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.     

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.     

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.     

New insights into the passive force enhancement in skeletal muscles

The steady-state isometric force following active stretching of a muscle is always greater than the steady-state isometric force obtained in a purely isometric contraction at the same length. This phenomenon has been termed "residual force enhancement" and it is associated with an active and a passive component. The origin of these components remains a matter of scientific debate. The purpose of this work was to test the hypothesis that the passive component of the residual force enhancement is caused by a passive structural element. In order to achieve this purpose, single fibers (n=6) from the lumbrical muscles of frog (Rana pipiens) were isolated and attached to a force transducer and a motor that could produce computer-controlled length changes. The passive force enhancement was assessed for three experimental conditions: in a normal Ringer's solution, and after the addition of 5 and 15mM 2,3-butanedione monoxime (BDM) which inhibits force production in a dose-dependent manner. If our hypothesis was correct, one would expect the passive force enhancement to be unaffected following BDM application. However, we found that increasing concentrations of BDM decreased the isometric forces, increased the normalized residual force enhancement, and most importantly for this study, increased the passive force enhancement. Furthermore, BDM decreased the rate of force relaxation after deactivation following active stretching of fibers, passive stretching in the Ringer's and BDM conditions produced the same passive force-sarcomere length relationship, and passive force enhancement required activation and force production. These results led to the conclusion that the passive force enhancement cannot be caused by a structural component exclusively as had been assumed up to date, but must be associated, directly or indirectly, with cross-bridge attachments upon activation and the associated active force.     

Molecular Basis of Force Development by Skeletal Muscles During and After Stretch

When activated skeletal muscles are stretched at slow velocities, force increases in two phases: (i) a fast increase, and (ii) a slow increase. The transition between these phases is commonly associated with the mechanical detachment of cross-bridges from actin. This phenomenon is referred to asforce enhancement during stretch. After the stretch, force decreases and reaches steady-state at levels that are higher than the force produced at the corresponding length during purely isometric contractions. This phenomenon is referred to asresidual force enhancement.The mechanisms behind the increase in force during and after stretch are still a matter of debate, and have physiological implications as human muscles perform stretch contractions continuously during daily activity. This paper briefly reviews the potential mechanisms to explain stretch forces, including an increased number of cross-bridges attached to actin, an increased strain in cross-bridges upon stretch, the influence of passive elements upon activation and sarcomere length non-uniformities.     

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.     

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.     

Cross-bridge behavior in rigor muscle

Properties of the rigor state in muscle can be explained by a simple cross-bridge model, of the type which has been suggested for active muscle, in which detachment of cross-bridges by ATP is excluded. Two attached cross-bridge states, with distinct force vs. distortion relationships, are required, in addition to a detached state, but the attached cross-bridge states in rigor muscle appear to differ significantly from the attached cross-bridge states in active muscle. The stability of the rigor force maintained in muscle under isometric conditions does not require exceptional stability of the attached cross-bridges, if the positions in which attachment of cross-bridges is allowed are limited so that the attachment of cross-bridges in positions which have minimum free energy is excluded. This explanation of the stability of the rigor state may also be applicable to the maintenance of stable rigor waves on flagella.     

Changes in force and stiffness during stretch of skeletal muscle fibers, effects of hypertonicity.

Slow stretch ramps (velocity: 0.17 fiber lengths s-1) were imposed during fused tetanic contractions of intact muscle fibers of the frog (1.4-3.0 degrees C; sarcomere length: 2.12-2.21 microns). Instantaneous force-extension relations were derived both under isometric conditions and during slow stretch by applying fast (0.2 ms) length steps to the fiber. An increase in tonicity (98 mM sucrose added to control Ringer solution) led to significant reduction of the maximum isometric tension but at the same time to marked increase in the force enhancement during slow stretch. The maximum force level reached during the stretch was affected very little. Experiments on relaxed fibers showed that recruitment of passive parallel elastic components were of no relevance for these effects. Hypertonicity slightly increased the instantaneous stiffness of the active fiber both in the presence and in the absence of stretch. The total extension of the undamped fiber elasticity was considerably reduced by increased tonicity under isometric conditions but was only slightly affected during slow stretch. The change in length of the undamped cross-bride elasticity upon stretch was thus greater in the hypertonic than in the normotonic solution suggesting a greater increase in force per cross-bridge in the hypertonic medium. The contractile effects are consistent with the assumptions that hypertonicity reduces the capability of the individual cross-bridge to produce active force and, furthermore, that hypertonicity has only minor effects on the number of attached cross-bridges and the maximum load-bearing capacity of the individual bridge.     

Residual force enhancement following eccentric induced muscle damage

During lengthening of an activated skeletal muscle, the force maintained following the stretch is greater than the isometric force at the same muscle length. This is termed residual force enhancement (RFE), but it is unknown how muscle damage following repeated eccentric contractions affects RFE. Using the dorsiflexors, we hypothesised muscle damage will impair the force generating sarcomeric structures leading to a reduction in RFE. Following reference maximal voluntary isometric contractions (MVC) in 8 young men (26.5±2.8y) a stretch was performed at 30°/s over a 30° ankle excursion ending at the same muscle length as the reference MVCs (30° plantar flexion). Surface electromyography (EMG) of the tibialis anterior and soleus muscles was recorded during all tasks. The damage protocol involved 4 sets of 25 isokinetic (30°/s) lengthening contractions. The same measures were collected at baseline and immediately post lengthening contractions, and for up to 10min recovery. Following the lengthening contraction task, there was a 30.3±6.4% decrease in eccentric torque (P<0.05) and 36.2±9.7% decrease in MVC (P<0.05) compared to baseline. Voluntary activation using twitch interpolation and RMS EMG amplitude of the tibialis anterior remained near maximal without increased coactivation for MVC. Contrary to our hypothesis, RFE increased (～100-250%) following muscle damage (P<0.05). It appears stretch provided a mechanical strategy for enhanced muscle function compared to isometric actions succeeding damage. Thus, active force of cross-bridges is decreased because of impaired excitation-contraction coupling but force generated during stretch remains intact because force contribution from stretched sarcomeric structures is less impaired.     

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.     

Activation dependence of stretch activation in mouse skinned myocardium: implications for ventricular function

Recent evidence suggests that ventricular ejection is partly powered by a delayed development of force, i.e., stretch activation, in regions of the ventricular wall due to stretch resulting from torsional twist of the ventricle around the apex-to-base axis. Given the potential importance of stretch activation in cardiac function, we characterized the stretch activation response and its Ca2+ dependence in murine skinned myocardium at 22 degrees C in solutions of varying Ca2+ concentrations. Stretch activation was induced by suddenly imposing a stretch of 0.5-2.5% of initial length to the isometrically contracting muscle and then holding the muscle at the new length. The force response to stretch was multiphasic: force initially increased in proportion to the amount of stretch, reached a peak, and then declined to a minimum before redeveloping to a new steady level. This last phase of the response is the delayed force characteristic of myocardial stretch activation and is presumably due to increased attachment of cross-bridges as a consequence of stretch. The amplitude and rate of stretch activation varied with Ca2+ concentration and more specifically with the level of isometric force prior to the stretch. Since myocardial force is regulated both by Ca2+ binding to troponin-C and cross-bridge binding to thin filaments, we explored the role of cross-bridge binding in the stretch activation response using NEM-S1, a strong-binding, non-force-generating derivative of myosin subfragment 1. NEM-S1 treatment at submaximal Ca2+-activated isometric forces significantly accelerated the rate of the stretch activation response and reduced its amplitude. These data show that the rate and amplitude of myocardial stretch activation vary with the level of activation and that stretch activation involves cooperative binding of cross-bridges to the thin filament. Such a mechanism would contribute to increased systolic ejection in response to increased delivery of activator Ca2+ during excitation-contraction coupling.     

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.     

Effects of oxidation on the power of chemically skinned rat soleus fibres

Oxidation alters calcium sensitivity, and decreases maximum isometric force (Po) and shortening velocity (Vmax) of single muscle fibres. To examine the effect of oxidation on the curvature of the force-velocity relationship, which determines muscle power in addition to Po and Vmax, skinned rat type I fibres were maximally activated at 15°C in a solution with pCa 4.5 and subjected to isotonic contractions before and after 4-min incubation in 50 mM H?O? (n=10) or normal relaxing solution (n=3). In five oxidised and four control fibres the rate of force redevelopment (ktr), following a rapid release and re-stretch, was measured. This gives a measure of the sum of the rate constants for cross-bridge attachment (f) and detachment (g?): (f+g?). H?O? reduced Po, Vmax and ktr by 19%, 21% and 24% respectively (P<0.001), while the shape of the force-velocity relationship was unchanged. Fitting data to the Huxley cross-bridge model suggested that oxidation decreased both the rate constant for cross-bridge attachment (f), and detachment of negatively strained cross-bridges (g?), similar to the effect of reduced activation. This suggests that oxidative modification is a possible cause of the variation in contractile properties between muscle fibres of the same type.     

Modeling residual force enhancement with generic cross-bridge models

The interaction of actin and myosin through cross-bridges explains much of muscle behavior. However, some properties of muscle, such as residual force enhancement, cannot be explained by current cross-bridge models. There is ongoing debate whether conceptual cross-bridge models, as pioneered by Huxley (A.F. Huxley, Muscle structure and theories of contraction, Prog. Biophys. Biophys. Chem. 7 (1957) 255) could, if suitably modified, fit experimental data showing residual force enhancement. Here we prove that there are only two ways to explain residual force enhancement with these ‘traditional’ cross-bridge models: the first requires cross-bridges to become stuck on actin (the stuck cross-bridge model) while the second requires that cross-bridges that are pulled off beyond a critical strain enter a ‘new’ unbound state that leads to a new force-producing cycle (the multi-cycle model). Stuck cross-bridge models cannot fit the velocity and stretch amplitude dependence of residual force enhancement, while the multi-cycle models can. The results of this theoretical analysis demonstrate that current kinetic models of cross-bridge action cannot explain the experimentally observed residual force enhancement. Either cross-bridges in the force-enhanced state follow a different kinetic cycle than cross-bridges in a ‘normal’ force state, or the assumptions underlying traditional cross-bridge models must be violated during experiments that show residual force enhancement.     

Characterization of cross-bridge elasticity and kinetics of cross-bridge cycling during force development in single smooth muscle cells

Force development in smooth muscle, as in skeletal muscle, is believed to reflect recruitment of force-generating myosin cross-bridges. However, little is known about the events underlying cross-bridge recruitment as the muscle cell approaches peak isometric force and then enters a period of tension maintenance. In the present studies on single smooth muscle cells isolated from the toad (Bufo marinus) stomach muscularis, active muscle stiffness, calculated from the force response to small sinusoidal length changes (0.5% cell length, 250 Hz), was utilized to estimate the relative number of attached cross-bridges. By comparing stiffness during initial force development to stiffness during force redevelopment immediately after a quick release imposed at peak force, we propose that the instantaneous active stiffness of the cell reflects both a linearly elastic cross-bridge element having 1.5 times the compliance of the cross-bridge in frog skeletal muscle and a series elastic component having an exponential length-force relationship. At the onset of force development, the ratio of stiffness to force was 2.5 times greater than at peak isometric force. These data suggest that, upon activation, cross-bridges attach in at least two states (i.e., low-force-producing and high-force-producing) and redistribute to a steady state distribution at peak isometric force. The possibility that the cross-bridge cycling rate was modulated with time was also investigated by analyzing the time course of tension recovery to small, rapid step length changes (0.5% cell length in 2.5 ms) imposed during initial force development, at peak force, and after 15 s of tension maintenance. The rate of tension recovery slowed continuously throughout force development following activation and slowed further as force was maintained. Our results suggest that the kinetics of force production in smooth muscle may involve a redistribution of cross-bridge populations between two attached states and that the average cycling rate of these cross-bridges becomes slower with time during contraction.     

The history dependence of force production in mammalian skeletal muscle following stretch-shortening and shortening-stretch cycles

The purpose of this study was to determine the history dependence of force production during and following stretch-shortening and shortening-stretch cycles in mammalian skeletal muscle. Thirty-three different isometric, stretch, shortening, stretch-shortening and shortening-stretch experiments were preformed in cat soleus (n=8) using previously established methods. Stretch-shortening and shortening-stretch cycles are not commutative with respect to the isometric forces following the length changes. Whereas force depression following shortening is virtually unaffected by previous stretching of the muscle, force enhancement following stretch depends in a dose-dependent manner on the amount of muscle shortening preceding the stretch. The history dependence of isometric force following shortening-stretch cycles can conveniently be modelled using an elastic (compressive and tensile) element that engages at the length of muscle activation. Such an "elastic" mechanism has been proposed by Edman and Tsuchiya (1996) (Edman, K.A. P., Tsuchiya, T., 1996. Strain of passive elements during force enhancement by stretch in frog mucle fibres. Journal of Physiology 490. 1, 191-205) based on experimental observations, and has been implemented theoretically in a rheological model of muscle (Forcinito et al., 1997) (Forcinito, M., Epstein, M., Herzog, W., 1997. Theoretical considerations on myofibril stiffness. Biophysics Journal 72, 1278-1286). The history dependence of isometric force following stretch-shortening cycles appears independent of the stretch preceding the shortening, except perhaps, if stretching occurs at very high speeds (i.e. 6-10 times fibre length per second). The results of this study are hard to reconcile with the two major mechanisms associated with history dependence of force production: sarcomere length non-uniformity (Edman et al., 1993) and stress-induced cross-bridge inhibition (Maréchal and Plaghki, 1979) (Maréchal, G., Plaghki, L., 1979. The deficit of the isometric tetanic tension redeveloped after a relase of frog muscle at a constant velocity. Journal of General Physiology 73, 453-467). It appears that studying the history dependence of force production under more functionally relevant conditions than has been done to date may provide new information that contributes to our understanding of possible mechanisms associated with force depression and force enhancement following muscular length changes.     

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.