The biochemical kinetics underlying actin movement generated by one and many skeletal muscle myosin molecules

To better understand how skeletal muscle myosin molecules move actin filaments, we determine the motion-generating biochemistry of a single myosin molecule and study how it scales with the motion-generating biochemistry of an ensemble of myosin molecules. First, by measuring the effects of various ligands (ATP, ADP, and P(i)) on event lifetimes, tau(on), in a laser trap, we determine the biochemical kinetics underlying the stepwise movement of an actin filament generated by a single myosin molecule. Next, by measuring the effects of these same ligands on actin velocities, V, in an in vitro motility assay, we determine the biochemistry underlying the continuous movement of an actin filament generated by an ensemble of myosin molecules. The observed effects of P(i) on single molecule mechanochemistry indicate that motion generation by a single myosin molecule is closely associated with actin-induced P(i) dissociation. We obtain additional evidence for this relationship by measuring changes in single molecule mechanochemistry caused by a smooth muscle HMM mutation that results in a reduced P(i)-release rate. In contrast, we observe that motion generation by an ensemble of myosin molecules is limited by ATP-induced actin dissociation (i.e., V varies as 1/tau(on)) at low [ATP], but deviates from this relationship at high [ATP]. The single-molecule data uniquely provide a direct measure of the fundamental mechanochemistry of the actomyosin ATPase reaction under a minimal load and serve as a clear basis for a model of ensemble motility in which actin-attached myosin molecules impose a load.     

A model to account for the elastic element in muscle crossbridges in terms of a bending myosin rod

We advance a structural model to account for the rapid elastic element seen in mechanical transient experiments on vertebrate skeletal muscle (A.F. Huxley & Simmons 1971 Nature, Lond. 233, 533-538). In contrast to other crossbridge models, ours does not envisage a myosin rod made up of two rigid portions connected by a hinge, but rather a gradually bending rod portion connecting the heads to the thick filament shaft. We propose that, in relaxed muscle, the subfragment 2 (S2) portion of the myosin rod is bound to the thick filament shaft by ionic interactions analogous to those between the light meromyosin (LMM) portions of the rod that constitute the body of the shaft. These interactions probably involve the alternating zones of positive and negative charge seen in myosin rod amino acid sequences. As the crossbridge cycle that generates tension begins, we propose that part of S2 detaches from the thick filament shaft and bends to enable the myosin head to attach to actin. When tension develops in the crossbridge, the S2 is straightened and more of it becomes detached from the shaft so that the junction between S2 and the myosin heads moves 3-4 nm axially. As tension declines at the end of the crossbridge stroke, we propose that S2 rebinds to the thick filament shaft and that this provides the restoring force to return the junction of the heads and S2 to its original axial position. Thus this movement would have the characteristics of an elastic element; detailed calculations indicate that it would have properties similar to those observed experimentally. Furthermore, this model can account for the radial attractive force seen in rigor and in contracting muscle, the decrease in stiffness when interfilament spacing is increased in skinned muscle, and the increased rate of proteolysis observed at the S2-LMM junction in contracting muscle.     

Force generation in single conventional actomyosin complexes under high dynamic load

The mechanical load borne by a molecular motor affects its force, sliding distance, and its rate of energy transduction. The control of ATPase activity by the mechanical load on a muscle tunes its efficiency to the immediate task, increasing ATP hydrolysis as the power output increases at forces less than isometric (the Fenn effect) and suppressing ATP hydrolysis when the force is greater than isometric. In this work, we used a novel 'isometric' optical clamp to study the mechanics of myosin II molecules to detect the reaction steps that depend on the dynamic properties of the load. An actin filament suspended between two beads and held in separate optical traps is brought close to a surface that is sparsely coated with motor proteins on pedestals of silica beads. A feedback system increases the effective stiffness of the actin by clamping the force on one of the beads and moving the other bead electrooptically. Forces measured during actomyosin interactions are increased at higher effective stiffness. The results indicate that single myosin molecules transduce energy nearly as efficiently as whole muscle and that the mechanical control of the ATP hydrolysis rate is in part exerted by reversal of the force-generating actomyosin transition under high load without net utilization of ATP.     

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.     

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 Lever Arm Effects a Mechanical Asymmetry of the Myosin-V-Actin Bond

Myosin-V is a two-headed molecular motor taking multiple ATP-dependent steps toward the plus end (forward) of actin filaments. At high mechanical loads, the motor processively steps toward the minus end (backward) even in the absence of ATP, whereas analogous forward steps cannot be induced. The detailed mechanism underlying this mechanical asymmetry is not known. We investigate the effect of force on individual single headed myosin-V constructs bound to actin in the absence of ATP. If pulled forward, the myosin-V head dissociates at forces twice as high than if pulled backward. Moreover, backward but not forward distances to the unbinding barrier are dependent on the lever arm length. This asymmetry of unbinding force distributions in a single headed myosin forms the basis of the two-headed asymmetry. Under load, the lever arm functions as a true lever in a mechanical sense.     

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 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 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.     

Inferring crossbridge properties from skeletal muscle energetics

Work is generated in muscle by myosin crossbridges during their interaction with the actin filament. The energy from which the work is produced is the free energy change of ATP hydrolysis and efficiency quantifies the fraction of the energy supplied that is converted into work. The purpose of this review is to compare the efficiency of frog skeletal muscle determined from measurements of work output and either heat production or chemical breakdown with the work produced per crossbridge cycle predicted on the basis of the mechanical responses of contracting muscle to rapid length perturbations. We review the literature to establish the likely maximum crossbridge efficiency for frog skeletal muscle (0.4) and, using this value, calculate the maximum work a crossbridge can perform in a single attachment to actin (33 × 10⁻²¹ J). To see whether this amount of work is consistent with our understanding of crossbridge mechanics, we examine measurements of the force responses of frog muscle to fast length perturbations and, taking account of filament compliance, determine the crossbridge force-extension relationship and the velocity dependences of the fraction of crossbridges attached and average crossbridge strain. These data are used in combination with a Huxley-Simmons-type model of the thermodynamics of the attached crossbridge to determine whether this type of model can adequately account for the observed muscle efficiency. Although it is apparent that there are still deficiencies in our understanding of how to accurately model some aspects of ensemble crossbridge behaviour, this comparison shows that crossbridge energetics are consistent with known crossbridge properties.     

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.     

Characterization of the myosin adenosine triphosphate (M.ATP) crossbridge in rabbit and frog skeletal muscle fibers.

In the presence of ATP and absence of Ca2+, muscle crossbridges have either MgATP or MgADP.Pi bound at the active site (S. B. Marston and R. T. Tregear, Nature [Lond.], 235:22:1972). The behavior of these myosin adenosine triphosphate (M.ATP) crossbridges, both in relaxed skinned rabbit psoas and frog semitendinosus fibers, was analyzed. At very low ionic strength, T = 5 degrees C, mu = 20 mM, these crossbridges spend a large fraction of the time attached to actin. In rabbit, the attachment rate constants at low salt are 10(4) - 10(5) s-1, and the detachment rate constants are approximately 10(4) s-1. When ionic strength is increased up to physiological values by addition of 140 mM potassium propionate, the major effect is a weakening of the crossbridge binding constant approximately 30-40-fold. This effect occurs because of a large decrease, approximately 100-fold, in the crossbridge attachment rate constants. The detachment rate constants decrease only 2-3-fold. The effect of ionic strength on crossbridge binding in the fiber is very similar to the effect of ionic strength on the binding of myosin subfragment-1 to unregulated actin in solution. Thus, the effect of increasing ionic strength in fibers appears to be a direct effect on crossbridge binding rather than an effect on troponin-tropomyosin. The finding that crossbridges with ATP bound at the active site can and do attach to actin over a wide range of ionic strengths strongly suggests that troponin-tropomyosin keeps a muscle relaxed by blocking a step subsequent to crossbridge attachment. Thus, rather than troponin-tropomyosin serving to keep a muscle relaxed by inhibiting attachment, it seems quite possible that the main way in which troponin-tropomyosin regulates muscle activity is by preventing the weakly-binding relaxed crossbridges from going on through the crossbridge cycle into more strongly-binding states.     

Why Muscle is an Efficient Shock Absorber

Skeletal muscles power body movement by converting free energy of ATP hydrolysis into mechanical work. During the landing phase of running or jumping some activated skeletal muscles are subjected to stretch. Upon stretch they absorb body energy quickly and effectively thus protecting joints and bones from impact damage. This is achieved because during lengthening, skeletal muscle bears higher force and has higher instantaneous stiffness than during isometric contraction, and yet consumes very little ATP. We wish to understand how the actomyosin molecules change their structure and interaction to implement these physiologically useful mechanical and thermodynamical properties. We monitored changes in the low angle x-ray diffraction pattern of rabbit skeletal muscle fibers during ramp stretch compared to those during isometric contraction at physiological temperature using synchrotron radiation. The intensities of the off-meridional layer lines and fine interference structure of the meridional M3 myosin x-ray reflection were resolved. Mechanical and structural data show that upon stretch the fraction of actin-bound myosin heads is higher than during isometric contraction. On the other hand, the intensities of the actin layer lines are lower than during isometric contraction. Taken together, these results suggest that during stretch, a significant fraction of actin-bound heads is bound non-stereo-specifically, i.e. they are disordered azimuthally although stiff axially. As the strong or stereo-specific myosin binding to actin is necessary for actin activation of the myosin ATPase, this finding explains the low metabolic cost of energy absorption by muscle during the landing phase of locomotion.     

Equilibrium muscle crossbridge behavior: The interaction of myosin crossbridges with actin

The interaction of myosin crossbridges with actin under equilibrium conditions is reviewed. Similarities and differences between the weakly- and strongly-binding interactions of myosin crossbridges with actin filaments are discussed. A precise, narrow definition of weakly- binding crossbridges is given. It is postulated that the fundamental interaction of crossbridges with actin is that the crossbridge heads are mobile after attachment in the first case but not in the second. It is argued that because the weakly-binding crossbridge heads are mobile after attachment, the heads appear to function independently of each other. The lack of head mobility in attached strongly-binding crossbridges makes the strongly-binding crossbridge heads appear to act cooperatively. This model of the strongly-binding crossbridge gives an explanation for two important and otherwise unexplained observations. It explains why the rate constant of force decay after a small stretch is a sigmoidal function of nucleotide analogue concentration, and why, in the presence of analogues or in rigor, the rate constant of force decay after a small stretch is often significantly slower than the rate constant for myosin subfragment-1 detachment from actin in solution. The model of the weakly-binding crossbridge accurately describes the behavior of the myosin·ATP crossbridge.     

Myosin cleft movement and its coupling to actomyosin dissociation

It has long been known that binding of actin and binding of nucleotides to myosin are antagonistic, an observation that led to the biochemical basis for the crossbridge cycle of muscle contraction. Thus ATP binding to actomyosin causes actin dissociation, whereas actin binding to the myosin accelerates ADP and phosphate release. Structural studies have indicated that communication between the actin- and nucleotide-binding sites involves the opening and closing of the cleft between the upper and lower 50K domains of the myosin head. Here we test the proposal that the cleft responds to actin and nucleotide binding in a reciprocal manner and show that cleft movement is coupled to actin binding and dissociation. We monitored cleft movement using pyrene excimer fluorescence from probes engineered across the cleft.     

Slip sliding away: load-dependence of velocity generated by skeletal muscle myosin molecules in the laser trap

Skeletal muscle's ability to shorten and lengthen against a load is a fundamental property, presumably reflecting the inherent load-dependence of the myosin molecular motor. Here we report the velocity of a single actin filament translocated by a mini-ensemble of skeletal myosin approximately 8 heads under constant loads up to 15 pN in a laser trap assay. Actin filament velocity decreased with increasing load hyberbolically, with unloaded velocity and stall force differing by a factor of 2 with [ATP] (30 vs. 100 muM). Analysis of actin filament movement revealed that forward motion was punctuated with rapid backward 60-nm slips, with the slip frequency increasing with resistive load. At stall force, myosin-generated forward movement was balanced by backward slips, whereas at loads greater than stall, myosin could no longer sustain forward motion, resulting in negative velocities as in eccentric contractions of whole muscle. Thus, the force-velocity relationship of muscle reflects both the inherent load-dependence of the actomyosin interaction and the balance between forward and reverse motion observed at the molecular level.     

Mutation of a conserved glycine in the SH1-SH2 helix affects the load-dependent kinetics of myosin

The ATP hydrolysis rate and shortening velocity of muscle are load-dependent. At the molecular level, myosin generates force and motion by coupling ATP hydrolysis to lever arm rotation. When a laser trap was used to apply load to single heads of expressed smooth muscle myosin (S1), the ADP release kinetics accelerated with an assistive load and slowed with a resistive load; however, ATP binding was mostly unaffected. To investigate how load is communicated within the motor, a glycine located at the putative fulcrum of the lever arm was mutated to valine (G709V). In the absence of load, stopped-flow and laser trap studies showed that the mutation significantly slowed the rates of ADP release and ATP binding, accounting for the ~270-fold decrease in actin sliding velocity. The load dependence of the mutant's ADP release rate was the same as that of wild-type S1 (WT) despite the slower rate. In contrast, load accelerated ATP binding by ~20-fold, irrespective of loading direction. Imparting mechanical energy to the mutant motor partially reversed the slowed ATP binding by overcoming the elevated activation energy barrier. These results imply that conformational changes near the conserved G709 are critical for the transmission of mechanochemical information between myosin's active site and lever arm.     

Myosin motor domain lever arm rotation is coupled to ATP hydrolysis

We have investigated coupling of lever arm rotation to the ATP binding and hydrolysis steps for the myosin motor domain. In several current hypotheses of the mechanism of force production by muscle, the primary mechanical feature is the rotation of a lever arm that is a subdomain of the myosin motor domain. In these models, the lever arm rotates while the myosin motor domain is free, and then reverses the rotation to produce force while it is bound to actin. These mechanical steps are coupled to steps in the ATP hydrolysis cycle. Our hypothesis is that ATP hydrolysis induces lever arm rotation to produce a more compact motor domain that has stored mechanical energy. Our approach is to use transient electric birefringence techniques to measure changes in hydrodynamic size that result from lever arm rotation when various ligands are bound to isolated skeletal muscle myosin motor domain in solution. Results for ATP and CTP, which do support force production by muscle fibers, are compared to those of ATPgammaS and GTP, which do not. Measurements are also made of conformational changes when the motor domain is bound to NDP's and PP(i) in the absence and presence of the phosphate analogue orthovanadate, to determine the roles the nucleoside moieties of the nucleotides have on lever arm rotation. The results indicate that for the substrates investigated, rotation does not occur upon substrate binding, but is coupled to the NTP hydrolysis step. The data are consistent with a model in which only substrates that produce a motor domain-NDP-P(i) complex as the steady-state intermediate make the motor domain more compact, and only those substrates support force production.     

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.     

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.