Active force-length relationship of human lower-leg muscles estimated from morphological data: a comparison of geometric muscle models

Muscle fibre lengths, pennation angles, and sarcomere lengths were measured (the latter by a diffraction technique) for each of the muscles of three embalmed lower-leg specimens. From these data and filament lengths from Walker & Schrodt (1973), the optimum fibre lengths were determined. Relationships between length and active force (at full activation) of the lower-leg muscles were calculated by use of (i) a unipennate muscle model, (ii) a bipennate model, and (iii) bipennate models in which the cosine of the pennation angle is approximated as length independent. It is concluded that the first two models are equally useful and that the use of the last models is discouraged in case of strongly pennated muscles. Non-uniformity of fibre parameters within one muscle appears to have little effect on the force-length relationship.     

Myosin thick filament lability induced by mechanical strain in airway smooth muscle.

Airway smooth muscle adapts to different lengths with functional changes that suggest plastic alterations in the filament lattice. To look for structural changes that might be associated with this plasticity, we studied the relationship between isometric force generation and myosin thick filament density in cell cross sections, measured by electron microscope, after length oscillations applied to the relaxed porcine trachealis muscle. Muscles were stimulated regularly for 12 s every 5 min. Between two stimulations, the muscles were submitted to repeated passive +/- 30% length changes. This caused tetanic force and thick-filament density to fall by 21 and 27%, respectively. However, in subsequent tetani, both force and filament density recovered to preoscillation levels. These findings indicate that thick filaments in airway smooth muscle are labile, depolymerization of the myosin filaments can be induced by mechanical strain, and repolymerization of the thick filaments underlies force recovery after the oscillation. This thick-filament lability would greatly facilitate plastic changes of lattice length and explain why airway smooth muscle is able to function over a large length range.     

Series-to-parallel transition in the filament lattice of airway smooth muscle.

Force-velocity curves measured at different times during tetani of sheep trachealis muscle were analyzed to assess whether velocity slowing could be explained by thick-filament lengthening. Such lengthening increases force by placing more cross bridges in parallel on longer filaments and decreases velocity by reducing the number of filaments spanning muscle length. From 2 s after the onset of stimulation, when force had achieved 42% of it final value, to 28 s, when force had been at its tetanic plateau for approximately 15 s, velocity decreases were exactly matched by force increases when force was adjusted for changes in activation, as assessed from the maximum power value in the force-velocity curves. A twofold change in velocity could be quantitatively explained by a series-to-parallel change in the filament lattice without any need to postulate a change in cross-bridge cycling rate.     

Filament lattice changes in smooth muscle assessed using birefringence

The long functional range of some types of smooth muscle has been the subject of recent study. It has been proposed that the muscle filament lattice adapts to longer lengths by placing more filaments in series and that lattice plasticity is facilitated by myosin filament evanescence, with filaments dissociating during relaxation and reforming upon activation. Support for these dynamic changes in the filament lattice has been provided partly by changes in contractile parameters at different times in the contraction-relaxation cycle at different lengths. If the changes in contractile parameters result from filament formation and dissociation, these structural changes must occur on the time scale of tension development and relaxation. To assess whether thick-filament formation could account for the contractile changes, we measured birefringence continuously during activation and relaxation and compared these optical changes with the time course of force development and relaxation. Birefringence is a well-known property of muscle; striations in skeletal and cardiac muscle result from the A-bands being anisotropic, i.e., birefringent, and it is now known that this optical property is due to the presence of myosin thick filaments in the A-bands. Thus, the strength of birefringence is expected to represent the density of thick filaments. Here, we describe the principle of the method, the techniques for recording the optical signals, some initial results, and discuss the interpretation of results and some limitations of the method.     

Muscle active force-length curve explained by an electrophysical model of interfilament spacing

The active isometric force-length relation (FLR) of striated muscle sarcomeres is central to understanding and modeling muscle function. The mechanistic basis of the descending arm of the FLR is well explained by the decreasing thin:thick filament overlap that occurs at long sarcomere lengths. The mechanistic basis of the ascending arm of the FLR (the decrease in force that occurs at short sarcomere lengths), alternatively, has never been well explained. Because muscle is a constant-volume system, interfilament lattice distances must increase as sarcomere length shortens. This increase would decrease thin and thick-filament electrostatic interactions independently of thin:thick filament overlap. To examine this effect, we present here a fundamental, physics-based model of the sarcomere that includes filament molecular properties, calcium binding, sarcomere geometry including both thin:thick filament overlap and interfilament radial distance, and electrostatics. The model gives extremely good fits to existing FLR data from a large number of different muscles across their entire range of measured activity levels, with the optimized parameter values in all cases lying within anatomically and physically reasonable ranges. A local first-order sensitivity analysis (varying individual parameters while holding the values of all others constant) shows that model output is most sensitive to a subset of model parameters, most of which are related to sarcomere geometry, with model output being most sensitive to interfilament radial distance. This conclusion is supported by re-running the fits with only this parameter subset being allowed to vary, which increases fit errors only moderately. These results show that the model well reproduces existing experimental data, and indicate that changes in interfilament spacing play as central a role as changes in filament overlap in determining the FLR, particularly on its ascending arm.     

Regulatory mechanism of length-dependent activation in skinned porcine ventricular muscle: role of thin filament cooperative activation in the Frank-Starling relation

Cardiac sarcomeres produce greater active force in response to stretch, forming the basis of the Frank-Starling mechanism of the heart. The purpose of this study was to provide the systematic understanding of length-dependent activation by investigating experimentally and mathematically how the thin filament “on–off” switching mechanism is involved in its regulation. Porcine left ventricular muscles were skinned, and force measurements were performed at short (1.9 µm) and long (2.3 µm) sarcomere lengths. We found that 3 mM MgADP increased Ca²⁺ sensitivity of force and the rate of rise of active force, consistent with the increase in thin filament cooperative activation. MgADP attenuated length-dependent activation with and without thin filament reconstitution with the fast skeletal troponin complex (sTn). Conversely, 20 mM of inorganic phosphate (Pi) decreased Ca²⁺ sensitivity of force and the rate of rise of active force, consistent with the decrease in thin filament cooperative activation. Pi enhanced length-dependent activation with and without sTn reconstitution. Linear regression analysis revealed that the magnitude of length-dependent activation was inversely correlated with the rate of rise of active force. These results were quantitatively simulated by a model that incorporates the Ca²⁺-dependent on–off switching of the thin filament state and interfilament lattice spacing modulation. Our model analysis revealed that the cooperativity of the thin filament on–off switching, but not the Ca²⁺-binding ability, determines the magnitude of the Frank-Starling effect. These findings demonstrate that the Frank-Starling relation is strongly influenced by thin filament cooperative activation.     

Thin-filament length correlates with fiber type in human skeletal muscle

Force production in skeletal muscle is proportional to the amount of overlap between the thin and thick filaments, which, in turn, depends on their lengths. Both thin- and thick-filament lengths are precisely regulated and uniform within a myofibril. While thick-filament lengths are essentially constant across muscles and species (～1.65 μm), thin-filament lengths are highly variable both across species and across muscles of a single species. Here, we used a high-resolution immunofluorescence and image analysis technique (distributed deconvolution) to directly test the hypothesis that thin-filament lengths vary across human muscles. Using deltoid and pectoralis major muscle biopsies, we identified thin-filament lengths that ranged from 1.19 ± 0.08 to 1.37 ± 0.04 μm, based on tropomodulin localization with respect to the Z-line. Tropomodulin localized from 0.28 to 0.47 μm further from the Z-line than the NH(2)-terminus of nebulin in the various biopsies, indicating that human thin filaments have nebulin-free, pointed-end extensions that comprise up to 34% of total thin-filament length. Furthermore, thin-filament length was negatively correlated with the percentage of type 2X myosin heavy chain within the biopsy and shorter in type 2X myosin heavy chain-positive fibers, establishing the existence of a relationship between thin-filament lengths and fiber types in human muscle. Together, these data challenge the widely held assumption that human thin-filament lengths are constant. Our results also have broad relevance to musculoskeletal modeling, surgical reattachment of muscles, and orthopedic rehabilitation.     

Ordering of the myofilament lattice in muscle fibers

The effect of pH on the muscle filament lattice in skinned rabbit psoas fibers was studied by X-ray diffraction. In relaxed fibers, the intensity of the 11 equatorial reflection, I11, remained constant between pH 7.0 and pH 6.0 and fell markedly when the pH was decreased to 5.5. The intensity of the 10 reflection was almost constant over this pH range. These results indicate that the thick-filament lattice is more stable than that of the thin filaments, and that the thin filaments are positioned within the thick-filament lattice by a charge-dependent force. In rigor fibers, the decrease in I11 over this pH range was much smaller, which shows that the thin filament lattice can also be stabilized by the presence of actomyosin crossbridges. These conclusions were confirmed by electron microscopy. Thus, the thin filaments can be positioned in the trigonal positions of the thick-filament lattice by two different mechanisms, one electrostatic and the other steric.     

Heat shock protein 20-mediated force suppression in forskolin-relaxed swine carotid artery

Increases in cyclic nucleotide levels induce smooth muscle relaxation by deactivation [reductions in myosin regulatory light chain (MRLC) phosphorylation (e.g., by reduced [Ca²⁺])] or force suppression (reduction in force without reduction in MRLC phosphorylation). Ser¹⁶-heat shock protein 20 (HSP20) phosphorylation is the proposed mediator of force suppression. We evaluated three potential hypotheses whereby Ser¹⁶-HSP20 phosphorylation could regulate smooth muscle force: 1) a threshold level of HSP20 phosphorylation could inactivate a thin filament as a whole, 2) phosphorylation of a single HSP20 could fully inactivate a small region of a thin filament, or 3) HSP20 phosphorylation could weakly inhibit myosin binding at either the thin- or thick-filament level. We tested these hypotheses by analyzing the dependence of force on Ser¹⁶-HSP20 phosphorylation in swine carotid media. First, we determined that swine HSP20 has a second phosphorylation site at Ser¹⁵⁷. Ser¹⁵⁷-HSP20 phosphorylation values were high and did not change during contractile activation or forskolin-induced relaxation. Forskolin significantly increased Ser¹⁶-HSP20 phosphorylation. The relationship between Ser¹⁶-HSP20 phosphorylation and force remained linear and was shifted downward in partially activated muscles relaxed with forskolin. Neither forskolin nor nitroglycerin induced actin depolymerization as detected using the F/G-actin ratio method in smooth muscle homogenates. These results suggest that force suppression does not occur in accordance with the first hypothesis (inactivation of a thin filament as a whole). Our data are more consistent with the second and third hypotheses that force suppression is mediated by full or partial inhibition of local myosin binding at the thin- or thick-filament level. cAMP; cGMP; nitric oxide; vascular smooth muscle     

Elastic properties of isolated thick filaments measured by nanofabricated cantilevers.

Using newly developed nanofabricated cantilever force transducers, we have measured the mechanical properties of isolated thick filaments from the anterior byssus retractor muscle of the blue mussel Mytilus edulis and the telson levator muscle of the horseshoe crab Limulus polyphemus. The single thick filament specimen was suspended between the tip of a flexible cantilever and the tip of a stiff reference beam. Axial stress was placed on the filament, which bent the flexible cantilever. Cantilever tips were microscopically imaged onto a photodiode array to extract tip positions, which could be converted into force by using the cantilever stiffness value. Length changes up to 23% initial length (Mytilus) and 66% initial length (Limulus) were fully reversible and took place within the physiological force range. When stretch exceeded two to three times initial length (Mytilus) or five to six times initial length (Limulus), at forces approximately 18 nN and approximately 7 nN, respectively, the filaments broke. Appreciable and reversible strain within the physiological force range implies that thick-filament length changes could play a significant physiological role, at least in invertebrate muscles.     

Flagellin redundancy in Caulobacter crescentus and its implications for flagellar filament assembly

Bacterial flagella play key roles in surface attachment and host-bacterial interactions as well as driving motility. Here, we have investigated the ability of Caulobacter crescentus to assemble its flagellar filament from six flagellins: FljJ, FljK, FljL, FljM, FljN, and FljO. Flagellin gene deletion combinations exhibited a range of phenotypes from no motility or impaired motility to full motility. Characterization of the mutant collection showed the following: (i) that there is no strict requirement for any one of the six flagellins to assemble a filament; (ii) that there is a correlation between slower swimming speeds and shorter filament lengths in ΔfljK ΔfljM mutants; (iii) that the flagellins FljM to FljO are less stable than FljJ to FljL; and (iv) that the flagellins FljK, FljL, FljM, FljN, and FljO alone are able to assemble a filament.     

Activation in a Skeletal Muscle Contraction Model with a Modification for Insect Fibrillar Muscle

A sliding filament model for muscle contraction is extended by including an activation mechanism based on the hypothesis that the binding of calcium by a regulating protein in the myofibrils must occur before the rate constant governing the making of interactions between cross-bridges and thin filament sites can take on nonzero values. The magnitude of the rate constant is proportional to the amount of bound calcium. The model's isometric twitch and rise of force in an isometric tetanus are similar to the curves produced by real muscles. It redevelops force after a quick release in an isometric tetanus faster than the initial rise. Quick release experiments on the model during an isometric twitch show that the “active state” curve produced is different from the postulated calcium binding curve. The force developed by the model can be increased by a small quick stretch delivered soon after activation to values near the maximum generated in an isometric tetanus. Following the quick stretch, the force remains near the tetanic maximum for a long time even though the calcium binding curve rises to a peak and subsequently decays by about 50%. The model satisfies the constraint of shortening with a constant velocity under a constant load. Modifications can be made in the model so that it produces the delayed force changes following step length changes characteristic of insect fibrillar muscle.     

Muscle-induced accelerations at maximum activation to assess individual muscle capacity during movement

Analyses of muscle-induced accelerations provide insight into how individual muscles contribute to motion. In previous studies, investigators have calculated muscle-induced accelerations on a per unit force basis to assess the potential of individual muscles to contribute to motion. However, because muscle force is a function of muscle activation, length, and shortening velocity, examining induced accelerations per unit force does not take into account how the capacity of individual muscles to produce force changes during movement. Alternatively, calculating a muscle's induced accelerations at maximum activation considers the extent to which the muscle can produce force during movement, as well as the potential of the muscle to accelerate the joints at each instant due to its moment arm(s) and the dynamics of the system. We computed both quantities for the major lower extremity muscles active during the stance phase of normal gait. We found that analyzing the induced accelerations at maximum activation in some cases led to a different interpretation of the muscles’ potential actions than analyzing the induced accelerations per unit force. For example, per unit force, gluteus maximus has a very large potential to accelerate the knee during single limb stance, but only a small potential to accelerate the knee at maximum activation due to this muscle operating in suboptimal regions of its force–length–velocity curve during the majority of stance. This new analysis technique will be useful in studying abnormal movement, when altered kinematics may influence the capacity of muscles to accelerate joints due to altered lengths and shortening velocities.     

A Nebulin Ruler Does Not Dictate Thin Filament Lengths

To generate force, striated muscle requires overlap between uniform-length actin and myosin filaments. The hypothesis that a nebulin ruler mechanism specifies thin filament lengths by targeting where tropomodulin (Tmod) caps the slow-growing, pointed end has not been rigorously tested. Using fluorescent microscopy and quantitative image analysis, we found that nebulin extended 1.01-1.03 μm from the Z-line, but Tmod localized 1.13-1.31 μm from the Z-line, in seven different rabbit skeletal muscles. Because nebulin does not extend to the thin filament pointed ends, it can neither target Tmod capping nor specify thin filament lengths. We found instead a strong correspondence between thin filament lengths and titin isoform sizes for each muscle. Our results suggest the existence of a mechanism whereby nebulin specifies the minimum thin filament length and sarcomere length regulates and coordinates pointed-end dynamics to maintain the relative overlap of the thin and thick filaments during myofibril assembly.     

Fibre operating lengths of human lower limb muscles during walking

Muscles actuate movement by generating forces. The forces generated by muscles are highly dependent on their fibre lengths, yet it is difficult to measure the lengths over which muscle fibres operate during movement. We combined experimental measurements of joint angles and muscle activation patterns during walking with a musculoskeletal model that captures the relationships between muscle fibre lengths, joint angles and muscle activations for muscles of the lower limb. We used this musculoskeletal model to produce a simulation of muscle-tendon dynamics during walking and calculated fibre operating lengths (i.e. the length of muscle fibres relative to their optimal fibre length) for 17 lower limb muscles. Our results indicate that when musculotendon compliance is low, the muscle fibre operating length is determined predominantly by the joint angles and muscle moment arms. If musculotendon compliance is high, muscle fibre operating length is more dependent on activation level and force-length-velocity effects. We found that muscles operate on multiple limbs of the force-length curve (i.e. ascending, plateau and descending limbs) during the gait cycle, but are active within a smaller portion of their total operating range.     

History-dependent properties of skeletal muscle myofibrils contracting along the ascending limb of the force–length relationship

There is a history dependence of skeletal muscle contraction: stretching activated muscles induces a long-lasting force enhancement, while shortening activated muscles induces a long-lasting force depression. These history-dependent properties cannot be explained by the current model of muscle contraction, and its mechanism is unknown. The purposes of this study were (i) to evaluate if force enhancement and force depression are present at short lengths (the ascending limb of the force–length (FL) relationship), (ii) to evaluate if the history-dependent properties are associated with sarcomere length (SL) non-uniformity and (iii) to determine the effects of cross-bridge (de)activation on force depression. Rabbit psoas myofibrils were isolated and attached between two microneedles for force measurements. Images of the myofibrils were projected onto a linear photodiode array for measurements of SL. Myofibrils were activated by either Ca²⁺ or MgADP; the latter induces cross-bridge attachment to actin independently of Ca²⁺. Activated myofibrils were subjected to three stretches or shortenings (approx. 4% SL at approx. 0.07 µm s⁻¹ sarcomere⁻¹) along the ascending limb of the FL relationship separated by periods (approx. 5 s) of isometric contraction. Force after stretch was higher than force after shortening at similar SLs. The differences in force could not be explained by SL non-uniformity. The FL relationship produced by Ca²⁺- and MgADP-activated myofibrils were similar in stretch experiments, but after shortening MgADP activation produced forces that were higher than Ca²⁺ activation. Since MgADP induces the formation of strongly bound cross-bridges, this result suggests that force depression following shortening is associated with cross-bridge deactivation.     

Thin filament length regulation in striated muscle sarcomeres: pointed-end dynamics go beyond a nebulin ruler

The actin (thin) filaments in striated muscle are highly regulated and precisely specified in length to optimally overlap with the myosin (thick) filaments for efficient myofibril contraction. Here, we review and critically discuss recent evidence for how thin filament lengths are controlled in vertebrate skeletal, vertebrate cardiac, and invertebrate (arthropod) sarcomeres. Regulation of actin polymerization dynamics at the slow-growing (pointed) ends by the capping protein tropomodulin provides a unified explanation for how thin filament lengths are physiologically optimized in all three muscle types. Nebulin, a large protein thought to specify thin filament lengths in vertebrate skeletal muscle through a ruler mechanism, may not control pointed-end actin dynamics directly, but instead may stabilize a large core region of the thin filament. We suggest that this stabilizing function for nebulin modifies the lengths primarily specified by pointed-end actin dynamics to generate uniform filament lengths in vertebrate skeletal muscle. We suggest that nebulette, a small homolog of nebulin, may stabilize a correspondingly shorter core region and allow individual thin filament lengths to vary according to working sarcomere lengths in vertebrate cardiac muscle. We present a unified model for thin filament length regulation where these two mechanisms cooperate to tailor thin filament lengths for specific contractile environments in diverse muscles.     

Effect of theophylline on the velocity of diaphragmatic muscle shortening

The present study examined the effect of theophylline on the shortening velocity of submaximally activated diaphragmatic muscle (i.e., muscles were activated by the use of a level of stimulation, 50 Hz, within the range of phrenic neural firing frequencies achieved during breathing, whereas maximum activation is achieved at 300 Hz). Experiments were performed in vitro on strips of diaphragmatic muscle obtained from 21 Syrian hamsters. Muscle shortening velocity was assessed during isotonic contractions against a range of afterloads, and Hill's characteristic equation was used to calculate velocity at zero load. In addition, unloaded shortening velocity was also measured by the slack test, i.e., from the time required for muscles to take up slack after a sudden reduction in muscle length. Theophylline (160 mg/l) increased the velocity of muscle shortening against a wide range of external loads (0-14 N/cm2) and increased the extrapolated unloaded velocity of shortening from 6.4 +/- 0.9 to 7.9 +/- 1.1 (SE) lengths/s (P less than 0.01). Theophylline reduced the time required to take up slack for any given step change in muscle length, increasing the unloaded velocity of shortening assessed by the slack test from 7.6 +/- 0.9 to 9.3 +/- 1.1 lengths/s (P less than 0.002). The effect of theophylline on diaphragmatic shortening velocity was evident at concentrations as low as 40 mg/l and increased progressively as theophylline concentrations were increased to 320 mg/l. Theophylline increased the shortening velocity of fatigued as well as fresh muscles.(ABSTRACT TRUNCATED AT 250 WORDS)     

Cardiac Myosin Binding Protein-C Is Essential for Thick-Filament Stability and Flexural Rigidity

Using atomic force microscopy, we examined the contribution of cardiac myosin binding protein-C (cMyBP-C) to thick-filament length and flexural rigidity. Native thick filaments were isolated from the hearts of transgenic mice bearing a truncation mutation of cMyBP-C (t/t) that results in no detectable cMyBP-C and from age-matched wild-type controls (+/+). Atomic force microscopy images of these filaments were evaluated with an automated analysis algorithm that identified filament position and shape. The t/t thick-filament length (1.48 ± 0.02 μm) was significantly (P < 0.01) shorter than +/+ (1.56 ± 0.02 μm). This 5%-shorter thick-filament length in the t/t was reflected in 4% significantly shorter sarcomere lengths of relaxed isolated cardiomyocytes of the t/t (1.97 ± 0.01 μm) compared to +/+ (2.05 ± 0.01 μm). To determine if cMyBP-C contributes to the mechanical properties of thick filaments, we used statistical polymer chain mechanics to calculate a per-filament-specific persistence length, an index of flexural rigidity directly proportional to Young's modulus. Thick-filament-specific persistence length in the t/t (373 ± 62 μm) was significantly lower than in +/+ (639 ± 101 μm). Accordingly, Young's modulus of t/t thick filaments was ∼60% of +/+. These results provide what we consider a new understanding for the critical role of cMyBP-C in defining normal cardiac output by sustaining force and muscle stiffness.     

Positive force feedback in bouncing gaits?

During bouncing gaits (running, hopping, trotting), passive compliant structures (e.g. tendons, ligaments) store and release part of the stride energy. Here, active muscles must provide the required force to withstand the developing tendon strain and to compensate for the inevitable energy losses. This requires an appropriate control of muscle activation. In this study, for hopping, the potential involvement of afferent information from muscle receptors (muscle spindles, Golgi tendon organs) is investigated using a two-segment leg model with one extensor muscle. It is found that: (i) positive feedbacks of muscle-fibre length and muscle force can result in periodic bouncing; (ii) positive force feedback (F+) stabilizes bouncing patterns within a large range of stride energies (maximum hopping height of 16.3 cm, almost twofold higher than the length feedback); and (iii) when employing this reflex scheme, for moderate hopping heights (up to 8.8 cm), an overall elastic leg behaviour is predicted (hopping frequency of 1.4-3 Hz, leg stiffness of 9-27 kN m(-1)). Furthermore, F+ could stabilize running. It is suggested that, during the stance phase of bouncing tasks, the reflex-generated motor control based on feedbacks might be an efficient and reliable alternative to central motor commands.