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 I_Na 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.     

A quantitative analysis of cardiac myocyte relaxation: a simulation study

The determinants of relaxation in cardiac muscle are poorly understood, yet compromised relaxation accompanies various pathologies and impaired pump function. In this study, we develop a model of active contraction to elucidate the relative importance of the [Ca2+]i transient magnitude, the unbinding of Ca2+ from troponin C (TnC), and the length-dependence of tension and Ca2+ sensitivity on relaxation. Using the framework proposed by one of our researchers, we extensively reviewed experimental literature, to quantitatively characterize the binding of Ca2+ to TnC, the kinetics of tropomyosin, the availability of binding sites, and the kinetics of crossbridge binding after perturbations in sarcomere length. Model parameters were determined from multiple experimental results and modalities (skinned and intact preparations) and model results were validated against data from length step, caged Ca2+, isometric twitches, and the half-time to relaxation with increasing sarcomere length experiments. A factorial analysis found that the [Ca2+]i transient and the unbinding of Ca2+ from TnC were the primary determinants of relaxation, with a fivefold greater effect than that of length-dependent maximum tension and twice the effect of tension-dependent binding of Ca2+ to TnC and length-dependent Ca2+ sensitivity. The affects of the [Ca2+]i transient and the unbinding rate of Ca2+ from TnC were tightly coupled with the effect of increasing either factor, depending on the reference [Ca2+]i transient and unbinding rate.     

Anisotropic conduction block and reentry in neonatal rat ventricular myocyte monolayers

Anisotropy can lead to unidirectional conduction block that initiates reentry. We analyzed the mechanisms in patterned anisotropic neonatal rat ventricular myocyte monolayers. Voltage and intracellular Ca (Ca(i)) were optically mapped under the following conditions: extrastimulus (S1S2) testing and/or tetrodotoxin (TTX) to suppress Na current availability; heptanol to reduce gap junction conductance; and incremental rapid pacing. In anisotropic monolayers paced at 2 Hz, conduction velocity (CV) was faster longitudinally than transversely, with an anisotropy ratio [AR = CV(L)/CV(T), where CV(L) and CV(T) are CV in the longitudinal and transverse directions, respectively], averaging 2.1 ± 0.8. Interventions decreasing Na current availability, such as S1S2 pacing and TTX, slowed CV(L) and CV(T) proportionately, without changing the AR. Conduction block preferentially occurred longitudinal to fiber direction, commonly initiating reentry. Interventions that decreased gap junction conductance, such as heptanol, decreased CV(T) more than CV(L), increasing the AR and causing preferential transverse conduction block and reentry. Rapid pacing resembled the latter, increasing the AR and promoting transverse conduction block and reentry, which was prevented by the Ca(i) chelator 1,2-bis oaminophenoxy ethane-N,N,N',N'-tetraacetic acid (BAPTA). In contrast to isotropic and uniformly anisotropic monolayers, in which reentrant rotors drifted and self-terminated, bidirectional anisotropy (i.e., an abrupt change in fiber direction exceeding 45°) caused reentry to anchor near the zone of fiber direction change in 77% of monolayers. In anisotropic monolayers, unidirectional conduction block initiating reentry can occur longitudinal or transverse to fiber direction, depending on whether the experimental intervention reduces Na current availability or decreases gap junction conductance, agreeing with theoretical predictions.     

The Ventral Photoreceptor Cells of Limulus : III. A voltage-clamp study

In the dark, the ventral photoreceptor of Limulus exhibits time-variant currents under voltage-clamp conditions; that is, if the membrane potential of the cell is clamped to a depolarized value there is an initial large outward current which slowly declines to a steady level. The current-voltage relation of the cell in the dark is nonlinear. The only ion tested which has any effect on the current-voltage relation is potassium; high potassium shifts the reversal potential towards zero and introduces a negative slope-conductance region. When the cell is illuminated under voltage-clamp conditions, an additional current, the light-induced current, flows across the cell membrane. The time course of this current mimics the time course of the light response (receptor potential) in the unclamped cell; namely, an initial transient phase is followed by a steady-state phase. The amplitude of the peak transient current can be as large as 60 times the amplitude of the steady-state current, while in the unclamped cell the amplitude of the peak transient voltage never exceeds 4 times the amplitude of the steady-state voltage. The current-voltage relations of the additional light-induced current obtained for different instants of time are also nonlinear, but differ from the current-voltage relations of the dark current. The ions tested which have the greatest effect on the light-induced current are sodium and calcium; low sodium decreases the current, while low calcium increases the current. The data strongly support the hypothesis that two systems of electric current exist in the membrane. Thus the total ionic current which flows in the membrane is accounted for as the sum of a dark current and a light-induced current.     

A computational model integrating electrophysiology, contraction, and mitochondrial bioenergetics in the ventricular myocyte

An intricate network of reactions is involved in matching energy supply with demand in the heart. This complexity arises because energy production both modulates and is modulated by the electrophysiological and contractile activity of the cardiac myocyte. Here, we present an integrated mathematical model of the cardiac cell that links excitation-contraction coupling with mitochondrial energy generation. The dynamics of the model are described by a system of 50 ordinary differential equations. The formulation explicitly incorporates cytoplasmic ATP-consuming processes associated with force generation and ion transport, as well as the creatine kinase reaction. Changes in the electrical and contractile activity of the myocyte are coupled to mitochondrial energetics through the ATP, Ca2+, and Na+ concentrations in the myoplasmic and mitochondrial matrix compartments. The pseudo steady-state relationship between force and oxygen consumption at various stimulus frequencies and external Ca2+ concentrations is reproduced in both model simulations and direct experiments in cardiac trabeculae under normoxic conditions, recapitulating the linearity between cardiac work and respiration in the heart. Importantly, the model can also reproduce the rapid time-dependent changes in mitochondrial NADH and Ca2+ in response to abrupt changes in workload. The steady-state and dynamic responses of the model were conferred by ADP-dependent stimulation of mitochondrial oxidative phosphorylation and Ca2+ -dependent regulation of Krebs cycle dehydrogenases, illustrating how the model can be used as a tool for investigating mechanisms underlying metabolic control in the heart.     

LabHEART: an interactive computer model of rabbit ventricular myocyte ion channels and Ca transport

An interactive computer program,LabHEART, was developed to simulate the action potential (AP), ioniccurrents, and Ca handling mechanisms in a rabbit ventricular myocyte.User-oriented, its design allows switching between voltage and currentclamp and easy on-line manipulation of key parameters to change theoriginal formulation. The model reproduces normal rabbit ventricularmyocyte currents, Ca transients, and APs. We also changed parameters to simulate data from heart failure (HF) myocytes, including reduced transient outward (I_to) and inward rectifying Kcurrents (I_K1), enhanced Na/Ca exchangeexpression, and reduced sarcoplasmic reticulum Ca-ATPase function, butunaltered Ca current density. These changes caused reduced Ca transientamplitude and increased AP duration (especially at lower frequency) asobserved experimentally. The model shows that the increased Na/Caexchange current (I_NaCa) in HF lowers theintracellular [Ca] threshold for a triggered AP from 800 to 540 nM. Similarly, the decrease in I_K1reduces the threshold to 600 nM. Changes in I_tohave no effect. Combining enhanced Na/Ca exchange with reducedI_K1 (as in HF) lowers the threshold to triggeran AP to 380 nM. These changes reproduce experimental results inHF, where the contributions of different factors are notreadily distinguishable. We conclude that the triggered APs thatcontribute to nonreentrant ventricular tachycardia in HF are dueapproximately equally (and nearly additively) to alterations inI_NaCa and I_K1. A freecopy of this software can be obtained athttp://www.meddean.luc.edu/lumen/DeptWebs/physio/bers.html.

     

Endothelium and myocyte cellular insulin receptor alterations in a rat model of myocardial infarction

Ischemic heart disease is considered to be one of the leading causes of death in adults. While extensive research on mechanisms contributing to the pathogenesis of myocardial infarction (MI) has been underway, it is not known whether insulin receptor characteristics and postreceptor signaling have been fully addressed as yet. Present work attempts to investigate whether the remodeling process effectively induces alteration(s) in insulin-binding characteristics at the coronary endothelium and cardiomyocytes using a rat heart model of MI. MI was induced by ligation of the left anterior descending coronary artery of adult male Sprague-Dawley rats. Two animal groups were used in the study: (i) sham-operated CHAPS-untreated and CHAPS-treated, and (ii) MI CHAPS-untreated and MI CHAPS-treated. A physical model describing 1:1 stoichiometry of reversible insulin binding to its receptors present on the endothelium and at cardiomyocytes after CHAPS treatment was considered for data analysis. Quantitation of the collected effluents after heart perfusion, the inlet at the aortic and outlet at the coronary sinus sites, were curve fitted using a first-order Bessel function, which determines the binding constants (k(n)), the reversible constant (k(-n)), the dissociation constant (k(d) = k(-n)/k(n)), and the residency time constant (tau = 1/k(-n)). In addition, hearts were excised, separated into right and left ventricles, and individually weighed, and areas of infarcted regions were measured. Results of the MI group showed significant increases in relative heart mass, left ventricle mass, and right ventricle mass normalized to total body mass. MI induced severe ischemia and irreversible myocardial injury as assessed by planimetry and histologic studies. The data showed differences in insulin receptor affinities at the endothelial and cardiac myocytes in the sham and in the MI-operated rats. The observed reduction in the binding affinity of insulin at the myocyte postinfarction may explain the pathogenic role of insulin in ischemic heart disease and, hence, resistance. Therefore, insulin administration during and post MI might be cardioprotective.     

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 Ca(2+), 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.     

Changes in excitation-contraction coupling in an isolated ventricular myocyte model of cardiac stunning

To investigate cardiac stunning, we recorded intracellular [Ca(2+)], contractions, and electrical activity in isolated guinea pig ventricular myocytes exposed to simulated ischemia and reperfusion. After equilibration, ischemia was simulated by exposing myocytes to hypoxia, acidosis, hyperkalemia, hypercapnia, lactate accumulation, and substrate deprivation for 30 min at 37 degrees C. Reperfusion was simulated by exposure to Tyrode solution. Field-stimulated myocytes exhibited stunning upon reperfusion. By 10 min of reperfusion, contraction amplitude decreased to 43.0 +/- 5.5% of preischemic values (n = 15, P < 0.05), although action potential configuration and sarcoplasmic reticulum Ca(2+) stores, assessed with caffeine, were normal. Diastolic [Ca(2+)] and Ca(2+) transients (fura 2) were also normal in stunned myocytes. In voltage-clamped cells, peak L-type Ca(2+) current was reduced to 47.4 +/- 4.5% of preischemic values at 10 min of reperfusion (n = 21, P < 0.05). Contractions elicited by Ca(2+)-induced Ca(2+) release and the voltage-sensitive release mechanism were both depressed in reperfusion. Our observations suggest that stunning is associated with reduced L-type Ca(2+) current but that alterations in Ca(2+) homeostasis and release are not directly responsible for stunning.     

A mathematical analysis of the action potential plateau duration of a human ventricular myocyte

The plateau phase of a human ventricular myocyte is analysed. The plateau duration is a function of the time required for a myocyte's transmembrane voltage to decrease by a certain voltage, DeltaV. The timing of the plateau is shown to be controlled by two slowly changing gate variables, the inactivation gate that controls the inward/depolarizing L-type calcium current and the inactivation gate that controls the outward/repolarizing slow rectifier potassium current. The amount of current controlled by these variables is a function of the net conductivity of the corresponding sodium and potassium channels. An equation is derived that relates action potential duration to these net conductivities and the time dependence of the slowly moving variables. This equation is used to estimate plateau duration for a given value of DeltaV. The initial conditions of the slowly moving inactivation variables are shown to affect plateau duration. These initial conditions depend on the amount of time that has elapsed between a previous repolarization and a current depolarization (diastolic interval). The analysis thus helps to quantify the characteristics of action potential duration restitution.     

Isometric contraction induces rapid myocyte remodeling in cultured rat right ventricular papillary muscles

The hypothesis that elevated systolic stress induces myocyte thickening has been difficult to test directly. We tested this hypothesis in working rat right ventricular papillary muscles using a recently developed technique for long-term muscle culture. Muscles were cultured for 36 h either isometrically at different levels of systolic stress or at physiological amounts and rates of shortening. Isometric contraction induced rapid increases in myocyte diameter regardless of the level of systolic stress, whereas control myocyte dimensions were maintained if physiological amounts and rates of systolic shortening were imposed. Myocyte thickening was accompanied by a significant decrease in cell length and number of sarcomeres in series along the long axis of the myocyte, suggesting that thickening may have occurred in part by rearrangement of existing sarcomeres. We conclude that the pattern of systolic shortening and/or diastolic lengthening regulates myocyte shape in working rat right ventricular papillary muscles, whereas systolic stress plays little or no role.     

A mathematical treatment of integrated Ca dynamics within the ventricular myocyte

We have developed a detailed mathematical model for Ca2+ handling and ionic currents in the rabbit ventricular myocyte. The objective was to develop a model that: 1), accurately reflects Ca-dependent Ca release; 2), uses realistic parameters, particularly those that concern Ca transport from the cytosol; 3), comes to steady state; 4), simulates basic excitation-contraction coupling phenomena; and 5), runs on a normal desktop computer. The model includes the following novel features: 1), the addition of a subsarcolemmal compartment to the other two commonly formulated cytosolic compartments (junctional and bulk) because ion channels in the membrane sense ion concentrations that differ from bulk; 2), the use of realistic cytosolic Ca buffering parameters; 3), a reversible sarcoplasmic reticulum (SR) Ca pump; 4), a scheme for Na-Ca exchange transport that is [Na]i dependent and allosterically regulated by [Ca]i; and 5), a practical model of SR Ca release including both inactivation/adaptation and SR Ca load dependence. The data describe normal electrical activity and Ca handling characteristics of the cardiac myocyte and the SR Ca load dependence of these processes. The model includes a realistic balance of Ca removal mechanisms (e.g., SR Ca pump versus Na-Ca exchange), and the phenomena of rest decay and frequency-dependent inotropy. A particular emphasis is placed upon reproducing the nonlinear dependence of gain and fractional SR Ca release upon SR Ca load. We conclude that this model is more robust than many previously existing models and reproduces many experimental results using parameters based largely on experimental measurements in myocytes.     

A computational model of the human left-ventricular epicardial myocyte

A computational model of the human left-ventricular epicardial myocyte is presented. Models of each of the major ionic currents present in these cells are formulated and validated using experimental data obtained from studies of recombinant human ion channels and/or whole-cell recording from single myocytes isolated from human left-ventricular subepicardium. Continuous-time Markov chain models for the gating of the fast Na(+) current, transient outward current, rapid component of the delayed rectifier current, and the L-type calcium current are modified to represent human data at physiological temperature. A new model for the gating of the slow component of the delayed rectifier current is formulated and validated against experimental data. Properties of calcium handling and exchanger currents are altered to appropriately represent the dynamics of intracellular ion concentrations. The model is able to both reproduce and predict a wide range of behaviors observed experimentally including action potential morphology, ionic currents, intracellular calcium transients, frequency dependence of action-potential duration, Ca(2+)-frequency relations, and extrasystolic restitution/post-extrasystolic potentiation. The model therefore serves as a useful tool for investigating mechanisms of arrhythmia and consequences of drug-channel interactions in the human left-ventricular myocyte.     

Bigendothelin-1 via p38-MAPK-dependent mechanism regulates adult rat ventricular myocyte contractility in sepsis

We tested the hypothesis that exogenous administration of the ET-1 precursor, bigET-1, would regulate adult rat ventricular myocyte (ARVM) contractility in a p38-mitogen activated protein kinase (p38-MAPK)-dependent mechanism during sepsis. Ventricular myocytes from adult rat hearts (both sham and septic) were stimulated to contract at 0.5 Hz and mechanical properties were evaluated using an IonOptix Myocam system. Immunoblot analysis was used to determine the phosphorylation of p38-MAPK and extracellular signal-regulated kinase 1/2 (ERK1/2). ARVMs were treated with vehicle, bigET-1 and inhibitors for 24 h and then subjected to functional and biochemical estimations. Septic ARVM displayed a distorted cell membrane and irregular network within the cells along with increased cell contractility as evidenced by elevated peak shortening (PS), maximal velocity of shortening (+dL/dt) and relengthening (-dL/dt) in comparison to sham ARVM. BigET-1 treatment caused ARVM enlargement in both sham and sepsis groups. BigET-1 (100 nM) produced an increase in ARVM contractility in sham group as compared to vehicle treatment. However, septic ARVM treated with bigET-1 exhibited unaltered ARVM contractility, and upregulated ET(B) receptors as compared to respective sham group. BigET-1 increased the concentration of ET-1 and upregulated phosphorylation of p38-MAPK but not of ERK1/2 in sham and septic ARVM. Furthermore, inhibition of p38-MAPK by SB203580 (10 microM) increased ARVM contractility in sham but not in sepsis group. BigET-1 reversed SB203580-induced increase in PS in sham group but accentuated it in sepsis group. BigET-1 also reversed SB203580-induced inhibition of p38-MAPK phosphorylation in sham but not in septic ARVM. SB203580 pretreatment followed by bigET-1 administration significantly decreased p38-MAPK phosphorylation and downregulated ET(B) receptor expression as compared to bigET-1 treatment per se in sepsis group but not in sham. We concluded that a bigET-1-induced non-responsive effect on septic ARVM contractile function could be due to upregulation of p38-MAPK phosphorylation and ET(B) receptor expression.     

The effects of hydrogen peroxide on intracellular calcium handling and contractility in the rat ventricular myocyte

Elevations in reactive oxygen species are implicated in many disease states and cause systolic and diastolic myocardial dysfunction. To understand the underlying cellular dysfunction, we characterised the effects of H?O? on [Ca(2+)](i) handling and contractility in the rat ventricular myocyte. This was achieved using patch clamping, [Ca(2+)](i) measurement using Fluo-3, video edge detection and confocal microscopy. All experiments were performed at 37°C. 200 μM H?O? resulted in a 44% decrease in the [Ca(2+)](i) transient amplitude, a 30% increase in diastolic [Ca(2+)](i) and an 18% decrease in the rate of systolic Ca(2+) removal. This was associated with a 61% reduction in systolic shortening, a contracture of 3 μm and a 42% increase in relaxation time respectively. The decrease in the [Ca(2+)](i) transient amplitude could be explained by a 27% decrease in SR Ca(2+) content. This, in turn results from a 22% decrease of SERCA activity. The decreased SR Ca(2+) content also provides a mechanism for a reduction in [Ca(2+)](i) spark frequency with no evidence for a Ca(2+) independent modification of ryanodine receptor open probability. We conclude that decreased SERCA activity is the major factor responsible for the changes of the systolic [Ca(2+)](i) transient.     

An integrative model of the cardiac ventricular myocyte incorporating local control of Ca2+ release

The local control theory of excitation-contraction (EC) coupling in cardiac muscle asserts that L-type Ca(2+) current tightly controls Ca(2+) release from the sarcoplasmic reticulum (SR) via local interaction of closely apposed L-type Ca(2+) channels (LCCs) and ryanodine receptors (RyRs). These local interactions give rise to smoothly graded Ca(2+)-induced Ca(2+) release (CICR), which exhibits high gain. In this study we present a biophysically detailed model of the normal canine ventricular myocyte that conforms to local control theory. The model formulation incorporates details of microscopic EC coupling properties in the form of Ca(2+) release units (CaRUs) in which individual sarcolemmal LCCs interact in a stochastic manner with nearby RyRs in localized regions where junctional SR membrane and transverse-tubular membrane are in close proximity. The CaRUs are embedded within and interact with the global systems of the myocyte describing ionic and membrane pump/exchanger currents, SR Ca(2+) uptake, and time-varying cytosolic ion concentrations to form a model of the cardiac action potential (AP). The model can reproduce both the detailed properties of EC coupling, such as variable gain and graded SR Ca(2+) release, and whole-cell phenomena, such as modulation of AP duration by SR Ca(2+) release. Simulations indicate that the local control paradigm predicts stable APs when the L-type Ca(2+) current is adjusted in accord with the balance between voltage- and Ca(2+)-dependent inactivation processes as measured experimentally, a scenario where common pool models become unstable. The local control myocyte model provides a means for studying the interrelationship between microscopic and macroscopic behaviors in a manner that would not be possible in experiments.     

A voltage-clamp study of the effects of colchicine on the squid giant axon

The effects of colchicine applied inside a squid giant axon were studied using voltage-clamp and internal perfusion techniques. It was found that colchicine selectively and reversibly suppresses the sodium conductance during excitation. The possible involvement of the microtubular structure in the functioning of the excitable channel is discussed.     

Multiphysics simulation of left ventricular filling dynamics using fluid-structure interaction finite element method

To relate the subcellular molecular events to organ level physiology in heart, we have developed a three-dimensional finite-element-based simulation program incorporating the cellular mechanisms of excitation-contraction coupling and its propagation, and simulated the fluid-structure interaction involved in the contraction and relaxation of the human left ventricle. The FitzHugh-Nagumo model and four-state model representing the cross-bridge kinetics were adopted for cellular model. Both ventricular wall and blood in the cavity were modeled by finite element mesh. An arbitrary Lagrangian Eulerian finite element method with automatic mesh updating has been formulated for large domain changes, and a strong coupling strategy has been taken. Using electrical analog of pulmonary circulation and left atrium as a preload and the windkessel model as an afterload, dynamics of ventricular filling as well as ejection was simulated. We successfully reproduced the biphasic filling flow consisting of early rapid filling and atrial contraction similar to that reported in clinical observation. Furthermore, fluid-structure analysis enabled us to analyze the wave propagation velocity of filling flow. This simulator can be a powerful tool for establishing a link between molecular abnormality and the clinical disorder at the macroscopic level.