Phase transition in force during ramp stretches of skeletal muscle.

Active glycerinated rabbit psoas fibers were stretched at constant velocity (0.1-3.0 lengths/s) under sarcomere length control. As observed by previous investigators, force rose in two phases: an initial rapid increase over a small stretch (phase I), and a slower, more modest rise over the remainder of the stretch (phase II). The transition between the two phases occurred at a critical stretch (LC) of 7.7 +/- 0.1 nm/half-sarcomere that is independent of velocity. The force at critical stretch (PC) increased with velocity up to 1 length/s, then was constant at 3.26 +/- 0.06 times isometric force. The decay of the force response to a small step stretch was much faster during stretch than in isometric fibers. The addition of 3 mM vanadate reduced isometric tension to 0.08 +/- 0.01 times control isometric tension (P0), but only reduced PC to 0.82 +/- 0.06 times P0, demonstrating that prepowerstroke states contribute to force rise during stretch. The data can be explained by a model in which actin-attached cross-bridges in a prepowerstroke state are stretched into regions of high force and detach very rapidly when stretched beyond this region. The prepowerstroke state acts as a mechanical rectifier, producing large forces during stretch but small forces during shortening.     

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.     

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.     

Force produced by isolated sarcomeres and half-sarcomeres after an imposed stretch

When a stretch is imposed to activated muscles, there is a residual force enhancement that persists after the stretch; the force is higher than that produced during an isometric contraction in the corresponding length. The mechanisms behind the force enhancement remain elusive, and there is disagreement if it represents a sarcomeric property, or if it is associated with length nonuniformities among sarcomeres and half-sarcomeres. The purpose of this study was to investigate the effects of stretch on single sarcomeres and myofibrils with predetermined numbers of sarcomeres (n = 2, 3. . . , 8) isolated from the rabbit psoas muscle. Sarcomeres were attached between two precalibrated microneedles for force measurements, and images of the preparations were projected onto a linear photodiode array for measurements of half-sarcomere length (SL). Fully activated sarcomeres were subjected to a stretch (5-10% of initial SL, at a speed of 0.3 μm·s(-1)·SL(-1)) after which they were maintained isometric for at least 5 s before deactivation. Single sarcomeres showed two patterns: 31 sarcomeres showed a small level of force enhancement after stretch (10.46 ± 0.78%), and 28 sarcomeres did not show force enhancement (-0.54 ± 0.17%). In these preparations, there was not a strong correlation between the force enhancement and half-sarcomere length nonuniformities. When three or more sarcomeres arranged in series were stretched, force enhancement was always observed, and it increased linearly with the degree of half-sarcomere length nonuniformities. The results show that the residual force enhancement has two mechanisms: 1) stretch-induced changes in sarcomeric structure(s); we suggest that titin is responsible for this component, and 2) stretch-induced nonuniformities of half-sarcomere lengths, which significantly increases the level of force enhancement.     

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.     

ULTRASTRUCTURE OF THE RESTING AND CONTRACTED STRIATED MUSCLE FIBER AT DIFFERENT DEGREES OF STRETCH

Passive stretch, isometric contraction, and shortening were studied in electron micrographs of striated, non-glycerinated frog muscle fibers. The artifacts due to the different steps of preparation were evaluated by comparing sarcomere length and fiber diameter before, during, and after fixation and after sectioning. Tension and length were recorded in the resting and contracted fiber before and during fixation. The I filaments could be traced to enter the A band between the A filaments on both sides of the I band, creating a zone of overlap which decreased linearly with stretch and increased with shortening. This is consistent with a sliding filament model. The decrease in the length of the A and I filaments during isometric contraction and the finding that fibers stretched to a sarcomere length of 3.7 µ still developed 30 per cent of the maximum tetanic tension could not be explained in terms of the sliding filament model. Shortening of the sarcomeres near the myotendinous junctions which still have overlap could account for only one-sixth of this tension, indicating that even those sarcomeres stretched to such a degree that there is a gap between A and I filaments are activated during isometric contraction (increase in stiffness). Shortening, too, was associated with changes in filament length. The diameter of A filaments remained unaltered with stretch and with isometric contraction. Shortening of 50 per cent was associated with a 13 per cent increase in A filament diameter. The area occupied by the fibrils and by the interfibrillar space increased with shortening, indicating a 20 per cent reduction in the volume of the fibrils when shortening amounted to 40 per cent.     

Stiffness and tension during and after sudden length changes of glycerinated single insect fibrillar muscle fibres

Rapid length changes were applied (within 0.2 ms or 0.4 ms) to single isometrically contracted glycerol extracted muscle fibres of the dorsal longitudinal muscle ofLethocerus maximus suspended in an Ca²⁺ and ATP containing solution at 20–23‡ C. Force transients and the fibre stiffness were measured during and after rapid length changes. At length changesbelow 0.5% of the initial fibre length (∼ 2.4 Μm sarcomere length) the mechanical transients were characterized as follows: (1) After stretch and after release the force regains at least partly the value of tension before the length change within a quick phase of tension recovery. The quick phase induced by stretch was nearly completed within 1–2 ms. (2) A pulse in length of 1.5 ms duration, i.e., a stretch followed by a release to the initial length or a release followed by a stretch to the initial length, was applied to the fibre. The force transient induced by this procedure regains after the second length change the value of the isometric tension before the procedure. (3) The stiffness was constant during each length change of the “pulse” and was equal during the first and the second length changes. These findings are predicted by the muscle contraction model of Huxley and Simmons (1971): The identical force before and after a length pulse may indicate that the rotation of cross bridges after the first length change is followed by a rotation into the original position after the second length change. The constancy of the stiffness during the length changes may indicate a Hookean elastic element of the cross bridge. The similarity of the stiffness during the first and the second length changes, i.e., before and after the quick phase, gives evidence that the quick phases after stretch and after release are not accompanied by a change in the net number of attached cross bridges. If stretches ofmore than 0.5% of the initial length were applied, the mechanical transient of the muscle fibre changed as follows: (1) An ultra fast tension decay phase (duration < 0.4 ms) was observed in addition to the slower decay phase induced by the smaller stretches. (2) If the initial stretch was followed by a release to the initial length, no fast recovery phase was observed, which returns the force to the value before the stretch. The reduced tension value persists for a longer period in time than 10 ms. (3) If the muscle was stretched and released repetitively an ultra fast quick phase was induced only by the first stretch. (4) The stiffness increased during stretch, but was found to be the same in the isometrically contracting muscle and after the quick tension decay phase following a large stretch. These findings indicate that the contraction model of Huxley and Simmons has to be extended by a further process additional to cross bridge rotation in case of large stretches (> 0.5%L ini). The findings are taken to indicate a rapid detachment and reattachment of overstrained cross bridges, i.e., a cross bridge slippage induced by large stretches.     

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.     

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.     

Dynamics of individual sarcomeres during and after stretch in activated single myofibrils

It is generally assumed that sarcomere lengths (SLs) change in isometric fibres following activation and following stretch on the descending limb of the force-length relationship, because of an inherent instability. Although this assumption has never been tested directly, instability and SL non-uniformity have been associated with several mechanical properties, such as 'creep' and force enhancement. The aim of this study was to test directly the hypothesis that sarcomeres are unstable on the descending limb of the force-length relationship. We used single myofibrils, isolated from rabbit psoas, that were attached to glass needles that allowed for controlled stretching of myofibrils. Images of the sarcomere striation pattern were projected onto a linear photodiode array, which was scanned at 20 Hz to produce dark-light patterns corresponding to the A- and I-bands, respectively. Starting from a mean SL of 2.55 +/- 0.07 microm, stretches of 11.2 +/- 1.6% of SL at a speed of 118.9 +/- 5.9 nm s(-1) were applied to the activated myofibrils (pCa(2+) = 4.75). SLs along the myofibril were non-uniform before, during and after the stretch, but with few exceptions, they remained constant during the isometric period before stretch, and during the extended isometric period after stretch. Sarcomeres never lengthened to a point beyond thick and thin filament overlap. We conclude that sarcomeres are non-uniform but generally stable on the descending limb of the force-length relationship.     

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.     

Similar effects of cooling and fatigue on eccentric and concentric force-velocity relationships in human muscle.

The purpose of this study was to investigate the effects of muscle temperature and fatigue during stretch (eccentric) and shortening (concentric) contractions of the maximally electrically activated human adductor pollicis muscle. After immersion of the lower arm in water baths of four different temperatures, the calculated muscle temperatures were 36.8, 31.6, 26.6, and 22.3 degrees C. Normalized (isometric force = 100%) eccentric force increased with stretch velocity to maximal values of 136.4 +/- 1.6 and 162.1 +/- 2.0% at 36.8 and 22.3 degrees C, respectively. After repetitive ischemic concentric contractions, fatigue was less at the lower temperatures, and at all temperatures the loss of eccentric force was smaller than the loss of isometric and concentric force. Consequently, normalized eccentric forces increased during fatigue to 159.7 +/- 4.6 and 185.7 +/- 7.3% at 36.8 and 22.3 degrees C, respectively. Maximal normalized eccentric force increased exponentially (r2 = 0.95) when Vmax was reduced by cooling and/or fatiguing contractions. This may indicate that a reduction in cross-bridge cycling rate could underlie the significant increases in normalized eccentric force found with cooling and fatigue.     

The conformation of myosin head domains in rigor muscle determined by X-ray interference

In the absence of adenosine triphosphate, the head domains of myosin cross-bridges in muscle bind to actin filaments in a rigor conformation that is expected to mimic that following the working stroke during active contraction. We used x-ray interference between the two head arrays in opposite halves of each myosin filament to determine the rigor head conformation in single fibers from frog skeletal muscle. During isometric contraction (force T(0)), the interference effect splits the M3 x-ray reflection from the axial repeat of the heads into two peaks with relative intensity (higher angle/lower angle peak) 0.76. In demembranated fibers in rigor at low force (<0.05 T(0)), the relative intensity was 4.0, showing that the center of mass of the heads had moved 4.5 nm closer to the midpoint of the myosin filament. When rigor fibers were stretched, increasing the force to 0.55 T(0), the heads' center of mass moved back by 1.1-1.6 nm. These motions can be explained by tilting of the light chain domain of the head so that the mean angle between the Cys(707)-Lys(843) vector and the filament axis increases by approximately 36 degrees between isometric contraction and low-force rigor, and decreases by 7-10 degrees when the rigor fiber is stretched to 0.55 T(0).     

Cross bridge slippage in skinned frog muscle fibres

Mechanically skinned single fibres of the semitendinosus muscles of Rana esculenta were investigated at ca. 4 degrees C. The fibres were activated by a Ca2+ jump technique, which allowed the development of a steady isometric tension within several seconds of entering a calcium rich solution at 4 degrees C. Sequences of length changes of different duration and amplitude were applied to the fibre. It could be demonstrated that the fibre behaved as a Hookean spring in the case of small amplitude length changes (up to 0.5% L0, ramp duration 0.5 ms) and that a sequence of length changes induced reversible changes in fibre state. In contrast, large stretches (greater than 1% L0) induced a muscle "give" if the stretch were not immediately preceded by a release. The data was interpreted on the basis of a strain induced detachment of cross bridges in combination with a rapid reattachment of presumably the same cross bridges in a discharged position. The rates of strain induced detachment and reattachment depended on the stretch amplitude. At amplitudes exceeding 2% L0 the rates were estimated to be at least several thousands per second.     

Effect of streptomycin on the active force of bioengineered heart muscle in response to controlled stretch

In this study, we describe a bioreactor system to deliver controlled stretch protocols to bioengineered heart muscle (BEHMs) and test the system when streptomycin (an aminoglycoside antibiotic, which blocks stretch-activated channels) is either added to or excluded from the culture medium. Streptomycin is a very commonly used component of cell culture antibiotic-antimycotic media additives, so its effects on muscle development and functional response to mechanical signals in vitro is worthy of investigation. Our hypothesis is that BEHMs will not adapt to the applied mechanical stretch protocol when streptomycin is present in the culture medium, but will do so when streptomycin is excluded. Bioengineered heart muscles were formed by culturing primary neonatal cardiac myocytes in a fibrin gel using a method previously developed in our laboratory. A custom bioreactor system was designed using SolidWorks and structural components manufactured using fusion deposition modeling. We utilized a stretch protocol of 1 Hz, 10% strain for 7 d. BEHMs were stretched in the presence and absence of streptomycin. As controls, BEHMs were maintained in a cell culture incubator with and without streptomycin. The contractile properties of all BEHMs were evaluated to determine the active force. We were able to demonstrate compatibility of the bioreactor system with BEHMs and were able to stretch 58 constructs with zero incidence of failure. When the BEHMs were stretched in the absence of streptomycin, the active force increased from a mean value of 51.7 +/- 5.6 (N = 10) to 102.4 +/- 16.3 muN (N = 10), with p < 0.05. However, BEHMs that were stretched in the presence of streptomycin did not show any significant increase in active force generation. The average active force of BEHMs increased from a mean value of 57.6 +/- 10.2 (N = 10) to 91.4 +/- 19.8 muN (N = 10) when stretched in the presence of streptomycin. In this study, we demonstrate compatibility of the a bioreactor system with BEHMs, stability of the BEHMs in response to stretch protocols, and significant functional improvement in response to controlled stretch only when streptomycin is excluded from the culture medium, supporting our hypothesis.     

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.     

Strain sensitivity and turnover rate of low force cross-bridges in contracting skeletal muscle fibers in the presence of phosphate.

Inorganic phosphate (Pi) decreases the isometric tension of skinned skeletal muscle fibers, presumably by increasing the relative fraction of a low force quaternary complex of actin, myosin, ADP, and Pi (A.M.ADP.Pi). At the same time, Pi gives rise to a fast relaxing mechanical component as detected by oscillations at 500 Hz. To characterize the dynamic properties of this A.M.ADP.Pi complex, the effect of Pi on the tension response to stretch was investigated with rabbit psoas fibers. A ramp stretch applied in the presence of 20 mM Pi increased tension more than in the control solution (0 mM Pi) but reduced the fast relaxing component to the control level. Thus, a stretch seems to convert the low force, fast relaxing A.M.ADP.Pi complex to a high force, slow relaxing form. However, the Pi-induced enhancement of the tension response was not observed until the fibers were stretched more than 0.4% of their length, suggesting that a critical cross-bridge extension of approximately 4 nm is required for this conversion. The rate constant of the attachment/detachment of this low force complex was estimated from the velocity dependence of the enhancement. It was approximately 10 s-1, in marked contrast to the A.M.ADP.Pi complex under low salt, relaxed conditions (approximately 10,000 s-1). The enhancement of the tension response was not observed when isometric tension was reduced by lowering free calcium, implying that calcium and Pi affect different steps in the actomyosin ATPase cycle during contraction.     

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.     

Human plantarflexor stiffness to multiple single-stretch trials.

The purpose of this investigation was to determine the influence of different stretch velocities, different rates of pre-stretch force development, and different pre-stretch muscle lengths on the intrinsic stiffness exhibited by the quasi-statically contracting active human plantarflexors during multiple single-stretch trials at 20-60% of maximum isometric contraction. Subjects were positioned prone, with the knee flexed 1.57 rad(90 degrees), shank stabilized, and foot secured in a hard plastic orthotic. Slowly increasing isometric plantarflexion force was produced until the plantarflexors were stretched by a rapid 0.2 rad (12 degrees) dorsiflexion movement. Plantarflexion forces and ankle positions were determined during these stretches as well as during resting stretches when the muscle was inactive. Resting forces were subtracted from the active trials, forces converted to torques, and stiffnesses determined for the first 62 ms of the stretch. The slope of the stiffness vs pre-stretch torque relationship averaged 4.30 +/- 0.34 Nm rad-1 Nm-1. Little difference was found between stiffness determined through the single-stretch method and the results of previous studies employing different mechanical inputs. Differences in stiffnesses with different stretching velocities were caused by computational artifact rather than by differences in intrinsic muscular reaction. Faster rates of pre-stretch force increase prior to the stretch resulted in slightly lower stiffnesses. Different pre-stretch muscle lengths apparently did not result in different stiffnesses. The shape of the torque vs displacement curve was remarkably insensitive to the planned manipulations of the testing conditions, responding in a stereotypical manner.     

Modeling the oscillation dynamics of activated airway smooth muscle strips

When strips of activated airway smooth muscle are stretched cyclically, they exhibit force-length loops that vary substantially in both position and shape with the amplitude and frequency of the stretch. This behavior has recently been ascribed to a dynamic interaction between the imposed stretch and the number of actin-myosin interactions in the muscle. However, it is well known that the passive rheological properties of smooth muscle have a major influence on its mechanical properties. We therefore hypothesized that these rheological properties play a significant role in the force-length dynamics of activated smooth muscle. To test the plausibility of this hypothesis, we developed a model of the smooth muscle strip consisting of a force generator in series with an elastic component. Realistic steady-state force-length loops are predicted by the model when the force generator obeys a hyperbolic force-velocity relationship, the series elastic component is highly nonlinear, and both elastic stiffness and force generation are adjusted so that peak loop force equals isometric force. We conclude that the dynamic behavior of airway smooth muscle can be ascribed in large part to an interaction between connective tissue rheology and the force-velocity behavior of contractile proteins.