Molecular dynamics simulations of evolved collective motions of atoms in the myosin motor domain upon perturbation of the ATPase pocket

A crucial point for mechanical force generation in actomyosin systems is how the energy released by ATP hydrolysis in the myosin motor domain gives rise to the movement of the myosin head along the actin filament. We assumed the signal of the ATP hydrolysis to be transmitted as modulated atomic vibrations from the nucleotide-binding site throughout the myosin head, and carried out 1-ns all-atom molecular dynamics simulations for that signal transmission. We distributed the released energy to atoms located around the ATPase pocket as kinetic energies and examined how the effect of disturbance extended throughout the motor domain. The result showed that the disturbance signal extended over the motor domain in 150 ps and induced slowly varying collective motions of atoms at the actin-binding site and the junction with the neck, both of which are relevant to the movement of the myosin head along the actin filament. We also performed a principal component analysis of thermal atomic motions for the motor domain, and the first principal component was consistent with the response to the disturbance given to the ATPase pocket.     

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.     

The N terminus of myosin-binding protein C extends toward actin filaments in intact cardiac muscle

Myosin and actin filaments are highly organized within muscle sarcomeres. Myosin-binding protein C (MyBP-C) is a flexible, rod-like protein located within the C-zone of the sarcomere. The C-terminal domain of MyBP-C is tethered to the myosin filament backbone, and the N-terminal domains are postulated to interact with actin and/or the myosin head to modulate filament sliding. To define where the N-terminal domains of MyBP-C are localized in the sarcomere of active and relaxed mouse myocardium, the relative positions of the N terminus of MyBP-C and actin were imaged in fixed muscle samples using super-resolution fluorescence microscopy. The resolution of the imaging was enhanced by particle averaging. The images demonstrate that the position of the N terminus of MyBP-C is biased toward the actin filaments in both active and relaxed muscle preparations. Comparison of the experimental images with images generated in silico, accounting for known binding partner interactions, suggests that the N-terminal domains of MyBP-C may bind to actin and possibly the myosin head but only when the myosin head is in the proximity of an actin filament. These physiologically relevant images help define the molecular mechanism by which the N-terminal domains of MyBP-C may search for, and capture, molecular binding partners to tune cardiac contractility.     

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.     

Movement of smooth muscle tropomyosin by myosin heads.

It has been proposed that during the activation of muscle contraction the initial binding of myosin heads to the actin thin filament contributes to switching on the thin filament and that this might involve the movement of actin-bound tropomyosin. The movement of smooth muscle tropomyosin on actin was investigated in this work by measuring the change in distance between specific residues on tropomyosin and actin by fluorescence resonance energy transfer (FRET) as a function of myosin head binding to actin. An energy transfer acceptor was attached to Cys374 of actin and a donor to the tropomyosin heterodimer at either Cys36 of the beta-chain or Cys190 of the alpha-chain. FRET changed for the donor at both positions of tropomyosin upon addition of skeletal or smooth muscle myosin heads, indicating a movement of the whole tropomyosin molecule. The changes in FRET were hyperbolic and saturated at about one head per seven actin subunits, indicating that each head cooperatively affects several tropomyosin molecules, presumably via tropomyosin's end-to-end interaction. ATP, which dissociates myosin from actin, completely reversed the changes in FRET induced by heads, whereas in the presence of ADP the effect of heads was the same as in its absence. The results indicate that myosin with and without ADP, intermediates in the myosin ATPase hydrolytic pathway, are effective regulators of tropomyosin position, which might play a role in the regulation of smooth muscle contraction.     

Geometrical factors influencing muscle force development. II. Radial forces.

If the subfragment-2 (S2) portion of the myosin cross-bridge to actin does not lie parallel to the myofilament axes then when a muscle fiber contracts, there will be a radial component to the cross-bridge force. When the subfragment-1 (S1) portion of the cross-bridge attaches to actin with its long axis projecting through the filament axis, the magnitude of the radial force depends upon the azimuthal location of the actin site, but when the attachment of the S1 to actin is slewed, as in the reconstruction of Moore et al. (J. Mol. Biol., 1970, 50:279-294), then for a single cross-bridge the radial component of the cross-bridge force is not quite so sensitive to actin site location and is approximately 0.1 the axial component. In both cases, the ratio of the radial to axial force decreases with decreasing filament separation. If the radial-axial force ratio for each cross-bridge is approximately 0.1, then at full overlap in a frog skeletal muscle fiber the radial component of the cross-bridge force accompanying full activation will exert a compressive pressure of approximately 5 X 10(-3) atm. This would have little effect upon an intact muscle fiber where the volume constraints are likely osmotic, but it might produce a 1-2% change in filament spacing in a "skinned" muscle fiber from which the sarcolemma had been removed. These computations assume that the S2 link between the S1 head and the myosin filament does not support a bending moment of shear. If it does, then the radial component of the cross-bridge will be either greater or less, depending on the specific cross-bridge geometry.     

Conformation of the myosin motor during force generation in skeletal muscle

Myosin motors drive muscle contraction, cytokinesis and cell locomotion, and members of the myosin superfamily have been implicated in an increasingly diverse range of cell functions. Myosin can displace a bound actin filament several nanometers in a single interaction. Crystallographic studies suggest that this 'working stroke' involves bending of the myosin head between its light chain and catalytic domains. Here we used X-ray fiber diffraction to test the crystallographic model and measure the interdomain bending during force generation in an intact single muscle fiber. The observed bending has two components: an elastic distortion and an active rotation that generates force. The average bend of the force-generating myosin heads in a muscle fiber is intermediate between those in crystal structures with different bound nucleotides, and the C-terminus of the head is displaced by 7 nm along the actin filament axis compared with the in vitro conformation seen in the absence of nucleotide.     

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.     

A model of muscle contraction based on the Langevin equation with actomyosin potentials

We propose a muscle contraction model that is essentially a model of the motion of myosin motors as described by a Langevin equation. This model involves one-dimensional numerical calculations wherein the total force is the sum of a viscous force proportional to the myosin head velocity, a white Gaussian noise produced by random forces and other potential forces originating from the actomyosin structure and intra-molecular charges. We calculate the velocity of a single myosin on an actin filament to be 4.9–49 μm/s, depending on the viscosity between the actomyosin molecules. A myosin filament with a hundred myosin heads is used to simulate the contractions of a half-sarcomere within the skeletal muscle. The force response due to a quick release in the isometric contraction is simulated using a process wherein crossbridges are changed forcibly from one state to another. In contrast, the force response to a quick stretch is simulated using purely mechanical characteristics. We simulate the force–velocity relation and energy efficiency in the isotonic contraction and adenosine triphosphate consumption. The simulation results are in good agreement with the experimental results. We show that the Langevin equation for the actomyosin potentials can be modified statistically to become an existing muscle model that uses Maxwell elements.     

An ionic–chemical–mechanical model for muscle contraction

The dynamic process underlying muscle contraction is the parallel sliding of thin actin filaments along an immobile thick myosin fiber powered by oar‐like movements of protruding myosin cross bridges (myosin heads). The free energy for functioning of the myosin nanomotor comes from the hydrolysis of ATP bound to the myosin heads. The unit step of translational movement is based on a mechanical‐chemical cycle involving ATP binding to myosin, hydrolysis of the bound ATP with ultimate release of the hydrolysis products, stress‐generating conformational changes in the myosin cross bridge, and relief of built‐up stress in the myosin power stroke. The cycle is regulated by a transition between weak and strong actin–myosin binding affinities. The dissociation of the weakly bound complex by addition of salt indicates the electrostatic basis for the weak affinity, while structural studies demonstrate that electrostatic interactions among negatively charged amino acid residues of actin and positively charged residues of myosin are involved in the strong binding interface. We therefore conjecture that intermediate states of increasing actin–myosin engagement during the weak‐to‐strong binding transition also involve electrostatic interactions. Methods of polymer solution physics have shown that the thin actin filament can be regarded in some of its aspects as a net negatively charged polyelectrolyte. Here we employ polyelectrolyte theory to suggest how actin–myosin electrostatic interactions might be of significance in the intermediate stages of binding, ensuring an engaged power stroke of the myosin motor that transmits force to the actin filament, and preventing the motor from getting stuck in a metastable pre‐power stroke state. We provide electrostatic force estimates that are in the pN range known to operate in the cycle.     

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.     

On the theory of muscle contraction: filament extensibility and the development of isometric force and stiffness.

The newly discovered extensibility of actin and myosin filaments challenges the foundation of the theory of muscle mechanics. We have reformulated A. F. Huxley's sliding filament theory to explicitly take into account filament extensibility. During isometric force development, growing cross-bridge tractions transfer loads locally between filaments, causing them to extend and, therefore, to slide locally relative to one another. Even slight filament extensibility implies that 1) relative displacement between the two must be nonuniform along the region of filament overlap, 2) cross-bridge strain must vary systematically along the overlap region, and importantly, 3) the local shortening velocities, even at constant overall sarcomere length, reduce force below the level that would have developed if the filaments had been inextensible. The analysis shows that an extensible filament system with only two states (attached and detached) displays three important characteristics: 1) muscle stiffness leads force during force development; 2) cross-bridge stiffness is significantly higher than previously assessed by inextensible filament models; and 3) stiffness is prominently dissociated from the number of attached cross-bridges during force development. The analysis also implies that the local behavior of one myosin head must depend on the state of neighboring attachment sites. This coupling occurs exclusively through local sliding velocities, which can be significant, even during isometric force development. The resulting mechanical cooperativity is grounded in fiber mechanics and follows inevitably from filament extensibility.     

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     

Smooth muscle and skeletal muscle myosins produce similar unitary forces and displacements in the laser trap.

Purified smooth muscle myosin in the in vitro motility assay propels actin filaments at 1/10 the velocity, yet produces 3-4 times more force than skeletal muscle myosin. At the level of a single myosin molecule, these differences in force and actin filament velocity may be reflected in the size and duration of single motion and force-generating events, or in the kinetics of the cross-bridge cycle. Specifically, an increase in either unitary force or duty cycle may explain the enhanced force-generating capacity of smooth muscle myosin. Similarly, an increase in attached time or decrease in unitary displacement may explain the reduced actin filament velocity of smooth muscle myosin. To discriminate between these possibilities, we used a laser trap to measure unitary forces and displacements from single smooth and skeletal muscle myosin molecules. We analyzed our data using mean-variance analysis, which does not rely on scoring individual events by eye, and emphasizes periods in the data with constant properties. Both myosins demonstrated multiple but similar event populations with discrete peaks at approximately +11 and -11 nm in displacement, and 1.5 and 3.5 pN in force. Mean attached times for smooth muscle myosin were longer than for skeletal-muscle myosin. These results explain much of the difference in actin filament velocity between these myosins, and suggest that an increased duty cycle is responsible for the enhanced force-generating capacity of smooth over skeletal-muscle myosin.     

3D structure of relaxed fish muscle myosin filaments by single particle analysis

To understand the structural changes involved in the force-producing myosin cross-bridge cycle in vertebrate muscle it is necessary to know the arrangement and conformation of the myosin heads at the start of the cycle (i.e. the relaxed state). Myosin filaments isolated from goldfish muscle under relaxing conditions and viewed in negative stain by electron microscopy (EM) were divided into segments and subjected to three-dimensional (3D) single particle analysis without imposing helical symmetry. This allowed the known systematic departure from helicity characteristic of vertebrate striated muscle myosin filaments to be preserved and visualised. The resulting 3D reconstruction reveals details to about 55 A resolution of the myosin head density distribution in the three non-equivalent head 'crowns' in the 429 A myosin filament repeat. The analysis maintained the well-documented axial perturbations of the myosin head crowns and revealed substantial azimuthal perturbations between crowns with relatively little radial perturbation. Azimuthal rotations between crowns were approximately 60 degrees , 60 degrees and 0 degrees , rather than the regular 40 degrees characteristic of an unperturbed helix. The new density map correlates quite well with the head conformations analysed in other EM studies and in the relaxed fish muscle myosin filament structure modelled from X-ray fibre diffraction data. The reconstruction provides information on the polarity of the myosin head array in the A-band, important in understanding the geometry of the myosin head interaction with actin during the cross-bridge cycle, and supports a number of conclusions previously inferred by other methods. The observed azimuthal head perturbations are consistent with the X-ray modelling results from intact muscle, indicating that the observed perturbations are an intrinsic property of the myosin filaments and are not induced by the proximity of actin filaments in the muscle A-band lattice. Comparison of the axial density profile derived in this study with the axial density profile of the X-ray model of the fish myosin filaments which was restricted to contributions from the myosin heads allows the identification of a non-myosin density peak associated with the azimuthally perturbed head crown which can be interpreted as a possible location for C-protein or X-protein (MyBP-C or -X). This position for C-protein is also consistent with the C-zone interference function deduced from previous analysis of the meridional X-ray pattern from frog muscle. It appears that, along with other functions, C-(X-) protein may have the role of slewing the heads of one crown so that they do not clash with the neighbouring actin filaments, but are readily available to interact with actin when the muscle is activated.     

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.     

Along the road not taken: how many myosin heads act on a single actin filament at any instant in working muscle?

We reconsider the use of stiffness measurements to estimate N, the number of myosin heads acting (working at any instant to produce tension) on a single actin filament in vertebrate striated muscle, and give reasons for our rejection of numbers produced from such measurements. We go on to present a different approach to the problem, citing and extending a model bearing on the value of N which is derived from other physiological and biochemical data and which offers insight into the fundamental actin-myosin contractile event as an impulsive force. New experimental data accumulating over the past decade support this model, in which the myosin heads act sequentially along the actin filament (this is an example of Conformational Spread). In this model only a single myosin head acts on a single actin filament to produce an impulse at any given instant in normally-contracting muscle, either in the isometric or the isotonic mode, so N?=?1. However, extra impulses occur within the same time frame after quick release of length or tension. The predictions of this sequential model are in striking agreement with a large body of recent detailed biophysical and biochemical evidence. We suggest that this warrants further in-depth experimental work, specifically to explore and test the sequential model and its implications.     

Myosin filament polymerization and depolymerization in a model of partial length adaptation in airway smooth muscle

Length adaptation in airway smooth muscle (ASM) is attributed to reorganization of the cytoskeleton, and in particular the contractile elements. However, a constantly changing lung volume with tidal breathing (hence changing ASM length) is likely to restrict full adaptation of ASM for force generation. There is likely to be continuous length adaptation of ASM between states of incomplete or partial length adaption. We propose a new model that assimilates findings on myosin filament polymerization/depolymerization, partial length adaptation, isometric force, and shortening velocity to describe this continuous length adaptation process. In this model, the ASM adapts to an optimal force-generating capacity in a repeating cycle of events. Initially the myosin filament, shortened by prior length changes, associates with two longer actin filaments. The actin filaments are located adjacent to the myosin filaments, such that all myosin heads overlap with actin to permit maximal cross-bridge cycling. Since in this model the actin filaments are usually longer than myosin filaments, the excess length of the actin filament is located randomly with respect to the myosin filament. Once activated, the myosin filament elongates by polymerization along the actin filaments, with the growth limited by the overlap of the actin filaments. During relaxation, the myosin filaments dissociate from the actin filaments, and then the cycle repeats. This process causes a gradual adaptation of force and instantaneous adaptation of shortening velocity. Good agreement is found between model simulations and the experimental data depicting the relationship between force development, myosin filament density, or shortening velocity and length.     

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.     

Flexibility of myosin-subfragment-1 in its complex with actin as revealed by fluorescence resonance energy transfer.

The flexibility of the acto-myosin complex in rigor conditions was characterized by measuring the temperature profile of normalized fluorescence resonance energy transfer efficiency, f' [Somogyi, B., Matkó, J., Papp, S., Hevessy, J., Welch, G.R. & Damjanovich, S. (1984) Biochemistry 23, 3403-3411]. Fluorescence acceptors were introduced to the Cys374 residues of actin and the donors were covalently attached either to Cys707 in the catalytic domain or to Cys177 in the essential light-chain of myosin S1. Fluorescence resonance energy transfer measurements revealed that the protein matrix between Cys374 of actin and Cys707 of S1 is rigid. In contrast, the link between the catalytic and light-chain-binding domains in myosin S1 is flexible. We have recently shown that the positional distribution of Cys707 was narrow relative to the actin filament, while that of the Cys177 was broad. Accordingly, the broad positional distribution of Cys177 is likely to be due to the large flexibility of the link between the catalytic and light-chain-binding domains. This flexibility is probably essential for the interdomain reorganization of the myosin head during the force generation process and for accommodating the symmetry difference between actin and myosin filaments to allow the formation of cross-bridges.