Free [ADP] and aerobic muscle work follow at least second order kinetics in rat gastrocnemius in vivo.

The relationship between free cytosolic [ADP] (and [P(i)]) and steady-state aerobic muscle work in rat gastrocnemius muscle in vivo using (31)P NMR was investigated. Anesthetized rats were ventilated and placed in a custom-built cradle fitted with a force transducer that could be placed into a 7-tesla NMR magnet. Muscle work was induced by supramaximal sciatic nerve stimulation that activated all fibers. Muscles were stimulated at 0.1, 0.2, 0.3, 0.4, 0.5, 0.8, 1.0, and 2.0 Hz until twitch force, phosphocreatine, and P(i) were unchanged between two consecutive spectra acquired in 4-min blocks (8-12 min). Parallel bench experiments were performed to measure total tissue glycogen, lactate, total creatine, and pyruvate in freeze-clamped muscles after 10 min of stimulation at each frequency. Up to 0.5 Hz, there was no significant change in muscle glycogen, lactate, and the lactate/pyruvate ratios between 8-12 min. At 0.8 Hz, there was a 17% fall in glycogen and a 65% rise in the muscle lactate with a concomitant fall in pH. Above this frequency, glycogen fell rapidly, lactate continued to rise, and ATP and pH declined. On the basis of these force and metabolic measurements, we estimated the maximal mitochondrial capacity (V(max)) to be 0.8 Hz. Free [ADP] was then calculated at each submaximal workload from measuring all the reactants of the creatine kinase equilibrium after adjusting the K'(CK) to the muscle temp (30 degrees C), pH, and pMg. We show that ADP (and P(i)) and tension-time integral follow a Hill relationship with at least a second order function. The K(0.5) values for free [ADP] and [P(i)] were 48 microM and 9 mM, respectively. Our data did not fit any form of the Michaelis-Menten equation. We therefore conclude that free cytosolic [ADP] and [P(i)] could potentially control steady-state oxidative phosphorylation in skeletal muscle in vivo.

The control of mitochondrial respiration by free cytosolic [ADP] and [P i ] remains highly controversial. The balanced reaction for oxidative phosphorylation is summarized in Reaction 1.
In 1952, Lardy and Wellman were among the first to propose that the rate of cellular respiration might be controlled by the products of ATP hydrolysis, namely free [ADP] or [P i ] (1,2). A few years later, Chance and Williams obtained apparent K m values of respiration of 20 M and 1.0 mM for free [ADP] and [P i ], respectively, in rat liver mitochondria (3). Chance suggested a greater role for free [ADP] than [P i ] in respiratory control since it would afford a greater sensitivity or gain to the system for a given increase in steady-state work (4 -6). In 1986, Katz and colleagues challenged the importance of free [ADP] on the basis of an invariant NMR determined [PCr]/[ATP] ratio in the in situ canine heart over a 3-5-fold increase in rate-pressure product, or oxygen consumption (42)(43)(44)(45)(46). Evidence against free [ADP] control was supported on theoretical grounds by the fact that a Michaelis-Menten function is inadequate to explain the observed high flux rates in vivo (7).
In an attempt to clarify what has become a very complex subject, Chance and colleagues proposed a modified Michaelis-Menten equation showing how control of cell respiration in vivo may be shared among the reactants in Reaction 1 (5). Chance further postulated that the relative contribution of each controller was dependent on the energetic state of the tissue (5). Notwithstanding the mounting evidence against free [ADP], its importance in the control of mitochondrial respiration has recently resurfaced with the 31 P NMR finding that the apparent kinetic order of [ADP] transduction is at least second order in intact human forearm (8). That free [ADP] and submaximal muscle work does not obey Michaelis-Menten kinetics has sparked a great deal of controversy (8,33). The aim of our study was to determine the relationship between free cytosolic [ADP] (and P i ) and tension-time integral (TTI) 1 in the rat gastrocnemius muscle in vivo. We show that free [ADP] (and P i ) and TTI followed an apparent second order function and that our data do not fit a Michaelis-Menten relationship.

EXPERIMENTAL PROCEDURES
Animal Preparation-Male Sprague-Dawley rats (350 -400 g body weight) were obtained from Animal Resources Center, Canningvale, Western Australia, Australia. Animals were housed in the James Cook University small animal facility with free access to food and water. Animals were anesthetized with an intraperitoneal injection of pentobarbital sodium (60 mg/kg), tracheotomized, and ventilated at the rate of 75 breaths/min with a tidal volume of ϳ25 ml to maintain arterial pH (7.4 Ϯ 0.5), pCO 2 (40 Ϯ 5 mmHg), and pO 2 (90 Ϯ 10 mmHg) (S.E.). Blood pH and gas tensions were analyzed using a Ciba-Corning 865 series analyzer. The right carotid artery was cannulated with heparinized (100 units/ml) polyethylene tubing connected to a Statham P23 XL pressure transducer coupled to a MacLab for continuous measurement of arterial blood pressure. Anesthesia was maintained by delivering 1% isofluorane in compressed air via artificial ventilation at a rate of 0.5 liter/min. The entire surgical procedure was performed on a thermostatically regulated heating pad (37°C).
Muscle Stimulation and Force Measurements-The right hindlimb was shaved, and two brass pins were driven through the calcaneum and tibial head with an electric drill. The animal was transferred to a purpose-built cradle pre-fitted with a 37°C water-heated pad, and the limb was immobilized by clamping the pins onto a mechanical ground in the cradle. For muscle stimulation, bipolar electrodes were attached to the right sciatic nerve exposed by blunt dissection of overlying tissue. The nerve was then severed distal to the electrodes. The tendon of the gastrocnemius muscle was freed from the leg and attached to a calibrated ultra precision mini load cell (Transducer Techniques, MDB10) with non-compliant 2.0 silk string. Isometric force development (newtons) was continuously displayed on a MacLab. The muscle was carefully denuded of overlying tissue avoiding arteries and veins, and covered with plastic film to prevent the exposed tissue from drying out. Muscles under these conditions maintained a constant internal temperature of 30 Ϯ 1°C throughout the experiment (n ϭ 5). Muscle temperature was measured in separate experiments using a YSI 500 series micro-implantable thermistor probe.
The muscle was adjusted to the length at which maximum twitch force was developed during a supramaximal contraction in response to a square-wave pulse (0.1 ms, 5-15 V). The TTI, defined as the sum of the area under the twitches over the acquisition period in the NMR spectra, was used as an index of muscle work with units of Newtons second (Ns). The twitch tension-time integral was found to be a linear function of stimulation frequency during steady-state aerobic work (data not shown). The equation to the line was TTI ϭ 46.98 stimulation frequency ϩ2.26 R 2 ϭ 0.99, giving a TTI at 0 Hz of 1.37 Ns. Each animal served as its own control precluding the need to normalize the data by muscle volume. The whole apparatus was introduced into the bore of an Oxford Instruments horizontal NMR magnet.
Nuclear Magnetic Resonance-31 P NMR experiments were performed at 121.47 MHz in the 110-mm bore of an Oxford 7.05-tesla superconducting magnet. A three-turn surface coil (14 mm outer diameter) was placed at the center of the gastrocnemius muscle and served as transmitter and receiver. A small latex balloon filled with a solution of 10 mM phenylphosphonic acid in saline was placed above the coil in the same geometrical arrangement as the muscle below and served as an external standard. Magnetic field homogeneity was optimized by observing the off-resonance proton signal of muscle water. The surface coil was tuned and matched to resonate at 121.47 MHz. All NMR experiments were performed using a radio frequency pulse of 10-s duration, which was transmitted at a near 90 o flip angle by the surface coil. 31 P NMR spectra were collected as 9600 data points using a sweep-width of 6000 Hz. The free induction decays were acquired over 0.8 s with an interpulse delay time of 1 s. The free induction decays were multiplied by a line broadening factor equivalent to 20 Hz to improve signal-to-noise ratio. Resultant line widths for the in vivo muscle experiments were typically 40 -60 Hz. The radio frequency pulse was not synchronized with a nerve stimulation. The advantage of 31 P NMR is that the method is noninvasive and provides continuous measurements of phosphorus metabolites in real time in one animal, including direct estimates of pH and free [Mg 2ϩ ]. The limitation of the NMR technique, as with conventional metabolic analysis, is that the measurements cannot discriminate the different contributions of fiber types.
Experimental Protocol and Definition of Steady State-Fully relaxed spectra with a relaxation delay of 20 s was collected for 30 min at the beginning of each experiment to determine the saturation correction factors for each of the phosphorus-containing compounds (see "Quantitation of NMR Spectra"). Control spectra were obtained for 7 min (256 transients) before the muscle was stimulated to contract isometrically at frequencies of 0.1, 0.2, 0.3, 0.4, and 0.5 Hz and either 0.8 Hz (n ϭ 4), 1 Hz (n ϭ 7), or 2 Hz (n ϭ 7). For each stimulation frequency in the three groups, spectra were acquired in 4-min blocks each with 128 transients. Muscles were allowed to recover for 20 min between each stimulation frequency to restore the contraction force and PCr and P i to prestimulation levels. The total time for each of the three protocols was about 3 h. The force and NMR data were then analyzed to establish a steady state in which twitch tension and PCr and P i were constant in two consecutive spectra (9,10). We showed that steady state was reached between 8 and 12 min of stimulation up to 0.8 Hz (see "Results").
Parallel experiments were carried out on the laboratory bench and muscles freeze-clamped following 10 min of stimulation at each of the frequencies using aluminum tongs pre-cooled in liquid nitrogen. The freeze-clamped muscles were ground to a fine powder under liquid nitrogen, the connective tissue was removed, and the powder kept at Ϫ80°C until analysis of lactate, glycogen, pyruvate, PCr, and Cr. Conversion of total tissue contents (micromoles/g wet weight) into intracellular concentrations (micromoles/ml) were carried out using our published extracellular space values and total tissue water contents reported for rat gastrocnemius in vivo (11). In the present study we also measured the extracellular spaces at 1 and 2 Hz and found them to be 18% and 17%, respectively. The values were not significantly different from the 16% we report in vivo (11).
Biochemical Assays-All chemicals used in the metabolic assays were purchased from either Sigma or Roche Molecular Biochemicals and were of the highest grade. Frozen tissue (ϳ100 mg) was homogenized in equal volumes of ice-cold 0.1 M HCl in methanol and 3.6% perchloric acid (12) using glass beads in a high speed Biospec mini-BeadBeater. The homogenate was centrifuged (9,000 ϫ g; 2 min) and a volume of acid-extract removed and mixed with an aliquot of KHCO 3 (0.3 and 0.2 M stocks) to neutralize (pH 6 -7). The supernatant was immediately measured either spectrophotometrically or fluorometrically for pyruvate, lactate, PCr, and creatine according to the methods of Passoneau and Lowry (12). Total tissue glycogen was measured separately according to the method of Passoneau (13). Briefly, 1 ml of 0.5 M NaOH was added to frozen tissue (ϳ50 mg) and heated in boiling water for 20 -30 min to remove tissue free glucose. The suspension was made acidic with a known volume of 12 N HCl (pH Ͻ 3.0). An aliquot of acid extract (ϳ50 l) was removed and added to 950 l of 200 mM acetate buffer (pH 4.7) containing amylo-␣-1,4-␣-1,6-glucosidase to digest tissue glycogen. Following 2 h of incubation, the acid extract was fluorometrically assayed for glucose (13).
Quantitation of NMR Spectra-31 P NMR spectral intensities for the phosphorus-containing compounds were determined by computer integration using the VNMRX software. Saturation correction factors were determined by taking the ratio of the area under a given peak with a 20-s relaxation delay to the area of the spectra with a 1-s relaxation delay. The mean correction factors for the 10 mM phenylphosphonic acid external standard, P i , PCr, and ␤-ATP were 2.20 Ϯ 0.05, 1.80 Ϯ 0.06, 1.56 Ϯ 0.0, and 1.22 Ϯ 0.02 (Ϯ S.E., n ϭ 18), respectively. Intracellular concentrations of the ␤-ATP, PCr, and P i were calculated by equating the spectral intensities of the saturation-corrected phosphorus metabolites to the spectral intensity of the saturation-corrected external standard (10 mM Intracellular pH (pH i ) was calculated from the chemical shift (␦, ppm) of P i relative to PCr in the 31 P spectra using the NMR version of the Henderson-Hasselbalch equation (1).
Intracellular free Mg 2ϩ concentration ([Mg 2ϩ ] i ) was calculated from the observed chemical shift difference (␦ ␣␤ ) in ppm between ␤-P and ␣-P resonances of ATP in the 31 P spectra using the modified form of the London equation (14),

Establishment of Steady-state and Apparent Aerobic V max of
Muscle-Steady-state was defined in terms of relatively constant TTI and concentrations of PCr and P i measured at the different stimulation frequencies in consecutive spectra acquired in 4-min blocks (Fig. 1). Mean values for TTI were similarly calculated in three blocks of 4 min to coincide with the NMR acquisition period. Fig. 1a shows no significant differences in TTI for the stimulation frequencies between 0.1 and 0.8 Hz over the 12-min time period. Significant changes were observed at 1 and 2 Hz. At all stimulation frequencies, PCr fell significantly during the first and second periods of acquisition (0 -8 min) (Fig. 1b). With the exception of 1 and 2 Hz, metabolic steady state was reached during the period between 8 and 12 min. A similar profile was found with the increase in muscle P i concentration at the different stimulation frequencies (Fig. 1c).
In parallel bench experiments, muscles were freeze-clamped following 10 min of stimulation and glycogen, lactate, and pyruvate were measured enzymatically (Table I). Up to 0.5 Hz, there was no significant difference in muscle glycogen, lactate, and pyruvate compared with controls. At 0.8 Hz, a significant rise in lactate and pyruvate (p Ͻ 0.05) was observed with a concomitant fall in glycogen. It was not until 1 and 2 Hz that glycogen fell as low as 30% of control, lactate increased up to 5-fold, and lactate/pyruvate ratio increased 3-fold (Table I). NMR determined cytosolic pH, also reported in Table I, was not significantly different from controls up to 0.5 Hz but significantly decreased from 7.203 to 7.050 at 0.8 Hz. On the basis of these changes in TTI and accompanying metabolic data, we estimated that the maximal mitochondrial capacity in rat gastrocnemius in situ under our conditions was around 0.8 Hz.

Changes in the PCr, ATP, Cr, Free [Mg 2ϩ ], and Calculation of Free [ADP] from the Creatine Kinase
Equilibrium-NMR determined PCr, ATP, P i , and free Mg 2ϩ in rat gastrocnemius muscle in vivo during the 8 -12 min of stimulation are reported in Table II. During submaximal steady-state work transitions, PCr fell in significantly different increments (p Ͻ 0.05) at each stimulation frequency up to 0.8 Hz (Table II). The work-induced fall in PCr was accompanied by a stoichiometric rise in intracellular P i concentration (Table II). It is noteworthy that ATP began to decrease at 2Hz when PCr was about 30% of the control value (Table II). ATP was not considered part of our aerobic steady-state criteria because it remained constant up to and including 1.0 Hz, presumably through PCr hydrolysis and the activation of anaerobic glycogenolysis (Tables I and II). Free [Mg 2ϩ ] was not significantly different up to 1 Hz but increased by 50% at 2 Hz.
Free cytosolic [ADP] was 17 M in the gastrocnemius prior to stimulation and increased with increasing stimulation frequency and tension-time integral (Fig. 2a). The equation to the line up to 0.8 Hz was TTI ϭ 46.984 ([ADP]) ϩ 2.2562 with R 2 ϭ 0.9945. When free [ADP] was plotted against TTI using the Hill relationship, given a V max of 39 Ns at 0.8 Hz, a Hill coefficient (n H ) of 2.4 was found (Fig. 2b). The equation to the line was log(TTI/V max Ϫ TTI) ϭ 2.38 (log ADP) Ϫ 4.00 with R 2 ϭ 0.99. The apparent K 0.5 of ADP for submaximal steady-state stimulation was 48 M. A similar analysis was performed with increases in cytosolic [P i ]. A Hill coefficient of 2.1 was obtained. The equation to the line was log(TTI/V max Ϫ TTI) ϭ 2.14(log[P i ]) Ϫ 2.08 with R 2 ϭ 0.96 (graph not shown). The apparent K 0.5 value of free [P i ] for submaximal steady-state work was 9.4 mM. The data for free cytosolic [ADP] (and free [P i ]) and TTI did not fit any form of the Michaelis-Menten function, i.e. the Lineweaver-Burke plot showed no tendency to intersect the y axis (Fig. 2c). Similarly, the Eadie-Hofstee and Hanes Plot followed no sensible form, leading to the calculation of a kinetic V max or apparent K m (plots not shown). DISCUSSION There has been much controversy in recent years about whether the relationship between oxygen consumption and free [ADP] follows a first order Michaelis-Menten function or higher order sigmoidal function. Our study shows that ADP and TTI follows a Hill relationship with at least a second order function. Before we discuss these findings in relation to other studies, it is important to first discuss the assumptions of our model that form the basis of our results. The assumptions are: 1) our study applies to submaximal steady-state levels of aerobic activity, 2) the maximal mitochondrial capacity for aerobic work in rat gastrocnemius was in the vicinity of 0.8 Hz, and 3) the tensiontime index provides a reliable estimate of oxygen consumption during steady-state work. Our first two assumptions were supported on the basis of our force and metabolic measurements in the magnet and on the bench. Fig. 1 clearly shows that no The points on the PCr and P i curves represent the time-averaged mean of the NMR spectra acquired in 4-min blocks. TTI values represent the sum of the area under the twitch over the acquisition period. The vertical bars represent the standard errors from the mean. The force and metabolic data from the three groups were pooled for the frequencies between 0.1 and 0.5 Hz, giving a total n value of 18. change occurred in twitch tension, PCr, and P i between the second and third spectra up to 0.8 Hz. Moreover, there was no significant change in muscle lactate, glycogen, and pH indicating a physiological and metabolic steady state (Tables I and II). Our study therefore differs from most in this area by experimentally determining the apparent maximum aerobic mitochondrial capacity (V max ) in situ not from fitting the data to a specific mathematical relation (8,(17)(18)(19). The third assumption, that tension-time index provides a reliable estimate of oxygen consumption, has been shown by many studies in the past for skeletal muscle (9, 10, 20 -24) and heart (25,26). For the rat hindlimb in vivo, Brindle et al. also have shown a linear function between tension-time integral and ATP turnover (23). Kushmerick and Paul also showed a linear relation between recovery oxygen consumption and TTI in frog sartorius (27).
Our Hill coefficient (n H ) for [ADP] and TTI of 2.4 for rat gastrocnemius in situ is consistent with the published work of 2.2 for human forearm muscle (8,19). Prior to the work of Jeneson et al. in 1996 (8), the relationship between steady-state work and free [ADP] had been assumed in vivo to follow a Michaelis-Menten function in rat leg muscle (28), cat perfused biceps (29), and human arm muscle (30). Some of the problems associated with these older kinetic analysis have been discussed by Kemp (31) and more recently by Jeneson et al. (8,32) with a reply from Portman et al. (33). The present study supports the idea that the relationship between oxygen consumption and free [ADP] follows at least a second order sigmoidal function.
In addition, the apparent K 0.5 of [ADP] of 48 M for tension time index (and oxygen consumption) we report in the present study is also consistent with some literature values. Again, this is a very controversial area. In 1989, Brindle and co-workers reported an apparent K m of at least 30 M for rat hindlimb in situ under steady-state submaximal exercise (23). These data have subsequently been recalculated to give an apparent K m of about 50 M (18,34). Similarly, Thompson and colleagues in 1995 studied phosphocreatine recovery in rat leg muscle in vivo and reported an apparent K m of ADP greater than 30 M. In ex vivo perfused cat biceps, Kushmerick and colleagues (29) calculated an apparent K m for free [ADP] of 23 M, a value similar to 26 M for rabbit gastrocnemius/soleus muscle groups in vivo (24). Better agreement is found with the work of Jeneson and co-workers (8), who calculated an apparent K 0.5 of ADP of 44 M in human forearm flexor muscle (8).
One possible concern that could be raised with our kinetic analysis is that the tension-time integral does not saturate with free [ADP] in vivo (Fig. 2a). This is to be expected in an intact muscle because of the recruitment of competing metabolic pathways and fuels to maintain ATP constant as the muscle approaches its maximal aerobic capacity. Indeed, in our study, ATP did not fall significantly until 2 Hz, which is far in excess of our estimate of aerobic V max for rat gastrocnemius based on lactate, glycogen, and pH values (Tables I and II). Because our system does not saturate in free [ADP] levels in situ, it does not therefore compromise our kinetic analysis.
Significance of Our Findings to the Control of Respiration in Vivo-A controller of mitochondrial steady-state oxygen consumption must fulfil a number of criteria. First, the pre-exercise steady-state level of the controller must be set at a concentration below or around its K 0.5 for oxygen consumption. Second, the controller must increase as oxygen consumption increases. Third, the controller must directly or indirectly regulate a specific rate-limiting enzyme(s) along the pathway. ADP has been a potential candidate for a role in regulating oxygen consumption for over 45 years (1,3). Other potential kinetic and thermodynamic controllers have been ATP (35) (17,43,44), and the oxygen concentration at cytochrome c (38,40). Our present study shows that the free cytosolic [ADP] fulfils these three criteria in rat gastrocnemius in vivo. However, on the basis of our data and others, it is premature to conclude that free [ADP] is the actual controller because we also show that free cytosolic [P i ] fulfils the same criteria. During increasing steady-state work, P i increased 8-fold from 3 to 16 mM up to 0.8 Hz (Figs. 1 and 2 and Table II). The apparent K 0.5 was calculated to be 9 mM and followed at least a second order relationship with tension time index. Our apparent K 0.5 for [P i ] of 9 mM for rat gastrocnemius is lower than the 19 mM reported for rabbit gastrocnemius (24). In our study neither change in free ADP or P i concentration with muscle work fit a Michaelis-Menten relationship. As Jeneson et al. (32) pointed out, the possibility also exists that the apparent overall kinetic order of the ADP-TTI relationship may also reflect [P i ] stimulation of respiration because in our model P i was found to lie within its apparent K 0.5 of 9.0 mM.
Another very interesting study relevant to our work is that of Arnold and Kadenbach (38), who in 1999 showed a sigmoidal relationship (average Hill coefficient of 2.9) between [ADP] and the activity of cytochrome c oxidase. From this relation, they suggested the possibility of regulation of respiration by intramitochondrial [ADP] (38). These authors, however, did not dismiss a role for [ADP] in the regulation of NADH dehydrogenase and cytochrome c reductase in the overall pacemaker of cell respiration (38). One difference between our study and theirs was Arnold and Kadenbach determined a matrix halfmaximal ADP stimulation of cytochrome c oxidase of 170 M (38). This value is over 3 times the "cytosolic" apparent K m of [ADP] we report for tension-time index (and presumably oxygen consumption). The highest cytosolic [ADP] we measured up to 0.8 Hz stimulation frequency was around 80 M (Table II). Arnold and Kadenbach do, however, note that mitochondrial membrane potential and the electrogenicity of the nature of the ATP/ADP carrier would result in a lower matrix ATP/ADP ratio due to higher [ADP], which they argue would be consistent with their kinetic work. We therefore conclude on the basis of our data that ADP and P i could potentially control incremental increases in steady-state work in skeletal muscle in vivo.