A dynamic model of excitation-contraction coupling during acidosis in cardiac ventricular myocytes

Extracellular acidification reveals the antiarrhythmic properties of amiodarone related to late sodium current-induced atrial arrhythmia

BACKGROUND

Amiodarone (AMIO) is an antiarrhythmic drug with the pKa in the physiological range. Here, we explored how mild extracellular pH (pHe) changes shape the interaction of AMIO with atrial tissue and impact its pharmacological properties in the classical model of sea anemone sodium channel neurotoxin type 2 (ATX) induced late sodium current (INa-Late) and arrhythmias.

METHOD

Isolated atrial cardiomyocytes from male Wistar rats and human embryonic kidney cells expressing SCN5A Na+ channels were used for patch-clamp experiments. Isolated right atria (RA) and left atria (LA) tissue were used for bath organ experiments.

RESULTS

A more acidophilic pHe caused negative inotropic effects on isolated RA and LA atrial tissue, without modification of the pharmacological properties of AMIO. A pHe of 7.0 changed the sodium current (INa) related components of the action potential (AP), which was enhanced in the presence of AMIO. ATXinduced arrhythmias in isolated RA and LA. Also, ATX prolonged the AP duration and enhanced repolarization dispersion in isolated cardiomyocytes in both pHe 7.4 and pHe 7.0. Pre-incubation of the isolated RA and LA and isolated atrial cardiomyocytes with AMIO prevented arrhythmias induced by ATX only at a pHe of 7.0. Moreover, AMIO was able to block INa-Late induced by ATX only at a pHe of 7.0.

CONCLUSION

The pharmacological properties of AMIO concerning healthy rat atrial tissue are not dependent on pHe. However, the prevention of arrhythmias induced by INa-Late is pHe-dependent. The development of drugs analogous to AMIO with charge stabilization may help to create more effective drugs to treat arrhythmias related to the INa-Late.

A mathematical model of ENaC and Slc26a6 regulation by CFTR in salivary gland ducts

Cystic fibrosis (CF) is a genetic disease caused by the mutations of cystic fibrosis transmembrane conductance regulator (CFTR), the cystic fibrosis transmembrane conductance regulator gene. Cftr is a critical ion channel expressed in the apical membrane of mouse salivary gland striated duct cells. Although Cftr is primarily a Cl- channel, its knockout leads to higher salivary Cl- and Na+ concentrations and lower pH. Mouse experiments show that the activation of Cftr upregulates epithelial Na+ channel (ENaC) protein expression level and Slc26a6 (a 1Cl-:2[Formula: see text] exchanger of the solute carrier family) activity. Experimentally, it is difficult to predict how much the coregulation effects of CFTR contribute to the abnormal Na+, Cl-, and [Formula: see text] concentrations and pH in CF saliva. To address this question, we construct a wild-type mouse salivary gland model and simulate CFTR knockout by altering the expression levels of CFTR, ENaC, and Slc26a6. By reproducing the in vivo and ex vivo final saliva measurements from wild-type and CFTR knockout animals, we obtain computational evidence that ENaC and Slc26a6 activities are downregulated in CFTR knockout in salivary glands.NEW & NOTEWORTHY This paper describes a salivary gland mathematical model simulating the ion exchange between saliva and the salivary gland duct epithelium. The novelty lies in the implementation of CFTR regulating ENaC and Slc26a6 in a CFTR knockout gland. By reproducing the experimental saliva measurements in wild-type and CFTR knockout glands, the model shows that CFTR regulates ENaC and Slc26a6 anion exchanger in salivary glands. The method could be used to understand the various cystic fibrosis phenotypes.

An ECG generative model of myocardial infarction

Background and Objective Computer-aided diagnosis (CAD) of Myocardial Infarction (MI) using machine learning depends on a large amount of clinical Electrocardiogram (ECG) data. Existing infarct ECG databases face the problem of class imbalance. Data augmentation using generative simulation models is a new approach to effectively address this problem. Methods A multiscale ECG generative model was established for ECG data augmentation. In the cellular layer, an ischemic Action Potential (AP) model was established to generate APs in cardiomyocytes with different transmural regions of infraction or different ischemic durations. In the tissue layer, a probability-driven cellular automata excitation propagation model was established to simulate the propagation speed and direction of excitation. An infarct tissue model and a coronary artery model were established to describe the spatiotemporal diversity of MI. A ventricle model, a human torso model, and a computational model of surface ECG based on field source theory were established in the heart-torso layer. Results The model generated pathological 12-lead ECGs of MI with different topography and different extent. When simulating different ventricular wall infarction, the lesions appear in the same leads as the clinical 12-lead ECG. The ST-segment decreases and the T-wave amplitude decreases, similar to the clinical ECG features when simulating subendocardial ischemia. The average fidelity of the 12-lead ECG the model generated is 95.6%, according to the designed DTW-GRA distance algorithm. Conclusions The generative model considers the electrophysiological properties of the natural heart, the pathology of myocardial infarction, and the diversity of clinical ECGs. The model can provide many reliable samples for machine learning of MI.

A Mathematical Model of Salivary Gland Duct Cells

Saliva is produced in two stages in the salivary glands: the secretion of primary saliva by the acinus and the modification of saliva composition to final saliva by the intercalated and striated ducts. In order to understand the saliva modification process, we develop a mathematical model for the salivary gland duct. The model utilises the realistic 3D structure of the duct reconstructed from an image stack of gland tissue. Immunostaining results show that TMEM16A and aquaporin are expressed in the intercalated duct cells and that ENaC is not. Based on this, the model predicts that the intercalated duct does not absorb Na\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ and Cl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^-$$\end{document}- like the striated duct but secretes a small amount of water instead. The input to the duct model is the time-dependent primary saliva generated by an acinar cell model. Our duct model produces final saliva output that agrees with the experimental measurements at various stimulation levels. It also shows realistic biological features such as duct cell volume, cellular concentrations and membrane potentials. Simplification of the model by omission of all detailed 3D structures of the duct makes a negligible difference to the final saliva output. This shows that saliva production is not sensitive to structural variation of the duct.

The mitochondrial pyruvate carrier at the crossroads of intermediary metabolism

Pyruvate metabolism, a central nexus of carbon homeostasis, is an evolutionarily conserved process and aberrant pyruvate metabolism is associated with and contributes to numerous human metabolic disorders including diabetes, cancer, and heart disease. As a product of glycolysis, pyruvate is primarily generated in the cytosol before being transported into the mitochondrion for further metabolism. Pyruvate entry into the mitochondrial matrix is a critical step for efficient generation of reducing equivalents and ATP and for the biosynthesis of glucose, fatty acids, and amino acids from pyruvate. However, for many years, the identity of the carrier protein(s) that transported pyruvate into the mitochondrial matrix remained a mystery. In 2012, the molecular-genetic identification of the mitochondrial pyruvate carrier (MPC), a heterodimeric complex composed of protein subunits MPC1 and MPC2, enabled studies that shed light on the many metabolic and physiological processes regulated by pyruvate metabolism. A better understanding of the mechanisms regulating pyruvate transport and the processes affected by pyruvate metabolism may enable novel therapeutics to modulate mitochondrial pyruvate flux to treat a variety of disorders. Herein, we review our current knowledge of the MPC, discuss recent advances in the understanding of mitochondrial pyruvate metabolism in various tissue and cell types, and address some of the outstanding questions relevant to this field.

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.

A Preliminary Computational Model for Hypoxic Acidosis in Cardiac Myocytes

Intracellular acidosis induced by hypoxia resulted from myocardial ischemia damages myocardium. However, the detailed mechanisms of hypoxic acidosis are not quantitatively explained. The purpose of this study is to create a novel computational model which can reproduce intracellular acidosis caused by myocardial ischemia. We constructed a computational model of myocardium, by using a mathematical ventricular cell model which includes pH regulation and a computational model of myocardial microcirculation for calculating extracellular conditions. The present model reproduced cellular hypoxia in an ischemic condition simulated by a reduced blood flow, and intracellular pH reduction in response to the hypoxia.

The Resting Potential and K+ Currents in Primary Human Articular Chondrocytes

Human transplant programs provide significant opportunities for detailed in vitro assessments of physiological properties of selected tissues and cell types. We present a semi-quantitative study of the fundamental electrophysiological/biophysical characteristics of human chondrocytes, focused on K⁺ transport mechanisms, and their ability to regulate to the resting membrane potential, E_m. Patch clamp studies on these enzymatically isolated human chondrocytes reveal consistent expression of at least three functionally distinct K⁺ currents, as well as transient receptor potential (TRP) currents. The small size of these cells and their exceptionally low current densities present significant technical challenges for electrophysiological recordings. These limitations have been addressed by parallel development of a mathematical model of these K⁺ and TRP channel ion transfer mechanisms in an attempt to reveal their contributions to E_m. In combination, these experimental results and simulations yield new insights into: (i) the ionic basis for E_m and its expected range of values; (ii) modulation of E_m by the unique articular joint extracellular milieu; (iii) some aspects of TRP channel mediated depolarization-secretion coupling; (iv) some of the essential biophysical principles that regulate K⁺ channel function in “chondrons.” The chondron denotes the chondrocyte and its immediate extracellular compartment. The presence of discrete localized surface charges and associated zeta potentials at the chondrocyte surface are regulated by cell metabolism and can modulate interactions of chondrocytes with the extracellular matrix. Semi-quantitative analysis of these factors in chondrocyte/chondron function may yield insights into progressive osteoarthritis.

Adaptation of the FK506 binding protein 1B to hibernation in bats

Hibernation is an adaptive strategy used by some animals to cope with cold and food shortage. The heart rate, overall energy need, body temperature, and many other physiological functions are greatly reduced during torpor but promptly return to normal levels upon arousal. The heartbeat of torpid bats can be hundreds fold lower than that of active bats, indicating that hibernating bats have a remarkable ability to control excitation-contraction coupling in cardiac muscle. FKBP1B (calstabin 2), a peptidyl-prolyl cis-trans isomerase, is critical for the regulation of excitation-contraction coupling. Whether FKBP1B is adapted to hibernation in bats is not known. Evolutionary analyses showed that the ω values of the Fkbp1b genes of 25 mammalian species are all less than 1, and amino acid sequence alignments revealed that FKBP1B proteins are highly conserved in mammals. The expression of the Fkbp1b gene was found to be elevated at both mRNA and protein levels in two distantly related bats (Rhinolophus ferrumequinum in Yinpterochiroptera and Myotis ricketti in Yangochiroptera) during torpor. Transcription factors such as YY1 and SPs were bioinformatically determined to have a higher binding affinity to the potential regulatory regions of Fkbp1b genes in hibernating than in non-hibernating mammals. This study provides new insights into the molecular evolution of Fkbp1b in adaptation to bat hibernation.

Bond graph modelling of the cardiac action potential: implications for drift and non-unique steady states

Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with respect to charge conservation in specific models. Here, we propose a general and systematic method of identifying conservation laws hidden in models of cardiac electrophysiology by using bond graphs, and develop a bond graph model of the cardiac action potential to study long-term behaviour. Bond graphs provide an explicit energy-based framework for modelling physical systems, which makes them well suited for examining conservation within electrophysiological models. We find that the charge conservation laws derived in previous studies are examples of the more general concept of a 'conserved moiety'. Conserved moieties explain model drift and non-unique steady states, generalizing the results from previous studies. The bond graph approach provides a rigorous method to check for drift and non-unique steady states in a wide range of cardiac action potential models, and can be extended to examine behaviours of other excitable systems.

Creating a Structurally Realistic Finite Element Geometric Model of a Cardiomyocyte to Study the Role of Cellular Architecture in Cardiomyocyte Systems Biology

With the advent of three-dimensional (3D) imaging technologies such as electron tomography, serial-block-face scanning electron microscopy and confocal microscopy, the scientific community has unprecedented access to large datasets at sub-micrometer resolution that characterize the architectural remodeling that accompanies changes in cardiomyocyte function in health and disease. However, these datasets have been under-utilized for investigating the role of cellular architecture remodeling in cardiomyocyte function. The purpose of this protocol is to outline how to create an accurate finite element model of a cardiomyocyte using high resolution electron microscopy and confocal microscopy images. A detailed and accurate model of cellular architecture has significant potential to provide new insights into cardiomyocyte biology, more than experiments alone can garner. The power of this method lies in its ability to computationally fuse information from two disparate imaging modalities of cardiomyocyte ultrastructure to develop one unified and detailed model of the cardiomyocyte. This protocol outlines steps to integrate electron tomography and confocal microscopy images of adult male Wistar (name for a specific breed of albino rat) rat cardiomyocytes to develop a half-sarcomere finite element model of the cardiomyocyte. The procedure generates a 3D finite element model that contains an accurate, high-resolution depiction (on the order of ~35 nm) of the distribution of mitochondria, myofibrils and ryanodine receptor clusters that release the necessary calcium for cardiomyocyte contraction from the sarcoplasmic reticular network (SR) into the myofibril and cytosolic compartment. The model generated here as an illustration does not incorporate details of the transverse-tubule architecture or the sarcoplasmic reticular network and is therefore a minimal model of the cardiomyocyte. Nevertheless, the model can already be applied in simulation-based investigations into the role of cell structure in calcium signaling and mitochondrial bioenergetics, which is illustrated and discussed using two case studies that are presented following the detailed protocol.

Mechanisms Underlying the Emergence of Post-acidosis Arrhythmia at the Tissue Level: A Theoretical Study

Acidosis has complex electrophysiological effects, which are associated with a high recurrence of ventricular arrhythmias. Through multi-scale cardiac computer modeling, this study investigated the mechanisms underlying the emergence of post-acidosis arrhythmia at the tissue level. In simulations, ten Tusscher-Panfilov ventricular model was modified to incorporate various data on acidosis-induced alterations of cellular electrophysiology and intercellular electrical coupling. The single cell models were incorporated into multicellular one-dimensional (1D) fiber and 2D sheet tissue models. Electrophysiological effects were quantified as changes of action potential profile, sink-source interactions of fiber tissue, and the vulnerability of tissue to the genesis of unidirectional conduction that led to initiation of re-entry. It was shown that acidosis-induced sarcoplasmic reticulum (SR) calcium load contributed to delayed afterdepolarizations (DADs) in single cells. These DADs may be synchronized to overcome the source-sink mismatch arising from intercellular electrotonic coupling, and produce a premature ventricular complex (PVC) at the tissue level. The PVC conduction can be unidirectionally blocked in the transmural ventricular wall with altered electrical heterogeneity, resulting in the genesis of re-entry. In conclusion, altered source-sink interactions and electrical heterogeneity due to acidosis-induced cellular electrophysiological alterations may increase susceptibility to post-acidosis ventricular arrhythmias.

Computational modeling of epithelial fluid and ion transport in the parotid duct after transfection of human aquaporin-1

Previous studies have shown that localized delivery of the aquaporin-1 (AQP1) gene to the parotid duct can restore saliva flow in minipigs following irradiation-induced salivary hypofunction. The resulting flow rate and electrochemistry of secreted saliva contradicts current understanding of ductal fluid transport. We hypothesized that changes in expression of ion transport proteins have occurred following AQP1 transfection. We use a mathematical model of ion and fluid transport across the parotid duct epithelial cells to predict the expression profile of ion transporters that are consistent with the experimental measurements of saliva composition and secretion rates. Using a baseline set of parameters, the model reproduces the data for the irradiated, non-AQP1-transfected case. We propose three scenarios which may have occurred after transfection, which differ in the location of the AQP1 gene. The first scenario places AQP1 within nonsecretory cells, and requires that epithelial sodium channel (ENaC) expression is greatly reduced (1.3% of baseline), and ductal bicarbonate concentration is increased from 40.6 to 137.0 mM, to drive water secretion into the duct. The second scenario introduces the AQP1 gene into all ductal cells. The final scenario has AQP1 primarily in the proximal duct cells which secrete water under baseline conditions. We find the change in the remaining cells includes a 95.8% reduction in ENaC expression, enabling us to reproduce all experimental ionic concentrations within 9 mM. These findings provide a mechanistic basis for the observations and will guide the further development of gene transfer therapy for salivary hypofunction.

NEW & NOTEWORTHY

Following transfection of aquaporin into the parotid ducts of minipigs with salivary hypofunction, the resulting increase in salivary flow rates contradicts current understanding of ductal fluid transport. We show that the change in saliva electrochemistry and flow rate can be explained by changes in expression of ion transporters in the ductal cell membranes, using a mathematical model replicating a single parotid duct.

Possible Mechanisms of Cardiac Contractile Dysfunction and Electrical Changes in Ammonium Chloride Induced Chronic Metabolic Acidosis in Wistar Rats

Metabolic acidosis could occur due to either endogenous acids accumulation or bicarbonate loss from the gastrointestinal tract or commonly from the kidney. This study aimed to investigate the possible underlying mechanism(s) of chronic acidosis-induced cardiac contractile and electrical changes in rats. Twenty four adult Wistar rats, of both sexes, were randomly divided into control group and chronic metabolic acidosis group, which received orally 0.28 M NH4Cl in the drinking water for 2 weeks. At the end of experimental period, systolic and diastolic blood pressure values were measured. On the day of sacrifice, rats were anesthetized by i.p. pentobarbitone (40 mg/kg b.w.), transthoracic echocardiography and ECG were performed. Blood samples were obtained from abdominal aorta for complete blood count and determination of pH, bicarbonate, chloride, sodium, potassium, troponin I, CK-MB, IL-6, renin and aldosterone levels. Hearts from both groups were studied for cardiac tissue IL-6 and aldosterone in addition to histopathological examination. Compared to control group, chronic metabolic acidosis group showed anemia, significant systolic and diastolic hypotension accompanied by significant reduction of ejection fraction and fraction of shortening, significant bradycardia, prolonged QTc interval and higher widened T wave as well as significantly elevated plasma levels of renin, aldosterone, troponin I, CK-MB and IL-6, and cardiac tissue aldosterone and IL-6. The left ventricular wall of the acidosis group showed degenerated myocytes with fibrosis and apoptosis. Thus, chronic metabolic acidosis induced negative inotropic and chronotropic effects and cardiomyopathy, possibly by elevated aldosterone and IL-6 levels released from the cardiac tissue.

A mathematical model of osteoclast acidification during bone resorption

Bone resorption by osteoclasts occurs through the creation of a sealed extracellular compartment (ECC), or pit, adjacent to the bone that is subsequently acidified through a complex biological process. The low pH of the pit dissolves the bone mineral and activates acid proteases that further break down the bone matrix. There are many ion channels, transporters, and soluble proteins involved in osteoclast mediated resorption, and in the past few years, there has been an increased understanding of the identity and properties of some key proteins such as the ClC-7 Cl^-/H⁺ antiporter and the H_V1 proton channel. Here we present a detailed mathematical model of osteoclast acidification that includes the influence of many of the key regulatory proteins. The primary enzyme responsible for acidification is the vacuolar H⁺-ATPase (V-ATPase), which pumps protons from the cytoplasm into the pit. Unlike the acidification of small lysosomes, the pit is so large that protons become depleted from the cytoplasm. Hence, proton buffering and production in the cytoplasm by carbonic anhydrase II (CAII) is potentially important for proper acidification. We employ an ordinary differential equations (ODE)-based model that accounts for the changes in ionic species in the cytoplasm and the resorptive pit. Additionally, our model tracks ionic flow between the cytoplasm and the extracellular solution surrounding the cell. Whenever possible, the properties of individual channels and transporters are calibrated based on electrophysiological measurements, and physical properties of the cell, such as buffering capacity, surface areas, and volumes, are estimated based on available data. Our model reproduces many of the experimental findings regarding the role of key proteins in the acidification process, and it allows us to estimate, among other things, number of active pumps, protons moved, and the influence of particular mutations implicated in disease.

Changes in Intracellular Na+ following Enhancement of Late Na+ Current in Virtual Human Ventricular Myocytes

The slowly inactivating or late Na+ current, INa-L, can contribute to the initiation of both atrial and ventricular rhythm disturbances in the human heart. However, the cellular and molecular mechanisms that underlie these pro-arrhythmic influences are not fully understood. At present, the major working hypothesis is that the Na+ influx corresponding to INa-L significantly increases intracellular Na+, [Na+]i; and the resulting reduction in the electrochemical driving force for Na+ reduces and (may reverse) Na+/Ca2+ exchange. These changes increase intracellular Ca2+, [Ca2+]i; which may further enhance INa-L due to calmodulin-dependent phosphorylation of the Na+ channels. This paper is based on mathematical simulations using the O'Hara et al (2011) model of baseline or healthy human ventricular action potential waveforms(s) and its [Ca2+]i homeostasis mechanisms. Somewhat surprisingly, our results reveal only very small changes (≤ 1.5 mM) in [Na+]i even when INa-L is increased 5-fold and steady-state stimulation rate is approximately 2 times the normal human heart rate (i.e. 2 Hz). Previous work done using well-established models of the rabbit and human ventricular action potential in heart failure settings also reported little or no change in [Na+]i when INa-L was increased. Based on our simulations, the major short-term effect of markedly augmenting INa-L is a significant prolongation of the action potential and an associated increase in the likelihood of reactivation of the L-type Ca2+ current, ICa-L. Furthermore, this action potential prolongation does not contribute to [Na+]i increase.

Regulation of cardiac cellular bioenergetics: mechanisms and consequences

The regulation of cardiac cellular bioenergetics is critical for maintaining normal cell function, yet the nature of this regulation is not fully understood. Different mechanisms have been proposed to explain how mitochondrial ATP production is regulated to match changing cellular energy demand while metabolite concentrations are maintained. We have developed an integrated mathematical model of cardiac cellular bioenergetics, electrophysiology, and mechanics to test whether stimulation of the dehydrogenase flux by Ca²⁺ or Pi, or stimulation of complex III by Pi can increase the rate of mitochondrial ATP production above that determined by substrate availability (ADP and Pi). Using the model, we show that, under physiological conditions the rate of mitochondrial ATP production can match varying demand through substrate availability alone; that ATP production rate is not limited by the supply of reducing equivalents in the form of NADH, as a result of Ca²⁺ or Pi activation of the dehydrogenases; and that ATP production rate is sensitive to feedback activation of complex III by Pi. We then investigate the mechanistic implications on cytosolic ion homeostasis and force production by simulating the concentrations of cytosolic Ca²⁺, Na⁺ and K⁺, and activity of the key ATPases, SERCA pump, Na⁺/K⁺ pump and actin-myosin ATPase, in response to increasing cellular energy demand. We find that feedback regulation of mitochondrial complex III by Pi improves the coupling between energy demand and mitochondrial ATP production and stabilizes cytosolic ADP and Pi concentrations. This subsequently leads to stabilized cytosolic ionic concentrations and consequentially reduced energetic cost from cellular ATPases.

A spatial model of fluid recycling in the airways of the lung

The genetic disease cystic fibrosis (CF) is a mutation in the cystic fibrosis transmembrane conductance regulator (CFTR) gene, and results in viscous mucus and impaired mucociliary clearance leading to chronic recurring pulmonary infections. Although extensive experimental research has been conducted over the last few decades, CF lung pathophysiology remains controversial. There are two competing explanations for the observed depletion of periciliary liquid (PCL) in CF lungs. The low volume hypothesis assumes fluid hyperabsorption through surface epithelia due to an over-active epithelial Na(+) channel (ENaC), and the low secretion hypothesis assumes inspissated mucins secreted from glands due to lack of serous fluid secreted from gland acini. We present a spatial mathematical model that reflects in vivo fluid recycling via submucosal gland (SMG) secretion, and absorption through surface epithelia. We then test the model in CF conditions by increasing ENaC open probability and decreasing SMG flux while simultaneously reducing CFTR open probability. Increasing ENaC activity only results in increased fluid absorption across surface epithelia, as seen in in vitro experiments. However, combining potential CF mechanisms results in markedly less fluid absorbed while providing the largest reduction in PCL volume, suggesting that a compromise in gland fluid secretion dominates over increased ENaC activity to decrease the amount of fluid transported transcellularly in CF lungs in vivo. Model results also indicate that a spatial model is necessary for an accurate calculation of total fluid transport, as the effects of spatial gradients can be severe, particularly in close proximity to the SMGs.

β-adrenergic effects on cardiac myofilaments and contraction in an integrated rabbit ventricular myocyte model

A five-state model of myofilament contraction was integrated into a well-established rabbit ventricular myocyte model of ion channels, Ca(2+) transporters and kinase signaling to analyze the relative contribution of different phosphorylation targets to the overall mechanical response driven by β-adrenergic stimulation (β-AS). β-AS effect on sarcoplasmic reticulum Ca(2+) handling, Ca(2+), K(+) and Cl(-) currents, and Na(+)/K(+)-ATPase properties was included based on experimental data. The inotropic effect on the myofilaments was represented as reduced myofilament Ca(2+) sensitivity (XBCa) and titin stiffness, and increased cross-bridge (XB) cycling rate (XBcy). Assuming independent roles of XBCa and XBcy, the model reproduced experimental β-AS responses on action potentials and Ca(2+) transient amplitude and kinetics. It also replicated the behavior of force-Ca(2+), release-restretch, length-step, stiffness-frequency and force-velocity relationships, and increased force and shortening in isometric and isotonic twitch contractions. The β-AS effect was then switched off from individual targets to analyze their relative impact on contractility. Preventing β-AS effects on L-type Ca(2+) channels or phospholamban limited Ca(2+) transients and contractile responses in parallel, while blocking phospholemman and K(+) channel (IKs) effects enhanced Ca(2+) and inotropy. Removal of β-AS effects from XBCa enhanced contractile force while decreasing peak Ca(2+) (due to greater Ca(2+) buffering), but had less effect on shortening. Conversely, preventing β-AS effects on XBcy preserved Ca(2+) transient effects, but blunted inotropy (both isometric force and especially shortening). Removal of titin effects had little impact on contraction. Finally, exclusion of β-AS from XBCa and XBcy while preserving effects on other targets resulted in preserved peak isometric force response (with slower kinetics) but nearly abolished enhanced shortening. β-AS effects on XBCa and XBcy have greater impact on isometric and isotonic contraction, respectively.

Dietary supplementation with either saturated or unsaturated fatty acids does not affect the mechanoenergetics of the isolated rat heart

It is generally recognized that increased consumption of polyunsaturated fatty acids, fish oil (FO) in particular, is beneficial to cardiac and cardiovascular health, whereas equivalent consumption of saturated fats is deleterious. In this study, we explore this divergence, adopting a limited purview: The effect of dietary fatty acids on the mechanoenergetics of the isolated heart per se. Mechanical indices of interest include left‐ventricular (LV) developed pressure, stroke work, cardiac output, coronary perfusion, and LV power. The principal energetic index is whole‐heart oxygen consumption, which we subdivide into its active and basal moieties. The primary mechanoenergetic index of interest is cardiac efficiency, the ratio of work performance to metabolic energy expenditure. Wistar rats were divided into three Diet groups and fed, ad libitum, reference (REF), fish oil‐supplemented (FO), or saturated fatty acid‐supplemented (SFA) food for 6 weeks. At the end of the dietary period, hearts were excised, mounted in a working‐heart rig, and their mechanoenergetic performance quantified over a range of preloads and afterloads. Analyses of Variance revealed no difference in any of the individual mechanoenergetic indices among the three Diet groups. In particular, we found no effect of prior dietary supplementation with either saturated or unsaturated fatty acids on the global efficiency of the heart.

Literature reports have claimed profound effects of dietary supplementation with either saturated or polyunsaturated fatty acids on the contractile efficiency of the heart – diminishing and enhancing efficiency, respectively. We have mimicked the experimental protocols used in those reports and find no effect of diet on any index of cardiac mechanoenergetics, including efficiency.

Role of CaMKII in post acidosis arrhythmias: a simulation study using a human myocyte model

Postacidotic arrhythmias have been associated to increased sarcoplasmic reticulum (SR) Ca(2+) load and Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) activation. However, the molecular mechanisms underlying these arrhythmias are still unclear. To better understand this process, acidosis produced by CO2 increase from 5% to 30%, resulting in intracellular pH (pHi) change from 7.15 to 6.7, was incorporated into a myocyte model of excitation-contraction coupling and contractility, including acidotic inhibition of L-type Ca(2+) channel (I(CaL)), Na(+)-Ca(2+) exchanger, Ca(2+) release through the SR ryanodine receptor (RyR2) (I(rel)), Ca(2+) reuptake by the SR Ca(2+) ATPase2a (I(up)), Na(+)-K(+) pump, K(+) efflux through the inward rectifier K(+) channel and the transient outward K(+) flow (I(to)) together with increased activity of the Na(+)-H(+) exchanger (I(NHE)). Simulated CaMKII regulation affecting I(rel), I(up), I(CaL), I(NHE) and I(to) was introduced in the model to partially compensate the acidosis outcome. Late Na(+) current increase by CaMKII was also incorporated. Using this scheme and assuming that diastolic Ca(2+) leak through the RyR2 was modulated by the resting state of this channel and the difference between SR and dyadic cleft [Ca(2+)], postacidotic delayed after depolarizations (DADs) were triggered upon returning to normal pHi after 6 min acidosis. The model showed that DADs depend on SR Ca(2+) load and on increased Ca(2+) leak through RyR2. This postacidotic arrhythmogenic pattern relies mainly on CaMKII effect on I(CaL) and I(up), since its individual elimination produced the highest DAD reduction. The model further revealed that during the return to normal pHi, DADs are fully determined by SR Ca(2+) load at the end of acidosis. Thereafter, DADs are maintained by SR Ca(2+) reloading by Ca(2+) influx through the reverse NCX mode during the time period in which [Na(+)]i is elevated.

Modulation of ventricular transient outward K⁺ current by acidosis and its effects on excitation-contraction coupling

The contribution of transient outward current (Ito) to changes in ventricular action potential (AP) repolarization induced by acidosis is unresolved, as is the indirect effect of these changes on calcium handling. To address this issue we measured intracellular pH (pHi), Ito, L-type calcium current (ICa,L), and calcium transients (CaTs) in rabbit ventricular myocytes. Intracellular acidosis [pHi 6.75 with extracellular pH (pHo) 7.4] reduced Ito by ~50% in myocytes with both high (epicardial) and low (papillary muscle) Ito densities, with little effect on steady-state inactivation and activation. Of the two candidate α-subunits underlying Ito, human (h)Kv4.3 and hKv1.4, only hKv4.3 current was reduced by intracellular acidosis. Extracellular acidosis (pHo 6.5) shifted Ito inactivation toward less negative potentials but had negligible effect on peak current at +60 mV when initiated from -80 mV. The effects of low pHi-induced inhibition of Ito on AP repolarization were much greater in epicardial than papillary muscle myocytes and included slowing of phase 1, attenuation of the notch, and elevation of the plateau. Low pHi increased AP duration in both cell types, with the greatest lengthening occurring in epicardial myocytes. The changes in epicardial AP repolarization induced by intracellular acidosis reduced peak ICa,L, increased net calcium influx via ICa,L, and increased CaT amplitude. In summary, in contrast to low pHo, intracellular acidosis has a marked inhibitory effect on ventricular Ito, perhaps mediated by Kv4.3. By altering the trajectory of the AP repolarization, low pHi has a significant indirect effect on calcium handling, especially evident in epicardial cells.

Regulation of ion gradients across myocardial ischemic border zones: a biophysical modelling analysis

The myocardial ischemic border zone is associated with the initiation and sustenance of arrhythmias. The profile of ionic concentrations across the border zone play a significant role in determining cellular electrophysiology and conductivity, yet their spatial-temporal evolution and regulation are not well understood. To investigate the changes in ion concentrations that regulate cellular electrophysiology, a mathematical model of ion movement in the intra and extracellular space in the presence of ionic, potential and material property heterogeneities was developed. The model simulates the spatial and temporal evolution of concentrations of potassium, sodium, chloride, calcium, hydrogen and bicarbonate ions and carbon dioxide across an ischemic border zone. Ischemia was simulated by sodium-potassium pump inhibition, potassium channel activation and respiratory and metabolic acidosis. The model predicted significant disparities in the width of the border zone for each ionic species, with intracellular sodium and extracellular potassium having discordant gradients, facilitating multiple gradients in cellular properties across the border zone. Extracellular potassium was found to have the largest border zone and this was attributed to the voltage dependence of the potassium channels. The model also predicted the efflux of [Formula: see text] from the ischemic region due to electrogenic drift and diffusion within the intra and extracellular space, respectively, which contributed to [Formula: see text] depletion in the ischemic region.

The relative influences of phosphometabolites and pH on action potential morphology during myocardial reperfusion: a simulation study

Myocardial ischemia-reperfusion (IR) injury represents a constellation of pathological processes that occur when ischemic myocardium experiences a restoration of perfusion. Reentrant arrhythmias, which represent a particularly lethal manifestation of IR injury, can result when ischemic tissue exhibits decreased excitability and/or changes of action potential duration (APD), conditions that precipitate unidirectional conduction block. Many of the cellular components that are involved with IR injury are modulated by pH and/or phosphometabolites such as ATP and phosphocreatine (PCr), all of which can be manipulated in vivo and potentially in the clinical setting. Using a mathematical model of the cardiomyocyte that we previously developed to study ischemia and reperfusion, we performed a series of simulations with the aim of determining whether pH- or phosphometabolite-related processes play a more significant role in generating changes in excitability and action potential morphology that are associated with the development of reentry. In our simulations, persistent shortening of APD, action potential amplitude (APA), and depolarization of the resting membrane potential were more severe when ATP and PCr availability were suppressed during reperfusion than when extracellular pH recovery was inhibited. Reduced phosphometabolite availability and pH recovery affected multiple ion channels and exchangers. Some of these effects were the result of direct modulation by phosphometabolites and/or acidosis, while others resulted from elevated sodium and calcium loads during reperfusion. In addition, increasing ATP and PCr availability during reperfusion was more beneficial in terms of increasing APD and APA than was increasing the amount of pH recovery. Together, these results suggest that therapies directed at increasing ATP and/or PCr availability during reperfusion may be more beneficial than perturbing pH recovery with regard to mitigating action potential changes that increase the likelihood of reentrant arrhythmias.

Computational approaches to understand cardiac electrophysiology and arrhythmias

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

Exceptional cardiac anoxia tolerance in tilapia (Oreochromis hybrid)

Anoxic survival requires the matching of cardiac ATP supply (i.e. maximum glycolytic potential, MGP) and demand (i.e. cardiac power output, PO). We examined the idea that the previously observed in vivo downregulation of cardiac function during exposure to severe hypoxia in tilapia (Oreochromis hybrid) represents a physiological strategy to reduce routine PO to within the heart's MGP. The MGP of the ectothermic vertebrate heart has previously been suggested to be ∼70 nmol ATP s(-1) g(-1), sustaining a PO of ∼0.7 mW g(-1) at 15°C. We developed an in situ perfused heart preparation for tilapia (Oreochromis hybrid) and characterized the routine and maximum cardiac performance under both normoxic (>20 kPa O(2)) and severely hypoxic perfusion conditions (<0.20 kPa O(2)) at pH 7.75 and 22°C. The additive effects of acidosis (pH 7.25) and chemical anoxia (1 mmol l(-1) NaCN) on cardiac performance in severe hypoxia were also examined. Under normoxic conditions, cardiac performance and myocardial oxygen consumption rate were comparable to those of other teleosts. The tilapia heart maintained a routine normoxic cardiac output (Q) and PO under all hypoxic conditions, a result that contrasts with the hypoxic cardiac downregulation previously observed in vivo under less severe conditions. Thus, we conclude that the in vivo downregulation of routine cardiac performance in hypoxia is not needed in tilapia to balance cardiac energy supply and demand. Indeed, the MGP of the tilapia heart proved to be quite exceptional. Measurements of myocardial lactate efflux during severe hypoxia were used to calculate the MGP of the tilapia heart. The MGP was estimated to be 172 nmol ATP s(-1) g(-1) at 22°C, and allowed the heart to generate a PO(max) of at least ∼3.1 mW g(-1), which is only 30% lower than the PO(max) observed with normoxia. Even with this MGP, the additional challenge of acidosis during severe hypoxia decreased maximum ATP turnover rate and PO(max) by 30% compared with severe hypoxia alone, suggesting that there are probably direct effects of acidosis on cardiac contractility. We conclude that the high maximum glycolytic ATP turnover rate and levels of PO, which exceed those measured in other ectothermic vertebrate hearts, probably convey a previously unreported anoxia tolerance of the tilapia heart, but a tolerance that may be tempered in vivo by the accumulation of acidotic waste during anoxia.

NHE inhibition does not improve Na(+) or Ca(2+) overload during reperfusion: using modeling to illuminate the mechanisms underlying a therapeutic failure

Reperfusion injury results from pathologies of cardiac myocyte physiology that develop when previously ischemic myocardium experiences a restoration of normal perfusion. Events in the development of reperfusion injury begin with the restoration of a proton gradient upon reperfusion, which then allows the sodium-proton exchanger (NHE) to increase flux, removing protons from the intracellular space while importing sodium. The resulting sodium overload drives increased reverse-mode sodium-calcium exchanger (NCX) activity, creating a secondary calcium overload that has pathologic consequences. One of the attempts to reduce reperfusion-related damage, NHE inhibition, has shown little clinical benefit, and only when NHE inhibitors are given prior to reperfusion. In an effort to further understand why NHE inhibitors have been largely unsuccessful, we employed a new mathematical cardiomyocyte model that we developed for the study of ischemia and reperfusion. Using this model, we simulated 20 minutes of ischemia and 10 minutes of reperfusion, while also simulating NHE inhibition by reducing NHE flux in our model by varying amounts and at different time points. In our simulations, when NHE inhibition is applied at the onset of reperfusion, increasing the degree of inhibition increases the peak sodium and calcium concentrations, as well as reducing intracellular pH recovery. When inhibition was instituted at earlier time points, some modest improvements were seen, largely due to reduced sodium concentrations prior to reperfusion. Analysis of all sodium flux pathways suggests that the sodium-potassium pump (NaK) plays the largest role in exacerbated sodium overload during reperfusion, and that reduced NaK flux is largely the result of impaired pH recovery. While NHE inhibition does indeed reduce sodium influx through that exchanger, the resulting prolongation of intracellular acidosis paradoxically increases sodium overload, largely mediated by impaired NaK function.

Myocardial ischemia, commonly observed when arteries supplying the heart become occluded, results when cardiac tissue receives inadequate blood perfusion. In order to minimize the amount of cardiac damage, ischemic tissue must be reperfused. However, reperfusion can result in deleterious effects that leave the heart muscle sicker than if the ischemia had been allowed to continue. Examples of these reperfusion injuries include lethal arrhythmias and an increased region of cell death. Some of the early events that result in reperfusion injury include changes in pH and an overload of sodium inside the cell. During reperfusion, the sodium-proton exchanger (NHE) removes protons from the cell in an effort to restore normal pH, in turn importing sodium ions. Many strategies have been attempted to prevent reperfusion injury, including inhibition of the NHE, with little clinical effect. Using a mathematical model that we developed to study ischemia and reperfusion in cardiac cells, we found that NHE inhibition produces more severe sodium overload, largely due to adverse consequences of the delayed pH recovery produced by NHE inhibition. These results suggest that NHE inhibition alone may not be a viable strategy, and that therapies which prolong intracellular acidosis may be problematic.

Mitochondrial energetics, pH regulation, and ion dynamics: a computational-experimental approach

We developed a computational model of mitochondrial energetics that includes Ca(2+), proton, Na(+), and phosphate dynamics. The model accounts for distinct respiratory fluxes from substrates of complex I and complex II, pH effects on equilibrium constants and enzyme kinetics, and the acid-base equilibrium distributions of energy intermediaries. We experimentally determined NADH and ΔΨ(m) in guinea pig mitochondria during transitions from de-energized to energized, or during state 2/4 to state 3 respiration, or into hypoxia and uncoupling, and compared the results with those obtained in model simulations. The model quantitatively reproduces the experimentally observed magnitude of ΔΨ(m), the range of NADH levels, respiratory fluxes, and respiratory control ratio upon transitions elicited by sequential additions of substrate and ADP. Simulation results are also able to mimic the change in ΔΨ(m) upon addition of phosphate to state 4 mitochondria, leading to matrix acidification and ΔΨ(m) polarization. The steady-state behavior of the integrated mitochondrial model qualitatively simulates the dependence of respiration on the proton motive force, and the expected flux-force relationships existing between respiratory and ATP synthesis fluxes versus redox and phosphorylation potentials. This upgraded mitochondrial model provides what we believe are new opportunities for simulating mitochondrial physiological behavior during dysfunctional states involving changes in pH and ion dynamics.

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

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

Integrative modeling of the cardiac ventricular myocyte

Cardiac electrophysiology is a discipline with a rich 50-year history of experimental research coupled with integrative modeling which has enabled us to achieve a quantitative understanding of the relationships between molecular function and the integrated behavior of the cardiac myocyte in health and disease. In this paper, we review the development of integrative computational models of the cardiac myocyte. We begin with a historical overview of key cardiac cell models that helped shape the field. We then narrow our focus to models of the cardiac ventricular myocyte and describe these models in the context of their subcellular functional systems including dynamic models of voltage-gated ion channels, mitochondrial energy production, ATP-dependent and electrogenic membrane transporters, intracellular Ca dynamics, mechanical contraction, and regulatory signal transduction pathways. We describe key advances and limitations of the models as well as point to new directions for future modeling research. WIREs Syst Biol Med 2011 3 392-413 DOI: 10.1002/wsbm.122

A mathematical model of the murine ventricular myocyte: a data-driven biophysically based approach applied to mice overexpressing the canine NCX isoform

Mathematical modeling of Ca(2+) dynamics in the heart has the potential to provide an integrated understanding of Ca(2+)-handling mechanisms. However, many previous published models used heterogeneous experimental data sources from a variety of animals and temperatures to characterize model parameters and motivate model equations. This methodology limits the direct comparison of these models with any particular experimental data set. To directly address this issue, in this study, we present a biophysically based model of Ca(2+) dynamics directly fitted to experimental data collected in left ventricular myocytes isolated from the C57BL/6 mouse, the most commonly used genetic background for genetically modified mice in studies of heart diseases. This Ca(2+) dynamics model was then integrated into an existing mouse cardiac electrophysiology model, which was reparameterized using experimental data recorded at consistent and physiological temperatures. The model was validated against the experimentally observed frequency response of Ca(2+) dynamics, action potential shape, dependence of action potential duration on cycle length, and electrical restitution. Using this framework, the implications of cardiac Na(+)/Ca(2+) exchanger (NCX) overexpression in transgenic mice were investigated. These simulations showed that heterozygous overexpression of the canine cardiac NCX increases intracellular Ca(2+) concentration transient magnitude and sarcoplasmic reticulum Ca(2+) loading, in agreement with experimental observations, whereas acute overexpression of the murine cardiac NCX results in a significant loss of Ca(2+) from the cell and, hence, depressed sarcoplasmic reticulum Ca(2+) load and intracellular Ca(2+) concentration transient magnitude. From this analysis, we conclude that these differences are primarily due to the presence of allosteric regulation in the canine cardiac NCX, which has not been observed experimentally in the wild-type mouse heart.

A metabolite-sensitive, thermodynamically constrained model of cardiac cross-bridge cycling: implications for force development during ischemia

We present a metabolically regulated model of cardiac active force generation with which we investigate the effects of ischemia on maximum force production. Our model, based on a model of cross-bridge kinetics that was developed by others, reproduces many of the observed effects of MgATP, MgADP, Pi, and H(+) on force development while retaining the force/length/Ca(2+) properties of the original model. We introduce three new parameters to account for the competitive binding of H(+) to the Ca(2+) binding site on troponin C and the binding of MgADP within the cross-bridge cycle. These parameters, along with the Pi and H(+) regulatory steps within the cross-bridge cycle, were constrained using data from the literature and validated using a range of metabolic and sinusoidal length perturbation protocols. The placement of the MgADP binding step between two strongly-bound and force-generating states leads to the emergence of an unexpected effect on the force-MgADP curve, where the trend of the relationship (positive or negative) depends on the concentrations of the other metabolites and [H(+)]. The model is used to investigate the sensitivity of maximum force production to changes in metabolite concentrations during the development of ischemia.

A model of Na+/H+ exchanger and its central role in regulation of pH and Na+ in cardiac myocytes

A new kinetic model of the Na(+)/H(+) exchanger (NHE) was developed by fitting a variety of major experimental findings, such as ion-dependencies, forward/reverse mode, and the turnover rate. The role of NHE in ion homeostasis was examined by implementing the NHE model in a minimum cell model including intracellular pH buffer, Na(+)/K(+) pump, background H(+), and Na(+) fluxes. This minimum cell model was validated by reconstructing recovery of pH(i) from acidification, accompanying transient increase in [Na(+)](i) due to NHE activity. Based on this cell model, steady-state relationships among pH(i), [Na(+)](I), and [Ca(2+)](i) were quantitatively determined, and thereby the critical level of acidosis for cell survival was predicted. The acidification reported during partial blockade of the Na(+)/K(+) pump was not attributed to a dissipation of the Na(+) gradient across the membrane, but to an increase in indirect H(+) production. This NHE model, though not adapted to the dimeric behavioral aspects of NHE, can provide a strong clue to quantitative prediction of degree of acidification and accompanying disturbance of ion homeostasis under various pathophysiological conditions.

Modeling the cardiac Na(+)/H (+) exchanger based on major experimental findings

Na(+)-H(+) exchanger (NHE) is the main acid extruder in cardiac myocytes. We review the experimental findings of ion-dependency of NHE activity, and the mathematical modeling developed so far. In spite of extensive investigation, many unsolved questions still remain. We consider that the precise description of NHE activity with mathematical models elucidates the roles of NHE in maintaining ionic homeostasis, especially under pathophysiological conditions.

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.

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.

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.

Single histidine button in cardiac troponin I sustains heart performance in response to severe hypercapnic respiratory acidosis in vivo

Intracellular acidosis is a profound negative regulator of myocardial performance. We hypothesized that titrating myofilament calcium sensitivity by a single histidine substituted cardiac troponin I (A164H) would protect the whole animal physiological response to acidosis in vivo. To experimentally induce severe hypercapnic acidosis, mice were exposed to a 40% CO(2) challenge. By echocardiography, it was found that systolic function and ventricular geometry were maintained in cTnI A164H transgenic (Tg) mice. By contrast, non-Tg (Ntg) littermates experienced rapid and marked cardiac decompensation during this same challenge. For detailed hemodymanic assessment, Millar pressure-conductance catheterization was performed while animals were treated with a beta-blocker, esmolol, during a severe hypercapnic acidosis challenge. Survival and load-independent measures of contractility were significantly greater in Tg vs. Ntg mice. This assay showed that Ntg mice had 100% mortality within 5 min of acidosis. By contrast, systolic and diastolic function were protected in Tg mice during acidosis, and they had 100% survival. This study shows that, independent of any beta-adrenergic compensation, myofilament-based molecular manipulation of inotropy by histidine-modified troponin I maintains cardiac inotropic and lusitropic performance and markedly improves survival during severe acidosis in vivo.

Mechanisms of transmurally varying myocyte electromechanics in an integrated computational model

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

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.

The balance between inactivation and activation of the Na+-K+ pump underlies the triphasic accumulation of extracellular K+ during myocardial ischemia

Ischemia-induced hyperkalemia (accumulation of extracellular K(+)) predisposes the heart to the development of lethal reentrant ventricular arrhythmias. This phenomenon exhibits a triphasic time course and is thought to be mediated by a combination of three mechanisms: 1) increased cellular K(+) efflux, 2) decreased cellular K(+) influx, and 3) shrinkage of the extracellular space. These ischemia-induced electrophysiological changes are driven by an impaired cellular metabolism. However, the relative contributions of these mechanisms, as well as the origin of the triphasic profile, have proven to be difficult to determine experimentally. In this study, the changes in metabolite concentrations that arise during 15 min of zero-flow global ischemia were incorporated into a dynamic model of cellular electrophysiology, which was extended to include a metabolically sensitive description of the Na(+)-K(+) pump and ATP-sensitive K(+) channel, in addition to cell volume regulation. The coupling of altered K(+) fluxes and cell volume regulation enables an integrative simulation of ischemic hyperkalemia. These simulations were able to quantitatively reproduce experimental measurements of the accumulation of extracellular K(+) during 15 min of simulated ischemia, both with respect to the degree of K(+) loss as well as the triphasic time course. Analysis of the model indicates that the inhibition of the Na(+)-K(+) pump is the dominant factor underlying this hyperkalemic behavior, accounting for approximately 85% of the observed extracellular K(+) accumulation. It was found that the balance between activation and inhibition of the Na(+)-K(+) pump, affected by the changing metabolite and ion concentrations (in particular, [ADP]), give rise to the triphasic profile associated with ischemic hyperkalemia.

Modeling hypertrophic IP3 transients in the cardiac myocyte

Cardiac hypertrophy is a known risk factor for heart disease, and at the cellular level is caused by a complex interaction of signal transduction pathways. The IP3-calcineurin pathway plays an important role in stimulating the transcription factor NFAT which binds to DNA cooperatively with other hypertrophic transcription factors. Using available kinetic data, we construct a mathematical model of the IP3 signal production system after stimulation by a hypertrophic alpha-adrenergic agonist (endothelin-1) in the mouse atrial cardiac myocyte. We use a global sensitivity analysis to identify key controlling parameters with respect to the resultant IP3 transient, including the phosphorylation of cell-membrane receptors, the ligand strength and binding kinetics to precoupled (with G(alpha)GDP) receptor, and the kinetics associated with precoupling the receptors. We show that the kinetics associated with the receptor system contribute to the behavior of the system to a great extent, with precoupled receptors driving the response to extracellular ligand. Finally, by reparameterizing for a second hypertrophic alpha-adrenergic agonist, angiotensin-II, we show that differences in key receptor kinetic and membrane density parameters are sufficient to explain different observed IP3 transients in essentially the same pathway.

A mathematical model of the slow force response to stretch in rat ventricular myocytes

We developed a model of the rat ventricular myocyte at room temperature to predict the relative effects of different mechanisms on the cause of the slow increase in force in response to a step change in muscle length. We performed simulations in the presence of stretch-dependent increases in flux through the Na(+)-H(+) exchanger (NHE) and Cl(-)-HCO(3)(-) exchanger (AE), stretch-activated channels (SAC), and the stretch-dependent nitric oxide (NO) induced increased open probability of the ryanodine receptors to estimate the capacity of each mechanism to produce the slow force response (SFR). Inclusion of stretch-dependent NHE & AE, SACs, and stretch-dependent NO effects caused an increase in tension following 15 min of stretch of 0.87%, 32%, and 0%, respectively. Comparing [Ca(2+)](i) dynamics before and after stretch in the presence of combinations of the three stretch-dependent elements, which produced significant SFR values (>20%), showed that the inclusion of stretch-dependent NO effects produced [Ca(2+)](i) transients, which were not consistent with experimental results. Further simulations showed that in the presence of SACs and the absence of stretch-dependent NHE & AE inhibition of NHE attenuated the SFR, such that reduced SFR in the presence of NHE blockers does not indicate a stretch dependence of NHE. Rather, a functioning NHE is responsible for a portion of the SFR. Based on our simulations we estimate that in rat cardiac myocytes at room temperature SACs play a significant role in producing the SFR, potentially in the presence of stretch-dependent NHE & AE and that NO effects, if any, must involve more mechanisms than just increasing the open probability of ryanodine receptors.

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

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