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.     

The length–tension curve in muscle depends on lattice spacing

Classic interpretations of the striated muscle length–tension curve focus on how force varies with overlap of thin (actin) and thick (myosin) filaments. New models of sarcomere geometry and experiments with skinned synchronous insect flight muscle suggest that changes in the radial distance between the actin and myosin filaments, the filament lattice spacing, are responsible for between 20% and 50% of the change in force seen between sarcomere lengths of 1.4 and 3.4 µm. Thus, lattice spacing is a significant force regulator, increasing the slope of muscle''s force–length dependence.     

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.     

Study of regulatory effect of tropomyosin on actin-myosin interaction in skeletal muscle by in vitro motility assay

The interaction between myosin and actin in striated muscle tissue is regulated by Ca²⁺ via thin filament regulatory proteins. Skeletal muscle possesses a whole pattern of myosin and tropomyosin isoforms. The regulatory effect of tropomyosin on actin-myosin interaction was investigated by measuring the sliding velocity of both actin and actin-tropomyosin filaments over fast and slow skeletal myosins using the in vitro motility assay. The actin-tropomyosin filaments were reconstructed with tropomyosin isoforms from striated muscle tissue. It was found that tropomyosins with different content of α-, β-, and γ-chains added to actin filaments affect the sliding velocity of filaments in different ways. On the other hand, the sliding velocity of filaments with the same content of α-, β-, and Γ-chains depends on myosin isoforms of striated muscle. The reciprocal effects of myosin and tropomyosin on actin-myosin interaction in striated muscle may play a significant role in maintenance of effective work of striated muscle both during ontogenesis and under pathological conditions.     

X-ray diffraction studies of the contractile mechanism in single muscle fibres

The molecular mechanism of muscle contraction was investigated in intact muscle fibres by X-ray diffraction. Changes in the intensities of the axial X-ray reflections produced by imposing rapid changes in fibre length establish the average conformation of the myosin heads during active isometric contraction, and show that the heads tilt during the elastic response to a change in fibre length and during the elementary force generating process: the working stroke. X-ray interference between the two arrays of myosin heads in each filament allows the axial motions of the heads following a sudden drop in force from the isometric level to be measured in situ with unprecedented precision. At low load, the average working stroke is 12 nm, which is consistent with crystallographic studies. The working stroke is smaller and slower at a higher load. The compliance of the actin and myosin filaments was also determined from the change in the axial spacings of the X-ray reflections following a force step, and shown to be responsible for most of the sarcomere compliance. The mechanical properties of the sarcomere depend on both the motor actions of the myosin heads and the compliance of the myosin and actin filaments.     

ANALYSIS OF MUSCLE CONTRACTION BY ULTRAVIOLET MICROBEAM DISRUPTION OF SARCOMERE STRUCTURE

In an effort to differentiate between the sliding filament theory for muscle contraction and alternative views which propose attachment between actin and myosin filaments at or across the H zone, rabbit psoas myofibrils were irradiated in various areas of the sarcomere with an ultraviolet microbeam. Irradiation of the I band appears to destroy the actin filaments; in vitro irradiation of F actin causes an irreversible depolymerization of the protein. Irradiation of the A band disorients the myosin but causes no apparent loss of dry mass. These effects are maximal at the wavelength of maximum absorption of the proteins involved. Actin filaments, released at the Z line of a sarcomere, are seen to slide into the A band on addition of ATP. Irradiation of a full A band prevents contraction, whereas irradiation of two-thirds of the A band, leaving a lateral edge intact, permits contraction at the non-irradiated edge. Thus contraction can occur in what is in essence only one-third of a sarcomere, eliminating any necessity for postulated H zone connections. These observations are in complete accord with the classical sliding filament theory but incompatible with either the contralateral filament hypothesis or the actin folding model for muscle contraction.     

Structure-function correlation in airway smooth muscle adapted to different lengths

Airway smooth muscle is able to adapt and maintain a nearly constant maximal force generation over a large length range. This implies that a fixed filament lattice such as that found in striated muscle may not exist in this tissue and that plastic remodeling of its contractile and cytoskeletal filaments may be involved in the process of length adaptation that optimizes contractile filament overlap. Here, we show that isometric force produced by airway smooth muscle is independent of muscle length over a twofold length change; cell cross-sectional area was inversely proportional to cell length, implying that the cell volume was conserved at different lengths; shortening velocity and myosin filament density varied similarly to length change: increased by 69.4% ± 5.7 (SE) and 76.0% ± 9.8, respectively, for a 100% increase in cell length. Muscle power output, ATPase rate, and myosin filament density also have the same dependence on muscle cell length: increased by 35.4% ± 6.7, 34.6% ± 3.4, and 35.6% ± 10.6, respectively, for a 50% increase in cell length. The data can be explained by a model in which additional contractile units containing myosin filaments are formed and placed in series with existing contractile units when the muscle is adapted at a longer length. muscle contraction; myosin filaments; ATPase activity; electron microscopy     

A mathematical model of the sarcomere mechanics of cross-striated muscle with consideration of the stretch and twist of actin filaments

A mathematical model of sarcomere mechanics, which takes into account the elongation of actin and myosin filaments and also twisting of the actin filaments in the sarcomere of striated muscle during contraction is presented. The model accounts for the experimentally observed phenomena of the stretch and twist of the actin filaments due to strong binding of myosin heads and the pulling force. Some model parameters were estimated from published experimental data. The results of modeling show that the twist of actin filaments can play a substantial role in the mechanical responses of contracting muscle fibers to step changes of their length.     

Behaviour of the crossbridges in stretched or compressed muscle fibres

The maximum chord of the myosin heads is comparable to the closest surface-to-surface spacing between the myofilaments in a muscle at the slack length. Therefore, when the sarcomere length increases or when the fibre is compressed, the surface-to-surface myofilament spacing becomes lower than the head long axis. We conclude that, in stretched or compressed fibres, some crossbridges cannot attach, owing to steric hindrance. When the amount of compression is limited, this hindrance may be overcome by a tilting of the heads in the plane perpendicular to the filament axes; in this case, there is no consequence as concerns the crossbridge properties. In highly compressed fibres, the crossbridges become progressively hindered and all the crossbridges are hindered for an axis-to-axis spacing representing about 60% of the spacing observed under zero external osmotic pressure. In this case, both the isometric tension and the ATPase activity of the fibre are zero. In fibres stretched up to 3.77 microns (sarcomere length corresponding to the disappearance of the overlap between the thick and the thin filaments), the ratio of hindered crossbridges over the functional crossbridges may be estimated at about 55%. In stretched fibres, a noticeable proportion of crossbridges are sterically hindered and the crossbridges performance (e.g. constants of attachment and detachment) depends on filament spacing, i.e. on sarcomere length. Therefore, we think it is probably impossible to consider the crossbridges as independent force converters, since this idea requires that the crossbridge properties are independent of sarcomere length. In this connection, all the experiments performed on osmotically compressed fibres are of major importance for the understanding of the true mechanisms of muscle contraction.     

Study of reciprocal effects of cardiac myosin and tropomyosin isoforms on actin-myosin interaction with in vitro motility assay

Interaction of myosin with actin in striated muscle is controlled by Ca²⁺ via thin filament associated proteins: troponin and tropomyosin. In cardiac muscle there is a whole pattern of myosin and tropomyosin isoforms. The aim of the current work is to study regulatory effect of tropomyosin on sliding velocity of actin filaments in the in vitro motility assay over cardiac isomyosins. It was found that tropomyosins of different content of α- and β-chains being added to actin filament effects the sliding velocity of filaments in different ways. On the other hand the velocity of filaments with the same tropomyosins depends on both heavy and light chains isoforms of cardiac myosin.     

Elastic behavior of connectin filaments during thick filament movement in activated skeletal muscle

Connectin (also called titin) is a huge, striated muscle protein that binds to thick filaments and links them to the Z-disc. Using an mAb that binds to connectin in the I-band region of the molecule, we studied the behavior of connectin in both relaxed and activated skinned rabbit psoas fibers by immunoelectron microscopy. In relaxed fibers, antibody binding is visualized as two extra striations per sarcomere arranged symmetrically about the M-line. These striations move away from both the nearest Z-disc and the thick filaments when the sarcomere is stretched, confirming the elastic behavior of connectin within the I- band of relaxed sarcomeres as previously observed by several investigators. When the fiber is activated, thick filaments in sarcomeres shorter than 2.8 microns tend to move from the center to the side of the sarcomere. This translocation of thick filaments within the sarcomere is accompanied by movement of the antibody label in the same direction. In that half-sarcomere in which the thick filaments move away from the Z-disc, the spacings between the Z-disc and the antibody and between the antibody and the thick filaments both increase. Conversely, on the side of the sarcomere in which the thick filaments move nearer to the Z-line, these spacings decrease. Regardless of whether I-band spacing is varied by stretch of a relaxed sarcomere or by active sliding of thick filaments within a sarcomere of constant length, the spacings between the Z-line and the antibody and between the antibody and the thick filaments increase with I-band length identically. These results indicate that the connectin filaments remain bound to the thick filaments in active fibers, and that the elastic properties of connectin are unaltered by calcium ions and cross-bridge activity.     

Sarcomeric pattern formation by actin cluster coalescence

Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells.     

Structural proteins in the myofilaments and regulation of contraction in vertebrate smooth muscle.

The contractile systems of vertebrate smooth and striated muscles are compared. Smooth muscles contain relatively large amounts of actin and tropomyosin organized into thin filaments, and smaller amounts of myosin in the form of thick filaments. The protein contents are consistent with observed thin:thick filament ratios of about 15-18:1 in smooth compared to 2:1 in striated muscle. The basic characteristics of both types of contractile proteins are similar; but there are a variety of quantitative differences in protein structures, enzymatic activities and filament stabilities. Biochemical and X-ray diffraction data generally support recent ultrastructural evidence concerning the organization of the myofilaments in smooth muscle, although a basic contractile unit comparable to the sarcomere in striated muscle has not been discerned. Myofilament interactions and contraction in smooth muscle are controlled by changes in the Ca2+ concentration. Recent evidence suggests the Ca2+-binding regulatory site is associated with the myosin in vertebrate smooth muscle (as in a variety of invertebrate muscles), rather than with troponin which is the regulatory protein associated with the thin filament in vertebrate striated muscle.     

Nebulin interacts with CapZ and regulates thin filament architecture within the Z-disc

The barbed ends of actin filaments in striated muscle are anchored within the Z-disc and capped by CapZ; this protein blocks actin polymerization and depolymerization in vitro. The mature lengths of the thin filaments are likely specified by the giant "molecular ruler" nebulin, which spans the length of the thin filament. Here, we report that CapZ specifically interacts with the C terminus of nebulin (modules 160-164) in blot overlay, solid-phase binding, tryptophan fluorescence, and SPOTs membrane assays. Binding of nebulin modules 160-164 to CapZ does not affect the ability of CapZ to cap actin filaments in vitro, consistent with our observation that neither of the two C-terminal actin binding regions of CapZ is necessary for its interaction with nebulin. Knockdown of nebulin in chick skeletal myotubes using small interfering RNA results in a reduction of assembled CapZ, and, strikingly, a loss of the uniform alignment of the barbed ends of the actin filaments. These data suggest that nebulin restricts the position of thin filament barbed ends to the Z-disc via a direct interaction with CapZ. We propose a novel molecular model of Z-disc architecture in which nebulin interacts with CapZ from a thin filament of an adjacent sarcomere, thus providing a structural link between sarcomeres.     

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.     

X-ray diffraction evidence for the extensibility of actin and myosin filaments during muscle contraction.

To clarify the extensibility of thin actin and thick myosin filaments in muscle, we examined the spacings of actin and myosin filament-based reflections in x-ray diffraction patterns at high resolution during isometric contraction of frog skeletal muscles and steady lengthening of the active muscles using synchrotron radiation as an intense x-ray source and a storage phosphor plate as a high sensitivity, high resolution area detector. Spacing of the actin meridional reflection at approximately 1/2.7 nm-1, which corresponds to the axial rise per actin subunit in the thin filament, increased about 0.25% during isometric contraction of muscles at full overlap length of thick and thin filaments. The changes in muscles stretched to approximately half overlap of the filaments, when they were scaled linearly up to the full isometric tension, gave an increase of approximately 0.3%. Conversely, the spacing decreased by approximately 0.1% upon activation of muscles at nonoverlap length. Slow stretching of a contracting muscle increased tension and increased this spacing over the isometric contraction value. Scaled up to a 100% tension increase, this corresponds to a approximately 0.26% additional change, consistent with that of the initial isometric contraction. Taken together, the extensibility of the actin filament amounts to 3-4 nm of elongation when a muscle switches from relaxation to maximum isometric contraction. Axial spacings of the layer-line reflections at approximately 1/5.1 nm-1 and approximately 1/5.9 nm-1 corresponding to the pitches of the right- and left-handed genetic helices of the actin filament, showed similar changes to that of the meridional reflection during isometric contraction of muscles at full overlap. The spacing changes of these reflections, which also depend on the mechanical load on the muscle, indicate that elongation is accompanied by slight changes of the actin helical structure possibly because of the axial force exerted by the actomyosin cross-bridges. Additional small spacing changes of the myosin meridional reflections during length changes applied to contracting muscles represented an increase of approximately 0.26% (scaled up to a 100% tension increase) in the myosin periodicity, suggesting that such spacing changes correspond to a tension-related extension of the myosin filaments. Elongation of the myosin filament backbone amounts to approximately 2.1 nm per half sarcomere. The results indicate that a large part (approximately 70%) of the sarcomere compliance of an active muscle is caused by the extensibility of the actin and myosin filaments; 42% of the compliance resides in the actin filaments, and 27% of it is in the myosin filaments.     

Passive force generation and titin isoforms in mammalian skeletal muscle.

When relaxed striated muscle cells are stretched, a resting tension is produced which is thought to arise from stretching long, elastic filaments composed of titin (also called connectin). Here, I show that single skinned rabbit soleus muscle fibers produce resting tension that is several-fold lower than that found in rabbit psoas fibers. At sarcomere lengths where the slope of the resting tension-sarcomere length relation is low, electron microscopy of skinned fibers indicates that thick filaments move from the center to the side of the sarcomere during prolonged activation. As sarcomeres are stretched and the resting tension sarcomere length relation becomes steeper, this movement is decreased. The sarcomere length range over which thick filament movement decreases is higher in soleus than in psoas fibers, paralleling the different lengths at which the slope of the resting tension-sarcomere length relations increase. These results indicate that the large differences in resting tension between single psoas and soleus fibers are due to different tensions exerted by the elastic elements linking the end of each thick filament to the nearest Z-disc, i.e., the titin filaments. Quantitative gel electrophoresis of proteins from single muscle fibers excludes the possibility that resting tension is less in soleus than in psoas fibers simply because they have fewer titin filaments. A small difference in the electrophoretic mobility of titin between psoas and soleus fibers suggests the alternate possibility that mammalian muscle cells use at least two titin isoforms with differing elastic properties to produce variations in resting tension.     

Fine structure and contraction of isolated muscle actomyosin

Summary A modified thread model of isolated cross-striated muscle actomyosin was produced, which a priori consisted of both actin and myosin filaments forming a random network. This modified model contracts to the same extent as the normal model which lacks myosin filaments prior to contraction.The striking difference in the contraction behavior of the two models indicates 1) that in the normal model myosin filament formation occurs during contraction and 2) that the pre-existence of myosin filaments in the modified model increases the speed of contraction. Hence, the sliding mechanism involving myosin filaments is able to operate at a higher speed than the sliding mechanism which utilizes oligomeric myosin.     

The stiffness of skeletal muscle in isometric contraction and rigor: the fraction of myosin heads bound to actin.

Step changes in length (between -3 and +5 nm per half-sarcomere) were imposed on isolated muscle fibers at the plateau of an isometric tetanus (tension T0) and on the same fibers in rigor after permeabilization of the sarcolemma, to determine stiffness of the half-sarcomere in the two conditions. To identify the contribution of actin filaments to the total half-sarcomere compliance (C), measurements were made at sarcomere lengths between 2.00 and 2.15 microm, where the number of myosin cross-bridges in the region of overlap between the myosin filament and the actin filament remains constant, and only the length of the nonoverlapped region of the actin filament changes with sarcomere length. At 2.1 microm sarcomere length, C was 3.9 nm T0(-1) in active isometric contraction and 2.6 nm T0(-1) in rigor. The actin filament compliance, estimated from the slope of the relation between C and sarcomere length, was 2.3 nm microm(-1) T0(-1). Recent x-ray diffraction experiments suggest that the myosin filament compliance is 1.3 nm microm(-1) T0(-1). With these values for filament compliance, the difference in half-sarcomere compliance between isometric contraction and rigor indicates that the fraction of myosin cross-bridges attached to actin in isometric contraction is not larger than 0.43, assuming that cross-bridge elasticity is the same in isometric contraction and rigor.