Muscle force, work and cost: a novel technique to revisit the Fenn effect

Muscle produces force by forming cross-bridges, using energy released from ATP. While the magnitude and duration of force production primarily determine the energy requirement, nearly a century ago Fenn observed that muscle shortening or lengthening influenced energetic cost of contraction. When work is done by the muscle, the energy cost is increased and when work is done on the muscle the energy cost is reduced. However, the magnitude of the 'Fenn effect' and its mirror ('negative Fenn effect') have not been quantitatively resolved. We describe a new technique coupling magnetic resonance spectroscopy with an in vivo force clamp that can directly quantify the Fenn effect [E=I+W, energy liberated (E) equals the energy cost of isometric force production (I) plus the work done (W)] and the negative Fenn effect (E=I-W) for one muscle, the first dorsal interosseous (FDI). ATP cost was measured during a series of contractions, each of which occurred at a constant force and for a constant duration, thus constant force-time integral (FTI). In all subjects, as the FTI increased with load, there was a proportional linear increase in energy cost. In addition, the cost of producing force greatly increased when the muscle shortened, and was slightly reduced during lengthening contraction. These results, though limited to a single muscle, contraction velocity and muscle length change, do quantitatively support the Fenn effect. We speculate that they also suggest that an elastic element within the FDI muscle functions to preserve the force generated within the cross-bridges.

High efficiency in human muscle: an anomaly and an opportunity?

Can human muscle be highly efficient in vivo? Animal muscles typically show contraction-coupling efficiencies <50% in vitro but a recent study reports that the human first dorsal interosseous (FDI) muscle of the hand has an efficiency value in vivo of 68%. We examine two key factors that could account for this apparently high efficiency value: (1) transfer of cross-bridge work into mechanical work and (2) the use of elastic energy to do external work. Our analysis supports a high contractile efficiency reflective of nearly complete transfer of muscular to mechanical work with no contribution by recycling of elastic energy to mechanical work. Our survey of reported contraction-coupling efficiency values puts the FDI value higher than typical values found in small animals in vitro but within the range of values for human muscle in vivo. These high efficiency values support recent studies that suggest lower Ca(2+) cycling costs in working contractions and a decline in cost during repeated contractions. In the end, our analysis indicates that the FDI muscle may be exceptional in having an efficiency value on the higher end of that reported for human muscle. Thus, the FDI muscle may be an exception both in contraction-coupling efficiency and in Ca(2+) cycling costs, which makes it an ideal muscle model system offering prime conditions for studying the energetics of muscle contraction in vivo.

Quantitative in vivo magnetic resonance spectroscopy using synthetic signal injection

Accurate conversion of magnetic resonance spectra to quantitative units of concentration generally requires compensation for differences in coil loading conditions, the gains of the various receiver amplifiers, and rescaling that occurs during post-processing manipulations. This can be efficiently achieved by injecting a precalibrated, artificial reference signal, or pseudo-signal into the data. We have previously demonstrated, using in vitro measurements, that robust pseudo-signal injection can be accomplished using a second coil, called the injector coil, properly designed and oriented so that it couples inductively with the receive coil used to acquire the data. In this work, we acquired nonlocalized phosphorous magnetic resonance spectroscopy measurements from resting human tibialis anterior muscles and used pseudo-signal injection to calculate the Pi, PCr, and ATP concentrations. We compared these results to parallel estimates of concentrations obtained using the more established phantom replacement method. Our results demonstrate that pseudo-signal injection using inductive coupling provides a robust calibration factor that is immune to coil loading conditions and suitable for use in human measurements. Having benefits in terms of ease of use and quantitative accuracy, this method is feasible for clinical use. The protocol we describe could be readily translated for use in patients with mitochondrial disease, where sensitive assessment of metabolite content could improve diagnosis and treatment.

Common phenotype of resting mouse extensor digitorum longus and soleus muscles: equal ATPase and glycolytic flux during transient anoxia

Rates of ATPase and glycolysis are several times faster in actively contracting mouse extensor digitorum longus muscle (EDL) than soleus (SOL), but we find these rates are not distinguishable at rest. We used a transient anoxic perturbation of steady state energy balance to decrease phosphocreatine (PCr) reversibly and to measure the rates of ATPase and of lactate production without muscle activation or contraction. The rate of glycolytic ATP synthesis is less than the ATPase rate, accounting for the continual PCr decrease during anoxia in both muscles. We fitted a mathematical model validated with properties of enzymes and solutes measured in vitro and appropriate for the transient perturbation of these muscles to experimental data to test whether the model accounts for the results. Simulations showed equal rates of ATPase and lactate production in both muscles. ATPase controls glycolytic flux by feedback from its products. Adenylate kinase function is critical because a rise in [AMP] is necessary to activate glycogen phosphorylase. ATPase is the primary source of H+ production. The sum of contributions of the 13 reactions of the glycogenolytic and glycolytic network to total proton load is negligible. The stoichiometry of lactate and H+ production is near unity. These results identify a default state of energy metabolism for resting muscle in which there is no difference in the metabolic phenotype of EDL and SOL. Therefore, additional control mechanisms, involving higher ATPase flux and [Ca2+], must exist to explain the well-known difference in glycolytic rates in fast-twitch and slow-twitch muscles in actively contracting muscle.

Lactic acidosis in vivo: testing the link between lactate generation and H+ accumulation in ischemic mouse muscle

The link between lactate generation and cellular acidosis has been questioned based on the possibility of H+ generation, independent of lactate production during glycolysis under physiological conditions. Here we test whether glycolytic H+ generation matches lactate production over a physiological pH and lactate range using ischemia applied to the hindlimb of a mouse. We measured the H+ generation and ATP level in vivo using 31P-magnetic resonance spectroscopy and chemically determined intracellular lactate level in the hindlimb muscles. No significant change was found in ATP content by chemical analysis (P>0.1), in agreement with the stoichiometric decline in phosphocreatine (20.2+/-1.2 mM) vs. rise in Pi (18.7+/-2.0 mM), as measured by 31P-magnetic resonance spectroscopy. A substantial drop in pH from 7.0 to 6.7 and lactate accumulation to 25 mM were found during 25 min of ischemia. The rise in H+ generation closely agreed with the accumulation of lactate, as shown by a close correlation with a slope near identity (0.98; r2=0.86). This agreement between glycolytic H+ production and elevation of lactate is confirmed by an analysis of the underlying reactions involved in glycolysis in vivo and supports the concept of lactic acidosis under conditions that substantially elevate lactate and drop pH. However, this link is expected to fail with conditions that deplete phosphocreatine, leading to net ATP hydrolysis and nonglycolytic H+ generation. Thus both direct measurements and an analysis of the stoichiometry of glycolysis in vivo support lactate acidosis as a robust concept for physiological conditions of the muscle cell.

Immune responses to AAV in canine muscle monitored by cellular assays and noninvasive imaging

We previously demonstrated that direct intramuscular injection of rAAV2 or rAAV6 in wild-type dogs resulted in robust T-cell responses to viral capsid proteins, and others have shown that cellular immunity to adeno-associated virus (AAV) capsid proteins coincided with liver toxicity and elimination of transgene expression in a human trial of hemophilia B. Here, we show that the heparin-binding ability of a given AAV serotype does not determine the induction of T-cell responses following intramuscular injection in dogs, and identify multiple epitopes in the AAV capsid protein that are recognized by T cells elicited by AAV injection. We also demonstrate that noninvasive magnetic resonance imaging (MRI) can accurately detect local inflammatory responses following intramuscular rAAV injection in dogs. These studies suggest that pseudotyping rAAV vectors to remove heparin-binding activity will not be sufficient to abrogate immunogenicity, and validate the utility of enzyme-linked immunosorbent spot (ELISpot) assay and MRI for monitoring immune and inflammatory responses following intramuscular injection of rAAV vectors in preclinical studies in dogs. These assays should be incorporated into future human clinical trials of AAV gene therapy to monitor immune responses.

Synthetic signal injection using inductive coupling

Conversion of MR signals into units of metabolite concentration requires a very high level of diligence to account for the numerous parameters and transformations that affect the proportionality between the quantity of excited nuclei in the acquisition volume and the integrated area of the corresponding peak in the spectrum. We describe a method that eases this burden with respect to the transformations that occur during and following data acquisition. The conceptual approach is similar to the ERETIC method, which uses a pre-calibrated, artificial reference signal as a calibration factor to accomplish the conversion. The distinguishing feature of our method is that the artificial signal is introduced strictly via induction, rather than radiation. We tested a prototype probe that includes a second RF coil rigidly positioned close to the receive coil so that there was constant mutual inductance between them. The artificial signal was transmitted through the second RF coil and acquired by the receive coil in parallel with the real signal. Our results demonstrate that the calibration factor is immune to changes in sample resistance. This is a key advantage because it removes the cumbersome requirement that coil loading conditions be the same for the calibration sample as for experimental samples. The method should be adaptable to human studies and could allow more practical and accurate quantification of metabolite content.

Contraction coupling efficiency of human first dorsal interosseous muscle

During working contractions, chemical energy in the form of ATP is converted to external work. The efficiency of this conversion, called 'contraction coupling efficiency', is calculated by the ratio of work output to energy input from ATP splitting. Experiments on isolated muscles and permeabilized fibres show the efficiency of this conversion has a wide range, 0.2-0.7. We measured the work output in contractions of a single human hand muscle in vivo and of the ATP cost of that work to calculate the contraction coupling efficiency of the muscle. Five subjects performed six bouts of rapid voluntary contractions every 1.5 s for 42 s (28 contractions, each with time to peak force < 150 ms). The bouts encompassed a 7-fold range of workloads. The ATP cost during work was quantified by measuring the extent of chemical changes within the muscle from (31)P magnetic resonance spectra. Contraction coupling efficiency was determined as the slope of paired measurements of work output and ATP cost at the five graded work loads. The results show that 0.68 of the chemical energy available from ATP splitting was converted to external work output. A plausible mechanism to account for this high value is a substantially lower efficiency for mitochondrial ATP synthesis. The method described here can be used to analyse changes in the overall efficiency determined from oxygen consumption during exercise that can occur in disease or with age, and to test the hypothesis that such changes are due to reduced contraction coupling efficiency.

Accurate myoglobin oxygen saturation by optical spectroscopy measured in blood-perfused rat muscle

Optical spectra were acquired from myoglobin and hemoglobin solutions and from the tibialis anterior muscle of Sprague-Dawley rats in the visible region (515 to 660 nm). Validation studies were performed on the in vitro spectra to demonstrate that partial least squares analysis of second-derivative spectra yields accurate measurements of myoglobin saturation in the presence of varying hemoglobin concentrations and saturations. When hemoglobin concentrations were varied between 0.25 and 4 times that of myoglobin, myoglobin saturations were measured with a root mean squared error (RMSE) of 4.9% (n = 56) over the full range from 0 to 1. Myoglobin saturations were also shown to be largely unaffected by hemoglobin saturation. RMSE values of only 1.7% (n = 77) were found when hemoglobin saturations were varied independently from myoglobin saturations. These in vitro validation studies represent the most complete and rigorous done to date using partial least squares analysis on myoglobin and hemoglobin spectra. Analysis of reflectance spectra from the rat hind limb yielded accurate measures of volume-averaged myoglobin fractional saturation in the presence of hemoglobin in vivo. Hemodilution showed that myoglobin fractional saturation measurements in the rat leg are not sensitive to changes in hematocrit, thereby confirming the results from solutions in vitro. Decreases in optical density of 11.3 +/- 3.0% (n = 3) were achieved while myoglobin saturation decreased by only 3.1 +/- 3.8%. Myoglobin saturation was significantly increased when the fraction of inspired O(2) was increased, showing that manipulations of myoglobin saturation are detectable and that myoglobin is not fully saturated in resting muscle. Together, these in vitro and in vivo studies show that cellular oxygenation derived from myoglobin fractional saturation can be measured accurately with little cross-talk from hemoglobin in the visible wavelength region, thereby extending optical spectroscopic studies of cellular and vascular oxygenation beyond the near-infrared regions previously studied.

Time-courses of perfusion and phosphocreatine in rat leg during low-level exercise and recovery

PURPOSE

To develop a noninvasive protocol for measuring local perfusion and metabolic demand in muscle tissue with sufficient sensitivity and time resolution to monitor kinetics at the onset of low-level exercise and during recovery.

MATERIALS AND METHODS

Capillary-level perfusion, the critical factor that determines oxygen and substrate delivery to active muscle, was measured by an arterial spin labeling (ASL) technique optimized for skeletal muscle. Phosphocreatine (PCr) kinetics, which signal the flux of oxidative phosphorylation, were measured by (31)P MR spectroscopy. Perfusion and PCr measurements were made in parallel studies before, during, and after three different intensities of low-level, stimulated exercise in rat hind limb.

RESULTS

The data reveal close coupling between the perfusion response and PCr changes. The onset and recovery time constants for PCr changes were independent of contractile force over the range of forces studied. Perfusion time constants during both onset of exercise and recovery tended to increase with contractile force.

CONCLUSION

These results demonstrate that the protocol implemented can be useful for probing the mechanisms that control skeletal muscle blood flow, the physiological limits to muscle performance, and the causes for the attenuated exercise-induced hyperemia observed in disease states.

Mild mitochondrial uncoupling impacts cellular aging in human muscles in vivo

Faster aging is predicted in more active tissues and animals because of greater reactive oxygen species generation. Yet age-related cell loss is greater in less active cell types, such as type II muscle fibers. Mitochondrial uncoupling has been proposed as a mechanism that reduces reactive oxygen species production and could account for this paradox between longevity and activity. We distinguished these hypotheses by using innovative optical and magnetic resonance spectroscopic methods applied to noninvasively measured ATP synthesis and O(2) uptake in vivo in human muscle. Here we show that mitochondrial function is unchanged with age in mildly uncoupled tibialis anterior muscle (75% type I) despite a high respiratory rate in adults. In contrast, substantial uncoupling and loss of cellular [ATP] indicative of mitochondrial dysfunction with age was found in the lower respiring and well coupled first dorsal interosseus (43-50% type II) of the same subjects. These results reject respiration rate as the sole factor impacting the tempo of cellular aging. Instead, they support mild uncoupling as a mechanism protecting mitochondrial function and contributing to the paradoxical longevity of the most active muscle fibers.

Dynamics of muscle glycogenolysis modeled with pH time course computation and pH-dependent reaction equilibria and enzyme kinetics

Cellular metabolites are moieties defined by their specific binding constants to H+, Mg2+, and K+ or anions without ligands. As a consequence, every biochemical reaction in the cytoplasm has an associated proton stoichiometry that is generally noninteger- and pH-dependent. Therefore, with metabolic flux, pH is altered in a medium with finite buffer capacity. Apparent equilibrium constants and maximum enzyme velocities, which are functions of pH, are also altered. We augmented an earlier mathematical model of skeletal muscle glycogenolysis with pH-dependent enzyme kinetics and reaction equilibria to compute the time course of pH changes. Analysis shows that kinetics and final equilibrium states of the closed system are highly constrained by the pH-dependent parameters. This kinetic model of glycogenolysis, coupled to creatine kinase and adenylate kinase, simulated published experiments made with a cell-free enzyme mixture to reconstitute the network and to synthesize PCr and lactate in vitro. Using the enzyme kinetic and thermodynamic data in the literature, the simulations required minimal adjustments of parameters to describe the data. These results show that incorporation of appropriate physical chemistry of the reactions with accurate kinetic modeling gives a reasonable simulation of experimental data and is necessary for a physically correct representation of the metabolic network. The approach is general for modeling metabolic networks beyond the specific pathway and conditions presented here.

FAWSETS perfusion measurements in exercising skeletal muscle

Arterial spin labeling (ASL) techniques are now recognized as valid tools for providing accurate measurements of cerebral and cardiac perfusion. The labeling process used with most ASL techniques creates two problems, magnetization transfer (MT) effects and arterial transit time effects, that require compensation. The compensation process limits time resolution and hinders absolute quantification. MT effects are particularly problematic in skeletal muscle because they are large and change rapidly during exercise. The protocol presented here was developed specifically for quantification of perfusion in exercising skeletal muscle. The ASL technique that was implemented, FAWSETS, eliminates MT effects and arterial transit times. Localized, single-voxel perfusion measurements were acquired from rat hind limbs at rest, during ischemia and during three different levels of stimulated exercise. The results demonstrate sufficient sensitivity to determine the time constants for perfusion changes at onset of, and during recovery from, exercise and to distinguish the differences in the amplitude of the perfusion response to different levels of exercise. Additional measurements were conducted to demonstrate insensitivity to MT effects. The exercise protocol is easily adaptable to phosphorous magnetic resonance measurements, allowing the possibility to acquire local measurements of perfusion and metabolism from the same tissue in future experiments.

Estimating in vitro mitochondrial oxygen consumption during muscle contraction and recovery: a novel approach that accounts for diffusion

A deconvolution algorithm, based on a Bayesian statistical framework and smoothing spline technique, is applied to reconstructing input functions from noisy measurements in biological systems. Deconvolution is usually ill-posed. However, placing a Bayesian prior distribution on the input function can make the problem well-posed. Using this algorithm and a computational model of diffusional oxygen transport in an approximately cylindrical muscle (about 0.5-mm diameter and 10-mm long mouse leg muscle), the time course of muscle oxygen uptake and mitochondrial oxygen consumption, both during isometric twitch contractions (at various frequencies) and the recovery period, is estimated from polarographic measurements of oxygen concentration on the muscle surface. An important feature of our experimental protocol is the availability of data for the apparatus characteristics. From these time courses, the actual mitochondrial consumption rates during resting and exercise states can be estimated. Mitochondrial oxygen consumption rate increased during stimulation to a maximum steady state value approximately five times of the resting value of 0.63 nmol/s/g wet weight for the stimulation conditions studied. Diffusion slowed the kinetic responses to the contraction but not the steady state fluxes during the stimulation interval.

Validation and advantages of FAWSETS perfusion measurements in skeletal muscle

This work discusses the strengths, limitations and validity of a novel arterial spin labeling technique when used specifically to measure perfusion in limb skeletal muscle. The technique, flow-driven arterial water stimulation with elimination of tissue signal (FAWSETS), offers several advantages over existing arterial spin labeling techniques. The primary goal of this study was to determine the perfusion signal response to changes in net hind limb flow that were independently verifiable. The range of perfusate flow was relevant to skeletal muscle during mild to moderate exercise. Localized, single voxel measurements were acquired from a 5 mm-thick slice in the isolated perfused rat hind limb at variable net flow rates. The results show that the perfusion signal is linearly proportional to net hind limb flow with a correlation coefficient of 0.974 (p = 0.0013). FAWSETS is especially well suited for studies of skeletal muscle perfusion, where it eliminates the need to compensate for magnetization transfer and arterial transit time effects. A conceptual discussion of the basic principles underlying these advantages is presented.

Three dimensional ultrasound analysis of fascicle orientation in human tibialis anterior muscle enables analysis of macroscopic torque at the cellular level

The purpose of this study was to test the hypothesis that the internal structure of the bipennate human tibialis anterior muscle is sufficiently homogenous throughout the muscle that the cellular stresses could be interpreted correctly from measurable anatomic properties and torque in the limb. This result is needed for facile comparison of extrinsic mechanical data and intrinsic energetic fluxes. Three-dimensional imaging of the fascicles of the human tibialis anterior muscle was made by capturing a series of ultrasound images while registering their location in space. Subsequent tracing of hundreds of structures in the ultrasound images with the use of custom software identified muscle boundaries, tendon surfaces, and fascicles as anatomic elements in 3-D space. The tendon was reconstructed as a mesh through the tracings identified as a component of the tendon. The angle of insertion of each identified fascicle at the tendon was calculated against the nearest normal in the mesh of the tendon. In three subjects the average angle of insertion of the fascicles onto the internal tendon was 11 degrees (coefficient of variation 40%). The angle decreased along the length of the muscle from approximately 15 degrees near the belly of the muscle to 6 degrees near the ankle in fascicles superior and inferior to the central tendon. The angle increased by several degrees during a voluntary contraction. Despite the differences in angles of insertion that can be measured, these distinctions have little significance for the distribution of forces along cellular axes within the muscle: the angles, their distribution within the muscle and change with contraction are small. For this bipennate muscle the cosine of the angle of insertion of the cellular bundles is always close to unity. Thus measurements of whole muscle mechanical data are simply related to mechanical stress of its cells.

Basal glycogenolysis in mouse skeletal muscle: in vitro model predicts in vivo fluxes

A previously published mammalian kinetic model of skeletal muscle glycogenolysis, consisting of literature in vitro parameters, was modified by substituting mouse specific Vmax values. The model demonstrates that glycogen breakdown to lactate is under ATPase control. Our criteria to test whether in vitro parameters could reproduce in vivo dynamics was the ability of the model to fit phosphocreatine (PCr) and inorganic phosphate (Pi) dynamic NMR data from ischemic basal mouse hindlimbs and predict biochemically-assayed lactate concentrations. Fitting was accomplished by optimizing four parameters--the ATPase rate coefficient, fraction of activated glycogen phosphorylase, and the equilibrium constants of creatine kinase and adenylate kinase (due to the absence of pH in the model). The optimized parameter values were physiologically reasonable, the resultant model fit the [PCr] and [Pi] timecourses well, and the model predicted the final measured lactate concentration. This result demonstrates that additional features of in vivo enzyme binding are not necessary for quantitative description of glycogenolytic dynamics.

Altered energetic properties in skeletal muscle of men with well-controlled insulin-dependent (type 1) diabetes

This study asked whether the energetic properties of muscles are changed by insulin-dependent diabetes mellitus (or type 1 diabetes), as occurs in obesity and type 2 diabetes. We used (31)P magnetic resonance spectroscopy to measure glycolytic flux, oxidative flux, and contractile cost in the ankle dorsiflexor muscles of 10 men with well-managed type 1 diabetes and 10 age- and activity-matched control subjects. Each subject performed sustained isometric muscle contractions lasting 30 and 120 s while attempting to maintain 70-75% of maximal voluntary contraction force. An altered glycolytic flux in type 1 diabetic subjects relative to control subjects was apparent from significant differences in pH in muscle at rest and at the end of the 120-s bout. Glycolytic flux during exercise began earlier and reached a higher peak rate in diabetic patients than in control subjects. A reduced oxidative capacity in the diabetic patients' muscles was evident from a significantly slower phosphocreatine recovery from a 30-s exercise bout. Our findings represent the first characterization of the energetic properties of muscle from type 1 diabetic patients. The observed changes in glycolytic and oxidative fluxes suggest a diabetes-induced shift in the metabolic profile of muscle, consistent with studies of obesity and type 2 diabetes that point to common muscle adaptations in these diseases.

Issues of exploration: human health and wellbeing during a mission to Mars

Today, the tools are in our hands to enable us to travel away from our home planet and become citizens of the solar system. Even now, we are seriously beginning to develop the robust infrastructure that will make the 21st century the Century of Space Travel. But this bold step must be taken with due concern for the health, safety and wellbeing of future space explorers. Our long experience with space biomedical research convinces us that, if we are to deal effectively with the medical and biomedical issues of exploration, then dramatic and bold steps are also necessary in this field. We can no longer treat the human body as if it were composed of muscles, bones, heart and brain acting independently. Instead, we must lead the effort to develop a fully integrated view of the body, with all parts connected and fully interacting in a realistic way. This paper will present the status of current (2000) plans by the National Space Biomedical Research Institute to initiate research in this area of integrative physiology and medicine. Specifically, three example projects are discussed as potential stepping stones towards the ultimate goal of producing a digital human. These projects relate to developing a functional model of the human musculoskeletal system and the heart.

A computational model for glycogenolysis in skeletal muscle

A dynamic model of the glycogenolytic pathway to lactate in skeletal muscle was constructed with mammalian kinetic parameters obtained from the literature. Energetic buffers relevant to muscle were included. The model design features stoichiometric constraints, mass balance, and fully reversible thermodynamics as defined by the Haldane relation. We employed a novel method of validating the thermodynamics of the model by allowing the closed system to come to equilibrium; the combined mass action ratio of the pathway equaled the product of the individual enzymes' equilibrium constants. Adding features physiologically relevant to muscle-a fixed glycogen concentration, efflux of lactate, and coupling to an ATPase--alowed for a steady-state flux far from equilibrium. The main result of our analysis is that coupling of the glycogenolytic network to the ATPase transformed the entire complex into an ATPase driven system. This steady-state system was most sensitive to the external ATPase activity and not to internal pathway mechanisms. The control distribution among the internal pathway enzymes-although small compared to control by ATPase-depended on the flux level and fraction of glycogen phosphorylase a. This model of muscle glycogenolysis thus has unique features compared to models developed for other cell types.

Energetics of muscle contraction: the whole is less than the sum of its parts

Understanding muscle energetics is a problem in optimizing supply of ATP to the demands of ATPases. The complexity of reactions and their fluxes to achieve this balance is greatly reduced by recognizing constraints imposed by the integration of common metabolites at fixed stoichiometry among modular units. ATPase is driven externally. Oxidative phosphorylation and glycogenolysis are the suppliers. We focus on their regulation which involves different controls, but reduces to two principles that enable facile experimental analysis of the supply and demand fluxes. The ratio of concentration of phosphocreatine (PCr) to ATP, not their individual values, sets the range of achievable concentrations of ADP in resting and active muscle (at fixed pH) in different cell types. This principle defines the fraction of available flux of oxidative phosphorylation utilized (at fixed enzyme activities). Then the kinetics of PCr recovery defines the kinetics of oxygen supply and substrate utilization. The second principle is the constancy of PCr and H(+) (lactate) production by glycogenolysis due to the coupling of ATPase and glycolysis. This principle enables glycogenolytic flux to be measured from intracellular proton loads. Further simplification occurs because the magnitude of the interacting fluxes and metabolite concentrations are specified within narrow limits when both the resting and active fluxes are quantified. Thus there is a small set of rules for assessing and understanding the thermodynamics and kinetics of muscle energetics.

Robert Ernest DAVIES. 17 August 1919 – 7 March 1993

Bob Davies was born at Barton–upon–Irwell, Lancaster, to Willian Owen Davies and Clarice Stella Davies (née Spencer) on 17 August 1919. His only sibling is a brother two years older, Arton Owen Davies. His father worked at a chemical factory, the Clayton Aniline Works in M's Educational Association, but only after raising her children did Stella Davies return to school and earn an MA and PhD at Manchester University. She obtained a position as a historian in the extramural staff of the university.

A metabolic control analysis of kinetic controls in ATP free energy metabolism in contracting skeletal muscle

A system analysis of ATP free energy metabolism in skeletal muscle was made using the principles of metabolic control theory. We developed a network model of ATP free energy metabolism in muscle consisting of actomyosin ATPase, sarcoplasmic reticulum (SR) Ca(2+)-ATPase, and mitochondria. These components were sufficient to capture the major aspects of the regulation of the cytosolic ATP-to-ADP concentration ratio (ATP/ADP) in muscle contraction and had inherent homeostatic properties regulating this free energy potential. As input for the analysis, we used ATP metabolic flux and the cytosolic ATP/ADP at steady state at six contraction frequencies between 0 and 2 Hz measured in human forearm flexor muscle by (31)P-NMR spectroscopy. We used the mathematical formalism of metabolic control theory to analyze the distribution of fractional kinetic control of ATPase flux and the ATP/ADP in the network at steady state among the components over this experimental range and an extrapolated range of stimulation frequencies (up to 10 Hz). The control analysis showed that the contractile actomyosin ATPase has dominant kinetic control of ATP flux in forearm flexor muscle over the 0- to 1.6-Hz range of contraction frequencies that resulted in steady states, as determined by (31)P-NMR. However, flux control begins to shift toward mitochondria at >1 Hz. This inversion of flux control from ATP demand to ATP supply control hierarchy progressed as the contraction frequency increased past 2 Hz and was nearly complete at 10 Hz. The functional significance of this result is that, at steady state, ATP free energy consumption cannot outstrip the ATP free energy supply. Therefore, this reduced, three-component muscle ATPase system is inherently homeostatic.

Cellular energetics analysis by a mathematical model of energy balance: estimation of parameters in human skeletal muscle

Cellular energy balance requires that the physiological demands by ATP-utilizing functions be matched by ATP synthesis to sustain muscle activity. We devised a new method of analysis of these processes in data from single individuals. Our approach is based on the logic of current information on the major mechanisms involved in this energy balance and can quantify not directly measurable parameters that govern those mechanisms. We use a mathematical model that simulates by ordinary, nonlinear differential equations three components of cellular bioenergetics (cellular ATP flux, mitochondrial oxidative phosphorylation, and creatine kinase kinetics). We incorporate data under resting conditions, during the transition toward a steady state of stimulation and during the transition during recovery back to the original resting state. Making use of prior information about the kinetic parameters, we fitted the model to previously published dynamic phosphocreatine (PCr) and inorganic phosphate (P(i)) data obtained in normal subjects with an activity-recovery protocol using (31)P nuclear magnetic resonance spectroscopy. The experiment consisted of a baseline phase, an ischemic phase (during which muscle stimulation and PCr utilization occurred), and an aerobic recovery phase. The model described satisfactorily the kinetics of the changes in PCr and P(i) and allowed estimation of the maximal velocity of oxidative phosphorylation and of the net ATP flux in individuals both at rest and during stimulation. This work lays the foundation for a quantitative, model-based approach to the study of in vivo muscle energy balance in intact muscle systems, including human muscle.

Glycolysis is independent of oxygenation state in stimulated human skeletal muscle in vivo

1. We tested the hypothesis that the cytoplasmic control mechanism for glycolysis is affected by the presence of oxygen during exercise. We used a comparison of maximal twitch stimulation under ischaemic and intact circulation in human wrist flexor and ankle dorsiflexor muscles. 31P magnetic resonance spectroscopy followed the phosphocreatine (PCr), Pi and pH dynamics at 6-9 s intervals. Glycolytic PCr synthesis was determined during stimulation from pH and tissue buffer capacity, as well as the oxidative phosphorylation rate. 2. Ischaemic vs. aerobic stimulation resulted in similar glycolytic fluxes in the two muscles. The onset of glycolysis occured after fifty to seventy stimulations and the extent of glycolytic PCr synthesis was directly proportional to the number of stimulations thereafter. 3. Two-fold differences in the putative feedback regulators of glycolysis, [Pi] and [ADP], were found between aerobic and ischaemic stimulation. The similar glycolytic fluxes in the face of these differences in metabolite levels eliminates feedback as a control mechanism in glycolysis. 4. These results demonstrate that glycolytic flux is independent of oxygenation state and metabolic feedback, but proportional to muscle activation. These results show a key role for muscle stimulation in the activation and maintenance of glycolysis. Further, this glycolytic control mechanism is independent of the feedback control mechanism that governs oxidative phosphorylation.

Do kinetics of ADP stimulation of mitochondria really change during myocardial maturation?

The following is the abstract of the article discussed in the subsequent letter:

Portman, Michael A., Yun Xiao, Ying Song, and Xue-Han Ning. Expression of adenine nucleotide translocator parallels maturation of respiratory control in heart in vivo. Am. J. Physiol. 273 ( Heart Circ. Physiol. 42): H1977–H1983, 1997.—Changes in the relationship between myocardial high-energy phosphates and oxygen consumption in vivo occur during development, implying that the mode of respiratory control undergoes maturation. We hypothesized that these maturational changes in sheep heart are paralleled by alterations in the adenine nucleotide translocator (ANT), which are in turn related to changes in the expression of this gene. Increases in myocardial oxygen consumption (MV˙o2) were induced by epinephrine infusion in newborn (0–32 h, n = 6) and mature sheep (30–32 days, n = 6), and high-energy phosphates were monitored with31P nuclear magnetic resonance. Western blot analyses for the ANT1and the β-subunit of F1-adenosinetriphosphatase (ATPase) were performed in these hearts and additional ( n = 9 total per group) as well as in fetal hearts (130–132 days of gestation, n = 5). Northern blot analyses were performed to assess for changes in steady-state RNA transcripts for these two genes. Kinetic analyses for the31P spectra data revealed that the ADP-MV˙o2relationship for the newborns conformed to a Michaelis-Menten model but that the mature data did not conform to first- or second-order kinetic control of respiration through ANT. Maturation from fetal to mature was accompanied by a 2.5-fold increase in ANT protein (by Western blot), with no detectable change in β-F1-ATPase. Northern blot data show that steady-state mRNA levels for ANT and β-F1-ATPase increased ∼2.5-fold from fetal to mature. These data indicate that 1) respiratory control pattern in the newborn is consistent with a kinetic type regulation through ANT, 2) maturational decreases in control through ANT are paralleled by specific increases in ANT content, and 3) regulation of these changes in ANT may be related to increases in steady-state transcript levels for its gene.

Energy balance in muscle activity: simulations of ATPase coupled to oxidative phosphorylation and to creatine kinase

Energy balance refers to the dynamic homeostasis of ATP and related forms of chemical potential within cells. This regulation is accomplished mainly by oxidative metabolism in most mammals. This homeostasis matches dynamically the energy demands of cellular ATPases (net decrease in chemical potential energy) with the energy supply by mitochondrial oxidative phosphorylation (net increase in chemical potential energy). Muscle cells are distinguished from most other cell types in their ability to attain energy balance with more than a 10-fold range of ATPase demand. Creatine kinase maintains a near to equilibrium flux: PCr + ADP<-->ATP + Cr. One important function of creatine kinase is to buffer ATP and ADP concentrations. A system of differential equations describe the coupled operation of cellular ATPase, creatine kinase and oxidative phosphorylation. These equations used experimentally measured concentrations of relevant metabolites and enzyme activities to simulate energy balance in muscle cells. The principle of energy balance is adequately illustrated by simulations with only a three component system.

Effect of viscosity on mechanics of single, skinned fibers from rabbit psoas muscle

Muscle contraction is highly dynamic and thus may be influenced by viscosity of the medium surrounding the myofilaments. Single, skinned fibers from rabbit psoas muscle were used to test this hypothesis. Viscosity within the myofilament lattice was increased by adding to solutions low molecular weight sugars (disaccharides sucrose or maltose or monosaccharides glucose or fructose). At maximal Ca2+ activation, isometric force (Fi) was inhibited at the highest solute concentrations studied, but this inhibition was not directly related to viscosity. Solutes readily permeated the filament lattice, as fiber diameter was unaffected by added solutes (except for an increased diameter with Fi < 30% of control). In contrast, there was a linear dependence upon 1/viscosity for both unloaded shortening velocity and also the kinetics of isometric tension redevelopment; these effects were unrelated to either variation in solution osmolarity or inhibition of force. All effects of added solute were reversible. Inhibition of both isometric as well as isotonic kinetics demonstrates that viscous resistance to filament sliding was not the predominant factor affected by viscosity. This was corroborated by measurements in relaxed fibers, which showed no significant change in the strain-rate dependence of elastic modulus when viscosity was increased more than twofold. Our results implicate cross-bridge diffusion as a significant limiting factor in cross-bridge kinetics and, more generally, demonstrate that viscosity is a useful probe of actomyosin dynamics.

A model of the inversion process in an arterial inversion experiment

A model of the behavior of spins moving through spatially varying gradient and B1 fields is presented. The model simulates the adiabatic behavior of flowing arterial water during a two-coil arterial inversion experiment. Predictions of the degree of inversion generated by the model are compared with flow phantom results for a wide range of gradient magnitudes, nominal B1 magnitudes, and flow velocities. The high level of agreement between the model and the flow phantom results indicates that the model can be used to help select efficient pulse sequence parameters when setting up an in vivo arterial inversion experiment. In addition, the model provides valuable insights into the adiabatic behavior of arterial spins. These insights could be useful in selecting an efficient surface coil geometry which achieves maximum inversion with a minimum B1 magnitude.

Non-invasive quantitative 31P MRS assay of mitochondrial function in skeletal muscle in situ

A method for non-invasive, quantitative 31P NMR spectroscopic investigation of mitochondrial function in human skeletal muscle in situ is described. High time resolution 31P NMR measurements of phosphocreatine, inorganic phosphate and ATP resonances were conducted on human forearm flexor muscle during involuntary twitch contraction at eight different frequencies. Mitochondrial and glyco(geno)lytic ATP synthesis fluxes, and the cytosolic free energy of ATP hydrolysis (delta GP), were calculated at incremental steady-states of energy balance. The covariation of mitochondrial ATP synthesis flux, JPMOP, and delta GP was quasi-linear over the physiological range of free energy values. Curve-fit analysis of the covariation yielded a maximal sustainable JPMOP of 0.24 +/- 0.06 mmol ATP l-1.s-1 and a midpoint potential, (delta GP)0.5, of 58.1 +/- 1.2 kJ/mole in the muscle cells.

Phosphorus metabolite distribution in skeletal muscle: quantitative bioenergetics using creatine analogs

The functional coupling of contractile activity to metabolic processes in skeletal, cardiac and smooth muscle has been extensively examined in the intact cell through the advent of 31P-NMR spectroscopy. The near-equilibrium formulation for creatine kinase (CK) has been used for the calculation of ADPfree and ATP chemical potential in many of these studies. However, control of the bulk cytoplasmic PCr/Cr ratio by the ATP/ADP ratio through CK implies that the ATP/ADP ratio is the same in all loci within the cell. Alternatively the cytoplasmic fraction of ATP and ADP must be so large that other 'compartments' do not influence the physicochemical properties of the bulk cytoplasm. By feeding creatine analogs to rodents, it is possible to test whether these synthetic analogs and the endogenous substrates obey simple rules of enzyme kinetics and equilibration. Two important concepts can be tested: (1) Are phosphorus metabolises fully visible to in vivo 31P-NMR measurements? (2) Does CK equilibrate with its substrates in the cytosol? It will be shown that in spite of localized enzymatic activity and microcompartments in the cell (such as mitochondria), creatine kinase equilibrates with its substrates in fast and slow skeletal muscles at rest. Therefore, the physicochemical properties of the cytosol are best described as freely mixing with respect to the bioenergetically important metabolites (PCr, ATP and phospho-analog) and fully quantifiable by 31P-NMR spectroscopy. It follows that only a narrow range of intercellular heterogeneity with respect to chemical potential is acceptable if bioenergetic processes (e.g. CK fluxes or regulation of oxidative phosphorylation) are to be meaningfully interpreted in a rigorous biochemical framework.

Skeletal muscle perfusion measurements using adiabatic inversion of arterial water

Quantitative NMR measurements of perfusion using magnetic labeling of arterial water have been demonstrated previously in several different highly perfused organs. The success of these previous experiments suggested that arterial labeling may be of use in measuring perfusion in skeletal muscle, where resting perfusion is very low and where increased perfusion after exercise is transient. In the experiments described in this paper, adiabatic inversion of arterial water has been used to make single-voxel measurements of perfusion in the lower hind limb of rats. At rest, the NMR results were quantified to yield a perfusion rate of about 13.8 ml/100g/min. After perturbation due to ischemic exercise, large relative changes in the NMR signal were observed. The peak change of about 2.5% of the NMR signal occurred shortly after perturbation and was followed by a return to resting levels over a period of about 4 min.

Activation of glycolysis in human muscle in vivo

We tested the cytoplasmic control mechanisms for glycolytic ATP synthesis in human wrist flexor muscles. The forearm was made ischemic and activated by maximal twitch stimulation of the median and ulnar nerves in 10 subjects. Kinetic changes in phosphocreatine, Pi, ADP, ATP, sugar phosphates, and pH were measured by 31P magnetic resonance spectroscopy at 7.1-s intervals. Proton production was determined from pH and tissue buffer capacity during stimulation. Glycolysis was activated between 30 and 50 stimulations, and the rate did not significantly change through the stimulation period. The independence of glycolytic rate on [Pi], [ADP], or [AMP] indicates that feedback regulation by these metabolites could not account for this activation of glycolysis. However, glycolytic H+ and ATP production increased sixfold from 0.5 to 3 Hz, indicating that glycolytic rate reflected muscle activation frequency. This dependence of glycolytic rate on muscle stimulation frequency and independence on metabolite levels is consistent with control of glycolysis by Ca2+.

Multiple equilibria of cations with metabolites in muscle bioenergetics

The multiple ionic forms of metabolites were evaluated at 37 degrees C for four reactions important in muscle contraction and recovery: 1) ATPase, 2) creatine kinase, 3) the Lohmann reaction, and 4) the Lohmann reaction reversed by coupling to glycogenolysis and glycolysis. Solution of the system of equations defining the multiple equilibria of the proton and cation complexes gives the concentration of each ionic form and a value for the proton stoichiometry for each reaction. The proton stoichiometric coefficients are unique for each reaction and are a function of pH because of differential binding of Mg2+ and K+ to adenine nucleotides, phosphocreatine, and Pi and because of different acidic dissociation constants for the metabolites. These results show the need to consider the binding of K+ in addition to the previously documented effects of Mg2+ in the cytoplasmic milieu. Commercially available software was used to show that related problems can be calculated readily on personal computers in applications similar to those described here.

Recovery after contraction of white muscle fibres from the dogfish Scyliorhinus canicula

Recovery after contraction of white muscle fibres of dogfish was investigated using 31P-NMR and measurements of heat production. The muscle fibres were stimulated to perform either a single isometric tetanus or a series of brief isometric tetani; the NMR measurements showed that approximately half of the phosphocreatine (PCr) was used. The period of activity was followed by a recovery period without stimulation. Both NMR and heat measurements agreed in showing that recovery was very slow, requiring at least 60 min for PCr resynthesis and for the production of recovery heat. The NMR results showed that changes in intracellular pH and in the concentrations of PCr and intracellular phosphate (Pi) had very similar time courses. Intracellular pH moved in the alkaline direction during the period of activity and then returned monotonically during recovery. The non-phosphate buffer power was 13.0 +/- 3.1 mmol l-1 intracellular water per pH unit (N = 4, mean +/- S.E.M.). The results are consistent with the view that oxidative processes resynthesize PCr during recovery, which is slow because of the low mitochondrial content of these muscle fibres.

The signal transduction function for oxidative phosphorylation is at least second order in ADP

To maintain ATP constant in the cell, mitochondria must sense cellular ATP utilization and transduce this demand to F0-F1-ATPase. In spite of a considerable research effort over the past three decades, no combination of signal(s) and kinetic function has emerged with the power to explain ATP homeostasis in all mammalian cells. We studied this signal transduction problem in intact human muscle using 31P NMR spectroscopy. We find that the apparent kinetic order of the transduction function of the signal cytosolic ADP concentration ([ADP]) is at least second order and not first order as has been assumed. We show that amplified mitochondrial sensitivity to cytosolic [ADP] harmonizes with in vitro kinetics of [ADP] stimulation of respiration and explains ATP homeostasis also in mouse liver and canine heart. This result may well be generalizable to all mammalian cells.

Activity-dependent induction of slow myosin gene expression in isolated fast-twitch mouse muscle

We demonstrate that direct electrical stimulation of isolated fast-twitch muscle in an organ culture system can induce expression of the slow myosin heavy chain (beta-MHC) gene, indicative of a phenotype transformation. Pairs of extensor digitorum longus (EDL) muscles were isolated from adult mice, incubated at resting length in separate chambers, and superfused with the same recirculated media One muscle was subjected to twitch stimulation (5-s trains of 5-Hz pulses at supramaximal voltage every minute), and force was recorded to assess function. The contralateral muscle was incubated without stimulation, to control for effects of the experimental preparation. Both muscle were rapidly frozen for RNA purification and oligo(dT)-primed reverse transcription; serial studies were carried out to 36 h. Polymerase chain reaction was performed utilizing primers specific for cytoplasmic beta-actin (beta-actin), a constitutive marker, and beta-MHC, a gene that is either inactive or expressed at very low levels in control EDL. After 30 h of stimulation, beta-MHC was consistently detected at a level severalfold higher in stimulated EDL than in incubated control EDL when band intensities were normalized to those of beta-actin. These results show that signals or fiber-specific transformations reside within the muscle and that this shift begins rapidly after induction of continuous stimulation.