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.     

Myosin step size. Estimation from slow sliding movement of actin over low densities of heavy meromyosin

We have estimated the step size of the myosin cross-bridge (d, displacement of an actin filament per one ATP hydrolysis) in an in vitro motility assay system by measuring the velocity of slowly moving actin filaments over low densities of heavy meromyosin on a nitrocellulose surface. In previous studies, only filaments greater than a minimum length were observed to undergo continuous sliding movement. These filaments moved at the maximum speed (Vo), while shorter filaments dissociated from the surface. We have now modified the assay system by including 0.8% methylcellulose in the ATP solution. Under these conditions, filaments shorter than the previous minimum length move, but significantly slower than Vo, as they are propelled by a limited number of myosin heads. These data are consistent with a model that predicts that the sliding velocity (v) of slowly moving filaments is determined by the product of vo and the fraction of time when at least one myosin head is propelling the filament, that is, v = vo [1-(1-ts/tc)N], where ts is the time the head is strongly bound to actin, tc is the cycle time of ATP hydrolysis, and N is the average number of myosin heads that can interact with the filament. Using this equation, the optimum value of ts/tc to fit the measured relationship between v and N was calculated to be 0.050. Assuming d = vots, the step size was then calculated to be between 10nm and 28 nm per ATP hydrolyzed, the latter value representing the upper limit. This range is within that of geometric constraint for conformational change imposed by the size of the myosin head, and therefore is not inconsistent with the swinging cross-bridge model tightly coupled with ATP hydrolysis.     

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.     

Characterization of in vitro motility assays using smooth muscle and cytoplasmic myosins

We have used two in vitro motility assays to study the relative movement of actin and myosin from turkey gizzards (smooth muscle) and human platelets. In the Nitella-based in vitro motility assay, myosin-coated polymer beads move over a fixed substratum of actin bundles derived from dissection of the alga, Nitella, whereas in the sliding actin filament assay fluorescently labeled actin filaments slide over myosin molecules adhered to a glass surface. Both assay systems yielded similar relative velocities using smooth muscle myosin and actin under our standard conditions. We have studied the effects of ATP, ionic strength, magnesium, and tropomyosin on the velocity and found that with the exception of the dependence on MgCl2, the two assays gave very similar results. Calcium over a concentration of pCa 8 to 4 had no effect on the velocity of actin filaments. Phosphorylated smooth muscle myosin propelled filaments of smooth muscle and skeletal muscle actin at the same rate. Phosphorylated smooth muscle and cytoplasmic myosin monomers also moved actin filaments, demonstrating that filament formation is not required for movement.     

A kinetic mechanism for the fast movement of Chara myosin

Endoplasmic streaming of characean cells of Nitella or Chara is known to be in the range 30-100 microm/second. The Chara myosin extracted from the cells and fixed onto a glass surface was found to move muscle actin filaments at a velocity of 60 microm/second. This is ten times faster than that of skeletal muscle myosin (myosin II). In this study, the displacement caused by single Chara myosin molecules was measured using optical trapping nanometry. The step size of Chara myosin was approximately 19nm. This step size is longer than that of skeletal muscle myosin but shorter than that of myosin V. The dwell time of the steps was relatively long, and this most likely resulted from two rate-limiting steps, the dissociation of ADP and the binding of ATP. The rate of ADP release from Chara myosin after the completion of the force-generation step was similar to that of myosin V, but was considerably slower than that of skeletal muscle myosin. The 19nm step size and the dwell time obtained could not explain the fast movement. The fast movement could be explained by the load-dependent release of ADP. As the load imposed on the myosin decreased, the rate of ADP release increased. We propose that the interaction of Chara myosin with an actin filament resulted in a negative load being imposed on other myosin molecules interacting with the same actin filament. This resulted in an accelerated release of ADP and the fast sliding movement.     

Transition from contractile to protractile distortions occurring along an actin filament sliding on myosin molecules

An ATP-activated actin filament sliding on myosin molecules exhibited mechanical distortions or fluctuations both longitudinally and transversally along the filament. Although actin filaments exhibited a uniform sliding movement longitudinally as the ATP concentration increased, the longitudinal fluctuations were found to vary their magnitude with the concentration. The magnitude of longitudinal fluctuations reached its maximum at approximately 100 microM of the ATP concentration. The local enhancement of the longitudinal fluctuations as responding to changes in the ATP concentration is associated with a critical phenomenon bridging the two different kinds of mechanical distortions, either contractile or protractile ones, occurring within a sliding actin filament.     

Class VI myosin moves processively along actin filaments backward with large steps.

Among a superfamily of myosin, class VI myosin moves actin filaments backwards. Here we show that myosin VI moves processively on actin filaments backwards with large ( approximately 36 nm) steps, nevertheless it has an extremely short neck domain. Myosin V also moves processively with large ( approximately 36 nm) steps and it is believed that myosin V strides along the actin helical repeat with its elongated neck domain that is critical for its processive movement with large steps. Myosin VI having a short neck cannot take this scenario. We found by electron microscopy that myosin VI cooperatively binds to an actin filament at approximately 36 nm intervals in the presence of ATP, raising a hypothesis that the binding of myosin VI evokes "hot spots" on actin filaments that attract myosin heads. Myosin VI may step on these "hot spots" on actin filaments in every helical pitch, thus producing processive movement with 36 nm steps.     

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.     

Modeling rigor cross-bridge patterns in muscle I. Initial studies of the rigor lattice of insect flight muscle.

We have undertaken some computer modeling studies of the cross-bridge observed by Reedy in insect flight muscle so that we investigate the geometric parameters that influence the attachment patterns of cross-bridges to actin filaments. We find that the appearance of double chevrons along an actin filament indicates that the cross-bridges are able to reach 10--14 nm axially, and about 90 degrees around the actin filament. Between three and five actin monomers are therefore available along each turn of one strand of actin helix for labeling by cross-bridges from an adjacent myosin filament. Reedy's flared X of four bridges, which appears rotated 60 degrees at successive levels on the thick filament, depends on the orientation of the actin filaments in the whole lattice as well as on the range of movement in each cross-bridge. Fairly accurate chevrons and flared X groupings can be modeled with a six-stranded myosin surface lattice. The 116-nm long repeat appears in our models as "beating" of the 14.5-nm myosin repeat and the 38.5-nm actin period. Fourier transforms of the labeled actin filaments indicate that the cross-bridges attach to each actin filament on average of 14.5 nm apart. The transform is sensitive to changes in the ease with which the cross-bridge can be distorted in different directions.     

Movement of myosin fragments in vitro: domains involved in force production

We have used the Nitella-based movement assay to localize the site of force production in myosin. Methods were developed to use nonfilamentous myosin or proteolytic fragments of myosin in place of the thick filaments used in the original assay. In the experiments described here, the tail of myosin or its subfragments is anchored via antibodies to the surface of small particles. Nonfilamentous myosin or its subfragments move along Nitella actin cables at speeds similar to those obtained with filamentous myosin. We generated short HMM, a myosin fragment containing the heads and only 400 A of the tail. Although short HMM lacks the "hinge" region proposed by Harrington to be the site of force generation, and is incapable of forming thick filaments, it moves along actin at speeds above 1 micron/sec. Therefore, neither a thick filament nor the carboxy-terminal 1100 A of the tail is required for movement along actin. The results indicate that force production occurs in or near the myosin heads.     

In vitro movement of actin filaments on gizzard smooth muscle myosin: requirement of phosphorylation of myosin light chain and effects of tropomyosin and caldesmon

ATP-dependent movement of actin filaments on smooth muscle myosin was investigated by using the in vitro motility assay method in which myosin was fixed on the surface of a coverslip in a phosphorylated or an unphosphorylated state. Actin filaments slid on gizzard myosin phosphorylated with myosin light chain kinase (MLCK) at a rate of 0.35 micron/s, but did not slide at all on unphosphorylated myosin. The movement of actin filaments on phosphorylated myosin was stopped by perfusion of phosphatase. Subsequent perfusion with a solution containing MLCK, calmodulin, and Ca2+ enabled actin filaments to move again. The sliding velocities on monophosphorylated and diphosphorylated myosin by MLCK were not different. Actin filaments did not move on myosin phosphorylated with protein kinase C (PKC). The sliding velocity on myosin phosphorylated with both MLCK and PKC was identical to that on myosin phosphorylated only with MLCK. Gizzard tropomyosin enhanced the sliding velocity to 0.76 micron/s. Gizzard caldesmon decreased the sliding velocity with increase in its concentration. At a 5-fold molar ratio of caldesmon to actin, the movement stopped completely. This inhibitory effect of caldesmon was relieved upon addition of excess calmodulin and Ca2+.     

Flexibility of myosin attachment to surfaces influences F-actin motion.

We have analyzed the dependence of actin filament sliding movement on the mode of myosin attachment to surfaces. Monoclonal antibodies (mAbs) that bind to three distinct sites were used to tether myosin to nitrocellulose-coated glass. One antibody reacts with an epitope on the regulatory light chain (LC2) located at the head-rod junction. The other two react with sites in the rod domain, one in the S2 region near the S2-LMM hinge, and the other at the C terminus of the myosin rod. This method of attachment provides a means of controlling the flexibility and density of myosin on the surface. Fast skeletal muscle myosin monomers were bound to the surfaces through the specific interaction with these mAbs, and the sliding movement of fluorescently labeled actin filaments was analyzed by video microscopy. Each of these antibodies produced stable myosin-coated surfaces that supported uniform motion of actin over the course of several hours. Attachment of myosin through the anti-S2 and anti-LMM mAbs yielded significantly higher velocities (10 microns/s at 30 degrees C) than attachment through anti-LC2 (4-5 microns/s at 30 degrees C). For each antibody, we observed a characteristic value of the myosin density for the onset of F-actin motion and a second critical density for velocity saturation. The specific mode of attachment influences the velocity of actin filaments and the characteristic surface density needed to support movement.     

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.     

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.     

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.     

Myosin filament polymerization and depolymerization in a model of partial length adaptation in airway smooth muscle

Length adaptation in airway smooth muscle (ASM) is attributed to reorganization of the cytoskeleton, and in particular the contractile elements. However, a constantly changing lung volume with tidal breathing (hence changing ASM length) is likely to restrict full adaptation of ASM for force generation. There is likely to be continuous length adaptation of ASM between states of incomplete or partial length adaption. We propose a new model that assimilates findings on myosin filament polymerization/depolymerization, partial length adaptation, isometric force, and shortening velocity to describe this continuous length adaptation process. In this model, the ASM adapts to an optimal force-generating capacity in a repeating cycle of events. Initially the myosin filament, shortened by prior length changes, associates with two longer actin filaments. The actin filaments are located adjacent to the myosin filaments, such that all myosin heads overlap with actin to permit maximal cross-bridge cycling. Since in this model the actin filaments are usually longer than myosin filaments, the excess length of the actin filament is located randomly with respect to the myosin filament. Once activated, the myosin filament elongates by polymerization along the actin filaments, with the growth limited by the overlap of the actin filaments. During relaxation, the myosin filaments dissociate from the actin filaments, and then the cycle repeats. This process causes a gradual adaptation of force and instantaneous adaptation of shortening velocity. Good agreement is found between model simulations and the experimental data depicting the relationship between force development, myosin filament density, or shortening velocity and length.     

A protein friction model of the actin sliding movement generated by myosin in mixtures of MgATP and MgGTP in vitro.

The sliding movement of an actin filament generated by myosin heads with MgGTP bound is much slower than that by those with MgATP bound. Nonetheless, there is a report that the actin sliding velocity at low (11-21 microM) MgATP concentrations is increased by the addition of MgGTP in a range of 1-3 mM, although the actin sliding velocity at these MgATP concentrations is larger than the maximum sliding velocity attained in the presence of MgGTP alone. The convex rise in the velocity was called "mutual sensitization of MgATP and MgGTP" in the report. Here we propose a theoretical model to account for the mutual sensitization of MgATP and MgGTP. The model is an extension of a protein friction model, accommodating the presence of two different substrates and assuming the presence of motile and non-motile myosins. This new model is in accord with the characteristics of the actin/myosin sliding movement experimentally observed in mixtures of MgATP and MgGTP. Comparison of the model with the experimental results implies that the non-motile and motile myosins are those with the "converse and correct" orientations of their heads with respect to the direction of the actin sliding movement in vitro.     

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.     

ATP-dependent movement of myosin in vitro: characterization of a quantitative assay

Sheetz and Spudich (1983, Nature (Lond.), 303:31-35) showed that ATP- dependent movement of myosin along actin filaments can be measured in vitro using myosin-coated beads and oriented actin cables from Nitella. To establish this in vitro movement as a quantitative assay and to understand better the basis for the movement, we have defined the factors that affect the myosin-bead velocity. Beads coated with skeletal muscle myosin move at a rate of 2-6 micron/s, depending on the myosin preparation. This velocity is independent of myosin concentration on the bead surface for concentrations above a critical value (approximately 20 micrograms myosin/2.5 X 10(9) beads of 1 micron in diameter). Movement is optimal between pH 6.8 and 7.5, at KCl concentrations less than 70 mM, at ATP concentrations greater than 0.1 mM, and at Mg2+ concentrations between 2 and 6 mM. From the temperature dependence of bead velocity, we calculate activation energies of 90 kJ/mol below 22 degrees C and 40 kJ/mol above 22 degrees C. Different myosin species move at their own characteristic velocities, and these velocities are proportional to their actin-activated ATPase activities. Further, the velocities of beads coated with smooth or skeletal muscle myosin correlate well with the known in vivo rates of myosin movement along actin filaments in these muscles. This in vitro assay, therefore, provides a rapid, reproducible method for quantitating the ATP- dependent movement of myosin molecules on actin.     

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.