Oxidative Phosphorylation K_0.5ADP In Vitro Depends on Substrate Oxidative Capacity: Insights from a Luciferase-Based Assay to Evaluate ADP Kinetic Parameters

Abstract

The K_0.5ADP of oxidative phosphorylation (OxPhos) identifies the cytosolic ADP concentration which elicits one-half the maximum OxPhos rate. This kinetic parameter is commonly measured to assess mitochondrial metabolic control sensitivity. Here we describe a luciferase-based assay to evaluate the ADP kinetic parameters of mitochondrial ATP production from OxPhos, adenylate kinase (AK), and creatine kinase (CK). The high sensitivity, reproducibility, and throughput of the microplate-based assay enabled a comprehensive kinetic assessment of all three pathways in mitochondria isolated from mouse liver, kidney, heart, and skeletal muscle. Carboxyatractyloside titrations were also performed with the assay to estimate the flux control strength of the adenine nucleotide translocase (ANT) over OxPhos in human skeletal muscle mitochondria. ANT flux control coefficients were 0.91 ± 0.07, 0.83 ± 0.06, and 0.51 ± 0.07 at ADP concentrations of 6.25, 12.5, and 25 μM, respectively, an [ADP] range which spanned the K_0.5ADP. The oxidative capacity of substrate combinations added to drive OxPhos was found to dramatically influence ADP kinetics in mitochondria from several tissues. In mouse skeletal muscle ten different substrate combinations elicited a 7-fold range of OxPhos V_max, which correlated positively (R² = 0.963) with K_0.5ADP values ranging from 2.3 ± 0.2 μM to 11.9 ± 0.6 μM. We propose that substrate-enhanced capacity to generate the protonmotive force increases the OxPhos K_0.5ADP because flux control at ANT increases, thus K_0.5ADP rises toward the dissociation constant, K_dADP, of ADP-ANT binding. The findings are discussed in the context of top-down metabolic control analysis.

INTRODUCTION

The cells of oxidative mammalian tissues, such as liver, kidney, heart, and skeletal muscle, match ATP breakdown with mitochondrial oxidative phosphorylation (OxPhos). Both feedforward and feedback control signals coordinate this balanced ATP turnover. In cardiac myocytes in vivo, feedforward (or parallel) control dominates, as indicated by little to no change in cellular energetic status in response to step changes in ATP turnover rate [1]. In contrast, skeletal muscle mitochondria substantially rely on cytosolic feedback signals in the form of ATP hydrolysis products [2, 3], which include ADP and inorganic phosphate (Pi) concentrations, as well as diminished ATP free energy (ΔG_ATP) [3, 4]. However, feedback activators of mitochondrial OxPhos can also inhibit ATP-utilizing sites [5, 6], which decreases cellular functional output [7, 8]; this reciprocal interplay reflects the connectivity property of metabolic control analysis [9]. Thus, mitochondrial sensitivity to the signals fundamentally influences cell ATP turnover and function [7].

The concentration of ADP required to elicit 50% of the maximum OxPhos rate, K_0.5ADP, is routinely assessed as an index of OxPhos control sensitivity [10–13]. Our primary objective was to develop a luciferase-based assay with good sensitivity and throughput for this purpose. In 1976 Lundin and coworkers [14] improved luciferase monitoring of ATP production by small quantities of mitochondria. Later, Lundin, Wibom, and Hultman, adapted the procedures specifically for the measurement of maximum oxidative phosphorylation rates by skeletal muscle mitochondria [15]. We used Lundin’s more recent review [16] to guide the development of our assay. Our procedure provides extreme sensitivity, along with excellent reproducibility and throughput, to evaluate the kinetic parameters of OxPhos, adenylate kinase (AK), and creatine kinase (CK). We first used the assay to assess the ADP kinetics of ATP production in all three pathways by mouse mitochondria isolated from liver, kidney, heart, and skeletal muscle. In intact contracting mammalian skeletal muscle, OxPhos K_0.5ADP values of 20–40 μM have been measured non-invasively using ³¹P-MRS methodology [2, 3, 17]. This same range of K_0.5ADP is observed when mitochondria are isolated and O₂ consumption rate (J_O2) is measured polarographically across a range of experimentally established ADP concentrations [18–21]. However, in vivo OxPhos rises in a markedly sigmoidal relationship to [ADP] with a Hill exponent, n_H, in the vicinity of 2.0 (Equation 1).

$$v=\frac{V_{\mathit{\text{max}}}}{\left(1+{\left(\frac{K_{0.5}ADP}{[ADP]}\right)}^{n_H}\right)}$$ (1)

In contrast, in vitro J_O2 ADP kinetics are usually described by a simple Michaelis-Menten model in which n_H ~ 1.0. The K_0.5ADP parameter is typically reported as “apparent K_MADP” (appK_MADP) [22] to emphasize that the kinetic constant relates to the entire oxidative pathway rather than one specific enzyme. Nevertheless, in vitro one specific enzyme, the adenine nucleotide translocase (ANT), has been reported to be the primary locus of OxPhos flux control [20, 23–25]. ANT exchanges ATP for ADP across the inner membrane, but only the free ion forms, ATP⁴⁻ and ADP³⁻, can bind to the transporter [26]. Thus, dominant control at ANT suggests a relationship between the OxPhos parameter expressed as K_0.5ADP³⁻ and the ANT-ADP dissociation constant, K_dADP³⁻, which is roughly 4 μM [27, 28]. Here we use the luciferase-based procedure to confirm and extend these findings of dominant ANT flux control at ANT. We then contrast the K_0.5ADP³⁻ values assessed in different tissue mitochondria with the K_dADP³⁻ of ANT binding. The results underscore the central role of ANT in OxPhos rate control, as well as the insight achieved when ADP binding and OxPhos kinetic constants are consistently expressed as the free ion, ADP³⁻ [20].

The maximum (state 3) O₂ consumption rate of mammalian skeletal muscle mitochondria depends on the oxidative substrates provided [29–31], yet in vitro ADP kinetics studies rarely consider the substrates used to drive respiration [11, 19, 20, 32, 33]. More recently it has been observed that substrate combinations with lower catalytic potential e.g., fatty acids, yield lower values of K_0.5ADP [18, 21, 34]. Therefore, our third objective was to determine the influence of substrate oxidative capacity on ADP kinetics. Skeletal muscle mitochondria oxidized ten different substrate combinations and showed linear dependence of K_0.5ADP with maximum OxPhos flux potential across a 7-fold range. We use top-down metabolic control analysis [8] to show that K_0.5ADP³⁻ rising toward the ANT-ADP K_dADP³⁻ in response to greater substrate capacity to generate the protonmotive force (Δp) is consistent with a concomitant rise in ANT flux control strength. Moreover, due to the bulk phase nature of Δp [35], this interpretation generalizes to all upstream steps involved in Δp production, for example the citrate cycle and the electron transport chain (ETC).

MATERIALS AND METHODS

Ethical Approval

Six healthy human volunteers took part in this study. All human participation was approved by the Institutional Review Board of the University of Arizona. Informed, written consent was obtained from all participants.

Mouse tissues were acquired in accordance with the guidelines regarding the care and use of animals by the Institutional Animal Care and Use Committee at the University of Arizona.

Mitochondrial Isolation Buffer Solutions

Human skeletal muscle biopsies were obtained from the vastus lateralis. Mitochondria were isolated as described [20]. Mouse liver and kidney mitochondria isolation involved only one buffer, a mannitol + sucrose (M-S) solution comprised of (mM): 220 mannitol, 70 sucrose, 10 Tris-HCl, and 1 EDTA, that was pH adjusted to 7.4 at 4°C. Heart and skeletal muscle mitochondria isolation used three buffer solutions, all pH adjusted to 7.5 at 4°C. Solution I was (mM): 100 KCl, 40 Tris-HCl, 10 Tris-Base, 5 MgCl₂, 1 EDTA, and 1 ATP; Solution II: 100 KCl, 40 Tris-HCl, 10 Tris-Base, 5 MgCl₂, 1 EDTA, 0.2 ATP, and 1.5% BSA (fatty acid free). Solution III contained no BSA but was otherwise identical to Solution II.

C57BL/6J male mice, 12 to 24 weeks of age on standard chow diet and water ad libitum, were used. On the day of the experiment mice were euthanized by CO₂ inhalation; tissues were then rapidly removed and placed on an inverted petri dish on ice previously primed with M-S solution. Tissue was cleaned of all visible fat and connective tissue. Liver and kidney mitochondria were isolated by a modification [36] of the procedure of Lardy and coworkers [37]. Heart and skeletal muscle (rodent and human) mitochondria were isolated as described in [20].

All final mitochondrial pellets were resuspended in M-S buffer. Protein concentrations (mg/ml) of final suspensions in rodent tissues were (mean ± SE) liver 15.1 ± 1.2, kidney 14.3 ± 0.8, heart 5.9 ± 0.8, and skeletal muscle 5.6 ± 0.4, and in human skeletal muscle 5.7 ± 1.1, as determined with the Lowry assay [38] using BSA as standard. Dilutions of these suspensions for the luciferase assay were also made in M-S buffer.

Biochemicals and ATP Determination Kit

Biochemicals were purchased from Sigma-Aldrich. ATP determination kits (Invitrogen Catalog #A22066) included D-luciferin, recombinant firefly luciferase enzyme (temperature optimum 28°C), dithiothreitol, and ATP standard. The kit assay buffer was not used. Below in Results the basic features of the assay and assay components are described. In addition, Supplement Table S-1B provides a description of assay reaction mix preparation.

ADP Kinetics Assays

Assays were carried out at 25°C in opaque-bottom 96-well plates using a Tecan Genios instrument. In all kinetic assays and standard curves, the final assay volume in each well was 200 μl. In kinetic assays additions to the well included 165 μl reaction mixture (RM), sufficient distilled H₂O to give a final assay volume of 200 μl, 5 μl of ADP, 10 μl of mitochondria diluted in M-S, inhibitors if any, and 10 μl of substrate mix to start the reaction. In the final 200 μl volume the RM components had the following concentrations in mM: 100 KCl, 50 MOPS, 20 Glucose, 1 EGTA, 5 MgCl₂, 10 K˙2 PO4, 1.0 dithiothreitol, 0.54 D-luciferin, luciferase, and 0.2 g% BSA, pH 7.0 at 25°C. Table S-1B contains further details. Luminescence in relative light units (RLU) was measured at one-minute intervals over 7–10 min assay durations. All ADP kinetic assays were done at least in duplicate.

ATP standard curves at 25°C were run by adding 5 μl of ATP stock (μM): 0, 20, 50, 100, 150, or 200 to give a range of ATP masses from 0 to 1000 pmol (0 – 5 μM). All kinetic assay components were checked for influence on the slope and stability of the ATP standard curve. ATP standard curves are shown in Supplemental Figures S-1 and S-2.

Kinetic assays measured the rate of ATP accumulation by following light emitted by luciferase. Assays at 25°C were run at eight levels of [ADP] (μM): 0, 1.563, 3.125, 6.25, 12.5, 25, 50, and 125 final concentrations, in a column of a 96-well plate. Unless stated otherwise, all OxPhos and CK assays contained 20 μM diadenosine pentaphosphate (AP₅A) to inhibit AK activity. Mitochondria given ADP and AP₅A did not produce measurable ATP unless either oxidative substrate or phosphocreatine (PCr) were added (see Results and Supplementary Figure 8a, 8b). OxPhos and CK assays were started by adding either oxidative substrate or 10 mM PCr. In the AK assays ADP served as the substrate and AP₅A was not included.

Oxidative Substrate Final Concentrations

Ten different oxidative substrates, some with inhibitors, were used in these studies. In most OxPhos experiments mitochondria oxidized 10 mM glutamate + 10 mM succinate (GS), which invariably gave the highest OxPhos rate of all substrate combinations in all mouse tissues, as well as human skeletal muscle. Other combinations were 10 mM glutamate + 2 mM malate (GM), 5 mM ascorbate + 1 mM TMPD (AT), 10 mM 2-oxoglutarate (2OG), 10 mM glutamate + 2 mM malate + 2 mM arsenite, an inhibitor of 2-oxoglutarate dehydrogenase (GMA), 30 mM pyruvate + 5 mM malate (PM), 20 μM palmitoyl-l-carnitine + 1 mM malate (PCM), 5 mM acetyl-carnitine + 1 mM malate (AcCM), 10 mM succinate + 5 μM rotenone (SR), and 10 mM glycerol-3-phosphate (G3P).

Analysis of ADP Kinetic Assays

Linear regression was used to determine the slope (RLU/min) of kinetic assay progress curves. Next, this slope was converted to ATP production rate (J_ATP) in units of pmol ATP/min using the slope of the ATP standard curve (RLU/pmol ATP). The kinetic parameters of the [ADP]:J_ATP relationship were then evaluated using the Excel Solver tool to minimize the residuals of a Michaelis-Menten nonlinear model with both [ADP] and the K_0.5ADP parameter raised to a Hill exponent (see Equation 1 above).

Metabolic Flux Control Assays

The flux control strength of the adenine nucleotide translocase (ANT) over OxPhos was measured in human skeletal muscle mitochondria oxidizing glutamate + succinate. Carboxyatractyloside (CAT), a high affinity inhibitor of ANT, was added at eight levels to titrate OxPhos measured with luciferase. Inhibitor titrations were performed at least in duplicate at three ADP concentrations, 6.25, 12.5, and 25 μM, a range which spans the K_0.5ADP for OxPhos. Into eight wells of reaction mix with 20 μM AP₅A were added mitochondria, one concentration of ADP, and one of eight levels of CAT (nM), 0, 0.25, 0.50, 1.0, 1.5, 1.875, 2.5, and 5.0. After 5 min of incubation to ensure equilibrium ANT-CAT binding, assays were initiated by the addition of glutamate + succinate.

Analysis of ANT Flux Control Assays

The flux control strength (C^J) of an enzyme in a metabolic pathway is defined [23, 24, 39] as the fractional change in pathway flux divided by the fractional change in enzyme abundance (or maximum activity):

$${\text{C}}^{\mathrm{J}}\text{=(dJ/J)/(dE/E)}$$ (2)

The fractional change in OxPhos flux at each CAT concentration was directly measured with the luciferase assay. The fraction of ANT occupied and inhibited by CAT was determined using the Easson-Steadman (E-S) equation [40] to estimate both the dissociation constant (K_d) of ANT-CAT binding and the concentration of ANT in the assay. The assumptions of the E-S equation and the evaluation of flux control strength are described in Results

Statistics

Slopes and goodness of fit were assessed with linear regression. Differences between two mean values were determined using unpaired t tests. Significance was accepted at p<0.05.

RESULTS

ATP Standard Curves

ATP standard curves are shown in Figures S-1 and S-2. Standard curves were linear with ATP addition, R² = 0.9993 ± 0.0001, n = 42. ATP signals were stable across time (Figures S-1 and S-2) indicating the absence of inhibitory product accumulation. ATP standard signal stability was also not affected by the addition of mitochondria and AP₅A either in the presence or absence of oligomycin. Standard curve slopes can be affected by assay components such as oxidative substrates and inhibitors. This must be accounted for by running ATP standards under the appropriate conditions; an example is shown in Figure S-2. It should be noted that inorganic phosphate (Pi) is a potent inhibitor of most luciferases [16]. In the present studies, 10 mM Pi was included in all assays and the appropriate volume of luciferase stock to add to the reaction mix was empirically determined. Thus, high but constant Pi concentration in the assay is not an issue. However, we were initially interested in using this assay to evaluate phosphate kinetic parameters, but this phosphate inhibition feature rendered that application impractical.

ADP Kinetic Assays

Excellent linearity with time, at every level of ADP, was consistently observed in kinetic assays of 7–10 min duration. A representative example is shown in Figure 1. The extreme sensitivity of luciferase-based ATP monitoring [16] enables the assay of very small quantities of mitochondrial protein. For example, in Figure 1 only 0.16 μg protein of mouse skeletal muscle mitochondria was added to each well. High sensitivity also minimizes net utilization of buffer constituents and accumulation of product (e.g., ATP), ensuring nearly steady state conditions. Consequently, assay progress curves were consistently linear across time with R² values approaching or equaling 0.99.

Figure 1.

Progress curves of kinetic assays. OxPhos of mouse skeletal muscle mitochondria oxidizing glutamate + succinate (10 mM + 10 mM). Adenylate kinase was inhibited with 20 μM AP₅A. Mitochondrial protein added to each well was 0.160 μg.

Although most commercially prepared ADP contains small amounts of contaminating ATP, this was not an issue of concern. Figure S-3 shows that in our hands ATP contamination of stock ADP solutions was 1.27%. Further, the linearity of this plot (R² = 0.999) up to an ADP concentration of 250 μM also indicates that an ADP level twice that of the highest used in our assays had no inhibitory effect on the ATP signal. We found it was unnecessary to remove ATP contamination from our ADP stocks, likely because the ATP levels are well below the K_MATP of potential ATP-utilizing reactions, for example, the F₁-ATPase activity of damaged mitochondria. In fact, as seen on the ordinate of Figure 1, the small but progressively higher initial RLU values resulting from this ATP contamination provided a helpful check that correct ADP stocks had been added to each well.

The progress curve slopes of Figure 1 (RLU/min) were converted to ATP production rates using an ATP standard curve (shown in Figure S-1) and the kinetic parameters of Equation 1 were then evaluated with nonlinear regression analysis to give results such as shown in Figure 2. An example of the analysis is given in Figure S-4. Examples of CK and AK analysis are provided in Figure S-5 and Figure S-6, respectively.

Figure 2.

Progress curves of Figure 1 converted to ATP production rates (J_ATP) and evaluated for kinetic parameters. Data are shown as unfilled circles and the solid line is the data fit to Equation 1.

K_0.5ADP = 11.9 μM, n_H = 1.28, and V_max = 103.7 pmol ATP/min (648 nmol min⁻¹ mg⁻¹)

Assay Dose-Response Linearity and Coefficient of Variation

Proportionality between ATP production rate and mitochondrial protein added was observed and the assay ADP concentration had no effect on dose-response linearity (see Figure S-7). The assay coefficient of variation (CV%) was calculated using 91 duplicate measurements collated from 13 mitochondrial preparations each assayed at 7 concentrations of ADP from 1.5 to 125 μM (Equation 3):

$$CV(\text{\%})=100x\sqrt{\frac{\mathrm{\Sigma }{\left(\frac{d}{m}\right)}^2}{2n}}$$ (3)

where d is the difference between two paired measurements, m is the mean of the pair, and n in this case is 91 pairs. The coefficient of variation of the 91 duplicates was 5.03%.

ADP Kinetics of ATP Production in Mouse Tissues

The ADP kinetic parameters for all three mitochondrial ATP production pathways in the four mouse tissues are given in Table 1. The control of oxidative ATP production was the primary focus of this study, but we additionally measured mitochondrial ATP production by adenylate kinase (AK) and creatine kinase (CK), which are both located in the intermembrane space. The parameter values in Table 1 were used to construct the kinetic curves shown in Figure 3.

Table 1:

ADP kinetic parameters for three pathways of ATP production by mitochondria isolated from the mouse tissues shown. The oxidative substrates were glutamate + succinate (10 mM + 10 mM). The substrate for creatine kinase (CK) was 10 mM phosphocreatine. For both OxPhos and CK 20 μM AP₅A was added to inhibit adenylate kinase (AK). AK phosphorylated the ADP added and AP₅A was not included. Units are μM for K_0.5ADP and nmol ATP min⁻¹ mg⁻¹ for V_max. n_H is unitless. Assay temperature was 25°C, pH 7.0, 10 mM inorganic phosphate, and total Mg²⁺ of 5 mM.

	Oxidative Phosphorylation				Adenylate Kinase				Creatine Kinase
K0.5AD P	Liver	Kidney	Heart	Muscle	Liver	Kidney	Heart	Muscle	Kidney	Heart	Muscle
Mean	22.3	12.1	12.5	11.9	84.0	64.3	54.9	78.0	37.8	24.4	36.3
SE	1.5	0.6	0.6	0.4	7.2	4.4	5.4	8.0	4.1	0.9	3.8
n	7	7	11	10	6	7	6	6	3	6	3
nH	Liver	Kidney	Heart	Muscle	Liver	Kidney	Heart	Muscle	Kidney	Heart	Muscle
Mean	1.33	1.45	1.35	1.19	1.53	1.74	1.85	1.68	1.00	1.00	1.07
SE	0.04	0.05	0.05	0.03	0.11	0.05	0.16	0.09	0.01	0.02	0.06
n	7	7	11	10	6	7	6	6	3	6	3
Vmax	Liver	Kidney	Heart	Muscle	Liver	Kidney	Heart	Muscle	Kidney	Heart	Muscle
Mean	59.9	109.9	242.4	553.5	171. 7	102.3	30.2	25.7	28.7	273.9	944.2
SE	4.5	6.0	8.0	31.3	23.7	15.0	3.9	5.4	3.7	50.5	188.0
n	7	7	11	10	6	7	6	6	3	6	3

Figure 3:

ATP production by OxPhos, AK, and CK in mouse mitochondria isolated from liver (panel A), kidney (panel B), heart (panel C), and skeletal muscle (panel D). Curves were constructed using the kinetic parameter values in Table 1.

In liver mitochondria CK activity was not detectable, in agreement with Saks and coworkers [41]. Liver mitochondria had very high AK V_max relative to OxPhos. AK kinetics were markedly sigmoidal, reflecting the cooperative ADP binding of the enzyme.

From a methodological standpoint, the liver results emphasize the need to inhibit AK with diadenosine pentaphosphate (AP₅A) when the experimental objective is to assess OxPhos or CK kinetics. As shown in Figure S-8a and Figure S-8b, AK activity was not detectable when AP₅A was present at 20 μM. It should be noted that the absence of ATP production when only ADP and AP₅A are added also indicates that mitochondria did not contain measurable endogenous oxidative substrate. This is consistent with the fact we are adding sub-microgram quantities of mitochondrial protein, which translates to less than 1.0 nl of matrix space, into 200 μl of reaction mix, a dilution factor exceeding 200,000.

In marked contrast to the liver, heart and skeletal muscle mitochondria exhibited low AK activity, particularly relative to OxPhos and CK. In heart (Figure 3C) and, especially, skeletal muscle (Figure 3D), mitochondrial ATP production via CK was highest. In kidney mitochondria (Figure 3B) the pattern of the three pathways was intermediate to that of liver and the striated muscle tissues.

In all tissue types the substrate combination eliciting the highest OxPhos rate was glutamate + succinate (GS), as shown for skeletal muscle in Fig. 4, heart in Fig. S-11, and liver Fig. S-12 (kidney not shown). Thus, glutamate + succinate was the oxidative substrate combination used in the comparison of ADP kinetic parameters across tissues shown in Table 1 and Figure 3, and in the determination of ANT flux control strength (Table 3).

Figure 4:

ADP kinetic assessment in mouse skeletal muscle mitochondria provided 10 different oxidative substrate combinations. Panel A shows how the substrate-dependent 7-fold range of maximum OxPhos rate linearly relates to the measured K_0.5ADP, y = 11.24x + 0.62, R² = 0.963. Panel B shows that as V_max and K_0.5ADP rise, the Hill exponent, n_H, concomitantly falls toward 1.0 i.e., the kinetics become more like a simple Michaelis-Menten model. Equation of the line in panel B: y=−0.636x+1.791, R²=0.607. Both panels illustrate the same 32 complete kinetic assessments carried out on 8 separate mitochondrial preparations. The substrates and inhibitors used were Glutamate (G), Succinate (S), Malate (M), Ascorbate+TMPD (AT), 2-oxoglutarate (2OG), Arsenite (A), Pyruvate (P), Palmitoyl-Carnitine (PC), Acetyl-Carnitine (AcC), Succinate + Rotenone (SR), and Glycerol-3-Phosphate (G3P). The final assay concentrations of each substrate combination and the inhibitors are listed in Materials and Methods.

Table 3:

ADP kinetic parameters and ANT flux control strength (C^J) assessed in human skeletal muscle mitochondria. ADP kinetics were evaluated as before. ANT flux control over OxPhos at three [ADP] (μM) was measured by titrating OxPhos with carboxyatractyloside. In all assays the oxidative substrates were glutamate + succinate and 20 μM AP₅A was added to inhibit adenylate kinase. One flux control assessment at 6.25 μM ADP was lost due to methodological problems.

	K0.5ADP	nH	Vmax	[ANT]	ANT CJ at Various [ADP]
	μM		nmol/min/mg	nmol/mg	6.25 μM	12.5 μM	25 μM
Mean	11.1	1.16	251.9	1.12	0.91	0.83	0.51*
SE	0.8	0.03	35.1	0.14	0.07	0.06	0.07
n	6	6	6	5	4	5	5

^*p = 0.035 vs 12.5 μM ADP

Liver K_0.5ADP for OxPhos was almost twofold higher than the other three tissues, p < 0.01, which were not different from each other. Skeletal muscle had the least sigmoidicity in its OxPhos kinetic response (lowest n_H exponent), p < 0.01 and the highest OxPhos V_max per mg mitochondrial protein, p < 0.01.

K_0.5ADP: ΣADP vs ADP³⁻

ADP and ATP bind to cations with variable affinity. All ADP concentrations mentioned to this point, for example the K_0.5ADP values in Table 1, have been the sum of all ionic forms, which can be symbolized ΣADP [42]. However, the adenine nucleotide translocase (ANT) binds ADP and ATP only in their free ion forms, ADP³⁻ and ATP⁴⁻ [26]. Magnesium is a major chelator of ADP (and ATP to an even greater extent) and the Mg²⁺ concentration in the respiration medium may vary substantially in different laboratories reporting kinetic assessments such as these. This is one reason it is helpful to express the K_0.5ADP in free ADP terms (K_0.5ADP³⁻). We have used the procedures of Chinopoulos and coworkers [43] to calculate the free [Mg²⁺] and [ADP⁻³] at each level of added ADP. In these experiments with total [Mg²⁺] of 5 mM, 10 mM [Pi], and pH 7.0, this adjustment gives an [ADP³⁻] which roughly equals the [ΣADP] divided by 6.4. Thus, the K_0.5ADP³⁻ (μM) for OxPhos in mouse liver, kidney, heart, and skeletal muscle determined here are, respectively, 3.5, 1.9, 1.9, and 1.9.

Related to the above, the absence of physiologically meaningful ATP ([ΣATP] < 5 μM) in these luciferase assays has two important, and counteracting, consequences on ADP kinetics. At physiological concentrations, ATP⁴⁻ competes with ADP³⁻ for binding to ANT [26, 44, 45] and its absence should therefore decrease K_0.5ADP. On the other hand, ATP binds to Mg⁺² almost 10 times more avidly than ADP [43, 46]. In this case, low [ATP] exposes ADP to roughly 3-fold higher free [Mg²⁺], thus substantially decreasing the fraction of the ΣADP pool available for ANT binding i.e., ADP³⁻. We directly compared estimates of OxPhos K_0.5ADP in both ΣADP and ADP³⁻ terms in the presence and absence of 5 mM ΣATP. The kinetics of ADP were simultaneously assessed in the same five preparations of mouse skeletal muscle mitochondria both polarographically, using a creatine kinase clamp [32, 47], and with the luciferase-based assay. In the polarographic creatine kinase clamp procedure O₂ consumption rate is continuously measured while the medium ADP concentration is clamped across a range of steady state values by adjusting the phosphocreatine to creatine ratio in the presence of 5 mM ATP and saturating creatine kinase [19, 20]. As reported in Table 2, polarography and luciferase gave similar K_0.5ADP values, 13.1 ± 1.3 and 11.9 ± 0.6 μM, respectively, when all ionic forms of ADP are considered (ΣADP). However, when expressed in terms of ADP³⁻, the clamp estimated a K_0.5ADP³⁻ over twofold higher than luciferase, 4.4 ± 0.4 vs 1.9 ± 0.1 μM, p = 0.003. Notably, the PCr clamp reconstitutes a more physiological assay environment than luciferase by providing closer to equilibrium conditions at the ADP:ATP exchange step [19] and ATP⁴⁻ competition with ADP³⁻ for binding to ANT [27]. Again, the buffer [ΣATP] in the luciferase assay never exceeds 5 μM, while in the clamp the buffer 5 mM ΣATP corresponds to [ATP⁴⁻] of roughly 320 – 340 μM [20].

Table 2.

ADP kinetic parameters determined with either polarography (and the “creatine kinase clamp”) at 37°C or the luciferase-based procedure at 25°C. Glutamate + Succinate (10 mM + 10 mM) were the oxidative substrates. The K_0.5 parameter is expressed in terms of all ionic forms of ADP (ΣADP), as well as the ionic form that binds to ANT (ADP³⁻).

	K0.5ADP (ΣADP)		K0.5ADP3−
	μM		μM
	Polarography	Luciferase	Polarography	Luciferase
Mean	13.1	11.9	4.4	1.9*
SE	1.3	0.6	0.4	0.1
n	5	5	5	5

^*p = 0.003 vs polarography

ANT Control of OxPhos Flux

As described in Materials and Methods, the flux control an enzyme exerts over a pathway can be estimated by measuring the fractional change in pathway flux divided by the fractional change in the abundance (or activity) of the enzyme. We measured ANT flux control strength over OxPhos in human skeletal muscle mitochondria oxidizing glutamate + succinate. ATP production was measured at eight levels of carboxyatractyloside (CAT). These inhibitor titrations were carried out at three ΣADP concentrations, 6.25, 12.5, and 25 μM, a range which spans the K_0.5ADP of 11.1 ± 0.8 μM (Table 3). The change in flux caused by each CAT level was directly measured with the luciferase assay. However, the denominator, the fraction of ANT bound and inactivated by CAT, had to account for the sub-microgram mitochondrial protein per assay; the concentration of ANT in the assay (see Fig S-9a) approximated the K_d of CAT binding [48]. To calculate the fraction of ANT bound to CAT we used the ligand conservation equation of Easson and Stedman [40, 49] (E-S equation), which provides estimates of both the ANT-CAT K_d and the concentration of ANT. Specifically applied to the present study the E-S equation is:

$$[\text{CAT}]/i=[\text{ANT}]+{\text{K}}_{\mathrm{d}}{(1-i)}^{-1}$$ (4)

where [CAT], [ANT], and K_d have the meanings described above and i is the relative inhibition of OxPhos caused by each CAT concentration. The results of each assay were analyzed using Equation 4 to estimate ANT concentration and the ANT-CAT K_d. However, it should be noted that the derivation of the E-S equation [40] assumes that the enzyme being studied has complete control of flux i.e., C^J = 1.0. Fortunately, in every mitochondrial preparation we assessed at low [ADP] (6.25 and/or 12.5 μM), the plots of (1-i)⁻¹ vs [CAT]/i were approximately linear, thus [ANT] and the ANT-CAT K_d could be estimated (see Fig S-9a for an example of the analysis). Further, consistent CAT-ANT K_d values were observed, 0.048 ± 0.002 nM (n=27). The y-intercept values ([ANT] in nM) were, as expected, more variable since they depend on the protein (mg/L) added to the assay and the ANT abundance (nmol/mg) of the mitochondrial sample. Flux control coefficients, C^J, were evaluated by measuring the fractional changes in flux and CAT-occupied ANT, (dJ/J)/(dANT/ANT), caused by the first CAT addition; an example is shown in Figure S-9b. Additionally, the entire titration of [CAT] and corresponding fluxes (J_ATP) were analyzed using the equation of Gellerich et al. [48] and nonlinear regression analysis; these estimates of control strength agreed with the simple procedure shown in Figure S-9b. Flux control results are reported in Table 3.

The (ΣADP) K_0.5ADP of 11.1 ± 0.8 μM for human skeletal muscle mitochondria oxidizing glutamate + succinate is similar (p = 0.39) to our previous human skeletal muscle data [20]. In that same study [20] the conventional polarographic procedure estimated the ANT flux control coefficient to be 0.82 at [ADP] close to the K_0.5ADP, also confirmed here. However, at [ADP] over twice the K_0.5ADP, 25 μM, ANT control strength fell substantially to 0.51 (Table 3). Finally, the ANT abundance of roughly 1 nmol/mg estimated with the luciferase assay and E-S analysis was also similar to the range reported for skeletal muscle [20, 50] and heart [24, 51] measured using polarography.

Effect of Substrate Supply on ADP Kinetic Parameters

The influence of substrate availability on the OxPhos ADP kinetics of mouse hindlimb skeletal muscle is shown in Figure 4. In 32 complete kinetic assessments carried out on 8 mitochondrial preparations, ten different substrate combinations were used. Figure 4A shows the linear relationship, R² = 0.963, between K_0.5ADP and V_max, which nearly regresses through the origin. Panel B of Figure 4 shows the Hill exponent, n_H, falls toward unity as flux and K_0.5ADP rise. Thus, high flux substrate combinations result in kinetics more similar to a simple Michaelis-Menten model. Essentially identical patterns were observed in human skeletal muscle mitochondria, albeit with fewer substrate combinations, as shown in Figure 5A and 5B. These are the same human mitochondrial preparations described in Table 3.

Figure 5:

Relationship between OxPhos V_max and K_0.5ADP (Panel A) and the Hill exponent, n_H, (Panel B) in 6 preparations of human skeletal muscle mitochondria oxidizing 4 different substrate combinations: GS, Glutamate + Succinate (10 mM + 10 mM), GM, Glutamate + Malate (10 mM + 2 mM), PM, Pyruvate + Malate (30 mM + 5 mM), and PCM, Palmitoyl-l-Carnitine + Malate (20 μM + 1 mM). Equations of the lines relating these mean values are in Panel A: y = 11.25x – 0.70, R² = 0.960 and in Panel B: y = −0.806x + 1.93, R² = 0.982. Scatterplots (n = 20 data points) of these relationships are shown in Figure S-14. In that case the equations of the lines are for Panel A: y = 10.92x – 0.39, R² = 0.893 and Panel B: y = − 0.722x + 1.86, R₂ = 0.530

Mitochondria isolated from several other sources gave similar results. These experiments are reported in Supplemental Data: Mouse heart (Figure S-11), mouse liver (Figure S-12), and L6 myotubes, which are differentiated rat skeletal muscle cells in culture (Figure S-13). Also shown (Figure S-10), are polarography data of linearly related state 3 O₂ consumption vs K_0.5ADP in mitochondria isolated from rat hindlimb muscle and avian flight muscle oxidizing 8 different substrate combinations from our previous work [18].

DISCUSSION

Luciferase Assay to Evaluate ADP Kinetics and Flux Control

The K_0.5ADP for OxPhos is a kinetic parameter widely used to assess both mitochondrial dysfunction in disease [11] and enhanced function due to exercise training [10, 12, 13]. We describe a convenient, reliable, and fast luciferase-based procedure capable of assessing mitochondrial ADP kinetics and flux control. With most research applications the extreme sensitivity offers practically no lower limit of detection; mitochondria isolated from cultured cells, for example the L6 cells used here, provide sufficient protein for hundreds of assays. Assays for ADP kinetics and flux control were routinely performed in duplicate by one individual in less than two hours. Polarography, by comparison, can assess additional fluxes of interest such as basal proton leak and uncoupled vs. coupled maximum ETC flux, but the assays require much more time and effort, in addition to orders of magnitude more mitochondrial protein. Further, if OxPhos is the process of interest, additional measurements or assumptions regarding proton leak or ATP/O coupling are necessary in polarographic studies.

Mitochondrial ATP Production in Mouse Tissues

Two characteristics of ATP production by liver mitochondria were noteworthy, AK activity and the K_0.5ADP for OxPhos. Oxidative ATP production by liver mitochondria exceeded that of AK up to about 50 μM [ADP], a little over twice the K_0.5ADP for OxPhos. Beyond that [ADP], ATP production by AK progressively outpaced OxPhos, up to a V_max that was almost 3-fold higher. We note briefly that the AK reaction, ADP + ADP → ATP + AMP, obviously cannot be viewed as a steady state source of ATP production. It can also be calculated (not shown) that hepatocyte metabolic rate, along with the mass of the cytosolic adenylate pool, preclude any meaningful AK contribution to metabolic capacitance during a transient rise in ATP demand [52]. The observed AK kinetics for the liver mitochondria exhibit a rapidly rising bi-directional catalytic competence as [ADP] rises (energy state falls) and oxidative phosphorylation becomes more competitive for ADP substrate. This pattern is consistent with the ability to maintain near-equilibrium in the AK reaction and an AMP signal proportional to the square of the [ADP]. Particularly in the liver, AMP activated protein kinase (AMPK) plays a central role in the maintenance of cellular energy homeostasis [53–56]. AMPK promotes oxidative substrate delivery, while it brakes ATP utilization [57]. Indeed, AMPK knockout in the liver impairs energy state defense [58].

The control of OxPhos was our primary focus. In this regard, the most notable outcome of the mouse tissue mitochondria in Table 1, which all oxidized glutamate + succinate, was the almost twofold higher K_0.5ADP observed in liver. The liver K_0.5ADP for OxPhos (22.3 μM), converts to a K_0.5ADP³⁻ of roughly 3.5 μM. This value is similar to ANT-ADP binding affinity, K_dADP³⁻, for which molecular dynamic modeling gives an estimate of 3.66 μM [28], in good agreement with experimental observations [27, 59]. In marked contrast, the ~12 μM K_0.5ADP of skeletal muscle, heart, and kidney converts to a K_0.5ADP³⁻ ~ 1.9 μM, about half the ANT K_dADP³⁻. Below we will propose that low relative ANT abundance in liver mitochondria [51, 60, 61] underlies the closer match between K_0.5ADP³⁻ and K_dADP³⁻ in this tissue. For now, we point out that ANT isoforms cannot explain higher liver K_0.5ADP. Two isoforms, ANT1 and ANT2, are found in mammalian liver, kidney, heart, and skeletal muscle mitochondria. Despite their different K_0.5ADP, liver and kidney have similar ANT2 relative abundances: 75% and 65%, respectively [62]. Kidney, heart, and skeletal muscle have similar K_0.5ADP, yet very different relative abundance in ANT1: 35%, 63%, and 81%, respectively [62]. Moreover, ANT isoforms have no obvious functional differences [63].

ANT ATP⁴⁻/ADP³⁻ binding and exchange

ANT is an inner membrane carrier which exchanges ADP for ATP, binding these adenylates exclusively in their free ion forms, ADP³⁻ and ATP⁴⁻ [26] at a site located at about the midpoint of the bilayer [63]. Operating in the “forward” direction ANT in its c-state (open toward the cytosol) binds ADP³⁻ in the intermembrane space, which changes the protein structure to the matrix-facing, m-state, in which ADP³⁻ can be released into the matrix [63, 64]. To complete one cycle of productive exchange, ATP⁴⁻ binds in the matrix, the conformation reverts to the c-state, and ATP⁴⁻ is released into the intermembrane space. ADP³⁻ binds to three positively charged residues, arginine and lysine, fully neutralizing all charges [28]. In contrast, although ATP⁴⁻ binds in the same location and with roughly similar affinity under deenergized conditions [27], one negative charge of bound ATP remains uncovered [45]. At physiological ratios of ATP/ADP, ATP⁴⁻ competition with ADP³⁻ increases the apparent K_MADP of the transport process [65]. This competition was evident in Table 2, where the more physiological conditions of the creatine kinase clamp i.e., extramitochondrial [ATP⁴⁻] > 300 μM, resulted in K_0.5ADP³⁻ over two times higher than in the luciferase assay (buffer [ΣATP] < 5 μM). Due to the charge difference in the exchange of cytosolic ADP³⁻ for matrix ATP⁴⁻, net flux at ANT is thermodynamically driven by the membrane potential, ΔΨ [65, 66].

ANT Control of OxPhos Flux

Previous studies that have taken care to assess only the flux control intrinsic to mitochondria themselves, thus excluding experimentally introduced rate-controlling enzymes such as hexokinase, have identified ANT as the major locus of OxPhos control in mitochondria isolated from rat liver, rabbit heart, and both rat and human skeletal muscle [20, 23, 24, 49]. Here we have confirmed the findings in human skeletal muscle and extended them to three concentrations of ADP, which span the K_0.5ADP. Importantly, these mitochondria oxidized the highest flux substrate combination, glutamate + succinate [30]. Control strength at ANT was especially strong, roughly 90% and 80%, at [ADP] below and near the K_0.5ADP, respectively. At 25 μM [ADP], over two times the K_0.5ADP, ANT control strength fell significantly to just over 50%. Many polarography studies, including our own [20], have shown that saturating ADP (state 3 respiration) reduces ANT flux control in striated muscle mitochondria to nearly zero [23, 50, 51]. We can infer, therefore, that control strength would continue to fall progressively as the ADP concentration increased above 25 μM. The findings of Kholodenko et al. in rabbit heart mitochondria [24], as well as our own preliminary data (not shown), support this assumption.

Effect of Oxidative Substrate on ADP Kinetics

In conformity with in vivo ³¹P-MRS studies [3, 17], we analyzed the ADP kinetics of OxPhos with a Michaelis-Menten type model with the K_0.5ADP and [ADP] terms raised to a Hill exponent, n_H (see Equation 1). We included a Hill exponent as an ad hoc parameter, simply to improve the estimate of K_0.5ADP. That goal was achieved, but the analytical approach also revealed the unexpected outcomes shown in Figure 4B and Figure 5B. As V_max and K_0.5ADP rose, the Hill exponent concomitantly fell, approaching simple Michaelis-Menten kinetics.

In this case, rather than reflecting higher order control by ADP [67], Hill coefficients appreciably in excess of 1.0 essentially described a near-linear [ADP]:J_ATP relationship abruptly transitioning to V_max, as shown in Figure 6. Figure S-15 clearly illustrates this phenomenon, contrasting the kinetic curves of glutamate + succinate and glycerol-3-phosphate, the highest and lowest V_max substrates, respectively.

Figure 6:

Kinetic responses of all 10 substrate combinations drawn using mean kinetic parameter values from the 8 separate mitochondrial preparations. ATP production rate is expressed relative to the V_max of Glutamate+Succinate (GS). Other substrates shown: G+Malate (GM), Ascorbate + TMPD (AscTMPD), 2-Oxoglutarate (OG), G+M+Arsenite (GMA), Pyruvate+M (PM), Acetyl-Carnitine+M (AcCM), Palmitoyl-Carnitine+M (PCM), Succinate+Rotenone (SR), and Glycerol-3-Phosphate (G3P).

Top-Down Metabolic Control Analysis (MCA)

The K_0.5ADP of OxPhos describes the response of the entire oxidative pathway. If all flux control were located at ANT up to V_max, then this K_0.5ADP would specifically reflect ANT kinetics. In this hypothetical case, since ADP binds to ANT as ADP³⁻, we would expect the values of K_0.5ADP³⁻ and ANT K_dADP³⁻ to be similar. This, in fact, is essentially the case for liver mitochondria oxidizing glutamate + succinate (this is discussed below). In contrast, the K_0.5ADP³⁻ for skeletal muscle mitochondria oxidizing glutamate + succinate was roughly half the K_dADP³⁻ and lower V_max substrates resulted in proportionally lower K_0.5ADP³⁻ values. We propose that augmented substrate oxidative capacity increases K_0.5ADP³⁻ toward the K_d of ANT-ADP³⁻ binding because flux control strength at ANT rises with the capacity to generate the protonmotive force (Δp). This interpretation is based on top-down, or modular, metabolic control analysis [68], which is conceptually illustrated in Figure 7.

Figure 7:

Top-down (modular) metabolic control analysis applied to the OxPhos pathway in the luciferase assay. The mitochondrion is conceptually viewed as comprised of two modules, Δp-producer and Δp-user with a common intermediate, Δp. Ten different oxidative substrate combinations were used to adjust, over a 7-fold range, the maximum rate of proton pumping by the Δp-producer module. The Δp generated by all 10 substrate combinations was utilized by the same Δp-user module. ADP acts as an external effector, which binds to, and activates, the Δp-user module, thus decreasing the rate control it exerts over the Δp-producer module. See text for further description. DH, substrate dehydrogenases; CAC, citric acid cycle; ETC, electron transport chain; C V, complex V; ANT, adenine nucleotide translocase.

Mitochondria are viewed as comprised of two modules, Δp-producer and Δp-user linked by their common intermediate, Δp [69]. The Δp-producer module contains all mitochondrial steps involved in substrate membrane transport and oxidation by dehydrogenases, as well as electron transport coupled to proton pumping. The Δp-user module contains the phosphate transporter, Complex V, and ANT. In top-down MCA terminology, the relationship between module activity and Δp is called elasticity, ε [8]; the Δp-producer module has negative elasticity to Δp (Δp “pushes back” against proton pumping by the producer module), while the Δp-user elasticity is positive (the electrophoretic effect of ΔΨ advancing ANT flux, for example). Our experimental intervention was to modify the Δp-producer module elasticity over a roughly 7-fold range with ten different oxidative substrate combinations. Importantly, all ten of these widely different Δp-producer elasticities interacted with the same Δp-user module responding to the same range of added ADP. The summation theorem of MCA states that the flux control coefficients of the two modules sum to 1.0 [9]:

$$C_{\mathit{\text{prod}}}^J+C_{\mathit{\text{user}}}^J=1.0$$ (5)

The connectivity property (Equation 6) describes the mutual dependence of the two modules on the common intermediate, Δp:

$$C_{\mathit{\text{prod}}}^J\ast {\epsilon }_{\mathrm{\Delta }p}^{\mathit{\text{prod}}}+C_{\mathit{\text{user}}}^J\ast {\epsilon }_{\mathrm{\Delta }p}^{\mathit{\text{user}}}=0$$ (6)

Equations 5 and 6 can be rearranged to give both flux control coefficients in terms of the elasticities (Equations 7 and 8) [69]:

$$C_{\mathit{\text{prod}}}^J=\frac{{\epsilon }_{\mathrm{\Delta }p}^{\mathit{\text{user}}}}{{\epsilon }_{\mathrm{\Delta }p}^{\mathit{\text{user}}}-{\epsilon }_{\mathrm{\Delta }p}^{\mathit{\text{prod}}}}$$ (7)

$$C_{\mathit{\text{user}}}^J=\frac{{\epsilon }_{\mathrm{\Delta }p}^{\mathit{\text{prod}}}}{{\epsilon }_{\mathrm{\Delta }p}^{\mathit{\text{prod}}}-{\epsilon }_{\mathrm{\Delta }p}^{\mathit{\text{user}}}}$$ (8)

As the buffer [ADP] rises, flux control at ANT falls (see Table 3), which means that control has been transferred to the Δp-producer module (Equation 5). Equation 7 describes this pattern. Rising [ADP] activates the Δp-user module, which increases its elasticity to Δp and transfers flux control to the Δp-producing module. Redistribution of control occurs regardless of the substrate supply, but the extent of the transfer is marginally greater if the elasticity of the Δp-producer is small, as it is with low V_max substrates. Equation 8 shows that higher substrate oxidative capacity i.e., more negative producer module elasticity, ${\epsilon }_{\mathrm{\Delta }p}^{\mathit{\text{prod}}}$, increases flux control strength at the user module, as predicted by Brand and coworkers 30 years ago [69]. Stated simply, an addition of ADP cannot increase OxPhos flux if the (Δp-user) module it activates has zero control of flux. For example, as shown in Figure S-15, when the oxidative substrate is Glycerol-3-Phosphate an increase in [ADP] from 12.5 μM to 25 μM increases OxPhos flux by less than 4%. In contrast, with Glutamate + Succinate, the same change in [ADP] increases ATP production by about 43%. In both cases the same Δp-user module was exposed to the same added increment in [ADP]. Thus, the extent to which ADP influences flux depends on the combination of Δp-user module flux control strength and its elasticity to ADP, which is described by another MCA concept, the partitioned response.

The Partitioned Response Coefficient

In Figure 7 ADP is viewed as an external effector on pathway flux. The effect of an ADP addition on flux is described by the partitioned response coefficient, R^J [9].

$$R_{eff}^J=C_{\mathit{\text{prod}}}^J\ast {\epsilon }_{eff}^{\mathit{\text{prod}}}+C_{\mathit{\text{user}}}^J\ast {\epsilon }_{eff}^{\mathit{\text{user}}}$$ (9)

where eff, the external effector, is ADP and ε is the elasticity of each module to ADP. The response of pathway flux to added ADP therefore depends on the control coefficient of each module and its elasticity to ADP.

Equation 9 summarizes the discussion above. High Δp-producer elasticity (high V_max substrates) relative to that of the Δp-user, gives ANT more control over a broader range of [ADP] (Equation 8). In this case the OxPhos K_0.5ADP³⁻ primarily reflects ANT kinetics. It is important to note this interpretation generalizes beyond the substrates supplied to the Δp-producer module; it also applies to the module itself. Because linear thermodynamic force-flow relationships operate down the entire oxidative pathway: Substrate → ΔGredox → Δp → ΔG_ATP [19], greater relative abundance in substrate dehydrogenases, citrate cycle, and/or ETC proteins would increase the capacity to generate Δp relative to the capacity of the Δp users to utilize it. In this case, enhanced defense of Δp thus, flux control at the user module, would allow K_0.5ADP³⁻ to approach K_dADP³⁻. As stated above, in liver mitochondria the measured OxPhos K_0.5ADP³⁻ and previously determined ANT K_dADP³⁻ (~4 μM) [27, 28] were similar. Interestingly, liver mitochondria have low ANT abundance relative to striated muscle and kidney, both per mg protein and per nmol cyt a [51, 60, 61], characteristics consistent with strong control of flux in the Δp-user module hence more closely matched values of K_0.5ADP and ANT K_dADP. In fact, in rat liver mitochondria oxidizing glutamate + malate, ANT maintains essentially complete flux control at respiration rates of roughly 50% state 3 [23]. Even more compelling, a flux control coefficient of 0.66 has been reported for liver mitochondria maximally activated by saturating (250 μM) ADP [70], a pattern of control dramatically different from that of striated muscle mitochondria [20, 24, 51]. In contrast, low V_max substrates result in the redistribution of control away from the user module and toward the Δp-producer module at lower [ADP³⁻], which widens the gap between K_0.5ADP³⁻ and K_dADP³⁻.

We interpret these data to indicate that any factor which influences the capacity for Δp production relative to its utilization correspondingly affects ANT flux control strength and the matching of OxPhos K_0.5ADP³⁻ to ANT K_dADP³⁻. Simulations in silico using a substantially modified version of Daniel Beard’s computational model of mitochondrial metabolism [71] are consistent with this interpretation. The same computational model also reproduces our luciferase and polarography assay results with excellent fidelity (unpublished data).

HIGHLIGHTS.

• Assay developed to evaluate ADP kinetic parameters requires < 1 μg mitochondrial protein.

• ANT flux control of OxPhos (%) was 91, 83, and 51 at [ADP] (μM) of 6.25, 12.5, and 25, respectively.

• The K_0.5ADP for OxPhos linearly depended on the oxidative capacity of respiratory substrates.