Contributions of HERG current to repolarization of the human ventricular action potential

Action potential repolarization in the mammalian heart is governed by interactions of a number of time- and voltage-dependent channel-mediated currents, as well as contributions from the Na⁺/Ca²⁺ exchanger and the Na⁺/K⁺ pump. Recent work has shown that one of the K⁺ currents (HERG) which contributes to repolarization in mammalian ventricle is a locus at which a number of point mutations can have significant functional consequences. In addition, the remarkable sensitivity of this K⁺ channel isoform to inhibition by a variety of pharmacological agents and clinical drugs has resulted in HERG being a major focus for Safety Pharmacology requirements.For these reasons we and others have attempted to define the functional role for HERG-mediated K⁺ currents in repolarization of the action potential in the human ventricle. Here, we describe and evaluate changes in the formulations for two K⁺ currents, I_K1 and HERG (or I_K,r), within the framework of ten Tusscher model of the human ventricular action potential. In this computational study, new mathematical formulations for the two nonlinear K⁺ conductances, I_K1 and HERG, have been developed based upon experimental data obtained from electrophysiological studies of excised human ventricular tissue and/or myocytes. The resulting mathematical model provides much improved simulations of the relative sizes and time courses of the K⁺ currents which modulate repolarization. Our new formulation represents an important first step in defining the mechanism(s) of repolarization of the membrane action potential in the human ventricle. Our overall goal is to understand the genesis of the T-wave of the human electrocardiogram.     

Frequency-dependent and proarrhythmogenic effects of FK-506 in rat ventricular cells

FK-506, a widely used immunosuppressant, has caused a few clinical cases with QT prolongation and torsades de pointe at high blood concentration. The proarrhytmogenic potential of FK-506 was investigated in single rat ventricular cells using the whole cell clamp method to record action potentials (APs) and ionic currents. Fluorescence measurements of Ca2+ transients were performed with indo-1 AM using a multiphotonic microscope. FK-506 (25 micromol/l) hyperpolarized the resting membrane potential (RMP; -3 mV) and prolonged APs (AP duration at 90% repolarization increased by 21%) at 0.1 Hz. Prolongation was enhanced by threefold at 3.3 Hz, and early afterdepolarizations (EADs) occurred in 59% of cells. EADs were prevented by stronger intracellular Ca2+ buffering (EGTA: 10 vs. 0.5 mmol/l in the patch pipette) or replacement of extracellular Na+ by Li+, which abolishes Na+/Ca2+ exchange [Na+/Ca2+ exchanger current (INaCa)]. In indo-1-loaded cells, FK-506 generated doublets of Ca(2+) transients associated with increased diastolic Ca2+ in one-half of the cells. FK-506 reversibly decreased the L-type Ca2+ current (ICaL) by 25%, although high-frequency-dependent facilitation of ICaL persisted, and decreased three distinct K+ currents: delayed rectifier K+ current (IK; >80%), transient outward K+ current (<20%), and inward rectifier K+ current (IK1; >40%). A shift in the reversal potential of IK1 (-5 mV) accounted for RMP hyperpolarization. Numerical simulations, reproducing all experimental effects of FK-506, and the use of nifedipine showed that frequency-dependent facilitation of ICaL plays a role in the occurrence of EADs. In conclusion, the effects of FK-506 on the cardiac AP are more complex than previously reported and include inhibitions of IK1 and ICaL. Alterations in Ca2+ release and INaCa may contribute to FK-506-induced AP prolongation and EADs in addition to the permissive role of ICaL facilitation at high rates of stimulation.     

Alteration of the transmembrane K+ gradient during development of delayed rectifier in isolated rat pulmonary arterial cells

The properties of the tail current associated with the delayed rectifier K+ current (IK) in isolated rat pulmonary artery smooth muscle cells were examined using the whole cell patch clamp technique. The tail currents observed upon repolarization to -60 mV after brief (e.g., 20 ms) or small (i.e. to potentials negative of 0 mV) depolarizations were outwardly directed, as expected given the calculated K+ reversal potential of -83 mV. The tail currents seen upon repolarization after longer (e.g., 500 ms) and larger (e.g., to +60 mV) depolarizations tended to be inwardly directed. Depolarizations of intermediate strength and/or duration were followed by biphasic tail currents, which were inwardly directed immediately upon repolarization, but changed direction and became outwardly directed before deactivation was complete. When cells were depolarized to +60 mV for 500 ms both IK and the subsequent inward tail current at -60 mV were similarly blocked by phencyclidine. Both IK and the inward tail current were also blocked by 4-aminopyridine. Application of progressively more depolarized 30 s preconditioning potentials inactivated IK, and reduced the inward tail current amplitude with a similar potential dependency. These results indicated that the inward tail current was mediated by IK. The reversal potential of the tail current became progressively more positive with longer depolarizations to +60 mV, shifting from -76.1 +/- 2.2 mV (n = 10) after a 20-ms step to -57.7 +/- 3.5 mV (n = 9) after a 500-ms step. Similar effects occurred when extracellular K+ and Na+ were replaced by choline. When extracellular K+ was raised to 50 mM, the tail current was always inwardly directed at -60 mV, but showed little change in amplitude as the duration of depolarization was increased. These observations are best explained if the dependencies of tail current direction and kinetics upon the duration of the preceding depolarization result from an accumulation of K+ at the external face of the membrane, possibly in membrane invaginations. A mathematical model which simulates the reversal potential shift and the biphasic kinetics of the tail current on this basis is presented.     

KvLQT1 modulates the distribution and biophysical properties of HERG. A novel alpha-subunit interaction between delayed rectifier currents

Cardiac repolarization is under joint control of the slow (IKs) and rapid (IKr) delayed rectifier currents. Experimental and clinical evidence indicates important functional interactions between these components. We hypothesized that there might be more direct interactions between the KvLQT1 and HERG alpha-subunits of IKs and IKr and tested this notion with a combination of biophysical and biochemical techniques. Co-expression of KvLQT1 with HERG in a mammalian expression system significantly accelerated HERG current deactivation at physiologically relevant potentials by increasing the contribution of the fast component (e.g. upon repolarization from +20 mV to -50 mV: from 20 +/- 3 to 32 +/- 5%, p < 0.05), making HERG current more like native IKr. In addition, HERG current density was approximately doubled (e.g. tail current after a step to +10 mV: 18 +/- 3 versus 39 +/- 7 pA/picofarad, p < 0.01) by co-expression with KvLQT1. KvLQT1 co-expression also increased the membrane immunolocalization of HERG by approximately 2-fold (p < 0.05). HERG and KvLQT1 co-immunolocalized in canine ventricular myocytes and co-immunoprecipitated in cultured Chinese hamster ovary cells as well as in native cardiac tissue, indicating physical interactions between HERG and KvLQT1 proteins in vitro and in vivo. Protein interaction assays also demonstrated binding of KvLQT1 (but not another K+ channel alpha-subunit, Kv3.4) to a C-terminal HERG glutathione S-transferase fusion protein. Co-expression with HERG did not affect the membrane localization or ionic current properties of KvLQT1. This study shows that the alpha-subunit of IKs can interact with and modify the localization and current-carrying properties of the alpha-subunit of IKr, providing potentially novel insights into the molecular function of the delayed rectifier current system.     

Characterization of two distinct depolarization-activated K+ currents in isolated adult rat ventricular myocytes

Depolarization-activated outward K+ currents in isolated adult rat ventricular myocytes were characterized using the whole-cell variation of the patch-clamp recording technique. During brief depolarizations to potentials positive to -40 mV, Ca(2+)-independent outward K+ currents in these cells rise to a transient peak, followed by a slower decay to an apparent plateau. The analyses completed here reveal that the observed outward current waveforms result from the activation of two kinetically distinct voltage-dependent K+ currents: one that activates and inactivates rapidly, and one that activates and inactivates slowly, on membrane depolarization. These currents are referred to here as Ito (transient outward) and IK (delayed rectifier), respectively, because their properties are similar (although not identical) to these K+ current types in other cells. Although the voltage dependences of Ito and IK activation are similar, Ito activates approximately 10-fold and inactivates approximately 30-fold more rapidly than IK at all test potentials. In the composite current waveforms measured during brief depolarizations, therefore, the peak current predominantly reflects Ito, whereas IK is the primary determinant of the plateau. There are also marked differences in the voltage dependences of steady-state inactivation of these two K+ currents: IK undergoes steady-state inactivation at all potentials positive to -120 mV, and is 50% inactivated at -69 mV; Ito, in contrast, is insensitive to steady-state inactivation at membrane potentials negative to -50 mV. In addition, Ito recovers from steady-state inactivation faster than IK: at -90 mV, for example, approximately 70% recovery from the inactivation produced at -20 mV is observed within 20 ms for Ito; IK recovers approximately 25-fold more slowly. The pharmacological properties of Ito and IK are also distinct: 4-aminopyridine preferentially attenuates Ito, and tetraethylammonium suppresses predominantly IK. The voltage- and time-dependent properties of these currents are interpreted here in terms of a model in which Ito underlies the initial, rapid repolarization phase of the action potential (AP), and IK is responsible for the slower phase of AP repolarization back to the resting membrane potential, in adult rat ventricular myocytes.     

Regulation of action potential duration under acute heat stress by I(K,ATP) and I(K1) in fish cardiac myocytes

The mechanism underlying temperature-dependent shortening of action potential (AP) duration was examined in the fish (Carassius carassius L.) heart ventricle. Acute temperature change from +5 to +18 degrees C (heat stress) shortened AP duration from 2.8 +/- 0.3 to 1.3 +/- 0.1 s in intact ventricles. In 56% (18 of 32) of enzymatically isolated myocytes, heat stress also induced reversible opening of ATP-sensitive K+ channels and increased their single-channel conductance from 37 +/- 12 pS at +8 degrees C to 51 +/- 13 pS at +18 degrees C (Q10 = 1.38) (P < 0.01; n = 12). The ATP-sensitive K+ channels of the crucian carp ventricle were characterized by very low affinity to ATP both at +8 degrees C [concentration of Tris-ATP that produces half-maximal inhibition of the channel (K1/2)= 1.35 mM] and +18 degrees C (K1/2 = 1.85 mM). Although acute heat stress induced ATP-sensitive K+ current (IK,ATP) in patch-clamped myocytes, similar heat stress did not cause any glibenclamide (10 microM)-sensitive changes in AP duration in multicellular ventricular preparations. Examination of APs and K+ currents from the same myocytes by alternate recording under current-clamp and voltage-clamp modes revealed that changes in AP duration were closely correlated with temperature-specific changes in the voltage-dependent rectification of the background inward rectifier K+ current IK1. In approximately 15% of myocytes (4 out of 27), IK,ATP-dependent shortening of AP followed the IK1-induced AP shortening. Thus heat stress-induced shortening of AP duration in crucian carp ventricle is primarily dependent on IK1. IK,ATP is induced only in response to prolonged temperature elevation or perhaps in the presence of additional stressors.     

Expression and Functional Characterization of the Human Ether-à-go-go-Related Gene (<Emphasis Type="Italic">HERG</Emphasis>) K<Superscript>+</Superscript> Channel Cardiac Splice Variant in <Emphasis Type="Italic">Xenopus laevis</Emphasis> Oocytes

HERG C_Cardiac, a C-terminal splice variant of the human ether-à-go-go-related gene (HERG A), was identified and found to be 100% homologous to HERG_USO. Real-time polymerase chain reaction data indicated that in the human heart HERG C_Cardiac mRNA was expressed eight times more than HERG A, whereas in human ventricular tissue it was expressed six times more than HERG A. A HERG C_Cardiac-green fluorescence protein (GFP) construct was heterologously expressed in Xenopus oocytes. Confocal micrographs revealed that HERG C_Cardiac was mainly expressed in the plasma membrane. HERG C_Cardiac channel expressed in oocytes produced slower inactivating outward currents and faster deactivating tail currents than those of HERG A channel. Equal amounts of HERG A and HERG C_Cardiac cRNA coinjected into oocytes formed intermediate HERG A + HERG C_Cardiac heteromultimers, which was reconfirmed by immunoprecipitation experiments with a HERG A N-terminal antibody. These heteromultimers had different inactivation, deactivation and activation kinetics from those of HERG A and HERG C_Cardiac channels. HERG A + HERG C_Cardiac heteromultimers significantly reduced the model action potential mean amplitude and increased the fast and slow inactivation τ values of the action potential repolarization phase, suggesting involvement of HERG A and HERG C_Cardiac heteromultimers in modulation of the refractory interval.     

Ionic currents underlying the action potential of Rana pipiens oocytes

Ionic currents in immature, ovulated Rana pipiens oocytes (metaphase I) were studied using the voltage-clamp technique. At this stage of maturity the oocyte can produce action potentials in response to depolarizing current or as an "off response" to hyperpolarizing current. Reducing external Na+ to 1/10 normal (choline substituted) eliminated the action potentials and both the negative-slope region and zero-crossing of the I-V relation. Reducing external Cl- to 1/10 or 1/100 normal (methanesulfonate substituted) lengthened the action potential. The outward current was reduced and a net inward current was revealed. By changing external Na+, Cl-, and K+ concentrations and using blocking agents (SITS, TEA), three voltage- and time-dependent currents were identified, INa, IK and ICl. The Na+ current activated at about 0 mV and reversed at very positive values which decreased during maturation. Inward Na+ current produced the upstroke of the action potential. During each voltage-clamp step the Na+ current activated slowly (seconds) and did not inactivate within many minutes. The Na+ current was not blocked by TTX at micromolar concentrations. The K+ current was present only in the youngest oocytes. Because IK was superimposed on a large leakage current, it appeared to reverse at the resting potential. When leakage currents were subtracted, the reversal potential for IK was more negative than -110 mV in Ringer's solution. IK was outwardly rectifying and strongly activated above -50 mV. The outward K+ current produced an after hyperpolarization at the end of each action potential. IK was blocked completely and reversibly by 20 mM external TEA. The Cl- current activated at about +10 mV and was outwardly rectifying. ICl was blocked completely and reversibly by 400 microM SITS added to the bathing medium. This current helped repolarize the membrane following an action potential in the youngest oocytes and was the only repolarizing current in more mature oocytes that had lost IK. The total leakage current had an apparently linear I-V relation and was separated into two components: a Na+ current (IN) and a smaller component carried by as yet unidentified ions.     

Tamoxifen inhibits Na+ and K+ currents in rat ventricular myocytes

Tamoxifen is an estrogen receptor antagonist used in the treatment of breast cancer. However, tamoxifen has been shown to induce QT prolongation of the electrocardiogram, thereby potentially causing life-threatening polymorphic ventricular arrhythmias. The purpose of the present study was to elucidate the electrophysiological mechanism(s) that underlie the arrhythmogenic effects of tamoxifen. We used standard ruptured whole cell and perforated patch-clamping techniques on rat ventricular myocytes to investigate the effects of tamoxifen on cardiac action potential (AP) waveforms and the underlying K+ currents. Tamoxifen (3 micromol/l) markedly prolonged AP duration, decreased maximal rate of depolarization, and decreased resting membrane potential. At this concentration, tamoxifen significantly depressed the Ca2+-independent transient outward K+ current (Ito), sustained outward delayed rectifier K+ current (Isus), inward rectifier K+ current (IK1), and Na+ current (INa) in the myocytes. Lower concentrations of tamoxifen (1 micromol/l) also decreased the resting membrane potential and significantly depressed IK1 to 79 +/- 5% (n = 5; at -120 mV) of pretreatment values. The results of this study indicate that inhibition of Ito, Isus, and IK1 by tamoxifen may underlie AP prolongation in cardiac myocytes and thereby contribute to prolonged QT interval observed in patients.     

Mathematical model of the neonatal mouse ventricular action potential

Therapies for heart disease are based largely on our understanding of the adult myocardium. The dramatic differences in action potential (AP) shape between neonatal and adult cardiac myocytes, however, indicate that a different set of molecular interactions in neonatal myocytes necessitates different treatment for newborns. Computational modeling is useful for synthesizing data to determine how interactions between components lead to systems-level behavior, but this technique has not been used extensively to study neonatal heart cell function. We created a mathematical model of the neonatal (day 1) mouse myocyte by modifying, on the basis of experimental data, the densities and/or formulations of ion transport mechanisms in an adult cell model. The new model reproduces the characteristic AP shape of neonatal cells, with a brief plateau phase and longer duration than the adult (action potential duration at 80% repolarization = 60.1 vs. 12.6 ms). The simulation results are consistent with experimental data, including 1) decreased density and altered inactivation of transient outward K+ currents, 2) increased delayed rectifier K+ currents, 3) Ca2+ entry through T-type as well as L-type Ca2+ channels, 4) increased Ca2+ influx through Na+/Ca2+ exchange, and 5) Ca2+ transients resulting from transmembrane Ca2+ entry rather than release from the sarcoplasmic reticulum (SR). Simulations performed with the model generated novel predictions, including increased SR Ca2+ leak and elevated intracellular Na+ concentration in neonatal compared with adult myocytes. This new model can therefore be used for testing hypotheses and obtaining a better quantitative understanding of differences between neonatal and adult physiology.     

Inhibition of HERG potassium channel current by the class 1a antiarrhythmic agent disopyramide

The Class 1a antiarrhythmic drug disopyramide (DISO) is associated with 'acquired' prolongation of the QT interval of the electrocardiogram (ECG). This potentially proarrhythmic effect is likely to reflect drug actions on ion channels involved in ventricular action potential repolarisation. In this study, we examined the effects of DISO on potassium channels encoded by HERG, as this K channel type has been implicated in both congenital and acquired long-QT syndromes (LQTS). Chinese hamster ovary cells were transiently transfected with HERG cDNA for subsequent whole cell patch clamp recording. HERG tail currents recorded at -40 mV following test pulses to +30 mV were inhibited in a dose-dependent fashion by DISO concentrations within the clinical range (IC50 = 7.23 +/- 0.72 microM; mean +/- SEM). Experiments with 10 microM DISO indicated that the degree of HERG blockade showed some voltage dependence. Further data obtained using an 'envelope of tails' protocol (pulse potential +40 mV) were consistent with a significant role for open-channel blockade at lower drug concentrations. At higher concentrations it is possible that blockade may have involved drug binding to both resting and open channels. Inhibition of the inactivation-deficient mutant HERG-S631A was comparable to that seen for wild-type HERG. Therefore, channel inactivation was not obligatory for DISO to exert its effect. Native delayed rectifier tail currents from rabbit isolated ventricular myocytes were also inhibited by DISO. We conclude (a) that DISO inhibits HERG encoded potassium channels at clinically relevant concentrations and (b) that this action may constitute the molecular basis for acquired LQTS associated with this drug.     

Properties of HERG channels stably expressed in HEK 293 cells studied at physiological temperature.

We have established stably transfected HEK 293 cell lines expressing high levels of functional human ether-a go-go-related gene (HERG) channels. We used these cells to study biochemical characteristics of HERG protein, and to study electrophysiological and pharmacological properties of HERG channel current at 35 degrees C. HERG-transfected cells expressed an mRNA band at 4.0 kb. Western blot analysis showed two protein bands (155 and 135 kDa) slightly larger than the predicted molecular mass (127 kDa). Treatment with N-glycosidase F converted both bands to smaller molecular mass, suggesting that both are glycosylated, but at different levels. HERG current activated at voltages positive to -50 mV, maximum current was reached with depolarizing steps to -10 mV, and the current amplitude declined at more positive voltages, similar to HERG channel current expressed in other heterologous systems. Current density at 35 degrees C, compared with 23 degrees C, was increased by more than twofold to a maximum of 53.4 +/- 6.5 pA/pF. Activation, inactivation, recovery from inactivation, and deactivation kinetics were rapid at 35 degrees C, and more closely resemble values reported for the rapidly activating delayed rectifier K+ current (I(Kr)) at physiological temperatures. HERG channels were highly selective for K+. When we used an action potential clamp technique, HERG current activation began shortly after the upstroke of the action potential waveform. HERG current increased during repolarization to reach a maximum amplitude during phases 2 and 3 of the cardiac action potential. HERG contributed current throughout the return of the membrane to the resting potential, and deactivation of HERG current could participate in phase 4 depolarization. HERG current was blocked by low concentrations of E-4031 (IC50 7.7 nM), a value close to that reported for I(Kr) in native cardiac myocytes. Our data support the postulate that HERG encodes a major constituent of I(Kr) and suggest that at physiological temperatures HERG contributes current throughout most of the action potential and into the postrepolarization period.     

Voltage-dependent block of cardiac inward-rectifying potassium current by monovalent cations

The inward-rectifying K+ current (IK1) in cat ventricular myocytes, like inward-rectifying K+ currents in many other preparations, exhibited a negative slope conductance region at hyperpolarized membrane potentials that was time-dependent. This was evident as an inactivation of inward current elicited by hyperpolarizing voltage-clamp pulses resulting in a negative slope region of the steady-state current-voltage relationship at potentials negative to -140 mV. Removing extracellular Na+ prevented the development of the negative slope in this voltage region, suggesting that Na+ can block IK1 channels in a time- and voltage-dependent manner. The time and voltage dependence of Cs+-induced block of IK1 was also examined. Cs+ blocked inward current in a manner similar to that of Na+, but the former was much more potent. The fraction of current blocked by Cs+ in the presence of Na+ was reduced in a time- and voltage-dependent manner, which suggested that these blocking ions compete for a common or at least similar site of action. In the absence of Na+, inactivation of IK1 could also be induced by both Cs+ and Li+. However, Li+ was less potent than Na+ in this respect. Calculation of the voltage sensitivity of current block by each of these ions suggests that the mechanism of block by each is similar.     

Structure of the HERG K+ channel S5P extracellular linker: role of an amphipathic alpha-helix in C-type inactivation

The HERG K+ channel has very unusual kinetic behavior that includes slow activation but rapid inactivation. These features are critical for normal cardiac repolarization as well as in preventing lethal ventricular arrhythmias. Mutagenesis studies have shown that the extracellular peptide linker joining the fifth transmembrane domain to the pore helix is critical for rapid inactivation of the HERG K+ channel. This peptide linker is also considerably longer in HERG K+ channels, 40 amino acids, than in most other voltage-gated K+ channels. In this study we show that a synthetic 42-residue peptide corresponding to this linker region of the HERG K+ channel does not have defined structural elements in aqueous solution; however, it displays two well defined helical regions when in the presence of SDS micelles. The helices correspond to Trp585-Ile593 and Gly604-Tyr611 of the channel. The Trp585-Ile593 helix has distinct hydrophilic and hydrophobic surfaces. The Gly604-Tyr611 helix corresponds to an N-terminal extension of the pore helix. Electrophysiological studies of HERG currents following application of exogenous S5P peptides show that the amphipathic helix in the S5P linker interacts with the pore region of the channel in a voltage-dependent manner.     

Long QT syndrome-associated mutations in the Per-Arnt-Sim (PAS) domain of HERG potassium channels accelerate channel deactivation

Mutations in the human ether-a-go-go-related gene (HERG) cause long QT syndrome, an inherited disorder of cardiac repolarization that predisposes affected individuals to life-threatening arrhythmias. HERG encodes the cardiac rapid delayed rectifier potassium channel that mediates repolarization of ventricular action potentials. In this study, we used the oocyte expression system and voltage clamp techniques to determine the functional consequences of eight long QT syndrome-associated mutations located in the amino-terminal region of HERG (F29L, N33T, G53R, R56Q, C66G, H70R, A78P, and L86R). Mutant subunits formed functional channels with altered gating properties when expressed alone in oocytes. Deactivation was accelerated by all mutations. Some mutants shifted the voltage dependence of channel availability to more positive potentials. Voltage ramps indicated that fast deactivation of mutant channels would reduce outward current during the repolarization phase of the cardiac action potential and cause prolongation of the corrected QT interval, QTc. The amino-terminal region of HERG was recently crystallized and shown to possess a Per-Arnt-Sim (PAS) domain. The location of these mutations suggests they may disrupt the PAS domain and interfere with its interaction with the S4-S5 linker of the HERG channel.     

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.     

Characterization of the inward-rectifying potassium current in cat ventricular myocytes

Whole-cell membrane currents were measured in isolated cat ventricular myocytes using a suction-electrode voltage-clamp technique. An inward-rectifying current was identified that exhibited a time-dependent activation. The peak current appeared to have a linear voltage dependence at membrane potentials negative to the reversal potential. Inward current was sensitive to K channel blockers. In addition, varying the extracellular K+ concentration caused changes in the reversal potential and slope conductance expected for a K+ current. The voltage dependence of the chord conductance exhibited a sigmoidal relationship, increasing at more negative membrane potentials. Increasing the extracellular K+ concentration increased the maximal level of conductance and caused a shift in the relationship that was directly proportional to the change in reversal potential. Activation of the current followed a monoexponential time course, and the time constant of activation exhibited a monoexponential dependence on membrane potential. Increasing the extracellular K+ concentration caused a shift of this relationship that was directly proportional to the change in reversal potential. Inactivation of inward current became evident at more negative potentials, resulting in a negative slope region of the steady state current-voltage relationship between -140 and -180 mV. Steady state inactivation exhibited a sigmoidal voltage dependence, and recovery from inactivation followed a monoexponential time course. Removing extracellular Na+ caused a decrease in the slope of the steady state current-voltage relationship at potentials negative to -140 mV, as well as a decrease of the conductance of inward current. It was concluded that this current was IK1, the inward-rectifying K+ current found in multicellular cardiac preparations. The K+ and voltage sensitivity of IK1 activation resembled that found for the inward-rectifying K+ currents in frog skeletal muscle and various egg cell preparations. Inactivation of IK1 in isolated ventricular myocytes was viewed as being the result of two processes: the first involves a voltage-dependent change in conductance; the second involves depletion of K+ from extracellular spaces. The voltage-dependent component of inactivation was associated with the presence of extracellular Na+.