A mathematical model of force transmission from intrafascicularly terminating muscle fibers

Many long skeletal muscles are comprised of fibers that terminate intrafascicularly. Force from terminating fibers can be transmitted through shear within the endomysium that surrounds fibers or through tension within the endomysium that extends from fibers to the tendon; however, it is unclear which pathway dominates in force transmission from terminating fibers. The purpose of this work was to develop mathematical models to (i) compare the efficacy of lateral (through shear) and longitudinal (through tension) force transmission in intrafascicularly terminating fibers, and (ii) determine how force transmission is affected by variations in the structure and properties of fibers and the endomysium. The models demonstrated that even though the amount of force that can be transmitted from an intrafascicularly terminating fiber is dependent on fiber resting length (the unstretched length at which passive stress is zero), endomysium shear modulus, and fiber volume fraction (the fraction of the muscle cross-sectional area that is occupied by fibers), fibers that have values of resting length, shear modulus, and volume fraction within physiologic ranges can transmit nearly all of their peak isometric force laterally through shearing of the endomysium. By contrast, the models predicted only limited force transmission ability through tension within the endomysium that extends from the fiber to the tendon. Moreover, when fiber volume fraction decreases to unhealthy ranges (less than 50%), the force-transmitting potential of terminating fibers through shearing of the endomysium decreases significantly. The models presented here support the hypothesis that lateral force transmission through shearing of the endomysium is an effective mode of force transmission in terminating fibers.     

Genetic Models in Applied Physiology. Merosin deficiency leads to alterations in passive and active skeletal muscle mechanics.

The role of extracellular elements on the mechanical properties of skeletal muscles is unknown. Merosin is an essential extracellular matrix protein that forms a mechanical junction between the sarcolemma and collagen. Therefore, it is possible that merosin plays a role in force transmission between muscle fibers and collagen. We hypothesized that deficiency in merosin may alter passive muscle stiffness, viscoelastic properties, and contractile muscle force in skeletal muscles. We used the dy/dy mouse, a merosin-deficient mouse model, to examine changes in passive and active muscle mechanics. After mice were anesthetized and the diaphragm or the biceps femoris hindlimb muscle was excised, passive length-tension relationships, stress-relaxation curves, or isometric contractile properties were determined with an in vitro biaxial mechanical testing apparatus. Compared with controls, extensibility was smaller in the muscle fiber direction and the transverse fiber direction of the mutant mice. The relaxed elastic modulus was smaller in merosin-deficient diaphragms compared with controls. Interestingly, maximal muscle tetanic stress was depressed in muscles from the mutant mice during uniaxial loading but not during biaxial loading. However, presence of transverse passive stretch increases maximal contractile stress in both the mutant and normal mice. Our data suggest that merosin contributes to muscle passive stiffness, viscoelasticity, and contractility and that the mechanism by which force is transmitted between adjacent myofibers via merosin possibly in shear.     

Mechanical Properties of the Sarcolemma and Myoplasm in Frog Muscle as a Function of Sarcomere Length

The elastimeter method was applied to the single muscle fiber of the frog semitendinosus to obtain the elastic moduli of the sarcolemma and myoplasm, as well as their relative contributions to resting fiber tension at different extensions. A bleb which was sucked into a flat-mouthed pipette at the fiber surface separated into an external sarcolemmal membrane and a thick inner myoplasmic region. Measurements showed that the sarcolemma does not contribute to intact fiber tension at sarcomere lengths below 3 µ. It was estimated that the sarcolemma contributed on the order of 10% to intact fiber tension at sarcomere lengths between 3 and 3.75 µ, and more so with further extension. Between these sarcomere lengths, the sarcolemma can be linearly extended and has a longitudinal elastic modulus of 5 x 10⁶ dyne/cm² (assuming a thickness of 0.1 µ). Resistance to deformation of the inner bleb region is due to myoplasmic elasticity. The myoplasmic elastic modulus was estimated by use of a model and was used to predict a fiber length-tension curve which agreed approximately with observations.     

Structural changes in single muscle fibers after stimulation at a low frequency

Direct stimulation of single muscle fibers from Xenopus laevis at a frequency of 1 Hz results in a decline of the peak isometric twitch tension after about 200 twitches. Fibers were chemically fixed in glutaraldehyde after a varying number of twitches and at several fatigue levels, and the ultrastructural appearance was compared with that of resting fibers treated by identical fixation methods. No gross structural abnormalities were observed but subtle changes occurred. The mitochondria of stimulated fibers contain granules of normal size and number. The inner crista width is constant but the matrix width is increased on stimulation. These changes would not compromise ATP production. The myofibrils are normal except for a slight swelling in the myosin lattice. The transverse system (T system) and sarcoplasmic reticulum are intact. The minor diameter of the transverse tubule (T tubule) is increased slightly in stimulated fibers. The gap between the T-TC membranes stays constant at about 110 A, but tiny connecting pillars are seen to cross this gap more frequently in stimulated fibers (21 +/- 5% triads) than in resting fibers (8 +/- 6%). In stimulated fibers there is a marked increase in the electron dense content of the terminal cisternae (TC). Inasmuch as the observed structural changes correlate with the number of twitches but not with the fatigue level, it is concluded that TC density and T-TC pillar formation are related to the normal mechanisms of excitation-contraction coupling.     

Finite element analysis of mechanics of lateral transmission of force in single muscle fiber

Most of the myofibers in long muscles of vertebrates terminate within fascicles without reaching either end of the tendon, thus force generated in myofibers has to be transmitted laterally through the extracellular matrix (ECM) to adjacent fibers; which is defined as the lateral transmission of force in skeletal muscles. The goal of this study was to determine the mechanisms of lateral transmission of force between the myofiber and ECM. In this study, a 2D finite element model of single muscle fiber was developed to study the effects of mechanical properties of the endomysium and the tapered ends of myofiber on lateral transmission of force. Results showed that most of the force generated is transmitted near the end of the myofiber through shear to the endomysium, and the force transmitted to the end of the model increases with increased stiffness of ECM. This study also demonstrated that the tapered angle of the myofiber ends can reduce the stress concentration near the myofiber end while laterally transmitting force efficiently.     

Palmitate oxidation in suspended skeletal muscle fibers from the rat

Palmitate oxidation in rat skeletal muscle was investigated with a suspension of intact isolated cells. M. flexor digitorum brevis was dissociated by a 6 h collagenase treatment to yield single myofibers of which 76% were viable. The contributions of 14CO2 and 14C-labeled acid-soluble intermediates to total oxidation products from palmitate were evaluated. The myofiber suspension exhibited a higher total oxidation rate than the isolated whole muscle, due to improved transport of palmitate to the sarcolemma. Addition of cytoplasmic cofactors L-carnitine, CoASH and ATP did not increase the palmitate oxidation. 14CO2 amounted to about 37% of oxidation products. With [1(-14)C]- and [16(-14)C]palmitate, the oxidation rates were equal. These findings indicate that the cellular integrity was well preserved. The oxidation rates were sharply decreased in fibers with damaged sarcolemmas, and in intact fibers when rotenon and antimycin A were applied. The damaged fibers restored the production of acid-soluble intermediates in the presence of cofactors. The results indicate that suspended skeletal myofibers are an adequate in vitro system for measurements of metabolic activities in the resting muscle.     

The composite structure of quail pectoralis muscle.

The twitch fibers of the quail pectoralis muscle were found to have one neuromuscular junction each, located in the middle third of the fiber. The length of isolated fibers varied between 8.8 and 33.2 mm, with mean and median values of 16 and 15.6 mm, respectively. The lengths of the fascicles from which the fibers were isolated varied between 30 and 51 mm. The muscle fibers taper at both ends. The neuromuscular junctions, revealed after histochemically reacting the intact muscle for acetyl cholinesterase activity, were arranged in discrete bands, separated by intervals of between 0.94 and 6.70 mm, with a mean value of 3.14 mm. The quail pectoralis muscle is thus composed of discontinuous, tapered muscle fibers, arranged in an overlapping series. It is therefore a muscle in which tension is transmitted laterally between muscle fibers.     

Cytological differentiation of human fetal skeletal muscle.

The ultrastructural differentiation of several different muscles was investigated in human fetuses ranging in age from 13 weeks to neonatal. At approximately 16 weeks of gestation cell cluster containing both myotubes and satellite cells lie enclosed by a newly formed basal lamina and show evidence of fusion. The development of organelles is evident in myoblasts, proceeds as the cells transform into myofibers, and continues in the neonate. Filament synthesis occurs primarily in the cell periphery where thin filaments appear to align themselves in relations to parallel arrays of ribosome-studded thick filaments: Z line formation follows the appearance of thin filaments. Intermediate filaments, approximately 10-12 nm thick, were also consistently observed in perinuclear regions and distal to filament assembly. Although sarcoplasmic reticulum (SR) development is closely related to fibril formation, connections between Z lines and SR are not consistent, thus supporting the conclusion that SR does not evoke the formation of the Z line. Bristlecoated vesicles appear to be the precursors of elements of the SR, possibly the lateral sacs. Development of the transverse tubules, as invaginations of the sarcolemma, is closely associated with the formation of lateral sacs since the latter occur along the sarcolemma as soon as transverse tubules appear. Cytological differentiation is similar, though not identical, in several different muscles. During the last trimester muscle fibers show some evidence of diversity mainly of variation in Z line width. In gerneral the results suggest that the sequence and stages of human myogenesis are similar to those of other species.     

Extracellular matrix and transmembrane linkages at the termination of intrafusal fibers and the outer capsule in chicken muscle spindles

Attachments of intrafusal fibers and of the outer spindle capsule at the far polar region were examined by immunohistochemistry in serially sectioned chicken leg muscles. Patterns of distribution of connective tissues and intracellular filaments suggest that, in this segment of the muscle spindle, intrafusal fibers bind laterally with the capsule. Contrary to extrafusal fibers at myotendinous junctions, folded plasmalemmas at the ends of intrafusal fibers were rare. Thus, there was little end-to-end interlocking between intrafusal fibers and the extracellular matrix. The tapered contours of terminating intrafusal fibers resembled those of extrafusal fibers which end in fascicles without tendinous connections. At points where the distal portions of intrafusal fibers closely adjoined and overlapped extrafusal fibers, α-actinin, vinculin, filamin, talin, β₁ integrin, spectrin, and dystrophin occurred with moderate to great frequency. It is generally accepted that these compounds are links in molecular chains that extend from the intracellular space across cell membranes to the extracellular matrix. Their location along substantial lengths of extrafusal fibers, distal capsule, and terminating intrafusal fibers suggests the presence of numerous transverse connections between elements of the terminal portion of the spindle and nonspindle tissues. Hence, it is likely that forces monitored by chicken spindles in muscles undergoing length changes are transferred from extrafusal fibers and extracellular matrix to the receptors in large part via lateral shear instead of by longitudinal tension. © 1996 Wiley-Liss, Inc.     

Identification of novel proteins unique to either transverse tubules (TS28) or the sarcolemma (SL50) in rabbit skeletal muscle

Novel proteins unique to either transverse tubules (TS28) or the sarcolemma (SL50) have been identified and characterized, and their in situ distribution in rabbit skeletal muscle has been determined using monoclonal antibodies. TS28, defined by mAb IXE112, was shown to have an apparent relative molecular mass of 28,000 D. Biochemical studies showed that TS28 is a minor membrane protein in isolated transverse tubular vesicles. Immunofluorescence and immunoelectron microscopical studies showed that TS28 is localized to the transverse tubules and in some subsarcolemmal vesicles possibly corresponding to the subgroup of caveolae connecting the transverse tubules with the sarcolemma. In contrast, TS28 is absent from the lateral portion of the sarcolemma. Immunofluorescence studies also showed that TS28 is more densely distributed in type II (fast) than in type I (slow) myofibers. Although TS28 and the 1,4-dihydropyridine receptor are both localized to transverse tubules and subsarcolemmal vesicles, TS28 is not a wheat germ agglutinin (WGA)-binding glycoprotein and does not appear to copurify with the 1,4-dihydropyridine receptor after detergent solubilization of transverse tubular membranes. SL50, defined by mAb IVD31, was shown to have an apparent relative molecular mass of 50,000 D. Biochemical studies showed that SL50 is not related to the 52,000-D (beta subunit) of the dihydropyridine receptor but does bind to WGA-Sepharose. Immunofluorescence labeling imaged by standard and confocal microscopy showed that SL50 is associated with the sarcolemma but apparently absent from the transverse tubules. Immunofluorescence labeling also showed that the density of SL50 in type II (fast) myofibers is indistinguishable from that of type I (slow) myofibers. The functions of TS28 and SL50 are presently unknown. However, the distinct distribution of TS28 to the transverse tubules and subsarcolemmal vesicles as determined by immunocytochemical labeling suggests that TS28 may be directly involved in excitation-contraction coupling. Our results demonstrate that, although transverse tubules are continuous with the sarcolemma, each of these membranes contain one or more unique proteins, thus supporting the idea that they each have a distinct protein composition.     

Peeled mammalian skeletal muscle fibers. Possible stimulation of Ca2+ release via a transverse tubule-sarcoplasmic reticulum mechanism

Single muscle fibers from rabbit soleus and adductor magnus and from semitendinosus muscles were peeled to remove the sarcolemma and then stimulated to release Ca2+ by (a) caffeine application or (b) ionic depolarization accomplished via substitution of choline chloride for potassium propionate at constant [K+] X [Cl-] in the bathing solution. Each stimulus, ionic or caffeine, elicited an isometric tension transient that appeared to be due to Ca2+ released from the sarcoplasmic reticulum (SR). The peak magnitude of the ionic (Cl- -induced) tension transient increased with increasing Cl- concentration. The application of ouabain to fibers after peeling had no effect on either type of tension transient. However, soaking the fibers in a ouabain solution before peeling blocked the Cl- -induced but not the caffeine-induced tension transient, which suggests that ouabain's site of action is extracellular, perhaps inside transverse tubules (TTs). Treating the peeled fibers with saponin, which should disrupt TTs to a greater extent than SR membrane, greatly reduced or eliminated the Cl- -induced tension transient without significantly altering the caffeine-induced tension transient. These results suggest that the Cl- -induced tension transient is elicited via stimulation of sealed, polarized TTs rather than via ionic depolarization of the SR.     

Extramuscular myofascial force transmission: experiments and finite element modeling

The specific purpose of the present study was to show that extramuscular myofascial force transmission exclusively has substantial effects on muscular mechanics. Muscle forces exerted at proximal and distal tendons of the rat extensor digitorium longus (EDL) were measured simultaneously, in two conditions (1) with intact extramuscular connections (2) after dissecting the muscles' extramuscular connections to a maximum extent without endangering circulation and innervation (as in most in situ muscle experiments). A finite element model of EDL including the muscles' extramuscular connections was used to assess the effects of extramuscular myofascial force transmission on muscular mechanics, primarily to test if such effects lead to distribution of length of sarcomeres within muscle fibers. In condition (1), EDL isometric forces measured at the distal and proximal tendons were significantly different (F(dist) > F(prox), DeltaF approximates maximally 40% of the proximal force). The model results show that extramuscular myofascial force transmission causes distributions of strain in the fiber direction (shortening in the proximal, lengthening in the distal ends of fibers) at higher lengths. This indicates significant length distributions of sarcomeres arranged in series within muscle fibers. Stress distributions found are in agreement with the higher distal force measured, meaning that the muscle fiber is no longer the unit exerting equal forces at both ends. Experimental results obtained in condition (2) showed no significant changes in the length-force characteristics (i.e., proximo-distal force differences were maintained). This shows that a muscle in situ has to be distinguished from a muscle that is truly isolated in which case the force difference has to be zero. We conclude that extramuscular myofascial force transmission has major effects on muscle functioning.     

Length-dependent electromechanical coupling in single muscle fibers

In single muscle fibers from the giant barnacle, a small decrease in muscle length decreases both the calcium activation and the peak isometric tension produced by a constant current stimulus. The effect is most pronounced if the length change immediately precedes the stimulation. In some cases, the decrease in tension with shortening can be accounted for almost entirely by a decrease in calcium release rather than changes in mechanical factors such as filament geometry. During the constant current stimulation the muscle membrane becomes more depolarized at longer muscle lengths than at the shorter muscle lengths. Under voltage clamp conditions, when the membrane potential is kept constant during stimulation, there is little length dependence of calcium release. Thus, the effect of length on calcium release is mediated through a change in membrane properties, rather than an effect on a subsequent step in excitation-contraction coupling. Stretch causes the unstimulated fiber membrane to depolarize by about l mV while release causes the fiber membrane to hyperpolarize by about the same amount. The process causing this change in potential has an equilibrium potential nearly 10 mV hyperpolarized from the resting level. This change in resting membrane potential with length may account for the length dependence of calcium release.     

SELECTIVE DISRUPTION OF THE SARCOTUBULAR SYSTEM IN FROG SARTORIUS MUSCLE : A Quantitative Study with Exogenous Peroxidase as a Marker

Skeletal muscles which have been soaked for 1 hr in a glycerol-Ringer solution and then returned to normal Ringer solution have a disrupted sarcotubular system. The effect is associated with the return to Ringer's since muscles have normal fine structure while still in glycerol-Ringer's. Karnovsky's peroxidase method was found to be a very reliable marker of extracellular space, filling 98.5% of the tubules in normal muscle. It was interesting to note that only 84.1% of the sarcomeres in normal muscle have transverse tubules. The sarcotubular system was essentially absent from glycerol-treated muscle fibers, only 2 % of the tubular system remaining connected to the extracellular space; the intact remnants were stumps extending only a few micra into the fiber. Thus, glycerol-treated muscle fibers provide a preparation of skeletal muscle with little sarcotubular system. Since the sarcoplasmic reticulum is not destroyed and the sarcolemma and myofilaments are intact in this preparation, of the properties of the sarcolemma may thus be separated from those of the tubular system.     

CARDIAC MUSCLE : A Comparative Study of Purkinje Fibers and Ventricular Fibers

With light and electron microscopy a comparison has been made of the morphology of ventricular (V) and Purkinje (P) fibers of the hearts of guinea pig, rabbit, cat, dog, goat, and sheep. The criteria, previously established for the rabbit heart, that V fibers are distinguished from P fibers by the respective presence and absence of transverse tubules is shown to be true for all animals studied. No evidence was found of a permanent connection between the sarcoplasmic reticulum and the extracellular space. The sarcoplasmic reticulum (SR) of V fibers formed couplings with the sarcolemma of a transverse tubule (interior coupling) and with the peripheral sarcolemma (peripheral coupling), whereas in P fibers the SR formed only peripheral couplings. The forms of the couplings were identical. The significance, with respect to excitation-contraction coupling, of the difference in the form of the couplings in cardiac versus skeletal muscle is discussed together with the electrophysiological implications of the differing geometries of bundles of P fibers from different animals.     

A non-cross-bridge stiffness in activated frog muscle fibers

Force responses to fast ramp stretches of various amplitude and velocity, applied during tetanic contractions, were measured in single intact fibers from frog tibialis anterior muscle. Experiments were performed at 14 degrees C at approximately 2.1 microm sarcomere length on fibers bathed in Ringer's solution containing various concentrations of 2,3-butanedione monoxime (BDM) to greatly reduce the isometric tension. The fast tension transient produced by the stretch was followed by a period, lasting until relaxation, during which the tension remained constant to a value that greatly exceeded the isometric tension. The excess of tension was termed "static tension," and the ratio between the force and the accompanying sarcomere length change was termed "static stiffness." The static stiffness was independent of the active tension developed by the fiber, and independent of stretch amplitude and stretching velocity in the whole range tested; it increased with sarcomere length in the range 2.1-2.8 microm, to decrease again at longer lengths. Static stiffness increased well ahead of tension during the tetanus rise, and fell ahead of tension during relaxation. These results suggest that activation increased the stiffness of some sarcomeric structure(s) outside the cross-bridges.     

Effects of nifedipine on the mechanical properties of sarcolemma and modulation of dynamics of the increase in the basal calcium level in fibers of rat soleus muscle under short-term hypogravity conditions

It has been shown that the modulation of the mechanical properties of sarcolemma mediated by nifedipine may be related to the dynamics of accumulation of calcium ions under short-term rat hindlimb suspension. The basal calcium level was measured with a fluorescent probe Fluo-4AM, the transverse stiffness of different parts of the contractile apparatus and sarcolemma was estimated by atomic force microscopy, and the content of desmin was determined by gel electrophoresis with immunoblotting. It has been found that nifedipine has a protective effect on muscle fibers under hypogravity by decreasing the degradation of desmin and proteins that determine the transverse stiffness of sarcolemma and the contractile apparatus, and the intensity of the increase in the basal calcium level. It was shown that selective blocking of L-channels leads to an increase in the basal calcium level in intact soleus fibers. At the same time, the transverse stiffness of sarcolemma and the contractile apparatus increases. The mechanism of this increase is still unclear, but it is thought to mediate the protective action of nifedipine.     

Hydrostatic compression in glycerinated rabbit muscle fibers.

Glycerinated muscle fibers isolated from rabbit psoas muscle, and a number of other nonmuscle elastic fibers including glass, rubber, and collagen, were exposed to hydrostatic pressures of up to 10 MPa (100 Atm) to determine the pressure sensitivity of their isometric tension. The isometric tension of muscle fibers in the relaxed state (passive tension) was insensitive to increased pressure, whereas the muscle fiber tension in rigor state increased linearly with pressure. The tension of all other fiber types (except rubber) also increased with pressure; the rubber tension was pressure insensitive. The pressure sensitivity of rigor tension was 2.3 kN/m2/MPa and, in comparison with force/extension relation determined at atmospheric pressure, the hydrostatic compression in rigor muscle fibers was estimated to be 0.03% Lo/MPa. As reported previously, the active muscle fiber tension is depressed by increased pressure. The possible underlying basis of the different pressure-dependent tension behavior in relaxed, rigor, and active muscle is discussed.     

Plasma membrane removal in rat skeletal muscle fibers reveals caveolin-3 hot-spots at the necks of transverse tubules

Caveolin-3, the muscle-specific isoform of the caveolae-associated protein caveolin, is often thought to be localized exclusively in the surface membrane in mature fibers and associated with transverse (t)-tubular system only transiently during development. Skeletal muscle fibers present a model where the surface membrane (sarcolemma) can be completely separated from the cell by mechanical dissection. Western blotting of matching portions of individual fibers from adult rat muscle in which the sarcolemma was either removed (skinned segment), or left in place (intact segment), revealed that ≥ 70% of caveolin-3 is actually located deeper in the fiber rather than in the sarcolemma itself. Triton solubility of caveolin-3 was no different between sarcolemmal and t-tubule compartments. Confocal immunofluorescence microscopy showed caveolin-3 present throughout the t-system in adult fibers, with ‘hot-spots’ at the necks of the tubules in the sub-sarcolemmal space. A similar representation was seen for the muscle specific voltage-dependent sodium channel Nav1.4 and it was found that at least some Nav1.4 co-immunoprecipitated with caveolin-3 in skinned muscle fibers. The caveolin-3 hot-spots just inside the opening of t-tubules may form regions that localize ion channels and kinases at the key place needed for efficient electrical transmission into the t-tubules as well as for other signaling processes.