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.     

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.     

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.     

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.     

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.     

Shortening-induced force depression is primarily caused by cross-bridges in strongly bound states

The steady-state isometric force following active muscle shortening is smaller than the corresponding force obtained for purely isometric contractions. This so-called residual force depression has been observed consistently for more than half a century, however its mechanism remains a matter of scientific debate. [Maréchal, G., Plaghki, L., 1979. The deficit of the isometric tetanic tension redeveloped after a release of frog muscle at a constant velocity. J. Gen. Physiol. 73, 453–467] suggested that force depression might be caused by alterations in the cross-bridge kinetics following muscle shortening, but there is no research studying force depression systematically for altered cross-bridge kinetic conditions. The purpose of this study was to investigate if force depression affects so-called weakly and strongly bound cross-bridges to the same degree. In order to achieve this aim, we modified the ratio of weakly to strongly bound cross-bridges with 2,3-butanedione monoxime (BDM) in single frog fibers. BDM inhibits the formation of strongly bound cross-bridges in a dose-dependent manner, thus the ratio of weakly to strongly bound cross-bridges could be altered in a systematic way. We found that the absolute amount of force depression was decreased by 50% while the relative amount was decreased by 12% in BDM exposed fibers compared to fibers in normal Ringer's solution. Furthermore, force depression was accompanied by a decrease in stiffness that was much greater in normal compared to BDM exposed fibers, leading to the conclusion that force depression was caused by an inhibition of cross-bridge attachment following fiber shortening and that this inhibition primarily affected cross-bridges in the strongly bound states.     

Mysteries of muscle contraction

According to the cross-bridge theory, the steady-state isometric force of a muscle is given by the amount of actin-myosin filament overlap. However, it has been known for more than half a century that steady-state forces depend crucially on contractile history. Here, we examine history-dependent steady-state force production in view of the cross-bridge theory, available experimental evidence, and existing explanations for this phenomenon. This is done on various structural levels, ranging from the intact muscle to the myofibrillar and isolated contractile protein level, so that advantages and limitations of the various preparations can be fully exploited and overcome. Based on experimental evidence, we conclude that steady-state force following active muscle stretching is enhanced, and this enhancement has a passive and an active component. The active component is associated with the cross-bridge kinetics, and the passive component is associated with a calcium-dependent increase in titin stiffness.     

Relationship between force and stiffness in muscle fibers after stretch.

The purpose of this study was to evaluate the relationship between force and stiffness after stretch of activated fibers, while simultaneously changing contractility by interfering with the cross-bridge kinetics and muscle activation. Single fibers dissected from lumbrical muscles of frogs were placed at a length 20% longer than the plateau of the force-length relationship, activated, and stretched by 5 and 10% of fiber length (speed: 40% fiber length/s). Experiments were conducted with maximal and submaximal stimulation in Ringer solution and with the addition of 2 and 5 mM of the myosin inhibitor 2,3-butanedione monoxime (BDM) to the solution. The steady-state force after stretch of an activated fiber was higher than the isometric force produced at the corresponding length in all conditions investigated. Lowering the frequency of stimulation decreased the force and stiffness during isometric contractions, but it did not change force enhancement and stiffness enhancement after stretch. Administration of BDM decreased the force and stiffness during isometric contractions, but it increased the force enhancement and stiffness enhancement after stretch. The relationship between force enhancement and stiffness suggests that the increase in force after stretch may be caused by an increase in the proportion of cross bridges attached to actin. Because BDM places cross bridges in a weakly bound, pre-powerstroke state, our results further suggest that force enhancement is partially associated with a recruitment of weakly bound cross bridges into a strongly bound state.     

Effect of temperature on residual force enhancement in single skeletal muscle fibers

It is well accepted that the steady-state isometric force following active stretching of a muscle is greater than the steady-state isometric force obtained in a purely isometric contraction at the same length. This property of skeletal muscle has been called residual force enhancement (FE). Despite decades of research the mechanisms responsible for FE have remained largely unknown. Based on previous studies showing increases in FE in fibers in which cross-bridges were biased towards weakly bound states, we hypothesized that FE might be associated with a stretch-induced facilitation of transitioning from weakly to strongly bound cross-bridges. In order to test this hypothesis, single fibers (n=11) from the lumbrical muscles of frog (Rana pipiens) were used to determine FE at temperatures of 7 and 20 degrees C. At the cold temperature, cross-bridges are biased towards weakly bound states, therefore we expected FE to be greater at 7 degrees C compared to 20 degrees C. The average FE was significantly greater at 7 degrees C (11.5+/-1.1%) than at 20 degrees C (7.8+/-1.0%), as expected. The enhancement of force/stiffness was also significantly greater at the low (13.3+/-1.4%) compared to the high temperature (5.6+/-1.7%), indicating an increased conversion from weakly to strongly bound cross-bridges at the low temperature. We conclude from the results of this study that muscle preparations that are biased towards weakly bound cross-bridge states show increased FE for given stretch conditions, thereby supporting the idea that FE might be caused, in part, by a stretch-induced facilitation of the conversion of weakly to strongly bound cross-bridges.     

Residual force enhancement in myofibrils and sarcomeres

Residual force enhancement has been observed following active stretch of skeletal muscles and single fibres. However, there has been intense debate whether force enhancement is a sarcomeric property, or is associated with sarcomere length instability and the associated development of non-uniformities. Here, we studied force enhancement for the first time in isolated myofibrils (n=18) that, owing to the strict in series arrangement, allowed for evaluation of this property in individual sarcomeres (n=79). We found consistent force enhancement following stretch in all myofibrils and each sarcomere, and forces in the enhanced state typically exceeded the isometric forces on the plateau of the force-length relationship. Measurements were made on the plateau and the descending limb of the force-length relationship and revealed gross sarcomere length non-uniformities prior to and following active myofibril stretching, but in contrast to previous accounts, revealed that sarcomere lengths were perfectly stable under these experimental conditions. We conclude that force enhancement is a sarcomeric property that does not depend on sarcomere length instability, that force enhancement varies greatly for different sarcomeres within the same myofibril and that sarcomeres with vastly different amounts of actin-myosin overlap produce the same isometric steady-state forces. This last finding was not explained by differences in the amount of contractile proteins within sarcomeres, vastly different passive properties of individual sarcomeres or (half-) sarcomere length instabilities, suggesting that the basic mechanical properties of muscles, such as force enhancement, force depression and creep, which have traditionally been associated with sarcomere instabilities and the corresponding dynamic redistribution of sarcomere lengths, are not caused by such instabilities, but rather seem to be inherent properties of the mechanisms of contraction.     

Considerations on the history dependence of muscle contraction.

When a skeletal muscle that is actively producing force is shortened or stretched, the resulting steady-state isometric force after the dynamic phase is smaller or greater, respectively, than the purely isometric force obtained at the corresponding final length. The cross-bridge model of muscle contraction does not readily explain this history dependence of force production. The most accepted proposal to explain both, force depression after shortening and force enhancement after stretch, is a nonuniform behavior of sarcomeres that develops during and after length changes. This hypothesis is based on the idea of instability of sarcomere lengths on the descending limb of the force-length relationship. However, recent evidence suggests that skeletal muscles may be stable over the entire range of active force production, including the descending limb of the force-length relationship. The purpose of this review was to critically evaluate hypotheses aimed at explaining the history dependence of force production and to provide some novel insight into the possible mechanisms underlying these phenomena. It is concluded that the sarcomere nonuniformity hypothesis cannot always explain the total force enhancement observed after stretch and likely does not cause all of the force depression after shortening. There is evidence that force depression after shortening is associated with a reduction in the proportion of attached cross bridges, which, in turn, might be related to a stress-induced inhibition of cross-bridge attachment in the myofilament overlap zone. Furthermore, we suggest that force enhancement is not associated with instability of sarcomeres on the descending limb of the force-length relationship and that force enhancement has an active and a passive component. Force depression after shortening and force enhancement after stretch are likely to have different origins.     

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.     

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.     

Cross-bridge induced force enhancement?

When a muscle is stretched while activated, its steady-state isometric force following stretch is greater than the corresponding purely isometric force. This so-called residual force enhancement (RFE) has been observed for half a century, yet its mechanism remains unknown. Recent experiments suggest that RFE is not caused by non-uniformities in sarcomere lengths, as had been assumed for a long time, and cannot be explained primarily with increases in passive force, but is directly related to the kinetics of the cross-bridge cycle. Specifically, it has been suggested that stretching an attached cross-bridge increases its dwell time and duty ratio; therefore, the proportion of attached cross-bridges in a muscle would be increased by stretch, thereby causing RFE. A three bead laser trap setup was used for testing single cross-bridge (myosin II) interactions with actin. Upon attachment of a cross-bridge, a stretch or shortening of the cross-bridge was applied with a force of about 1.0 pN. The hypothesis that stretching a single cross-bridge increases its dwell time and duty ratio was rejected. However, stretching caused an increase in the average steady-state force per cross-bridge (3.4±0.4 pN; n=433) compared to shortening (1.9±0.3 pN; n=689). Therefore, based on the results of this study, RFE cannot be explained by an increased duty ratio and the associated increase in proportion of attached cross-bridges, but might be associated with an increased force per cross-bridge.     

Mechanical work as predictor of force enhancement and force depression

The steady-state force following active muscle shortening or stretch differs from the maximum isometric force associated with the final length. This phenomenon proves that the isometric force production is not only dependent on current muscle length and length time derivative, but depends on the preceding contraction history. Isolated extensor digitorum longus and soleus muscles from mice (NMRI strain) were used to investigate the force produced by a muscle, and some parameters hypothetically influencing this history-dependent force modification. The muscles were pre-stimulated at a fixed length, then different stretch/shortening episodes were introduced, whereafter changes of the active force were recorded while the muscles were held isometrically to approach a steady-state force before de-stimulation. The mechanical work during active stretch and shortening was evaluated by integrating the product of force and ramp velocity over the length-varying period. The results show a negative linear correlation between the force modification and the mechanical work produced on or by the muscle, continuous between shortening and stretch. A corresponding modification of the passive force component following each stimulation was also observed. The conclusion is that the isometric force attained after stretch or shortening is well described by an asymptotic force which is determined by the mechanical work.     

Effects of shortening on stretch-induced force enhancement in single skeletal muscle fibers

The main purpose of this study was to evaluate the effects of shortening on the stretch-induced force enhancement in single muscle fibers, and indirectly test the hypothesis that force enhancement may be associated with the engagement of a passive element upon activation. Fibers were placed on the descending limb of the force-length relationship, and stretch and shortening contractions were performed. Fibers underwent two sets of shortening-stretch cycles. First, fibers were shortened by a fixed amplitude and speed (10% fiber length, and at 40% fiber length/s), and then were stretched (10% fiber length, and at 40% fiber length/s) immediately following shortening, or 500 or 1000 ms following the shortening. Second, fibers were shortened by varying amounts (5%, 10% and 15% fiber length) and at a constant speed (40% fiber length/s) immediately preceding a given fiber stretch (10% fiber length, and at 40% fiber length/s). When stretching was immediately preceded by shortening, force enhancement was decreased proportionally with the shortening magnitude. When intervals were introduced between shortening and stretch, the effects of shortening on the stretch-induced force enhancement became less prominent. We concluded that, in contrast to published suggestions, shortening affects the stretch-induced force enhancement in an amplitude-dependent manner in single fibers, as it does in whole muscles, but this effect is diminished by increasing the time period between the shortening and stretch phases.     

Residual force enhancement and force depression in human single muscle fibres

Residual force depression (rFD) and residual force enhancement (rFE) are intrinsic contractile properties of muscle. rFD is characterized as a decrease in steady-state isometric force following active shortening compared with a purely isometric contraction at the same muscle length and level of activation. By contrast, isometric force is increased following active lengthening compared to a reference isometric contraction at the same muscle length and level of activation; this is termed rFE. To date, there have been no investigations of rFD and rFE in human muscle fibres, therefore the purpose of this study was to determine whether rFD and rFE occur at the single muscle fibre level in humans. rFD and rFE were investigated in maximally activated single muscle fibres biopsied from the vastus lateralis of healthy adults. To induce rFD, fibres were activated and shortened from an average sarcomere length (SL) of 3.2–2.6 μm. Reference isometric contractions were performed at an average SL of 2.6 μm. To induce rFE, fibres were actively lengthened from an average SL of 2.6–3.2 μm and a reference isometric contraction was performed at an average SL of 3.2 μm. Isometric steady-state force was lower following active shortening (p < 0.05), and higher following active lengthening (p < 0.05), as compared to the reference isometric contractions. We demonstrated rFD and rFE in human single fibres which is consistent with previous animal models. The non-responder phenomenon often reported in rFE studies involving voluntary contractions at the whole human level was not observed at the single fibre level.     

Increased Residual Force Enhancement in Older Adults Is Associated with a Maintenance of Eccentric Strength

Despite an age-related loss of voluntary isometric and concentric strength, muscle strength is well maintained during lengthening muscle actions (i.e., eccentric strength) in old age. Additionally, in younger adults during lengthening of an activated skeletal muscle, the force level observed following the stretch is greater than the isometric force at the same muscle length. This feature is termed residual force enhancement (RFE) and is believed to be a combination of active and passive components of the contractile apparatus. The purpose of this study was to provide an initial assessment of RFE in older adults and utilize aging as a muscle model to explore RFE in a system in which isometric force production is compromised, but structural mechanisms of eccentric strength are well-maintained. Therefore, we hypothesised that older adults will experience greater RFE compared with young adults. Following a reference maximal voluntary isometric contraction (MVC) of the dorsiflexors in 10 young (26.1±2.7y) and 10 old (76.0±6.5y) men, an active stretch was performed at 15°/s over a 30° ankle joint excursion ending at the same muscle length as the reference MVCs (40° of plantar flexion). Any additional torque compared with the reference MVC therefore represented RFE. In older men RFE was ∼2.5 times greater compared to young. The passive component of force enhancement contributed ∼37% and ∼20% to total force enhancement, in old and young respectively. The positive association (R ² = 0.57) between maintained eccentric strength in old age and RFE indicates age-related mechanisms responsible for the maintenance of eccentric strength likely contributed to the observed elevated RFE. Additionally, as indicated by the greater passive force enhancement, these mechanisms may be related to increased muscle series elastic stiffness in old age.     

Muscular force production after concentric contraction

The steady-state force following active shortening does not reach the maximum isometric force associated with the final length. Isolated extensor digitorum longus and soleus muscles from mice (NMRI strain) were used to investigate the force produced by a muscle, and some parameters hypothetically influencing this shortening-induced force depression. The muscles were pre-stimulated at fixed length, shortened and then held isometrically to give maximum post-shortening forces, before de-stimulation. The shortening magnitude was 0.18, 0.36 or 0.72mm (about 2-7% of optimal length), time of shortening was chosen as 0.03, 0.06 and 0.12s, and final length as +0.72, 0 and -0.72mm, related to optimal length. The mechanical work during active shortening was evaluated by integrating the product of force and shortening velocity over the shortening period. The results show a positive correlation between the force depression and the mechanical work, whereas the force depression was not correlated to the velocity of shortening. Depression of the passive force component was also observed following all stimulations. Experiments show that the fully stimulated redevelopment of isometric force following concentric contraction follows a time function similar to the creation of force when isometric muscle is initially stimulated. The conclusion is that the isometric force development after active shortening can be well described by an asymptotic force which is decided by the produced work, and the initial isometric time constant.     

Cross-bridge mechanism of residual force enhancement after stretching in a skeletal muscle

A muscle model that uses a modified Langevin equation with actomyosin potentials was used to describe the residual force enhancement after active stretching. Considering that the new model uses cross-bridge theory to describe the residual force enhancement, it is different from other models that use passive stretching elements. Residual force enhancement was simulated using a half sarcomere comprising 100 myosin molecules. In this paper, impulse is defined as the integral of an excess force from the steady isometric force over the time interval for which a stretch is applied. The impulse was calculated from the force response due to fast and slow muscle stretches to demonstrate the viscoelastic property of the cross-bridges. A cross-bridge mechanism was proposed as a way to describe the residual force enhancement on the basis of the impulse results with reference to the compliance of the actin filament. It was assumed that the period of the actin potential increased by 0.5% and the amplitude of the potential decreased by 0.5% when the half sarcomere was stretched by 10%. The residual force enhancement after 21.0% sarcomere stretching was 6.9% of the maximum isometric force of the muscle; this value was due to the increase in the number of cross-bridges.