State-dependent radial elasticity of attached cross-bridges in single skinned fibres of rabbit psoas muscle

Elastic energy storage and radial forces in the myofilament lattice depend on sarcomere length

We most often consider muscle as a motor generating force in the direction of shortening, but less often consider its roles as a spring or a brake. Here we develop a fully three-dimensional spatially explicit model of muscle to isolate the locations of forces and energies that are difficult to separate experimentally. We show the strain energy in the thick and thin filaments is less than one third the strain energy in attached cross-bridges. This result suggests the cross-bridges act as springs, storing energy within muscle in addition to generating the force which powers muscle. Comparing model estimates of energy consumed to elastic energy stored, we show that the ratio of these two properties changes with sarcomere length. The model predicts storage of a greater fraction of energy at short sarcomere lengths, suggesting a mechanism by which muscle function shifts as force production declines, from motor to spring. Additionally, we investigate the force that muscle produces in the radial or transverse direction, orthogonal to the direction of shortening. We confirm prior experimental estimates that place radial forces on the same order of magnitude as axial forces, although we find that radial forces and axial forces vary differently with changes in sarcomere length.

Locomotion requires energy. Very fast locomotion requires a larger amount of energy than muscle can produce in such a short time period, thus muscle must use energy that it previously produced and stored as elastic deformation. Cyclical or repeated movements can be directly powered by muscle, but energy may be conserved in such cases through elastic energy storage. Traditionally we've looked primarily at tendons, insect exoskeletons, and bones as locations where this energy is stored. However, a small but growing body of literature has recently suggested the backbone filament proteins in muscle act as elastic storage locations. We suggest that the myosin motors themselves are capable of storing more energy than the filaments, energy that may be released to power very fast movements or reduce the cost of cyclical movements. We further suggest that this energy is stored in the radial deformations of myosin motors, in a direction that is perpendicular to the axis of muscle shortening.

Structure and functional characteristics of rat's left ventricle cardiomyocytes under antiorthostatic suspension of various duration and subsequent reloading

The goal of the research was to identify the structural and functional characteristics of the rat's left ventricle under antiorthostatic suspension within 1, 3, 7 and 14 days, and subsequent 3 and 7-day reloading after a 14-day suspension. The transversal stiffness of the cardiomyocyte has been determined by the atomic force microscopy, cell respiration—by polarography and proteins content—by Western blotting. Stiffness of the cortical cytoskeleton increases as soon as one day after the suspension and increases up to the 14th day, and starts decreasing during reloading, reaching the control level after 7 days. The stiffness of the contractile apparatus and the intensity of cell respiration also increases. The content of non-muscle isoforms of actin in the cytoplasmic fraction of proteins does not change during the whole experiment, as does not the beta-actin content in the membrane fraction. The content of gamma-actin in the membrane fraction correlates with the change in the transversal stiffness of the cortical cytoskeleton. Increased content of alpha-actinin-1 and alpha-actinin-4 in the membrane fraction of proteins during the suspension is consistent with increased gamma-actin content there. The opposite direction of change of alpha-actinin-1 and alpha-actinin-4 content suggests their involvement into the signal pathways.

Transversal stiffness of fibers and desmin content in leg muscles of rats under gravitational unloading of various durations

The aim of this research was the analysis of structural changes in various parts of the sarcolemma and contractile apparatus of muscle fibers by measuring their transversal stiffness by atomic force microscopy under gravitational unloading. Soleus, medial gastrocnemius, and tibialis anterior muscles of Wistar rats were the objects of the study. Gravitational unloading was carried out by antiorthostatic suspension of hindlimbs for 1, 3, 7, and 12 days. It was shown that the transversal stiffness of different parts of the contractile apparatus of soleus muscle fibers decreases during gravitational unloading in the relaxed, calcium-activated, and rigor states, the fibers of the medial gastrocnemius show no changes, whereas the transversal stiffness of tibialis anterior muscle increases. Thus the transversal stiffness of the sarcolemma in the relaxed state is reduced in all muscles, which may be due to the direct action of gravity as an external mechanical factor that can influence the tension on a membrane. The change of sarcolemma stiffness in activated fibers, which is due probably to the transfer of tension from the contractile apparatus, correlates with the dynamics of changes in the content of desmin.

Transversal stiffness and Young's modulus of single fibers from rat soleus muscle probed by atomic force microscopy

The structural integrity of striated muscle is determined by extra-sarcomere cytoskeleton that includes structures that connect the Z-disks and M-bands of a sarcomere to sarcomeres of neighbor myofibrils or to sarcolemma. Mechanical properties of these structures are not well characterized. The surface structure and transversal stiffness of single fibers from soleus muscle of the rat were studied with atomic force microscopy in liquid. We identified surface regions that correspond to projections of the Z-disks, M-bands, and structures between them. Transversal stiffness of the fibers was measured in each of these three regions. The stiffness was higher in the Z-disk regions, minimal between the Z-disks and the M-bands, and intermediate in the M-band regions. The stiffness increased twofold when relaxed fibers were maximally activated with calcium and threefold when they were transferred to rigor (ATP-free) solution. Transversal stiffness of fibers heavily treated with Triton X-100 was about twice higher than that of the permeabilized ones, however, its regional difference and the dependence on physiological state of the fiber remained the same. The data may be useful for understanding mechanics of muscle fibers when it is subjected to both axial and transversal strain and stress.

Effects of sustained length-dependent activation on in situ cross-bridge dynamics in rat hearts

The cellular basis of the length-dependent increases in contractile force in the beating heart has remained unclear. Our aim was to investigate whether length-dependent mediated increases in contractile force are correlated with myosin head proximity to actin filaments, and presumably the number of cross-bridges activated during a contraction. We therefore employed x-ray diffraction analyses of beat-to-beat contractions in spontaneously beating rat hearts under open-chest conditions simultaneous with recordings of left ventricle (LV) pressure-volume. Regional x-ray diffraction patterns were recorded from the anterior LV free wall under steady-state contractions and during acute volume loading (intravenous lactate Ringers infusion at 60 ml/h, <5 min duration) to determine the change in intensity ratio (I(1,0)/I(1,1)) and myosin interfilament spacing (d(1,0)). We found no significant change in end-diastolic (ED) intensity ratio, indicating that the proportion of myosin heads in proximity to actin was unchanged by fiber stretching. Intensity ratio decreased significantly more during the isovolumetric contraction phase during volume loading than under baseline contractions. A significant systolic increase in myosin head proximity to actin filaments correlated with the maximum rate of pressure increase. Hence, a reduction in interfilament spacing at end-diastole ( approximately 0.5 nm) during stretch increased the proportion of cross-bridges activated. Furthermore, our recordings suggest that d(1,0) expansion was inversely related to LV volume but was restricted during contraction and sarcomere shortening to values smaller than the maximum during isovolumetric relaxation. Since ventricular volume, and presumably sarcomere length, was found to be directly related to interfilament spacing, these findings support a role for interfilament spacing in modulating cross-bridge formation and force developed before shortening.

Apparent elastic modulus and hysteresis of skeletal muscle cells throughout differentiation

The effect of differentiation on the transverse mechanical properties of mammalian myocytes was determined by using atomic force microscopy. The apparent elastic modulus increased from 11.5 +/- 1.3 kPa for undifferentiated myoblasts to 45.3 +/- 4.0 kPa after 8 days of differentiation (P < 0.05). The relative contribution of viscosity, as determined from the normalized hysteresis area, ranged from 0.13 +/- 0.02 to 0.21 +/- 0.03 and did not change throughout differentiation. Myosin expression correlated with the apparent elastic modulus, but neither myosin nor beta-tubulin were associated with hysteresis. Microtubules did not affect mechanical properties because treatment with colchicine did not alter the apparent elastic modulus or hysteresis. Treatment with cytochalasin D or 2,3-butanedione 2-monoxime led to a significant reduction in the apparent elastic modulus but no change in hysteresis. In summary, skeletal muscle cells exhibited viscoelastic behavior that changed during differentiation, yielding an increase in the transverse elastic modulus. Major contributors to changes in the transverse elastic modulus during differentiation were actin and myosin.

Time-resolved X-ray diffraction by skinned skeletal muscle fibers during activation and shortening

Force, sarcomere length, and equatorial x-ray reflections (using synchrotron radiation) were studied in chemically skinned bundles of fibers from Rana temporaria sartorius muscle, activated by UV flash photolysis of a new photolabile calcium chelator, NP-EGTA. Experiments were performed with or without compression by 3% dextran at 4 degrees C. Isometric tension developed at a similar rate (t(1/2) = 40 +/- 5 ms) to the development of tetanic tension measured in other studies (Cecchi et al., 1991). Changes in intensity of equatorial reflections (I(11) t(1/2), 15-19 ms; I(10) t(1/2), 24-26 ms) led isometric tension development and were faster than for tetanus. During shortening at 0.14P(o), I(10) and I(11) changes were partially reversed (18% and 30%, respectively, compressed lattice), in agreement with intact cell data. In zero dextran, activation caused a compression of A-band lattice spacing by 0.7 nm. In 3% dextran, activation caused an expansion of 1.4 nm, consistent with an equilibrium spacing of 45 nm. But, in both cases, discharge of isometric tension by shortening caused a rapid lattice expansion of 1.0-1.1 nm, suggesting discharge of a compressive cross-bridge force, with or without compression by dextran, and the development of an additional expansive force during activation. In contrast to I(10) and I(11) data, these findings for lattice spacing did not resemble intact fiber data.

In vivo x-ray diffraction of indirect flight muscle from Drosophila melanogaster

Small-angle x-ray diffraction from isolated muscle preparations is commonly used to obtain time-resolved structural information during contraction. We extended this technique to the thoracic flight muscles of living fruit flies, at rest and during tethered flight. Precise measurements at 1-ms time resolution indicate that the myofilament lattice spacing does not change significantly during oscillatory contraction. This result is consistent with the notion that a net radial force maintains the thick filaments at an equilibrium interfilament spacing of approximately 56 nm throughout the contractile cycle. Transgenic flies with amino-acid substitutions in the conserved phosphorylation site of the myosin regulatory light chain (RLC) exhibit structural abnormalities that can explain their flight impairment. The I(20)/I(10) equatorial intensity ratio of the mutant fly is 35% less than that of wild type, supporting the hypothesis that myosin heads that lack phosphorylated RLC remain close to the thick filament backbone. This new experimental system facilitates investigation of the relation between molecular structure and muscle function in living organisms.

Backward movements of cross-bridges by application of stretch and by binding of MgADP to skeletal muscle fibers in the rigor state as studied by x-ray diffraction

The effects of the applied stretch and MgADP binding on the structure of the actomyosin cross-bridges in rabbit and/or frog skeletal muscle fibers in the rigor state have been investigated with improved resolution by x-ray diffraction using synchrotron radiation. The results showed a remarkable structural similarity between cross-bridge states induced by stretch and MgADP binding. The intensities of the 14.4- and 7.2-nm meridional reflections increased by approximately 23 and 47%, respectively, when 1 mM MgADP was added to the rigor rabbit muscle fibers in the presence of ATP-depletion backup system and an inhibitor for muscle adenylate kinase or by approximately 33 and 17%, respectively, when rigor frog muscle was stretched by approximately 4.5% of the initial muscle length. In addition, both MgADP binding and stretch induced a small but genuine intensity decrease in the region close to the meridian of the 5.9-nm layer line while retaining the intensity profile of its outer portion. No appreciable influence was observed in the intensities of the higher order meridional reflections of the 14.4-nm repeat and the other actin-based reflections as well as the equatorial reflections, indicating a lack of detachment of cross-bridges in both cases. The changes in the axial spacings of the actin-based and the 14.4-nm-based reflections were observed and associated with the tension change. These results indicate that stretch and ADP binding mediate similar structural changes, being in the correct direction to those expected for that the conformational changes are induced in the outer portion distant from the catalytic domain of attached cross-bridges. Modeling of conformational changes of the attached myosin head suggested a small but significant movement (about 10-20 degrees) in the light chain-binding domain of the head toward the M-line of the sarcomere. Both chemical (ADP binding) and mechanical (stretch) intervensions can reverse the contractile cycle by causing a backward movement of this domain of attached myosin heads in the rigor state.

A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus

The constitutive law of the material comprising any structure is essential for mechanical analysis since this law enables calculation of the stresses from the deformations and vice versa. To date, there is no constitutive law for actively contracting myocardial tissue. Using 2,3-butanedione monoxime to protect the myocardium from mechanical trauma, we subjected thin midwall slices of rabbit myocardium to multiaxial stretching first in the passive state and then during steady-state barium contracture or during tetani in ryanodine-loaded tissue. Assuming transverse isotropy in both the passive and active conditions, we used our previously described methods (Humphrey et al., 1990a) to obtain both passive and active constitutive laws. The major results of this study are: (1) This is the first multiaxial constitutive law for actively contracting mammalian myocardium. (2) The functional forms of the constitutive law for barium contracture and ryanodine-induced tetani are the same but differ from those in the passive state. Hence, one cannot simply substitute differing values for the coefficients of the passive law to describe the active tissue properties. (3) There are significant stresses developed in the cross-fiber direction (more than 40 percent of those in the fiber direction) that cannot be attributed to either deformation effects or nonparallel muscle fibers. These results provide the foundation for future mechanical analyses of the heart.

ATPase kinetics on activation of rabbit and frog permeabilized isometric muscle fibres: a real time phosphate assay

1. The rate of appearance of inorganic phosphate (Pi) and hence the ATPase activity of rabbit psoas muscle in single permeabilized muscle fibres initially in rigor was measured following laser flash photolysis of the P3-1-(2-nitrophenyl)ethyl ester of ATP (NPE-caged ATP) in the presence and absence of Ca2+. Pi appearance was monitored from the fluorescence signal of a Pi-sensitive probe, MDCC-PBP, a coumarin-labelled A197C mutant of the phosphate-binding protein from Escherichia coli. Fibres were immersed in oil to optimize the fluorescence signal and to obviate diffusion problems. The ATPase activity was also measured under similar conditions from the rate of NADH disappearance using an NADH-linked coupled enzyme assay. 2. On photolysis of NPE-caged ATP in the presence of Ca2+ at 20 degrees C, the fluorescence increase of MDCC-PBP was non-linear with time. ATPase activity was 41 s-1 in the first turnover based on a myosin subfragment 1 concentration of 150 microM. This was calculated from a linear regression of the fluorescence signal reporting 20-150 microM of Pi release. Tension was at 67% of its isometric level by the time 150 microM Pi was released. ATPase activities were 36 and 31 s-1 for Pi released in the ranges of 150-300 microM and 300-450 microM, respectively. The ATPase activity had a Q10 value of 2.9 based on measurements at 5, 12 and 20 degrees C. 3. An NADH-linked assay showed the ATPase activity had a lower limit of 12.7 s-1 at 20 degrees C. The response to photolytic release of ADP showed that the rate of NADH disappearance was partially limited by the flux through the coupled reactions. Simulations indicated that the linked assay data were consistent with an initial ATPase activity of 40 s-1. 4. On photolysis of NPE-caged ATP in the absence of Ca2+ the ATPase activity was 0.11 s-1 at 20 degrees C with no discernible rapid transient phase of Pi release during the first turnover of the ATPase. 5. To avoid the rigor state, the ATPase rate in the presence of Ca2+ was also measured on activation from the relaxed state by photolytic release of Ca2+ from a caged Ca2+ compound, nitrophenyl-EGTA. At 5 degrees C the ATPase rate was 5.8 and 4.0 s-1 in the first and second turnovers, respectively. These rates are comparable to those when NPE-caged ATP was used. 6. The influence of ADP and Pi on the ATPase activities was measured using the MDCC-PBP and NADH-linked assays, respectively. ADP (0.5 mM) decreased the initial ATPase rate by 23%. Pi (10 mM) had no significant effect. Inhibition by ADP, formed during ATP hydrolysis, contributed to the decrease of ATPase activity with time. 7. The MDCC-PBP assay and NPE-caged ATP were used to measure the ATPase rate in single permeabilized muscle fibres of the semitendinosus muscle of the frog. At 5 degrees C in the presence of Ca2+ the ATPase activity was biphasic being 15.0 s-1 during the first turnover (based on 180 microM myosin subfragment 1). Tension was 74% of its isometric level by the time 180 microM Pi was released. During the third turnover the ATPase rate decreased to about 20% of that during the first turnover. 8. ATPase activity in isometric rabbit muscle fibres during the first few turnovers is about an order of magnitude greater than that when a steady state is reached. Possible reasons and the consequences for understanding the mechanism of muscular contraction are discussed.

Orientation of intermediate nucleotide states of indane dione spin-labeled myosin heads in muscle fibers

We have used electron paramagnetic resonance to study the orientation of myosin heads in the presence of nucleotides and nucleotide analogs, to induce equilibrium states that mimic intermediates in the actomyosin ATPase cycle. We obtained electron paramagnetic resonance spectra of an indane dione spin label (InVSL) bound to Cys 707 (SH1) of the myosin head, in skinned rabbit psoas muscle fibers. This probe is rigidly immobilized on the catalytic domain of the head, and the principal axis of the probe is aligned nearly parallel to the fiber axis in rigor (no nucleotide), making it directly sensitive to axial rotation of the head. On ADP addition, all of the heads remained strongly bound to actin, but the spectral hyperfine splitting increased by 0.55 +/- 0.02 G, corresponding to a small but significant axial rotation of 7 degrees. Adenosine 5'-(adenylylim-idodiphosphate) (AMPPNP) or pyrophosphate reduced the actomyosin affinity and introduced a highly disordered population of heads similar to that observed in relaxation. For the remaining oriented population, pyrophosphate induced no significant change relative to rigor, but AMPPNP induced a slight but probably significant rotation (2.2 degrees +/- 1.6 degrees), in the direction opposite that induced by ADP. Adenosine 5'-O-(3-thiotriphosphate) (ATP gamma S) relaxed the muscle fiber, completely dissociated the heads from actin, and produced disorder similar to that in relaxation by ATP. ATP gamma S plus Ca induced a weak-binding state with most of the actin-bound heads disordered. Vanadate had negligible effect in the presence of ADP, but in isometric contraction vanadate substantially reduced both force and the fraction of oriented heads. These results are consistent with a model in which myosin heads are disordered early in the power stroke (weak-binding states) and rigidly oriented later in the power stroke (strong-binding states), whereas transitions among the strong-binding states induce only slight changes in the axial orientation of the catalytic domain.

Structural changes in the actomyosin cross-bridges associated with force generation

It is generally thought that to generate active force in muscle, myosin heads (cross-bridges) that are attached to actin undergo large-scale conformational changes. However, evidence for conformational changes of the attached cross-bridges associated with force generation has been ambiguous. In this study, we took advantage of the recent observation that cross-bridges that are weakly attached to actin in a relaxed muscle are apparently in attached preforce-generating states. The experimental conditions were chosen such that there were large fractions of cross-bridges attached under relaxing and activating conditions, and high-resolution equatorial x-ray diffraction patterns obtained under these conditions were compared. Changes brought about by activation in the two innermost intensities, I10 and I11, did not follow the familiar reciprocal changes. Instead, there was almost no change in I11, whereas I10 decreased by 34%. Together with the changes found in the higher-order reflections, the results suggest that the structure of the attached force-generating cross-bridges differs from that of the weakly bound, preforce-generating cross-bridges and possibly also differs from that of the cross-bridges in rigor. These observations support the concept that force generation involves a transition between distinct structural states of the actomyosin cross-bridges.