Stoichiometry of Na⁺-Ca²⁺ exchange in inside-out patches excised from guinea-pig ventricular myocytes

Abstract

1. The stoichiometry (n_x) of cardiac Na⁺-Ca²⁺ exchange was examined by measuring the reversal potential of the Na⁺-Ca²⁺ exchange current (I_Na-Ca) in large inside-out patches, ‘macro patches’, excised from intact guinea-pig ventricular cells.

2. Cytoplasmic application of Na⁺ (Na⁺_i) or Ca²⁺ (Ca²⁺_i) induced I_Na-Ca which showed properties similar to I_Na-Ca in the giant membrane patch. The outward I_Na-Ca was depressed by an exchanger inhibitory peptide, XIP.

3. The reversal potential of the XIP-sensitive current indicated that n_x was ≈4 (3·6-4·2) at 9–40 mM Na⁺_i, and n_x tended to increase as Na⁺_i was increased. Proteolysis by trypsin did not significantly affect the stoichiometry. Similar results were obtained from the reversal potential of I_Na-Ca that was induced by application of both Na⁺_i and Ca²⁺_i.

4. At 0·1 μM Ca²⁺_i, n_x was ≈4 (3·7-4·4) at 6–25 mM Na⁺_i and tended to increase as Na⁺_i was increased. When Ca²⁺_i was changed from 0·1 to 1 and 1000 μM at constant 50 mM Na⁺_i, the value was ≈4 (3·6-4·4).

5. When the extracellular Na⁺ (Na⁺_o) and Ca²⁺ (Ca²⁺_o) concentrations were varied in the presence of 25 or 9 mM Na⁺_i and 1 μM Ca²⁺_i, n_x was almost constant (≈4) over the range 0·3-20 mM Ca²⁺_o and 10–145 mM Na⁺_o.

6. These results indicated that the stoichiometry of Na⁺-Ca²⁺ exchange is different from generally accepted 3Na⁺:1Ca²⁺, and suggested that the stoichiometry is either 4Na⁺:1Ca²⁺ or variable depending on Na⁺_i and Ca²⁺_i.

Operation of the cardiac Na⁺-Ca²⁺ exchange is primarily determined by the transsarcolemmal electrochemical gradients of both Na⁺ and Ca²⁺ (Mullins, 1977). Thus, the reversal potential of Na⁺-Ca²⁺ exchange is dependent on the stoichiometry of the exchange. A model of 4Na⁺:1Ca²⁺ exchange was originally proposed by Mullins (1977) based on energetic considerations and the sensitivity of Ca²⁺ fluxes to membrane potential. Later, a 3Na⁺:1Ca²⁺ exchange was suggested, based on measurements of ion fluxes (Pitts, 1979; Wakabayashi & Goshima, 1981; Reeves & Hale, 1984), intracellular Na⁺ and/or Ca²⁺ concentrations (Axelsen & Bridge, 1985; Sheu & Fozzard, 1985; Crespo et al. 1990) and reversal potential of I_Na-Ca (Ehara et al. 1989; Noma et al. 1991; Matsuoka & Hilgemann, 1992). However, accurate measurement of reversal potential was difficult in the whole-cell clamp studies, because of accumulation and depletion of the intracellular ions (Ehara et al. 1989; Noma et al. 1991). This problem was considered to be negligible in the giant membrane patch developed by Hilgemann (1989). However, since the giant membrane patch uses ‘bleb’ membrane instead of intact sarcolemma, the properties of Na⁺-Ca²⁺ exchange might have been altered during bleb formation.

We developed a new method of obtaining large inside-out patches, ‘macro patches’, from intact ventricular cells, and succeeded in recording I_Na-Ca. In this study, the stoichiometry was re-examined by measuring the reversal potential of I_Na-Ca using an exchanger inhibitory peptide, XIP (Li et al. 1991; Chin et al. 1993; Matsuoka et al. 1993). The reversal potential supported a stoichiometry of 4Na⁺:1Ca²⁺ rather than 3Na⁺:1Ca²⁺, and suggested that the stoichiometry may change with ionic concentrations on the cytoplasmic side of the membrane.

Preliminary data were presented in the 43rd annual meeting of the Biophysical Society (Matsuoka et al. 1999).

METHODS

Isolation of myocytes

Guinea-pigs (200–300 g) were deeply anaesthetized by intraperitoneal injection of pentobarbitone sodium (> 0.1 mg g⁻¹). Single ventricular myocytes were isolated by intra-coronary perfusion of the heart with nominally Ca²⁺-free Tyrode solution containing collagenase (0.4 mg ml⁻¹, Sigma type I) for 15 min (Powell et al. 1980; Fujioka et al. 1998). The myocytes were used for the macro patch experiment within 8 h.

Macro patch and giant membrane patch formation

Patch pipettes for the macro patch were prepared using a two-step pipette puller (Narishige PB-7, Japan) from borosilicate glass capillaries (o.d. = 2.0 mm, i.d. = 1.4 mm; Hilgenberg, Germany). The inner tip diameter was 5–7 μm and the electrical resistance was 0.3-0.8 MΩ when filled with pipette solutions (see below). A seal resistance of 2–5 GΩ could be formed by applying gentle negative pressure (10–20 cmH₂O) for several minutes. The patch excision was usually established by blowing the attached cell with a solution stream from a theta capillary located near the cell (see below).

The giant membrane patch study was carried out in a manner similar to that described by Hilgemann (1995). In brief, the isolated guinea-pig ventricular myocytes were stored overnight at 4°C in a high K⁺, low Cl⁻ solution for bleb formation. The tip of the patch electrode was 10–15 μm in diameter, and was coated with a mixture of Parafilm (American National Can), and light and heavy mineral oil (Sigma) (approximately 1:1:1 ratio in weight).

Electrophysiology

Voltage clamp was conducted with a patch clamp amplifier (Axopatch 200B; Axon Instruments, Inc., Foster City, CA, USA). The holding potential was set to 0 mV. The membrane current was filtered at 100–500 Hz by a low-pass filter, and sampled at 50–100 Hz by an A/D converter (ADX-98H; Canopus, Japan). The current-voltage (I–V) relationship was recorded with ramp voltage pulses (dV/dt= 0.72 V s⁻¹) as previously described (Fujioka et al. 1998), and the membrane current and voltage were sampled at 1.6 kHz. The reversal potential was obtained as the zero current potential of a function which was fitted to I_Na-Ca by the least-squares method (Stein, 1986; Matsuoka & Hilgemann, 1992). The equation is:

(1)

where K_em is e^(V/53.4), I is membrane current, V is membrane voltage (in mV), and values of a, b, c and d were adjusted to experimental data. All statistical data are shown as means ±s.d. In some experiments, the cytoplasmic solution containing 0.5 mg ml⁻¹ trypsin (Sigma) was applied to the cytoplasmic surface of the patch for 15–20 s to deregulate the exchanger.

Ion concentration jump

The patch pipette with the excised inside-out patch membrane was positioned near the theta glass capillary (o.d. = 1.5 mm, i.d. = 1.3 mm, and septum = 0.05 mm; Iwaki Glass Co., Ltd, Chiba, Japan), in which two kinds of cytoplasmic solution flowed. Ion concentration jumps were performed by moving a piezo translator (Murata MFG Co., Ltd, Kyoto, Japan), on which the theta glass was mounted, with 20–30 V voltage pulses (Jonas, 1995). The temperature of the cytoplasmic solutions at the outlet of the theta capillary was 36–37°C.

Solutions and chemicals

The control Tyrode solution contained (mM): NaCl, 140; KCl, 5.4; CaCl₂, 1.8; MgCl₂, 0.5; NaH₂PO₄, 0.33; glucose, 5.5; and Hepes, 5 (pH = 7.4/NaOH). The high K⁺, low Cl⁻ solution contained: KCl, 25; glutamate, 70; KH₂PO₄, 10; taurine, 10; EGTA, 0.5; glucose, 11; and Hepes, 10 (pH = 7.3/KOH). A pipette solution used to activate the outward I_Na-Ca contained (mM): N-methyl-D-glucamine (NMDG), 100; aspartate, 100; Hepes, 5; TEA-Cl, 20; ouabain, 0.05; CaCl₂, 5; MgCl₂, 2; CsCl, 2; BaCl₂, 2; and nicardipine, 0.002 (pH = 7.4/NMDG). The pipette solution used for the inward I_Na-Ca contained: NaOH, 100; aspartate, 100; Hepes, 5; TEA-Cl, 20; ouabain 0.05; EGTA, 0.1; MgCl₂, 2; CsCl, 2; BaCl₂, 2; and nicardipine, 0.002 (pH = 7.4/NMDG). A standard pipette solution used for reversal potential measurements contained: NaOH, 145; aspartate, 145; Hepes, 5; TEA-Cl, 20; ouabain, 0.05; CaCl₂, 2; MgCl₂, 2; CsCl, 2; BaCl₂, 2; and nicardipine, 0.002 (pH = 7.4/HCl).

Ba²⁺ (2 mM) was included in the pipette solutions to suppress background current (Ehara et al. 1989). Recently Trac et al. (1997) reported Na⁺-Ba²⁺ exchange current in giant patches from Xenopus oocytes expressing NCX1. In macro patches of the present study, however, cytoplasmic Na⁺ barely induced a substantial outward current in the presence of 2 mM Ba²⁺_o and no Ca²⁺_o. Therefore, we assumed that Na⁺-Ba²⁺ exchange current is negligible under the present conditions.

Standard cytoplasmic solution with 100 mM Na⁺ contained: NaOH, 100; EGTA, 10; Hepes, 20; aspartate, 100; TEA-Cl, 20; CsCl, 20; CaCl₂, 8.79; and MgCl₂, 1.11 (pH = 7.2/NMDG). Cytoplasmic solutions containing various Na⁺ concentrations were prepared by replacement of NaOH with LiOH. Free Ca²⁺ and Mg²⁺ concentrations were calculated with a software developed by Bers et al. (1994) and were 1.0 μM and 1.0 mM, respectively. The free Mg²⁺ concentration was fixed to 1 mM when free Ca²⁺ was changed. XIP was purchased from the Peptide Institute, Inc. (Osaka, Japan).

RESULTS

Inward and outward I_Na-Ca

The application of Ca²⁺₁ or Na⁺_i to the macro patch induced a measurable inward or outward current only in the presence of counter ions at the extracellular side of the patch membrane. The Ca²⁺₁-induced inward current was mostly time independent (Fig. 1a), and half-maximum concentration (K_h) for Ca²⁺₁ was 7.4 ± 2.6 μM (n= 10) when fitted to the Hill equation. The Na⁺_i-induced outward current partially decayed (Fig. 1B) in a similar manner to the Na⁺-dependent inactivation characteristics of I_Na-Ca (Hilgemann et al. 1992b). Removal of Ca²⁺₁ depressed the Na⁺_i-induced outward current. When measured at the initial peak of the outward current, K_h for Na⁺_i was 21.1 ± 1.0 mM (n= 4) at 1 μM Ca²⁺₁, and K_h for Ca²⁺₁ to activate the current was 0.3 ± 0.1 μM (n= 10) at 100 mM Na⁺. Partial proteolysis of the patch by trypsin eliminated these regulatory mechanisms, i.e. the Na⁺-dependent inactivation and the Ca²⁺ activation, and augmented the outward current. It is notable that 1 μM Ca²⁺₁ did not significantly affect the background current (‘a – c’ in Fig. 1B). An exchanger inhibitory peptide (XIP; Li et al. 1991; Chin et al. 1993; Matsuoka et al. 1993) inhibited control (not shown) and deregulated (Fig. 1C) exchange current, reversibly. It should also be noted that the background XIP-sensitive (‘a – c’ in Fig. 1C) current is small. These properties of the Ca²⁺₁- or Na⁺_i-induced currents were in good agreement with I_Na-Ca in the giant membrane patch from the cardiac ‘bleb’ (Hilgemann et al. 1992a,b) and from Xenopus oocytes expressing NCX1 (Matsuoka et al. 1993, 1997). We conclude that the macro patch technique is suitable for the analysis of I_Na-Ca. The inward I_Na-Ca and the outward I_Na-Ca after the trypsin treatment were almost time independent, suggesting that ion depletion and accumulation near the patch membrane are small. The accumulation/depletion issue will be further argued in Discussion.

Figure 1. I_Na-Ca in the ‘macro patch’.

A, 10 μM Ca²⁺_i-induced inward I_Na-Ca. Na⁺₀= 100 mM, Ca²⁺_o= 0 mM, and Na⁺_i= 0 mM. Ca²⁺_i was increased from 0 to 10 μM during the period indicated. Right panel is the I–V relation of I_Na-Ca (‘b – a’), which was obtained as a difference current in the presence and absence of 10 μM Ca²⁺_i. B, 100 mM Na⁺_i-induced outward I_Na-Ca. Na⁺₀= 0 mM and Ca²⁺_o= 5 mM. Na⁺_i (100 mM) was applied in the presence and absence of 1 μM Ca²⁺_i. Then the cytoplasmic side of the patch was treated by trypsin for 20 s. The I–V relations in the presence (‘b – a’) and absence (‘d – c’) of 1 μM Ca²⁺_i, and I–V relation after trypsin treatment (‘f – e’) were superimposed. Note that 1 μM Ca²⁺_i did not affect background current (‘a – c’). C, inhibition of I_Na-Ca by XIP. The patch was pretreated with trypsin. XIP (0.2 μM) reversibly inhibited 100 mM Na⁺_i-induced I_Na-Ca. Note that the effect of XIP on the background current was small (‘a – c’). Data in A, B and C were obtained from different patches.

Reversal potential of I_Na-Ca

The stoichiometry (n_x) of Na⁺-Ca²⁺ exchange can be determined by measuring the equilibrium potential (E_Na-Ca) at known concentrations of Na⁺ and Ca²⁺ according to the following equation:

(2)

where E_Na and E_Ca are the equilibrium potentials of Na⁺ and Ca²⁺, respectively (Mullins, 1977).

To dissect I_Na-Ca from the rest of the membrane current, the current was recorded in the presence and absence of 0.2 μM XIP (half-maximal inhibition at 0.1 μM; Li et al. 1991; Chin et al. 1993; Matsuoka et al. 1993) and I_Na-Ca was obtained as the difference current. To eliminate the Na⁺_i-dependent inactivation, the patch was pretreated with trypsin. Under the control condition of 145 mM Na⁺₀, 2 mM Ca²⁺_o, 9 mM Na⁺_i, and 1 μM Ca²⁺₁, 0.2 μM XIP shifted the holding current outwardly (left panel in Fig. 2a). The I–V relation of XIP-sensitive current is shown in the right panel of Fig. 2a (‘b – a’). Note that background conductance did not significantly change after the activation of I_Na-Ca (‘c – a’). The XIP-sensitive current was obtained at various values of Na⁺_i (Fig. 2B). Fitting eqn (1) (dotted line) to the record determined a reversal potential of −29.5 mV at 40 mM Na⁺_i. The reversal potential shifted to +5.0, +15.0 and +42.5 mV, as Na⁺_i was decreased to 25, 15 and 9 mM, respectively. We further confirmed its selective block of I_Na-Ca by applying XIP under conditions in which I_Na-Ca was suppressed. In fact, the XIP-sensitive current was negligible as shown in Fig. 2C when I_Na-Ca was suppressed beforehand by removing Ca²⁺₁ in trypsin-untreated patches (n= 3).

Figure 2. XIP-sensitive I_Na-Ca.

A, XIP-sensitive current. Na⁺₀= 145 mM, Ca²⁺_o= 2 mM, Na⁺_i= 9 mM and Ca²⁺_i= 1 μM. XIP (0.2 μM) suppressed inward I_Na-Ca at the holding potential (left panel) in the trypsin-treated patch. The XIP-sensitive current (‘b – a’) is shown in the right panel. Note that the background current did not significantly change (‘c – a’). B, I–V relation of the XIP-sensitive current at different Na⁺_i. XIP (0.2 μM)-sensitive currents at 40, 25, 15 and 9 mM Na⁺_i are shown. Dotted curves are fitting functions and arrows indicate reversal potentials. C, effect of XIP on the background current. XIP (0.2 μM)-sensitive current in the presence of 100 mM Na⁺_i and 0 μM Ca²⁺_i is shown (Na⁺₀= 145 mM, Ca²⁺_o= 2 mM, trypsin-untreated patch).

Measurements of the reversal potential of the XIP-sensitive current were plotted against Na⁺_i on a semilogarithmic scale in Fig. 3a (open circles). The experimental values largely deviated from E_Na-Ca of 3Na⁺:1Ca²⁺ exchange, and were close to E_Na-Ca of 4Na⁺:1Ca²⁺ exchange. When the data were fitted with eqn (2), assuming that Na⁺ and Ca²⁺ concentrations around the exchanger were equal to those of bulk solutions (145 mM Na⁺₀, 2 mM Ca²⁺_o and 1 μM Ca²⁺₁) and that stoichiometry is fixed, n_x was 4.1 (continuous line). However, the slope of the experimental values seems less steep than either the fitted line (n_x= 4.1) or the theoretical line for n_x= 4 (dotted line). Alternatively in Fig. 3B, n_x was calculated at individual Na⁺_i concentrations (open circles). There was a tendency for n_x to increase as Na⁺_i was increased. The calculated values were 3.3 ± 0.8 (n= 3), 3.6 ± 0.4 (n= 7), 3.9 ± 0.2 (n= 7), 4.1 ± 0.3 (n= 7), 4.2 ± 0.3 (n= 7) and 4.9 ± 0.8 (n= 3) at 6, 9, 15, 25, 40 and 100 mM Na⁺_i, respectively.

Figure 3. Reversal potentials and stoichiometry of the XIP-sensitive current.

A, Na⁺_i concentration-reversal potential relationship. Dotted lines indicate theoretical E_Na-Ca of 4Na⁺:1Ca²⁺ and 3Na⁺:1Ca²⁺ exchange, respectively, and the continuous line is the fitted function (n_x= 4.1). Data were obtained from trypsin-treated patches (^, 7 patches) and non-trypsin-treated patches (•, 6 patches). B, Na⁺_i concentration- stoichiometry relationship. n_x was calculated from the experimental data in A using eqn (2). Na⁺₀= 145 mM, Ca²⁺_o= 2 mM and Ca²⁺_i= 1 μM. The number of values at each Na⁺_i concentration was 3–7.

In the experiments described above, the regulatory mechanisms were eliminated with 0.5 mg ml⁻¹ trypsin to avoid the development of the Na⁺-dependent inactivation during the ramp pulse. To exclude a possibility that partial proteolysis altered the stoichiometry, the measurement was repeated without the trypsin treatment (filled circles in Fig. 3). Although the XIP-sensitive component was relatively small under this condition, the reversal potentials and the calculated n_x were similar to those from trypsin-treated patches. The fitted n_x for the entire data was 3.7 (data not shown), and n_x at each Na⁺_i concentration increased from ∼3 to ∼4 as Na⁺_i was increased. Therefore, we assumed that the proteolysis did not alter the stoichiometry.

To exclude any possibility that XIP modulated the stoichiometry in addition to blocking the exchange activity, the reversal potential was also measured without using XIP by recording the membrane currents induced by simultaneous application of Na⁺_i and Ca²⁺₁ (Na⁺_i,Ca²⁺₁-induced current). In the trypsin-pretreated patch, simultaneous application of 12 mM Na⁺_i and 1 μM Ca²⁺₁ induced inward I_Na-Ca at the membrane potential of 0 mV (left panel in Fig. 4a). Its difference current reversed at about +28 mV (‘b – a’). The background current was stable (‘c – a’ in Fig. 4a) in the time scale of several tens of seconds. Currents induced by 12–50 mM Na⁺_i and 1 μM Ca²⁺₁ are shown in Fig. 4B. We considered that the background conductance was not significantly affected by the jump of Na⁺_i and Ca²⁺₁ concentrations, because no substantial current was induced by 100 mM Na⁺_i (Fig. 4C) in the absence of both Na⁺₀ and Ca²⁺_o in the pipette. Similar results were obtained in a total of four patches. Ca²⁺₁ at a concentration of 30 μM did not induce significant current either (data not shown).

Figure 4. Na⁺_i,Ca²⁺_i-induced I_Na-Ca.

A, I_Na-Ca induced by application of Na⁺_i and Ca²⁺_i. Na⁺₀= 145 mM, Ca²⁺_o= 2 mM. The patch was pretreated with trypsin. An application of 12 mM Na⁺_i and 1 μM Ca²⁺_i induced an inward I_Na-Ca at the holding potential (left panel). The I–V relation of the current (‘b – a’) is shown in the right panel. Note that background current did not change significantly after the activation of I_Na-Ca (‘c – a’). B, the I–V relation at different Na⁺_i concentrations. The Na⁺_i concentration was changed from 12 to 50 mM in a patch with the same protocol as A. C, 100 mM Na⁺_i-induced current in the absence of both Na⁺₀ and Ca²⁺_o in the pipette solution. Na⁺₀ was replaced by NMDG.

We plotted these results in Fig. 5. The data were again obtained from both trypsin-treated (open squares) and -untreated patches (filled squares). The result was consistent with that from the XIP-sensitive I_Na-Ca. The fitted n_x was 4.3 (continuous line) and 3.8 (not shown) in the trypsin-treated and -untreated patches, respectively. With the data from the trypsin-treated patch, n_x at individual Na⁺_i concentrations was 3.2 ± 0.2 (n= 3, 6 mM), 3.6 ± 0.2 (n= 3, 9 mM), 4.2 ± 0.2 (n= 4, 12 mM), 3.9 ± 0.1 (n= 4, 20 mM), 3.8 ± 0.1 (n= 4, 30 mM), 4.1 ± 0.1 (n= 4, 50 mM) and 5.5 ± 0.6 (n= 5, 100 mM).

Figure 5. Reversal potentials and stoichiometry of the Na⁺_i,Ca²⁺_i-induced I_Na-Ca.

A, Na⁺_i concentration-reversal potential relationship. Dotted lines indicate theoretical E_Na-Ca of 4Na⁺:1Ca²⁺ and 3Na⁺:1Ca²⁺ exchange, respectively, and the continuous line is the fitted function (n_x= 4.3). Data were from trypsin-treated patches (□, 9 patches) and non-trypsin-treated patches (▪, 9 patches). B, Na⁺_i concentration-stoichiometry relationship. n_x was calculated from the data in A using eqn (2).

Mullins & Brinley (1975) suggested a possibility that stoichiometry is variable depending on Ca²⁺₁ concentration. This hypothesis was tested at 10-fold lower Ca²⁺₁ (0.1 μM) in trypsin-treated patches. I_Na-Ca was isolated as either 0.8 μM XIP-sensitive current (circles) or Na⁺_i,Ca²⁺₁-induced current (squares, in Fig. 6a). The reversal potentials were clearly different from an E_Na-Ca of 3Na⁺:1Ca²⁺ exchange, and were closer to an E_Na-Ca expected for 4Na⁺:1Ca²⁺ exchange at Na⁺_i concentrations of less than 25 mM. At 40 and 100 mM Na⁺_i, the reversal potential even deviated from an E_Na-Ca of 4Na⁺:1Ca²⁺. When eqn (2) was fitted to the data from XIP-sensitive current at 6–40 mM Na⁺_i, the fitted n_x was 4.3 (continuous line). The calculated n_x (lower panel of Fig. 6a) again increased as Na⁺_i was increased. n_x values of the XIP-sensitive current were 3.7 ± 0.3 (n= 4), 4.0 ± 0.2 (n= 4), 4.3 ± 0.2 (n= 4), 4.4 ± 0.2 (n= 3), 5.0 ± 0.9 (n= 3) and 8.7 ± 2.8 (n= 3) at 6, 9, 15, 25, 40 and 100 mM Na⁺_i, respectively.

Figure 6. Ca²⁺_i dependence of the reversal potential.

All patches were pretreated with trypsin. Data were obtained from the 0.2 or 0.8 μM XIP-sensitive current (^) and from the Na⁺_i,Ca²⁺_i-induced current (□). The two dotted lines have the same meanings as in Fig. 5. A, Na⁺_i concentration-reversal potential (upper panel) and -stoichiometry (lower panel) relationships at 0.1 μM Ca²⁺_i. Na⁺₀= 145 mM and Ca²⁺_o= 2 mM. Data were from 6 patches. The continuous line is the fitted function (n_x= 4.3). B, Ca²⁺_i concentration-reversal potential (upper panel) and -stoichiometry (lower panel) relationships. Na⁺₀= 145 mM, Ca²⁺_o= 2 mM and Na⁺_i= 50 mM. Data were from 7 patches. The continuous line is the fitted function (n_x= 4.6).

The above finding necessitated examination of the reversal potential under a variety of ionic conditions. Figure 6B illustrates measurements of the reversal potential over a range of Ca²⁺₁ concentrations in the presence of constant 50 mM Na⁺_i. Although the measurements slightly shifted to positive potentials from an E_Na-Ca of 4Na⁺:1Ca²⁺, the slope of the relationship was compatible with n_x= 4. The value of n_x required to fit the data of the XIP-sensitive current was 4.6 (continuous line), and n_x tended to decrease as Ca²⁺₁ was increased. This result and also results in Figs 3, 5 and 6A may suggest that the stoichiometry is dependent on Na⁺_i and Ca²⁺₁ concentrations. n_x of the XIP-sensitive current was 4.6 ± 0.5 (n= 3), 4.3 ± 0.3 (n= 4) and 3.6 ± 0.6 (n= 4) at 0.1 μM, 1 μM and 1 mM Ca²⁺₁, respectively. The calculated n_x at 10 and 100 μM free Ca²⁺ was remarkably variable, probably because free Ca²⁺ could not be accurately adjusted with EGTA. Therefore, these data were omitted from the plot.

The reversal potential was also measured at various Ca²⁺_o concentrations in the presence of 25 mM Na⁺_i and 1 μM Ca²⁺₁ (Fig. 7a) and at various Na⁺₀ concentrations in the presence of 9 mM Na⁺_i and 1 μM Ca²⁺₁ (Fig. 7B). n_x fitted to data from the XIP-sensitive current was 4.2 (continuous line in Fig. 7a) and 4.3 (continuous line in Fig. 7B), respectively. It is notable that the deviation of n_x from the theoretical E_Na-Ca of 4Na⁺:1Ca²⁺ exchange was small in these experiments. These results may support a fixed stoichiometry of 4Na⁺:1Ca²⁺.

Figure 7. Na⁺₀ and Ca²⁺_o concentration dependencies of the reversal potential.

A, Ca²⁺_o concentration-reversal potential (upper panel) and -stoichiometry (lower panel) relationships. Na⁺₀= 145 mM, Na⁺_i= 25 mM and Ca²⁺_i= 1 μM. The fitted n_x is 4.2 (continuous line). Data were from 17 patches. B, Na⁺₀ concentration-reversal potential (upper panel) and -stoichiometry (lower panel) relationships. Ca²⁺_o= 2 mM, Na⁺_i= 9 mM and Ca²⁺_i= 1 μM. The fitted n_x is 4.3 (continuous line). Data were from 24 patches. All the data were obtained from the 0.2 μM XIP-sensitive current (^) and from the Na⁺_i,Ca²⁺_i-induced current (□) in trypsin-treated patches. In each case the two dotted lines have the same meanings as in Fig. 5.

The 3Na⁺:1Ca²⁺ exchange was suggested in the giant membrane patch excised from the ‘bleb’ (Matsuoka & Hilgemann, 1992). This method allows complete replacement of the test solutions at the inner side of the membrane as in the present macro patch. However, the measurement of the reversal potential of I_Na-Ca was not as systematic as in the present study and XIP was not used. Therefore, we re-measured the reversal potential of I_Na-Ca in giant membrane patches, which were not pretreated with trypsin (Fig. 8). Indeed the reversal potentials measured at 6 and 9 mM Na⁺_i corresponded well to the 3Na⁺:1Ca²⁺ exchange. However, as Na⁺_i was increased, the reversal potential deviated from the theory of 3Na⁺:1Ca²⁺ exchange in both the XIP-sensitive current (circles) and the Na⁺_i,Ca²⁺₁-induced current (squares). The change in n_x was similar to that in the macro patch (Figs 3 and 5). Close inspection of the data in the previous study (Matsuoka & Hilgemann, 1992) reveals essentially the same deviation of the experimental data at higher ionic concentrations. At Na⁺_i higher than 25 mM, the reversal potential of the Na⁺_i,Ca²⁺₁-induced current was more negative than that of the XIP-sensitive current. This might be explained by assuming an outward background current induced by the application of Na⁺_i was superimposed on I_Na-Ca.

Figure 8. Reversal potential of I_Na-Ca in the giant membrane patch from cardiac bleb.

A, Na⁺_i concentration-reversal potential relation. Na⁺₀= 145 mM, Ca²⁺_o= 2 mM and Ca²⁺_i= 1 μM. Data were from the 0.2 μM XIP-sensitive current (^) and from the Na⁺_i,Ca²⁺_i-induced current (□). B, Na⁺_i concentration- stoichiometry relation. In A and B the two dotted lines have the same meanings as in Fig. 5. The number of values at each point was 3–5.

DISCUSSION

The excised inside-out macro patch developed in the present study was smaller in membrane area than the giant membrane patch applied to the bleb membrane of cardiac myocytes (Hilgemann, 1989, 1995). However, this macro patch allowed us to record an I_Na-Ca, which showed essentially the same characteristics as I_Na-Ca in the giant membrane patch (Fig. 1). The use of intact membrane may make this method preferable to that of the giant membrane patch. To examine the stoichiometry of cardiac Na⁺-Ca²⁺ exchange, we measured the reversal potential of I_Na-Ca in a wide range of Na⁺ and Ca²⁺ on both sides of the patch membrane. I_Na-Ca was recorded as either the XIP-sensitive current or the current induced by applying Na⁺_i and Ca²⁺₁. Surprisingly to us, the reversal potential of I_Na-Ca thus isolated suggested 4Na⁺:1Ca²⁺ rather than 3Na⁺:1Ca²⁺ exchange, provided that n_x is constant. On the other hand, the calculated n_x had a tendency to change depending on Na⁺_i and Ca²⁺₁ concentrations. Thus, we find it necessary to reconsider the fixed stoichiometry of 3Na⁺:1Ca²⁺ described in previous studies (Pitts, 1979; Wakabayashi & Goshima, 1981; Reeves & Hale, 1984; Axelsen & Bridge, 1985; Sheu & Fozzard, 1985; Ehara et al. 1989; Crespo et al. 1990; Noma et al. 1991; Matsuoka & Hilgemann, 1992).

In the whole-cell clamp experiment, intracellular ion concentrations were not completely controlled by ion diffusion from the attached pipette, as suggested by the reversal potential change during the activation of I_Na-Ca (Ehara et al. 1989; Noma et al. 1991). In fact, the previous results (Ehara et al. 1989; Crespo et al. 1990; Noma et al. 1991) can be explained by a 4Na⁺:1Ca²⁺ exchange, provided that actual intracellular Na⁺ and Ca²⁺ concentrations were slightly higher and lower, respectively, than the pipette solution. A similar ion concentration change might occur in flux measurements (Pitts, 1979; Wakabayashi & Goshima, 1981; Reeves & Hale, 1984). Crespo et al. (1990) demonstrated that the intracellular Ca²⁺ concentration was consistent with a 3Na⁺:1Ca²⁺ exchange stoichiometry. However, their conclusion is valid under the condition that the exchanger is the only Ca²⁺ pathway across the sarcolemma. Other Ca²⁺ pathways, such as sarcolemmal Ca²⁺-ATPase, might contribute to the control of intracellular Ca²⁺ more than they estimated, as recently demonstrated in rat ventricular cells by Choi & Eisner (1999).

Provided that Na⁺ and Ca²⁺ concentrations effective for the exchanger are equal to those in the bulk solutions, and that the stoichiometry is not fixed, the present experimental data suggest that n_x increases with increasing Na⁺_i (Figs 3, 5 and 6A) or with decreasing Ca²⁺₁ (Fig. 6B). At 1 μM Ca²⁺₁, n_x was ∼4 (3.6-4.1) at 9–50 mM Na⁺_i. But n_x tended to decrease to ∼3 at 6 mM Na⁺_i, and increase to more than 4 at 100 mM Na⁺_i. A small amount of contamination of background current might significantly affect the estimation of stoichiometry at lower Na⁺_i concentrations, where the difference in E_Na-Ca between 3Na⁺:1Ca²⁺ and 4Na⁺:1Ca²⁺ exchange becomes smaller (Figs 3 and 5). However, at 0.1 μM Ca²⁺₁ (Fig. 6a), the theoretical difference was larger, and the Na⁺_i-dependent increase of n_x was more obvious. In the presence of either 9 or 25 mM Na⁺_i and various Na⁺₀ or Ca²⁺_o concentrations (Fig. 7), the fitted n_x was ∼4 (4.2 and 4.3) and was in agreement with the values at corresponding Na⁺_i concentrations in the Na⁺_i-n_x relation (Figs 3 and 5). At 50 mM Na⁺_i and various Ca²⁺₁ concentrations (Fig. 6B), the fitted n_x was 4.6 and larger than the value at either 9 or 25 mM Na⁺_i (Fig. 7). These findings also support the Na⁺_i dependence of stoichiometry. n_x with constant 0.1 μM Ca²⁺₁ (Fig. 6a) tended to be larger at individual Na⁺_i concentrations than the corresponding value obtained with 1 μM Ca²⁺₁ (Figs 3 and 5). These findings suggest that n_x is dependent on Na⁺_i and Ca²⁺₁, and are consistent with the suggestion by Mullins & Brinley (1975) that stoichiometry is variable depending on the Ca²⁺₁ concentration. If the stoichiometry is dependent on Na⁺_i and Ca²⁺₁, the 3Na⁺:1Ca²⁺ exchange, which the previous studies suggested, may still be applicable at Na⁺_i less than 6 mM and Ca²⁺₁ more than 1 μM.

The variable stoichiometry may imply that the Na⁺-Ca²⁺ exchange consists of two reactions, i.e. 3Na⁺:1Ca²⁺ and 4 or more Na⁺: 1Ca²⁺ exchange reactions. The latter reaction would become dominant as Na⁺_i was increased. Alternatively the exchanger may change its structure of ion binding site as Na⁺_i was increased, so that the affinity for Na⁺_i decreases. The mechanism of the affinity change is unknown. However, the Na⁺-dependent inactivation is not related to this process, because elimination of the Na⁺-dependent inactivation by trypsin did not significantly change the reversal potentials. At present, no biochemical and structural information supporting the variable stoichiometry is available. However, the idea of variable stoichiometry has been proposed in other transporters, such as Na⁺,K⁺-ATPase (Candia & Cook, 1986; Blostein & Polvani, 1991) and sarcoplasmic reticulum Ca²⁺ pump (Johnson et al. 1985). Further studies are needed to clarify the transport mechanism of the Na⁺-Ca²⁺ exchanger.

The Na⁺_i-dependent change in stoichiometry may be beneficial for Ca²⁺ extrusion when intracellular Na⁺ increases. The increase of Na⁺_i moves E_Na-Ca to negative potentials so that it decreases Ca²⁺ extrusion. However, if the stoichiometry changes from 3Na⁺:1Ca²⁺ to 4Na⁺:1Ca²⁺, the negative shift of E_Na-Ca would be decreased. As a result, the decrease of Ca²⁺ extrusion would be attenuated.

If the stoichiometry is different from 3Na⁺:1Ca²⁺ under physiological conditions, Ca²⁺ movement through the sarcolemmal Na⁺-Ca²⁺ exchange must be re-estimated. The exchanger with 4Na⁺:1Ca²⁺ stoichiometry may carry 0.5Ca²⁺ per charge of I_Na-Ca. This value is half of that with 3Na⁺:1Ca²⁺ exchange. However, the driving force for Ca²⁺ extrusion is larger in the 4Na⁺:1Ca²⁺ exchange than that for 3Na⁺:1Ca²⁺ exchange. At resting potential (-80 mV, 10 mM Na⁺_i, 145 mM Na⁺₀, 2 mM Ca²⁺_o), if Ca²⁺₁ is equilibrated only with the exchanger, Ca²⁺₁ would be 0.11 nM. This value is obviously too low. The Ca²⁺ regulation mechanism would play an important role in preventing the extreme decrease of Ca²⁺₁. Thus, the exchange inactivates at lower Ca²⁺₁ concentrations.

Contamination of the background current

If the genuine stoichiometry is 3Na⁺:1Ca²⁺, deviation of the reversal potential from theoretical E_Na-Ca might be artificially generated by contamination by background current. To test this possibility, background Na⁺ conductance was examined under conditions in which the exchanger was suppressed by removal of regulatory Ca²⁺₁ (‘d – c’ in Fig. 1B) and by removal of both Na⁺₀ and Ca²⁺_o (Fig. 4C). In both experiments, background Na⁺-sensitive conductance was small. Theoretically, a positive shift of the reversal potential of the Na⁺_i,Ca²⁺₁-inducd current (I_Na-Ca) would be caused by a contamination of inward background current. This is possible if the Li⁺ conductance of the background current system was larger than the Na⁺ conductance. When Li⁺_i was replaced by Na⁺_i, outward background current would decrease and the reversal potential of the difference current (Na⁺_i,Ca²⁺₁-inducd current) would shift positively. However, in the experiment shown in Fig. 1B, the application of 100 mM Na⁺_i, which was the largest Na⁺ concentration jump in the present study, induced no inward current (‘d – c’).

An alternative mechanism for the contaminating background current would be a conductance activated by the application of Na⁺_i or Ca²⁺₁, such as Na⁺_i-activated K⁺ current (Kameyama et al. 1984) and Ca²⁺₁-activated Cl⁻ current (Zygmunt & Gibbons, 1991). The former is unlikely because no K⁺ was added in the test solutions. The latter should reverse at the equilibrium potential of Cl⁻, i.e. ∼+15 mV in the present study (Cl⁻_o= 34 mM and Cl⁻_i= 60 mM), when activated. However, the application of 1 μM Ca²⁺₁ failed to induce such a current (‘a – c’ in Fig. 1B).

To exclude contamination of background current in the XIP-sensitive current, the effect of 0.2 μM XIP on the background current was tested under conditions in which I_Na-Ca was suppressed by removal of both Na⁺₀ and Na⁺_i (‘a – c’ in Fig. 1C) and by removal of regulatory Ca²⁺ (Fig. 2C). Indeed, the background XIP-sensitive current was small in both cases. It might be argued that this experimental evidence does not necessarily exclude the possibility of contaminating background current, because the XIP-sensitive background current might be induced only under the ionic conditions for measuring I_Na-Ca; i.e. in the presence of Na⁺₀, Na⁺_i and Ca²⁺₁. However, the above considerations make these Na⁺- or Ca²⁺-mediated conductances unlikely under the present experimental conditions.

Time-dependent change of the background conductance would also affect our results. If a background non-selective conductance increased during the activation of I_Na-Ca, the reversal potential of I_Na-Ca, which was obtained as the difference before and during the I_Na-Ca activation, would shift towards zero potential. However, in the majority of patches, the background current did not significantly change before and after the activation of I_Na-Ca, as demonstrated in both the XIP-sensitive (Fig. 2a) and the Na⁺_i,Ca²⁺₁-induced I_Na-Ca (Fig. 4a).

Taken together, the foregoing arguments indicate that the contamination of background current in both protocols for the isolation of I_Na-Ca is not large enough to account for 3Na⁺:1Ca²⁺ exchange.

Ion accumulation and depletion during I_Na-Ca activation

An alternative source of experimental error is that ion concentrations at the ion-binding sites of the exchange molecule were not exactly the same as those of the bulk solutions. Na⁺ and Ca²⁺ might accumulate or deplete in a narrow space between the membrane and the glass surface, which was generated by the invagination of the patch membrane into the electrode tip (‘omega-shape’ formation, Sakmann & Neher, 1995). The finding that I_Na-Ca after trypsin treatment did not decay with time (Figs 1B and C, and 4A) does not necessarily exclude the possibility of ion accumulation and depletion, which might have saturated in this narrow cleft within the activation phase of I_Na-Ca. The ion flux via both the exchanger and the leak conductance works to decrease the concentration gradient across a part of the patch membrane facing the narrow cleft as long as the membrane potential was clamped at 0 mV. Thus the reversal potential of I_Na-Ca, which was generated by a fractional population of the exchanger facing the narrow cleft, might artificially shift towards zero potential and result in a less steep relationship between the reversal potential and the ion concentrations even if the stoichiometry is fixed to 3Na⁺:1Ca²⁺. However, the relatively high concentrations in the extracellular solution (Na⁺₀= 145 mM, Ca²⁺_o= 2 mM) probably make this effect smaller. Furthermore, it should be noted that the slope of the reversal potential-ion concentration relation was well explained with a fixed 4Na⁺:1Ca²⁺ exchange when extracellular ion concentrations were varied (Fig. 7). However, we could not completely exclude the rapid concentration change in this narrow cleft on activating I_Na-Ca, since no appropriate method to examine this possibility is available at the present time.

The ‘omega-shape’ formation of patch membrane might cause significant delay of ion diffusion over the distance from the bulk solution to the patch membrane. Na⁺ and Ca²⁺ would deplete and accumulate, respectively, under the patch membrane when the outward I_Na-Ca was activated, if the ion flux through the exchanger was significantly larger compared to the ion diffusion flux. This ion accumulation and depletion would also make the reversal potential shift towards zero potential. To address this problem, the distance between the pipette tip and the patch membrane, and the ion flux through both the exchanger and pipette diffusion were evaluated by analysing the time course of the I_Na-Ca activation and attenuation induced by the ion concentration jump.

In a trypsin-treated patch, 50 mM Na⁺_i-induced I_Na-Ca reached steady state within 30 ms (Fig. 9a). Half-maximal time (t_1/2) for the activation was 14.3 ms (10.4 ± 5.1 ms, four patches). The 50 mM Na⁺_i-induced current was attenuated by an additional jump of Ca²⁺₁ from 0 to 2 mM. However, there was a substantial delay of the inhibition (Fig. 9B): t_1/2 was 108.6 ms (73.2 ± 42.7 ms, four patches). These time courses presumably reflect Na⁺ and Ca²⁺ diffusion from the electrode tip to the patch membrane, since the binding of these ions to the carrier should be much faster. The timing of solution change at the electrode tip was obtained by measuring current response to junction potential change. The patch membrane was disrupted after recording I_Na-Ca, and the bath solution was changed from the control Tyrode solution to 20 % diluted Tyrode solution (Fig. 9C). Time 0 in Fig. 9a and B is the time when the current response began.

Figure 9. Simulation of ion flux in the inside-out patch.

A, activation of outward I_Na-Ca. The pipette solution contains 0 mM Na⁺₀ and 5 mM Ca²⁺_o. The patch was pretreated with trypsin. Na⁺_i (50 mM)-induced I_Na-Ca and simulated I_Na-Ca with the patch distance of 4, 6, 8 and 10 μm (smooth curves from left to right) are superimposed. B, suppression of outward I_Na-Ca by Ca²⁺_i. Ca²⁺ (2 mM: 10 mM EGTA + 12 mM CaCl₂) inhibited the 50 mM Na⁺-induced I_Na-Ca. Simulated I_Na-Ca with the patch distance of 4, 6, 8 and 10 μm (smooth curves from left to right) are also superimposed. C, open-tip response. Current response to bath solution change from the control Tyrode solution to 20 % diluted Tyrode solution was recorded after disruption of the patch membrane. Data from A, B and C were from the same pipette. D, simulation of I_Na-Ca, and Na⁺ and Ca²⁺ concentrations in a compartment just under the membrane. Na⁺ (50 mM) and Ca²⁺ (1 μM) were added at the bulk cytoplasmic space at time 0. I_Na-Ca had an I_max of 10 pA (upper panel). Na⁺ simulation in the middle panel had I_max values of 10 pA, 10 nA and 10 μA, and the results are superimposed (a, b and c). Ca²⁺ simulation in the bottom panel had I_max values of 10 pA (a), 10 nA (b) and 10 μA (c).

The ion diffusion to the patch membrane was simulated using a similar model to the one by Qin et al. (1991). A space between the patch membrane and the tip was divided into 100 compartments along the axis of the pipette, and the diffusion of ions between the adjacent compartments was integrated. Pipette tip diameter was 5 μm and the patch distance was changed from 4 to 10 μm. Diffusion coefficients of Na⁺ and Ca²⁺ were 1.33 × 10⁻⁹ and 0.79 × 10⁻⁹ m² s⁻¹, respectively (Hille, 1992). The diffusion coefficient of both EGTA and Ca²⁺-bound EGTA was 3 × 10⁻¹⁰ m² s⁻¹, and Ca²⁺ binding and unbinding rate constants of EGTA were 2 × 10⁶ M⁻¹ s⁻¹ and 0.4 s⁻¹, respectively (Hellam & Podolsky, 1969). I_Na-Ca was calculated as follows:

where Na and Ca are Na⁺ and Ca²⁺ concentrations in a compartment adjacent to the membrane, K_Na and K_Ca are dissociation constants of Na⁺ and Ca²⁺, and 18 mM and 0.008 mM, respectively. The maximum current, I_max was set to 7–10 pA to obtain the same amplitude as the experimental value. Na⁺ and Ca²⁺ fluxes through the exchange current were calculated with a 3Na⁺:1Ca²⁺:1charge relation. Simulated I_Na-Ca is superimposed on the current traces in Fig. 9a and B with the patch distance of 4, 6, 8 and 10 μm (from left to right). In this model, the retarded diffusion of Ca²⁺ compared to Na⁺ is due to Ca²⁺ binding to 10 mM EGTA. The slightly shallow slope of I_Na-Ca on the activation and attenuation compared to the simulation might be due to distribution of the exchanger at various distances from the electrode tip on the omega-shaped membrane. The simulation suggests that the patch distance was approximately 8 μm. In a total of four patches, the estimated distance was 4–8 μm.

With the foregoing model, we calculated the ion concentrations just under the membrane upon application of both Na⁺_i and Ca²⁺₁ (Fig. 9D). The patch distance was 8 μm. Bulk Na⁺_i and Ca²⁺₁ were changed from 0 mM and 0 μM (+10 mM EGTA) to 50 mM and 1 μM, respectively, at time 0. The upper trace is a simulated I_Na-Ca (I_max= 10 pA). The Na⁺ concentration was simulated with different amplitudes of I_Na-Ca (I_max= 10 pA, 10 nA and 10 μA). The three results are superimposed in the middle panel (a, b and c). In all cases, the Na⁺ concentration reached steady state within 30 ms. The Na⁺ concentration after the 20 s activation was 50.00, 50.00 and 49.96 mM, respectively. The Ca²⁺ concentration with the different amplitudes of I_Na-Ca is shown in the bottom panel. The peak Ca²⁺ concentration was reached within 600 ms. The steady-state Ca²⁺ concentration was 1.000, 1.001 and 2.014 μM, respectively. Significant Ca²⁺ accumulation occurred only when the amplitude of I_Na-Ca was more than several microamps, this amplitude being unrealistic compared to the usual experimental amplitudes (1–15 pA). Furthermore, even if the patch distance was set to be twice as large (16 μm), the steady-state ion concentrations were the same as those in the bulk solution (I_max= 10 pA). Therefore, the possibility of ion accumulation and depletion on the cytoplasmic side of the patch membrane is unlikely in the macro patch. An error due to the diffusion delay is also unlikely, because the I–V relation was measured 10–12 s after the activation of I_Na-Ca, which is enough for the ion diffusion (Figs 2 and 4).

If the ‘ion well’ connected to the cytoplasmic Na⁺ binding site (Läuger, 1987) exists, it generates a Na⁺ gradient between the cytoplasmic Na⁺ binding site and bulk cytoplasmic solution. The Na⁺ concentration at the bottom of the ‘ion well’ would be lower than that of the cytoplasmic solution when the membrane was hyperpolarized. However, as far as Na⁺_i and Ca²⁺₁ share a common binding site in the same ‘ion well’, the concentration gradient for Ca²⁺ should balance the effect of the Na⁺ gradient and the reversal potential should follow E_Na-Ca determined by the bulk solutions.