Anushka Michailova

Modeling β-Adrenergic Control of Cardiac Myocyte Contractility in Silico

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 β1-adrenergic receptor, and manipulating the affinity of Gsα 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.

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

We extended the model of the ventricular myocyte by Winslow et al. (Circ. Res 1999, 84:571-586) by incorporating 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). The results indicate that, under normal conditions, Ca(2+) binding by low-affinity ATP and diffusion of CaATP may affect the amplitude and time course of intracellular Ca(2+) signals. The model also suggests that a fall in ATP/ADP ratio significantly reduces sarcoplasmic Ca(2+) content, increases diastolic Ca(2+), lowers systolic Ca(2+), increases Ca(2+) influx through L-type channels, and decreases the efficiency of the Na(+)/Ca(2+) exchanger in extruding Ca(2+) during periodic voltage-clamp stimulation. The analysis suggests that the most important reason for these changes during metabolic inhibition is the down-regulation of the sarcoplasmic Ca(2+)-ATPase pump by reduced diastolic MgATP levels. High Ca(2+) concentrations developed near the membrane might have a greater influence on Mg(2+), ATP, and ADP concentrations than that of the lower Ca(2+) concentrations in the bulk myoplasm. The model predictions are in general agreement with experimental observations measured under normal and pathological conditions.

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

•  We have developed a detailed computational model of a cardiac Ca2+ spark based on a three dimensional reconstruction of electron tomograms. •  Our model predicts near total junctional Ca2+ depletion after the spark, while regional Ca2+ reserve is preserved. The local Ca2+ gradient inferred by these findings reconciles previous model predictions with experimental measurements. •  Differences in local distribution of calsequestrin have a profound impact on spark termination time, as reported by Fluo5, solely based on its Ca2+ buffering capacity. •  The SERCA pump can prolong spark release time by pumping Ca2+ back into the junctional SR during the spark.

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 (Ca2+). To investigate how the t-tubule microanatomy 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.

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 Ca2+-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 Ca2+ release in the regulation of cytosolic and nuclear Ca2+ 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 Ca2+ store. The observation that the nucleus is surrounded by its own putative Ca2+ store raises the possibility that nuclear IP3-dependent Ca2+ release plays a critical role in ETC. This provides a potential mechanism of regulation that acts locally and autonomously from the global cytosolic Ca2+ signal underlying ECC. Moreover, there is evidence that: (i) the sarcoplasmic reticulum (SR) and NE are a single contiguous Ca2+ store; (ii) the nuclear pore complex is the major gateway for Ca2+ and macromolecules to pass between the cytosol and the nucleoplasm; (iii) the inner membrane of the NE hosts key Ca2+ handling proteins including the Na+/Ca2+ 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 Ca2+ signaling domain equipped with its own ion channels and transporters that allow for complex local Ca2+ signals. Many experimental and modeling approaches have been used for the study of intracellular Ca2+ signaling but the key to the understanding of the dual role of Ca2+ mediating ECC and ECT lays in quantitative differences of local [Ca2+] in the nuclear and cytosolic compartment. In this review, we discuss the state of knowledge regarding the origin and the physiological implications of nuclear Ca2+ transients in different cardiac cell types (adult atrial and ventricular myocytes) as well as experimental and mathematical approaches to study Ca2+ and IP3 signaling in the cytosol and nucleus. In particular, we focus on the concept that highly localized Ca2+ signals are required to translocate and activate Ca2+-dependent transcription factors (e.g., nuclear factor of activated T-cells, NFAT; histone deacetylase, HDAC) through phosphorylation/dephosphorylation processes.

Fractional factorial design for parameter sweep experiments using Nimrod/E

The techniques of formal experimental design and analysis are powerful tools for scientists and engineers. However, these techniques are currently underused for experiments conducted with computer models. This has motivated the incorporation of experimental design functionality into the Nimrod tool chain. Nimrod has been extensively used for exploration of the response of models to their input parameters; the addition of experimental design tools will combine the efficiency of carefully designed experiments with the power of distributed execution. This paper describes the incorporation of one type of design, the fractional factorial design, and associated analysis tools, into the Nimrod framework. The result provides a convenient environment that automates the design of an experiment, the execution of the jobs on a computational grid and the return of results, and which assists in the interpretation of those results. Several case studies are included which demonstrate various aspects of this approach.

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

Abstract 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 Gaussian kernel functions is employed to generate implicit models for biomolecules. The coefficients in the summation are designed as functions of the structure indices, which specify the structures at a certain level and enable a local resolution control on the biomolecular surface. A method called neighboring search is adopted to locate the grid points close to the expected biomolecular surface, and reduce the number of grids to be analyzed. For a specific grid point, a KD-tree or bounding volume hierarchy is applied to search for the atoms contributing to its density computation, and faraway atoms are ignored due to the decay of Gaussian kernel functions. In addition to density map construction, three modes are also employed and compared during mesh generation and quality improvement to generate high quality tetrahedral meshes: CPU sequential, multi-core CPU parallel and GPU parallel. We have applied our algorithm to several large proteins and obtained good results.

Modeling Effects of L-Type Ca2+ Current and Na+-Ca2+ Exchanger on Ca2+ 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 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 intracellular 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 sarcoplasmic 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 understanding of the contributions of L-type and Na+/Ca2+ exchanger fluxes to intracellular Ca2+ dynamics.

Multiscale modeling in rodent ventricular myocytes

This paper indicates that in ventricular myocytes when the SR (sarcoplasmic reticulum) is pharmacologically inhibited, the intracellular Ca²⁺concentration rapidly increases during Ca²⁺ entrance (0-70 ms), whereas the decay of Ca²⁺ is slow; in the absence of fluorescent dye, large Ca²⁺ concentration gradients might develop near the cell membrane; intracellular Ca²⁺ distribution is tightly regulated by the localization of Ca²⁺transporter proteins along the sarcolemma and strongly relays on the presence of mobile and stationary Ca²⁺ buffers. These studies also imply that in ventricular cells with intact and functional SR, the Ca²⁺ signal most likely would spread faster along the t-tubular system, surface membrane than to the cell interior and that in the absence of Ca²⁺ dye high Ca²⁺ gradients under the surface membrane and more uniform Ca²⁺ distribution in the cell interior might be expected.

Effects of Magnesium on Cardiac Excitation-Contraction Coupling

Objective: Magnesium regulates a large number of cellular processes. Small changes in intracellular free Mg2+ ([Mg2+]i) may have important effects on cardiac excitability and contractility. We investigated the effects of [Mg2+]i on cardiac excitation-contraction coupling. Methods: We used our ionic-metabolic model that incorporates equations for Ca2+ and Mg2+ buffering and transport by ATP and ADP and equations for MgATP regulation of ion transporters (Na+-K+ pump, sarcolemmal and sarcoplasmic Ca2+ pumps). Results: Model results indicate that variations in cytosolic Mg2+ level might sensitively affect diastolic and systolic Ca2+, sarcoplasmic Ca2+ content, Ca2+ influx through L-type channels, efficiency of the Na+/Ca2+ exchanger and action potential shape. The analysis suggests that the most important reason for the observed effects is a modified normal function of sarcoplasmic Ca2+-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.