Accuracy and precision of quantitative ³¹P-MRS measurements of human skeletal muscle mitochondrial function

Abstract

Although theoretically sound, the accuracy and precision of ³¹P-magnetic resonance spectroscopy (³¹P-MRS) approaches to quantitatively estimate mitochondrial capacity are not well documented. Therefore, employing four differing models of respiratory control [linear, kinetic, and multipoint adenosine diphosphate (ADP) and phosphorylation potential], this study sought to determine the accuracy and precision of ³¹P-MRS assessments of peak mitochondrial adenosine-triphosphate (ATP) synthesis rate utilizing directly measured peak respiration (State 3) in permeabilized skeletal muscle fibers. In 23 subjects of different fitness levels, ³¹P-MRS during a 24-s maximal isometric knee extension and high-resolution respirometry in muscle fibers from the vastus lateralis was performed. Although significantly correlated with State 3 respiration (r = 0.72), both the linear (45 ± 13 mM/min) and phosphorylation potential (47 ± 16 mM/min) models grossly overestimated the calculated in vitro peak ATP synthesis rate (P < 0.05). Of the ADP models, the kinetic model was well correlated with State 3 respiration (r = 0.72, P < 0.05), but moderately overestimated ATP synthesis rate (P < 0.05), while the multipoint model, although being somewhat less well correlated with State 3 respiration (r = 0.55, P < 0.05), most accurately reflected peak ATP synthesis rate. Of note, the PCr recovery time constant (τ), a qualitative index of mitochondrial capacity, exhibited the strongest correlation with State 3 respiration (r = 0.80, P < 0.05). Therefore, this study reveals that each of the ³¹P-MRS data analyses, including PCr τ, exhibit precision in terms of mitochondrial capacity. As only the multipoint ADP model did not overstimate the peak skeletal muscle mitochondrial ATP synthesis, the multipoint ADP model is the only quantitative approach to exhibit both accuracy and precision.

as the atp generated during recovery from exercise is driven almost exclusively by oxidative metabolism (6, 51), the rate of phosphocreatine (PCr) recovery is commonly used as an indicator of skeletal muscle mitochondrial phosphorylation “capacity” or function (19, 59). Given the mono-exponential behavior of PCr kinetics postexercise (41), a common approach has been to utilize PCr τ or the rate constant (k) to qualitatively assess muscle mitochondrial function (43). Quantitative approaches relying on models of respiratory control have also been proposed to estimate mitochondrial capacity in vivo. For instance, kinetic models of respiratory control by the phosphorylation potential (ADP·Pi/ATP, the Kinetic Phosphorylation Potential model) (66) or ADP (4, 17) (the Kinetic ADP model), have been used to estimate the peak rate of mitochondrial ATP synthesis (V_max). To improve the accuracy of this estimate, a refinement of the latter approach using a multipoint analysis of the recovery (the Multipoint ADP model) has also been proposed (21). An additional, frequently used method is based on the central role played by the creatine kinase reaction in the intracellular communication between the sites of ATP demand and synthesis (the Linear model) (21), and is derived from the electrical analog model of respiratory control (43). However, the accuracy and precision of these quantitative approaches of estimating mitochondrial capacity compared with the direct measurement of mitochondrial functional capacity is uncommon.

This not well-validated array of ³¹P-MRS data analysis approaches to assess mitochondrial function in vivo complicates comparisons between studies and, as they can lead to different conclusions, may call into question the generalization of ³¹P-MRS results (33). Therefore to appropriately facilitate the widespread use of ³¹P-MRS, it is critical to evaluate the relationship between each model of respiratory control and intrinsic mitochondrial respiration capacity, measured in vitro, to clarify whether one approach is preferable to the others. Interestingly, some validation with in vitro techniques has been performed for these ³¹P-MRS-based approaches (5, 28, 32, 42). However, these comparisons were likely somewhat affected by the fact that ³¹P-MRS provides a physiologically relevant functional assessment of muscle mitochondrial properties within the environment of the muscle, whereas enzymatic activities measure the maximal flux at specific points along the metabolic pathway. Thus, the latter, may not accurately reflect maximal oxidative phosphorylation flux in skeletal muscle (2). Similarly, respiration measurements in isolated mitochondria, although providing a more direct measurement, may be affected by the biased selection of a particular mitochondrial population and the disruption of mitochondrial interactions during the isolation procedure, which in turn can alter mitochondrial function (26, 50). However, this issue appears to have been overcome by the development of the in vitro permeabilized fiber technique, which seems to preserve most of the functional properties of the skeletal muscle mitochondria (26, 50).

Therefore, the purpose of this study, employing comprehensive in vivo and in vitro analyses, was to determine the accuracy and precision of the peak mitochondrial ATP synthesis rates of four models of respiratory control (linear, kinetic, and multipoint ADP, and phosphorylation potential) against State 3 respiration directly assessed in permeabilized skeletal muscle fibers. We hypothesized that all the ³¹P-MRS data analysis approaches would be significantly correlated with State 3 respiration assessed in vitro. However, on the basis of previous studies (19, 27, 33), we hypothesized that the peak ATP synthesis rates estimated with the linear and phosphorylation potential models would overestimate those calculated from State 3 respiration in vitro.

METHODS

Subjects.

Following informed consent procedures, 23 (20 males, 3 females) subjects, exhibiting a variety of physical activity levels, participated in this study (Table 1). All subjects were nonsmokers, free of diabetes and known cardiovascular, peripheral vascular, neuromuscular, or pulmonary disease. Additionally, none of the subjects were taking medications known to affect muscle function. The women, who were all premenopausal, were studied in the MR scanner during days 1–7 of their menstrual cycle to standardize the influence of female hormones. The study was approved by the Institutional Review Boards of both the University of Utah and the Salt Lake City Veterans Affairs Medical Center.

Table 1.

Subject characteristics

Characteristics
Anthropometric characteristics
Age, yr	25 ± 4
Height, cm	169 ± 37
Weight, kg	73 ± 12
BMI, kg/m2	24 ± 4
Thigh volume, L	4.9 ± 1.2
Functional characteristics
Steps per day	8,459 ± 2,764
Moderate to vigorous activity, min/day	51 ± 19
Blood and plasma characteristics
Glucose, mg/dl	79 ± 11
Cholesterol, mg/dl	170 ± 24
Triglycerides, mg/dl	99 ± 35
HDL, mg/dl	55 ± 13
LDL, mg/dl	104 ± 21
WBC, K/μl	5.4 ± 1.0
RBC, M/μl	5.2 ± 0.4
Hemoglobin, g/dl	15.6 ± 1.1
Hematocrit, %	45 ± 3
Neutrophil, K/μl	2.9 ± 0.9
Lymphocyte, K/μl	2.0 ± 0.7
Monocyte, K/μl	0.4 ± 0.1

Values are expressed as means ± SD; n = 23. Body mass index, BMI; high-density lipoprotein, HDL; low-density lipoprotein, LDL; white blood cells, WBC; red blood cells, RBC.

Exercise protocol.

On the first day, participants were familiarized with testing procedures and performed preliminary assessments. On a separate day, subjects performed the isometric knee extension exercise in the whole body MRI system (TimTrio 2.9T; Siemens Medical Systems, Erlangen, Germany). While positioned supine, the knee of the dominant leg was fixed at ∼135° over a custom-built apparatus, and the foot was attached to a strain gauge (SSM-AJ-250; Interface, Scottsdale, AZ). To minimize hip movement and back extension during the contraction, participants were secured to the bed with nonelastic straps placed over the hips and the thigh of the leg being interrogated. The force signal was collected with a sample frequency of 100 Hz, converted from analog-to-digital (MP150, Biopac Systems), and recorded on a personal computer (Acknowledge, Biopac Systems). Each participant performed two baseline/practice maximum voluntary contractions (MVC) of ∼5–10 s duration with 1 min of recovery between each. After ∼10 min of rest and 4 min of baseline data collection, subjects performed a maximal voluntary isometric contraction for 24 s followed by 5 min of recovery. Based on preliminary testing, this protocol was designed to elicit a substantial depletion in PCr content without inducing acidosis, as this is known to complicate the interpretation of the PCr recovery kinetics. On a separate day, a percutaneous biopsy of the vastus lateralis muscle ∼3.5 cm deep, 15 cm proximal to the knee and slightly distal to the ventral mid-line of the muscle was obtained from the same leg. The 5-mm diameter biopsy needle (Bergström) was attached to sterile tubing and a syringe to apply a negative pressure to assist in the muscle sample collection (12). Immediately after the muscle sample (∼100 mg) was removed from the leg, a portion of the sample (∼20 mg) was immersed in ice-cold biopsy preservation fluid (BIOPS) for respiratory analysis (47) (in mM: 2.77 CaK²EGTA, 7.23 K₂EGTA, 20 imidazole, 50 K⁺MES, 20 taurine, 0.5 dithiothreitol, 6.56 MgCl₂, 5.77 ATP, 15 PCr, pH 7.1). Visits were separated by at least 7 days to ensure adequate healing from the biopsy procedure or enough recovery from the exercise. All experimental trials were performed in a thermoneutral environment (∼20°C) and following an overnight fast.

31P-MRS.

MRS was performed using a clinical 2.9T MRI system (Tim-Trio; Siemens Medical Solutions, Erlangen, Germany) operating at 49.9 MHz for ³¹P resonance. ³¹P-MRS data were acquired with a ³¹P-proton (¹H) dual-surface coil with linear polarization (Rapid Biomedical, Rimpar, Germany) positioned above the quadriceps. The ³¹P single-loop coil diameter was 125 mm, which surrounded the 110-mm ¹H coil loop. After a three-plane scout proton image, advanced localized volume shimming was performed. Before each experiment, two fully relaxed ³¹P-MRS spectra were acquired at rest with three averages per spectrum and a repetition time (TR) of 30 s. Then, ³¹P-MRS data acquisition was performed throughout the rest-exercise-recovery protocol using an FID (free-induction-decay) pulse sequence with a 2.56 ms adiabatic half-passage excitation RF (radio frequency) pulse and the following parameters (TR = 2 s, receiver bandwidth = 5 kHz, 1,024 data points, and 3 averages per spectrum). Saturation factors were quantified by the comparison between fully relaxed (TR = 30 s) and partially relaxed (TR = 2s) spectra.

Relative concentrations of phosphocreatine [PCr], inorganic phosphate [Pi], phosphodiester (PDE), and [ATP] were obtained by a time domain-fitting routine using the AMARES algorithm (64) incorporated into the CSIAPO software (38). Intracellular pH was calculated from the chemical shift difference between the Pi and PCr signals (58). The free cytosolic [ADP] was calculated from [PCr] and pH using the creatine kinase (CK) equilibrium constant (K_CK = 1.66 × 10⁹ M⁻¹) and the assumption that PCr represents 85% of the total creatine content (16). The resting concentrations were calculated from the average peak areas of the two relaxed spectra (TR = 30 s; n = 3) recorded at rest and assuming an 8.2 mM [ATP] under these conditions.

31P-MRS data analysis.

PCr recovery kinetics was determined by fitting the PCr time-dependent changes during the recovery period to a single exponential curve described by the following equation:

$$[\text{PCr}]\hspace{0.17em}(t)\hspace{0.17em}=\hspace{0.17em}{[\text{PCr}]}_{\text{end}}\hspace{0.17em}+\hspace{0.17em}{[\text{PCr}]}_{\text{cons}}(1\hspace{0.17em}-\hspace{0.17em}{\text{e}}^{-(t/\tau )})$$

where [PCr]_end is the concentration of [PCr] measured at end of exercise and [PCr]_cons refers to the amount of PCr consumed at the end of the exercise session, and τ reflects the time constant of the recovery, a relative measure of muscle oxidative capacity (21, 42–44). The initial rate of PCr resynthesis (Vi) was calculated as follows:

$$Vi\hspace{0.17em}=\hspace{0.17em}k\hspace{0.17em}\times {[\text{PCr}]}_{\text{cons}}$$

in which [PCr]_cons represents the amount of PCr consumed at the end of exercise and the rate constant, k = 1/τ.

On the basis of the assumption that in the absence of an oxygen limitation and changes in mitochondrial redox balance, phosphate potential ([Pi] × [ADP]/[ATP]) controls the rate of oxidative phosphorylation with a K_m of 0.11 (66), we calculated V_{max pp} (kinetic phosphorylation potential model) as follows:

$$V_{\max \hspace{0.17em}\text{pp}}\hspace{0.17em}=\hspace{0.17em}Vi\hspace{0.17em}(1\hspace{0.17em}+\hspace{0.17em}[K_{\text{m}}/({[\text{Pi}]}_{\text{end}}\hspace{0.17em}\times \hspace{0.17em}{[\text{ADP}]}_{\text{end}}/[\text{ATP}])])$$

Based on the sigmoid relationship between the oxidative ATP production rate and free cytosolic ADP concentration (kinetic ADP model), V_{max ADP} (in mM/min) was calculated using the initial rate of PCr synthesis during the recovery period and [ADP] obtained at the end of exercise as previously described (60):

$$V_{\max \hspace{0.17em}\text{ADP}}\hspace{0.17em}=\hspace{0.17em}Vi\hspace{0.17em}[1+{(K_{\text{m}}/{[\text{ADP}]}_{\text{end}})}^{2.2}]$$

By use of multipoint analysis (21, 35), the control of respiration rate by ADP was fitted using nonlinear least square techniques from the following function (multiple-point ADP model) (67):

$$Vi\hspace{0.17em}=\hspace{0.17em}(V_{\max \hspace{0.17em}\text{mp}}\times {[\text{ADP}]}^{nH})/({K_m}^{nh}\hspace{0.17em}+\hspace{0.17em}{[\text{ADP}]}^{nh})$$

in which n_H is the Hill coefficient, K_m is the ADP value at half-maximal Vi, and V_{max mp} is the maximal ADP-stimulated respiration rate. Although we acknowledge that even in absence of ADP there is some mitochondrial respiration (uncoupled respiration), the minimal ADP-stimulated respiration rate (V_min) was not included in the model, as the estimation of this parameter has poor accuracy due to the low signal-to-noise ratio of the respiration rate and [ADP] in the resting state.

According to the linear model of oxidative phosphorylation described by Meyer (43), the theoretical peak rate of oxidative phosphorylation can be estimated as the product of k_PCr and resting [PCr] using the following equation (linear model) (21):

$$V_{\max \hspace{0.17em}\text{lin}}\hspace{0.17em}=\hspace{0.17em}k\hspace{0.17em}\times \hspace{0.17em}{\text{PCr}}_{\text{rest}}$$

Model variables were determined with an iterative process by minimizing the sum of squared residuals (RSS) between the fitted function and the observed values. Goodness of fit was assessed by visual inspection of the residual plot and the frequency plot distribution of the residuals, χ² values and the coefficient of determination (r²) calculated as follows:

$$r^2\hspace{0.17em}=\hspace{0.17em}1\hspace{0.17em}-\hspace{0.17em}({\text{SS}}_{\text{reg}}/{\text{SS}}_{\text{tot}})$$

with SS_reg representing the sum of squares of the residuals from the fit and SS_tot being the sum of squares of the residuals from the mean.

Mitochondrial respiration.

Muscle samples were prepared and permeabilized for mitochondrial respiration analysis as previously described (47). Briefly, BIOPS-immersed fibers were carefully separated with fine-tip forceps and subsequently bathed in a BIOPS-based saponin solution (50 μg saponin/ml BIOPS) for 30 min. Following saponin treatment, muscle fibers were rinsed twice in ice-cold mitochondrial respiration fluid (MIR05, in mM: 110 sucrose, 0.5 EGTA, 3 MgCl₂, 60 K-lactobionate, 20 taurine, 10 KH₂PO₄, and 20 HEPES, and BSA 1 g/l, pH 7.1) for 10 min each rinse. After the muscle sample was gently dabbed with a paper towel to remove excess fluid, the wet weight of the sample was measured using a standard calibrated scale (2–4 mg). The muscle fibers were then placed in the respiration chamber (Oxytherm, Hansatech Instruments, UK) in 2 ml of MIR05 solution and warmed to 37°C. MIR05 was air saturated with O₂ concentrations of ∼190 to ∼175 μM O₂ from the start to finish of the experiments. After allowing the muscle 10 min to equilibrate, mitochondrial respiratory function was assessed in duplicate. State 2 respiration was measured after the addition of malate (2 mM), and glutamate (10 mM) in saturating concentrations. State 3 respiration with electron flux through CI was measured after the addition of ADP (5 mM), and maximal coupled respiration (State 3) with convergent electron flux through CI + CII was achieved by adding saturating concentrations of succinate (10 mM) to the respiration chamber. This combination of substrates was chosen to reconstitute the operation of the tricarboxylic acid cycle and prevent the depletion of key metabolites from the mitochondrial matrix, thus providing suitable conditions for evaluating maximal physiological oxidative phosphorylation capacity (7). Then, cytochrome c (10 μM) was added to test for outer mitochondrial membrane integrity. Only samples demonstrating intact mitochondrial membrane integrity (<10% increase in respiration in response to cytochrome c) were included in this analysis. Assuming a P/O ratio of 2.47 (3) and muscle density of 1.049 kg/l, the maximal ADP-stimulated respiration was converted into ATP synthesis rate (mM·min⁻¹·l⁻¹) to assess the accuracy of the quantitative ³¹P-MRS data analysis approaches.

Thigh volume.

Thigh volume and quadriceps muscle mass were calculated based on thigh leg circumference (3 sites: distal, middle, and proximal), thigh length, and skinfold measurements (18), a method that has demonstrated excellent agreement with thigh volume assessed with ¹H-MR imaging.

Physical activity level.

Both a subjective modified physical activity level (PAL) recall questionnaire and objective accelerometer data were used to assess physical activity. The PAL questionnaire included items regarding the average type, frequency, intensity, and duration of physical activity in any given week. After receiving standardized operating instructions, subjects wore the accelerometer (GT1M; Actigraph, Pensacola, FL) for 7 continuous days, with adherence automatically assessed by the data output. Average daily physical activity was expressed as steps per day and the time spent in moderate to vigorous physical activity. Based on the recommendations of the manufacturer of the accelerometer, thresholds for sedentary, light, and moderate to vigorous activity were defined as <99, 100-1,959, and 1,952+ counts/min, respectively.

Statistical analysis.

The assessment of differences between baseline and exercise was performed with either paired t-tests or nonparametric Wilcoxon tests, where appropriate (Statsoft, version 5.5; Statistica, Tulsa, Oklahoma). Potential relationships between variables were assessed using Pearson's correlation analysis or the nonparametric Spearman rank order correlation. Statistical significance was accepted at P < 0.05. Results are presented as means ± SD in tables and means ± SE in the figures for clarity.

RESULTS

High-energy phosphate compounds, intracellular pH, and mitochondrial function in vivo.

Intracellular metabolite concentrations and pH at rest and at the end of the exercise are summarized in Table 2. Unlike pH, which was not significantly different from baseline after exercise (P > 0.05), PCr was significantly decreased (P < 0.01), and both Pi and ADP were significantly increased compared with baseline (P < 0.01).

Table 2.

Muscle metabolites and pH at rest and in response to knee-extensor exercise, and parameters of mitochondrial function measured by ³¹P-MRS

	Resting	End Exercise
Concentrations	Means SD	Means SD	P
	31 ± 4	16 ± 5	*
Pi, mM	1 ± 0.6	11 ± 3	*
ADP, μM	8 ± 1	64 ± 26	*
pH	6.98 ± 0.03	6.97 ± 0.09
PCr recovery kinetics and mitochondrial function
Time constant, s	44 ± 11
Vmax ADP multipoint, mM/min	20 ± 5
Km, μM	25 ± 6
Hill coefficient	2.6 ± 0.8

Values expressed as means ± SD. PCr, phosphocreatine; Pi, inorganic phosphate; ADP, adenosine diphosphate; PDE, phosphodiester; K_m, ADP value at half-maximal oxidative ATP synthesis rate.

^*P < 0.01, significantly different from baseline.

Typical examples of the PCr dynamics during the recovery period as well as the relationship between PCr resynthesis rate and ADP in a representative subject are displayed in Fig. 1. The mean PCr τ and kinetic parameters estimated with the multiple-point ADP model are presented in Table 2. V_max from the linear and phosphorylation potential models were significantly higher than V_max from the kinetic and multiple-point ADP models (P < 0.05; Fig. 2). In addition, the peak ATP synthesis rates from the linear, phosphorylation potential, and ADP kinetic models were significantly higher than the ATP synthesis rate calculated from State 3 CI + CII in vitro (P < 0.05; Fig. 2).

Fig. 1.

Typical example of postexercise [PCr] resynthesis with respect to time, fitted according to a monoexponential function (A) and the corresponding PCr resynthesis rate (mM/min) with respect to ADP concentration, a key regulator of mitochondrial respiration, fitted according to a sigmoid function (B). IC 95, 95% confidence interval of the time constant; n_H, Hill coefficient; and K_m, ADP value at half-maximal oxidative ATP synthesis rate.

Fig. 2.

Peak rates of mitochondrial ATP synthesis based on respiratory control models by the phosphorylation potential (kinetic phosphorylation potential model), ADP using two parameters (kinetic ADP model) or a multipoint analysis (multiple-point ADP model), and the electrical analog model of respiratory (linear model). Dashed line, peak rate of mitochondrial ATP synthesis estimated from the maximal ADP-stimulated respiration in vitro assuming a P/O ratio of 2.47. *P < 0.05, significantly different from ADP models; #P < 0.05, significantly different from calculated in vitro value.

Respiration in permeabilized fibers and relationship with in vivo measurements.

State 2 respiration was 16.5 ± 10.2 ρM·s⁻¹·mg⁻¹ wet wt and reached 45.6 ± 12.6 ρM·s⁻¹·mg⁻¹ wet wt during State 3 respiration due to convergent electron flux through Complex I and II. As illustrated in Fig. 3, State 3 CI + CII was significantly correlated with PCr τ (r = 0.8, P < 0.05; Fig. 3A) and V_max from all four models (r = 0.55–0.72, P < 0.05; Fig. 3, B–E).

Fig. 3.

Relationships between maximal ADP-stimulated respiration with convergent electron flux through Complex I and Complex II and in vivo indexes of mitochondrial capacity, i.e., the PCr recovery time constant (indirect method; A), the peak rate of mitochondrial ATP synthesis estimated based on a model of respiratory control by the phosphorylation potential (kinetic phosphorylation potential model; B), ADP using two parameters (kinetic ADP model; C) or multipoint analysis (multiple-point ADP model; D), the electrical analog model of respiratory control (linear model; E).

DISCUSSION

This study, employing comprehensive in vivo and in vitro metabolic analyses, sought to determine the accuracy and precision of the peak mitochondrial ATP synthesis rates of four models of respiratory control (linear, kinetic, and multipoint ADP and phosphorylation potential). Consistent with our first hypothesis, in terms of precision, V_max calculated from each of the quantitative models of respiratory control correlated with the State 3 respiration in vitro (r = 0.55 to 0.72). Although not the primary aim of the study, the PCr τ, a qualitative index of mitochondrial capacity, exhibited the strongest association with State 3 respiration in vitro (r = 0.80). However, in terms of accuracy, the peak ATP synthesis rates from the linear, phosphorylation potential, and ADP kinetic models were significantly higher than the ATP synthesis rate calculated from the State 3 respiration in vitro. Therefore, this study reveals that each of the ³¹P-MRS data analysis approaches, including the PCr τ, provides evidence of being precise. However, only the multipoint ADP model did not overstimate the peak rate of skeletal muscle mitochondrial ATP synthesis, supportive of the conclusion that this is the only quantitative model exhibiting both accuracy and precision.

Accuracy and precision of ³¹P-MRS mitochondrial function measurements.

An important finding of this study was that the State 3 respiration with convergent electron flux through CI and CII in permeabilized fibers from the vastus lateralis muscle correlated significantly, although to somewhat differing degrees, with all four of the quantitative ³¹P-MRS approaches to assess mitochondrial phosphorylation capacity in the quadriceps of the same cohort of subjects (r = 0.55 to 0.72; Fig. 3). In addition, although not the primary aim of the study, we observed that the PCr τ, a qualitative index of mitochondrial capacity, demonstrated a strong correlation with State 3 respiration (r = 0.80, P < 0.05). Consistent with our results, some of these ³¹P-MRS indexes of mitochondrial capacity have previously been documented to correlate with in vitro markers of mitochondrial content or function (5, 28, 32, 42). In accord with the current findings (Fig. 3E), the peak rate of mitochondrial ATP synthesis from the linear model has previously been correlated with State 3, CI and CII respiration in both isolated mitochondria from young adults (r = 0.71) (28) and permeabilized fibers from older individuals (r = 0.69)(5). Furthermore, citrate synthase activity (r = 0.63 to 0.64), a marker of mitochondrial content (31), demonstrated a good agreement with the peak rate of mitochondrial ATP synthesis from the kinetic ADP model (r = 0.64) in the calf muscle of young adults (32). In addition, an extensive review of the literature recently confirmed the consistency of the ADP kinetics model with direct invasive measurements of muscle O₂ consumption using a common analytical framework (19). Previous investigations have documented that the τ/rate constant of PCr recovery kinetics exhibit moderate to good agreement (r = 0.48 to 0.84) with citrate synthase activity in the human calf (32, 42) and rat gastrocnemius muscles (44). In addition, the injection of a CI inhibitor elicited a parallel decrease in the PCr recovery rate constant measured by ³¹P-MRS and the State 3 respiration from CI in isolated mitochondria from the tibialis anterior of rats (62). Therefore, taken together, these findings strongly support the use of ³¹P-MRS to assess the functional properties of skeletal muscle mitochondria in vivo.

It is interesting to note that the correlation coefficients observed in the current study between the in vitro and in vivo measurements of mitochondrial function appear to be slightly higher than the values reported in previous studies (28, 32, 42). This apparently better agreement may originate from the permeabilized fiber technique employed in the current study to assess the mitochondrial properties in vitro. Indeed, it has been advocated that the permeabilized fiber approach enables the assessment of all cellular populations of mitochondria and preserves the integrity of the mitochondria, thus providing a more physiological measurement of mitochondrial respiration (26, 50). Interestingly, although used as an external control in this study, by means of construct validity, the high level of agreement between the in vivo measurements of mitochondrial function and the assessment of mitochondrial respiratory capacity in permeabilized fibers lends further credence to this technique.

Of note, the τ/rate constant of PCr recovery kinetics and the kinetic ADP model have previously exhibited good agreement with citrate synthase activity, but not with cytochrome c oxidase activity (32). However, it should be acknowledged that the maximal flux at specific points of the metabolic pathway does not necessarily accurately reflect the maximal oxidative phosphorylation flux (2). Specifically, it is unclear whether cytochrome c oxidase, which is the terminal complex of the mitochondrial electron transport chain, is an appropriate mitochondrial biomarker, as the flux through the electron transport chain is usually in excess relative to the maximal flux through ATP synthase (7). Also, while citrate synthase activity closely reflects mitochondrial content in the skeletal muscle of healthy adults (31), the muscle respiratory capacity normalized for mitochondrial content can vary substantially between healthy individuals with different activity levels (15). Therefore, based on these considerations regarding the use of mitochondrial enzyme activity to assess metabolic capacity, this approach may not fully reflect the functional capacity of the mitochondria, or at least not as closely as the State 3, complex I and II respiration in permeabilized fibers, as employed in the current study.

Comparing in vivo approaches to assess mitochondrial function.

A both unique and novel aspect of the present study was the aim to assess the relationship between four quantitative ³¹P-MRS methods of determining mitochondrial capacity and mitochondrial respiration capacity measured in permeabilized fibers as an index of precision. Although there was some range in the strength of the relationships (r = 0.55 to 0.72), with the multipoint ADP model demonstrating the weakest relationship, each model exhibited a level of precision, as all were significantly related to State 3 respiration measured in vitro (Table 3). It is also worth noting that, although a qualitative index of mitochondrial capacity, the PCr τ actually demonstrated the closest association with State 3 (r = 0.80; Fig. 3), suggestive of a greater precision with this method compared with the quantitative approaches. Although the level of precision is an important parameter when one is trying to establish the best approach to use when studying mitochondrial function in vivo, a thorough interpretation of the implications of the current results requires that the reliability and experimental conditions, which may influence this assessment, also be considered.

Table 3.

Summary of the positive, + and negative, − accuracy and precision findings for ³¹P-MRS analysis approaches for assessing mitochondrial capacity in skeletal muscle

Approach	Accuracy	Precision
PCr time constant	NA	+
Linear	−	+
ADP kinetic	−	+
ADP multipoint	+	+
Phosphorylation potential	−	+

Phosphocreatine, PCr; not applicable, NA; adenosine diphosphate, ADP.

Both the PCr τ and the peak rate of mitochondrial ATP synthesis from the linear model are influenced by the PCr content, pH, and H⁺ efflux (14, 37, 56, 63), which can, in turn, negatively affect the reproducibility of these indexes (34). This shortcoming can, however, be overcome, as in the present study, by using a short exercise bout to prevent metabolic acidosis (28). In such a scenario, PCr τ appears to be a good approach to qualitatively assess skeletal muscle mitochondrial capacity across individuals with a wide spectrum of activity levels. In this regard, the subjects recruited in this study exhibited a variety of physical activity levels, resulting in a large range of values for the PCr time constant (∼20–70 s), consistent with the published literature in young healthy individuals [∼25 s (65), ∼40 s (61), 30–50 s (48), and 30–70 s (55)]. Of note, from a quantitative standpoint, the peak rate of mitochondrial ATP synthesis determined using the electrical analog model significantly overestimated muscle mitochondrial capacity (∼45 mM/min; Fig. 2) and was significantly greater than the models relying on ADP as the key regulator for mitochondrial respiration. Interestingly, the calculated peak ATP synthesis determined in vitro was substantially lower than the value obtained utilizing the linear model in the present study and far below common values documented in the literature using this approach (>100 mM/min) (28, 29), further confirming that the linear method tends to overestimate the peak rate of mitochondrial ATP synthesis. This overestimation might stem from the fact that the V_max calculated using this approach is beyond the range of the linear approximation (PCr between 20 and 70% of total Cr) required by the electric analog model (43) and therefore would require some additional modeling of the nonlinear characteristics of the mitochondrial capacity (43). Also, although extensively used in the literature, this approach is also questionable from a conceptual standpoint, because, in addition to the PCr τ, it is dependent on resting [PCr], which has been established to be inversely proportional to the number of type I oxidative skeletal muscle fibers (24). In other words, this implies that muscle fibers with greater oxidative potential and mitochondrial volume density (type I oxidative fibers) exhibit lower [PCr], which according to the mathematical formulation of this model, would, incorrectly, translate into lower mitochondrial capacity.

The estimated V_max with the phosphorylation potential model was also considerably higher than the calculated ATP synthesis rate from permeabilized fiber respiration in vitro. This systematic error potentially arises from the arbitrary value set for the K_m (0.11 mM) (66), which has yet to be experimentally confirmed. In light of these issues, and considering that the reproducibility of this method has yet to be established, other methods should be preferred to quantify muscle mitochondrial capacity from ³¹P-MRS measurements.

Although significantly higher, the ADP model provided an estimation of the peak rate of oxidative ATP synthesis that was more compatible with the currently calculated in vitro values (24 vs. 14 mM/min, P < 0.05) and those estimated from the literature in untrained subjects (∼16–28 mM/min) (7). Interestingly, it has been documented that the peak rate of mitochondrial ATP synthesis from the kinetic ADP model is independent of pH (56) and exhibits high reproducibility (1, 34, 57). Therefore, in combination with the very good association exhibited between this index and mitochondrial respiratory capacity assessed in vitro (Fig. 3), this approach appears to provide both a precise and a reproducible measurement of mitochondrial capacity across a variety of exercise conditions. In the future, greater accuracy with this method may be achieved by directly measuring total creatine content, using, perhaps, dynamic ³¹P-MRS in combination with ¹H-MRS (20).

The multipoint ADP model was the only analytical approach exhibiting both accuracy and precision compared with the in vitro measurements (Table 3; Figs. 2 and 3). However, it should be recognized that the large PCr depletion and limited pH changes induced by the exercise protocol employed in this study facilitated the analysis of the recovery period with the multipoint ADP model. Indeed, due to the need for high time resolution, large metabolic changes, and the greater complexity of this model, unless analyses specific to the sensitivity of mitochondrial respiration to ADP are important components of a study (i.e., the K_m and Hill coefficient), the simple kinetic ADP model may, ultimately, be preferable to the multipoint ADP approach.

Experimental considerations.

An important aspect of the present study was to quantitatively compare the ATP synthesis rates estimated with four models in vivo and State 3 respiration measured in vitro in permeabilized skeletal muscle fibers, this latter approach being used as an external control. Although preserving most of the functional properties of the mitochondria (26, 50), it should, however, be acknowledged that this in vitro preparation still features some inherent physiological differences with the assessment of mitochondrial function by ³¹P-MRS. This, in turn, may have resulted in some variations of the estimated rates for muscle phosphorylation capacity (Fig. 2). First, [O₂] in the respiration chamber is supraphysiological ([O₂] > 175 μM, 37°C), and the diffusion of O₂ to the mitochondria is facilitated by the permeabilization of the plasma membrane. In contrast, in vivo the intracellular O₂ partial pressure of the skeletal muscle is much lower (52, 54), and the plasma membrane is intact, potentially limiting mitochondrial ATP synthesis rate (9–11, 36). Second, spontaneous muscle contraction (46) or collapse of the cytoskeleton (25), potentially restricting respiratory capacity, have been reported during the assessment of respiration in vitro. Third, the mechanisms of respiratory control might substantially differ in vivo and in vitro. Specifically, reducing equivalents (NADH and FADH) and ADP are all provided in saturating concentrations in vitro. On the other hand, calcium (Ca²⁺) oscillations, which play a key role in the activation of mitochondrial respiration in vivo (22, 23), are in small and constant concentrations in the buffer solution used in vitro. Together, these differences in the regulatory parameters for oxidative phosphorylation between the two experimental approaches are likely associated with different mechanisms of metabolic control. Therefore, although both ³¹P-MRS and the permeabilized fiber approach provide a functional assessment of muscle mitochondrial properties within the environment of the muscle, it should be recognized that the conversion of respiratory rates from permeabilized fibers to in vivo conditions is subject to some inherent uncertainty.

Mitochondrial respiratory capacity was measured in vitro at a temperature of 37°C. Given the short duration of the exercise (24 s) and the thermoneutral temperature of the MR scanner (∼20°C), the exercise-induced rise in muscle temperature was likely less than 0.2–0.3°C (8). Accordingly, the temperature difference between the two experimental conditions was considered negligible; therefore, the in vitro metabolic rates were not adjusted for this factor when extrapolated to in vivo conditions.

One could question the consequence on our conclusions based on the sampling of different volumes with the ³¹P-MRS and biopsy techniques. Indeed, based on the dimension and the sensitivity of the surface coil, the MR signal originated from a much larger sample volume [vastus lateralis, vastus medialis, rectus femoris, and to a small extent from the vastus intermedius (48)] compared with the rather small muscle biopsy sample collected in the vastus lateralis (∼6–10 mg). Together, the volume difference and the known variability sample to sample with the biopsy technique (39, 40) may potentially have contributed to some of the quantitative differences observed in the estimate of ATP synthesis rates in vivo and in vitro (Fig. 2). Additionally, this difference would have augmented the variance of the correlation between the respiratory capacity in vitro and the ³¹P-MRS indexes of mitochondrial phosphorylation capacity. However, two lines of evidence suggest that our findings were not greatly confounded by this factor. First, the muscle recruitment during knee-extension exercise is homogeneous (53,) and the four muscles composing the quadriceps appear to exhibit similar metabolic properties in humans (48). Second, the four models in vivo were rather tightly correlated to the in vitro measurement of mitochondrial respiratory capacity (r = 0.55 to 0.80; Fig. 3) suggesting that the biopsy samples were representative of the quadriceps.

In addition to the consistent lack of a cytochrome c response during the in vitro experiments, the maximal coupled respiration with convergent electron flux through CI + CII (26–70 ρM·s⁻¹·mg⁻¹) was also within the span of values previously reported in the literature [∼27 ρM·s⁻¹·mg⁻¹ (49), 30–80 ρM·s⁻¹·mg⁻¹ (13), ∼70 ρM·s⁻¹·mg⁻¹ (30), 10–70 ρM·s⁻¹·mg⁻¹ (45)], confirming the quality of the muscle fiber preparations.

Conclusion.

In summary, this study has revealed that each of the ³¹P-MRS data analysis approaches, including the PCr τ, provides evidence of being precise. However, only the multipoint ADP model did not overstimate the peak rate of skeletal muscle mitochondrial ATP synthesis, supportive of the conclusion that this is the only quantitative model exhibiting both accuracy and precision.

GRANTS

This work was funded in part by grants from the Flight Attendant Medical Research Institute (FAMRI), NIH National Heart, Lung, and Blood Institute (K99 HL-125756, PO1 HL-091830), and the Veteran's Administration Rehabilitation Research and Development Service (E6910-R, E1697-R, E1433-P, and E9275-L).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

G.L., J.R.G., J.D.T., C.R.H., Y.L.F., E.-K.J., and R.S.R. conception and design of research; G.L., J.R.G., J.D.T., C.R.H., R.S.G., S.Y.P., E.-K.J., and R.S.R. performed experiments; G.L., J.R.G., J.D.T., C.R.H., S.Y.P., and Y.L.F. analyzed data; G.L. interpreted results of experiments; G.L. prepared figures; G.L. drafted manuscript; G.L., J.R.G., J.D.T., C.R.H., Y.L.F., E.-K.J., and R.S.R. edited and revised manuscript; G.L., J.R.G., J.D.T., C.R.H., R.S.G., S.Y.P., Y.L.F., E.-K.J., and R.S.R. approved final version of manuscript.