An energetic model of muscle contraction

Does the intercept of the heat-stress relation provide an accurate estimate of cardiac activation heat?

KEY POINTS

The heat of activation of cardiac muscle reflects the metabolic cost of restoring ionic homeostasis following a contraction. The accuracy of its measurement depends critically on the abolition of crossbridge cycling. We abolished crossbridge activity in isolated rat ventricular trabeculae by use of blebbistatin, an agent that selectively inhibits myosin II ATPase. We found cardiac activation heat to be muscle length independent and to account for 15-20% of total heat production at body temperature. We conclude that it can be accurately estimated at minimal muscle length.

ABSTRACT

Activation heat arises from two sources during the contraction of striated muscle. It reflects the metabolic expenditure associated with Ca²⁺ pumping by the sarcoplasmic reticular Ca²⁺ -ATPase and Ca²⁺ translocation by the Na⁺ /Ca²⁺ exchanger coupled to the Na⁺ ,K⁺ -ATPase. In cardiac preparations, investigators are constrained in estimating its magnitude by reducing muscle length to the point where macroscopic twitch force vanishes. But this experimental protocol has been criticised since, at zero force, the observed heat may be contaminated by residual crossbridge cycling activity. To eliminate this concern, the putative thermal contribution from crossbridge cycling activity must be abolished, at least at minimal muscle length. We achieved this using blebbistatin, a selective inhibitor of myosin II ATPase. Using a microcalorimeter, we measured the force production and heat output, as functions of muscle length, of isolated rat trabeculae from both ventricles contracting isometrically at 5 Hz and at 37°C. In the presence of blebbistatin (15 μmol l^-1 ), active force was zero but heat output remained constant, at all muscle lengths. Activation heat measured in the presence of blebbistatin was not different from that estimated from the intercept of the heat-stress relation in its absence. We thus reached two conclusions. First, activation heat is independent of muscle length. Second, residual crossbridge heat is negligible at zero active force; hence, the intercept of the cardiac heat-force relation provides an estimate of activation heat uncontaminated by crossbridge cycling. Both results resolve long-standing disputes in the literature.

Cardiac activation heat remains inversely dependent on temperature over the range 27-37°C

The relation between heat output and stress production (force per cross-sectional area) of isolated cardiac tissue is a key metric that provides insight into muscle energetic performance. The heat intercept of the relation, termed "activation heat," reflects the metabolic cost of restoring transmembrane gradients of Na(+) and K(+) following electrical excitation, and myoplasmic Ca(2+) concentration following its release from the sarcoplasmic reticulum. At subphysiological temperatures, activation heat is inversely dependent on temperature. Thus one may presume that activation heat would decrease even further at body temperature. However, this assumption is prima facie inconsistent with a study, using intact hearts, which revealed no apparent change in the combination of activation and basal metabolism between 27 and 37°C. It is thus desired to directly determine the change in activation heat between 27 and 37°C. In this study, we use our recently constructed high-thermal resolution muscle calorimeter to determine the first heat-stress relation of isolated cardiac muscle at 37°C. We compare the relation at 37°C to that at 27°C to examine whether the inverse temperature dependence of activation heat, observed under hypothermic conditions, prevails at body temperature. Our results show that activation heat was reduced (from 3.5 ± 0.3 to 2.3 ± 0.3 kJ/m(3)) at the higher temperature. This leads us to conclude that activation metabolism continues to decline as temperature is increased from hypothermia to normothermia and allows us to comment on results obtained from the intact heart by previous investigators.

Muscle heat: a window into the thermodynamics of a molecular machine

The contraction of muscle is characterized by the development of force and movement (mechanics) together with the generation of heat (metabolism). Heat represents that component of the enthalpy of ATP hydrolysis that is not captured by the microscopic machinery of the cell for the performance of work. It arises from two conceptually and temporally distinct sources: initial metabolism and recovery metabolism. Initial metabolism comprises the hydrolysis of ATP and its rapid regeneration by hydrolysis of phosphocreatine (PCr) in the processes underlying excitation-contraction coupling and subsequent cross-bridge cycling and sliding of the contractile filaments. Recovery metabolism describes those process, both aerobic (mitochondrial) and anaerobic (cytoplasmic), that produce ATP, thereby allowing the regeneration of PCr from its hydrolysis products. An equivalent partitioning of muscle heat production is often invoked by muscle physiologists. In this formulation, total enthalpy expenditure is separated into external mechanical work (W) and heat (Q). Heat is again partitioned into three conceptually distinct components: basal, activation, and force dependent. In the following mini-review, we trace the development of these ideas in parallel with the development of measurement techniques for separating the various thermal components.

The efficiency of muscle contraction

When a muscle contracts and shortens against a load, it performs work. The performance of work is fuelled by the expenditure of metabolic energy, more properly quantified as enthalpy (i.e., heat plus work). The ratio of work performed to enthalpy produced provides one measure of efficiency. However, if the primary interest is in the efficiency of the actomyosin cross-bridges, then the metabolic overheads associated with basal metabolism and excitation-contraction coupling, together with those of subsequent metabolic recovery process, must be subtracted from the total heat and work observed. By comparing the cross-bridge work component of the remainder to the Gibbs free energy of hydrolysis of ATP, a measure of thermodynamic efficiency is achieved. We describe and quantify this partitioning process, providing estimates of the efficiencies of selected steps, while discussing the errors that can arise in the process of quantification. The dependence of efficiency on animal species, fibre-type, temperature, and contractile velocity is considered. The effect of contractile velocity on energetics is further examined using a two-state, Huxley-style, mathematical model of cross-bridge cycling that incorporates filament compliance. Simulations suggest only a modest effect of filament compliance on peak efficiency, but progressively larger gains (vis-à-vis the rigid filament case) as contractile velocity approaches Vmax. This effect is attributed primarily to a reduction in the component of energy loss arising from detachment of cross-bridge heads at non-zero strain.

Inhibition of cross-bridge formation has no effect on contraction-associated phosphorylation of p38 MAPK in mouse skeletal muscle

Mitogen-activated protein kinases (MAPKs), in particular p38 MAPK, are phosphorylated in response to contractile activity, yet the mechanism for this is not understood. We tested the hypothesis that the force of contraction is responsible for p38 MAPK phosphorylation in skeletal muscle. Extensor digitorum longus (EDL) muscles isolated from adult male Swiss Webster mice were stimulated at fixed length at 10 Hz for 15 min and then subjected to Western blot analysis for the phosphorylation of p38 MAPK and ERK1/2. Contralateral muscles were fixed at resting length and were not stimulated. Stimulated muscles showed a 2.5-fold increase in phosphorylated p38 MAPK relative to nonstimulated contralateral controls, and there was no change in the phosphorylation of ERK1/2. When contractile activity was inhibited with N-benzyl-p-toluene sulfonamide (BTS), a specific inhibitor of actomyosin ATPase, force production decreased in both a time- and concentration-dependent manner. Preincubation with 25, 75, and 150 microM BTS caused 78+/-4%, 97+/-0.2%, and 99+/-0.2% inhibition in contractile force, respectively, and was stable after 30 min of treatment. Fluorescence measurements demonstrated that Ca2+ cycling was minimally affected by BTS treatment. Surprisingly, BTS did not suppress the level of p38 MAPK phosphorylation in stimulated muscles. These data do not support the view that force generation per se activates p38 MAPK and suggest that other events associated with contraction must be responsible.

Cardiac energetics: sense and nonsense

1. The background to current ideas in cardiac energetics is outlined and, in the genomic era, the need is stressed for detailed knowledge of mouse heart mechanics and energetics. 2. The mouse heart is clearly different to the rat in terms of its excitation-contraction (EC) coupling and the common assumption that heart rate difference between mice and humans will account for the eightfold difference in myocardial oxygen consumption is wrong, because the energy per beat of the mouse heart is approximately one-third that of the human heart. 3. In vivo evidence suggests that there may well be an eightfold species difference in the non-beating metabolism of mice and human hearts. It is speculated that the magnitude of basal metabolism in the heart is regulatable and that, in the absence of perfusion, it falls to approximately one-quarter of its in vivo rate and that in clinical conditions, such as hibernation, it probably decreases; its magnitude may be controlled by the endothelium. 4. The active energy balance sheet is briefly discussed and it is suggested that the activation heat accounts for 20-25% of the active energy per beat and cross-bridge turnover accounts for the balance. It is argued that force, not shortening, is the major determinant of cardiac energy usage. 5. The outcome of recent cardiac modelling with variants of the Huxley and Hill/Eisenberg models is described. It has been necessary to invoke 'loose coupling' to replicate the low cardiac energy flux measured at low afterloads (medium to high velocities of shortening). 6. Lastly, some of the unexplained or 'nonsense' energetic data are outlined and eight unsolved problems in cardiac energetics are discussed.

Comparison of the cardiac force-time integral with energetics using a cardiac muscle model

Several investigators have found experimentally that the force-time integral varies non-linearly with energy expenditure over the course of a cardiac contraction. Also, recent research findings have indicated that the crossbridge cycle to ATP hydrolysis ratio in muscle fiber systems may not be coupled with a one-to-one ratio. In order to investigate these findings, Huxley's sliding filament crossbridge muscle model coupled with parallel and series elastic components was simulated to examine the behavior of the crossbridge energy utilization and force-time integral vs time. Crossbridge (CB) energy utilization was determined by considering the ATP hydrolysis for the crossbridge cycling, and this CB energy was compared with the force-length energy in a contraction. This CB energy was calculated in both isometric and isotonic contractions as a function of contraction time and compared to the force-time integral. Simulation results demonstrated that the ratio of the force-time integral to CB energy varies strongly throughout the cardiac cycle for both isometric and isotonic cases, as has been observed experimentally. Simulations also showed that using the force-length energy component of energy vs the CB energy gave a better correlation between the total energetic predictions and the force-time integral, agreeing with recent finding that the crossbridge cycle to ATP hydrolysis ratio may not be coupled one-to-one, especially at lower force levels.

Myocardial mechanics and the Fenn effect determined from a cardiac muscle crossbridge model

A three-element cardiac muscle fibre model, utilising Huxley's sliding filament theory for the contractile element and coupled with parallel and series elastic components, was simulated to see if it were possible to predict the cardiac Fenn effect. The force/length energy (FLE) was computed in both isometric and isotonic contractions, as a function of muscle fibre length (preload) in the isometric case and afterload in the isotonic contraction case. Simulation results demonstrated that isotonic contractions produced a greater FLE than isometric contractions at every corresponding afterload, with the difference being equal to the work produced in the isotonic case, which is characteristic of the Fenn effect. The maximum energy utilisation was observed at maximum force isometric contractions, as has been experimentally observed in cardiac muscle. Changing the stiffness of the series elastic component did not change the Fenn-effect behaviour. Fenn-effect plots using crossbridge energy predictions showed behaviour similar to the FLE plots, but the FLE: crossbridge energy ratio declined with decreasing force even though the efficiency has been experimentally found to be constant.

Activation heat in rabbit cardiac muscle

1. Activation heat was estimated myothermically in right ventricular papillary muscles of rabbits using several different methods. 2. Gradual pre-shortening of muscles to a length (lmin) where no active force development took place upon stimulation led to relatively low estimates of activation heat (1.59 +/- 0.26-2.06 +/- 0.57 mJ g-1 blotted wet weight, mean +/- S.E.M., n = 10). 3. Quick releases applied during the latency period, before force development, from lmax to various muscle lengths allowed a heat-stress relation to be established. The zero-stress intercept of this relation estimated the activation heat to be 3.27 +/- 0.40 mJ g-1; this was close to the experimentally measured value of 3.46 +/- 0.39 mJ g-1 (mean +/- S.E.M., n = 23) found by quick release from lmax to lmin. 4. The magnitude of the activation heat measured by the quick-release technique is dependent upon the extracellular Ca2+ concentration and there is good correlation between activation heat magnitude and peak developed stress. 5. In agreement with expectations based on the aequorin data of Allen & Kurihara (1982) a prolonged period of time spent at a short length is shown to depress the subsequently determined activation heat. 6. Hyperosmotic solutions (2.5 x normal) only abolished active stress development at low stimulus rates (0.2 Hz) and the activation heat measured at lmax under these conditions was 2.03 +/- 0.12 mJ g-1 (mean +/- S.E.M., n = 6). This value was significantly lower than the latency release estimate of activation heat in the same preparations (2.93 +/- 0.39 mJ g-1). 7. The latency release method of estimating activation heat results in activation heat values that account for approximately 30% of total active energy flux per contraction; a fraction comparable to that found in skeletal muscle. Calculations based on the data suggest that, under our experimental conditions, total Ca2+ release per beat lies between 50 and 100 nmol g-1 wet weight which would produce less than half-maximal myofibrillar ATPase activity when allowance is made for the passive Ca2+-buffering capacity of the myocardial cell.

Effects of cross reinnervation on the energetics of rat skeletal muscle

Experiments were carried out to investigate the changes which occur in the energy production of cross reinnervated fast and slow twitch skeletal muscles. Rat soleus (SOL) and extensor digitorum longus (EDL) muscles were used in myothermic experiments. It was found that the energy production of cross reinnervated skeletal muscle is largely determined by the source of the nervous innervation; as are the dynamic and histological properties of mammalian skeletal muscle. There was an increase in the energy production of crossed soleus muscle and a concomitant reduction in the energy production of crossed EDL. The changes observed correlated well with the measured changes in the force-velocity properties.

Stress as an index of metabolic cost in papillary muscle of the cat

Active stress, stress-time integral (STI) and total heat production of cat right ventricular papillary muscles were recorded during brief trains of isometric twitch contractions at muscle lengths less than or equal to optimal length. Individual muscles were subjected to a 10 degree C change in temperature, a change of stimulus frequency and the addition of isoprenaline sulphate (10(-7) mol. 1(-1). The STI-heat and stress-heat data were subjected respectively to linear and quadratic regression analyses. For both relations, the intercept (stress-independent heat) was unaffected by the frequency change, doubled by the temperature decrease and trebled by the addition of isoprenaline. None of the treatments had a significant effect on the first or second order coefficients of the stress-heat relation. The slope of the STI-heat relation was halved by lowering the temperature, increased 50% by the addition of isoprenaline and unaffected by stimulus frequency. Thus the energetic cost of a given stress increment was constant across conditions while that for a given STI increment was not. Stress is the better mechanical index of myocardial energy cost when the inotropic state is changing.

The effects of temperature on the energetics of rat papillary muscle

The mechanical and myothermic responses of left ventricular papillary muscles from adult rats have been examined at 20 degrees and at 27 degrees C. Contraction trains of six isometric or isotonic twitches at 1/6 Hz were used to establish the heat-stress and load-enthalpy relations respectively. Peak isometric stress was slightly higher at 20 degrees than at 27 degrees C (45 vs. 41 mN/mm2) and was inversely related to muscle cross-sectional area. The stress-independent heat component, identified with the activation heat, was 75% greater at the lower temperature. The stress-dependent heat component, identified with the heat of actin-myosin interaction, was unaffected by temperature. In isotonic experiments the external work performance was similar at both temperatures but the heat liberation was significantly enhanced at the lower temperature so that mechanical efficiency (external work/enthalpy) was reduced. Evidence is presented suggesting that the preparations were not O2-diffusion limited at either temperature. The results are discussed in terms of known functional anomalies of rat cardiac tissue.

Energetics of shortening muscles in twitches and tetanic contractions. II. Force-determined shortening heat

The extra heat liberation accompanying muscular shortening, the force-determined shortening heat, is defined as the difference between the heat produced when shortening occurs and that produced in an isometric contraction developing the same amount of force and performing the same amount of internal work. Based on this definition, the initial energy production in twitches and tetanic contractions (E) is given by E = A + f (P, t) + alpha(F)x + W, where A is the activation heat, f(P, t), the tension-related heat (a heat production associated with the development and maintenance of tension), alpha(F)x, the force-determined shortening heat, and W, the external work. It is demonstrated that this equation accurately accounts for the time-course of heat evolution and the total initial energy production in both twitches and tetani at 0 degrees C. The force-determined shortening heat is liberated, during shortening, in direct proportion to (a) the distance shortened, and (b) the force against which shortening occurs. The normalized value of the force-determined shortening heat coefficient, alpha(F)/P(o), is the same in both the twitch and the tetanus. Finally, this formulation of the muscle's energy production also accounts for the total energy production in afterload isotonic twitches at 20 degrees C, where a Fenn effect is not demonstrable.