Sliding distance per ATP molecule hydrolyzed by myosin heads during isotonic shortening of skinned muscle fibers.

We measured isotonic sliding distance of single skinned fibers from rabbit psoas muscle when known and limited amounts of ATP were made available to the contractile apparatus. The fibers were immersed in paraffin oil at 20 degrees C, and laser pulse photolysis of caged ATP within the fiber initiated the contraction. The amount of ATP released was measured by photolyzing 3H-ATP within fibers, separating the reaction products by high-pressure liquid chromatography, and then counting the effluent peaks by liquid scintillation. The fiber stiffness was monitored to estimate the proportion of thick and thin filament sites interacting during filament sliding. The interaction distance, Di, defined as the sliding distance while a myosin head interacts with actin in the thin filament per ATP molecule hydrolyzed, was estimated from the shortening distance, the number of ATP molecules hydrolyzed by the myosin heads, and the stiffness. Di increased from 11 to 60 nm as the isotonic tension was reduced from 80% to 6% of the isometric tension. Velocity and Di increased with the concentration of ATP available. As isotonic load was increased, the interaction distance decreased linearly with decrease of the shortening velocity and extrapolated to 8 nm at zero velocity. Extrapolation of the relationship between Di and velocity to saturating ATP concentration suggests that Di reaches 100-190 nm at high shortening velocity. The interaction distance corresponds to the sliding distance while cross-bridges are producing positive (working) force plus the distance while they are dragging (producing negative forces). The results indicate that the working and drag distances increase as the velocity increases. Because Di is larger than the size of either the myosin head or the actin monomer, the results suggest that for each ATPase cycle, a myosin head interacts mechanically with several actin monomers either while working or while producing drag.     

Smooth muscle myosin cross-bridge interactions modulate actin filament sliding velocity in vitro

Although it is generally believed that phosphorylation of the regulatory light chain of myosin is required before smooth muscle can develop force, it is not known if the overall degree of phosphorylation can also modulate the rate at which cross-bridges cycle. To address this question, an in vitro motility assay was used to observe the motion of single actin filaments interacting with smooth muscle myosin copolymers composed of varying ratios of phosphorylated and unphosphorylated myosin. The results suggest that unphosphorylated myosin acts as a load to slow down the rate at which actin is moved by the faster cycling phosphorylated cross-bridges. Myosin that was chemically modified to generate a noncycling analogue of the "weakly" bound conformation was similarly able to slow down phosphorylated myosin. The observed modulation of actin velocity as a function of copolymer composition can be accounted for by a model based on mechanical interactions between cross-bridges.     

Direct observation of molecular motility by light microscopy

We used video-fluorescence microscopy to directly observe the sliding movement of single fluorescently labeled actin filaments along myosin fixed on a glass surface. Single actin filaments labeled with phalloidin-tetramethyl-rhodamine, which stabilizes the filament structure of actin, could be seen very clearly and continuously for at least 60 min in 02-free solution, and the sensitivity was high enough to see very short actin filaments less than 40 nm long that contained less than eight dye molecules. The actin filaments were observed to move along double-headed and, similarly, single-headed myosin filaments on which the density of the heads varied widely in the presence of ATP, showing that the cooperative interaction between the two heads of the myosin molecule is not essential to produce the sliding movement. The velocity of actin filament independent of filament length (greater than 1 micron) was almost unchanged until the density of myosin heads along the thick filament was decreased from six heads/14.3 nm to 1 head/34 nm. This result suggests that five to ten heads are sufficient to support the maximum sliding velocity of actin filaments (5 micron/s) under unloaded conditions. In order for five to ten myosin heads to achieve the observed maximum velocity, the sliding distance of actin filaments during one ATP cycle must be more than 60 nm.     

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.     

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.     

Cooperative actions between myosin heads bring effective functions

A recent study with single molecule measurements has reported that muscle myosin, a molecular motor, stochastically generates multiple steps along an actin filament associated with the hydrolysis of a single ATP molecule [Kitamura, K., Tokunaga, M., Esaki, S., Iwane, A.H., Yanagida, T., 2005. Mechanism of muscle contraction based on stochastic properties of single actomyosin motors observed in vitro. Biophysics 1, 1-19]. We have built a model reproducing such a stochastic movement of a myosin molecule incorporated with ATPase reaction cycles and demonstrated that the thermal fluctuation was a key for the function of myosin molecules [Esaki, S., Ishii, Y., Yanagida, T., 2003. Model describing the biased Brownian movement of myosin. Proc. Jpn. Acad. 79 (Ser B), 9-14]. The size of the displacement generated during the hydrolysis of single ATP molecules was limited within a half pitch of an actin filament when a single myosin molecules work separately. However, in muscle the size of the displacement has been reported to be greater than 60 nm [Yanagida, T., Arata, T., Oosawa, F., 1985. Sliding distance of actin filament induced by a myosin crossbridge during one ATP hydrolysis cycle. Nature 316, 366-369; Higuchi et al., 1991]. The difference suggests cooperative action between myosin heads in muscle. Here we extended the model built for an isolated myosin head to a system in which myosin heads are aligned in muscle arrangement to understand the cooperativity between heads. The simulation showed that the rotation of the actin filament [Takezawa, Y., Sugimoto, Y., Wakabayashi, K., 1998. Extensibility of the actin and myosin filaments in various states of skeletal muscles as studied by X-ray diffraction. Adv. Exp. Med. Biol. 453, 309-317; Wakabayashi, K., Ueno, Y., Takezawa, Y., Sugimoto, Y., 2001. Muscle contraction mechanism: use of X-ray synchrotron radiation. Nat. Enc. Life Sci. 1-11] associated with the release of ATPase products and binding of ATP as well as interaction between myosin heads allowed the myosin filament to move greater than a half pitch of the actin filament while a single ATP molecule is hydrolyzed. Our model demonstrated that the movement is loosely coupled to the ATPase cycle as observed in muscle.     

Calcium regulates scallop muscle by changing myosin flexibility

Muscle myosins are molecular motors that convert the chemical free energy available from ATP hydrolysis into mechanical displacement of actin filaments, bringing about muscle contraction. Myosin cross-bridges exert force on actin filaments during a cycle of attached and detached states that are coupled to each round of ATP hydrolysis. Contraction and ATPase activity of the striated adductor muscle of scallop is controlled by calcium ion binding to myosin. This mechanism of the so-called “thick filament regulation” is quite different to vertebrate striated muscle which is switched on and off via “thin filament regulation” whereby calcium ions bind to regulatory proteins associated with the actin filaments. We have used an optically based single molecule technique to measure the angular disposition adopted by the two myosin heads whilst bound to actin in the presence and absence of calcium ions. This has allowed us to directly observe the movement of individual myosin heads in aqueous solution at room temperature in real time. We address the issue of how scallop striated muscle myosin might be regulated by calcium and have interpreted our results in terms of the structures of smooth muscle myosin that also exhibit thick filament regulation. This paper is not being submitted elsewhere and the authors have no competing financial interests     

An accelerated state of myosin-based actin motility

We use an in vitro motility assay to determine the biochemical basis for a hypermotile state of myosin-based actin sliding. It is widely assumed that the sole biochemical determinant of actin-sliding velocities, V, is actin-myosin detachment kinetics (1/tauon), yet we recently reported that, above a critical ATP concentration of approximately 100 microM, V exceeds the detachment limit by more than 2-fold. To determine the biochemical basis for this hypermotile state, we measure the effects of ATP and inorganic phosphate, Pi, on V and observe that at low [ATP] V decreases as ln [Pi], whereas above 100 microM ATP the hypermotile V is independent of Pi. The ln [Pi] dependence of V at low [ATP] is consistent with a macroscopic model of muscle shortening, similar to Hill's contractile component, which predicts that V varies linearly with an internal force (Hill's active state) that drives actin movement against the viscous drag of myosin heads strongly bound to actin (Hill's dashpot). At high [ATP], we suggest that the hypermotile V is caused by shear thinning of the resistive population of strongly bound myosin heads. Our data and analysis indicate that, in addition to contributions from tauon and myosin's step size, d, V is influenced by the biochemistry of myosin's working step as well as resistive properties of actin and myosin.     

Disorder induced in nonoverlap myosin cross-bridges by loss of adenosine triphosphate.

Adenosine triphosphate-dependent changes in myosin filament structure have been directly observed in whole muscle by electron microscopy of thin sections of rapidly frozen, demembranated frog sartorius specimens. In the presence of ATP the thick filaments show an ordered, helical array of cross-bridges except in the bare zone. In the absence of ATP they show two distinct appearances: in the region of overlap with actin, there is an ordered, rigorlike array of cross-bridges between the thick and thin filaments, whereas in the nonoverlap region (H-zone) the myosin heads move away from the thick filament backbone and lose their helical order. This result suggests that the presence of ATP is necessary for maintenance of the helical array of cross-bridges characteristic of the relaxed state. The primary effect of ATP removal on the myosin heads appears to be weaken their binding to the thick filament backbone; released heads that are close to an actin filament subsequently form a new actin-based, ordered array.     

Actin-crosslinking protein regulation of filament movement in motility assays: a theoretical model.

The interaction of single actin filaments on a myosin-coated coverslip has been modeled by several authors. One model adds a component of "frictional drag" by myosin heads that oppose movement of the actin filaments. We have extended this concept by including the resistive drag from actin crosslinking proteins to understand better the relationship among crosslinking number, actin-myosin force generation, and motility. The validity of this model is supported by agreement with the experimental results from a previous study in which crosslinking proteins were added with myosin molecules under otherwise standard motility assay conditions. The theoretical relationship provides a means to determine many physical parameters that characterize the interaction between a single actin filament and a single actin-crosslinking molecule (various types). In particular, the force constant of a single filamin molecule is calculated as 1.105 pN, approximately 3 times less than a driving myosin head (3.4 pN). Knowledge of this parameter and others derived from this model allows a better understanding of the interaction between myosin and the actin/actin-binding protein cytoskeleton and the role of actin-binding proteins in the regulation and modulation of motility.     

An ionic–chemical–mechanical model for muscle contraction

The dynamic process underlying muscle contraction is the parallel sliding of thin actin filaments along an immobile thick myosin fiber powered by oar‐like movements of protruding myosin cross bridges (myosin heads). The free energy for functioning of the myosin nanomotor comes from the hydrolysis of ATP bound to the myosin heads. The unit step of translational movement is based on a mechanical‐chemical cycle involving ATP binding to myosin, hydrolysis of the bound ATP with ultimate release of the hydrolysis products, stress‐generating conformational changes in the myosin cross bridge, and relief of built‐up stress in the myosin power stroke. The cycle is regulated by a transition between weak and strong actin–myosin binding affinities. The dissociation of the weakly bound complex by addition of salt indicates the electrostatic basis for the weak affinity, while structural studies demonstrate that electrostatic interactions among negatively charged amino acid residues of actin and positively charged residues of myosin are involved in the strong binding interface. We therefore conjecture that intermediate states of increasing actin–myosin engagement during the weak‐to‐strong binding transition also involve electrostatic interactions. Methods of polymer solution physics have shown that the thin actin filament can be regarded in some of its aspects as a net negatively charged polyelectrolyte. Here we employ polyelectrolyte theory to suggest how actin–myosin electrostatic interactions might be of significance in the intermediate stages of binding, ensuring an engaged power stroke of the myosin motor that transmits force to the actin filament, and preventing the motor from getting stuck in a metastable pre‐power stroke state. We provide electrostatic force estimates that are in the pN range known to operate in the cycle.     

Cross-bridge number, position, and angle in target zones of cryofixed isometrically active insect flight muscle

Electron micrographic tomograms of isometrically active insect flight muscle, freeze substituted after rapid freezing, show binding of single myosin heads at varying angles that is largely restricted to actin target zones every 38.7 nm. To quantify the parameters that govern this pattern, we measured the number and position of attached myosin heads by tracing cross-bridges through the three-dimensional tomogram from their origins on 14.5-nm-spaced shelves along the thick filament to their thin filament attachments in the target zones. The relationship between the probability of cross-bridge formation and axial offset between the shelf and target zone center was well fitted by a Gaussian distribution. One head of each myosin whose origin is close to an actin target zone forms a cross-bridge most of the time. The probability of cross-bridge formation remains high for myosin heads originating within 8 nm axially of the target zone center and is low outside 12 nm. We infer that most target zone cross-bridges are nearly perpendicular to the filaments (60% within 11 degrees ). The results suggest that in isometric contraction, most cross-bridges maintain tension near the beginning of their working stroke at angles near perpendicular to the filament axis. Moreover, in the absence of filament sliding, cross-bridges cannot change tilt angle while attached nor reach other target zones while detached, so may cycle repeatedly on and off the same actin target monomer.     

Muscle cross-bridges bound to actin are disordered in the presence of 2,3-butanedione monoxime.

Electron paramagnetic resonance spectroscopy was used to monitor the orientation of muscle cross-bridges attached to actin in a low force and high stiffness state that may occur before force generation in the actomyosin cycle of interactions. 2,3-butanedione monoxime (BDM) has been shown to act as an uncompetitive inhibitor of the myosin ATPase that stabilizes a myosin.ADP.P(i) complex. Such a complex is thought to attach to actin at the beginning of the powerstroke. Addition of 25 mM BDM decreases tension by 90%, although stiffness remains high, 40-50% of control, showing that cross-bridges are attached to actin but generate little or no force. Active cross-bridge orientation was monitored via electron paramagnetic resonance spectroscopy of a maleimide spin probe rigidly attached to cys-707 (SH-1) on the myosin head. A new labeling procedure was used that showed improved specificity of labeling. In 25 mM BDM, the probes have an almost isotropic angular distribution, indicating that cross-bridges are highly disordered. We conclude that in the pre-powerstroke state stabilized by BDM, cross-bridges are attached to actin, generating little force, with a large portion of the catalytic domain of the myosin heads disordered.     

Effect of low pH on single skeletal muscle myosin mechanics and kinetics

Acidosis (low pH) is the oldest putative agent of muscular fatigue, but the molecular mechanism underlying its depressive effect on muscular performance remains unresolved. Therefore, the effect of low pH on the molecular mechanics and kinetics of chicken skeletal muscle myosin was studied using in vitro motility (IVM) and single molecule laser trap assays. Decreasing pH from 7.4 to 6.4 at saturating ATP slowed actin filament velocity (V(actin)) in the IVM by 36%. Single molecule experiments, at 1 microM ATP, decreased the average unitary step size of myosin (d) from 10 +/- 2 nm (pH 7.4) to 2 +/- 1 nm (pH 6.4). Individual binding events at low pH were consistent with the presence of a population of both productive (average d = 10 nm) and nonproductive (average d = 0 nm) actomyosin interactions. Raising the ATP concentration from 1 microM to 1 mM at pH 6.4 restored d (9 +/- 3 nm), suggesting that the lifetime of the nonproductive interactions is solely dependent on the [ATP]. V(actin), however, was not restored by raising the [ATP] (1-10 mM) in the IVM assay, suggesting that low pH also prolongs actin strong binding (t(on)). Measurement of t(on) as a function of the [ATP] in the single molecule assay suggested that acidosis prolongs t(on) by slowing the rate of ADP release. Thus, in a detachment limited model of motility (i.e., V(actin) approximately d/t(on)), a slowed rate of ADP release and the presence of nonproductive actomyosin interactions could account for the acidosis-induced decrease in V(actin), suggesting a molecular explanation for this component of muscular fatigue.     

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.     

The neck domain of myosin II primarily regulates the actomyosin kinetics, not the stepsize

In order to study the role of the neck domain of myosin in muscle contraction, we measured the steps of individual myosin II molecules engineered to have no neck domain (light chain-binding domain) by optical trapping nanometry. The actin filament and myosin cofilaments interacted on a glass surface to minimize the angle between them, and to minimize the interaction between myosin and the glass surface. The results showed that the average myosin stepsize did not change much when the neck domain was removed, but the sliding velocity decreased approximately fivefold. Furthermore, the duration of steps for neckless myosin was several times longer at saturated ATP concentration, indicating that the slower velocity was due to a slower dissociation rate of myosin heads from actin. From these data, we conclude that the neck domain of myosin-II primarily regulates the actomyosin kinetics, not the mechanics.     

Forces measured with micro-fabricated cantilevers during actomyosin interactions produced by filaments containing different myosin isoforms and loop 1 structures

Background

There is evidence that the actin-activated ATP kinetics and the mechanical work produced by muscle myosin molecules are regulated by two surface loops, located near the ATP binding pocket (loop 1), and in a region that interfaces with actin (loop 2). These loops regulate force and velocity of contraction, and have been investigated mostly in single molecules. There is a lack of information of the work produced by myosin molecules ordered in filaments and working cooperatively, which is the actual muscle environment.

Methods

We use micro-fabricated cantilevers to measure forces produced by myosin filaments isolated from mollusk muscles, skeletal muscles, and smooth muscles containing variations in the structure of loop 1 (tonic and phasic myosins). We complemented the experiments with in-vitro assays to measure the velocity of actin motility.

Results

Smooth muscle myosin filaments produced more force than skeletal and mollusk myosin filaments when normalized per filament overlap. Skeletal muscle myosin propelled actin filaments in a higher sliding velocity than smooth muscle myosin. The values for force and velocity were consistent with previous studies using myosin molecules, and suggest a close correlation with the myosin isoform and structure of surface loop 1.

General significance

The technique using micro-fabricated cantilevers to measure force of filaments allows for the investigation of the relation between myosin structure and contractility, allowing experiments to be conducted with an array of different myosin isoforms. Using the technique we observed that the work produced by myosin molecules is regulated by amino-acid sequences aligned in specific loops.     

Enhancement of the sliding velocity of actin filaments in the presence of ATP analogue: AMP-PNP

The sliding velocity of actin filaments was found to increase in the presence of ATP analogues. At 0.5 mM ATP, the presence of 2.0 mM of AMP-PNP enhanced the filament velocity from 3.2 up to 4.5 microm/s. However, 2 mM ADP decreased the velocity down to 1.1 microm/s. The results suggest that the complex conformations of myosin cross-bridges interacting with an actin filament in the presence of ATP analogues makes the entire filament move faster.     

Modeling residual force enhancement with generic cross-bridge models

The interaction of actin and myosin through cross-bridges explains much of muscle behavior. However, some properties of muscle, such as residual force enhancement, cannot be explained by current cross-bridge models. There is ongoing debate whether conceptual cross-bridge models, as pioneered by Huxley (A.F. Huxley, Muscle structure and theories of contraction, Prog. Biophys. Biophys. Chem. 7 (1957) 255) could, if suitably modified, fit experimental data showing residual force enhancement. Here we prove that there are only two ways to explain residual force enhancement with these ‘traditional’ cross-bridge models: the first requires cross-bridges to become stuck on actin (the stuck cross-bridge model) while the second requires that cross-bridges that are pulled off beyond a critical strain enter a ‘new’ unbound state that leads to a new force-producing cycle (the multi-cycle model). Stuck cross-bridge models cannot fit the velocity and stretch amplitude dependence of residual force enhancement, while the multi-cycle models can. The results of this theoretical analysis demonstrate that current kinetic models of cross-bridge action cannot explain the experimentally observed residual force enhancement. Either cross-bridges in the force-enhanced state follow a different kinetic cycle than cross-bridges in a ‘normal’ force state, or the assumptions underlying traditional cross-bridge models must be violated during experiments that show residual force enhancement.