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.     

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.     

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.     

A physical model of ATP-induced actin-myosin movement in vitro.

The nature of the mechanism limiting the velocity of ATP-induced unidirectional movements of actin-myosin filaments in vitro is considered. In the sliding process two types of "cyclic" interactions between myosin heads and actin are involved, i.e., productive and nonproductive. In the productive interaction, myosin heads split ATP and generate a force which produces sliding between actin and myosin. In the nonproductive interaction "cycle," on the other hand, myosin heads rapidly attach to and detach from actin "reversibly," i.e., without splitting ATP or generating an active force. Such a nonproductive interaction "cycle" causes irreversible dissipation of sliding energy into heat, because the myosin cross-bridges during this interaction are passive elastic structures. This consideration has led us to postulate that such cross-bridges, in effect, exert viscous-like frictional drag on moving elements. Energetic considerations suggest that this frictional drag is much greater than the hydrodynamic viscous drag. We present a model in which the sliding velocity is limited by the balance between the force generated by myosin cross-bridges in the productive interaction and the frictional drag exerted by other myosin cross-bridges in the nonproductive interaction. The model is consistent with experimental findings of in vitro sliding, including the dependence of velocity on ATP concentration, as well as the sliding velocity of co-polymers of skeletal muscle myosin and phosphorylated and unphosphorylated smooth muscle myosins.     

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.     

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.     

The unit event of sliding of the chemo-mechanical enzyme composed of myosin and actin with regulatory proteins

Various myosin-actin systems do not always show the same sliding behaviors. To make the situation clear, discussions are concentrated on the unit event of sliding of the chemo-mechanical enzyme composed of a single myosin head and a single actin filament with regulatory proteins. The popular idea of the one-to-one correspondence between the chemical state and the physical state or between the chemical reaction step and the physical conformational change is reexamined. It is likely that the sites and the modes of interaction between myosin head and actin filament during the ATP hydrolysis are more multiple and variable, and the input-output coupling in the chemo-mechanical enzyme is loose.     

Chemomechanical coupling in actomyosin system: An approach by in vitro movement assay and kinetic analysis of ATP hydrolysis by shortening myofibrils

On the basis of our recent studies of the sliding distance of actin filaments during one ATP cycle on the surface of myosin-coated glass surface and ATP hydrolysis by rapidly shortening myofibrils, the molecular mechanism of chemomechanical coupling is considered. We conclude that the myosin head can repeat many active cyclic interactions with actins to drive the actin filaments over a long distance during one ATP cycle, and that the distance is variable depending on the load.     

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.     

Cell motility and thermodynamic fluctuations tailoring quantum mechanics for biology

Cell motility underlying muscle contraction is an instance of thermodynamics tailoring quantum mechanics for biology. Thermodynamics is intrinsically multi-agential in admitting energy consumers in the form of energy-deficient thermodynamic fluctuations. The onset of sliding movement of an actin filament on myosin molecules in the presence of ATP molecules to be hydrolyzed demonstrates that thermodynamic fluctuations transform their nature so as to accommodate themselves to energy transduction subject to the first law of thermodynamics. The transition from transversal to longitudinal fluctuations of an actin filament with the increase of ATP concentration coincides with the change in the nature of energy consumers acting upon thermal energy in the light of the first law, eventually embodying a uniform sliding movement of an actin filament.     

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.     

A modelized distribution of actomyosin interactions in the vertebrate cardiac muscle

Preliminary assumption of this model is that interactions between actin and myosin presupposes an exact three-dimensional geometrical correspondence between sites, due to the very short time constants present under physiological conditions. Only small and controlled torsions of the actin filaments are accepted. The model uses geometrical information concerning orientations and dimensions of myosin crossbridges and actin monomeres to modelize the distribution of their inter-actions. An orientation map of actin sites in the cross-section perpendicular to the filament axis is proposed, adapted to the specific filament array of vertebrate muscle. Orientation of myosin crossbridges follows Luther's rules. According to the model, any interaction between actin and myosin implies the superimposition of their respective cross-sectional planes. The axial length of actin monomere is 55 A; the distance between two crossbridges along the myosin filament axis is 143 A. The following properties are derived: 1) The shortening step of the sliding actin filament must be a multiple of 11 A (highest common factor). Taking into account the staggered disposition of the two actin strands and the presence of two heads for each cross-bridge, the most probable value for this shortening step is equal to 99 A. A specific scheme is proposed to describe the shortening process. The behavior of the modelized crossbridge does not need any elastic structure--2) Planes situated at 715 A (lowest common multiple) of actin and myosin coinciding planes are also in coincidence. In a hemi-sarcomere the maximal number of these planes, referred to as simultaneously activable planes, is 10 (20 if both myosin heads are considered). The proportion of interactions authorized by the site orientations is 1/12. In the model, the concept of randomly recruited crossbridges is replaced by a discretized recruitment, based on geometrical properties at an ultrastructural level. The proposed distribution is homogeneous: it can be extended radially in the sarcomere and authorizes the actin filament sliding in the whole physiological range under the control of a dual activation function, reproducing Ca++ temporal and spatial distribution.     

Mechanism of formation of actomyosin interface

Force generation in muscle results from binding of myosin to F-actin. ATP binding to myosin provides energy to dissociate actomyosin complex while the hydrolysis of ATP is needed for re-binding of myosin to F-actin. At the end of each cycle myosin and actin form a tight complex with a substantial interface area. We investigated the dynamics of formation of actomyosin interface in presence and absence of nucleotides by quenched flow cross-linking technique. We showed previously that myosin head (subfragment 1, S1) directly interacts with at least two monomers in the actin filament. The quenched flow cross-linking experiments revealed that the initial contact (in presence or absence of nucleotides) occurs between loop 635-647 of S1 and 1-12 N-terminal residues of one actin and, then, the second contact forms between loop 567-574 of S1 and the N terminus of the second actin. The distance between these two loops in S1 corresponds to the distance between N termini of two actins in the same strand (53 A) but is smaller than that between two actins from the different strands (102 A). The formation of the actomyosin complex proceeds in ordered sequence: S1 initially binds to one actin then binds with the second actin located in the same strand but probably closer to the barbed end of F-actin. The presence of nucleotides slows down the interaction of S1 with the second actin, which correlates with recently proposed cleft movement in a 50 kDa domain of S1. The sequential mechanism of formation of actomyosin interface starting from one end and developing towards the barbed end might be involved in force generation and directional movement in actin-myosin system.     

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.     

Cross-bridge attachment during high-speed active shortening of skinned fibers of the rabbit psoas muscle: implications for cross-bridge action during maximum velocity of filament sliding

To characterize the kinetics of cross-bridge attachment to actin during unloaded contraction (maximum velocity of filament sliding), ramp-shaped stretches with different stretch-velocities (2-40,000 nm per half-sarcomere per s) were applied to actively contracting skinned fibers of the rabbit psoas muscle. Apparent fiber stiffness observed during such stretches was plotted versus the speed of the imposed stretch (stiffness-speed relation) to derive the rate constants for cross-bridge dissociation from actin. The stiffness-speed relation obtained for unloaded shortening conditions was shifted by about two orders of magnitude to faster stretch velocities compared to isometric conditions and was almost identical to the stiffness-speed relation observed in the presence of MgATPgammaS at high Ca(2+) concentrations, i.e., under conditions where cross-bridges are weakly attached to the fully Ca(2+) activated thin filaments. These data together with several control experiments suggest that, in contrast to previous assumptions, most of the fiber stiffness observed during high-speed shortening results from weak cross-bridge attachment to actin. The fraction of strongly attached cross-bridges during unloaded shortening appears to be as low as some 1-5% of the fraction present during isometric contraction. This is about an order of magnitude less than previous estimates in which contribution of weak cross-bridge attachment to observed fiber stiffness was not considered. Our findings imply that 1) the interaction distance of strongly attached cross-bridges during high-speed shortening is well within the range consistent with conventional cross-bridge models, i.e., that no repetitive power strokes need to be assumed, and 2) that a significant part of the negative forces that limit the maximum speed of filament sliding might originate from weak cross-bridge interactions with actin.     

Electron tomography of swollen rigor fibers of insect flight muscle reveals a short and variably angled S2 domain

Subfragment 2 (S2), the segment that links the two myosin heads to the thick filament backbone, may serve as a swing-out adapter allowing crossbridge access to actin, as the elastic component of crossbridges and as part of a phosphorylation-regulated on-off switch for crossbridges in smooth muscle. Low-salt expansion increases interfilament spacing (from 52 nm to 67 nm) of rigor insect flight muscle fibers and exposes a tethering segment of S2 in many crossbridges. Docking an actoS1 atomic model into EM tomograms of swollen rigor fibers identifies in situ for the first time the location, length and angle assignable to a segment of S2. Correspondence analysis of 1831 38.7 nm crossbridge repeats grouped self-similar forms from which class averages could be computed. The full range of the variability in angles and lengths of exposed S2 was displayed by using class averages for atomic fittings of acto-S1, while S2 was modeled by fitting a length of coiled-coil to unaveraged individual repeats. This hybrid modeling shows that the average length of S2 tethers along the thick filament (except near the tapered ends) is approximately 10 nm, or 16% of S2's total length, with an angular range encompassing 90 degrees axially and 120 degrees azimuthally. The large range of S2 angles indicates that some rigor bridges produce positive force that must be balanced by others producing drag force. The short tethering segment clarifies constraints on the function of S2 in accommodating variable myosin head access to actin. We suggest that the short length of S2 may also favor intermolecular head-head interactions in IFM relaxed thick filaments.     

Enhancing the staggered fluctuations of an actin filament sliding on Chara myosin

We examined both longitudinal and transversal fluctuations of displacements of an actin filament sliding upon Chara myosin molecules. Although the magnitude of transversal fluctuations remained rather independent of ATP concentration, the longitudinal ones were found to increase their magnitude as the concentration increased. In addition, the longitudinal fluctuations gradually increased as the sliding velocity of the filament increased.     

Myosin head mechanical performance under different conformational change mechanisms

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

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.     

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.