Up-and-down movement of a sliding actin filament in the in vitro motility assay

We observed a three-dimensional up-and-down movement of an actin filament sliding on heavy mero-myosin (HMM) molecules in an in vitro motility assay. The up-and-down movement occurred along the direction perpendicular to the planar glass plane on which the filament demonstrated a sliding movement. The height length of the up-and-down movement was measured by monitoring the extent of diminishing fluorescent emission from the marker attached to the filament in the evanescent field of attenuation. The height lengths whose distribution exhibits a local maximum were found around the two values, 150 nm and 90 nm, separately. This undulating three-dimensional movement of an actin filament suggests that the interactions between myosin (HMM) molecules and the actin filament may temporally be modulated during its sliding movement.     

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.     

Unidirectional movement of an actin filament taking advantage of temperature gradients

An actin filament with heat acceptors attached to its Cys374 residue in each actin monomer could move unidirectionally even under heat pulsation alone, while in the total absence of both ATP and myosin. The prime driver for the movement was temperature gradients operating between locally heated portions on an actin filament and its cooler surroundings. In this report, we investigated how the mitigation of the temperature gradients induces a unidirectional movement of an actin filament. We then observed the transversal fluctuations of the filament in response to heat pulsation and their transition into longitudinally unidirectional movement. The transition was significantly accelerated when Cys374 and Lys336 were simultaneously excited within an actin monomer. These results suggest that the mitigation of the temperature gradients within each actin monomer first went through the energy transformation to transversal fluctuations of the filament, and then followed by the transformation further down to longitudinal movements of the filament. The faster mitigation of temperature gradients within actin monomer helps build up the transition from the transversal to longitudinal movements of the filament by coordinating the interaction between the neighboring monomers.     

Onset of the sliding movement of an actin filament on myosin molecules: from isotropic to anisotropic fluctuations

An actin filament contacting myosin molecules increased the fluctuation intensity of the filamental displacement as the ATP concentration increased. In particular, fluctuations in the filamental displacement in the planar plane in which the sliding movement takes place were isotropic at a low ATP concentration, and became anisotropic as the concentration increased. The build-up of the sliding movement of an actin filament was associated with the transformation from isotropic to anisotropic fluctuations of the filamental displacement.     

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.     

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.     

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.     

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 Motors Drive Long Range Alignment of Actin Filaments

The bulk alignment of actin filament sliding movement, powered by randomly oriented myosin molecules, has been observed and studied using an in vitro motility assay. The well established, actin filament gliding assay is a minimal experimental system for studying actomyosin motility. Here, we show that when the assay is performed at densities of actin filaments approaching those found in living cells, filament gliding takes up a preferred orientation. The oriented patterns of movement that we have observed extend over a length scale of 10–100 μm, similar to the size of a mammalian cell. We studied the process of filament alignment and found that it depends critically upon filament length and density. We developed a simple quantitative measure of filament sliding orientation and this enabled us to follow the time course of alignment and the formation and disappearance of oriented domains. Domains of oriented filaments formed spontaneously and were separated by distinct boundaries. The pattern of the domain structures changed on the time scale of several seconds and the collision of neighboring domains led to emergence of new patterns. Our results indicate that actin filament crowding may play an important role in structuring the leading edge of migrating cells. Filament alignment due to near-neighbor mechanical interactions can propagate over a length scale of several microns; much greater than the size of individual filaments and analogous to a log drive. Self-alignment of actin filaments may make an important contribution to cell polarity and provide a mechanism by which cell migration direction responds to chemical cues.     

Longitudinal Distortions and Transversal Fluctuations of an Actin Filament Sliding on Myosin Molecules

An actin filament sliding on myosin moleculesdemonstrates both longitudinal distortions and transversal fluctuationswith the linear dimension far exceeding the diameter of an actinmonomer. Local swaying of a single actin filament was identified byreading speckled fluorescent markers attached on the filament. Theaccuracy of reading each speckled marker was about 10.4 nm (r.m.s.).Longitudinal distortions of an actin filament at a low ATP concentrationof 20 M were as much as 0.5 m for the average filament lengthof 5.4 m. The magnitude of transversal fluctuations was as much as60 nm, that was independent of the filament length. Both longitudinaldistortions and transversal fluctuations are suggested to play a pivotalrole for facilitating a smooth sliding movement of an actin filament.     

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.     

Crossbridge and tropomyosin positions observed in native, interacting thick and thin filaments

Tropomyosin movements on thin filaments are thought to sterically regulate muscle contraction, but have not been visualized during active filament sliding. In addition, although 3-D visualization of myosin crossbridges has been possible in rigor, it has been difficult for thick filaments actively interacting with thin filaments. In the current study, using three-dimensional reconstruction of electron micrographs of interacting filaments, we have been able to resolve not only tropomyosin, but also the docking sites for weak and strongly bound crossbridges on thin filaments. In relaxing conditions, tropomyosin was observed on the outer domain of actin, and thin filament interactions with thick filaments were rare. In contracting conditions, tropomyosin had moved to the inner domain of actin, and extra density, reflecting weakly bound, cycling myosin heads, was also detected, on the extreme periphery of actin. In rigor conditions, tropomyosin had moved further on to the inner domain of actin, and strongly bound myosin heads were now observed over the junction of the inner and outer domains. We conclude (1) that tropomyosin movements consistent with the steric model of muscle contraction occur in interacting thick and thin filaments, (2) that myosin-induced movement of tropomyosin in activated filaments requires strongly bound crossbridges, and (3) that crossbridges are bound to the periphery of actin, at a site distinct from the strong myosin binding site, at an early stage of the crossbridge cycle.     

Super helix formation of actin filaments in an in vitro motile system.

Muscle contraction results from relative sliding of actin and myosin filaments. However, the possibility that actin filaments twist or rotate during sliding has not yet been experimentally investigated. We found that a super helix of an actin filament is formed in an in vitro motile system. This fact suggests that an actin filament twists and rotates due to a torque component of a sliding force generated at cross-bridges.     

Direct inhibition of the actomyosin motility by local anesthetics in vitro.

Using a recently developed in vitro motility assay, we have demonstrated that local anesthetics directly inhibit myosin-based movement of single actin filaments in a reversible dose-dependent manner. This is the first reported account of the actions of local anesthetics on purified proteins at the molecular level. In this study, two tertiary amine local anesthetics, lidocaine and tetracaine, were used. The inhibitory action of the local anesthetics on actomyosin sliding movement was pH dependent; the anesthetics were more potent at higher pH values, and this reaction was accompanied by an increased proportion of the uncharged form of the anesthetics. QX-314, a permanently charged derivative of lidocaine, had no effect on actomyosin sliding movement. These results indicate that the uncharged form of local anesthetics is predominantly responsible for the inhibition of actomyosin sliding movement. The local anesthetics inhibited sliding movement but hardly interfered with the binding of actin filaments to myosin on the surface or with actomyosin ATPase activity at low ionic strength. To characterize the actomyosin interaction in the presence of anesthetics, we measured the binding and breaking force of the actomyosin complex. The binding of actin filaments to myosin on the surface was not affected by lidocaine at low ionic strength. The breaking force, measured using optical tweezers, was approximately 1.5 pN per micron of an actin filament, which was much smaller than in rigor and isometric force. The binding and breaking force greatly decreased with increasing ionic strength, indicating that the remaining interaction is ionic in nature. The result suggests that the binding and ATPase of actomyosin are governed predominantly by ionic interaction, which is hardly affected by anesthetics; whereas the force generation requires hydrophobic interaction, which plays a major part of the strong binding and is blocked by anesthetics, in addition to the ionic interaction.     

Slowly modulating fluctuations as mesoscopic distortions occurring on an actin filament

An actin filament sliding on myosin molecules exhibits fluctuating or staggered movements as responding to changes in the ATP concentration. We previously observed that fluctuations in the sliding velocity enhanced in a manner being independent of the magnitude of the velocity. The present study focused upon a single actin filament bound to a glass surface through avidin–biotin bonding to examine those fluctuations inherent to the filament in the presence of heavy meromyosin. The auto-correlation analysis revealed that the relaxation time of fluctuations in the filamental displacement obtains its maximum value at about 100 μM of the ATP concentration in the ambient, while the magnitude of the fluctuations gradually increased with an increase of the concentration. Furthermore, the measurement of the fluorescence intensity from the markers fixed on the filament demonstrated an enhancement of the negative correlation between the measured peak intensity and the spatial spreading of its intensity over the range of 0–200 μM of the ATP concentration, as indicating both development and mitigation of local distortions occurring within the filament.     

Velocity of myosin-based actin sliding depends on attachment and detachment kinetics and reaches a maximum when myosin-binding sites on actin saturate

Molecular motors such as kinesin and myosin often work in groups to generate the directed movements and forces critical for many biological processes. Although much is known about how individual motors generate force and movement, surprisingly, little is known about the mechanisms underlying the macroscopic mechanics generated by multiple motors. For example, the observation that a saturating number, N, of myosin heads move an actin filament at a rate that is influenced by actin–myosin attachment and detachment kinetics is accounted for neither experimentally nor theoretically. To better understand the emergent mechanics of actin–myosin mechanochemistry, we use an in vitro motility assay to measure and correlate the N-dependence of actin sliding velocities, actin-activated ATPase activity, force generation against a mechanical load, and the calcium sensitivity of thin filament velocities. Our results show that both velocity and ATPase activity are strain dependent and that velocity becomes maximized with the saturation of myosin-binding sites on actin at a value that is 40% dependent on attachment kinetics and 60% dependent on detachment kinetics. These results support a chemical thermodynamic model for ensemble motor mechanochemistry and imply molecularly explicit mechanisms within this framework, challenging the assumption of independent force generation.     

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.     

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.     

Inhibition of the relative movement of actin and myosin by caldesmon and calponin.

Contractile activity of myosin II in smooth muscle and non-muscle cells requires phosphorylation of myosin by myosin light chain kinase. In addition, these cells have the potential for regulation at the thin filament level by caldesmon and calponin, both of which bind calmodulin. We have investigated this regulation using in vitro motility assays. Caldesmon completely inhibited the movement of actin filaments by either phosphorylated smooth muscle myosin or rabbit skeletal muscle heavy meromyosin. The amount of caldesmon required for inhibition was decreased when tropomyosin is present. Similarly, calponin binding to actin resulted in inhibition of actin filament movement by both smooth muscle myosin and skeletal muscle heavy meromyosin. Tropomyosin had no effect on the amount of calponin needed for inhibition. High concentrations of calmodulin (10 microM) in the presence of calcium completely reversed the inhibition. The nature of the inhibition by the two proteins was markedly different. Increasing caldesmon concentrations resulted in graded inhibition of the movement of actin filaments until complete inhibition of movement was obtained. Calponin inhibited actin sliding in a more "all or none" fashion. As the calponin concentration was increased the number of actin filaments moving was markedly decreased, but the velocity of movement remained near control values.     

Movement of the actin filament bundle in Mytilus sperm: a new mechanism is proposed

An actin filament bundle approximately 2-5 microns in length is present in the sperm of the blue mussel, Mytilus. In unfired sperm this bundle extends from the midpiece through a canal in the center of the nucleus to terminate on the membrane limiting the inside of the cone-shaped acrosomal vacuole. The bundle is composed of 45-65 actin filaments which are hexagonally packed and regularly cross-bridged together to form an actin paracrystal so well ordered that it has six nearly equal faces. Upon induction of the acrosomal reaction, a needle-like process is formed in a few seconds. Within this process is the actin filament bundle which appears unchanged in filament number and packing as determined by optical diffraction methods. Using fluorescein-conjugated phalloidin we were able to establish that the bundle does not change length but instead is projected anteriorly out of the midpiece and nuclear canal like an arrow. Existing mechanisms to explain this extension cannot apply. Specifically, the bundle does not increase in length (no polymerization), does not change its organization (no change in actin twist), does not change filament number (no filament sliding), and cannot move by myosin (wrong polarity). Thus we are forced to look elsewhere for a mechanism and have postulated that at least a component of this movement, or cell elongation, is the interaction of the actin filament bundle with the plasma membrane.