Slow Ca2+ Efflux by Ca2+/H+ Exchange in Cardiac Mitochondria Is Modulated by Ca2+ Re-uptake via MCU, Extra-Mitochondrial pH, and H+ Pumping by FOF1-ATPase

Mitochondrial (m) Ca2+ influx is largely dependent on membrane potential (ΔΨm), whereas mCa2+ efflux occurs primarily via Ca2+ ion exchangers. We probed the kinetics of Ca2+/H+ exchange (CHEm) in guinea pig cardiac muscle mitochondria. We tested if net mCa2+ flux is altered during a matrix inward H+ leak that is dependent on matrix H+ pumping by ATPm hydrolysis at complex V (FOF1-ATPase). We measured [Ca2+]m, extra-mitochondrial (e) [Ca2+]e, ΔΨm, pHm, pHe, NADH, respiration, ADP/ATP ratios, and total [ATP]m in the presence or absence of protonophore dinitrophenol (DNP), mitochondrial uniporter (MCU) blocker Ru360, and complex V blocker oligomycin (OMN). We proposed that net slow influx/efflux of Ca2+ after adding DNP and CaCl2 is dependent on whether the ΔpHm gradient is/is not maintained by reciprocal outward H+ pumping by complex V. We found that adding CaCl2 enhanced DNP-induced increases in respiration and decreases in ΔΨm while [ATP]m decreased, ΔpHm gradient was maintained, and [Ca2+]m continued to increase slowly, indicating net mCa2+ influx via MCU. In contrast, with complex V blocked by OMN, adding DNP and CaCl2 caused larger declines in ΔΨm as well as a slow fall in pHm to near pHe while [Ca2+]m continued to decrease slowly, indicating net mCa2+ efflux in exchange for H+ influx (CHEm) until the ΔpHm gradient was abolished. The kinetics of slow mCa2+ efflux with slow H+ influx via CHEm was also observed at pHe 6.9 vs. 7.6 by the slow fall in pHm until ΔpHm was abolished; if Ca2+ reuptake via the MCU was also blocked, mCa2+ efflux via CHEm became more evident. Of the two components of the proton electrochemical gradient, our results indicate that CHEm activity is driven largely by the ΔpHm chemical gradient with H+ leak, while mCa2+ entry via MCU depends largely on the charge gradient ΔΨm. A fall in ΔΨm with excess mCa2+ loading can occur during cardiac cell stress. Cardiac cell injury due to mCa2+ overload may be reduced by temporarily inhibiting FOF1-ATPase from pumping H+ due to ΔΨm depolarization. This action would prevent additional slow mCa2+ loading via MCU and permit activation of CHEm to mediate efflux of mCa2+. HIGHLIGHTS - We examined how slow mitochondrial (m) Ca2+ efflux via Ca2+/H+ exchange (CHEm) is triggered by matrix acidity after a rapid increase in [Ca2+]m by adding CaCl2 in the presence of dinitrophenol (DNP) to permit H+ influx, and oligomycin (OMN) to block H+ pumping via FOF1-ATP synthase/ase (complex V).- Declines in ΔΨm and pHm after DNP and added CaCl2 were larger when complex V was blocked.- [Ca2+]m slowly increased despite a fall in ΔΨm but maintained pHm when H+ pumping by complex V was permitted.- [Ca2+]m slowly decreased and external [Ca2+]e increased with declines in both ΔΨm and pHm when complex V was blocked.- ATPm hydrolysis supports a falling pHm and redox state and promotes a slow increase in [Ca2+]m.- After rapid Ca2+ influx due to a bolus of CaCl2, slow mCa2+ efflux by CHEm occurs directly if pHe is low.

There is a well-known direct correlation between m and mCa 2+ uptake based on the Nernst equation; a more polarized gradient (Chinopoulos and Adam-Vizi, 2010;Chinopoulos, 2011), equals the proton motive force, pmf. However, it is not known how the magnitude, rate, and route of mCa 2+ uptake or release in cardiac muscle cell mitochondria is affected by manipulating the IMM [H + ] m gradient by allowing mATP hydrolysis, which would result in H + pumping and better maintain the [H + ] gradient when m is low, vs. blocking mATP hydrolysis (no H + pumping with collapsing [H + ]) and lower m . Exposure of mitochondria to external (e) CaCl 2 when the IMM is fully charged (high m ), defined here by the presence of substrate in state 2 conditions without an induced inward H + leak, promotes rapid voltagedependent mCa 2+ uptake via MCU (Hoppe, 2010). In contrast, decreased net mCa 2+ uptake might be expected during a protonophore-induced inward H + leak if H + influx leads to Ca 2+ efflux. However, an inward H + flux that slowly decreases m can still result in a slow, continued uptake of mCa 2+ (Delcamp et al., 1998;Di Lisa and Bernardi, 1998) due to the influx of positive charges without an effect on the [H + ] m , and more so with a fall in [H + ] m gradient from the added influx of H + in the presence of a protonophore.
Our aim was to mechanistically examine the slow mode kinetics of mCa 2+ influx/efflux in cardiac cell mitochondria. The conditions under which CHE m may occur in cardiac mitochondria are unknown. We proposed that an induced, net influx of H + is coupled to net mCa 2+ efflux by activation of CHE m in the face of continued mCa 2+ uptake via the MCU in partially depolarized m mitochondria. In addition, if the extra-mitochondrial milieu is acidic, pH m would slowly decrease as mH + entry by mCHE m is exchanged for mCa 2+ efflux in Ca 2+ overloaded mitochondria. We postulated that CHE m is activated under conditions of slow a H + influx and a high m[Ca 2+ ], and especially when H + pumping by complex V, stimulated by the lowered m, is prevented. To carry out our aim, we examined the time dependent changes in m , [Ca 2+ ] m and pH m , and extra-mitochondrial [Ca 2+ ] e and pH e , after a bolus of CaCl 2 either by inducing an inward H + leak that causes an outward pumping of H + by complex V, or by altering the extra-mitochondrial pH e .
In one set of experiments, we challenged isolated energized mitochondria with a bolus of CaCl 2 in the absence or presence of increasing concentrations of the protonophore 2,4dinitrophenol (DNP) in the absence or presence of the complex V inhibitor oligomycin (OMN) to block ATP hydrolysis-induced H + pumping, and or Ru360 to block the reuptake of Ca 2+ via the MCU. To understand how DNP, OMN, and Ru360 dynamically alter [Ca 2+ ] m or [Ca 2+ ] e after a bolus of CaCl 2 , we considered it crucial to also dynamically measure m , pH m , and NADH, as well as mitochondrial respiration (extent of uncoupling), total [ATP] m , and ATP m /ADP m ratio. In another set of isolated mitochondrial experiments, we directly induced mCa 2+ efflux via CHE m after CaCl 2 loading by altering the Na +free medium from a control pH e of 7.15 to either pH 7.6 or 6.9. We show that secondary Ca 2+ influx vs. efflux is [H + ] m dependent.  (Heinen et al., 2007;Huang et al., 2007;Aldakkak et al., 2010;Haumann et al., 2010) (all fluorescence probes from Invitrogen TM -Thermo Fisher Scientific). Respiration (Clark electrode) and ATP m (bioluminescence) and ATP m /ADP m ratio (HPLC, luminometry) were also measured. The experimental buffer, mitochondrial substrates, and drugs were Na + -free to prevent activation of NCE m by extra-mitochondrial Na + . The inactivity of the NCE was verified by comparing data from these experiments to data from experiments with added CGP-37157, a known mitochondrial NCE m inhibitor (data not shown).

Experimental Protocols
Medium pH e -Induced Changes in pH m The experimental buffer was identical to that described above except that in addition to the pH 7.15 buffer, buffers at pH 6.9 and 7.6 were prepared by titration with HCl and KOH, respectively. The residual EGTA carried over from the isolation buffer to the experimental buffer resulted in an ionized extramitochondrial [Ca 2+ ] e of <200 nM (Figure 1). To measure changes in [Ca 2+ ] e after adding a bolus of 40 µM CaCl 2 , each pH buffer contained Fura 4 F penta-K + salt. The K D 's for Ca 2+ were calculated and corrected for each buffer pH because pH affects the binding of Ca 2+ to the fluorescence dye (see section "Supplementary Materials S.1.4, S.1.8"). In other experiments, pH m and m were measured using BCECF-AM and TMRM fluorescent dyes, respectively. Experiments were initiated at t = 30 s when mitochondria were added to the FIGURE 1 | Changes in buffer [Ca 2+ ] e (A), matrix pH m (B), and m (C) over time after adding 40 µM CaCl 2 (210 s) at extra-mitochondrial pH e 7.6, 7.15, and 6.9 with or without 1 µM Ru360 (300 s) to inhibit additional mCa 2+ uptake via MCU. Note the rapid fall in [Ca 2+ ] e due to fast mCa 2+ uptake via the MCU and the following slow rise in [Ca 2+ ] e (Ca 2+ efflux) (A), slow decline in pH m (B), and slow depolarization of m (C) at pH 6.9 (each line = mean of 3-4 replicates from 12 guinea pig hearts for each fluorescence measurement). Note in the pH 6.9 medium the faster rate of mCa 2+ efflux (A) over time when MCU was blocked, and the faster declines in pH m (B) and m (C) over time when MCU was not blocked. buffer; at t = 90 s pyruvic acid (PA, 0.5 mM) was added, followed by a bolus of 40 µM CaCl 2 at t = 210 s to initiate rapid mCa 2+ uptake via MCU. Note that in guinea pig cardiac mitochondria, the respiratory control index (RCI) is higher in the presence of pyruvate alone (Heinen et al., 2007;Blomeyer et al., 2013;Boelens et al., 2013) than with pyruvate plus malate (Riess et al., 2008). For some experiments, 1 µM Ru360 (or vehicle, 0.1% DMSO) was added at t = 300 s shortly after adding CaCl 2 to block Ca 2+ reuptake into mitochondria via MCU after the Ca 2+ was extruded from mitochondria. At the end (1700 s) of each experiment, the potent protonophore, carbonyl cyanide m-chlorophenyl hydrazone (CCCP, 4 µM) was given to completely abolish the pH gradient and depolarize m . Data for each pH group were collected in mitochondrial suspensions from the same heart; approximately 8-10 hearts were used for each fluorescent probe. At pH 7.15, adding 40 µM CaCl 2 , which increased extra-mitochondrial [Ca 2+ ] e into the 1 µM range and increased the initial [Ca 2+ ] m to approximately 500 nM (Figures 1, 2), is unlikely to induce membrane permeability transition pore (mPTP) opening. However, to test the possibility of mPTP opening, 500 nM cyclosporine A (CsA), a modulator of cyclophilin D required to open mPTP, was given before adding CaCl 2 in several experiments at pH e 6.9 and 7.15.

Protonophore-Induced Changes in pH m
Experiments were initiated at t = −120 s; at t = −90 s, mitochondria were added to the experimental buffer (time line, Figure 3); external pH e was 7.15. At t = 0 s, pyruvic acid (PA, 0.5 mM) was added to the mitochondria suspended in the experimental buffer, followed by 0, 10, 20, 30, or 100 µM DNP, a mild protonophore, at t = 90 s, followed by the addition of de-ionized H 2 O, 10, or 25 µM CaCl 2 at t = 225 s. The 90 s period allowed for full m polarization  . Buffer pH = 7.15. Data obtained from 10 hearts with 4-5 replicates per heart. For P < 0.05: * after DNP vs. before DNP; # after CaCl 2 vs. before CaCl 2 ; † late (700 s) vs. early (215 s) after CaCl 2 . and stabilization of pH m and NADH. In some experiments (see section "Supplementary Results S.2.4" and Supplementary Figure S.6), 100 nM Ru360 was added at t = 300 s, after the addition of CaCl 2 , to block any reuptake of mCa 2+ by the MCU that was extruded by CHE m . For the OMN treated groups, 10 µM OMN was added to the experimental buffer at the start of the experimental protocol (Figure 3). At the end of each experiment CCCP was added at t = 760 s to maximally depolarize m . DNP, Ru360, OMN, and CCCP were each dissolved initially in DMSO and then in buffer to yield a final buffer concentration for DMSO of 0.1 to 0.4% (wt/vol). Each drug or DMSO alone was added to a final volume of 10 µL. To test for mPTP opening, CsA was given before adding 20 or 30 µM DNP and 25 µM CaCl 2 in several experiments conducted at pH e 7.15.

Statistical Analyses
Data were summarized at 500, 1000, and 1500 s (for Figures 1, 2) for external buffer-induced changes in pH m on [Ca 2+ ] e . Data were summarized for protonophore-induced changes in pH m on [Ca 2+ ] m at 80 s (after adding PA), 215 s (after adding DNP), 275 s (early after adding CaCl 2 ), and 700 s (late after adding CaCl 2 ) (e.g., Figure 4). All data points were presented and expressed as average ± SEM. Repeated measure ANOVAs followed by a post hoc analyses using Student-Newman-Keuls' test was performed to determine statistically significant differences among groups. A P-value < 0.05 (two-tailed) was considered significant. See Figure legends

CHE m Activation Was Exposed by Efflux of Ca 2+ With Influx of H + and Was Greater If MCU Was Inhibited
Direct evidence for CHE m activation was observed by acidifying the extra-mitochondrial buffer (low pH e ), which subsequently decreased the matrix pH m slowly over time (Figure 1). With NCE m and Na + /H + (NHE m ) inactivated by using Na + -free solutions and substrates, fast mCa 2+ influx via the MCU, induced after adding 40 µM CaCl 2 at pH 6.9, was followed by a slow mCa 2+ efflux over time ∼(300-1700 s) as shown by the increase in extra-mitochondrial [Ca 2+ ] e from <200 nM to nearly 4500 nM in the absence of Ru360 ( Figure 1A). When Ru360 was added 90 s after adding CaCl 2 , [Ca 2+ ] e rose even more over the first 1000 s, indicating blockade of Ca 2+ recycling via the MCU and revealing the total mCa 2+ effluxed via CHE m . In the pH 6.9 plus Ru360 group the mean rate (slope) of increase in [Ca 2+ ] e (mCa 2+ efflux) over time (300-1700 s) was 1.5 ± 0.1 nM/s, pH 0.4 units). This was greater than in the pH 6.9 minus Ru360 group (1.0 ± 0.2 nM/s over 300-1000 s), suggesting that approximately 1/3 of the mCa 2+ extruded was retaken up across the IMM via the MCU. In contrast, mCa 2+ efflux was not observed in the pH 7.6 medium without Ru360, and minimally at 1500 s at pH 7.6 with Ru360. There was less mCa 2+ efflux at pH 7.15 ± Ru360 compared to pH 6.9 ± Ru360. However, even at pH 7.15 ± Ru360, there were similar steady declines in pH e while net slow Ca 2+ efflux was noted only in the plus Ru360 groups, indicating Ca 2+ re-uptake via MCU. Therefore, in the acidic extra-mitochondrial medium, slow decreases in pH m (H + influx) were accompanied by slow increases in mCa 2+ efflux, indicating CHE m activity. Eventually, matrix acidification was more pronounced in the pH 6.9 medium ( pH 0.62 units) in the absence of Ru360 than in all other groups so that over time as H + influx was exchanged for Ca 2+ efflux the IMM pH gradient was eventually obliterated, halting Ca 2+ efflux ( Figure 1B). Eventually, because of mCa 2+ influx, near complete depolarization of m occurred in the pH 6.9 medium ( Figure 1C), as shown by little change after adding CCCP, and by the complete depolarization of m when Ca 2+ recycling via the MCU was permitted (minus Ru360 group). Although adding CaCl 2 at an external pH e of 6.9 led eventually to near complete dissipation of m , when CsA was first added to the buffer, CsA prevented the gradual, slow extrusion of mCa 2+ and declines in pH m and m induced by adding CaCl 2 at pH e 6.9 indicating a complete lack of CHE m activity (see section  (Figure 2) indicates maximal mCa 2+ efflux occurred in the pH e 6.9 medium (largest IMM ( H + ] gradient), much less so in the pH 7.15 medium, and not at all in the pH 7.6 medium. Ca 2+ efflux was accentuated in the presence of Ru360 given just after the added CaCl 2 bolus (Figure 2). The difference (arrow) between the absence and presence of Ru360 indicates the rapid reuptake (recycling) of Ca 2+ via MCU on extrusion via CHE m . Thus total Ca 2+ efflux was greater in the pH 6.9 group when MCU was not blocked because [H + ] m rose higher than when MCU was blocked. The steep, vertical increase in mCa 2+ efflux at the highest [H + ] m in the pH 6.9 group resulted from cessation of mCa 2+ reuptake via MCU due to depolarization of m ( Figure 1C). The net amount of H + entering mitochondria per Ca 2+ exiting mitochondria may be indeterminate because much of the H + entering is pumped out via the respiratory enzyme complexes.

Mitochondrial Membrane Potential ( m ) Was Depressed by DNP After Adding CaCl 2
In the protonophore series of experiments (time line, Figure 3), DNP alone decreased m slightly as assessed by rodamine-123 (R123) (Huang et al., 2007) (Figure 4), in a concentrationdependent manner, except at 100 µM DNP, which alone fully (+OMN) or nearly (−OMN) depolarized m . m was estimated as % of maximal depolarization, where the baseline after adding substrate with OMN signifies full polarization (0%) and addition of CCCP denotes complete depolarization (100%). Adding 10 µL of 0.1% DMSO (DNP vehicle) or 10 µM DNP had no significant effect when given before CaCl 2 , whereas adding 20, 30, or 100 µM DNP before 10 µM CaCl 2 reduced the R123 m signals by 12.7, 18.7, and 92.4% vs. DMSO (Figure 4A), respectively. In the presence of OMN (Figure 4C), adding 20, 30, or 100 µM DNP before 10 µM CaCl 2 increased the fluorescence signal intensities (i.e., depolarized m ) by 16.2, 33.0, and 99.0%, respectively, vs. DMSO (0%). Overall, before adding either   (Figures 6C,D) of OMN shows that the average initial, rapid increase in [Ca 2+ ] m via the MCU was much faster after adding 25 µM CaCl 2 than after 10 µM CaCl 2 in the ± OMN groups; this initial rate of mCa 2+ uptake decreased as m fell with added DNP. The initial rate of increase in [Ca 2+ ] m during the first 7 s after adding 10 µM CaCl 2 ( Figure 5C) decreased from 8 to 2 nM/s (DNP 0-100 µM). After adding 25 µM CaCl 2 (Figure 5D), the rate decreased from 88 to 20 nM/s. In the presence of OMN (Figures 6C,D), the initial increases in [Ca 2+ ] m in fully coupled mitochondria (no DNP) were larger than those in the absence of OMN (Figures 6C,D vs. Figures 5C,D). With OMN present, the initial increases in [Ca 2+ ] m decreased from 30 to 4 nM/s after adding 10 µM CaCl 2 and from 130 to 13 nM/s after adding 25 µM CaCl 2 , Thus the initial rates of increase in [Ca 2+ ] m with 10 µM CaCl 2 were consistently faster in the presence of OMN (Figure 6C vs. Figure 5C), and at 25 µM CaCl 2 , with or without 10 µM DNP (Figure 6D vs. Figure 5D). A summary of slope data collected between 300 and 750 s, i.e., after the initial, rapid increase in [Ca 2+ ] m via the MCU with added 10 µM CaCl 2 , demonstrates a much slower and smaller (pM/s) gradual increase in [Ca 2+ ] m over time in the absence of OMN with a threefold greater slope after 30 µM DNP vs. DMSO ( Figure 5E). After adding 25 µM CaCl 2 , the slow increase in [Ca 2+ ] m was about fourfold higher after 20 µM DNP vs. DMSO ( Figure 5F). The secondary slow rise in [Ca 2+ ] m was about 1000 times slower than the initial fast phase and roughly dependent on both the amount of mCa 2+ that was taken up initially just after adding CaCl 2 and the extent of m depolarization. In contrast, in the presence of OMN under the same conditions of added CaCl 2 and DNP, the slope data showed slow and small declines (rather than increases) in [Ca 2+ ] m over time (Figures 6E,F). The slow rate of extrusion of mCa 2+ by CHE m when complex V was blocked with OMN ( Figures 6E,F) became greater when mCa 2+ entry via the MCU was greater (Figures 6 A,B).

Matrix pH Remained Steady Without OMN but Fell With OMN-Induced Block of Complex V
Baseline matrix pH m was approximately 7.55 in each group after adding PA and before adding DNP (Figures 7A-D). In the absence of OMN, adding 10-30 µM DNP did not result in a significant net decrease in pH m ; however, 100 µM DNP markedly decreased pH m (Figures 7A,B). This effect to collapse the pH m gradient was proportional to the collapse of the m gradient (Figure 4). In the absence of OMN, adding CaCl 2 had no appreciable effect on pH m ( m partially depolarized) even in the presence of DNP, except for 100 µM DNP, when pH m fell markedly ( m fully depolarized) (Figures 7A,B). In the absence of OMN, H + influx was matched by H + pumping as pH m did not change appreciably. In contrast, in the presence of OMN there was a strong DNP concentrationdependent fall in matrix pH m (Figures 7C,D)

Mitochondrial Redox State Remained Steady Without OMN but Fell With OMN-Induced Block of Complex V
A reduced redox state is associated with maintenance of pH m . Adding the substrate PA increased the redox state (more reduced) as determined by high NADH autofluorescence (Figure 8).
In the absence of OMN, adding 10 to 30 µM DNP ± 10 or 25 µM CaCl 2 (Figures 8A,B) did not cause a significant change in NADH. NADH was unchanged despite up to 60% decrease in m fluorescence (Figures 4A,B) after adding DNP and CaCl 2 . However, when complex V was blocked by OMN (Figures 8C,D), there was significant oxidation (low NADH) by DNP in a concentration dependent manner. In contrast to the condition without OMN, with OMN present as little as a 20% fall in m fluorescence (Figures 4C,D) led to a more oxidized NADH state. Moreover, NADH was fully oxidized at 20 µM DNP with OMN present (Figures 8C,D), and the oxidized state was not altered significantly by adding CaCl 2 after DNP. In the absence or presence of CaCl 2 , NADH  (Figures 9A,B). There was no change in basal [ATP] m after adding PA. DNP, at 10 µM, did not significantly change [ATP] before or after adding CaCl 2 (Figures 9A,B) (Figures 9A,B). In the presence of OMN (Figures 9C,D)

Ca 2+/ H + Exchange Activity Is Identified by Manipulating IMM [H + ] and [Ca 2+ ] Gradients
We provide firm support for a role of CHE m in maintaining homeostasis of Ca 2+ against H + under certain conditions in cardiac cell mitochondria that may mimic some sequelae of cardiac IR injury. Our results: (1) furnish direct evidence for CHE m activity by the secondary, slow increases in matrix Ca 2+ efflux coupled to slow increases in matrix H + influx, when both NCE and NHE activities are blocked, and particularly, when MCU-dependent mCa 2+ re-uptake is blocked with Ru360; (2) demonstrate that respiration increases while m decreases mildly, whereas pH m and redox state are relatively maintained when inducing a matrix inward H + leak with DNP before adding CaCl 2 ; adding CaCl 2 results in a secondary, slow increase in [Ca 2+ ] m that slowly depolarizes m ; (3) show that with permissive H + influx, but inhibited outward H + pumping at complex V, adding CaCl 2 causes larger decreases in m , pH m , and NADH and results in a slow decrease in [Ca 2+ ] m ; (4) indicate that blocking complex V with OMN to prevent H + pumping causes m to further decrease after adding CaCl 2 because the influx of mCa 2+ via the MCU is not opposed by H + pumping at complex V; (5) suggest that the lack of a slow fall or rise in [Ca 2+ ] m in the presence of 100 µM DNP is due to the loss of mdependent mCa 2+ uptake by MCU; (6) point out that only in partially depolarized mitochondria does added CaCl 2 result in a pH m -independent gradual increase in [Ca 2+ ] m that is reciprocated by H + pumping to maintain pH m ; preventing matrix acidification is associated with a maintained redox state; and (7) show that the decrease in [ATP] in the absence of OMN supports ATP hydrolysis with H + pumping. These two scenarios, ±OMN, are depicted graphically in Figure 10A vs. Figure 10B.

Net Mitochondrial Ca 2+ Influx Occurs via MCU and Net Ca 2+ Efflux Can Occur via Ca 2+ /H + Exchange
The dependence of rapid MCU-mediated mCa 2+ uptake on m has been examined extensively (Gunter and Pfeiffer, 1990;Gunter et al., 1994;Dash et al., 2009;Haumann et al., 2010). But our study demonstrates that net m[Ca 2+ ] can additionally increase slowly via the MCU, and that this happens when pH m is relatively maintained despite a decline in m resulting from the DNP-mediated inward H + flux and after the initial rapid Ca 2+ influx via MCU. A gradual increase in [Ca 2+ ] m at the expense of maintaining the pH m may be deleterious to mitochondrial function. We propose that this secondary rise in net [Ca 2+ ] m results from an adequate m with Ru360dependent slow mCa 2+ influx, which eventually leads to a slow, continued fall in m . Because H + pumping at complex V maintains the [H + ] m gradient, mCa 2+ efflux via CHE m in exchange for mH + influx due to the H + leak is likely masked by mCa 2+ re-uptake. Thus, the DNP-induced H + leak and the concomitant dissipation of the IMM [H + ] gradient, when FIGURE 10 | Schema depicting putative role of MCU and CHE m on slow Ca 2+ influx and efflux, respectively, during stepwise depolarization with DNP with un-inhibited (i.e., minus OMN) (A) vs. inhibited (B) F O F 1 -ATPsynthase(ase) (i.e., plus OMN) after a bolus addition of CaCl 2 to the mitochondrial medium. (A) (1) DNP permits H + entry that tends to (2) decrease m , which enhances H + pumping by respiratory complexes, including (3) F O F 1 -ATPase, so that pH m does not decrease appreciably and m is partially supported (2). Adding CaCl 2 further depolarizes m by allowing more cationic (Ca 2+ ) charges into the matrix via the MCU (4). Over time, in the range of a 20-60% decline in m , pH m remains unchanged as (5) H + is pumped out (3) in exchange for permissive H + entry (1) in triggering additional slow mCa 2+ uptake by MCU and causing m to decrease further. CHE m is inhibited by the lack (pH 7.6) of matrix acidity (5) and NCE m and NHE m are inactivated by the lack of substrate and buffer Na + (6). (B) Alternatively, when F O F 1 -ATPase is inhibited (3), matrix acidity gradually increases (pH 6.9), m is less supported (2) and Ca 2+ slowly exits (CHE m ) in exchange for slow H + entry due to DNP (5). This sequence triggers a net loss of mCa 2+ even though uptake of Ca 2+ via the MCU continues, as shown by a greater efflux of mCa 2+ by CHE m when additional mCa 2+ uptake via MCU is blocked by Ru360 (4). DNP, dinitrophenol; ETC, electron transport chain; IMS, inner membrane space; MCU, mitochondrial Ca 2+ uniporter; OMN, oligomycin; TCA, tricarboxylic acid. countered by H + pumping at complex V (in addition to other complexes), can maintain the pH m and support the pmf ( m + RT/F pH m ) (Dzbek and Korzeniewski, 2008 (Gursahani and Schaefer, 2004). In contrast, when ATP m hydrolysis is prevented, pH m slowly decreases toward pH e with a greater fall in m ; the slow H + influx is accompanied by a slow net fall in [Ca 2+ ] m mediated by CHE m even though the extruded Ca 2+ is recycled via the MCU. Since H + influx (DNP-induced leak) is not countered by reciprocal H + pumping to restore pH m , the slow influx of H + is exchanged for slow Ca 2+ efflux via CHE m until the pH gradient is dissipated.
Ca 2+ and H + gradients across the IMM are largely dependent on m and pH gradients resulting from H + pumping by respiratory complexes. Ionic homeostasis requires one cation efflux pathway to oppose another cation influx pathway and vice versa. Cation exchangers fulfill this need. Unlike mCa 2+ uptake via MCU, which is dependent on m and on the chemical gradient, exchange of Ca 2+ and H + via CHE m may or may not be dependent on m (Rottenberg and Marbach, 1990;Gunter et al., 1991). But the direction of Ca 2+ and H + flux mediated solely by CHE m is dependent on a large IMM [H + ] or [Ca 2+ ] gradient to shuttle Ca 2+ or H + across the IMM. This can be expressed by an electroneutral J CHE flux equation (Tewari et al., 2014), calculated here in the presence and absence of OMN (see section "Supplementary Results S.2.8" and Supplementary Figure S.10). J CHE flux analysis of our data suggests that slow mCa 2+ influx could have occurred via CHE m in the absence of OMN, whereas mCa 2+ efflux could have occurred in the presence of OMN. Indeed, we have provided strong support for slow net mCa 2+ efflux mediated by CHE m (despite slow mCa 2+ uptake by MCU) when complex V cannot pump H + in the presence of OMN.
Although CHE m likely occurs both in the absence or presence of OMN, our results suggest that the observed secondary, slow influx of mCa 2+ influx (minus OMN) is due primarily to reuptake by a Ru360 sensitive mechanism, presumably MCU, that may overwhelm any CHE m activity. This is because Ru360 blocked the slow rise in [Ca 2+ ] m and the slow fall in [Ca 2+ ] e , thus supporting MCU as the mediator of the slow mCa 2+ influx. The J CHE flux equation only monitors differences in [H + ] and [Ca 2+ ] on either side of the IMM and does not rely on effects of the pH m gradient on H + pumping or the m gradient on mCa 2+ uptake via MCU. Thus the secondary, slow mCa 2+ uptake after the initial CaCl 2 bolus (Figures 5A,B,E,F) appears to be a direct effect of H + pumping by complex V (minus OMN) to maintain the pH m charge gradient and support the pmf although m continues to fall due to the continued mCa 2+ influx. On the other hand, inhibiting ATP m hydrolysis (Figures 9C,D) to prevent H + pumping not only enhances the fall in m (Figures 4C,D) to retard further mCa 2+ loading by the MCU, but also permits slow CHE m -mediated mCa 2+ efflux (Figures 6A,B,E,F) in exchange for mH + influx until the diminishing pH m gradient is abolished (Figures 7C,D).
Alternatively, we demonstrated CHE m activity by acidifying the external medium before adding CaCl 2 , while blocking NCE m and NHE m activities by using Na + free buffer and substrates. We observed a slowly increasing [Ca 2+ ] e coupled to a slowly increasing [H + ] m . We used Ru360 to expose the net amount of mCa 2+ efflux via CHE m by blocking the effluxed Ca 2+ from re-entering via MCU (Figures 1, 2). It is unlikely that 0.1-1 µM Ru360 inhibits CHE m because Ru360 did not block mCa 2+ efflux (Figures 1, 2), only mCa 2+ influx. Of course, Ru360 might block another mode of non-MCU Ca 2+ uptake. Our proposed mechanism is described schematically in Figures 10A,B. We postulate that CHE m activity is completely inhibited if the matrix remains alkaline (large pH m gradient), thus exposing net Ca 2+ uptake via MCU. The slow increases in [Ca 2+ ] m that we observed previously (Haumann et al., 2010) likely represent net slow mCa 2+ via MCU (reference Figure 5).
A leucine zipper EF hand-containing trans-membrane protein (LETM1) found in non-mammalian cells is thought to be a molecular component of CHE m (Jiang et al., 2009;Shao et al., 2016). Knockdown and expression of LETM1 in a number of cell lines support its role in Ca 2+ /H + exchange, particularly in mitochondria (Jiang et al., 2013;Doonan et al., 2014). Alternatively, other studies (Nowikovsky et al., 2004(Nowikovsky et al., , 2012Froschauer et al., 2005;Malli and Graier, 2010;Austin et al., 2017) support that LETM1 either does not mediate Ca 2+ efflux (De Marchi et al., 2014) or that it mediates K + /H + and/or Na + /H + exchange, so conclusive genetic evidence for CHE requires more study. It is important to note that the elusive CHE protein appears to be insensitive to MCU inhibitors, i.e., ruthenium red (RR) compounds (Bernardi et al., 1984), and to CGP-37157, the NCE inhibitor (Tsai et al., 2014). The present study explores for the first time the kinetics of CHE m activity in relation to MCU activity in cardiac cell mitochondria.
m < E REV−ATPase Promotes ATP Hydrolysis F O F 1 -ATPsynthase/ase directionality is governed by m and its "reversal potential" E REV−ATPase , which in turn is dependent on the concentration of the reactants ATP/ADP, and H + (Metelkin et al., 2009;Chinopoulos and Adam-Vizi, 2010;. Additional factors of E REV that affect the direction and rate of ATP synthesis/hydrolysis are the free [P i ] and the H + m /ATP m coupling ratio, n (Cross and Muller, 2004). When m becomes less negative than E REV , which depends on a high [ATP] m and pH m , but a low [ADP] m , H + ejection by complex V becomes thermodynamically favorable (Metelkin et al., 2009;Chinopoulos and Adam-Vizi, 2010;Chinopoulos, 2011). E REV−ATPase can occur when m falls between −130 and −100 mV, depending on matrix [ATP] m /[ADP] m , [P i ] m , pH m , and the coupling ratio Chinopoulos, 2011). Others (Leyssens et al., 1996;Bains et al., 2006;Chinopoulos and Adam-Vizi, 2010) have observed that a fall in m caused by a protonophore, such as DNP or CCCP, can induce ATP hydrolysis through reversal of F O F 1 -ATPsynthase. The consequent H + pumping by complex V would tend to partially restore m to offset the protonophoreinduced decreases in pH m and m as discussed above. The electrical gradient m and the H + chemical gradient [H + ] m together contribute to the total pmf that powers the synthesis of ATP; when pmf is not maintained, hydrolysis of matrix ATP occurs. Previous studies have also furnished indirect evidence for reversal of F O F 1 -ATPsynthase under conditions of reduced mCa 2+ uptake and a fully depolarized m with CCCP (Leyssens et al., 1996;Bains et al., 2006). ATP m hydrolysis has been reported to occur in vivo during cardiac ischemia (Grover et al., 2004), but the in vivo m at which this occurs is not known. Here we show how a DNP-induced fall in m induces ATP hydrolysis.
In the absence of OMN, the lack of a fall in ATP levels after adding 10 µM DNP indicated that ATP m hydrolysis (Figure 9) did not occur because m remained relatively stable before adding CaCl 2 . However, adding CaCl 2 resulted in a gradual, but large, fall in m over time. In the presence of 20 µM DNP and 25 µM CaCl 2 , ATP hydrolysis occurred (20-25% of maximum) with a decrease in m at an IMM gradient of approximately 0.35 pH m units (Figures 7A,B). A faster rate of ATP hydrolysis was indicated by the additional fall in [ATP] m over time after adding 30 µM DNP and CaCl 2 . The DNP-induced falls in m were accompanied by reduced ATP m /ADP m ratios (see section "Supplementary Materials S.1.11, S1.12 and Supplementary Results S.2.9") indicating consumption of ATP, as also shown by the lower [ATP] m (Figures 9A,B). A calculation of available matrix ATP is given (see section "Supplementary Results S.2.10"). In the presence of 100 µM DNP and added CaCl 2 , m was maximally depolarized (Figures 4A,B), the pH m gradient was abolished (Figures 7A,B), and NADH was oxidized (Figures 8A,B), indicating that ATP m hydrolysis was insufficient to maintain the pmf. This contrasts to the situation with 10-30 µM DNP where pmf was supported largely by the pH m gradient, as also reflected by the maintained NADH redox state. m is normally fully polarized when complex V is blocked by OMN (Valdez et al., 2006;Brand and Nicholls, 2011); however, the effect of DNP to slightly decrease m was intensified when OMN was present, particularly after adding 25 µM CaCl 2 that intensifies the depolarization of m in the presence of DNP. This effect of DNP in the absence of OMN indicates that ATP hydrolysis indeed supported the pH m via H + pumping even at a relatively small decline in m with DNP. With OMN present, ATP hydrolysis cannot occur (Figures 9C,D) and so complex V cannot contribute to maintaining pH m ; therefore, the low pH m accompanied by a high [Ca 2+ ] m must have activated CHE m .

Changes in pH m , [Ca 2+ ] m , and NADH Are Larger With OMN Than Without OMN
An interesting observation of our study is the contribution of complex V to maintain the pH m gradient (and thus supporting the pmf ) whereby the H + leak is compensated by augmented H + pumping by complex V; this resulted in slow mCa 2+ influx ("Ca 2+ leak") that could be blocked by Ru360, which indicates the influx likely occurred via MCU. But if compensatory H + pumping is blocked by OMN, the matrix becomes acidic, the pH m gradient falls lower, and slow mCa 2+ efflux occurs via CHE m thus masking the slow mCa 2+ influx ( Figure 10B). Evidence for H + pumping during ATP hydrolysis during DNP-mediated H + influx was provided by the maintenance of an alkaline pH m ; moreover, pH m indeed fell when H + pumping was blocked by OMN. Similarly, if mitochondria reside in an acidic environment (Figures 1, 2), [H + ] m falls as [Ca 2+ ] e rises, indicating CHE m . Indeed, in a previous study it was reported that adding lactic acid to a Na + free mitochondrial suspension increased buffer Ca 2+ by 43% (Gambassi et al., 1993); it was suggested that Ca 2+ was extruded as H + influx caused H + ions to compete with Ca 2+ ions for mitochondrial binding sites (Gambassi et al., 1993). We furnish direct evidence for a link between Ca 2+ efflux with H + influx in mammalian cardiac muscle mitochondria, when Na + is absent and the MCU is blocked after adding CaCl 2 .
NADH levels remained unchanged after adding DNP and CaCl 2 (Figures 8A,B); this likely reflects the faster state 2 respiration (Supplementary Figure S2) since the inward H + leak by DNP was balanced by H + pumping from complex V as well as from complexes I, III, and IV. Only at 100 µM DNP with CaCl 2 , which fully depolarized m (Figures 4A,B), did DNP result in a lower pH m (Figures 7A,B) and a more oxidized redox state, i.e., a decrease in NADH (Figures 8A,B). It is likely that an increase in F O F 1 -ATPase activity plus a faster TCA cycle turnover (increased NADH/NAD + ratio) can result in maintained NADH levels despite the DNP-induced H + leak. In the presence of OMN, however, NADH was gradually oxidized (Figures 8C,D) along with the fall in pH m (Figures 7C,D); this scenario likely occurred because the additional H + pumping by complex V to support m was blocked. We observed that adding CaCl 2 alone did not significantly change NADH levels in this model, which is consistent with our earlier study (Haumann et al., 2010). Although an increase in [Ca 2+ ] m can stimulate NADH producing dehydrogenases McCormack and Denton, 1980;Wan et al., 1989;Brandes and Bers, 1997), our experiments were conducted at maximal [Ca 2+ ] m values below the K 0.5 of 1 µM Ca 2+ at which these dehydrogenases are reported to be activated McCormack and Denton, 1980 (Huang et al., 2007)). This indicated that the driving force for both Ca 2+ and H + would remain inward despite H + pumping at complex V to attempt to re-establish the pH m gradient by compensating for the DNP-mediated H + influx. Based on our estimated m and the calculated Ca 2+ and H + equilibrium potentials driving both Ca 2+ and H + inward, we conclude that the outward H + pumping by complex V (in addition to complexes I, III, IV) was sufficient to compensate for the continued inward influx of H + mediated by DNP thus restoring the pH m gradient, but not the pmf, and thus preventing activation of CHE m . Ru360 blocked this additional uptake of mCa 2+ by the MCU so that [Ca 2+ ] e did not continue to fall.
We predict that the major conduit for both fast and slow mCa 2+ influx under our experimental conditions occurs primarily via the MCU. The efflux of Ca 2+ via the CHE m is slow so we expect the re-uptake of Ca 2+ via the MCU also would be slow. Although the J CHE flux equation alone predicted that slow mCa 2+ (Figures 4A-D), [Ca 2+ ] m did not rise as it did in the presence of DNP (Figures 5A,B) when pH m was maintained (Figures 7A,B). This suggests that the secondary, slow uptake of mCa 2+ is indirectly related to H + pumping due to the decline in [H + ] m to support the pmf ; the additional, slow mCa 2+ uptake by the MCU occurs because of the remaining charge gradient ( m ) and Ca 2+ chemical gradient.
In contrast, in the presence of OMN the kinetics of the delayed, slow mCa 2+ efflux via CHE m under conditions of reduced m and low pH m are different. Our estimates of (Huang et al., 2007) of −60 to −70 mV at 700 s with OMN present are much lower than without OMN; this is likely due to dissipation of both pH m and m gradients because H + pumping by complex V to support pH m (and m ) was blocked. With OMN present, we estimated Nernst potentials of +13 and +6 mV, respectively, for Ca 2+ and H + (calculated at 700 s). Based on these Nernst potentials the driving forces for both Ca 2+ and H + would remain inward with OMN present, although their Nernst potentials are reversed compared to those in the absence of OMN. With the slow inward driving force for H + , unmatched by H + pumping at complex V, pH m approached pH e and net [Ca 2+ ] m became lowered due to CHE m . Because inhibiting the MCU with Ru360 caused a robust increase in [Ca 2+ ] e , this indicated the Ca 2+ effluxed via CHE m re-enters via the MCU unless this pathway is blocked. Under the unique condition of collapsed m (100 µM DNP) and pH m gradients, the secondary, slow uptake of mCa 2+ is absent (Figures 5A,B, black lines) so that the decline in [Ca 2+ ] m via CHE m is fully observed (Figures 6A,B). Thus, a fall in pH e strongly supports net mCa 2+ efflux via CHE m even though the Nernst potentials indicate continued slow mCa 2+ influx (via MCU), which indeed occurs if there is remaining m . This means that net Ca 2+ efflux due to CHE m (Figures 1, 2 and Supplementary Figure S.6) can be exposed by blocking the MCU after the initial bolus of CaCl 2 to prevent further mCa 2+ uptake. CHE m is predicted by the J CHE equation to favor mCa 2+ efflux in exchange for mH + influx based on matrix and buffer ion concentrations obtained with OMN present (Supplementary Figure S.10). Our prediction assumes that Ca 2+ is exchanged for 2H + with equal affinities for both cations, or a higher affinity for H + . Does Transient, Low Conductance mPTP Also Shuttle Ca 2+ Across the IMM in These Experiments?
Inducing a partial m depolarization was reported to cause a slow influx of mCa 2+ through low conductance mPTP opening (Saotome et al., 2005). CsA prevented both an increase in mCa 2+ and the release of the small molecule calcein during simulated ischemia in cardiomyocytes suggesting that transient mPTP opening during ischemia allowed mCa 2+ influx (Seidlmayer et al., 2015). In the present study adding CaCl 2 in the presence of DNP or an acidic buffer caused falls in m , so could low conductance mPTP opening have contributed to the secondary, slow increase or decrease in m [Ca 2+ ] we observed in the absence or presence of OMN? We doubt this for the following reasons: (1) ROS, adenine nucleotide levels, and other factors are believed to contribute to mPTP formation during IR injury. But in our study we did not utilize IR to induce increases in Ca 2+ and ROS or decreases in pH m or m ; (2) Altering just the driving force for protons across the IMM using DNP or external pH to exchange Ca 2+ ion for H + ions is not compatible for a mechanism to cause or prevent formation of mPTP but it is for inducing mCHE activity; (3) Transient mPTP formation is controversial and based largely on the utility of calcein or other small particles to mark mitochondrial release of small molecules with free flowing ions such as Ca 2+ (Petronilli et al., 1999); (4) CsA-sensitive transient mPTP opening in individual mitochondria of cardiac myocytes is quite rare even with elevated m[Ca 2+ ] or exposure to H 2 O 2 (Lu et al., 2016); (4) CsA, or its inhibition of the peptidyl prolyl cis-trans isomerase activity of cyclophilin D, has known and unknown effects on mitochondrial function that may be unrelated to mPTP formation (Giorgio et al., 2010). Some interpretations on effects of cyclophilin D, via CsA, may pertain to changes in Ca 2+ flux due to mCHE rather than transitional mPTP opening.

CSA Ceases Activation of CHE m
CsA unexpectedly stopped the secondary CaCl 2 -induced effects attributed to CHE m . CsA ceased all apparent CHE m activity after adding CaCl 2 when pH e was 6.9 or 7.15, as assessed by measurements of extra-matrix [Ca 2+ ] e , pH m , and m (Supplementary Figures S.1A-C). CsA did not blunt the partial m depolarization induced by DNP alone at pH e 7.15, but did delay full m depolarization induced by adding CaCl 2 after DNP (Supplementary Figures S.7A,B). We do not believe the slow, attenuated decreases in extrusion of Ca 2+ or slow fall in matrix pH observed in the presence of CsA are directly related to inhibition of permanent or transient mPTP opening. CsA did not directly prevent the m depolarization that occurs during CHE m or with addition of DNP alone. In the absence of CsA (Figures 1A-C), the observed changes in pH m , external [Ca 2+ ] e , and m , induced by adding CaCl 2 at extra-matrix pH 6.9, occurred very slowly over 25-30 min; this is indicative of slow cation exchange activity, not mPTP. Moreover, full m depolarization was incomplete. CsA or its inhibition of cyclophilin D may obviate the conditions for matrix H + influx or mCa 2+ efflux as well as Ca 2+ recycling via the MCU. CsA may prevent dissipation of the pH gradient when the external pH is low. Since the results obtained in the presence of CsA are not compatible with preventing or delaying mPTP opening, the effects of CsA in this setting are unclear. Additional experiments will be needed to delineate the mechanism of CsA on preventing CHE m .

Other Potential Limitations of the Study
One important limitation of our study is the lack of a selective inhibitor of CHE m to aid in defining a more precise mechanism of action. Since the gene code for LETM1 and its protein sequence are known, point mutations (Tsai et al., 2014) and knockdowns (Jiang et al., 2013;Doonan et al., 2014) in mammalian models will be helpful to assess mechanisms and kinetics of this cation antiporter; but it remains unclear if LETM1 mediates CHE m exclusively, or at all. Another limitation is that mitochondria were examined outside their normal milieu so that the contributions of ATP synthesis by glycolysis and ATP hydrolysis for cellular metabolic support could not be assessed. Experiments were conducted at room temperature at which metabolism would be lower and buffering capacity different than at 37 • C. The activity of CHE m during cardiac IR is unknown and mCa 2+ efflux in cardiac mitochondria may occur primarily via the NCE m and not CHE m . Nevertheless, induction of CHE m could occur in vivo during IR injury under very specific circumstances of trans-IMM cationic imbalance. Evaluation of CHE m activity in cardiac myocytes after IR injury should be helpful to design protective strategies using this mechanism.

CONCLUSION
This study furnishes new insights into the bioenergetic and dynamic mechanisms in cardiac cell mitochondria of delayed, slow mCa 2+ influx via the MCU, and mCa 2+ efflux via the pH mdependent CHE m . We demonstrate the kinetics of slow changes in mCa 2+ loading/unloading that are linked to unblocked vs. blocked ATP m hydrolysis to decrease vs. increase pH m , respectively, after partial depolarization by DNP. We found that after an initial CaCl 2 bolus there is slow mCa 2+ influx (Ca 2+ leak) through a Ru360-sensitive pathway if H + pumping counteracts a H + leak; however, there is net slow mCa 2+ efflux that overrides m -mediated Ca 2+ influx that is activated via CHE m if there is a high pH m gradient. In cardiac mitochondria, the rapid and slow mode of uptake of mCa 2+ appears to be dependent primarily on the trans-membrane [Ca 2+ ] and m gradients if outward H + pumping counteracts inward H + entry. In contrast, slow extrusion of mCa 2+ by CHE m appears to be dependent primarily on the [ H + ] m gradient induced by H + influx/leak by DNP or by an acidic pH e . Importantly, if NCE m and NHE m are inactivated, blocking complex V might prevent delayed Ca 2+ overload and instead stimulate Ca 2+ extrusion via CHE m if there is an inward H + leak. In intact cells, this can also serve to preserve TCA cycle-generated ATP, i.e., substrate level phosphorylation. Such passive homeostatic balance of [Ca 2+ ] m may occur during cardiac injury when there is mCa 2+ loading accompanied by declines in NADH redox state, pH m and m . We conclude that the differences in the rate and magnitude of mCa 2+ influx/efflux in partially depolarized mitochondria, in the presence or absence of F O F 1− ATPase activity, can be ascribed to the underlying changes in pmf components, pH m and m , after rapid mCa 2+ loading.

AUTHOR CONTRIBUTIONS
DS proposed the study and its initial design. JH conducted most experiments, carried out initial statistical analysis, constructed initial figures, and participated in design, interpretation and writing. AG, AB, CB, CN, and MB conducted supporting experiments. AC, W-MK, and RD participated in theoretical interpretation of the results and text editing. DS and AC supervised the team in subsequent experimental designs, interpretation of results, and manuscript construction and writing.

FUNDING
This project was supported by grants from the National Institutes of Health (R01HL089514, R01HL095122 and 5T35HL072483) and the Veterans Administration (Merit Review BX820405P and BX002539).