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

Generalizing the isothermal efficiency by using Gaussian distributions

Unlike the Carnot heat engine efficiency published in 1824, an isothermal efficiency derived from thermodynamics and information theory can be applied to biological systems. The original approach by Pierce and Cutler in 1959 to derive the isothermal efficiency equation came from Shannon's channel capacity of 1949 and from Felker's 1952 determination of the minimum energy dissipation needed to gain a bit. In 1991 and 2010 Schneider showed how the isothermal efficiency equation can be applied to molecular machines and that this can be used to explain why several molecular machines are 70% efficient. Surprisingly, some macroscopic biological systems, such as whole ecosystems, are also 70% efficient but it is hard to see how this could be explained by a thermodynamic and molecular theory. The thesis of this paper is that the isothermal efficiency can be derived without using thermodynamics by starting from a set of independent Gaussian distributions. This novel derivation generalizes the isothermal efficiency equation for use at all levels of biology, from molecules to ecosystems.

Metabolic Cost of Activation and Mechanical Efficiency of Mouse Soleus Muscle Fiber Bundles During Repetitive Concentric and Eccentric Contractions

Currently available data on the energetics of isolated muscle preparations are based on bouts of less than 10 muscle contractions, whereas metabolic energy consumption is mostly relevant during steady state tasks such as locomotion. In this study we quantified the energetics of small fiber bundles of mouse soleus muscle during prolonged (2 min) series of contractions. Bundles (N = 9) were subjected to sinusoidal length changes, while measuring force and oxygen consumption. Stimulation (five pulses at 100 Hz) occurred either during shortening or during lengthening. Movement frequency (2-3 Hz) and amplitude (0.25-0.50 mm; corresponding to ± 4-8% muscle fiber strain) were close to that reported for mouse soleus muscle during locomotion. The experiments were performed at 32°C. The contributions of cross-bridge cycling and muscle activation to total metabolic energy expenditure were separated using blebbistatin. The mechanical work per contraction cycle decreased sharply during the first 10 cycles, emphasizing the importance of prolonged series of contractions. The mean ± SD fraction of metabolic energy required for activation was 0.37 ± 0.07 and 0.56 ± 0.17 for concentric and eccentric contractions, respectively (both 0.25 mm, 2 Hz). The mechanical efficiency during concentric contractions increased with contraction velocity from 0.12 ± 0.03 (0.25 mm 2 Hz) to 0.15 ± 0.03 (0.25 mm, 3 Hz) and 0.16 ± 0.02 (0.50 mm, 2 Hz) and was -0.22 ± 0.08 during eccentric contractions (0.25 mm, 2 Hz). The percentage of type I fibers correlated positively with mechanical efficiency during concentric contractions, but did not correlate with the fraction of metabolic energy required for activation.

Neurophysics Assessment of the Muscle Bioenergy Generated by Transcranial Magnetic Stimulation

The content of the rectified motor evoked potential (MEP) induced by transcranial magnetic stimulation (TMS) has ambiguously been assessed without the precision that energy calculation deserves. This fact has misled data interpretation and misguided biomedical interventions. To definitively fill the gap that exits in the neurophysics processing of these signals, we computed, in Walls (W^), the bioenergy within the rectified MEP recorded from the human first digitorum index (FDI) muscle at rest and under isometric contraction. We also gauged the biowork exerted by this muscle. Here we show that bioenergy and biowork can accurately and successfully be assessed, validated, and determined in W^ from MEP signals induced by TMS, regardless of knowing the mathematical expression of the function of the signal. Our novel neurophysics approach represents a dramatic paradigm shift in analysis and interpretation of the content of the MEP and will give a true meaning to the content of rectified signals. Importantly, this innovative approach allowed unveiling that women exerted more bioenergy than men at the magnetic stimulations used in this study. Revisitation of conclusions drawn from studies published elsewhere assessing rectified EMG signals that have used ambiguous units is strongly recommended.

Neurophysics Assessment of the Muscle Bioenergy Generated by Transcranial Magnetic Stimulation

The content of the rectified motor evoked potential (MEP) induced by transcranial magnetic stimulation (TMS) has ambiguously been assessed without the precision that energy calculation deserves. This fact has misled data interpretation and misguided biomedical interventions. To definitively fill the gap that exits in the neurophysics processing of these signals, we computed, in Walls ( W ^ ), the bioenergy within the rectified MEP recorded from the human first digitorum index (FDI) muscle at rest and under isometric contraction. We also gauged the biowork exerted by this muscle. Here we show that bioenergy and biowork can accurately and successfully be assessed, validated, and determined in W ^ from MEP signals induced by TMS, regardless of knowing the mathematical expression of the function of the signal. Our novel neurophysics approach represents a dramatic paradigm shift in analysis and interpretation of the content of the MEP and will give a true meaning to the content of rectified signals. Importantly, this innovative approach allowed unveiling that women exerted more bioenergy than men at the magnetic stimulations used in this study. Revisitation of conclusions drawn from studies published elsewhere assessing rectified EMG signals that have used ambiguous units is strongly recommended.

Limit to steady-state aerobic power of skeletal muscles

Like any other kind of cell, muscle cells produce energy by oxidizing the fuel substrate that they absorb together with the needed oxygen from the surroundings. Oxidation occurs entirely within the cell. It means that the reactants and products of reaction must at some time be dissolved in the cell's cytosol. If a cell operates at steady state, its cytosol composition remains constant. Therefore, the cytosol in a muscle that produces work at steady state must contain a constant amount of fuel, oxygen, and product of reaction dissolved in it. The greater the power produced, the higher the concentration of these solutes. There is a limit, however, to the maximum amount of solutes that the cytosol can contain without damaging the cell. General thermodynamic arguments, which are reviewed in this paper, help relate this limit to the dehydration and overhydration limits of the cell. The present analysis shows that the same limits entail a limit to the maximum power that a muscle can produce at steady state. This limit depends on the composition of the fuel mixture used by the muscle. The analysis also determines the number of fuel carbon atoms that must be oxidized in parallel within a cell to produce a given power. It may well happen that a muscle cannot reach the maximum attainable power because it cannot activate all the parallel oxidation paths that are needed to produce it. This may be due to a series of reasons ranging from health issues to a lack of training. The paper shows how the methods of indirect calorimetry can provide all the experimental data needed to determine the actual number of parallel oxidation paths that at steady state must be active in a muscle in a given exercise. A diagram relating muscle power to the number of parallel oxidation paths and fuel composition is finally presented. It provides a means to assess the power capacity of animal muscles and can be applied to evaluate their fitness, stamina, margins for improvement, and athletic potential.

A mathematical model for pressure-based organs behaving as biological pressure vessels

We introduce a mathematical model that describes the allometry of physical characteristics of hollow organs behaving as pressure vessels based on the physics of ideal pressure vessels. The model was validated by studying parameters such as body and organ mass, systolic and diastolic pressures, internal and external dimensions, pressurization energy and organ energy output measurements of pressure-based organs in a wide range of mammals and birds. Seven rules were derived that govern amongst others, lack of size efficiency on scaling to larger organ sizes, matching organ size in the same species, equal relative efficiency in pressurization energy across species and direct size matching between organ mass and mass of contents. The lung, heart and bladder follow these predicted theoretical relationships with a similar relative efficiency across various mammalian and avian species; an exception is cardiac output in mammals with a mass exceeding 10 kg. This may limit massive body size in mammals, breaking Cope's rule that populations evolve to increase in body size over time. Such a limit was not found in large flightless birds exceeding 100 kg, leading to speculation about unlimited dinosaur size should dinosaurs carry avian-like cardiac characteristics.

Mitochondria to motion: optimizing oxidative phosphorylation to improve exercise performance

Mitochondria oxidize substrates to generate the ATP that fuels muscle contraction and locomotion. This review focuses on three steps in oxidative phosphorylation that have independent roles in setting the overall mitochondrial ATP flux and thereby have direct impact on locomotion. The first is the electron transport chain, which sets the pace for oxidation. New studies indicate that the electron transport chain capacity per mitochondria declines with age and disease, but can be revived by both acute and chronic treatments. The resulting higher ATP production is reflected in improved muscle power output and locomotory performance. The second step is the coupling of ATP supply from O2 uptake (mitochondrial coupling efficiency). Treatments that elevate mitochondrial coupling raise both exercise efficiency and the capacity for sustained exercise in both young and old muscle. The final step is ATP synthesis itself, which is under dynamic control at multiple sites to provide the 50-fold range of ATP flux between resting muscle and exercise at the mitochondrial capacity. Thus, malleability at sites in these subsystems of oxidative phosphorylation has an impact on ATP flux, with direct effects on exercise performance. Interventions are emerging that target these three independent subsystems to provide many paths to improve ATP flux and elevate the muscle performance lost to inactivity, age or disease.

Limits to anaerobic energy and cytosolic concentration in the living cell

For many physical systems at any given temperature, the set of all states where the system's free energy reaches its largest value can be determined from the system's constitutive equations of internal energy and entropy, once a state of that set is known. Such an approach is fraught with complications when applied to a living cell, because the cell's cytosol contains thousands of solutes, and thus thousands of state variables, which makes determination of its state impractical. We show here that, when looking for the maximum energy that the cytosol can store and release, detailed information on cytosol composition is redundant. Compatibility with cell's life requires that a single variable that represents the overall concentration of cytosol solutes must fall between defined limits, which can be determined by dehydrating and overhydrating the cell to its maximum capacity. The same limits are shown to determine, in particular, the maximum amount of free energy that a cell can supply in fast anaerobic processes, starting from any given initial state. For a typical skeletal muscle in normal physiological conditions this energy, i.e., the maximum anaerobic capacity to do work, is calculated to be about 960 J per kg of muscular mass. Such energy decreases as the overall concentration of solutes in the cytosol is increased. Similar results apply to any kind of cell. They provide an essential tool to understand and control the macroscopic response of single cells and multicellular cellular tissues alike. The applications include sport physiology, cell aging, disease produced cell damage, drug absorption capacity, to mention the most obvious ones.

What limits performance during whole-body incremental exercise to exhaustion in humans?

To determine the mechanisms causing task failure during incremental exercise to exhaustion (IE), sprint performance (10 s all-out isokinetic) and muscle metabolites were measured before (control) and immediately after IE in normoxia (P(IO2) 143 mmHg) and hypoxia (P(IO2): 73 mmHg) in 22 men (22 ± 3 years). After IE, subjects recovered for either 10 or 60 s, with open circulation or bilateral leg occlusion (300 mmHg) in random order. This was followed by a 10 s sprint with open circulation. Post-IE peak power output (W(peak)) was higher than the power output reached at exhaustion during IE (P < 0.05). After 10 and 60 s recovery in normoxia, W(peak) was reduced by 38 ± 9 and 22 ± 10% without occlusion, and 61 ± 8 and 47 ± 10% with occlusion (P < 0.05). Following 10 s occlusion, W(peak) was 20% higher in hypoxia than normoxia (P < 0.05), despite similar muscle lactate accumulation ([La]) and phosphocreatine and ATP reduction. Sprint performance and anaerobic ATP resynthesis were greater after 60 s compared with 10 s occlusions, despite the higher [La] and [H(+)] after 60 s compared with 10 s occlusion recovery (P < 0.05). The mean rate of ATP turnover during the 60 s occlusion was 0.180 ± 0.133 mmol (kg wet wt)(-1) s(-1), i.e. equivalent to 32% of leg peak O2 uptake (the energy expended by the ion pumps). A greater degree of recovery is achieved, however, without occlusion. In conclusion, during incremental exercise task failure is not due to metabolite accumulation or lack of energy resources. Anaerobic metabolism, despite the accumulation of lactate and H(+), facilitates early recovery even in anoxia. This points to central mechanisms as the principal determinants of task failure both in normoxia and hypoxia, with lower peripheral contribution in hypoxia.

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.

Elevated energy coupling and aerobic capacity improves exercise performance in endurance-trained elderly subjects

Increased maximal oxygen uptake (V(O(2)max)), mitochondrial capacity and energy coupling efficiency are reported after endurance training (ET) in adult subjects. Here we test whether leg exercise performance (power output of the legs, P(max), at V(O(2)max)) reflects these improvements with ET in the elderly. Fifteen male and female subjects were endurance trained for a 6 month programme, with 13 subjects (69.5 ± 1.2 years old, range 65-80 years old; n = 7 males; n = 6 females) completing the study. This training significantly improved P(max) (Δ17%; P = 0.003), V(O(2)max) (Δ5.4%; P = 0.021) and the increment in oxygen uptake (V(O(2))) above resting (ΔV(O(2)m-r) = V(O(2)max) - V(O(2)rest; Δ9%; P < 0.02). In addition, evidence of improved energy coupling came from elevated leg power output per unit V(O(2))at the aerobic capacity [Δ(P(max)/ΔV(O(2)m-r)); P = 0.02] and during submaximal exercise in the ramp test as measured by delta efficiency (ΔP(ex)/ΔV(O(2)); P = 0.04). No change was found in blood lactate, muscle glycolysis or fibre type. The rise in P(max) paralleled the improvement in muscle oxidative phosphorylation capacity (ATP(max)) in these subjects. In addition, the greater exercise energy coupling [Δ(P(max)/ΔV(O(2)m-r)) and delta efficiency] was accompanied by increased mitochondrial energy coupling as measured by elevated ATP production per unit mitochondrial content in these subjects. These results suggest that leg exercise performance benefits from elevations in energy coupling and oxidative phosphorylation capacity at both the whole-body and muscle levels that accompany endurance training in the elderly.

Exercise efficiency of low power output cycling

Exercise efficiency at low power outputs, energetically comparable to daily living activities, can be influenced by homeostatic perturbations (e.g., weight gain/loss). However, an appropriate efficiency calculation for low power outputs used in these studies has not been determined. Fifteen active subjects (seven females, eight males) performed 14, 5-min cycling trials: two types of seated rest (cranks vertical and horizontal), passive (motor-driven) cycling, no-chain cycling, no-load cycling, cycling at low (10, 20, 30, 40 W), and moderate (50, 60, 80, 100, 120 W) power outputs. Mean delta efficiency was 57% for low power outputs compared to 41.3% for moderate power outputs. Means for gross (3.6%) and net (5.7%) efficiencies were low at the lowest power output. At low power outputs, delta and work efficiency values exceeded theoretical values. In conclusion, at low power outputs, none of the common exercise efficiency calculations gave values comparable to theoretical muscle efficiency. However, gross efficiency and the slope and intercept of the metabolic power vs mechanical power output regression provide insights that are still valuable when studying homeostatic perturbations.