Shortening Heat Research Articles

Resolving an inconsistency in the estimation of the energy for excitation of cardiac muscle contraction.

In the excitation of muscle contraction, calcium ions interact with transmembrane transporters. This process is accompanied by energy consumption and heat liberation. To quantify this activation energy or heat in the heart or cardiac muscle, two non-pharmacological approaches can be used. In one approach using the "pressure-volume area" concept, the same estimate of activation energy is obtained regardless of the mode of contraction (either isovolumic/isometric or ejecting/shortening). In the other approach, an accurate estimate of activation energy is obtained only when the muscle contracts isometrically. If the contraction involves muscle shortening, then an additional component of heat associated with shortening is liberated, over and above that of activation. The present study thus examines the reconcilability of the two approaches by performing experiments on isolated muscles measuring contractile force and heat output. A framework was devised from the experimental data to allow us to replicate several mechanoenergetics results gleaned from the literature. From these replications, we conclude that the choice of initial muscle length (or ventricular volume) underlies the divergence of the two approaches in the estimation of activation energy when the mode of contraction involves shortening (ejection). At low initial muscle lengths, the heat of shortening is relatively small, which can lead to the misconception that activation energy is contraction mode independent. In fact, because cardiac muscle liberates heat of shortening when allowed to shorten, estimation of activation heat must be performed only under isometric (isovolumic) contractions. We thus recommend caution when estimating activation energy using the "pressure-volume area" concept.

Energetics Equivalent of the Cardiac Force-Length End-Systolic Zone: Implications for Contractility and Economy of Contraction.

We have recently demonstrated the existence of a region on the cardiac mechanics stress-length plane, which we have designated “The cardiac end-systolic zone.” The zone is defined as the area on the pressure-volume (or stress-length) plane within which all stress-length contraction profiles reach their end-systolic points. It is enclosed by three boundaries: the isometric end-systolic relation, the work-loop (shortening) end-systolic relation, and the zero-active stress isotonic end-systolic relation. The existence of this zone reflects the contraction-mode dependence of the cardiac end-systolic force-length relations, and has been confirmed in a range of cardiac preparations at the whole-heart, tissue and myocyte levels. This finding has led us to speculate that a comparable zone prevails for cardiac metabolism. Specifically, we hypothesize the existence of an equivalent zone on the energetics plane (heat vs. stress), and that it can be attributed to the recently-revealed heat of shortening in cardiac muscle. To test these hypotheses, we subjected trabeculae to both isometric contractions and work-loop contractions over wide ranges of preloads and afterloads. We found that the heat-stress relations for work-loop contractions were distinct from those of isometric contractions, mirroring the contraction mode-dependence of the stress-length relation. The zone bounded by these contraction-mode dependent heat-stress relations reflects the heat of shortening. Isoproterenol-induced enhancement of contractility led to proportional increases in the zones on both the mechanics and energetics planes, thereby supporting our hypothesis.

Experimental and modelling evidence of shortening heat in cardiac muscle.

Heat associated with muscle shortening has been repeatedly demonstrated in skeletal muscle, but its existence in cardiac muscle remains contentious after five decades of study. By iterating between experiments and computational modelling, we show compelling evidence for the existence of shortening heat in cardiac muscle and reveal, mechanistically, the source of this excess heat. Our results clarify a long-standing uncertainty in the field of cardiac muscle energetics. We provide a revised partitioning of cardiac muscle energy expenditure to include this newly revealed thermal component. When a muscle shortens against an afterload, the heat that it liberates is greater than that produced by the same muscle contracting isometrically at the same level of force. This excess heat is defined as 'shortening heat', and has been repeatedly demonstrated in skeletal muscle but not in cardiac muscle. Given the micro-structural similarities between these two muscle types, and since we imagine that shortening heat is the thermal accompaniment of cross-bridge cycling, we have re-examined this issue. Using our flow-through microcalorimeter, we measured force and heat generated by isolated rat trabeculae undergoing isometric contractions at different muscle lengths and work-loop (shortening) contractions at different afterloads. We simulated these experimental protocols using a thermodynamically constrained model of cross-bridge cycling and probed the mechanisms underpinning shortening heat. Predictions generated by the model were subsequently validated by a further set of experiments. Both our experimental and modelling results show convincing evidence for the existence of shortening heat in cardiac muscle. Its magnitude is inversely related to the afterload or, equivalently, directly related to the extent of shortening. Computational simulations reveal that the heat of shortening arises from the cycling of cross-bridges, and that the rate of ATP hydrolysis is more sensitive to change of muscle length than to change of afterload. Our results clarify a long-standing uncertainty in the field of cardiac muscle energetics.

Shortening Heat In Cardiac Muscle

The ‘heat of shortening’ in muscle was first demonstrated by Fenn (1923). Tectanically‐contracting skeletal muscle, released to shorten at a fixed afterload, was shown to produce heat at a rate in excess of the steady‐state isometric heat rate. Subsequent studies in the following decades have provided ample evidence to support the existence of shortening heat in skeletal muscle. The situation is much less clear in cardiac muscle. Using the ‘latency release’ method, Holroyd and Gibbs (1992) showed that no heat was liberated when cardiac muscle was shortened against zero afterload. Adding legitimacy to the latency release protocol, its use showed the existence of shortening heat in both fast‐twitch and slow‐twitch hind‐limb muscles of the rat. (Holroyd et al., 1996). Since that time, the existence of shortening heat in cardiac muscle seems not to have been further investigated, leaving the field in the curious situation that shortening heat is present in skeletal muscle but not in cardiac muscle, despite their micro‐structural similarities. Since it must be imagined that shortening heat is the thermal accompaniment of cross‐bridge cycling, and its attendant thermogenic ATP hydrolysis, we undertake a re‐examination of the issue. We do so using two independent approaches.Firstly, we quantify shortening heat in isolated preparations (right ventricular trabeculae carneae) from rat hearts. Trabeculae were dissected from the left ventricles of 14–16 week old male Sprague‐Dawley rats and mounted in a flow‐through microcalorimeter at 32 °C, as previously described (Taberner et al., 2011). The muscle was subjected to a series of steady‐state trains of isotonic contractions at progressively diminishing afterloads, and isometric contractions at progressively diminishing muscle lengths. Shortening heat is defined as the difference in twitch heat between these two modes of contractions at a given afterload. Secondly, experimental findings are complemented by predictions of cross‐bridge ATP hydrolysis from a thermodynamically‐constrained, mathematical model of cardiac muscle mechano‐energetics (Tran et al., 2010). In both cases we exploit the difference of enthalpy‐load relations between isometric and isotonic contractions, while ensuring that comparisons are performed at the same peak force.Our experimental results confirm the existence of shortening heat in rat trabeculae. The magnitude of shortening heat was inversely related to the afterload and was a monotonically‐increasing function of the ‘extent of shortening’. Computational simulations reveal that the heat of shortening arises from the cycling of cross‐bridges, and that, even at very low afterloads where no external work is done, there is always a component of energy that is dissipated as heat.

The Biomechanical Relevance of the Mathematical Models of Torque-Angle and Torque-Velocity Relationships

Mathematical models of torque-velocity and torque-angle relationships on different muscle groups and joints allow at least two things: (1) to generate and analyze characteristic curves based on experimental data and to assess their dynamics during neurogenic or myogenic dysfunctions, or to use them as a criterion for the changes in the level of training; and (2) to generate the predictive torque equations for various joints. Based on our previous studies [1-4] and on the classical force-velocity relationship of Hill [5], in this report we discuss the biomechanical relevance of mathematical models of torque-velocity and torque-angle relationships with polynomials, cubic splines and exponential functions. The cases concern different muscle groups and joints, as well as a comparative analysis of data between trained and untrained subjects, demonstrating the possibilities of mathemamical modelling to differentiate the changes in the force profile of skeletal muscles as a response to long-term adaptation to training. [1] Kanelov, I., Pencheva, N., Stefanov, S., Milanov, P., Dimitriev, M. (2014) Concentric torque-velocity realtionships of the elbow flexors and extensors in healthy females. Book of Abstracts, 19th Annual Congress of the European College of Sport Science 2nd - 5th July 2014, Amsterdam – The Netherlands. [2] Kanelov I., Koroleova G., Milanov P. Pencheva N. (2016) Impact of the joint angular positions on the peak torque of elbow flexors and extensors in healthy males. Research in Kinesiology, (in press). [3] Koroleova, G., Mavrevski, R., Kanelov, I., Pencheva, N., Milanov, P. (2015) Assessment of elbow torque-velocity curve fitting with different optimization criteria. Book of Abstracts, 20th Annual Congress of the European College of Sport Science, 24th - 27th June 2015, Malmo, Sweden. [4] Pencheva, N., Kokova, M., Dencheva, S. (2012) Torque-angle relationships of the elbow flexors and extensors in healthy females. Book of Abstracts, 18th Annual Congress of the European College of Sport Science, 26th - 29th June 2013, Barcelona, Spain. [5] Hill A. V. (1938) The heat of shortening and the dynamic constraints of muscle, Proceedings of the Royal Society B: Biological Sciences, 126 (843), p. 136-195.

An Energetic Model of Low Frequency Isometric Neuromuscular Electrical Stimulation.

The objective of this study was to evaluate whether an adapted Hill-type model of muscle energetics could account for the relatively high energy turnover observed during low frequency isometric Neuromuscular Electrical Stimulation (NMES). A previously validated Hill-based model was adapted to estimate the energy consumption due to muscle activation, force maintenance and internal shortening of the muscle during isometric NMES. Quadriceps muscle model parameters were identified for 10 healthy subjects based on the experimentally measured torque response to isometric stimulation at 8 Hz. Model predictions of torque and energy consumption rates across the stimulation range 1-12 Hz were compared with experimental data recorded from the same subjects. The model provided estimates in close agreement with the experimental values for the group mean energy consumption rate across the frequency range tested, (R adj (2) = 0.98), although prediction of individual data points for all frequencies and all subjects was more variable, (R adj (2) = 0.70). The model suggests that approximately one-third of the energy between 4 and 6 Hz is due to shortening heat. The model provides a means of identifying optimal therapeutic stimulation patterns for sustained incremental oxygen uptake at minimum torque output for a given muscle and provides insight into the energetic components involved.

English

Introduction The works of AV Hill and coworkers, AF Huxley and followers, Eisenberg and coworkers, Lombardi and coworkers are rapidly sketched. This hypothesis discusses the possible uncertainties in the interpretation of data in proposed mechanisms of skeletal muscle contraction. The hypothesis In the Huxley-Simmons model, the elastic element must be stretched by one-dimensional fluctuations (Brownian motions) before any chemical change in state. The transition rates are made realistic by assuming that three or more attached states are necessary. Evaluation of hypothesis Some of the concepts generally accepted in the models of muscle contraction are cast in doubt. They are: the lack of consideration of the water–protein interactions; the belief that viscosity is irrelevant in the economy of muscle contraction; the concept of the drag stroke; the significance of the Huxley-Simmons manoeuvre; the possible interference of the equipment on the measurements; and the lack of consideration of the acceleration of the load. Conclusion The lack of consideration of the above items may compromise the correct building of the model of muscle contraction. Introduction Hill’s work AV Hill and coworkers investigated muscle contraction for more than 40 years. The beauty of their work is that the mechanical measurements were always accompanied by thermodynamic measurements. As a matter of fact, contraction velocity, tension, work produced, energy output and heat released were always concomitantly measured. Two fundamental concepts were established: 1) the relation between the contraction velocity and the tension produced. Hill’s equation1 (Figure 1): (P + a) (v + b) = (P0 + a) b where, a and b are constants and 2) that the extra heat produced in shortening a given distance varies with the load, so that the constant α of the heat of shortening for frog sartorii at 0°C, is given by2 (Figure 2): α = 0.16 (± 0.015) P0 + 0.18 (± 0.027) P The sliding filament model In the initial hypothesis of AF Huxley3, the amplitude of the power stroke was a function of the available thermal energy. It was also assumed that at maximum velocity, where tension equals zero, the net positive force exerted by myosin heads attached in the power stroke equals the net negative force exerted by heads that have been carried into the drag-stroke region. In a second model, AF Huxley and Simmons4 assumed that, after attachment, the cross-bridges rotate from one to the next of a few positions with progressively lower potential energy while stretching a 40 nm long elastic linkage. At the end of the rotation, the detachment of myosin head was caused by the hydrolysis of ATP. The model of Eisenberg et al. In the model of Huxley and Simmons4, the elastic element must be stretched by one-dimensional fluctuations (Brownian motion) before any transition may occur, as a consequence, to make the transition rates realistic, three or more attached states are necessary. Eisenberg et al.5, on the contrary, assume that in the transitions, elasticity and chemical changes of state are linked. The conformational change of the attached cross-bridge therefore affects both the free energy and the force exerted by the crossbridge. Further, the model of Eisenberg et al.5 predicts that the number of the attached cross-bridges (and not their force) decreases with the shortening velocity. The length of the power stroke and the force delivered by the motors The response of the cross-bridge to the same output of mechanical energy may be threefold: (1) weak force and large motion, (2) strong force and short motion and (3) variable force/distance ratio depending on the load. According to AF Huxley, the response of the cross-bridge is of the weak force – large motion3, with a ~10 nm power stroke4. It is, however, most likely that that the force/ distance ratio changes with the load. This possibility was first formulated theoretically by Worthington and Elliott6, then experimentally by Piazzesi et al.7, who proposed the step size to decrease from 7 nm at zero load to 4 nm at 80% of the isometric load. * Corresponding author Email: enrico.grazi@unife.it Dipartimento di Biochimica e Biologia Molecolare, Universita di Ferrara, Via Borsari 46, 44100 Ferrara, Italy

Interventricular comparison of the energetics of contraction of trabeculae carneae isolated from the rat heart

We compare the energetics of right ventricular and left ventricular trabeculae carneae isolated from rat hearts. Using our work-loop calorimeter, we subjected trabeculae to stress-length work (W), designed to mimic the pressure-volume work of the heart. Simultaneous measurement of heat production (Q) allowed calculation of the accompanying change of enthalpy (H = W + Q). From the mechanical measurements (i.e. stress and change of length), we calculated work, shortening velocity and power. In combination with heat measurements, we calculated activation heat (Q(A)), crossbridge heat (Q(xb)) and two measures of cardiac efficiency: 'mechanical efficiency' ((mech) = W/H) and 'crossbridge efficiency' ((xb) = W/(H - Q(A))). With respect to their left ventricular counterparts, right venticular trabeculae have higher peak shortening velocity, and higher peak mechanical efficiency, but with no difference of stress development, twitch duration, work performance, shortening power or crossbridge efficiency. That is, the 35% greater maximum mechanical efficiency of right venticular than left ventricular trabeculae (13.6 vs. 10.2%) is offset by the greater metabolic cost of activation (Q(A)) in the latter. When corrected for this difference, crossbridge efficiency does not differ between the ventricles.

IMPROVEMENT OF PRODUCTION TECHNOLOGYCOMPOTE WITH GRAPES FROM THE SHF EMF

The experimental results warming of canned in an electromagnetic microwave field. Some new modes of heat sterilization using preheating of the grapes in the microwave EMF. Revealed that the use of pre-microwave heating of berries in the banks before pouring syrup saves heat, shortening heat sterilization regimes compote over 30% and the quality of the finished product.

A macroscopic ansatz to deduce the Hill relation

In this study, we derive the hyperbolic force–velocity relation of concentric muscular contraction, first formulated empirically by A.V. Hill in 1938, from three essential model assumptions: (1) the structural assembly of three well-known elements – i.e. active, parallel damping, and serial – fulfilling a force equilibrium, (2) the parallel damping coefficient explicitly depending on muscle force output and three parameters, and (3) the kinematic gearing ratio between active and serial element being assigned to a parameter. The energy source within the muscle represented by the force of the active element is an additional fifth parameter. As a result we find the Hill “constants” A and B as functions of our five model parameters. Using A and B values from literature on experimental data, we predict heat power release of our model. By calculating enthalpy rate and mechanical efficiency, we compare the model heat power to predictions from another Hill-type model, to Hill's original findings, and to findings from modern muscle heat measurements. We reconsider why the biggest share of heat rate during isometric contractions (maintenance heat) and the velocity-dependent heat rate during concentric contractions in addition to maintenance heat rate (shortening heat rate) may be traced back to the same mechanism represented by the kinematic gearing ratio. Namely, we suggest that the serial element transfers attachment–detachment fluctuations of actin–myosin crossbridges within one sarcomere to others in the same sarcomere and to those in parallel and in series. Numerically, in case of negligible passive muscular damping, we find the ratio between A and isometric force (relative A) to depend exclusively on the kinematic gearing ratio, whereas the maintenance heat rate scales with the square of relative A. Moreover, this mechanical coupling internal to the muscle fibres may also be behind the macroscopic force dependency of the overall parallel damping coefficient.

Large-scale models reveal the two-component mechanics of striated muscle.

This paper provides a comprehensive explanation of striated muscle mechanics and contraction on the basis of filament rotations. Helical proteins, particularly the coiled-coils of tropomyosin, myosin and α-actinin, shorten their H-bonds cooperatively and produce torque and filament rotations when the Coulombic net-charge repulsion of their highly charged side-chains is diminished by interaction with ions. The classical “two-component model” of active muscle differentiated a “contractile component” which stretches the “series elastic component” during force production. The contractile components are the helically shaped thin filaments of muscle that shorten the sarcomeres by clockwise drilling into the myosin cross-bridges with torque decrease (= force-deficit). Muscle stretch means drawing out the thin filament helices off the cross-bridges under passive counterclockwise rotation with torque increase (= stretch activation). Since each thin filament is anchored by four elastic α-actinin Z-filaments (provided with force-regulating sites for Ca2+ binding), the thin filament rotations change the torsional twist of the four Z-filaments as the “series elastic components”. Large scale models simulate the changes of structure and force in the Z-band by the different Z-filament twisting stages A, B, C, D, E, F and G. Stage D corresponds to the isometric state. The basic phenomena of muscle physiology, i. e. latency relaxation, Fenn-effect, the force-velocity relation, the length-tension relation, unexplained energy, shortening heat, the Huxley-Simmons phases, etc. are explained and interpreted with the help of the model experiments.

Teaching from classic papers: Hill's model of muscle contraction

A. V. Hill's 1938 paper "The heat of shortening and the dynamic constants of muscle" is an enduring classic, presenting detailed methods, meticulous experiments, and the model of muscle contraction that now bears Hill's name. Pairing a simulation based on Hill's model with a reading of his paper allows students to follow his thought process to discover key principles of muscle physiology and gain insight into how to develop quantitative models of physiological processes. In this article, the experience of the author using this approach in a graduate biomedical engineering course is outlined, along with suggestions for adapting this approach to other audiences.

Evaluation of a Hill based muscle model for the energy cost and efficiency of muscular contraction

The purpose of this study was to evaluate a Hill-based mathematical model of muscle energetics and to disclose inconsistencies in existing experimental data. For this purpose, we simulated iso-velocity contractions of mouse fast twitch EDL and slow twitch SOL fibers, and we compared the outcome to experimental results. The experimental results were extracted from two studies published in the literature, which were based on the same methodology but yielded different outcomes (B96 and B93). In the model, energy cost was modeled as the sum of heat and work. Parameters used to model heat rate were entirely independent of the experimental data-sets. Parameters describing the mechanical behavior were derived from both experimental studies. The model was found to accurately predict the muscle energetics and mechanical efficiency of data-set B96. The model could not, however, replicate the energetics and efficiency of SOL and EDL that were found in data-set B93. The model overestimated the shortening heat rate of EDL but, surprisingly, also the mechanical work rate for both muscles. This was surprising since mechanical characteristics of the model were derived directly from the experimental data. It was demonstrated that the inconsistencies in data-set B93 must have been due to some unexplained confounding artifact. It was concluded that the presented model of muscle energetics is valid for iso-velocity contractions of mammalian muscle since it accurately predicts experimental results of an independent data-set (B96). In addition, the model appeared to be helpful in revealing inconsistencies in a second data-set (B93).

Muscle contraction: energy rate equations in relation to efficiency and step-size distance

We derive the energy rate equation for muscle contraction. Our equation has only two parameters m, the maintenance heat rate and 1/ S, the shortening heat coefficient. The impulsive model (previously described in earlier papers) provides a physical basis for parameter 1/ S as well as for constants a and b in Hill’s force–velocity equation. We develop new theory and relate the efficiency and the step-size distance to our energy rate equation. Correlation between the efficiency and the step-size distance is established. The various numbers are listed in Table 1: we use data from five different muscles in the literature. In summary, our analysis strongly supports the impulsive model as the correct model of contraction.

Dynamic optimization of human walking.

A three-dimensional, neuromusculoskeletal model of the body was combined with dynamic optimization theory to simulate normal walking on level ground. The body was modeled as a 23 degree-of-freedom mechanical linkage, actuated by 54 muscles. The dynamic optimization problem was to calculate the muscle excitation histories, muscle forces, and limb motions subject to minimum metabolic energy expenditure per unit distance traveled. Muscle metabolic energy was calculated by slimming five terms: the basal or resting heat, activation heat, maintenance heat, shortening heat, and the mechanical work done by all the muscles in the model. The gait cycle was assumed to be symmetric; that is, the muscle excitations for the right and left legs and the initial and terminal states in the model were assumed to be equal. Importantly, a tracking problem was not solved. Rather only a set of terminal constraints was placed on the states of the model to enforce repeatability of the gait cycle. Quantitative comparisons of the model predictions with patterns of body-segmental displacements, ground-reaction forces, and muscle activations obtained from experiment show that the simulation reproduces the salient features of normal gait. The simulation results suggest that minimum metabolic energy per unit distance traveled is a valid measure of walking performance.

An explanation of shortening heat generation and mechanical performance enhancement during muscle stretch.

Titin is an extraordinary long multidomain protein spanning half of the sarcomeric unit. One end of the titin filament is known to emerge from the Z-line, but the precise localization of the other end is still a matter of debate. Assuming that titin filaments connect the Z-line to the tips of thin filaments in the opposite half of the sarcomere, the behavior of an actively contracting muscle during mechanical stretch, as well as the mechanism of muscle shortening heat generation, can be easily explained if one considers that titin filaments are involved not only in the passive elasticity of the muscle but also in the force and heat generation during contraction.

Shortening heat in slow- and fast-twitch muscles of the rat.

Shortening heat has been reported in several amphibian skeletal muscles. In this investigation, shortening heat has been investigated in both soleus and extensor digitorum longus (EDL) muscles of young rats. The procedure involved shortening the muscles through two different distances, at near maximum velocity and at the onset of a summated twitch from different initial lengths. At the end of the shortening period, the muscle contracted isometrically, and the stress and associated heat production were recorded. These heat-stress data were compared with heat-stress data of isometric twitches at different initial lengths. There was a parallel upward shift in energy output when shortening occurred, indicating the presence of a shortening heat. Shortening heat increased with the distance shortened in soleus, but this was not the case for EDL. The values for the shortening heat coefficient for both muscle types are slightly higher than those reported for amphibian skeletal muscle and suggest that shortening heat is a significant component of the energy output of mammalian skeletal muscle.

The energetics of shortening amphibian cardiac muscle.

An isolated amphibian cardiac muscle preparation, toad ventricular strip, was used to examine the energetics of shortening. Simultaneous measurements of force and length changes and the associated heat production were made. Both the isometric heat/stress and the enthalpy (heat+work)/load relationships were similar to those previously reported in mammalian cardiac muscle. The activation metabolism was higher in this preparation and, like its mammalian counterpart, was length dependent. The heat production measured in an isometric contraction was approximately 50% higher than that observed at the same stress level in rodent mammalian cardiac muscle. This did not affect the maximum isotonic mechanical efficiency (work divided by enthalpy) of the preparation which, at an afterload of 20% of the maximum stress was 18.1 +/- 1.7% (n = 8). There was no evidence for a shortening heat component in this preparation during isotonic contractions. It appears therefore that the energetics of shortening amphibian cardiac muscle closely resemble the energetics of mammalian cardiac tissue.

Is there a shortening-heat component in mammalian cardiac muscle contraction?

It has been suggested that there is a shortening-heat component that is an extra liberation of heat on shortening above that due to the external work, which contributes to the total energy expenditure of the beating heart. The presence of a shortening heat component was studied in isolated papillary muscles from the right ventricle of rabbits killed by cervical dislocation. At the onset of a contraction, muscles were shortened from various initial lengths through fixed distances at near maximum velocity before being allowed to develop force at the new length; the heat production accompanying such contractions was measured. The measured heat was compared with heat values predicted from previously established heat-stress curves obtained by using either preshortening or latency release methods. There was no shortening-related increment in heat output per contraction when comparison was made to a control heat-stress curve, obtained using the latency release method. An increase in heat production of 10% was observed with long shortening distances when comparison was made to a control heat-stress curve obtained by preshortening the muscles; however, this difference is most likely due to an underestimate of the magnitude of the activation heat component in these control heat-stress curves. An increase in isometric heat production due to maintained stretch per se was observed. The present data indicate that it is unlikely that there is a significant shortening heat component when cardiac muscle shortens. The absence of such a metabolic component may account for the rapid fall off in total enthalpy output in isotonic contractions at low to medium afterloads when compared with the skeletal muscle data.

The theory of sliding filament models for muscle contraction. I. The two-state model

The mechanical and thermal properties of Huxley's 1957 sliding filament model for striated muscle contraction are reconsidered, with emphasis on general relationships between two-state models and muscle behaviour. New empirical forms for the rate functions f(x) and g(x) are proposed, which give an improved fit to experiments. A specific procedure, based on the shortening heat, for determining model parameters is described and applied to various choices of rate functions. The change in slope of the tension-velocity curve observed by Katz is shown to require at least one discontinuity in the binding rate f(x), and a general formula is given. The two-state model also gives a symmetric cusp in the ATP-rate vs velocity curve at v = 0. The theory is extended to time-varying situations and applied to transient responses following isometric activation by tetanus (including latency relaxation), and unloaded and after-loaded contractions. The early burst of heat production can also be fitted by assigning appropriate values to the heats of binding and dissociation.