Myosin head mechanical performance under different conformational change mechanisms

The present paper puts forward a mathematical approach to model the conformational changes of the myosin head due to ATP hydrolysis, which determine the head swinging and consequent sliding of the actin filament. Our aim is to provide a simple but effective model simulating myosin head performance to be integrated into the overall model of sarcomere mechanics under development at our Laboratory (J. Biomech. 34 (2001) 1607). We began by exploring myosin head mechanics in recent findings about myosin ultrastructure, morphology and energetics in order to calculate the working stroke distance (WS) and the force transmitted to the actin filament during muscle contraction. Two different working stroke mechanisms were investigated, assuming that the swinging of the myosin head occurs either as a consequence of purely conformational changes (Science 261 (1993a) 58) or by thermally driven motion (ratchet mechanism) followed by conformational changes (Cell 99 (1999) 421). Our results show that force and WS values vary markedly between the two models. The maximum force generated is about 10 pN for the first model and 31 pN for the second model, and the WSs are about 13 and 4 nm, respectively. These results are then discussed and compared with published data. The experimental data used for comparison are scarce and non-homogeneous; hence, the final remarks do not lead to definite conclusions. In any event, relatively speaking, the first model is more coherent with experimental findings.     

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 possible mechanism for determining the directionality of myosin molecular motors

There is a large superfamily of myosins, which play various fundamental roles in cellular motility. In this superfamily, most of myosins, including myosins II and V, move to the barbed end of an actin filament, whereas myosin VI was found to move in the opposite direction to the pointed end. Although myosin VI has structural differences compared with the other myosins, the mechanism for the reversal of the directionality has not been satisfactorily explained by conventional theories for myosin motility, including the widely accepted lever-arm hypothesis. In this paper, a simple mechanism for determining the directionality is proposed. The mechanism assumes that the driving force for the power stroke is caused by elastic energy stored within a myosin molecule at the joint between the head and the neck. The elastic energy originates from the attractive force between myosin and actin, and accumulates during the docking process. The energy of ATP is used to reduce the attractive force between myosin and actin and to facilitate the dissociation of these molecules. Therefore, it is not directly engaged in the power stroke. With this mechanism, the directionality of the myosin motility is simply determined by the direction of the neck with respect to the head in the dissociated configuration. This structural difference is actually observed in myosin VI. The same mechanism also explains the behavior of a backward moving engineered myosin. Computer simulations demonstrated the feasibility of this working mechanism.     

Muscle contraction: a mechanism of energy transduction

A mechanism of muscle contraction is presented in which energy from the hydrolysis of MgATP is transferred directly to conformational strain in a flexible segment of the myosin head. That segment is proximal to both the active site and the subfragment 1—subfragment 2 hinge (the portion of the myosin molecule that connects each of its two enzymatically active globular heads to the long thin helical body). This proximity allows configurational changes at the active site, which are an intrinsic part of the enzymatic mechanism, to impose a localized strain, or distortion, near the hinge. The energy, trapped in the protein this way, is subsequently used for mechanical work when other enzymatically-induced conformational changes free the strained segment of the myosin head to unbend. As this happens, the head rotates and the distal end (opposite the hinge) attaches to the actin filament and pulls on it. In this mechanism, actin interacts with myosin in two different ways: (1) at the active site where it activates a step in the hydrolysis of MgATP that frees the head to rotate; (2) at the distal end of myosin, where it forms the grip through which the rotating head pulls on the actin filament. The first interaction allows actin to initiate primary movement of the myosin head; the second directs the force and allows the movement of the head to be used for the sliding motion of the actin and myosin filaments during contraction. In this model, there are also two different energy transfers: one occurs in the transduction process itself when energy from hydrolysis is trapped as conformational distortion in the hinge region; the other occurs, reversibly, when actin and myosin form and then break the distal grip; in this second transfer there is no net energy change in the course of a cycle. A chemical mechanism is suggested to explain actin-activation of hydrolysis at the active site-hinge region.     

A monomeric myosin VI with a large working stroke

Myosin VI is involved in a wide variety of intracellular processes such as endocytosis, secretion and cell migration. Unlike almost all other myosins so far studied, it moves towards the minus end of actin filaments and is therefore likely to have unique cellular properties. However, its mechanism of force production and movement is not understood. Under our experimental conditions, both expressed full-length and native myosin VI are monomeric. Electron microscopy using negative staining revealed that the addition of ATP induces a large conformational change in the neck/tail region of the expressed molecule. Using an optical tweezers-based force transducer we found that expressed myosin VI is nonprocessive and produces a large working stroke of 18 nm. Since the neck region of myosin VI is short (it contains only a single IQ motif), it is difficult to reconcile the 18 nm working stroke with the classical 'lever arm mechanism', unless other structures in the molecule contribute to the effective lever. A possible model to explain the large working stroke of myosin VI is presented.     

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.     

Forces measured with micro-fabricated cantilevers during actomyosin interactions produced by filaments containing different myosin isoforms and loop 1 structures

Background

There is evidence that the actin-activated ATP kinetics and the mechanical work produced by muscle myosin molecules are regulated by two surface loops, located near the ATP binding pocket (loop 1), and in a region that interfaces with actin (loop 2). These loops regulate force and velocity of contraction, and have been investigated mostly in single molecules. There is a lack of information of the work produced by myosin molecules ordered in filaments and working cooperatively, which is the actual muscle environment.

Methods

We use micro-fabricated cantilevers to measure forces produced by myosin filaments isolated from mollusk muscles, skeletal muscles, and smooth muscles containing variations in the structure of loop 1 (tonic and phasic myosins). We complemented the experiments with in-vitro assays to measure the velocity of actin motility.

Results

Smooth muscle myosin filaments produced more force than skeletal and mollusk myosin filaments when normalized per filament overlap. Skeletal muscle myosin propelled actin filaments in a higher sliding velocity than smooth muscle myosin. The values for force and velocity were consistent with previous studies using myosin molecules, and suggest a close correlation with the myosin isoform and structure of surface loop 1.

General significance

The technique using micro-fabricated cantilevers to measure force of filaments allows for the investigation of the relation between myosin structure and contractility, allowing experiments to be conducted with an array of different myosin isoforms. Using the technique we observed that the work produced by myosin molecules is regulated by amino-acid sequences aligned in specific loops.     

Electric dipole theory and thermodynamics of actomyosin molecular motor in muscle contraction

Movements in muscles are generated by the myosins which interact with the actin filaments. In this paper we present an electric theory to describe how the chemical energy is first stored in electrostatic form in the myosin system and how it is then released and transformed into work. Due to the longitudinal polarized molecular structure with the negative phosphate group tail, the ATP molecule possesses a large electric dipole moment (p(0)), which makes it an ideal energy source for the electric dipole motor of the actomyosin system. The myosin head contains a large number of strongly restrained water molecules, which makes the ATP-driven electric dipole motor possible. The strongly restrained water molecules can store the chemical energy released by ATP binding and hydrolysis processes in the electric form due to their myosin structure fixed electric dipole moments (p(i)). The decrease in the electric energy is transformed into mechanical work by the rotational movement of the myosin head, which follows from the interaction of the dipoles p(i) with the potential field V(0) of ATP and with the potential field Psi of the actin. The electrical meaning of the hydrolysis reaction is to reduce the dipole moment p(0)-the remaining dipole moment of the adenosine diphosphate (ADP) is appropriately smaller to return the low negative value of the electric energy nearly back to its initial value, enabling the removal of ADP from the myosin head so that the cycling process can be repeated. We derive for the electric energy of the myosin system a general equation, which contains the potential field V(0) with the dipole moment p(0), the dipole moments p(i) and the potential field psi. Using the previously published experimental data for the electric dipole of ATP (p(0) congruent with 230 debye) and for the amount of strongly restrained water molecules (N congruent with 720) in the myosin subfragment (S1), we show that the Gibbs free energy changes of the ATP binding and hydrolysis reaction steps can be converted into the form of electric energy. The mechanical action between myosin and actin is investigated by the principle of virtual work. An electric torque always appears, i.e. a moment of electric forces between dipoles p(0) and p(i)(/M/ > or = 16 pN nm) that causes the myosin head to function like a scissors-shaped electric dipole motor. The theory as a whole is illustrated by several numerical examples and the results are compared with experimental results.     

Force generation, work, and coupling in molecular motors.

A mechanism is proposed for molecular motors in which force is generated by a protein conformational change driven by binding energy (in muscle, that of myosin with actin as well as with ATP, ADP, or Pi). Work, the product of the force generated by one myosin or kinesin molecule (F) and the distance over which it acts (d), is a function of a ratio of dissociation constants before and after the contractile step: F.d < RT ln(KAe/KAc). From published data the ratio is > 2 x 10(4), which can be explained by conversion of a surface complex to an enclosed, or partly enclosed, complex. Although the complex performing the work stroke is in unstrained conformation, the complex after the work stroke is much more stable, owing to binding forces; the latter, however, is destabilized by the load, which thereby opposes the contractile conformational change, countering the force-generating reaction. The connection between the free energy release and work is implicit in the mechanism, inasmuch as coupling, like force generation, depends on conformational changes driven by binding energy (internal rather than external work being involved in coupling). The principles apply whether ATP or an ion gradient drives the system. At high load, in muscle, the mechanism allows for a summation of the forces generated by several myosin molecules.     

A simulation model of the conventional kinesin based on the Driven-by-Detachment mechanism

Kinesins are molecular motors that unidirectionally move along microtubules using the chemical energy of ATP. Although the core structure of kinesins is similar to that of myosins, the lever-arm hypothesis, which is widely accepted as a plausible mechanism to explain the behaviors of myosins, cannot be directly applied to kinesins. Masuda has proposed a mechanochemical process called the ‘Driven-by-Detachment (DbD)’ mechanism to explain the characteristic behaviors of myosins, including the backward movement of myosin VI and the loose coupling phenomenon of myosin II. The DbD mechanism assumes that the energy of ATP is mainly used to detach a myosin head from an actin filament by temporarily reducing the affinity of the myosin against the actin. After the affinity is recovered, the detached head has potential energy originating from the attractive force between the myosin and the actin. During the docking process, the potential energy is converted into elastic energy within the myosin molecule, and the intramolecular elastic energy is finally used to produce the power strokes. In the present paper, the DbD mechanism was used to explain the hand-over-hand motion of the conventional kinesin. The neck linker of the kinesin is known to determine the directionality of the motility but, in this paper, it was assumed that the neck linker was not directly engaged in the power strokes, which were driven by the attractive force between the kinesin head and the microtubule. Based on this assumption, simple mechanical simulations showed that the model of a kinesin dimer processively moved along a microtubule protofilament, if the affinity of the kinesin against the microtubule is appropriately controlled. Moreover, if an external force was applied to the center of the kinesin dimer, the dimer moved backward along a microtubule, as observed in experimental motility assays.     

MgATP binding changes neither the shape nor the flexibility of the heads of single myosin molecules.

The structural mechanism by which myosin heads exert force is unknown. One possibility is that the tight binding of the heads to actin drives them into a force-generating configuration. Another possibility is that the force-generating conformational change is inherent to the myosin heads. In this case the heads would make force by changing their shape according to the species of nucleotide in their active sites, the tight attachment to actin serving only to provide traction. To test this latter possibility, we used negative stain electron microscopy to search for a MgATP-induced shape change in the heads of single myosin molecules. We compared the heads of 10S smooth muscle myosin monomers (wherein MgATP is trapped at the active site) with the MgATP-free heads of 6S monomers. We found that to a resolution of about 2 nm, MgATP binding to the unrestrained myosin head does not drive it to change its shape or its flexibility. This result suggests that the head makes force by virtue of an induced fit to actin.     

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.     

Nonlinear increase of elongation rate of actin filaments with actin monomer concentration

The nonlinear increase of the elongation rate of actin filaments above the critical monomer concentration was investigated by nucleated polymerization of actin. Significant deviations from linearity were observed when actin was polymerized in the presence of magnesium ions. When magnesium ions were replaced by potassium or calcium ions, no deviations from linearity could be detected. The nonlinearity was analyzed by two simple assembly mechanisms. In the first model, if the ATP hydrolysis by polymeric actin is approximately as fast as the incorporation of monomers into filaments, terminal subunits of lengthening filaments are expected to carry to some extent ADP. As ADP-containing subunits dissociate from the ends of actin filaments faster than ATP-containing subunits, the rate of elongation of actin filaments would be nonlinearly correlated with the monomer concentration. In the second model (conformational change model), actin monomers and filament subunits were assumed to occur in two conformations. The association and dissociation rates of actin molecules in the two conformations were thought to be different. The equilibrium distribution between the two conformations was assumed to be different for monomers and filament subunits. The ATP hydrolysis was thought to lag behind polymerization and conformational change. As under the experimental conditions the rate of ATP hydrolysis by polymeric actin was independent of the concentration of filament ends, the observed nonlinear increase of the rate of elongation with the monomer concentration above the critical monomer concentration was unlikely to be caused by ATP hydrolysis at the terminal subunits. The conformational change model turned out to be the simplest assembly mechanism by which all available experimental data could be explained.     

Electron microscopic evidence for the myosin head lever arm mechanism in hydrated myosin filaments using the gas environmental chamber

Muscle contraction results from an attachment–detachment cycle between the myosin heads extending from myosin filaments and the sites on actin filaments. The myosin head first attaches to actin together with the products of ATP hydrolysis, performs a power stroke associated with release of hydrolysis products, and detaches from actin upon binding with new ATP. The detached myosin head then hydrolyses ATP, and performs a recovery stroke to restore its initial position. The strokes have been suggested to result from rotation of the lever arm domain around the converter domain, while the catalytic domain remains rigid. To ascertain the validity of the lever arm hypothesis in muscle, we recorded ATP-induced movement at different regions within individual myosin heads in hydrated myosin filaments, using the gas environmental chamber attached to the electron microscope. The myosin head were position-marked with gold particles using three different site-directed antibodies. The amplitude of ATP-induced movement at the actin binding site in the catalytic domain was similar to that at the boundary between the catalytic and converter domains, but was definitely larger than that at the regulatory light chain in the lever arm domain. These results are consistent with the myosin head lever arm mechanism in muscle contraction if some assumptions are made.     

Excited hydrogen bonds in the molecular mechanism of muscle contraction.

The mechanism of muscle contraction is considered. The hydrolysis of an ATP molecule is assumed to produce the excitation of hydrogen bonds A--H...B between electronegative atoms A and B, which are contained in the myosin head and actin filament. This excitation energy epsilon f depends on the interatomic distance AB = R and generates the tractive force f = -delta epsilon f/delta R, that makes atoms AB approach each other. The swing of the myosin head results in macroscopic mutual displacement of actin and myosin polymers. The motion of the actin filament under the action of this force is studied. The conditions under which a considerable portion of the excitation energy converts into the potential tension energy of the actin filament are analysed, and the probability of higher muscle efficiency existence is discussed.     

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.     

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.     

Calcium regulates scallop muscle by changing myosin flexibility

Muscle myosins are molecular motors that convert the chemical free energy available from ATP hydrolysis into mechanical displacement of actin filaments, bringing about muscle contraction. Myosin cross-bridges exert force on actin filaments during a cycle of attached and detached states that are coupled to each round of ATP hydrolysis. Contraction and ATPase activity of the striated adductor muscle of scallop is controlled by calcium ion binding to myosin. This mechanism of the so-called “thick filament regulation” is quite different to vertebrate striated muscle which is switched on and off via “thin filament regulation” whereby calcium ions bind to regulatory proteins associated with the actin filaments. We have used an optically based single molecule technique to measure the angular disposition adopted by the two myosin heads whilst bound to actin in the presence and absence of calcium ions. This has allowed us to directly observe the movement of individual myosin heads in aqueous solution at room temperature in real time. We address the issue of how scallop striated muscle myosin might be regulated by calcium and have interpreted our results in terms of the structures of smooth muscle myosin that also exhibit thick filament regulation. This paper is not being submitted elsewhere and the authors have no competing financial interests     

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.     

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.