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

Radial stiffness characteristics of the overlap regions of sarcomeres in isolated skeletal myofibrils in pre-force generating state

We have studied the stiffness of myofilament lattice in sarcomeres in the pre-force generating state, which was realized by a relaxing reagent, BDM (butane dione monoxime). First, the radial stiffness for the overlap regions of sarcomeres of isolated single myofibrils was estimated from the resulting decreases in diameter by osmotic pressure applied with the addition of Dextran. Then, the radial stiffness was also estimated from force-distance curve measurements with AFM technology. The radial stiffness for the overlap regions thus obtained was composed of a soft and a rigid component. The soft component visco-elastically changed in a characteristic fashion depending on the physiological conditions of myofibrils, suggesting that it comes from cross-bridge structures. BDM treatments significantly affected the soft radial component of contracting myofibrils depending on the approach velocity of cantilever: It was nearly equal to that in the contracting state at high approach velocity, whereas as low as that in the relaxing state at low approach velocity. However, comparable BDM treatments greatly suppressed the force production and the axial stiffness in contracting glycerinated muscle fibers and also the sliding velocity of actin filaments in the in vitro motility assay. Considering that BDM shifts the cross-bridge population from force generating to pre-force generating states in contracting muscle, the obtained results strongly suggest that cross-bridges in the pre-force generating state are visco-elastically attached to the thin filaments in such a binding manner that the axial stiffness is low but the radial stiffness significantly high similar to that in force generating state.

Myosin head mechanical performance under different conformational change mechanisms

The present paper puts forward a mathematical approach to model the conformational changes of the myosin head due to ATP hydrolysis, which determine the head swinging and consequent sliding of the actin filament. Our aim is to provide a simple but effective model simulating myosin head performance to be integrated into the overall model of sarcomere mechanics under development at our Laboratory (J. Biomech. 34 (2001) 1607). We began by exploring myosin head mechanics in recent findings about myosin ultrastructure, morphology and energetics in order to calculate the working stroke distance (WS) and the force transmitted to the actin filament during muscle contraction. Two different working stroke mechanisms were investigated, assuming that the swinging of the myosin head occurs either as a consequence of purely conformational changes (Science 261 (1993a) 58) or by thermally driven motion (ratchet mechanism) followed by conformational changes (Cell 99 (1999) 421). Our results show that force and WS values vary markedly between the two models. The maximum force generated is about 10 pN for the first model and 31 pN for the second model, and the WSs are about 13 and 4 nm, respectively. These results are then discussed and compared with published data. The experimental data used for comparison are scarce and non-homogeneous; hence, the final remarks do not lead to definite conclusions. In any event, relatively speaking, the first model is more coherent with experimental findings.

An asymmetry in the phosphate dependence of tension transients induced by length perturbation in mammalian (rabbit psoas) muscle fibres

The effects of inorganic phosphate (P(i), a product released during ATP hydrolysis in active muscle) on tension transients induced by length perturbation (approximately 0.3 ms) were examined in chemically skinned (0.5 % Brij), maximally Ca(2+)-activated rabbit psoas muscle fibres at 10 degrees C (ionic strength 200 mM, pH 7.1). In one type of experiment, the tension transients induced by length release and stretch of a standard amplitude (0.4-0.5 % of L(o), muscle fibre length) were examined at a range of added [P(i)] (range 3-25 mM). The steady active tension was depressed approximately 45 % with 25 mM added P(i). The initial tension recovery (from T(1), extreme tension reached after length step, to T(2), tension after quick recovery) was analysed by half-time measurement and also by exponential curve fitting - extracting a fast (phase 2a) and a slow (phase 2b) component. The tension decay after a stretch became faster with increased [P(i)], whereas the quick tension rise induced by a length release was insensitive to added P(i). Consequently, the asymmetry in the speed of tension recovery from stretch and release was reduced at high [P(i)]. A plot of the phase 2b rate (or 1/half-time) of tension decay after stretch versus [P(i)] was approximately hyperbolic and showed saturation at higher [P(i)] levels. In a second type of experiment, the tension transients induced by length steps of different amplitudes were examined in control (no added P(i)) and in the presence of 25 mM added P(i). Over a range of length step amplitudes (up to 1 % L(0)), the tension decay after stretch was consistently faster in the presence of P(i) than in the control; this was particularly pronounced in phase 2b. The rate of tension rise after length release remained high but similar in the presence and absence of added P(i). These observations indicate that a stretch and release perturb different molecular steps in the crossbridge cycle. The P(i) sensitivity of tension decay (phase 2b) after stretch is similar to that seen using other perturbations (e.g. [P(i)] jumps, hydrostatic pressure jumps and temperature jumps and sinusoidal length oscillations). The results indicate that the P(i)-sensitive force generation identified in previous studies is strain sensitive (as expected), but it is seen only with respect to positive strain (stretches).

Sarcomeric visco-elasticity of chemically skinned skeletal muscle fibres of the rabbit at rest

The giant muscle protein titin (connectin), contained in the gap filament that connect a thick filament to the Z-line in a sarcomere, is generally considered to be responsible for the passive force (tension) and visco-elasticity in resting striated muscle. However, whether it can account for all the features of the resting tension response remains unclear. In this paper, we examine the basic features of the 'sarcomeric visco-elasticity' in a single resting mammalian muscle fibre and attempt to account for various tension components on the basis of known structural features of a sarcomere. At sarcomere length of approximately 2.6 microm, the force response to a ramp stretch of 2-5% is complex but can be resolved into four functionally different components. The behaviour displayed by the components ranges from pure viscous type (directly proportional to stretch velocity, ranging from 0.1 to 30 lengths s(-1)) to predominantly elastic type (insensitive to stretch velocity at 1-2 s time scale); simulations show two components of visco-elasticity with characteristically different relaxation times. The velocity-sensitive components (only) are enhanced by filament lattice compression (dextran - 500 kD) and by increased medium viscosity (dextran - 12 kD); also, the relaxation time of visco-elasticity is longer with increased medium viscosity. Amplitude of all the components and the relaxation time of visco-elasticity are increased at longer sarcomere length (range approximately 2.5 - 3.0 microm). The study, and quantitative analyses, extend our previous work on intact muscle fibres and suggest that the velocity-sensitive tension components in intact sarcomere arise from interactions between sarcomeric filaments, filament segments and inter-filamentary medium; the two components of visco-elasticity arise from distinct regions of titin (connectin) molecules.

Z/I and A-band lattice spacings in frog skeletal muscle: effects of contraction and osmolarity

A-band and Z-line/I-band lattice spacings were measured by small-angle X-ray diffraction from relaxed and isometrically-contracting whole frog sartorius muscles with lattice spacings reduced or swollen by changing the osmolarity of the bathing solution. A-band spacing increased by approximately 3% upon isometric contraction at reduced lattice spacings (245-356 mOsm) and decreased by approximately 1% at swollen spacings (172 mOsm), similarly to the behaviour of skinned muscles upon changing from the relaxed state to rigor. The Z/I lattice underwent a significant lattice expansion (3-8%) upon isometric contraction at all osmolarities, in qualitative agreement (but quantitative disagreement) with results from electron microscopy on mammalian skeletal muscle. Lattice areas calculated for the Z/I and A-band lattices indicate a barrel-shaped sarcomere in the resting state, which may provide a partial explanation for how longitudinal forces produced in the A-band can produce a radial expansive force in the Z-line during contraction. The radial component of cross-bridge stiffness was calculated from the A-band data for contracting muscle, using a lattice stability model incorporating structural, osmotic and electrostatic forces. The calculations gave a radial cross-bridge stiffness during contraction of about 9 x 10(5) N m-2, and outward radial force per thick filament in normal Ringer's solution of 6 x 10(-9) N, corresponding to a radial force per cross-bridge of 10(-11) N.

The filament lattice of striated muscle

The filament lattice of striated muscle is an overlapping hexagonal array of thick and thin filaments within which muscle contraction takes place. Its structure can be studied by electron microscopy or X-ray diffraction. With the latter technique, structural changes can be monitored during contraction and other physiological conditions. The lattice of intact muscle fibers can change size through osmotic swelling or shrinking or by changing the sarcomere length of the muscle. Similarly, muscle fibers that have been chemically or mechanically skinned can be compressed with bathing solutions containing very large inert polymeric molecules. The effects of lattice change on muscle contraction in vertebrate skeletal and cardiac muscle and in invertebrate striated muscle are reviewed. The force developed, the speed of shortening, and stiffness are compared with structural changes occurring within the lattice. Radial forces between the filaments in the lattice, which can include electrostatic, Van der Waals, entropic, structural, and cross bridge, are assessed for their contributions to lattice stability and to the contraction process.

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.

Nucleotides increase the internal flexibility of filaments of dephosphorylated Acanthamoeba myosin II

The actin-activated Mg(2+)-ATPase activity of Acanthamoeba myosin II minifilaments is dependent both on Mg2+ concentration and on the state of phosphorylation of three serine sites at the C-terminal end of the heavy chains. Previous electric birefringence experiments on minifilaments showed a large dependence of signal amplitude on the phosphorylation state and Mg2+ concentration, consistent with large changes in filament flexibility. These observations suggested that minifilament stiffness was important for function. We now report that the binding of nucleotides to dephosphorylated minifilaments at Mg2+ concentrations needed for optimal activity increases the flexibility by about 10-fold, as inferred from the birefringence signal amplitude increase. An increase in flexibility with nucleotide binding is not observed for dephosphorylated minifilaments at lower Mg2+ concentrations or for phosphorylated minifilaments at any Mg2+ concentrations examined. The relaxation times for minifilament rotations that are sensitive to the conformation myosin heads are also observed to depend on phosphorylation, Mg2+ concentration, and nucleotide binding. These latter experiments indicate that the actin-activated Mg2+ concentration, and nucleotide binding. These latter experiments indicate that the actin-activated Mg(2+)-ATPase activity of Acanthamoeba myosin II correlates with both changes in myosin head conformation and the ability of minifilaments to cycle between stiff and flexible conformations coupled to nucleotide binding and release.

Myosin head orientation and mobility during isometric contraction: effects of osmotic compression

We have correlated the mobility and the generation of force of myosin heads by applying radial compression to isometrically contracting muscle fibers. Osmotic pressure was produced by dextran T-500, and its effect on the orientation and mobility of myosin heads labeled with N-(1-oxy-2,2,5,5-tetramethyl-4-pyperidinyl)maleimide was observed by conventional and saturation-transfer electron paramagnetic resonance methods. A biphasic behavior is spectral changes coinciding with the tension dependence was observed as the fibers were compressed. At diameters above the equilibrium spacing, the large myosin head disorder characteristic during contraction in the absence of compression was largely maintained, whereas the mobility decreased threefold, from tauR approximately 25 microseconds to approximately 80-90 microseconds. The inhibition of fast microsecond motions was not accompanied by tension loss, implying that these motions are not necessary for force generation. At diameters below the equilibrium spacing, both the disorder and the mobility decreased dramatically in parallel with the tension inhibition, suggesting that slower microsecond motions and the disorder of the myosin head are necessary for muscle function.

Parallel inhibition of active force and relaxed fiber stiffness by caldesmon fragments at physiological ionic strength and temperature conditions: additional evidence that weak cross-bridge binding to actin is an essential intermediate for force generation

Previously we showed that stiffness of relaxed fibers and active force generated in single skinned fibers of rabbit psoas muscle are inhibited in parallel by actin-binding fragments of caldesmon, an actin-associated protein of smooth muscle, under conditions in which a large fraction of cross-bridges is weakly attached to actin (ionic strength of 50 mM and temperature of 5 degrees C). These results suggested that weak cross-bridge attachment to actin is essential for force generation. The present study provides evidence that this is also true for physiological ionic strength (170 mM) at temperatures up to 30 degrees C, suggesting that weak cross-bridge binding to actin is generally required for force generation. In addition, we show that the inhibition of active force is not a result of changes in cross-bridge cycling kinetics but apparently results from selective inhibition of weak cross-bridge binding to actin. Together with our previous biochemical, mechanical, and structural studies, these findings support the proposal that weak cross-bridge attachment to actin is an essential intermediate on the path to force generation and are consistent with the concept that isometric force mainly results from an increase in strain of the attached cross-bridge as a result of a structural change associated with the transition from a weakly bound to a strongly bound actomyosin complex. This mechanism is different from the processes responsible for quick tension recovery that were proposed by Huxley and Simmons (Proposed mechanism of force generation in striated muscle. Nature. 233:533-538.) to represent the elementary mechanism of force generation.

Distinct molecular processes associated with isometric force generation and rapid tension recovery after quick release

It was proposed by Huxley and Simmons (Nature 1971, 233:533-538) that force-generating cross-bridges are attached to actin in several stable positions. In this concept, isometric force is generated by the same mechanism as the quick tension recovery after an abrupt release of length; i.e., when crossbridges proceed from the first postulated stable position to the second and/or subsequent positions, resulting in straining of the elastic elements within the cross-bridges. Therefore, isometric force is generated by cross-bridges in the second or even subsequent stable positions. However, through mechanical measurements of skinned rabbit psoas muscle fibers, we found that during isometric contraction only the first stable state is significantly occupied; i.e., isometric force is generated by cross-bridges in the first of the stable states. Thus, isometric force and the quick tension recovery appear to result from two distinctly different molecular processes. We propose that isometric force results from a structural change in the actomyosin complex associated with the transition from a weakly bound configuration to a strongly bound configuration before the reaction steps in the Huxley-Simmons model, whereas a major component of quick tension recovery originates from transitions among the subsequent strongly bound states. Mechanical, biochemical, and structural evidence for the two distinct processes is summarized and reviewed.

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.

Orientation and dynamics of myosin heads in aluminum fluoride induced pre-power stroke states: an EPR study

We have determined the orientation and dynamics of the putative pre-power stroke crossbridges in skinned muscle fibers labeled with maleimide spin-label at Cys-707 of myosin. Orientation was measured using electron paramagnetic resonance (EPR) and mobility by saturation transfer EPR. The crossbridges are trapped in the pre-power stroke conformation in the presence of aluminum fluoride, Ca, and ATP. In agreement with data published for unlabeled fibers (Chase et al., 1994), spin-labeled muscle fibers display 42.5% of rigor stiffness, without the generation of force. The trapped crossbridges are as disordered as the relaxed heads, but their microsecond dynamics are significantly restricted. Modeling of the immobile fraction (35%), in terms of attached heads as estimated from stiffness, suggests that the bound heads rotate with a correlation time tau r = 150-400 microseconds, as compared to tau r = 3 microseconds for the heads in relaxed fibers. These "strongly" attached myosin heads, at orientations other than in rigor, are a candidate for the state from which head rotation generates force, as postulated by H. E. Huxley (1969). Ordering of the heads may well be the structural event driving the generation of force.