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

From in vivo plasma composition to in vitro cardiac electrophysiology and in silico virtual heart: the extracellular calcium enigma

In spite of its potential impact on simulation results, the problem of setting the appropriate Ca(2+) concentration ([Ca(2+)](o)) in computational cardiac models has not yet been properly considered. Usually [Ca(2+)](o) values are derived from in vitro electrophysiology. Unfortunately, [Ca(2+)](o) in the experiments is set significantly far (1.8 or 2 mM) from the physiological [Ca(2+)] in blood (1.0-1.3 mM). We analysed the inconsistency of [Ca(2+)](o) among in vivo, in vitro and in silico studies and the dependence of cardiac action potential (AP) duration (APD) on [Ca(2+)](o). Laboratory measurements confirmed the difference between standard extracellular solutions and normal blood [Ca(2+)]. Experimental data on human atrial cardiomyocytes confirmed literature data, demonstrating an inverse relationship between APD and [Ca(2+)](o). Sensitivity analysis of APD on [Ca(2+)](o) for five of the most used cardiac cell models was performed. Most of the models responded with AP prolongation to increases in [Ca(2+)](o), i.e. opposite to the AP shortening observed in vitro and in vivo. Modifications to the Ten Tusscher-Panfilov model were implemented to demonstrate that qualitative consistency among in vivo, in vitro and in silico studies can be achieved. The Courtemanche atrial model was used to test the effect of changing [Ca(2+)](o) on quantitative predictions about the effect of K(+) current blockade. The present analysis suggests that (i) [Ca(2+)](o) in cardiac AP models should be changed from 1.8 to 2 mM to approximately 1.15 mM in order to reproduce in vivo conditions, (ii) the sensitivity to [Ca(2+)](o) of ventricular AP models should be improved in order to simulate real conditions, (iii) modifications to the formulation of Ca(2+)-dependent I(CaL) inactivation can make models more suitable to analyse AP when [Ca(2+)](o) is set to lower physiological values, and (iv) it could be misleading to use non-physiological high [Ca(2+)](o) when the quantitative analysis of in vivo pathophysiological mechanisms is the ultimate aim of simulation.

Coupling contraction, excitation, ventricular and coronary blood flow across scale and physics in the heart

In this study, we review the development and application of multi-physics and multi-scale coupling in the construction of whole-heart physiological models. Through an examination of recent computational modelling developments, we analyse the significance of coupling mechanisms for the increased understanding of cardiac function in the areas of excitation-contraction, coronary blood flow and ventricular fluid mechanical coupling. Within these physiological domains, we demonstrate and discuss the importance of model parametrization, imaging-based model anatomy and computational implementation.

The relative role of refractoriness and source-sink relationship in reentry generation during simulated acute ischemia

During acute myocardial ischemia, reentrant episodes may lead to ventricular fibrillation (VF), giving rise to potentially mortal arrhythmias. VF has been traditionally related to dispersion of refractoriness and more recently to the source-sink relationship. Our goal is to theoretically investigate the relative role of dispersion of refractoriness and source-sink mismatch in vulnerability to reentry in the specific situation of regional myocardial acute ischemia. The electrical activity of a regionally ischemic tissue was simulated using a modified version of the Luo-Rudy dynamic model. Ischemic conditions were varied to simulate the time-course of acute ischemia. Our results showed that dispersion of refractoriness increased with the severity of ischemia. However, no correlation between dispersion of refractoriness and the width of the vulnerable window was found. Additionally, in approximately 50% of the reentries, unidirectional block (UDB) took place in cells completely recovered from refractoriness. We examined patterns of activation after premature stimulation and they were intimately related to the source-sink relationship, quantified by the safety factor (SF). Moreover, the isoline where the SF dropped below unity matched the area where propagation failed. It was concluded that the mismatch of the source-sink relationship, rather than solely refractoriness, was the ultimate cause of the UDB leading to reentry. The SF represents a very powerful tool to study the mechanisms responsible for reentry.

A physiome standards-based model publication paradigm

In this era of widespread broadband Internet penetration and powerful Web browsers on most desktops, a shift in the publication paradigm for physiome-style models is envisaged. No longer will model authors simply submit an essentially textural description of the development and behaviour of their model. Rather, they will submit a complete working implementation of the model encoded and annotated according to the various standards adopted by the physiome project, accompanied by a traditional human-readable summary of the key scientific goals and outcomes of the work. While the final published, peer-reviewed article will look little different to the reader, in this new paradigm, both reviewers and readers will be able to interact with, use and extend the models in ways that are not currently possible. Here, we review recent developments that are laying the foundations for this new model publication paradigm. Initial developments have focused on the publication of mathematical models of cellular electrophysiology, using technology based on a CellML- or Systems Biology Markup Language (SBML)-encoded implementation of the mathematical models. Here, we review the current state of the art and what needs to be done before such a model publication becomes commonplace.

A thermodynamic model of the cardiac sarcoplasmic/endoplasmic Ca(2+) (SERCA) pump

We present a biophysically based kinetic model of the cardiac SERCA pump that consolidates a range of experimental data into a consistent and thermodynamically constrained framework. The SERCA model consists of a number of sub-states with partial reactions that are sensitive to Ca(2+) and pH, and to the metabolites MgATP, MgADP, and Pi. Optimization of model parameters to fit experimental data favors a fully cooperative Ca(2+)-binding mechanism and predicts a Ca(2+)/H(+) counter-transport stoichiometry of 2. Moreover, the order of binding of the partial reactions, particularly the binding of MgATP, proves to be a strong determinant of the ability of the model to fit the data. A thermodynamic investigation of the model indicates that the binding of MgATP has a large inhibitory effect on the maximal reverse rate of the pump. The model is suitable for integrating into whole-cell models of cardiac electrophysiology and Ca(2+) dynamics to simulate the effects on the cell of compromised metabolism arising in ischemia and hypoxia.

Genetically determined differences in sodium current characteristics modulate conduction disease severity in mice with cardiac sodium channelopathy

Conduction slowing of the electric impulse that drives the heartbeat may evoke lethal cardiac arrhythmias. Mutations in SCN5A, which encodes the pore-forming cardiac sodium channel alpha subunit, are associated with familial arrhythmia syndromes based on conduction slowing. However, disease severity among mutation carriers is highly variable. We hypothesized that genetic modifiers underlie the variability in conduction slowing and disease severity. With the aim of identifying such modifiers, we studied the Scn5a(1798insD/+) mutation in 2 distinct mouse strains, FVB/N and 129P2. In 129P2 mice, the mutation resulted in more severe conduction slowing particularly in the right ventricle (RV) compared to FVB/N. Pan-genomic mRNA expression profiling in the 2 mouse strains uncovered a drastic reduction in mRNA encoding the sodium channel auxiliary subunit beta4 (Scn4b) in 129P2 mice compared to FVB/N. This corresponded to low to undetectable beta4 protein levels in 129P2 ventricular tissue, whereas abundant beta4 protein was detected in FVB/N. Sodium current measurements in isolated myocytes from the 2 mouse strains indicated that sodium channel activation in myocytes from 129P2 mice occurred at more positive potentials compared to FVB/N. Using computer simulations, this difference in activation kinetics was predicted to explain the observed differences in conduction disease severity between the 2 strains. In conclusion, genetically determined differences in sodium current characteristics on the myocyte level modulate disease severity in cardiac sodium channelopathies. In particular, the sodium channel subunit beta4 (SCN4B) may constitute a potential genetic modifier of conduction and cardiac sodium channel disease.

The mechanism and significance of the slow changes of ventricular action potential duration following a change of heart rate

This article reviews the effects of changes of heart rate on the ventricular action potential duration. These can be divided into short term (fractions of a second), resulting from the kinetics of recovery of membrane currents, through to long term (up to days), resulting from changes of protein expression. We concentrate on the medium-term changes (time course of the order of 100 s). These medium-term changes occur in isolated tissues and in the intact human heart. They may protect against cardiac arrhythmias. Finally, we discuss the cellular mechanisms responsible for these changes.

Re-evaluating the efficacy of beta-adrenergic agonists and antagonists in long QT-3 syndrome through computational modelling

AIMS

Long QT syndrome (LQTS) is a heterogeneous collection of inherited cardiac ion channelopathies characterized by a prolonged electrocardiogram QT interval and increased risk of sudden cardiac death. Beta-adrenergic blockers are the mainstay of treatment for LQTS. While their efficacy has been demonstrated in LQTS patients harbouring potassium channel mutations, studies of beta-blockers in subtype 3 (LQT3), which is caused by sodium channel mutations, have produced ambiguous results. In this modelling study, we explore the effects of beta-adrenergic drugs on the LQT3 phenotype.

METHODS AND RESULTS

In order to investigate the effects of beta-adrenergic activity and to identify sources of ambiguity in earlier studies, we developed a computational model incorporating the effects of beta-agonists and beta-blockers into an LQT3 mutant guinea pig ventricular myocyte model. Beta-activation suppressed two arrhythmogenic phenomena, transmural dispersion of repolarization and early after depolarizations, in a dose-dependent manner. However, the ability of beta-activation to prevent cardiac conduction block was pacing-rate-dependent. Low-dose beta-blockade by propranolol reversed the beneficial effects of beta-activation, while high dose (which has off-target sodium channel effects) decreased arrhythmia susceptibility.

CONCLUSION

These results demonstrate that beta-activation may be protective in LQT3 and help to reconcile seemingly conflicting results from different experimental models. They also highlight the need for well-controlled clinical investigations re-evaluating the use of beta-blockers in LQT3 patients.

Estimating atrial action potential duration from electrograms

Electrogram analysis is important in clinical and experimental settings. Activation recovery interval (ARI) has been used to measure ventricular action potential duration (APD) but its suitability for the atria has not been addressed. Mapping of atrial repolarization may be especially important during nerve stimulation since large heterogenous APD changes may manifest. This study assessed the utility of estimating APD in the atria using electrograms. A computer model of the atria was used to compute electrograms. Two different atrial waveforms were used, as well as two ventricular. APD was modulated with an acetylcholine- (ACh) dependent potassium channel and varying the spatial ACh distribution. ARI was computed, as well as the area under the repolarization wave (ATa). APD was measured by four methods. Atrial electrograms were also compared to monophasic action potentials recorded from a dog. ARI computed from atrial action potentials was not very precise, with errors ranging over 30 ms. Determining changes in APD induced by changing [ACh] yielded larger errors. Conversely, ventricular action potentials produced ARIs that very closely correlated with APD, and changes in APD . Positive ATa indicated regions of shortened APD, and islands of ACh release were clearly demarcated by ATa polarity. Experimentally, ARI was able to detect changes in APD, but did not measure APD well. The faster rate of ventricular repolarization produces larger currents that are less susceptible to electrotonic coupling effects, improving correlation with APD. ARI most closely correlated with APD measured as a fixed threshold above rest. Atrial APs produce electrograms that can be used to detect changes in APD. This may be improved by decreasing coupling. The ATa is a robust measure for precisely identifying spatial APD heterogeneities.

Modelling and measuring electromechanical coupling in the rat heart

Tension-dependent binding of Ca(2+) to troponin C in the cardiac myocyte has been shown to play an important role in the regulation of Ca(2+) and the activation of tension development. The significance of this regulatory mechanism is quantified experimentally by the quantity of Ca(2+) released following a rapid change in the muscle length. Using a computational, coupled, electromechanics cell model, we have confirmed that the tension dependence of Ca(2+) binding to troponin C, rather than cross-bridge kinetics or the rate of Ca(2+) uptake by the sarcoplasmic reticulum, determines the quantity of Ca(2+) released following a length step. This cell model has been successfully applied in a continuum model of the papillary muscle to analyse experimental data, suggesting the tension-dependent binding of Ca(2+) to troponin C as the likely pathway through which the effects of localized impaired tension generation alter the Ca(2+) transient. These experimental results are qualitatively reproduced using a three-dimensional coupled electromechanics model. Furthermore, the model predicts that changes in the Ca(2+) transient in the viable myocardium surrounding the impaired region are amplified in the absence of tension-dependent binding of Ca(2+) to troponin C.

Properties and ionic mechanisms of action potential adaptation, restitution, and accommodation in canine epicardium

Computational models of cardiac myocytes are important tools for understanding ionic mechanisms of arrhythmia. This work presents a new model of the canine epicardial myocyte that reproduces a wide range of experimentally observed rate-dependent behaviors in cardiac cell and tissue, including action potential (AP) duration (APD) adaptation, restitution, and accommodation. Model behavior depends on updated formulations for the 4-aminopyridine-sensitive transient outward current (I(to1)), the slow component of the delayed rectifier K(+) current (I(Ks)), the L-type Ca(2+) channel current (I(Ca,L)), and the Na(+)-K(+) pump current (I(NaK)) fit to data from canine ventricular myocytes. We found that I(to1) plays a limited role in potentiating peak I(Ca,L) and sarcoplasmic reticulum Ca(2+) release for propagated APs but modulates the time course of APD restitution. I(Ks) plays an important role in APD shortening at short diastolic intervals, despite a limited role in AP repolarization at longer cycle lengths. In addition, we found that I(Ca,L) plays a critical role in APD accommodation and rate dependence of APD restitution. Ca(2+) entry via I(Ca,L) at fast rate drives increased Na(+)-Ca(2+) exchanger Ca(2+) extrusion and Na(+) entry, which in turn increases Na(+) extrusion via outward I(NaK). APD accommodation results from this increased outward I(NaK). Our simulation results provide valuable insight into the mechanistic basis of rate-dependent phenomena important for determining the heart's response to rapid and irregular pacing rates (e.g., arrhythmia). Accurate simulation of rate-dependent phenomena and increased understanding of their mechanistic basis will lead to more realistic multicellular simulations of arrhythmia and identification of molecular therapeutic targets.

Proarrhythmic defects in Timothy syndrome require calmodulin kinase II

BACKGROUND

Timothy syndrome (TS) is a disease of excessive cellular Ca(2+) entry and life-threatening arrhythmias caused by a mutation in the primary cardiac L-type Ca(2+) channel (Ca(V)1.2). The TS mutation causes loss of normal voltage-dependent inactivation of Ca(V)1.2 current (I(Ca)). During cellular Ca(2+) overload, the calmodulin-dependent protein kinase II (CaMKII) causes arrhythmias. We hypothesized that CaMKII is a part of the proarrhythmic mechanism in TS.

METHODS AND RESULTS

We developed an adult rat ventricular myocyte model of TS (G406R) by lentivirus-mediated transfer of wild-type and TS Ca(V)1.2. The exogenous Ca(V)1.2 contained a mutation (T1066Y) conferring dihydropyridine resistance, so we could silence endogenous Ca(V)1.2 with nifedipine and maintain peak I(Ca) at control levels in infected cells. TS Ca(V)1.2-infected ventricular myocytes exhibited the signature voltage-dependent inactivation loss under Ca(2+) buffering conditions, not permissive for CaMKII activation. In physiological Ca(2+) solutions, TS Ca(V)1.2-expressing ventricular myocytes exhibited increased CaMKII activity and a proarrhythmic phenotype that included action potential prolongation, increased I(Ca) facilitation, and afterdepolarizations. Intracellular dialysis of a CaMKII inhibitory peptide, but not a control peptide, reversed increases in I(Ca) facilitation, normalized the action potential, and prevented afterdepolarizations. We developed a revised mathematical model that accounts for CaMKII-dependent and CaMKII-independent effects of the TS mutation.

CONCLUSIONS

In TS, the loss of voltage-dependent inactivation is an upstream initiating event for arrhythmia phenotypes that are ultimately dependent on CaMKII activation.

Microstructure-based Monte Carlo simulation of Ca2+ dynamics evoking cardiac calcium channel inactivation

Ca(2+) dynamics underlying cardiac excitation-contraction coupling are essential for heart functions. In this study, we constructed microstructure-based models of Ca(2+) dynamics to simulate Ca(2+) influx through individual L-type Calcium channels (LCCs), an effective Ca(2+) diffusion within the cytoplasmic space and in the dyadic space, and the experimentally observed calcium-dependent inactivation (CDI) of the LCCs induced by local and global Ca(2+) sensing. The models consisted of LCCs with distal and proximal Ca(2+) (Calmodulin-Ca(2+) complex) binding sites. In one model, the intra-cellular space was organelle-free cytoplasmic space, and the other was with a dyadic space including sarcoplasmic reticulum membrane. The Ca(2+) dynamics and CDI of the LCCs in the model with and without the dyadic space were then simulated using the Monte Carlo method. We first showed that an appropriate set of parameter values of the models with effectively extra-slow Ca(2+) diffusion enabled the models to reproduce major features of the CDI process induced by the local and global sensing of Ca(2+) near LCCs as measured with single and two spatially separated LCCs by Imredy and Yue (Neuron. 1992;9:197-207). The effective slow Ca(2+) diffusion might be due to association and dissociation of Ca(2+) and Calmodulin (CaM). We then examined how the local and global CDIs were affected by the presence of the dyadic space. The results suggested that in microstructure modeling of Ca(2+) dynamics in cardiac myocytes, the effective Ca(2+) diffusion under CaM-Ca(2+) interaction, the nanodomain structure of LCCs for detailed CDI, and the geometry of subcellular space for modeling dyadic space should be considered.

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.

CellML and associated tools and techniques

We have, in the last few years, witnessed the development and availability of an ever increasing number of computer models that describe complex biological structures and processes. The multi-scale and multi-physics nature of these models makes their development particularly challenging, not only from a biological or biophysical viewpoint but also from a mathematical and computational perspective. In addition, the issue of sharing and reusing such models has proved to be particularly problematic, with the published models often lacking information that is required to accurately reproduce the published results. The International Union of Physiological Sciences Physiome Project was launched in 1997 with the aim of tackling the aforementioned issues by providing a framework for the modelling of the human body. As part of this initiative, the specifications of the CellML mark-up language were released in 2001. Now, more than 7 years later, the time has come to assess the situation, in particular with regard to the tools and techniques that are now available to the modelling community. Thus, after introducing CellML, we review and discuss existing editors, validators, online repository, code generators and simulation environments, as well as the CellML Application Program Interface. We also address possible future directions including the need for additional mark-up languages.

Physiological properties of hERG 1a/1b heteromeric currents and a hERG 1b-specific mutation associated with Long-QT syndrome

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

Reconstructing subsurface electrical wave orientation from cardiac epi-fluorescence recordings: Monte Carlo versus diffusion approximation

The development of voltage-sensitive dyes has revolutionized cardiac electrophysiology and made optical imaging of cardiac electrical activity possible. Photon diffusion models coupled to electrical excitation models have been successful in qualitatively predicting the shape of the optical action potential and its dependence on subsurface electrical wave orientation. However, the accuracy of the diffusion equation in the visible range, especially for thin tissue preparations, remains unclear. Here, we compare diffusion and Monte Carlo (MC) based models and we investigate the role of tissue thickness. All computational results are compared to experimental data obtained from intact guinea pig hearts. We show that the subsurface volume contributing to the epi-fluorescence signal extends deeper in the tissue when using MC models, resulting in longer optical upstroke durations which are in better agreement with experiments. The optical upstroke morphology, however, strongly correlates to the subsurface propagation direction independent of the model and is consistent with our experimental observations.

Molecular basis of cardiac action potential repolarization

The action potential (AP) is generated by transport of ions through transmembrane ion channels. Rate dependence of AP repolarization is a fundamental property of cardiac cells, and its modification by disease or drugs can lead to fatal arrhythmias. Using a computational biology approach, we investigated the gating kinetics of the rapid (IKr) and slow (IKs) K+ currents during the AP in order to provide insight into the molecular basis of their role in AP repolarization. Results show that IKr intensifies during the late AP plateau by progressively recovering from inactivation and generating a pronounced late peak of open-state occupancy. The delayed peak makes IKr an effective determinant of AP repolarization. IKs builds an available reserve of channels in closed states near the open state that can open rapidly to generate current during the AP repolarization phase. By doing so, IKs can provide repolarizing current when other currents (e.g., IKr) are compromised by disease or drugs, thus preventing excessive AP prolongation and arrhythmic activity.

Enhancement of ventricular gap-junction coupling by rotigaptide

AIMS

Rotigaptide is proposed to exert its anti-arrhythmic effects by improving myocardial gap-junction communication. To directly investigate the mechanisms of rotigaptide action, we treated cultured neonatal murine ventricular cardiomyocytes with clinical pharmacological doses of rotigaptide and directly determined its effects on gap-junctional currents.

METHODS AND RESULTS

Neonatal murine ventricular cardiomyocytes were enzymatically isolated and cultured for 1-4 days. Primary culture cell pairs were subjected to dual whole cell patch-clamp procedures to directly measure gap-junctional currents (I(j)) and voltage (V(j)). Rotigaptide (0-350 nM) was applied overnight or acutely perfused into 35 mm culture dishes. Rotigaptide (35-100 nM) acutely and chronically increased the resting gap-junction conductance (g(j)), and normalized steady-state minimum g(j) (G(min)) by 5-20%. Higher concentrations produced a diminishing response, which mimics the observed therapeutic efficacy of the drug. The inactivation kinetics was similarly slowed in a therapeutic concentration-dependent manner without affecting the V(j) dependence of inactivation or recovery. The effects of 0-100 nM rotigaptide on ventricular g(j) during cardiac action potential propagation were accurately modelled by computer simulations which demonstrate that clinically effective concentrations of rotigaptide can partially reverse conduction slowing due to decreases in g(j) and inactivation.

CONCLUSION

These results demonstrate that therapeutic concentrations of rotigaptide increase the resting gap-junction conductance and reduce the magnitude and kinetics of steady-state inactivation in a concentration-dependent manner. Rotigaptide may be effective in treating re-entrant forms of cardiac arrhythmias by improving conduction and preventing the formation of re-entrant circuits in partially uncoupled myocardium.

In silico risk assessment for drug-induction of cardiac arrhythmia

The main components of repolarization reserve for the ventricular action potential (AP) are the rapid (I(Kr)) and slow (I(Ks)) delayed outward K(+) currents. While many drugs block I(Kr) and cause life-threatening arrhythmias including torsades de pointes, the frequency of arrhythmias varies between different I(Kr)-blockers. Different types of block of I(Kr) cause distinct phenotypes of prolongation of action potential duration (APD), increase in transmural dispersion of repolarization (TDR) and, accordingly, occurrence of torsades de pointes. Therefore the assessment of a drug's proarrhythmic risk requires a method that provides quantitative and comprehensive comparison of the effects of different forms of I(Kr)-blockade upon APDs and TDR. However, most currently available methods are not adapted to such an extensive comparison. Here, we introduce I(Kr)-I(Ks) two-dimensional maps of APD and TDR as a novel risk-assessment method. Taking the kinetics of I(Kr)-blockade into account, APDs can be calculated upon a ventricular AP model which systematically alters the magnitudes of I(Kr) and I(Ks). The calculated APDs are then plotted on a map where the x axis represents the conductance of I(Kr) while the y axis represents that of I(Ks). TDR is simulated with models corresponding to APs in epicardial, midcardial and endocardial myocardium. These two-dimensional maps of APD and TDR successfully account for differences in the risk resulting from three distinct types of I(Kr)-blockade which correspond to the effects of dofetilide, quinidine and vesnarinone. This method may be of use to assess the arrhythmogenic risk of various I(Kr)-blockers.

Subepicardial phase 0 block and discontinuous transmural conduction underlie right precordial ST-segment elevation by a SCN5A loss-of-function mutation

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

Sex, age, and regional differences in L-type calcium current are important determinants of arrhythmia phenotype in rabbit hearts with drug-induced long QT type 2

In congenital and acquired long QT type 2, women are more vulnerable than men to torsade de pointes. In prepubertal rabbits (and children), the arrhythmia phenotype is reversed; however, females still have longer action potential durations than males. Thus, sex differences in K(+) channels and action potential durations alone cannot account for sex-dependent arrhythmia phenotypes. The L-type calcium current (I(Ca,L)) is another determinant of action potential duration, Ca(2+) overload, early afterdepolarizations (EADs), and torsade de pointes. Therefore, sex, age, and regional differences in I(Ca,L) density and in EAD susceptibility were analyzed in epicardial left ventricular myocytes isolated from the apex and base of prepubertal and adult rabbit hearts. In prepubertal rabbits, peak I(Ca,L) at the base was 22% higher in males than females (6.4+/-0.5 versus 5.0+/-0.2 pA/pF; P<0.03) and higher than at the apex (6.4+/-0.5 versus 5.0+/-0.3 pA/pF; P<0.02). Sex differences were reversed in adults: I(Ca,L) at the base was 32% higher in females than males (9.5+/-0.7 versus 6.4+/-0.6 pA/pF; P<0.002) and 28% higher than the apex (9.5+/-0.7 versus 6.9+/-0.5 pA/pF; P<0.01). Apex-base differences in I(Ca,L) were not significant in adult male and prepubertal female hearts. Western blot analysis showed that Ca(v)1.2alpha levels varied with sex, maturity, and apex-base, with differences similar to variations in I(Ca,L); optical mapping revealed that the earliest EADs fired at the base. Single myocyte experiments and Luo-Rudy simulations concur that I(Ca,L) elevation promotes EADs and is an important determinant of long QT type 2 arrhythmia phenotype, most likely by reducing repolarization reserve and by enhancing Ca(2+) overload and the propensity for I(Ca,L) reactivation.

Minimal model for human ventricular action potentials in tissue

Modeling the dynamics of wave propagation in human ventricular tissue and studying wave stability require models that reproduce realistic characteristics in tissue. We present a minimal ventricular (MV) human model that is designed to reproduce important tissue-level characteristics of epicardial, endocardial and midmyocardial cells, including action potential (AP) amplitudes and morphologies, upstroke velocities, steady-state action potential duration (APD) and conduction velocity (CV) restitution curves, minimum APD, and minimum diastolic interval. The model is then compared with three previously published human ventricular cell models, the Priebe and Beuckelmann (PB), the Ten Tusscher-Noble-Noble-Panfilov (TNNP), and the Iyer-Mazhari-Winslow (IMW). For the first time, the stability of reentrant waves for all four models is analyzed, and quantitative comparisons are made among the models in single cells and in tissue. The PB, TNNP, and IMW models exhibit quantitative differences in APD and CV rate adaptation, as well as completely different reentrant wave dynamics of quasi-breakup, stability, and breakup, respectively. All the models have dominant frequencies comparable to clinical values except for the IMW model, which has a large range of frequencies extending beyond the clinical range for both ventricular tachycardia (VT) and ventricular fibrillation (VF). The TNNP and IMW models possess a large degree of short-term memory and we show for the first time the existence of memory in CV restitution. The MV model also can be fitted to reproduce the dynamics of other models and is computationally more efficient: the times required to simulate the MV, TNNP, PB and IMW models follow the ratio 1:31:50:8084.

Extracting intramural wavefront orientation from optical upstroke shapes in whole hearts

Information about intramural propagation of electrical excitation is crucial to understanding arrhythmia mechanisms in thick ventricular muscle. There is currently a controversy over whether it is possible to extract such information from the shape of the upstroke in optical mapping recordings. We show that even in the complex geometry of a whole guinea pig heart, optical upstroke morphology reveals the 3D wavefront orientation near the surface. To characterize the upstroke morphology, we use V(F)(*), the fractional level at which voltage-sensitive fluorescence, V(F), has maximal time derivative. Low values of V(F)(*)( approximately 0.2) indicate a wavefront moving away from the surface, high values of V(F)(*) ( approximately 0.6) a wavefront moving toward the surface, and intermediate values of V(F)(*) ( approximately 0.4) a wavefront moving parallel to the surface. We further performed computer simulations using Luo-Rudy II electrophysiology and a simplified 3D geometry. The simulated V(F)(*) maps for free wall and apical stimulations as well as for sinus rhythm are in good quantitative agreement with the averaged experimental results. Furthermore, computer simulations show that the effect of the curvature of the heart on wave propagation is negligible.

Bradycardic onset of spiral wave re-entry: structural substrates

AIMS

The least understood aspect of re-entrant cardiac arrhythmias is how they start spontaneously. The known mechanisms for re-entry induction involve the application of premature electrical stimuli or rapid pacing, whereas in a clinical setting, re-entry often occurs at normal heart rates. Here, we propose a physiological mechanism of re-entry onset at normal and slow heart rates, which is based on structurally determined heterogeneities.

METHODS AND RESULTS

Using a two-dimensional tissue model with Luo-Rudy II kinetics, we study electrical propagation in the presence of macroscopic coupling heterogeneities. We find that spiral wave re-entry occurs if steep and smooth coupling gradients are situated side by side, with the critical steepness depending on the frequency of stimulation. We demonstrate how bradycardia can unmask a slow endogenous pacemaker in a poorly coupled region, subsequently leading to spiral wave re-entry.

CONCLUSION

In the presence of coupling heterogeneities, a single excitation coming from the less coupled region may induce spiral wave re-entry.

Reentry in survived subepicardium coupled to depolarized and inexcitable midmyocardium: insights into arrhythmogenesis in ischemia phase 1B

BACKGROUND

Delayed ventricular arrhythmias during acute myocardial ischemia (1B arrhythmias) are associated with an increase in tissue impedance and are most likely sustained in a thin subepicardial layer.

OBJECTIVE

The goal of this study was to test the hypothesis that heterogeneous uncoupling between depolarized midmyocardium and surviving subepicardium results in heterogeneous refractoriness in the latter, providing the reentry substrate after a premature beat.

METHODS

A 3-dimensional bidomain slab was constructed comprising a normal subepicardial layer coupled to a slightly depolarized (-80 to -60 mV) but inexcitable midmyocardium. Experimentally measured tissue impedance served as input for the model. Four stages of heterogeneous uncoupling between the 2 layers were simulated, each corresponding to an experimental ischemic impedance value. Effective refractory periods (ERP), conduction velocities, and inducibility of reentry were examined.

RESULTS

Heterogeneous uncoupling resulted in subepicardial ERP dispersion, allowing reentry to occur. The minimum ERP dispersion needed to induce reentry was 28 ms. Reentry induction was only possible in this model at the 2 intermediate stages of uncoupling, and only when midmyocardial resting membrane potential was more negative than -60 mV. Complete uncoupling of the layers resulted in normal subepicardial conduction without arrhythmias. The minimum length of the reentrant pathway was 2.5 cm, comparable to 2.4 cm reported in previous experiments.

CONCLUSION

Heterogeneous uncoupling to a negative sink such as depressed inexcitable midmyocardium may be a substrate for ischemia 1B arrhythmias. Total uncoupling removes the arrhythmogenic substrate.

Intra-myocardial cusp waves and their manifestation in optical mapping signals

The rotating fiber orientation within the cardiac wall substantially affects the electrical propagation and can cause intra-myocardial cusp waves. Numerical simulations have shown that the cusps form in layers where propagation is perpendicular to the fiber orientation and lead to complex wave front morphologies. They can travel across layers and break through at the epi- or endocardial surfaces where they cause apparent accelerations of propagation. The validation of these results remains a major experimental challenge. In the present study, we investigate both computationally and experimentally how intramural cusp waves can be detected using optical imaging. Our simulations show that cusps alter the optical upstroke morphology and can be detected well before they reach the surface (up to 1 mm deep). Experiments in Langendorff-perfused guinea pig hearts are consistent with our numerical findings.

The role of mechanoelectric feedback in vulnerability to electric shock

Experimental and clinical studies have shown that ventricular dilatation is associated with increased arrhythmogenesis and elevated defibrillation threshold; however, the underlying mechanisms remain poorly understood. The goal of the present study was to test the hypothesis that (1) stretch-activated channel (SAC) recruitment and (2) geometrical deformations in organ shape and fiber architecture lead to increased arrhythmogenesis by electric shocks following acute ventricular dilatation. To elucidate the contribution of these two factors, the study employed, for the first time, a combined electro-mechanical simulation approach. Acute dilatation was simulated in a model of rabbit ventricular mechanics by raising the LV end-diastolic pressure from 0.6 (control) to 4.2 kPa (dilated). The output of the mechanics model was used in the electrophysiological model. Vulnerability to shocks was examined in the control, the dilated ventricles, and in the dilated ventricles that also incorporated currents through SAC as a function of local strain, by constructing vulnerability grids. Results showed that dilatation-induced deformation alone decreased upper limit of vulnerability (ULV) slightly and did not result in increased vulnerability. With SAC recruitment in the dilated ventricles, the number of shock-induced arrhythmia episodes increased by 37% (from 41 to 56) and the lower limit of vulnerability (LLV) decreased from 9 to 7 V/cm, while ULV did not change. The heterogeneous activation of SAC caused by the heterogeneous fiber strain in the ventricular walls was the main reason for increased vulnerability to electric shocks since it caused dispersion of electrophysiological properties in the tissue, resulting in postshock unidirectional block and establishment of reentry.

Computational biology of cardiac myocytes: proposed standards for the physiome

Predicting information about human physiology and pathophysiology from genomic data is a compelling, but unfulfilled goal of post-genomic biology. This is the aim of the so-called Physiome Project and is, undeniably, an ambitious goal. Yet if we can exploit even a small proportion of the rich and varied experimental data currently available, significant insights into clinically important aspects of human physiology will follow. To achieve this requires the integration of data from disparate sources into a common framework. Extrapolation of available data across species, laboratory techniques and conditions requires a quantitative approach. Mathematical models allow us to integrate molecular information into cellular, tissue and organ-level, and ultimately clinically relevant scales. In this paper we argue that biophysically detailed computational modelling provides the essential tool for this process and, furthermore, that an appropriate framework for annotating, databasing and critiquing these models will be essential for the development of integrative computational biology.

Multi-scale computational modelling in biology and physiology

Recent advances in biotechnology and the availability of ever more powerful computers have led to the formulation of increasingly complex models at all levels of biology. One of the main aims of systems biology is to couple these together to produce integrated models across multiple spatial scales and physical processes. In this review, we formulate a definition of multi-scale in terms of levels of biological organisation and describe the types of model that are found at each level. Key issues that arise in trying to formulate and solve multi-scale and multi-physics models are considered and examples of how these issues have been addressed are given for two of the more mature fields in computational biology: the molecular dynamics of ion channels and cardiac modelling. As even more complex models are developed over the coming few years, it will be necessary to develop new methods to model them (in particular in coupling across the interface between stochastic and deterministic processes) and new techniques will be required to compute their solutions efficiently on massively parallel computers. We outline how we envisage these developments occurring.

Progesterone regulates cardiac repolarization through a nongenomic pathway: an in vitro patch-clamp and computational modeling study

BACKGROUND

Female sex is an independent risk factor for torsade de pointes in long-QT syndrome. In women, QT interval and torsade de pointes risk fluctuate dynamically during the menstrual cycle and pregnancy. Accumulating clinical evidence suggests a role for progesterone; however, the effect of progesterone on cardiac repolarization remains undetermined.

METHODS AND RESULTS

We investigated the effects of progesterone on action potential duration and membrane currents in isolated guinea pig ventricular myocytes. Progesterone rapidly shortened action potential duration, which was attributable mainly to enhancement of the slow delayed rectifier K+ current (I(Ks)) under basal conditions and inhibition of L-type Ca2+ currents (I(Ca,L)) under cAMP-stimulated conditions. The effects of progesterone were mediated by nitric oxide released via nongenomic activation of endothelial nitric oxide synthase; this signal transduction likely takes place in the caveolae because sucrose density gradient fractionation experiments showed colocalization of the progesterone receptor c-Src, phosphoinositide 3-kinase, Akt, and endothelial nitric oxide synthase with KCNQ1, KCNE1, and Ca(V)1.2 in the caveolae fraction. We used computational single-cell and coupled-tissue action potential models incorporating the effects of progesterone on I(Ks) and I(Ca,L); the model reproduces the fluctuations of cardiac repolarization during the menstrual cycle observed in women and predicts the protective effects of progesterone against rhythm disturbances in congenital and drug-induced long-QT syndrome.

CONCLUSIONS

Our data show that progesterone modulates cardiac repolarization by nitric oxide produced via a nongenomic pathway. A combination of experimental and computational analyses of progesterone effects provides a framework to understand complex fluctuations of QT interval and torsade de pointes risks in various hormonal states in women.

Fast drug action solving from cardiac action potential by model fitting in a sampled parameter space

Model-based predictive approaches have been receiving increasing attention as a valuable tool to reduce cost in drug development. In this work, a model-fitting-based approach for solving drug actions using cardiac action potential recordings is investigated. Contribution of major ion currents in cardiac membrane excitation has been intensively studied. Cardiac cell models nowadays reproduce APs very precisely. Giving a test AP, the activities of involved ion channels can be determined by fitting the cell model to reproduce the test AP. Using experimental APs recordings both before and after drug dose, drug actions can be estimated by changes in channel activity. Due to the high computational cost in calculating cardiac models, a fast approach using only precalculated sample set is proposed. The searching strategy in the sampled space is divided into two steps: in the first step, the sample of best similarity comparing with the test AP is selected; then response surface approximation using the neighboring samples is followed and the estimation value is obtained by the approximated surface. This approach showed quite good estimation accuracy for a large number of simulation tests. Experiments using animal AP recordings from drug dose trials were also exemplified in which case the ICaL inhibition effect of nifedipine [10] was correctly discovered.

Analysis of damped oscillations during reentry: a new approach to evaluate cardiac restitution

Reentry is a mechanism underlying numerous cardiac arrhythmias. During reentry, head-tail interactions of the action potential can cause cycle length (CL) oscillations and affect the stability of reentry. We developed a method based on a difference-delay equation to determine the slopes of the action potential duration and conduction velocity restitution functions, known to be major determinants of reentrant arrhythmogenesis, from the spatial period P and the decay length D of damped CL oscillations. Using this approach, we analyzed CL oscillations after the induction of reentry and the resetting of reentry with electrical stimuli in rings of cultured neonatal rat ventricular myocytes grown on microelectrode arrays and in corresponding simulations with the Luo-Rudy model. In the experiments, P was larger and D was smaller after resetting impulses compared to the induction of reentry, indicating that reentry became more stable. Both restitution slopes were smaller. Consistent with the experimental findings, resetting of simulated reentry caused oscillations with gradually increasing P, decreasing D, and decreasing restitution slopes. However, these parameters remained constant when ion concentrations were clamped, revealing that intracellular ion accumulation stabilizes reentry. Thus, the analysis of CL oscillations during reentry opens new perspectives to gain quantitative insight into action potential restitution.

Role of maximum rate of depolarization in predicting action potential duration during ventricular fibrillation

During ventricular fibrillation (VF) only 39% of the variation in action potential duration (APD) is accounted for by the previous diastolic interval [DI((n-1))], i.e., restitution, and the previous APD [APD((n-1))], i.e., memory. We tested the hypothesis that a characteristic of the AP upstroke, the maximum rate of depolarization (V(max)), also helps account for its APD. A floating microelectrode was used to make transmembrane recordings at 16,000 samples/s from the anterior left ventricular wall during four 20-s episodes of VF in each of six pigs. V(max), time from V(max) to 60% repolarization (APD(60)), and DI were calculated throughout all episodes. Stepwise linear regression was used to determine how well each APD(60) (APD(60n)) was predicted by V(max) of that AP, the four previous DIs (n-1, n - 2, n - 3, n - 4), and the three previous APD(60)s (n-1, n - 2, n - 3). V(max) entered in the regression equation significantly more often (86% of VF episodes) than either APD((n-1)) (47% of episodes) or DI((n-1)) (58% of episodes). When these three variables entered first or second, their coefficients were almost always positive, consistent with a longer APD associated with 1) a larger V(max), 2) a longer APD((n-1)), and 3) a longer DI((n-1)). R(2) of the regression for all entered variables was 0.51 +/- 0.01 (mean +/- SD). During the first 20 s of VF in swine, V(max) is a more important determinant of APD than the previous DI (restitution) or the previous APD (memory). All variables together account for only one-half of APD variation during VF.

A model of the guinea-pig ventricular cardiac myocyte incorporating a transverse-axial tubular system

A model of the guinea-pig cardiac ventricular myocyte has been developed that includes a representation of the transverse-axial tubular system (TATS), including heterogeneous distribution of ion flux pathways between the surface and tubular membranes. The model reproduces frequency-dependent changes of action potential shape and intracellular ion concentrations and can replicate experimental data showing ion diffusion between the tubular lumen and external solution in guinea-pig myocytes. The model is stable at rest and during activity and returns to rested state after perturbation. Theoretical analysis and model simulations show that, due to tight electrical coupling, tubular and surface membranes behave as a homogeneous whole during voltage and current clamp (maximum difference 0.9 mV at peak tubular INa of -38 nA). However, during action potentials, restricted diffusion and ionic currents in TATS cause depletion of tubular Ca2+ and accumulation of tubular K+ (up to -19.8% and +3.4%, respectively, of bulk extracellular values, at 6 Hz). These changes, in turn, decrease ion fluxes across the TATS membrane and decrease sarcoplasmic reticulum (SR) Ca2+ load. Thus, the TATS plays a potentially important role in modulating the function of guinea-pig ventricular myocyte in physiological conditions.

Computer simulation of wild-type and mutant human cardiac Na+ current

Long QT syndrome (LQTS) and Brugada syndrome (BrS) are inherited diseases predisposing to ventricular arrhythmias and sudden death. Genetic studies linked LQTS and BrS to mutations in genes encoding for cardiac ion channels. Recently, two novel missense mutations at the same codon in the gene encoding the cardiac Na+ channel (SCN5A) have been identified: Y1795C (causing the LQTS phenotype) and Y1795H (causing the BrS phenotype). Functional studies in HEK293 cells showed that both mutations alter the inactivation of Na+ current and cause a sustained Na+ current upon depolarisation. In this paper, a nine state Markov model was used to simulate the Na+ current in wild-type Na+ cardiac channel and the current alterations observed in Y1795C and Y1795H mutant channels. The model includes three distinct closed states, a conducting open state and five inactivation states (one fast-, two intermediate- and two closed-inactivation). Transition rates between these states were identified on the basis of previously published voltage-clamp experiments. The model was able to reproduce the experimental Na+ current in mutant channels just by altering the assignment of model parameters with respect to wild-type case. Parameter assignment was validated by performing action potential clamp experiments and comparing experimental and simulated I(Na) current. The Markov model was subsequently introduced in the Luo-Rudy model of ventricular myocyte to investigate "in silico" the consequences on the ventricular cell action potential of the two mutations. Coherently with their phenotypes, the Y1795C mutation prolongs the action potential, while the Y1795H mutation causes only negligible changes in action potential morphology.

Calcium-regulating peptide hormones and blood electrolytic balance in chronic heart failure

Calcium-regulating system is important for the functional activity of myocardium. However, little is known about the role of this system in the pathogenesis of cardiovascular diseases. Blood samples from the patients with chronic heart failure (CHF) caused by ischaemic disease (coronary artery disease) (NYHA class I-IV) were used to analyze the levels of calcium, inorganic phosphate, sodium, potassium, parathyroid hormone (PTH) and parathyroid hormone-related protein (PTHrP). The heart beat rate and arterial blood pressure were chosen as additional tests for the functional status of cardiovascular system. The alteration of electrolytes homeostasis was found dependent on the severity of the pathology being maximally expressed in the NYHA class IV patients. Similar tendency was demonstrated for circulating PTH and PTHrP with the highest blood concentrations observed in patients of the NYHA class III and IV. The extent of these changes was found more pronounced in the female patients. It is suggested that the calcium-regulating hormonal system is involved in the pathogenesis of the ischaemic heart disease; however the sharp increase of PTH and PTHrP at the severe stages of pathology may play a compensatory role in maintaining the heart function.

A guide to modelling cardiac electrical activity in anatomically detailed ventricles

One of the most recent trends in cardiac electrophysiology is the development of integrative anatomically accurate models of the heart, which include description of cardiac activity from sub-cellular and cellular level to the level of the whole organ. In order to construct this type of model, a researcher needs to collect a wide range of information from books and journal articles on various aspects of biology, physiology, electrophysiology, numerical mathematics and computer programming. The aim of this methodological article is to survey recent developments in integrative modelling of electrical activity in the ventricles of the heart, and to provide a practical guide to the resources and tools that are available for work in this exciting and challenging area.

Vulnerability to reentry in a regionally ischemic tissue: a simulation study

Sudden cardiac death is mainly provoked by arrhythmogenic processes. During myocardial ischemia many malignant arrhythmias, such as reentry, take place and can degenerate into ventricular fibrillation. It is thus of great interest to unravel the intricate mechanisms underlying the initiation and maintenance of a reentry. In this computational study, we analyze the probability of reentry during different stages of the acute phase of ischemia. We also aimed at the understanding of the role of its main components: hypoxia, hyperkalemia, and acidosis analyzing the intricate ionic mechanisms responsible for reentry generation. We simulated the electrical activity of a ventricular tissue affected by regional ischemia based on a modified version of the Luo-Rudy model (LRd00). The ischemic conditions were varied to simulate different stages of this pathology. After premature stimulation, we evaluated the vulnerability to reentry. We obtained an unimodal behavior for the vulnerable window as ischemia progressed, peaking at the eighth minute after the onset of ischemia where the vulnerable window yielded 58 ms. Under more severe conditions the vulnerable window decreased and became zero for minute 8.75. The present work provides insight into the mechanisms of reentry generation during ischemia, highlighting the role of acidosis and hypoxia when hyperkalemia is present.

Upregulation of KCNE1 induces QT interval prolongation in patients with chronic heart failure

BACKGROUND

Prolongation of the action potential duration (APD) is observed in ventricular myocytes isolated from the failing heart. The rapid component (I(Kr)) and the slow component (I(Ks)) of the delayed-rectifier potassium current (I(K)) are major determinants of the APD, but less information is available on the genomic modulation of I(K) in the remodeled human heart. The aim of the current study was to examine the relationship between I(K) transcripts and QT interval in surface electrocardiogram in patients with chronic heart failure (CHF).

METHODS AND RESULTS

Total RNA was extracted from right ventricle endomyocardial biopsy samples in 21 CHF patients (age: 53+/-4 years, mean +/- SEM). The KCNH2 and KCNQ1 levels did not differ significantly between controls (New York Heart Association (NYHA) I, n=10) and CHF patients (NYHA II or III, n=11), whereas the KCNE1 level was significantly higher in CHF patients than in controls (relative mRNA levels normalized to GAPDH expression: 6.16+/-0.31 vs 7.70+/-0.46, p<0.05). The KCNE1/KCNQ1 ratio was higher in CHF patients than in controls (0.92+/-0.02 vs 1.06+/-0.05, p<0.05) and the KCNE1-KCNQ1 ratio was positively correlated with QT interval (r=0.70, p<0.05). Increasing the KCNE1 concentration caused a shift in activation voltage and slowed the activation kinetics of the KCNE1-KCNQ1 currents expressed in Xenopus oocytes. Prolongation of the APD and decrease in I(Ks) with increasing the amount of KCNE1 concentration were well predicted in a computer simulation.

CONCLUSIONS

In mild-to-moderate CHF patients, the relative abundance of KCNE1 compared to KCNQ1 genes, at least in part, might contribute to the preferential prolongation of QT interval through reducing the net outward current during the plateau of the action potential.

Regulation of Ca2+ and electrical alternans in cardiac myocytes: role of CAMKII and repolarizing currents

Alternans of cardiac repolarization is associated with arrhythmias and sudden death. At the cellular level, alternans involves beat-to-beat oscillation of the action potential (AP) and possibly Ca(2+) transient (CaT). Because of experimental difficulty in independently controlling the Ca(2+) and electrical subsystems, mathematical modeling provides additional insights into mechanisms and causality. Pacing protocols were conducted in a canine ventricular myocyte model with the following results: 1) CaT alternans results from refractoriness of the sarcoplasmic reticulum Ca(2+) release system; alternation of the L-type calcium current has a negligible effect; 2) CaT-AP coupling during late AP occurs through the sodium-calcium exchanger and underlies AP duration (APD) alternans; 3) increased Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) activity extends the range of CaT and APD alternans to slower frequencies and increases alternans magnitude; its decrease suppresses CaT and APD alternans, exerting an antiarrhythmic effect; and 4) increase of the rapid delayed rectifier current (I(Kr)) also suppresses APD alternans but without suppressing CaT alternans. Thus CaMKII inhibition eliminates APD alternans by eliminating its cause (CaT alternans) while I(Kr) enhancement does so by weakening CaT-APD coupling. The simulations identify combined CaMKII inhibition and I(Kr) enhancement as a possible antiarrhythmic intervention.

Calsequestrin mutation and catecholaminergic polymorphic ventricular tachycardia: a simulation study of cellular mechanism

OBJECTIVES

Patients with a missense mutation of the calsequestrin 2 gene (CASQ2) are at risk for catecholaminergic polymorphic ventricular tachycardia. This mutation (CASQ2(D307H)) results in decreased ability of CASQ2 to bind Ca2+ in the sarcoplasmic reticulum (SR). In this theoretical study, we investigate a potential mechanism by which CASQ2(D307H) manifests its pro-arrhythmic consequences in patients.

METHODS

Using simulations in a model of the guinea pig ventricular myocyte, we investigate the mutation's effect on SR Ca2+ storage, the Ca2+ transient (CaT), and its indirect effect on ionic currents and membrane potential. We model the effects of isoproterenol (ISO) on Ca(V)1.2 (the L-type Ca2+ current, I(Ca(L))) and other targets of beta-adrenergic stimulation.

RESULTS

ISO increases I(Ca(L)), prolonging action potential (AP) duration (Control: 172 ms, +ISO: 207 ms, at cycle length of 1500 ms) and increasing CaT (Control: 0.79 microM, +ISO: 1.61 microM). ISO increases I(Ca(L)) by reducing the fraction of channels which undergo voltage-dependent inactivation and increasing transitions from a non-conducting to conducting mode of channel gating. CASQ2(D307H) reduces SR storage capacity, thereby reducing the magnitude of CaT (Control: 0.79 microM, CASQ2(D307H): 0.52 microM, at cycle length of 1500 ms). The combined effect of CASQ2(D307H) and ISO elevates SR free Ca2+ at a rapid rate, leading to store-overload-induced Ca2+ release and delayed afterdepolarization (DAD). If resting membrane potential is sufficiently elevated, the Na+-Ca2+ exchange-driven DAD can trigger I(Na) and I(Ca(L)) activation, generating a triggered arrhythmogenic AP.

CONCLUSIONS

The CASQ2(D307H) mutation manifests its pro-arrhythmic consequences due to store-overload-induced Ca2+ release and DAD formation due to excess free SR Ca2+ following rapid pacing and beta-adrenergic stimulation.

Analysis of QT Interval Prolongation With Heart Failure by Simulation of Repolarization Process

It has been postulated that action potential duration (APD) is prolonged and I<inf>Ks</inf>, a slow component of delayed rectifier potassium current, decreases in heart failure. We have reported that QT interval is prolonged and expression weight of KCNE1, coding I<inf>Ks</inf>channel, increases in patients with heart failure. Since it is known that increase in KCNE1 increases the maximum conductance of I<inf>Ks</inf>channel, the mechanism of APD prolongation is not explained by over expression of KCNE1. In this study, we construct a cardiac membrane action potential simulation model based on the experimental data from Xenopus oocytes expressed KCNQ1 and KCNE1 to investigate the relationship between increase in KCNE1 and APD. In addition, we investigated effect of reduction in Ca²⁺-independent transient outward potassium current (I<inf>to</inf>) on APD in heart failure. In simulation, APD at 5ng KCNE1 was 180.96ms, which was 4.63% longer than that at 1ng KCNE1 (APD=172.96ms) and 55.9% longer than that at 0.2ng KCNE1 (APD=110.96ms. In the cases of KCNQ1 alone and 0.2ng KCNE1 coinjected, APD shortened as density of I<inf>to</inf>decreased, and APD prolonged as density of I<inf>to</inf>decreased in other cases. This study shows that increase in KCNE1 expression level makes maximum conductance of I<inf>Ks</inf>channel increase and I<inf>Ks</inf>channel open slowly and conductance of I<inf>Ks</inf>channel decrease according to the APD time scale. Therefore increasing the KCNE1 expression level may prolong APD with this mechanism. This method of constructing a simulation model based on experiments helps to explain the relationship between potassium currents and QT interval prolongation.

The evolution of CellML

CellML is an open XML-based markup language for describing and exchanging mathematical models of biological processes. While CellML was originally designed to describe and exchange models of cellular and subcellular processes, the design principles that were applied to the construction of a language with this relatively narrow focus are equally applicable to the specification of a language with a much wider scope. In this paper we describe the structure of CellML, how the language is evolving to broaden its scope, and what tools are being developed to facilitate its use.

Incorporation of myofilament activation mechanics into a lumped model of the human heart

The success and usefulness of lumped cardiovascular models are directly dependent on the physiological fidelity of their formulation. In most existing lumped formulations for the heart, the compliance of the chamber is modeled based on its electrical analog, the capacitor. This has traditionally resulted in the use of a pre-described time-varying stiffness modulus for simulating the cardiac contractions. Unfortunately, such a time-varying stiffness does not include any physiological contractile machinery and thus no dependency on fiber sarcomere length and intracellular calcium concentrations, key mechanisms responsible for proper cardiac function. In this paper a lumped cardiovascular model is presented that is based on the incorporation of detailed myofilament activation for simulating the ventricular calcium binding and cross-bridging mechanism. Upon validation against experimental data, it is shown that the new myofilament activation-based model considerably increases the physiological validity and internal consistency of the cardiovascular simulations in comparison to the traditional variable compliance-based models. It is also shown, through specific case studies, that the present model can serve as a quick response tool for testing various hypotheses concerning the impact of the calcium binding and crossbridge kinetics on the overall performance of the cardiovascular system.