Calcium and IP3 dynamics in cardiac myocytes: experimental and computational perspectives and approaches.

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).

Multi-core CPU or GPU-accelerated Multiscale Modeling for Biomolecular Complexes.

Multi-scale modeling plays an important role in understanding the structure and biological functionalities of large biomolecular complexes. In this paper, we present an efficient computational framework to construct multi-scale models from atomic resolution data in the Protein Data Bank (PDB), which is accelerated by multi-core CPU and programmable Graphics Processing Units (GPU). A multi-level summation of Gaus-sian kernel functions is employed to generate implicit models for biomolecules.

Sensitivity of rabbit ventricular action potential and Ca²⁺ dynamics to small variations in membrane currents and ion diffusion coefficients.

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.

Molecular and subcellular-scale modeling of nucleotide diffusion in the cardiac myofilament lattice.

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.

Modeling effects of L-type ca(2+) current and na(+)-ca(2+) exchanger on ca(2+) trigger flux in rabbit myocytes with realistic T-tubule geometries.

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.

Slow Calcium-Depolarization-Calcium waves may initiate fast local depolarization waves in ventricular tissue.

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.

Modelling cardiac calcium sparks in a three-dimensional reconstruction of a calcium release unit.

Triggered release of Ca2+ from an individual sarcoplasmic reticulum (SR) Ca(2+) release unit (CRU) is the fundamental event of cardiac excitation–contraction coupling, and spontaneous release events (sparks) are the major contributor to diastolic Ca(2+) leak in cardiomyocytes. Previous model studies have predicted that the duration and magnitude of the spark is determined by the local CRU geometry, as well as the localization and density of Ca(2+) handling proteins. We have created a detailed computational model of a CRU, and developed novel tools to generate the computational geometry from electron tomographic images.

Multiscale modeling of calcium dynamics in ventricular myocytes with realistic transverse tubules.

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.

Numerical analysis of Ca2+ signaling in rat ventricular myocytes with realistic transverse-axial tubular geometry and inhibited sarcoplasmic reticulum.

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.

Multiscale modeling in rodent ventricular 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].

Effects of Mg2+, pH and PCr on cardiac excitation-metabolic coupling.

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+).

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.

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.

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.

Modeling beta-adrenergic control of cardiac myocyte contractility in silico.

The beta-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 beta-adrenergic signaling with excitation-contraction coupling was formulated, and each subsystem was validated with independent biochemical and physiological measurements.

Spatiotemporal features of Ca2+ buffering and diffusion in atrial cardiac myocytes with inhibited sarcoplasmic reticulum.

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.