Fenn Effect Research Articles

Weakly-Bound, Non-Linear Elastic Cross-Bridges are Required to Self-Consistently Model the FENN Effect, Force Velocity and Tension Transients in Muscle Fibers

Weakly-Bound, Non-Linear Elastic Cross-Bridges are Required to Self-Consistently Model the FENN Effect, Force Velocity and Tension Transients in Muscle Fibers

Muscle Measurements Show Weakly Bound Cross-Bridges Act as a Viscous Drag

Molecular measurements of muscle myosin interacting with actin are described by a four-state mechanochemical model. The model contains two bound states, where myosin is attached to actin, and two unbound states, where myosin does not interact with actin. However, previous experiments in solution and on muscle fibers suggest another short-lived interaction between myosin and actin, the weakly bound state. While each of the two bound states can be directly observed at the single molecule level, this third, weakly bound, state is too brief to observe with the typical resolution of these experiments (∼1ms). Does this weakly bound state contribute to muscle force generation and, if so, what is its role? To begin addressing these questions, we compared two models, 1) a four-state model (lacking a weakly bound state) and 2) a five-state model (including a weakly bound state), to published experimental measurements made with whole muscles or muscle fibers. We found that both models fit classical measurements of heat generation as a function of work done by a muscle (the Fenn effect), and measurements of shortening rate as a function of resistive force (the Hill force-velocity relation). However, only the five-state model describes both data sets with a consistent set of parameters. Additionally, both models predict a phenomenon called stretch-activation, defined as a delayed increase in force following rapid lengthening of an otherwise isometric muscle. However, experimental results show the delayed increase in force upon stretch is preceded by an initial peak (phase I) and transient decrease (phase II) in force. Phase II is missing in the four-state model, but present in the five-state model. These results are consistent with the weakly bound state acting as a viscous drag on the thin filament.

Effects of cross-bridge compliance on the force-velocity relationship and muscle power output.

Muscles produce force and power by utilizing chemical energy through ATP hydrolysis. During concentric contractions (shortening), muscles generate less force compared to isometric contractions, but consume greater amounts of energy as shortening velocity increases. Conversely, more force is generated and less energy is consumed during eccentric muscle contractions (lengthening). This relationship between force, energy use, and the velocity of contraction has important implications for understanding muscle efficiency, but the molecular mechanisms underlying this behavior remain poorly understood. Here we used spatially-explicit, multi-filament models of Ca2+-regulated force production within a half-sarcomere to simulate how force production, energy utilization, and the number of bound cross-bridges are affected by dynamic changes in sarcomere length. These computational simulations show that cross-bridge binding increased during slow-velocity concentric and eccentric contractions, compared to isometric contractions. Over the full ranges of velocities that we simulated, cross-bridge cycling and energy utilization (i.e. ATPase rates) increased during shortening, and decreased during lengthening. These findings are consistent with the Fenn effect, but arise from a complicated relationship between velocity-dependent cross-bridge recruitment and cross-bridge cycling kinetics. We also investigated how force production, power output, and energy utilization varied with cross-bridge and myofilament compliance, which is impossible to address under typical experimental conditions. These important simulations show that increasing cross-bridge compliance resulted in greater cross-bridge binding and ATPase activity, but less force was generated per cross-bridge and throughout the sarcomere. These data indicate that the efficiency of force production decreases in a velocity-dependent manner, and that this behavior is sensitive to cross-bridge compliance. In contrast, significant effects of myofilament compliance on force production were only observed during isometric contractions, suggesting that changes in myofilament compliance may not influence power output during non-isometric contractions as greatly as changes in cross-bridge compliance. These findings advance our understanding of how cross-bridge and myofilament properties underlie velocity-dependent changes in contractile efficiency during muscle movement.

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.

A re-interpretation of the rate of tension redevelopment (k TR) in active muscle

A slackening to zero tension by large length release (~20%) and a restretch of active muscle fibres cause a fall and a redevelopment in tension. According to the model of Brenner (Proc Natl Acad Sci USA 85(9):3265-3269, 1988), the rate constant of tension redevelopment (k TR) is the sum of attachment and detachment rate constants, hence is limited by the fast reaction. Here we propose a model in which, after restretch, cross-bridges cycle many times by stretching series elastic elements, hence k(TR) is limited by a slow reaction. To set up this model, we made an assumption that the stepping rate (v) decreases linearly with tension (F), which is consistent with the Fenn effect. The distance traveled by a cross-bridge stretches series elastic elements with stiffness σ. With these assumptions, we set up a first order differential equation, which results in an exponential time course with the rate constant k(TR) = ση(0)ν(0)(1 - λ)/F(1), where λ = ν(1)/ν(0), η = step size, the subscript 0 indicates unloaded condition, and the subscript 1 indicate isometric condition. We demonstrate that the ATP hydrolysis rate (=[myosin head]/ν(0)) is proportionate to k(TR) as the ambient temperature is changed, and that the published data fit to this relationship well if λ = 0.28. We conclude that k(TR) is limited by the cross-bridge turnover rate; hence it represents the rate constant of the slowest reaction of the cross-bridge cycle, i.e. the ADP isomerization step before ADP is released.

A New Theory on k(TR) with Series Elastic Elements

It has been known that when the length of active muscle fiber is released suddenly by ∼15% and re-stretched, tension falls to 0, then it redevelops exponentially with the rate constant ktr. The rise of tension has been interpreted to represent the force generation step (partial cross-bridge cycle). Here we propose a model, in which cross-bridges cycle many times in this period by stretching series elastic elements. One assumption needed is either the step size (η) or the stepping rate (v) decreases linearly with tension(F): η=η0{1-F(t)/F0} (1), or ν = ν0{1-F(t)/F0} (2), where F0 is isometric tension; η0 is step size and ν0 is the number of steps/sec without load. Eqs. 1 and 2 are mathematical representations of the Fenn effect. Distance travelled by cross-bridges in time dt is ηvdt, which stretches series elastic with stiffness σ. Thus, the increase in tension is: dF=σvηdt. By using Eq. 1 or 2, we get: dF/dt+kF=kF0 (3), where k=ση0ν0/F0 (4). By solving Eq. 3 with F(0)=0, we get F(t)=F0{1-exp(-kt)} (5). Eq. 5 is a good approximation of tension time course which deduced kTR. From Eq. 4, it can be concluded that kTR is proportionately related to the turn over rate (ν0). Because ATPase=M0ν0 (M0 is myosin concentration), k=ATPase•ση0/F0M0 (6). Our available data on rabbit psoas fibers on kTR and ATPase at 10°C–25°C demonstrate that these are proportionately related, as predicted by Eq. 6. Our data further demonstrate that kTR and 2πa (slowest rate constant of tension transients) are linearly related by 2πa=0.71kTR+0.89s−1, demonstrating that 2πa is also limited by the turn over rate. In the two state model with attachment rate (f) and detachment rate (g), the turnover rate is v0=fg/(f+g), hence kTR=(ση0/F0)(fg)/(f+g) (limited by a slow reaction). Therefore, kTR≠ f+g (limited by a fast reaction).

Does negative work cost less

The Fenn effect states that the cost of producing work by muscle is higher than producing no work at all. Here we evaluate whether negative work costs even less. We measured the cost of force production in contractions where work (concentric), no work (isometric) and negative work (eccentric) were done using a new apparatus for measuring human muscle mechanics and energetics in vivo. Our mechanical apparatus allows measurements at the same force, displacement and duration for all contraction types simultaneous with magnetic resonance (MRI) measures of the ATP cost. This unique suite of controls and measurements in the same individual allows for a direct comparison of the cost of force production (ATP/(kN·s)) between the different types of contractions. Contrary to our original thought negative work during eccentric contractions (20±4 ATP/(kN·s)) had the same cost of force production as no work (18±6 ATP/(kN·s)) in an isometric contraction but both were less than half the cost of force production (53±9 ATP/(kN·s)) in a concentric working contraction. This suggests a common mechanism underlies the cost of force in contractions that produce no work and negative work, which is more economical than force production in contractions that generate positive work. The key difference appears to be that the generation of movement requires more energy than contractions that are static or resist movement during force production. So contrary to the natural extension of the Fenn effect, negative work is not cheaper but costs the same as no work at all.

Effects of Speed and Slope on Ski Skating Efficiency and Kinematics

Cross-country skiing is performed at varying speeds and slopes where a skier continuously needs to alter his technique in order to ski efficient. PURPOSE: To investigate the effects of speed and slope on gross efficiency (GE) and kinematics while treadmill roller skiing employing the skating G3 technique. METHODS: Seven male elite skiers performed nine 5-min submaximal stages. These stages were matched for low, moderate and high metabolic rates at inclinations of 2% (12, 17 and 22 km·h-1), 5% (9, 12 and 16 km·h-1) and 8% (6, 9 and 12 km·h-1), respectively. Oxygen uptake, respiratory exchange ratio and blood lactate concentration were used to determine physiological response and calculate metabolic rate. Work against gravity and friction determined work rate. GE was calculated as work rate divided by metabolic rate. Kinematics were analyzed using the Qualisys Pro Reflex system (Qualisys AB, Gothenburg, Sweden). RESULTS: A linear relationship between work rate and metabolic rate was found for each of the three different slopes (all P < 0.05). At the matched metabolic rates, work rates were always higher on steeper slopes (all P < 0.05). GE was consistently higher on steeper slopes, but increased at higher speed for all slopes, i.e, GE increased from ∼10% (at 2% inclination and 12 km·h-1) up to ∼16% (at 8% inclination and 12 km·h-1) (all P < 0.05). Cycle rate (CR) increased, whereas cycle time and cycle length decreased, both with increased speed and slope (all P < 0.05). Strong inter-individual correlations were found between GE and CR at the highest speed for all three slopes (all r = ∼0.90, P < 0.05). CONCLUSION: A linear relationship between work rate and metabolic rate, i.e., "Fenn effect", was found for cross-country skiing when treadmill roller skiing using a standardized slope and technique. Thus, GE slightly increases with speed from low to high metabolic rates. However, skiers show a higher efficiency and are able to obtain higher work rates on steeper slopes at a given metabolic rate. They do this by increasing CR, which is in contradiction with general findings in the literature. Yet, all skiers employ higher CR on steeper slopes, more efficient skiers were able to employ longer cycle lengths and lower cycle rates.

Efficiency in cycling: a review

We focus on the effect of cadence and work rate on energy expenditure and efficiency in cycling, and present arguments to support the contention that gross efficiency can be considered to be the most relevant expression of efficiency. A linear relationship between work rate and energy expenditure appears to be a rather consistent outcome among the various studies considered in this review, irrespective of subject performance level. This relationship is an example of the Fenn effect, described more than 80 years ago for muscle contraction. About 91% of all variance in energy expenditure can be explained by work rate, with only about 10% being explained by cadence. Gross efficiency is strongly dependent on work rate, mainly because of the diminishing effect of the (zero work-rate) base-line energy expenditure with increasing work rate. The finding that elite athletes have a higher gross efficiency than lower-level performers may largely be explained by this phenomenon. However, no firm conclusions can be drawn about the energetically optimal cadence for cycling because of the multiple factors associated with cadence that affect energy expenditure.

The energetics of allosteric regulation of ADP release from myosin heads

Myosin molecules are involved in a wide range of transport and contractile activities in cells. A single myosin head functions through its ATPase reaction as a force generator and as a mechanosensor, and when two or more myosin heads work together in moving along an actin filament, the interplay between these mechanisms contributes to collective myosin behaviors. For example, the interplay between force-generating and force-sensing mechanisms coordinates the two heads of a myosin V molecule in its hand-over-hand processive stepping along an actin filament. In muscle, it contributes to the Fenn effect and smooth muscle latch. In both examples, a key force-sensing mechanism is the regulation of ADP release via interhead forces that are generated upon actin-myosin binding. Here we present a model describing the mechanism of allosteric regulation of ADP release from myosin heads as a change, DeltaDeltaG(-D), in the standard free energy for ADP release that results from the work, Deltamicro(mech), performed by that myosin head upon ADP release, or DeltaDeltaG(-D) = Deltamicro(mech). We show that this model is consistent with previous measurements for strain-dependent kinetics of ADP release in both myosin V and muscle myosin II. The model makes explicit the energetic cost of accelerating ADP release, showing that acceleration of ADP release during myosin V processivity requires approximately 4 kT of energy whereas the energetic cost for accelerating ADP release in a myosin II-based actin motility assay is only approximately 0.4 kT. The model also predicts that the acceleration of ADP release involves a dissipation of interhead forces. To test this prediction, we use an in vitro motility assay to show that the acceleration of ADP release from both smooth and skeletal muscle myosin II correlates with a decrease in interhead force. Our analyses provide clear energetic constraints for models of the allosteric regulation of ADP release and provide novel, testable insights into muscle and myosin V function.

Force generation examined by laser temperature‐jumps in shortening and lengthening mammalian (rabbit psoas) muscle fibres

We examined the tension change induced by a rapid temperature jump (T-jump) in shortening and lengthening active muscle fibres. Experiments were done on segments of permeabilized single fibres (length (L0) ∼2 mm, sarcomere length 2.5 μm) from rabbit psoas muscle; [MgATP] was 4.6 mm, pH 7.1, ionic strength 200 mm and temperature ∼9°C. A fibre was maximally Ca2+-activated in the isometric state and a ∼3°C, rapid (< 0.2 ms), laser T-jump applied when the tension was approximately steady in the isometric state, or during ramp shortening or ramp lengthening at a limited range of velocities (0–0.2 L0 s−1). The tension increased to 2- to 3 × P0 (isometric force) during ramp lengthening at velocities > 0.05 L0 s−1, whereas the tension decreased to about < 0.5 × P0 during shortening at 0.1–0.2 L0 s−1; the unloaded shortening velocity was ∼1 L0 s−1 and the curvature of the force–shortening velocity relation was high (a/P0 ratio from Hill's equation of ∼0.05). In isometric state, a T-jump induced a tension rise of 15–20% to a new steady state; by curve fitting, the tension rise could be resolved into a fast (phase 2b, 40–50 s−1) and a slow (phase 3, 5–10 s−1) exponential component (as previously reported). During steady lengthening, a T-jump induced a small instantaneous drop in tension, followed by recovery, so that the final tension recorded with and without a T-jump was not significantly different; thus, a T-jump did not lead to a net increase of tension. During steady shortening, the T-jump induced a pronounced tension rise and both its amplitude and the rate (from a single exponential fit) increased with shortening velocity; at 0.1–0.2 L0 s−1, the extent of fibre shortening during the T-jump tension rise was estimated to be ∼1.2% L0 and it was shorter at lower velocities. At a given shortening velocity and over the temperature range of 8–30°C, the rate of T-jump tension rise increased with warming (Q10 ≈ 2.7), similar to phase 2b (endothermic force generation) in isometric muscle. Results are discussed in relation to the previous findings in isometric muscle fibres which showed that a T-jump promotes an early step in the crossbridge–ATPase cycle that generates force. In general, the finding that the T-jump effect on active muscle tension is pronounced during shortening, but is depressed/inhibited during lengthening, is consistent with the expectations from the Fenn effect that energy liberation (and acto-myosin ATPase rate) in muscle are increased during shortening and depressed/inhibited during lengthening.

Force Generation in Single Conventional Actomyosin Complexes under High Dynamic Load

The mechanical load borne by a molecular motor affects its force, sliding distance, and its rate of energy transduction. The control of ATPase activity by the mechanical load on a muscle tunes its efficiency to the immediate task, increasing ATP hydrolysis as the power output increases at forces less than isometric (the Fenn effect) and suppressing ATP hydrolysis when the force is greater than isometric. In this work, we used a novel ‘isometric’ optical clamp to study the mechanics of myosin II molecules to detect the reaction steps that depend on the dynamic properties of the load. An actin filament suspended between two beads and held in separate optical traps is brought close to a surface that is sparsely coated with motor proteins on pedestals of silica beads. A feedback system increases the effective stiffness of the actin by clamping the force on one of the beads and moving the other bead electrooptically. Forces measured during actomyosin interactions are increased at higher effective stiffness. The results indicate that single myosin molecules transduce energy nearly as efficiently as whole muscle and that the mechanical control of the ATP hydrolysis rate is in part exerted by reversal of the force-generating actomyosin transition under high load without net utilization of ATP.

Temperature-jump-induced (endothermic) muscle force generation is sensitive to filament sliding, demonstrating the Fenn effect

Temperature-jump-induced (endothermic) muscle force generation is sensitive to filament sliding, demonstrating the Fenn effect

The Sarcomeric Control of Energy Conversion

The Frank-Starling Law, Fenn Effect, and Suga's suggestions of cardiac muscle constant contractile efficiency establish the dependence of cardiac mechanics and energetics on the loading conditions. Consistent with these observations, this review suggests that the sarcomere control of contraction consists of two dominant feedbacks: (1) a cooperativity mechanism (positive feedback), whereby the number of force-generating cross-bridges (XBs) determines the affinity of calcium binding to the troponin regulatory protein; and (2) a mechanical (negative) feedback, whereby the filament shortening velocity affects the rate of XB turnover from the force to the non-force generating conformation. The study explains the roles of these feedbacks in providing the adaptive control of energy consumption by the loading conditions and validates the dependence of the cooperativity mechanism on the number of strong XBs. The cooperativity mechanism regulates XB recruitment. It explains the cardiac force-length calcium relationship, the related Frank-Starling Law of the heart, and the adaptive control of new XB recruitment and the associated adenosine triphosphate (ATP) consumption. The mechanical feedback explains the force-velocity relationship and the constant and high-contractile efficiency. These mechanisms were validated by testing the force responses to large amplitude (100 nm/sarcomere) sarcomere length (SL) oscillations, in intact tetanized trabeculae (utilizing 30 microM cyclopiazonic). The force responses to large-length oscillations lag behind the imposed oscillations at low extracellular calcium concentration ([Ca(2+)](0)) and slow frequencies (<4 Hz, 25 degrees C), yielding counterclockwise hystereses in the force-length plane. The force was higher during shortening than during lengthening. The area within these hystereses corresponds to the external work generated from new XB recruitment during each oscillation, and it is determined by the delay in the force response. Characterization of the delayed response and its dependence on the SL, force, and calcium allows identification of the regulation of XB recruitment. The direct dependence of the phase on force indicates that XB recruitment is determined directly by the force (i.e., the number of strong XBs) and indirectly by SL or calcium. The suggested feedbacks determine cardiac energetics: 1) the constant and high contractile efficiency is an intrinsic property of the single XB, due to the mechanical feedback; and 2) the XBs are the myocyte sensors that modulate XB recruitment in response to length and load changes through the cooperativity mechanism.

Adenosine diphosphate and strain sensitivity in myosin motors

The release of adenosine diphosphate (ADP) from the actomyosin cross-bridge plays an important role in the adenosine-triphosphate-driven cross-bridge cycle. In fast contracting muscle fibres, the rate at which ADP is released from the cross-bridge correlates with the maximum shortening velocity of the muscle fibre, and in some models the rate of ADP release defines the maximum shortening velocity. In addition, it has long been thought that the rate of ADP release could be sensitive to the load on the cross-bridge and thereby provide a molecular explanation of the Fenn effect. However, direct evidence of a strain-sensitive ADP-release mechanism has been hard to come by for fast muscle myosins. The recently published evidence for a strain-sensing mechanism involving ADP release for slower muscle myosins, and in particular non-muscle myosins, is more compelling and can provide the mechanism of processivity for motors such as myosin V. It is therefore timely to examine the evidence for this strain-sensing mechanism. The evidence presented here will argue that a strain-sensitive mechanism of ADP release is universal for all myosins but the basic mechanism has evolved in different ways for different types of myosin. Furthermore, this strain-sensing mechanism provides a way of coordinating the action of multiple myosin motor domains in a single myosin molecule, or in complex assemblies of myosins over long distances without invoking a classic direct allosteric or cooperative communication between motors.

Load-dependent kinetics of force production by smooth muscle myosin measured with optical tweezers.

Muscle contraction is driven by the cyclical interaction of myosin with actin, coupled with ATP hydrolysis. Myosin attaches to actin, forming a crossbridge that produces force and movement as it tilts or rocks into subsequent bound states before finally detaching. It has been hypothesized that the kinetics of one or more of these mechanical transitions are dependent on load, allowing muscle to shorten quickly under low load, but to sustain tension economically, with slowly cycling crossbridges under high load conditions. The idea that muscle biochemistry depends on mechanical output is termed the 'Fenn effect'. However, the molecular details of how load affects the kinetics of a single crossbridge are unknown. Here, we describe a new technique based on optical tweezers to rapidly apply force to a single smooth muscle myosin crossbridge. The crossbridge produced movement in two phases that contribute 4 nm + 2 nm of displacement. Duration of the first phase depended in an exponential manner on the amplitude of applied load. Duration of the second phase was much less affected by load, but was significantly shorter at high ATP concentration. The effect of load on the lifetime of the bound crossbridge is to prolong binding when load is high, but to accelerate release when load is low or negative.

The off rate of Ca(2+) from troponin C is regulated by force-generating cross bridges in skeletal muscle.

The effects of dissociation of force-generating cross bridges on intracellular Ca(2+), pCa-force, and pCa-ATPase relationships were investigated in mouse skeletal muscle. Mechanical length perturbations were used to dissociate force-generating cross bridges in either intact or skinned fibers. In intact muscle, an impulse stretch or release, a continuous length vibration, a nonoverlap stretch, or an unloaded shortening during a twitch caused a transient increase in intracellular Ca(2+) compared with that in isometric controls and resulted in deactivation of the muscle. In skinned fibers, sinusoidal length vibrations shifted pCa-force and pCa-actomyosin ATPase rate relationships to higher Ca(2+) concentrations and caused actomyosin ATPase rate to decrease at submaximal Ca(2+) and increase at maximal Ca(2+) activation. These results suggest that dissociation of force-generating cross bridges during a twitch causes the off rate of Ca(2+) from troponin C to increase (a decrease in the Ca(2+) affinity of troponin C), thus decreasing the Ca(2+) sensitivity and resulting in the deactivation of the muscle. The results also suggest that the Fenn effect only exists at maximal but not submaximal force-activating Ca(2+) concentrations.

Muscle contraction as a Markov process. I: Energetics of the process.

Force generation during muscle contraction can be understood in terms of cyclical length changes in segments of actin thin filaments moving through the three-dimensional lattice of myosin thick filaments. Recent anomalies discovered in connection with analysis of myosin step sizes in in vitro motility assays and with skinned fibres can be rationalized by assuming that ATP hydrolysis on actin accompanies these length changes. The paradoxically rapid regeneration of tension in quick release experiments, as well as classical energetic relationships, such as Hill's force-velocity curve, the Fenn effect, and the unexplained enthalpy of shortening, can be given mutually self-consistent explanations with this model. When muscle is viewed as a Markov process, the vectorial process of chemomechanical transduction can be understood in terms of lattice dependent transitions, wherein the phosphate release steps of the myosin and actin ATPases depend only on occurrence of allosteric changes in neighbouring molecules. Tropomyosin has a central role in coordinating the steady progression of these cooperative transitions along actin filaments and in gearing up the system in response to higher imposed loads.

Muscle contraction as a Markov process I: energetics of the process

Force generation during muscle contraction can be understood in terms of cyclical length changes in segments of actin thin filaments moving through the three-dimensional lattice of myosin thick filaments. Recent anomalies discovered in connection with analysis of myosin step sizes in in vitro motility assays and with skinned fibres can be rationalized by assuming that ATP hydrolysis on actin accompanies these length changes. The paradoxically rapid regeneration of tension in quick release experiments, as well as classical energetic relationships, such as Hill's force–velocity curve, the Fenn effect, and the unexplained enthalpy of shortening, can be given mutually self-consistent explanations with this model. When muscle is viewed as a Markov process, the vectorial process of chemomechanical transduction can be understood in terms of lattice dependent transitions, wherein the phosphate release steps of the myosin and actin ATPases depend only on occurrence of allosteric changes in neighbouring molecules. Tropomyosin has a central role in coordinating the steady progression of these cooperative transitions along actin filaments and in gearing up the system in response to higher imposed loads.

Evidence for the load-dependent mechanical efficiency of individual myosin heads in skeletal muscle fibers activated by laser flash photolysis of caged calcium in the presence of a limited amount of ATP.

Although a contracting muscle regulates its energy output depending on the load imposed on it ("Fenn effect"), the mechanism underlying the load-dependent energy output remains obscure. To explore the possibility that the mechanical efficiency, with which chemical energy derived from ATP hydrolysis is converted into mechanical work, of individual myosin heads changes in a load-dependent manner, we examined the auxotonic shortening of glycerinated rabbit psoas muscle fibers, containing ATP molecules almost equal in number to the myosin heads, after laser-flash photolysis of caged calcium. Immediately before laser-flash activation, almost all of the myosin heads in the fiber are in the state M.ADP.Pi, and can undergo only one ATP hydrolysis cycle after activation. When the fibers were activated to shorten under various auxotonic loads, the length, force, and power output changes were found to be scaled according to the auxotonic load. Both the power and energy outputs were maximal under a moderate auxotonic load. The amount of M.ADP.Pi utilized at a time after activation was estimated from the amount of isometric force developed after interruption of fiber shortening. This amount was minimal in the isometric condition and increased nearly in proportion to the distance of fiber shortening. These results are taken as evidence that the efficiency of chemomechanical energy conversion in individual myosin heads changes in a load-dependent manner.