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.     

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.     

Lattice shrinkage with increasing resting tension in stretched, single skinned fibers of frog muscle.

The 1,0 lattice spacing d1,0 in chemically and mechanically skinned single fibers of frog muscle was measured at various sarcomere lengths, L, in the range from L = 2.1 to 6.0 microns by an x-ray diffraction method. In chemically skinned fibers, d1,0 decreased with a similar slope to that of mechanically skinned fibers up to L congruent to 3 microns, but beyond this point d1,0 steeply decreased with further stretching. This steep decrease in d1,0 could be ascribed mainly to an increase in the compressing force associated with the longitudinal extension of a remnant of the sarcolemma. In mechanically skinned fibers, the gradual decrease in d1,0 continued beyond filament overlap (L greater than or equal to 3.5 microns) and was highly proportional to a resting tension. This decrease in d1,0 at L greater than or equal to 3.5 microns could be ascribed to an increase in the force exerted by lateral elastic components, which is proportional to the longitudinal resting tension. A conceptual model is proposed of a network structure of elastic components in a sarcomere.     

Lattice swelling with the selective digestion of elastic components in single-skinned fibers of frog muscle.

Changes in the 1.0 lattice spacing during trypsin (0.25 micrograms/ml) treatment in mechanically skinned single fibers of frog muscle was examined by an x-ray diffraction method at various sarcomere lengths. The resting tension of a relaxed fiber was decreased by trypsin treatment but the stiffness of a rigor fiber was not, suggesting that elastic components were selectively digested. With progression of the digestion, the lattice spacing increased remarkably at longer sarcomere lengths and finally became independent of the sarcomere length. The increase in the lattice spacing was proportional to the decrease in the resting tension. These results support our previous suggestion (Higuchi, H., and Y. Umazume, 1986, Biophys. J., 50:385-389) that the lattice spacing decreases at long lengths due to compressive force exerted by a lateral elastic component that connects thick filaments to an axial elastic component. Consequently, it is unlikely that the decrease in the lattice spacing is determined by a decrease in the repulsive force between thick and thin filaments with stretching a fiber.     

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.     

Time-resolved changes in equatorial x-ray diffraction and stiffness during rise of tetanic tension in intact length-clamped single muscle fibers.

We report the first time-resolved x-ray diffraction studies on tetanized intact single muscle fibers of the frog. The 10, 11, 20, 21, 30, and Z equatorial reflections were clearly resolved in the relaxed fiber. The preparation readily withstood 100 1-s duration (0.4-s beam exposure) tetani at 4 degrees C (less than 4% decline of force and no deterioration in the 10, 11 equatorial intensity ratio at rest or during activation). Equatorial intensity changes (10 and 11) and fiber stiffness led tension (t1/2 lead 20 ms at 4 degrees C) during the tetanus rise and lagged during the isometric phase of relaxation. These findings support the existence of a low force cross-bridge state during the rise of tetanic tension and isometric relaxation that is not evident at the tetanus plateau. In "fixed end" tetani lattice expansion occurred with a time course similar to stiffness during the tetanus rise. During relaxation, lattice spacing increased slightly, while the sarcomere length remained isometric, but underwent large changes after the "shoulder" of tension. Under length clamp control, lattice expansion during the tetanus rise was reduced or abolished, and compression (2%) of the lattice was observed. A lattice compression is predicted by certain cross-bridge models of force generation (Schoenberg, M. 1980. Biophys. J. 30:51-68; Schoenberg, M. 1980. Biophys. J. 30:69-78).     

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.     

Changes in the lateral filament spacing of skinned muscle fibres when cross-bridges attach

When a skinned fibre prepared from frog skeletal muscle goes from the relaxed to the rigor state at a sarcomere length of about 2.2 μm, the 1, 0 transverse spacing of the filament lattice, measured by X-ray diffraction, decreases by about 11%. In measurements at various sarcomere lengths, the decrease in the spacing was approximately proportional to the degree of overlap between the thick and thin filaments. This suggests that the shrinkage of the lattice is caused by a lateral force produced by cross-bridges. In order to estimate the magnitude of the lateral force, the decrease of spacing between relaxed and rigor states was compared with the shrinkage caused osmotically by adding a high molecular weight polymer, polyvinylpyrrolidone, to the bathing solution. The results indicate that the lateral force produced per unit length of thick filament in the overlap zone is of the same order of magnitude as the axially directed force produced during maximum isometric contraction (10^?10 to 10^?9 N/μm).Experiments in the presence of a high concentration of polyvinylpyrrolidone (100 g/l) show that when the lattice spacing is decreased osmotically beyond a certain value, the lateral force produced when the fibre goes into rigor changes its direction, causing the lattice to swell. This result can be explained by assuming that there is an optimum interfilament spacing at which the cross-bridges produce no lateral force. At other spacings, the lateral force tends to displace the filament lattice toward that optimum value.     

CONTRACTILITY AND ULTRASTRUCTURE IN GLYCEROL-EXTRACTED MUSCLE FIBERS : II. Ultrastructure in Resting and Shortened Fibers

Glycerol-extracted rabbit psoas muscle fibers were examined by electron microscopy both before and after ATP-induced isotonic shortening. Ultrastructural changes were correlated with the initial sarcomere length and the degree of shortening. The ultrastructural appearance of the resting fiber at rest length was identical with that described by H. E. Huxley and Hanson. At sarcomere lengths greater than 3.7 to 3.8 µ, the A and I filaments were detached and separated by a gap. The presence of "gap" filaments was confirmed, and evidence is presented which indicates that these filaments form connections between the ends of the A and I filaments. Shortening from initial sarcomere lengths at which the filaments overlapped took place through sliding of the filaments. If shortening was initiated from sarcomere lengths at which there was a gap, a narrowing of the I band was brought about by a curling of the I filaments at the boundary between the A and I bands. No evidence could be found that the I filaments moved into the A band.     

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     

Adaptive response of pulmonary arterial smooth muscle to length change.

Hypervasoconstriction is associated with pulmonary hypertension and dysfunction of the pulmonary arterial smooth muscle (PASM) is implicated. However, relatively little is known about the mechanical properties of PASM. Recent advances in our understanding of plastic adaptation in smooth muscle may shed light on the disease mechanism. In this study, we determined whether PASM is capable of adapting to length changes (especially shortening) and regain its contractile force. We examined the time course of length adaptation in PASM in response to step changes in length and to length oscillations mimicking the periodic stretches due to pulsatile arterial pressure. Rings from sheep pulmonary artery were mounted on myograph and stimulated using electrical field stimulation (12-16 s, 20 V, 60 Hz). The length-force relationship was determined at L(ref) to 0.6 L(ref), where L(ref) was a reference length close to the in situ length of PASM. The response to length oscillations was determined at L(ref), after the muscle was subjected to length oscillation of various amplitudes for 200 s at 1.5 Hz. Release (or stretch) of resting PASM from L(ref) to 0.6 (and vice versa) was followed by a significant force recovery (73 and 63%, respectively), characteristic of length adaptation. All recoveries of force followed a monoexponential time course. Length oscillations with amplitudes ranging from 5 to 20% L(ref) caused no significant change in force generation in subsequent contractions. It is concluded that, like many smooth muscles, PASM possesses substantial capability to adapt to changes in length. Under pathological conditions, this could contribute to hypervasoconstriction in pulmonary hypertension.     

X-ray evidence for radial cross-bridge movement and for the sliding filament model in actively contracting skeletal muscle

Equatorial X-ray diffraction patterns have been studied from muscles at rest, during contraction and in rigor. It is confirmed that the relative intensity ($\text{I}\text{1,0}\text{I}\text{1,1}$) of the two main equatorial reflections depends both on the sarcomere length and on the state of the muscle; in any one state the ratio $\text{I}\text{1,0}\text{I}\text{1,1}$ increases as the sarcomere length of the muscle increases, while at any fixed sarcomere length the ratio is smaller for contracting muscle than for resting muscle and smaller still for rigor muscles. The change of $\text{I}\text{1,0}\text{I}\text{1,1}$ with change of state at constant sarcomere length is interpreted as being due to radial movement of cross-bridges: the average movement during contraction being about 40% of that in rigor.Over the whole range of sarcomere length studied (between 1.8 and 2.7 μm) there was no evidence for any change in lattice spacing when a muscle contracts isometrically.Muscles were studied generating tension after they had shortened actively against a load. The lattice spacings and intensity ratio $\text{I}\text{1,0}\text{I}\text{1,1}$ both changed during active shortening in a way entirely consistent with the sliding filament theory of contraction.     

Compliance of thin filaments in skinned fibers of rabbit skeletal muscle.

The mechanical compliance (reciprocal of stiffness) of thin filaments was estimated from the relative compliance of single, skinned muscle fibers in rigor at sarcomere lengths between 1.8 and 2.4 micron. The compliance of the fibers was calculated as the ratio of sarcomere length change to tension change during imposition of repetitive cycles of small stretches and releases. Fiber compliance decreased as the sarcomere length was decreased below 2.4 micron. The compliance of the thin filaments could be estimated from this decrement because in this range of lengths overlap between the thick and thin filaments is complete and all of the myosin heads bind to the thin filament in rigor. Thus, the compliance of the overlap region of the sarcomere is constant as length is changed and the decrease in fiber compliance is due to decrease of the nonoverlap length of the thin filaments (the I band). The compliance value obtained for the thin filaments implies that at 2.4-microns sarcomere length, the thin filaments contribute approximately 55% of the total sarcomere compliance. Considering that the sarcomeres are approximately 1.25-fold more compliant in active isometric contractions than in rigor, the thin filaments contribute approximately 44% to sarcomere compliance during isometric contraction.     

Passive tension in cardiac muscle: contribution of collagen, titin, microtubules, and intermediate filaments.

The passive tension-sarcomere length relation of rat cardiac muscle was investigated by studying passive (or not activated) single myocytes and trabeculae. The contribution of collagen, titin, microtubules, and intermediate filaments to tension and stiffness was investigated by measuring (1) the effects of KCl/KI extraction on both trabeculae and single myocytes, (2) the effect of trypsin digestion on single myocytes, and (3) the effect of colchicine on single myocytes. It was found that over the working range of sarcomeres in the heart (lengths approximately 1.9-2.2 microns), collagen and titin are the most important contributors to passive tension with titin dominating at the shorter end of the working range and collagen at longer lengths. Microtubules made a modest contribution to passive tension in some cells, but on average their contribution was not significant. Finally, intermediate filaments contributed about 10% to passive tension of trabeculae at sarcomere lengths from approximately 1.9 to 2.1 microns, and their contribution dropped to only a few percent at longer lengths. At physiological sarcomere lengths of the heart, cardiac titin developed much higher tensions (> 20-fold) than did skeletal muscle titin at comparable lengths. This might be related to the finding that cardiac titin has a molecular mass of 2.5 MDa, 0.3-0.5 MDa smaller than titin of mammalian skeletal muscle, which is predicted to result in a much shorter extensible titin segment in the I-band of cardiac muscle. Passive stress plotted versus the strain of the extensible titin segment showed that the stress-strain relationships are similar in cardiac and skeletal muscle. The difference in passive stress between cardiac and skeletal muscle at the sarcomere level predominantly resulted from much higher strains of the I-segment of cardiac titin at a given sarcomere length. By expressing a smaller titin isoform, without changing the properties of the molecule itself, cardiac muscle is able to develop significant levels of passive tension at physiological sarcomere lengths.     

Structural states in the Z band of skeletal muscle correlate with states of active and passive tension

In skeletal muscle Z bands, the ends of the thin contractile filaments interdigitate in a tetragonal array of axial filaments held together by periodically cross-connecting Z filaments. Changes in these two sets of filaments are responsible for two distinct structural states observed in cross section, the small-square and basketweave forms. We have examined Z bands and A bands in relaxed, tetanized, stretched, and stretched and tetanized rat soleus muscles by electron microscopy and optical diffraction. In relaxed muscle, the A-band spacing decreases with increasing load and sarcomere length, but the Z lattice remains in the small-square form and the Z spacing changes only slightly. In tetanized muscle at sarcomere lengths up to 2.7 micron, the Z lattice assumes the basketweave form and the Z spacing is increased. The increased Z spacing is not the result of sarcomere shortening. Further, passive tension is not sufficient to cause this change in the Z lattice; active tension is necessary.     

Passive and active tension in single cardiac myofibrils.

Single myofibrils were isolated from chemically skinned rabbit heart and mounted in an apparatus described previously (Fearn et al., 1993; Linke et al., 1993). We measured the passive length-tension relation and active isometric force, both normalized to cross sectional area. Myofibrillar cross sectional area was calculated based on measurements of myofibril diameter from both phase-contrast images and electron micrographs. Passive tension values up to sarcomere lengths of approximately 2.2 microns were similar to those reported in larger cardiac muscle specimens. Thus, the element responsible for most, if not all, passive force of cardiac muscle at physiological sarcomere lengths appears to reside within the myofibrils. Above 2.2 microns, passive tension continued to rise, but not as steeply as reported in multicellular preparations. Apparently, structures other than the myofibrils become increasingly important in determining the magnitude of passive tension at these stretched lengths. Knowing the myofibrillar component of passive tension allowed us to infer the stress-strain relation of titin, the polypeptide thought to support passive force in the sarcomere. The elastic modulus of titin is 3.5 x 10(6) dyn cm-2, a value similar to that reported for elastin. Maximum active isometric tension in the single myofibril at sarcomere lengths of 2.1-2.3 microns was 145 +/- 35 mN/mm2 (mean +/- SD; n = 15). This value is comparable with that measured in fixed-end contractions of larger cardiac specimens, when the amount of nonmyofibrillar space in those preparations is considered. However, it is about 4 times lower than the maximum active tension previously measured in single skeletal myofibrils under similar conditions (Bartoo et al., 1993).     

Plasticity in canine airway smooth muscle

The large volume changes of some hollow viscera require a greater length range for the smooth muscle of their walls than can be accommodated by a fixed array of sliding filaments. A possible explanation is that smooth muscles adapt to length changes by forming variable numbers of contractile units in series. To test for such plasticity we examined the muscle length dependence of shortening velocity and compliance, both of which will vary directly with the number of thick filaments in series. Dog tracheal smooth muscle was studied because its cells are arrayed in long, straight, parallel bundles that span the length of the preparation. In experiments where muscle length was changed, both compliance and velocity showed a strong dependence on muscle length, varying by 1.7-fold and 2.2-fold, respectively, over a threefold range of length. The variation in isometric force was substantially less, ranging from a 1.2- to 1.3-fold in two series of experiments where length was varied by twofold to an insignificant 4% variation in a third series where a threefold length range was studied. Tetanic force was below its steady level after both stretches and releases, and increased to a steady level with 5-6 tetani at 5 min intervals. These results suggest strongly that the number of contractile units in series varies directly with the adapted muscle length. Temporary force depression after a length change would occur if the change transiently moved the filaments from their optimum overlap. The relative length independence of the adapted force is explained by the reforming of the filament lattice to produce optimum force development, with commensurate changes of velocity and compliance.     

Myofascial force transmission causes interaction between adjacent muscles and connective tissue: effects of blunt dissection and compartmental fasciotomy on length force characteristics of rat extensor digitorum longus muscle.

Muscles within the anterior tibial compartment (extensor digitorum longus: EDL, tibialis anterior: TA, and extensor hallucis longus muscles: EHL) and within the peroneal compartment were excited simultaneously and maximally. The ankle joint was fixed kept at 90 degrees. For EDL length force characteristics were determined. This was performed first with the anterior tibial compartment intact (1), and subsequently after: (2) blunt dissection of the anterior and lateral interface of EDL and TA. (3) Full longitudinal lateral fasciotomy of the anterior tibial compartment. (4) Full removal of TA and EHL muscles. Length-force characteristics were changed significantly by these interventions. Blunt dissection caused a force decrease of approximately 10% at all lengths, i.e., without changing EDL optimum or active slack lengths. This indicates that intermuscular connective tissue mediates significant interactions between adjacent muscles. Indications of its relatively stiff mechanical properties were found both in the physiological part of the present study, as well as the anatomical survey of connective tissue. Full lateral compartmental fasciotomy increased optimum length and decreased active slack length, leading to an increase of length range (by approximately 47%), while decreasing optimal force. As a consequence an increase in force for the lower length range was found. Such changes of length force characteristics are compatible with an increased distribution of fiber mean sarcomere length. On the basis of these results, it is concluded that extramuscular connective tissue has a sufficiently stiff connection to intramuscular connective tissue to be able to play a role in force transmission. Therefore, in addition to intramuscular myofascial force transmission, extramuscular force transmission has to be considered within intact compartments of limbs. A survey of connective tissue structures within the compartment indicated sheet-like neuro-vascular tracts to be major components of extramuscular connective tissue with connections to intramuscular connective tissue stroma. Removal of TA and EHL yielded yet another decrease of force (mean for optimal force approximately 10%). No significant changes of optimum and active slack lengths could be shown in this case. It is concluded that myofascial force transmission should be taken into account when considering muscular function and its coordination, and in clinical decisions regarding fasciotomy and repetitive strain injury.     

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.     

The positional stability of thick filaments in activated skeletal muscle depends on sarcomere length: evidence for the role of titin filaments

Electron microscopy was used to study the positional stability of thick filaments in isometrically contracting skinned rabbit psoas muscle as a function of sarcomere length at 7 degrees C. After calcium activation at a sarcomere length of 2.6 micron, where resting stiffness is low, sarcomeres become nonuniform in length. The dispersion in sarcomere length is complete by the time maximum tension is reached. A-bands generally move from their central position and continue moving toward one of the Z-discs after tension has reached a plateau at its maximum level. The lengths of the thick and thin filaments remain constant during this movement. The extent of A-band movement during contraction depends on the final length of the individual sarcomere. After prolonged activation, all sarcomeres between 1.9 and 2.5 micron long exhibit A-bands that are adjacent to a Z-disc, with no intervening I-band. Sarcomeres 2.6 or 2.7 micron long exhibit a partial movement of A-bands. At longer sarcomere lengths, where the resting stiffness exceeds the slope of the active tension-length relation, the A-bands remain perfectly centered during contraction. Sarcomere symmetry and length uniformity are restored upon relaxation. These results indicate that the central position of the thick filaments in the resting sarcomere becomes unstable upon activation. In addition, they provide evidence that the elastic titin filaments, which join thick filaments to Z-discs, produce almost all of the resting tension in skinned rabbit psoas fibers and act to resist the movement of thick filaments away from the center of the sarcomere during contraction.