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

Modeling CICR in rat ventricular myocytes: voltage clamp studies

<p>Abstract</p> <p>Background</p> <p>The past thirty-five years have seen an intense search for the molecular mechanisms underlying calcium-induced calcium-release (CICR) in cardiac myocytes, with voltage clamp (VC) studies being the leading tool employed. Several VC protocols including lowering of extracellular calcium to affect <it>Ca</it>²⁺loading of the sarcoplasmic reticulum (SR), and administration of blockers caffeine and thapsigargin have been utilized to probe the phenomena surrounding SR <it>Ca</it>²⁺release. Here, we develop a deterministic mathematical model of a rat ventricular myocyte under VC conditions, to better understand mechanisms underlying the response of an isolated cell to calcium perturbation. Motivation for the study was to pinpoint key control variables influencing CICR and examine the role of CICR in the context of a physiological control system regulating cytosolic <it>Ca</it>²⁺concentration ([<it>Ca</it>²⁺]<it>_myo</it>).</p> <p>Methods</p> <p>The cell model consists of an electrical-equivalent model for the cell membrane and a fluid-compartment model describing the flux of ionic species between the extracellular and several intracellular compartments (cell cytosol, SR and the dyadic coupling unit (DCU), in which resides the mechanistic basis of CICR). The DCU is described as a controller-actuator mechanism, internally stabilized by negative feedback control of the unit's two diametrically-opposed <it>Ca</it>²⁺channels (trigger-channel and release-channel). It releases <it>Ca</it>²⁺flux into the cyto-plasm and is in turn enclosed within a negative feedback loop involving the SERCA pump, regulating[<it>Ca</it>²⁺]<it>_myo</it>.</p> <p>Results</p> <p>Our model reproduces measured VC data published by several laboratories, and generates graded <it>Ca</it>²⁺release at high <it>Ca</it>²⁺gain in a homeostatically-controlled environment where [<it>Ca</it>²⁺]<it>_myo</it>is precisely regulated. We elucidate the importance of the DCU elements in this process, particularly the role of the ryanodine receptor in controlling SR <it>Ca</it>²⁺release, its activation by trigger <it>Ca</it>²⁺, and its refractory characteristics mediated by the luminal SR <it>Ca</it>²⁺sensor. Proper functioning of the DCU, sodium-calcium exchangers and SERCA pump are important in achieving negative feedback control and hence <it>Ca</it>²⁺homeostasis.</p> <p>Conclusions</p> <p>We examine the role of the above <it>Ca</it>²⁺regulating mechanisms in handling various types of induced disturbances in <it>Ca</it>²⁺levels by quantifying cellular <it>Ca</it>²⁺balance. Our model provides biophysically-based explanations of phenomena associated with CICR generating useful and testable hypotheses.</p

Changes in Intracellular Na+ following Enhancement of Late Na+ Current in Virtual Human Ventricular Myocytes

The slowly inactivating or late Na+ current, INa-L, can contribute to the initiation of both atrial and ventricular rhythm disturbances in the human heart. However, the cellular and molecular mechanisms that underlie these pro-arrhythmic influences are not fully understood. At present, the major working hypothesis is that the Na+ influx corresponding to I(Na-L)significantly increases intracellular Na+, [Na]; and the resulting reduction in the electrochemical driving force for Na+ reduces and (may reverse) Na+/Ca2+ exchange. These changes increase intracellular Ca2+, [Ca2+]; which may further enhance I(Na-L)due to calmodulindependent phosphorylation of the Na+ channels. This paper is based on mathematical simulations using the O'Hara et al (2011) model of baseline or healthy human ventricular action potential waveforms(s) and its [Ca2(+)]; homeostasis mechanisms. Somewhat surprisingly, our results reveal only very small changes (<= 1.5 mM) in [Na] even when INa-L is increased 5-fold and steady-state stimulation rate is approximately 2 times the normal human heart rate (i.e. 2 Hz). Previous work done using well-established models of the rabbit and human ventricular action potential in heart failure settings also reported little or no change in [Na] when I(Na-L)was increased. Based on our simulations, the major short-term effect of markedly augmenting I(Na-L)is a significant prolongation of the action potential and an associated increase in the likelihood of reactivation of the L-type Ca2+ current, Ica-L. Furthermore, this action potential prolongation does not contribute to [Na]; increase.This work was supported by (i) the "VI Plan Nacional de Investigacion Cientifica, Desarrollo e Innovacion Tecnologica" from the Ministerio de Economia y Competitividad of Spain (grant number TIN2012-37546-C03-01) and the European Commission (European Regional Development Funds-ERDF-FEDER), (ii) by the Direccion General de Politica Cientifica de la Generalitat Valenciana (grant number GV/2013/119), and by (iii), Programa Prometeo (PROMETEO/2016/088) de la Conselleria d'Educacio Formacio I Ocupacio, Generalitat Valenciana. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.K Cardona; Trénor Gomis, BA.; W Giles (2016). Changes in Intracellular Na+ following Enhancement of Late Na+ Current in Virtual Human Ventricular Myocytes. PLoS ONE. 11(11). https://doi.org/10.1371/journal.pone.0167060S111

Different Densities of Na-Ca Exchange Current in T-Tubular and Surface Membranes and Their Impact on Cellular Activity in a Model of Rat Ventricular Cardiomyocyte

The ratio of densities of Na-Ca exchanger current ( NaCa ) in the t-tubular and surface membranes ( NaCa -ratio) computed from the values of NaCa and membrane capacitances ( m ) measured in adult rat ventricular cardiomyocytes before and after detubulation ranges between 1.7 and 25 (potentially even 40). Variations of action potential waveform and of calcium turnover within this span of the NaCa -ratio were simulated employing previously developed model of rat ventricular cell incorporating separate description of ion transport systems in the t-tubular and surface membranes. The increase of NaCa -ratio from 1.7 to 25 caused a prolongation of APD (duration of action potential at 90% repolarisation) by 12, 9, and 6% and an increase of peak intracellular Ca 2+ transient by 45, 2+ transient was a consequence of a higher Ca 2+ load in sarcoplasmic reticulum induced by the increased Ca 2+ cycling between the surface and t-tubular membranes. However, the reason for large differences in the NaCa -ratio assessed from measurements in adult rat cardiomyocytes remains to be explained

Different Densities of Na-Ca Exchange Current in T-Tubular and Surface Membranes and Their Impact on Cellular Activity in a Model of Rat Ventricular Cardiomyocyte

The ratio of densities of Na-Ca exchanger current (INaCa) in the t-tubular and surface membranes (INaCa-ratio) computed from the values of INaCa and membrane capacitances (Cm) measured in adult rat ventricular cardiomyocytes before and after detubulation ranges between 1.7 and 25 (potentially even 40). Variations of action potential waveform and of calcium turnover within this span of the INaCa-ratio were simulated employing previously developed model of rat ventricular cell incorporating separate description of ion transport systems in the t-tubular and surface membranes. The increase of INaCa-ratio from 1.7 to 25 caused a prolongation of APD (duration of action potential at 90% repolarisation) by 12, 9, and 6% and an increase of peak intracellular Ca2+ transient by 45, 19, and 6% at 0.1, 1, and 5 Hz, respectively. The prolonged APD resulted from the increase of INaCa due to the exposure of a larger fraction of Na-Ca exchangers to higher Ca2+ transients under the t-tubular membrane. The accompanying rise of Ca2+ transient was a consequence of a higher Ca2+ load in sarcoplasmic reticulum induced by the increased Ca2+ cycling between the surface and t-tubular membranes. However, the reason for large differences in the INaCa-ratio assessed from measurements in adult rat cardiomyocytes remains to be explained

Role of t-tubules in the control of trans-sarcolemmal ion flux and intracellular Ca2+ in a model of the rat cardiac ventricular myocyte

The t-tubules of mammalian ventricular myocytes are invaginations of the surface membrane that form a complex network within the cell, with restricted diffusion to the bulk extracellular space. The trans-sarcolemmal flux of many ions, including Ca2+, occurs predominantly across the t-tubule membrane and thus into and out of this restricted diffusion space. It seems possible, therefore, that ion concentration changes may occur in the t-tubule lumen, which would alter ion flux across the t-tubule membrane. We have used a computer model of the ventricular myocyte, incorporating a t-tubule compartment and experimentally determined values for diffusion between the t-tubule lumen and bulk extracellular space, and ion fluxes across the t-tubule membrane, to investigate this possibility. The results show that influx and efflux of different ion species across the t-tubule membrane are similar, but not equal. Changes of ion concentration can therefore occur close to the t-tubular membrane, thereby altering trans-sarcolemmal ion flux and thus cell function, although such changes are reduced by diffusion to the bulk extracellular space. Slowing diffusion results in larger changes in luminal ion concentrations. These results provide a deeper understanding of the role of the t-tubules in normal cell function, and are a basis for understanding the changes that occur in heart failure as a result of changes in t-tubule structure and ion fluxes.</p

Quantification of t-tubule area and protein distribution in rat cardiac ventricular myocytes

International audienceThe transverse (t-) tubules of cardiac ventricular myocytes are invaginations of the surface membrane that form a complex network within the cell. Many of the key proteins involved in excitation-contraction coupling appear to be located predominantly at the t-tubule membrane. Despite their importance, the fraction of cell membrane within the t-tubules remains unclear: measurement of cell capacitance following detubulation suggests approximately 32%, whereas optical measurements suggest up to approximately 65%. We have, therefore, investigated the factors that may account for this discrepancy. Calculation of the combinations of t-tubule radius, length and density that produce t-tubular membrane fractions of 32% or 56% suggest that the true fraction is at the upper end of this range. Assessment of detubulation using confocal and electron microscopy suggests that incomplete detubulation can account for some, but not all of the difference. High cholesterol, and a consequent decrease in specific capacitance, in the t-tubule membrane, may also cause the t-tubule fraction calculated from the loss of capacitance following detubulation to be underestimated. Correcting for both of these factors results in an estimate that is still lower than that obtained from optical measurements suggesting either that optical methods overestimate the fraction of membrane in the t-tubules, or that other, unknown, factors, reduce the apparent fraction obtained by detubulation. A biophysically realistic computer model of a rat ventricular myocyte, incorporating a t-tubule network, is used to assess the effect of the altered estimates of t-tubular membrane fraction on the calculated distribution of ion flux pathways

Cardiac cell modelling: observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field