Millisecond-scale biochemical response to change in strain

Muscle fiber contraction involves the cyclical interaction of myosin cross-bridges with actin filaments, linked to hydrolysis of ATP that provides the required energy. We show here the relationship between cross-bridge states, force generation, and Pi release during ramp stretches of active mammalian skeletal muscle fibers at 20°C. The results show that force and Pi release respond quickly to the application of stretch: force rises rapidly, whereas the rate of Pi release decreases abruptly and remains low for the duration of the stretch. These measurements show that biochemical change on the millisecond timescale accompanies the mechanical and structural responses in active muscle fibers. A cross-bridge model is used to simulate the effect of stretch on the distribution of actomyosin cross-bridges, force, and Pi release, with explicit inclusion of ATP, ADP, and Pi in the biochemical states and length-dependence of transitions. In the simulation, stretch causes rapid detachment and reattachment of cross-bridges without release of Pi or ATP hydrolysis.     

Flash and smash: rapid freezing of muscle fibers activated by photolysis of caged ATP.

A new approach was used to study transient structural states of cross-bridges during activation of muscle fibers. Rabbit skinned muscle fibers were rapidly and synchronously activated from the rigor state by photolysis of caged ATP in the presence of Ca2+. At several different times during the switch from rigor to fully active tension development, the fibers were rapidly frozen on a liquid helium-cooled metal block, freeze-substituted, and examined in an electron microscope. The limits of structural preservation and resolution with this technique were analyzed. We demonstrate that the resolution of our images is sufficient to draw the following conclusions about cross-bridge structure. Rigor cross-bridges point away from the Z-line and most of them are wider near the thin filaments than near the backbone of the thick filaments. In contrast, cross-bridges in actively contracting fibers stretch between the thick and thin filaments at a variable angle, and are uniformly thin. Diffraction patterns computed from contracting muscle show layer lines both at 38 and 43 nm indicating that active cross-bridges contribute mass to both the actin- and myosin-based helical periodicities. The images obtained from fibers frozen 20 ms after release of ATP show a mixture of rigor and active type cross-bridge configurations. There is little evidence of cross-bridges with the rigor shape by 50 ms, and the difference in configurations between 50 and 300 ms after photolysis is surprisingly subtle.     

Rigor-force producing cross-bridges in skeletal muscle fibers activated by a substoichiometric amount of ATP

Isometric skinned muscle fibers were activated by the photogeneration of a substoichiometric amount of ATP and their cross-bridge configurations examined during the development of the rigor force by x-ray diffraction and electron microscopy. By the photogeneration of approximately 100 microM ATP, approximately 2/3 of the concentration of the myosin heads in a muscle fiber, muscle fibers originally in the rigor state showed a transient drop of the force and then produced a long-lasting rigor force (approximately 50% of the maximal active force), which gradually recovered to the original force level with a time constant of approximately 4 s. Associated with the photoactivation, muscle fibers revealed small but distinct changes in the equatorial x-ray diffraction that run ahead of the development of force. After reaching a plateau of force, long-lasting intensity changes in the x-ray diffraction pattern developed in parallel with the force decline. Two-dimensional x-ray diffraction patterns and electron micrographs of the sectioned muscle fibers taken during the period of 1-1.9 s after the photoactivation were basically similar to those from rigor preparations but also contained features characteristic of fully activated fibers. In photoactivated muscle fibers, some cross-bridges bound photogenerated ATP and underwent an ATP hydrolysis cycle whereas a significant population of the cross-bridges remained attached to the thin actin filaments with no available ATP to bind. Analysis of the results obtained indicates that, during the ATP hydrolysis reaction, the cross-bridges detached from actin filaments and reattached either to the same original actin monomers or to neighboring actin monomers. The latter cross-bridges contribute to produce the rigor force by interacting with the actin filaments, first producing the active force and then being locked in a noncycling state(s), transforming their configuration on the actin filaments to stably sustain the produced force as a passive rigor force.     

Cross-bridge duty cycle in isometric contraction of skeletal myofibrils

During interaction of actin with myosin, cross-bridges impart mechanical impulses to thin filaments resulting in rotations of actin monomers. Impulses are delivered on the average every tc seconds. A cross-bridge spends a fraction of this time (ts) strongly attached to actin, during which it generates force. The "duty cycle" (DC), defined as the fraction of the total cross-bridge cycle that myosin spends attached to actin in a force generating state (ts/ tc), is small for cross-bridges acting against zero load, like freely shortening muscle, and increases as the load rises. Here we report, for the first time, an attempt to measure DC of a single cross-bridge in muscle. A single actin molecule in a half-sarcomere was labeled with fluorescent phalloidin. Its orientation was measured by monitoring intensity of the polarized TIRF images. Actin changed orientation when a cross-bridge bound to it. During isometric contraction, but not during rigor, actin orientation oscillated between two values, corresponding to the actin-bound and actin-free state of the cross-bridge. The average ts and tc were 3.4 and 6 s, respectively. These results suggest that, in isometrically working muscle, cross-bridges spend about half of the cycle time attached to actin. The fact that 1/ tc was much smaller than the ATPase rate suggests that the bulk of the energy of ATP hydrolysis is used for purposes other than performance of mechanical work.     

Mathematical simulation of muscle cross-bridge cycle and force-velocity relationship

Muscle contraction underlies many essential functions such as breathing, heart beating, locomotion, regulation of blood pressure, and airway resistance. Active shortening of muscle is the result of cycling of myosin cross-bridges that leads to sliding of myosin filaments relative to actin filaments. In this study, we have developed a computer program that allows us to alter the rates of transitions between any cross-bridge-states in a stochastic cycle. The cross-bridge states within the cycle are divided into six attached (between myosin cross-bridges and actin filaments) states and one detached state. The population of cross-bridges in each of the states is determined by the transition rates throughout the cycle; differential equations describing the transitions are set up as a cyclic matrix. A method for rapidly obtaining steady-state exact solutions for the cyclic matrix has been developed to reduce computation time and avoid the divergence problem associated with numerical solutions. In the seven-state model, two power strokes are assumed for each cross-bridge cycle, one before the release of inorganic phosphate, and one after. The characteristic hyperbolic force-velocity relationship observed in muscle contraction can be reproduced by the model. Deviation from the single hyperbolic behavior at low velocities can be mimicked by allowing the rate of cross-bridge-attachment to vary with velocity. The effects of [ATP], [ADP], and [P(i)] are simulated by changing transition rates between specific states. The model has revealed new insights on how the force-velocity characteristics are related to the state transitions in the cross-bridge cycle.     

Changes in orientation of actin during contraction of muscle

It is well documented that muscle contraction results from cyclic rotations of actin-bound myosin cross-bridges. The role of actin is hypothesized to be limited to accelerating phosphate release from myosin and to serving as a rigid substrate for cross-bridge rotations. To test this hypothesis, we have measured actin rotations during contraction of a skeletal muscle. Actin filaments of rabbit psoas fiber were labeled with rhodamine-phalloidin. Muscle contraction was induced by a pulse of ATP photogenerated from caged precursor. ATP induced a single turnover of cross-bridges. The rotations were measured by anisotropy of fluorescence originating from a small volume defined by a narrow aperture of a confocal microscope. The anisotropy of phalloidin-actin changed rapidly at first and was followed by a slow relaxation to a steady-state value. The kinetics of orientation changes of actin and myosin were the same. Extracting myosin abolished anisotropy changes. To test whether the rotation of actin was imposed by cross-bridges or whether it reflected hydrolytic activity of actin itself, we labeled actin with fluorescent ADP. The time-course of anisotropy change of fluorescent nucleotide was similar to that of phalloidin-actin. These results suggest that orientation changes of actin are caused by dissociation and rebinding of myosin cross-bridges, and that during contraction, nucleotide does not dissociate from actin.     

Models in which many cross-bridges attach simultaneously can explain the filament movement per ATP split during muscle contraction

Contractile filaments in skeletal muscle are moved by less than 2 nm for each ATP used. If just one cross-bridge is attached to each thin filament at any instant then this distance represents the fundamental myosin cross-bridge step size (i.e. the distance one cross-bridge moves a thin filament in one ATP-splitting cycle). However, most contraction models assume many cross-bridges are attached at any instant along each thin filament. The purpose of this study was to establish whether the net filament sliding per ATP used could be explained quantitatively in terms of a cross-bridge model in which multiple cross-bridges are attached along each thin filament. It was found that the relationship between net filament sliding per ATP split and the load against which the muscle shortens is compatible with such a model and furthermore predicts that the cross-bridge step size is between 7.5 and 12.5 nm over most of the range of loads. These values were similar for different muscle fibre types.     

Straightening Out the Elasticity of Myosin Cross-Bridges

In a contracting muscle, myosin cross-bridges extending from thick filaments pull the interdigitating thin (actin-containing) filaments during cyclical ATP-driven interactions toward the center of the sarcomere, the structural unit of striated muscle. Cross-bridge attachments in the sarcomere have been reported to exhibit a similar stiffness under both positive and negative forces. However, in vitro measurements on filaments with a sparse complement of heads detected a decrease of the cross-bridge stiffness at negative forces attributed to the buckling of the subfragment 2 tail portion. Here, we review some old and new data that confirm that cross-bridge stiffness is nearly linear in the muscle filament lattice. The implications of high myosin stiffness at positive and negative strains are considered in muscle fibers and in nonmuscle intracellular cargo transport.     

Spin-label study of actin-myosin-nucleotide interactions in contracting glycerinated muscle fibers

This paper presents the results of simultaneous measurements of the electron paramagnetic resonance signal of spin-label bound to myosin cross-bridges and the mechanical response of glycerol-treated rabbit psoas fibers under isometric contraction. No observable change has been detected in vitro in the local motion of spin-label bound to myosin-ATP with conventional electron paramagnetic resonance techniques when F-actin is added, even under conditions where more than 30% of the myosin is expected to be in an attached state. In contrast, a clear change in the spin-label mobility is observed when cross-bridges are attached to thin filaments. Similar spectra are also observed when cross-bridges are in the rigor state or in an attached state in the presence of 5′-adenylyl imidodiphosphate in place of ATP. A good proportionality is found between the change in the electron paramagnetic resonance signal and the tension when substrate concentration is varied under conditions where no appreciable amount of rigor complex is present. Thus, by assuming 0 and 100% attachment in the relaxed and rigor states, respectively, the extent of cross-bridge attachment can be estimated; it is about 80% at a relatively low ATP concentration where the maximum tension is observed, while it is about 35% in the millimolar range of ATP concentration. A consistent explanation can be given for the spectra obtained both in solution and in the fiber, provided that two distinct states, the preactive and active states, exist in cross-bridges attached to thin filaments. The contribution of intermediate complexes to the force generation is discussed. The effect of Ca²⁺ control on cross-bridge attachment is also studied at various concentrations of substrate.     

Rotation of the lever arm of Myosin in contracting skeletal muscle fiber measured by two-photon anisotropy

The rotation of the lever arm of myosin cross-bridges is believed to be responsible for muscle contraction. To resolve details of this rotation, it is necessary to observe a single cross-bridge. It is still impossible to do so in muscle fiber, but it is possible to investigate a small population of cross-bridges by simultaneously activating myosin in a femtoliter volume by rapid release of caged ATP. In earlier work, in which the number of observed cross-bridges was limited to approximately 600 by confocal microscopy, we were able to measure the rates of cross-bridge detachment and rebinding. However, we were unable to resolve the power stroke. We speculated that the reason for this was that the number of observed cross-bridges was too large. In an attempt to decrease this number, we used two-photon microscopy which permitted observation of approximately 1/2 as many cross-bridges as before with the same signal/noise ratio. With the two-photon excitation, the number of cross-bridges was small enough to resolve the beginning of the power stroke. The results indicated that the power stroke begins approximately 170 ms after the rigor cross-bridge first binds ATP.     

Structural changes in isometrically contracting insect flight muscle trapped following a mechanical perturbation

The application of rapidly applied length steps to actively contracting muscle is a classic method for synchronizing the response of myosin cross-bridges so that the average response of the ensemble can be measured. Alternatively, electron tomography (ET) is a technique that can report the structure of the individual members of the ensemble. We probed the structure of active myosin motors (cross-bridges) by applying 0.5% changes in length (either a stretch or a release) within 2 ms to isometrically contracting insect flight muscle (IFM) fibers followed after 5-6 ms by rapid freezing against a liquid helium cooled copper mirror. ET of freeze-substituted fibers, embedded and thin-sectioned, provides 3-D cross-bridge images, sorted by multivariate data analysis into ~40 classes, distinct in average structure, population size and lattice distribution. Individual actin subunits are resolved facilitating quasi-atomic modeling of each class average to determine its binding strength (weak or strong) to actin. ~98% of strong-binding acto-myosin attachments present after a length perturbation are confined to "target zones" of only two actin subunits located exactly midway between successive troponin complexes along each long-pitch helical repeat of actin. Significant changes in the types, distribution and structure of actin-myosin attachments occurred in a manner consistent with the mechanical transients. Most dramatic is near disappearance, after either length perturbation, of a class of weak-binding cross-bridges, attached within the target zone, that are highly likely to be precursors of strong-binding cross-bridges. These weak-binding cross-bridges were originally observed in isometrically contracting IFM. Their disappearance following a quick stretch or release can be explained by a recent kinetic model for muscle contraction, as behaviour consistent with their identification as precursors of strong-binding cross-bridges. The results provide a detailed model for contraction in IFM that may be applicable to contraction in other types of muscle.     

Compliant realignment of binding sites in muscle: transient behavior and mechanical tuning.

The presence of compliance in the lattice of filaments in muscle raises a number of concerns about how one accounts for force generation in the context of the cross-bridge cycle--binding site motions and coupling between cross-bridges confound more traditional analyses. To explore these issues, we developed a spatially explicit, mechanochemical model of skeletal muscle contraction. With a simple three-state model of the cross-bridge cycle, we used a Monte Carlo simulation to compute the instantaneous balance of forces throughout the filament lattice, accounting for both thin and thick filament distortions in response to cross-bridge forces. This approach is compared to more traditional mass action kinetic models (in the form of coupled partial differential equations) that assume filament inextensibility. We also monitored instantaneous force generation, ATP utilization, and the dynamics of the cross-bridge cycle in simulations of step changes in length and variations in shortening velocity. Three critical results emerge from our analyses: 1) there is a significant realignment of actin-binding sites in response to cross-bridge forces, 2) this realignment recruits additional cross-bridge binding, and 3) we predict mechanical behaviors that are consistent with experimental results for velocity and length transients. Binding site realignment depends on the relative compliance of the filament lattice and cross-bridges, and within the measured range of these parameters, gives rise to a sharply tuned peak for force generation. Such mechanical tuning at the molecular level is the result of mechanical coupling between individual cross-bridges, mediated by thick filament deformations, and the resultant realignment of binding sites on the thin filament.     

Activating efficiency of Ca2+ and cross-bridges as measured by phosphate analog release

To assess the activating efficiency of Ca2+ and cross-bridges, the release rates of phosphate analogs from skinned fibers were estimated from the recovery of contractility and that of stiffness. Estimations were performed based on the assumptions that contractility was indicative of the population of analog-free myosin heads and that stiffness reflected the population of formed cross-bridges. Aluminofluoride (AlFx) and orthovanadate (Vi) were used as phosphate analogs with mechanically skinned fibers from rabbit psoas muscle. The use of the analogs enabled the functional assessment of activation level in the total absence of ATP. Fibers loaded with the analogs gradually recovered contractility and stiffness in normal plain rigor solution. The addition of Ca2+ to the plain rigor solution significantly accelerated their recovery, whereas ADP had no appreciable effect. ATP plus Ca2+(contracting condition) accelerated the recovery by several tens of times. These results indicate that the cross-bridges formed during contraction have prominent activating efficiency, which is indispensable to attain full activation. A comparison between the activating efficiency evaluated from stiffness and that from contractility suggested that Ca2+ is more potent in accelerating the binding of actin to analog-bound myosin heads whereas cross-bridges mainly accelerate the subsequent analog-releasing step.     

The mechanism of muscle contraction

Knowledge of the mechanism of contraction has been obtained from studies of the interaction of actin and myosin in solution, from an elucidation of the structure of muscle fibers, and from measurements of the mechanics and energetics of fiber contraction. Many of the states and the transition rates between them have been established for the hydrolysis of ATP by actin and myosin subfragments in solution. A major goal is to now understand how the kinetics of this interaction are altered when it occurs in the organized array of the myofibril. Early work on the structure of muscle suggested that changes in the orientation of myosin cross-bridges were responsible for the generation of force. More recently, fluorescent and paramagnetic probes attached to the cross-bridges have suggested that at least some domains of the cross-bridges do not change orientation during force generation. A number of properties of active cross-bridges have been defined by measurements of steady state contractions of fibers and by the transients which follow step changes in fiber length or tension. Taken together these studies have provided firm evidence that force is generated by a cyclic interaction in which a myosin cross-bridge attaches to actin, exerts force through a "powerstroke" of 12 nm, and is then released by the binding of ATP. The mechanism of this interaction at the molecular level remains unknown.     

Bridgelike interconnections between thick filaments in stretched skeletal muscle fibers observed by the freeze-fracture method

The ultrastructure of frog semitendinosus muscle was explored using the freeze-fracture, deep-etch, rotary-shadowing technique. Mechanically skinned fibers were stretched to decrease or eliminate the overlap of thick and thin filaments before rapid freezing with liquid propane. In relaxed, contracting, and rigor fibers, a significant number of bridgelike interconnections, distinct from those observed in the M-region, were observed between adjacent thick filaments in the non-overlap region. Their half-length and diameter corresponded approximately to the known dimensions of the cross-bridge (or myosin S-1). The interconnection may thus be formed by the binding of two apposed cross-bridges projecting from adjacent thick filaments. Fixation with 0.5% glutaraldehyde for 5-10 min before freezing effectively preserved these structures. The results indicate that the interconnections are genuine structures that appear commonly in stretched muscle fibers. They may play a role in stabilizing the thick filament lattice, and possibly in the contractile process.     

Cross-bridge movements during a slow length change of active muscle.

Tension changes caused by slow stretch or release of actively contracting muscle are accompanied by axial displacements of myosin heads (i.e., cross-bridges) from the positions characteristic of isometric contraction. The direction of the axial displacement appears to affect the rate of cross-bridge detachment or reattachment during muscle-length changes.     

Structural characterization of the binding of Myosin*ADP*Pi to actin in permeabilized rabbit psoas muscle

When myosin is attached to actin in a muscle cell, various structures in the filaments are formed. The two strongly bound states (A*M*ADP and A*M) and the weakly bound A*M*ATP states are reasonably well understood. The orientation of the strongly bound myosin heads is uniform ("stereospecific" attachment), and the attached heads exhibit little spatial fluctuation. In the prehydrolysis weakly bound A*M*ATP state, the orientations of the attached myosin heads assume a wide range of azimuthal and axial angles, indicating considerable flexibility in the myosin head. The structure of the other weakly bound state, A*M*ADP*P(i), however, is poorly understood. This state is thought to be the critical pre-power-stroke state, poised to make the transition to the strongly binding, force-generating states, and hence it is of particular interest for understanding the mechanism of contraction. However, because of the low affinity between myosin and actin in the A*M*ADP*P(i) state, the structure of this state has eluded determination both in isolated form and in muscle cells. With the knowledge recently gained in the structures of the weakly binding M*ATP, M*ADP*P(i) states and the weakly attached A*M*ATP state in muscle fibers, it is now feasible to delineate the in vivo structure of the attached state of A*M*ADP*P(i). The series of experiments presented in this article were carried out under relaxing conditions at 25 degrees C, where approximately 95% of the myosin heads in the skinned rabbit psoas muscle contain the hydrolysis products. The affinity for actin is enhanced by adding polyethylene glycol (PEG) or by lowering the ionic strength in the bathing solution. Solution kinetics and binding constants were determined in the presence and in the absence of PEG. When the binding between actin and myosin was increased, both the myosin layer lines and the actin layer lines increased in intensity, but the intensity profiles did not change. The configuration (mode) of attachment in the A*M*ADP*P(i) state is thus unique among the intermediate attached states of the cross-bridge ATP hydrolysis cycle. One of the simplest explanations is that both myosin filaments and actin filaments are stabilized (e.g., undergo reduced spatial fluctuations) by the attachment. The alignment of the myosin heads in the thick filaments and the alignment of the actin monomers in the thin filaments are improved as a result. The compact atomic structure of M*ADP*P(i) with strongly coupled domains may contribute to the unique attachment configuration: the "primed" myosin heads may function as "transient struts" when attached to the thin filaments.     

Suppression of muscle contraction by vanadate. Mechanical and ligand binding studies on glycerol-extracted rabbit fibers

The suppression of tension development by orthovanadate (Vi) was studied in mechanical experiments and by measuring the binding of radioactive Vi and nucleotides to glycerol-extracted rabbit muscle fibers. During active contractions, Vi bound to the cross-bridges and suppressed tension with an apparent second-order rate constant of 1.34 X 10(3) M-1s-1. The half-saturation concentration for tension suppression was 94 microM Vi. The incubation of fibers in Vi relaxing or rigor solutions prior to initiation of active contractions had little effect on the initial rise of active tension. The addition of adenosine diphosphate (ADP) and Vi to fibers in rigor did not cause relaxation. Suppression of tension only developed during cross-bridge cycling. After slow relaxation from rigor in 1 mM Vi and low (50 microM) MgATP concentration (0 Ca2+), radioactive Vi and ADP were trapped within the fiber. This finding indicated the formation of a stable myosin X ADP X Vi complex, as has been reported in biochemical experiments with isolated myosin. Vi and ADP trapped within the fibers were released only by subsequent cross-bridge attachment. Vi and ADP were preferentially trapped under conditions of cross-bridge cycling in the presence of ATP rather than in relaxed fibers or in rigor with ADP. These results indicate that in the normal cross-bridge cycle, inorganic phosphate (Pi) is released from actomyosin before ADP. The resulting actomyosin X ADP intermediate can bind Vi and Pi. This intermediate probably supports force. Vi behaves as a close analogue of Pi in muscle fibers, as it does with isolated actomyosin.     

Muscular contraction and cytoplasmic streaming: A new general hypothesis

Several experiments point out that some crossbridges remain attached to the thin filaments at rest. It is assumed, in this paper, that these cross-bridges exert mechanical tractions on the thin filaments, directed from the thin to the thick filaments. When contraction is triggered off, a conformational change of the attached crossbridges is induced by the chemical energy released from ATP splitting. This conformational change leads to the reduction of the mechanical tensions. The electrostatic repulsive forces between the filaments become therefore automatically preponderant. This phenomenon induces a sideways expansion of the filament lattice and, taking into account the elasticity of muscle, a contraction in the direction of the filaments. This model accounts for the most important physiological and thermodynamical properties of muscle (tension-length curves, responses to quick stretch and quick release, Fenn effect, Hill's relation, behaviour of skinned fibres). It is directly applicable to all kinds of muscles and to cytoplasmic streaming, provided only actin, but not necessarily myosin, filaments are present in the cell.