Model study of ATP and ADP buffering, transport of Ca(2+) and Mg(2+), and regulation of ion pumps in ventricular myocyte

Nampt controls skeletal muscle development by maintaining Ca2+ homeostasis and mitochondrial integrity

Objective

NAD⁺ is a co-factor and substrate for enzymes maintaining energy homeostasis. Nicotinamide phosphoribosyltransferase (NAMPT) controls NAD⁺ synthesis, and in skeletal muscle, NAD⁺ is essential for muscle integrity. However, the underlying molecular mechanisms by which NAD⁺ synthesis affects muscle health remain poorly understood. Thus, the objective of the current study was to delineate the role of NAMPT-mediated NAD⁺ biosynthesis in skeletal muscle development and function.

Methods

To determine the role of Nampt in muscle development and function, we generated skeletal muscle-specific Nampt KO (SMNKO) mice. We performed a comprehensive phenotypic characterization of the SMNKO mice, including metabolic measurements, histological examinations, and RNA sequencing analyses of skeletal muscle from SMNKO mice and WT littermates.

Results

SMNKO mice were smaller, with phenotypic changes in skeletal muscle, including reduced fiber area and increased number of centralized nuclei. The majority of SMNKO mice died prematurely. Transcriptomic analysis identified that the gene encoding the mitochondrial permeability transition pore (mPTP) regulator Cyclophilin D (Ppif) was upregulated in skeletal muscle of SMNKO mice from 2 weeks of age, with associated increased sensitivity of mitochondria to the Ca²⁺-stimulated mPTP opening. Treatment of SMNKO mice with the Cyclophilin D inhibitor, Cyclosporine A, increased membrane integrity, decreased the number of centralized nuclei, and increased survival.

Conclusions

Our study demonstrates that NAMPT is crucial for maintaining cellular Ca²⁺ homeostasis and skeletal muscle development, which is vital for juvenile survival.

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NAD⁺ salvage capacity is important for skeletal muscle development and survival.

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Skeletal muscle-specific Nampt knockout mice exhibit a dystrophy-like phenotype.

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Nampt deletion alters Ca²⁺ homeostasis and impairs mitochondrial function.

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Low NAD⁺ levels signals mitochondrial permeability transition pore opening.

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Cyclosporin A treatment improves sarcolemma integrity and increases survival rate.

Modulations of Cardiac Functions and Pathogenesis by Reactive Oxygen Species and Natural Antioxidants

Homeostasis in the level of reactive oxygen species (ROS) in cardiac myocytes plays a critical role in regulating their physiological functions. Disturbance of balance between generation and removal of ROS is a major cause of cardiac myocyte remodeling, dysfunction, and failure. Cardiac myocytes possess several ROS-producing pathways, such as mitochondrial electron transport chain, NADPH oxidases, and nitric oxide synthases, and have endogenous antioxidation mechanisms. Cardiac Ca²⁺-signaling toolkit proteins, as well as mitochondrial functions, are largely modulated by ROS under physiological and pathological conditions, thereby producing alterations in contraction, membrane conductivity, cell metabolism and cell growth and death. Mechanical stresses under hypertension, post-myocardial infarction, heart failure, and valve diseases are the main causes for stress-induced cardiac remodeling and functional failure, which are associated with ROS-induced pathogenesis. Experimental evidence demonstrates that many cardioprotective natural antioxidants, enriched in foods or herbs, exert beneficial effects on cardiac functions (Ca²⁺ signal, contractility and rhythm), myocytes remodeling, inflammation and death in pathological hearts. The review may provide knowledge and insight into the modulation of cardiac pathogenesis by ROS and natural antioxidants.

Plasticity in striatal dopamine release is governed by release-independent depression and the dopamine transporter

Mesostriatal dopaminergic neurons possess extensively branched axonal arbours. Whether action potentials are converted to dopamine output in the striatum will be influenced dynamically and critically by axonal properties and mechanisms that are poorly understood. Here, we address the roles for mechanisms governing release probability and axonal activity in determining short‐term plasticity of dopamine release, using fast‐scan cyclic voltammetry in the ex vivo mouse striatum. We show that brief short‐term facilitation and longer short term depression are only weakly dependent on the level of initial release, i.e. are release insensitive. Rather, short-term plasticity is strongly determined by mechanisms which govern axonal activation, including K⁺‐gated excitability and the dopamine transporter, particularly in the dorsal striatum. We identify the dopamine transporter as a master regulator of dopamine short‐term plasticity, governing the balance between release‐dependent and independent mechanisms that also show region‐specific gating.

Dopamine release in the striatum has important roles in action selection and in disorders such as Parkinson’s disease. The authors here show that short-term plasticity of dopamine release is strongly determined by axonal activation and dopamine transporters.

Cyclosporin A Increases Mitochondrial Buffering of Calcium: An Additional Mechanism in Delaying Mitochondrial Permeability Transition Pore Opening

Regulation of mitochondrial free Ca²⁺ is critically important for cellular homeostasis. An increase in mitochondrial matrix free Ca²⁺ concentration ([Ca²⁺]_m) predisposes mitochondria to opening of the permeability transition pore (mPTP). Opening of the pore can be delayed by cyclosporin A (CsA), possibly by inhibiting cyclophilin D (Cyp D), a key regulator of mPTP. Here, we report on a novel mechanism by which CsA delays mPTP opening by enhanced sequestration of matrix free Ca²⁺. Cardiac-isolated mitochondria were challenged with repetitive CaCl₂ boluses under Na⁺-free buffer conditions with and without CsA. CsA significantly delayed mPTP opening primarily by promoting matrix Ca²⁺ sequestration, leading to sustained basal [Ca²⁺]_m levels for an extended period. The preservation of basal [Ca²⁺]_m during the CaCl₂ pulse challenge was associated with normalized NADH, matrix pH (pH_m), and mitochondrial membrane potential (ΔΨ_m). Notably, we found that in PO₄³⁻ (P_i)-free buffer condition, the CsA-mediated buffering of [Ca²⁺]_m was abrogated, and mitochondrial bioenergetics variables were concurrently compromised. In the presence of CsA, addition of P_i just before pore opening in the P_i-depleted condition reinstated the Ca²⁺ buffering system and rescued mitochondria from mPTP opening. This study shows that CsA promotes P_i-dependent mitochondrial Ca²⁺ sequestration to delay mPTP opening and, concomitantly, maintains mitochondrial function.

Nucleotide Binding in an Engineered Recombinant Ca2+-ATPase N-Domain

A recombinant Ca²⁺-ATPase nucleotide binding domain (N-domain) harboring the mutations Trp552Leu and Tyr587Trp was expressed and purified. Chemical modification by N-bromosuccinimide and fluorescence quenching by acrylamide showed that the displaced Trp residue was located at the N-domain surface and slightly exposed to solvent. Guanidine hydrochloride-mediated N-domain unfolding showed the low structural stability of the α6-loop-α7 motif (the new Trp location) located near the nucleotide binding site. The binding of nucleotides (free and in complex with Mg²⁺) to the engineered N-domain led to significant intrinsic fluorescence quenching (ΔF_max ∼ 30%) displaying a saturable hyperbolic pattern; the calculated affinities decreased in the following order: ATP > ADP = ADP-Mg²⁺ > ATP-Mg²⁺. Interestingly, it was found that Ca²⁺ binds to the N-domain as monitored by intrinsic fluorescence quenching (ΔF_max ∼ 12%) with a dissociation constant (K_d) of 50 μM. Notably, the presence of Ca²⁺ (200 μM) increased the ATP and ADP affinity but favored the binding of ATP over that of ADP. In addition, binding of ATP to the N-domain generated slight changes in secondary structure as evidenced by circular dichroism spectral changes. Molecular docking of ATP to the N-domain provided different binding modes that potentially might be the binding stages prior to γ-phosphate transfer. Finally, the nucleotide binding site was studied by fluorescein isothiocyanate labeling and molecular docking. The N-domain of Ca²⁺-ATPase performs structural dynamics upon Ca²⁺ and nucleotide binding. It is proposed that the increased affinity of the N-domain for ATP mediated by Ca²⁺ binding may be involved in Ca²⁺-ATPase activation under normal physiological conditions.

Carnitine modulates crucial myocardial adenosine triphosphatases and acetylcholinesterase enzyme activities in choline-deprived rats

Choline is an essential nutrient, and choline deficiency has been associated with cardiovascular morbidity. Choline is also the precursor of acetylcholine (cholinergic component of the heart's autonomic nervous system), whose levels are regulated by acetylcholinesterase (AChE). Cardiac contraction-relaxation cycles depend on ion gradients established by pumps like the adenosine triphosphatases (ATPases) Na(+)/K(+)-ATPase and Mg(2+)-ATPase. This study aimed to investigate the impact of dietary choline deprivation on the activity of rat myocardial AChE (cholinergic marker), Na(+)/K(+)-ATPase, and Mg(2+)-ATPase, and the possible effects of carnitine supplementation (carnitine, structurally relevant to choline, is used as an adjunct in treating cardiac diseases). Adult male albino Wistar rats were distributed among 4 groups, and were fed a standard or choline-deficient diet for one month with or without carnitine in their drinking water (0.15% w/v). The enzyme activities were determined spectrophotometrically in the myocardium homogenate. Choline deficiency seems to affect the activity of the aforementioned parameters, but only the combination of choline deprivation and carnitine supplementation increased myocardial Na(+)/K(+)-ATPase activity along with a concomitant decrease in the activities of Mg(2+)-ATPase and AChE. The results suggest that carnitine, in the setting of choline deficiency, modulates cholinergic myocardial neurotransmission and the ATPase activity in favour of cardiac work efficiency.

ADP protects cardiac mitochondria under severe oxidative stress

ADP is not only a key substrate for ATP generation, but also a potent inhibitor of mitochondrial permeability transition pore (mPTP). In this study, we assessed how oxidative stress affects the potency of ADP as an mPTP inhibitor and whether its reduction of reactive oxygen species (ROS) production might be involved. We determined quantitatively the effects of ADP on mitochondrial Ca(2+) retention capacity (CRC) until the induction of mPTP in normal and stressed isolated cardiac mitochondria. We used two models of chronic oxidative stress (old and diabetic mice) and two models of acute oxidative stress (ischemia reperfusion (IR) and tert-butyl hydroperoxide (t-BH)). In control mitochondria, the CRC was 344 ± 32 nmol/mg protein. 500 μmol/L ADP increased CRC to 774 ± 65 nmol/mg protein. This effect of ADP seemed to relate to its concentration as 50 μmol/L had a significantly smaller effect. Also, oligomycin, which inhibits the conversion of ADP to ATP by F0F1ATPase, significantly increased the effect of 50 μmol/L ADP. Chronic oxidative stress did not affect CRC or the effect of 500 μmol/L ADP. After IR or t-BH exposure, CRC was drastically reduced to 1 ± 0.2 and 32 ± 4 nmol/mg protein, respectively. Surprisingly, ADP increased the CRC to 447 ± 105 and 514 ± 103 nmol/mg protein in IR and t-BH, respectively. Thus, it increased CRC by the same amount as in control. In control mitochondria, ADP decreased both substrate and Ca(2+)-induced increase of ROS. However, in t-BH mitochondria the effect of ADP on ROS was relatively small. We conclude that ADP potently restores CRC capacity in severely stressed mitochondria. This effect is most likely not related to a reduction in ROS production. As the effect of ADP relates to its concentration, increased ADP as occurs in the pathophysiological situation may protect mitochondrial integrity and function.

Luminal Ca2+ controls activation of the cardiac ryanodine receptor by ATP

The synergic effect of luminal Ca²⁺, cytosolic Ca²⁺, and cytosolic adenosine triphosphate (ATP) on activation of cardiac ryanodine receptor (RYR2) channels was examined in planar lipid bilayers. The dose–response of RYR2 gating activity to ATP was characterized at a diastolic cytosolic Ca²⁺ concentration of 100 nM over a range of luminal Ca²⁺ concentrations and, vice versa, at a diastolic luminal Ca²⁺ concentration of 1 mM over a range of cytosolic Ca²⁺ concentrations. Low level of luminal Ca²⁺ (1 mM) significantly increased the affinity of the RYR2 channel for ATP but without substantial activation of the channel. Higher levels of luminal Ca²⁺ (8–53 mM) markedly amplified the effects of ATP on the RYR2 activity by selectively increasing the maximal RYR2 activation by ATP, without affecting the affinity of the channel to ATP. Near-diastolic cytosolic Ca²⁺ levels (<500 nM) greatly amplified the effects of luminal Ca²⁺. Fractional inhibition by cytosolic Mg²⁺ was not affected by luminal Ca²⁺. In models, the effects of luminal and cytosolic Ca²⁺ could be explained by modulation of the allosteric effect of ATP on the RYR2 channel. Our results suggest that luminal Ca²⁺ ions potentiate the RYR2 gating activity in the presence of ATP predominantly by binding to a luminal site with an apparent affinity in the millimolar range, over which local luminal Ca²⁺ likely varies in cardiac myocytes.

A three-dimensional simulation model of cardiomyocyte integrating excitation-contraction coupling and metabolism

Recent studies have revealed that Ca(2+) not only regulates the contraction of cardiomyocytes, but can also function as a signaling agent to stimulate ATP production by the mitochondria. However, the spatiotemporal resolution of current experimental techniques limits our investigative capacity to understand this phenomenon. Here, we created a detailed three-dimensional (3D) cardiomyocyte model to study the subcellular regulatory mechanisms of myocardial energetics. The 3D cardiomyocyte model was based on the finite-element method, with detailed subcellular structures reproduced, and it included all elementary processes involved in cardiomyocyte electrophysiology, contraction, and ATP metabolism localized to specific loci. The simulation results were found to be reproducible and consistent with experimental data regarding the spatiotemporal pattern of cytosolic, intrasarcoplasmic-reticulum, and mitochondrial changes in Ca(2+); as well as changes in metabolite levels. Detailed analysis suggested that although the observed large cytosolic Ca(2+) gradient facilitated uptake by the mitochondrial Ca(2+) uniporter to produce cyclic changes in mitochondrial Ca(2+) near the Z-line region, the average mitochondrial Ca(2+) changes slowly. We also confirmed the importance of the creatine phosphate shuttle in cardiac energy regulation. In summary, our 3D model provides a powerful tool for the study of cardiac function by overcoming some of the spatiotemporal limitations of current experimental approaches.

Multi-Scale Continuum Modeling of Biological Processes: From Molecular Electro-Diffusion to Sub-Cellular Signaling Transduction

This article provides a brief review of multi-scale modeling at the molecular to cellular scale, with new results for heart muscle cells. A finite element-based simulation package (SMOL) was used to investigate the signaling transduction at molecular and sub-cellular scales (http://mccammon.ucsd.edu/smol/, http://FETK.org) by numerical solution of time-dependent Smoluchowski equations and a reaction-diffusion system. At the molecular scale, SMOL has yielded experimentally-validated estimates of the diffusion-limited association rates for the binding of acetylcholine to mouse acetylcholinesterase using crystallographic structural data. The predicted rate constants exhibit increasingly delayed steady-state times with increasing ionic strength and demonstrate the role of an enzyme's electrostatic potential in influencing ligand binding. At the sub-cellular scale, an extension of SMOL solves a non-linear, reaction-diffusion system describing Ca²⁺ ligand buffering and diffusion in experimentally-derived rodent ventricular myocyte geometries. Results reveal the important role for mobile and stationary Ca²⁺ buffers, including Ca²⁺ indicator dye. We found that the alterations in Ca²⁺-binding and dissociation rates of troponin C (TnC) and total TnC concentration modulate subcellular Ca²⁺ signals. Model predicts that reduced off-rate in whole troponin complex (TnC, TnI, TnT) versus reconstructed thin filaments (Tn, Tm, actin) alters cytosolic Ca²⁺ dynamics under control conditions or in disease-linked TnC mutations. The ultimate goal of these studies is to develop scalable methods and theories for integration of molecular-scale information into simulations of cellular-scale systems.

Cardiac models in drug discovery and development: a review

Cardiovascular diseases are among the leading causes of death in the developed world. Developing novel therapies for diseases like heart failure is crucial, but this is hampered by the high attrition rate in drug development. The withdrawal of drugs at the final hurdle of approval is mostly because of their unpredictable effects on normal cardiac rhythm. The advent of cardiac computational modeling in the last 5 decades has aided the understanding of heart function significantly. Recently, these models increasingly have been applied toward designing and understanding therapies for cardiac disease. This article will discuss how cellular models of electrophysiology, cell signaling, and metabolism have been used to investigate pharmacologic therapies for cardiac diseases including arrhythmia, ischemia, and heart failure.

Mitochondrial free [Ca2+] increases during ATP/ADP antiport and ADP phosphorylation: exploration of mechanisms

ADP influx and ADP phosphorylation may alter mitochondrial free [Ca2+] ([Ca2+](m)) and consequently mitochondrial bioenergetics by several postulated mechanisms. We tested how [Ca2+](m) is affected by H2PO4(-) (P(i)), Mg2+, calcium uniporter activity, matrix volume changes, and the bioenergetic state. We measured [Ca2+](m), membrane potential, redox state, matrix volume, pH(m), and O2 consumption in guinea pig heart mitochondria with or without ruthenium red, carboxyatractyloside, or oligomycin, and at several levels of Mg2+ and P(i). Energized mitochondria showed a dose-dependent increase in [Ca2+](m) after adding CaCl2 equivalent to 20, 114, and 485 nM extramatrix free [Ca2+] ([Ca2+](e)); this uptake was attenuated at higher buffer Mg2+. Adding ADP transiently increased [Ca2+](m) up to twofold. The ADP effect on increasing [Ca2+](m) could be partially attributed to matrix contraction, but was little affected by ruthenium red or changes in Mg2+ or P(i). Oligomycin largely reduced the increase in [Ca2+](m) by ADP compared to control, and [Ca2+](m) did not return to baseline. Carboxyatractyloside prevented the ADP-induced [Ca2+](m) increase. Adding CaCl2 had no effect on bioenergetics, except for a small increase in state 2 and state 4 respiration at 485 nM [Ca2+](e). These data suggest that matrix ADP influx and subsequent phosphorylation increase [Ca2+](m) largely due to the interaction of matrix Ca2+ with ATP, ADP, P(i), and cation buffering proteins in the matrix.

Models of cardiac excitation-contraction coupling in ventricular myocytes

Mathematical and computational modeling of cardiac excitation-contraction coupling has produced considerable insights into how the heart muscle contracts. With the increase in biophysical and physiological data available, the modeling has become more sophisticated with investigations spanning in scale from molecular components to whole cells. These modeling efforts have provided insight into cardiac excitation-contraction coupling that advanced and complemented experimental studies. One goal is to extend these detailed cellular models to model the whole heart. While this has been done with mechanical and electrophysiological models, the complexity and fast time course of calcium dynamics have made inclusion of detailed calcium dynamics in whole heart models impractical. Novel methods such as the probability density approach and moment closure technique which increase computational efficiency might make this tractable.

A biophysically based mathematical model for the kinetics of mitochondrial Na+-Ca2+ antiporter

Sodium-calcium antiporter is the primary efflux pathway for Ca(2+) in respiring mitochondria, and hence plays an important role in mitochondrial Ca(2+) homeostasis. Although experimental data on the kinetics of Na(+)-Ca(2+) antiporter are available, the structure and composition of its functional unit and kinetic mechanisms associated with the Na(+)-Ca(2+) exchange (including the stoichiometry) remains unclear. To gain a quantitative understanding of mitochondrial Ca(2+) homeostasis, a biophysical model of Na(+)-Ca(2+) antiporter is introduced that is thermodynamically balanced and satisfactorily describes a number of independent data sets under a variety of experimental conditions. The model is based on a multistate catalytic binding mechanism for carrier-mediated facilitated transport and Eyring's free energy barrier theory for interconversion and electrodiffusion. The model predicts the activating effect of membrane potential on the antiporter function for a 3Na(+):1Ca(2+) electrogenic exchange as well as the inhibitory effects of both high and low pH seen experimentally. The model is useful for further development of mechanistic integrated models of mitochondrial Ca(2+) handling and bioenergetics to understand the mechanisms by which Ca(2+) plays a role in mitochondrial signaling pathways and energy metabolism.

Magnesium gating of cardiac gap junction channels

We aimed to study kinetics of modulation by intracellular Mg(2+) of cardiac gap junction (Mg(2+) gate). Paired myocytes of guinea-pig ventricle were superfused with solutions containing various concentrations of Mg(2+). In order to rapidly apply Mg(2+) to one aspect of the gap junction, the non-junctional membrane of one of the pair was perforated at nearly the connecting site by pulses of nitrogen laser beam. The gap junction conductance (G(j)) was measured by clamping the membrane potential of the other cell using two-electrode voltage clamp method. The laser perforation immediately increased G(j), followed by slow G(j) change with time constant of 3.5 s at 10 mM Mg(2+). Mg(2+) more than 1.0 mM attenuated dose-dependently the gap junction conductance and lower Mg(2+) (0.6 mM) increased G(j) with a Hill coefficient of 3.4 and a half-maximum effective concentration of 0.6 mM. The time course of G(j) changes was fitted by single exponential function, and the relationship between the reciprocal of time constant and Mg(2+) concentration was almost linear. Based on the experimental data, a mathematical model of Mg(2+) gate with one open state and three closed states well reproduced experimental results. One-dimensional cable model of thirty ventricular myocytes connected to the Mg(2+) gate model suggested a pivotal role of the Mg(2+) gate of gap junction under pathological conditions.

A biophysically based mathematical model for the kinetics of mitochondrial calcium uniporter

Ca2+ transport through mitochondrial Ca2+ uniporter is the primary Ca2+ uptake mechanism in respiring mitochondria. Thus, the uniporter plays a key role in regulating mitochondrial Ca2+. Despite the importance of mitochondrial Ca2+ to metabolic regulation and mitochondrial function, and to cell physiology and pathophysiology, the structure and composition of the uniporter functional unit and kinetic mechanisms associated with Ca2+ transport into mitochondria are still not well understood. In this study, based on available experimental data on the kinetics of Ca2+ transport via the uniporter, a mechanistic kinetic model of the uniporter is introduced. The model is thermodynamically balanced and satisfactorily describes a large number of independent data sets in the literature on initial or pseudo-steady-state influx rates of Ca2+ via the uniporter measured under a wide range of experimental conditions. The model is derived assuming a multi-state catalytic binding and Eyring's free-energy barrier theory-based transformation mechanisms associated with the carrier-mediated facilitated transport and electrodiffusion. The model is a great improvement over the previous theoretical models of mitochondrial Ca2+ uniporter in the literature in that it is thermodynamically balanced and matches a large number of independently published data sets on mitochondrial Ca2+ uptake. This theoretical model will be critical in developing mechanistic, integrated models of mitochondrial Ca2+ handling and bioenergetics which can be helpful in understanding the mechanisms by which Ca2+ plays a role in mediating signaling pathways and modulating mitochondrial energy metabolism.

Mg2+ protects adult beating cardiomyocytes against ischaemia

Although Mg2+ reduces infarct size in whole heart models of ischaemia/reperfusion, the cardioprotective effect of Mg2+ at the cellular level is still a controversial issue. Therefore, we tested whether Mg2+ protects cardiomyocytes against ischaemia. To accomplish this aim we used an experimental model of ischaemia that utilises single beating adult cardiomyocytes in which oxygen tension is tightly regulated without the use of oxygen scavengers or metabolic inhibitors. Taking all these into consideration, this model is probably closer to in vivo conditions than the majority of previously published cellular models of ischaemia. We found that the addition of extracellular Mg2+ (8 mM) increased the survival of cells exposed to ischaemia. As sarcolemma and mitochondria are end-effectors of cardioprotective signalling, we examined whether Mg2+ regulates sarcolemmal and mitochondrial events. Mg2+ (8 mM) did not affect the whole cell K+ current as revealed by patch clamp electrophysiology. Experiments with laser confocal microscopy and the mitochondrial membrane potential-sensitive dye, JC-1, showed that Mg2+ (8 mM) did not affect ischaemia-induced mitochondrial membrane depolarisation. However, a significantly lower JC-1 ratio was required to kill cells under control conditions than cells treated with Mg2+ (8 mM). Based on the obtained data, we conclude that Mg2+ protects single beating cardiomyocytes against ischaemia by increasing cellular resistance to the consequences of mitochondrial membrane depolarisation in the cytosol.

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.

Excitation-contraction coupling and mitochondrial energetics

Cardiac excitation-contraction (EC) coupling consumes vast amounts of cellular energy, most of which is produced in mitochondria by oxidative phosphorylation. In order to adapt the constantly varying workload of the heart to energy supply, tight coupling mechanisms are essential to maintain cellular pools of ATP, phosphocreatine and NADH. To our current knowledge, the most important regulators of oxidative phosphorylation are ADP, Pi, and Ca2+. However, the kinetics of mitochondrial Ca2+-uptake during EC coupling are currently a matter of intense debate. Recent experimental findings suggest the existence of a mitochondrial Ca2+ microdomain in cardiac myocytes, justified by the close proximity of mitochondria to the sites of cellular Ca2+ release, i. e., the ryanodine receptors of the sarcoplasmic reticulum. Such a Ca2+ microdomain could explain seemingly controversial results on mitochondrial Ca2+ uptake kinetics in isolated mitochondria versus whole cardiac myocytes. Another important consideration is that rapid mitochondrial Ca2+ uptake facilitated by microdomains may shape cytosolic Ca2+ signals in cardiac myocytes and have an impact on energy supply and demand matching. Defects in EC coupling in chronic heart failure may adversely affect mitochondrial Ca2+ uptake and energetics, initiating a vicious cycle of contractile dysfunction and energy depletion. Future therapeutic approaches in the treatment of heart failure could be aimed at interrupting this vicious cycle.

An unconditionally stable numerical method for the Luo–Rudy 1 model used in simulations of defibrillation

Numerical simulations of defibrillation using the Bidomain model coupled to a model of membrane kinetics represent a serious numerical challenge. This is because very high voltages close to defibrillation electrodes demand that extreme time step restrictions be placed on standard numerical schemes, e.g. the forward Euler scheme. A common solution to this problem is to modify the cell model by simple if-tests applied to several equations and rate functions. These changes are motivated by numerical problems rather than physiology, and should therefore be avoided whenever possible. The purpose of this paper is to present a numerical scheme that handles the original model without modifications and which is unconditionally stable for the Luo-Rudy phase 1 model. This also shows that the cell model is mathematically well-behaved, even in the presence of very high voltages. Our theoretical results are illustrated by numerical computations.

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.

Spatial and temporal Ca2+, Mg2+, and ATP2- dynamics in cardiac dyads during calcium release

We have constructed a three-dimensional reaction-diffusion model of the mammalian cardiac calcium release unit. We analyzed effects of diffusion coefficients, single channel current amplitude, density of RyR channels, and reaction kinetics of ATP(2-) with Ca(2+) and Mg(2+) ions on spatiotemporal concentration profiles of Ca(2+), Mg(2+), and ATP(2-) in the dyadic cleft during Ca(2+) release. The model revealed that Ca(2+) concentration gradients persist near RyRs in the steady state. Even with low number of open RyRs, peak [Ca(2+)] in the dyadic space reached values similar to estimates of luminal [Ca(2+)] in approximately 1 ms, suggesting that during calcium release the Ca(2+) gradient moves from the cisternal membrane towards the boundary of the dyadic space with the cytosol. The released Ca(2+) bound to ATP(2-), and thus substantially decreased ATP(2-) concentration in the dyadic space. The released Ca(2+) could also replace Mg(2+) in its complex with ATP(2-) during first milliseconds of release if dissociation of MgATP was fast. The results suggest that concentration changes of Ca(2+), Mg(2+), and ATP(2-) might be large and fast enough to reduce dyadic RyR activity. Thus, under physiological conditions, termination of calcium release may be facilitated by the synergic effect of the construction and chemistry of mammalian cardiac dyads.

Contributions of sustained INa and IKv43 to transmural heterogeneity of early repolarization and arrhythmogenesis in canine left ventricular myocytes

The roles of sustained components of I(Na) and I(Kv43) in shaping the action potentials (AP) of myocytes isolated from the canine left ventricle (LV) have not been studied in detail. Here we investigate the hypothesis that these two currents can contribute substantially to heterogeneity of early repolarization and arrhythmic risk. Quantitative data from voltage-clamp and expression profiling experiments were used to complete meaningful modifications to an existing "local control" model of canine midmyocardial myocyte excitation-contraction coupling for epicardial and endocardial cells. We include 1) heterogeneous I(Kv43), I(Ks), and I(SERCA) density; 2) modulation of I(Kv43) by Kv channel interacting protein type 2 (KChIP2) channel subunits; 3) a possible Ca(2+)-dependent open-state inactivation of I(Kv43); and 4) a sustained component of the inward Na(+) current, I(NaL). The resulting simulations illustrate ways in which KChIP2- and Ca(2+)-dependent control of I(Kv43) can result in a sustained outward current that can neutralize I(NaL) in a rate- and myocyte subtype-dependent manner. Both these currents appear to play significant roles in modulating AP duration and rate dependence in midmyocardial myocytes. Furthermore, an increased ratio of I(Kv43) to I(NaL) is capable of protecting epicardial myocytes from the early afterdepolarizations resulting from the SCN5A-I1768V mutation-induced increase in I(NaL). Experimentally observed transmural differences in Ca(2+) handling, including greater sarcoplasmic reticulum Ca(2+) content and faster Ca(2+) transient decay rates on the epicardium, were recapitulated in our simulations. By design, these models allow upward integration into organ models or may be used as a basis for further investigations into cellular heterogeneities.

Dictyostelium myosin-IE is a fast molecular motor involved in phagocytosis

Class I myosins are single-headed motor proteins, implicated in various motile processes including organelle translocation, ion-channel gating, and cytoskeleton reorganization. Here we describe the cellular localization of myosin-IE and its role in the phagocytic uptake of solid particles and cells. A complete analysis of the kinetic and motor properties of Dictyostelium discoideum myosin-IE was achieved by the use of motor domain constructs with artificial lever arms. Class I myosins belonging to subclass IC like myosin-IE are thought to be tuned for tension maintenance or stress sensing. In contrast to this prediction, our results show myosin-IE to be a fast motor. Myosin-IE motor activity is regulated by myosin heavy chain phosphorylation, which increases the coupling efficiency between the actin and nucleotide binding sites tenfold and the motile activity more than fivefold. Changes in the level of free Mg(2+) ions, which are within the physiological range, are shown to modulate the motor activity of myosin-IE by inhibiting the release of adenosine diphosphate.

Inhibition of cAMP-dependent protein kinase under conditions occurring in the cardiac dyad during a Ca2+ transient

The space between the t-tubule invagination and the sarcoplasmic reticulum (SR) membrane, the dyad, in ventricular myocytes has been predicted to experience very high [Ca2+] for short periods of time during a Ca2+ transient. The dyadic space accommodates many protein kinases responsible for the regulation of Ca2+ handling proteins of the cell. We show in vitro that cAMP-dependent protein kinase (PKA) is inhibited by high [Ca2+] through a shift in the ratio of CaATP/MgATP toward CaATP. We further generate a three-dimensional mathematical model of Ca2+ and ATP diffusion within dyad. We use this model to predict the extent to which PKA would be inhibited by an increased CaATP/MgATP ratio during a Ca2+ transient in the dyad in vivo. Our results suggest that under normal physiological conditions a myocyte paced at 1 Hz would experience up to 55% inhibition of PKA within the cardiac dyad, with inhibition averaging 5% throughout the transient, an effect which becomes more pronounced as the myocyte contractile frequency increases (at 7 Hz, PKA inhibition averages 28% across the dyad throughout the duration of a Ca2+ transient).

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

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

Multiscale modeling of cardiac cellular energetics

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

Cardiac systems biology

As more detailed molecular information accumulates on the biology of the heart and other complex systems in health and disease, the need for new integrative analyses and tools is growing. Systems biology and bioengineering seek to use high-throughput technologies and integrative computational analysis to construct networks of the interactions between molecular components in the system, to develop systems models of their functionally integrated biological properties, and to incorporate these systems models into structurally integrated multi-scale models for predicting clinical phenotypes. This review gives examples of recent applications using these approaches to elucidate the electromechanical function of the heart in aging and disease.

Regulation of heart insulin receptor tyrosine kinase activity by magnesium and spermine

Insulin action and aspects of the insulin-signaling pathway have been studied in the heart although the direct regulation of the heart's insulin receptor has not been explored. This study describes the first purification and characterization of the mammalian (rabbit, rat and bovine) heart insulin receptor. The rabbit heart IR showed maximum insulin binding of 18 microg/mg (approximately 1 mole insulin/mole (alpha2beta2) receptor) and a curvilinear Scatchard plot with a high affinity KD for insulin binding of approximately 4 nM at optimal pH (7.8) and NaCl concentration (150 mM). The insulin receptor tyrosine kinase activity was stimulated by insulin, Mg2+ (half-maximum response at approximately 5.6-10.6 nM and approximately 8.5 mM, respectively) and by the physiological polyamines, spermine and spermidine. The stimulation by Mg2+ and the polyamines occurred with and without insulin. These characteristics of the heart insulin receptor provide a mechanism for regulating the activity of the receptor's tyrosine kinase activity by the intracellular free Mg2+ concentration and the polyamines in the absence and presence of insulin.

Functionally and structurally integrated computational modeling of ventricular physiology

Computational biology is integrative in several ways. Functionally, computational models are valuable for integrating the many interacting processes within biochemical networks and the many interacting physiological subsystems within the cell. Structurally detailed models provide a way of integrating across scales of biological organization from molecule to organism. Data integration across diverse laboratory and clinical measurements is another unique strength of computational biology. We describe examples of all three categories of integration by using recent advances in modeling cardiac excitation-contraction coupling and whole-heart electromechanics in health and disease.

Modeling regulation of cardiac KATP and L-type Ca2+ currents by ATP, ADP, and Mg2+

Changes in cytosolic free Mg(2+) and adenosine nucleotide phosphates affect cardiac excitability and contractility. To investigate how modulation by Mg(2+), ATP, and ADP of K(ATP) and L-type Ca(2+) channels influences excitation-contraction coupling, we incorporated equations for intracellular ATP and MgADP regulation of the K(ATP) current and MgATP regulation of the L-type Ca(2+) current in an ionic-metabolic model of the canine ventricular myocyte. The new model: 1), quantitatively reproduces a dose-response relationship for the effects of changes in ATP on K(ATP) current, 2), simulates effects of ADP in modulating ATP sensitivity of K(ATP) channel, 3), predicts activation of Ca(2+) current during rapid increase in MgATP, and 4), demonstrates that decreased ATP/ADP ratio with normal total Mg(2+) or increased free Mg(2+) with normal ATP and ADP activate K(ATP) current, shorten action potential, and alter ionic currents and intracellular Ca(2+) signals. The model predictions are in agreement with experimental data measured under normal and a variety of pathological conditions.

Multi-scale modelling and the IUPS physiome project

We review the development of models of cellular and tissue function and in particular address issues of multi-scale modelling, including the transition from stochastic models to continuum models and the incorporation of cell and tissue structure. The heart is used as an example of linking models at the molecular level to cell, tissue and organ level function.

Changes in Mg2+ ion concentration and heavy chain phosphorylation regulate the motor activity of a class I myosin

Class I myosins are single-headed motor proteins implicated in various motile processes including organelle translocation, ion channel gating, and cytoskeleton reorganization. Dictyostelium discoideum myosin-ID belongs to subclass 1alpha, whose members are thought to be tuned for rapid sliding. The direct analysis of myosin-ID motor activity is made possible by the production of single polypeptide constructs carrying an artificial lever arm. Using these constructs, we show that the motor activity of myosin-ID is activated 80-fold by phosphorylation at the TEDS site. TEDS site phosphorylation acts by stabilizing the actomyosin complex and increasing the coupling between actin binding and the release of hydrolysis products. A surprising effect of Mg(2+) ions on in vitro motility was discovered. Changes in the level of free Mg(2+) ions within the physiological range are shown to modulate motor activity by inhibiting ADP release. Our results indicate that higher concentrations of free Mg(2+) ions stabilize the tension-bearing actin myosin ADP state and shift the system from the production of rapid movement toward the generation of tension.

Effects of Magnesium on Cardiac Excitation-Contraction Coupling

OBJECTIVE

Magnesium regulates a large number of cellular processes. Small changes in intracellular free Mg(2+) ([Mg(2+)](i)) may have important effects on cardiac excitability and contractility. We investigated the effects of [Mg(2+)](i) on cardiac excitation-contraction coupling.

METHODS

We used our ionic-metabolic model that incorporates equations for Ca(2+) and Mg(2+) buffering and transport by ATP and ADP and equations for MgATP regulation of ion transporters (Na(+)-K(+) pump, sarcolemmal and sarcoplasmic Ca(2+) pumps).

RESULTS

Model results indicate that variations in cytosolic Mg(2+) level might sensitively affect diastolic and systolic Ca(2+), sarcoplasmic Ca(2+) content, Ca(2+) influx through L-type channels, efficiency of the Na(+)/Ca(2+) exchanger and action potential shape. The analysis suggests that the most important reason for the observed effects is a modified normal function of sarcoplasmic Ca(2+)-ATPase pump by altered diastolic MgATP levels.

CONCLUSION

The model is able to reproduce qualitatively a sequence of events that correspond well with experimental observations during cardiac excitation-contraction coupling in mammalian ventricular myocytes.

Computational physiology and the Physiome Project

Bioengineering analyses of physiological systems use the computational solution of physical conservation laws on anatomically detailed geometric models to understand the physiological function of intact organs in terms of the properties and behaviour of the cells and tissues within the organ. By linking behaviour in a quantitative, mathematically defined sense across multiple scales of biological organization--from proteins to cells, tissues, organs and organ systems--these methods have the potential to link patient-specific knowledge at the two ends of these spatial scales. A genetic profile linked to cardiac ion channel mutations, for example, can be interpreted in relation to body surface ECG measurements via a mathematical model of the heart and torso, which includes the spatial distribution of cardiac ion channels throughout the myocardium and the individual kinetics for each of the approximately 50 types of ion channel, exchanger or pump known to be present in the heart. Similarly, linking molecular defects such as mutations of chloride ion channels in lung epithelial cells to the integrated function of the intact lung requires models that include the detailed anatomy of the lungs, the physics of air flow, blood flow and gas exchange, together with the large deformation mechanics of breathing. Organizing this large body of knowledge into a coherent framework for modelling requires the development of ontologies, markup languages for encoding models, and web-accessible distributed databases. In this article we review the state of the field at all the relevant levels, and the tools that are being developed to tackle such complexity. Integrative physiology is central to the interpretation of genomic and proteomic data, and is becoming a highly quantitative, computer-intensive discipline.

Modeling the isolated cardiac myocyte

Computer modeling of cardiac myocytes has flourished in recent years. Models have evolved from mathematical descriptions of ionic channels alone to more sophisticated formulations that include calcium transport mechanisms, ATP production and metabolic pathways. The increased complexity is fueled by the new data available in the field. The continuous production of experimental data has led to the evolution of increasingly refined descriptions of the phenomena by modelers. Integrating the numerous systems involved in cardiac myocyte homeostasis makes the use of computer models necessary due to the unreliability of intuitive approaches. However the complexity of the model should not imply a cumbersome operation of the program. As with any tool, computer models have to be easy to operate or their strength will be diminished and potential users will not benefit fully from them. The contribution of the computer modeler to their respective biological fields will be more successful and enduring if modelers devote sufficient time to implement their equations into a model with user-friendly characteristics.

Parameter estimation in cardiac ionic models

We examine the problem of parameter estimation in mathematical models of excitable cell cardiac electrical activity using the well-known Beeler-Reuter (1977) ionic equations for the ventricular action potential. The estimation problem can be regarded as equivalent to the accurate reconstruction of ionic current kinetics and amplitudes in an excitable cell model, given only action potential experimental data. We show that in the Beeler-Reuter case, all ionic currents may be reasonably reconstructed using an experimental design consisting of action potential recordings perturbed by pseudo-random injection currents. The Beeler-Reuter model was parameterised into 63 parameters completely defining all membrane current amplitudes and kinetics. Total membrane current was fitted to model-generated experimental data using a 'data-clamp' protocol. The experimental data consisted of a default action-potential waveform and an optional series of perturbed waveforms generated by current injections. Local parameter identifiability was ascertained from the reciprocal condition value (1/lambda) of the Hessian at the known solution. When fitting to a single action potential waveform, the model was found to be over-determined, having a 1/lambda value of approximately 3.6e-14. This value improved slightly to approximately 1.4e-10 when an additional 2 perturbed waveforms were included in the fitting process, suggesting that the additional data did not overly improve the identifiability problem. The additional data, however, did allow the accurate reconstruction of all ionic currents. This indicates that by appropriate experimental design, it may be possible to infer the properties of underlying membrane currents from observation of transmembrane potential waveforms perturbed by pseudo-random currents.

The computational integrated myocyte: a view into the virtual heart

The presentation outlines an integrative approach for developing a computational model of cardiomyocytes. A modular approach is proposed, and strategies of linking the modules (intermediary metabolism, electrophysiology, and mechanics) of the model are presented. A strong recommendation is given toward an integrated system approach backed by experimental validation.

An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release

The local control theory of excitation-contraction (EC) coupling in cardiac muscle asserts that L-type Ca(2+) current tightly controls Ca(2+) release from the sarcoplasmic reticulum (SR) via local interaction of closely apposed L-type Ca(2+) channels (LCCs) and ryanodine receptors (RyRs). These local interactions give rise to smoothly graded Ca(2+)-induced Ca(2+) release (CICR), which exhibits high gain. In this study we present a biophysically detailed model of the normal canine ventricular myocyte that conforms to local control theory. The model formulation incorporates details of microscopic EC coupling properties in the form of Ca(2+) release units (CaRUs) in which individual sarcolemmal LCCs interact in a stochastic manner with nearby RyRs in localized regions where junctional SR membrane and transverse-tubular membrane are in close proximity. The CaRUs are embedded within and interact with the global systems of the myocyte describing ionic and membrane pump/exchanger currents, SR Ca(2+) uptake, and time-varying cytosolic ion concentrations to form a model of the cardiac action potential (AP). The model can reproduce both the detailed properties of EC coupling, such as variable gain and graded SR Ca(2+) release, and whole-cell phenomena, such as modulation of AP duration by SR Ca(2+) release. Simulations indicate that the local control paradigm predicts stable APs when the L-type Ca(2+) current is adjusted in accord with the balance between voltage- and Ca(2+)-dependent inactivation processes as measured experimentally, a scenario where common pool models become unstable. The local control myocyte model provides a means for studying the interrelationship between microscopic and macroscopic behaviors in a manner that would not be possible in experiments.

Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell

We developed an improved mathematical model for a single primary pacemaker cell of the rabbit sinoatrial node. Original features of our model include 1) incorporation of the sustained inward current (I(st)) recently identified in primary pacemaker cells, 2) reformulation of voltage- and Ca(2+)-dependent inactivation of the L-type Ca(2+) channel current (I(Ca,L)), 3) new expressions for activation kinetics of the rapidly activating delayed rectifier K(+) channel current (I(Kr)), and 4) incorporation of the subsarcolemmal space as a diffusion barrier for Ca(2+). We compared the simulated dynamics of our model with those of previous models, as well as with experimental data, and examined whether the models could accurately simulate the effects of modulating sarcolemmal ionic currents or intracellular Ca(2+) dynamics on pacemaker activity. Our model represents significant improvements over the previous models, because it can 1) simulate whole cell voltage-clamp data for I(Ca,L), I(Kr), and I(st); 2) reproduce the waveshapes of spontaneous action potentials and ionic currents during action potential clamp recordings; and 3) mimic the effects of channel blockers or Ca(2+) buffers on pacemaker activity more accurately than the previous models.

Ionic charge conservation and long-term steady state in the Luo-Rudy dynamic cell model

It has been postulated that cardiac cell models accounting for changes in intracellular ion concentrations violate a conservation principle, and, as a result, computed parameters (e.g., ion concentrations and transmembrane potential, V(m)) drift in time, never attaining steady state. To address this issue, models have been proposed that invoke the charge conservation principle to calculate V(m) from ion concentrations ("algebraic" method), rather than from transmembrane current ("differential" method). The aims of this study are to compare model behavior during prolonged periods of pacing using the algebraic and differential methods, and to address the issue of model drift. We pace the Luo-Rudy dynamic model of a cardiac ventricular cell and compare the time-dependent behavior of computed parameters using the algebraic and differential methods. When ions carried by the stimulus current are taken into account, the algebraic and differential methods yield identical results and neither shows drift in computed parameters. The present study establishes the proper pacing protocol for simulation studies of cellular behavior during long periods of rapid pacing. Such studies are essential for mechanistic understanding of arrhythmogenesis, since cells are subjected to rapid periodic stimulation during many arrhythmias.