Ionic Mechanisms of Propagated Repolarization in a One-Dimensional Strand of Human Ventricular Myocyte Model.

Although repolarization has been suggested to propagate in cardiac tissue both theoretically and experimentally, it has been challenging to estimate how and to what extent the propagation of repolarization contributes to relaxation because repolarization only occurs in the course of membrane excitation in normal hearts. We established a mathematical model of a 1D strand of 600 myocytes stabilized at an equilibrium potential near the plateau potential level by introducing a sustained component of the late sodium current (INaL). By applying a hyperpolarizing stimulus to a small part of the strand, we succeeded in inducing repolarization which propagated along the strand at a velocity of 1~2 cm/s. The ionic mechanisms responsible for repolarization at the myocyte level, i.e., the deactivation of both the INaL and the L-type calcium current (ICaL), and the activation of the rapid component of delayed rectifier potassium current (IKr) and the inward rectifier potassium channel (IK1), were found to be important for the propagation of repolarization in the myocyte strand. Using an analogy with progressive activation of the sodium current (INa) in the propagation of excitation, regenerative activation of the predominant magnitude of IK1 makes the myocytes at the wave front start repolarization in succession through the electrical coupling via gap junction channels.

Mechanisms Underlying Spontaneous Action Potential Generation Induced by Catecholamine in Pulmonary Vein Cardiomyocytes: A Simulation Study.

Cardiomyocytes and myocardial sleeves dissociated from pulmonary veins (PVs) potentially generate ectopic automaticity in response to noradrenaline (NA), and thereby trigger atrial fibrillation. We developed a mathematical model of rat PV cardiomyocytes (PVC) based on experimental data that incorporates the microscopic framework of the local control theory of Ca2+ release from the sarcoplasmic reticulum (SR), which can generate rhythmic Ca2+ release (limit cycle revealed by the bifurcation analysis) when total Ca2+ within the cell increased. Ca2+ overload in SR increased resting Ca2+ efflux through the type II inositol 1,4,5-trisphosphate (IP3) receptors (InsP3R) as well as ryanodine receptors (RyRs), which finally triggered massive Ca2+ release through activation of RyRs via local Ca2+ accumulation in the vicinity of RyRs. The new PVC model exhibited a resting potential of -68 mV. Under NA effects, repetitive Ca2+ release from SR triggered spontaneous action potentials (APs) by evoking transient depolarizations (TDs) through Na+/Ca2+ exchanger (APTDs). Marked and variable latencies initiating APTDs could be explained by the time courses of the α1- and ß1-adrenergic influence on the regulation of intracellular Ca2+ content and random occurrences of spontaneous TD activating the first APTD. Positive and negative feedback relations were clarified under APTD generation.

Modeling analysis of inositol 1,4,5-trisphosphate receptor-mediated Ca2+ mobilization under the control of glucagon-like peptide-1 in mouse pancreatic ß-cells.

Glucagon-like peptide-1 (GLP-1) is an intestinally derived blood glucose-lowering hormone that potentiates glucose-stimulated insulin secretion from pancreatic ß-cells. The secretagogue action of GLP-1 is explained, at least in part, by its ability to stimulate cAMP production so that cAMP may facilitate the release of Ca(2+) from inositol trisphosphate receptor (IP3R)-regulated Ca(2+) stores. However, a quantitative model has yet to be provided that explains the molecular mechanisms and dynamic processes linking GLP-1-stimulated cAMP production to Ca(2+) mobilization. Here, we performed simulation studies to investigate how GLP-1 alters the abilities of Ca(2+) and IP3 to act as coagonists at IP3R Ca(2+) release channels. A new dynamic model was constructed based on the Kaftan model, which demonstrates dual steady-state allosteric regulation of the IP3R by Ca(2+) and IP3. Data obtained from ß-cells were then analyzed to understand how GLP-1 facilitates IP3R-mediated Ca(2+) mobilization when UV flash photolysis is used to uncage Ca(2+) and IP3 intracellularly. When the dynamic model for IP3R activation was incorporated into a minimal cell model, the Ca(2+) transients and oscillations induced by GLP-1 were successfully reconstructed. Simulation studies indicated that transient and oscillatory responses to GLP-1 were produced by sequential positive and negative feedback regulation due to fast activation and slow inhibition of the IP3R by Ca(2+). The slow rate of Ca(2+)-dependent inhibition was revealed to provide a remarkable contribution to the time course of the decay of cytosolic Ca(2+) transients. It also served to drive and pace Ca(2+) oscillations that are significant when evaluating how GLP-1 stimulates insulin secretion.

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

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

Cell-specific models of hiPSC-CMs developed by the gradient-based parameter optimization method fitting two different action potential waveforms.

Parameter optimization (PO) methods to determine the ionic current composition of experimental cardiac action potential (AP) waveform have been developed using a computer model of cardiac membrane excitation. However, it was suggested that fitting a single AP record in the PO method was not always successful in providing a unique answer because of a shortage of information. We found that the PO method worked perfectly if the PO method was applied to a pair of a control AP and a model output AP in which a single ionic current out of six current species, such as IKr, ICaL, INa, IKs, IKur or IbNSC was partially blocked in silico. When the target was replaced by a pair of experimental control and IKr-blocked records of APs generated spontaneously in human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), the simultaneous fitting of the two waveforms by the PO method was hampered to some extent by the irregular slow fluctuations in the Vm recording and/or sporadic alteration in AP configurations in the hiPSC-CMs. This technical problem was largely removed by selecting stable segments of the records for the PO method. Moreover, the PO method was made fail-proof by running iteratively in identifying the optimized parameter set to reconstruct both the control and the IKr-blocked AP waveforms. In the lead potential analysis, the quantitative ionic mechanisms deduced from the optimized parameter set were totally consistent with the qualitative view of ionic mechanisms of AP so far described in physiological literature.

Steady-state solutions of cell volume in a cardiac myocyte model elaborated for membrane excitation, ion homeostasis and Ca2+ dynamics.

The cell volume continuously changes in response to varying physiological conditions, and mechanisms underlying volume regulation have been investigated in both experimental and theoretical studies. Here, general formulations concerning cell volume change are presented in the context of developing a comprehensive cell model which takes Ca(2+) dynamics into account. Explicit formulas for charge conservation and steady-state volumes of the cytosol and endoplasmic reticulum (ER) are derived in terms of membrane potential, amount of ions, Ca(2+)-bound buffer molecules, and initial cellular conditions. The formulations were applied to a ventricular myocyte model which has plasma-membrane Ca(2+) currents with dynamic gating mechanisms, Ca(2+)-buffering reactions with diffusive and non-diffusive buffer proteins, and Ca(2+) uptake into or release from the sarcoplasmic reticulum (SR) accompanied by compensatory cationic or anionic currents through the SR membrane. Time-dependent volume changes in cardiac myocytes induced by varying extracellular osmolarity or by action potential generation were successfully simulated by the novel formulations. Through application of bifurcation analysis, the existence and uniqueness of steady-state solutions of the cell volume were validated, and contributions of individual ion channels and transporters to the steady-state volume were systematically analyzed. The new formulas are consistent with previous fundamental theory derived from simple models of minimum compositions. The new formulations may be useful for examination of the relationship between cell function and volume change in other cell types.

Gradient-based parameter optimization method to determine membrane ionic current composition in human induced pluripotent stem cell-derived cardiomyocytes.

Premature cardiac myocytes derived from human induced pluripotent stem cells (hiPSC-CMs) show heterogeneous action potentials (APs), probably due to different expression patterns of membrane ionic currents. We developed a method for determining expression patterns of functional channels in terms of whole-cell ionic conductance (Gx) using individual spontaneous AP configurations. It has been suggested that apparently identical AP configurations can be obtained using different sets of ionic currents in mathematical models of cardiac membrane excitation. If so, the inverse problem of Gx estimation might not be solved. We computationally tested the feasibility of the gradient-based optimization method. For a realistic examination, conventional 'cell-specific models' were prepared by superimposing the model output of AP on each experimental AP recorded by conventional manual adjustment of Gxs of the baseline model. Gxs of 4-6 major ionic currents of the 'cell-specific models' were randomized within a range of ± 5-15% and used as an initial parameter set for the gradient-based automatic Gxs recovery by decreasing the mean square error (MSE) between the target and model output. Plotting all data points of the MSE-Gx relationship during optimization revealed progressive convergence of the randomized population of Gxs to the original value of the cell-specific model with decreasing MSE. The absence of any other local minimum in the global search space was confirmed by mapping the MSE by randomizing Gxs over a range of 0.1-10 times the control. No additional local minimum MSE was obvious in the whole parameter space, in addition to the global minimum of MSE at the default model parameter.

Systems analysis of GLP-1 receptor signaling in pancreatic ß-cells.

Glucagon-like peptide-1 (GLP-1) elevates intracellular concentration of cAMP ([cAMP]) and facilitates glucose-dependent insulin secretion in pancreatic ß-cells. There has been much evidence to suggest that multiple key players such as the GLP-1 receptor, G(s) protein, adenylate cyclase (AC), phosphodiesterase (PDE), and intracellular Ca(2+) concentration ([Ca(2+)]) are involved in the regulation of [cAMP]. However, because of complex interactions among these signaling factors, the kinetics of the reaction cascade as well as the activities of ACs and PDEs have not been determined in pancreatic ß-cells. We have constructed a minimal mathematical model of GLP-1 receptor signal transduction based on experimental findings obtained mostly in ß-cells and insulinoma cell lines. By fitting this theoretical reaction scheme to key experimental records of the GLP-1 response, the parameters determining individual reaction steps were estimated. The model reconstructed satisfactorily the dynamic changes in [cAMP] and predicted the activities of cAMP effectors, protein kinase A (PKA), and cAMP-regulated guanine nucleotide exchange factor [cAMP-GEF or exchange protein directly activated by cAMP (Epac)] during GLP-1 stimulation. The simulations also predicted the presence of two sequential desensitization steps of the GLP1 receptor that occur with fast and very slow reaction rates. The cross talk between glucose- and GLP-1-dependent signal cascades for cAMP synthesis was well reconstructed by integrating the direct regulation of AC and PDE by [Ca(2+)]. To examine robustness of the signaling system in controlling [cAMP], magnitudes of AC and PDE activities were compared in the presence or absence of GLP-1 and/or the PDE inhibitor IBMX.(1).

Minor contribution of cytosolic Ca2+ transients to the pacemaker rhythm in guinea pig sinoatrial node cells.

The question of the extent to which cytosolic Ca(2+) affects sinoatrial node pacemaker activity has been discussed for decades. We examined this issue by analyzing two mathematical pacemaker models, based on the "Ca(2+) clock" (C) and "membrane clock" (M) hypotheses, together with patch-clamp experiments in isolated guinea pig sinoatrial node cells. By applying lead potential analysis to the models, the C mechanism, which is dependent on potentiation of Na(+)/Ca(2+) exchange current via spontaneous Ca(2+) release from the sarcoplasmic reticulum (SR) during diastole, was found to overlap M mechanisms in the C model. Rapid suppression of pacemaker rhythm was observed in the C model by chelating intracellular Ca(2+), whereas the M model was unaffected. Experimental rupturing of the perforated-patch membrane to allow rapid equilibration of the cytosol with 10 mM BAPTA pipette solution, however, failed to decrease the rate of spontaneous action potential within ∼30 s, whereas contraction ceased within ∼3 s. The spontaneous rhythm also remained intact within a few minutes when SR Ca(2+) dynamics were acutely disrupted using high doses of SR blockers. These experimental results suggested that rapid disruption of normal Ca(2+) dynamics would not markedly affect spontaneous activity. Experimental prolongation of the action potentials, as well as slowing of the Ca(2+)-mediated inactivation of the L-type Ca(2+) currents induced by BAPTA, were well explained by assuming Ca(2+) chelation, even in the proximity of the channel pore in addition to the bulk cytosol in the M model. Taken together, the experimental and model findings strongly suggest that the C mechanism explicitly described by the C model can hardly be applied to guinea pig sinoatrial node cells. The possible involvement of L-type Ca(2+) current rundown induced secondarily through inhibition of Ca(2+)/calmodulin kinase II and/or Ca(2+)-stimulated adenylyl cyclase was discussed as underlying the disruption of spontaneous activity after prolonged intracellular Ca(2+) concentration reduction for >5 min.

Characterization of the cardiac Na+/K+ pump by development of a comprehensive and mechanistic model.

A large amount of experimental data on the characteristics of the cardiac Na(+)/K(+) pump have been accumulated, but it remains difficult to predict the quantitative contribution of the pump in an intact cell because most measurements have been made under non-physiological conditions. To extrapolate the experimental findings to intact cells, we have developed a comprehensive Na(+)/K(+) pump model based on the thermodynamic framework (Smith and Crampin, 2004) of the Post-Albers reaction cycle combined with access channel mechanisms. The new model explains a variety of experimental results for the Na(+)/K(+) pump current (I(NaK)), including the dependency on the concentrations of Na(+) and K(+), the membrane potential and the free energy of ATP hydrolysis. The model demonstrates that both the apparent affinity and the slope of the substrate-I(NaK) relationship measured experimentally are affected by the composition of ions in the extra- and intracellular solutions, indirectly through alteration in the probability distribution of individual enzyme intermediates. By considering the voltage dependence in the Na(+)- and K(+)-binding steps, the experimental voltage-I(NaK) relationship could be reconstructed with application of experimental ionic compositions in the model, and the view of voltage-dependent K(+) binding was supported. Re-evaluation of charge movements accompanying Na(+) and K(+) translocations gave a reasonable number for the site density of the Na(+)/K(+) pump on the membrane. The new model is relevant for simulation of cellular functions under various interventions, such as depression of energy metabolism.

A novel method to quantify contribution of channels and transporters to membrane potential dynamics.

The action potential, once triggered in ventricular or atrial myocytes, automatically proceeds on its time course or is generated spontaneously in sinoatrial node pacemaker cells. It is induced by complex interactions among such cellular components as ion channels, transporters, intracellular ion concentrations, and signaling molecules. We have developed what is, to our knowledge, a new method using a mathematical model to quantify the contribution of each cellular component to the automatic time courses of the action potential. In this method, an equilibrium value, which the membrane potential is approaching at a given moment, is calculated along the time course of the membrane potential. The calculation itself is based on the time-varying conductance and the reversal potentials of individual ion channels and electrogenic ion transporters. Since the equilibrium potential moves in advance of the membrane potential change, we refer to it as the lead potential, V(L). The contribution of an individual current was successfully quantified by comparing dV(L)/dt before and after fixing the time-dependent change of a component of interest, such as the variations in the open probability of a channel or the turnover rate of an ion transporter. In addition to the action potential, the lead-potential analysis should also be applicable in all types of membrane excitation in many different kinds of cells.

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.

Role of Mg(2+) block of the inward rectifier K(+) current in cardiac repolarization reserve: A quantitative simulation.

Different K(+) currents serve as "repolarization reserve" or a redundant repolarizing mechanism that protects against excessive prolongation of the cardiac action potential and therefore arrhythmia. Impairment of the inward rectifier K(+) current (I(K1)) has been implicated in the pathogenesis of cardiac arrhythmias. The characteristics of I(K1) reflect the kinetics of channel block by intracellular cations, primarily spermine (a polyamine) and Mg(2+), whose cellular levels may vary under various pathological conditions. However, the relevance of endogenous I(K1) blockers to the repolarization reserve is still not fully understood in detail. Here we used a mathematical model of a cardiac ventricular myocyte which quantitatively reproduces the dynamics of I(K1) block to examine the effects of the intracellular spermine and Mg(2+) concentrations, through modifying I(K1), on the action potential repolarization. Our simulation indicated that an I(K1) transient caused by relief of Mg(2+) block flows during early phase 3. Increases in the intracellular spermine/Mg(2+) concentration, or decreases in the intracellular Mg(2+) concentration, to levels outside their normal ranges prolonged action potential duration by decreasing the I(K1) transient. Moreover, reducing both the rapidly activating delayed rectifier current (I(Kr)) and the I(K1) transient caused a marked retardation of repolarization and early afterdepolarization because they overlap in the voltage range at which they flow. Our results indicate that the I(K1) transient caused by relief of Mg(2+) block is an important repolarizing current, especially when I(Kr) is reduced, and that abnormal intracellular free spermine/Mg(2+) concentrations may be a missing risk factor for malignant arrhythmias in I(Kr)-related acquired (drug-induced) and congenital long QT syndromes.

A new integrated method for analyzing heart mechanics using a cell-hemodynamics-autonomic nerve control coupled model of the cardiovascular system.

A model of the cardiovascular system coupling cell, hemodynamics, and autonomic nerve control function is proposed for analyzing heart mechanics. We developed a comprehensive cardiovascular model with multi-physics and multi-scale characteristics that simulates the physiological events from membrane excitation of a cardiac cell to contraction of the human heart and systemic blood circulation and ultimately to autonomic nerve control. A lumped parameter model is used to compute the systemic and pulmonary circulations interacting with the cardiac cell mechanism. For autonomic control of the cardiovascular system, we used the approach suggested by Heldt et al. [2002. Computational modeling of cardiovascular response to orthostatic stress. J. Appl. Physiol. 92, 1239-1254] (Heldt model), including baroreflex and cardiopulmonary reflexes. We assumed sympathetic and parasympathetic pathways for the nerve control system. The cardiac muscle response to these reflex control systems was implemented using the activation-level changes in the L-type calcium channel and sarcoplasmic/endoplasmic reticulum calcium ATPase function based on experimental observations. Using this model, we delineated the cellular mechanism of heart contractility mediated by nerve control function. To verify the integrated method, we simulated a 10% hemorrhage, which involves cardiac cell mechanics, circulatory hemodynamics, and nerve control function. The computed and experimental results were compared. Using this methodology, the state of cardiac contractility, influenced by diverse properties such as the afterload and nerve control systems, is easily assessed in an integrated manner.

Simulation analysis of intracellular Na+ and Cl- homeostasis during beta 1-adrenergic stimulation of cardiac myocyte.

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

A simulation study on the activation of cardiac CaMKII delta-isoform and its regulation by phosphatases.

Although the highly conserved Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) is known to play an essential role in cardiac myocytes, its involvement in the frequency-dependent acceleration of relaxation is still controversial. To investigate the functional significance of CaMKII autophosphorylation and its regulation by protein phosphatases (PPs) in heart, we developed a new mathematical model for the CaMKIIdelta isoform. Due to better availability of experimental data, the model was first adjusted to the kinetics of the neuronal CaMKIIalpha isoform and then converted to a CaMKIIdelta model by fitting to kinetic data of the delta isoform. Both models satisfactorily reproduced experimental data of the CaMKII-calmodulin interaction, the autophosphorylation rate, and the frequency dependence of activation. The level of autophosphorylated CaMKII cumulatively increased upon starting the Ca(2+) stimulation at 3 Hz in the delta model. Variations in PP concentration remarkably affected the frequency-dependent activation of CaMKIIdelta, suggesting that cellular PP activity plays a key role in adjusting CaMKII activation in heart. The inhibitory effect of PP was stronger for CaMKIIalpha compared to CaMKIIdelta. Simulation results revealed a potential involvement of CaMKIIdelta autophosphorylation in the frequency-dependent acceleration of relaxation at physiological heart rates and PP concentrations.

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

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

Regulation of the glucose supply from capillary to tissue examined by developing a capillary model.

A new glucose transport model relying upon diffusion and convection across the capillary membrane was developed, and supplemented with tissue space and lymph flow. The rate of glucose utilization (J util) in the tissue space was described as a saturation function of glucose concentration in the interstitial fluid (C glu,isf), and was varied by applying a scaling factor f to J max. With f = 0, the glucose diffusion ceased within ~20 min. While, with increasing f, the diffusion was accelerated through a decrease in C glu,isf, but the convective flux remained close to resting level. When the glucose supplying capacity of the capillary was measured with a criterion of J util /J max = 0.5, the capacity increased in proportion to the number of perfused capillaries. A consistent profile of declining C glu,isf along the capillary axis was observed at the criterion of 0.5 irrespective of the capillary number. Increasing blood flow scarcely improved the supplying capacity.

Ionic mechanisms of cardiac cell swelling induced by blocking Na+/K+ pump as revealed by experiments and simulation.

Although the Na(+)/K(+) pump is one of the key mechanisms responsible for maintaining cell volume, we have observed experimentally that cell volume remained almost constant during 90 min exposure of guinea pig ventricular myocytes to ouabain. Simulation of this finding using a comprehensive cardiac cell model (Kyoto model incorporating Cl(-) and water fluxes) predicted roles for the plasma membrane Ca(2+)-ATPase (PMCA) and Na(+)/Ca(2+) exchanger, in addition to low membrane permeabilities for Na(+) and Cl(-), in maintaining cell volume. PMCA might help maintain the [Ca(2+)] gradient across the membrane though compromised, and thereby promote reverse Na(+)/Ca(2+) exchange stimulated by the increased [Na(+)](i) as well as the membrane depolarization. Na(+) extrusion via Na(+)/Ca(2+) exchange delayed cell swelling during Na(+)/K(+) pump block. Supporting these model predictions, we observed ventricular cell swelling after blocking Na(+)/Ca(2+) exchange with KB-R7943 or SEA0400 in the presence of ouabain. When Cl(-) conductance via the cystic fibrosis transmembrane conductance regulator (CFTR) was activated with isoproterenol during the ouabain treatment, cells showed an initial shrinkage to 94.2 +/- 0.5%, followed by a marked swelling 52.0 +/- 4.9 min after drug application. Concomitantly with the onset of swelling, a rapid jump of membrane potential was observed. These experimental observations could be reproduced well by the model simulations. Namely, the Cl(-) efflux via CFTR accompanied by a concomitant cation efflux caused the initial volume decrease. Then, the gradual membrane depolarization induced by the Na(+)/K(+) pump block activated the window current of the L-type Ca(2+) current, which increased [Ca(2+)](i). Finally, the activation of Ca(2+)-dependent cation conductance induced the jump of membrane potential, and the rapid accumulation of intracellular Na(+) accompanied by the Cl(-) influx via CFTR, resulting in the cell swelling. The pivotal role of L-type Ca(2+) channels predicted in the simulation was demonstrated in experiments, where blocking Ca(2+) channels resulted in a much delayed cell swelling.

simBio: a Java package for the development of detailed cell models.

Quantitative dynamic computer models, which integrate a variety of molecular functions into a cell model, provide a powerful tool to create and test working hypotheses. We have developed a new modeling tool, the simBio package (freely available from ), which can be used for constructing cell models, such as cardiac cells (the Kyoto model from Matsuoka et al., 2003, 2004 a, b, the LRd model from Faber and Rudy, 2000, and the Noble 98 model from Noble et al., 1998), epithelial cells (Strieter et al., 1990) and pancreatic beta cells (Magnus and Keizer, 1998). The simBio package is written in Java, uses XML and can solve ordinary differential equations. In an attempt to mimic biological functional structures, a cell model is, in simBio, composed of independent functional modules called Reactors, such as ion channels and the sarcoplasmic reticulum, and dynamic variables called Nodes, such as ion concentrations. The interactions between Reactors and Nodes are described by the graph theory and the resulting graph represents a blueprint of an intricate cellular system. Reactors are prepared in a hierarchical order, in analogy to the biological classification. Each Reactor can be composed or improved independently, and can easily be reused for different models. This way of building models, through the combination of various modules, is enabled through the use of object-oriented programming concepts. Thus, simBio is a straightforward system for the creation of a variety of cell models on a common database of functional modules.