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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]

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]

Calcium plays a crucial role in excitation-contraction coupling (ECC), but it is also a pivotal second messenger activating Ca(2+)-dependent transcription factors in a process termed excitation-transcription coupling (ETC). Evidence accumulated over the past decade indicates a pivotal role of inositol 1,4,5-trisphosphate receptor (IP3R)-mediated Ca(2+) release in the regulation of cytosolic and nuclear Ca(2+) signals. IP3 is generated by stimulation of plasma membrane receptors that couple to phospholipase C (PLC), liberating IP3 from phosphatidylinositol 4,5-bisphosphate (PIP2). An intriguing aspect of IP3 signaling is the presence of the entire PIP2-PLC-IP3 signaling cascade as well as the presence of IP3Rs at the inner and outer membranes of the nuclear envelope (NE) which functions as a Ca(2+) store. The observation that the nucleus is surrounded by its own putative Ca(2+) store raises the possibility that nuclear IP3-dependent Ca(2+) release plays a critical role in ETC. This provides a potential mechanism of regulation that acts locally and autonomously from the global cytosolic Ca(2+) signal underlying ECC. Moreover, there is evidence that: (i) the sarcoplasmic reticulum (SR) and NE are a single contiguous Ca(2+) store; (ii) the nuclear pore complex is the major gateway for Ca(2+) and macromolecules to pass between the cytosol and the nucleoplasm; (iii) the inner membrane of the NE hosts key Ca(2+) handling proteins including the Na(+)/Ca(2+) exchanger (NCX)/GM1 complex, ryanodine receptors (RyRs), nicotinic acid adenine dinucleotide phosphate receptors (NAADPRs), Na(+)/K(+) ATPase, and Na(+)/H(+) exchanger. Thus, it appears that the nucleus represents a Ca(2+) signaling domain equipped with its own ion channels and transporters that allow for complex local Ca(2+) signals. Many experimental and modeling approaches have been used for the study of intracellular Ca(2+) signaling but the key to the understanding of the dual role of Ca(2+) mediating ECC and ECT lays in quantitative differences of local [Ca(2+)] in the nuclear and cytosolic compartment. In this review, we discuss the state of knowledge regarding the origin and the physiological implications of nuclear Ca(2+) transients in different cardiac cell types (adult atrial and ventricular myocytes) as well as experimental and mathematical approaches to study Ca(2+) and IP3 signaling in the cytosol and nucleus. In particular, we focus on the concept that highly localized Ca(2+) signals are required to translocate and activate Ca(2+)-dependent transcription factors (e.g., nuclear factor of activated T-cells, NFAT; histone deacetylase, HDAC) through phosphorylation/dephosphorylation processes.

Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions., (Copyright © 2013 The Authors. Published by Elsevier Inc. All rights reserved.)

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.

The transverse tubular system of rabbit ventricular myocytes consists of cell membrane invaginations (t-tubules) that are essential for efficient cardiac excitation-contraction coupling. In this study, we investigate how t-tubule micro-anatomy, L-type Ca(2+) channel (LCC) clustering, and allosteric activation of Na(+)/Ca(2+) exchanger by L-type Ca(2+) current affects intracellular Ca(2+) 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(+)/Ca(2+) exchanger, sarcolemmal Ca(2+) pump, and sarcolemmal Ca(2+) leak), and stationary and mobile Ca(2+) 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 intracellular Ca(2+). We obtained parameters from voltage-clamp protocols of L-type Ca(2+) current and line-scan recordings of Ca(2+) concentration profiles in rabbit cells, in which the sarcoplasmic reticulum is disabled. Our model results agree with experimental measurements of global Ca(2+) transient in myocytes loaded with 50 μM Fluo-3. We found that local Ca(2+) concentrations within the cytosol and sub-sarcolemma, as well as the local trigger fluxes of Ca(2+) crossing the cell membrane, are sensitive to details of t-tubule micro-structure and membrane Ca(2+) flux distribution. The model additionally predicts that local Ca(2+) trigger fluxes are at least threefold to eightfold higher than the whole-cell Ca(2+) trigger flux. We found also that the activation of allosteric Ca(2+)-binding sites on the Na(+)/Ca(2+) exchanger could provide a mechanism for regulating global and local Ca(2+) trigger fluxes in vivo. Our studies indicate that improved structural and functional models could improve our understanding of the contributions of L-type and Na(+)/Ca(2+) exchanger fluxes to intracellular Ca(2+) dynamics.

The t-tubules 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 (Ca(2+)). To investigate how the t-tubule microanatomy and the distribution of membrane Ca(2+) flux affect cardiac excitation-contraction coupling we developed a 3-D continuum model of Ca(2+) 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 Ca(2+) signaling requires more accurate knowledge of the t-tubule ultra-structure and Ca(2+) flux distribution along the sarcolemma. The results reveal the important role for mobile and stationary Ca(2+) buffers, including the Ca(2+) 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 Ca(2+) transients was found when the Ca(2+) flux was heterogeneously distributed along the sarcolemma. In the absence of fluorescence dye, strongly non-uniform Ca(2+) signals are predicted. Even at modest elevation of Ca(2+), reached during Ca(2+) influx, large and steep Ca(2+) gradients are found in the narrow sub-sarcolemmal space. The model predicts that the branched t-tubule structure and changes in the normal Ca(2+) flux density along the cell membrane support initiation and propagation of Ca(2+) waves in rat myocytes.

There is a growing body of experimental evidence suggesting that the Ca(2+) signaling in ventricular myocytes is characterized by a high gradient near the cell membrane and a more uniform Ca(2+) distribution in the cell interior [1]--[7]. An important reason for this phenomenon might be that in these cells the t-tubular system forms a network of extracellular space, extending deep into the cell interior. This allows the electrical signal, that propagates rapidly along the cell membrane, to reach the vicinity of the sarcoplasmic reticulum (SR), where intracellular Ca(2+) required for myofilament activation is stored [1], [8]--[11]. Early studies of cardiac muscle showed that the t-tubules are found at intervals of about 2 lm along the longitudinal cell axis in close proximity to the Z-disks of the sarcomeres [12]. Subsequent studies have demonstrated that the t-tubular system has also longitudinal extensions [9]--[11], [13].

A tight coupling between ionic currents, intracellular Ca2+ homeostasis, cytosolic [ADP] and deltaG of ATP hydrolysis underlies the regulation of cardiac cell function. As more experimental detail on the biochemistry and biophysics of these complex processes and their interactions accumulates, the intuitive interpretation of the new findings becomes increasingly impractical. For this reason we developed detailed biophysical model that couples Ca2+ signaling, cell electrophysiology and bioenergetics with the main interactions between phosphorylated species (ATP, ADP, AMP, PCr, Cr, P(i)) and Lewis cytosolic acids (Na+, K+, Mg2+, H+). The results indicate that the increase in free cytosolic Mg2+ (0.2-5 mM) systematically shortens the action potential duration. The analysis suggests that that under physiological conditions a pH decrease accompanied by a free Mg2+ increase tends to counteract an [ADP] increase due to PCr depletion. The model reproduces qualitatively a sequence of events that correlates well with the experimental data.

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.

Ca(2+) signaling in cells is largely governed by Ca(2+) diffusion and Ca(2+) binding to mobile and stationary Ca(2+) buffers, including organelles. To examine Ca(2+) signaling in cardiac atrial myocytes, a mathematical model of Ca(2+) diffusion was developed which represents several subcellular compartments, including a subsarcolemmal space with restricted diffusion, a myofilament space, and the cytosol. The model was used to quantitatively simulate experimental Ca(2+) signals in terms of amplitude, time course, and spatial features. For experimental reference data, L-type Ca(2+) currents were recorded from atrial cells with the whole-cell voltage-clamp technique. Ca(2+) signals were simultaneously imaged with the fluorescent Ca(2+) indicator Fluo-3 and a laser-scanning confocal microscope. The simulations indicate that in atrial myocytes lacking T-tubules, Ca(2+) movement from the cell membrane to the center of the cells relies strongly on the presence of mobile Ca(2+) buffers, particularly when the sarcoplasmic reticulum is inhibited pharmacologically. Furthermore, during the influx of Ca(2+) large and steep concentration gradients are predicted between the cytosol and the submicroscopically narrow subsarcolemmal space. In addition, the computations revealed that, despite its low Ca(2+) affinity, ATP acts as a significant buffer and carrier for Ca(2+), even at the modest elevations of [Ca(2+)](i) reached during influx of Ca(2+).