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1 Introduction

Intracellular oxygen levels in the microenvironment of mitochondria are the result of a dynamic balance between oxygen transport to tissues through the respiratory cascade [1] and oxygen utilization by the mitochondrial respiratory electron transport system [2]. At any physiological steady state, a metabolic perturbation of oxygen demand leads to a shift of intracellular oxygen concentration (decrease after stimulation or increase after arrest), unless effective control of oxygen supply exerts a compensatory effect to maintain intracellular oxygen levels within a regulated range. Conversely, an environmental perturbation from normoxic to hypoxic or hyperoxic levels modifies the variables of oxygen transport and the metabolic capacity for oxygen consumption is compromised if mitochondrial oxygen pressures are changed below the level of kinetic saturation. Three elements, therefore, are responsible for controlling cellular oxygenation: the environmental oxygen level, oxygen transport and respiratory metabolism.

This review is focused on cellular and mitochondrial respiration, under the control of extracellular or mitochondrial oxygen pressure (Section 2). In Section 3, we summarize our experience gained by application of high-resolution respirometry to the study of isolated mitochondria and intact cells under conditions of varying oxygen concentrations. Extending the comprehensive review on mitochondrial oxygen kinetics published in 1995 [3], we discuss in Section 4 possible explanations for discrepancies on the p 50 of mitochondrial respiration, i.e. the partial pressure at which respiration rate is 50% of flux at kinetic oxygen saturation. There is a >200-fold range of mitochondrial p 50 reported in the literature. Whereas instrumental and methodological artefacts are responsible for the major part of this large range, a 10-fold variation of p 50 is due to turnover of cytochrome c oxidase (between the minimum of respiration compensating for leak and fully ADP-stimulated respiration) and variation between different mitochondrial sources and various small cells. In Section 5, we relate the p 50 of mitochondrial respiration to intracellular oxygen regimes under normoxia and hypoxia, discussing the theoretical consequences of the actual p 50 of mitochondrial respiration under physiological conditions, for energy homeostasis and mitochondrial excess capacities, oxygen sensing and signalling responses to hypoxia. In particular, comparison of the p 50 in isolated mitochondria and intact cells supports the direct measurement of high intracellular oxygen gradients in cardiomyocytes [4, 5], in contrast to the comparatively negligible intracellular oxygen gradients in small cells [6].

2 Mitochondrial and Cellular Oxygen Kinetics

2.1 Isolated Mitochondria

Mitochondrial respiration is a hyperbolic function of oxygen partial pressure, p O2,

$$j_{{\rm{O}}_{\rm{2}} } = \frac{{p_{{\rm{O}}_{\rm{2}} } }}{{p_{{\rm{50}}} + p_{{\rm{O}}_{\rm{2}} } }}$$
((1))

where j O2 is the rate expressed relative to the maximum pathway flux, J max, observed at kinetic oxygen saturation in a defined metabolic state. Characteristic metabolic states of isolated mitochondria, incubated with selected substrate combinations (e.g. pyruvate, malate, glutamate, succinate), are (i) OXPHOS (State 3 [7]; maximally ADP-stimulated oxidative phosphorylation; but see [8]), and (ii) LEAK (State 4 [7]; minimum oxygen flux required to compensate for proton leak, slip and cation cycling, without providing ADP or by inhibiting phosphorylation; for discussion see [9]). J max, therefore, is a complex function of coupling and electron supply through the mitochondrial electron transport system to cytochrome c oxidase. Similarly, the maximum reaction velocity of an enzyme, V max, varies as a function of the concentrations of other substrates and enzyme concentration, [E]. The enzyme turnover, V max/[E], or pathway flux, J max, exert an influence on the apparent Michaelis-Menten constant, K m′, or p 50. The p 50 of mitochondrial respiration, therefore, depends on the metabolic state. If catalytic efficiency, V max/K m′, is constant, then K m′ and p 50 increase in direct proportion to enzyme turnover [10]. In addition to substrate and ADP supply [11], coupling of electron transport to phosphorylation modifies the p 50 of cellular and mitochondrial respiration [2, 12, 13]. Since the present review is focussed on mitochondrial physiology, we will not consider uncoupled states which provide a measure of the capacity of the electron transport system, ETS.

2.2 Intact Cells

In the ROUTINE state, cell respiration is controlled by physiological aerobic ATP demand at routine steady-state ADP levels, which result from the dynamic balance of ATP production (aerobic and glycolytic) and cellular ATP utilization. After inhibition of electron transport, e.g. by 0.5 µM myxothiazol, residual oxygen consumption (ROX) is observed which is subtracted from total oxygen consumption to obtain mitochondrial ROUTINE respiration. As shown by the inhibitory effect of oligomycin, which inhibits ATP synthase and induces a LEAK respiratory state, ROUTINE respiration is about two to four times higher than LEAK respiration, and is thus significantly less than OXPHOS capacity, which may be six to ten times the LEAK respiration, as expressed by the respiratory control ratio [14, 15].

In addition to the enzymatically catalyzed oxygen consumption, the oxygen dependence of cell respiration is controlled by oxygen gradients related to oxygen transport from the extracellular medium to the mitochondria. The oxygen pressure difference, Δp cell, between the extracellular medium and the average mitochondrion is a function of cell size, cell shape, mitochondrial distribution and oxygen flux. At half-maximum oxygen flux, oxygen gradients are 50% of their maximum at unlimited flux, and maximum Δp cell = 2·Δp 50 can be calculated as the p 50 difference of respiration in intact cells and isolated mitochondria, at comparable metabolic states [6],

$$\Delta p_{50} \, = \,p_{50,{\rm{cell}}} \, - \,p_{50,{\rm{mito}}} $$
((2))

For comparison of mitochondria and cells, respiration is expressed as oxygen flux per mitochondrial protein, J O2 [pmol·s–1·mg−1], or relative to a mitochondrial marker such as aa 3 content or citrate synthase activity. Cell respiration is frequently expressed as oxygen flow per number of cells, I O2 [pmol·s−1·10−6], which is an extensive quantity and varies with cell size and mitochondrial content [16]. High oxygen flow in large and active cells, such as cardiomyocytes, results in proportionally high Δp 50 [6].

3 Oxygen Kinetics and High-Resolution Respirometry

3.1 Nanomolar Resolution of Oxygen Concentration

Measurement of mitochondrial oxygen kinetics presents an experimental challenge [3, 17, 18], considering the demands set on oxygen monitoring with high sensitivity and high time resolution. High-resolution respirometry (HRR) was developed for routine measurement of low volume-specific oxygen flux and low, sub-micro molar oxygen concentration [3]. The instrumental and methodological basis of HRR (Oxygraph-2 k; OROBOROS INSTRUMENTS, Austria; www.oroboros.at) has been discussed in detail [11]. Since 2001, HRR was improved further in a second generation of instruments (Oxygraph-2 k) with reduced signal noise (Fig. 1; compare Fig. 3) as achieved by higher temperature stability, improved stirring and advanced electronics and mechanical design. The HRR features most important for oxygen kinetics are summarized briefly: (1) The experimental chamber and sealings are made of inert materials which do not store and release dissolved oxygen (no Perspex, no Teflon coated stirrers). (2) Unstirred layers are minimized by effective stirring, and gas-aqueous phase boundaries are avoided to exclude uncontrolled oxygen gradients. (3) Polarographic oxygen sensors (POS) with a large cathode, inserted into the precisely thermostated O2k-chamber (±0.001°C) yield a linear signal with low noise over a 500,000-fold dynamic range. Noise decreases with declining oxygen pressure, which eliminates the requirement for smoothing in the low-oxygen range and ensures high time resolution. (4) Accurate oxygen calibrations are obtained at air saturation and zero oxygen concentration, with correction for signal drift in the nanomolar concentration range. (5) High digital resolution (2 nM) and data recording at intervals of one second are a basis for deconvolution of the oxygen signal with the calibrated first-order exponential time constant of the POS, and for calculating oxygen flux, J V,O2 [pmol·s−1·ml−1], as the time derivative of oxygen concentration. (6) Errors of oxygen flux are minimized by on-line correction for instrumental background, calibrated by measurement of residual oxygen back-diffusion into the system and oxygen consumption by the POS over the entire experimental oxygen range. (7) Concentrations of mitochondria or cells are varied in a range compatible with instrumental sensitivity, time resolution and steady-state enzyme kinetics. In this range, measurement of p 50 must be independent of sample concentration or transition time. (8) Before aerobic-anoxic transitions, oxygen flux must be sufficiently stable to exclude time effects superimposed over oxygen dependence of respiration. In addition, reversibility and stability of respiration are evaluated after re-oxygenation, which is particularly important in prolonged experiments with steady-state oxygen levels. (9) By selecting oxygen pressures <1.1 kPa for hyperbolic analysis [3], oxygen levels >10 times the p 50 are covered, without extending to non-physiological high oxygen pressures. (10) Non-linear hyperbolic fits of the flux/oxygen pressure relation are tested by evaluation of residuals rather than linearity of double-reciprocal plots [19].

Fig. 1
figure 2_1_117031_1_En

Oxygen kinetics of respiration of 32D cells in a closed chamber (2 ml mitochondrial respiration medium MiR05; OROBOROS Oxygraph-2 k; 5.106 cells.ml−1, 37°C). a. Oxygen concentration (continuous line) and volume-specific oxygen flux (circles) as a function of time during the aerobic-anoxic transition. The oxygen signal was corrected for the time constant (τ = 2.8 s) of the O2 sensor. Oxygen flux was corrected for instrumental background. b. Hyperbolic fit (continuous line) in the low-oxygen range of oxygen flux (circles) as a function of oxygen concentration or oxygen pressure (oxygen solubility 9.71 µM/kPa). Maximum flux, J V,max, was 66 pmol·s−1·ml−1. Corresponding to the low maximum flow, I max, of 13 pmol·s−1·ml−1 in the endogenous ROUTINE state, the p 50 was 0.028 kPa (0.21 mmHg; 0.27 µM). After re-oxygenation and dilution of the cells by a factor of 0.94–4.7.106 cells.ml−1 (due to injections of aerobic respiration medium; not shown), respiratory flow (per cell) returned to the initial value, and the p 50 was 0.022 kPa in a second aerobic-anoxic transition (dashed line, showing the lower volume-specific flux at the lower cell density)

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3.2 High-Resolution Oxygen Kinetics: Effects of Cell Density and Cell Activity

Mouse parental promyeloid 32D cells [20] are small cells grown in suspension in RPMI 1640 (PAA Laboratories Pasching, Austria). Figure 1a shows typical traces of oxygen concentration and oxygen flux during an aerobic-anoxic transition. Flux was a hyperbolic function of oxygen concentration with a p 50 of 0.028 and 0.022 kPa in the first and second transition, at I max of 13 pmol·s−1·10−6 (Fig. 1b). Oxygen flow of intact 32D cells varied between cultures, with identical or occasionally very low activities of cells incubated in mitochondrial respiration medium MiR05 (compared to cell culture medium RPMI; Fig. 2a). The “intracellular” mitochondrial respiration medium is not physiological, but is frequently used in respiratory studies with cells, when plasma membrane permeabilization is effected as part of the titration protocol in the Oxygraph-2 k chamber [16]. The lowest values of oxygen flow in MiR05 are representative of an inactive respiratory state, as shown by comparison with oligomycin-inhibited respiration of cells measured in RPMI (Fig. 2a). In Fig. 2b, p 50 values from the same experiments are plotted against volume-specific ROUTINE oxygen flux, which was varied from 16 to 260 pmol·s−1·ml−1 by incubation of each cell culture at two different cell concentrations in the range of 2·106–11·106 cells/ml. Cell density exerts its effect not only on volume-specific flux, J V,max, but may also modulate cell-specific oxygen flow, I max (for HUVEC, see [12]). As reported previously [12, 13, 18], variation of mitochondrial or cell density provides an essential test for instrumental time resolution and kinetic consistency of p 50 values.

Fig. 2
figure 2_2_117031_1_En

Oxygen kinetics of respiration of 32D cells incubated in cell culture medium RPMI (full symbols) or mitochondrial respiration medium MiR05 (open symbols). a. Dependence of p 50 on oxygen flow (per 106 cells). * and + indicate averages from two parallel determinations of ROUTINE and LEAK respiration, respectively, with 32D-vRAF cells. b. Independence of p 50 on oxygen flux (per ml of cell suspension), in paired experiments at two dilutions of cell concentration [x106 cells/ml]: 2.5 and 5.0 (triangles); 2.9 and 10.0 (circles); 2.5 and 10.6 (squares); 1.9 and 8.5 (diamonds). Each symbol indicates a single aerobic-anoxic transition

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Variation of oxygen flow (per cell; Fig. 2a) in paired experiments with the same cell culture (Fig. 2b) was due to different levels of activity in the ROUTINE state. The corresponding range in turnover of cytochrome c oxidase explains the linear dependence of p 50 on cell respiration (Fig. 2a). Variation of cell size and mitochondrial content provides an alternative mechanism for variation of respiratory activity per cell [16]. At constant mitochondrial p 50 (constant turnover of cytochrome c oxidase), however, cellular p 50 would not vary with oxygen flow per cell, except if intracellular gradients and Δp 50 (Eq. 2) increase with cell size in different cultures.

The linear increase of p 50 as a function of oxygen flow (per cell; Fig. 2a) indicates varying enzyme turnover at constant mitochondrial content per cell, which was further supported by the constant citrate synthase activity per cell (data not shown). Additional support for our interpretation in terms of variation of mitochondrial activity stems from independent control experiments with 32D-vRAF cells suspended in RPMI and pharmacological intervention with respiratory activity. When ROUTINE respiration was inhibited by oligomycin (2 µg/ml), the p 50 declined proportional to the reduced LEAK respiratory flow. These results are comparable to the decrease of p 50 in isolated mitochondria from the active OXPHOS state to the passive LEAK state ( [2, 13, 21]; Table 1). A linear dependence of the K m′ of cytochrome c oxidase on enzyme turnover [10] was shown conclusively in the bacterial enzyme [22, 23].

Table 1 p 50 of mitochondrial respiration in different metabolic states of coupled respiration (LEAK: resting, not ADP-activated; OXPHOS: active, ADP-activated; ROUTINE: under physiological control of activation in intact cells). Respiratory flux at kinetic oxygen saturation, J max, is expressed in pmol/(s·unit x); if unit x is cell number, then J max becomes I max. J Vma x is flux per volume of incubation medium. A: p 50 in isolated mitochondria (mt) and small cells. B: Results in closed systems with J Vma x above 500 pmol.s−1 .ml− 1 [13], and in closed and open systems with apparent problems of oxygen heterogeneity. C: p 50 based on intracellular p O2 reported by myoglobin in large muscle cells and tissues
Full size table

Respiratory flow in the ROUTINE state of 32D cells in RPMI averaged 18.4 ± 3.7 pmol·s−1·10−6 (N = 39; compare [15]), and the corresponding p 50 was 0.051 ± 0.012 kPa (= 0.38 mmHg; c 50 = 0.48 µM; Table 1). The 32D cell volume is 0.0009 ± 0.0001 mm3 (0.9 pL), determined in a CASY1 TT system (Schärfe System, Reutlingen, Germany). These cells are comparable to human umbilical vein endothelial cells (HUVEC) in terms of cell volume, ROUTINE respiration, electron transport capacity after uncoupling and p 50 [12, 15].

We have not determined the oxygen kinetics of mitochondria isolated from 32D cells, but may compare the cellular p 50 with results on mitochondria isolated from rat liver and rat heart, which is 0.016 and 0.020 kPa in the passive LEAK state and 0.035 and 0.057 kPa in the active OXPHOS state with substrates for Complex I or succinate + rotenone for Complex II ( [2, 13]; Fig. 3a, b). Since the substrate combination for Complex I+II exerts an additive effect and stimulates OXPHOS capacity to a higher level of cytochrome c oxidase turnover [9], the p 50 in the active OXPHOS state of Complex I- or Complex II-respiration is quite comparable to turnover conditions in the ROUTINE state. Taken together, these data indicate that the small intracellular oxygen gradients (Eq. 2) in 32D cells are close to the limit of detection. Similar conclusions are drawn [6] from the oxygen kinetics of HUVEC (ROUTINE I O2 = 30–50 pmol·s−1·10−6 and p 50 = 0.05–0.08 kPa [12]) and human fibroblasts (ROUTINE I O2 = 50 pmol·s−1·10−6 and p 50 = 0.04–0.08 kPa [24, 25], where oxygen flow, I O2, is given per number of cells).

Fig. 3
figure 2_3_117031_1_En

Oxygen flux per volume of incubation medium, J V,O2 [pmol·s−1·ml−1], as a function of oxygen pressure, p O2, in the low-oxygen range <1.1 kPa, in active heart mitochondria (OXPHOS, 1 mM ADP, 1 mM ATP, 2 mM pyruvate, 5 mM malate; 30°C), at different mitochondrial protein concentrations [mg/ml]. Protein-specific flux at kinetic oxygen saturation, J max, is 4.5 nmol·s−1·mg−1 independent of protein concentration. Similarly, the p 50 is independent of protein concentration (a and b), whereas the increase of p 50 (c) is an experimental artefact at protein concentrations >0.15 mg/ml, corresponding to volume-specific J max >500 pmol·s−1·ml−1. From [13]

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4 Discussion

4.1 Comparative Mitochondrial Physiology and p50 of Mitochondrial Respiration

Extending previous reviews on oxygen kinetics of mitochondrial respiration [3, 6], Table 1A and Fig. 4 summarize p 50 and respiration in isolated, coupled mitochondria incubated with physiological substrates and in intact small cells. With a focus on mitochondrial physiology, no data are included on (i) uncoupled respiration [3, 12, 13, 18]; (ii) the isolated step of cytochrome c oxidase with artificial substrates, and (iii) large cells (hepatocytes, cardiomyocytes) where oxygen gradients are significant [4, 6]. In addition to rat liver, rat heart and various mammalian cell types, a large variety of mitochondrial sources has been tested, including plants [26], brine shrimp embryos (Artemia [27]), and frog skeletal muscle [28]. Considering this broad spectrum of comparative mitochondrial physiology and respiratory states from LEAK to ROUTINE and OXPHOS, the range of p 50 from 0.01 to 0.11 kPa (0.08–0.75 mmHg) is remarkably consistent, and independent of measurement in closed or open chambers if methodological criteria are met as summarized above (Section 3.1; [3]).

Fig. 4
figure 2_4_117031_1_En

p 50 for respiration of isolated, coupled mitochondria and intact small cells. a: p 50 measured in closed, well stirred respirometry chambers with aerobic-anoxic transitions as a function of volume-specific oxygen flux. The critical range >500 pmol·s−1·ml−1 is hatched. b: Closed systems; hatched areas (a) high volume-specific flux, correspondingly fast aerobic-anoxic transitions and insufficient time resolution (Fig. 3c), and (b) EPR oxymetry without stirring. c: Open systems; hatched areas (c) indicate results obtained with an identical GAP instrument including a gas phase. Experimental details and references in Table 1

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Close agreement of p 50 for small cells and isolated mitochondria suggests that Δp 50 (Eq. 2) is in the order of 0.01–0.03 kPa (Table 1A). A 10- to 20-fold higher Δp cell has been reported by delayed fluorescence of endogenous protoporphyrin in small cells [29], which is not supported by a model of oxygen diffusion [18].

Comparison of results reported for identical experimental models (e.g. isolated rat liver mitochondria or HUVEC; Table 1A, B) suggests that discrepancies of p 50 are primarily related to methodological issues. The scatter of reported p 50 values increased dramatically since 2003 (Fig. 4). Consideration of fundamental instrumental and experimental criteria helps to discriminate between physiological variability and experimental bias (Fig. 3). In several cases, separation of facts and artefacts on oxygen kinetics is impossible without extending the studies in question by methodological tests, particularly variation of mitochondrial or cell density (Fig. 2; [12, 13]).

4.2 Methodological Limitations of Closed Systems

The basis of oxygen kinetic measurements in closed respirometry systems [30] is the measurement of oxygen flux in aerobic-anoxic transitions (Fig. 1). To compensate for low instrumental resolution, high mitochondrial concentrations (>0.2 mg mitochondrial protein/ml) have been used to achieve accurate measurement of oxygen flux. Under these conditions, rapid aerobic-anoxic transitions present a potential problem as pointed out by Britton Chance more than 40 years ago: “It is probable that the enzyme concentrations were so high under our experimental conditions that the enzyme passed too rapidly through the first order region for an accurate measurement of the K m value” [10]. Direct experimental evidence for the magnitude of such inaccuracies was provided by using a large range of mitochondrial densities for measurement of oxygen kinetics [13]. Volume-specific oxygen flux is shown as a function of oxygen pressure at increasing protein concentrations of isolated rat heart mitochondria (Fig. 3). The p 50 is 0.035 kPa in the active OXPHOS state, as measured at protein concentrations ranging from 0.02 to 0.12 mg/ml (Fig. 3a,b). At higher mitochondrial concentrations, volume-specific fluxes >500 pmol·s−1·ml−1 result in artificially high p 50 values (Fig. 3c).

Correction of the oxygen signal for the exponential time constant of the POS [3] is important but insufficient at high flux when the aerobic-anoxic transition time is too short (Fig. 4a). At densities of 0.2–0.5 mg/ml (25°C) of rat liver and heart mitochondria in the passive LEAK state, volume-specific fluxes are in the range of 50–100 pmol·s−1·ml−1, which are optimum for oxygen kinetics and result in a reproducible p 50 of 0.02 kPa [3, 27, 31, 32] (Table 1A). In contrast, even high-resolution respirometry cannot resolve short transition times <30–40 s from 10 µM to zero oxygen at high volume-specific flux >500 pmol·s−1·ml−1 in closed chambers, which explains the erroneously high p 50 of 0.15 kPa for rat liver and heart mitochondria [32] respiring in the active OXPHOS state (Table 1B; Fig. 4a).

Varying human umbilical vein endothelial cell (HUVEC) density in a three-fold range from 0.6·106 to 2.0·106 cells/ml, maximum oxygen flow and p 50 of ROUTINE respiration vary by a factor of 1.4, from 35 to 49 pmol·s−1·10−6 and from 0.052 to 0.075 kPa, respectively, in endothelial growth medium without inhibitor [12]. In contrast, a 6-fold higher p 50 of 0.44 kPa was reported for HUVEC in the presence of L-NMMA (NOS inhibitor) with 31·106 cells/ml and corresponding high volume-specific flux [33]. Instruments with high O2 back-diffusion [33, 34] are particularly sensitive to artefacts of rapid aerobic-anoxic transitions (Fig. 4a).

In electron paramagnetic resonance (EPR) oxymetry, small numbers of cells can be studied in micro chambers of 50 µl volume [35]. Without sufficient stirring, oxygen gradients develop in diffusion zones around cells [35], comparable to the diffusion zone towards the POS membrane [36]. Although diffusion conditions across unstirred POS are simpler to model in comparison to suspended cells, corrections are inherently inaccurate and the only satisfactory solution for measurement of dissolved oxygen is obtained by vigorous stirring, as in HRR. Taking oxygen diffusion in unstirred EPR oxymetry into consideration reduces the estimate of p 50 for respiration of endothelial cells two-fold [35], but the corrected p 50 values remain highly sensitive to cell density (2·106–5·106 cells/ml; Table 1B). The minimum oxygen pressure, p #, at which cessation of respiration in EPR oxymetry indicates equilibrium to be established within mitochondria, is at 0.05 kPa [35] (in the range of p 50 from HRR), whereas the thermodynamic equilibrium p O2 is 0.0003 kPa for coupled mitochondrial oxygen reduction [3]. Perhaps oxygen diffusion through the tube sealing clay contributes to the high p # in capillaries used for EPR oxymetry. The sensitivity (>2-fold) of p # on diffusion corrections indicates that it is not a thermodynamic equilibrium property, since diffusion gradients are dissipated in the approach to equilibrium. Further uncertainties may result from high noise of flux and lack of temperature control in EPR oxymetry. The diffusion model applied for correction in EPR oxymetry assumes that the diffusion zone increases as a steady function of time [35], whereas experimental validation – using the POS as a test system – suggests that a steady-state is reached after a short period of a few minutes. Wall effects are not considered, nor potential effects of cell aggregation in the confinement of a 50 µl capillary [35]. Taken together, these difficulties may explain the high apparent p 50 derived from EPR oxymetry (Fig. 4b).

4.3 Variation of p50 in Open Systems

Using a steady-state approach with oxygen transfer from the gas to aqueous phase (GAP), Sugano et al. [21] report a p 50 of 0.08 kPa in active pigeon heart mitochondria at a protein concentration of 0.2 mg/ml (Table 1A). At 10 mg/ml, however, Cole et al. [37] obtained a p 50 of 0.005 kPa in active rat skeletal muscle mitochondria. Using the identical instrumental GAP respirometry system, a p 50 of 0.37 kPa was reported for rat liver mitochondria in the passive LEAK state [38], 75 times higher than in ADP-stimulated rat skeletal muscle mitochondria [37] (Fig. 4c). In contrast to the well established direct proportionality between p 50 and turnover of cytochrome c oxidase [10–13, 22, 26, 28], the p 50 obtained by GAP respirometry was paradoxically higher in the quiescent LEAK state compared to the active OXPHOS state [38]. GAP respirometry, therefore, yields inconsistent results on mitochondrial oxygen kinetics (Fig. 4c). Under conditions of very high flux [37], oxygen gradients between the gas and aqueous phases and towards the oxygen sensor at the bottom of the chamber may explain differences between the mitochondrial response to oxygen pressure in the heterogeneous system and the much lower p 50 reported by the POS in GAP respirometry. This does not explain, however, why the reported p 50 increases as the volume specific flux declines in this GAP respirometric system (Table 1B). In addition, previous claims that the p 50 may be lower in closed than open systems [39] are rejected with reference to the literature summarized over the past 40 years in general and to discrepancies of GAP respirometry in particular (Fig. 4, Table 1).

4.4 Variation of p50 In Vivo

Living cells provide an in vivo model that can be studied in vitro, both in closed measuring systems or open systems at steady state. The p 50 of mitochondrial respiration in vivo varies as a function of metabolic state (turnover of cytochrome c oxidase), as observed in living cells (Fig. 2). The 1H nuclear magnetic resonance signal of deoxymyoglobin provides an elegant means of monitoring intracellular oxygen saturation in vivo, reducing Δp 50 (Eq. 2) to the effects of intracellular oxygen gradients. Using this approach in perfused rat heart [40], maximally active human skeletal muscle [41] and mouse skeletal muscle at rest or stimulated by uncoupling [42], p 50 values of mitochondrial respiration range from 0.07 to 0.2 kPa (Table 1C), whereas the p 50 in resting rat cardiomyocytes is 0.015 based on intracellular p O2 derived from spectrophotometric myoglobin saturation measurements [43]. The dependence of cellular or tissue respiration on average myoglobin saturation does not accurately reflect the p 50 of mitochondrial respiration. Direct comparison would require modelling of the distribution of mitochondria [44] over the range of local oxygen pressures as determined by intracellular oxygen gradients [4], and particularly evaluation of anoxic core regions [5] and their effect on the overall response of tissue or cell respiration under these heterogeneous oxygen conditions. A mitochondrial p 50 of 0.067 has been derived from a model of brain oxygen supply [45].

5 Conclusions

The p 50 of mitochondrial respiration in the range of 0.02–0.05 kPa (0.15–0.4 mmHg) indicates close matching of the affinity of cytochrome c oxidase to the demands imposed on enzyme function in the low-oxygen environment within cells. 86% myoglobin saturation (2 kPa O2) in normoxic resting mouse skeletal muscle [42] supports full (99%) respiratory capacity of mitochondria in the LEAK state (Table 1A). At maximum aerobic exercise in human muscle, however, myoglobin saturation is 50% (p O2 = 0.3–0.4 kPa) [41, 46], which implies an oxygen limitation to 0.9 of maximum mitochondrial capacity, assuming homogenous oxygen distribution. Short-term performance at the extreme of maximum aerobic muscle power induces physiological, intracellular hypoxia at environmental normoxia, if we consider oxygen limitation by >5% as a criterion of defining bioenergetic hypoxia.

In contrast, with a p 50 as high as 0.4 kPa (3 mmHg; Table 1B), mitochondrial activity would be limited to 0.44 of respiratory capacity at 50% myoglobin saturation. Even at an intracellular oxygen pressure of 4–5 kPa in liver [47], respiration rate would reach only 0.9 of capacity. Such high p 50 values of mitochondrial respiration are experimental artefacts resulting from high volume-specific flux in closed chambers (Fig. 4a) and of diffusion limitation in unstirred systems (Fig. 4b). Internally inconsistent results on p 50 from open GAP respirometry indicate a methodological problem which remains unresolved (Fig. 4c). Several recent studies on the inhibition of cytochrome c oxidase by NO report erroneously high p 50 in the absence of inhibitor [33, 34, 39]. A critical evaluation is required whether or not these methodological deficiencies extend into the higher oxygen range where NO inhibits cytochrome c oxidase, a compensatory shift may occur of cytochrome redox states [33, 48] and mitochondrial ROS production may be affected.

At half-maximum aerobic power, myoglobin saturation in skeletal muscle is increased to 70% (p O2 = 0.9 kPa [46]), corresponding to oxygen limitation of 5% with a p 50 of 0.05 kPa. An intracellular p O2 of 1–2 kPa at modest routine activity, therefore, is the normoxic mitochondrial microenvironment in skeletal muscle, and the high affinity of mitochondrial respiration for oxygen prevents significant oxygen limitation under these conditions. On the other hand, a p 50 of 0.02–0.05 kPa is not excessively low and thus provides the potential for mitochondria to function as a bioenergetic oxygen sensor and playing a role in oxygen signalling and adaptation to hypoxia [49, 50].