracellular ion changes (Na+, K+, Ca2+ and Cl-), contraction, cell volume, and oxidative phosphorylation. An application of isoproterenol to the model cell resulted in the shortening of action potential duration (APD) after a transient prolongation, the increases in both Ca2+ transient and cell shortening, and the decreases in both Cl- concentration and cell volume. These results are consistent with experimental data. Increasing the density of ICFTR shortened APD and augmented the peak amplitudes of the L-type Ca2+ current (ICaL) and the Ca2+ transient during the beta1-adrenergic stimulation. This indirect inotropic effect was elucidated by the increase in the driving force of ICaL via a decrease in plateau potential. Our model reproduced the experimental data demonstrating the decrease in intracellular Na+ during the beta-adrenergic stimulation at 0 or 0.5 Hz electrical stimulation. The decrease is attributable to the increase in Na+ affinity of Na+/K+ pump by protein kinase A. However it was predicted that Na+increases at higher beating rate because of larger Na+ influx through forward Na+/Ca2+ exchange. It was demonstrated that dynamic changes in Na+ and Cl- fluxes remarkably affect the inotropic action of isoproterenol in the ventricular myocytes.

Cardiac beta-adrenergic signaling: from subcellular microdomains to heart failure

beta-adrenergic signaling plays a central role in the neurohumoral regulation of the heart and the progression of heart failure. Initially thought to be a simple linear cascade, this complex network is now recognized to utilize cross-talk with numerous other pathways, spatial compartmentation, and feedback control to coordinate cardiac electrophysiology, contractility, and adaptive remodeling. Here, we review recent basic insights and novel quantitative approaches that are leading to a more comprehensive understanding of beta-adrenergic signaling and thus motivate new therapeutic strategies for cardiac disease.

Modeling transmural heterogeneity of K(ATP) current in rabbit ventricular myocytes

To investigate the mechanisms regulating excitation-metabolic coupling in rabbit epicardial, midmyocardial, and endocardial ventricular myocytes we extended the LabHEART model (Puglisi JL and Bers DM. Am J Physiol Cell Physiol 281: C2049-C2060, 2001). We incorporated equations for Ca(2+) and Mg(2+) buffering by ATP and ADP, equations for nucleotide regulation of ATP-sensitive K(+) channel and L-type Ca(2+) channel, Na(+)-K(+)-ATPase, and sarcolemmal and sarcoplasmic Ca(2+)-ATPases, and equations describing the basic pathways (creatine and adenylate kinase reactions) known to communicate the flux changes generated by intracellular ATPases. Under normal conditions and during 20 min of ischemia, the three regions were characterized by different I(Na), I(to), I(Kr), I(Ks), and I(Kp) channel properties. The results indicate that the ATP-sensitive K(+) channel is activated by the smallest reduction in ATP in epicardial cells and largest in endocardial cells when cytosolic ADP, AMP, PCr, Cr, P(i), total Mg(2+), Na(+), K(+), Ca(2+), and pH diastolic levels are normal. The model predicts that only K(ATP) ionophore (Kir6.2 subunit) and not the regulatory subunit (SUR2A) might differ from endocardium to epicardium. The analysis suggests that during ischemia, the inhomogeneous accumulation of the metabolites in the tissue sublayers may alter in a very irregular manner the K(ATP) channel opening through metabolic interactions with the endogenous PI cascade (PIP(2), PIP) that in turn may cause differential action potential shortening among the ventricular myocyte subtypes. The model predictions are in qualitative agreement with experimental data measured under normal and ischemic conditions in rabbit ventricular myocytes.

Compartmentation of cAMP signaling in cardiac myocytes: a computational study

Receptor-mediated changes in cAMP production play an essential role in sympathetic and parasympathetic regulation of the electrical, mechanical, and metabolic activity of cardiac myocytes. However, responses to receptor activation cannot be easily ascribed to a uniform increase or decrease in cAMP activity throughout the entire cell. In this study, we used a computational approach to test the hypothesis that in cardiac ventricular myocytes the effects of beta(1)-adrenergic receptor (beta(1)AR) and M(2) muscarinic receptor (M(2)R) activation involve compartmentation of cAMP. A model consisting of two submembrane (caveolar and extracaveolar) microdomains and one bulk cytosolic domain was created using published information on the location of beta(1)ARs and M(2)Rs, as well as the location of stimulatory (G(s)) and inhibitory (G(i)) G-proteins, adenylyl cyclase isoforms inhibited (AC5/6) and stimulated (AC4/7) by G(i), and multiple phosphodiesterase isoforms (PDE2, PDE3, and PDE4). Results obtained with the model indicate that: 1), bulk basal cAMP can be high ( approximately 1 microM) and only modestly stimulated by beta(1)AR activation ( approximately 2 microM), but caveolar cAMP varies in a range more appropriate for regulation of protein kinase A ( approximately 100 nM to approximately 2 microM); 2), M(2)R activation strongly reduces the beta(1)AR-induced increases in caveolar cAMP, with less effect on bulk cAMP; and 3), during weak beta(1)AR stimulation, M(2)R activation not only reduces caveolar cAMP, but also produces a rebound increase in caveolar cAMP following termination of M(2)R activity. We conclude that compartmentation of cAMP can provide a quantitative explanation for several aspects of cardiac signaling.

The contribution of genes involved in potassium-recycling in the inner ear to noise-induced hearing loss

Noise-induced hearing loss (NIHL) is one of the most important occupational diseases and, after presbyacusis, the most frequent cause of hearing loss. NIHL is a complex disease caused by an interaction between environmental and genetic factors. The various environmental factors involved in NIHL have been relatively extensively studied. On the other hand, little research has been performed on the genetic factors responsible for NIHL. To test whether the variation in genes involved in coupling of cells and potassium recycling in the inner ear might partly explain the variability in susceptibility to noise, we performed a case-control association study using 35 SNPs selected in 10 candidate genes on a total of 218 samples selected from a population of 1,261 Swedish male noise-exposed workers. We have obtained significant differences between susceptible and resistant individuals for the allele, genotype, and haplotype frequencies for three SNPs of the KCNE1 gene, and for the allele frequencies for one SNP of KCNQ1 and one SNP of KCNQ4. Patch-clamp experiments in high K+-concentrations using a Chinese hamster ovary (CHO) cell model were performed to investigate the possibility that the KCNE1-p.85N variant (NT_011512.10:g.21483550G>A; NP_00210.2:p.Asp85Asn) was causative for high noise susceptibility. The normalized current density generated by KCNQ1/KCNE1-p.85N channels, thus containing the susceptibility variant, differed significantly from that from wild-type channels. Furthermore, the midpoint potential of KCNQ1/KCNE1-p.85N channels (i.e., the voltage at which 50% of the channels are open) differed from that of wild-type channels. Further genetic and physiological studies will be necessary to confirm these findings.

Computational biology in the study of cardiac ion channels and cell electrophysiology

The cardiac cell is a complex biological system where various processes interact to generate electrical excitation (the action potential, AP) and contraction. During AP generation, membrane ion channels interact nonlinearly with dynamically changing ionic concentrations and varying transmembrane voltage, and are subject to regulatory processes. In recent years, a large body of knowledge has accumulated on the molecular structure of cardiac ion channels, their function, and their modification by genetic mutations that are associated with cardiac arrhythmias and sudden death. However, 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 beta-adrenergic cascade on the cell electrophysiological function.

Compartmentation of cyclic nucleotide signaling in the heart: the role of A-kinase anchoring proteins

The activation of the cyclic nucleotide protein kinase A (PKA) and PKG by their respective second messengers is responsible for the modulation of many cellular functions in the heart including cardiac hypertrophy, strength of contraction, and ion flux. However, several studies have revealed that a general increase in cyclic nucleotide concentration in the cell is not sufficient for the specific regulation of target proteins. These studies found that PKA and PKG must be colocalized with their targets to ensure spatial-temporal control of substrate phosphorylation. This compartmentation of cyclic nucleotide signaling is accomplished by tethering the protein kinases with their respective substrates through the association with scaffolding proteins. For cAMP signaling, A-kinase anchoring proteins (AKAPs) provide a molecular mechanism for cAMP compartmentation, allowing for the precise control of PKA-mediated phosphorylation events. (cAMP, PKA, AKAP, PKG).

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

INTRODUCTION

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

METHODS AND RESULTS

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

SUMMARY

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

Strategies and Tactics in Multiscale Modeling of Cell-to-Organ Systems

Modeling is essential to integrating knowledge of human physiology. Comprehensive self-consistent descriptions expressed in quantitative mathematical form define working hypotheses in testable and reproducible form, and though such models are always "wrong" in the sense of being incomplete or partly incorrect, they provide a means of understanding a system and improving that understanding. Physiological systems, and models of them, encompass different levels of complexity. The lowest levels concern gene signaling and the regulation of transcription and translation, then biophysical and biochemical events at the protein level, and extend through the levels of cells, tissues and organs all the way to descriptions of integrated systems behavior. The highest levels of organization represent the dynamically varying interactions of billions of cells. Models of such systems are necessarily simplified to minimize computation and to emphasize the key factors defining system behavior; different model forms are thus often used to represent a system in different ways. Each simplification of lower level complicated function reduces the range of accurate operability at the higher level model, reducing robustness, the ability to respond correctly to dynamic changes in conditions. When conditions change so that the complexity reduction has resulted in the solution departing from the range of validity, detecting the deviation is critical, and requires special methods to enforce adapting the model formulation to alternative reduced-form modules or decomposing the reduced-form aggregates to the more detailed lower level modules to maintain appropriate behavior. The processes of error recognition, and of mapping between different levels of model complexity and shifting the levels of complexity of models in response to changing conditions, are essential for adaptive modeling and computer simulation of large-scale systems in reasonable time.

Ensemble of Linear Models for Predicting Drug Properties

We propose a new classification method for the prediction of drug properties, called random feature subset boosting for linear discriminant analysis (LDA). The main novelty of this method is the ability to overcome the problems with constructing ensembles of linear discriminant models based on generalized eigenvectors of covariance matrices. Such linear models are popular in building classification-based structure-activity relationships. The introduction of ensembles of LDA models allows for an analysis of more complex problems than by using single LDA, for example, those involving multiple mechanisms of action. Using four data sets, we show experimentally that the method is competitive with other recently studied chemoinformatic methods, including support vector machines and models based on decision trees. We present an easy scheme for interpreting the model despite its apparent sophistication. We also outline theoretical evidence as to why, contrary to the conventional AdaBoost ensemble algorithm, this method is able to increase the accuracy of LDA models.

Transmural electrophysiological heterogeneities in action potential duration increase the upper limit of vulnerability

Transmural dispersion in action potential duration (APD) has been shown to contribute to arrhythmia induction in the heart. However, its role in termination of lethal arrhythmias by defibrillation shocks has never been examined. The goal of this study is to investigate how transmural dispersion in APD affects cardiac vulnerability to electric shocks, in an attempt to better understand the mechanisms behind defibrillation failure. This study used a three- dimensional, geometrically accurate finite element bidomain rabbit ventricular model. Transmural heterogeneities in ionic currents were incorporated based on experimental data to generate the transmural APD profile recorded in adult rabbits during pacing. Results show that the incorporation of transmural APD heterogeneities in the model causes an increase in the upper limit of vulnerability from 26.7 V/cm in the homogeneous APD ventricles to 30.5 V/cm in the ventricles with heterogeneous transmural APD profile. Examination of shock-end virtual electrode polarisation and postshock electrical activity reveals that the higher ULV in the heterogeneous model is caused by increased dispersion in postshock repolarisation within the LV wall, which increases the likelihood of the establishment of intramural re-entrant circuits.

An ionic model of stretch-activated and stretch-modulated currents in rabbit ventricular myocytes

AIMS

To develop an ionic model of stretch-activated and stretch-modulated currents in rabbit ventricular myocytes consistent with experimental observations, that can be used to investigate the role of these currents in intact myocardium.

METHODS AND RESULTS

A non-specific cation-selective stretch-activated current I(ns), was incorporated into the Puglisi-Bers ionic model of epicardial, endocardial and midmyocardial ventricular myocytes. Using the model, we predict a reduction in action potential duration at 20% repolarization (APD(20)) and action potential amplitude, an elevated resting transmembrane potential and either an increase or decrease in APD(90), depending on the reversal potential of I(ns). A stretch-induced decrease in I(K1) (70%), plus a small I(ns) current (g(ns) = 10 pS), results in a reduction in APD(20) and increase in APD(90), and a reduced safety factor for conduction. Increasing I(K1) (150%) plus a large I(ns) current (g(ns) = 40 pS), also leads to a reduction in APD(20) and increase in APD(90), but with a greater safety factor. Endocardial and midmyocardial cells appear to be the most sensitive to stretch-induced changes in action potential. The addition of the K(+)-specific stretch-activated current (SAC) I(Ko) results in action potential shortening.

CONCLUSION

Transmural heterogeneity of I(Ko) may reduce repolarization gradients in intact myocardium caused by intrinsic ion channel densities, nonuniform strains and electrotonic effects.

A strategy for integrative computational physiology

Organ function (the heart beat for example) can only be understood through knowledge of molecular and cellular processes within the constraints of structure-function relations at the tissue level. A quantitative modeling framework that can deal with these multiscale issues is described here under the banner of the International Union of Physiological Sciences Physiome Project.

Multiscale modeling of cardiac cellular energetics

Multiscale modeling is essential to integrating knowledge of human physiology starting from genomics, molecular biology, and the environment through the levels of cells, tissues, and organs all the way to integrated systems behavior. The lowest levels concern biophysical and biochemical events. The higher levels of organization in tissues, organs, and organism are complex, representing the dynamically varying behavior of billions of cells interacting together. Models integrating cellular events into tissue and organ behavior are forced to resort to simplifications to minimize computational complexity, thus reducing the model's ability to respond correctly to dynamic changes in external conditions. Adjustments at protein and gene regulatory levels shortchange the simplified higher-level representations. Our cell primitive is composed of a set of subcellular modules, each defining an intracellular function (action potential, tricarboxylic acid cycle, oxidative phosphorylation, glycolysis, calcium cycling, contraction, etc.), composing what we call the "eternal cell," which assumes that there is neither proteolysis nor protein synthesis. Within the modules are elements describing each particular component (i.e., enzymatic reactions of assorted types, transporters, ionic channels, binding sites, etc.). Cell subregions are stirred tanks, linked by diffusional or transporter-mediated exchange. The modeling uses ordinary differential equations rather than stochastic or partial differential equations. This basic model is regarded as a primitive upon which to build models encompassing gene regulation, signaling, and long-term adaptations in structure and function. During simulation, simpler forms of the model are used, when possible, to reduce computation. However, when this results in error, the more complex and detailed modules and elements need to be employed to improve model realism. The processes of error recognition and of mapping between different levels of model form complexity are challenging but are essential for successful modeling of large-scale systems in reasonable time. Currently there is to this end no established methodology from computational sciences.