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Na⁺ current through K_ATP channels: consequences for Na⁺ and K⁺ fluxes during early myocardial ischemia

Institut für Physiologie, Abt. Herz-Kreislauf-Physiologie, Friedrich-Schiller-Universität Jena, D-07740 Jena, Germany

Submitted 18 March 2003 ; accepted in final form 12 August 2003

	ABSTRACT

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
During early myocardial ischemia, the myocytes are loaded with Na⁺, which in turn leads to Ca²⁺ overload and cell death. The pathway of the Na⁺ influx has not been fully elucidated. The aim of the study was to quantify the Na⁺ inward current through sarcolemmal K_ATP channels (I_KATP,Na) in anoxic isolated cardiomyocytes at the actual reversal potential (V_rev) and to estimate the contribution of this current to the Na⁺ influx in the ischemic myocardium. I_KATP,Na was determined in excised single channel patches of mouse ventricular myocytes and macropatches of Xenopus laevis oocytes expressing SUR2A/Kir6.2 channels. In the presence of K⁺ ions, the respective permeability ratios for Na⁺ to K⁺ ions, P_Na/P_K, were close to 0.01. Only in the presence of Na⁺ ions on both sides of the membrane was I_KATP,Na similarly large to that calculated from the permeability ratio P_Na/P_K, indicative of a Na⁺ influx that is largely independent of the K⁺ efflux at V_rev. With the use of a peak K_ATP channel conductance in anoxic cardiomyocytes of 410 nS, model simulations for a myocyte within the ischemic myocardium showed that the amplitude of the Na⁺ influx and K⁺ efflux is even larger than the respective fluxes by the Na⁺-K⁺ pump and all other background fluxes. These results suggest that during early ischemia the Na⁺ influx through K_ATP channels essentially contributes to the total Na⁺ influx and that it also balances the K⁺ efflux through K_ATP channels.

heart; K⁺ efflux; Na⁺ influx

The time course of anoxia-induced opening of these channels in isolated myocytes (35, 57) approximately fits the time course of K⁺ accumulation during the first 5 to 10 min of global ischemia (7). This time interval will be termed in the following as "early ischemia." However, also severe objections against a relevant contribution of K_ATP channels exist: 1) excised patch measurements showed that half-maximum activation of K_ATP channels appears only at several tens of micromoles, whereas the measured cytosolic [ATP] in the ischemic myocardium was determined in the millimolar range (17, 64). 2) Opening of highly selective K⁺ channels shifts the membrane potential closer to the K⁺ equilibrium potential, thereby counteracting the K⁺ efflux. 3) The question as to which counter-ion balances the K⁺ efflux through K_ATP channels is still unanswered. Objection 1 might be put into perspective by the recent discovery of strong modulatory effects of phosphatidylinositol-phosphates (5, 21) or long-chain acyl-coenzyme A esters (39) on the inhibitory effect of ATP. Objections 2 and 3 are unresolved until today. An influx of Na⁺ ions might balance the K⁺ efflux and most studies in the ischemic heart indeed showed that intracellular [Na⁺]([Na⁺]_i) rises at a rate of 0.5–1 mM/min (for a review, see Ref. 62). In the hypoxic myocardium, Fiolet and co-workers (17) observed that the time course of the intracellular Na⁺ accumulation even mirrors that of the extracellular K⁺ accumulation. Functionally, intracellular Na⁺ accumulation may lead to detrimental Ca⁺ overload, resulting in cell necrosis. The most likely molecular mechanism underlying the Ca²⁺ overload is that increased intracellular Na⁺ reduces the Na⁺ gradient across the membrane, which in turn diminishes the driving force for the Na⁺/Ca²⁺ exchange to extrude Ca²⁺ ions out of the cell (18, 38).

Concerning the pathway along which Na⁺ ions enters the cells in the ischemic myocardium, the Na⁺/H⁺ exchange has been reported to contribute significantly to the intracellular Na⁺ accumulation (2, 48), thereby extruding protons produced by anaerobic metabolism. Because in the action of an exchange the movements of both ions are strictly coupled, the Na⁺/H⁺ exchange cannot balance the K⁺ efflux. Alternatively, voltage-dependent Na⁺ channels might form a respective Na⁺ pathway. It has been shown that they gain continuous activity at the resting potential by application of the ischemic metabolite lysophosphatitylcholine (10, 59). A significant contribution of both Na⁺ channels and the Na⁺/H⁺ exchange to the anoxic Na⁺ rise was reported in isolated ventricular myocytes (16). It is not clear, however, whether the time course of induction of continuous Na⁺ channel activity can match that of the rapid extracellular K⁺ accumulation during early ischemia. A further possible pathway for Na⁺ ions is nonspecific cation channels (for a review, see Ref. 12), which, however, have not been demonstrated to happen during early ischemia or anoxia.

Because of these many uncertainties, alternative K⁺ efflux mechanisms have also been considered: evidence has been presented that the K⁺ efflux is coupled to the efflux of lactate (20, 58) that is massively produced in ischemic cells. K⁺ might also couple to either P_i (42) or Cl^– and Na⁺ (Na⁺-K⁺-Cl^– cotransport; Ref. 44).

The present study had the aim to reevaluate the low permeability of K_ATP channels for Na⁺ ions because the conductance generated by the K_ATP channels under the conditions of metabolic impairment is so large (34) that the permeation of the nearly impermeant Na⁺ ions might become relevant. For K_ATP channels in cardiomyocytes, a high K⁺ selectivity has been demonstrated (29). The exact permeability ratio P_Na/P_K, however, has not been determined to our knowledge. Instead, the permeability ratio was determined for K_ATP channels in skeletal muscle [0.15 (54)] and pancreatic -cells [0.007 for Na⁺ inward current (3)], channels that contain the same pore-forming Kir6.2 subunit as the cardiac channels (for a review, see Ref. 4). These values indicate that K_ATP channels are highly selective for K⁺ over Na⁺ ions. However, the magnitude of Na⁺ current through K_ATP channels in a cardiomyocyte does not only depend on the permeability ratio P_Na/P_K but also on the conductance generated by the channels and the actual driving force. If the conductance generated by K_ATP channels dominates the overall conductance of the cell membrane, then the Na⁺ influx through the K_ATP channels can even approximately balance the K⁺ efflux through the same channels. In this work, the Na⁺ current through wild-type and recombinant K_ATP channels was quantified in both the presence and absence of K⁺ ions at the reversal potential and it is shown that it is of similar magnitude under both conditions. Model calculations for an ischemic cardiomyocyte show that under ischemic conditions, sarcolemmal K_ATP channels are an important player for both the early K⁺ accumulation in the extracellular space and the early Na⁺ accumulation in the intracellular space.

	METHODS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Preparation of mouse ventricular myocytes. Mouse ventricular myocytes were prepared at 37°C as described previously (35). In brief, the heart was perfused on a Langendorff apparatus for 5 min with a solution containing (in mM) 140.0 NaCl, 5.8 KCl, 0.5 KH₂PO₄, 0.4 Na₂HPO₄, 0.9 MgSO₄, 11.1 glucose, and 10.0 HEPES, pH 7.1 (NaOH). The perfusion was continued for 25 min with the same solution supplemented with 10 µM CaCl₂ and 150 mg/l collagenase (Sigma type I, Worthington Biochemical or Biochrom). The ventricles were cut and agitated in KB solution containing (in mM) 50.0 glutamic acid, 20.0 HEPES, 20.0 taurine, 10.0 glucose, 3.0 MgSO₄, 0.5 EGTA, 30.0 KCl, and 30.0 KH₂PO₄, pH 7.3 (KOH). The cells were stored in KB solution at room temperature until experimental use.

Synthesis of cRNA. Plasmids containing the cDNAs of murine Kir6.2 (accession no. D50581 [GenBank] ) and SUR2A (accession no. AF003531 [GenBank] ) were kindly provided by Dr. B. Fakler (University of Freiburg). The coding regions were flanked by the 5'- and 3'-untranslated regions of the Xenopus laevis -globin gene to increase the translation efficiency in the oocytes. Capped cRNA was synthesized in vitro using SP6 RNA polymerase after linearization of the plasmids with MluI.

Preparation of X. laevis oocytes and RNA injection. Oocytes were obtained surgically from adult females of X. laevis. The oocytes were treated for 60–90 min with 1.2 mg/ml collagenase (Type CLS II, Biochrom) and manually dissected. They were injected with 40–70 nl of a solution containing a mixture of cRNA specific for SUR2A and Kir6.2. The oocytes were incubated at 18°C in Barth medium until experimental use within 6 days after injection.

Electrophysiology. Current measurements in excised patches were performed with standard techniques (Axopatch 200B amplifier; Axon Instruments). The patch pipettes were prepared from borosilicate glass and the tips were heat polished. The resistance of the patch pipettes was 0.7–1.8 M. Excision of the patches was performed 30 s after the formation of the giga seal. For single channel measurements, the pipettes were coated with Sylgard 184 (Dow Corning, Midland, MI). In each inside-out patch, the efficacy of 2 mM ATP (either as Na⁺ or K⁺ salt depending on the subsequent experiments) to block the K_ATP channel current (I_KATP) was tested. The remaining leakage current was used for off-line subtraction in the analysis. Single-channel events were recorded at constant voltage. Macroscopic currents were recorded by applying voltage ramps (slope 0.16 V/s) applied every 2 s. Measurements were started only after the initial rundown was finished and I_KATP had an approximately constant amplitude. The measurements in excised patches were performed at room temperature 22 ± 1°C. The on-line filter (4-pole Bessel) was set to 5 kHz, and the data were later off-line filtered with a Gaussian algorithm to 1 kHz. The sampling rate was 10 kHz (12-bit resolution).

Measurements of whole cell currents in cardiomyocytes were conducted with patch pipettes of a resistance of 0.7–1.7 M. The currents used to determine the conductance of the cell at maximally open K_ATP channels were recorded with a discontinuous single-electrode voltage clamp (dSEVC) amplifier (SEC 05L/H, npi Electronics). This amplifier has been shown to be particularly appropriate for measuring large currents in cardiomyocytes because it avoids errors inferred by the series resistance (34). The switching frequency was set to a value between 40 and 50 kHz. Intervals for recording of voltage and current injection were equally long. Current measurements were conducted with voltage ramps (slope 0.16 V/s) running from –90 to –40 mV every 5 s. The holding potential was set to –80 mV and the temperature was 37°C. Current-clamp experiments in cardiomyocytes were carried out at room temperature with an Axopatch 200B amplifier. The on-line filter (4-pole Bessel) was set to 5 kHz. The sampling rate was 10 kHz (12-bit resolution).

The ISO2 patch-clamp soft- and hardware (MFK, Niedernhausen, Germany) was used to control the experiments.

Anoxia. I_KATP in cardiomyocytes was induced by anoxia (6). The oxygen tension (PO₂) near the cell was continuously monitored as described previously (35). In brief, the phosphorescence dye Pdmeso-tetra(4-carboxyphenyl)porphin (PTP) was added to the bath solution (0.4 g/l) and PO₂ was determined by evaluating the phosphorescence life time of PTP (35, 40). Anoxic bath solution was obtained by dialyzing the solution with pure nitrogen across the wall of an oxygen-permeable silicon tubing (35). The bath was kept free of oxygen by insulation with ultra pure argon (6, 55).

Solutions used in electrophysiology. The compositions of the solutions used to determine the permeability ratio P_Na/P_K in excised patches are shown and explained in Table 1. The activity coefficients for Na⁺ and K⁺ ions, _Na and _K, were determined from the concentrations of all ions in the solution by the approximation proposed by Guggenheim (19)

(1)

where z_i is the valence of the ion i, I is the total ionic strength of the solution given by c_iz_i², c^o is the standard concentration of 1 M, and A is an empirical factor of 0.5243 M^–1/2. _i,j is the interaction coefficient describing the interactions between the central ion and oppositely charged surrounding ions. _i,j may be reasonably approximated by 0.1 |z_iz_j| (14). B and a are constants whose values were set to 3.318 x 10⁹ m^–1 and 0.3 nm, respectively (8, 50). The activities a_Na=_Na[Na⁺] and a_K=_K[K⁺] for the solutions used to determine permeability ratios are shown in Table 1.

For measurement of whole cell currents in cardiomyocytes under anoxia, the patch pipettes were filled with a solution containing (in mM) 150.0 KCl, 5.0 HEPES, 10 EGTA, and 1 CaCl₂, pH 7.3 (KOH). The bath solution contained (in mM) 150.0 NaCl, 5.4 KCl, 2.5 or 3.6 CaCl₂, 0.5 MgCl₂, and 10.0 HEPES, pH 7.4 (NaOH). For current-clamp experiments, the pipettes were filled with 150.0 KCl, 10 NaCl, 5.0 HEPES, 10 EGTA, and 1 CaCl₂, pH 7.3 (KOH) and the bath solution contained 125.0 NaCl, 25.0 KCl, 2.5 CaCl₂, and 10.0 HEPES, pH 7.4 (NaOH). For reduction of Na in the bath solution to 5 mM, 120 mM NaCl were replaced by equimolar Tris·HCl.

Glibenclamide (Sigma, St. Louis, MO) and rilmakalim (kindly provided by Dr. H. Goegelein, Frankfurt, Germany) were dissolved in dimethylsulfoxide (1 and 20 mM stock solution, respectively).

Measurement of cardiomyocyte volume. The volume of mouse ventricular myocytes was determined with a confocal laser-scanning microscope (LSM 510, Carl-Zeiss-Jena) after the cell membrane was stained with the dye FM1–43 (Molecular Probes) in KB medium. Rod-shaped cells were randomly selected. The volume was calculated from the three-dimensional reconstruction of the myocytes with the software implemented in the confocal microscope.

Data evaluation, statistics, and modeling. The single channel current amplitude was determined with conventional procedures by building histograms and fitting them with Gaussian functions implemented in the ISO2 program. Curve fits were performed with the ORIGIN 6.1 software (Microcal). Statistical analysis was conducted with standard software. Student's t-test was used to test for statistical significance using the P < 0.05 criterion. Model simulations were performed with an own software. Time-dependent changes of ion concentrations were modeled with first-order differential equations that were numerically resolved with a Runge-Kutta routine. The largest time steps had a duration of 0.1 s.

	RESULTS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Permeability ratio P_Na/P_K. In a first approach, we determined the permeability ratio P_Na/P_K in excised patches of cardiomyocytes by analyzing single-channel currents. Single-channel measurements provide the advantage that small changes of leakage and open probability do not influence the results. Three solution pairs were employed to cover the voltage range between –82 and –25 mV. Composition, activity of K⁺ and Na⁺ ions, and calculated Nernst potential for K⁺ of the three solution pairs (1–3) are shown in Table 1. Typical single channel currents at different voltages are shown in Fig. 1A, top. The voltages were corrected for the measured junction potentials (Table 1). The amplitude of the unitary currents was plotted as function of voltage and the data points were fitted with the Goldman-Hodgkin-Katz (GHK) current equation (with i_KATP = i_KATP,K + i_KATP,Na) according to

(2)

V is the voltage, F is the Faraday constant, R is the molar gas constant, T is the temperature in Kelvins, and z is the charge of the ions. a_x indicates the respective activity of Na⁺ or K⁺ ions (Table 1), where i is the inside and o is the outside of the membrane. The calculated permeability ratios P_Na/P_K for solution pairs 1 through 3 were 0.0127 ± 0.0077 (n = 5), 0.0054 ± 0.0021 (n = 10), and 0.0069 ± 0.0057 (n = 5), respectively. Because these values were statistically indistinguishable, the permeability ratio P_Na/P_K was considered to be voltage independent between –82 and –25 mV. The data were therefore lumped together yielding a mean permeability ratio P_Na/P_K of 0.0076 ± 0.0017 (n = 20). This value is similar to that obtained in pancreatic -cells for external Na⁺ (3).

View larger version (11K): [in this window] [in a new window]   Fig. 1. Permeability ratio PNa/PK in excised patches of cardiomyocytes at 0 mM ATP in the bath. A: representative current recordings (top) in a patch containing a single KATP channel at different voltages recorded with solution pair 2 (Table 1). The amplitude of the single channel currents was plotted as function of voltage and fitted with the Goldman-Hodgkin-Katz (GHK) equation (Eq. 2; diagram) yielding for this particular patch the indicated permeability ratio PNa/PK. B: current recording of a macroscopic current with solution pair 4 (Table 1) following a voltage ramp. The leak current, recorded at 2 mM ATP, was subtracted. Intersection of the trace with the abscissa indicates the reversal potential (Vrev), which calculates with Eq. 3 to a permeability ratio PNa/PK of 0.015.

Because the permeability ratio P_Na/P_K is critical for the conclusions of this report, it was determined with a second approach from the reversal potential of macroscopic SUR2A/Kir6.2 currents. For these experiments, solution pair 4 was used (Table 1). In the oocyte expression system, macroscopic currents could be analyzed because the channel density per patch is higher than in cardiomyocytes and eventually overlapping endogenous currents are only small. Voltage ramps were applied and the leakage current, recorded in the presence of 2 mM ATP, was subtracted to isolate I_KATP. Figure 1B shows a typical current trace. The reversal potential (V_rev) was determined and the permeability ratio P_Na/P_K was obtained by using the GHK voltage equation according to

(3)

The variables have the same meanings as described above. Statistically, the permeability ratio P_Na/P_K was 0.0105 ± 0.0026 (n = 6). The main results of this section on native and recombinant cardiac K_ATP channels are that P_Na is approximately one-hundredth of P_K and that the P_Na/P_K ratio is independent of voltage between –82 and –26 mV, a voltage range covering the resting potential of cardiomyocytes at both control and ischemic conditions.

Na⁺ current through K_ATP channels. The use of the GHK equations to unravel the Na⁺ and K⁺ current through K_ATP channels at V_rev implies that both current components are independent. If so, then the macroscopic Na⁺ current through K_ATP channels (I_KATP,Na) should be measurable directly in the absence of K⁺ ions. Figure 2A shows a representative experiment in an excised macropatch with SUR2A/Kir6.2 channels with equal Na⁺ concentrations in bath and pipette (solution o4 in Table 1) in which 60% of the inward current recorded at 0 mM ATP (control) was blocked by 2 mM ATP and the block was reversible. Similar results were observed in 11 other patches. Figure 2B shows that glibenclamide (100 nM), a specific K_ATP channel blocker, was as effective as 2 mM ATP to block I_KATP,Na. Similar results were observed in five other patches. The current component remaining after either ATP or glibenclamide was considered to be the leakage current. Not shown are the following control experiments: 1) patches from either water-injected (n = 5) or SUR2A-injected oocytes (n = 5) did not generate any ATP-sensitive current; 2) niflumic acid (0.3 mM), a blocker of chloride channels, did not affect the ATP-sensitive extra current (n = 4); and 3) when replacing 142.1 mM NaCl in the pipette by an equal amount of N-methyl-D-glucamine chloride, the ATP-sensitive current was outward over the whole voltage range between –140 and 80 mV (n = 4). Conclusively, the ATP- and glibenclamide-sensitive current was a Na⁺ current through K_ATP channels.

View larger version (15K): [in this window] [in a new window]   Fig. 2. Macropatch Na+ current (IKATP,Na) through SUR2A/Kir6.2 channels expressed in an oocyte with Na+ and no K+ ions on both sides of the membrane (solution o4). The currents were elicited by voltage ramps from –80 to 20 mV. A: ATP block. The current component reversibly blocked by ATP (2 mM) is IKATP,Na. The traces were recorded in the same patch. B: glibenclamide block. After washout of ATP (2 mM), IKATP,Na appeared (control). Glibenclamide (100 nM) blocked IKATP,Na similarly effective as did before ATP. The traces were recorded in the same patch.

To test whether or not the measured Na⁺ current through K_ATP channels in the absence of K⁺ ions is similar in amplitude to the not directly measurable Na⁺ current in the presence of K⁺ ions, the following strategy was chosen: in excised macropatches containing SUR2A/Kir6.2 channels, currents generated by ramp pulses were measured with solution pair 4. These currents were fitted with an extended GHK current equation according to

(4)

The term {1 + exp[(V – V_h)/s]} accounts for the voltage-dependent Na⁺ block of I_KATP that increases at more depolarized potentials (25). V_h and s are the voltage of half-maximum block and a slope parameter, respectively. The other variables have the same meanings as described above. Figure 3A shows an example of such a fit yielding the indicated permeability ratio P /P_K. Also shown are the underlying Na⁺ and K⁺ current components.

View larger version (12K): [in this window] [in a new window]   Fig. 3. Relationship of the measured Na+ current in the presence of K+ ions to that in the absence of K+ ions in macropatches (SUR2A/Kir6.2 expressed in oocytes). The currents were recorded by applying appropriate voltage ramps. Leakage currents, determined by application of 2 mM ATP, were subtracted. A: IKATP in the presence of K+. The current (noisy trace), induced by a voltage ramp, was recorded with solution pair 4 (Table 1). The trace was fitted with Eq. 4 (superimposed smooth curve) and the underlying Na+ and K+ currents (IKATP,Na and IKATP,K) are indicated. The parameters were PNa = 3.84 cm3·s–1, PK = 508.24 cm–3·s–1, Vh = –29.82 mV, s = 25.83 mV. B: IKATP,Na in the absence of K+ ions in the same macropatch as in A (noisy trace). The current trace was recorded with symmetrical Na+ concentrations (solution o4 on both sides of the membrane; Table 1). The smooth curve represents the current calculated with Eq. 4 for solution o4. The parameters were the same as those in A.

The parameters (see Fig. 3) were then used to compute the Na⁺ current at symmetric Na⁺ activities (solution o4 on both sides of the membrane), which allowed us to compare the calculated Na⁺ current with the measured Na⁺ current directly (Fig. 3B). As a result, the measured Na⁺ current showed a similar voltage dependence but an amplitude of only 65% (–80 mV) of that of the calculated Na⁺ current. Also statistically, the measured Na⁺ current was significantly smaller than the calculated Na⁺ current (67 ± 9%; n = 6), which might be due to differences in permeation or in gating. The conclusion is that the Na⁺ current through K_ATP channels in the absence of K⁺ is somewhat smaller but not dramatically different from that in the presence of K⁺ ions, indicative of a relatively independent permeation of both ions. Therefore, the Na⁺ current measured in the absence of K⁺ ions reflects roughly the Na⁺ current flowing through the K_ATP channels in the presence of K⁺ ions.

We finally tested whether the lack of external K⁺ ions has enhanced the Na⁺ current through K_ATP channels in the sense of an anomalous mole-fraction dependence, which is the effect that the conductance of ion channels goes through a minimum as a function of the ratio of ion concentrations (23). In the case of an anomalous mole-fraction dependence, the continuous increase of the external K⁺ concentration from zero should first decrease the Na⁺ inward current until it further increases because the much better permeable K⁺ ions would pass the channels themselves. To this end, we filled the tip of the pipette with symmetric Na⁺ solution (solution o4) and the rest of the pipette with a modified solution o4 in which all Na⁺ (140 mM) was replaced by equimolar K⁺. One may obtain a situation that initially Na⁺ current through K_ATP channels is present and the concentration of K⁺ ions would increase continuously by diffusion. Figure 4 shows respective currents from the beginning of the experiment and at a time at which the inward current has already significantly increased while V_rev was shifted to more positive values. The time courses of both V_rev and current amplitude at –75 mV (Fig. 4B) show that the diffusion-induced increase of the external K⁺ concentration did not produce a minimum of the current. Similar results were obtained in five other patches. The interpretation is that there is no anomalous mole-fraction dependence for K⁺ and Na⁺, which further supports the notion of an independent permeation of both ions.

View larger version (16K): [in this window] [in a new window]   Fig. 4. Current through KATP channels at continuously increasing K+ concentration at the extracellular side starting from 0 (SUR2A/Kir6.2 expressed in oocytes). The tip of the pipette was filled with solution o4 (Table 1) and the rest of the pipettes with solution o4 containing K+ instead of Na+ ions. A: current traces induced by voltage ramps at the beginning of the experiment () and 10 min later after K+ ions had reached the outside of the patch by diffusion (). B: time course of Vrev (top) and the current amplitude at –75 mV (mean of all sampling points between –80 and –70 mV; bottom). Two millimoles of ATP were applied to the bath to test for leakage. The current amplitude did not pass a minimum, suggesting independent permeation of both ions.

To demonstrate the relevance of the Na⁺ influx through K_ATP channels at the actual resting potential (V_rest), current-clamp recordings in whole cardiomyocytes were performed with variable extracellular Na⁺ concentration while the K⁺ concentration in the bath and the pipette was kept constant. K_ATP channels were opened by the specific opener rilmakalim (20 µM) (36). The experiments were performed at room temperature to keep the rundown of I_KATP (57) slow. The extracellular K⁺ concentration ([K⁺]_o) was set to 25 mM to stabilize V_rest. A typical experiment is shown in Fig. 5. Initially, extracellular [Na⁺] ([Na⁺]_o) was 125 mM. Before switching to current clamp (* in Fig. 5, bottom), the conductance G at V_rev was determined under voltage clamp by a ramp pulse [G = 28 nS; top left current-voltage (I-V)] relationship). After switching to current clamp, V_rest was –38 mV, which was by 8 mV positive to the calculated Nernst potential for K⁺ ions (–46 mV). Lowering [Na⁺]_o to 5 mM [intracellular [K⁺] (([K⁺]_i) and [K⁺]_o were unchanged]) shifted V_rest to –30 mV and the effect was reversible. After switching back to voltage clamp and increasing [Na⁺]_o to 125 mM (end of the first trace in Fig. 5, bottom), rilmakalim was applied until G reached an approximately stable value (G = 77 nS; ** in Fig. 5, bottom; top right I-V relationship). When switching to current clamp, the cell was hyperpolarized by 2 to –40 mV, suggesting that the P_Na/P_K ratio for K_ATP channels was somewhat smaller than for the background conductance but that it was also relevant because at a three times larger G (presence of rilmakalim) perfectly K⁺-selective K_ATP channels would have caused larger hyperpolarization. Moreover, when lowering [Na⁺]_o at three times larger G, perfectly K⁺-selective K_ATP channels would have caused only one-third of the depolarization compared with control conditions. The result, however, was that the amount of depolarization induced by lowering [Na⁺]_o was similar in the absence and presence of rilmakalim, which further substantiates a roughly similar P_Na/P_K ratio for K_ATP channels and the background conductance and thus a functionally relevant P_Na value for K_ATP channels. Similar results were observed in three other cells.

View larger version (14K): [in this window] [in a new window]   Fig. 5. Dependence of the resting membrane potential (Vrest) in a mouse cardiomyocyte on extracellular [Na+] ([Na+]o) at closed (left) and open KATP channels (right). The pipette contained (in mM) 150 K+ and 10 Na+, the bath 25 K+ and either 125 or 5 Na+. KATP channels were opened by 20 µM rilmakalim. Bottom: plot of Vrest as a function of time recorded in the current-clamp mode. The top current-voltage relationships indicate currents in response to voltage ramps (–100 to 80 mV in 500 ms) recorded in the voltage-clamp mode before switching to the current-clamp mode under control conditions (*; left) and after opening of KATP channels by rilmakalim (**; right). The conductance G at Vrev is indicated. Lowering [Na+]o generates a similarly large depolarization of Vrest at closed and open KATP channels.

Determination of the maximum conductance of K_ATP channels in cardiomyocytes. To estimate consequences of the above results for the metabolically impaired myocardium, the whole cell I_KATP was determined in mouse cardiomyocytes that were exposed to anoxia at the temperature of 37°C. The whole cell current at the time of the maximum I_KATP was measured (35, 57). Application of ramp pulses from –90 to –40 mV induced approximately linear currents (Fig. 6). The maximum conductance (G_KATP,max) was determined by fitting a line. Statistically, the anoxia-induced conductance was 410 ± 86 nS (n = 8), which is significantly larger than the rilmakalim-induced current at room temperature. The time interval between starting anoxia and the maximum I_KATP was 153 ± 43 s.

View larger version (13K): [in this window] [in a new window]   Fig. 6. Anoxia-induced maximum conductance GKATP,max at Vrev in a mouse cardiomyocyte. Application of a ramp from –90 to –40 mV induced an approximately linear current (dots). The leak current, determined under normoxic conditions, was subtracted. The large noise level was inferred by the switching of the single-electrode amplifier. GKATP,max was determined by fitting a line to the trace.

Simulation of K_ATP channel mediated K⁺ and Na⁺ fluxes in the myocardium. The consequences of the determined permeability ratio P_Na/P_K, the voltage dependence of the block of I_KATP, and the maximal conductance G_KATP in a cardiomyocyte for the K⁺ and Na⁺ fluxes during anoxia were estimated by computer simulation for a cardiomyocyte embedded in the myocardium. The equations used to model the individual current components are described in the APPENDIX. The approach was to define the total volume of the cell, the relative intra- and extracellular water space, to calculate the K⁺ and Na⁺ fluxes under control conditions, and finally to calculate the changes of the concentrations of K⁺ and Na⁺ ions in the intra- and extracellular space in response to a typical time course of anoxia-induced I_KATP. It should be emphasized that all ion fluxes considered herein were calculated for the actual computed V_rev that itself changes. All ion currents involved in excitation were ignored because during acute stop-flow ischemia, excitation ceases rapidly. It was therefore reasonable to assume that initially the driving action of the Na⁺-K⁺ pump is exactly balanced by only one "background" mechanism that contains all mechanisms carrying K⁺ ions outwardly and Na⁺ ions inwardly.

The mean volume of the myocytes, determined with the confocal microscope (see METHODS), was 37 ± 10 pl (n = 14). The relative intra- and extracellular water space were assumed to equal those in the rat myocardium (15). The respective values were 73.1 and 26.9%. The extracellular space includes the interstitium and the plasma.

The total transmembrane current of Na⁺ ions across the membrane, I_Na, was described by

(5a)

where I_p,Na and I_b,Na are the Na⁺ currents carried by the Na⁺-K⁺ pump and the background current, respectively. The total transmembrane current of K⁺ ions, I_K, across the membrane was analogously described according to

(5b)

Each current depends on the activity of the ions on both sides of the membrane and on the actual V_rev. In addition, I_KATP and I_p were modeled to depend on the cytosolic ATP concentration (see APPENDIX).

The activities a_x of the Na⁺ and K⁺ ions on the inside (suffix i) and the outside (suffix o) of the membrane were described with the following first-order differential equations

(6a)

(6b)

(6c)

(6d)

where V_i and V_o are intra- and extracellular volume.

Figure 7 shows the result of a simulation. The K_ATP channel opening (appearance of G_KATP) is associated with much larger Na⁺ and K⁺ fluxes across the membrane than generated by the Na⁺-K⁺ pump and all background pathways. The consequence is that the Na⁺ and K⁺ concentrations on both sides of the membrane change significantly in the time range of minutes. a_K,o increases with a time scale that is similar to that observed during early ischemia (22, 24). The concomitant rise of a_Na,i is smaller than that of a_K,o because of the larger intracellular volume with respect to the extracellular volume. The Na⁺-K⁺ pump cannot balance this extra flow. It transiently increases its transport rate due to depolarization and the increase of a_Na,i. In this simulation, it was assumed that its activity finally ceases because of the lack of ATP. It is particularly noticeable that the magnitude of the Na⁺ flux through the K_ATP channels at the actual V_rev clearly exceeds that of all background mechanisms despite the fact that Na⁺ ions have a permeability of less than 1% of that of K⁺ ions. The reason for this large flux of Na⁺ ions through the K_ATP channels is the large number of channels activated by ATP depletion.

View larger version (14K): [in this window] [in a new window]   Fig. 7. Simulation of Na+ and K+ currents and activities in a cardiomyocyte during early ischemia. GKATP is the whole cell conductance generated by the opening of KATP channels, Vrev is the actual reversal potential that is a function of the ion activities aNa,i and aK,i at the intracellular and aNa,o and aK,o at the extracellular side of the membrane. Ip,Na and Ip,K are currents carried by the Na+-K+ pump, IKATP,Na and IKATP,K are currents through KATP channels, and Ib,Na and Ib,K are background currents consisting of all Na+ and K+ currents apart from Ip and IKATP. The convention for the currents is that an outward current of positively charged ions is upwardly directed. In this simulation, [ATP] was assumed to drop from an initial value of 5 to 0 mM according to the indicated time course. The equations used for the simulations are shown in the APPENDIX. Opening of the KKATP channels induced severe changes of the ion activities and Vrev. For further explanation, see text.

Figure 8 shows a respective simulation in which only one parameter was changed: the [ATP] was not allowed to decay to zero but fell to a low steady-state value as 5 µM, e.g., to simulate low glycolytic activity. Consequently, the activity of the Na⁺-K⁺ pump is not inhibited by substrate deprivation (K_m,ATP = 1 µM). The pump currents I_p,Na and I_p,K increase and remain increased due to depolarization and Na⁺ load of the cell. Despite this significantly different situation compared with the simulation in Fig. 7, opening of K_ATP channels causes a massive change of V_rev and the Na⁺ and K⁺ activities on both sides of the membrane. These results show that the dominating influence of the K_ATP channels on the K⁺ accumulation during early ischemia does not depend critically on the specific equations adopted for the pump. This conclusion also holds for the background current.

View larger version (13K): [in this window] [in a new window]   Fig. 8. Simulation of Na+ and K+ currents and activities in a cardiomyocyte during early ischemia similar to Fig. 7 with the only difference that [ATP] did not drop to values below 5 µM, which is 5 times the half-saturation value of the substrate binding site of the Na+-K+ pump. Even at nearly fully active pump, the effect of the opening of the KATP channels on the ion activities is substantial, K+ ions accumulate to a similar degree as under the condition of a rapidly inhibited Na+-K+ pump. For further explanation, see text.

	DISCUSSION

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
The main results of the present report are 1) despite a low permeability ratio P_Na/P_K of only 0.01, the Na⁺ current through K_ATP channels is of relevant amplitude at the actual V_rev. 2) The Na⁺ current through K_ATP channels does not largely depend on the concentration of K⁺ ions. 3) The Na⁺ influx through K_ATP channels at V_rev can balance even large K⁺ efflux as typically observed during early ischemia. 4) Model simulations for the conditions of early ischemia show that the amplitudes of the Na⁺ influx and K⁺ efflux are large compared with the fluxes by the Na⁺-K⁺ pump and all background fluxes present under control conditions. It is therefore suggested that during early ischemia both the extracellular K⁺ accumulation and the intracellular Na⁺ accumulation are essentially mediated by the massive opening of K_ATP channels.

Modeling the ion currents at V_rev. The experimental results of this report showed that the conductance determined for anoxia-induced opening of K_ATP channels (G_KATP) suffices to generate significant Na⁺ influx at the actual V_rev. Because under the anoxic and other metabolically compromised conditions G_KATP dominates the total membrane conductance, it is particularly noteworthy that at the actual V_rev, which equals in an unclamped cell the actual resting potential, the Na⁺ influx through K_ATP channels approximately resembles the K⁺ efflux and both fluxes are large compared with those mediated by the Na⁺-K⁺ pump. K_ATP channels therefore simply overstrain the capacity of the Na⁺-K⁺ pump, even if its activity is maximally enhanced by the increase of the intracellular Na⁺ activity and the shift of the reversal potential to more depolarized voltages (Fig. 8).

The Na⁺ and K⁺ currents through K_ATP channels, I_KATP,Na and I_KATP,K, respectively, were modeled with an equation according to the GHK theory and an empirical term to describe the inward rectification due to the voltage-dependent block of Na⁺ ions (25). The resulting Eq. 4 described I_KATP well (Fig. 3A). Because in the voltage range between –80 and 20 mV I_KATP,Na showed a similar degree of inward rectification (Fig. 3B) as the total I_KATP, it seemed to be justified to also include the voltage-dependent block for I_KATP,Na. As permeability ratio, the smaller determined value of 0.0076, obtained from excised single channel patches in cardiomyocytes, was used to avoid any overestimation of the role of the K_ATP channels. The maximal K_ATP channel conductance in a whole cardiomyocyte was large (G_KATP,max = 410 nS). Because errors inferred by uncompensated series resistance could be avoided when using the dSEVC amplifier, the determined G_KATP,max was considered to be a realistic value of the conductance under those experimental conditions.

The background currents I_b,Na and I_b,K were modeled with a very simple assumption: for control conditions, they were set to exactly balance the currents I_p,Na and I_p,K generated by the Na⁺-K⁺ pump, and a voltage dependence according to the GHK theory was assumed. For a quiescent cardiomyocyte at normoxic conditions, this approach is a conditio sine qua non because only then a stable resting potential is possible. The voltage dependence of the background conductance was modeled according to the results of Sakmann and Trube (51), which is certainly reasonable for the dominating I_b,K. One might argue that it is illegitimate to confer this approach to I_b,Na. Indeed, under ischemic conditions, the Na⁺ influx by both persistent Na⁺ channels (10, 59) and the Na⁺/H⁺ exchange can significantly enhance the Na⁺ influx compared with our assumptions.

Concerning the persistent Na⁺ current, the published results are controversial whether this current plays a role during ischemia and, if yes, how large it is and how rapidly it appears. Because of these uncertainties, a Na⁺ current through voltage-dependent Na⁺ channels was not included in the model. Anyway, the effect of any further Na⁺ conductance in the membrane would cause a larger deviation of V_rev from the K⁺ equilibrium potential and thus a larger K⁺ efflux and a more rapid depolarization of V_rev compared with Figs. 7 and 8. Thus the conclusions derived for the meaning of the Na⁺ current through K_ATP channels would be qualitativly unaffected by an additional conductance for Na⁺ ions.

Not considered in the modeling of the background current was also the putative increase of the Na⁺/H⁺ exchange activity, which should be present because of elevated intracellular levels of protons produced by switching to the anaerobic metabolism. Because the Na⁺/H⁺ exchange is not electrogenic, its interference would be confined to an accelerated decrease of the driving force for Na⁺ ions. The modeling in this report would be affected, respectively, but the main conclusions upon the Na⁺ current through K_ATP channels would not be questioned.

The considerations upon Na⁺ ions can be generalized to all other conductances serving as pathway for counter-ions to the K⁺ efflux during ischemia: additional ion conductances would always cause an even larger K⁺ efflux if V_rev shifts to more depolarizing potentials.

Intracellular Na⁺ accumulation. Intracellular accumulation of Na⁺ ions during acute ischema has been consistently documented. With the use of nuclear magnetic resonance measurements, a doubling of [Na⁺]_i was observed in the ischemic myocardium after 13 to 20 min (45, 48). Yan and co-workers (63) observed a doubling of [Na⁺]_i after 15 min of ischemia with the use of ion-sensitive microelectrodes. Knopf and coworkers (33), working with extracellular ion-sensitive electrodes, calculated a Na⁺ influx already during the first 2 min of global ischemia in the rat heart. Considering the way Na⁺ ions enters the cells, two main pathways are discussed. 1) The Na⁺/H⁺ exchange has been considered because 5-(N-ethyl-N-isopropyl)amiloride (EIPA) and amiloride were effective to inhibit the Na⁺ accumulation (45, 48). In isolated cardiomyocytes, HOE-642, a more specific blocker of the Na⁺/H⁺ exchange, has also been shown to inhibit Na⁺ accumulation (16). 2) Voltage-dependent Na⁺ channels have been viewed to form the second relevant pathway. Experimental evidence comes from measurement of Na⁺ accumulation in the ischemic myocardium that could be partly blocked by the local anesthetic and Na⁺ channel blocker lidocaine (11, 60). In isolated cardiomyocytes, the experimental results are controversial. Hypoxia was shown to increase a persistent Na⁺ current, which, however, was not present at the normal resting potential (28) but only at –60 mV and more positive voltages. A noninactivating Na⁺ current could also be induced by the ischemic metabolite lysophosphatidylcholine (10, 59). In contrast, Mejia-Alvarez and Marban (43) reported evidence against any contribution of voltage-dependent Na⁺ channels to the intracellular Na⁺ accumulation in metabolically inhibited cardiomyocytes. Tetrodotoxin (TTX), a specific blocker of voltage-dependent Na⁺ channels, was shown to inhibit the intracellular increase of Na⁺ ions in anoxic Tyrode solution but not in a solution simulating ischemia (16). These results obtained from isolated myocytes give rise to doubts whether in the quiescent myocardium a TTX-sensitive Na⁺ current persists. If one takes into further account that the lidocaine effects in the ischemic myocardium were obtained at the concentration of 200 µM (11, 60) while the drug blocks cardiac K_ATP channels with an IC₅₀ of only 43 µM (46), one might suggest in the light of the present results that the role of a Na⁺ influx through K_ATP channels is of greater relevance than that through voltage-dependent Na⁺ channels.

Besides the two main pathways for the Na⁺ influx during ischemia, other pathways were brought into consideration: the Na⁺/Ca²⁺ exchange is conceivable to play a role (53), extruding Ca²⁺ ions from intracellular to the extracellular space. At least for quiescent myocytes, it seems unlikely that a respectively large amount of Ca²⁺ ions first enters the cells to cause a respectively large Na⁺ accumulation because the cells would die immediately. Further pathways are Ca²⁺-activated nonspecific cation channels (13), the Na⁺-K⁺-2Cl^– and the Na⁺-Cl^– cotransport (53). However, experimental evidence for a relevant contribution of these mechanisms to the ion movements during early ischemia is still lacking.

In the present study, a novel pathway mediating Na⁺ influx in the anoxic/ischemic myocardium has been proposed and its capacity has been estimated. The evidence is compelling that the Na⁺ current through K_ATP channels becomes one of the leading conductances during early ischemia, possibly even the leading conductance. Our line of evidence is indirectly strengthened by a previous report in which we showed that amiloride as well as its derivatives EIPA and dichlorobenzamil block K_ATP channels much more effectively than the Na⁺/H⁺ or Na⁺/Ca⁺ exchange (9). Consequently, in all studies where these drugs were used to identify one of the exchanges, K_ATP channels must have been blocked, too. Our results therefore suggest that also in these experiments an essential action of the drugs was exerted on K_ATP channels conducting Na⁺ ions.

Extracellular K⁺ accumulation and V_rev. The mechanisms underlying the characteristic triphasic time course of the extracellualar K⁺ accumulation are still poorly understood. The present work provides novel arguments to take sarcolemmal K_ATP channels into more serious consideration again after they have been sorted out by numerous investigators because of the severe objections summarized in the introduction part. With the results of this report and those on alterations of the ATP sensitivity of the channels by various membrane constituents (5, 21), none of these objections is left. Furthermore, the time course of early K⁺ accumulation predicted from the experiments in isolated cardiomyocytes under anoxic conditions approximately fits with measured time courses in the ischemic myocardium (22, 24, 62). The results of the present study therefore strongly suggest that K_ATP channels are a major player for the early K⁺ accumulation.

The fact that our model simulations produced somewhat larger K⁺ accumulations than observed experimentally may find explanations in uncertainties with the assumptions and species differences. In addition, one should also take into account that in the tissue not all myocytes must respond simultaneously, which should decrease the amplitude of K⁺ accumulation. Furthermore, nothing is known about an eventual influence of the nonmyocardial cardiac cells. They might, for instance, buffer extracellular K⁺ ions. When considering the time course of the simulated depolarization of V_rev, it is two to three times faster than that measured in globally ischemic pig hearts (31). Using the same arguments as to explain the larger K⁺ accumulation and taking further into account that the experiments of Kléber (31) were performed at a lower temperature (31–33°C) than the measurements on which our simulations are based (37°C), then the time course of the simulated depolarization of V_rev also fits reasonably well with experimental time courses.

The a_K,o curves in Figs. 7 and 8 approximately reflect the time course of the early two phases of K⁺ accumulation. The early rising phase is caused by the large G_KATP. The second phase is characterized either by a flat increase of a_K,o in the case that the Na⁺-K⁺ pump ceases its activity rapidly (Fig. 7) or an approximately constant a_K,o level in the case that the K⁺-Na⁺ pump preserves its activity due to sufficient basic ATP levels (Fig. 8). Hence, the balance between transiently opening K_ATP channels and the remaining activity of the Na⁺-K⁺ pump finally defines whether the second phase of K⁺ accumulation is either slowly increasing or constant and it may even become decreasing if G_KATP is smaller. All cases were observed experimentally in previous studies (31, 33, 61, 62). This interpretation of the second phase of K⁺ accumulation fits with the observation of Weiss and Shine (61) who abolished the plateau phase of K⁺ accumulation with cardiac glycosides, specific blockers of the Na⁺-K⁺ pump. Finally, it should be mentioned that the time course of the K⁺ accumulation in Figs. 7 or 8 could be easily extended by a slow component describing the development of an irreversible damage of the membrane (32). As a result, the typical triphasic time course of the ischemic extracellular K⁺ accumulation would be fully reproduced.

Identification of an essential Na⁺ influx through open K_ATP channels might also question pharmacological strategies with K_ATP channel openers because opening of these channels would not only produce beneficial effects on the myocardium, to increase the excitation threshold and shorten the action potential, but also a maleficient effect, to increase [Na⁺]_i and, via the action of the Na⁺/Ca²⁺ exchange, to increase intracellular [Ca²⁺], thereby damaging the cells.

	APPENDIX

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX REFERENCES

 
Currents Carried by Na⁺-K⁺ Pump

Modeling the activity of the Na⁺-K⁺ pump was based on the equations described by Luo and Rudy (41) for a guinea pig myocyte. The corresponding current (I_p) in the presence of high intracellular ATP levels is given by

(7)

with the voltage-dependent parameter f_NaK = 1/{1 + 0.1245 exp[–0.1V_revF/(RT)] + 0.0365 exp[–V_revF/(RT)]}, the a_Na,o dependence factor = [exp (a_Na,o/67.3) – 1]/7, K_m,Nai = 10 mM, K_m,Ko = 1.5 mM, and I_NaK = 1.3 pA/pF. T was set to 310 K. V_rev is the actual membrane voltage that is the resultant of the reversal potentials of all contributing mechanisms at the actual intracellular and extracellular activities of K⁺ and Na⁺ ions. The cell membrane capacitance C_cell was set to 84 pF (27).

In extension to the equations of Luo and Rudy (41), under our conditions the activity of the Na⁺-K⁺ pump could be assumed to depend on the cytosolic [ATP] because at mitochondrial blockade the [ATP] has been shown to drop to very low levels (1), although it is not clear, however, whether or not it drops to values below the half saturation of the substrate binding site [K_m,ATP 1 µM (30)]. To test the influence of an either working or blocked Na⁺-K⁺ pump, an additional ATP-dependent factor f_ATP = [ATP]/([ATP] + K_m,ATP), with K_m,ATP = 1 µM, was introduced. As shown in Figs. 7 and 8, a more precise modeling of the ATP dependence of the Na⁺-K⁺ pump, including, e.g., the regulatory binding site, was of subsidiary influence because the effects of a massive K_ATP channel opening dominate the total Na⁺ and K⁺ fluxes across the cell membrane. The time course of the [ATP] drop was modeled with an equation to generate a drop resembling that observed by Allue et al. (1) after treatment with cyanide and 2-deoxyglucose (1 min for the drop from 3 to 0.25 mM)

(8)

The control ATP concentration ([ATP]₀) was set to 5 mM. t is the time (in s), the value of 100 simulates the latency of the ATP drop (in s), and the value of 18 generates the indicated speed of the [ATP] drop. The fluxes of Na⁺ and K⁺ ions by the pump at the actual V_rev were calculated by assuming a 3:2 stoichiometry and they were treated in the dimension of a current yielding I_p,Na = 3 I_p and I_p,K = –2 I_p.

Background Currents

The background current (I_b) was assumed to include all Na⁺ and K⁺ currents apart from those carried by the Na⁺-K⁺ pump and the K_ATP channels. Under steady-state (control) conditions, that must exist at the resting potential, both the inward flux of K⁺ and the outward flux of Na⁺ ions by the pump must be exactly balanced by the reverse fluxes. We therefore set the control background Na⁺ current I_b,Na = –I_p,Na and the control background K⁺ current I_b,K = –I_p,K. To estimate the contribution of the background currents carried by both ions at changing V_rev and ion concentrations, the following approach was chosen: assuming independent fluxes of Na⁺ and K⁺ ions, the equilibrium potentials for each ion species were calculated with the Nernst equation according to

(9a)

(9b)

The initial value of the reversal potential of the background current (V_b,rev,0) was set to –85 mV, which is by 3.8 mV positive to the equilibrium potential for K⁺ as calculated with the Nernst equation and thus matches the experimental result that potassium-selective I_K1 channels dominate the total conductance of the cell membrane at the resting potential (51). The conductance generated by each of the ions at V_b,rev,0 was obtained by

(10a)

(10b)

The empirical factor ([K⁺]_o/3.6)^0.54 describes the flat dependence of these conductances on a_K,o (50), which was also assumed to be valid for G_b,Na. None of the results of the simulation did critically depend on the factor (a_K,o/3.6)^0.54. The actual values for I_b,Na and I_b,K at any V_rev and ion activity were calculated with

(11a)

(11b)

K_ATP Channel Currents

The time course of the conductance G_KATP generated by the K_ATP channels was modeled in the following way: the amplitude of G_KATP was assumed to be governed by the cytosolic [ATP] given by Eq. 8. Then G_KATP was modeled by

(12)

G_KATP,max was obtained from the measurements in this study (410 nS). The [ATP] generating half-maximum I_KATP current (IC₅₀) and the Hill coefficient (H) were set to 25 µM and 2, respectively (37). r(t) is a factor describing the rundown of I_KATP during metabolic inhibition (57)

(13)

r(t) was set to 1 until the time t_s when [ATP] had decreased to values below IC₅₀ and it then decayed with a time constant = 75 s (56). These values generated a typical time course of both appearance and disappearance of G_KATP (35, 57).

I_KATP = I_KATP,Na + I_KATP,K was calculated by Eq. 4 with V = V_rev. As in the experimental sections, P_K and P_Na are the whole cell permeabilities of the K_ATP channels for K⁺ and Na⁺ ions, respectively. Because d(I_KATP)/dV_rev should equal G_KATP, the measured conductance of K_ATP channels in a whole cell (410 nS) at V_rev, and the ratio (P_KATP,Na/P_KATP,K) was known (0.0076; obtained from the single channel experiments), Eq. 4 was differentiated and P_K and P_Na were calculated according to

(14)

with

P_Na was calculated according to

(15)

V_rev

The actual V_rev was calculated by numerically solving the equation

(16)

	ACKNOWLEDGMENTS

 
The authors are indebted to Dr. T. Baukrowitz for comments on the manuscript and to S. Bernhardt, K. Schoknecht, and A. Kolchmeier for excellent technical assistance.

GRANTS

The work was supported by the Deutsche Forschungsgemeinschaft and the Interdisciplinary Center for Clinical Research Jena.

	FOOTNOTES

 

Address for reprint requests and other correspondence: K. Benndorf, Institut für Physiologie, Abt. Herz-Kreislauf-Physiologie, Friedrich-Schiller-Universität Jena, Teichgraben 8, D-07740 Jena, Germany (E-mail: kben{at}mti-n.unijena.de).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

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