Modelling the cardiac transverse-axial tubular system

Different effects of cardiomyocyte contractile activity on transverse and axial tubular system luminal content dynamics

BACKGROUND

Efficient excitation-contraction coupling of mammalian ventricular cardiomyocytes depends on the transverse-axial tubular system (TATS), a network of surface membrane invaginations. TATS enables tight coupling of sarcolemmal and sarcoplasmic reticulum membranes, which is essential for rapid Ca2+-induced Ca2+ release, and uniform contraction upon electrical stimulation. The majority of TATS in healthy ventricular cardiomyocytes is composed of transverse tubules (TT, ∼90 % of TATS in rabbit). The remainder consists of mostly axial tubules (AT), which are less abundant and less well studied. In disease, however, the relative abundance of TT and AT changes. The mechanisms and relevance of this change are not known, and understanding them requires a more targeted effort to study the dynamics of AT structure and function. While TATS content is continuous with the interstitial space, it is contained within a domain of restricted diffusion. We have previously shown that TT are cyclically squeezed during stretch and contraction. This can contribute to TT content mixing and accelerates luminal content exchange with the environment. Here, we explore the effects of cardiomyocyte stretch and contraction on AT.

METHODS

TATS structure and diffusion dynamics were studied using 3D electron tomography of rabbit left ventricular cardiomyocytes, preserved at rest or during contraction, and ventricular tissue preserved at rest or during stretch, as well as live-cell TATS content exchange measurements.

RESULTS

We show (i) that cardiomyocyte contraction is associated with an increase in the apparent speed of diffusion of TT content that scales with beating rate and degree of cell shortening. In contrast, (ii) AT develop membrane folds and constrictions during contraction, (iii) with no effect of contraction on luminal exchange dynamics, while (iv) cardiomyocyte stretch is associated with AT straightening and AT and TT 'squeezing' that (v) supports an acceleration of the apparent speed of diffusion in AT and TT. Finally, (vi) we present a simple computational model outlining the potential relevance of AT in healthy and diseased cells.

CONCLUSIONS

Our results indicate that TT and AT are differently affected by the cardiac contractile cycle, and suggest that AT may play a role in ensuring TATS network content homogeneity in diseased cardiomyocytes. Further research is needed to explore the interplay of structural and functional remodelling of different TATS components in failing myocardium.

Mechanisms of spontaneous Ca2+ release-mediated arrhythmia in a novel 3D human atrial myocyte model: II. Ca2+ -handling protein variation

Disruption of the transverse-axial tubule system (TATS) in diseases such as heart failure and atrial fibrillation occurs in combination with changes in the expression and distribution of key Ca2+ -handling proteins. Together this ultrastructural and ionic remodelling is associated with aberrant Ca2+ cycling and electrophysiological instabilities that underlie arrhythmic activity. However, due to the concurrent changes in TATs and Ca2+ -handling protein expression and localization that occur in disease it is difficult to distinguish their individual contributions to the arrhythmogenic state. To investigate this, we applied our novel 3D human atrial myocyte model with spatially detailed Ca2+ diffusion and TATS to investigate the isolated and interactive effects of changes in expression and localization of key Ca2+ -handling proteins and variable TATS density on Ca2+ -handling abnormality driven membrane instabilities. We show that modulating the expression and distribution of the sodium-calcium exchanger, ryanodine receptors and the sarcoplasmic reticulum (SR) Ca2+ buffer calsequestrin have varying pro- and anti-arrhythmic effects depending on the balance of opposing influences on SR Ca2+ leak-load and Ca2+ -voltage relationships. Interestingly, the impact of protein remodelling on Ca2+ -driven proarrhythmic behaviour varied dramatically depending on TATS density, with intermediately tubulated cells being more severely affected compared to detubulated and densely tubulated myocytes. This work provides novel mechanistic insight into the distinct and interactive consequences of TATS and Ca2+ -handling protein remodelling that underlies dysfunctional Ca2+ cycling and electrophysiological instability in disease. KEY POINTS: In our companion paper we developed a 3D human atrial myocyte model, coupling electrophysiology and Ca2+ handling with subcellular spatial details governed by the transverse-axial tubule system (TATS). Here we utilize this model to mechanistically examine the impact of TATS loss and changes in the expression and distribution of key Ca2+ -handling proteins known to be remodelled in disease on Ca2+ homeostasis and electrophysiological stability. We demonstrate that varying the expression and localization of these proteins has variable pro- and anti-arrhythmic effects with outcomes displaying dependence on TATS density. Whereas detubulated myocytes typically appear unaffected and densely tubulated cells seem protected, the arrhythmogenic effects of Ca2+ handling protein remodelling are profound in intermediately tubulated cells. Our work shows the interaction between TATS and Ca2+ -handling protein remodelling that underlies the Ca2+ -driven proarrhythmic behaviour observed in atrial fibrillation and may help to predict the effects of antiarrhythmic strategies at varying stages of ultrastructural remodelling.

Fraction of the T-Tubular Membrane as an Important Parameter in Cardiac Cellular Electrophysiology: A New Way of Estimation

The transverse-axial tubular system (t-tubules) plays an essential role in excitation-contraction coupling in cardiomyocytes. Its remodelling is associated with various cardiac diseases. Numerous attempts were made to analyse characteristics essential for proper understanding of the t-tubules and their impact on cardiac cell function in health and disease. The currently available methodical approaches related to the fraction of the t-tubular membrane area produce diverse data. The widely used detubulation techniques cause irreversible cell impairment, thus, distinct cell samples have to be used for estimation of t-tubular parameters in untreated and detubulated cells. Our proposed alternative method is reversible and allows repetitive estimation of the fraction of t-tubular membrane (f t) in cardiomyocytes using short-term perfusion of the measured cell with a low-conductive isotonic sucrose solution. It results in a substantial increase in the electrical resistance of t-tubular lumen, thus, electrically separating the surface and t-tubular membranes. Using the whole-cell patch-clamp measurement and the new approach in enzymatically isolated rat atrial and ventricular myocytes, a set of data was measured and evaluated. The analysis of the electrical equivalent circuit resulted in the establishment of criteria for excluding measurements in which perfusion with a low conductivity solution did not affect the entire cell surface. As expected, the final average f t in ventricular myocytes (0.337 ± 0.017) was significantly higher than that in atrial myocytes (0.144 ± 0.015). The parameter f t could be estimated repetitively in a particular cell (0.345 ± 0.021 and 0.347 ± 0.023 in ventricular myocytes during the first and second sucrose perfusion, respectively). The new method is fast, simple, and leaves the measured cell intact. It can be applied in the course of experiments for which it is useful to estimate both the surface and t-tubular capacitance/area in a particular cell.

Exploring the Coordination of Cardiac Ion Channels With Action Potential Clamp Technique

The patch clamp technique underwent continual advancement and developed numerous variants in cardiac electrophysiology since its introduction in the late 1970s. In the beginning, the capability of the technique was limited to recording one single current from one cell stimulated with a rectangular command pulse. Since that time, the technique has been extended to record multiple currents under various command pulses including action potential. The current review summarizes the development of the patch clamp technique in cardiac electrophysiology with special focus on the potential applications in integrative physiology.

Beat-by-Beat Cardiomyocyte T-Tubule Deformation Drives Tubular Content Exchange

Supplemental Digital Content is available in the text.

The sarcolemma of cardiomyocytes contains many proteins that are essential for electromechanical function in general, and excitation-contraction coupling in particular. The distribution of these proteins is nonuniform between the bulk sarcolemmal surface and membrane invaginations known as transverse tubules (TT). TT form an intricate network of fluid-filled conduits that support electromechanical synchronicity within cardiomyocytes. Although continuous with the extracellular space, the narrow lumen and the tortuous structure of TT can form domains of restricted diffusion. As a result of unequal ion fluxes across cell surface and TT membranes, limited diffusion may generate ion gradients within TT, especially deep within the TT network and at high pacing rates.

Diffusional and Electrical Properties of T-Tubules Are Governed by Their Constrictions and Dilations

Cardiac t-tubules (TTs) form a network of complex surface membrane invaginations that is essential for proper excitation-contraction coupling. Although electron and optical microscopy studies provided a wealth of important information about the structure of TTs, assessing their functional properties remains a challenge. In this study, we investigated the diffusional accessibility of TTs in intact isolated adult mouse ventricular myocytes using, to our knowledge, a novel fluorescence-based assay. In this approach, a small part of TTs is first locally filled with fluorescent dextran and then its diffusion out of TTs is monitored after rapid removal of extracellular dextran. In normal cells, diffusion of 3 kDa dextran is characterized by an average time constant of 3.9 ± 1.2 s with the data ranging from 1.8 to 10.5 s. The data are consistent with essentially free diffusion of dextran in TTs although measurable contribution of binding is also evident. TT fluorescence is abolished in cells treated with high concentration of formamide or after hyposmotic stress. Importantly, the assay we use allows for quantitative, repetitive measurements of subtle dynamic changes in TT structure of the same cell that are not possible to observe with other approaches. In particular, dextran diffusion rate decreases two-to-threefold during cell swelling, suggesting significant structural remodeling of TTs. Computer modeling shows that diffusional accessibility and electrical properties of TTs are primarily determined by the constrictions and dilations of individual TTs and that, from a functional perspective, TTs cannot be considered as a network of cylinders of the same average diameter. Constriction/dilation model of cardiac TTs is in a quantitative agreement with previous high-resolution microscopy studies of TT structure and alternative measurements of diffusional and electrical time constants of TTs. The data also show that the apparent electrical length constant of cardiac TTs is likely several-fold smaller than that estimated in earlier studies.

Quantitative assessment of passive electrical properties of the cardiac T-tubular system by FRAP microscopy

Well-coordinated activation of all cardiomyocytes must occur on every heartbeat. At the cell level, a complex network of sarcolemmal invaginations, called the transverse-axial tubular system (TATS), propagates membrane potential changes to the cell core, ensuring synchronous and uniform excitation-contraction coupling. Although myocardial conduction of excitation has been widely described, the electrical properties of the TATS remain mostly unknown. Here, we exploit the formal analogy between diffusion and electrical conductivity to link the latter with the diffusional properties of TATS. Fluorescence recovery after photobleaching (FRAP) microscopy is used to probe the diffusion properties of TATS in isolated rat cardiomyocytes: A fluorescent dextran inside TATS lumen is photobleached, and signal recovery by diffusion of unbleached dextran from the extracellular space is monitored. We designed a mathematical model to correlate the time constant of fluorescence recovery with the apparent diffusion coefficient of the fluorescent molecules. Then, apparent diffusion is linked to electrical conductivity and used to evaluate the efficiency of the passive spread of membrane depolarization along TATS. The method is first validated in cells where most TATS elements are acutely detached by osmotic shock and then applied to probe TATS electrical conductivity in failing heart cells. We find that acute and pathological tubular remodeling significantly affect TATS electrical conductivity. This may explain the occurrence of defects in action potential propagation at the level of single T-tubules, recently observed in diseased cardiomyocytes.

Small membrane permeable molecules protect against osmotically induced sealing of t-tubules in mouse ventricular myocytes

Cardiac t-tubules are critical for efficient excitation-contraction coupling but become significantly remodeled during various stress conditions. However, the mechanisms by which t-tubule remodeling occur are poorly understood. Recently, we demonstrated that recovery of mouse ventricular myocytes after hyposmotic shock is associated with t-tubule sealing. In this study, we found that the application of Small Membrane Permeable Molecules (SMPM) such as DMSO, formamide and acetamide upon washout of hyposmotic solution significantly reduced the amount of extracellular dextran trapped within sealed t-tubules. The SMPM protection displayed sharp biphasic concentration dependence that peaks at ∼140 mM leading to >3- to 4-fold reduction in dextran trapping. Consistent with these data, detailed analysis of the effects of DMSO showed that the magnitude of normalized inward rectifier tail current (IK1,tail), an electrophysiological marker of t-tubular integrity, was increased ∼2-fold when hyposmotic stress was removed in the presence of 1% DMSO (∼140 mM). Analysis of dynamics of cardiomyocytes shrinking during resolution of hyposmotic stress revealed only minor increase in shrinking rate in the presence of 1% DMSO, and cell dimensions returned fully to prestress values in both control and DMSO groups. Application and withdrawal of 10% DMSO in the absence of preceding hyposmotic shock induced classical t-tubule sealing. This suggests that the biphasic concentration dependence originated from an increase in secondary t-tubule sealing when high SMPM concentrations are removed. Overall, the data suggest that SMPM protect against sealing of t-tubules following hyposmotic stress, likely through membrane modification and essentially independent of their osmotic effects.

Isolation and Mechanical Measurements of Myofibrils from Human Induced Pluripotent Stem Cell-Derived Cardiomyocytes

Tension production and contractile properties are poorly characterized aspects of excitation-contraction coupling of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs). Previous approaches have been limited due to the small size and structural immaturity of early-stage hiPSC-CMs. We developed a substrate nanopatterning approach to produce hiPSC-CMs in culture with adult-like dimensions, T-tubule-like structures, and aligned myofibrils. We then isolated myofibrils from hiPSC-CMs and measured the tension and kinetics of activation and relaxation using a custom-built apparatus with fast solution switching. The contractile properties and ultrastructure of myofibrils more closely resembled human fetal myofibrils of similar gestational age than adult preparations. We also demonstrated the ability to study the development of contractile dysfunction of myofibrils from a patient-derived hiPSC-CM cell line carrying the familial cardiomyopathy MYH7 mutation (E848G). These methods can bring new insights to understanding cardiomyocyte maturation and developmental mechanical dysfunction of hiPSC-CMs with cardiomyopathic mutations.

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The contractile properties of hiPSC-CM myofibrils have not been previously studied

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hiPSC-CMs cultured on nanopatterned surfaces develop elongated, aligned myofibrils

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hiPSC-CMs myofibrils have contractile properties similar to human fetal myofibrils

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hiPSC-CMs can be used to study development of genetically based cardiac diseases

An integrated finite element simulation of cardiomyocyte function based on triphasic theory

In numerical simulations of cardiac excitation-contraction coupling, the intracellular potential distribution and mobility of cytosol and ions have been mostly ignored. Although the intracellular potential gradient is small, during depolarization it can be a significant driving force for ion movement, and is comparable to diffusion in terms of net flux. Furthermore, fluid in the t-tubules is thought to advect ions to facilitate their exchange with the extracellular space. We extend our previous finite element model that was based on triphasic theory to examine the significance of these factors in cardiac physiology. Triphasic theory allows us to study the behavior of solids (proteins), fluids (cytosol) and ions governed by mechanics and electrochemistry in detailed subcellular structures, including myofibrils, mitochondria, the sarcoplasmic reticulum, membranes, and t-tubules. Our simulation results predicted an electrical potential gradient inside the t-tubules at the onset of depolarization, which corresponded to the Na(+) channel distribution therein. Ejection and suction of fluid between the t-tubules and the extracellular compartment during isometric contraction were observed. We also examined the influence of t-tubule morphology and mitochondrial location on the electrophysiology and mechanics of the cardiomyocyte. Our results confirm that the t-tubule structure is important for synchrony of Ca(2+) release, and suggest that mitochondria in the sub-sarcolemmal region might serve to cancel Ca(2+) inflow through surface sarcolemma, thereby maintaining the intracellular Ca(2+) environment in equilibrium.

Targeting cardiomyocyte Ca2+ homeostasis in heart failure

Improved treatments for heart failure patients will require the development of novel therapeutic strategies that target basal disease mechanisms. Disrupted cardiomyocyte Ca²⁺ homeostasis is recognized as a major contributor to the heart failure phenotype, as it plays a key role in systolic and diastolic dysfunction, arrhythmogenesis, and hypertrophy and apoptosis signaling. In this review, we outline existing knowledge of the involvement of Ca²⁺ homeostasis in these deficits, and identify four promising targets for therapeutic intervention: the sarcoplasmic reticulum Ca²⁺ ATPase, the Na⁺-Ca²⁺ exchanger, the ryanodine receptor, and t-tubule structure. We discuss experimental data indicating the applicability of these targets that has led to recent and ongoing clinical trials, and suggest future therapeutic approaches.

Effect of ion concentration changes in the limited extracellular spaces on sarcolemmal ion transport and Ca2+ turnover in a model of human ventricular cardiomyocyte

We have developed a computer model of human cardiac ventricular myocyte (CVM), including t-tubular and cleft spaces with the aim of evaluating the impact of accumulation-depletion of ions in restricted extracellular spaces on transmembrane ion transport and ionic homeostasis in human CVM. The model was based on available data from human CVMs. Under steady state, the effect of ion concentration changes in extracellular spaces on [Ca²⁺]_i-transient was explored as a function of critical fractions of ion transporters in t-tubular membrane (not documented for human CVM). Depletion of Ca²⁺ and accumulation of K⁺ occurring in extracellular spaces slightly affected the transmembrane Ca²⁺ flux, but not the action potential duration (APD₉₀). The [Ca²⁺]_i-transient was reduced (by 2%–9%), depending on the stimulation frequency, the rate of ion exchange between t-tubules and clefts and fractions of ion-transfer proteins in the t-tubular membrane. Under non-steady state, the responses of the model to changes of stimulation frequency were analyzed. A sudden increase of frequency (1–2.5 Hz) caused a temporal decrease of [Ca²⁺] in both extracellular spaces, a reduction of [Ca²⁺]_i-transient (by 15%) and APD₉₀ (by 13 ms). The results reveal different effects of activity-related ion concentration changes in human cardiac t-tubules (steady-state effects) and intercellular clefts (transient effects) in the modulation of membrane ion transport and Ca²⁺ turnover.

Emerging mechanisms of T-tubule remodelling in heart failure

Cardiac excitation-contraction coupling occurs primarily at the sites of transverse (T)-tubule/sarcoplasmic reticulum junctions. The orderly T-tubule network guarantees the instantaneous excitation and synchronous activation of nearly all Ca(2+) release sites throughout the large ventricular myocyte. Because of the critical roles played by T-tubules and the array of channels and transporters localized to the T-tubule membrane network, T-tubule architecture has recently become an area of considerable research interest in the cardiovascular field. This review will focus on the current knowledge regarding normal T-tubule structure and function in the heart, T-tubule remodelling in the transition from compensated hypertrophy to heart failure, and the impact of T-tubule remodelling on myocyte Ca(2+) handling function. In the last section, we discuss the molecular mechanisms underlying T-tubule remodelling in heart disease.

Spatial variability in T-tubule and electrical remodeling of left ventricular epicardium in mouse hearts with transgenic Gαq overexpression-induced pathological hypertrophy

Pathological left ventricular hypertrophy (LVH) is consistently associated with prolongation of the ventricular action potentials. A number of previous studies, employing various experimental models of hypertrophy, have revealed marked differences in the effects of hypertrophy on action potential duration (APD) between myocytes from endocardial and epicardial layers of the LV free wall. It is not known, however, whether pathological LVH is also accompanied by redistribution of APD among myocytes from the same layer in the LV free wall. In the experiments here, LV epicardial action potential remodeling was examined in a mouse model of decompensated LVH, produced by cardiac-restricted transgenic Gαq overexpression. Confocal linescanning-based optical recordings of propagated action potentials from individual in situ cardiomyocytes across the outer layer of the anterior LV epicardium demonstrated spatially non-uniform action potential prolongation in transgenic hearts, giving rise to alterations in spatial dispersion of epicardial repolarization. Local density and distribution of anti-Cx43 mmune reactivity in Gαq hearts were unchanged compared to wild-type hearts, suggesting preservation of intercellular coupling. Confocal microscopy also revealed heterogeneous disorganization of T-tubules in epicardial cardiomyocytes in situ. These data provide evidence of the existence of significant electrical and structural heterogeneity within the LV epicardial layer of hearts with transgenic Gαq overexpression-induced hypertrophy, and further support the notion that a small portion of electrically well connected LV tissue can maintain dispersion of action potential duration through heterogeneity in the activities of sarcolemmal ionic currents that control repolarization. It remains to be examined whether other experimental models of pathological LVH, including pressure overload LVH, similarly exhibit alterations in T-tubule organization and/or dispersion of repolarization within distinct layers of LV myocardium.

The interaction of Ca2+ with sarcomeric proteins: role in function and dysfunction of the heart

The hallmarks of the normal heartbeat are both rapid onset of contraction and rapid relaxation as well as an inotropic response to both increased end-diastolic volume and increased heart rate. At the microscopic level, Ca(2+) plays a crucial role in normal cardiac contraction. This paper reviews the cycle of Ca(2+) fluxes during the normal heartbeat, which underlie the coupling between excitation and contraction and permit a highly synchronized action of cardiac sarcomeres. Length dependence of the response of the regulatory sarcomeric proteins mediates the Frank-Starling Law of the heart. However, Ca(2+) transport may go astray in heart disease such as in congestive heart failure, and both jeopardize systole and diastole and triggering arrhythmias. The interaction between weak and strong segments in nonuniform cardiac muscle allows partial preservation of force of contraction but may further lead to mechanoelectric feedback or reverse excitation-contraction coupling mediating an early diastolic Ca(2+) transient caused by the rapid force decrease during the relaxation phase. These rapid force changes in nonuniform muscle may cause arrhythmogenic Ca(2+) waves to propagate by the activation of neighboring sarcoplasmic reticulum by diffusing Ca(2+) ions.

The structure and function of cardiac t-tubules in health and disease

The transverse tubules (t-tubules) are invaginations of the cell membrane rich in several ion channels and other proteins devoted to the critical task of excitation-contraction coupling in cardiac muscle cells (cardiomyocytes). They are thought to promote the synchronous activation of the whole depth of the cell despite the fact that the signal to contract is relayed across the external membrane. However, recent work has shown that t-tubule structure and function are complex and tightly regulated in healthy cardiomyocytes. In this review, we outline the rapidly accumulating knowledge of its novel roles and discuss the emerging evidence of t-tubule dysfunction in cardiac disease, especially heart failure. Controversy surrounds the t-tubules' regulatory elements, and we draw attention to work that is defining these elements from the genetic and the physiological levels. More generally, this field illustrates the challenges in the dissection of the complex relationship between cellular structure and function.

Electromechanical coupling in the cardiac myocyte; stretch-arrhythmia feedback

The macroscopic hallmarks of the normal heartbeat are rapid onset of contraction and rapid relaxation and an inotropic response to both increased end diastolic volume and increased heart rate. At the microscopic level, the calcium ion (Ca(2+)) plays a crucial role in normal cardiac contraction. This paper reviews the cycle of Ca(2+) fluxes during the normal heartbeat, which underlie the coupling between excitation and contraction (ECC) and permit a highly synchronized action of cardiac sarcomeres. Length dependence of the response of the regulatory sarcomeric proteins mediates the Frank-Starling Law of the heart. However, Ca(2+) transport may go astray in heart disease and both jeopardize the exquisite mechanism of systole and diastole and triggering arrhythmias. The interplay between weakened and strong segments in nonuniform cardiac muscle may further lead to mechanoelectric feedback-or reverse excitation contraction coupling (RECC) mediating an early diastolic Ca(2+) transient caused by the rapid force decrease during the relaxation phase. These rapid force changes in nonuniform muscle may cause arrhythmogenic Ca(2+) waves to propagate by activation of neighbouring SR by diffusing Ca(2+) ions.

Ca efflux via the sarcolemmal Ca ATPase occurs only in the t-tubules of rat ventricular myocytes

The transverse (t-) tubule network is an important site for Ca influx and release during excitation-contraction coupling in cardiac ventricular myocytes; however, its role in Ca extrusion is less clear. The present study was designed to investigate the relative contributions of Ca extrusion pathways across the t-tubule and surface membranes. Ventricular myocytes were isolated from the hearts of adult male Wistar rats and detubulated using formamide. Intracellular Ca was monitored using fluo-3 and confocal microscopy. Caffeine (20 mmol/L) was used to induce SR Ca release; carboxyeosin (20 μmol/L) and nickel (10 mmol/L) were used to inhibit the sarcolemmal Ca ATPase and Na/Ca exchanger (NCX) respectively. Carboxyeosin decreased the rate constant of decay of the caffeine-induced Ca transient in control cells, but had no effect in detubulated cells, suggesting that Ca extrusion via the Ca ATPase occurs only across the t-tubule membrane. However nickel decreased the rate constant of the caffeine-induced Ca transient in control and detubulated cells, although its effect was greater in control cells, suggesting that Ca extrusion via NCX occurs across the surface and t-tubule membranes. The PKA inhibitor H-89 (10 μmol/L) was used to investigate the role of basal PKA activity in Ca extrusion; H-89 appeared to have no effect on Ca extrusion via the Ca ATPase, but reduced Ca extrusion via NCX at the t-tubules but not the surface membrane. Thus it appears that Ca extrusion via the sarcolemmal Ca ATPase occurs only at the t-tubules, and is not regulated by basal PKA activity, while Ca extrusion via NCX occurs across both the surface and t-tubule membranes, but predominantly across the t-tubule membrane due, in part, to localised stimulation of NCX by PKA at the t-tubules. This may be important in heart disease, in which changes in t-tubule structure and protein phosphorylation occur.

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. 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.

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]. 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].

Uniform action potential repolarization within the sarcolemma of in situ ventricular cardiomyocytes

Previous studies have speculated, based on indirect evidence, that the action potential at the transverse (t)-tubules is longer than at the surface membrane in mammalian ventricular cardiomyocytes. To date, no technique has enabled recording of electrical activity selectively at the t-tubules to directly examine this hypothesis. We used confocal line-scan imaging in conjunction with the fast response voltage-sensitive dyes ANNINE-6 and ANNINE-6plus to resolve action potential-related changes in fractional dye fluorescence (DeltaF/F) at the t-tubule and surface membranes of in situ mouse ventricular cardiomyocytes. Peak DeltaF/F during action potential phase 0 depolarization averaged -21% for both dyes. The shape and time course of optical action potentials measured with the water-soluble ANNINE-6plus were indistinguishable from those of action potentials recorded with intracellular microelectrodes in the absence of the dye. In contrast, optical action potentials measured with the water-insoluble ANNINE-6 were significantly prolonged compared to the electrical recordings obtained from dye-free hearts, suggesting electrophysiological effects of ANNINE-6 and/or its solvents. With either dye, the kinetics of action potential-dependent changes in DeltaF/F during repolarization were found to be similar at the t-tubular and surface membranes. This study provides what to our knowledge are the first direct measurements of t-tubule electrical activity in ventricular cardiomyocytes, which support the concept that action potential duration is uniform throughout the sarcolemma of individual cells.

The role of mammalian cardiac t-tubules in excitation-contraction coupling: experimental and computational approaches

The sarcolemmal membrane of mammalian cardiac ventricular myocytes is characterized by the presence of invaginations called transverse tubules (t-tubules). Transverse tubules occur at the Z-line as transverse elements with longitudinal extensions. While the existence of t-tubules has been known for some time, recent experimental studies have suggested that their structure and function are more complex than previously believed. There are, however, aspects of t-tubule function that are not currently amenable to experimental investigation, but can be investigated using computational and mathematical approaches. Such studies have helped elucidate further the possible role of t-tubules in cell function. This review summarizes recent experimental and complementary computational studies which highlight the important role of t-tubules in cardiac excitation-contraction coupling.

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

The 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.

A model of the guinea-pig ventricular cardiac myocyte incorporating a transverse-axial tubular system

A model of the guinea-pig cardiac ventricular myocyte has been developed that includes a representation of the transverse-axial tubular system (TATS), including heterogeneous distribution of ion flux pathways between the surface and tubular membranes. The model reproduces frequency-dependent changes of action potential shape and intracellular ion concentrations and can replicate experimental data showing ion diffusion between the tubular lumen and external solution in guinea-pig myocytes. The model is stable at rest and during activity and returns to rested state after perturbation. Theoretical analysis and model simulations show that, due to tight electrical coupling, tubular and surface membranes behave as a homogeneous whole during voltage and current clamp (maximum difference 0.9 mV at peak tubular INa of -38 nA). However, during action potentials, restricted diffusion and ionic currents in TATS cause depletion of tubular Ca2+ and accumulation of tubular K+ (up to -19.8% and +3.4%, respectively, of bulk extracellular values, at 6 Hz). These changes, in turn, decrease ion fluxes across the TATS membrane and decrease sarcoplasmic reticulum (SR) Ca2+ load. Thus, the TATS plays a potentially important role in modulating the function of guinea-pig ventricular myocyte in physiological conditions.