A new approach to the determination of tubular membrane capacitance: passive membrane electrical properties under reduced electrical conductivity of the extracellular solution.

The transverse-axial tubular system (tubular system) of cardiomyocytes plays a key role in excitation-contraction coupling. To determine the area of the tubular membrane in relation to the area of the surface membrane, indirect measurements through the determination of membrane capacitances are currently used in addition to microscopic methods. Unlike existing electrophysiological methods based on an irreversible procedure (osmotic shock), the proposed new approach uses a reversible short-term intermittent increase in the electrical resistance of the extracellular medium. The resulting increase in the lumen resistance of the tubular system makes it possible to determine separate capacitances of the tubular and surface membranes. Based on the analysis of the time course of the capacitive current, computational relations were derived to quantify the elements of the electrical equivalent circuit of the measured cardiomyocyte including both capacitances. The exposition to isotonic low-conductivity sucrose solution is reversible which is the main advantage of the proposed approach allowing repetitive measurements on the same cell under control and sucrose solutions. Experiments on rat ventricular cardiomyocytes (n = 20) resulted in the surface and tubular capacitance values implying the fraction of tubular capacitance/area of 0.327 ± 0.018. We conclude that the newly proposed method provides results comparable to the data obtained by the currently used detubulation method and, in addition, by being reversible, allows repeated evaluation of surface and tubular membrane parameters on the same cell.

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.

Aminophylline at clinically relevant concentrations affects inward rectifier potassium current in a dual way.

Bronchodilator aminophylline may induce atrial or less often ventricular arrhythmias. The mechanism of this proarrhythmic side effect has not been fully explained. Modifications of inward rectifier potassium (Kir) currents including IK1 are known to play an important role in arrhythmogenesis; however, no data on the aminophylline effect on these currents have been published. Hence, we tested the effect of aminophylline (3-100 µM) on IK1 in enzymatically isolated rat ventricular myocytes using the whole-cell patch-clamp technique. A dual steady-state effect of aminophylline was observed; either inhibition or activation was apparent in individual cells during the application of aminophylline at a given concentration. The smaller the magnitude of the control IK1, the more likely the activation of the current by aminophylline and vice versa. The effect was reversible; the relative changes at -50 and -110 mV did not differ. Using IK1 channel population model, the dual effect was explained by the interaction of aminophylline with two different channel populations, the first one being inhibited and the second one being activated. Considering various fractions of these two channel populations in individual cells, varying effects observed in the measured cells could be simulated. We propose that the dual aminophylline effect may be related to the direct and indirect effect of the drug on various Kir2.x subunits forming the homo- and heterotetrameric IK1 channels in a single cell. The observed IK1 changes induced by clinically relevant concentrations of aminophylline might contribute to arrhythmogenesis related to the use of this bronchodilator in clinical medicine.

Divergent estimates of the ratio between Na+-Ca2+ current densities in t-tubular and surface membranes of rat ventricular cardiomyocytes.

The ratio between Na+-Ca2+ exchange current densities in t-tubular and surface membranes of rat ventricular cardiomyocytes (JNaCa-ratio) estimated from electrophysiological data published to date yields strikingly different values between 1.7 and nearly 40. Possible reasons for such divergence were analysed by Monte Carlo simulations assuming both normal and log-normal distribution of the measured data. The confidence intervals CI95 of the mean JNaCa-ratios computed from the reported data showed an overlap of values between 1 and 3, and between 0.3 and 4.3 in the case of normal and log-normal distribution, respectively. Further analyses revealed that the published high values likely result from a large scatter of data due to transmural differences in JNaCa, dispersion of cell membrane capacitances and variability in incomplete detubulation. Taking into account the asymmetric distribution of the measured data, the reduction of mean current densities after detubulation and the substantially smaller CI95 of lower values of the mean JNaCa-ratio, the values between 1.6 and 3.2 may be considered as the most accurate estimates. This implies that 40 to 60% of Na+-Ca2+ exchanger is located at the t-tubular membrane of adult rat ventricular cardiomyocytes.

Distribution of data in cellular electrophysiology: Is it always normal?

The distribution of data presented in many electrophysiological studies is presumed to be normal without any convincing evidence. To test this presumption, the cell membrane capacitance and magnitude of inward rectifier potassium currents were recorded by the whole-cell patch clamp technique in rat atrial myocytes. Statistical analysis of the data showed that these variables were not distributed normally. Instead, a positively skewed distribution appeared to be a better approximation of the real data distribution. Consequently, the arithmetic mean, used inappropriately in such data, may substantially overestimate the true mean value characterizing the central tendency of the data. Moreover, a large standard deviation describing the variance of positively skewed data allowed 95% confidence interval to include unrealistic negative values. We therefore conclude that the normality of the electrophysiological data should be tested in every experiment and, if rejected, the positively skewed data should be more accurately characterized by the median and interpercentile range or, if justified (namely in the case of log-normal and gamma data distribution), by the geometric mean and the geometric standard deviation.

A new simple approach to estimation of membrane capacitance from current responses to voltage clamp steps.

A variety of techniques of cell capacitance measurement have been proposed and applied in cellular electrophysiology. They are mostly based on the evaluation of membrane current responses to small changes in the membrane voltage. One of the currently used approaches applies the least-squares fit of an exponential current decay in response to voltage clamped rectangular pulses. In this study, we propose an alternative simpler approach to evaluation of the exponential parts in the current responses to square wave stimulation and present preliminary results of membrane capacitance evaluation. It is based on the property of the exponential function that has not yet been used to measure membrane capacitance. The time constant and the asymptote of the exponential waveform are unambiguously determined by the values read at three points separated by a constant time interval. In order to minimize the effect of noise and deviations from the exponential waveform, the triplet of points is designed to slide along the time axis. The results of the proposed approach and those previously evaluated by the least squares method are comparable. The method described may be advantageous for continuously recording changes in membrane capacitance.

Current density as routine parameter for description of ionic membrane current: is it always the best option?

The current density (J) is a parameter routinely used to characterize individual ionic membrane currents. Its evaluation is based on the presumption that the magnitude of whole-cell ionic membrane current (I) is directly proportional to the cell membrane capacitance (C), i.e. I positively and strongly correlates with C and the regression line describing I-C relation intersects the y-axis close to the origin of coordinates. We aimed to prove the presumption in several examples and find whether the conversion of I to J could be always beneficial. I-C relation was analysed in several potassium currents, measured in rat atrial myocytes (in inward rectifier currents, IK1, and both the constitutively active and acetylcholine-induced components of acetylcholine-sensitive current, IK(Ach)CONST and IK(Ach)ACH), and in rat ventricular myocytes (transient outward current Ito). I-C correlation was estimated by the Pearson coefficient (r). A coefficient (k) was newly suggested describing deviation of the regression intercept from zero in currents with considerable r value. Based on mathematical simulations, I was satisfactorily proportional to C when r ≥ 0.6 and k ≤ 0.2 which was fulfilled in IK1 and IK(Ach)ACH (r = 0.84, k = 0.20, and r = 0.61, k = 0.06, respectively). I-C correlation was significantly positive, but weak in IK(Ach)CONST (r = 0.42), and virtually missing in Ito (r = 0.04). The impaired I-C proportionality in IK(Ach)CONST and Ito likely reflects heterogeneity of the channel expression. We conclude that the conversion of I to J should be avoided when I-C proportionality is absent. Otherwise, serious misinterpretation of data may arise.

The intriguing effect of ethanol and nicotine on acetylcholine-sensitive potassium current IKAch: Insight from a quantitative model.

Recent experimental work has revealed unusual features of the effect of certain drugs on cardiac inwardly rectifying potassium currents, including the constitutively active and acetylcholine-induced components of acetylcholine-sensitive current (IKAch). These unusual features have included alternating susceptibility of the current components to activation and inhibition induced by ethanol or nicotine applied at various concentrations, and significant correlation between the drug effect and the current magnitude measured under drug-free conditions. To explain these complex drug effects, we have developed a new type of quantitative model to offer a possible interpretation of the effect of ethanol and nicotine on the IKAch channels. The model is based on a description of IKAch as a sum of particular currents related to the populations of channels formed by identical assemblies of different α-subunits. Assuming two different channel populations in agreement with the two reported functional IKAch-channels (GIRK1/4 and GIRK4), the model was able to simulate all the above-mentioned characteristic features of drug-channel interactions and also the dispersion of the current measured in different cells. The formulation of our model equations allows the model to be incorporated easily into the existing integrative models of electrical activity of cardiac cells involving quantitative description of IKAch. We suppose that the model could also help make sense of certain observations related to the channels that do not show inward rectification. This new ionic channel model, based on a concept we call population type, may allow for the interpretation of complex interactions of drugs with ionic channels of various types, which cannot be done using the ionic channel models available so far.

Inward rectifying potassium currents resolved into components: modeling of complex drug actions.

Inward rectifier potassium currents (I Kir,x) belong to prominent ionic currents affecting both resting membrane voltage and action potential repolarization in cardiomyocytes. In existing integrative models of electrical activity of cardiac cells, they have been described as single current components. The proposed quantitative model complies with findings indicating that these channels are formed by various homomeric or heteromeric assemblies of channel subunits with specific functional properties. Each I Kir,x may be expressed as a total of independent currents via individual populations of identical channels, i.e., channels formed by the same combination of their subunits. Solution of the model equations simulated well recently observed unique manifestations of dual ethanol effect in rat ventricular and atrial cells. The model reflects reported occurrence of at least two binding sites for ethanol within I Kir,x channels related to slow allosteric conformation changes governing channel conductance and inducing current activation or inhibition. Our new model may considerably improve the existing models of cardiac cells by including the model equations proposed here in the particular case of the voltage-independent drug-channel interaction. Such improved integrative models may provide more precise and, thus, more physiologically relevant results.

Nicotine at clinically relevant concentrations affects atrial inward rectifier potassium current sensitive to acetylcholine.

Nicotine abuse is associated with variety of diseases including arrhythmias, most often atrial fibrillation (AF). Altered inward rectifier potassium currents including acetylcholine-sensitive current I K(Ach) are known to be related to AF pathogenesis. Since relevant data are missing, we aimed to investigate I K(Ach) changes at clinically relevant concentrations of nicotine. Experiments were performed by the whole cell patch clamp technique at 23 ± 1 °C on isolated rat atrial myocytes. Nicotine was applied at following concentrations: 4, 40 and 400 nM; ethanol at 20 mM (∼0.09%). Nicotine at 40 and 400 nM significantly activated constitutively active component of I K(Ach) with the maximum effect at 40 nM (an increase by ∼100%); similar effect was observed at -110 and -50 mV. Changes at 4 nM nicotine were negligible on average. Coapplication of 40 nM nicotine and 20 mM ethanol (which is also known to activate this current) did not show cumulative effect. In the case of acetylcholine-induced component of I K(Ach), a dual effect of nicotine and its correlation with the current magnitude in control were apparent: the current was increased by nicotine in the cells showing small current in control and vice versa. The effect of 40 and 400 nM nicotine on acetylcholine-induced component of I K(Ach) was significantly different at -110 and -50 mV. We conclude that nicotine at clinically relevant concentrations significantly increased constitutively active component of I K(Ach) and showed a dual effect on its acetylcholine-induced component, similarly as ethanol. Synchronous application of nicotine and ethanol did not cause additive effect.

Effect of ethanol at clinically relevant concentrations on atrial inward rectifier potassium current sensitive to acetylcholine.

Alcohol intoxication tends to induce arrhythmias, most often the atrial fibrillation. To elucidate arrhythmogenic mechanisms related to alcohol consumption, the effect of ethanol on main components of the ionic membrane current is investigated step by step. Considering limited knowledge, we aimed to examine the effect of clinically relevant concentrations of ethanol (0.8-80 mM) on acetylcholine-sensitive inward rectifier potassium current I K(Ach). Experiments were performed by the whole-cell patch clamp technique at 23 ± 1 °C on isolated rat and guinea-pig atrial myocytes, and on expressed human Kir3.1/3.4 channels. Ethanol induced changes of I K(Ach) in the whole range of concentrations applied; the effect was not voltage dependent. The constitutively active component of I K(Ach) was significantly increased by ethanol with the maximum effect (an increase by ∼100 %) between 8 and 20 mM. The changes were comparable in rat and guinea-pig atrial myocytes and also in expressed human Kir3.1/3.4 channels (i.e., structural correlate of I K(Ach)). In the case of the acetylcholine-induced component of I K(Ach), a dual ethanol effect was apparent with a striking heterogeneity of changes in individual cells. The effect correlated with the current magnitude in control: the current was increased by eth-anol in the cells showing small current in control and vice versa. The average effect peaked at 20 mM ethanol (an increase of the current by ∼20 %). Observed changes of action potential duration agreed well with the voltage clamp data. Ethanol significantly affected both components of I K(Ach) even in concentrations corresponding to light alcohol consumption.

Acute effects of ethanol on action potential and intracellular Ca(2+) transient in cardiac ventricular cells: a simulation study.

Alcohol consumption may result in electrocardiographic changes and arrhythmias, at least partly due to effects of ethanol on cardiac ionic currents. Contractility and intracellular Ca(2+) dynamics seem to be altered as well. In this study, we integrated the available (mostly animal) experimental data into previously published models of the rat and human ventricular myocytes to assess the share of ionic current components in ethanol-induced changes in AP configuration and cytosolic Ca(2+) transient in ventricular cardiomyocytes. The rat model reproduced well the experimentally observed changes in AP duration (APD) under ethanol (slight prolongation at 0.8 mM and shortening at ≥8 mM). These changes were almost exclusively caused by the ethanol-induced alterations of I K1. The cytosolic Ca(2+) transient decreased gradually with the increasing ethanol concentration as a result of the ethanol-induced inhibition of I Ca. In the human model, ethanol produced a dose-dependent APD lengthening, dominated by ethanol effect on I Kr, the key repolarising current in human ventricles. This effect might contribute to the clinically observed proarrhythmic effects of ethanol in predisposed individuals.

Effect of Ca2+ efflux pathway distribution and exogenous Ca2+ buffers on intracellular Ca2+ dynamics in the rat ventricular myocyte: a simulation study.

We have used a previously published computer model of the rat cardiac ventricular myocyte to investigate the effect of changing the distribution of Ca(2+) efflux pathways (SERCA, Na(+)/Ca(2+) exchange, and sarcolemmal Ca(2+) ATPase) between the dyad and bulk cytoplasm and the effect of adding exogenous Ca(2+) buffers (BAPTA or EGTA), which are used experimentally to differentially buffer Ca(2+) in the dyad and bulk cytoplasm, on cellular Ca(2+) cycling. Increasing the dyadic fraction of a particular Ca(2+) efflux pathway increases the amount of Ca(2+) removed by that pathway, with corresponding changes in Ca(2+) efflux from the bulk cytoplasm. The magnitude of these effects varies with the proportion of the total Ca(2+) removed from the cytoplasm by that pathway. Differences in the response to EGTA and BAPTA, including changes in Ca(2+)-dependent inactivation of the L-type Ca(2+) current, resulted from the buffers acting as slow and fast "shuttles," respectively, removing Ca(2+) from the dyadic space. The data suggest that complex changes in dyadic Ca(2+) and cellular Ca(2+) cycling occur as a result of changes in the location of Ca(2+) removal pathways or the presence of exogenous Ca(2+) buffers, although changing the distribution of Ca(2+) efflux pathways has relatively small effects on the systolic Ca(2+) transient.

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.

Estimation of rate constants of drug binding to open channels of cardiac transient outward current.

An improved approach to the evaluation of the rate constants of drugs binding to the open channel underlying the transient outward potassium current I(t0) is described. It is based on an analysis of a quantitative model formulated by a set of twelve differential equations. The rate constants are calculated from the time constants resulting from an approximation of the time course of apparent inactivation of the recorded I(t0) by two exponentials in the absence and by three exponentials in the presence of a blocking agent. The model study confirmed significantly higher accuracy in comparison with the existing electrophysiological method.

Effect of antipsychotic drug perphenazine on fast sodium current and transient outward potassium current in rat ventricular myocytes.

Antipsychotic drug perphenazine belongs to the phenothiazine group commonly reported to induce ECG changes and tachyarrhythmias. Data about its effect on ionic membrane currents in cardiomyocytes are missing. We analyzed the effect of perphenazine (0.1-100 microM) on fast sodium current I (Na) and transient outward potassium current I (to) in enzymatically isolated rat right ventricular myocytes by the whole-cell patch-clamp technique at room temperature. Perphenazine reversibly blocked I (Na) (reducing its amplitude; IC(50) = 1.24 +/- 0.10 microM) and I (to) (accelerating its apparent inactivation with a slight decrease of its amplitude; IC(50) = 38.2 +/- 3.5 microM, evaluated from changes of the time integral). The fast time constant of I (to) inactivation was significantly decreased in a concentration-dependent manner (IC(50) = 30.0 +/- 6.6 microM). Both blocks were use and frequency dependent at 3.3 Hz. We conclude that perphenazine causes concentration-, use-, and frequency-dependent block of I (Na) and I (to) . Computer simulations suggest that perphenazine interacts preferentially with I (Na) channels in inactivated states and with I (to) channels in both open and open-inactivated states.

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.

The functional role of cardiac T-tubules explored in a model of rat ventricular myocytes.

The morphology of the cardiac transverse-axial tubular system (TATS) has been known for decades, but its function has received little attention. To explore the possible role of this system in the physiological modulation of electrical and contractile activity, we have developed a mathematical model of rat ventricular cardiomyocytes in which the TATS is described as a single compartment. The geometrical characteristics of the TATS, the biophysical characteristics of ion transporters and their distribution between surface and tubular membranes were based on available experimental data. Biophysically realistic values of mean access resistance to the tubular lumen and time constants for ion exchange with the bulk extracellular solution were included. The fraction of membrane in the TATS was set to 56%. The action potentials initiated in current-clamp mode are accompanied by transient K+ accumulation and transient Ca2+ depletion in the TATS lumen. The amplitude of these changes relative to external ion concentrations was studied at steady-state stimulation frequencies of 1-5 Hz. Ca2+ depletion increased from 7 to 13.1% with stimulation frequency, while K+ accumulation decreased from 4.1 to 2.7%. These ionic changes (particularly Ca2+ depletion) implicated significant decrease of intracellular Ca2+ load at frequencies natural for rat heart.