Calcium Activation of Heart Mitochondrial Oxidative Phosphorylation RAPID KINETICS OF mV˙ O 2 , NADH, AND LIGHT SCATTERING*

Parallel activation of heart mitochondria NADH and ATP production by Ca 2 1 has been shown to involve the Ca 2 1 -sensitive dehydrogenases and the F 0 F 1 -ATPase. In the current study we hypothesize that the response time of Ca 2 1 -activated ATP production is rapid enough to support step changes in myocardial workload ( ; 100 ms). To test this hypothesis, the rapid kinetics of Ca 2 1 activation of mV˙ O 2 , [NADH], and light scattering were eval- uated in isolated porcine heart mitochondria at 37 °C using a variety of optical techniques. The addition of Ca 2 1 was associated with an initial response time (IRT) of mV˙ O 2 that was dose-dependent with a minimum IRT of 0.27 6 0.02 s ( n 5 41) at 535 n M Ca 2 1 . The IRTs for NADH fluorescence and light scattering in response to Ca 2 1 additions were similar to mV˙ O 2 . The Ca 2 1 IRT for mV˙ O 2 was significantly shorter than 1.6 m M ADP (2.36 6 0.47 s; p < 0.001, n 5 13), 2.2 m M P i (2.32 6 0.29, p < 0.001, n 5 13), or 10 m M creatine (15.6. 6 1.18 s, p < 0.001, n 5 18) under similar experimental conditions. Calcium effects were inhibited with 8 m M ruthenium red (2.4 6 0.31 s; p < 0.001, n 5 16) and reversed pellet

The maintenance of a steady state energy metabolism, by the appropriate orchestration of mitochondrial energy conversion with work, is a common process in many cells (1)(2)(3)(4). The cytosolic transduction systems involved in this balance of work with mitochondrial oxidative phosphorylation has been proposed to involve at least four putative cytosolic signaling systems. These include cytosolic concentrations of ADP and P i (5), creatine (6 -9), and/or Ca 2ϩ (10 -15). The ADP and P i levels have been proposed to serve as cytosolic signals to the mitochondria, changing in proportion to work (i.e. ATPase activity). Therefore, ADP and P i , the key substrates for ATP production in the mitochondria, are believed to control ATP production by limiting the substrate for the synthesis reaction (5). Creatine, another putative cytosolic feedback metabolite related to the free ADP levels, is generated by the rapid cytosolic ATPase and creatine kinase reactions (6 -9, 16 -23) in the cytosol. The localization of creatine phosphokinase (CPK) 1 at the myofilaments and the inner mitochondria space to generate creatine in the cytosol from ADP and re-derive ADP in the inner membrane space provided a logical "facilitated diffusion" of ADP to the mitochondrion. Due to its higher concentration, creatine (ϳ10 mM) in cytosol (24,25) is thought to generate a higher "net" diffusional flux when compared with micromolar [ADP] in cytosol. This creatine kinase shuttle has been proposed in various forms over the years (for review see Ref. 26). Finally, Ca 2ϩ has also been proposed as another transducer between cytosolic work and mitochondrial metabolism; however, the mechanism of this activation is thought to occur differently than the proposed feedback models for ADP, P i , and creatine. Work at the myofilaments and ion transport by the sarcoplasmic reticulum and sarcolemmal membrane pumps are thought to be stimulated by Ca 2ϩ in parallel with mitochondrial ATP production. The activation of the contractile apparatus of the heart by Ca 2ϩ has been well characterized (for review see Ref. 27) as well as its effects on Ca 2ϩ ion transport (for review see Ref. 28). In the mitochondria, Ca 2ϩ has long been suggested to modulate Ca 2ϩsensitive dehydrogenase (10,11) as well as F 0 F 1 -ATPase activity (13)(14)(15). This parallel activation scheme relies on Ca 2ϩ having rapid, as well as similar, kinetics for modulating work and mitochondrial metabolism.
In the intact cell it is likely that all of these regulatory processes may be playing some role in the energy homeostasis. The relative importance of these different pathways might be related to the relative speed at which metabolism can respond to these cytosolic signals that could conceivably be changing simultaneously in the cell. Despite the fact that these models of mitochondrial regulation have been in the literature for many years, there is very little information on the rapid kinetics of these putative signaling molecules on oxidative phosphorylation. The purpose of this study was to determine the rapid kinetics of heart mitochondria to extramitochondrial concentrations of these putative cytosolic signaling markers. This was accomplished using isolated porcine heart mitochondria and rapid optical techniques to follow NADH, light scattering (volume), and oxygen consumption in response to step increases in these potential cytosolic signaling molecules. * The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

MATERIALS AND METHODS
Mitochondria Isolation-Heart mitochondria were isolated from anesthetized pig according to Ref. 15 and were within the guidelines listed in the Animal Care and Welfare Act (7 United States Congress 2142, section 13). Buffers use in the isolation, washing, and experimentation are presented in Table I. The mitochondria were isolated and washed in solution A, and the final preparation was suspended in solution B. To ensure that chloride, at the concentrations used in buffer B (Table I), did not detach creatine kinase from the inner mitochondrial membrane (29), mitochondria were in some cases resuspended in buffer A (Table I).
Fluorescence Dye Loading-Approximately 90% of the resuspended mitochondria were loaded with 5-(6)-carboxy-2Ј-7Ј-dichlorofluorescein diacetate, succinimidyl ester (CF; Molecular Probes, Eugene OR) at 1 nmol of CF⅐nmol of Cyt a Ϫ1 to provide an optical correction for primary and secondary optical filters in the sample (31).
To monitor mitochondrial matrix free [Ca 2ϩ ], mitochondria were loaded with RHOD 2 at 7.66 Ϯ 1.07 nmol of RHOD 2⅐nmol of Cyt a Ϫ1 (n ϭ 9) by incubation at 0°C for 10 min in a 30 mM solution of RHOD 2-AM (Molecular Probes Inc, R-1244) dissolved in Me 2 SO with trace amounts of Pluronic F-127 (Molecular Probes, P-6867). In all cases, loaded mitochondria were washed and repelleted three times, with the third pellet resuspended in plain buffer B, or A where appropriate, at 26.8 Ϯ 1.85 nmol of Cyt a ⅐ml Ϫ1 (n ϭ 31). The intra-and extramitochondrial RHOD 2 content was determined in mitochondria preincubated at 37°C for 6 min. RHOD 2-loaded mitochondria were pelleted at 4000 ϫ g in an Ependorff centrifuge (model 5415C) for 2 min, and the supernatant was collected as the extramitochondrial pool. The pelleted mitochondria were resuspended in buffer C containing 2% Triton X to minimize sample light scattering. Total RHOD 2 in the Triton X-treated pellet and supernatant were determined spectrophotometrically (Lambda 3B, PerkinElmer Life Sciences) at the peak absorbance (545 nm), with two reference wavelengths (i.e. 520 and 590 nm) to correct for nonspecific absorbance in the samples. The absorbance of RHOD 2 at 545 nm was confirmed to be [Ca 2ϩ ]-insensitive and independent of esterase cleavage (data not shown). The extinction coefficient for RHOD 2 determined from this three-point method was 40.12 mM Ϫ1 ⅐cm Ϫ1 at the peak absorbance, which was ϳ2-fold lower than reported extinction at this wavelength (Molecular Probes Inc.). Based on this, the [RHOD 2] of the mitochondria was 3.01 Ϯ 0.11 nmol of RHOD 2⅐nmol of Cyt a Ϫ1 compared with 161.7 Ϯ 0.009 pmol of RHOD 2⅐ml Ϫ1 in the extramitochondrial space. At the concentration of mitochondria used in these studies (4 nmol of Cyt a ⅐ml Ϫ1 ), this corresponds to a 5.06 Ϯ 0.21% (n ϭ 9) contamination of RHOD 2 in the non-mitochondrial space.
To determine the role of the extramitochondrial dye to the Ca 2ϩ effects observed, the fraction of dye cleaved in the two compartments must be determined. Since the acetoxymethyl ester form of RHOD 2 is Ca 2ϩ -insensitive and would not contribute to any Ca 2ϩ -dependent fluorescence signal changes, the cleaved form of [RHOD 2] was determined from standard curves between the total RHOD 2 content (measured by absorbance) and fluorescence enhancement in the presence and absence of Ca 2ϩ . Samples from the supernatant and resuspended pellet, with and without Ca 2ϩ , were then compared with standard curves, determined for the potassium salt form of the dye (Molecular Probes Inc., R14220), to estimate the cleaved fraction. If 100% cleavage had occurred, then the ratio of fluorescence to absorbance in the presence of Ca 2ϩ should be the same in the samples as in the standard curve. The fractional decrease in the Ca 2ϩ -dependent fluorescence normalized to the total [RHOD 2] was taken as the portion of uncleaved dye. By using this approach, the fractional cleavage of the dye was 58.4 Ϯ 4.6 and 99.4 Ϯ 58.4% (n ϭ 22) in the mitochondrial and extramitochondrial space, respectively. Taking the relative distribution of the dye content between the mitochondria and extracellular space, along with the relative cleavage of the dye, the total contribution of the extramitochondrial space to the Ca 2ϩ -sensitive fluorescence signal is less than 8.05 Ϯ 0.34% (n ϭ 22) in ⌬OD.
Preparation Quality and Incubation Conditions-The quality of each preparation was determined from the respiratory control ratio (RCR) of mV O 2 . ADP-driven respiration was stimulated with a single addition of 1.6 mM ADP, and the subsequent State 4 rate was determined using a polarographic O 2 electrode in buffer B. This approach permitted direct comparison of RCR values with our previous work and provided a mechanism for production of optical standards, required for NADH determinations (see below).
To deplete mitochondria of endogenous Ca 2ϩ , all preparations were incubated for 6 min in buffer C (Table I) at 37°C. This procedure resulted in a matrix free [Ca 2ϩ ] of 1.26 Ϯ 0.17 nM (n ϭ 61), as determined by matrix RHOD 2 fluorescence (see "NADH and RHOD 2 Fluorescence"), and was similar to previous reports for Ca 2ϩ -depleted mitochondrial preparations (32). To estimate the rate and response times for inorganic phosphate (P i ), mitochondria were incubated in buffer D or H (Table I), where P i was incremented after G/M (5 mM) and ATPase (1.6 IU⅐ml Ϫ1 ).
In an effort to optimize creatine (Cr)-driven respiration, a series of experiments were performed with five different buffers (C, E-G, and G 0 ). Initial studies were performed in buffer C, in the absence of ADP, and were driven with a single bolus of Cr, which match physiological levels (10 mM final) in cardiac tissue (33). Reports from Saks and co-workers (35) have suggested that excess chloride (Ͼ50 mM) and auto-oxidation may result in low creatine kinase turnover rates (34 -36) in isolated mitochondria (29). To test these hypothesizes several incubation buffers were used; buffer E (Table I) attempted to reduce the level of auto-oxidation with the addition of 0.5 mM dithiothreitol, whereas buffers F and G were formulated to lower the level of free chloride to near-physiologic levels (37). Since, under normal isolation procedures, mitochondria are resuspended in buffer B which contains Ͼ140 mM chloride, a subpopulation was prepared and reconstituted in buffer A, and the experiment was performed in buffer G (buffer G 0 ), therefore testing this hypothesis. Under these conditions (buffers E-G 0 ), incubations and experimental substrate additions were performed as described for buffer C; however, since ADP has been shown to lower the K m for creatine kinase enzyme (38), 0.4 IU⅐ml Ϫ1 ATPase was added to provide a constant ADP background. Finally, in an effort to compare the maximal creatine-stimulated rates in buffer G with ADP and P i , experiments were performed in buffers G and H (Table I), respectively. Postincubation, carbon substrates, ATPase, and Ca 2ϩ were added to the suspension in series while optical data were collected (see below).
Calculated free [Ca 2ϩ ] in each buffer was based on affinity constants previously reported (39). Where appropriate, data are presented as calculated free concentrations. In those cases where 0 nM or "nominally zero" Ca 2ϩ are indicated, no additional Ca 2ϩ was added to the media. In general, mitochondria experiments were performed at 1 nmol of Cyt a ⅐ml Ϫ1 ; however, RHOD 2 experiments were performed at higher concentrations of mitochondria (4 nmol of Cyt a ⅐ml Ϫ1 ) to increase the RHOD 2 signal to noise ratio.
Chamber Mixing Kinetics-The kinetic effects of metabolites and Ca 2ϩ were the primary interest of this work. Thus, the determination of the inherent mixing rates in the experimental chamber was critical for the interpretation of the data. The chamber mixing kinetics was determined optically by monitoring the absorption of Hb during its injection into the chamber, as described previously (40). A single bolus of Hb was injected into the chamber containing deactivated mitochondria while monitoring the Hb optical absorbance. This permitted the determination of system-mixing times at the appropriate temperature, ionic strength, and viscosity. These studies revealed a response time of 0.184 Ϯ 0.03 s (n ϭ 15), approximately double the spectral acquisition rate (100 ms⅐spectrum Ϫ1 ).
Oxygen Consumption (mV O 2 )-For the determination of rapid changes in oxygen consumption, the oxygen-sensitive optical absorption of extramitochondrial hemoglobin was used as described previously (40). Standard hemoglobin dissociation curves were generated daily by monitoring Hb absorbance at 561 and 549 nm (an isosbestic reference) in a mitochondria/Hb suspension oxidizing 800 M glutamate ϩ malate (G/M) at State 4 respiration while the O 2 tension was monitored with the polarographic electrode. By using these data, a standard curve of F sat and %O 2 was constructed and was constrained over the intervals 0 Յ F sat Յ1 and 0% Յ %O 2 Յ21%, respectively. These data were then interpolated using a cubic spline to approximate a continuous function and were then mathematically inverted providing a lookup table where %O 2 could be evaluated for each F sat obtained from experimental spectra (see Ref. 40).
All mitochondrial respiratory measurements were carried out between 0 and 15% O 2 saturation (0 to 0.982 F sat ) and anoxia (40). By using the standard curve as a lookup table, soluble O 2 in the chamber (nmol O 2 ) for each experimental spectra (sO 2 (n)) was calculated as shown in Equation 1, where %O 2 (n) is the percent oxygen in the chamber for "n" spectra Calcium and Oxidative Phosphorylation, Rapid Kinetics derived from the lookup table; ␣ is the solubility of oxygen in buffer for a given salt content and temperature in nmol⅐ml Ϫ1 , and V C is the volume of the chamber in ml. The oxygen solubility used was 199 nmol⅐ml Ϫ1 at 37°C (41). Similarly, given F sat (n) for each experimental spectrum, total O 2 bound to Hb (HbO 2 (n)), in nmol of O 2 , was calculated as shown in Equation 2, where F sat (n) is the fractional saturation of Hb for n spectra; [Hb] is the concentration of hemoglobin in the chamber in nmol⅐ml Ϫ1 ; ␤ is the capacitance of O 2 per nmol of Hb in nmol, and V C is the volume of the chamber in ml. Combining Equations 1 and 2, the total oxygen content (nanomoles of O 2 ) of the reaction chamber at n spectra ([O 2 ](n)) was calculated as given in Equation 3.
Since all spectra were acquired at fixed intervals (100 ms), differentiating these with respect to time yields oxygen consumption rates in nmol of O 2 ⅐nmol Cyt a Ϫ1 ⅐min Ϫ1 (see Equation 4), ␦t is the interval over which the decrease occurred in seconds; Cyt a is the cytochrome aa 3 content in nmol⅐ml Ϫ1 , and V c is the chamber volume in ml. NADH and RHOD 2 Fluorescence-Reduced pyridine dinucleotides (NADH) were monitored in parallel experiments using the same chamber mixing system as for the mV O 2 ; however, excitation and light collection were provided on the same side of the chamber (0 o ) with the RP400-7 UV-visible reflectance probe (Ocean Optics Inc.). Excitation was provided with a 500-watt Hg/Xe arc lamp (Oriel Inc., models 68811 and 66011) fitted with a 360 nm band-pass filter (Edmund Scientific Inc. model 46085). The result was a primary spectral line centered at 360 Ϯ 10 nm, which was coupled to the six fibers of the excitation arm of the reflectance probe. Detection of NADH was provided with a linear CCD array (Ocean Optics Inc., model PC2000), described for mV O 2 , coupled to the receive arm of the reflectance probe. Data were digitally sampled over the spectral bandwidth of 335-1064 nm at 10 Hz with a 12 Bit A/D converter as described for mV O 2 .
To correct for potential non-linear amplitude response of the linear diode array over the spectral bandwidth used in these studies, and to calculated true irradiance, spectra were collected for a 3100 K calibrated black body source (Ocean Optics Inc., model LS-1). Theoretical calculations of black body irradiation for 3100 K were performed using Plank's equation (Equation 5): where is wavelength bound by 335 nm Յ Յ1064 nm; hc is Plank's constant 1240 eV⅐nm; K b is Boltzmann's constant for black body irradiation 8.617 ϫ 10 Ϫ5 eV⅐K Ϫ1 , and T is the source filament temperature in K. Given this, detector quantum efficiency (Q eff ) was determined between theoretical (Ir bb ) estimates and the calibrated source (Ir cal ) at 3100 K for all wavelengths (): Provided the function described in Equation 6, corrected irradiance for each spectrum (Ir corr (n)) was calculated as shown in Equation 7, where Ir raw (,n) is the raw data at the "nth" spectrum collected for each wavelength (); Ir dark is the dark current of the detector at each , and Q eff is the quantum efficiency of the detector for each . By using the formulation in Equations 5-7, control spectra were obtained in fully oxidized (0.067 mM ADP) and reduced (5 mM G/M) mitochondria in the absence and presence of CF. Given these, model spectra for NADH (M NADH ) and CF (M CF ) were constructed by difference. Spectra modeling excitation light bleed through (M EBT ) were obtained from G-10 Sephadex beads (size 40 -120 m, Sigma) at 1 mg⅐ml Ϫ1 . Model spectra (M NADH , M CF , and M EBT ) were fitted and com-pared with a multiple linear regression to each experimental spectra, n, yielding the coefficients for NADH (I NADH ), CF (I CF ), and EBT (I EBT ) as described previously (31). Coefficients for each experimental spectra (n) were calculated as shown in Equation 8, For studies where matrix free Ca 2ϩ was monitored, additional difference spectra were constructed in the absence and presence of Ca 2ϩ , permitting the construction of model spectra for RHOD 2 (M RHOD ). As with NADH, estimates of matrix free [Ca 2ϩ ] were determined from calculated model coefficient described by Equation 9, By using the coefficients for NADH or RHOD 2 with CF, the I NADH ⅐I CF Ϫ1 or I RHOD ⅐I CF Ϫ1 ratios could be calculated, providing a method for eliminating both primary and secondary inner filter effects on NADH and RHOD 2, respectively. Estimates of free matrix [Ca 2ϩ ] were determined using a K d of 570 nM as shown in Equation 10, where estimates of maximal RHOD 2 fluorescence (F max ) were determined at the end of each experiment in the presence of excess Ca 2ϩ (10 M) plus 10 M Br-A234187 (Sigma, B-7272). Regression coefficients for RHOD 2 fluorescence (I RHOD ⅐I CF

Ϫ1
) post-Ca 2ϩ depletion approached zero and were taken to represent minimal RHOD 2 fluorescence (F min ).
In all cases, regressions were performed iteratively until the sum of squares convergence was achieved using the Marquardt-Levenberg algorithm written in IDL (Research Systems Inc., version 5.2). The algorithm provides the following: 1) the coefficients of the model spectra; 2) standard deviation for the coefficients; 3) an F test for fit between model and experimental data; and 4) multiple linear correlation coefficients for the fitted spectra. The degree of concordance between model and experimental spectra was high both within (0.993 Ϯ 0.0004, average n ϭ 9355⅐study Ϫ1 , p Յ 0.0001) and between (0.993 Ϯ 0.0006, total n ϭ 122050, p Յ 0.0001) experimental studies.
Since NADH levels are in dynamic flux between CaDH production and cytochrome consumption, calculations of changes in [NADH] to a new steady state can be described by "jump" or transition kinetics (42) using the following bimolecular Equation 11, where ␦(⌬x) and ␦t are the changes in product x for a given change in time t. k 1 and k 2 are the reaction rate constants in the forward and reverse directions of the initial step, whereas k 3 is the forward reaction rate constant in the formation of the product x. s o , ⌬x o , t, and are the initial [substrate], initial change in [product], time, and time constants, respectively. As the limit of t approaches 0 it yields Equation 11, thus permitting estimates of NADH production rate from initial rates shown in Equation 12, where the initial rates of product formation are described by the rate constants k 1 , k 2 , and k 3 and the initial concentrations of substrate and the change in product formation, yielding a simple linear equation. Given the relations described by Equations 11 and 12, the initial rate of NADH formation can be described by a simple linear system and therefore is dominated by the forward rate constant (k 1 ) of the reaction and the initial [substrate] (42). By using the derivations from Equations 8 and 11-12, and the acquisition rate per spectra (100 ms⅐spectra Ϫ1 ), NADH levels could be differentiated with respect to time, yielding the initial rate of change for NADH (mV NADH ) in I NADH ⅐I CF Ϫ1 ⅐Cyt a Ϫ1 ⅐min Ϫ1 (see Equation 13), ) is the change in scattering corrected NADH levels, and ␦t is the time interval in seconds over which the data were differentiated; Cyt a is the content of cytochrome aa 3 in the media in nmol⅐ml Ϫ1 , and V c is the chamber volume in ml.
Light Scattering-Light scattering was used as an indirect measure of mitochondrial volume changes. Mitochondrial volume was of interest in this study since Ca 2ϩ is known to modulate matrix volume, and possibly mitochondrial metabolism (43). Therefore, volume changes could provide possible insight into the mechanisms, which underlie rapid mitochondrial kinetics. Illumination was provided by a tungstenhalogen source (Titan Tool Inc., model F0-150) coupled to the optical chamber via liquid light guide. The transmitted light (180 o from incident source) was detected using the receive arm of the reflection probe (Ocean Optics Inc., model RP400 -7 UV-visible), coupled to a linear CCD array, and was sampled as described for Hb experiments. Mitochondria were placed in the chamber at 1 nmol of Cyt a ⅐ml Ϫ1 , and incident light was adjusted via mechanical iris to permit collection of the full dynamic range over the spectral bandwidth (360 -1064 nm). Additionally, a sample of the source light (S 0 ) was collected, permitting calculations of light scattering ( s ) with the units of optical difference (⌬OD) as shown in Equation 14, where S 0 is the block average of 5 spectra obtained from the tungstenhalogen source, and S 1 is the optical intensity for the mitochondrial suspension at n spectra. Since spectra were acquired at regular intervals, as with O 2 and NADH, differentiating s with respect to time for discrete wavelengths () yields Equation 15 in ⌬OD⅐Cyt a Ϫ1 ⅐min Ϫ1 , where s ((n)) is the light scattering for a given cytochrome isosbestic wavelength (455, 510, 520, 540, 575, and 630 nm) at n spectra; ␦t is the interval over which the data was differentiated in seconds; Cyt a is the cytochrome aa 3 content in nmol⅐ml Ϫ1 , and V c is the chamber volume in ml. mV s represents the initial rates for light scattering in this system. Since the relationship between mitochondrial volume and light scattering is complex, this measure can only be considered an estimate of mitochondrial swelling rates in response to these perturbations. Optical Time Stamp (OTS)-Addition of oxidizable carbon substrates, ATPase, and experimental substrates (i.e. Ca 2ϩ , ADP, creatine, G/M, ruthenium red, or EGTA) were added serially and optically time stamped upon addition. The optical time stamp was generated by exciting an external tungsten source filtered with a 530 Ϯ 20 nm bandpass filter (Fig. 1). The resulting flash of light caused a brief (ϳ100 ms) green shift in the spectral line at the point of addition. This green shift in the spectra when post-processed using Equations 1-15 resulted in a downward deflection in the signal intensity at the point where the addition was made. In all cases the OTS was at least 2-fold greater than the noise at the point of addition, permitting precise determination of when the addition was made.
IRT Determination-The IRT of the mitochondria to the experimental perturbation was calculated by selecting two ROI. The first ROI placed just prior to the addition and the second just post to the addition were used to demark the boundaries over which two least squares linear regressions were performed. Based on the slopes and intercepts from this analysis, the regression lines for each ROI were interpolated over the entire data range selected by both ROIs. The intersection of the two regression lines represented the initial point where the transition to the new slope occurred. The IRT was then calculated as the difference in time from the middle of the OTS to the point of intersection. Provided this methodology, which was based on a statistical framework, an unbiased estimate of the response time of the system could be made. Analytical derivation of IRT, presented under the "Appendix," can be shown to be essentially identical to the conventionally used in exponential fits of time varying data. Given this, it is reasoned that in the absence of exponentially time varying functions, as observed for mV O 2 , NADH, or s , reliable estimates of " " could be calculated by IRT.
Electron Microscopy-Porcine hearts were isolated from anesthetized pigs according to Ref. 15 and were retrograde-perfused via coronary arteries with normal saline, followed by fixative solution containing 2.5% glutaraldehyde in 100 mM cacodylate buffer (pH 7.2) and 250 mM CaCl 2 at 25°C. Tissue blocks from the apex, epi-, and endocardium were further fixed in the same fixative for 4 h (25°C). Following fixation, tissue blocks were washed three times in Sabatini's solution (100 mM cacodylate buffer with 6.8% sucrose). All samples were then postfixed with 1% osmium tetroxide in 100 mM cacodylate buffer (pH 7.2) for an additional hour and washed three times in Sabatini's solution. The samples were passed through a graded series of alcohols followed by treatment with propylene oxide, a 1:1 Epon/propylene oxide mix, and three changes in pure epon. Polymerization was performed at 60°C overnight. Ultra-thin sections were cut with a Leica Ultracut UCT ultra-microtome, stained with uranyl acetate and lead citrate, and examined with a transmission electron microscope (JEOL 1000X) at accelerating voltage of 60 kV.
Data and Statistical Analysis-Initial data processing for O 2 , NADH, and light scattering were performed using Equations 1-15 with custom programs written in IDL (Research Systems Inc., version 5.2). Postprocessing of initial rates before and after "substrate" additions were performed by a least squares linear regression, also in a custom program written in IDL (Research Systems Inc., version 5.2). The resulting analysis determines the following: 1) the regression coefficients; 2) the equation of the line describing the relationship; and 3) the probability that the slope of the line is not significantly different from zero. Individual slopes between treatments for mV O 2 , mV NADH , and mV s , and IRTs were compared using a multifactor-dependent variable t test (Statistica version 5.0, Statsoft Inc.). Where appropriate, values are expressed as mean Ϯ 1 S.E. In all cases, the fiduciary level of significance was taken at p Յ 0.05.

RESULTS
Mitochondrial Characterization-Oxygen consumption was tightly coupled to ATP phosphorylation in this preparation with an average respiratory control ratio (RCR) of 14.3 Ϯ 0.41 (n ϭ 31) and ranged between 10.5 and 18.7 while oxidizing G/M. Mitochondria with RCR below 8 were not used in these studies. In all cases, RCR estimates of mitochondrial integrity were performed in buffer B (Table I) with 5 mM G/M, 2 mM P i , and a single addition of 1.3 mM ADP at 37°C. This methodology permitted direct comparison with our previous work (15,44) and allowed for model spectra for NADH and CF to be collected for fluorescence standards (31).
Calcium, ADP, P i , and Creatine Activation of Oxygen Consumption-A typical mV O 2 time course for evaluating the effects of Ca 2ϩ is shown in Fig. 1A. The addition of carbon substrates to Ca 2ϩ -depleted mitochondria in buffer C resulted in an increase in mV O 2 , consistent with a repolarization of ⌬ post-depletion (15). Once at steady state, exogenous ATPase was added to the media, providing a constant generation of ADP. In all cases steady state was achieved for several seconds before additional experimental perturbations were made. An OTS was applied during the additions of "substrates," thus providing a method for evaluating IRT as outlined under the "Materials and Methods." The addition of Ca 2ϩ resulted in an immediate increase in respiration, and an expanded time course is presented in Fig. 1B. Calculation of IRT for Ca 2ϩ was determined from regression analysis performed over two ROIs, just prior to and after the substrate addition. IRT was evaluated as the time difference between the OTS and point of intersection of the two slopes. The IRT for Ca 2ϩ was estimated to be 0.27 Ϯ 0.02 s, which was virtually the same as the chamber mixing kinetics (Fig. 2B). By using the above setup, the effects of [Ca 2ϩ ] on IRT and mV O 2 were evaluated between nominally zero (0 nM) and 1835 nM free Ca 2ϩ and are presented in Fig. 2A and Table II. The addition of Ca 2ϩ from 0 to 535 nM resulted in a incremental decrease in IRT, with the largest difference from control (ϳ9fold) occurring at the optimal [Ca 2ϩ ] of 535 nM. Oxygen consumption increased in a dose-dependent manor with [Ca 2ϩ ] through 535 nM (Table II). However, [Ca 2ϩ ] in excess of 1000 nM increased IRT by nearly 10-fold, and mV O 2 decreased by approximately 20% indicating significant Ca 2ϩ inhibition and possible Ca 2ϩ overload.
To test the reversibility of the Ca 2ϩ effects, EGTA was added to the chamber to reduce [Ca 2ϩ ] by ϳ150 nM, as calculated (39). The reduction in [Ca 2ϩ ] resulted in a decrease in mV O 2 by 17% in the steady state from the full 535 nM Ca 2ϩ stimulation. The IRT for this extraction of Ca 2ϩ (1.55 Ϯ 0.14 s) was much slower than the maximum rate of activation by Ca 2ϩ (0.27 Ϯ 0.02 s) but did demonstrate reversibility of the Ca 2ϩ effect. The slow off-kinetic of Ca 2ϩ might be influenced by the fact that Ca 2ϩ was not returned to nominally zero values with the EGTA addition.
The respiratory time response to Ca 2ϩ was compared with other putative cytosolic transducers including ADP, P i , creatine as well as carbon substrate additions. The results of these studies are presented in Fig. 2B and Table III. Several inter-  Table I. P i experiments were performed in buffers D and H. Creatine experiments indicated by G 0 signify mitochondria resuspended in buffer A and respiring in buffer G. ADP IRT listed represent State 4 to ADP-driven transition while oxidizing 5 mM G/M ϩ 535 nM Ca 2ϩ . Cr rates reported in buffer C are for mitochondria oxidizing 5 mM G/M ϩ 535 Ca 2ϩ . Creatine experiments in buffers E-G 0 were performed as in buffer C; however, 0.4 IU⅐ml Ϫ1 ATPase was present to lower the K m for creatine kinase (29). ATPase additions denoted by were for mitochondria oxidizing 1.5 mM G/M ϩ 535 nM Ca 2ϩ prior to final substrate addition. ATPase additions denoted by ␣-␥ were for mitochondria oxidizing ␣-ketoglutarate, pyruvate, or malate, respectively. IRTs reported for RuRed and EGTA were at 8 and 160 M, respectively. In all cases data are presented as means Ϯ S.E., and significance is indicated on the figure with square brackets indicating the grouping. esting comparisons can be made from these data. First, the respiratory response to Ca 2ϩ (535 nM) was an order of magnitude faster than ADP (2.36 Ϯ 0.47 s), P i (2.32 Ϯ 0.29 s), or carbon substrate additions (3.31 Ϯ 0.42 s) in buffer C, and Ͼ25 and 10-fold higher than ADP (8.90 Ϯ 0.47 s) and P i (3.20 Ϯ 1.38 s) in buffers G and H, respectively. This implies that Ca 2ϩ increases the efficiency of the reaction rate more effectively than ADP or P i additions alone. Creatine (10 mM) was added to State 4 mitochondria oxidizing 5 mM G/M ϩ 535 nM Ca 2ϩ in buffer C. The creatine-stimulated rate increased mV O 2 by ϳ5fold over State 4 rate (Table III); however, this rate was 3.6and 5.3-fold lower than the ADP-and Ca 2ϩ -stimulated rates, respectively. Similarly, IRTs for creatine were more than 6 and 50 times longer than for the ADP or Ca 2ϩ , respectively.
The fact that both mV O 2 and IRT were substantially slower from creatine when compared with ADP or Ca 2ϩ suggested that creatine kinase activity may have been reduced by either autooxidation (34 -36) or excessive chloride (Ͼ50 mM) (29) in the media. To test this, creatine studies were performed in buffers E-G 0 with 0.4 IU⅐ml Ϫ1 ATPase and are presented in Fig. 2B and Table III. The addition of dithiothreitol alone (i.e. buffer E, Table I), to minimize oxidation effects, did not significantly alter the overall kinetics when compared with experiments performed in buffer C. On the contrary, reducing Cl Ϫ to physiological levels with the impermeant anion methane sulfonate (buffer F, Table I) significantly shortened the IRT by 1.6-fold; however, these changes were not accompanied by significant changes in mV O 2 (Table III). Interestingly, when both K ϩ and Cl Ϫ were lowered in tandem by replacement with sucrose (buffers G and G 0 , Table I), the IRTs for Cr-stimulated respiration were indistinguishable from those obtained for ADP or P i in buffer C (Fig. 2B). These shorter IRT were accompanied by a Ͼ2-fold increase in mV O 2 over those obtained in either buffer C or E; however, these rates remained ϳ1.2-(buffer G) and ϳ1.7fold (buffer G 0 ) lower than those observed for ADP additions alone in buffer C and were on average ϳ2-fold lower than rates observed for Ca 2ϩ (Table III). Combined these data suggest that of all the putative cytosolic transducers that could modify mitochondrial respiration, Ca 2ϩ had the shortest response time with the greatest dynamic range in mV O 2 .
Extramitochondrial increase in [Ca 2ϩ ] rapidly stimulates mV O 2 in a dose-dependent manner when added to a previously Ca 2ϩ -depleted preparation. However, it is unlikely that an initial condition of nominally zero [Ca 2ϩ ] is physiological. Thus, serial additions of Ca 2ϩ were evaluated to establish whether the effects of [Ca 2ϩ ] on respiration were not dependent on the nominally zero initial conditions. In these studies, ATPase additions were made accompanied by only 60 nM Ca 2ϩ , which was ϳ30% of the Ca 2ϩ K 0.5 (Table V) (Table III) and the IRT (Fig. 2B). These data suggest that activation by Ca 2ϩ is not strongly dependent on initial [Ca 2ϩ ] conditions as long as the concentration changes remain in the dose-dependent region.
To evaluate the matrix dependence of extramitochondrial [Ca 2ϩ ] perturbations, experiments were performed in the presence of 8 M Ruthenium Red (RuRed). Addition of RuRed to the media prior to Ca 2ϩ addition resulted in a significantly longer IRT and was approximately 8-fold greater than that observed for Ca 2ϩ addition alone. The increase in IRT was accompanied by a 1.2-fold lower maximal rate than for 535 nM Ca 2ϩ alone, thus demonstrating partial matrix Ca 2ϩ inhibition at this concentration of RuRed. Concentrations higher than 8 M were attempted to inhibit completely this activation by Ca 2ϩ ; however, significant optical artifacts prevented accurate rate determinations and therefore are not reported.
Calcium Activation of NADH Production-To compare with the mV O 2 results, parallel kinetic experiments were performed for NADH production with variable Ca 2ϩ additions. A typical time course of scatter corrected NADH is presented in Fig. 3A. Mitochondria were placed in the chamber and allowed to Ca 2ϩdeplete for 6 min prior to substrate addition. Upon G/M addition, [NADH] rapidly increased and reached steady state within ϳ10 s. Once at steady state, respiration was initiated with a 1.6 IU⅐ml Ϫ1 addition of ATPase, which resulted in a rapid decline in [NADH]. Once a constant NADH level was achieved, a single bolus of Ca 2ϩ was added, which increased by 150% with 535 nM Ca 2ϩ addition. The IRT for NADH were calculated as the difference in time between the OTS and the point of intersection of the two regression lines as per previous (Fig. 3B). In addition, initial rates of NADH production (mV NADH ) with [Ca 2ϩ ] were determined as described under "Materials and Methods." The results of the IRT and mV NADH analyses with variable [Ca 2ϩ ] are presented in Fig. 4. NADH response times, like mV O 2 , were non-linearly correlated with [Ca 2ϩ ], with the apparent optima occurring at 535 nM free Ca 2ϩ (Fig. 4A). At concentrations greater than 1000 nM, however, IRTs increases by more than 4-fold and were consistent with trends observed for mV O 2 . Calculations of mV NADH with [Ca 2ϩ ] showed a similar non-linear relationship to that observed with IRT, with a maximal rates increasing by 50-fold over base line at 535 nM Ca 2ϩ . At high [Ca 2ϩ ] (Ͼ1000 nM) mV NADH decreased by approximately 40% consistent with the decline in mV O 2 observed over this same range (Table II).
Calcium and Light Scattering-Light scattering, an indirect measure of mitochondria swelling, was monitored to determine if changes in mitochondrial volume were accompanying the metabolic changes observed with mV O 2 and mV NADH . A typical time course plot of mitochondrial absorbance is illustrated in Fig. 5 for 6 cytochrome isosbestic wavelengths. The addition of G/M to substrate and Ca 2ϩ -depleted mitochondria caused an increase in light scattering (decreased ⌬OD) at all isosbestic wavelengths. This decrease in transmitted light is consistent with a change in refractive index of the suspension and is mediated via an increase in matrix water content, cristae unfolding, and mitochondrial swelling during substrate accumulation. Upon steady state, ADP-driven respiration was initiated with a single addition of 1.6 IU⅐ml Ϫ1 ATPase, resulting in an increase in ⌬OD, consistent with mitochondrial contraction. At steady state respiration, a single bolus of Ca 2ϩ was added to  t test). In all cases data are from mitochondria oxidizing 5 mM G/M as the carbon source and were Ca 2ϩ -depleted prior to treatment as described under "Materials and Methods" in buffer C. Data are presented as means Ϯ 1 S.E. the suspension, resulting in a marked increase in light scattering and/or mitochondrial swelling. As described previously, ROIs were drawn prior to and post Ca 2ϩ addition, and from these estimates the rate of ⌬OD change and IRTs were determined ( Fig. 5 and Table IV). Interestingly, calculated IRTs at all wavelengths showed little variation with [Ca 2ϩ ] and were on average 1.9 Ϯ 0.5-and 4.9 Ϯ 0.9-fold shorter than calculate IRTs for mV NADH and mV O 2 , respectively.
Analysis of mV s time course data with [Ca 2ϩ ] showed a strong non-linear dependence of mV s with Ca 2ϩ dose (Fig. 6A). Interestingly, at [Ca 2ϩ ] in excess of 500 nM the maximal amplitude of light scattering, and therefore mitochondria swelling, was achieved with little increase at progressively higher dose (Fig. 6A). A summary of this analysis for all studies is presented in Fig. 6B, which illustrates saturation kinetics of mV s with [Ca 2ϩ ], and a K 0.5 of 175 nM (Table V). Ca 2ϩ above 1000 nM caused the highest rate of light scattering and showed the greatest attenuation in mV NADH and mV O 2 (Figs. 4B and 5B and Table II) consistent with damage to the mitochondria ATP production capacity.
Kinetics of Mitochondrial Matrix [Ca 2ϩ ]-To confirm further that the metabolic effects were due to matrix Ca 2ϩ accumulation, matrix Ca 2ϩ was monitored using RHOD 2 loaded in the mitochondrial matrix. Loading as described under "Materials and Methods" resulted in a high degree of compartmental specificity, with 92.0 Ϯ 0.33% (n ϭ 22) of the Ca 2ϩ -sensitive RHOD 2 signal originating from the loaded mitochondrial matrix. A typical time course for RHOD 2-loaded mitochondria is presented in Fig. 7. The addition of carbon substrates and ATPase resulted in no changes in RHOD 2 fluorescence signal as determined by I RHOD ⅐I CF Ϫ1 . The addition of 535 nM Ca 2ϩ resulted in a rapid increase in matrix free Ca 2ϩ with an IRT not significantly different from chamber mixing times (Fig. 7A). To con-firm further the matrix dependence of these changes, the specific Ca 2ϩ uniport inhibitor Ru360 (Calbiochem, product 557440) was added in excess (20 M) to block Ca 2ϩ transport via this mechanism. The steady state matrix Ca 2ϩ level was reduced by ϳ50% after a Ca 2ϩ bolus. The IRT was also apparently lengthened by Ru360; however, the IRT was still within the sampling rate of the system (50 ms⅐spectrum Ϫ1 ). Since the Nyquist could not be properly satisfied, no estimates of IRT for Ca 2ϩ uptake could be made. By using Equations 9 and 10, estimates of matrix free Ca 2ϩ post-depletion were 1.26 Ϯ 0.17 nM, while after 535 nM Ca 2ϩ addition, in the presence and absence of excess Ru360, were 519.9 Ϯ 54.17 (n ϭ 32) and 273.6 Ϯ 30.28 nM (n ϭ 29), respectively.

DISCUSSION
These data are consistent with the notion that extramitochondrial Ca 2ϩ can rapidly modulate mitochondrial ATP production rates within ϳ200 ms. Determination of IRT for Ca 2ϩ effects on mV O 2 , NADH, light scattering, and RHOD 2 were on the order of the chamber mixing times (Fig. 2B), suggesting that the kinetics could even be more rapid.
The effects of Ca 2ϩ on mV O 2 are assumed to represent the effects of Ca 2ϩ on ATP production rate and may be caused by the matrix influx of Ca 2ϩ . These conclusions are supported by our previous observations that mitochondrial uncoupling by Ca 2ϩ is minimal at concentrations below 600 nM (15). Furthermore, a correlation between mV O 2 and direct measurements of ATP production has also been established in this system (15). Finally, the metabolic effects observed with Ca 2ϩ , increased mV O 2 , and [NADH] are not consistent with an uncoupling of oxygen consumption from ATP production by the influx of Ca 2ϩ ions alone, which should decrease [NADH] while increasing mV O 2 .
Evidence that changes in matrix Ca 2ϩ were responsible for TABLE III Oxygen consumption rates and regression statistics with calcium and substrates r 2 and n are the combined regression coefficient and number of observations. In all cases the level of significance relative to a slope of zero for linear regressions used for the IRT determination was p Յ 0.0001. Data represent mitochondria oxidizing 5 mM G/M as the oxidizable carbon source and were Ca 2ϩ -depleted in experimental buffer indicated by parentheses (i.e. (C) indicates buffer C) prior to intervention as described under "Materials and Methods." Creatine experiments indicated by (G 0 ) signify mitochondria resuspended in buffer A and respiring in buffer F. Oxygen consumption rates 1 and 2 correspond to the first and second substrate additions, respectively. ADP rates listed represent State 4 to ADP-driven transition while oxidizing 5 mM G/M ϩ 535 nM Ca 2ϩ . Creatine (Cr) rates reported in buffer C are for mitochondria oxidizing 5 mM G/M ϩ 535 nM Ca 2ϩ . Creatine experiments in buffers D-F 0 were performed as in buffer C; however, 0.4 IU ⅐ ml Ϫ1 ATPase was present to lower the K m value for creatine kinase (38). P i experiments were performed in buffers D and H, which contained 0.25 mM P i and were maximally stimulated with 2 mM bolus. Rates reported for Ruthenium Red (RuRed) and EGTA were at 8 and 160 M, respectively. In all cases, data are presented as means Ϯ 1 S.E. these metabolic effects of extramitochondrial Ca 2ϩ were obtained by the partial inhibition of these effects with RuRed, and the kinetics of matrix [Ca 2ϩ ] were detected with RHOD 2. The partial inhibition of the metabolic effects of Ca 2ϩ by RuRed as well as the partial inhibition of Ca 2ϩ uptake by Ru360 suggests that Ruthenium Red-insensitive Ca 2ϩ uptake mechanisms exists in this preparation. These results are similar to the recent results (45) demonstrating a partial inhibition of mitochondria Ca 2ϩ uptake by RuRed in intact heart cells. The nature of this RuRed-insensitive transport mechanism is unknown but is consistent with previous descriptions of the rapid uptake mode in liver mitochondria (46,47). Matrix Ca 2ϩ could effect ATP production at several levels including an increase in [NADH] or ⌬ driving force via CaDH activation (11,15,48) or activation of the F 0 F 1 -ATPase (15). The current data are consistent with both of these mechanisms. The rapid increase in [NADH] observed with Ca 2ϩ is consistent with an activation of CaDH. These data suggest that the CaDH are being activated in ϳ200 ms, although taking seconds to reach maximum values (Fig. 3). This is consistent with previous data on the activation of pyruvate and 2-oxoglutarate dehydrogenases in mitochondria (49,50). These results suggest that the activation of CaDH and increase in metabolic driving force through an increase in [NADH] was one of the rapid metabolic response mechanisms initiated by Ca 2ϩ .
In previous work, it was shown that increases in F 0 F 1 -ATPase activity were very significant in Ca 2ϩ activation of heart mitochondrial ATP production in the steady state (15). Similar data have been recently obtained by skeletal muscle mitochondria (51). Although the IRT for NADH and mV O 2 were similar (Figs. 2 and 4), closer inspection of the NADH and mV O 2 time courses revealed a monotonic increase in [NADH] (Fig.  3B), whereas the increase in mV O 2 was almost a simple step function at the current temporal resolution (Fig. 1B). This result was surprising since several other studies have demonstrated a linear relationship between [NADH] and mV O 2 in mitochondria (44,52) and cells (53) in the steady state with varying substrate delivery. These rapid kinetic effects of Ca 2ϩ suggest that the increase in NADH driving force alone was not linearly related to mV O 2 , and some other factors regulating ATP production must play a role. The likely site of this activation is an increase in the F 0 F 1 -ATPase synthetic flux in conjunction with the increase in CaDH as demonstrated previously (15).
The mechanism of Ca 2ϩ activation of F 0 F 1 -ATPase synthetic rate is unknown; however, Ca 2ϩ has been shown to modify cardiac mitochondrial volume in vitro (31,54). Halstrap and co-workers (55) have suggested that mitochondrial volume changes observed in liver, and stimulated by Ca 2ϩ , may play a role in activation of oxidative phosphorylation through the pyrophosphate stimulation pathway. Since matrix volume can be rapidly followed using light scattering techniques (56), we used this approach to evaluate whether matrix volume changes were kinetically associated with the observed metabolic effects of Ca 2ϩ . Calcium additions resulted in a rapid increase in light scattering consistent with an increase in matrix volume and were concomitant with increases in [NADH] and mV O 2 . Similar volume effects of Ca 2ϩ have been observed in liver (55,(57)(58)(59)(60)(61)(62) and heart (31, 54) mitochondria. It is unclear whether increases in volume are due solely to matrix Ca 2ϩ influx or to indirect mechanisms such as the production of new matrix osmolytes, or changes in other ion permeabilities. Since net Ca 2ϩ entry into the matrix in cardiac mitochondria is very low, with an estimated value of ϳ500 mOsm (see Fig. 7), it is therefore unlikely that it represents the primary osmolyte which elicits these changes (63,64). It is more probable that the changes observed are reflective of either elevated osmolyte production or an alteration in ion permeability of the inner membrane, where Ca 2ϩ serves as the second messenger. The most likely ion permeability change would be for K ϩ , as this ion plays a key role in the regulation of mitochondrial volume. Studies in liver mitochondria seem to support this contention showing that changes in volume with Ca 2ϩ are due to specific alterations in K ϩ permeability (for review see Ref. 11). The fact that the rate of light scattering (mV s ) was strongly dependent on [Ca 2ϩ ], and IRT was not, may indicate that the effects of Ca 2ϩ on light scattering were occurring much faster than the  IRT and n are the initial response time in seconds and the number of observations, respectively. In all cases the level of significance relative to a slope of zero for linear regressions used for the IRT determination was p Յ 0.0001. [Ca 2ϩ ] are calculated free levels based on affinity constants described previously (39). Data are presented as means Ϯ 1 S.E. In all cases data are from mitochondria oxidizing 5 mM G/M as the carbon source and were Ca 2ϩ -depleted prior to treatment as described under "Materials and Methods."  Table IV. mixing time of the system resulting in the observed constant IRT value as a function of Ca 2ϩ concentration. Despite the mechanism of Ca 2ϩ -induced volume changes, it is clear that Ca 2ϩ additions increased mV s , with the largest magnitude change occurring between 172 and 535 nM, which was consistent with the calculated K 0.5 for [NADH] and mV O 2 effects with Ca 2ϩ (ϳ175 nM; Table IV). Given this correlation, it is reasonable to speculate that changes in matrix volume could contribute to the stimulation of mV O 2 and mV NADH observed and is consistent with previous studies in rat liver mitochondria (see Ref. 55). Further investigations are required to establish the role of matrix volume on the Ca 2ϩ metabolic effects in cardiac mitochondria.
For Ca 2ϩ to serve effectively as a rapid modulator (i.e. stimulate or inhibit) of mitochondrial oxidative phosphorylation in the 25-600 nM concentration range, the off-kinetics (i.e. removal of Ca 2ϩ ) of the process would need to be similar to the on-kinetics (i.e. addition of Ca 2ϩ ) that were the focus of this study. We attempted to estimate the off-kinetics with the addition of exogenous EGTA to the chamber. This revealed that the metabolic effects of Ca 2ϩ were in fact reversible, but the kinetics was significantly slower (1.55 Ϯ 0.14 s, n ϭ 6) compared with the on kinetics (0.27 Ϯ 0.02 s, n ϭ 43). The slower off kinetics might be due to the incomplete removal of Ca 2ϩ by the solubility limited concentration of EGTA or the kinetics of EGTA Ca 2ϩ binding. A more rapid and complete trap of Ca 2ϩ is required to effectively quantitate the off-kinetics in this system. If the off-kinetics for Ca 2ϩ transport is slow, then this phenomenon might contribute an "asymmetric" temporal response to work or hypoxia transitions observed as metabolic overshoots in heart (65,66) and skeletal muscle (67).
It is interesting to compare the kinetics of Ca 2ϩ with P i and ADP, the other putative cytosolic modulators (5) of mitochondrial ATP production. The direct addition of near-saturating levels of ADP or P i alone resulted in a much slower mV O 2 response (Ͼ2 s) than Ca 2ϩ additions (Fig. 2B). This implies that the net effects of Ca 2ϩ are occurring faster than the initiation of serial transport of ADP or P i into the matrix and ADP phosphorylation by the F 0 F 1 -ATPase under near-optimal conditions. Similar kinetics for ADP activation of ATP production (1-2.5 s) has been reported for rat liver mitochondria (68,69). These data suggest that mitochondrial ATP production is more responsive, kinetically, to changes in [Ca 2ϩ ] than [ADP] or [P i ]. The delay in ATP production after the addition of ADP has been ascribed to the slow transport of ADP into the matrix space through the adenylate translocase. However, in heart mitochondria the translocase does not significantly contribute to the overall rate limitation of ATP production since uncoupled rates of respiration are similar to the State 3 rate (15,44,70 (71) in less than ϳ2 ms. Thus, the delay in ATP production with ADP additions is likely due to other factors such as the buffering of ADP in the matrix (72) and the fact that the ratio of ATP:ADP Ϫ1 is critical (73) in the operation of cytochrome oxidase (74 -77) as well as the F 0 F 1 -ATPase (71,78). Finally, since the initial conditions these experiments had near-physiological levels of ATP (3.4 mM), the matrix ATP: ADP Ϫ1 ratio may have played a significant role in this delayed response to ADP. If the matrix ATP was very high before the addition of ADP, the large amounts of ADP would have to be exchanged before approaching the free ATP:ADP Ϫ1 of ϳ2, as observed in intact rat hearts (79) and human skeletal muscle (80). The time required to reset the ATP:ADP Ϫ1 ratio could contribute to the delay observed for the ADP effect on respiration.
Creatine has been suggested to be more efficient in delivering ADP to the matrix than extramitochondrial ADP alone (19 -21, 24, 81-83). In this model, it has been suggested that local ADP synthesis, transfer to adenine nucleotide translocase, and subsequent respiration was preferential to simple exogenous bolus additions of ADP (81). Coupled to cytosolic creatine kinase, this might lead to a faster cytosolic transduction system than ADP alone. To test this hypothesis, creatine in the presence of ATP was used to generate ADP via the endogenous CPK in heart mitochondria. Using step increases of 10 mM creatine in the presence of ATP and P i resulted in very slow IRT responses (15.6 Ϯ 1.2 s) using our standard conditions (buffer C). To ensure that the creatine kinase enzyme was preserved in the mitochondrial membranes, several additional studies were performed. A thiol (S-H)-reducing agent dithiothreitol (0.5 mM) was added (buffer E) to prevent auto-oxidation of the CPK complex (34 -36); however, no improvement in IRT was observed. Alternatively, chloride in excess of (Ͼ50 mM) has been implicated in the loss of CPK function, which was reasoned to be due to the detachment of CPK from the adenine nucleotide translocase complex in the inner mitochondrial membrane (29). To test this possibility, experiments were performed in only 32 mM Cl Ϫ as the balanced anions to Na ϩ , Mg 2ϩ , and ATP. Under these conditions, the creatine IRT was shorter (Fig. 2B). To investigate the effects of inorganic ions further, experiments were performed in sucrose-based buffer, i.e. buffers G and G 0 , after reconstitution in either buffer B or buffer A, respectively. By using these systems, results from our studies could then be directly compared with previous findings for Cr respiration performed in similar media (20,21,24,29,38,82,84). Interestingly, the findings in buffers G and G 0 show a marked reduction in the creatine-driven IRT for mV O 2 values, which were comparable to those observed for ADP in buffer C (Fig. 2B). Similarly, mV O 2 increased by more than 100% for both preparations (Table III) in the sucrose buffers and were comparable to previous work (20,21,29,38,82). These findings are difficult to interpret, as the preparations are absent of Ͼ120 mM K ϩ normally seen in the cytosol, an ion known to play a major role in matrix volume regulation. Interestingly, when one compares the Cr results from buffer F, which contains physiologic levels of ions, with buffers G or G 0 , it is clear that only under the extreme conditions of low K ϩ and Cl Ϫ does one achieve elevated Cr rates and faster IRT (Table III), and this suggests that great caution be exercised when comparing results in dissimilar media. In any event, under optimal conditions for Cr, the IRT for mV O 2 was still 2 orders of magnitude longer than for Ca 2ϩ in our studies. Combined, these data illustrate that the metabolic effects of Ca 2ϩ occur at least 2 orders of magnitude faster than all other putative cytosolic signaling molecules tested and lend credence to the hypothesis that Ca 2ϩ may be capable of responding to step changes in cytosolic work.
In the current study, the IRT was estimated for Ca 2ϩ transport, and metabolic effects were found to occur well under 200 ms. Traditionally, matrix accumulation of Ca 2ϩ has been thought to occur too slowly to respond to cyclic changes in [Ca 2ϩ ] c (64,85,86). This discrepancy might in part be due to the methodological differences between studies. One issue has been the temperature at which these studies are conducted. The current studies were performed at 37°C, whereas much of the earlier work (87)(88)(89)(90)(91) was performed at significantly lower temperatures. Temperature correcting these data, assuming a linear dependence on temperature and a Q 10 of 2, does not resolve this issue, since these transport studies are still 5-7-fold slower. One possibility is that the Ca 2ϩ transport process is not linearly dependent on temperature due to phase transitions in the inner membrane lipid (92); however, this needs to be experimentally evaluated. All of the Ca 2ϩ observed effects in the current study could only be observed if the mitochondria were prepared with great care not to expose them to large concentrations of Ca 2ϩ (i.e. in situ perfusion of heart with Ca 2ϩ buffer solutions) as well as an ϳ6-min Ca 2ϩ depletion at 37°C in the absence of carbon substrates. This could result in much different initial conditions for matrix Ca 2ϩ levels when compared with previous work. Some evidence for rapid Ca 2ϩ uptake mechanisms has been found in mitochondria both in vitro and in intact cells. Recent work by Gunter and co-workers (46,47) demonstrated mitochondrial Ca 2ϩ uptake mechanisms in liver with similar kinetics as those described in the current study, and which showed reduced RuRed sensitivity. Similarly, studies in RHOD 2-loaded intact rabbit myocytes have also demonstrated RuRed insensitivity (45), suggesting this mechanism of transport is not an artifact of the isolation process. Moreover, studies in isolated astrocytes (89), neuroblastomas (93), hepatocytes (87), and cardiac myocytes (45, 88, 94 -97) have also shown rapid matrix Ca 2ϩ accumulation that is linked to phasic cycling of cytosolic Ca 2ϩ waves. Most interestingly, Rizzuto et al. (98,99), using a targeted Ca 2ϩ -sensitive fluorescent protein to complex IV, have shown that hormone-induced SR (ER) Ca 2ϩ release propagates directly into the mitochondria in approximately 1 s. Moreover, work in SR and complex IV co-loaded HeLa cells illustrates the close coupling of SR Ca 2ϩ release and mitochondrial uptake (100). These latter results suggest that more rapid mechanisms for Ca 2ϩ uptake may be present in cardiac mitochondria than suggested by previous work. Further characterization of these rapid Ca 2ϩ transport mechanisms will be required to establish the molecular mechanisms and pathways involved.
The current work is consistent with a rapid mechanism for the modulation of matrix Ca 2ϩ and mitochondrial oxidative phosphorylation by extramitochondrial Ca 2ϩ . The rapid metabolic effects of Ca 2ϩ observed were consistent with both the CaDH and F 0 F 1 -ATPase activation as described previously (15) for steady state oxidative phosphorylation. The speed of this process has only been estimated to occur in less than 200 ms due to technical limitations of the current experimental approach; however, this time constant is more than adequate to have extramitochondrial Ca 2ϩ regulate oxidative phosphorylation during work transitions in the heart (for example see Ref. 101). The [Ca 2ϩ ] dependence of this process is consistent with the physiological variations in Ca 2ϩ found in intact cells assuming no intracellular compartmentation of SR calcium release around the mitochondria. However, the morphological basis for a more direct coupling between mitochondrial Ca 2ϩ and SR release in the heart is clearly present as previously proposed by Rizzuto et al. (100) in other systems. Both scanning and transmission electron micrographs have shown a close association of the SR with mitochondria located between the Z lines of each myocyte sarcomere. An example from one of these studies is presented in Fig. 8. This tight morphological association of the SR with the mitochondria might further enhance the coupling of matrix Ca 2ϩ and associated metabolic effects with the contraction and active ion transport processes also activated by the SR Ca 2ϩ release, resulting in a balanced activation of metabolism with the mechanical and ion transport work in the myocyte.
The present study contains several limitations that should be recognized. First, since the isolation of mitochondria requires mechanical sheer force to remove them, it is possible that mitochondria in these preparations do not reflect the true capacity of those in the intact cell. Based on our RCR data, it would appear that minimal loss occurred, as the coupling (RCR) was maintained on average greater than 14 at 37°C and is on average more than double those reported for similar preparations. Despite this, it is difficult to determine if isolated mitochondria actually reflect the true capacity of the tissue in vivo (44). Second, the Ca 2ϩ depletion procedure is problematic, as it is difficult to know what resting matrix [Ca 2ϩ ] is in vivo. Based on this, it is difficult to assess whether our depletion protocol accurately represents the normal condition in intact hearts or whether a highly non-physiological condition is being evaluated. The obvious concern is that the matrix Ca 2ϩ levels are artificially low resulting in magnified Ca 2ϩ effects. Although this may be occurring at some level, results from the split Ca 2ϩ addition study, which looked at serial Ca 2ϩ additions up to 535 nM, do not support this contention. Third, the kinetic resolution of these studies was limited by the mixing characteristics of the chamber. Based on previous work that suggested very slow Ca 2ϩ transport kinetics, we assumed that the chamber mixing characteristics would not be a problem. However, all of the Ca 2ϩ -dependent effects were apparently influenced by the ϳ200-ms mixing kinetics of the chamber. To overcome this limitation, a near instantaneous delivery of Ca 2ϩ would be possible using caged Ca 2ϩ probes which are now commercially available. This might permit the further refinement of these rapid kinetic effects of Ca 2ϩ on mitochondrial metabolism. Finally, the delivery of Ca 2ϩ in isolated cells and perfused hearts has been shown to be phasic with the cardiac cycle. Since only a single bolus of Ca 2ϩ was used at a fixed [ATPase] in this study, it is difficult to know if the metabolic responses observed occur when Ca 2ϩ levels are appropriately cycled. This fundamental limitation could be eliminated in future studies by phasically adding Ca 2ϩ , again using caged Ca 2ϩ , and sub-maximal photolysis along with appropriate buffers.

APPENDIX
In the ROI just prior to the addition (t Յ t 0 ), if the reaction is assumed to be in quasi-steady state, then the rate of oxygen consumption is constant as shown in Equation A1, In the ROI following the addition (t Ն t 0 ), the reaction is assumed to reach a new quasi-steady state after an exponential transition in the rate of oxygen consumption from v 0 to v 1 : Integrating this expression with the initial condition that [O 2 ] ϭ c 0 at t ϭ t 0 yields Equation A4, This expression is asymptotic to the line (Equation A5): The line in the first ROI and the asymptote in the second ROI intersect at t ϭ t 0 defined by the condition shown in Equation  A6: under "Materials and Methods." Appendix Fig. A1A illustrates the time course of simulated [O 2 ] data and the methods by which t 0 and t i were assigned. Since the IRT was observed to range between 100 and 15,000 ms, model data sets were constructed with known exponential time constants in this range and compared with calculated IRT measurements. The results of this analysis are plotted under "Appendix" Fig. A1B. The concordance between these two measures was very high (R 2 ϭ 0.9995, n ϭ 12) with the line describing the trend being nearly that of identity ( ϭ 0.857 (IRT) Ϫ0.005). Calculations of estimated error for IRT revealed a consistent 13.7 Ϯ 3.6% underestimate (n ϭ 12). The fact that the IRT was consistently shorter than the true " " under these conditions is largely based in user defined errors in selecting ROIs and intersections. Moreover, the bulk of this error was for values that were extremely long (Ͼ6,000 ms). Based on these data and the analytical formulations above, it was reasoned that for step transitions with rapid responses and that show little exponential character on the current time scale, IRT was a reliable estimate of the transition time constant .