Modulation of passive force in single skeletal muscle fibres

In this study, we investigated the effects of activation and stretch on the passive force-sarcomere length relationship in skeletal muscle. Single fibres from the lumbrical muscle of frogs were placed at varying sarcomere lengths on the descending limb of the force-sarcomere length relationship, and tetanic contractions, active stretches and passive stretches (amplitudes of ca 10% of fibre length at a speed of 40% fibre length/s) were performed. The passive forces following stretch of an activated fibre were higher than the forces measured after isometric contractions or after stretches of a passive fibre at the corresponding sarcomere length. This effect was more pronounced at increased sarcomere lengths, and the passive force-sarcomere length relationship following active stretch was shifted upwards on the force axis compared with the corresponding relationship obtained following isometric contractions or passive stretches. These results provide strong evidence for an increase in passive force that is mediated by a length-dependent combination of stretch and activation, while activation or stretch alone does not produce this effect. Based on these results and recently published findings of the effects of Ca2+ on titin stiffness, we propose that the observed increase in passive force is caused by the molecular spring titin.     

Force enhancement above the initial isometric force on the descending limb of the force-length relationship

Edman et al. (J. General Physiol. 80 (1982) 769) observed in single fibres of frog that the steady-state forces following active fibre stretch were greater than the purely isometric force obtained at the length from which the stretch was initiated. Operating on the descending limb of the force-length relationship, such a result can only be explained within the framework of the sarcomere length non-uniformity theory, if some fibre segments shortened during the fibre stretch. However, such a result was not found, leaving Edman's observation unexplained. Force enhancement above the initial isometric force has not been investigated systematically in whole muscle, and therefore it is not known whether this property is also part of whole muscle mechanics. The purpose of this study was to test if the steady-state forces following active stretch of cat semitendinosus were greater than the corresponding purely isometric forces at the muscle length from which the stretch was started. Cat semitendinosus was stretched by various amounts on the descending limb of the force-length relationship, and the steady-state forces following these stretches were compared to the corresponding isometric forces at the initial and final muscle lengths. In 109 of 131 tests, the steady-state forces following stretching were greater than the isometric forces at the initial muscle lengths. Force enhancement increased with increasing amounts of stretching, and force enhancement above the initial isometric force was more likely to occur following stretches of great compared to small amplitude. Passive forces following active muscle stretching were often significantly greater than the passive forces at the same muscle length following an isometric contraction or a passive stretching of the muscle. This observation was made consistently at the longest muscle lengths tested. It appears, therefore, that there is a passive force that accounts for part of the force enhancement above the isometric force at the initial muscle length, and that provides increased passive force when a muscle is actively, rather than passively, stretched at long muscle lengths. We conclude that cat semitendinosus demonstrates steady-state force enhancement above the corresponding purely isometric force at the initial muscle length on the descending limb of the force-length relationship for many contractile conditions, and that a unique, and so far undetected, passive, parallel element contributes to this force enhancement, particularly at long muscle lengths where muscle is assumed to be most vulnerable to injuries associated with sarcomere length instability.     

Muscle architecture and force-velocity relationships in humans

The in vivo torque-velocity relationships of the knee extensors (KE), knee flexors (KF), ankle plantarflexors (PF), and ankle dorsiflexors (DF) were determined in 12 untrained subjects using an isokinetic testing device (Cybex II). These data were then matched to the predicted maximum forces and shortening velocities derived from muscle architectural determinations made on three hemipelvectomies (36). The torque-velocity curves of all muscle groups resembled that predicted by Hill's (19, 20) equation except at the higher forces and lower velocities. The peak torques occurred at mean velocities ranging from 41-62 rad X s-1 for the KE, KF, and PF. Although the peak torque of the DF occurred at the isometric loading condition, it was also lower than that predicted by Hill's equation. The muscle fiber length and physiological cross-sectional area measurements indicate that the architecture of the human leg musculature has a major influence on the torque-velocity characteristics. These data corroborate previous findings (24) that some neural inhibitory mechanism exists in the control of the leg musculature, which limits the maximum forces that could be produced under optimal stimulating conditions.     

The effects of muscle stretching and shortening on isometric forces on the descending limb of the force-length relationship

The purpose of this study was to examine the effects of stretching and shortening on the isometric forces at different lengths on the descending limb of the force-length relationship. Cat soleus (N = 10) was stretched and shortened by various amounts on the descending limb of the force-length relationship, and the steady-state forces following these dynamic contractions were compared to the isometric forces at the corresponding muscle lengths. We found a shift of the force-length relationship to greater force values following muscle stretching, and to smaller force values following muscle shortening. Shifts in both directions critically depended on the magnitude of stretching/shortening and the final muscle length. We confirm recent findings that the steady-state isometric force following some stretch conditions clearly exceeded the maximal isometric forces at optimum muscle length, and that force enhancement was associated with an increase in the passive force, i.e., a passive force enhancement. When the passive force enhancement was subtracted from the total force enhancement, forces following stretch were always equal to or smaller than the isometric force at optimum muscle length. Together, these findings led to the conclusions: (a). that force enhancement is composed of an "active and a "passive" component; (b). that the "passive" component of force enhancement allows for forces greater than the maximal isometric forces at the muscle's optimum length; and (c). that force enhancement and force depression are critically affected by muscle length and stretch/shortening amplitude.     

Stretch-induced,steady-state force enhancement in single skeletal muscle fibers exceeds the isometric force at optimum fiber length

Stretch-induced force enhancement has been observed in a variety of muscle preparations and on structural levels ranging from single fibers to in vivo human muscles. It is a well-accepted property of skeletal muscle. However, the mechanism causing force enhancement has not been elucidated, although the sarcomere-length non-uniformity theory has received wide support. The purpose of this paper was to re-investigate stretch-induced force enhancement in frog single fibers by testing specific hypotheses arising from the sarcomere-length non-uniformity theory. Single fibers dissected from frog tibialis anterior (TA) and lumbricals (n=12 and 22, respectively) were mounted in an experimental chamber with physiological Ringer's solution (pH=7.5) between a force transducer and a servomotor length controller. The tetantic force-length relationship was determined. Isometric reference forces were determined at optimum length (corresponding to the maximal, active, isometric force), and at the initial and final lengths of the stretch experiments. Stretch experiments were performed on the descending limb of the force-length relationship after maximal tetanic force was reached. Stretches of 2.5-10% (TA) and 5-15% lumbricals of fiber length were performed at 0.1-1.5 fiber lengths/s. The stretch-induced, steady-state, active isometric force was always equal or greater than the purely isometric force at the muscle length from which the stretch was initiated. Moreover, for stretches of 5% fiber length or greater, and initiated near the optimum length of the fiber, the stretch-enhanced active force always exceeded the maximal active isometric force at optimum length. Finally, we observed a stretch-induced enhancement of passive force. We conclude from these results that the sarcomere length non-uniformity theory alone cannot explain the observed force enhancement, and that part of the force enhancement is associated with a passive force that is substantially greater after active compared to passive muscle stretch.     

The mechanical response of active human muscle during and after stretch

Five subjects contracted forearm supinator muscles which were stretched after development of maximal isometric torque. The ratio of torque at the end of stretch over isometric torque at that position was calculated as excess torque. Excess torque increased with stretch velocity and decreased with stretch amplitude, and it was not dependent upon final muscle length. The rate of decay of torque following stretch could not be shown to depend upon stretch variables. The absence of significant changes in myoelectric activity suggested that with high initial forces, reflex activity did not account for the observed changes. Time-constants of decay (0.15 s to 1.8 s) were much greater than time-constants of rise (approx. 0.07 s) of isometric torque at the same muscle length. This indicates that interaction of series elastic and contractile elements is not the sole cause of prolonged torque following stretch. It is concluded that stretch temporarily enhances the intrinsic contractile properties of a group of human muscles in a manner similar to, but quantitatively different from that seen in isolated muscle preparations.     

Measurement of active muscle stiffness with and without the stretch reflex

The purpose of the present study was to evaluate active muscle stiffness with the stretch reflex according to changes (in 110-ms period after stretching) in torque and fascicle length during slower angular velocity (peak angular velocity of 100 deg·s⁻¹) in comparison with active muscle stiffness without the stretch reflex (in 60-ms period after stretching) during slower and faster (peak angular velocity of 250 deg·s⁻¹) angular velocities. Active muscle stiffness in the medial gastrocnemius muscle was calculated according to changes in estimated muscle force and fascicle length with slower and faster stretching during submaximal isometric contractions (10–90% maximal voluntary contractions). Active muscle stiffness significantly increased for both angular velocities and analyzed periods as torque levels exerted became higher. The effects of angular velocities and the interaction between angular velocities and torque levels were not significantly different between 250 deg·s⁻¹ (in 60-ms period after stretching) and 100 deg·s⁻¹ (in 110-ms period after stretching) conditions. The effects of the analyzed periods and the interaction between analyzed periods and torque levels were not significantly different between the analyzed periods (60-ms and 110-ms periods after stretching) for the 100 deg·s⁻¹ condition. Furthermore, active muscle stiffness measured during the same angular velocity had significant correlations between those calculated in the different analyzed periods, whereas those under 250 deg·s⁻¹ (60-ms period after stretching) did not correlate with those under 100 deg·s⁻¹ (110-ms period after stretching). These results suggest that active muscle stiffness is not influenced by the stretch reflex.     

Pre-power stroke cross bridges contribute to force during stretch of skeletal muscle myofibrils

When activated skeletal muscle is stretched, force increases in two phases. This study tested the hypothesis that the increase in stretch force during the first phase is produced by pre-power stroke cross bridges. Myofibrils were activated in sarcomere lengths (SLs) between 2.2 and 2.5 microm, and stretched by approximately 5-15 per cent SL. When stretch was performed at 1 microms-1SL-1, the transition between the two phases occurred at a critical stretch (SLc) of 8.4+/-0.85 nm half-sarcomere (hs)-1 and the force (critical force; Fc) was 1.62+/-0.24 times the isometric force (n=23). At stretches performed at a similar velocity (1 microms-1SL-1), 2,3-butanedione monoxime (BDM; 1 mM) that biases cross bridges into pre-power stroke states decreased the isometric force to 21.45+/-9.22 per cent, but increased the relative Fc to 2.35+/-0.34 times the isometric force and increased the SLc to 14.6+/-0.6 nm hs-1 (n=23), suggesting that pre-power stroke cross bridges are largely responsible for stretch forces.     

Residual force enhancement after lengthening is present during submaximal plantar flexion and dorsiflexion actions in humans.

Stretch of an activated muscle causes a transient increase in force during the stretch and a sustained, residual force enhancement (RFE) after the stretch. The purpose of this study was to determine whether RFE is present in human muscles under physiologically relevant conditions (i.e., when stretches were applied within the working range of large postural leg muscles and under submaximal voluntary activation). Submaximal voluntary plantar flexion (PF(v)) and dorsiflexion (DF(v)) activation was maintained by providing direct visual feedback of the EMG from soleus or tibialis anterior, respectively. RFE was also examined during electrical stimulation of the plantar flexion muscles (PF(s)). Constant-velocity stretches (15 degrees /s) were applied through a range of motion of 15 degrees using a custom-built ankle torque motor. The muscles remained active throughout the stretch and for at least 10 s after the stretch. In all three activation conditions, the stable joint torque measured 9-10 s after the stretch was greater than the isometric joint torque at the final joint angle. When expressed as a percentage of the isometric torque, RFE values were 7, 13, and 12% for PF(v), PF(s), DF(v), respectively. These findings indicate that RFE is a characteristic of human skeletal muscle and can be observed during submaximal (25%) voluntary activation when stretches are applied on the ascending limb of the force-length curve. Although the underlying mechanisms are unclear, it appears that sarcomere popping and passive force enhancement are insufficient to explain the presence of RFE in these experiments.     

Force during stretches of rat skeletal muscles after hypertonia at short and long lengths

Following injection of tetanus toxin into rat gastrocnemius muscle to produce hypertonia, plantar flexor muscles were allowed to shorten (S, n=5) without restraint or held lengthened (L, n=3) by splinting. Saline injected rats served as control (n=5). One week after injection, peak forces during 3 stretches with passive muscles and acute isometric force deficits produced by 15 stretches of electrically stimulated muscles were examined under pentobarbital anesthesia. Isometric force and mass of plantar flexors were similar in S rats but 16% lower in L rats compared to control. Peak passive forces were highest in S rats but not different between L rats and control. At the end of the stretch protocol, isometric force deficits were 26% larger in S rats compared to L rats and 17% smaller in L rats compared to control. Acute isometric force deficits produced by stretches of active skeletal muscles were dependent on the muscle length maintained during hypertonia. Our animal model could be used to test rehabilitation interventions during hypertonia of skeletal muscles.     

A non-cross-bridge stiffness in activated frog muscle fibers

Force responses to fast ramp stretches of various amplitude and velocity, applied during tetanic contractions, were measured in single intact fibers from frog tibialis anterior muscle. Experiments were performed at 14 degrees C at approximately 2.1 microm sarcomere length on fibers bathed in Ringer's solution containing various concentrations of 2,3-butanedione monoxime (BDM) to greatly reduce the isometric tension. The fast tension transient produced by the stretch was followed by a period, lasting until relaxation, during which the tension remained constant to a value that greatly exceeded the isometric tension. The excess of tension was termed "static tension," and the ratio between the force and the accompanying sarcomere length change was termed "static stiffness." The static stiffness was independent of the active tension developed by the fiber, and independent of stretch amplitude and stretching velocity in the whole range tested; it increased with sarcomere length in the range 2.1-2.8 microm, to decrease again at longer lengths. Static stiffness increased well ahead of tension during the tetanus rise, and fell ahead of tension during relaxation. These results suggest that activation increased the stiffness of some sarcomeric structure(s) outside the cross-bridges.     

Residual force enhancement exceeds the isometric force at optimal sarcomere length for optimized stretch conditions.

Residual force enhancement (FE) following stretch of an activated muscle is a well accepted property of skeletal muscle contraction. However, the mechanism underlying FE remains unknown. A crucial assumption on which some proposed mechanisms are based is the idea that forces in the enhanced state cannot exceed the steady-state isometric force at a sarcomere length associated with optimal myofilament overlap. Although there are a number of studies in which forces in the enhanced state were compared with the corresponding isometric forces on the plateau of the force-length relationship, these studies either did not show enhanced forces above the plateau or, if they did, they lacked measurements of sarcomere lengths confirming the plateau region. Here, we revisited this question by optimizing stretch conditions and measuring the average sarcomere lengths in isolated fibers, and we found that FE exceeded the maximal isometric reference force obtained at the plateau of the force-length relationship consistently (mean+/-SD: 4.8+/-2.1%) and by up to 10%. When subtracting the passive component of FE from the total FE, the enhanced forces remained greater than the isometric plateau force (mean+/-SD: 4.3+/-2.0%). Calcium-induced increases in passive forces, known to be present in single fibers and myofibrils, are too small to account for the FE observed here. We conclude that FE cannot be explained exclusively with a stretch-induced development of sarcomere length nonuniformities, that FE in single fibers may be associated with the recruitment of additional contractile force, and that isometric steady-state forces in the enhanced state are not uniquely determined by sarcomere lengths.     

Acceleration of stretch activation in murine myocardium due to phosphorylation of myosin regulatory light chain

The regulatory light chains (RLCs) of vertebrate muscle myosins bind to the neck region of the heavy chain domain and are thought to play important structural roles in force transmission between the cross-bridge head and thick filament backbone. In vertebrate striated muscles, the RLCs are reversibly phosphorylated by a specific myosin light chain kinase (MLCK), and while phosphorylation has been shown to accelerate the kinetics of force development in skeletal muscle, the effects of RLC phosphorylation in cardiac muscle are not well understood. Here, we assessed the effects of RLC phosphorylation on force, and the kinetics of force development in myocardium was isolated in the presence of 2,3-butanedione monoxime (BDM) to dephosphorylate RLC, subsequently skinned, and then treated with MLCK to phosphorylate RLC. Since RLC phosphorylation may be an important determinant of stretch activation in myocardium, we recorded the force responses of skinned myocardium to sudden stretches of 1% of muscle length both before and after treatment with MLCK. MLCK increased RLC phosphorylation, increased the Ca(2+) sensitivity of isometric force, reduced the steepness of the force-pCa relationship, and increased both Ca(2+)-activated and Ca(2+)-independent force. Sudden stretch of myocardium during an otherwise isometric contraction resulted in a concomitant increase in force that quickly decayed to a minimum and was followed by a delayed redevelopment of force, i.e., stretch activation, to levels greater than pre-stretch force. MLCK had profound effects on the stretch activation responses during maximal and submaximal activations: the amplitude and rate of force decay after stretch were significantly reduced, and the rate of delayed force recovery was accelerated and its amplitude reduced. These data show that RLC phosphorylation increases force and the rate of cross-bridge recruitment in murine myocardium, which would increase power generation in vivo and thereby enhance systolic function.     

Cross-bridge attachment during high-speed active shortening of skinned fibers of the rabbit psoas muscle: implications for cross-bridge action during maximum velocity of filament sliding

To characterize the kinetics of cross-bridge attachment to actin during unloaded contraction (maximum velocity of filament sliding), ramp-shaped stretches with different stretch-velocities (2-40,000 nm per half-sarcomere per s) were applied to actively contracting skinned fibers of the rabbit psoas muscle. Apparent fiber stiffness observed during such stretches was plotted versus the speed of the imposed stretch (stiffness-speed relation) to derive the rate constants for cross-bridge dissociation from actin. The stiffness-speed relation obtained for unloaded shortening conditions was shifted by about two orders of magnitude to faster stretch velocities compared to isometric conditions and was almost identical to the stiffness-speed relation observed in the presence of MgATPgammaS at high Ca(2+) concentrations, i.e., under conditions where cross-bridges are weakly attached to the fully Ca(2+) activated thin filaments. These data together with several control experiments suggest that, in contrast to previous assumptions, most of the fiber stiffness observed during high-speed shortening results from weak cross-bridge attachment to actin. The fraction of strongly attached cross-bridges during unloaded shortening appears to be as low as some 1-5% of the fraction present during isometric contraction. This is about an order of magnitude less than previous estimates in which contribution of weak cross-bridge attachment to observed fiber stiffness was not considered. Our findings imply that 1) the interaction distance of strongly attached cross-bridges during high-speed shortening is well within the range consistent with conventional cross-bridge models, i.e., that no repetitive power strokes need to be assumed, and 2) that a significant part of the negative forces that limit the maximum speed of filament sliding might originate from weak cross-bridge interactions with actin.     

Motor unit recruitment patterns during reflex compensation of muscle yield investigated by computer simulations

 An important function of the stretch reflex in the soleus muscle in the decerebrate cat preparation is to compensate for the tendency of muscle suddenly to yield during ramp increases in length. As the level of background (i.e. pre-stretch) force increases, there is a systematic change in the curvature of the force trajectory during this reflex compensation, from concave to convex with respect to increasing force. The hypothesis that this change in curvature was due to background force-dependent changes in the recruitment pattern of motor units was investigated with a combined computer simulation/ experimental technique. The simulation consisted of 20 model motor units for the soleus muscle, each based on a distributed moment muscle model. The timing of recruitment of the motor units was optimized to allow the simulation outputs to fit a set of experimental data records on the reflex response to stretch initiated at five different levels of pre-stretch force. The resulting recruitment patterns showed that a tendency for recruitment to be concentrated progressively in the early portion of the stretch as pre-stretch force increased could account for the changes in reflex force curvature. These results are consistent with the skewed distribution of intrinsic electrical thresholds of motoneurons, in which low-threshold units are much more frequent than high-threshold ones. Therefore the changes in recruitment pattern and reflex force curvature may be due primarily to the intrinsic properties of motoneurons. Received: 18 September 1995/Accepted in revised form: 21 May 1996     

Active force inhibition and stretch-induced force enhancement in frog muscle treated with BDM.

There is evidence that the stretch-induced residual force enhancement observed in skeletal muscles is associated with 1) cross-bridge dynamics and 2) an increase in passive force. The purpose of this study was to characterize the total and passive force enhancement and to evaluate whether these phenomena may be associated with a slow detachment of cross bridges. Single fibers from frog lumbrical muscles were placed at a length 20% longer than the plateau of the force-length relationship, and active and passive stretches (amplitudes of 5 and 10% of fiber length and at a speed of 40% fiber length/s) were performed. Experiments were conducted in Ringer solution and with the addition of 2, 5, and 10 mM of 2,3-butanedione monoxime (BDM), a cross-bridge inhibitor. The steady-state active and passive isometric forces after stretch of an activated fiber were higher than the corresponding forces measured after isometric contractions or passive stretches. BDM decreased the absolute isometric force and increased the total force enhancement in all conditions investigated. These results suggest that total force enhancement is directly associated with cross-bridge kinetics. Addition of 2 mM BDM did not change the passive force enhancement after 5 and 10% stretches. Addition of 5 and 10 mM did not change (5% stretches) or increased (10% stretches) the passive force enhancement. Increasing stretch amplitudes and increasing concentrations of BDM caused relaxation after stretch to be slower, and because passive force enhancement is increased at the greatest stretch amplitudes and the highest BDM concentrations, it appears that passive force enhancement may be related to slow-detaching cross bridges.     

Series elasticity in frog sartorius muscle during release and stretch

When a stretch is applied to an isolated muscle during tetanic stimulation, the force developed is higher than the maximal isometric tension (Po). This force puts the series elastic component (SEC) under tension and in a domain which is not well defined in terms of tension-extension curve. In the present work, an attempt was made to determine the stiffness of the SEC for tensions greater than Po, using the sartorius muscle of the frog. For this purpose, rapid releases and stretches of different amplitudes were given during maximal isometric contractions. Plotting normalized tension (P/Po) against normalized length changes (negative or positive extensions, delta L/Lo.10(2] produced a tension-extension curve. The slopes of the linear part of each relationship on both sides of Po indicated an increase in SEC stiffness when the muscle was rapidly stretched. Furthermore, the transient character of the increase in stiffness was studied by measuring SEC stiffness during rapid releases applied at various time intervals after stretches: the muscle was found to be stiffer as the time interval was shorter. The results are discussed in terms of (i) non-linear behaviour of the passive and active parts of the SEC, (ii) enhancement of storage and release of potential energy.     

Muscle activation and the isokinetic torque-velocity relationship of the human triceps surae

The influence of muscle activation and the time allowed for torque generation on the angle-specific torque-velocity relationship of the triceps surae was studied during plantar flexion using supramaximal electrical stimulation and a release technique on six male subjects [mean (SD) age 25 (4) years]. Torque-velocity data were obtained under different levels of constant muscle activation by varying the stimulus frequency and the time allowed for isometric torque generation prior to release and isokinetic shortening. To eliminate the effects of the frequency response on absolute torque the isokinetic data were normalized to the maximum isometric torque values at 0.44 rad. There were no significant differences in the normalized torques generated at any angular velocity using stimulus frequencies of 20, 50 or 80 Hz. When the muscle was stimulated at 50 Hz the torques obtained after a 400 ms and 1 s pre-release isometric contraction did not differ significantly. However, with no pre-release contraction significantly less torque was generated at all angular velocities beyond 1.05 rad · s^–1 when compared with either the 200, 400 ms or 1 s condition. With a 200 ms pre-release contraction significantly less torque was generated at angular velocities beyond 1.05 rad · s^–1 when compared with the 400 ms or 1 s conditions. It would seem that the major factor governing the shape of the torque-velocity curve at a constant level of muscle activation is the time allowed for torque generation.     

Force enhancement and relaxation rates after stretch of activated muscle fibres

The residual force enhancement following muscle stretch might be associated with an increase in the proportion of attached cross-bridges, as supported by stiffness measurements. In this case, it could be caused by an increase in the attachment or a decrease in the detachment rate of cross-bridges, or a combination of the two. The purpose of this study was to investigate if the stretch-induced force enhancement is related to cross-bridge attachment/detachment kinetics. Single muscle fibres dissected from the lumbrical muscle of frog were place at a length approximately 20% longer than the plateau of the force-length relationship; they were maximally activated, and after full isometric force was reached, ramp stretches were imposed with amplitudes of 5 and 10% fibre length, at a speed of 40% fibre length s(-1). Experiments were performed in Ringer's solution, and with the addition of 2, 5 and 10 nM of 2,3-butanedione monoxime (BDM), a drug that places cross-bridges in a pre-power-stroke, state, inhibiting force production. The total force following stretch was higher than the corresponding force measured after isometric contraction at the corresponding length. This residual force enhancement was accompanied by an increase relaxation time. BDM, which decreases force production during isometric contractions, considerably increased the relative levels of force enhancement. BDM also increased relaxation times after stretch, beyond the levels observed during reference contractions in Ringer's solution, and beyond isometric control tests at the corresponding BDM concentrations. Together, these results support the idea that force enhancement is caused, at least in part, by a decrease in cross-bridge detachment rates, as manifested by the increased relaxation times following fibre stretch.     

A comparison of the mechanical behavior of the cat soleus muscle with a distribution-moment model

A state-variable model for skeletal muscle, termed the "Distribution-Moment Model," is derived from A. F. Huxley's 1957 model of molecular contraction dynamics. The state variables are the muscle stretch and the three lowest-order moments of the bond-distribution function (which represent, respectively, the contractile tissue stiffness, the muscle force, and the elastic energy stored in the contractile tissue). The rate equations of the model are solved under various conditions, and compared to experimental results for the cat soleus muscle subjected to constant stimulation. The model predicts several observed effects, including yielding of the muscle force in constant velocity stretches, different "force-velocity relations" in isotonic and isovelocity experiments, and a decrease of peak force below the isometric level in small-amplitude sinusoidal stretches. Chemical energy and heat rates predicted by the model are also presented.