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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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 as an entangled quantum coherence.

Cell motility underlying muscle contraction is imputed to a macroscopic quantum mechanical coherence actualized locally in the body of a biological organism. Actin-activated myosin ATPase activity functions as a heat sink operating effectively at an extremely low temperature. Extraction of heat energy from the actin filament can help condensing the atomic degrees of freedom constituting the filament into a macroscopic quantum state carrying a nonvanishing linear momentum. Sliding movement of an actin filament on myosin molecules while hydrolyzing ATP molecules is a consequence of the quantum mechanical coherence due to an extremely slow release of energy stored in an ATP molecule.     

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.     

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.     

The internalist enterprise on constructing cell motility in a bottom-up manner.

Quantum coherence in the biological realm is constructed internally in a bottom-up manner. In particular, an actin filament sliding on myosin molecules in the presence of ATP to be hydrolyzed as a functional unit of muscle contraction exhibits magnetization as a marker of quantum coherence. The uniqueness of quantum coherence in biology is found in precipitating synchronous time in interaction from the interacting energy quanta, each of which has carried with itself synchronous time unique to the quantum in isolation. It exhibits a marked contrast to quantum coherence met in low temperature physics, in the latter of which no transformation of the nature of synchronous time is entertained.     

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.     

A deterministic mechanism producing the loose coupling phenomenon observed in an actomyosin system

Myosins are molecular motors that convert the chemical energy of ATP into mechanical work called a power stroke. Class II myosin engaged in muscle contraction is reported to show a "loose coupling phenomenon", in which the number of power strokes is greater than the number of ATP hydrolyses. This phenomenon cannot be explained by the lever-arm hypothesis, which is currently accepted as a standard theory for myosin motility. In this paper, a model is proposed to reproduce the loose coupling phenomenon. The model is based on a mechanochemical process called "Driven by Detachment (DbD)" mechanism, which assumes that the energy of the power strokes originates from the potential energy generated by the attractive force between myosin and actin. During the docking process, the potential energy is converted into an intramolecular strain in a myosin molecule, which drives the power stroke after the myosin is firmly attached to an actin filament. The energy of ATP is used to temporarily reduce the attractive force and to increase the potential energy. Therefore, it is not directly linked to the power strokes. When myosin molecules work as an aggregate, the sliding movement of a myosin filament driven by the power strokes of some myosin heads makes other myosin heads that have completed their power strokes detach from the actin without consuming ATP. Under the DbD mechanism, these passively detached myosins can be again engaged in power strokes after the next attachment to actin. As a result, the number of power strokes becomes greater than the number of ATP hydrolyses, and the loose coupling phenomenon will be observed. A theoretical analysis indicates that the efficiency of converting the potential energy into intramolecular elastic energy determines the number of power strokes per each ATP hydrolysis. Computer simulations showed that the DbD mechanism actually produced the loose coupling phenomenon. A critical requirement for this mechanism is that ATP must preferentially facilitate the detachment of myosins that have completed their power strokes, but are still strongly attached to the actin. This requirement may be fulfilled by ATP hydrolysis tightly depending on the conformation of a myosin molecule.     

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.     

Tropomyosin as a regulator of the sliding movement of actin filaments

We examined the capacity of tropomyosin molecules regulating the sliding movement of actin filaments on myosin molecules in the presence of ATP molecules to be hydrolyzed. For this objective, we prepared tropomyosin molecules modified to be a little bit stiffer compared to the intact ones by applying a fixed cross-linker between a pair of twisted tropomyosin monomers. The cross-linked tropomyosin molecules, when complexed with actin filaments, were found to inhibit the sliding movement of the filaments on myosin molecules even in the absence of calcium-regulated troponin molecules. It is then suggested that the mechanical flexibility of tropomyosin molecules may be instrumental to actualizing the proper functional regulation of the sliding movement of actin filaments.     

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.     

Troponin is a potential regulator for actomyosin interactions

Troponin extracted from rabbit skeletal muscle directly binds to an actin filament in a molar ratio of 1:1 even in the absence of tropomyosin. An actin filament decorated with troponin did not exhibit significant difference from pure actin filaments in the maximum rate of actomyosin ATP hydrolysis and the sliding velocity of the filament examined by means of an in vitro motility assay. However, the relative number of troponin-bound actin filaments moving in the absence of calcium ions decreased to half that in their presence. The amount of HMM bound to the filaments was less than 4% of actin monomers in the presence of TNs. In addition, actin filaments could not move when Tn molecules were bound in the molar ratio of about 1:1 although they sufficiently bind to myosin heads. These results indicate that troponin can transform an actin monomer within a filament into an Off-state without sterically blocking of the myosin-binding sites with tropomyosin molecules.     

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.