Optimum power output and structural design of sarcomeres

A model of a "general" sarcomere is presented for the calculation of power output as a function of (i) contraction range, (ii) contraction velocity, (iii) muscle fibre stimulation (active state) and (iv) structural parameters of the sarcomere (i.e. lengths of actin, myosin, and bare zone on myosin, and thickness of the Z-disc). The model is applicable to virtually all types of striated muscle fibres. By computer simulation, particular combinations of actin and myosin lengths were found that maximize the specific power output for particular functional demands, specified in terms of contraction range and contraction velocity. The accuracy of the prediction of the optimum sarcomere design by the model depends on the quality of its input, i.e. the available knowledge of the in vivo spectrum of contraction velocities and sarcomere excursions. Predictions of sarcomere design from model simulations were compared with ultrastructural data from the literature. With the present model, the complete variation in the ratio of myosin length over actin length (from about 1.05 down to 0.65, as observed in insect and vertebrate sarcomeres) can be explained as a series of adaptations for optimum power output from a small to a large contraction range, respectively.     

Differential serial sarcomere number adaptations in knee extensor muscles of rats is contraction type dependent.

Sarcomerogenesis, or the addition of sarcomeres in series within a fiber, has a profound impact on the performance of a muscle by increasing its contractile velocity and power. Sarcomerogenesis may provide a beneficial adaptation to prevent injury when a muscle consistently works at long lengths, accounting for the repeated-bout effect. The association between eccentric exercise, sarcomerogenesis and the repeated-bout effect has been proposed to depend on damage, where regeneration allows sarcomeres to work at shorter lengths for a given muscle-tendon unit length. To gain additional insight into this phenomenon, we measured fiber dynamics directly in the vastus lateralis (VL) muscle of rats during uphill and downhill walking, and we measured serial sarcomere number in the VL and vastus intermedius (VI) after chronic training on either a decline or incline grade. We found that the knee extensor muscles of uphill walking rats undergo repeated active concentric contractions, and therefore they suffer no contraction-induced injury. Conversely, the knee extensor muscles during downhill walking undergo repeated active eccentric contractions. Serial sarcomere numbers change differently for the uphill and downhill exercise groups, and for the VL and VI muscles. Short muscle lengths for uphill concentric-biased contractions result in a loss of serial sarcomeres, and long muscle lengths for downhill eccentric-biased contractions result in a gain of serial sarcomeres.     

Length dependence of active force production in skeletal muscle.

The sliding filament and cross-bridge theories of muscle contraction provide discrete predictions of the tetanic force-length relationship of skeletal muscle that have been tested experimentally. The active force generated by a maximally activated single fiber (with sarcomere length control) is maximal when the filament overlap is optimized and is proportionally decreased when overlap is diminished. The force-length relationship is a static property of skeletal muscle and, therefore, it does not predict the consequences of dynamic contractions. Changes in sarcomere length during muscle contraction result in modulation of the active force that is not necessarily predicted by the cross-bridge theory. The results of in vivo studies of the force-length relationship suggest that muscles that operate on the ascending limb of the force-length relationship typically function in stretch-shortening cycle contractions, and muscles that operate on the descending limb typically function in shorten-stretch cycle contractions. The joint moments produced by a muscle depend on the moment arm and the sarcomere length of the muscle. Moment arm magnitude also affects the excursion (length change) of a muscle for a given change in joint angle, and the number of sarcomeres arranged in series within a muscle fiber determines the sarcomere length change associated with a given excursion.     

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.     

Lack of correspondence between histochemical and structural fiber typing in antennal muscles of the rock lobster Palinurus vulgaris.

1. Sarcomere lengths and fine structure were examined in three histochemical fiber types of antennal muscles of the rock lobster. 2. Sarcomere lengths are distributed over a continuum of values from 6.5 to 19 microns. 3. Although a correlation between ATPase activity and sarcomere length is demonstrated, fibers with high ATPase activity do not have the sarcomere length typical of fast contracting fibers. 4. These fibers deviated from the typical fast structure in having long sarcomeres (greater than 6.5 microns) and in having some unusual ultrastructural characteristics (absence of the H-band, presence of Z-tubules, high thin to thick ratio, 5:1) associated with other more classical features. 5. This finding demonstrates that sarcomere length measurements do not always accurately predict the physiological performance of a single muscle fiber. 6. The fiber type composition of two antagonistic antennal muscles is compared and the functional significance of the results is discussed with respect to their role in behavior.     

Polarized light observations on striated muscle contraction in a mite

Contraction of individual sarcomeres within the living mite Tarsonemus sp. was observed by polarized light microscopy. In unflattened animals the usual range of contraction was such that the minimum sarcomere length approximated the length of the A region, and the maximum sarcomere length was about twice the length of the A region. The central sarcomeres of the dorsal metapodosomal muscles were observed in detail. The A band length increased slightly with increasing sarcomere length since the regression of I region length on sarcomere length had an average slope of 0.91. When the A band length in a sarcomere which was shortening was compared with the length when the same sarcomere lengthened, no significant difference was seen. The A band of each sarcomere seemed to act as a not too rigid limit to further shortening; this agreed with the reversible shortening of a muscle in which the A band had been experimentally shortened. An H region was visible at long sarcomere lengths and was not visible at short sarcomere lengths, even when the muscle was actively shortening. The rate of change of H region length with sarcomere length suggested that I filament length may increase as sarcomere length increases. Despite this effect and the small increase in A length with sarcomere length, the results are considered to be consistent with a model in which shortening occurs by the relative movement of A and I filaments, with little or no change in length of either set of filaments. Sarcomere shortening was clearly associated with an increase in the retardation of the A region.     

Sarcomere reorganization in mite muscle.

The number of sarcomeres in a given muscle of the mite Tarsonemus randsi was constant in both larval and adult stages, with the exception of the two medial dorsal metapodosomal muscles in males. These muscles have three sarcomeres in larvae and one sarcomere in adults. This change in sarcomere number within a muscle was observed in the living animal by polarized light microscopy using parthenogenetically derived male larvae. Initially the transforming muscles shortened slowly (hours) and the appearance of the sarcomeres was comparable to that seen during normal contraction. With continued shortening there was apposition of adjacent A bands and disappearance of clearly visible Z lines, but no loss of birefringence. Over the next 12 hr there was further shortening of the muscle and loss of birefringence. This was apparent as shortening of the three apposed A regions to the length of a single A band with a small increase in muscle width and no increase in the peak retardation of the birefringent region. The observations are discussed in terms of differential loss of the A filaments of the two terminal sarcomeres.     

Ultrastructural diversity in motor units of crustacean stomach muscles

The physiological and ultrastructural properties of muscle fiber.s comprising three motor units in the gastric mill of blue crabs are described. In their contractile properties muscle fibers in all motor units are similar and resemble the slow type fibers in crustacean limb muscles. The majority of fibers generate large excitatory post-synaptic potentials which do not facilitate strongly. Structurally two types of fibers are found. The one type has long sarcomeres (greater than 6 mum), thin to thick myofilament ratios of 5-6:1 and diads located near the ends of the A-band. The other type has shorter sarcomeres (less than 6 mum), thin to thick myofilament ratios of 3:1 and diads located at mid sarcomere level. Both types of fibers occur within a single motor unit and this differs from the vertebrate situation. Furthermore, the finding of fibers with a low thin to thick myofilament ratio of 3:1 demonstrates that they are not exclusive to fast type crustacean muscle but also occur in slow stomach muscles.     

Overextended sarcomeres regain filament overlap following stretch

Sarcomere overextension has been widely implicated in stretch-induced muscle injury. Yet, sarcomere overextensions are typically inferred based on indirect evidence obtained in muscle and fibre preparations, where individual sarcomeres cannot be observed during dynamic contractions. Therefore, it remains unclear whether sarcomere overextensions are permanent following injury-inducing stretch-shortening cycles, and thus, if they can explain stretch-induced force loss. We tested the hypothesis that overextended sarcomeres can regain filament overlap in isolated myofibrils from rabbit psoas muscles. Maximally activated myofibrils (n=13) were stretched from an average sarcomere length of 2.6±0.04μm by 0.9μm sarcomere(-1) at a speed of 0.1μm sarcomere(-1)s(-1) and immediately returned to the starting lengths at the same speed (sarcomere strain=34.1±2.3%). Myofibrils were then allowed to contract isometrically at the starting lengths (2.6μm) for ～30s before relaxing. Force and individual sarcomere lengths were measured continuously. Out of the 182 sarcomeres, 35 sarcomeres were overextended at the peak of stretch, out of which 26 regained filament overlap in the shortening phase while 9 (～5%) remained overextended. About 35% of the sarcomeres with initial lengths on the descending limb of the force-length relationship and ～2% of the sarcomeres with shorter initial lengths were overextended. These findings provide first ever direct evidence that overextended sarcomeres can regain filament overlap in the shortening phase following stretch, and that the likelihood of overextension is higher for sarcomeres residing initially on the descending limb.     

A quantitative model of intersarcomere dynamics during fixed-end contractions of single frog muscle fibers.

A numerical model of a muscle fiber as 400 sarcomeres, identical except for their initial lengths, was used to simulate fixed-end tetanic contractions of frog single fibers at sarcomere lengths above the optimum. The sarcomeres were represented by a lumped model, constructed from the passive and active sarcomere length-tension curves, the force-velocity curve, and the observed active elasticity of a single frog muscle fiber. An intersarcomere force was included to prevent large disparities in lengths of neighboring sarcomeres. The model duplicated the fast rise, slow creep rise, peak, and slow decline of tension seen in tetanic contractions of stretched living fibers. Decreasing the initial non-uniformity of sarcomere length reduced the rate of rise of tension during the creep phase, but did not decrease the peak tension reached. Limitations of the model, and other processes that might contribute to the shape of the fixed end tetanic tension record are discussed. Taking account of model and experimental results, it is concluded that the distinctive features of the tension records of fixed end tetanic contraction at lengths beyond optimum can be explained by internal motion within the fiber.     

Sarcomere Mechanics in Capillary Endothelial Cells

Tension generation in endothelial cells of the aorta, spleen, and eye occurs in actin stress fibers, and is necessary for normal cell function. Sarcomeres are the tension-generating units of actin stress fibers in endothelial cells. How sarcomeres generate and maintain tension in stress fibers is not well understood. Using femtosecond laser ablation, we severed living stress fibers and measured sarcomere contraction under zero tension. The length of the sarcomere decreased in two phases: an instantaneous initial response, followed by a slower change in length attributed to myosin activity. The latter phase ceased abruptly after a minimum sarcomere length was reached, suggesting a rigid resistance that prevents further contraction. Furthermore, severed, contracted stress fibers did not relax when treated with myosin inhibitors, indicating that contracted stress fibers do not store elastic potential energy. These novel measurements combined with modeling suggest that myosin-generated forces in adjacent sarcomeres are directly in balance, and argue against sarcomere models with springlike elements in parallel with myosin contractile elements. We propose a new model for tension generation in the sarcomere, which provides a mechanistic interpretation for our observations and previous observations of inhomogeneous sarcomere contraction and apparent stress fiber viscoelastic behavior.     

Length-tension relation in Limulus striated muscle

Laser diffraction techniques coupled with simultaneous tension measurements were used to determine the length-tension relation in intact, small (0.5-mm thick, 10-mm wide, 20-25-mm long) bundles of a Limulus (horseshoe crab) striated muscle, the telson levator muscle. This muscle differs from the model vertebrate systems in that the thick filaments are not of a constant length, but shorten from 4.9 to approximately 2.0 micrometers as the sarcomeres shorten from 7 to 3 micrometers. In the Limulus muscle, the length-tension relation plateaued to an average maximum tension of 0.34 N/mm2 at a sarcomere length of 6.5 micrometers (Lo) to 8.0 micrometers. In the sarcomere length range from 3.8 to 12.5 micrometers, the muscle developed 50% or more of the maximum tension. When the sarcomere lengths are normalized (expressed as L/Lo) and the Limulus data are compared to those from frog muscle, it is apparent that Limulus muscle develops tension over a relatively greater range of sarcomere lengths.     

Residual force enhancement in myofibrils and sarcomeres

Residual force enhancement has been observed following active stretch of skeletal muscles and single fibres. However, there has been intense debate whether force enhancement is a sarcomeric property, or is associated with sarcomere length instability and the associated development of non-uniformities. Here, we studied force enhancement for the first time in isolated myofibrils (n=18) that, owing to the strict in series arrangement, allowed for evaluation of this property in individual sarcomeres (n=79). We found consistent force enhancement following stretch in all myofibrils and each sarcomere, and forces in the enhanced state typically exceeded the isometric forces on the plateau of the force-length relationship. Measurements were made on the plateau and the descending limb of the force-length relationship and revealed gross sarcomere length non-uniformities prior to and following active myofibril stretching, but in contrast to previous accounts, revealed that sarcomere lengths were perfectly stable under these experimental conditions. We conclude that force enhancement is a sarcomeric property that does not depend on sarcomere length instability, that force enhancement varies greatly for different sarcomeres within the same myofibril and that sarcomeres with vastly different amounts of actin-myosin overlap produce the same isometric steady-state forces. This last finding was not explained by differences in the amount of contractile proteins within sarcomeres, vastly different passive properties of individual sarcomeres or (half-) sarcomere length instabilities, suggesting that the basic mechanical properties of muscles, such as force enhancement, force depression and creep, which have traditionally been associated with sarcomere instabilities and the corresponding dynamic redistribution of sarcomere lengths, are not caused by such instabilities, but rather seem to be inherent properties of the mechanisms of contraction.     

SALS, a WH2-domain-containing protein, promotes sarcomeric actin filament elongation from pointed ends during Drosophila muscle growth

Organization of actin filaments into a well-organized sarcomere structure is critical for muscle development and function. However, it is not completely understood how sarcomeric actin/thin filaments attain their stereotyped lengths. In an RNAi screen in Drosophila primary muscle cells, we identified a gene, sarcomere length short (sals), which encodes an actin-binding, WH2 domain-containing protein, required for proper sarcomere size. When sals is knocked down by RNAi, primary muscles display thin myofibrils with shortened sarcomeres and increased sarcomere number. Both loss- and gain-of-function analyses indicate that SALS may influence sarcomere lengths by promoting thin-filament lengthening from pointed ends. Furthermore, the complex localization of SALS and other sarcomeric proteins in myofibrils reveals that the full length of thin filaments is achieved in a two-step process, and that SALS is required for the second elongation phase, most likely because it antagonizes the pointed-end capping protein Tropomodulin.     

Leverage and muscle type in crab chelae (Crustacea: Brachyura)

The chelae of Cancer pagurus and Macropipus depurator were examined with respect to mechanical advantage. The closer muscles were investigated with respect to sarcomere length in the constituent fibres and to the force developed by the whole muscle during isometric contraction. Cancer chelae have a relatively high mechanical advantage, 0.329 ± 001. Cancer closer muscles contain a high proportion of fibres with long sarcomeres, mean lengths mostly falling between 12 and 15 μm, and develop a maximum stress of about 496 kN.m⁻² during contraction. These figures are typical for "slow" crustacean muscle. The chelae of M. depurator are dimorphic. In one, the strong chela, the mechanical advantage is 0.248 ± 0.066 while in the other, the fast chela, the mechanical advantage is 0.177 ± 0.006. M. depurator closer muscles contain fibres with mean sarcomere lengths mostly falling between 6 and 10 μm. The muscle develops a maximum stress of about 145 kN.m⁻² during contraction. These figures are typical of "intermediate" crustacean muscles. "Fast" muscle fibres with short sarcomeres (about 30 um) were found in the chelae of both Cancer and M. depurator but were much commoner in the latter. Thus in Cancer a high mechanical advantage is correlated with slow muscle while in M. depurator lower mechanical advantages are broadly correlated with faster muscle. Consistent correlation between mechanical advantage and muscle type in the dimorphic chelae of M. depurator , however, is lacking. No consistent regionation of fibres with similar properties was found in the muscles.     

Measuring muscle and joint geometry parameters of a shoulder for modeling purposes.

An extensive set of muscle and joint geometry parameters was measured of the right shoulder of an embalmed male. For all muscles the optimal muscle fiber length was determined by laser diffraction measurements of sarcomere length. In addition, tendon length and physiological cross-sectional area were determined. The parameter set was needed to enhance the reliability of a computer model of the shoulder (Van der Helm, 1994a,b Journal of Biomechanics 27, 527-550, 551-569). With the model, an abduction of the arm was simulated in seven positions, at 30 degrees intervals. In each of the simulated arm positions, actual sarcomere lengths were calculated from the lengths of 104 muscle elements, distributed over 16 shoulder muscles. For most muscle elements, the simulated abduction appeared to take place within the sarcomere length range in which the muscle elements can exert force. The muscle elements can then act on the ascending limb as well as on the plateau and on the descending limb of the relative force-length curves of sarcomeres. The produced data set is not only important for the refinement of shoulder modeling, but also for functional analyses of shoulder movements in general.     

Mechanical principles of effects of botulinum toxin on muscle length–force characteristics: An assessment by finite element modeling

Recent experiments involving muscle force measurements over a range of muscle lengths show that effects of botulinum toxin (BTX) are complex e.g., force reduction varies as a function of muscle length. We hypothesized that altered conditions of sarcomeres within active parts of partially paralyzed muscle is responsible for this effect. Using finite element modeling, the aim was to test this hypothesis and to study principles of how partial activation as a consequence of BTX affects muscle mechanics. In order to model the paralyzing effect of BTX, only 50% of the fascicles (most proximal, or middle, or most distal) of the modeled muscle were activated. For all muscle lengths, a vast majority of sarcomeres of these BTX-cases were at higher lengths than identical sarcomeres of the BTX-free muscle. Due to such “longer sarcomere effect”, activated muscle parts show an enhanced potential of active force exertion (up to 14.5%). Therefore, a muscle force reduction originating exclusively from the paralyzed muscle fiber populations, is compromised by the changes of active sarcomeres leading to a smaller net force reduction. Moreover, such “compromise to force reduction” varies as a function of muscle length and is a key determinant of muscle length dependence of force reduction caused by BTX. Due to longer sarcomere effect, muscle optimum length tends to shift to a lower muscle length. Muscle fiber–extracellular matrix interactions occurring via their mutual connections along full peripheral fiber lengths (i.e., myofascial force transmission) are central to these effects. Our results may help improving our understanding of mechanisms of how the toxin secondarily affects the muscle mechanically.     

Sarcomere Length Nonuniformity and Force Regulation in Myofibrils and Sarcomeres

The smallest contractile unit in striated muscles is the sarcomere. Although some of the classic features of contraction assume a uniform behavior of sarcomeres within myofibrils, the occurrence of sarcomere length nonuniformities has been well recognized for years, but it is yet not well understood. In the past years, there has been a great advance in experiments using isolated myofibrils and sarcomeres that has allowed scientists to directly evaluate sarcomere length nonuniformity. This review will focus on studies conducted with these preparations to develop the hypotheses that 1) force production in myofibrils is largely altered and regulated by intersarcomere dynamics and that 2) the mechanical work of one sarcomere in a myofibril is transmitted to other sarcomeres in series. We evaluated studies looking into myofibril activation, relaxation, and force changes produced during activation. We conclude that force production in myofibrils is largely regulated by intersarcomere dynamics, which arises from the cooperative work of the contractile and elastic elements within a myofibril.     

Skeletal muscle design to meet functional demands

Skeletal muscles are length- and velocity-sensitive force producers, constructed of a vast array of sarcomeres. Muscles come in a variety of sizes and shapes to accomplish a wide variety of tasks. How does muscle design match task performance? In this review, we outline muscle''s basic properties and strategies that are used to produce movement. Several examples are provided, primarily for human muscles, in which skeletal muscle architecture and moment arms are tailored to a particular performance requirement. In addition, the concept that muscles may have a preferred sarcomere length operating range is also introduced. Taken together, the case is made that muscles can be fine-tuned to perform specific tasks that require actuators with a wide range of properties.     

Flight muscle function in Drosophila requires colocalization of glycolytic enzymes.

Structural relationships between the myofibrillar contractile apparatus and the enzymes that generate ATP for muscle contraction are not well understood. We explored whether glycolytic enzymes are localized in Drosophila flight muscle and whether localization is required for function. We find that glycerol-3-phosphate dehydrogenase (GPDH) is localized at Z-discs and M-lines. The glycolytic enzymes aldolase and glyceraldehyde-3-phosphate dehydrogenase (GAPDH) are also localized along the sarcomere with a periodic pattern that is indistinguishable from that of GPDH localization. Furthermore, localization of aldolase and GAPDH requires simultaneous localization of GPDH, because aldolase and GAPDH are not localized along the sarcomere in muscles of strains that carry Gpdh null alleles. In an attempt to understand the process of glycolytic enzyme colocalization, we have explored in more detail the mechanism of GPDH localization. In flight muscle, there is only one GPDH isoform, GPDH-1, which is distinguished from isoforms found in other tissues by having three C-terminal amino acids: glutamine, asparagine, and leucine. Transgenic flies that can produce only GPDH-1 display enzyme colocalization similar to wild-type flies. However, transgenic flies that synthesize only GPDH-3, lacking the C-terminal tripeptide, do not show the periodic banding pattern of localization at Z-discs and M-lines for GPDH. In addition, neither GAPDH nor aldolase colocalize at Z-discs and M-lines in the sarcomeres of muscles from GPDH-3 transgenic flies. Failure of the glycolytic enzymes to colocalize in the sarcomere results in the inability to fly, even though the full complement of active glycolytic enzymes is present in flight muscles. Therefore, the presence of active enzymes in the cell is not sufficient for muscle function; colocalization of the enzymes is required. These results indicate that the mechanisms by which ATP is supplied to the myosin ATPase, for muscle contraction, requires a highly organized cellular system.