Mechanochemical coupling in actomyosin energy transduction studied by in vitro movement assay

In order to study the mechanochemical coupling in actomyosin energy transduction, the sliding distance of an actin filament induced by one ATP hydrolysis cycle was obtained by using an in vitro movement assay that permitted quantitative and simultaneous measurements of (1) the movements of single fluorescently labeled actin filaments on myosin bound to coverslip surfaces and (2) the ATPase rates. The sliding distance was determined as (the working stroke time in one ATPase cycle, tws) x (the filament velocity, v). tws was obtained from the ATPase turnover rate of myosin during the sliding (kt), the ATP hydrolysis time (delta t) and the ON-rate at which myosin heads enter into the working stroke state when they encounter actin (kON); tws approximately 1/kt-delta t-1/kON. kt was estimated from the ATPase rates of the myosin-coated surface during the sliding of actin filaments. delta t has been determined as less than 1/100 per second, kON was estimated by analyzing the movements of very short (40 nm) filaments. The resulting sliding distance during one ATP hydrolysis cycle near zero load was greater than 100 nm, which is about ten times longer than that expected for a single attachment-detachment cycle between an actin and a myosin head. This leads to the conclusion that the coupling between the ATPase and attachment-detachment cycles is not determined rigidly in a one-to-one fashion.     

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.     

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.     

Mechanics and models of the myosin motor

In striated muscles, shortening comes about by the sliding movement of thick filaments, composed mostly of myosin, relative to thin filaments, composed mostly of actin. This is brought about by cyclic action of 'cross-bridges' composed of the heads of myosin molecules projecting from a thick filament, which attach to an adjacent thin filament, exert force for a limited time and detach, and then repeat this cycle further along the filament. The requisite energy is provided by the hydrolysis of a molecule of adenosine triphosphate to the diphosphate and inorganic phosphate, the steps of this reaction being coupled to mechanical events within the cross-bridge. The nature of these events is discussed. There is good evidence that one of them is a change in the angle of tilt of a 'lever arm' relative to the 'catalytic domain' of the myosin head which binds to the actin filament. It is suggested here that this event is superposed on a slower, temperature-sensitive change in the orientation of the catalytic domain on the actin filament. Many uncertainties remain.     

Myosin cross-bridge mechanics: geometrical determinants for continuous sliding

Advances in experimental techniques have provided new details on the molecular mechanisms governing the cross-bridge kinetics. Nevertheless, the issue of micromechanics of sliding is still debated. In particular, uncertainty exists regarding the myosin filament arrangement and structure and the mechanics of the myosin head with respect to the working stroke distance (WS) and the duty ratio (r), i.e. the fraction of the ATPase cycle time the myosin head is attached to the actin filament. The object of the present work is to provide a theoretical framework to correlate different features of cross-bridge mechanics; the main hypothesis is that the attachment between the actin filament and the surrounding myosin filaments has to be continuous through the sliding (continuous sliding hypothesis) in order to maximise the effect of the myosin head performance. A 3-D model of the sliding mechanism based on a geometrical approach is presented, which is able to identify the architectures that accomplish the continuous sliding under unloaded conditions. About 200 different configurations have been simulated by changing the myosin head binding range, i.e. its ability to reach an actin binding site from its rest position, WS, the myosin head orientation and the actin filament orientation. Only few configurations were consistent with the continuous sliding hypothesis. Depending on the parameter set adopted, the percentage of attached heads (%AH) calculated ranges between 4% and 28%, r between 0.08 and 0.02 s⁻¹, and the sliding velocity between 0.7 and 10.6 μm/s. In all the cases, results were not affected by the WS value.     

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.     

Probing Muscle Myosin Motor Action: X-Ray (M3 and M6) Interference Measurements Report Motor Domain Not Lever Arm Movement

The key question in understanding how force and movement are produced in muscle concerns the nature of the cyclic interaction of myosin molecules with actin filaments. The lever arm of the globular head of each myosin molecule is thought in some way to swing axially on the actin-attached motor domain, thus propelling the actin filament past the myosin filament. Recent X-ray diffraction studies of vertebrate muscle, especially those involving the analysis of interference effects between myosin head arrays in the two halves of the thick filaments, have been claimed to prove that the lever arm moves at the same time as the sliding of actin and myosin filaments in response to muscle length or force steps. It was suggested that the sliding of myosin and actin filaments, the level of force produced and the lever arm angle are all directly coupled and that other models of lever arm movement will not fit the X-ray data. Here, we show that, in addition to interference across the A-band, which must be occurring, the observed meridional M3 and M6 X-ray intensity changes can all be explained very well by the changing diffraction effects during filament sliding caused by heads stereospecifically attached to actin moving axially relative to a population of detached or non-stereospecifically attached heads that remain fixed in position relative to the myosin filament backbone. Crucially, and contrary to previous interpretations, the X-ray interference results provide little direct information about the position of the myosin head lever arm; they are, in fact, reporting relative motor domain movements. The implications of the new interpretation are briefly assessed.     

Troponin is a potential regulator for actomyosin interactions

Troponin extracted from rabbit skeletal muscle directly binds to an actin filament in a molar ratio of 1:1 even in the absence of tropomyosin. An actin filament decorated with troponin did not exhibit significant difference from pure actin filaments in the maximum rate of actomyosin ATP hydrolysis and the sliding velocity of the filament examined by means of an in vitro motility assay. However, the relative number of troponin-bound actin filaments moving in the absence of calcium ions decreased to half that in their presence. The amount of HMM bound to the filaments was less than 4% of actin monomers in the presence of TNs. In addition, actin filaments could not move when Tn molecules were bound in the molar ratio of about 1:1 although they sufficiently bind to myosin heads. These results indicate that troponin can transform an actin monomer within a filament into an Off-state without sterically blocking of the myosin-binding sites with tropomyosin molecules.     

Inorganic polyphosphate hydrolysis catalyzed by skeletal muscular actomyosin complexes is uncoupled with motility

Hydrolysis of the triphosphate moiety of ATP, catalyzed by myosin, induces alterations in the affinity of the myosin heads for actin filaments via conformational changes, thereby causing motility of the actomyosin complexes. To elucidate the contribution of the triphosphate group attached to adenosine, we examined the enzymatic activity of heavy meromyosin (HMM) with actin filaments for inorganic tripolyphosphate (3PP) using a Malachite green method and evaluated using fluorescence microscopy the effects of 3PP on actin filament motility on HMM-coated glass slides. In the presence of MgCl₂, HMM hydrolyzed 3PP at a maximum rate of 0.016 s⁻¹ HMM⁻¹, which was four times lower than the hydrolysis rate of ATP. Tetrapolyphosphate (4PP) was hydrolyzed at a rate similar to that of 3PP hydrolysis. The hydrolysis rates of 3PP and 4PP were enhanced by roughly 10-fold in the presence of actin filaments. In motility assays, the presence of polyphosphates did not lead to the sliding movement of actin filaments. Moreover, in the presence of ATP at low concentrations, the sliding velocity of actin filaments decreased as the concentration of added polyphosphate increased, indicating a competitive binding of polyphosphate to myosin heads with ATP. These results suggested that the energy produced by standalone triphosphate hydrolysis did not induce the unidirectional motion of actomyosin and that the link between triphosphate and adenosine was crucial for motility.     

Dynamic conformational changes due to the ATP hydrolysis in the motor domain of myosin: 10-ns molecular dynamics simulations

Muscle contraction is caused by directed movement of myosin heads along actin filaments. This movement is triggered by ATP hydrolysis, which occurs within the motor domain of myosin. The mechanism for this intramolecular process remains unknown owing to a lack of ways to observe the detailed motions of each atom in the myosin molecule. We carried out 10-ns all-atom molecular dynamics simulations to investigate the types of dynamic conformational changes produced in the motor domain by the energy released from ATP hydrolysis. The results revealed that the thermal fluctuations modulated by perturbation of ATP hydrolysis are biased in one direction that is relevant to directed movement of the myosin head along the actin filament.     

Cross-bridge action: present views, prospects, and unknowns

When the sliding filament hypothesis was proposed in 1953-1954, existing evidence showed that (1) contributions to tension were given by active sites uniformly distributed within each zone of filament overlap and (2) each site functioned cyclically. These sites were identified by electron microscopy as cross-bridges between the two filaments, formed of the heads of myosin molecules projecting from a thick filament and attaching to a thin filament. The angle of these cross-bridges was found to be different at rest and in rigor, suggesting that the event causing relative motion of the filaments was a change of the angle of the cross-bridges. At first, it seemed likely that the whole cross-bridge rotated about its attachment to actin, but when the atomic structures of actin and myosin were obtained by X-ray crystallography, a possible hinge was found between the "catalytic domain" which attaches to the actin filament and the "light-chain domain" which appears to act as a lever arm. Two attitudes of the lever arm are now well established, the transition between them being driven by a conformational change coupled to some step in the hydrolysis of ATP, but several recent observations suggest that this is not the whole story: a third attitude has been shown by X-ray crystallography; a non-muscle myosin has been shown to produce its working stroke in two steps; and there are suggestions that an additional displacement of the filaments is produced by a change in the attitude of the catalytic domain on the thin filament.     

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.     

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.     

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.     

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.     

Thermal activation energy for bidirectional movement of actin along bipolar tracks of myosin filaments

Previous in vitro motility assays using bipolar myosin thick filaments demonstrated that actin filaments were capable of moving in both directions along the myosin filament tracks. The movements; however, were slower in the direction leading away from the central bare zone than towards it. To understand the mechanism underlying these different direction-dependent motilities, we have examined the effects of temperature on the velocities of the bidirectional movements along reconstituted myosin filaments. Activation energies of the movements were determined by Arrhenius plots at high and low concentrations of ATP. As a result, the thermal activation energy of the movement away from the central bare zone was significantly higher than that of the movement toward the zone. Given that the backward movement away from the central bare zone would cause the myosin heads to be constrained and the stiffness of the cross-bridges to increase, these results suggest that elastic energy required for the cross-bridge transition is supplied by thermal fluctuations.     

Twirling Motion of Actin Filaments in Gliding Assays with Nonprocessive Myosin Motors

We present a model study of gliding assays in which actin filaments are moved by nonprocessive myosin motors. We show that even if the power stroke of the motor protein has no lateral component, the filaments will rotate around their axis while moving over the surface. Notably, the handedness of this twirling motion is opposite from that of the actin filament structure. It stems from the fact that the gliding actin filament has target zones, where its subunits point toward the surface and are therefore more accessible for myosin heads. Each myosin head has a higher binding probability before it reaches the center of the target zone than afterwards, which results in a left-handed twirling. We present a stochastic simulation and an approximative analytical solution. The calculated pitch of the twirling motion depends on the filament velocity (ATP concentration). It reaches ∼400 nm for low speeds and increases with higher speeds.     

3D structure of relaxed fish muscle myosin filaments by single particle analysis

To understand the structural changes involved in the force-producing myosin cross-bridge cycle in vertebrate muscle it is necessary to know the arrangement and conformation of the myosin heads at the start of the cycle (i.e. the relaxed state). Myosin filaments isolated from goldfish muscle under relaxing conditions and viewed in negative stain by electron microscopy (EM) were divided into segments and subjected to three-dimensional (3D) single particle analysis without imposing helical symmetry. This allowed the known systematic departure from helicity characteristic of vertebrate striated muscle myosin filaments to be preserved and visualised. The resulting 3D reconstruction reveals details to about 55 A resolution of the myosin head density distribution in the three non-equivalent head 'crowns' in the 429 A myosin filament repeat. The analysis maintained the well-documented axial perturbations of the myosin head crowns and revealed substantial azimuthal perturbations between crowns with relatively little radial perturbation. Azimuthal rotations between crowns were approximately 60 degrees , 60 degrees and 0 degrees , rather than the regular 40 degrees characteristic of an unperturbed helix. The new density map correlates quite well with the head conformations analysed in other EM studies and in the relaxed fish muscle myosin filament structure modelled from X-ray fibre diffraction data. The reconstruction provides information on the polarity of the myosin head array in the A-band, important in understanding the geometry of the myosin head interaction with actin during the cross-bridge cycle, and supports a number of conclusions previously inferred by other methods. The observed azimuthal head perturbations are consistent with the X-ray modelling results from intact muscle, indicating that the observed perturbations are an intrinsic property of the myosin filaments and are not induced by the proximity of actin filaments in the muscle A-band lattice. Comparison of the axial density profile derived in this study with the axial density profile of the X-ray model of the fish myosin filaments which was restricted to contributions from the myosin heads allows the identification of a non-myosin density peak associated with the azimuthally perturbed head crown which can be interpreted as a possible location for C-protein or X-protein (MyBP-C or -X). This position for C-protein is also consistent with the C-zone interference function deduced from previous analysis of the meridional X-ray pattern from frog muscle. It appears that, along with other functions, C-(X-) protein may have the role of slewing the heads of one crown so that they do not clash with the neighbouring actin filaments, but are readily available to interact with actin when the muscle is activated.     

Calcium regulation of thin filament movement in an in vitro motility assay.

The ability of calcium to regulate thin filament sliding velocity was studied in an in vitro motility assay system using cardiac troponin and tropomyosin and rhodamine-phalloidin-labeled skeletal actin and skeletal heavy meromyosin to propel the filaments. Measurements showed that both the number of thin filaments sliding and their sliding speed (Sf) were dependent on the calcium concentration in the range of pCa 5 to 9. Thin filament motility was completely inhibited only if troponin and tropomyosin were added at a concentration of 100 nM to the motility assay solution and the pCa was more than 8. The filament sliding speed was dependent on the pCa in a noncooperative fashion (Hill coefficient = 1) and reached maximum at 5 microns/s at a pCa of 5. The number of filaments moving uniformly decreased from > 90% at pCa 5-6 to near zero in less than 1 pCa unit. This behavior may be explained by a hypothesis in which the regulatory proteins control the number of cross-bridge heads interacting with the thin filaments rather than the rate at which they individually hydrolyze ATP or translocate the thin filaments.     

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