Mathematical Model of Mouse Embryonic Cardiomyocyte Excitation–Contraction Coupling

Excitation–contraction (E–C) coupling is the mechanism that connects the electrical excitation with cardiomyocyte contraction. Embryonic cardiomyocytes are not only capable of generating action potential (AP)-induced Ca²⁺ signals and contractions (E–C coupling), but they also can induce spontaneous pacemaking activity. The spontaneous activity originates from spontaneous Ca²⁺ releases from the sarcoplasmic reticulum (SR), which trigger APs via the Na⁺/Ca²⁺ exchanger (NCX). In the AP-driven mode, an external stimulus triggers an AP and activates voltage-activated Ca²⁺ intrusion to the cell. These complex and unique features of the embryonic cardiomyocyte pacemaking and E–C coupling have never been assessed with mathematical modeling. Here, we suggest a novel mathematical model explaining how both of these mechanisms can coexist in the same embryonic cardiomyocytes. In addition to experimentally characterized ion currents, the model includes novel heterogeneous cytosolic Ca²⁺ dynamics and oscillatory SR Ca²⁺ handling. The model reproduces faithfully the experimentally observed fundamental features of both E–C coupling and pacemaking. We further validate our model by simulating the effect of genetic modifications on the hyperpolarization-activated current, NCX, and the SR Ca²⁺ buffer protein calreticulin. In these simulations, the model produces a similar functional alteration to that observed previously in the genetically engineered mice, and thus provides mechanistic explanations for the cardiac phenotypes of these animals. In general, this study presents the first model explaining the underlying cellular mechanism for the origin and the regulation of the heartbeat in early embryonic cardiomyocytes.     

A theory for the membrane potential of living cells

We give an explicit formula for the membrane potential of cells in terms of the intracellular and extracellular ionic concentrations, and derive equations for the ionic currents that flow through channels, exchangers and electrogenic pumps. We demonstrate that the work done by the pumps equals the change in potential energy of the cell, plus the energy lost in downhill ionic fluxes through the channels and exchangers. The theory is illustrated in a simple model of spontaneously active cells in the cardiac pacemaker. The model predicts the experimentally observed intracellular ionic concentration of potassium, calcium and sodium. Likewise, the shapes of the simulated action potential and five membrane currents are in good agreement with experiment. We do not see any drift in the values of the concentrations in a long time simulation, and we obtain the same asymptotic values when starting from the full equilibrium situation with equal intracellular and extracellular ionic concentrations. Received: 9 December 1998 / Revised version: 30 August 1999 / Accepted: 15 October 1999     

Contribution of BKCa-Channel Activity in Human Cardiac Fibroblasts to Electrical Coupling of Cardiomyocytes-Fibroblasts

Cardiac fibroblasts are involved in the maintenance of myocardial tissue structure. However, little is known about ion currents in human cardiac fibroblasts. It has been recently reported that cardiac fibroblasts can interact electrically with cardiomyocytes through gap junctions. Ca²⁺-activated K⁺ currents (I _K[Ca]) of cultured human cardiac fibroblasts were characterized in this study. In whole-cell configuration, depolarizing pulses evoked I _K(Ca) in an outward rectification in these cells, the amplitude of which was suppressed by paxilline (1 μM) or iberiotoxin (200 nM). A large-conductance, Ca²⁺-activated K⁺ (BK_Ca) channel with single-channel conductance of 162 ± 8 pS was also observed in human cardiac fibroblasts. Western blot analysis revealed the presence of α-subunit of BK_Ca channels. The dynamic Luo-Rudy model was applied to predict cell behavior during direct electrical coupling of cardiomyocytes and cardiac fibroblasts. In the simulation, electrically coupled cardiac fibroblasts also exhibited action potential; however, they were electrically inert with no gap-junctional coupling. The simulation predicts that changes in gap junction coupling conductance can influence the configuration of cardiac action potential and cardiomyocyte excitability. I _k(Ca) can be elicited by simulated action potential waveforms of cardiac fibroblasts when they are electrically coupled to cardiomyocytes. This study demonstrates that a BK_Ca channel is functionally expressed in human cardiac fibroblasts. The activity of these BK_Ca channels present in human cardiac fibroblasts may contribute to the functional activities of heart cells through transfer of electrical signals between these two cell types.     

A computational model of pig ventricular cardiomyocyte electrophysiology and calcium handling: Translation from pig to human electrophysiology

The pig is commonly used as an experimental model of human heart disease, including for the study of mechanisms of arrhythmia. However, there exist differences between human and porcine cellular electrophysiology: The pig action potential (AP) has a deeper phase-1 notch, a longer duration at 50% repolarization, and higher plateau potentials than human. Ionic differences underlying the AP include larger rapid delayed-rectifier and smaller inward-rectifier K⁺-currents (I_Kr and I_K1 respectively) in humans. AP steady-state rate-dependence and restitution is steeper in pigs. Porcine Ca²⁺ transients can have two components, unlike human. Although a reliable computational model for human ventricular myocytes exists, one for pigs is lacking. This hampers translation from results obtained in pigs to human myocardium. Here, we developed a computational model of the pig ventricular cardiomyocyte AP using experimental datasets of the relevant ionic currents, Ca²⁺-handling, AP shape, AP duration restitution, and inducibility of triggered activity and alternans. To properly capture porcine Ca²⁺ transients, we introduced a two-step process with a faster release in the t-tubular region, followed by a slower diffusion-induced release from a non t-tubular subcellular region. The pig model behavior was compared with that of a human ventricular cardiomyocyte (O’Hara-Rudy) model. The pig, but not the human model, developed early afterdepolarizations (EADs) under block of I_K1, while I_Kr block led to EADs in the human but not in the pig model. At fast rates (pacing cycle length = 400 ms), the human cell model was more susceptible to spontaneous Ca²⁺ release-mediated delayed afterdepolarizations (DADs) and triggered activity than pig. Fast pacing led to alternans in human but not pig. Developing species-specific models incorporating electrophysiology and Ca^2+-handling provides a tool to aid translating antiarrhythmic and arrhythmogenic assessment from the bench to the clinic.     

Cardiomyocyte dysfunction during the chronic phase of Chagas disease

Chagas disease, which is caused by the parasite Trypanosoma cruzi, is an important cause of heart failure. We investigated modifications in the cellular electrophysiological and calcium-handling characteristics of an infected mouse heart during the chronic phase of the disease. The patch-clamp technique was used to record action potentials (APs) and L-type Ca²⁺ and transient outward K⁺ currents. [Ca²⁺]_i changes were determined using confocal microscopy. Infected ventricular cells showed prolonged APs, reduced transient outward K⁺ and L-type Ca²⁺ currents and reduced Ca²⁺ release from the sarcoplasmic reticulum. Thus, the chronic phase of Chagas disease is characterised by cardiomyocyte dysfunction, which could lead to heart failure.     

Colchicine modulates calcium homeostasis and electrical property of HL‐1 cells

Colchicine is a microtubule disruptor that reduces the occurrence of atrial fibrillation (AF) after an operation or ablation. However, knowledge of the effects of colchicine on atrial myocytes is limited. The aim of this study was to determine if colchicine can regulate calcium (Ca²⁺) homeostasis and attenuate the electrical effects of the extracellular matrix on atrial myocytes. Whole‐cell clamp, confocal microscopy with fluorescence, and western blotting were used to evaluate the action potential and ionic currents of HL‐1 cells treated with and without (control) colchicine (3 nM) for 24 hrs. Compared with control cells, colchicine‐treated HL‐1 cells had a longer action potential duration with smaller intracellular Ca²⁺ transients and sarcoplasmic reticulum (SR) Ca²⁺ content by 10% and 47%, respectively. Colchicine‐treated HL‐1 cells showed a smaller L‐type Ca²⁺ current, reverse mode sodium–calcium exchanger (NCX) current and transient outward potassium current than control cells, but had a similar ultra‐rapid activating outward potassium current and apamin‐sensitive small‐conductance Ca²⁺‐activated potassium current compared with control cells. Colchicine‐treated HL‐1 cells expressed less SERCA2a, total, Thr17‐phosphorylated phospholamban, Cav1.2, CaMKII, NCX, Kv1.4 and Kv1.5, but they expressed similar levels of the ryanodine receptor, Ser16‐phosphorylated phospholamban and Kv4.2. Colchicine attenuated the shortening of the collagen‐induced action potential duration in HL‐1 cells. These findings suggest that colchicine modulates the atrial electrical activity and Ca²⁺ regulation and attenuates the electrical effects of collagen, which may contribute to its anti‐AF activity.     

Cardiomyocytes hypertrophic status after myocardial infarction determines distinct types of arrhythmia: Role of the ryanodine receptor

The mechanisms responsible for sudden cardiac death in heart failure (HF) are unclear. We investigated early and delayed afterdepolarizations (EADs, DADs) in HF. Cardiomyocytes were enzymatically isolated from the right ventricle (RV) and the septum of rats 8 weeks after myocardial infarction (MI) and sham-operated animals. Membrane capacitance, action potentials (AP) and ionic currents were measured by whole-cell patch-clamp. The [Ca²⁺]_i transients and Ca²⁺ sparks were recorded with Fluo-4 during fluorescence measurements. Arrhythmia was triggered in 40% of MI cells (not in sham) using trains of 5 stimulations at 2.0 Hz. EADs and DADs occurred in distinct cell populations both in the RV and the septum. EADs occurred in normal-sized PMI cells (<230 pF), whereas DADs occurred in hypertrophic PMI cells (>230 pF). All cells exhibited prolonged APs due to reduced I_to current. However, additional modifications in Ca²⁺-dependent ionic currents occurred in hypertrophic cells: a decrease in the inward rectifier K⁺ current I_K1, and a slowing of L-type Ca²⁺ current inactivation which was responsible for the lack of adaptation of APs to abrupt changes in the pacing rate. The occurrence of spontaneous Ca²⁺ sparks, reflecting ryanodine receptor (RyR2) diastolic activity, increased with hypertrophy. The [Ca²⁺]_i transient amplitude, sarcoplasmic reticulum (SR) Ca²⁺ load and Ca²⁺ sparks amplitude were all inversely correlated with cell size. We conclude that the trophic status of cardiomyocytes determines the type of cellular arrhythmia in MI rats, based on differential electrophysiological remodeling which may reflect early-mild and late-severe or differential modifications in the RyR2 function.     

Ionic currents during the action potential in the molluscan neurone with the self-clamp technique

The ionic currents during the action potential in the F1 neurone of Helix aspersa were investigated, using the Self-Clamp Technique. A spontaneous action potential was recorded and then replayed, both in its direct and in its inverted form, to the same cell in voltage clamp and in control conditions. Under various experimental conditions such as treatment with the specific ionic channels blockers tetrodotoxin, lanthanum, 4-aminopyridine or tetraethylammonium, as well as low sodium and low calcium external media, the single ionic currents were detected by stimulating the membrane with the direct pulse only. The Self-Clamp Technique allowed the measuring of the following parameters, in their real time course during the action potential: a) the total action currents; b) the pharmacologically blocked ionic components; c) the ionic components which remained insensitive to the agents used (residual currents). These data were compared with those obtained by applying conventional rectangular pulses in voltage clamp. The membrane capacity was measured with the Self-Clamp Technique and the recorded currents were normalized assuming a specific capacity of 4 μF/cm². The isolated ionic components were directly compared with the total action currents to evaluate the degree to which blockage was complete. The electric charge transported by each ionic specimen was evaluated as well as the individual ionic amounts. The sodium influx was 3.18 ± 0.55 pM/cm² per impulse (9 cells), calcium influx 1.03 ± 0.37 pM/cm² per impulse (10 cells). A value of 6.37 ± 1.03 pM/cm² per impulse was found for the potassium outflux, with a probable overestimation of about 1 pM/cm² per impulse (9 cells).     

Properties of the charibdotoxin-sensitive component of Ca2+-dependent K+ current in smooth muscle cells of the guinea pigTaenia Coli

Using the voltage-clamp technique, we investigated transmembrane ion currents in isolated smooth muscle cells of the guinea pigtaenia coli. In our study, we identified and studied a charibdotoxin-sensitive component of Ca²⁺-dependent K⁺ current carried through the channels of high conductance (in most publications called “big conductance,”I _BK(Ca)). This component was completely blocked by 100 nM charibdotoxin and by tetraethylammonium in concentrations as low as 1 mM.I _BK(Ca) demonstrated fast kinetics of inactivation, which nearly coincided with that of Ca²⁺ current. In addition to the dependence on Ca²⁺ concentration, this current also showed voltage-dependent properties: with a rise in the level of depolarization its amplitude increased. In many cells, depolarizing shifts in the membrane potential evoke spontaneous outward currents. Such currents probably represent the secondary effect of cyclic Ca²⁺ release from the caffeine-sensitive intracellular stores that result in short-term activation of charibdotoxin-sensitive Ca²⁺-dependent K⁺ channels.     

A quantitative model for linking Na+/Ca2+ exchanger to SERCA during refilling of the sarcoplasmic reticulum to sustain [Ca2+] oscillations in vascular smooth muscle

We have developed a quantitative model for the creation of cytoplasmic Ca²⁺ gradients near the inner surface of the plasma membrane (PM). In particular we simulated the refilling of the sarcoplasmic reticulum (SR) via PM–SR junctions during asynchronous [Ca²⁺]_i oscillations in smooth muscle cells of the rabbit inferior vena cava. We have combined confocal microscopy data on the [Ca²⁺]_i oscillations, force transduction data from cell contraction studies and electron microscopic images to build a basis for computational simulations that model the transport of calcium ions from Na⁺/Ca²⁺ exchangers (NCX) on the PM to sarcoplasmic/endoplasmic reticulum Ca²⁺ ATPase (SERCA) pumps on the SR as a three-dimensional random walk through the PM–SR junctional cytoplasmic spaces. Electron microscopic ultrastructural images of the smooth muscle cells were elaborated with software algorithms to produce a very clear and dimensionally accurate picture of the PM–SR junctions. From this study, we conclude that it is plausible and possible for enough Ca²⁺ to pass through the PM–SR junctions to replete the SR during the regenerative Ca²⁺ release, which underlies agonist induced asynchronous Ca²⁺ oscillations in vascular smooth muscle.     

The Circadian Clock Gene Period1 Connects the Molecular Clock to Neural Activity in the Suprachiasmatic Nucleus

The neural activity patterns of suprachiasmatic nucleus (SCN) neurons are dynamically regulated throughout the circadian cycle with highest levels of spontaneous action potentials during the day. These rhythms in electrical activity are critical for the function of the circadian timing system and yet the mechanisms by which the molecular clockwork drives changes in the membrane are not well understood. In this study, we sought to examine how the clock gene Period1 (Per1) regulates the electrical activity in the mouse SCN by transiently and selectively decreasing levels of PER1 through use of an antisense oligodeoxynucleotide. We found that this treatment effectively reduced SCN neural activity. Direct current injection to restore the normal membrane potential partially, but not completely, returned firing rate to normal levels. The antisense treatment also reduced baseline [Ca²⁺]i levels as measured by Fura2 imaging technique. Whole cell patch clamp recording techniques were used to examine which specific potassium currents were altered by the treatment. These recordings revealed that the large conductance [Ca²⁺]i-activated potassium currents were reduced in antisense-treated neurons and that blocking this current mimicked the effects of the anti-sense on SCN firing rate. These results indicate that the circadian clock gene Per1 alters firing rate in SCN neurons and raise the possibility that the large conductance [Ca²⁺]i-activated channel is one of the targets.     

Use of thapsigargin to study Ca2+ homeostasis in cardiac cells

Several reports have documented that thapsigargin is a potent inhibitor of the SR Ca²⁺ ATPase isolated from cardiac or skeletal muscle. We have characterized the specificity of this agent in intact rat cardiac myocytes using cells maintained in the whole cell voltage clamp configuration. We have shown that thapsigargin decreases the magnitude of the Ca²⁺ transient and the twitch by about 80% while it slows the decay rate for these responses. These changes were not accompanied by any alterations in sarcolemmal currents or in the trigger Ca²⁺ generated by the inward calcium current. Taken together these results reveal that the action of thapsigargin is restricted to the SR Ca²⁺ ATPase in intact cardiac myocytes. Furthermore, it is demonstrated unambiguously that SR intracellular Ca²⁺ stores are an absolute requirement for the development of contractile tension in rat heart myocytes. It is shown that thapsigargin is a valuable probe to examine the importance of SR pools of Ca²⁺ and the role of the Ca²⁺ ATPase in intact myocytes as well as in genetically altered heart cells.     

Parameter estimation in cardiac ionic models

We examine the problem of parameter estimation in mathematical models of excitable cell cardiac electrical activity using the well-known Beeler–Reuter (1977) ionic equations for the ventricular action potential. The estimation problem can be regarded as equivalent to the accurate reconstruction of ionic current kinetics and amplitudes in an excitable cell model, given only action potential experimental data. We show that in the Beeler–Reuter case, all ionic currents may be reasonably reconstructed using an experimental design consisting of action potential recordings perturbed by pseudo-random injection currents.

The Beeler–Reuter model was parameterised into 63 parameters completely defining all membrane current amplitudes and kinetics. Total membrane current was fitted to model-generated experimental data using a ‘data-clamp’ protocol. The experimental data consisted of a default action-potential waveform and an optional series of perturbed waveforms generated by current injections. Local parameter identifiability was ascertained from the reciprocal condition value (1/λ) of the Hessian at the known solution. When fitting to a single action potential waveform, the model was found to be over-determined, having a 1/λ value of 3.6e−14. This value improved slightly to 1.4e−10 when an additional 2 perturbed waveforms were included in the fitting process, suggesting that the additional data did not overly improve the identifiability problem. The additional data, however, did allow the accurate reconstruction of all ionic currents. This indicates that by appropriate experimental design, it may be possible to infer the properties of underlying membrane currents from observation of transmembrane potential waveforms perturbed by pseudo-random currents.     

Cardiac action potential duration and calcium regulation in males and females

Adult women have longer QT intervals compared with men of a similar age, indicating differences in the speed of repolarisation of the ventricles. We investigate the influences of gender on ventricular electrophysiology and intracellular Ca²⁺ regulation of the guinea pig heart. Comparing sexually mature animals, females exhibited a significantly longer APD. Peak L-type Ca²⁺ current (I_CaL) was larger in females and when this current was inhibited with nifedipine the gender differences in APD were removed. APD differences also disappeared when the SR was depleted of Ca²⁺. Inactivation of I_CaL during a clamp step is faster in females but slower during an action potential and SR Ca²⁺ content is larger. We suggest that gender differences in APD result from variation in the kinetics of I_CaL stemming from alterations to Ca²⁺ release.     

Predicting Local SR Ca Dynamics during Ca Wave Propagation in Ventricular Myocytes

Of the many ongoing controversies regarding the workings of the sarcoplasmic reticulum (SR) in cardiac myocytes, two unresolved and interconnected topics are 1), mechanisms of calcium (Ca²⁺) wave propagation, and 2), speed of Ca²⁺ diffusion within the SR. Ca²⁺ waves are initiated when a spontaneous local SR Ca²⁺ release event triggers additional release from neighboring clusters of SR release channels (ryanodine receptors (RyRs)). A lack of consensus regarding the effective Ca²⁺ diffusion constant in the SR (D_Ca,SR) severely complicates our understanding of whether dynamic local changes in SR [Ca²⁺] can influence wave propagation. To address this problem, we have implemented a computational model of cytosolic and SR [Ca²⁺] during Ca²⁺ waves. Simulations have investigated how dynamic local changes in SR [Ca²⁺] are influenced by 1), D_Ca,SR; 2), the distance between RyR clusters; 3), partial inhibition or stimulation of SR Ca²⁺ pumps; 4), SR Ca²⁺ pump dependence on cytosolic [Ca²⁺]; and 5), the rate of transfer between network and junctional SR. Of these factors, D_Ca,SR is the primary determinant of how release from one RyR cluster alters SR [Ca²⁺] in nearby regions. Specifically, our results show that local increases in SR [Ca²⁺] ahead of the wave can potentially facilitate Ca²⁺ wave propagation, but only if SR diffusion is relatively slow. These simulations help to delineate what changes in [Ca²⁺] are possible during SR Ca²⁺release, and they broaden our understanding of the regulatory role played by dynamic changes in [Ca²⁺]_SR.     

A Model of Action Potentials and Fast Ca Dynamics in Pancreatic β-Cells

We examined the ionic mechanisms mediating depolarization-induced spike activity in pancreatic β-cells. We formulated a Hodgkin-Huxley-type ionic model for the action potential (AP) in these cells based on voltage- and current-clamp results together with measurements of Ca²⁺ dynamics in wild-type and Kv2.1 null mouse islets. The model contains an L-type Ca²⁺ current, a “rapid” delayed-rectifier K⁺ current, a small slowly-activated K⁺ current, a Ca²⁺-activated K⁺ current, an ATP-sensitive K⁺ current, a plasma membrane calcium-pump current and a Na⁺ background current. This model, coupled with an equation describing intracellular Ca²⁺ homeostasis, replicates β-cell AP and Ca²⁺ changes during one glucose-induced spontaneous spike, the effects of blocking K⁺ currents with different inhibitors, and specific complex spike in mouse islets lacking Kv2.1 channels. The currents with voltage-independent gating variables can also be responsible for burst behavior. Original features of this model include new equations for L-type Ca²⁺ current, assessment of the role of rapid delayed-rectifier K⁺ current, and Ca²⁺-activated K⁺ currents, demonstrating the important roles of the Ca²⁺-pump and background currents in the APs and bursts. This model provides acceptable fits to voltage-clamp, AP, and Ca²⁺ concentration data based on in silico analysis.     

Simulations of the cardiac action potential based on the Hodgkin-Huxley kinetics with the use of Microsoft Excel spreadsheets

The purpose of this study was to develop a method to simulate the cardiac action potential using a Microsoft Excel spreadsheet. The mathematical model contained voltage-gated ionic currents that were modeled using either Beeler-Reuter (B-R) or Luo-Rudy (L-R) phase 1 kinetics. The simulation protocol involves the use of in-cell formulas directly typed into a spreadsheet. The capability of spreadsheet iteration was used in these simulations. It does not require any prior knowledge of computer programming, although the use of the macro language can speed up the calculation. The normal configuration of the cardiac ventricular action potential can be well simulated in the B-R model that is defined by four individual ionic currents, each representing the diffusion of ions through channels in the membrane. The contribution of Na+ inward current to the rate of depolarization is reproduced in this model. After removal of Na+ current from the model, a constant current stimulus elicits an oscillatory change in membrane potential. In the L-R phase 1 model where six types of ionic currents were defined, the effect of extracellular K+ concentration on changes both in the time course of repolarization and in the time-independent K+ current can be demonstrated, when the solutions are implemented in Excel. Using the simulation protocols described here, the users can readily study and graphically display the underlying properties of ionic currents to see how changes in these properties determine the behavior of the heart cell. The method employed in these simulation protocols may also be extended or modified to other biological simulation programs.     

Mitogen-activated Ca++ channels in human B lymphocytes

Two complementary experimental methods have been used to examine mitogen-induced transmembrane conductances in human B cells using the Daudi cell line as a model for human B cell activation. Spectrofluorometry was used to investigate mitogen-induced changes in [Ca⁺⁺]_i and transmembrane potential. Activation of human B cells with anti-μ antibodies resulted in a biphasic rise in [Ca⁺⁺]_i, the second phase being mediated by the influx of extracellular Ca⁺⁺. Ca⁺⁺ influx was inhibited by high [K⁺]e, suggesting that this influx was transmembrane potential sensitive. Membrane currents of Daudi cells were investigated using voltage clamp techniques. Before mitogenic stimulation, the cells were electrically quiet. Within several minutes of the addition of anti-μ antibodies to the bath solution, inward currents were observed at negative voltages. Whole-cell currents changed instantly with voltage steps and were transmembrane potential sensitive in that at potentials more positive than ?40 mV no currents were detectable. A similar conductance was also activated by the introduction of IP₃ into the intracellular solution, suggesting that IP₃ generation after surface IgM crosslinking is involved in the activation of this conductance. Both anti-μ and IP³ induced currents were blocked by 1 mM La⁺⁺⁺, which is known to block Ca⁺⁺ channels. These results strongly support the presence of membrane Ca⁺⁺ channels in human B cells that function in the early stages of activation. Changes in transmembrane potential appear to be important in regulating Ca⁺⁺ influx. These mechanisms work in concert to regulate the level of [Ca⁺⁺]_i during the early phases of human B cell activation. © 1993 Wiley-Liss, Inc.     

Voltage-dependent ionic conductances in the human malignant astrocytoma cell line U87-MG

Although the human malignant astrocytoma cell line U87-MG has been used in numerous studies, few findings are available on the properties of its membrane ion conductances. Characterization of the ion channels expressed in these cells will make it possible to study membrane ion conductance changes when a receptor is activated by its ligand. This will help to elucidate the functional properties of these receptors and their signal-transduction pathways in pathophysiological events. This work studied the voltage-dependent ionic conductances of U87-MG cells using the Whole-Cell Recording patch-clamp technique. Six types of voltage-dependent ionic currents were identified: (i) a TEA-, 4-AP- and CTX-sensitive Ca²⁺-dependent K⁺ current, (ii) a transient K⁺ current inhibited by 4-AP, (iii) an inwardly rectifying K⁺ current blocked by Ba²⁺ and 4-AP, (iv) a DIDS- and SITS-sensitive Cl^? current, (v) a TTX-sensitive Na⁺ conductance and (vi) a L-type Ca²⁺ conductance activated by BayK-8644 and inhibited by Ni and the L-type Ca²⁺ channel inhibitor, nifedipine. In addition, electrical depolarizations elicited inward currents due to voltage-independent, Ca²⁺-dependent K⁺ influx against the electrochemical gradient, probably via an ouabain-sensitive Na⁺-K⁺ pump.