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.     

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.     

The mechanisms of the residual force enhancement after stretch of skeletal muscle: non-uniformity in half-sarcomeres and stiffness of titin

When activated skeletal muscles are stretched, the force increases significantly. After the stretch, the force decreases and reaches a steady-state level that is higher than the force produced at the corresponding length during purely isometric contractions. This phenomenon, referred to as residual force enhancement, has been observed for more than 50 years, but the mechanism remains elusive, generating considerable debate in the literature. This paper reviews studies performed with single muscle fibres, myofibrils and sarcomeres to investigate the mechanisms of the stretch-induced force enhancement. First, the paper summarizes the characteristics of force enhancement and early hypotheses associated with non-uniformity of sarcomere length. Then, it reviews new evidence suggesting that force enhancement can also be associated with sarcomeric structures. Finally, this paper proposes that force enhancement is caused by: (i) half-sarcomere non-uniformities that will affect the levels of passive forces and overlap between myosin and actin filaments, and (ii) a Ca(2+)-induced stiffness of titin molecules. These mechanisms are compatible with most observations in the literature, and can be tested directly with emerging technologies in the near future.     

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.     

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.     

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.     

Is titin a ‘winding filament’? A new twist on muscle contraction

Recent studies have demonstrated a role for the elastic protein titin in active muscle, but the mechanisms by which titin plays this role remain to be elucidated. In active muscle, Ca(2+)-binding has been shown to increase titin stiffness, but the observed increase is too small to explain the increased stiffness of parallel elastic elements upon muscle activation. We propose a 'winding filament' mechanism for titin's role in active muscle. First, we hypothesize that Ca(2+)-dependent binding of titin's N2A region to thin filaments increases titin stiffness by preventing low-force straightening of proximal immunoglobulin domains that occurs during passive stretch. This mechanism explains the difference in length dependence of force between skeletal myofibrils and cardiac myocytes. Second, we hypothesize that cross-bridges serve not only as motors that pull thin filaments towards the M-line, but also as rotors that wind titin on the thin filaments, storing elastic potential energy in PEVK during force development and active stretch. Energy stored during force development can be recovered during active shortening. The winding filament hypothesis accounts for force enhancement during stretch and force depression during shortening, and provides testable predictions that will encourage new directions for research on mechanisms of muscle contraction.     

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.     

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.     

Does stretching velocity affect residual force enhancement?

It is thought that the magnitude of residual force enhancement (RFE) is not affected by stretch velocity. However, the range of stretch velocities studied in previous investigations has been limited to slow and moderate velocities. High velocities of muscle stretching are associated with a loss of force and incomplete cross-bridge attachment to actin, thus creating a unique set of eccentric conditions referred to as slippage. The purpose of this study was to extend the relationship between stretch velocity and RFE to high velocities. We hypothesized that slippage at high velocities might affect RFE. We stretched cat soleus muscles for 4 mm to the plateau of the force-length relationship at speeds of 2, 4, 8, 16, 32, 64 mm/s to induce RFE, and slippage for the fastest condition. For each RFE test, a corresponding isometric reference test was conducted. Residual force enhancement was quantified as the relative increase in isometric steady state force between the experimental stretch and the isometric reference tests. Residual force enhancement was similar for all stretch speeds, as expected, with the exception of the fastest speed (64 mm/s), which was associated with slippage and no significant RFE. These results suggest that if stretch speeds are too fast, and are associated with slippage, RFE is abolished. We conclude from these findings that proper cross-bridge engagement is required during eccentric muscle action to produce RFE.     

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.     

Stretch of active muscle during the declining phase of the calcium transient produces biphasic changes in calcium binding to the activating sites

In voltage-clamped barnacle single muscle fibers, muscle shortening during the declining phase of the calcium transient increases myoplasmic calcium. This extra calcium is probably released from the activating sites by a change in affinity when cross-bridges break (Gordon, A. M., and E. B. Ridgway, 1987. J. Gen. Physiol. 90:321-340). Stretching the muscle at similar times causes a more complex response, a rapid increase in intracellular calcium followed by a transient decrease. The amplitudes of both phases increase with the rate and amplitude of stretch. The rapid increase, however, appears only when the muscle is stretched more than approximately 0.4%. This is above the length change that produces the breakpoint in the force record during a ramp stretch. This positive phase in response to large stretches is similar to that seen on equivalent shortening at the same point in the contraction. For stretches at different times during the calcium transient, the peak amplitude of the positive phase has a time course that is delayed relative to the calcium transient, while the peak decrease during the negative phase has an earlier time course that is more similar to the calcium transient. The amplitudes of both phases increase with increasing strength of stimulation and consequent force. When the initial muscle the active force. A large decrease in length (which drops the active force to zero) decreases the extra calcium seen on a subsequent restretch. After such a shortening step, the extra calcium on stretch recovers (50 ms half time) toward the control level with the same time course as the redeveloped force. Conversely, stretching an active fiber decreases the extra calcium on a subsequent shortening step that is imposed shortly afterward. Enhanced calcium binding due to increased length alone cannot explain our data. We hypothesize that the calcium affinity of the activating sites increases with cross-bridge attachment and further with cross-bridge strain. This accounts for the biphasic response to stretch as follows: cross-bridges detached by stretch first decrease calcium affinity, then upon reattachment increase calcium affinity due to the strained configuration brought on by the stretch. The experiments suggest that cross-bridge attachment and strain can modify calcium binding to the activating sites in intact muscle.     

Does residual force enhancement increase with increasing stretch magnitudes?

It is generally accepted that force enhancement in skeletal muscles increases with increasing stretch magnitudes. However, this property has not been tested across supra-physiological stretch magnitudes and different muscle lengths, thus it is not known whether this is a generic property of skeletal muscle, or merely a property that holds for small stretch magnitudes within the physiological range. Six cat soleus muscles were actively stretched with magnitudes varying from 3 to 24 mm at three different parts of the force–length relationship to test the hypothesis that force enhancement increases with increasing stretch magnitude, independent of muscle length. Residual force enhancement increased consistently with stretch amplitudes on the descending limb of the force–length relationship up to a threshold value, after which it reached a plateau. Force enhancement did not increase with stretch amplitude on the ascending limb of the force–length relationship. Passive force enhancement was observed for all test conditions, and paralleled the behavior of the residual force enhancement. Force enhancement increased with stretch magnitude when stretching occurred at lengths where there was natural passive force within the muscle. These results suggest that force enhancement does not increase unconditionally with increasing stretch magnitude, as is generally accepted, and that increasing force enhancement with stretch appears to be tightly linked to that part of the force–length relationship where there is naturally occurring passive force.     

Effects of sustained length-dependent activation on in situ cross-bridge dynamics in rat hearts

The cellular basis of the length-dependent increases in contractile force in the beating heart has remained unclear. Our aim was to investigate whether length-dependent mediated increases in contractile force are correlated with myosin head proximity to actin filaments, and presumably the number of cross-bridges activated during a contraction. We therefore employed x-ray diffraction analyses of beat-to-beat contractions in spontaneously beating rat hearts under open-chest conditions simultaneous with recordings of left ventricle (LV) pressure-volume. Regional x-ray diffraction patterns were recorded from the anterior LV free wall under steady-state contractions and during acute volume loading (intravenous lactate Ringers infusion at 60 ml/h, <5 min duration) to determine the change in intensity ratio (I_1,0/I_1,1) and myosin interfilament spacing (d_1,0). We found no significant change in end-diastolic (ED) intensity ratio, indicating that the proportion of myosin heads in proximity to actin was unchanged by fiber stretching. Intensity ratio decreased significantly more during the isovolumetric contraction phase during volume loading than under baseline contractions. A significant systolic increase in myosin head proximity to actin filaments correlated with the maximum rate of pressure increase. Hence, a reduction in interfilament spacing at end-diastole (∼0.5 nm) during stretch increased the proportion of cross-bridges activated. Furthermore, our recordings suggest that d_1,0 expansion was inversely related to LV volume but was restricted during contraction and sarcomere shortening to values smaller than the maximum during isovolumetric relaxation. Since ventricular volume, and presumably sarcomere length, was found to be directly related to interfilament spacing, these findings support a role for interfilament spacing in modulating cross-bridge formation and force developed before shortening.     

Critical sarcomere extension required to recruit a decaying component of extra force during stretch in tetanic contractions of frog skeletal muscle fibers

29 single frog skeletal muscle fibers were stretched during fused tetanic contractions. The force increase during stretch exhibited a breakpoint at a critical length change (average: 16.6 nm per one-half sarcomere) that was independent of velocity of stretch and of sarcomere length between 1.8 and 2.8 microns. After stretch there was an early decaying force component with a force-extension curve similar to that during stretch, which disappeared over approximately 2 s. This component was removed by a small, quick release, leaving a longer- lasting component. The critical amplitude of release required to produce this result was found by clamping the fiber to a load at which there was zero velocity of shortening. This amplitude increased with time up to the angle in the force record during stretch, was constant for the remainder of the stretch, and decreased with time after the end of stretch; it was consistently less than the critical amplitude of stretch required to reach the breakpoint of force enhancement during stretch but was also independent of sarcomere length. The force drop accompanying the critical release showed a small increase up to an optimum magnitude at 2.4--2.7 microns sarcomere length, with a decrease at longer lengths.     

Cross-bridge kinetics, cooperativity, and negatively strained cross- bridges in vertebrate smooth muscle. A laser-flash photolysis study

The effects of laser-flash photolytic release of ATP from caged ATP [P3-1(2-nitrophenyl)ethyladenosine-5'-triphosphate] on stiffness and tension transients were studied in permeabilized guinea pig protal vein smooth muscle. During rigor, induced by removing ATP from the relaxed or contracting muscles, stiffness was greater than in relaxed muscle, and electron microscopy showed cross-bridges attached to actin filaments at an approximately 45 degree angle. In the absence of Ca2+, liberation of ATP (0.1-1 mM) into muscles in rigor caused relaxation, with kinetics indicating cooperative reattachment of some cross-bridges. Inorganic phosphate (Pi; 20 mM) accelerated relaxation. A rapid phase of force development, accompanied by a decline in stiffness and unaffected by 20 mM Pi, was observed upon liberation of ATP in muscles that were released by 0.5-1.0% just before the laser pulse. This force increment observed upon detachment suggests that the cross-bridges can bear a negative tension. The second-order rate constant for detachment of rigor cross-bridges by ATP, in the absence of Ca2+, was estimated to be 0.1-2.5 X 10(5) M-1s-1, which indicates that this reaction is too fast to limit the rate of ATP hydrolysis during physiological contractions. In the presence of Ca2+, force development occurred at a rate (0.4 s-1) similar to that of intact, electrically stimulated tissue. The rate of force development was an order of magnitude faster in muscles that had been thiophosphorylated with ATP gamma S before the photochemical liberation of ATP, which indicates that under physiological conditions, in non-thiophosphorylated muscles, light-chain phosphorylation, rather than intrinsic properties of the actomyosin cross-bridges, limits the rate of force development. The release of micromolar ATP or CTP from caged ATP or caged CTP caused force development of up to 40% of maximal active tension in the absence of Ca2+, consistent with cooperative attachment of cross-bridges. Cooperative reattachment of dephosphorylated cross-bridges may contribute to force maintenance at low energy cost and low cross-bridge cycling rates in smooth muscle.     

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.     

Evidence of residual force enhancement for multi-joint leg extension

Force enhancement is a well accepted property of skeletal muscle and has been observed at all structural levels ranging from single myofibrils to voluntarily activated m. quadriceps femoris in vivo. However, force enhancement has not been studied for multi-joint movements like human leg extension; therefore knowledge about its relevance in daily living remains limited. The purpose of this study was to determine whether there is force enhancement during maximal voluntary multi-joint leg extension. Human leg extension was studied (n=22) on a motor driven leg press dynamometer where external reaction forces under the feet as well as activity of 8 lower extremity muscles were measured. In addition, torque in the ankle and knee joints was calculated using inverse dynamics. The steady-state isometric force, joint torques, and muscle activation after active stretch (20° stretch amplitude at 60°/s) were compared with the corresponding values obtained during isometric reference contractions. There was consistent force enhancement during and following stretch for both forces and joint torques. Potentiation during stretch reached values between 26% and 30%, while a significant force enhancement of 10.5–12.3% and 4.3–7.4% remained 0.5–1 and 2.5–3 s after stretch, respectively. During stretch, EMG signals of m. gastrocnemius medialis and lateralis were significantly increased, while following stretch all analyzed muscles showed the same activity as during the reference contractions. We conclude from these results that force enhancement exists in everyday movements and should be accounted for when analyzing or modelling human movement.     

A multi-scale continuum model of skeletal muscle mechanics predicting force enhancement based on actin–titin interaction

Although recent research emphasises the possible role of titin in skeletal muscle force enhancement, this property is commonly ignored in current computational models. This work presents the first biophysically based continuum-mechanical model of skeletal muscle that considers, in addition to actin–myosin interactions, force enhancement based on actin–titin interactions. During activation, titin attaches to actin filaments, which results in a significant reduction in titin’s free molecular spring length and therefore results in increased titin forces during a subsequent stretch. The mechanical behaviour of titin is included on the microscopic half-sarcomere level of a multi-scale chemo-electro-mechanical muscle model, which is based on the classic sliding-filament and cross-bridge theories. In addition to titin stress contributions in the muscle fibre direction, the continuum-mechanical constitutive relation accounts for geometrically motivated, titin-induced stresses acting in the muscle’s cross-fibre directions. Representative simulations of active stretches under maximal and submaximal activation levels predict realistic magnitudes of force enhancement in fibre direction. For example, stretching the model by 20 % from optimal length increased the isometric force at the target length by about 30 %. Predicted titin-induced stresses in the muscle’s cross-fibre directions are rather insignificant. Including the presented development in future continuum-mechanical models of muscle function in dynamic situations will lead to more accurate model predictions during and after lengthening contractions.     

History-dependence of isometric muscle force: effect of prior stretch or shortening amplitude

It is well-recognised that steady-state isometric muscle force is decreased following active shortening (force depression, FD) and increased following active stretch (force enhancement, FE). It has also been demonstrated that passive muscle force is increased following active stretch (passive FE). Several studies have reported that FD increases with shortening amplitude and that FE and passive FE increase with stretch amplitude. Here, we investigate whether these trends continue with further increases in shortening or stretch amplitude. Experiments were performed using in situ cat soleus muscles (n=8 for FD; n=7 for FE and passive FE). FD, FE and passive FE were measured after shortening or stretch contractions that covered as wide a range of amplitudes as practically possible without damaging the muscles. FD increased approximately linearly with shortening amplitude, over the full range of amplitudes investigated. This is consistent with the hypothesis that FD arises from a stress-induced inhibition of crossbridges. FE increased with stretch amplitude only up to a point, and then levelled off. Passive FE, and the transient increase in force at the end of stretch, showed relationships to stretch amplitude that were qualitatively very similar to the relationship for FE, increasing only until the same critical stretch amplitude had been reached. We conclude that FE and passive FE do not increase with stretch amplitude under all circumstances. This finding has important consequences for determining the mechanisms underlying FE and passive FE because any mechanism that is proposed to explain them must be able to predict it.