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.     

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.     

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.     

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.     

Staggered movement of an actin filament sliding on myosin molecules in the presence of ATP

An actin filament sliding on myosin molecules in the presence of an extremely low concentration of ATP exhibited a staggered movement. Longitudinally sliding movement of the filament was frequently interrupted by its non-sliding, fluctuating movements both in the longitudinal and transversal directions. Intermittent sliding movements of an actin filament indicate establishment of a coordination of ATP-mediated active sites distributed along the filament.     

Communicative interaction of myosins along an actin filament in the presence of ATP

Myosin molecules contacting an actin filament in the presence of ATP were found to regulate the filamental fluctuations due to ATP hydrolysis in a communicative manner along the filament. As an evidence of the occurrence of the communication, ATP-activated fluctuating displacements of the filament in the direction perpendicular to its longitudinal axis were identified to propagate at a finite velocity not less than about 0.2 μm/s unidirectionally along the filament.     

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.     

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.     

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.     

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.     

Molecular and Subcellular-Scale Modeling of Nucleotide Diffusion in the Cardiac Myofilament Lattice

Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions.     

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.     

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.     

Molecular and Subcellular-Scale Modeling of Nucleotide Diffusion in the Cardiac Myofilament Lattice

Contractile function of cardiac cells is driven by the sliding displacement of myofilaments powered by the cycling myosin crossbridges. Critical to this process is the availability of ATP, which myosin hydrolyzes during the cross-bridge cycle. The diffusion of adenine nucleotides through the myofilament lattice has been shown to be anisotropic, with slower radial diffusion perpendicular to the filament axis relative to parallel, and is attributed to the periodic hexagonal arrangement of the thin (actin) and thick (myosin) filaments. We investigated whether atomistic-resolution details of myofilament proteins can refine coarse-grain estimates of diffusional anisotropy for adenine nucleotides in the cardiac myofibril, using homogenization theory and atomistic thin filament models from the Protein Data Bank. Our results demonstrate considerable anisotropy in ATP and ADP diffusion constants that is consistent with experimental measurements and dependent on lattice spacing and myofilament overlap. A reaction-diffusion model of the half-sarcomere further suggests that diffusional anisotropy may lead to modest adenine nucleotide gradients in the myoplasm under physiological conditions.     

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.     

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.     

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.     

Quantitation of liquid-crystalline ordering in F-actin solutions.

Actin filaments (F-actin) are important determinants of cellular shape and motility. These functions depend on the collective organization of numerous filaments with respect to both position and orientation in the cytoplasm. Much of the orientational organization arises spontaneously through liquid crystal formation in concentrated F-actin solutions. In studying this phenomenon, we found that solutions of purified F-actin undergo a continuous phase transition, from the isotropic state to a liquid crystalline state, when either the mean filament length or the actin concentration is increased above its respective threshold value. The phase diagram representing the threshold filament lengths and concentrations at which the phase transition occurs is consistent with that predicted by Flory's theory on solutions of noninteracting, rigid cylinders (Flory, 1956b). However, in contrast to other predictions based on this model, we found no evidence for the coexistence of isotropic and anisotropic phases. Furthermore, the phase transition proved to be temperature dependent, which suggests the existence of orientation-dependent interfilament interactions or of a temperature-dependent filament flexibility. We developed a simple method for growing undistorted fluorescent acrylodan-labeled F-actin liquid crystals; and we derived a simple theoretical treatment by which polarization-of-fluorescence measurements could be used to quantitate, for the first time, the degree of spontaneous filament ordering (nematic order parameter) in these F-actin liquid crystals. This order parameter was found to increase monotonically with both filament length and concentration. Actin liquid crystals can readily become distorted by a process known as "texturing." Zigzaging and helicoidal liquid crystalline textures which persisted in the absence of ATP were observed through the polarizing microscope. Possible texturing mechanisms are discussed.     

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.     

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.