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To investigate the mechanisms regulating excitation-metabolic coupling in rabbit epicardial, midmyocardial, and endocardial ventricular myocytes we extended the LabHEART model (Puglisi JL and Bets DM. Am J Physiol Cell Physiol 281: C2049-C2060, 2001). We incorporated equations for [Ca.sup.2+] and [Mg.sup.2+] buffering by ATP and ADP, equations for nucleotide regulation of ATP-sensitive [K.sup.+] channel and L-type [Ca.sup.2+] channel, [Na.sup.+]-[K.sup.+]-ATPase, and sarcolemmal and sarcoplasmic [Ca.sup.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 rain of ischemia, the three regions were characterized by different [I.sub.Na],[I.sub.to], [I.sub.Kr][I.sub.Ks] and [I.sub.Kp] channel properties. The results indicate that the ATP-sensitive [K.sup.+] channel is activated by the smallest reduction in ATP in epicardial cells and largest in endocardial cells when cytosolic ADP, AMP, PCr, Cr, [P.sub.i], total [Mg.sup.2+], [Na.sup.+], [K.sup.+], [Ca.sup.2+], and pH diastolic levels are normal. The model predicts that only [K.sub.ATP] ionophore (Kit6.2 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 KATP channel opening through metabolic interactions with the endogenous PI cascade (PI[P.sub.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. ATP-sensitive [K.sup.+] channel; creatine and adenylate kinase reactions; phosphatidylinositol phosphates; heart; mathematical model

Little is known about how small variations in ionic currents and Ca2+ and Na+ diffusion coefficients impact action potential and Ca2+ dynamics in rabbit ventricular myocytes. We applied sensitivity analysis to quantify the sensitivity of Shannon et al. model (Biophys. J., 2004) to 5%-10% changes in currents conductance, channels distribution, and ion diffusion in rabbit ventricular cells. We found that action potential duration and Ca2+ peaks are highly sensitive to 10% increase in L-type Ca2+ current; moderately influenced by 10% increase in Na+-Ca2+ exchanger, Na+-K+ pump, rapid delayed and slow transient outward K+ currents, and Cl-background current; insensitive to 10% increases in all other ionic currents and sarcoplasmic reticulum Ca2+ fluxes. Cell electrical activity is strongly affected by 5% shift of L-type Ca2+ channels and Na+-Ca2+ exchanger in between junctional and submembrane spaces while Ca2+-activated Cl--channel redistribution has the modest effect. Small changes in submembrane and cytosolic diffusion coefficients for Ca2+, but not in Na+ transfer, may alter notably myocyte contraction. Our studies highlight the need for more precise measurements and further extending and testing of the Shannon et al. model. Our results demonstrate usefulness of sensitivity analysis to identify specific knowledge gaps and controversies related to ventricular cell electrophysiology and Ca2+ signaling. [ABSTRACT FROM AUTHOR]

The transverse tubular system of rabbit ventricular myocytes consists of cell membrane invaginations (t-tubules) that are essential for efficient cardiac excitation-contraction cou-pling. In this study, we investigate how t-tubule micro-anatomy, L-type Ca2+ channel (LCC) clustering, and allosteric activation of Na+/Ca2+ exchanger by L-type Ca2+ current affects intracellular Ca2+ dynamics. Our model includes a realistic 3D geometry of a single t-tubule and its surrounding half-sarcomeres for rabbit ventricular myocytes. The effects of spatially distributed membrane ion-transporters (LCC, Na+/Ca2+ exchanger, sarcolemmal Ca2+ pump, and sarcolemmal Ca2+ leak), and stationary and mobile Ca2+ buffers (troponin C, ATP, calmodulin, and Fluo-3) are also considered.We used a coupled reaction-diffusion system to describe the spatio-temporal concentration profiles of free and buffered intracel-lular Ca2+.We obtained parameters from voltage-clamp protocols of L-type Ca2+ current and line-scan recordings of Ca2+ concentration profiles in rabbit cells, in which the sar-coplasmic reticulum is disabled. Our model results agree with experimental measurements of global Ca2+ transient in myocytes loaded with 50 μM Fluo-3.We found that local Ca2+ concentrations within the cytosol and sub-sarcolemma, as well as the local trigger fluxes of Ca2+ crossing the cell membrane, are sensitive to details of t-tubule micro-structure and membrane Ca2+ flux distribution. The model additionally predicts that local Ca2+ trigger fluxes are at least threefold to eightfold higher than the whole-cell Ca2+ trigger flux. We found also that the activation of allosteric Ca2+-binding sites on the Na+/Ca2+ exchanger could provide a mechanism for regulating global and local Ca2+ trigger fluxes in vivo. Our studies indicate that improved structural and functional models could improve our under-standing of the contributions of L-type and Na+/Ca2+ exchanger fluxes to intracellular Ca2+ dynamics. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various papers within the issue on topics including biomedical engineering, computational biology and the role of ontologies in biology.

Spatial-temporal Ca^2+ dynamics due to Ca^2+ release, buffering, and reuptaking plays a central role in studying excitation–contraction (E–C) coupling in both normal and diseased cardiac myocytes. In this paper, we employ two numerical methods, namely, the meshless method and the finite element method, to model such Ca^2+ behaviors by solving a nonlinear system of reaction–diffusion partial differential equations at two scales. In particular, a subcellular model containing several realistic transverse tubules (or t-tubules) is investigated and assumed to reside at different locations relative to the cell membrane. To this end, the Ca^2+ concentration calculated from the whole-cell modeling is adopted as part of the boundary constraint in the subcellular model. The preliminary simulations show that Ca^2+ concentration changes in ventricular myocytes are mainly influenced by calcium release from t-tubules. [ABSTRACT FROM AUTHOR]

The t-tubule's of mammalian ventricular myocytes are invaginations of the cell membrane that occur at each Z-line. These invaginations branch within the cell to form a complex network that allows rapid propagation of the electrical signal, and hence synchronous rise of intracellular calcium (Ca2+). To investigate how the t-tubulemicroanatomy and the distribution of membrane Ca2+ flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca2+ signaling, buffering and diffusion in rat ventricular myocytes. The transverse-axial t-tubule geometry was derived from light microscopy structural data. To solve the nonlinear reaction-diffusion system we extended SMOL software tool (http://mccammon.ucsd.edu/smol/). The analysis suggests that the quantitative understanding of the Ca2+ signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca2+ flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca2+ buffers, including the Ca2+ indicator dye. In agreement with experiment, in the presence of fluorescence dye and inhibited sarcoplasmic reticulum, the lack of detectible differences in the depolarization-evoked Ca2+ transients was found when the Ca2+ flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca2+ signals are predicted. Even at modest elevation of Ca2+, reached during Ca2+ influx, large and steep Ca2+ gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca2+ flux density along the cell membrane support initiation and propagation of Ca2+ waves in rat myocytes. [ABSTRACT FROM AUTHOR]

The article presents a discussion on the developed three dimensional (3-D) continuum model used for the laboratory observation of calcium ion (Ca2+) properties on rat myocytes. It provides information on the geometrical model and structural data observed and gathered on the rat's ventricular muscle cell. It also investigates mechanisms involving the basic principles of excitation-contraction (EC) coupling propagation in the observed ventricular myocytes. The study also reveals that the local Ca2+ spatiotemporal features signals that relies on the axial and cell surface diffusion distances.

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 Ca2+ and Mg2+ buffering by ATP and ADP, equations for nucleotide regulation of ATP-sensitive K+ channel and L-type Ca2+ channel, Na+-K+-ATPase, and sarcolemmal and sarcoplasmic Ca2+-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 mm of ischemia, the three regions were characterized by different INa, Ito, IKr, IKs, and IKp 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, Pi, total Mg2+, Na+, K+, Ca2+, and pH diastolic levels are normal. The model predicts that only KATP 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 KATP channel opening through metabolic interactions with the endogenous PI cascade (PIP2, 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. [ABSTRACT FROM AUTHOR]

The β-adrenergic signaling pathway regulates cardiac myocyte contractility through a combination of feedforward and feedback mechanisms. We used systems analysis to investigate how the components and topology of this signaling network permit neurohormonal control of excitation-contraction coupling in the rat ventricular myocyte. A kinetic model integrating β-adrenergic signaling with excitation-contraction coupling was formulated, and each subsystem was validated with independent biochemical and physiological measurements. Model analysis was used to investigate quantitatively the effects of specific molecular perturbations. 3-Fold overexpression of adenylyl cyclase in the model allowed an 85% higher rate of cyclic AMP synthesis than an equivalent overexpression of β[sub 1]-adrenergic receptor, and manipulating the affinity of G[sub s]α for adenylyl cyclase was a more potent regulator of cyclic AMP production. The model predicted that less than 40% of adenylyl cyclase molecules may be stimulated under maximal receptor activation, and an experimental protocol is suggested for validating this prediction. The model also predicted that the endogenous heat-stable protein kinase inhibitor may enhance basal cyclic AMP buffering by 68% and increasing the apparent Hill coefficient of protein kinase A activation from 1.0 to 2.0. Finally, phosphorylation of the L-type calcium channel and phospholamban were found sufficient to predict the dominant changes in myocyte contractility, including a 2.6× increase in systolic calcium (inotropy) and a 28% decrease in calcium half-relaxation time (lusitropy). By performing systems analysis, the consequences of molecular perturbations in the β-adrenergic signaling network may be understood within the context of integrative cellular physiology. [ABSTRACT FROM AUTHOR]

Abstract: Intercellular calcium waves in cardiac myocytes are a well-recognized, if incompletely understood, phenomenon. In a variety of preparations, investigators have reported multi-cellular calcium waves or triggered propagated contractions, but the mechanisms of propagation and pathological importance of these events remain unclear. Here, we review existing experimental data and present a computational approach to investigate the mechanisms of multi-cellular calcium wave propagation. Over the past 50 years, the standard modeling paradigm for excitable cardiac tissue has seen increasingly detailed models of the dynamics of individual cells coupled in tissue solely by intercellular and interstitial current flow. Although very successful, this modeling regime has been unable to capture two important phenomena: 1) the slow intercellular calcium waves observed experimentally, and 2) how intercellular calcium events resulting in delayed after depolarizations at the cellular level could overcome a source-sink mismatch to initiate depolarization waves in tissue. In this paper, we introduce a mathematical model with subcellular spatial resolution, in which we allow both inter- and intracellular current flow and calcium diffusion. In simulations of coupled cells employing this model, we observe: a) slow inter-cellular calcium waves propagating at about 0.1 mm/s, b) faster Calcium-Depolarization-Calcium (CDC) waves, traveling at about 1 mm/s, and c) CDC-waves that can set off fast depolarization-waves (50 cm/s) in tissue with varying gap-junction conductivity. [Copyright &y& Elsevier]