Cytoplasmic Na⁺-dependent modulation of mitochondrial Ca²⁺ via electrogenic mitochondrial Na⁺–Ca²⁺ exchange

Abstract

To clarify the role of mitochondrial Na⁺–Ca²⁺ exchange (NCX_mito) in regulating mitochondrial Ca²⁺ (Ca²⁺_mito) concentration at intact and depolarized mitochondrial membrane potential (ΔΨ_mito), we measured Ca²⁺_mito and ΔΨ_mito using fluorescence probes Rhod-2 and TMRE, respectively, in the permeabilized rat ventricular cells. Applying 300 nm cytoplasmic Ca²⁺ (Ca²⁺_c) increased Ca²⁺_mito and this increase was attenuated by cytoplasmic Na⁺ (Na⁺_c) with an IC₅₀ of 2.4 mm. To the contrary, when ΔΨ_mito was depolarized by FCCP, a mitochondrial uncoupler, Na⁺_c enhanced the Ca²⁺_c-induced increase in Ca²⁺_mito with an EC₅₀ of about 4 mm. This increase was not significantly affected by ruthenium red or cyclosporin A. The inhibition of NCX_mito by CGP-37157 further increased Ca²⁺_mito when ΔΨ_mito was intact, while it suppressed the Ca²⁺_mito increase when ΔΨ_mito was depolarized, suggesting that ΔΨ_mito depolarization changed the exchange mode from forward to reverse. Furthermore, ΔΨ_mito depolarization significantly reduced the Ca²⁺_mito decrease via forward mode, and augmented the Ca²⁺_mito increase via reverse mode. When the respiratory chain was attenuated, the induction of the reverse mode of NCX_mito hyperpolarized ΔΨ_mito, while ΔΨ_mito depolarized upon inducing the forward mode of NCX_mito. Both changes in ΔΨ_mito were remarkably inhibited by CGP-37157. The above experimental data indicated that NCX_mito is voltage dependent and electrogenic. This notion was supported theoretically by computer simulation studies with an NCX_mito model constructed based on present and previous studies, presuming a consecutive and electrogenic Na⁺–Ca²⁺ exchange and a depolarization-induced increase in Na⁺ flux. It is concluded that Ca²⁺_mito concentration is dynamically modulated by Na⁺_c and ΔΨ_mito via electrogenic NCX_mito.

Mitochondria in the cardiac myocyte have been recognized as Ca²⁺ stores, in addition to their role as energy providers that synthesise a large proportion of ATP required for maintaining heart function. Mitochondrial Ca²⁺ (Ca²⁺_mito) activates matrix dehydrogenases (pyruvate dehydrogenase, isocitrate dehydrogenase and α-ketoglutarate dehydrogenase) (McCormack et al. 1990) and may also activate F₀/F₁-ATPase (Territo et al. 2000). The overall effect of elevated Ca²⁺_mito may be the up-regulation of oxidative phosphorylation and the acceleration of ATP synthesis (McCormack et al. 1990; Balaban, 2002; Matsuoka et al. 2004; Jo et al. 2006). On the other hand, the excessive rise in Ca²⁺_mito triggers the mitochondrial permeability transition pore (PTP) resulting in pathological cell injury and death (Weiss et al. 2003; Brookes et al. 2004; Hajnoczky et al. 2006). Therefore, the Ca²⁺_mito concentration must be kept within the proper range to maintain physiological mitochondrial function.

In cardiac mitochondria, Ca²⁺ uptake and removal is mainly mediated via the mitochondrial Ca²⁺ uniporter and the Na⁺–Ca²⁺ exchange (NCX_mito) (Gunter & Pfeiffer, 1990; Bernardi, 1999; Brookes et al. 2004), respectively. The mitochondria Ca²⁺ uniporter is driven by the mitochondrial membrane potential (ΔΨ_mito) (Rottenberg & Scarpa, 1974; O'Rourke, 2007) and a recent patch clamp study demonstrated that it is an ion channel highly selective to Ca²⁺ (Kirichok et al. 2004). On the other hand, the dependence of NCX_mito on ΔΨ_mito has been controversial and an electrophysiological approach for measuring current mediated via NCX_mito has not succeeded.

NCX_mito was first discovered by Carafoli et al. (1974). Electrogenic or voltage-dependent Na⁺–Ca²⁺ exchange was suggested by their later studies demonstrating the higher Hill coefficient (n_H) for Na⁺_c (∼3) and the attenuation of Na⁺-dependent Ca²⁺ efflux by ΔΨ_mito depolarization induced by an uncoupler (Crompton et al. 1976, 1977). A later study by Jung et al. (1995) further supported this notion by measuring matrix pH and Ca²⁺ with fluorescence probes. To the contrary, Affolter & Carafoli (1980) demonstrated that ΔΨ_mito did not alter when the Ca²⁺ efflux via NCX_mito was induced and suggested NCX_mito is electroneutral. Brand (1985) also suggested the voltage-independent exchange by demonstrating that Ca²⁺ efflux via NCX_mito was not affected by A23187, which catalyses Ca²⁺–2H⁺ exchange. Wingrove & Gunter (1986) supported this idea by in-depth measurements of the Na⁺_c and Ca²⁺_c dependences (n_H= 2.0 and 1.0, respectively). Therefore, it is a prerequisite to clarify whether NCX_mito depends on ΔΨ_mito in order to quantitatively understand the mechanisms regulating Ca²⁺_mito concentration.

ΔΨ_mito depolarizes under various pathological conditions such as ischaemia/reperfusion (see reviews, for example, Weiss et al. 2003). Under such circumstance, cytoplasmic Na⁺ (Na⁺_c) as well as Ca²⁺ (Ca²⁺_c) concentrations increase (Pierce & Czubryt, 1995; Piper et al. 2003). While the increase in Ca²⁺_c concentration leads to the accumulation of Ca²⁺ in mitochondria, only limited information is available about how Na⁺_c affects Ca²⁺_mito concentration and NCX_mito activity when ΔΨ_mito is depolarized (Smets et al. 2004; Saotome et al. 2005). Saotome et al. (2005) recently reported a slight decrease in the affinity for Na⁺_c of the Ca²⁺ efflux via NCX_mito when ΔΨ_mito was dissipated, which is in contrast to the larger effect found by Crompton et al. (1977).

In the present study, we aimed to clarify how the changes in Na⁺_c concentration and ΔΨ_mito modulate the Ca²⁺_mito concentration of cardiac mitochondria, and how NCX_mito is involved in the modulation. Our experimental and simulation studies indicated that NCX_mito is voltage dependent and electrogenic. Because of this feature, NCX_mito dynamically changes the exchange mode (forward or reverse) and modulates the Ca²⁺_mito concentration in a manner dependent on Na⁺_c and ΔΨ_mito.

Methods

Cell isolation

Ventricular myocytes were obtained from male Wister rats (body wt, 250–350 g) in a similar manner to recent articles (Lin et al. 2006; Shioya, 2007). This protocol was approved by the Animal Research Committee in the Graduate School of Medicine, Kyoto University. In brief, Wister rats were anaesthetized by intraperitoneal administration of pentobarbitone sodium (> 0.1 mg g⁻¹). The heart was quickly excised after thoracotomy and mounted on a Langendorff apparatus to perfuse through the coronary artery with a Ca²⁺-free cell isolation buffer (CIB) at 37°C. After 8–10 min perfusion to clear the blood and to stop the heart beating, the CIB solution containing 0.2 mm Ca²⁺, collagenase (Type II, 1 mg ml⁻¹ Worthington), protease (Type XIV, 0.05 mg ml⁻¹ Sigma-Aldrich) and trypsin (Type I, 0.05 mg ml⁻¹ Sigma-Aldrich) was perfused for 10–15 min. The left ventricle was then cut into small pieces and was shaken gently for 5–10 min in the CIB solution, to which 0.3 mm Ca²⁺ and 1 mg ml⁻¹ bovine serum albumin (Sigma-Aldrich) were added. Finally, isolated myocytes were transferred to the CIB solution containing 1 mm Ca²⁺ and then stored in a modified DMEM solution.

Solutions and drugs

The CIB solutions contained (mm): 130 NaCl, 5.4 KCl, 0.5 MgCl₂, 0.33 NaH₂PO₄, 22 glucose, 1 l-gutamine, 0.1 EGTA, 25 Hepes, and 0.01 units ml⁻¹ insulin (pH 7.4 with NaOH). The modified DMEM solution was prepared by adding 20 mm NaCl, 25 mm Hepes to DMEM (without NaHCO₃, MP Biomedicals) (pH 7.4 with NaOH). The bath solution contained (mm): 118 KCl, 10 EGTA, 10 Hepes, 3 K₂ATP, 2 potassium pyruvate, 1 K₂HPO₄, 2 succinic acid, 0.1 K-ADP, 2 malic acid, and 2 potassium glutamic acid (pH 7.2 with KOH). Free Mg²⁺ and Ca²⁺ concentrations, which were calculated by WinMAXC software (Patton et al. 2004), were adjusted to be 1 mm and 300–800 nm, respectively, by adding 4.02–4.99 mm MgCl₂ and 6.65–8.41 mm CaCl₂. Na⁺_c concentration was changed from 0 to 50 mm by replacing KCl with equimolar NaCl.

Ruthenium red (an inhibitor of the mitochondrial Ca²⁺ uniportor), cyclosporin A (an inhibitor of PTP), antimycin A (an inhibitor of complex III of the mitochondrial electron transport chain), oligomycin (an inhibitor of F₀/F₁-ATPase), NS1619 (an opener of mitochondrial Ca²⁺-activated K⁺ channel), and carbonyl cyanide 4-(trifluoromethoxy) phenylhydrazone (FCCP, an ionopore of protons) were purchased from Sigma-Aldrich, and CGP-37157 (an inhibitor of NCX_mito) was from Tocris Cookson Inc. SM20550 (an inhibitor of mitochondrial Na⁺–H⁺ exchange) was a kind gift from Dainippon Sumitomo Phama. CGP-37157 (20 mm), cyclosporin A (1 mm), antimycin A (10 mm), oligomycin (10 mm), FCCP (1 mm) and NS1619 (10 mm) were dissolved in DMSO as stock solutions. The final concentration of DMSO in the bath solution was 0.01–0.1%. Cyclosporin A (0.1 μm) was added to the bath solution when ΔΨ_mito was depolarized or mitochondria were preloaded with a high Ca²⁺_c (600 or 800 nm) unless otherwise stated. 2,3-butaedione monoxine (20 mm; BDM; Sigma-Aldrich) was added to the bath solution to reduce contraction artifacts when applying a high Ca²⁺_c concentration (600 or 800 nm).

The bath solution was changed within 2–3 s by using a perfusion system (ValveLink8, AutoMate Scientifi Inc., USA).

Measurement of Ca²⁺_mito and ΔΨ_mito in permeabilized myocytes

The myocytes were loaded with TMRE (an indicator for the mitochondrial membrane potential; Molecular Probes, Eugene, OR, USA), a permeant AM-ester form of Rhod-2 (a cationic indicator for Ca²⁺; Molecular Probes), or MitoTracker Green (a mitochondria-specific dye; Molecular Probes). To remove the fluorescence dyes from cytoplasm and to facilitate access to mitochondria, sarcolemmal membrane was permeabilized by applying a Ca²⁺-free bath solution containing saponin (0.1 mg ml⁻¹) for 1 min, according to previous studies (Fry et al. 1984; Sedova & Blatter, 2000; Saotome et al. 2005). Fluorescence images were obtained at 36–37°C by using a laser scanning confocal microscope (FV500 Olympus, Japan) with a ×40 water-immersion objective lens. All the images were recorded by a single scan every 10 or 20 s, except for those in Fig. 1 (an average of five consecutive scans). Myocytes loaded with TMRE or Rhod-2 were excited at 543 nm, and the fluorescence images at > 560 nm (TMRE) or 560–600 nm (Rhod-2) were obtained. When co-loaded with MitoTracker Green (excitation; 488 nm) and Rhod-2 (excitation: 543 nm), fluorescence images at 505–525 nm and 560–600 nm, respectively, were sequentially obtained.

Figure 1. Measurement of Ca²⁺_mito and ΔΨ_mito.

A, confocal images of a myocyte loaded with TMRE before (a) and after (b) saponin treatment, and 4 min after applying 1 μm FCCP and 2 μm oligomycin (c). B, time course of TMRE fluorescence change with (•) or without (○) applying 1 μm FCCP and 2 μm oligomycin (FCCP + Olig). C, confocal images of a myocyte co-loaded with Rhod-2 and MitoTracker Green after saponin treatment. Rhod-2 images before (a) and 5 min after (b) applying 600 nm Ca²⁺, MitoTracker Green image 5 min after applying 600 nm Ca²⁺ (c), and a merged image of Rhod-2 and MitoTracker Green image (d). D, time course of Rhod-2 fluorescence change. In A and C, the colour scale of fluorescence intensity is denoted on the right side (arbitrary units) and a bar indicates 5 μm in each image. In B and D, the TMRE and Rhod-2 fluorescences were normalized to the first one after the saponin treatment.

The fluorescence intensity (F) of TMRE or Rhod-2 within the cell area was obtained by subtracting a background component as follows:

where F_cell and F_background are an average of fluorescence from the entire cell area and the extracellular area, respectively.

For the measurement of ΔΨ_mito, the myocytes were loaded with 25 nm TMRE for 10 min at room temperature. To reduce TMRE fluorescence loss, 12.5 nm TMRE was added to the bath solution. Figure 1A demonstrates TMRE fluorescence images before (a) and after (b) the saponin treatment (0 Ca²⁺). The fluorescence pattern was similar to that of MitoTracker Green in Fig. 1Cc and fluorescence in the extracellular area was almost negligible (3–4% of cellular area). The saponin treatment decreased the TMRE fluorescence about by 20%, but did not affect the mitochondrial alignment. Most of the remaining fluorescence reflects ΔΨ_mito, whose value is about −150 to −180 mV under the normal condition (Nicholls & Budd, 2000). Applying 1 μm FCCP and 2 μm oligomycin abolished the TMRE fluorescence (Fig. 1Ac; 3 min after), indicating depolarization of ΔΨ_mito. The TMRE fluorescence was stable over 10 min as shown in Fig. 1B (open circles). In the present study, ΔΨ_mito was depolarized with a variety of procedures illustrated by an example in Fig. 1B (filled circles; 1 μm FCCP and 2 μm oligomycin (FCCP + Olig.)) and change of ΔΨ_mito (mV) was estimated according to a study by O'Reilly et al. (2003) as follows:

where F₀ and F₁ are an average fluorescence intensity of TMRE in the cell area, from which the background fluorescence was subtracted, before and after the procedures, respectively. Table 1 summarizes the change of ΔΨ_mito and the half-time to steady state (t_1/2).

Table 1.

Summary of ΔΨ_mito change

	Estimated change in ΔΨmito (mV)	t1/2 (s)
Sub(−)	78 ± 25	132 ± 34 (n = 6)
FCCP	104 ± 4	30 ± 4 (n = 10)
FCCP + Olig	101 ± 4	36 ± 10 (n = 7)
Anti + Olig	104 ± 3	87 ± 26 (n = 7)
NS1619	75 ± 21	282 ± 91 (n = 7)
NS1619 + Sub(−)	97 ± 11	154 ± 47 (n = 10)

Sub(−); removal of mitochondrial substrates (potassium pyruvate, K₂HPO₄, succinic acid, K-ADP, malic acid, and potassium glutamic acid); FCCP; 1 μm FCCP; FCCP + Olig; 1 μm FCCP and 2 μm oligomycin; Anti + Olig; 10 μm antimycin A and 2 μm oligomycin; NS1619; 10 μm NS1619; and NS1619 + Sub(−); 10 μm NS1619 without the mitochondrial substrates.

For the measurement of Ca²⁺_mito, rat myocytes were loaded with 5 μm Rhod-2 for 60 min at 4°C as described in previous studies (Trolinger et al. 1997; Jo et al. 2006). Rhod-2 was located also in the cytoplasm after the loading (data not shown), but the saponin treatment greatly washed it out (Fig. 1Ca). Localization of Rhod-2 in mitochondria was confirmed in the myocytes by further loading of 200 nm MitoTracker Green for 30 min at 37°C. The Rhod-2 fluorescent was slightly visible after the saponin treatment (Fig. 1Ca; 0 nm Ca²⁺), while the fluorescence from unloaded control myocytes was not detectable (not shown). Applying Ca²⁺ remarkably but locally increased the fluorescence intensity (Fig. 1Cb; 5 min after applying 600 nm Ca²⁺). Figure 1Cc is an image of MitoTracker Green from the same cell and a merged image of panel b and c is shown in panel d, indicating that fluorescences of Rhod-2 and MitoTracker Green were largely co-localized. On average, 96 ± 3% (n = 5) of the MitoTracker Green fluorescence co-localized with the Rhod-2 fluorescence. Therefore we concluded that the Rhod-2 almost exclusively monitors Ca²⁺ in mitochondria under the present experimental conditions. The Rhod-2 fluorescence was stable over 10 min and did not show significant photo bleaching as shown in Fig. 1D.

Statistical analysis

Data are presented as mean ± s.d. Statistical analyses were performed by one-factor ANOVA using StatView (SAS Institute Inc.). Multiple and two-group comparisons were performed according to Student–Newman–Keul's method and Student's t test, respectively. P < 0.05 was considered significant.

A computer model of NCX_mito

A computer model of NCX_mito was constructed using Visual Studio 2005 (Microsoft). Details are described in the Appendix.

Results

Na⁺_c dependence of Ca²⁺_mito

Dependence of Ca²⁺_mito concentration on Na⁺_c was first examined at intact ΔΨ_mito in Fig. 2. An increase in Ca²⁺_c from 0 to 300 nm greatly augmented Ca²⁺_mito, which was measured by Rhod-2, in the absence of Na⁺_c (white circles). The rise was 9.2 ± 2.8 times on average and it took about 10 min to reach steady state. The rise of Rhod-2 fluorescence was almost completely inhibited by 7 μm ruthenium red (grey triangles), an inhibitor of the mitochondrial Ca²⁺ uniporter (IC₅₀= 9 nm; Kirichok et al. 2004), supporting the previous notion that the Ca²⁺ uniporter is the dominant mechanism of Ca²⁺_mito influx (Gunter & Pfeiffer, 1990; Bernardi, 1999). The maximum Ca²⁺_mito level decreased with increasing Na⁺_c concentration. Averages of the maximum increase were 5.5, 3.4, 2.3 and 1.4 times in the presence of 2, 6, 20 and 50 mm Na⁺_c, respectively. The Na⁺_c-dependent decrease is most probably due to Ca²⁺_mito removal via NCX_mito. Fitting a Hill equation to the maximum Rhod-2 fluorescence levels yielded a half-inhibitory concentration (IC₅₀) of 2.4 mm Na⁺ (Fig. 2B).

Figure 2. Effects of Na⁺_c on Ca²⁺_mito.

A, Ca²⁺_c-induced Ca²⁺_mito increase at intact ΔΨ_mito. Ca²⁺_c (300 nm) was added in the presence of various concentrations of Na⁺_c as denoted at the top and right of graph. Ruthenium red (RR; 7 μm) was added to the Na⁺-free solution (grey triangles, n = 10). The Rhod-2 fluorescence was normalized to the one before applying Ca²⁺_c. B, Na⁺_c dependence of Ca²⁺_mito. The maximum increases of Rhod-2 fluoresce in A (9.2 ± 2.8, 5.5 ± 1.6, 3.4 ± 0.7, 2.3 ± 0.7 and 1.4 ± 0.2 times, in the presence of 0, 2, 6, 20 and 50 mm Na⁺_c, respectively) were plotted against Na⁺_c concentration. The curve is a fitted equation: 1.0 + 8.2/(1 + (Na⁺_c/2.4)^0.9). n = 4–23. C, Ca²⁺_c-induced Ca²⁺_mito increase at depolarized ΔΨ_mito. The same protocol as in A was repeated in the presence of 1 μm FCCP. RR (7 μm) was added to the solution containing 20 mm Na⁺ (grey triangles, n = 9). D, the maximum increases of Rhod-2 fluoresce (○) in C (1.7 ± 0.2, 2.5 ± 0.3, 3.3 ± 0.4 and 2.4 ± 0.4 times in the presence of 0, 6, 20 and 50 mm Na⁺_c, respectively) were plotted. The curve is a fitted equation: 1.7 + 1.2/(1 + (4.3/Na⁺_c)^3.0). n = 5–11. Data with cyclosporin A (•) are 1.5 ± 0.2, 2.2 ± 0.3, 3.0 ± 0.5 and 2.6 ± 0.4 times in the presence of 0, 6, 20 and 50 mm Na⁺_c, respectively. n = 4–7. The maximum increases were not significantly different in the absence and presence of the drug at each Na⁺_c concentration.

On the other hand, an opposite Na⁺_c dependence was obtained when ΔΨ_mito was depolarized. In Fig. 2C, the myocytes were first superfused with the bath solution containing 1 μm FCCP, which greatly depolarized ΔΨ_mito (see Table 1). Applying 300 nm Ca²⁺ increased the Rhod-2 fluorescence only 1.7 times in the absence of Na⁺_c. However, with 6 or 20 mm Na⁺_c, the rise was augmented to 2.5 and 3.1 times, respectively. A further increase of Na⁺_c to 50 mm attenuated the fluorescence intensity. The half-effective concentration (EC₅₀) for Na⁺_c was about 4 mm (Fig. 2D). Under this experimental condition, the Ca²⁺_c-induced Ca²⁺_mito increase might be due to mechanism(s) different from the Ca²⁺ uniporter because the Ca²⁺ influx through the channel was likely to be largely attenuated when ΔΨ_mito is depolarized (Rottenberg & Scarpa, 1974; O'Rourke, 2007). Consistent with this notion, ruthenium red did not significantly affect the Ca²⁺_mito increase (Fig. 2C; grey triangles; 20 mm Na⁺_c+ 7 μm ruthenium red). The involvement of PTP in the Ca²⁺_c-induced Ca²⁺_mito increase is probably small because addition of 0.1 μm cyclosporin A, which is a potent inhibitor of PTP (IC₅₀= 25 nm; McGuinness et al. 1990), to the bath solution did not greatly affect the Ca²⁺_mito increase (filled circles in Fig. 2D).

One of the major Ca²⁺ handling mechanisms of cardiac mitochondria is NCX_mito, which exchanges Ca²⁺_mito for Na⁺_c (Crompton et al. 1976, 1977; Bernardi, 1999). We hypothesized that NCX_mito is involved in the Ca²⁺_c-induced Ca²⁺_mito increase at both intact and depolarized ΔΨ_mito. This hypothesis was first tested pharmacologically in Fig. 3. As we expected, applying 30 μm CGP-37157, which almost completely suppresses NCX_mito (IC₅₀= 0.36 μm; Cox et al. 1993; also see Fig. 4A), after the application of 300 nm Ca²⁺_c and 6 mm Na⁺_c induced a further increase in the Rhod-2 fluorescence when ΔΨ_mito was intact (Fig. 3A). This result indicates that the forward mode of NCX_mito operates under this condition, attenuating Ca²⁺_mito increase due to Ca²⁺ influx through the Ca²⁺ uniporter. To the contrary, when ΔΨ_mito was depolarized by 1 μm FCCP (Fig. 3B), CGP-37157 attenuated the increase in Rhod-2 fluorescence (3.4 versus 1.4 times, P < 0.05) and a removal of the drug induced a fluorescence increase. This result suggested that the Ca²⁺_mito increase was mediated by the Ca²⁺ influx through the reverse mode of NCX_mito, not via the Ca²⁺ uniporter. Therefore, it was suggested that NCX_mito mediates the Na⁺_c-dependent Ca²⁺_mito extrusion (forward mode of exchange) when ΔΨ_mito is intact, while the exchange mode reverses when ΔΨ_mito depolarizes. Dependences of NCX_mito on Na⁺_c and ΔΨ_mito were studied in detail in the following experiments.

Figure 3. Effects of NCX_mito inhibition on Ca²⁺_c-induced Ca²⁺_mito increase.

A, inhibition of forward mode of NCX_mito at normal ΔΨ_mito. After reaching a steady state of Rhod-2 fluorescence, 30 μm CGP-37157 was added to the bath solution. n = 6. Representative images of a myocyte loaded with Rhod-2 before (a) and after (b) adding Ca²⁺_c, and 15 min after applying CGP-37157 (c) are shown in the lower panel. B, inhibition of reverse mode of NCX_mito at depolarized ΔΨ_mito. The protocol is the same as in Fig. 2C and 30 μm CGP-37157 was added prior to the application of 300 nm Ca²⁺_c (•, n = 5). The maximum increase with and without CGP-37157 was significantly different. Representative images are shown in the lower panel. The colour scale of fluorescence intensity is denoted on the right side (arbitrary units) and a bar indicates 10 μm.

Figure 4. Na⁺_c dependence of Ca²⁺ efflux via forward mode of NCX_mito.

A, time course of Ca²⁺_mito decrease. The myocytes were preloaded with 300 nm Ca²⁺_c and Ca²⁺ efflux via forward mode of NCX_mito was induced by applying the bath solution with no Ca²⁺ and various Na⁺_c as denoted on the right of graph. CGP-37157 (30 μm) was added to the solution with 6 mm Na⁺ (•). The Rhod-2 fluorescence was normalized to that before changing the solution. B, Na⁺_c dependence of initial decay velocity of Ca²⁺ efflux. The initial decay velocity of Ca²⁺ efflux (2.1 ± 0.4, 3.1 ± 1.3, 13.3 ± 7.1, 39.7 ± 5.9, 76.2 ± 13.9 and 56.5 ± 13.9% min⁻¹ in the presence of 0, 0.3, 0.6, 1, 6 and 20 mm Na⁺_c, respectively) was fitted by a Hill equation: 2.2 + 64.2/(1 + (0.9/Na⁺_c)^3.8). n = 4–7.

Ca²⁺ efflux through the forward mode of NCX_mito

In Fig. 4, the Na⁺_c dependence of the forward mode of NCX_mito was studied under the condition where NCX_mito mainly operates Ca²⁺ efflux from mitochondria. The myocytes were first preloaded with Ca²⁺ by superfusing with bath solution containing 300 nm Ca²⁺_c and no Na⁺_c until the Rhod-2 fluorescence reached a steady state. Switching the bath solution to one containing no Ca²⁺_c and 6 mm Na⁺_c induced a decay of Rhod-2 fluorescence with a half-time to steady state (t_1/2) of about 60 s (open circles). With 30 μm CGP-37157 (filled circles) or no Na⁺ (open triangles), the decay was significantly attenuated and did not reach a steady state within 30 min. The initial decay velocity (% min⁻¹) was plotted against Na⁺_c concentration (Fig. 4B). The half-maximum concentration (K_1/2) of Na⁺_c was about 1 mm, a value which is comparable to the IC₅₀ in Fig. 2B. The high Hill coefficient (n_H= 3.8) suggests that more than three Na⁺ are transported.

The voltage dependence of NCX_mito has been controversial. To directly address this issue, we measured ΔΨ_mito in TMRE-loaded myocytes. When the Ca²⁺ efflux via NCX_mito was induced with the same protocol as in Fig. 4 (6 mm Na⁺_c), no significant change in the TMRE fluoresence was observed (data not shown). This result is consistent with experiments by Affolter & Carafoli (1980), but inconsistent with the ΔΨ_mito dependence suggested in Figs 2 and 3. Since ΔΨ_mito is largely maintained by H⁺ pumping via the respiratory chain (Nicholls & Budd, 2000), NCX_mito-induced membrane potential change might be compensated by the respiratory chain. As expected, a large decline of the TMRE fluorescence (depolarization) was induced upon the activation of Ca²⁺ efflux via NCX_mito (open circles, Fig. 4A) when the respiratory chain was suppressed by removing mitochondria substrates (potassium pyruvate, K₂HPO₄, succinic acid, K-ADP, malic acid and potassium glutamic acid). The decline of TMRE fluorescence was largely attenuated by CGP-37157 (closed circles, Fig. 5A) and was significantly suppressed without mitochondria pre-loading with Ca²⁺ (triangles, Fig. 5A). These data demonstrated that the Ca²⁺ efflux via the forward mode of NCX_mito depolarizes ΔΨ_mito. The direction of ΔΨ_mito change is consistent with that expected in plasma membrane NCX, in which positive charge is supposed to move concurrently with Na⁺ flux (Hilgemann et al. 1991; Matsuoka & Hilgemann, 1992; Powell et al. 1993). The above results indicated that NCX_mito is electrogenic.

Figure 5. Voltage dependence of forward mode of NCX_mito.

A, ΔΨ_mito change upon activation of forward mode of NCX_mito with (•, n = 4) and without (○, n = 6) 30 μm CGP-37157. TMRE fluorescence was normalized to the one before changing the bath solution to that containing 6 mm Na⁺ and no Ca²⁺. Mitochondria were preloaded with Ca²⁺ for 10 min with the protocol in Fig. 4. Without Ca²⁺ preloading, no remarkable change in TMRE fluorescence was induced (▵, n = 5). B, ΔΨ_mito dependence of forward mode of NCX_mito in intact (Control) and depolarized mitochondria preloaded with 300 nm Ca²⁺_c. The initial decay velocity of Rhod-2 fluorescence was measured at control and depolarized ΔΨ_mito by 1 μm FCCP, 10 μm antimycin A and 2 μm oligomycin (Anti + Olig), 10 μm NS1619, and 10 μm NS1619 without mitochondrial substrates (NS1619 + Sub(−)). The initial decay velocity was not significantly different among the five groups. n = 5–24. C, ΔΨ_mito dependence of forward mode of NCX_mito in mitochondria preloaded with 800 nm Ca²⁺_c. The initial decay velocity was measured at control and depolarized ΔΨ_mito by FCCP or Anti + Olig. The initial decay velocity of FCCP or Anti + Olig was significantly smaller than the control group (*P < 0.05). n = 7–11. In these experiments, 0.1 μm cyclosporin A was added to inhibit PTP.

The ΔΨ_mito dependence of Ca²⁺ efflux via NCX_mito was studied in Fig. 5B. ΔΨ_mito was altered by several procedures: 1 μm FCCP (an ionopore of proton), 10 μm antimycin A (an inhibitor of complex III of the mitochondrial electron transport chain, IC₅₀= 13 nm; Cherednichenko et al. 2004) and 2 μm oligomycin (an inhibitor of F₀/F₁-ATPase, IC₅₀≈ 0.3 μm; Van Dyke et al. 1984) (Anti + Olig.), 10 μm NS1619 (an opener of mitochondrial Ca²⁺-activated K⁺ channel; Sato et al. 2005), and 10 μm NS1619 without mitochondrial substrates (NS1619 + Sub(−)). It was estimated that these procedures depolarized the mitochondrial membrane by approximately 104, 104, 75 and 97 mV on average, respectively (see Table 1). In Fig. 5B, Rhod-2-loaded myocytes were first pre-loaded with 300 nm Ca²⁺_c until reaching a steady state; these conditions were maintained for 5–12 min to allow ΔΨ_mito to reach a new steady state. Then the Ca²⁺ efflux was induced in a manner similar to Fig. 4A (6 mm Na⁺). However, the initial decay velocity of Rhod-2 fluorescence was not significantly different between intact and depolarized mitochondria. Our computer model predicted, as shown later in Fig. 7, that the Ca²⁺ efflux via NCX_mito is more steeply dependent on ΔΨ_mito at higher Ca²⁺_mito. In line with this prediction, the initial decay velocity was largely slowed by the ΔΨ_mito depolarization (FCCP, Anti + Oligo) when mitochondria was pre-loaded with 800 nm Ca²⁺ (Fig. 5C). The contribution of PTP and Ca²⁺ uniporter to the Rhod-2 fluorescence decay was unlikely, because no significant difference was found in the initial decay velocity at intact ΔΨ_mito with or without ruthenium red, which was added after the pre-loading (71.2 ± 9.6 versus 76.7 ± 13.9% min⁻¹) and cyclosporin A (78.9 ± 18.0 versus 76.7 ± 13.9% min⁻¹). These data indicated that the Ca²⁺ efflux via the forward mode of NCX_mito is dependent on ΔΨ_mito. However, the Ca²⁺ efflux might be saturated at negative ΔΨ_mito when Ca²⁺_mito concentration is lower.

Figure 7. Effects of Na⁺_c on depolarization-induced Ca²⁺_mito increase by 1 μm FCCP (A) or 10 μm antimycin A and 2 μm oligomycin (B).

The protocol is the same as in Fig. 6A. Removal of Na⁺_c significantly attenuated the depolarization-induced Ca²⁺_mito increase. Data are with 20 mm Na⁺_c (○: n = 7, A; n = 7, B) and without Na⁺_c (•: n = 5, A; n = 6, B).

Ca²⁺ influx through the reverse mode of NCX_mito

The voltage dependence of the reverse mode of NCX_mito was studied in Fig. 6. In this series of experiments, 7 μm ruthenium red, 0.1 μm cyclosporin A and 10 μm SM20550 (IC₅₀= 10 nm; Yamamoto et al. 2000) were added to the bath solution to suppress the mitochondrial Ca²⁺ uniporter, PTP, and the mitochondrial Na⁺–H⁺ exchange, respectively. Applying 600 nm Ca²⁺_c did not significantly increase the Rhod-2 fluorescence, but membrane depolarization by 1 μm FCCP and 2 μm oligomycin (FCCP + Olig, Fig. 6A) remarkably augmented the Rhod-2 fluorescence (Na⁺_c= 20 mm). Essentially the same result was obtained with 1 μm FCCP alone (Fig. 7A), or 10 μm antimycin A and 2 μm oligomycin (Anti + Olig, Fig. 7B). CGP-37157 (30 μm) did not significantly affect the Rhod-2 fluorescence with 600 nm Ca²⁺_c at the intact Ψ_mito, but greatly attenuated the depolarization-induced Ca²⁺_mito rise (data not shown), indicating that the Ca²⁺_mito increase is mediated via the reverse mode of NCX_mito. Although FCCP might induce mitochondrial ATP depletion via the reverse of F₀/F₁-ATPase (Nicholls & Budd, 2000) and Ca²⁺ release from sarcoplasmic reticulum (Landolfi et al. 1998), these effects were not involved in the Ca²⁺_mito increase because no significant difference was found both in the maximum increase of Ca²⁺_mito (Fig. 6B) and the change of ΔΨ_mito (Table 1) among the procedures with FCCP, FCCP + Olig, and Anti + Olig. However, lesser ΔΨ_mito depolarization by NS1619 or NS1619 + Sub(−) tended to induce a lower increase in Ca²⁺_mito. This suggested a strong voltage dependence of the reverse mode of NCX_mito. To further confirm the voltage-dependent nature of the reverse mode of NCX_mito, we measured the change in ΔΨ_mito with TMRE upon inducing the reverse mode of NCX_mito (Fig. 6C). Applying 600 nm Ca²⁺ to the myocyte that was treated with the NS1619 + Sub(−) procedure increased the TMRE fluorescence twofold (triangles), indicating membrane hyperpolarization. A larger increase in the TMRE fluorescence was induced in myocytes treated with Anti + Olig (open circles) probably because of larger activity of NCX_mito (see Fig. 6B). CGP-37157 significantly inhibited the fluorescence increase (filled circles, Fig. 6C). These data indicated that NCX_mito is electrogenic also in the reverse mode. The direction of ΔΨ_mito change was opposite to that induced by the forward mode of NCX_mito (Fig. 5A), and consistent with the notion that the Na⁺ translocation step is electrogenic.

Figure 6. Voltage dependence of reverse mode of NCX_mito.

A, the increase in Ca²⁺_mito change upon ΔΨ_mito depolarization. Ca²⁺ (600 nm) was added as denoted at the top of graph under the conditions that Ca²⁺ uniporter and PTP were suppressed. Na⁺_c concentration was 20 mm. Depolarization by 1 μm FCCP and 2 μm oligomycin (FCCP + Olig) significantly augmented the Rhod-2 fluorescence. B, summary of Ca²⁺_mito increase induced by five depolarization procedures. The maximum increases of Rhod-2 florescence were 4.6 ± 0.9, 4.8 ± 0.7, 4.7 ± 0.7, 1.3 ± 0.3 and 2.7 ± 0.6 times, respectively, in the presence of FCCP, FCCP + Olig, Anti + Olig, NS1619, and NS1619 + Sub(−). n = 5–27. The maximum increase by NS1619 or NS1619 + Sub(−) was significantly small than the other groups (*P < 0.05). C, ΔΨ_mito change upon activation of reverse mode of NCX_mito. The myocytes loaded with TMRE were superfused with the bath solution containing Anti + Olig or NS1619 + Sub(−). The reverse mode of NCX_mito was induced by adding 600 nm Ca²⁺_c with (•) and without (○ and ▵) CGP-37157. n = 5–10.

The Na⁺_c dependence of the reverse mode of NCX_mito was studied in Fig. 7. Although the reverse mode of NCX_mito was expected to be enhanced by removing Na⁺_c, the Na⁺_c removal almost completely abolished the depolarization-induced Ca²⁺_mito increase by FCCP alone (Fig. 7A) or antimycin A and oligomycin (Anti + Olig, Fig. 7B). These results are consistent with data in Fig. 2, but apparently conflict with the general characteristics of plasma membrane NCX.

The above experimental findings strongly indicated that the Na⁺_c-dependent Ca²⁺_mitodecrease at intact ΔΨ_mito and increase at depolarized ΔΨ_mito are mediated via voltage-dependent and electrogenic NCX_mito. We further studied dependences of NCX_mito on Na⁺_c and ΔΨ_mito by computer simulations.

Simulation study on NCX_mito

As described in the Appendix, our computer model of NCX_mito assumed the following hypotheses: (i) electrogenic 3Na⁺/1Ca²⁺ exchange, (ii) the carrier-bound 3Na⁺ has one positive charge, and (iii) a consecutive exchange which consists of two states of the carrier (E₁ and E₂). We examined how this model can explain our and previous experimental data. In Fig. 8A, the voltage dependence of Ca²⁺ efflux was simulated at various Ca²⁺_mito; 300 nm (black dashed line), 1000 nm (grey line) and 3000 nm (green line). The saturation of the Ca²⁺ efflux with 300 nm Ca²⁺_mito at negative ΔΨ_mito is in agreement with the result in Fig. 5B. However, increasing Ca²⁺_mito steepened the voltage dependence. The steep ΔΨ_mito dependence at higher Ca²⁺_mito concentrations is in agreement with the present (Fig. 5C) and previous experiment by Crompton et al. (1977) demonstrating that depolarization by an uncoupler attenuated the Na⁺_c-dependent Ca²⁺ efflux from isolated mitochondria pre-loaded with 1000–3000 nm Ca²⁺_c. The voltage dependence of the reverse mode of NCX_mito was simulated under the experimental conditions of Fig. 6 (Fig. 8B). We assumed a linear relationship between Na⁺_c and Na⁺ in the mitochondrial matrix (Na⁺_mito) according to experimental data by Jung et al. (1992) as described in the Appendix; Na⁺_c/Na⁺_mito= 8.6 at intact ΔΨ_mito (red line in Fig. 8B) and Na⁺_c/Na⁺_mito= 2.2 at depolarized ΔΨ_mito (blue line in Fig. 8B). It was predicted that the Ca²⁺ influx is negligible at intact ΔΨ_mito (−180 to about −150 mV), but the ΔΨ_mito depolarization and the following increase in Na⁺_mito permeability strongly augment the Ca²⁺ influx at ΔΨ_mito more than −100 mV (red line in Fig. 8B). These results are comparable to the experimental result in Fig. 6A. The Na⁺_c dependence of the reverse model of NCX_mito at depolarized ΔΨ_mito was studied in Fig. 8C. Increasing Na⁺_c monotonically attenuated the Ca²⁺ influx when a constant Na⁺_mito (4 mm) was assumed (black dashed line in upper panel of Fig. 8C) because of the competitive inhibition of the Ca²⁺_c binding by Na⁺_c. If the ratio of Na⁺_c/Na⁺_mito under the normal condition (8.6) was assumed, no significant increase in the Ca²⁺ influx was evoked (blue line in the upper panel of Fig. 8C). This is because the probability of carriers bound with Na⁺_c and Na⁺_mito (P(E₁Na) and P(E₂Na), respectively) did not significantly increase (grey dashed line and blue line in lower panel of Fig. 8C). However, if the ratio under the depolarized condition (2.2) was assumed, P(E₁Na) and P(E₂Na) remarkably increased as increasing Na⁺_c (black dashed line and red line in the lower panel of Fig. 8C), and the Ca²⁺ influx augmented as increasing Na⁺_c and peaked approximately at 20 mm Na⁺_c (red line in upper panel of C). This relation is consistent with the experimental finding in Fig. 2D.

Figure 8. Simulation of net Ca²⁺ flux via NCX_mito.

A, relation between net Ca²⁺ flux and ΔΨ_mito of forward mode of NCX_mito. Ca²⁺_mito= 300, 1000 and 3000 nm as denoted at the left of graph. Na⁺_c= 6 mm, Ca²⁺_c= 0 and Na⁺_mito= Na⁺_c/8.6 mm. B, relation between net Ca²⁺ flux and ΔΨ_mito of reverse mode of NCX_mito. Na⁺_c= 20 mm, Ca²⁺_c= 600 nm, Ca²⁺_mito= 0, and with Na⁺_mito= Na⁺_c/2.2 (red line) or Na⁺_c/8.6 mm (blue line). C, Na⁺_c dependence of Ca²⁺ influx via reverse mode (upper panel), and P(E₂Na) and P(E₁Na) (at lower panel). Ca²⁺_mito= 0, Ca²⁺_c= 300 nm and ΔΨ_mito= 0 mV. At upper panel, Na⁺_mito was set to a fixed value (4 mm, black dashed line), Na⁺_c/8.6 (blue line), and Na⁺_c/2.2 mm (red line), respectively. In lower panel, P(E₂Na) and P(E₁Na) were plotted setting Na⁺_mito= Na⁺_c/8.6 (blue line and grey dashed line, respctively) and Na⁺_mito= Na⁺_c/2.2 mm (red and black dashed line, respectively). D, effects of Na⁺_c on Ca²⁺ efflux via forward mode of NCX_mito. Upper and lower panels represent the net Ca²⁺ flux–ΔΨ relationship and the ΔΨ dependence of P(E₁Na) (continuous lines) and P(E₂Ca) (dashed lines). Na⁺_mito= Na⁺_c/8.6 mm, Ca²⁺_mito= 1000 nm, and Ca²⁺_c= 0. Na⁺_c is denoted at right of graph.

The above simulation results demonstrated that the voltage-dependent nature of NCX_mito plays key roles in regulating Ca²⁺_mito concentration, and predicted that the increase in mitochondrial Na⁺ permeability at depolarized ΔΨ_mito contributes to the apparently opposite Na⁺_c dependence of the reverse mode of NCX_mito.

Discussion

The voltage dependence or electrogenicity of NCX_mito has been controversial since NCX_mito was first discovered by Carafoli et al. (1974). In the present study, we for the first time recorded the ΔΨ_mito change upon inducing the forward and reverse mode of NCX_mito. This finding strongly indicated that NCX_mito is electrogenic. The direction of ΔΨ_mito change suggested that net positive charge moves in the direction of net Na⁺ flux, or that net negative charge moves in the direction of net Ca²⁺ flux. The Na⁺ translocation step of NCX_mito may be a major electrogenic step, analogously to the plasma membrane NCX (Hilgemann et al. 1991; Matsuoka & Hilgemann, 1992; Powell et al. 1993). The latter is also possible as shown in plasma membrane NCX (Niggli & Lederer, 1991). Affolter & Carafoli (1980) failed to observe the ΔΨ_mito change upon inducing the Na⁺_c-dependent Ca²⁺ efflux from isolated mitochondria. The ΔΨ_mito change induced by NCX_mito might be easily compensated by H⁺ pumping via the respiratory chain. This hypothesis was validated in the experiment of Fig. 5A where the expected change in ΔΨ_mito was observed when the respiratory chain was inhibited.

The voltage dependence of NCX_mito may depend on ionic conditions. The Na⁺_c-dependent Ca²⁺ efflux from mitochondria preloaded with a relatively low concentration of Ca²⁺_c (300 nm) was not significantly affected by ΔΨ_mito depolarization (Fig. 5B), but it was indeed affected when preloaded with higher Ca²⁺_c (800 nm, Fig. 5C). The latter finding was consistent with the data of Crompton et al. (1977) demonstrating that ΔΨ_mito depolarization by an uncoupler greatly attenuated the Na⁺_c-dependent Ca²⁺ efflux from isolated mitochondria preloaded with 1000–3000 nm Ca²⁺_c. Our computer simulation predicted that the slope of net Ca²⁺ flux of the forward mode of NCX_mito depends on Ca²⁺_mito concentration (Fig. 8A) and supported the experimental findings. Our computer model further predicted that the Na⁺_c concentration also affects the slope of voltage dependence as shown in Fig. 8D. The increase in Na⁺_c concentration augmented the probability of exchanger bound with Na⁺_c (P(E₁Na)) and that with Ca²⁺_mito (P(E₂Ca)) at higher ΔΨ_mito, resulting in the augmentation of Ca²⁺ efflux at higher ΔΨ_mito and the attenuation of the voltage dependence. On the other hand, a substantial increase in the Ca²⁺ influx via the reverse mode of NCX_mito was induced by the ΔΨ_mito depolarization (Fig. 6A). This marked effect of depolarization is probably due to the steep voltage dependence of NCX_mito under the experimental conditions (20 mm Na⁺_c, Fig. 8B). Details of the voltage dependence of NCX_mito remain to be clarified by direct measurement of NCX_mito-associated current.

Saotome et al. (2005) suggested that ΔΨ_mito dissipation does not remarkably affect Ca²⁺ efflux via NCX_mito when preloaded with 300 nm Ca²⁺_c. Their findings might be in line with our conclusion. However, in their experiments, about a half of the Ca²⁺ efflux was mediated via non-NCX_mito mechanism(s) which was insensitive to Na⁺_c and diltiazem (an inhibitor of NCX_mito), and the speed of the Ca²⁺ efflux was slower. Experimental temperature (22 versus 37°C) might affect the turnover rate of NCX_mito.

As demonstrated in the current and previous studies (Sedova & Blatter, 2000; Malli et al. 2003), Na⁺_c significantly affects Ca²⁺_mito concentration through the forward mode of NCX_mito. However, a variety of K_1/2 values of NCX_mito for Na⁺_c has been reported in cardiac myocytes and other cells, ranging from 1 to 12 mm (Crompton et al. 1976, 1978; Coll et al. 1982; Fry et al. 1984; Wingrove & Gunter, 1986; Sedova & Blatter, 2000; Saotome et al. 2005; Fig. 4B from our data). Our computer simulation predicted that the affinity for Na⁺_c is decreased by the ΔΨ_mito depolarization, the increase in Ca²⁺_mito or increase in Ca²⁺_c concentration (data not shown). Thus the variability of the K_1/2 value is probably, at least in part, caused by the experimental conditions employed.

The most puzzling finding was the Na⁺_c dependence of the reverse mode of NCX_mito. The dependence was opposite to the general characteristics of plasma membrane NCX and the NCX_mito model (the black dashed line of the upper panel in Fig. 8C). However, the NCX_mito model well reproduced the experimentally obtained Na⁺_c dependence by adopting the relationship between Na⁺_c and Na⁺_mito in isolated mitochondria (Jung et al. 1992). Griffiths (1999) found that metabolic inhibition induced the collapse of ΔΨ_mito and the Ca²⁺_mito increase in rat cardiomyocytes and the Ca²⁺_mito increase was attenuated by CGP-37157. Similar results were obtained in metabolically inhibited renal epithelial cells of Madin–Darby canine kidney (MDCK) and concomitant increases in Na⁺_c and Na⁺_mito were observed (Smets et al. 2004; Baron et al. 2005). It is logically expected that the increase in Na⁺_cattenuates the reverse mode of NCX_mito. However, as demonstrated by the present experiments and computer simulation, the increase in Na⁺_c up to 50 mm still induced significant Ca²⁺ influx via NCX_mito when ΔΨ_mito was depolarized because of a possible increase in the Na⁺ permeability of the mitochondrial membrane.

Several pathways of mitochondrial Na⁺ flux have been proposed; Na⁺–H⁺ exchange for Na⁺ efflux, and NCX_mito, Na⁺ channel and PTP for Na⁺ influx (Bernardi, 1999). Monocarboxylic acid transporter (lactate or pyruvate – Na⁺ cotransporter; Takeo & Tanonaka, 2004) and mitochondrial K_ATP channels (Bernardinelli et al. 2006) may be another route for Na⁺ influx. Although mechanisms of the depolarization-induced increase in Na⁺ permeability has not been clarified, it might be speculated that the depolarization procedures employed in this study increased mitochondrial H⁺, which in turn attenuated H⁺ gradient across the mitochondrial membrane and inhibited Na⁺ efflux via Na⁺–H⁺ exchanger. In our preliminary experiments, no remarkable difference was observed in the depolarization-induced Ca²⁺_mito increase with or without SM20550, an inhibitor of mitochondrial Na⁺–H⁺ exchange. This might indicate that the Na⁺–H⁺ exchanger was already suppressed when ΔΨ_mito was depolarized.

In this study, we did not calibrate Rhod-2 fluorescence due to the difficulty of accurate calibration, and assumed a linear relationship between the Rhod-2 fluorescence and Ca²⁺_mito concentration because the almost proportional relation to Ca²⁺_mito concentration of Hela cells was reported in the range that the intensity greatly changes (Collins et al. 2001). Similarly, the absolute value of ΔΨ_mito could not be obtained in this study. The values of K_1/2 and ΔΨ_mito may be slightly different if accurate calibrations of Rhod-2 and TMRE signals are achieved, but our conclusion about the voltage-dependent and electrogenic property of NCX_mito will be still valid. Our computer model is the first one that can well reproduce a wide range of experimental data of cardiac NCX_mito, but has several limitations because of the lack of quantitative experimental data about NCX_mito, such as the current–voltage relationship, affinities for Na⁺_mito and Ca²⁺_mito, and the stoichiometry. Further experimental studies are needed to refine the model.

In summary, the cardiac NCX_mito is voltage dependent and electrogenic. The voltage- and Na⁺_c-dependent natures of NCX_mito dynamically modulate Ca²⁺_mito concentration in the cardiac myocyte.

Appendix

A model of NCX_mito

A computer model of NCX_mito was constructed based on a general scheme proposed by Crompton et al. (1977) and a computer model of sarcolemmal 3Na⁺–1Ca²⁺ exchange (Powell et al. 1993) (Fig. 9). E₁ and E₂ are states that an ion binding site faces, cytoplasm and mitochondrial matrix, respectively. Instantaneous binding of Na⁺ and Ca²⁺ to the carrier was assumed and the probability of the ion-bound carrier in the E₁ and E₂ states was expressed as follows.

Figure 9. Dependence of NCX_mito model on Na⁺_c and Ca²⁺_c.

A, a scheme of NCX_mito model. B, linear relations between Na⁺_c and Na⁺_mito at intact (grey) and depolarized (black) ΔΨ_mito reproduced from Jung et al. (1992). C, Na⁺_c dependence of Ca²⁺ efflux via forward mode of NCX_mito. The continous line is a model simulation (Na⁺_mito= Na⁺_c/8.6 mm, Ca²⁺_mito= 300 nm, Ca²⁺_c= 0 and ΔΨ_mito=−180 mV). Circles are experimental data from Fig. 4B in the present study. D, Ca²⁺_c dependence of Ca²⁺ influx via reverse mode of NCX_mito. The continous line is a model simulation (Na⁺_mito= 25 mm, Na⁺_c= 0, Ca²⁺_mito= 0 and ΔΨ_mito= 0 mV). Circles are experimental data by Paucek & Jabůrek (2004).

The Na⁺-bound carrier was assumed to have one positive charge and rate constants (k₁–k₄) were expressed as follows.

where F is Faraday's constant (96.4867 C mmol⁻¹), R is the gas constant (8.3143 C mV K⁻¹ mmol⁻¹), and T is absolute temperature (310 K).

Steady state probability that the exchanger locates in E₁ and E₂ state P(E₁total) and P(E₂total) and net Ca²⁺ flux were calculated as below.

Reversal potential of the NCX_mito current, which can be calculated with the Na⁺ flux rate, should be the same as the equilibrium potential of 3Na⁺–1Ca²⁺ exchange (E_Na/Ca).

This assumption yields a following constraint

The values of the dissociation constant were determined so as to fit experimental data and this constraint.

In the present experiments, Na⁺_mito concentration might change when changing Na⁺_c. Na⁺_mito concentration was estimated by the linear relation between Na⁺_c and Na⁺_mito, which was obtained in isolated mitochondria by Jung et al. (1992); Na⁺_c/Na⁺_mito= 8.6 at intact ΔΨ_mito (grey line in Fig. 9B) and Na⁺_c/Na⁺_mito= 2.2 at depolarized ΔΨ_mito (black line in Fig. 9B).

Figure 9C and D demonstrates the Na⁺_c dependence of the forward mode and the Ca²⁺_c dependence of the reverse mode of NCX_mito, respectively. Dissociation constants for Na⁺_c and Ca²⁺_c were determined to fit experimental data in Fig. 4B and data of Ca²⁺ and Na⁺ fluxes measurement from reconstructed beef heart NCX_mito by Paucek & Jabůrek (2004). The Na⁺_c dependence of Ca²⁺ efflux via forward mode NCX_mito is also in agreement with the data of Paucek & Jabůrek (2004) under their experimental conditions (0 mV, 10 μm Ca²⁺_mito, 0 Na⁺_mito and 0 Ca²⁺_c).