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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Hydrolysis of ATP by polymerized actin depends on the bound divalent cation but not profilin.

Growing evidence suggests that the nucleotide bound to actin filaments serves as a timer to control actin filament turnover during cell motility (Pollard, T. D., Blanchoin, L., and Mullins, R. D. (2000) Annu. Rev. Biophys. Biomol. Struct. 29, 545-576). We re-examined the hydrolysis of ATP by polymerized actin using mechanical quenched-flow methods to improve temporal resolution. The rate constant for ATP hydrolysis by polymerized Mg actin is 0.3 s(-1), 3-fold faster than that measured manually. The ATP hydrolysis rate is similar when Mg ATP actin elongates either the pointed end or the barbed end of filaments. Polymerized Ca actin hydrolyzes ATP at 0.05 s(-1). Mg ATP actin saturated with profilin can elongate barbed ends at >60 s(-1), 2 orders of magnitude faster than ATP hydrolysis (0.3 s(-1)). Given that profilin binds to a surface on actin that is buried in the Holmes model of the actin filament, we expect that profilin will block subunit addition at the barbed end of a filament. Profilin must move from this site at rates much faster than it dissociates from monomers (4 s(-1)). ATP hydrolysis is not required for this movement.     

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.     

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.     

Quantitative analysis of extension-torsion coupling of actin filaments

Actin filaments have a double-helix structure consisting of globular actin molecules. In many mechanical cellular activities, such as cell movement, division, and shape control, modulation of the extensional and torsional dynamics of the filament has been linked to regulatory actin-binding protein functions. Therefore, it is important to quantitatively evaluate extension-torsion coupling of filament to better understand the actin filament dynamics. In the present study, the extension-torsion coupling was investigated using molecular dynamics simulations. We constructed a model for the actin filament consisting of 14 actin subunits in an ionic solvent as a minimal functional unit, and analyzed longitudinal and twisting Brownian motions of the filament. We then derived the expected value of energy associated with extension and torsion at equilibrium, and evaluated the extension-torsion stiffness of the filament from the thermal fluctuations obtained from the MD simulations. The results demonstrated that as the analyzed sampling-window duration was increased, the extension-torsion coupling stiffness evaluated on a nanosecond scale tended to converge to a value of 7.6×10(-11) N. The results obtained from this study will contribute to the understanding of biomechanical events, under mechanical tension and torque, involving extension-torsion coupling of filaments.     

Molecular dynamics simulation of a myosin subfragment-1 docking with an actin filament

Myosins are typical molecular motor proteins, which convert the chemical energy of ATP into mechanical work. The fundamental mechanism of this energy conversion is still unknown. To explain the experimental results observed in molecular motors, Masuda has proposed a theory called the “Driven by Detachment (DbD)” mechanism for the working principle of myosins. Based on this theory, the energy used during the power stroke of the myosins originates from the attractive force between a detached myosin head and an actin filament, and does not directly arise from the energy of ATP. According to this theory, every step in the myosin working process may be reproduced by molecular dynamics (MD) simulations, except for the ATP hydrolysis step. Therefore, MD simulations were conducted to reproduce the docking process of a myosin subfragment-1 (S1) against an actin filament. A myosin S1 directed toward the barbed end of an actin filament was placed at three different positions by shifting it away from the filament axis. After 30 ns of MD simulations, in three cases out of ten trials on average, the myosin made a close contact with two actin monomers by changing the positions and the orientation of both the myosin and the actin as predicted in previous studies. Once the docking was achieved, the distance between the myosin and the actin showed smaller fluctuations, indicating that the docking is stable over time. If the docking was not achieved, the myosin moved randomly around the initial position or moved away from the actin filament. MD simulations thus successfully reproduced the docking of a myosin S1 with an actin filament. By extending the similar MD simulations to the other steps of the myosin working process, the validity of the DbD theory may be computationally demonstrated.     

Polymerization of ADP-actin and ATP-actin under sonication and characteristics of the ATP-actin equilibrium polymer

Polymerization under sonication has been developed as a new method to study the rapid polymerization of actin with a large number of elongating sites. The theory proposed assumes that filaments under sonication are maintained at a constant length by the constant input of energy. The data obtained for the reversible polymerization of ADP-actin under sonication have been successfully analyzed according to the proposed model and, therefore, validate the model. The results obtained for the polymerization of ATP-actin under sonication demonstrate the involvement of ATP hydrolysis in the polymerization process. At high actin concentration, polymerization was fast enough, as compared to ATP hydrolysis on the F-actin, to obtain completion of the reversible polymerization of ATP-actin before significant hydrolysis of ATP occurred. A critical concentration of 3 microM was determined as the ratio of the dissociation and association rate constants for the interaction of ATP-actin with the ATP filament ends in 1 mM MgCl2, 0.2 mM ATP. The plot of the rate of elongation of filaments versus actin monomer concentration exhibited an upward deviation at high actin concentration that is consistent with this result. The fact that F-actin at steady state is more stable than the ATP-F-actin polymer at equilibrium suggests that the interaction between ADP-actin and ATP-actin subunits at the end of the ATP-capped filament is much stronger than the interaction between two ATP-actin subunits.     

Cofilin tunes the nucleotide state of actin filaments and severs at bare and decorated segment boundaries

Actin-based motility demands the spatial and temporal coordination of numerous regulatory actin-binding proteins (ABPs), many of which bind with affinities that depend on the nucleotide state of actin filament. Cofilin, one of three ABPs that precisely choreograph actin assembly and organization into comet tails that drive motility in vitro, binds and stochastically severs aged ADP actin filament segments of de novo growing actin filaments. Deficiencies in methodologies to track in real time the nucleotide state of actin filaments, as well as cofilin severing, limit the molecular understanding of coupling between actin filament chemical and mechanical states and severing. We engineered a fluorescently labeled cofilin that retains actin filament binding and severing activities. Because cofilin binding depends strongly on the actin-bound nucleotide, direct visualization of fluorescent cofilin binding serves as a marker of the actin filament nucleotide state during assembly. Bound cofilin allosterically accelerates P(i) release from unoccupied filament subunits, which shortens the filament ATP/ADP-P(i) cap length by nearly an order of magnitude. Real-time visualization of filament severing indicates that fragmentation scales with and occurs preferentially at boundaries between bare and cofilin-decorated filament segments, thereby controlling the overall filament length, depending on cofilin binding density.     

Actin binding proteins that change extent and rate of actin monomer-polymer distribution by different mechanisms

Actin binding proteins control actin assembly and disassembly by altering the critical concentration and by changing the kinetics of polymerization. All of these control mechanisms in some way or the other make use of the energy of hydrolysis of actin-bound ATP. Capping of barbed filament ends increases the critical concentration as long as ATP hydrolysis maintains a difference in the actin monomer binding constants of the two ends. A further increase in the critical concentration on adding a second cap, tropomodulin, to the other, pointed filament end also requires ATP hydrolysis as described by the model presented here. Changes in the critical concentration are amplified into much larger changes of the monomer pool by actin sequestering proteins, provided their actin binding equilibrium constants fall within a relatively narrow range around the values for the two critical concentrations of actin. Cofilin greatly speeds up treadmilling, which requires ATP hydroysis, by increasing the rate constant of depolymerization. Profilin increases the rate of elongation at the barbed filament end, coupled to a lowering of the critical concentration, only if ATP hydrolysis makes profilin binding to the barbed end independent of its binding constant for actin monomers.     

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.     

The assembly of MreB, a prokaryotic homolog of actin

MreB, a major component of the bacterial cytoskeleton, exhibits high structural homology to its eukaryotic counterpart actin. Live cell microscopy studies suggest that MreB molecules organize into large filamentous spirals that support the cell membrane and play a key shape-determining function. However, the basic properties of MreB filament assembly remain unknown. Here, we studied the assembly of Thermotoga maritima MreB triggered by ATP in vitro and compared it to the well-studied assembly of actin. These studies show that MreB filament ultrastructure and polymerization depend crucially on temperature as well as the ions present on solution. At the optimal growth temperature of T. maritima, MreB assembly proceeded much faster than that of actin, without nucleation (or nucleation is highly favorable and fast) and with little or no contribution from filament end-to-end annealing. MreB exhibited rates of ATP hydrolysis and phosphate release similar to that of F-actin, however, with a critical concentration of approximately 3 nm, which is approximately 100-fold lower than that of actin. Furthermore, MreB assembled into filamentous bundles that have the ability to spontaneously form ring-like structures without auxiliary proteins. These findings suggest that despite high structural homology, MreB and actin display significantly different assembly properties.     

Calcium regulation of thin filament movement in an in vitro motility assay.

The ability of calcium to regulate thin filament sliding velocity was studied in an in vitro motility assay system using cardiac troponin and tropomyosin and rhodamine-phalloidin-labeled skeletal actin and skeletal heavy meromyosin to propel the filaments. Measurements showed that both the number of thin filaments sliding and their sliding speed (Sf) were dependent on the calcium concentration in the range of pCa 5 to 9. Thin filament motility was completely inhibited only if troponin and tropomyosin were added at a concentration of 100 nM to the motility assay solution and the pCa was more than 8. The filament sliding speed was dependent on the pCa in a noncooperative fashion (Hill coefficient = 1) and reached maximum at 5 microns/s at a pCa of 5. The number of filaments moving uniformly decreased from > 90% at pCa 5-6 to near zero in less than 1 pCa unit. This behavior may be explained by a hypothesis in which the regulatory proteins control the number of cross-bridge heads interacting with the thin filaments rather than the rate at which they individually hydrolyze ATP or translocate the thin filaments.