Feedback Regulation and Time Hierarchy of Oxidative Phosphorylation in Cardiac Mitochondria

Abstract

To determine how oxidative ATP synthesis is regulated in the heart, the responses of cardiac mitochondria oxidizing pyruvate to alterations in [ATP], [ADP], and inorganic phosphate ([P_i]) were characterized over a range of steady-state levels of extramitochondrial [ATP], [ADP], and [P_i]. Evolution of the steady states of the measured variables with the flux of respiration shows that: (1) a higher phosphorylation potential is achieved by mitochondria at higher [P_i] for a given flux of respiration; (2) the time hierarchy of oxidative phosphorylation is given by phosphorylation subsystem, electron transport chain, and substrate dehydrogenation subsystems listed in increasing order of their response times; (3) the matrix ATP hydrolysis mass action ratio [ADP] × [P_i]/[ATP] provides feedback to the substrate dehydrogenation flux over the entire range of respiratory flux examined in this study; and finally, (4) contrary to previous models of regulation of oxidative phosphorylation, [P_i] does not modulate the activity of complex III.

Introduction

The phosphorylation potential, defined as the Gibbs free energy of the ATP hydrolysis reaction (${\Delta }_{\mathit{r}}{\mathit{G}}_{\text{ATPase}}$), provides the chemical driving force for cellular function. Most of the ATP synthesized in the mammalian heart is synthesized from oxidative phosphorylation in mitochondria (OxPhos), where the free energy of terminal oxidation of carbon substrates is transduced into the extramitochondrial phosphorylation potential. The extramitochondrial phosphorylation potential is defined by ${\Delta }_{\mathit{r}}{G}_{\text{ATPase}}={\Delta }_r{\mathit{G}}_{\text{ATPase}}^0+\text{log}\left(\left[\text{ADP}\right]\left[{\text{P}}_{\text{i}}\right]/\left[\text{ATP}\right]\right)$, where [ATP], [ADP], and [P_i] denote the concentrations of ATP, ADP, and P_i and ${\Delta }_{\mathit{r}}{G}_{\text{ATPase}}^0$ is the reference free energy of the ATP hydrolysis reaction at specified physiological temperature, pH, and free cation concentrations (1). The regulation of [ATP], [ADP], and [P_i] in vivo, achieved by the interplay between processes hydrolyzing ATP and mitochondrial ATP synthesis, has been a source of longstanding debate in cardiac energetics (2, 3).

Initial investigations on isolated mitochondria revealed that mitochondria respired and phosphorylated ADP in response to changes in [ADP] and [P_i] (4, 5, 6, 7, 8). However, observations in intact tissue showing no detectable change in [ADP] and [P_i] during changes in work rate (9) stimulated a search for controllers of OxPhos other than [ADP] and [P_i] for over two decades (3). A series of studies on isolated mitochondria demonstrated that with appropriate choice of carbon substrates and experimental conditions, which were not physiological, significant stimulation of respiration by Ca²⁺ was possible (10, 11). Because Ca²⁺ mediates excitation-contraction coupling and the resulting contractile ATP demand, Ca²⁺ concentration was postulated as an open-loop signal, stimulating changes in ATP synthesis to match changes in ATP demand (2, 12). While the in situ observations on the relative stability in myocardial [ADP] were reproduced in subsequent studies (13, 14, 15), many subsequent studies have reported marked increases in [P_i] from baseline state with increasing cardiac work (16, 17, 18, 19, 20, 21, 22). Overall, the observed relationships among oxygen consumption, [ADP], and [P_i] shown in those and other studies (16, 17, 18, 19, 20, 21, 22) demonstrate that feedback from products of ATP hydrolysis could explain the control of OxPhos in vivo. Theoretical analysis of these data (3, 5, 7, 16, 17, 23, 24) predicts that this feedback represents the dominant controller of oxidative ATP synthesis in vivo. In this context, previous studies on isolated mitochondria have mainly demonstrated that [P_i] reduced the apparent ADP half-saturation constant and increased the apparent maximal velocity for respiration (5, 7). The nature of feedback from [ADP] and [P_i] to the mitochondrial enzymes constituting OxPhos and their response time hierarchy governing the quantitative relationship among OxPhos flux and [ADP] and [P_i] are unknown. In the current study, time hierarchy of a biochemical system is defined as the relative order of response times of individual system components with respect to overall system flux. More formally, time hierarchy is defined as the separation in time constants or turnover times of the components of a metabolic system (25, 26, 27). To elucidate the feedback regulation of OxPhos, one must measure not only respiration but also other state variables governing mitochondrial function such as NADH/NAD, inner membrane potential (Δψ), cytochrome c²⁺/(cytochrome c²⁺ + cytochrome c³⁺), extramitochondrial, or matrix [ADP]/[ATP] and [P_i]. Evolution of the steady-state values of those variables over a range of steady-state OxPhos fluxes provides us with a means to infer the underlying time hierarchy and feedback structure of OxPhos (25).

In the current study we measured fluxes of respiration (ATP synthesis) in response to ATP demand in a system based on isolated cardiac mitochondria consuming physiological substrates at physiological temperature while measuring several mitochondrial variables in parallel. These experiments were conducted under conditions designed to vary [ADP] and [P_i] over physiologically relevant ranges to reveal the dynamics of the system. The changes in the steady-state values of the measured variables over a range of respiratory fluxes revealed the response time hierarchy of the system and that [P_i] feedback is essential in addition to feedback from [ADP]/[ATP] in the matrix.

Materials and Methods

Isolation of mitochondria

Mitochondria were isolated from 12- to 15-week-old Wistar rat hearts by differential centrifugation as detailed in Vinnakota et al. (28). The heart was cannulated in situ and perfused with ice-cold cardioplegia solution for 5 min. The heart was then extracted, minced, and homogenized in the presence of protease (5 U/mL in 2.5 mL finally diluted to 25 mL) in the isolation buffer. The homogenate was centrifuged twice at 8000g to wash the protease, discarding the supernatant each time. The resuspended pellet was centrifuged at 700g discarding the pellet and the supernatant containing mitochondria-rich fraction was centrifuged at 8000g. The mitochondria-rich pellet from the final spin was resuspended in a small volume of the isolation buffer and stored on ice for the duration of the experiments. Citrate synthase activity was determined in the preparation using Srere’s method (29) and a mitochondrial concentration equivalent to 0.337 U CS activity/mL was employed for all experiments unless stated otherwise.

Enzymes and buffers

All reagents were purchased from Sigma (St. Louis, MO) unless stated otherwise. Myokinase and pyruvate kinase were desalted in 1 mM phosphate buffer pH 6.8 using an Amicon Ultra-15 Centrifugal Filter devices with a 3 KDa cutoff (Millipore, Billerica, MA). Three centrifugations at 5000g of 85 min each were performed to desalt myokinase and pyruvate kinase. Apyrase was reconstituted in 5 mM MOPS and 0.1% BSA. All enzymes were aliquoted, stored at −20°C in the presence of 0.1% BSA, and each aliquot was used only once. Respiration buffer consisted of 5 mM ATP, 2.5 mM sodium pyruvate, 0.5 mM malate, 5 mM or 1 mM Pi, 6 mM MgCl₂, 107 Mm KCl, 1 mM EGTA, and 50 mM MOPS at pH 7.2. Decylubiquinone was reduced using Rieske’s protocol for experiments testing P_i activation of complex III (30).

High-resolution respirometry and tetraphenyl phosphonium potentiometry

Five steady states in respiratory flux spanning a 10-fold range and their methods of reconstitution are listed here in the order of increasing ATP synthesis flux: (1) LEAK state, where mitochondria respire to maintain membrane potential in response to dissipation by proton leak and other ion circuits, was obtained using 19 U/mL pyruvate kinase and 2 mM phosphoenol pyruvate to maximize ATP/ADP ratio; (2) state 3.5, where mitochondria are respiring to meet ATP demand due to ATPases in the preparation hydrolyzing MgATP; (3) by the addition of 0.2 U/mL of apyrase, an ATP hydrolyzing enzyme; (4) by the addition of 0.4 U/mL apyrase; and (5) by the addition of 0.8 U/mL apyrase. In the final three states, mitochondria are respiring to synthesize ATP in response to ATP hydrolysis due to both the ATPases in the mitochondrial preparation and the added apyrase. Because apyrase has a small ADPase activity, myokinase was added to keep the adenine nucleotide pool exchangeable. The flux of respiration at 37°C was measured in an Oroboros Oxygraph 2K high-resolution respirometer (Oroboros Instruments, Innsbruck, Austria), where the oxygen concentration in a closed chamber is measured by an amperometric sensor. See Fig. 1 A for representative traces of oxygen consumption flux in the LEAK state, state 3.5 and with 0.8 U/mL apyrase. Lipophilic cation tetraphenyl phosphonium (TPP⁺) uptake was measured to obtain the value of mitochondrial inner membrane potential. TPP⁺ concentration in the oxygraph chamber was measured by a TPP⁺ selective electrode, where the electrode potential with respect to a reference electrode is a linear function of the logarithm of the TPP⁺ concentration in the buffer. A calibration curve was generated before each membrane potential measurement and the TPP⁺ uptake by mitochondria in a given respiratory state was measured as the difference between TPP⁺ concentration before adding the mitochondria (3 μM) and the concentration measured during the respiratory steady state obtained after adding mitochondria and necessary enzymes. See Fig. 1 B for representative recordings of TPP⁺ calibration and uptake measurements. The inner membrane potential (Δψ) was computed assuming a Nernst equilibrium distribution across the inner mitochondrial membrane with negligible membrane binding and a matrix water space of 1 μL/0.674 U CS. The value Δψ was measured in the LEAK state, state 3.5, and with 0.8 U/mL apyrase additions.

Figure 1.

Time course data of respiration, TPP⁺ uptake, NADH, and difference spectra of cyt c²⁺. Respiration, NADH, and TPP⁺ data are shown for LEAK, state 3.5, and 0.8 U/mL apyrase states (see Materials and Methods). (A) Representative recordings of time courses of respiration fluxes approaching steady states during LEAK, state 3.5, and with 0.8 U/mL apyrase. A respiratory steady state is reached by 150 s and the maximal respiration is higher with 5 mM initial [P_i]. (B) Representative traces of TPP electrode calibration and mitochondrial uptake measurements for 1 mM initial [P_i] experiments. TPP is injected in steps of 0.5 μM from starting at 1 μM and increasing to 3 μM, after which mitochondria and necessary enzymes and substrates are injected to obtain the desired respiratory state. The TPP uptake is highest in the LEAK state and decreases toward the 0.8 U/mL apyrase state due to depolarization of the mitochondrial inner membrane. (C) Representative recordings of NADH fluorescence for 1 mM initial [P_i] experiments normalized with respect to maximally reduced and oxidized endpoints. NADH becomes more oxidized as the steady-state respiratory flux increases. (D) Time-averaged absorbance difference spectra of cyt c²⁺α-band at maximally reduced state and during respiratory steady states LEAK, state 3.5, and 0.8 U/mL apyrase state with respect to the maximally oxidized state of cyt c. The maximally oxidized state of cyt c was obtained by incubating mitochondria in respiration buffer without any carbon substrates and further confirmed with the addition of antimycin A. The normalized absorbance difference is equal to cyt c²⁺/(cyt c²⁺ + cyt c³⁺) (E) The raw absorbance difference between mitochondria treated with cyanide resulting in a maximally reduced state, and the maximally oxidized state between 500 and 625 nm, showing the peak of the cytochrome c²⁺α-band at 551 nm and the nearest isosbestic point at 541 nm, where the difference spectrum reaches a zero value. To see this figure in color, go online.

Optical spectroscopy

NADH was measured by fluorescence in a Varioskan Flash multimode plate reader (Thermo Fisher Scientific, Asheville, NC) where the end points for maximally reduced and oxidized states were obtained by using rotenone and FCCP, respectively, as described previously in Vinnakota et al. (11, 28). Mitochondria were suspended in a total volume of 1 mL in respiration buffer in each well of a 24-well microplate along with enzymes and substrates corresponding to the desired respiratory state. Fluorescence emission was recorded at 470 nm with 350 nm excitation every 7 s for 308 s, which was followed by the addition of rotenone or FCCP and the recording of end point fluorescence for 273 s (see Fig. 1 C). Cytochrome c²⁺ fraction was measured by absorbance in an OLIS clarity spectrophotometer (OLIS, Bogart, GA) equipped with a 8.8 mL optical integrating cavity using a white LED light source and a Fourier transform spectrometer as the detector where the end points for maximally reduced and oxidized states were obtained by treating mitochondria with cyanide and antimycin A, respectively. The optical integrating cavity provided a 12-fold path-length magnification at 551 nm (31) but did not completely eliminate light scattering due to the turbidity of the mitochondrial suspension, which changes dynamically due to mitochondrial volume changes. Absorbance spectrum of mitochondrial suspension was recorded between 400 and 600 nm every 3 s. In agreement with published values in the literature (32), we observed that the α-band of cyt c²⁺ absorbance has a peak at 551 nm and the closest isosbestic point at 541 nm, where the spectra corresponding to maximally oxidized and reduced states of cyt c²⁺ intersect. The time course of measured absorbance recorded for a given respiratory state at 55L nm was normalized with respect to the absorbance at the isosbestic point (541 nm) to correct for changes in absorbance due to light scattering by mitochondria (see Fig. 1 D). Cyt c²⁺ absorbance was measured in the LEAK state, state 3.5, and with 0.8 U/mL apyrase additions, whereas NADH fluorescence was measured in all of the respiratory steady states.

Perchlorate quenching and extraction for ADP measurement, and high performance liquid chromatography-based ADP measurement

Mitochondrial respiratory steady states were reconstituted as described above in 2 mL cuvettes in a cuvette holder maintained at 37°C using a circulating water bath. The reconstituted system was quenched at 150 s and 180 s after the initiation of respiration by adding 260 μL of the suspension to 65 μL of 6 M perchloric acid (HClO₄) stored on ice. The quenched aliquots were centrifuged at 13,500 RPM for 10 min at 4°C to remove the acid-denatured protein. The recovered supernatant was neutralized by using 9.6 M KOH with 50 mM MOPS stored on ice, then centrifuged at 13,500 RPM for 10 min at 4°C to remove the precipitated KClO₄, filtered, aliquoted, and stored at −80°C until further analysis. The content of ADP in the extracted samples was measured by high performance liquid chromatography using an ion pairing method (mobile phase A = 0.1 M KH₂PO₄ + 4 mM tetrabutylammonium hydrogen sulfate pH 6; mobile phase B = A:methanol, 70:30, pH 7.2; 0.6 mL/min flow rate; gradient program 0 min – 0% B, 5 min – 0% B, 10 min – 100% B, 14 min – 100% B, 19 min – 0% B, 24 min 0% B; UV absorbance detection at 259 nm) on a Luna C18 column ((2) 150 mm length, 4.6 mm inner diameter, 3 μm particle size; Phenomenex, Torrance, CA) and quantified using a calibration curve generated by external standards.

Data analysis and curve fitting

Relationships between steady-state J_O2 and measured redox variables were fitted to empirical descriptors using orthogonal distance regression using ODRPACK 2.1 (33, 34) provided in SciPy (35), a Python-based open source software library for scientific computing. The computations were performed using the IPython environment (36). Ninety-five percent confidence interval estimates for the fitted parameters were compared between data from 5 mM [P_i]₀ and 1 mM [P_i]₀ experiments to determine whether the fitted relationships were different with statistical significance. NADH, Δψ, and cyt c²⁺/(cyt c²⁺ + cyt c³⁺) data were fitted to empirical functions of J_O2, $\text{exp}\left(a{J}_{\text{O}2}^{-b}\right)$, $a{J}_{\text{O}2}^{-b}$, and $a{J}_{\text{O}2}^b$, respectively, where a and b are adjustable parameters that are distinct for each data type. Curve fits to the experimental data are presented in Fig. 2.

Figure 2.

Relationships between steady-state values of the measured variables. (A) J_O2 versus [ADP] plot and a fit to the expression V_max [ADP][P_i]/(K_ADP+[ADP])(K_Pi+[P_i]) (solid line) show that a single K_ADP and K_Pi can describe the relationship between [ADP], [P_i] and J_O2. (B) Contour plot of J_O2 as a function of both [ADP] and [P_i] showing the [ADP], [P_i] concentrations spanned in this study, and J_O2 data and contours of constant J_O2 (in μmol/min/U CS) in [ADP], [P_i] space. (C) J_O2 plotted against the free energy of the ATP hydrolysis (Δ_rG_ATPase) reaction in the cytosol showing that at higher [P_i], mitochondria can synthesize ATP at a higher Δ_rG_ATPase for a given ATP synthesis flux. (D) Normalized steady-state NADH plotted against J_O2 showing the oxidation of NADH with increase in J_O2 and no distinguishable difference between 5 mM [P_i]₀ and 1 mM [P_i]₀ experiments. (Solid line) Power-law fit exp(2.21J_O2^−0.38) to the entire data set. (E) The value Δψ plotted against J_O2 shows depolarization with increasing flux of respiration, demonstrating that the phosphorylation subsystem, which consumes the proton electrochemical gradient, is the fastest component of OxPhos (solid line, 137.47J_O2^−0.068). (F) Cyt c²⁺ normalized with respect to total cyt c plotted against J_O2 shows no difference between the curves for 1 mM [P_i]₀ and 5 mM [P_i]₀ experiments (solid line, 0.48J_O2^−0.21), contradicting prior reports in the literature on the role of [P_i] in modulating the cytochrome c redox state via complex III. Data in all figures were plotted as mean ± SD, where the number of biological replicates was 3–6 for J_O2 data, 2 for [ADP] data, 3–6 for NADH data, 3 for all Δψ except in state 3.5 (i.e., 1) at 1 mM [P_i]₀, and 2 for all cyt c²⁺ data. To see this figure in color, go online.

Results and Discussion

Fig. 1 shows representative data collected by respirometry (oxygen flux, J_O2), absorbance spectroscopy (cytochrome c²⁺ fraction), fluorometry (NADH level), and TPP⁺ uptake using a TPP⁺-selective electrode to measure membrane potential as detailed in the Materials and Methods. The steady-state data for all of the variables are plotted in Fig. 2.

Kinetics of steady-state J_O2 driven by changes in extramitochondrial [ADP] and [P_i]

All of the key relationships between quasi-steady-state variables assayed in this study are plotted in Fig. 2. Fig. 2, A and B, plots the measured relationship between J_O2 and extramitochondrial [ADP] and [P_i], showing that increasing concentrations of substrates for oxidative phosphorylation increases oxidative flux. The continuous curves plotted in the figure are orthogonal distance regression fits to a product of two hyperbolic functions V_max [ADP][P_i]/(K_ADP+[ADP])(K_Pi+[P_i]), which shows that [P_i] increases the apparent V_max of OxPhos. Bishop and Atkinson (5) reported that [P_i] feedback also decreased the apparent Michaelis-Menten constant for ADP (K_ADP) in addition to increasing the apparent V_max. We do not observe changes in K_ADP in our data, which is likely due to the relatively narrow range of [P_i] spanned in our study compared to the study of Bishop and Atkinson (5), where [P_i] was maintained at 2, 10, and 25 mM. Current estimates of in vivo [P_i] in the myocardium are submillimolar at rest and ∼2 mM at maximal work (16, 17), which is spanned in our preparation except for the submillimolar concentrations. The lower end of the physiological range is not possible to maintain in our in vitro reconstituted system. In our system, changes in [P_i] from an initial value are determined by a mass conservation constraint resulting from closed adenylate and phosphate pools, resulting in a monotonic change in the steady-state [P_i] and [ADP] with the flux of respiration. This variation in [P_i] and [ADP] enabled the estimation of the apparent half-saturation constants, K_ADP = 31.38 ± 7.56 μM and K_Pi = 1.14 ± 0.22 mM. In summary we show that increasing [P_i] increases the overall turnover rate of OxPhos primarily through an apparent V_max effect, which enables mitochondria to generate a higher extramitochondrial $\left|{\Delta }_r{G}_{\text{ATPase}}\right|$ for a given flux of ATP synthesis (see Fig. 2 C). In situ estimates of steady-state [ADP] and [P_i] during rest and maximal work in the rat heart from the study of Headrick et al. (17) predict a 3.5-fold increase in OxPhos flux based on our estimates of K_ADP and K_Pi, which exceeds the 2.5-fold increase in the rate pressure product measured in their study. The contributions of changes in [ADP] and [P_i] to the predicted 3.5-fold change in OxPhos flux from rest to exercise are 2 and 1.74, respectively, and are nearly equal within experimental error. As Headrick et al. (17) report, the estimated contributions of changes in [ADP] and [P_i] to the changes in the flux of OxPhos are critically dependent on the measurement of resting [P_i]. A reliable measurement of resting [P_i] in the heart in vivo has not been reported to our knowledge.

Steady states in NADH and membrane potential examined against J_O2 reveal system response time hierarchy

Fig. 2, D–F, shows normalized NADH, membrane potential (Δψ) and fraction of cytochrome c in reduced state cyt c²⁺ plotted against J_O2. These relationships were fitted to parsimonious functions to test whether those functions were different for the two different initial concentrations (denoted by the subscript 0) of inorganic phosphate used: 1 mM [P_i]₀ and 5 mM [P_i]₀. We found there were no statistically significant differences in those relationships due to [P_i]₀, and that each of those relationships could effectively be described by a single function.

The concentrations of NADH and NAD constitute a conserved pool whose steady-state values change according to the balance between NADH-generating fluxes (pyruvate dehydrogenase complex and TCA cycle dehydrogenases) and respiratory chain complex I oxidizing NADH. Because the steady-state NADH decreases with increasing J_O2, this means that the substrate dehydrogenation fluxes generating NADH and FADH₂ have longer response times than the electron transport chain when the ATP demand is changed. When ATP demand is increased, there is a net oxidation of NADH by the respiratory chain, followed by a response of the dehydrogenases, which achieve a steady-state balance at lower [NADH] for higher J_O2. The magnitude of the change in NADH per unit change in J_O2 is highest at the resting J_O2 and decreases toward a much smaller value near maximal J_O2, indicating that the response time of substrate dehydrogenation approaches that of the electron transport chain at higher respiratory rates.

The common intermediate of OxPhos between the respiration and phosphorylation components is the proton-motive force across the inner membrane. Under our experimental buffer ionic conditions the primary contributor to the proton motive force is the electrical potential difference Δψ (37). A plot of Δψ versus J_O2 in Fig. 2 C shows that increasing flux of ATP synthesis depolarizes the inner membrane, implying that the phosphorylation subsystem, consisting of the ATP synthase, adenine nucleotide translocator, and the phosphate carrier (which is driven by the stoichiometric translocation of ∼3.7 protons from the intermembrane space to the matrix space OxPhos (38, 39)), is the fastest responding component of OxPhos. Also, the net depolarization per unit J_O2 is not different between 1 and 5 mM [P_i]₀ within the limits of experimental error. Similar to the relationship for [NADH], the net depolarization per unit J_O2 decreases with increasing J_O2.

Cytochrome c redox steady-state data show an increase with respiration, and show no difference in this relationship for 1 vs. 5 mM [P_i]₀. A plausible explanation for the increase in cyt c²⁺, while NADH decreases with J_O2, could be different sensitivities of complexes I and IV to membrane potential. This interpretation is investigated in depth by Bazil et al. (40) using a computer model to analyze these data.

In summary, the results presented in Fig. 2 represent the load characteristic (25) defined as the response of mitochondrial state variables to ATP demand flux, elucidating the underlying response time hierarchy. These results imply that in response to an increase in ATP demand, ATP delivery, and synthesis causes depolarization of the inner membrane, leading to an increase in respiratory flux, which leads to a net oxidation of NADH, which leads to a response in dehydrogenase flux from the TCA cycle. If, for example, an increase in phosphate arising from ATP hydrolysis stimulated a rapid compensatory response in TCA cycle flux, then the dehydrogenase flux response would not necessarily be the last subsystem in responding and we would not necessarily have seen a decrease in NADH with increasing J_O2.

A simplified model for the feedback control of OxPhos: testing the [P_i] activation of complex III

Based on respiration data and in some instances data on [NADH], Δψ, and cyt c²⁺, several conceptual and theoretical models for oxidative phosphorylation have been proposed (41, 42, 43). While most theoretical models have not considered the effects of [P_i] as a potential regulator of OxPhos, Bishop and Atkinson (5, 7) demonstrated a clear kinetic effect of [P_i] on cardiac mitochondria consuming pyruvate coupled to ATP synthesis. In 1979, Bishop (7) postulated that [P_i] could act as a regulator of OxPhos in vivo in the heart based on his experiments on isolated rat cardiac mitochondria respiring on pyruvate. More recently Bose et al. (37), studied the effect of [P_i] on mitochondria respiring on glutamate/malate at 0 and 3 mM [P_i]. Bose et al. (37) measured respiration, [NADH], Δψ and cyt c²⁺/(cyt c²⁺ + cyt c³⁺), and proposed that [P_i] may modulate OxPhos by activating generation of [NADH], by modulating the flux of electron transfer from cytochrome b to cyt c, and as a substrate for F₁F_OATPase.

Based on the analysis of data from Bose et al. (37), Beard (42) developed a computational model based on mass action kinetics where [P_i] feedback modulates the flux of NADH generation and flux of cyt c reduction by directly modulating the activity of complex III, and determined that of the proposed effects of P_i on the respiratory chain, only the effect on complex III represented a putative explanation of the effects observed by Bose et al. (37). Specifically, a testable prediction of the Beard model is that a change in [P_i] from 1 to 5 mM causes a threefold increase in complex III activity. We tested this prediction in this study by assaying the respiration in uncoupled mitochondria with complex I blocked by rotenone and reduced decylubiquinone acting as a sole substrate directly feeding electrons into complex III. Respiration measurements show no difference in complex III activity due to [P_i] as shown in Fig. 3, disproving the hypothesis that phosphate directly affects the activity of complex III in cardiac mitochondria. Analysis of data from this study by Bazil et al. (44, 45) using independently identified kinetic models for ETC enzymes indeed shows that the intrinsic kinetics of ETC enzymes can explain the observations from this study without a direct modulation of complex III enzyme activity. It is concluded that the apparent effects of P_i on complex III reported by Bose et al. (37) and incorporated into the model of Beard (42) likely resulted from P_i-dependent substrate transport and non-steady-state experimental conditions.

Figure 3.

Decylubiquinol-driven respiration at 1 mM [P_i] and 5 mM [P_i]. Representative time courses of mitochondrial respiration at 1 and 5 mM [P_i] using decylubiquinol, which is a substrate for complex III, as the sole substrate show no difference in the apparent activity of complex III due to differences in [P_i]. To see this figure in color, go online.

[P_i] feedback due to mass action at F₁F_OATPase and at succinyl CoA synthetase

In this section we examine the feedback of [P_i] to the overall NADH generation flux J_DH. J_DH is equivalent to a stoichiometric fraction ϕ_N × J_O2, where ϕ_N = 0.8 (4NADH out of five reducing equivalents (4NADH+1QH2)) for the complete oxidation of a pyruvate molecule starting from the pyruvate dehydrogenase complex (PDC) followed by a complete span of the TCA. P_i is a substrate for the phosphate transporter and the F₁F_OATPase in the phosphorylation subsystem, and for the reaction catalyzed by succinyl CoA synthetase in the TCA cycle generating reducing equivalents. Data in Fig. 2 show that the F₁F_OATPase, together with the adenine nucleotide translocator and phosphate carrier, responds to change in ATP demand faster than upstream components of the respiratory chain. Evidence in the literature (46, 47, 48) suggests that the magnitude of free energy span of the F₁F_OATPase is <3 kJ/mol, which places this reaction closer to equilibrium compared to the adenine nucleotide translocator. Based on a near-equilibrium approximation to the F₁F_OATPase reaction, and assuming a negligible pH gradient so that [P_i] in the extramitochondrial space is equilibrated with [P_i]_x due to the high activity of the phosphate transporter, we are able to estimate the mass action ratio: the ATP hydrolysis reaction X_ATPase, is defined as ${\left[\text{ADP}\right]}_{\text{x}}{\left[{\text{P}}_{\text{i}}\right]}_{\text{x}}\text{/}{\left[\text{ATP}\right]}_{\text{x}}$ using the expression $\text{exp}\left[\left({\Delta }_r{G}_{\text{ATPase}}^0-n_{A}F\Delta \psi \right)/RT\right]$, and the concentration ratio [ADP]_x/[ATP]_x in the mitochondrial matrix (denoted by the subscript x for concentration variables) for given values of Δψ and [P_i]_o. In the expression used to estimate X_ATPase, n_A is the number of protons translocated through the F₁F_OATPase per ATP synthesized whose value is estimated to be 8:3 based on structural information for the mammalian enzyme (39), and F is the Faraday constant whose value is 96,500 Coulombs/mole. The estimated mass action ratio of the ATP hydrolysis reaction X_ATPase in the matrix is plotted as a function of J_DH in Fig. 4 A for the respiratory steady states where both Δψ and J_DH were measured. We also utilized the phenomenological relationship between J_DH and Δψ shown in Fig. 2 E, and calculated X_ATPase as a continuous function of J_DH. Direct calculations of X_ATPase from data (symbols) and those from the curve fit to Δψ data in Fig. 4 A show qualitative agreement between both. The monotonic and near-linear behavior of J_DH versus X_ATPase indicates the strong feedback between energy state and substrate dehydrogenation flux in the mitochondrial matrix.

Figure 4.

Potential feedback controller for OxPhos. In the steady-state NADH generation flux, J_DH is equivalent to a stoichiometric fraction ϕ_N × J_O2, where ϕ_N = 0.8 (4NADH/(4NADH+1QH2)) for a complete span of the TCA cycle starting from the conversion of pyruvate to acetyl CoA at the pyruvate dehydrogenase complex. To examine the potential for several state variables known to provide feedback to J_DH by participating as substrates in the reactions of the PDC and the TCA cycle, we plot J_DH against the mass action ratio of the ATP hydrolysis reaction in the matrix X_ATPase in (A), [ADP]_x/[ATP]_x in (B), and 1-NADH/(NAD+NADH) in (C).

Plotting J_DH versus the ratio [ADP]_x/[ATP]_x in Fig. 4 B indicates that J_DH is not uniquely determined by [ADP]_x/[ATP]_x, which means that the TCA cycle flux cannot be a function of [ADP]_x/[ATP]_x alone. We also examine J_DH as a function of NAD in Fig. 4 C. While J_DH increases with increasing NAD, the flux becomes insensitive to NAD as the flux increases. Therefore, NAD may provide kinetic feedback over low flux ranges (from the leak state until mid-range values of respiration) but not at higher values unless the sensitivity to NAD changes at high fluxes. In summary, of the quantities examined in Fig. 4, the X_ATPase is the only factor that may provide kinetic feedback for the substrate dehydrogenase flux over the entire observed range of respiratory flux.

Implications for in vivo cardiac mitochondrial function and limits to interpretation

Key questions on the control of mitochondrial ATP synthesis in vivo that have fueled much of the controversy in this field are: (1) what are the contributions of feedback from [ADP] and [P_i] to the control of ATP synthesis flux? and (2) does [NADH] generation follow the flux of its demand or does it drive the electron transport chain flux? Our results in this study indicate that [ADP] and [P_i] can provide sufficient feedback to account for the entire range of mitochondrial respiratory flux due to ATP synthesis, and that NADH and Δψ measurements reflect that they follow ATP demand in the isolated reconstituted system. Furthermore, as previously discussed in our results, [ADP] and [P_i] can potentially account for the range of ATP synthesis flux observed in situ in rat hearts (17). However, measurement of resting [P_i] in the heart in situ is necessary to definitively estimate the contribution of [P_i] in relation to that of [ADP], and to ascertain whether the entire range of respiration can be explained.

Studies by Ashruf et al. (49) showed that NADH oxidized in response to increase in work (oxygen consumption) in Langendorff-perfused rat hearts where the hearts were perfused with buffer containing either 5.5 mM glucose or 10 mM pyruvate while ensuring tissue normoxia using a vasodilator in the perfusate. Chapman (50) and Chapman et al. (51) also reported oxidation of NADH with isometric force generation in isolated rabbit heart trabeculae incubated in the presence of pyruvate and glucose. A similar relationship between NADH and work was observed in well-oxygenated isolated myocytes (52).

The isolated reconstituted system studied in this article differs from the in vivo system in several aspects. The increase in ATP hydrolysis rate in vivo is due to calcium-mediated excitation-contraction coupling, which results in a parallel increase in cytosolic [Ca²⁺] whereas we do not have any calcium increase with the flux of ATP hydrolysis in our mitochondrial preparation. The relationship among [ATP], [ADP], and [P_i] is constrained in vivo by the near-equilibrium creatine kinase and adenylate kinase reactions and the conservation of total adenine nucleotides, creatine, and total exchangeable phosphate, which results in buffering of [ATP], and much smaller changes in [ADP] when compared to those in [P_i] with changing ATP hydrolysis fluxes. In contrast, our experimental system shows an equimolar increase of [ADP] and [P_i] due to the lack of an ATP buffering system such as the creatine kinase reaction. Despite these differences, we do show that feedback from [ADP] and [P_i] is sufficient to support mitochondrial ATP synthesis over a wide range of ATP hydrolysis fluxes in our preparation. Additionally, we show key properties of mitochondrial response to demand that permit inference of the effects of feedback from [ADP] and [P_i] in vivo, and as a corollary, the presence and magnitude of any feedforward controllers that might be contributing to mitochondrial ATP synthesis flux.

In summary, this study reports measurements of key mitochondrial variables obtained using physiological substrates, ionic conditions, and temperature over a range of steady-state respiration fluxes in an isolated reconstituted mitochondrial preparation. Results demonstrate: (1) a higher phosphorylation potential is achieved by mitochondria at 5 mM [P_i] than at 1 mM [P_i] for a given flux of respiration; (2) the component of the of the oxidative phosphorylation systems that responds fastest to changes in ATP demand is the F₁F_oATPase together with nucleotide and phosphate transport, followed by the electron transport chain and substrate dehydrogenation systems in increasing order of response times; (3) the matrix ATP hydrolysis mass action ratio [ADP] × [P_i]/[ATP] provides feedback to the substrate dehydrogenation flux over the entire range of respiratory flux examined in this study; and finally, (4) contrary to previous models of regulation of oxidative phosphorylation, [P_i] does not directly modulate the activity of complex III.

Author Contributions

K.C.V., J.N.B., and D.A.B designed the study; K.C.V., F.V.d.B., R.W.W., and J.N.B. acquired the data; and K.C.V., J.N.B., F.V.d.B., R.W.W., and D.A.B. wrote the article.

Editor: Godfrey Smith.