Lattice spacing changes accompanying isometric tension development in intact single muscle fibers.

The myosin lattice spacing of single intact muscle fibers of the frog, Rana temporaria, was studied in Ringer's solution (standard osmolarity 230 mOsm) and hyper- and hypotonic salines (1.4 and 0.8 times standard osmolarity respectively) in the relaxed state, during "fixed end" tetani, and during shortening, using synchrotron radiation. At standard tonicity, a tetanus was associated with an initial brief lattice expansion (and a small amount of sarcomere shortening), followed by a slow compression (unaccompanied by sarcomere length changes). In hypertonic saline (myosin lattice compressed by 8.1%), these spacing changes were suppressed, in hypotonic saline (lattice spacing increased by 7.5%), they were enhanced. During unloaded shortening of activated fibers, a rapid lattice expansion occurred at all tonicities, but became larger as tonicity was reduced. This expansion was caused in part by the change in length of the preparation, but also by a recoil of a stressed radial compliance associated with axial force. The lattice spacing during unloaded shortening was equal to or occasionally greater than predicted for a relaxed fiber at that sarcomere length, indicating that the lattice compression associated with activation is rapidly reversed upon loss of axial force. Lattice recompression occurred upon termination of shortening under standard and hypotonic conditions, but was almost absent under hypertonic conditions. These observations indicate that axial cross-bridge tension is associated with a compressive radial force in intact muscle fibers at full overlap; however, this radial force exhibits a much greater sensitivity to lattice spacing than does the axial force.     

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.     

Filament lattice of frog striated muscle. Radial forces, lattice stability, and filament compression in the A-band of relaxed and rigor muscle.

Repulsive pressure in the A-band filament lattice of relaxed frog skeletal muscle has been measured as a function of interfilament spacing using an osmotic shrinking technique. Much improved chemical skinning was obtained when the muscles were equilibrated in the presence of EGTA before skinning. The lattice shrank with increasing external osmotic pressure. At any specific pressure, the lattice spacing in relaxed muscle was smaller than that of muscle in rigor, except at low pressures where the reverse was found. The lattice spacing was the same in the two states at a spacing close to that found in vivo. The data were consistent with an electrostatic repulsion over most of the pressure range. For relaxed muscle, the data lay close to electrostatic pressure curves for a thick filament charge diameter of approximately 26 nm, suggesting that charges stabilizing the lattice are situated about midway along the thick filament projections (HMM-S1). At low pressures, observed spacings were larger than calculated, consistent with the idea that thick filament projections move away from the filament backbone. Under all conditions studied, relaxed and rigor, at short and very long sarcomere lengths, the filament lattice could be modeled by assuming a repulsive electrostatic pressure, a weak attractive pressure, and a radial stiffness of the thick filaments (projections) that differed between relaxed and rigor conditions. Each thick filament projection could be compressed by approximately 5 or 2.6 nm requiring a force of 1.3 or 80 pN for relaxed and rigor conditions respectively.     

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.     

Effects of pressure on equatorial x-ray fiber diffraction from skeletal muscle fibers.

When skeletal muscle fibers are subjected to a hydrostatic pressure of 10 MPa (100 atmospheres), reversible changes in tension occur. Passive tension from relaxed muscle is unaffected, rigor tension rises, and active tension falls. The effects of pressure on muscle structure are unknown: therefore a pressure-resistant cell for x-ray diffraction has been built, and this paper reports the first study of the low-angle equatorial patterns of pressurized relaxed, rigor, and active muscle fibers, with direct comparisons from the same chemically skinned rabbit psoas muscle fibers at 0.1 and 10 MPa. Relaxed and rigor fibers show little change in the intensity of the equatorial reflections when pressurized to 10 MPa, but there is a small, reversible expansion of the lattice of 0.7 and 0.4%, respectively. This shows that the order and stability of the myofilament lattice is undisturbed by this pressure. The rise in rigor tension under pressure is thus probably due to axial shortening of one or more components of the sarcomere. Initial results from active fibers at 0.1 MPa show that when phosphate is added the lattice spacing and equatorial intensities change toward their relaxed values. This indicates cross-bridge detachment, as expected from the reduction in tension that phosphate induces. 10 MPa in the presence of phosphate at 11 degrees C causes tension to fall by a further 12%, but not change is detected in the relative intensity of the reflections, only a small increase in lattice spacing. Thus pressure appears to increase the proportion of attached cross-bridges in a low-force state.     

Myosin crossbridge orientation in demembranated muscle fibres studied by birefringence and X-ray diffraction measurements

Muscle contraction is generally thought to involve changes in the orientation of myosin crossbridges during their ATP-driven cyclical interaction with actin. We have investigated crossbridge orientation in equilibrium states of the crossbridge cycle in demembranated fibres of frog and rabbit muscle, using a novel combination of techniques: birefringence and X-ray diffraction. Muscle birefringence is sensitive to both crossbridge orientation and the transverse spacing of the contractile filament lattice. The latter was determined from the equatorial X-ray diffraction pattern, allowing accurate characterization of the orientation component of birefringence changes. We found that this component decreased when relaxed muscle fibres were put into rigor at rest length, and when either the ionic strength or temperature of relaxed fibres was lowered. In each case the birefringence decrease was accompanied by an increase in the intensity of the (1,1) equatorial X-ray reflection relative to that of the (1,0) reflection. When fibres that had been stretched largely to eliminate overlap between actin- and myosin-containing filaments were put into rigor, there was no change in the orientation component of the birefringence. When isolated myosin subfragment-1 was bound to these rigor fibres, the orientation component of the birefringence increased. The birefringence changes at rest length are likely to be due to changes in the orientation of myosin crossbridges, and in particular of the globular head region of the myosin molecules. In relaxed fibres from rabbit muscle, at 100 mM ionic strength, 15 degrees C, the long axis of the heads appears to be relatively well aligned with the filament axis. When fibres are put into rigor, or the temperature or ionic strength is lowered, the degree of alignment decreases and there is a transfer of crossbridge mass towards the actin-containing filaments.     

Force enhancement and relaxation rates after stretch of activated muscle fibres

The residual force enhancement following muscle stretch might be associated with an increase in the proportion of attached cross-bridges, as supported by stiffness measurements. In this case, it could be caused by an increase in the attachment or a decrease in the detachment rate of cross-bridges, or a combination of the two. The purpose of this study was to investigate if the stretch-induced force enhancement is related to cross-bridge attachment/detachment kinetics. Single muscle fibres dissected from the lumbrical muscle of frog were place at a length approximately 20% longer than the plateau of the force-length relationship; they were maximally activated, and after full isometric force was reached, ramp stretches were imposed with amplitudes of 5 and 10% fibre length, at a speed of 40% fibre length s(-1). Experiments were performed in Ringer's solution, and with the addition of 2, 5 and 10 nM of 2,3-butanedione monoxime (BDM), a drug that places cross-bridges in a pre-power-stroke, state, inhibiting force production. The total force following stretch was higher than the corresponding force measured after isometric contraction at the corresponding length. This residual force enhancement was accompanied by an increase relaxation time. BDM, which decreases force production during isometric contractions, considerably increased the relative levels of force enhancement. BDM also increased relaxation times after stretch, beyond the levels observed during reference contractions in Ringer's solution, and beyond isometric control tests at the corresponding BDM concentrations. Together, these results support the idea that force enhancement is caused, at least in part, by a decrease in cross-bridge detachment rates, as manifested by the increased relaxation times following fibre stretch.     

Relationship between force and stiffness in muscle fibers after stretch.

The purpose of this study was to evaluate the relationship between force and stiffness after stretch of activated fibers, while simultaneously changing contractility by interfering with the cross-bridge kinetics and muscle activation. Single fibers dissected from lumbrical muscles of frogs were placed at a length 20% longer than the plateau of the force-length relationship, activated, and stretched by 5 and 10% of fiber length (speed: 40% fiber length/s). Experiments were conducted with maximal and submaximal stimulation in Ringer solution and with the addition of 2 and 5 mM of the myosin inhibitor 2,3-butanedione monoxime (BDM) to the solution. The steady-state force after stretch of an activated fiber was higher than the isometric force produced at the corresponding length in all conditions investigated. Lowering the frequency of stimulation decreased the force and stiffness during isometric contractions, but it did not change force enhancement and stiffness enhancement after stretch. Administration of BDM decreased the force and stiffness during isometric contractions, but it increased the force enhancement and stiffness enhancement after stretch. The relationship between force enhancement and stiffness suggests that the increase in force after stretch may be caused by an increase in the proportion of cross bridges attached to actin. Because BDM places cross bridges in a weakly bound, pre-powerstroke state, our results further suggest that force enhancement is partially associated with a recruitment of weakly bound cross bridges into a strongly bound state.     

Non-specific termination of simian virus 40 DNA replication.

Axial X-ray diffraction patterns have been studied from relaxed, contracted and rigor vertebrate striated muscles at different sarcomere lengths to determine which features of the patterns depend on the interaction of actin and myosin. The intensity of the myosin layer lines in a live, relaxed muscle is sometimes less in a stretched muscle than in the muscle at rest-length; the intensity depends not only on the sarcomere length but on the time that has elapsed since dissection of the muscle. The movement of cross-bridges giving rise to these intensity changes are not caused solely by the withdrawal of actin from the A-band.When a muscle contracts or passes into rigor many changes occur that are independent of the sarcomere length: the myosin layer lines decrease in intensity to about 30% of their initial value when the muscle contracts, and disappear completely when the muscle passes into rigor. Both in contracting and rigor muscles at all sarcomere lengths the spacings of the meridional reflections at 143 Å and 72 Å are 1% greater than from a live relaxed muscle at rest-length. It is deduced that the initial movement of cross-bridges from their positions in resting muscle does not depend on the interaction of each cross-bridge with actin, but on a conformational change in the backbone of the myosin filament: occurring as a result of activation. The possibility is discussed that the conformational change occurs because the myosin filament, like the actin filament, has an activation control mechanism. Finally, all the X-ray diffraction patterns are interpreted on a model in which the myosin filament can exist in one of two possible states: a relaxed state which gives a diffraction pattern with strong myosin layer lines and an axial spacing of 143.4 Å, and an activated state which gives no layer lines but a meridional spacing of 144.8 Å.     

Active force inhibition and stretch-induced force enhancement in frog muscle treated with BDM.

There is evidence that the stretch-induced residual force enhancement observed in skeletal muscles is associated with 1) cross-bridge dynamics and 2) an increase in passive force. The purpose of this study was to characterize the total and passive force enhancement and to evaluate whether these phenomena may be associated with a slow detachment of cross bridges. Single fibers from frog lumbrical muscles were placed at a length 20% longer than the plateau of the force-length relationship, and active and passive stretches (amplitudes of 5 and 10% of fiber length and at a speed of 40% fiber length/s) were performed. Experiments were conducted in Ringer solution and with the addition of 2, 5, and 10 mM of 2,3-butanedione monoxime (BDM), a cross-bridge inhibitor. The steady-state active and passive isometric forces after stretch of an activated fiber were higher than the corresponding forces measured after isometric contractions or passive stretches. BDM decreased the absolute isometric force and increased the total force enhancement in all conditions investigated. These results suggest that total force enhancement is directly associated with cross-bridge kinetics. Addition of 2 mM BDM did not change the passive force enhancement after 5 and 10% stretches. Addition of 5 and 10 mM did not change (5% stretches) or increased (10% stretches) the passive force enhancement. Increasing stretch amplitudes and increasing concentrations of BDM caused relaxation after stretch to be slower, and because passive force enhancement is increased at the greatest stretch amplitudes and the highest BDM concentrations, it appears that passive force enhancement may be related to slow-detaching cross bridges.     

Effects of the number of actin-bound S1 and axial force on X-ray patterns of intact skeletal muscle

Effects of the number of actin-bound S1 and of axial tension on x-ray patterns from tetanized, intact skeletal muscle fibers were investigated. The muscle relaxant, BDM, reduced tetanic M3 meridional x-ray reflection intensity (I(M3)), M3 spacing (d(M3)), and the equatorial I(11)/I(10) ratio in a manner consistent with a reduction in the fraction of S1 bound to actin rather than by generation of low-force S1-actin isomers. At complete force suppression, I(M3) was 78% of its relaxed value. BDM distorted dynamic I(M3) responses to sinusoidal length oscillations in a manner consistent with an increased cross-bridge contribution to total sarcomere compliance, rather than a changed S1 lever orientation in BDM. When the number of actin-bound S1 was varied by altering myofilament overlap, tetanic I(M3) at low overlap was similar to that in high [BDM] (79% of relaxed I(M3)). Tetanic d(M3) dependence on active tension in overlap experiments differed from that observed with BDM. At high BDM, tetanic d(M3) approached its relaxed value (14.34 nm), whereas tetanic d(M3) at low overlap was 14.50 nm, close to its value at full overlap (14.56 nm). This difference in tetanic d(M3) behavior was explicable by a nonlinear thick filament compliance which is extended by both active and passive tension.     

Donnan potentials from striated muscle liquid crystals. Lattice spacing dependence.

Electrochemical potentials were measured as a function of myofilament packing density in crayfish striated muscle. The A-band striations are supramolecular smectic B1 lattice assemblies of myosin filaments and the I-band striations are nematic liquid crystals of actin filaments. Both A- and I-bands generate potentials derived from the fixed charge that is associated with structural proteins. In the reported experiments, filament packing density was varied by osmotically reducing lattice volume. The electrochemical potentials were measured from the A- and I-bands in the relaxed condition over a range of lattice volumes. From the measurements of relative cross-sectional area, unit-cell volume (obtained by low-angle x-ray diffraction) and previously determined effective linear charge densities (Aldoroty, R.A., N.B. Garty, and E.W. April, 1985, Biophys. J., 47:89-96), Donnan potentials can be predicted for any amount of compression. In the relaxed condition, the predicted Donnan potentials correspond to the measured electrochemical potentials. In the rigor condition, however, a net increase in negative charge associated with the myosin filament is observed. The predictability of the data demonstrates the applicability of Donnan equilibrium theory to the measurement of electrochemical potentials from liquid-crystalline systems. Moreover, the relationship between filament spacing and the Donnan potential is consistent with the concept that surface charge provides the necessary electrostatic force to stabilize the myofilament lattice.     

Mechanical and structural properties underlying contraction of skeletal muscle fibers after partial 1-ethyl-3-[3-dimethylamino)propyl]carbodiimide cross-linking.

We show prolonged contraction of permeabilized muscle fibers of the frog during which structural order, as judged from low-angle x-ray diffraction, was preserved by means of partial cross-linking of the fibers using the zero-length cross-linker 1-ethyl-3-[3-dimethylamino)propyl]carbodiimide. Ten to twenty percent of the myosin cross-bridges were cross-linked, allowing the remaining 80-90% to cycle and generate force. These fibers displayed a well-preserved sarcomeric order and mechanical characteristics similar to those of intact muscle fibers. The intensity of the brightest meridional reflection at 14.5 nm, resulting from the projection of cross-bridges evenly spaced along the myofilament length, decreased by 60% as a relaxed fiber was deprived of ATP and entered the rigor state. Upon activation of a rigorized fiber by the addition of ATP, the intensity of this reflection returned to 97% of the relaxed value, suggesting that the overall orientation of cross-bridges in the active muscle was more perpendicular to the filament axis than in rigor. Following a small-amplitude length step applied to the active fibers, the reflection intensity decreased for both releases and stretches. In rigor, however, a small stretch increased the amplitude of the reflection by 35%. These findings show the close link between cross-bridge orientation and tension changes.     

Radial equilibrium lengths of actomyosin cross-bridges in muscle.

Radial equilibrium lengths of the weakly attached, force-generating, and rigor cross-bridges are determined by recording their resistance to osmotic compression. Radial equilibrium length is the surface-to-surface distance between myosin and actin filaments at which attached cross-bridges are, on average, radially undistorted. We previously proposed that differences in the radial equilibrium length represent differences in the structure of the actomyosin cross-bridge. Until now the radial equilibrium length had only been determined for various strongly attached cross-bridge states and was found to be distinct for each state examined. In the present work, we demonstrate that weakly attached cross-bridges, in spite of their low affinity for actin, also exert elastic forces opposing osmotic compression, and they are characterized by a distinct radial equilibrium length (12.0 nm vs. 10.5 nm for force-generating and 13.0 nm for rigor cross-bridge). This suggests significant differences in the molecular structure of the attached cross-bridges under these conditions, e.g., differences in the shape of the myosin head or in the docking of the myosin to actin. Thus, the present finding supports our earlier conclusion that there is a structural change in the attached cross-bridge associated with the transition from a weakly bound configuration to the force-generating configuration. The implications for imposing spatial constraints on modeling actomyosin interaction in the filament lattice are discussed.     

Mechanical anisotropy of inflated elastic tissue from the pig aorta

Uniaxial and biaxial mechanical properties of purified elastic tissue from the proximal thoracic aorta were studied to understand physiological load distributions within the arterial wall. Stress–strain behaviour was non-linear in uniaxial and inflation tests. Elastic tissue was 40% stiffer in the circumferential direction compared to axial in uniaxial tests and～100% stiffer in vessels at an axial stretch ratio of 1.2 or 1.3 and inflated to physiological pressure. Poisson’s ratio v_θz averaged 0.2 and v_zθ increased with circumferential stretch from ～0.2 to ～0.4. Axial stretch had little impact on circumferential behaviour. In intact (unpurified) vessels at constant length, axial forces decreased with pressure at low axial stretches but remained constant at higher stretches. Such a constant axial force is characteristic of incrementally isotropic arteries at their in vivo dimensions. In purified elastic tissue, force decreased with pressure at all axial strains, showing no trend towards isotropy. Analysis of the force–length–pressure data indicated a vessel with v_θz≈0.2 would stretch axially 2–4% with the cardiac pulse yet maintain constant axial force. We compared the ability of 4 mathematical models to predict the pressure-circumferential stretch behaviour of tethered, purified elastic tissue. Models that assumed isotropy could not predict the stretch at zero pressure. The neo-Hookean model overestimated the non-linearity of the response and two non-linear models underestimated it. A model incorporating contributions from orthogonal fibres captured the non-linearity but not the zero-pressure response. Models incorporating anisotropy and non-linearity should better predict the mechanical behaviour of elastic tissue of the proximal thoracic aorta.     

Filament interaction monitored by light scattering in skinned fibers

The intensity of light scattered by chemically skinned rabbit psoas fibers in relaxed, rigor, and activated states was monitored at 90 degrees to the incident beam. In the relaxed state, scattering varied in proportion to the volume of muscle in the beam. Scattering increased to 2.3 times the resting value when rigor was induced by withdrawal of MgATP or when the myofibrils were activated by the caffeine-induced release of Ca from the sarcoplasmic reticulum. The rigor-induced increase in scattering decreased monotonically when MgATP was reintroduced stepwise (0-100 microM). This decrease in scattering was accompanied by an increase in tension up to an optimum MgATP level of approximately 10 microM, and then tension decreased at higher concentrations (10-100 microM). The increase in scattering during both rigor and activation was dependent upon fiber length. At lengths when thick-thin filament overlap was near zero, the light signal due to rigor and activation fell to within 10% of the signal for the relaxed fiber at that length. The signal during rigor increased only minimally (approximately 10%) when stretch (approximately 1%) was applied. This increase in signal was small despite a measured 5- to 10-fold increase in tension and an estimated twofold increase in stiffness. Thus, the increased light scattering caused by rigor and activation depends on filament overlap and not tension, stiffness, or substrate binding.     

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.     

Transients in orientation of a fluorescent cross-bridge probe following photolysis of caged nucleotides in skeletal muscle fibres.

In muscle fibres labelled with iodoacetamidotetramethylrhodamine at Cys707 of the myosin heavy chain, the probes have been reported to change orientation when the fibre is activated, relaxed or put into rigor. In order to test whether these motions are indications of the cross-bridge power stroke, we monitored tension and linear dichroism of the probes in single glycerol-extracted fibres of rabbit psoas muscle during mechanical transients initiated by laser pulse photolysis of caged ATP and caged ADP. In rigor dichroism is negative, indicating average probe absorption dipole moments oriented more than 54.7 degrees away from the fibre axis. During activation from rigor induced by photoliberation of ATP from caged ATP in the presence of calcium, the dichroism reversed sign promptly (half-time 12.5 ms for 500 microM-ATP) upon release of ATP, but then changed only slightly during tension development 20 to 100 milliseconds later. During the onset of rigor following transfer of the fibre from an ATP-containing relaxing solution to a rigor medium lacking ATP, force generation preceded the change in dichroism. The dichroism change occurred slowly (half-time 47 s), because binding of ADP to sites within the muscle fibre limited its rate of diffusion out of the fibre. When ADP was introduced or removed, the dichroism transient was similar in time course and magnitude to that obtained after the introduction or removal of ATP. Neither adding nor removing ADP produced substantial changes in force. These results demonstrate that orientation of the rhodamine probes on the myosin head reflects mainly structural changes linked to nucleotide binding and release, rather than rotation of the cross-bridge during force generation.     

Axial and radial forces of cross-bridges depend on lattice spacing

Nearly all mechanochemical models of the cross-bridge treat myosin as a simple linear spring arranged parallel to the contractile filaments. These single-spring models cannot account for the radial force that muscle generates (orthogonal to the long axis of the myofilaments) or the effects of changes in filament lattice spacing. We describe a more complex myosin cross-bridge model that uses multiple springs to replicate myosin's force-generating power stroke and account for the effects of lattice spacing and radial force. The four springs which comprise this model (the 4sXB) correspond to the mechanically relevant portions of myosin's structure. As occurs in vivo, the 4sXB's state-transition kinetics and force-production dynamics vary with lattice spacing. Additionally, we describe a simpler two-spring cross-bridge (2sXB) model which produces results similar to those of the 4sXB model. Unlike the 4sXB model, the 2sXB model requires no iterative techniques, making it more computationally efficient. The rate at which both multi-spring cross-bridges bind and generate force decreases as lattice spacing grows. The axial force generated by each cross-bridge as it undergoes a power stroke increases as lattice spacing grows. The radial force that a cross-bridge produces as it undergoes a power stroke varies from expansive to compressive as lattice spacing increases. Importantly, these results mirror those for intact, contracting muscle force production.     

Radial stiffness of frog skinned muscle fibers in relaxed and rigor conditions.

Radial stiffness in various conditions of mechanically skinned fibers of semitendinosus muscle of Rana catesbeiana was determined by compressing the fiber with polyvinylpyrrolidone (PVP K-30, Mr = 40,000) in incubating solution. The change in width (D) of fibers with increasing and decreasing PVP concentrations was highly reproducible at a range 0-6% PVP. Radial stiffness of relaxed fibers was almost independent of the sarcomere length. On the other hand, radial stiffness of rigor fibers showed a linear relation against the sarcomere length. These results indicate that cross-bridge attachment would be a major factor in the increase of the radial stiffness. Radial stiffness of relaxed and rigor fibers was (2.14 +/- 0.52) X 10(4) N/m2 (mean +/- SD) and (8.76 +/- 2.04) X 10(4) N/m2, respectively, at the relative fiber width (D/D0) of 0.92, where D0 denotes the fiber width in the rigor solution at 0% PVP. Radial stiffness of a fiber in a rigor solution containing pyrophosphate (PPi) was between those of relaxed and rigor fibers, i.e., (4.76 +/- 0.86) X 10(4) N/m2 at D/Do of 0.92. In PPi and rigor solutions, radial stiffness reversibly increased to around 150 and 130%, respectively, in the presence of 10(-6) M Ca2+. To explain these results, especially the Ca2+-induced change in the radial stiffness, some factor in addition to the number of attached cross-bridges has to be taken into account. The variation of radial stiffness under various conditions will be discussed in relation to the possible manner of cross-bridge attachment.