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Logo of jphysiolThe Journal of Physiology SiteMembershipSubmissionJ Physiol
J Physiol. Dec 1, 2002; 545(Pt 2): 453–461.
Published online Nov 1, 2002. doi:  10.1113/jphysiol.2002.025866
PMCID: PMC2290698

Stoichiometry of NA+−CA2+ exchange is 3:1 in guinea-pig ventricular myocytes

Abstract

In single guinea-pig ventricular myocytes, we examined the stoichiometry of Na+-Ca2+ exchange (NCX) by measuring the reversal potential (ENCX) of NCX current (INCX) and intracellular Ca2+ concentration ([Ca2+]i) with the whole-cell voltage-clamp technique and confocal microscopy, respectively. With given ionic concentrations in the external and pipette solutions, the predicted ENCX were −73 and −11 mV at 3:1 and 4:1 stoichiometries, respectively. ENCX measured were −69 ± 2 mV (n = 11), −47 ± 1 mV (n = 14) and −15 ± 1 mV (n = 15) at holding potentials (HP) of −73, −42 and −11 mV, respectively. Thus, ENCX almost coincided with HP, indicating that [Ca2+]i and/or [Na+]i changed due to INCX flow. Shifts of ENCXENCX) were measured by changing [Ca2+]o or [Na+]o. The measured values of ΔENCX were almost always smaller than those expected theoretically at a stoichiometry of either 3:1 or 4:1. Using indo-1 fluorescence, [Ca2+]i measured under the whole-cell voltage-clamp supported a 3:1 but not 4:1 stoichiometry. To prevent Ca2+ accumulation, we inhibited INCX with Ni2+ and re-examined ENCX during washing out Ni2+. With HP at predicted ENCX at a 3:1 stoichiometry, ENCX developed was close to predicted ENCX and did not change with time. However, with HP at predicted ENCX for a 4:1 stoichiometry, ENCX developed initially near a predicted ENCX for a 3:1 stoichiometry and shifted toward ENCX for a 4:1 stoichiometry with time. We conclude that the stoichiometry of cardiac NCX is 3:1.

Na+-Ca2+ exchange (NCX) is a key regulator of intracellular Ca2+ in cardiac myocytes. Ca2+ is extruded in exchange with Na+ reversibly. Transport of Na+ and Ca2+ via NCX is sequential, not simultaneous (Kananshvili, 1990; Li & Kimura, 1991; Niggli & Lederer, 1991). The energy for transport depends on the Na+ and Ca2+ concentration gradients across the membrane, the membrane voltage and the stoichiometry (Mullins, 1979; Blaustein & Lederer, 1999). ATP is not an energy source for NCX but it is an intracellular activator possibly via phospholipid metabolism (Hilgemann & Ball, 1996).

Initially, Mullins (1979) proposed a 4:1 stoichiometry of NCX based on thermodynamic grounds. However, in cardiac myocytes the stoichiometry has been considered to be 3:1 based on measurements of ion fluxes (Pitts, 1979; Wakabayashi & Goshima, 1981; Reeves & Hale, 1984), [Na+]i and/or [Ca2+]i (Axelsen & Bridge, 1985; Sheu & Fozzard, 1985; Crespo et al. 1990) and the reversal potential of INCX (ENCX) (Kimura et al. 1986, 1987; Ehara et al. 1989; Yasui & Kimura, 1990). However, recently Fujioka et al. (2000) reported that the stoichiometry of NCX in guinea-pig ventricular cells was 4:1 or variable from measurements of ENCX with the inside-out ‘macro-patch’ method, thus challenging the stoichiometry of 3:1. More recently, with whole-cell voltage-clamp, Dong et al. (2002) also reported 4:1 stoichiometry of NCX1.1 expressed in HEK cells. Therefore, we re-examined the stoichiometry of NCX in guinea-pig cardiac ventricular myocytes by simultaneously measuring ENCX and [Ca2+]i with the whole-cell voltage-clamp and confocal microscopy, respectively.

Our preliminary data were presented at the Cellular and Molecular Physiology of Sodium-Calcium Exchange meeting of the 2001 American Physiological Society as an abstract (Hinata et al. 2001).

Methods

Isolation of cells

All experiments were performed in accordance with the regulations of the Animal Research Committee of Fukushima Medical University. Male guinea-pigs weighing 250-400 g were anaesthetized by intraperitoneal injection of 250 mg kg−1 sodium pentobarbital with 2.5 U g−1 heparin. The chest was opened under artificial ventilation, the aorta was cannulated in situ, and the heart was removed. After washing out the blood with Tyrode solution, the heart was mounted in a Langendorff perfusion system. The perfusate was changed to Ca2+-free Tyrode solution to stop the heartbeat and then to one containing 0.01 % (w/v) collagenase (Wako, Osaka, Japan) and 0.002 % (w/v) alkaline protease (Nagase, Tokyo, Japan). After about 20 min, the collagenase was washed out by perfusing a high K+, low Cl solution (modified KB solution; Isenberg & Klöckner, 1982). Cardiac ventricular tissue was cut into pieces in the modified KB solution and shaken to isolate the cells. The cell suspension was stored at 4 °C and the myocytes were used for the experiment within 8 h. The temperature of the bath solution was maintained at 36 ± 0.5 °C with a water jacket. Tyrode solution contained (mm): NaCl 140, KCl 5.4, CaCl2 1.8, MgCl2 1, NaH2PO4 0.33, glucose 5.5 and Hepes (4, (2-hydroxyethyl)-1-piperazine-ethanesulfonic acid)-NaOH 5 (pH 7.4). The modified KB solution contained (mm): KOH 70, l-glutamic acid 50, KCl 40, taurine 20, KH2PO4 20, MgCl2 3, glucose 10, EGTA 0.2 and Hepes-KOH 10 (pH 7.2).

Patch-clamp recording

Membrane currents were recorded by the whole-cell patch-clamp method using pCLAMP7 software (Axon Instruments, Foster City, CA, USA). Single cardiac ventricular cells were placed in a recording chamber (1 ml volume) attached to an inverted microscope (Nikon, Tokyo, Japan) and were superfused with the Tyrode solution at a rate of 5 ml min−1. Patch pipettes were forged from 1.3 mm diameter glass capillaries (Nihon Rikagaku Kikai, Tokyo) with a two-stage microelectrode puller (pp-83, Narishige, Tokyo, Japan). The pipette resistance was 3-5 MΩ when filled with the pipette solution. The composition of the pipette solution was (mm): NaCl 20, BAPTA (1,2-bis (2-aminophenoxy)-ethane-N,N,N’,N’-tetraacetic acid) 20, CaCl2 9, 9.5 or 10 (calculated free Ca2+ concentrations, 184, 200 or 226 nm, respectively), CsOH 120, aspartic acid 50, MgCl2 3, MgATP 5 and Hepes 20 (pH 7.2 with aspartic acid). In some experiments, 10 mm instead of 9 mm CaCl2 was used in the pipette solution. Calculated ENCX at 9 and 10 mm added Ca2+ were respectively −73 and −68 mV at 3:1, and −11 and −8 mV at 4:1. Since the results at 10 mm were similar to those with 9 mm CaCl2, the data were included. The extracellular solution contained (mm): NaCl 140, CaCl2 1, MgCl2 1, ouabain 0.02, nifedipine or D600 0.01, ryanodine 0.01 and Hepes-NaOH 5 (pH 7.2). Nifedipine and D600 were used to block Ca2+ channels and neither drug affected INCX. The electrode was connected to a patch-clamp amplifier (CEZ-2300, Nihon Kohden, Tokyo, Japan). Recording signals were filtered at 2.5 kHz bandwidth, and the series resistance was compensated.

Ramp pulses of 500 ms duration were given with 10 s intervals in the experiments shown in Fig. 1 and Fig. 2 and with 3 s intervals in the experiment shown in Fig. 4 and Fig. 5. The ramp pulse was initially depolarized from a holding potential of −60 to +20 mV, then hyperpolarized to −100 mV and depolarized back to the holding potential at a speed of 680 mV s−1. The stoichiometry was determined by an equilibrium potential of NCX (ENCX), which is given by the following equation: ENCX + (nENa - ECa)/(n - 2) where n is a stoichiometry of Na+, and ENa and ECa are equilibrium potentials of Na+ and Ca2+, respectively. The descending limb of the ramp was used to plot I-V curves without capacitative current compensation. Ca2+ current, K+ currents, Na+-K+ pump current and Ca2+ release channels of the sarcoplasmic reticulum were blocked by nifedipine or D600, Cs+, ouabain and ryanodine in the external solution, respectively.

Figure 1
ENCX at 1 and 2 mm [Ca2+]o at three different HPs
Figure 2
Effect of raising [Na+]o on ENCX at three different HPs
Figure 4
Effects of −90 mV HP (ENCX at a 3:1 stoichiometry) and −20 mV HP (ENCX at a 4:1 stoichiometry) on ENCX during the recovery from Ni2+ inhibition
Figure 5
Effects of −20 mV HP (ENCX at a 3:1 stoichiometry) and −90 mV HPs on ENCX during the recovery of INCX from Ni2+ inhibition

Measurement of [Ca2+]i

The whole-cell voltage-clamp was performed using a CEZ-2400 amplifier (Nihon Kohden, Tokyo, Japan). Two-dimensional Ca2+ images were obtained by a fast scanning confocal fluorescent microscopy (Nikon RCM-8000; Nikon, Tokyo, Japan) equipped with a Fluor 40 × 1.15 NA, water immersion objective lens (Nikon, Tokyo, Japan) and Ratio3 software (Nikon, Tokyo, Japan). Recordings were started at least 5 min after rupturing the patch membrane to allow 100 μm indo-1 (Dojin, Kumamoto, Japan) to diffuse into the cell from the pipette. The excitation wavelength from an argon ion laser was 351 nm and the emission wavelengths were 405 and 485 nm. The resolution of the microscopy was approximately 0.4 μm × 0.3 μm × 1.5 μm (x, y and z) by the measurement using fluorescent beads. The Ca2+ image was scanned over a full frame (512 pixels × 512 pixels; 170 μm × 140 μm). Calibration of the indo-1 signal was performed in vitro using the pipette solution containing 20 mm BAPTA with various concentrations of added Ca2+. The following equation was used : [Ca2+]i + Kd(Rmin - R)/(R - Rmax), where Kd is the dissociation constant of indo-1 (217 nm), R is the fluorescence ratio and Rmin and Rmax are the fluorescence ratios in the absence of and with saturation of Ca2+, respectively (Dissociation Constant Calculator; Molecular Probes, Eugene, USA).

In vivo calibration of indo-1 would be better than in vitro calibration, because the Kd value of indo-1 has been reported to be higher in vivo than in vitro (Negulescu & Machen, 1990; Harkins et al. 1993; Kawanishi et al. 1994; Bassani et al. 1995). However, in vivo calibrations reported were in general performed with acetoxymethyl (AM) form of indo-1 in intact cells where the cell interior was not dialysed with a pipette solution containing a high concentration of calcium chelator such as BAPTA. In the present study, the cell was dialysed with a pipette solution containing indo-1 and 20 mm BAPTA, and this might have made in vivo Kd value of indo-1 similar to the in vitro value. Therefore we used in vitro calibration of indo-1 for [Ca2+]i. All the recordings were carried out at 36 ± 1 °C.

Data analysis

All the values are presented as means ± s.e.m. (number of experiments). Student's t test and analysis of variance were used for the statistical analyses. P values of less than 0.05 were considered to be significant.

Results

Measurement of ENCX by changing [Ca2+]o at different holding potentials

To determine the stoichiometry of NCX, we measured ENCX by a brief application of 1 mm Ni2+, a selective NCX inhibitor, to the external solution. The holding potential (HP) was set at −73 mV which was the predicted ENCX value for a 3:1 stoichiometry at 140 mm [Na+]o, 1 mm [Ca2+]o, 20 mm [Na+]i, 184 nm [Ca2+]i. Figure 1A shows concatenated current responses to ramp voltage pulses given every 10 s at −73 mV HP. Pulse intervals were omitted from the figure to clearly demonstrate the holding current level. [Ca2+]o was initially at 1 mm and was raised to 2 mm. Ni2+ (1 mm) was added briefly to the external solution to block INCX in order to measure ENCX at each [Ca2+]o. Figure 1B and C illustrate the current-voltage (I-V) relation curves of the control (a, c) and in the presence of 1 mm Ni2+ (b, d) at 1 and 2 mm [Ca2+]o, respectively. Figure 1D shows difference I-V curves of the Ni2+-sensitive currents from Fig. 1B (a - b) and Fig. 1C (c - d). ENCX of (a - b) was −70 mV and ENCX of (c - d) was −76 mV. Therefore, ENCX was shifted by −6 mV upon changing [Ca2+]o from 1 to 2 mm at −73 mV HP, which was smaller than the theoretical value (-18 mV) at a 3:1 but close to that (-9 mV) at a 4:1 stoichiometry.

Using the same protocol, we measured ENCX and shifts of ENCXENCX) at two other HPs: −11 mV, a theoretical ENCX at a 4:1 stoichiometry (Fig. 1F) and −42 mV (Fig. 1E) which is the middle value between −11 and −73 mV. In addition, [Ca2+]o was lowered from 1 to 0.5 mm at each HP (figures not shown) and ΔENCX were evaluated. The results are summarized in Table 1.

Table 1
Summarized results of experiments represented in Figs 1 and and22

We tested whether the currents measured were purely due to NCX operation, and were not contaminated by other currents through, for example, Ca2+-activated non-selective cation channels, stretch-operated cation channels, Ca2+-activated Cl channels or incompletely inactivating Na+ channels. At −11 mV HP, 20 μm tetrodotoxin (TTX) and 100 μm niflumic acid did not affect the current, indicating that incompletely inactivating Na+ current and Cl currents were not contaminated. Gadolinium at 100 μm inhibited the current with a reversal potential near −11 mV HP, which was almost identical to that inhibited by subsequently added KB-R7943, confirming that gadolinium inhibited INCX (Zhang & Hancox, 2000) and that the stretch-operated cation current was not involved. KB-7943 and Ni2+ inhibited currents with similar reversal potentials near −11 mV HP, indicating that the involvement of non-selective cation current was unlikely, because KB-R7943 does not inhibit a Ca2+-activated non-selective cation current (unpublished data).

As seen in Table 1, the measured ENCX values were different at three different HPs, even though the ionic conditions were the same. ENCX almost coincided with each HP. The values of ΔENCX were smaller than expected at stoichiometries of 3:1 and 4:1 with each intervention at almost all HPs, although some values are close to those expected at a stoichiometry of 4:1. These results suggested that [Ca2+]i and/or [Na+]i were altered by INCX flow.

Measurement of ENCX by changing [Na+]o

Since changing [Ca2+]o appeared to change [Ca2+]i and/or [Na+]i, we next measured ΔENCX upon changing [Na+]o, because changing [Na+]o might affect [Ca2+]i and/or [Na+]i less dramatically. A representative concatenated current response is shown in Fig. 2A. Currents during the pulse intervals were omitted in Fig. 2A. The protocol was the same as that for Fig. 1. Figure 2B and C illustrate I-V curves of the control (a, c) and in the presence of 1 mm Ni2+ (b, d) at 140 and 200 mm [Na+]o, respectively, at −73 mV HP. Figure 1D shows difference I-V curves of the Ni2+-sensitive currents from Fig. 2B (a - b) at 140 mm [Na+]o and from Fig. 2C (c - d) at 200 mm [Na+]i. ENCX of (a - b) was −70 mV and ENCX of (c - d) was −50 mV. ΔENCX was 22 ± 1 mV (n = 5) upon changing [Na+]o from 140 to 200 mm at −73 mV HP. We performed this experiment at the two other HPs and the results are presented in Table 1. ΔENCX was smaller as HPs were less negative. ΔENCX was close to that expected at 4:1 at −42 and −73 mV HP but was significantly smaller at −11 mV than that expected at 4:1 and 3:1. This result indicated that changing [Na+]o also changed [Ca2+]i and/or [Na+]i.

Measurement of [Ca2+]i

In the above experiments, ΔENCX was sometimes close to that expected at a stoichiometry of 4:1, but other times it was significantly smaller than that expected at a stoichiometry of 4:1, which was even further smaller than that expected at a stoichiometry of 3:1. In addition, ENCX depended on HP. These results suggested that intracellular ion concentrations, especially [Ca2+]i, were changed by INCX flow because [Na+]i was more diffusible than [Ca2+]i in the cell, especially in the presence of BAPTA. Therefore, we measured [Ca2+]i and ENCX simultaneously with 100 μm indo-1 in the pipette solution using confocal fluorescent microscopy under the whole-cell voltage-clamp. Representative images of the same cell at two different HPs are shown in Fig. 3. Ionic conditions were the same as those at 1 mm [Ca2+]o and 140 mm [Na+]o in Fig. 1 and Fig. 2. Initially HP was at −11 mV (Fig. 3A) and then it was changed to −73 mV (Fig. 3B) in this cell and the reverse order of HPs was also tested. Recordings were continued for at least 5 min after rupturing the patch membrane or after changing the membrane potential. At −11 mV HP, [Ca2+]i was 374 ± 38 nm (n = 16) (Fig. 3A) and ENCX was −13 ± 1 mV (n = 5). In contrast, in the same cell at −73 mV HP, [Ca2+]i was 173 ± 11 nm (n = 13) and ENCX was −70 ± 1 mV (n = 5). The predicted [Ca2+]i was 184 nm at −73 and −11 mV at stoichiometries of 3:1 and 4:1, respectively. The [Ca2+]i of 173 ± 11 nm at −73 mV HP was close to the predicted value at a stoichiometry of 3:1, while 374 ± 38 nm at −11 mV was too high for a 4:1 stoichiometry. Thus, the results of [Ca2+]i measurements supported a 3:1 stoichiometry.

Figure 3
[Ca2+]i measurement with indo-1 at two different HPs

Measurement of ENCX during the recovery from Ni2+-inhibition

Since [Ca2+]i was in accordance with a 3:1 stoichiometry, we attempted to measure ENCX again by the whole-cell clamp with a protocol which would minimize ionic concentration change due to INCX flow. We inhibited INCX completely with 5 mm Ni2+ at the onset of the whole-cell clamp and examined ENCX during the recovery of INCX after washing out Ni2+ (Fig. 4). We at first performed the experiment using the same ionic conditions used in Fig. 1 at −73 and −11 mV HP. However the difference in the reversal potential was not clear between the two HPs. Therefore we employed an external solution containing higher concentrations of 200 mm [Na+]o and 9 mm [Ca2+]o and a pipette solution containing 20 mm Na+ and 200 nm free Ca2+ (20 mm BAPTA and 9.5 mm Ca2+). The external solution is hyperosmotic and may modulate the magnitude of INCX, but does not affect ENCX (Wright et al. 1995). The predicted ENCX was −100 mV at a 3:1 stoichiometry and −20 mV at a 4:1 stoichiometry. Representative concatenated current responses at −90 mV HP are shown in Fig. 4A and at −20 mV HP in Fig. 4B. Ramp pulse interval was 3 s instead of 10 s. Ni2+ at 5 mm was added to the external solution at the beginning of the whole-cell clamp and was washed out after about 5 min. Figure 4C shows the difference I-V curves at −90 mV HP. ENCX developed at around −90 mV and did not change with time. In contrast, at −20 mV HP, ENCX of the difference I-V curves appeared initially at around −70 mV and shifted toward −20 mV with time (Fig. 4D). As shown in Table 2, the average steady state values coincided with a 3:1 stoichiometry but not with a 4:1 stoichiometry.

Table 2
Summarized results of experiments represented in Fig. 4

To further confirm our results, we performed the above protocol under the ionic conditions where a theoretical ENCX was approximately −20 mV at a 3:1 stoichiometry. With 200 mm [Na+]o, 0.5 mm [Ca2+]o, 20 mm [Na+]i and 226 nm [Ca2+]i, ENCX calculated is −21 mV at a 3:1 stoichiometry. Figure 5A shows representative concatenated currents recorded at −20 mV HP. Figure 5C shows the difference I-V curves obtained by subtraction as labelled. ENCX developed initially near the holding potential of −22 ± 2 mV (n = 5) and did not shift with time. Steady state ENCX after about 36 s was −25 ± 2 mV (n = 5) (Table 3). This result also supports a 3:1 stoichiometry. In contrast, under the same ionic conditions, when HP was held at −90 mV, a significantly more negative HP than ENCX at a 3:1 stoichiometry, ENCX developed initially at −19 ± 4 mV (n = 5) and shifted to a steady state ENCX of −32 ± 10 mV (n = 5) after 36 s. Thus when HP was away from expected ENCX, the initial ENCX soon after washing out Ni2+ coincided with the value expected for a 3:1 stoichiometry but then shifted with time. These data strongly support that the stoichiometry of NCX is 3:1 rather than 4:1.

Table 3
Summarized results of experiments represented in Fig. 5

Discussion

When we measured ENCX at three different HPs, −11, −42 and −73 mV, ENCX almost coincided with HP even though the compositions of the external and pipette solutions were identical. Furthermore, when we measured the ENCX shifts (ΔENCX) by changing [Ca2+]o or [Na+]o, ΔENCX values were closer to that expected at a 4:1 stoichiometry than 3:1 or most often smaller than those expected for both 4:1 and 3:1 stoichiometries at any of the HPs. The most likely cause of the smaller ΔENCX upon changing [Ca2+]o and [Na+]o was that Ca2+ and/or Na+ accumulated (or depleted) under the membrane because INCX approached NCX equilibrium at a given holding potential. In addition, 1 mm Ni2+ did not inhibit INCX completely and thus INCX flow during Ni2+ inhibition allowed [Ca2+]i and/or [Na+]i change. Contamination of other currents such as non-inactivating Na+ current and Cl currents could be denied, because 20 μm tetrodotoxin (TTX) and 100 μm niflumic acid did not affect the current at −11 and −73 mV HP. Gadolinium at 100 μm inhibited the current with the reversal potential near −11 mV HP, which was identical to that inhibited further by subsequently added KB-R7943. This confirmed that gadolinium inhibited INCX (Zhang & Hancox, 2000) and that a stretch-activated cation current was not involved. Contamination of Ca2+-activated nonselective cation current was also negated because KB-R7943- and Ni+-inhibited currents had similar reversal potentials while KB-R7943 does not inhibit the Ca2+-activated cation current (unpublished data).

The fact that ENCX tended to coincide with a holding potential at any ionic concentration indicates that the method we employed in Fig. 1 and Fig. 2 for measuring ENCX to determine the stoichiometry had serious limitations. To overcome this difficulty, we measured [Ca2+]i with indo-1 fluorescence using confocal microscopy under the voltage-clamp. [Ca2+]i at −73 mV HP, or ENCX at a 3:1 stoichiometry, was 173 ± 11 nm (n = 13). Thus the value was almost consistent with the theoretical [Ca2+]i of 184 nm. However, under the same ionic conditions, [Ca2+]i at −11 mV HP, or ENCX at a 4:1 stoichiometry, was 374 ± 38 nm (n = 16). This value was significantly higher than the theoretical value of 184 nm. In addition, in spite of using the same cell, [Ca2+]i were significantly changed between the two different HPs. This was a surprising result because [Ca2+]i accumulated even in the presence of 20 mm BAPTA. Thus, the [Ca2+]i measurement supported a 3:1 but not a 4:1 stoichiometry.

We performed the whole-cell voltage-clamp experiment again and examined ENCX with a different protocol, as shown in Fig. 4 and Fig. 5. We initially inhibited INCX almost completely with 5 mm Ni2+ instead of 1 mm Ni2+, and then washed out Ni2+ to measure ENCX during the recovery of INCX from Ni2+ inhibition. When the HP was at ENCX for a 3:1 stoichiometry, the ENCX developed initially near the theoretical value for a 3:1 stoichiometry and did not change with time (Fig. 4A and C, Fig. 5A and C). In contrast, when the HP was at the theoretical ENCX for a 4:1 stoichiometry, which was more positive than a 3:1 ENCX (Fig. 4B and D), or when the HP was significantly more negative than a 3:1 ENCX (Fig. 5B and D), INCX developed initially with ENCX closed to that expected for a 3:1 stoichiometry and then shifted with time toward each HP (Tables 2 and and3).3). These results also support a 3:1 stoichiometry.

We learned from this study that it is rather difficult to control [Ca2+]i even with 20 mm BAPTA in the pipette solution under the whole-cell voltage-clamp when INCX flowed. In other words, NCX has a strong tendency to approach its equilibrium at a holding potential by changing [Ca2+]i and/or [Na+]i, and this is why ENCX tends to coincide with a given holding potential at a steady state. Recently, using the whole-cell voltage-clamp, Dong et al. (2002) reported 4:1 stoichiometry by measuring ENCX of NCX1.1 overexpressed in HEK cells. Although their data of ENCX fitted to theoretically expected 4:1 stoichiometry, they used a fixed holding potential of 0 mV with a rather low concentration of 10 mm EGTA or BAPTA in the pipette solution and therefore there is a possibility that ENCX they measured were shifted to the holding potential of 0 mV, and thus apparently fitted to 4:1 rather than 3:1 stoichiometry. This possibility is also discussed for the macro-patch data in the following.

Fujioka et al. (2000) concluded that the stoichiometry was 4:1 or variable depending on external and cytoplasmic Ca2+ or Na+ concentrations. They examined ENCX with inside-out macro-patches which they estimated to be devoid of [Ca2+]i accumulation. However, based on our present results we suspect that [Ca2+]i accumulation might have occurred on the cytoplasmic side of the inside-out macro-patch membrane in their experiment for the following reasons. First, they used a rather low concentration of 10 mm EGTA as a Ca2+ chelator added to a high concentration of 8.79 mm CaCl2 to give 1 μm free Ca2+ in the cytoplasmic solution. EGTA has Ca2+ binding kinetics slower than that of BAPTA (Tsien, 1980). Our data indicated that it was difficult to control [Ca2+]i even with 20 mm BAPTA in the pipette solution. Second, they fixed the holding potential at 0 mV, which was good to avoid interference by a Ca2+-activated non-selective cation current that reverses at 0 mV (Ehara et al. 1988), but it might have facilitated Ca2+ accumulation during the outward INCX flow at 0 mV. For example, under the ionic conditions of Fujioka et al. (2000) with 145 mm [Na+]o, 50 mm [Na+]i, 2 mm [Ca2+]o and 1 μm [Ca2+]i, the theoretical ENCX at a 3:1 stoichiometry was −117 mV, while the ENCX they measured was around −50 mV, which they interpreted as an ENCX at a 4:1 stoichiometry. However, this may have been due to [Ca2+]i accumulation rather than a 4:1 stoichiometry, because if [Ca2+]i rose to 10 μm, ENCX would be −56 mV at a 3:1 stoichiometry. Fujioka et al. (2000) demonstrated that INCX of 1.5 pA was induced by 50 mm [Na+]i at 0 mV, which could induce Ca2+ influx of 5 μm s−1 by roughly estimating the space under the macro-patch membrane as a half sphere with 6 μm diameter and thus an increase of [Ca2+]i to 10 μm might be possible due to INCX flow.

Third, the data of Fujioka et al. (2000) indicated that the stoichiometry was closer to 3:1 when [Na+]i was lower (≈9 mm) or [Ca2+]i was higher (100 μm) at fixed concentrations of 145 mm [Na+]o and 2 mm [Ca2+]o, and that the stoichiometry was 4 or more when [Na+]i was higher (9-40 mm) or [Ca2+]i was lower (0.1-10 μm). Higher [Na+]i induced larger Ca2+ influx leading to Ca2+ accumulation on the cytoplasmic side of the membrane, especially at lower [Ca2+]i. This tendency was seen in both macro-patch and giant-patch data, but was more prominent in the macro-patch than the giant-patch (Fujioka et al. 2000). This may have led to their conclusion of a 4:1 or 5:1 stoichiometry.

Where does Ca2+ accumulate in the macro-patch? The macro-patch is very likely to maintain the complex structure of the cardiac surface membrane including the T-tubules (Davis et al. 2001), unlike the smooth giant-patch obtained from the fully extended ‘bleb’ membrane of the relaxed myocyte (Collins et al. 1992). NCX molecules are more densely localized in the transverse tubules than the surface membrane (Frank et al. 1992; Yang et al. 2002). Activity of these localized NCX may lead to Ca2+ accumulation in a limited space under the membrane. Accumulation effects were also seen in the giant-patch data (Fujioka et al. 2000), which may indicate that there may be a limited space for rapid diffusion to occur just under the NCX molecules. Although Fujioka et al. (2000) simulated ion flux in the inside-out patch membrane, simulated curves do not always appear to fit the experimentally obtained curve. Thus there may be a limited space immediately under the NCX molecule which prevents immediate free diffusion with the bulk solution.

We conclude that the stoichiometry of cardiac Na+-Ca2+ exchange is 3:1.

Acknowledgments

We thank Dr Isao Matsuoka for his valuable discussion, and Dr Tomoyuki Ono and Ms Sanae Sato for their excellent technical assistance. This work was supported by Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (11357020, 13670092).

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