Role of individual ionic current systems in ventricular cells hypothesized by a model study

Effective suppression of Ih and INa caused by capsazepine, known to be a blocker of TRPV1 receptor

A synthetic inhibitor of capsaicin-induced TRPV1 channel activation is called capsazepine (CPZ). In this study, we aimed to explore the effects of CPZ on hyperpolarization-activated cationic current (Ih) and voltage-gated Na + current (INa) in pituitary tumor (GH3) cells. Through patch-clamp recordings, we found that CPZ concentration-dependently inhibited Ih amplitude and slowed its activation time course. The IC50 and KD values were 3.1 and 3.16 μM, respectively. CPZ also shifted the steady-state activation curve of Ih towards a more hyperpolarized potential. However, there was no change in the gating charge of the curve. A modified Markovian model predicted the CPZ-induced decrease in the voltage-dependent hysteresis of Ih. CPZ suppressed INa in GH3 cells, without altering its activation or inactivation time course. Additionally, exposure to CPZ reduced spontaneous firing. These findings suggest that CPZ's inhibitory effects on Ih and INa are direct and not dependent on vanilloid receptor binding. This could provide light on an unidentified ionic mechanism influencing the membrane excitability of neurons and endocrine or neuroendocrine cells in vivo.

Identification and characterisation of functional Kir6.1-containing ATP-sensitive potassium channels in the cardiac ventricular sarcolemmal membrane

BACKGROUND AND PURPOSE

The canonical Kir6.2/SUR2A ventricular KATP channel is highly ATP-sensitive and remains closed under normal physiological conditions. These channels activate only when prolonged metabolic compromise causes significant ATP depletion and then shortens the action potential to reduce contractile activity. Pharmacological activation of KATP channels is cardioprotective, but physiologically, it is difficult to understand how these channels protect the heart if they only open under extreme metabolic stress. The presence of a second KATP channel population could help explain this. Here, we characterise the biophysical and pharmacological behaviours of a constitutively active Kir6.1-containing KATP channel in ventricular cardiomyocytes.

EXPERIMENTAL APPROACH

Patch-clamp recordings from rat ventricular myocytes in combination with well-defined pharmacological modulators was used to characterise these newly identified K+ channels. Action potential recording, calcium (Fluo-4) fluorescence measurements and video edge detection of contractile function were used to assess functional consequences of channel modulation.

KEY RESULTS

Our data show a ventricular K+ conductance whose biophysical characteristics and response to pharmacological modulation were consistent with Kir6.1-containing channels. These Kir6.1-containing channels lack the ATP-sensitivity of the canonical channels and are constitutively active.

CONCLUSION AND IMPLICATIONS

We conclude there are two functionally distinct populations of ventricular KATP channels: constitutively active Kir6.1-containing channels that play an important role in fine-tuning the action potential and Kir6.2/SUR2A channels that activate with prolonged ischaemia to impart late-stage protection against catastrophic ATP depletion. Further research is required to determine whether Kir6.1 is an overlooked target in Comprehensive in vitro Proarrhythmia Assay (CiPA) cardiac safety screens.

Computational modeling of electromechanical coupling in human cardiomyocyte applied to study hypertrophic cardiomyopathy and its drug response

BACKGROUND AND OBJECTIVE

Knowledge of electromechanical coupling in cardiomyocyte and how it is influenced by various pathophysiological factors is fundamental to understanding the pathogenesis of myocardial disease and its response to medication, which is however hard to be thoroughly addressed by clinical/experimental studies due to technical limitations. At this point, computational modeling offers an alternative approach. The main objective of the study was to develop a computational model capable of simulating the process of electromechanical coupling and quantifying the roles of various factors in play in the human left ventricular cardiomyocyte.

METHODS

A new electrophysiological model was firstly built by combining several existing electrophysiological models and incorporating the mechanism of electrophysiological homeostasis, which was subsequently coupled to models representing the cross-bridge dynamics and active force generation during excitation-contraction coupling and the passive mechanical properties of cardiomyocyte to yield an integrative electromechanical model. Model parameters were calibrated or optimized based on a large amount of experimental data. The resulting model was applied to delineate the characteristics of electromechanical coupling and explore underlying determinant factors in hypertrophic cardiomyopathy (HCM) cardiomyocyte, as well as quantify their changes in response to different medications.

RESULTS

Model predictions captured the major electromechanical characteristics of cardiomyocyte under both normal physiological and HCM conditions. In comparison with normal cardiomyocyte, HCM cardiomyocyte suffered from systemic changes in both electrophysiological and mechanical variables. Numerical simulations of drug response revealed that Mavacamten and Metoprolol could both reduce the active contractility and alleviate calcium overload but had marked differential influences on many other electromechanical variables, which theoretically explained why the two drugs have differential therapeutic effects. In addition, our numerical experiments demonstrated the important role of compensatory ion transport in maintaining electrophysiological homeostasis and regulating cytoplasmic volume.

CONCLUSIONS

A sophisticated computational model has the advantage of providing quantitative and integrative insights for understanding the pathogenesis and drug responses of HCM or other myocardial diseases at the level of cardiomyocyte, and hence may contribute as a useful complement to clinical/experimental studies. The model may also be coupled to tissue- or organ-level models to strengthen the physiological implications of macro-scale numerical simulations.

Models of the cardiac L-type calcium current: A quantitative review

The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.

SBML to bond graphs: From conversion to composition

The Systems Biology Markup Language (SBML) is a popular software-independent XML-based format for describing models of biological phenomena. The BioModels Database is the largest online repository of SBML models. Several tools and platforms are available to support the reuse and composition of SBML models. However, these tools do not explicitly assess whether models are physically plausible or thermodynamically consistent. This often leads to ill-posed models that are physically impossible, impeding the development of realistic complex models in biology. Here, we present a framework that can automatically convert SBML models into bond graphs, which imposes energy conservation laws on these models. The new bond graph models are easily mergeable, resulting in physically plausible coupled models. We illustrate this by automatically converting and coupling a model of pyruvate distribution to a model of the pentose phosphate pathway.

Bifurcations and Proarrhythmic Behaviors in Cardiac Electrical Excitations

The heart is a hierarchical dynamic system consisting of molecules, cells, and tissues, and acts as a pump for blood circulation. The pumping function depends critically on the preceding electrical activity, and disturbances in the pattern of excitation propagation lead to cardiac arrhythmia and pump failure. Excitation phenomena in cardiomyocytes have been modeled as a nonlinear dynamical system. Because of the nonlinearity of excitation phenomena, the system dynamics could be complex, and various analyses have been performed to understand the complex dynamics. Understanding the mechanisms underlying proarrhythmic responses in the heart is crucial for developing new ways to prevent and control cardiac arrhythmias and resulting contractile dysfunction. When the heart changes to a pathological state over time, the action potential (AP) in cardiomyocytes may also change to a different state in shape and duration, often undergoing a qualitative change in behavior. Such a dynamic change is called bifurcation. In this review, we first summarize the contribution of ion channels and transporters to AP formation and our knowledge of ion-transport molecules, then briefly describe bifurcation theory for nonlinear dynamical systems, and finally detail its recent progress, focusing on the research that attempts to understand the developing mechanisms of abnormal excitations in cardiomyocytes from the perspective of bifurcation phenomena.

Kir Channel Molecular Physiology, Pharmacology, and Therapeutic Implications

For the past two decades several scholarly reviews have appeared on the inwardly rectifying potassium (Kir) channels. We would like to highlight two efforts in particular, which have provided comprehensive reviews of the literature up to 2010 (Hibino et al., Physiol Rev 90(1):291-366, 2010; Stanfield et al., Rev Physiol Biochem Pharmacol 145:47-179, 2002). In the past decade, great insights into the 3-D atomic resolution structures of Kir channels have begun to provide the molecular basis for their functional properties. More recently, computational studies are beginning to close the time domain gap between in silico dynamic and patch-clamp functional studies. The pharmacology of these channels has also been expanding and the dynamic structural studies provide hope that we are heading toward successful structure-based drug design for this family of K⁺ channels. In the present review we focus on placing the physiology and pharmacology of this K⁺ channel family in the context of atomic resolution structures and in providing a glimpse of the promising future of therapeutic opportunities.

Evolution of mathematical models of cardiomyocyte electrophysiology

Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.

In Silico Assessment of Class I Antiarrhythmic Drug Effects on Pitx2-Induced Atrial Fibrillation: Insights from Populations of Electrophysiological Models of Human Atrial Cells and Tissues

Electrical remodelling as a result of homeodomain transcription factor 2 (Pitx2)-dependent gene regulation was linked to atrial fibrillation (AF) and AF patients with single nucleotide polymorphisms at chromosome 4q25 responded favorably to class I antiarrhythmic drugs (AADs). The possible reasons behind this remain elusive. The purpose of this study was to assess the efficacy of the AADs disopyramide, quinidine, and propafenone on human atrial arrhythmias mediated by Pitx2-induced remodelling, from a single cell to the tissue level, using drug binding models with multi-channel pharmacology. Experimentally calibrated populations of human atrial action po-tential (AP) models in both sinus rhythm (SR) and Pitx2-induced AF conditions were constructed by using two distinct models to represent morphological subtypes of AP. Multi-channel pharmaco-logical effects of disopyramide, quinidine, and propafenone on ionic currents were considered. Simulated results showed that Pitx2-induced remodelling increased maximum upstroke velocity (dVdtmax), and decreased AP duration (APD), conduction velocity (CV), and wavelength (WL). At the concentrations tested in this study, these AADs decreased dVdtmax and CV and prolonged APD in the setting of Pitx2-induced AF. Our findings of alterations in WL indicated that disopyramide may be more effective against Pitx2-induced AF than propafenone and quinidine by prolonging WL.

The ForceLAB simulator: Application to the comparison of current models of cardiomyocyte contraction

Mathematical models are useful tools in the study of physiological phenomena. However, due to differences in assumptions and formulations, discrepancy in simulations may occur. Among the models for cardiomyocyte contraction based on Huxley's cross-bridge cycling, those proposed by Negroni and Lascano (NL) and Rice et al. (RWH) are the most frequently used. This study was aimed at developing a computational tool, ForceLAB, which allows implementing different contraction models and modifying several functional parameters. As an application, electrically-stimulated twitches triggered by an equal Ca²⁺ input and steady-state force x pCa relationship (pCa = -log of the molar free Ca²⁺ concentration) simulated with the NL and RWH models were compared. The equilibrium Ca²⁺-troponin C (TnC) dissociation constant (K_d) was modified by changing either the association (k_on) or the dissociation (k_off) rate constant. With the NL model, raising K_d by either maneuver decreased monotonically twitch amplitude and duration, as expected. With the RWH model, in contrast, the same K_d variation caused increase or decrease of peak force depending on which rate constant was modified. Additionally, force x pCa curves simulated using Ca²⁺ binding constants estimated in cardiomyocytes bearing wild-type and mutated TnC were compared to curves previously determined in permeabilized fibers. Mutations increased k_on and k_off, and decreased K_d. Both models produced curves fairly comparable to the experimental ones, although sensitivity to Ca²⁺ was greater, especially with RWH model. The NL model reproduced slightly better the qualitative changes associated with the mutations. It is expected that this tool can be useful for teaching and investigation.

Current applications of mathematical models of the interstitial cells of Cajal in the gastrointestinal tract

The interstitial cells of Cajal (ICC) form interconnected networks throughout the gastrointestinal (GI) tract. ICC act as the pacemaker cells that initiate the rhythmic bioelectrical slow waves and intermediary between the GI musculature and nerves, both of which are critical to GI motility. Disruptions to the number of ICC and the integrity of ICC networks have been identified as a key pathophysiological mechanism in a number of clinically challenging GI disorders. The current analyses of ICC generally rely on either functional recordings taken directly from excised tissue or morphological analysis based on images of labeled ICC, where the structural-functional relationship is investigated in an associative manner rather than mechanistically. On the other hand, computational physiology has played a significant role in facilitating our understanding of a number of physiological systems in both health and disease, and investigations in the GI field are beginning to incorporate several mathematical models of the ICC. The main aim of this review is to present the major modeling advances in GI electrophysiology, in order to introduce a multi-scale framework for mathematically quantifying the functional consequences of ICC degradation at both cellular and tissue scales. The outcomes will inform future investigators utilizing modeling techniques in their studies. This article is categorized under: Metabolic Diseases > Computational Models.

Differentiating the effects of β-adrenergic stimulation and stretch on calcium and force dynamics using a novel electromechanical cardiomyocyte model

Cardiac electrophysiology and mechanics are strongly interconnected. Calcium is crucial in this complex interplay through its role in cellular electrophysiology and sarcomere contraction. We aim to differentiate the effects of acute β-adrenergic stimulation (β-ARS) and cardiomyocyte stretch (increased sarcomere length) on calcium-transient dynamics and force generation, using a novel computational model of cardiac electromechanics. We implemented a bidirectional coupling between the O'Hara-Rudy model of human ventricular electrophysiology and the MechChem model of sarcomere mechanics through the buffering of calcium by troponin. The coupled model was validated using experimental data from large mammals or human samples. Calcium transient and force were simulated for various degrees of β-ARS and initial sarcomere lengths. The model reproduced force-frequency, quick-release, and isotonic contraction experiments, validating the bidirectional electromechanical interactions. An increase in β-ARS increased the amplitudes of force (augmented inotropy) and calcium transient, and shortened both force and calcium-transient duration (lusitropy). An increase in sarcomere length increased force amplitude even more, but decreased calcium-transient amplitude and increased both force and calcium-transient duration. Finally, a gradient in relaxation along the thin filament may explain the nonmonotonic decay in cytosolic calcium observed with high tension. Using a novel coupled human electromechanical model, we identified differential effects of β-ARS and stretch on calcium and force. Stretch mostly contributed to increased force amplitude and β-ARS to the reduction of calcium and force duration. We showed that their combination, rather than individual contributions, is key to ensure force generation, rapid relaxation, and low diastolic calcium levels.NEW & NOTEWORTHY This work identifies the contribution of electrical and mechanical alterations to regulation of calcium and force under exercise-like conditions using a novel human electromechanical model integrating ventricular electrophysiology and sarcomere mechanics. By better understanding their individual and combined effects, this can uncover arrhythmogenic mechanisms in exercise-like situations. This publicly available model is a crucial step toward understanding the complex interplay between cardiac electrophysiology and mechanics to improve arrhythmia risk prediction and treatment.

Mathematical model of the ventricular action potential and effects of isoproterenol-induced cardiac hypertrophy in rats

Mathematical action potential (AP) modeling is a well-established but still-developing area of research to better understand physiological and pathological processes. In particular, changes in AP mechanisms in the isoproterenol (ISO) -induced hypertrophic heart model are incompletely understood. Here we present a mathematical model of the rat AP based on recordings from rat ventricular myocytes. In our model, for the first time, all channel kinetics are defined with a single type of function that is simple and easy to apply. The model AP and channels dynamics are consistent with the APs recorded from rats for both Control (absence of ISO) and ISO-treated cases. Our mathematical model helps us to understand the reason for the prolongation in AP duration after ISO application while ISO treatment helps us to validate our mathematical model. We reveal that the smaller density and the slower gating kinetics of the transient K⁺ current help explain the prolonged AP duration after ISO treatment and the increasing amplitude of the rapid and the slow inward rectifier currents also contribute to this prolongation alongside the flux in Ca²⁺ currents. ISO induced an increase in the density of the Na⁺ current that can explain the faster upstroke. We believe that AP dynamics from rat ventricular myocytes can be reproduced very well with this mathematical model and that it provides a powerful tool for improved insights into the underlying dynamics of clinically important AP properties such as ISO application.

Cardiomyocyte calcium handling in health and disease: Insights from in vitro and in silico studies

Calcium (Ca²⁺) plays a central role in cardiomyocyte excitation-contraction coupling. To ensure an optimal electrical impulse propagation and cardiac contraction, Ca²⁺ levels are regulated by a variety of Ca²⁺-handling proteins. In turn, Ca²⁺ modulates numerous electrophysiological processes. Accordingly, Ca²⁺-handling abnormalities can promote cardiac arrhythmias via various mechanisms, including the promotion of afterdepolarizations, ion-channel modulation and structural remodeling. In the last 30 years, significant improvements have been made in the computational modeling of cardiomyocyte Ca²⁺ handling under physiological and pathological conditions. However, numerous questions involving the Ca²⁺-dependent regulation of different macromolecular complexes, cross-talk between Ca²⁺-dependent regulatory pathways operating over a wide range of time scales, and bidirectional interactions between electrophysiology and mechanics remain to be addressed by in vitro and in silico studies. A better understanding of disease-specific Ca²⁺-dependent proarrhythmic mechanisms may facilitate the development of improved therapeutic strategies. In this review, we describe the fundamental mechanisms of cardiomyocyte Ca²⁺ handling in health and disease, and provide an overview of currently available computational models for cardiomyocyte Ca²⁺ handling. Finally, we discuss important uncertainties and open questions about cardiomyocyte Ca²⁺ handling and highlight how synergy between in vitro and in silico studies may help to answer several of these issues.

Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.

A Formal Approach for Scalable Simulation of Gastric ICC Electrophysiology

OBJECTIVE

Efficient and accurate organ models are crucial for closed-loop validation of implantable medical devices. This paper investigates bio-electric slow wave modeling of the stomach, so that gastric electrical stimulator (GES) can be validated and verified prior to implantation. In particular, we consider high-fidelity, scalable, and efficient modeling of the pacemaker, Interstitial cells of Cajal (ICC), based on the formal hybrid input output automata (HIOA) framework.

METHODS

Our work is founded in formal methods, a collection of mathematically sound techniques originating in computer science for the design and validation of safety-critical systems. We modeled each ICC cell using an HIOA. We also introduce an HIOA path model to capture the electrical propagation delay between cells in a network. The resultant network of ICC cells can simulate normal and diseased action potential propagation patterns, making it useful for device validation.

RESULTS

The simulated slow wave of a single ICC cell had high correlation ( ≈ 0.9) with the corresponding biophysical models.

CONCLUSIONS

The proposed model is able to simulate the slow wave activity of a network of ICC cells with high-fidelity for device validation.

SIGNIFICANCE

The proposed HIOA model is significantly more efficient than the corresponding biophysical models, scales to larger networks of ICC cells, and is capable of simulating varying propagation patterns. This has the potential to enable verification and validation of implantable GESs in closed-loop with gastrointestinal models in the future.

A new myofilament contraction model with ATP consumption for ventricular cell model

A new contraction model of cardiac muscle was developed by combining previously described biochemical and biophysical models. The biochemical component of the new contraction model represents events in the presence of Ca2+-crossbridge attachment and power stroke following inorganic phosphate release, detachment evoked by the replacement of ADP by ATP, ATP hydrolysis, and recovery stroke. The biophysical component focuses on Ca2+ activation and force (F b) development assuming an equivalent crossbridge. The new model faithfully incorporates the major characteristics of the biochemical and biophysical models, such as F b activation by transient Ca2+ ([Ca2+]-F b), [Ca2+]-ATP hydrolysis relations, sarcomere length-F b, and F b recovery after jumps in length under the isometric mode and upon sarcomere shortening after a rapid release of mechanical load under the isotonic mode together with the load-velocity relationship. ATP consumption was obtained for all responses. When incorporated in a ventricular cell model, the contraction model was found to share approximately 60% of the total ATP usage in the cell model.

Computational motility models of neurogastroenterology and neuromodulation

The success of neuromodulation therapies, particularly in the brain, spinal cord, and peripheral nerves, has been greatly aided by computational, biophysical models. However, treating gastrointestinal disorders with electrical stimulation has been much less explored, partly because the mode of action of such treatments is unclear, and selection of stimulation parameters is often empirical. Progress in gut neuromodulation is limited by the comparative lack of biophysical models capable of simulating neuromodulation of gastrointestinal function. Here, we review the recently developed biophysical models of electrically-active cells in the gastrointestinal system that contribute to motility. Biophysical models are replacing phenomenologically-defined models due to advancements in electrophysiological characterization of key players in the gut: enteric neurons, smooth muscle fibers, and interstitial cells of Cajal. In this review, we explore existing biophysically-defined cellular and network models that contribute to gastrointestinal motility. We focus on recent models that are laying the groundwork for modeling electrical stimulation of the gastrointestinal system. Developing models of gut neuromodulation will improve our mechanistic understanding of these treatments, leading to better parameterization, selectivity, and efficacy of neuromodulation to treat gastrointestinal disorders. Such models may have direct clinical translation to current neuromodulation therapies, such as sacral nerve stimulation.

External K+ dependence of strong inward rectifier K+ channel conductance is caused not by K+ but by competitive pore blockade by external Na

Strong inward rectifier K⁺ (sKir) channels determine the membrane potentials of many types of excitable and nonexcitable cells, most notably the resting potentials of cardiac myocytes. They show little outward current during membrane depolarization (i.e., strong inward rectification) because of the channel blockade by cytoplasmic polyamines, which depends on the deviation of the membrane potential from the K⁺ equilibrium potential (V - E_K) when the extracellular K⁺ concentration ([K⁺]_out) is changed. Because their open-channel conductance is apparently proportional to the "square root" of [K⁺]_out, increases/decreases in [K⁺]_out enhance/diminish outward currents through sKir channels at membrane potentials near their reversal potential, which also affects, for example, the repolarization and action-potential duration of cardiac myocytes. Despite its importance, however, the mechanism underlying the [K⁺]_out dependence of the open sKir channel conductance has remained elusive. By studying Kir2.1, the canonical member of the sKir channel family, we first show that the outward currents of Kir2.1 are observed under the external K⁺-free condition when its inward rectification is reduced and that the complete inhibition of the currents at 0 [K⁺]_out results solely from pore blockade caused by the polyamines. Moreover, the noted square-root proportionality of the open sKir channel conductance to [K⁺]_out is mediated by the pore blockade by the external Na⁺, which is competitive with the external K⁺ Our results show that external K⁺ itself does not activate or facilitate K⁺ permeation through the open sKir channel to mediate the apparent external K⁺ dependence of its open channel conductance. The paradoxical increase/decrease in outward sKir channel currents during alternations in [K⁺]_out, which is physiologically relevant, is caused by competition from impermeant extracellular Na^.

Community effect of cardiomyocytes in beating rhythms is determined by stable cells

The community effect of cardiomyocytes was investigated in silico by the change in number and features of cells, as well as configurations of networks. The theoretical model was based on experimental data and accurately reproduced recently published experimental results regarding coupled cultured cardiomyocytes. We showed that the synchronised beating of two coupled cells was tuned not to the cell with a faster beating rate, but to the cell with a more stable rhythm. In a network of cardiomyocytes, a cell with low fluctuation, but not a hight frequency, became a pacemaker and stabilised the beating rhythm. Fluctuation in beating rapidly decreased with an increase in the number of cells (N), almost irrespective of the configuration of the network, and a cell comes to have natural and stable beating rhythms, even for N of approximately 10. The universality of this community effect lies in the fluctuation-dissipation theorem in statistical mechanics.

Developmental changes in the balance of glycolytic ATP production and oxidative phosphorylation in ventricular cells: A simulation study

The developmental program of the heart requires accurate regulation to ensure continuous circulation and simultaneous cardiac morphogenesis, because any functional abnormalities may progress to congenital heart malformation. Notably, energy metabolism in fetal ventricular cells is regulated in a manner that differs from adult ventricular cells: fetal cardiomyocytes generally have immature mitochondria and fetal ventricular cells show greater dependence on glycolytic ATP production. However, although various characteristics of energy metabolism in fetal ventricular cells have been reported, to our knowledge, a quantitative description of the contributions of these factors to fetal ventricular cell functions has not yet been established. Here, we constructed a mathematical model to integrate various characteristics of fetal ventricular cells and predicted the contribution of each characteristic to the maintenance of intracellular ATP concentration and sarcomere contraction under anoxic conditions. Our simulation results demonstrated that higher glycogen content, higher hexokinase activity, and lower creatine concentration helped prolong the time for which ventricular cell contraction was maintained under anoxic conditions. The integrated model also enabled us to quantitatively assess the contributions of factors related to energy metabolism in ventricular cells. Because fetal cardiomyocytes exhibit similar energy metabolic profiles to stem cell-derived cardiomyocytes and those in the failing heart, an improved understanding of these fetal ventricular cells will contribute to a better comprehension of the processes in stem cell-derived cardiomyocytes or under pathological conditions.

Activation of the Ca2+-sensing receptors increases currents through inward rectifier K+ channels via activation of phosphatidylinositol 4-kinase

Inward rectifier K⁺ channels are important for maintaining normal electrical function in many cell types. The proper function of these channels requires the presence of membrane phosphoinositide 4,5-bisphosphate (PIP₂). Stimulation of the Ca²⁺-sensing receptor CaR, a pleiotropic G protein-coupled receptor, activates both G_q/11, which decreases PIP₂, and phosphatidylinositol 4-kinase (PI-4-K), which, conversely, increases PIP₂. How membrane PIP₂ levels are regulated by CaR activation and whether these changes modulate inward rectifier K⁺ are unknown. In this study, we found that activation of CaR by the allosteric agonist, NPSR568, increased inward rectifier K⁺ current (I _K1) in guinea pig ventricular myocytes and currents mediated by Kir2.1 channels exogenously expressed in HEK293T cells with a similar sensitivity. Moreover, using the fluorescent PIP₂ reporter tubby-R332H-cYFP to monitor PIP₂ levels, we found that CaR activation in HEK293T cells increased membrane PIP₂ concentrations. Pharmacological studies showed that both phospholipase C (PLC) and PI-4-K are activated by CaR stimulation with the latter played a dominant role in regulating membrane PIP₂ and, thus, Kir currents. These results provide the first direct evidence that CaR activation upregulates currents through inward rectifier K⁺ channels by accelerating PIP₂ synthesis. The regulation of I _K1 plays a critical role in the stability of the electrical properties of many excitable cells, including cardiac myocytes and neurons. Further, synthetic allosteric modulators that increase CaR activity have been used to treat hyperparathyroidism, and negative CaR modulators are of potential importance in the treatment of osteoporosis. Thus, our results provide further insight into the roles played by CaR in the cardiovascular system and are potentially valuable for heart disease treatment and drug safety.

A computational model of a human single sinoatrial node cell

For the investigation of the spontaneous rhythmical activity response in the application of cardiac neuromodulation, we formulated a human sinoatrial node (SAN) cell model. With the aim of decreasing elevated heart rate (HR), we want to establish a hardware-in-the-loop system including this model for the analysis of optimal stimulation patterns of the neurostimulation system. Base model structures are adopted from rabbit SAN cell models available in literature and conveyed with Hodgkin-Huxley-type model equations describing the complex time and voltage dependent activation and deactivation processes of individual ion channels. The resulting model consists of 15 currents which are currently known to be responsible for the generation of the membrane action potential (AP). The model reproduces AP frequencies equivalent to those measured in isolated human SAN cells with a resulting HR of 71.8 bpm. Model validation via simulation of the inhibitory effect of ivabradine showed accordance with experimental results obtained in human studies. Furthermore, we could validate the model in regard to its HR effects upon parasympathetic stimulation with results obtained in a human trial study.

A human ventricular myocyte model with a refined representation of excitation-contraction coupling

Cardiac Ca(2+)-induced Ca(2+) release (CICR) occurs by a regenerative activation of ryanodine receptors (RyRs) within each Ca(2+)-releasing unit, triggered by the activation of L-type Ca(2+) channels (LCCs). CICR is then terminated, most probably by depletion of Ca(2+) in the junctional sarcoplasmic reticulum (SR). Hinch et al. previously developed a tightly coupled LCC-RyR mathematical model, known as the Hinch model, that enables simulations to deal with a variety of functional states of whole-cell populations of a Ca(2+)-releasing unit using a personal computer. In this study, we developed a membrane excitation-contraction model of the human ventricular myocyte, which we call the human ventricular cell (HuVEC) model. This model is a hybrid of the most recent HuVEC models and the Hinch model. We modified the Hinch model to reproduce the regenerative activation and termination of CICR. In particular, we removed the inactivated RyR state and separated the single step of RyR activation by LCCs into triggering and regenerative steps. More importantly, we included the experimental measurement of a transient rise in Ca(2+) concentrations ([Ca(2+)], 10-15 μM) during CICR in the vicinity of Ca(2+)-releasing sites, and thereby calculated the effects of the local Ca(2+) gradient on CICR as well as membrane excitation. This HuVEC model successfully reconstructed both membrane excitation and key properties of CICR. The time course of CICR evoked by an action potential was accounted for by autonomous changes in an instantaneous equilibrium open probability of couplons. This autonomous time course was driven by a core feedback loop including the pivotal local [Ca(2+)], influenced by a time-dependent decay in the SR Ca(2+) content during CICR.

Myokit: A simple interface to cardiac cellular electrophysiology

Myokit is a new powerful and versatile software tool for modeling and simulation of cardiac cellular electrophysiology. Myokit consists of an easy-to-read modeling language, a graphical user interface, single and multi-cell simulation engines and a library of advanced analysis tools accessible through a Python interface. Models can be loaded from Myokit's native file format or imported from CellML. Model export is provided to C, MATLAB, CellML, CUDA and OpenCL. Patch-clamp data can be imported and used to estimate model parameters. In this paper, we review existing tools to simulate the cardiac cellular action potential to find that current tools do not cater specifically to model development and that there is a gap between easy-to-use but limited software and powerful tools that require strong programming skills from their users. We then describe Myokit's capabilities, focusing on its model description language, simulation engines and import/export facilities in detail. Using three examples, we show how Myokit can be used for clinically relevant investigations, multi-model testing and parameter estimation in Markov models, all with minimal programming effort from the user. This way, Myokit bridges a gap between performance, versatility and user-friendliness.

Hair cell-type dependent expression of basolateral ion channels shapes response dynamics in the frog utricle

The dynamics of vestibular afferent responses are thought to be strongly influenced by presynaptic properties. In this paper, by performing whole-cell perforated-patch experiments in the frog utricle, we characterized voltage-dependent currents and voltage responses to current steps and 0.3–100 Hz sinusoids. Current expression and voltage responses are strongly related to hair cell type. In particular, voltage responses of extrastriolar type eB (low pass, −3 dB corner at 52.5 ± 12.8 Hz) and striolar type F cells (resonant, tuned at 60 ± 46 Hz) agree with the dynamics (tonic and phasic, respectively) of the afferent fibers they contact. On the other hand, hair cell release (measured with single-sine membrane ΔCm measurements) was linearly related to Ca in both cell types, and therefore did not appear to contribute to dynamics differences. As a tool for quantifying the relative contribution of basolateral currents and other presynaptic factors to afferent dynamics, the recorded current, voltage and release data were used to build a NEURON model of the average extrastriolar type eB and striolar type F hair cell. The model contained all recorded conductances, a basic mechanosensitive hair bundle and a ribbon synapse sustained by stochastic voltage-dependent Ca channels, and could reproduce the recorded hair cell voltage responses. Simulated release obtained from eB-type and F-type models display significant differences in dynamics, supporting the idea that basolateral currents are able to contribute to afferent dynamics; however, release in type eB and F cell models does not reproduce tonic and phasic dynamics, mainly because of an excessive phase lag present in both cell types. This suggests the presence in vestibular hair cells of an additional, phase-advancing mechanism, in cascade with voltage modulation.

Implementation of Contraction to Electrophysiological Ventricular Myocyte Models, and Their Quantitative Characterization via Post-Extrasystolic Potentiation

Heart failure (HF) affects over 5 million Americans and is characterized by impairment of cellular cardiac contractile function resulting in reduced ejection fraction in patients. Electrical stimulation such as cardiac resynchronization therapy (CRT) and cardiac contractility modulation (CCM) have shown some success in treating patients with HF. Computer simulations have the potential to help improve such therapy (e.g. suggest optimal lead placement) as well as provide insight into the underlying mechanisms which could be beneficial. However, these myocyte models require a quantitatively accurate excitation-contraction coupling such that the electrical and contraction predictions are correct. While currently there are close to a hundred models describing the detailed electrophysiology of cardiac cells, the majority of cell models do not include the equations to reproduce contractile force or they have been added ad hoc. Here we present a systematic methodology to couple first generation contraction models into electrophysiological models via intracellular calcium and then compare the resulting model predictions to experimental data. This is done by using a post-extrasystolic pacing protocol, which captures essential dynamics of contractile forces. We found that modeling the dynamic intracellular calcium buffers is necessary in order to reproduce the experimental data. Furthermore, we demonstrate that in models the mechanism of the post-extrasystolic potentiation is highly dependent on the calcium released from the Sarcoplasmic Reticulum. Overall this study provides new insights into both specific and general determinants of cellular contractile force and provides a framework for incorporating contraction into electrophysiological models, both of which will be necessary to develop reliable simulations to optimize electrical therapies for HF.

Ca2+ dysregulation in the endoplasmic reticulum related to Alzheimer's disease: A review on experimental progress and computational modeling

Alzheimer's disease (AD) is a devastating, incurable neurodegenerative disease affecting millions of people worldwide. Dysregulation of intracellular Ca(2+) signaling has been observed as an early event prior to the presence of clinical symptoms of AD and is believed to be a crucial factor contributing to its pathogenesis. The progressive and sustaining increase in the resting level of cytosolic Ca(2+) will affect downstream activities and neural functions. This review focuses on the issues relating to the increasing Ca(2+) release from the endoplasmic reticulum (ER) observed in AD neurons. Numerous research papers have suggested that the dysregulation of ER Ca(2+) homeostasis is associated with mutations in the presenilin genes and amyloid-β oligomers. These disturbances could happen at many different points in the signaling process, directly affecting ER Ca(2+) channels or interfering with related pathways, which makes it harder to reveal the underlying mechanisms. This review paper also shows that computational modeling is a powerful tool in Ca(2+) signaling studies and discusses the progress in modeling related to Ca(2+) dysregulation in AD research.

Cellular cardiac electrophysiology modeling with Chaste and CellML

Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model code is auto-generated at compile or run time; it never has to be manually edited. We use ontological annotation to identify model variables describing certain biological quantities (membrane voltage, capacitance, etc.) to allow us to import any relevant CellML models into the Chaste framework in consistent units and to interact with them via consistent interfaces. This approach provides a great deal of flexibility for analysing different models of the same system. Chaste provides a wide choice of numerical methods for solving the ordinary differential equations that describe the models. Fixed-timestep explicit and implicit solvers are provided, as discussed in previous work. Here we introduce the Rush–Larsen and Generalized Rush–Larsen integration techniques, made available via symbolic manipulation of the model equations, which are automatically rearranged into the forms required by these approaches. We have also integrated the CVODE solvers, a ‘gold standard’ for stiff systems, and we have developed support for symbolic computation of the Jacobian matrix, yielding further increases in the performance and accuracy of CVODE. We discuss some of the technical details of this work and compare the performance of the available numerical methods. Finally, we discuss how this is generalized in our functional curation framework, which uses a domain-specific language for defining complex experiments as a basis for comparison of model behavior.

EAD and DAD mechanisms analyzed by developing a new human ventricular cell model

It has long been suggested that the Ca(2+)-mechanisms are largely involved in generating the early afterdepolarization (EAD) as well as the delayed afterdepolarization (DAD). This view was examined in a quantitative manner by applying the lead potential analysis to a new human ventricular cell model. In this ventricular cell model, the tight coupled LCC-RyR model (CaRU) based on local control theory (Hinch et al. 2004) and ion channel models mostly based on human electrophysiological data were included to reproduce realistic Ca(2+) dynamics as well as the membrane excitation. Simultaneously, the Ca(2+) accumulation near the Ca(2+) releasing site was incorporated as observed in real cardiac myocytes. The maximum rate of ventricular repolarization (-1.02 mV/ms) is due to IK1 (-0.55 mV/ms) and the rest is provided nearly equally by INCX (-0.20 mV/ms), INaL (-0.16 mV/ms) and INaT (-0.13 mV/ms). These INaL and INaT components are due to closure of the voltage gate, which remains partially open during the plateau potential. DADs could be evoked by applying high-frequency stimulations supplemented by a partial Na(+)/K(+) pump inhibition, or by a microinjection of Ca(2+). EADs was evoked by retarding the inactivation of INaL. The lead potential (VL) analysis revealed that IK1 and IKr played the primary role to reverse the AP repolarization to depolarizing limb of EAD. ICaL and INCX amplified EAD, while the remaining currents partially antagonized dVL/dt. The maximum rate of rise of EAD was attributable to the rapid activation of both ICaL (45.5%) and INCX (54.5%).

The cardiac muscle duplex as a method to study myocardial heterogeneity

This paper reviews the development and application of paired muscle preparations, called duplex, for the investigation of mechanisms and consequences of intra-myocardial electro-mechanical heterogeneity. We illustrate the utility of the underlying combined experimental and computational approach for conceptual development and integration of basic science insight with clinically relevant settings, using previously published and new data. Directions for further study are identified.

The mitochondrial Na+-Ca2+ exchanger, NCLX, regulates automaticity of HL-1 cardiomyocytes

Mitochondrial Ca²⁺ is known to change dynamically, regulating mitochondrial as well as cellular functions such as energy metabolism and apoptosis. The NCLX gene encodes the mitochondrial Na⁺-Ca²⁺ exchanger (NCX_mit), a Ca²⁺ extrusion system in mitochondria. Here we report that the NCLX regulates automaticity of the HL-1 cardiomyocytes. NCLX knockdown using siRNA resulted in the marked prolongation of the cycle length of spontaneous Ca²⁺ oscillation and action potential generation. The upstrokes of action potential and Ca²⁺ transient were markedly slower, and sarcoplasmic reticulum (SR) Ca²⁺ handling were compromised in the NCLX knockdown cells. Analyses using a mathematical model of HL-1 cardiomyocytes demonstrated that blocking NCX_mit reduced the SR Ca²⁺ content to slow spontaneous SR Ca²⁺ leak, which is a trigger of automaticity. We propose that NCLX is a novel molecule to regulate automaticity of cardiomyocytes via modulating SR Ca²⁺ handling.

Spiral-wave dynamics in a mathematical model of human ventricular tissue with myocytes and fibroblasts

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, one-, and two-sided MF couplings. Our studies of MF units elucidate the dependence of the action-potential (AP) morphology on parameters such as , the fibroblast resting-membrane potential, the fibroblast conductance , and the MF gap-junctional coupling . Furthermore, we find that our MF composite can show autorhythmic and oscillatory behaviors in addition to an excitable response. Our 2D studies use (a) both homogeneous and inhomogeneous distributions of fibroblasts, (b) various ranges for parameters such as , and , and (c) intercellular couplings that can be zero-sided, one-sided, and two-sided connections of fibroblasts with myocytes. We show, in particular, that the plane-wave conduction velocity decreases as a function of , for zero-sided and one-sided couplings; however, for two-sided coupling, decreases initially and then increases as a function of , and, eventually, we observe that conduction failure occurs for low values of . In our homogeneous studies, we find that the rotation speed and stability of a spiral wave can be controlled either by controlling or . Our studies with fibroblast inhomogeneities show that a spiral wave can get anchored to a local fibroblast inhomogeneity. We also study the efficacy of a low-amplitude control scheme, which has been suggested for the control of spiral-wave turbulence in mathematical models for cardiac tissue, in our MF model both with and without heterogeneities.

Contribution of quantitative changes in individual ionic current systems to the embryonic development of ventricular myocytes: a simulation study

Early embryonic rodent ventricular cells exhibit spontaneous action potential (AP), which disappears in later developmental stages. Here, we used 3 mathematical models-the Kyoto, Ten Tusscher-Panfilov, and Luo-Rudy models-to present an overview of the functional landscape of developmental changes in embryonic ventricular cells. We switched the relative current densities of 9 ionic components in the Kyoto model, and 160 of 512 representative combinations were predicted to result in regular spontaneous APs, in which the quantitative changes in Na(+) current (I Na) and funny current (I f) made large contributions to a wide range of basic cycle lengths. In all three models, the increase in inward rectifier current (I K1) before the disappearance of I f was predicted to result in abnormally high intracellular Ca(2+) concentrations. Thus, we demonstrated that the developmental changes in APs were well represented, as I Na increased before the disappearance of I f, followed by a 10-fold increase in I K1.

An integrative model of the cardiovascular system coupling heart cellular mechanics with arterial network hemodynamics

The current study proposes a model of the cardiovascular system that couples heart cell mechanics with arterial hemodynamics to examine the physiological role of arterial blood pressure (BP) in left ventricular hypertrophy (LVH). We developed a comprehensive multiphysics and multiscale cardiovascular model of the cardiovascular system that simulates physiological events, from membrane excitation and the contraction of a cardiac cell to heart mechanics and arterial blood hemodynamics. Using this model, we delineated the relationship between arterial BP or pulse wave velocity and LVH. Computed results were compared with existing clinical and experimental observations. To investigate the relationship between arterial hemodynamics and LVH, we performed a parametric study based on arterial wall stiffness, which was obtained in the model. Peak cellular stress of the left ventricle and systolic blood pressure (SBP) in the brachial and central arteries also increased; however, further increases were limited for higher arterial stiffness values. Interestingly, when we doubled the value of arterial stiffness from the baseline value, the percentage increase of SBP in the central artery was about 6.7% whereas that of the brachial artery was about 3.4%. It is suggested that SBP in the central artery is more critical for predicting LVH as compared with other blood pressure measurements.

Hyperpolarization-activated current, If, in mathematical models of rabbit sinoatrial node pacemaker cells

A typical feature of sinoatrial (SA) node pacemaker cells is the presence of an ionic current that activates upon hyperpolarization. The role of this hyperpolarization-activated current, I_f, which is also known as the “funny current” or “pacemaker current,” in the spontaneous pacemaker activity of SA nodal cells remains a matter of intense debate. Whereas some conclude that I_f plays a fundamental role in the generation of pacemaker activity and its rate control, others conclude that the role of I_f is limited to a modest contribution to rate control. The ongoing debate is often accompanied with arguments from computer simulations, either to support one's personal view or to invalidate that of the antagonist. In the present paper, we review the various mathematical descriptions of I_f that have been used in computer simulations and compare their strikingly different characteristics with our experimental data. We identify caveats and propose a novel model for I_f based on our experimental data.

Na/K pump regulation of cardiac repolarization: insights from a systems biology approach

The sodium-potassium pump is widely recognized as the principal mechanism for active ion transport across the cellular membrane of cardiac tissue, being responsible for the creation and maintenance of the transarcolemmal sodium and potassium gradients, crucial for cardiac cell electrophysiology. Importantly, sodium-potassium pump activity is impaired in a number of major diseased conditions, including ischemia and heart failure. However, its subtle ways of action on cardiac electrophysiology, both directly through its electrogenic nature and indirectly via the regulation of cell homeostasis, make it hard to predict the electrophysiological consequences of reduced sodium-potassium pump activity in cardiac repolarization. In this review, we discuss how recent studies adopting the systems biology approach, through the integration of experimental and modeling methodologies, have identified the sodium-potassium pump as one of the most important ionic mechanisms in regulating key properties of cardiac repolarization and its rate dependence, from subcellular to whole organ levels. These include the role of the pump in the biphasic modulation of cellular repolarization and refractoriness, the rate control of intracellular sodium and calcium dynamics and therefore of the adaptation of repolarization to changes in heart rate, as well as its importance in regulating pro-arrhythmic substrates through modulation of dispersion of repolarization and restitution. Theoretical findings are consistent across a variety of cell types and species including human, and widely in agreement with experimental findings. The novel insights and hypotheses on the role of the pump in cardiac electrophysiology obtained through this integrative approach could eventually lead to novel therapeutic and diagnostic strategies.

A CellML simulation compiler and code generator using ODE solving schemes

: Models written in description languages such as CellML are becoming a popular solution to the handling of complex cellular physiological models in biological function simulations. However, in order to fully simulate a model, boundary conditions and ordinary differential equation (ODE) solving schemes have to be combined with it. Though boundary conditions can be described in CellML, it is difficult to explicitly specify ODE solving schemes using existing tools. In this study, we define an ODE solving scheme description language-based on XML and propose a code generation system for biological function simulations. In the proposed system, biological simulation programs using various ODE solving schemes can be easily generated. We designed a two-stage approach where the system generates the equation set associating the physiological model variable values at a certain time t with values at t + Δt in the first stage. The second stage generates the simulation code for the model. This approach enables the flexible construction of code generation modules that can support complex sets of formulas. We evaluate the relationship between models and their calculation accuracies by simulating complex biological models using various ODE solving schemes. Using the FHN model simulation, results showed good qualitative and quantitative correspondence with the theoretical predictions. Results for the Luo-Rudy 1991 model showed that only first order precision was achieved. In addition, running the generated code in parallel on a GPU made it possible to speed up the calculation time by a factor of 50. The CellML Compiler source code is available for download at http://sourceforge.net/projects/cellmlcompiler.

An image-based model of the whole human heart with detailed anatomical structure and fiber orientation

Many heart anatomy models have been developed to study the electrophysiological properties of the human heart. However, none of them includes the geometry of the whole human heart. In this study, an anatomically detailed mathematical model of the human heart was firstly reconstructed from the computed tomography images. In the reconstructed model, the atria consisted of atrial muscles, sinoatrial node, crista terminalis, pectinate muscles, Bachmann's bundle, intercaval bundles, and limbus of the fossa ovalis. The atrioventricular junction included the atrioventricular node and atrioventricular ring, and the ventricles had ventricular muscles, His bundle, bundle branches, and Purkinje network. The epicardial and endocardial myofiber orientations of the ventricles and one layer of atrial myofiber orientation were then measured. They were calculated using linear interpolation technique and minimum distance algorithm, respectively. To the best of our knowledge, this is the first anatomically-detailed human heart model with corresponding experimentally measured fibers orientation. In addition, the whole heart excitation propagation was simulated using a monodomain model. The simulated normal activation sequence agreed well with the published experimental findings.

A kinematic approach for efficient and robust simulation of the cardiac beating motion

Computer simulation techniques for cardiac beating motions potentially have many applications and a broad audience. However, most existing methods require enormous computational costs and often show unstable behavior for extreme parameter sets, which interrupts smooth simulation study and make it difficult to apply them to interactive applications. To address this issue, we present an efficient and robust framework for simulating the cardiac beating motion. The global cardiac motion is generated by the accumulation of local myocardial fiber contractions. We compute such local-to-global deformations using a kinematic approach; we divide a heart mesh model into overlapping local regions, contract them independently according to fiber orientation, and compute a global shape that satisfies contracted shapes of all local regions as much as possible. A comparison between our method and a physics-based method showed that our method can generate motion very close to that of a physics-based simulation. Our kinematic method has high controllability; the simulated ventricle-wall-contraction speed can be easily adjusted to that of a real heart by controlling local contraction timing. We demonstrate that our method achieves a highly realistic beating motion of a whole heart in real time on a consumer-level computer. Our method provides an important step to bridge a gap between cardiac simulations and interactive applications.

How the Hodgkin-Huxley equations inspired the Cardiac Physiome Project

Early modelling of cardiac cells (1960-1980) was based on extensions of the Hodgkin-Huxley nerve axon equations with additional channels incorporated, but after 1980 it became clear that processes other than ion channel gating were also critical in generating electrical activity. This article reviews the development of models representing almost all cell types in the heart, many different species, and the software tools that have been created to facilitate the cardiac Physiome Project.

Direct effects of esmolol and landiolol on cardiac function, coronary vasoactivity, and ventricular electrophysiology in guinea-pig hearts

The ultra-short acting, selective β(1)-adrenergic antagonists landiolol and esmolol are widely used perioperatively; however, little is known about their acute direct actions on the heart. The current study utilized the Langendorff perfused heart system to measure changes in cardiac function and hemodynamics in response to each drug. Furthermore, electrophysiological analysis was performed on isolated ventricular myocytes. Direct application of esmolol significantly decreased systolic left ventricular pressure and heart rate at concentrations > 10 µM, while it dose-dependently increased coronary perfusion pressure. Esmolol also shortened the action potential duration (APD) in a concentration-dependent manner, an action maintained even when the delayed rectifier K(+) current or ATP sensitive K(+) current was blocked. Moreover, esmolol inhibited both the inward rectifier K(+) current (I(K1)) and the L-type Ca(2+) current (I(CaL)) and increased the outward current dose-dependently. In contrast, landiolol had minimal cardiac effects. In the Kyoto Model computer simulation, inhibition of either I(K1) or I(CaL) alone failed to shorten the APD; however, an additional increase in the time-independent outward current caused shortening of the APD, equal to that induced by esmolol. In conclusion, esmolol directly inhibits cardiac performance significantly more so than landiolol, an effect revealed to be at least in part mediated by esmolol-induced APD shortening.

A general CellML simulation code generator using ODE solving scheme description

To cope with the complexity of the biological function simulation models, model representation with description language is becoming popular. However, simulation software itself becomes complex in these environment, thus, it is difficult to modify target computation resources or numerical calculation methods or simulation conditions. Typical biological function simulation software consists of 1) model equation, 2) boundary conditions and 3) ODE solving scheme. Introducing the description model file such as CellML is useful for generalizing the first point and partly second point, however, third point is difficult to handle. We introduce a simulation software generation system which use markup language based description of ODE solving scheme together with cell model description file. By using this software, we can easily generate biological simulation program code with different ODE solving schemes. To show the efficiency of our system, experimental results of several simulation models with different ODE scheme and different computation resources are shown.

Pivotal role of mitochondrial Na⁺₋Ca²⁺ exchange in antigen receptor mediated Ca²⁺ signalling in DT40 and A20 B lymphocytes

Cytoplasmic Ca(2+) concentration ([Ca(2+)](i)) increases upon activation of antigen-receptor in lymphocytes. Mitochondria have been suggested to regulate the [Ca(2+)](i) response, but the molecular mechanisms and the roles are poorly understood. To clarify them, we carried out a combination study of mathematical simulations and knockout or knockdown of NCLX, a gene candidate for the mitochondrial Na(+)-Ca(2+) exchanger (NCX(mit)), in B lymphocytes. A mathematical model of Ca(2+) dynamics in B lymphocytes demonstrated that NCX(mit) inhibition reduces basal Ca(2+) content of endoplasmic reticulum (ER) and suppresses B-cell antigen receptor (BCR)-mediated [Ca(2+)](i) rise. The predictions were validated in DT40 B lymphocytes of heterozygous NCLX knockout (NCLX(+/-)). In NCLX(+/-) cells, mitochondrial Ca(2+) efflux via NCX(mit) was strongly decelerated, suggesting NCLX is a gene responsible for NCX(mit) in B lymphocytes. Consistent with the predictions, ER Ca(2+) content declined and [Ca(2+)](i) hardly rose upon BCR activation in NCLX(+/-) cells. ER Ca(2+) uptake was reduced to ∼58% of the wild-type (WT), while it was comparable to WT when mitochondrial respiration was disturbed. Essentially the same results were obtained by a pharmacological inhibition or knockdown of NCLX by siRNA in A20 B lymphocytes. Unexpectedly, ER Ca(2+) leak was augmented and co-localization of mitochondria with ER was lower in NCLX(+/-) and NCLX silenced cells. Taken together, we concluded that NCLX is a key Ca(2+) provider to ER, and that NCLX-mediated Ca(2+) recycling between mitochondria and ER is pivotal in B cell responses to antigen.

A computational model of cytosolic and mitochondrial [ca] in paced rat ventricular myocytes

We carried out a series of experiment demonstrating the role of mitochondria in the cytosolic and mitochondrial Ca(2+) transients and compared the results with those from computer simulation. In rat ventricular myocytes, increasing the rate of stimulation (1~3 Hz) made both the diastolic and systolic [Ca(2+)] bigger in mitochondria as well as in cytosol. As L-type Ca(2+) channel has key influence on the amplitude of Ca(2+)-induced Ca(2+) release, the relation between stimulus frequency and the amplitude of Ca(2+) transients was examined under the low density (1/10 of control) of L-type Ca(2+) channel in model simulation, where the relation was reversed. In experiment, block of Ca(2+) uniporter on mitochondrial inner membrane significantly reduced the amplitude of mitochondrial Ca(2+) transients, while it failed to affect the cytosolic Ca(2+) transients. In computer simulation, the amplitude of cytosolic Ca(2+) transients was not affected by removal of Ca(2+) uniporter. The application of carbonyl cyanide 4-(trifluoromethoxy) phenylhydrazone (FCCP) known as a protonophore on mitochondrial membrane to rat ventricular myocytes gradually increased the diastolic [Ca(2+)] in cytosol and eventually abolished the Ca(2+) transients, which was similarly reproduced in computer simulation. The model study suggests that the relative contribution of L-type Ca(2+) channel to total transsarcolemmal Ca(2+) flux could determine whether the cytosolic Ca(2+) transients become bigger or smaller with higher stimulus frequency. The present study also suggests that cytosolic Ca(2+) affects mitochondrial Ca(2+) in a beat-to-beat manner, however, removal of Ca(2+) influx mechanism into mitochondria does not affect the amplitude of cytosolic Ca(2+) transients.

Cardiac electromechanical models: from cell to organ

The heart is a multiphysics and multiscale system that has driven the development of the most sophisticated mathematical models at the frontiers of computational physiology and medicine. This review focuses on electromechanical (EM) models of the heart from the molecular level of myofilaments to anatomical models of the organ. Because of the coupling in terms of function and emergent behaviors at each level of biological hierarchy, separation of behaviors at a given scale is difficult. Here, a separation is drawn at the cell level so that the first half addresses subcellular/single-cell models and the second half addresses organ models. At the subcellular level, myofilament models represent actin–myosin interaction and Ca-based activation. The discussion of specific models emphasizes the roles of cooperative mechanisms and sarcomere length dependence of contraction force, considered to be the cellular basis of the Frank–Starling law. A model of electrophysiology and Ca handling can be coupled to a myofilament model to produce an EM cell model, and representative examples are summarized to provide an overview of the progression of the field. The second half of the review covers organ-level models that require solution of the electrical component as a reaction–diffusion system and the mechanical component, in which active tension generated by the myocytes produces deformation of the organ as described by the equations of continuum mechanics. As outlined in the review, different organ-level models have chosen to use different ionic and myofilament models depending on the specific application; this choice has been largely dictated by compromises between model complexity and computational tractability. The review also addresses application areas of EM models such as cardiac resynchronization therapy and the role of mechano-electric coupling in arrhythmias and defibrillation.

Simulation of developmental changes in action potentials with ventricular cell models

During cardiomyocyte development, early embryonic ventricular cells show spontaneous activity that disappears at a later stage. Dramatic changes in action potential are mediated by developmental changes in individual ionic currents. Hence, reconstruction of the individual ionic currents into an integrated mathematical model would lead to a better understanding of cardiomyocyte development. To simulate the action potential of the rodent ventricular cell at three representative developmental stages, quantitative changes in the ionic currents, pumps, exchangers, and sarcoplasmic reticulum (SR) Ca(2+) kinetics were represented as relative activities, which were multiplied by conductance or conversion factors for individual ionic systems. The simulated action potential of the early embryonic ventricular cell model exhibited spontaneous activity, which ceased in the simulated action potential of the late embryonic and neonatal ventricular cell models. The simulations with our models were able to reproduce action potentials that were consistent with the reported characteristics of the cells in vitro. The action potential of rodent ventricular cells at different developmental stages can be reproduced with common sets of mathematical equations by multiplying conductance or conversion factors for ionic currents, pumps, exchangers, and SR Ca(2+) kinetics by relative activities.

Experiment-model interaction for analysis of epicardial activation during human ventricular fibrillation with global myocardial ischaemia

We describe a combined experiment-modelling framework to investigate the effects of ischaemia on the organisation of ventricular fibrillation in the human heart. In a series of experimental studies epicardial activity was recorded from 10 patients undergoing routine cardiac surgery. Ventricular fibrillation was induced by burst pacing, and recording continued during 2.5 min of global cardiac ischaemia followed by 30 s of coronary reflow. Modelling used a 2D description of human ventricular tissue. Global cardiac ischaemia was simulated by (i) decreased intracellular ATP concentration and subsequent activation of an ATP sensitive K⁺ current, (ii) elevated extracellular K⁺ concentration, and (iii) acidosis resulting in reduced magnitude of the L-type Ca²⁺ current I(Ca,L). Simulated ischaemia acted to shorten action potential duration, reduce conduction velocity, increase effective refractory period, and flatten restitution. In the model, these effects resulted in slower re-entrant activity that was qualitatively consistent with our observations in the human heart. However, the flattening of restitution also resulted in the collapse of many re-entrant waves to several stable re-entrant waves, which was different to the overall trend we observed in the experimental data. These findings highlight a potential role for other factors, such as structural or functional heterogeneity in sustaining wavebreak during human ventricular fibrillation with global myocardial ischaemia.