The relationship between free and total calcium concentrations in the matrix of liver and brain mitochondria.

Three sequential phases of mitochondrial calcium accumulation can be distinguished: matrix dehydrogenase regulation, buffering of extramitochondrial free calcium, and finally activation of the permeability transition. Relationships between these phases, free and total matrix calcium concentration, and phosphate concentration are investigated in rat liver and brain mitochondria. Slow, continuous calcium infusion is employed to avoid transient bioenergetic consequences of bolus additions. Liver and brain mitochondria undergo permeability transitions at precise matrix calcium loads that are independent of infusion rate. Cytochrome c release precedes the permeability transition. Cyclosporin A enhances the loading capacity in the presence or absence of acetoacetate. A remarkably constant free matrix calcium concentration, in the range 1-5 microM as monitored by matrix-loaded fura2-FF, was observed when total matrix calcium was increased from 10 to at least 500 nmol of calcium/mg of protein. Increasing phosphate decreased both the free matrix calcium and the matrix calcium-loading capacity. Thus the permeability transition is not triggered by a critical matrix free calcium concentration. The rate of hydrogen peroxide detection by Amplex Red decreased during calcium infusion arguing against a role for oxidative stress in permeability pore activation in this model. A transition between a variable and buffered matrix free calcium concentration occurred at 10 nmol of total matrix calcium/mg protein. The solubility product of amorphous Ca3(PO4)2 is consistent with the observed matrix free calcium concentration, and the matrix pH is proposed to play the major role in maintaining the low matrix free calcium concentration.


From the Buck Institute for Age Research, Novato, California 94945
Three sequential phases of mitochondrial calcium accumulation can be distinguished: matrix dehydrogenase regulation, buffering of extramitochondrial free calcium, and finally activation of the permeability transition. Relationships between these phases, free and total matrix calcium concentration, and phosphate concentration are investigated in rat liver and brain mitochondria. Slow, continuous calcium infusion is employed to avoid transient bioenergetic consequences of bolus additions. Liver and brain mitochondria undergo permeability transitions at precise matrix calcium loads that are independent of infusion rate. Cytochrome c release precedes the permeability transition. Cyclosporin A enhances the loading capacity in the presence or absence of acetoacetate. A remarkably constant free matrix calcium concentration, in the range 1-5 M as monitored by matrix-loaded fura2-FF, was observed when total matrix calcium was increased from 10 to at least 500 nmol of calcium/mg of protein. Increasing phosphate decreased both the free matrix calcium and the matrix calciumloading capacity. Thus the permeability transition is not triggered by a critical matrix free calcium concentration. The rate of hydrogen peroxide detection by Amplex Red decreased during calcium infusion arguing against a role for oxidative stress in permeability pore activation in this model. A transition between a variable and buffered matrix free calcium concentration occurred at 10 nmol of total matrix calcium/mg protein. The solubility product of amorphous Ca 3 (PO 4 ) 2 is consistent with the observed matrix free calcium concentration, and the matrix pH is proposed to play the major role in maintaining the low matrix free calcium concentration.
Isolated mitochondria from a variety of sources possess a large but finite capacity to accumulate and retain Ca 2ϩ (for reviews see Refs. 1 and 2). When this limit is exceeded, mitochondria assemble a pore in their inner membrane that is non-selectively permeable to ions and solutes up to 1.4 kDa (for review see Ref. 3). It is unclear what exactly defines Ca 2ϩ overload and how this triggers the permeability transition. Phosphate (P i ) is required for massive Ca 2ϩ loading of the matrix and a variety of evidence suggests that a calcium phosphate complex is formed within the matrix once about 10 nmol of Ca 2ϩ /mg has been accumulated. First, phosphate is required for extensive matrix Ca 2ϩ loading that can exceed 1 M total Ca 2ϩ concentration before swelling can be observed (1,2). Sec-ond, over a wide range of total matrix Ca 2ϩ (͚Ca 2ϩ m ) 1 the activity of the Ca 2ϩ efflux pathways in both liver and brain mitochondria are inversely related to the free P i concentration but independent of ͚Ca 2ϩ m , consistent with a matrix free Ca 2ϩ , [Ca 2ϩ ] m , that is governed by the solubility product of a calcium phosphate complex and is suboptimal for maximal activity of the efflux pathways of liver or brain mitochondria (4,5). Third, mitochondria can maintain a remarkably constant setpoint when ͚Ca 2ϩ m is varied widely (6), indicating that the activity of the efflux pathway, and hence [Ca 2ϩ ] m , is not varying. Fourth, mitochondria accumulating Ca 2ϩ in the presence of excess phosphate extrude 1 H ϩ per Ca 2ϩ accumulated, consistent with the formation of Ca 3 (PO 4 ) 2 in the matrix (7). Finally, P i -depleted mitochondria in the presence of acetate as permeant anion show an increasing efflux activity with increasing Ca 2ϩ load and fail to maintain a setpoint that is independent of ͚Ca 2ϩ m (4). All of these observations are consistent with a matrix Ca 2ϩ phosphate complex that obeys mass-action relationships to maintain a low [Ca 2ϩ ] m . However, any complex must be freely reversible, since the physiological complex is capable of dissociating into Ca 2ϩ and P i immediately following mitochondrial depolarization, allowing the two ions to exit the mitochondrion on their individual carriers (5).
Mitochondrial Ca 2ϩ loading has almost invariably been investigated by the addition of one or more bolus additions of Ca 2ϩ , each of which induces a non-steady-state condition in which mitochondrial respiration, membrane potential and redox status change with time. Even multiple, relatively small, Ca 2ϩ additions result in repetitive partial mitochondrial depolarizations and bioenergetic demands. In addition, it is highly likely that the calcium phosphate complex formed in response to a rapid increase in [Ca 2ϩ ] m following a bolus addition may differ from that formed when Ca 2ϩ is slowly accumulated, since many forms of calcium phosphate are thermodynamically unstable and spontaneously interconvert (8).
In this study we first investigate the capacity of liver and brain mitochondria to accumulate Ca 2ϩ when the cation is slowly infused into the incubation, allowing the mitochondria to accumulate the cation continuously, with minimal bioenergetic demands. Second we monitor the matrix free Ca 2ϩ concentrations during such loading in order to establish whether the supposed matrix buffering actually occurs, and finally we attempt to determine whether any relationship exists between matrix free Ca 2ϩ and the initiation of the permeability transition.
Preparation of Rat Liver Mitochondria (RLM)-Mitochondria were isolated from 6-week-old Wistar rats. The liver was homogenized in 125 mM sucrose, 125 mM mannitol, 5 mM Hepes, 1 mM EGTA, pH 7.2 and centrifuged at 1000 ϫ g for 10 min at 4°C. The supernatant was then centrifuged for 10 min at 8 000 ϫ g at 4°C. The resulting pellet was resuspended and centrifuged for 10 min at 8500 ϫ g at 4°C. The upper layer of this pellet was removed by gentle pipetting and the lower mitochondrial pellet resuspended in 0.5 ml of 250 mM sucrose, 16 M BSA, 5 mM Hepes, pH 7.2.
Preparation of Rat Brain Mitochondria (RBM)-The cerebral cortices of two 6-week-old rats were rapidly removed into 20 ml of ice-cold isolation buffer (320 mM sucrose, 5 mM Tes, 1 mM EGTA, pH 7.2) and homogenized. The homogenate was centrifuged at 1000 ϫ g for 5 min at 4°C. The supernatant was centrifuged at 8500 ϫ g for 10 min, and the resulting pellet resuspended in 1 ml of isolation buffer. This was layered onto a discontinuous gradient consisting of 1 ml of 6% Ficoll, 0.5 ml of 9% Ficoll, and 4.5 ml of 12% Ficoll (all prepared in isolation buffer) and centrifuged at 75,000 ϫ g for 30 min. The myelin, synaptosomal, and free mitochondrial fractions formed respectively above the 6% layer, as a doublet within the 9% layer and as a pellet. The pellet was resuspended in 250 mM sucrose, 16 M bovine serum albumin, 10 mM Tes, pH 7.2 and centrifuged at 8000 ϫ g before being resuspended in this last buffer to 10 -20 mg of protein/ml by the Bradford protein assay.
Mitochondrial Ca 2ϩ Accumulation-0.1 mg of mitochondrial protein was suspended in 2 ml of incubation medium (100 mM NaCl, 25 mM Hepes, pH 7.2, 1 g/ml oligomycin, 2 mM sodium phosphate, and 0.5 mM ADP unless otherwise stated. A NaCl-based medium was used as this was shown in an earlier study (4) to give optimal respiratory control. Experiments with RLM utilized 2 mM succinate as substrate in the presence of 1 M rotenone; those with RBM utilized 5 mM glutamate plus 5 mM malate or 5 mM pyruvate plus 5 mM malate. Experiments were performed at 37°C in stirred cuvettes in a PerkinElmer LS-50B fluorimeter. CaCl 2 additions were made either as bolus additions or as gradual infusions with a Braun Perfusor (FT Scientific Instruments, Glos., UK) modified to take a Hamilton microsyringe (5).
Depletion of Endogenous Phosphate-Isolated mitochondria were depleted of endogenous phosphate by incubation with 1 mM glucose, 0.75 units/ml hexokinase, 1 mM MgCl 2 , 5 mM glutamate, 5 mM malate ,and 0.5 mM ADP in incubation medium at 37°C for 5 min in the presence of substrate as previously described (5).
Mitochondrial Free Ca 2ϩ -RBM (0.1 mg of protein) were incubated in 25 l of 250 mM sucrose, 10 mM Tes, 80 M fura2-FF AM, 16 M BSA, pH 7.2 on ice for 30 min and then at room temperature for 30 min. Any contaminating synaptosomes were permeabilized by addition of 1 ml of 250 mM sucrose, 16 M albumin, 5 mM Hepes, pH 7.2 containing 0.01% digitonin for the last 5 min of the incubation. The mitochondria were then centrifuged for 1 min at 10,000 ϫ g, the pellet resuspended in 1 ml of 250 mM sucrose, 16 M BSA, 5 mM Hepes, pH 7.2 and recentrifuged. The pellet was finally resuspended in 20 l of the same medium and used immediately.
Estimation of [Ca] m in Equilibrium with Amorphous Tricalcium Phosphate as a Function of pH m -The following dissociation constants were taken for phosphate, pK 1 ϭ 2.13, pK 2 ϭ 7.2, pK 3 ϭ 12.39 (10). A representative value for the K sp for amorphous Ca 3 (PO 4 ) 2 of 3 ϫ 10 Ϫ30 was assumed, as published values from vary from 10 Ϫ26 to 10 Ϫ33. Equilibrium was assumed across the membrane via the phosphate carrier for an H 2 PO 4 Ϫ /OH Ϫ antiport (11). As the calculation was intended to show how [Ca 2ϩ ] m in equilibrium with Ca 3 (PO 4 ) 2 could vary with pH and [P i ] e rather than report definitive values, no attempt was made to correct for activity coefficients of the charged species in the highly non-ideal conditions within the matrix.
Mitochondrial Light Scattering, Membrane Potential, H 2 O 2 Production, and NAD(P) Pool Redox Status-All parameters were monitored in a stirred cuvette at 37°C in the LS50B fluorimeter. Mitochondrial light scattering was monitored at 625 nm. Changes in membrane potential were followed qualitatively by the fluorescence quenching of tetramethylrhodamine methyl ester (549 nm excitation, 575 nm emission). H 2 O 2 production was monitored fluorimetrically with 1 M Amplex Red and 0.75 units/ml horseradish peroxidase (563 nm excitation, 587 nm emission). Changes in NAD(P)H fluorescence were monitored at 350 nm excitation, 450 nm emission.
Cytochrome c Release-Release of cytochrome c was monitored by removing 100-l samples from the cuvette during an experiment and centrifuging to separate mitochondrial pellet and supernatant. Samples were separated and visualized by Western blotting. The blot was blocked with 5% albumin in TBS-Tween (25 mM Tris-HCl, pH 7.6, 150 mM NaCl, 0.05% Tween 20) and then incubated with 1:2500 mouse anti-cytochrome c antibody in TBS-Tween plus 1% BSA followed by 1:2500 sheep anti-mouse antibody-horseradish peroxidase conjugate in TBS-Tween containing 1% BSA prior to enhanced chemiluminescence (ECL) detection (Amersham Biosciences).

Rat Liver Mitochondrial Ca 2ϩ -loading Capacity during
Steady Ca 2ϩ Infusion-The capacity of RLM to accumulate Ca 2ϩ in the presence of phosphate, and ADP is dependent upon the mode of addition (Fig. 1). A single bolus addition of 450 nmol of Ca 2ϩ /mg initiates a permeability transition within 15 min, whereas 12 smaller additions of 50 nmol of Ca 2ϩ /mg can be made to a parallel preparation, while the steady infusion of Ca 2ϩ at a rate of 85 nmol/mg/min allowed 800 nmol/mg to be accumulated before the permeability transition was observed.
As previously demonstrated (5) the steady infusion of Ca 2ϩ into a mitochondrial incubation results in an initial increase in external Ca 2ϩ concentration ([Ca 2ϩ ] e ) until the uniporter is sufficiently active to accumulate Ca 2ϩ at a rate equal to that at which Ca 2ϩ is being added to the external medium (i.e. the infusion rate plus the activity of the mitochondrial Ca 2ϩ efflux pathway). Subsequently, and for as long as the activities of the uniporter and efflux pathway remain constant, Ca 2ϩ is accumulated into the matrix at the same rate that it is delivered to A would be predicted from the catastrophic consequences of removing the proton-impermeability of the inner membrane, permeability pore opening in individual mitochondria is associated with a virtually instantaneous collapse of membrane potential (12,13). The resultant discharge of Ca 2ϩ into the medium may trigger Ca 2ϩ overload in adjacent mitochondria, leading to a chain reaction in which the entire mitochondrial population is seen to undergo the permeability transition in a short period of time. In order to minimize this effect in the present study, and also to ensure that anoxia did not occur during prolonged Ca 2ϩ infusions, a very low mitochondrial protein concentration (0.05 mg/ml incubation) was used in most of these experiments.
Changes in mitochondrial membrane potential, NAD(P) ϩ reduction, light scattering and cytochrome c retention were monitored in parallel with the Ca 2ϩ infusion (Fig. 2). At the single mitochondrion level, the inner membrane permeabilization associated with the permeability transition results in an immediate collapse in membrane potential (13) and consequent loss of matrix Ca 2ϩ . A complicating factor therefore in conventional studies with mitochondrial populations is that this released Ca 2ϩ can be taken up by adjacent mitochondria, either masking the initiation of the permeability transition, or triggering a chain reaction by inducing Ca 2ϩ overload. Since the release of cytochrome c is an irreversible consquence of outer membrane rupture following the permeability transition, the experiment depicted in Fig. 2d, was performed to monitor the time course of release of the cytochrome during continuous infusion. Samples were taken from the cuvette during the Ca 2ϩ infusion and rapidly centrifuged to pellet the mitochondria through silicone oil. Extensive cytochrome c release is first seen just before the massive release of matrix Ca 2ϩ due to the permeability transition (sample iv). This suggests that a significant proportion of the mitochondria in the cuvette have undergone the transition by this stage. The modest increase in external free Ca 2ϩ indicates that surrounding mitochondria accumulate Ca 2ϩ from their depolarized neighbors, which would be predicted to facilitate in turn their depolarization and propagation of the transition throughout the incubation. A permeability transition-independent release of cytochrome c from rat brain mitochondria has been reported previously (14), although in that case it was induced by a single massive bolus addition of Ca 2ϩ (3200 nmol/mg) and could therefore be due to transient osmotic swelling of the matrix prior to formation of the osmotically inactive calcium phosphate complex.
No change in the extent of TMRM ϩ quenching could be detected until shortly before the onset of the permeability transition (Fig. 2a). In contrast to Ca 2ϩ , whose distribution is the consequence of a dynamic balance between independent uptake and efflux pathways, TMRM ϩ responds in a Nernstian manner to the membrane potential. A permeability transition in a fraction of the mitochondria is therefore not masked by reuptake of the membrane potential indicator by the residual mitochondria. For example, collapse in the membrane potential in 50% of the mitochondria would halve the aggregate matrix volume in which the TMRM ϩ is accumulated, releasing the probe and decreasing the quenching in the cuvette.
Light scattering increased steadily during the infusion (Fig.  2b). Since this parameter is a function of the difference in refractive index between the matrix and medium, it is likely that what is being observed is an increase in matrix refractive index due to the formation of a calcium phosphate complex rather than a physical contraction of the matrix (14). NAD(P)H fluorescence also increases as Ca 2ϩ is infused (Fig.  2c). As will be seen below (Fig. 8) [Ca 2ϩ ] m is almost invariant over the range where the increased fluorescence signal is observed and so it is unlikely that the signal increases as a result of Ca 2ϩ -dependent substrate dehydrogenase activation (15). Since fluorescence is sensitive to the environment, it is equally possible that the fluorescence change reflects a change in matrix environment rather than increased reduction.
By altering the speed of the infusion pump it is possible to determine whether the onset of the permeability transition is influenced by the rate or the extent of matrix Ca 2ϩ loading. Varying the infusion rate from 42.5 to 170 nmol of Ca 2ϩ /mg/ min had no effect upon the capacity of the liver mitochondria to  accumulate Ca 2ϩ (Fig. 3a). In the presence of the permeability transition inhibitor cyclosporin A (Fig. 3b) the capacity increased almost 3-fold and again seemed independent of the rate of infusion, although a slight decrease in capacity was observed for the slowest infusion.
Oxidation of RLM matrix NADH by acetoacetate in the absence of exogenous adenine nucleotides facilitates the permeability transition in response to bolus additions of Ca 2ϩ (16). It has recently been reported (17) that acetoacetate activates a low conductance form of the permeability transition pore in RLM, that is sensitive to cyclosporin A and manifests itself as an increase in the rate of Ca 2ϩ efflux observed following ruthenium red addition, but without a detectable loss of membrane potential. Under the present conditions, NADH oxidation induced by acetoacetate does not increase the steady-state rate of Ca 2ϩ efflux from the mitochondria, since that would be reflected in an increased steady-state [Ca 2ϩ ] e and none can be detected (Fig. 4), but instead the capacity of the mitochondria to accumulate Ca 2ϩ is considerably decreased. Importantly this effect of acetoacetate is still observed in the presence of 1 M cyclosporin and ADP (Fig. 4).
Relationship between Free and Total Matrix Ca 2ϩ Concentrations during Ca 2ϩ Infusion-Preincubation of isolated mitochondria with fluorescent Ca 2ϩ indicators can allow sufficient loading to occur to monitor matrix free Ca 2ϩ concentrations (15, 18 -24). In our hands it was difficult to achieve a reliable extent of loading with RLM and so subsequent experiments were performed with RBM.
The low affinity fura analog fura2-FF (K d ϭ 5.5 M) was found to load into the mitochondrial matrix as the acetoxymethyl ester and to be hydrolyzed sufficiently to enable changes in [Ca 2ϩ ] m to be followed. Since mitochondrial autofluorescence, due primarily to NAD(P)H at the wavelengths employed, changes at the onset of the permeability transition (Fig. 2) in most experiments this was corrected for by parallel determinations in the absence of loaded dye.
The hypothesis on which these studies were based was that changes in [Ca 2ϩ ] m in the presence of excess phosphate would be largely buffered by the formation of calcium phosphate complexes. In order initially to assess the ability of the loaded fura2-FF to detect changes in [Ca 2ϩ ] m therefore, mitochondria were extensively depleted of endogenous P i by preincubation with ADP, glucose and hexokinase, as previously described (5), and acetate was added as permeant anion to prevent build up of a pH gradient. Since calcium acetate is highly soluble it would be predicted that [Ca 2ϩ ] m would rise with Ca 2ϩ load. Fig.  5   matrix dehydrogenases increases with [Ca 2ϩ ] e (15) while under extensive loading conditions the activity of the efflux pathways is invariant with matrix Ca 2ϩ load but varies inversely with the matrix free phosphate (5). Fig. 6 shows the transition between these two phases of matrix Ca 2ϩ loading. When isolated mitochondria are suspended in incubation media similar to that used here, there is sufficient contaminating Ca 2ϩ in the medium and residual Ca 2ϩ in the matrix such that the initial loading condition when [Ca 2ϩ ] m varies with Ca 2ϩ load is not seen. On addition of 10 -30 M EGTA, a sharp decline in the steady-state [Ca 2ϩ ] e was observed as ͚Ca m decreased from 10 to 3 nmol/mg (Fig. 6), consistent with a decrease in free matrix Ca 2ϩ (5). In contrast, additions of Ca 2ϩ caused little increase in steady-state [Ca 2ϩ ] e , indicating that the setpoint had been attained.
Since inefficiency of the [Ca 2ϩ ] e buffering in the presence of acetate contrasts so much with that seen in the presence of excess P i (Fig. 1), the inference is that the latter allows [Ca 2ϩ ] m to be essentially independent of ͚Ca m over the range where a setpoint is observed, in the present preparation from 20 nmol/mg (Fig. 6) to 500 nmol/mg ͚Ca m (Fig. 1). Studies to investigate this were performed on RBM. Since RBM have been reported to respond to Ca 2ϩ addition differently from liver mitochondria (38) the basic infusion was repeated (Fig. 7). RBM maintain a high membrane potential and NAD(P)H reduction until the onset of the permeability transition in the same way as liver mitochondria.
This was tested in the experiments depicted in Fig. 8a (Fig. 8b), and this may represent the initiation of the permeability transition, which would allow matrix fura2-FF to be released and equilibrate with [Ca 2ϩ ] e . The relationship between [Ca 2ϩ ] m and ͚Ca 2ϩ m is shown in more detail in Fig. 8c. Based on a matrix volume of 1 l/mg the ratio of bound/free Ca 2ϩ in the matrix can reach 150,000 in Ca 2ϩ -loaded rat brain mitochondria.
It is frequently assumed that the permeability transition is triggered by an increase in matrix free Ca 2ϩ , however increasing external phosphate decreases the capacity of mitochondria to accumulate Ca 2ϩ before the permeability transition is activated (25). If the assumption is correct that [Ca 2ϩ ] m is defined by the solubility product of a calcium phosphate complex, then [Ca 2ϩ ] m would be buffered at lower values by the increased matrix P i . This is confirmed in Fig. 9. Increasing external P i from 2 to 5 mM decreases the capacity of brain mitochondria to buffer [Ca 2ϩ ] e by almost 50%; however, the [Ca 2ϩ ] m at which the permeability transition was activated in the presence of 5 mM P i was substantially lower than that in the presence of 2 mM P i . It can be concluded that the permeability transition is not triggered by an increased [Ca 2ϩ ] m . Consistent with this, cyclosporin A has no effect on the relationship between [Ca 2ϩ ] m and ͚Ca 2ϩ m during Ca 2ϩ infusion (Fig. 10). Cyclosporin A more than doubled the capacity of the mitochondria to accumulate and retain Ca 2ϩ without affecting the relationship between ͚Ca 2ϩ m and [Ca 2ϩ ] m until the permeability transition is activated.
The release of hydrogen peroxide from brain mitochondria oxidizing NAD-linked substrates is membrane potential-dependent, and bolus additions of Ca 2ϩ decrease H 2 O 2 release monitored by Amplex Red to an extent that can be correlated with a decrease in membrane potential (26). Since slow Ca 2ϩ infusion occurs independently of any significant depolarization (Fig. 2), H 2 O 2 -dependent Amplex Red oxidation in the presence of cyclosporin A was monitored during infusion of Ca 2ϩ (Fig.  11). Compared with a parallel blank infusion there was a slow decline in the rate. It is thus not evident that the permeability transition can be ascribed to a Ca 2ϩ -dependent oxidative stress.

DISCUSSION
Matrix Free Ca 2ϩ -A series of studies performed 10 -15 years ago established that free Ca 2ϩ concentrations within the matrices of isolated liver and heart mitochondria varied over a range from 0.1 to 2 M under conditions of limited matrix Ca 2ϩ loading, i.e. Ͻ10 nmol/mg of protein (15, 18 -23, 27). Three approaches were taken, a null-point technique in which extramitochondrial free Ca 2ϩ was adjusted until the addition of the Ca 2ϩ ionophore A23187 caused no net flux of Ca 2ϩ (18,28), determination from the activation state of Ca 2ϩ -dependent matrix dehydrogenases (15,23) and loading or entrapment of optical Ca 2ϩ indicators (15,19,20,23,27). Under these conditions matrix free Ca 2ϩ varied with external free Ca 2ϩ in a way consistent with physiological control of matrix dehydrogenase activities (for review see Ref. 29).
In reported using matrix-targeted aequorins (30), although the in vitro calibration technique employed has recently been criticized (31), since with an in situ calibration, values close to those obtained with Rhod-2 have been obtained (31). However, since aequorin is consumed by Ca 2ϩ , it is not suitable for the meas-urement of long term steady-state concentrations as studied here.
Matrix Total Ca 2ϩ -A limitation with the above studies is that total Ca 2ϩ is generally not determined in parallel, and so it is not possible to draw conclusions about the chelation of matrix Ca 2ϩ or how this changes with matrix load. In 1978 the first studies were performed in which steady-state extramitochondrial free Ca 2ϩ concentrations ([Ca 2ϩ ] e ) were monitored during extensive matrix Ca 2ϩ loading (4,5,31). In the presence of excess P i and physiological concentrations of adenine nucleotides, liver (6), and brain (4) mitochondria were able to restore a [Ca 2ϩ ] e that was independent of matrix Ca 2ϩ load from 10 to almost 1000 nmol of Ca 2ϩ /mg.
Analysis of the individual kinetics of the Ca 2ϩ uniporter and efflux pathways indicated that this setpoint was the consequence of a kinetic balance between the activities of a uniporter highly dependent upon [Ca 2ϩ ] e and an efflux pathway activity apparently totally insensitive to changes in total matrix Ca 2ϩ over this range (5). This latter in turn could be due either to saturation of the efflux pathway by [Ca 2ϩ ] m or to a [Ca 2ϩ ] m that was essentially independent of matrix Ca 2ϩ load over this range. Two experiments supported the latter alternative and indicated that complexation of Ca 2ϩ with matrix P i helped to maintain a constant [Ca 2ϩ ] m . First the activity of the RLM efflux pathway was inversely related to the P i concentration (5) and second when acetate replaced P i as permeant anion the Ca 2ϩ efflux activity, and hence the setpoint increased continuously with matrix load (5).
While such studies were initially criticized as being nonphysiological, the advent of digital Ca 2ϩ imaging demonstrated that cytoplasmic free Ca 2ϩ ([Ca 2ϩ ] c ) in excitable cells undergoes large excursions far exceeding the setpoint values obtained with isolated mitochondria (33), and it is now established that in situ mitochondria can accumulate large amounts of Ca 2ϩ when the local [Ca 2ϩ ] c is above 0.5 M and release Ca 2ϩ to the cytoplasm when [Ca 2ϩ ] c is restored to basal values (e.g. Ref. 34). It is however apparent that monitoring [Ca 2ϩ ] m of in situ mitochondria provides little information on the extent of total Ca 2ϩ accumulation within the matrix. Thus in repetitively stimulated lizard motor nerve terminals the sustained clearance of cytoplasmic Ca 2ϩ by mitochondria fails to increase [Ca 2ϩ ] m above 1 M regardless of stimulation frequency or the amount of accumulated Ca 2ϩ (35). The present study shows (Fig. 8) that [Ca 2ϩ ] m of isolated rat brain mitochondria changes by less than 20% when total matrix Ca 2ϩ is increased from about 10 to 400 nmol/mg. These two aspects of mitochondrial Ca 2ϩ accumulation are not mutually incompatible, and as shown in Fig. 6, there is a smooth transition from the region where [Ca 2ϩ ] m varies with Ca 2ϩ load to the invariant region associated with a constant setpoint and buffered [Ca 2ϩ ] m .
The Nature of the Matrix Calcium Phosphate Complex-Although much evidence points to the presence of a calcium phosphate complex within the matrix of loaded mitochondria, its nature remains obscure, due largely to the considerable complexity and variability of biologically relevant calcium phosphate forms (for review see Ref. 10). Additionally, investigations are hindered by the ability of the presumed matrix complex instantly to dissociate into Ca 2ϩ and P i when the Ca 2ϩ -loaded mitochondria are depolarized, so that Ca 2ϩ exits via the reversal of the uniporter, and P i exits via the P i transporter (5).
The formation of a calcium phosphate complex within the matrix that is in equilibrium with 5 mM free phosphate but with only 2 M [Ca 2ϩ ] m (Fig. 8) has to be reconciled with the ability to prepare physiological extracellular buffers containing similar phosphate concentrations but one-thousand times higher free Ca 2ϩ concentrations. Similarly, external Ca 2ϩ electrodes or low affinity extramitochondrial Ca 2ϩ indicators show that Ca 2ϩ released from Ca 2ϩ -loaded mitochondria into P icontaining media remains in solution even though the [Ca 2ϩ ] e is much higher than the [Ca 2ϩ ] m indicated by the matrixloaded fura2-FF (Figs. 9 and 10). The contrast between the ability of polarized mitochondria to retain enormous amounts of Ca 2ϩ within their matrices and the rapid and almost complete release of the ion when the mitochondria are depolarized is additionally puzzling since the concentration gradients of free Ca 2ϩ and P i across the polarized membrane appear to be so small (Fig. 8), [Ca 2ϩ ] m being limited by the solubility product of the complex and [P i ] m being defined from the external P i and the transmembrane pH gradient.
Hydroxyapatite can be detected in fixed and dessicated samples, but it is generally accepted that this is an artifact (36). In an artificial cytoplasm in the presence of ATP, amorphous Ca 3 (PO 4 ) 2 is initially formed when millimolar Ca 2ϩ is titrated, particularly at pH 7.5-8.0 (corresponding to the matrix pH) and is stable for prolonged periods (8). At external pH 7.0, the mitochondrial uptake of one Ca 2ϩ in the presence of excess P i is accompanied by the net extrusion of one proton (7), consistent with the rapid formation of Ca 3 (PO 4 ) 2 (Fig. 12).
Reported values for the ion activity product (solubility product) of amorphous Ca 3 (PO 4 ) 2 differ widely in the literature, from 2 ϫ 10 Ϫ33 to 1.6 ϫ 10 Ϫ25 . It is not easy to find the original references in which these constants were determined, and in any case the mitochondrial matrix is perhaps as far from an ideal solution as it is possible to imagine, but nevertheless the solubility properties of this calcium salt provides a way to understand a number of apparently conflicting aspects of calcium storage in the mitochondrial matrix. Thus it is not immediately apparent how micromolar free Ca 2ϩ concentrations could form such a complex with P i within the mitochondrial matrix, while much higher free Ca 2ϩ concentrations can coexist with millimolar P i in physiological incubation media without precipitation. Secondly, if the gradient of free Ca 2ϩ concentration across the inner membrane is really so small (1-4-fold) as is indicated by this and other studies, why is a high membrane potential required to retain Ca 2ϩ within the matrix and why does the addition of protonophore lead to such a massive and rapid efflux of Ca 2ϩ and P i ? The answer may lie in the high pH dependence of the Ca 2ϩ concentration that is in equilibrium with amorphous Ca 3 (PO 4 ) 2 (Fig. 12) 3Ϫ species increases as the third power of pH m . Maintenance of the solubility product for Ca 3 (PO 4 ) 2 thus means that the concentration of free matrix Ca 2ϩ in equilibrium with the complex decreases as the second power of the matrix pH and as the two-thirds power of the total external phosphate concentration (Fig. 12) Ϫ / OH Ϫ antiport. a, amorphous tricalcium phosphate, Ca 3 (PO 4 ) 2 , forms in the matrix, a H ϩ /Ca 2ϩ ratio of 1 is seen in the external medium. b, CaHPO 4 formation gives a H ϩ /Ca 2ϩ ratio of 0.5. c, Ca(HPO 4 ) 2 formation gives a H ϩ /Ca 2ϩ ratio of Ϫ1. d, hydroxyapatite formation would be associated with a H ϩ /Ca 2ϩ ratio of 1.1. e, matrix free Ca 2ϩ concentration ([Ca] m ) in equilibrium with either amorphous tricalcium phosphate (TCA, K sp ϭ 3 ϫ 10 Ϫ30 ) or hydroxyapatite (HAP, K sp ϭ 1 ϫ 10 Ϫ59 ) for two concentrations of total external phosphate (2 and 5 mM) and as a function of matrix pH. The three dissociation constants for phosphate were taken as: pK 1 ϭ 2.13, pK 2 ϭ 7.2, pK 3 ϭ 12.39 (10). Note that the gradient of the PO 4 3Ϫ anion varies as the third power of the pH gradient across the inner membrane, thus matrix acidification from pH 8.0 to pH 7.0 would decrease the matrix PO 4 3Ϫ concentration by a factor of 1000. At a constant solubility product for Ca 3 (PO 4 ) 2 , this would raise the [Ca 2ϩ ] m in equilibrium with the complex by 100-fold. In the presence of 5 mM total P i , an indicated [Ca 2ϩ ] m of 2.1 M would correspond to a matrix pH close to 7.7, i.e. 0.5 pH units alkaline with respect to the medium. rary reversal of ⌬pH following addition of a protonophore would thus be predicted to facilitate dissociation of the complex, liberating free Ca 2ϩ and facilitating its rapid efflux via reversal of the uniporter in response to the concomitant collapse of ⌬ m .
The Relationship between Bolus Ca 2ϩ Additions and Continuous Infusion-This is the second study in which we have utilized slow, continuous Ca 2ϩ infusion in order to investigate mitochondrial Ca 2ϩ transport. In the first (5) we determined the kinetics of the rat liver mitochondrial Ca 2ϩ uniporter by infusing the cation at different rates and determining the value at which [Ca 2ϩ ] e stabilized, i.e. when the uniporter activity exactly balanced that of the infusion rate plus the activity of the efflux pathway. Uniporter activity was found to increase as an exponential function of [Ca 2ϩ ] e until respiration became rate-limiting (5).
It is extraordinarily complex to analyze mitochondrial Ca 2ϩ transport and sequestration in response to a bolus addition of the cation when [Ca 2ϩ ] e , ⌬ m , light scattering, phosphate transport, and calcium phosphate complex formation are all changing rapidly with time (see e.g. Ref. 38). The present study removes much of this complexity by monitoring Ca 2ϩ sequestration in the matrix when the cation is infused sufficiently slowly to minimize the bioenergetic load, and hence effects on ⌬ m . This is of particular relevance since it has been proposed that the permeability transition pore is activated by a lowering of the membrane potential (39). Infusion also allows ample time for calcium phosphate complexes to form in the matrix; it is possible that the permeability-transition-independent release of cytochrome c seen when large Ca 2ϩ boluses (400 -2100 nmol/mg of protein) are given to brain mitochondria (38) is a consequence of a high free matrix Ca 2ϩ before complex formation occurs, particularly since phosphate transport follows Ca 2ϩ entry and is initiated by the enhanced transmembrane pH gradient.
Relevance to in Vivo Mitochondrial Ca 2ϩ Transport-It is becoming increasingly apparent that brain mitochondria in situ can accumulate Ca 2ϩ under a variety of physiological and pathological conditions such as epilepsy (40), ischemia (41,42), and concussive brain injury (43). At the same time there is active debate as to whether the permeability transition participates in neuronal ischemic death and whether permeability transition inhibitors are neuroprotective (9, 32, 37, 44 -46). It is clearly important to establish the factors that define the Ca 2ϩ -loading capacity of brain mitochondria. Two scenarios may be envisaged, one in which in situ brain mitochondria load with Ca 2ϩ rapidly in response to a sudden dramatic increase in free cytoplasmic Ca 2ϩ , for example due to repetitive firing of voltage-activated Ca 2ϩ channels, and one in which they slowly accumulate the cation in response to a slow uncompensated inward leak of the cation across the plasma membrane. The present study may be of relevance to the latter. It is apparent that phosphate plays a major role in defining the capacity of the mitochondria; it would of importance to determine whether cytoplasmic phosphate is in excess or is limiting under the above conditions of mitochondrial Ca 2ϩ loading.