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.     

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     

Myosin V passing over Arp2/3 junctions: branching ratio calculated from the elastic lever arm model

Myosin V is a two-headed processive motor protein that walks in a hand-over-hand fashion along actin filaments. When it encounters a filament branch, formed by the Arp2/3 complex, it can either stay on the straight mother filament, or switch to the daughter filament. We study both probabilities using the elastic lever arm model for myosin V. We calculate the shapes and bending energies of all relevant configurations in which the trail head is bound to the actin filament before Arp2/3 and the lead head is bound either to the mother or to the daughter filament. Based on the assumption that the probability for a head to bind to a certain actin subunit is proportional to the Boltzmann factor obtained from the elastic energy, we calculate the mother/daughter filament branching ratio. Our model predicts a value of 27% for the daughter and 73% for the mother filament. This result is in good agreement with recent experimental data.     

Direct Measurements of Local Coupling between Myosin Molecules Are Consistent with a Model of Muscle Activation

Muscle contracts due to ATP-dependent interactions of myosin motors with thin filaments composed of the proteins actin, troponin, and tropomyosin. Contraction is initiated when calcium binds to troponin, which changes conformation and displaces tropomyosin, a filamentous protein that wraps around the actin filament, thereby exposing myosin binding sites on actin. Myosin motors interact with each other indirectly via tropomyosin, since myosin binding to actin locally displaces tropomyosin and thereby facilitates binding of nearby myosin. Defining and modeling this local coupling between myosin motors is an open problem in muscle modeling and, more broadly, a requirement to understanding the connection between muscle contraction at the molecular and macro scale. It is challenging to directly observe this coupling, and such measurements have only recently been made. Analysis of these data suggests that two myosin heads are required to activate the thin filament. This result contrasts with a theoretical model, which reproduces several indirect measurements of coupling between myosin, that assumes a single myosin head can activate the thin filament. To understand this apparent discrepancy, we incorporated the model into stochastic simulations of the experiments, which generated simulated data that were then analyzed identically to the experimental measurements. By varying a single parameter, good agreement between simulation and experiment was established. The conclusion that two myosin molecules are required to activate the thin filament arises from an assumption, made during data analysis, that the intensity of the fluorescent tags attached to myosin varies depending on experimental condition. We provide an alternative explanation that reconciles theory and experiment without assuming that the intensity of the fluorescent tags varies.     

GFP-tagged regulatory light chain monitors single myosin lever-arm orientation in a muscle fiber

Myosin is the molecular motor in muscle-binding actin and executing a power stroke by rotating its lever arm through an angle of approximately 70 degrees to translate actin against resistive force. A green fluorescent protein (GFP)-tagged human cardiac myosin regulatory light chain (HCRLC) was constructed to study in situ lever arm orientation one molecule at a time by polarized fluorescence emitted from the GFP probe. The recombinant protein physically and functionally replaced the native RLC on myosin lever arms in the thick filaments of permeabilized skeletal muscle fibers. Detecting single molecules in fibers where myosin concentration reaches 300 microM is accomplished using total internal reflection fluorescence microscopy. With total internal reflection fluorescence, evanescent field excitation, supercritical angle fluorescence detection, and CCD detector pixel size limits detection volume to just a few attoliters. Data analysis manages both the perturbing effect of the TIR interface on probe emission and the effect of high numerical aperture collection of light. The natural myosin concentration gradient in a muscle fiber allows observation of fluorescence polarization from C-term GFP-tagged HCRLC exchanged myosin from regions in the thick filament containing low and high myosin concentrations. In rigor, cross-bridges at low concentration at the end of the thick filament maintain GFP dipole moments at two distinct polar angles relative to the fiber symmetry axis. The lower angle, where the dipole is nearly parallel to fiber axis, is more highly populated than the alternative, larger angle. Cross-bridges at higher concentration in the center of the thick filament are oriented in a homogeneous band at approximately 45 degrees to the fiber axis. The data suggests molecular crowding impacts myosin conformation, implying mutual interactions between cross-bridges alter how the muscle generates force. The GFP-tagged RLC is a novel probe to assess single-lever-arm orientation characteristics in situ.     

Myosin V is a left-handed spiral motor on the right-handed actin helix

Myosin V is a two-headed, actin-based molecular motor implicated in organelle transport. Previously, a single myosin V molecule has been shown to move processively along an actin filament in discrete approximately 36 nm steps. However, 36 nm is the helical repeat length of actin, and the geometry of the previous experiments may have forced the heads to bind to, or halt at, sites on one side of actin that are separated by 36 nm. To observe unconstrained motion, we suspended an actin filament in solution and attached a single myosin V molecule carrying a bead duplex. The duplex moved as a left-handed spiral around the filament, disregarding the right-handed actin helix. Our results indicate a stepwise walking mechanism in which myosin V positions and orients the unbound head such that the head will land at the 11th or 13th actin subunit on the opposing strand of the actin double helix.     

Unconstrained steps of myosin VI appear longest among known molecular motors

Myosin VI is a two-headed molecular motor that moves along an actin filament in the direction opposite to most other myosins. Previously, a single myosin VI molecule has been shown to proceed with steps that are large compared to its neck size: either it walks by somehow extending its neck or one head slides along actin for a long distance before the other head lands. To inquire into these and other possible mechanism of motility, we suspended an actin filament between two plastic beads, and let a single myosin VI molecule carrying a bead duplex move along the actin. This configuration, unlike previous studies, allows unconstrained rotation of myosin VI around the right-handed double helix of actin. Myosin VI moved almost straight or as a right-handed spiral with a pitch of several micrometers, indicating that the molecule walks with strides slightly longer than the actin helical repeat of 36 nm. The large steps without much rotation suggest kinesin-type walking with extended and flexible necks, but how to move forward with flexible necks, even under a backward load, is not clear. As an answer, we propose that a conformational change in the lifted head would facilitate landing on a forward, rather than backward, site. This mechanism may underlie stepping of all two-headed molecular motors including kinesin and myosin V.     

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.     

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.     

Smooth muscle myosin cross-bridge interactions modulate actin filament sliding velocity in vitro

Although it is generally believed that phosphorylation of the regulatory light chain of myosin is required before smooth muscle can develop force, it is not known if the overall degree of phosphorylation can also modulate the rate at which cross-bridges cycle. To address this question, an in vitro motility assay was used to observe the motion of single actin filaments interacting with smooth muscle myosin copolymers composed of varying ratios of phosphorylated and unphosphorylated myosin. The results suggest that unphosphorylated myosin acts as a load to slow down the rate at which actin is moved by the faster cycling phosphorylated cross-bridges. Myosin that was chemically modified to generate a noncycling analogue of the "weakly" bound conformation was similarly able to slow down phosphorylated myosin. The observed modulation of actin velocity as a function of copolymer composition can be accounted for by a model based on mechanical interactions between cross-bridges.     

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.     

The Antiparallel Dimerization of Myosin X Imparts Bundle Selectivity for Processive Motility

Myosin X is an unconventional actin-based molecular motor involved in filopodial formation, microtubule-actin filament interaction, and cell migration. Myosin X is an important component of filopodia regulation, localizing to tips of growing filopodia by an unclear targeting mechanism. The native α-helical dimerization domain of myosin X is thought to associate with antiparallel polarity of the two amino acid chains, making myosin X the only myosin that is currently considered to form antiparallel dimers. This study aims to determine if antiparallel dimerization of myosin X imparts selectivity toward actin bundles by comparing the motility of parallel and antiparallel dimers of myosin X on single and fascin-bundled actin filaments. Antiparallel myosin X dimers exhibit selective processivity on fascin-bundled actin and are only weakly processive on single actin filaments below saturating [ATP]. Artificial forced parallel dimers of myosin X are robustly processive on both single and bundled actin, exhibiting no selectivity. To determine the relationship between gating of the reaction steps and observed differences in motility, a mathematical model was developed to correlate the parameters of motility with the biochemical and mechanical kinetics of the dimer. Results from the model, constrained by experimental data, suggest that the probability of binding forward, toward the barbed end of the actin filament, is lower in antiparallel myosin X on single actin filaments compared to fascin-actin bundles and compared to constructs of myosin X with parallel dimerization.     

Orientation of the N-terminal lobe of the myosin regulatory light chain in skeletal muscle fibers

The orientation of the N-terminal lobe of the myosin regulatory light chain (RLC) in demembranated fibers of rabbit psoas muscle was determined by polarized fluorescence. The native RLC was replaced by a smooth muscle RLC with a bifunctional rhodamine probe attached to its A, B, C, or D helix. Fiber fluorescence data were interpreted using the crystal structure of the head domain of chicken skeletal myosin in the nucleotide-free state. The peak angle between the lever axis of the myosin head and the fiber or actin filament axis was 100—110° in relaxation, isometric contraction, and rigor. In each state the hook helix was at an angle of ～40° to the lever/filament plane. The in situ orientation of the RLC D and E helices, and by implication of its N- and C-lobes, was similar in smooth and skeletal RLC isoforms. The angle between these two RLC lobes in rigor fibers was different from that in the crystal structure. These results extend previous crystallographic evidence for bending between the two lobes of the RLC to actin-attached myosin heads in muscle fibers, and suggest that such bending may have functional significance in contraction and regulation of vertebrate striated muscle.     

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.     

The conformation of myosin head domains in rigor muscle determined by X-ray interference

In the absence of adenosine triphosphate, the head domains of myosin cross-bridges in muscle bind to actin filaments in a rigor conformation that is expected to mimic that following the working stroke during active contraction. We used x-ray interference between the two head arrays in opposite halves of each myosin filament to determine the rigor head conformation in single fibers from frog skeletal muscle. During isometric contraction (force T(0)), the interference effect splits the M3 x-ray reflection from the axial repeat of the heads into two peaks with relative intensity (higher angle/lower angle peak) 0.76. In demembranated fibers in rigor at low force (<0.05 T(0)), the relative intensity was 4.0, showing that the center of mass of the heads had moved 4.5 nm closer to the midpoint of the myosin filament. When rigor fibers were stretched, increasing the force to 0.55 T(0), the heads' center of mass moved back by 1.1-1.6 nm. These motions can be explained by tilting of the light chain domain of the head so that the mean angle between the Cys(707)-Lys(843) vector and the filament axis increases by approximately 36 degrees between isometric contraction and low-force rigor, and decreases by 7-10 degrees when the rigor fiber is stretched to 0.55 T(0).     

High flexibility of the actomyosin crossbridge resides in skeletal muscle myosin subfragment-2 as demonstrated by a new single molecule assay

Popular views of force generation in muscle indicate that a lever arm in the myosin head initiates displacement of the thin filament. However, this lever arm is attached to the thick filament backbone by a flexible combination of coiled coils and hinges in the myosin subfragment-2 (S2); therefore, efficient force generation depends on tension development in this linking structure. Herein, a single molecule assay is developed to examine the flexibility of the intact S2 relative to that of the myosin head. Fluorescently labeled myosin rod is polymerized onto a single myosin molecule that is bound to actin, and the resulting Brownian motion of the rod is analyzed at video rates by digital image processing. Complete rotations of the rod suggest significant amounts of random coil in the linking structure. The close similarity of twist rates for double-headed and single-headed myosin indicates that most of the flexibility originates at or beyond the first pitch of coiled coil in S2 and most likely at the hinge connecting S2 and the light meromyosin. The myosin head has a smaller but still detectable impact on this flexibility, since the addition of ADP to the rigor crossbridge produces differential effects on the torsional characteristics of double-headed versus single-headed myosin.     

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.     

A new muscle contractile system composed of a thick filament lattice and a single actin filament

To bridge the gap between the contractile system in muscle and in vitro motility assay, we have devised an A-band motility assay system. A glycerinated skeletal myofibril was treated with gelsolin to selectively remove the thin filaments and expose a single A-band. A single bead-tailed actin filament trapped by optical tweezers was made to interact with the inside or the outer surface of the A-band, and the displacement of the bead-tailed filament was measured in a physiological ionic condition by phase-contrast and fluorescence microscopy. We observed large back-and-forth displacement of the filament accompanied by a large change in developed force. Despite this large tension fluctuation, we found that the average force was proportional to the overlap inside and outside the A-band up to approximately 150 nm and 300 nm from the end of the A-band, respectively. Consistent with the difference in the density of myosin molecules, the average force per unit length of the overlap inside the A-band (the time-averaged force/myosin head was approximately 1 pN) was approximately twice as large as that outside. Thus, we conclude that the A-band motility assay system described here is suitable for studying force generation on a single actin filament, and its sliding movement within a regular three-dimensional thick filament lattice.     

Affinity for MgADP and force of unbinding from actin of myosin purified from tonic and phasic smooth muscle

Smooth muscle is unique in its ability to maintain force at low MgATP consumption. This property, called the latch state, is more prominent in tonic than phasic smooth muscle. Studies performed at the muscle strip level have suggested that myosin from tonic muscle has a greater affinity for MgADP and therefore remains attached to actin longer than myosin from phasic muscle, allowing for cross-bridge dephosphorylation and latch-bridge formation. An alternative hypothesis is that after dephosphorylation, myosin reattaches to actin and maintains force. We investigated these fundamental properties of smooth muscle at the molecular level. We used an in vitro motility assay to measure actin filament velocity (nu(max)) when propelled by myosin purified from phasic or tonic muscle at increasing [MgADP]. Myosin was 25% thiophosphorylated and 75% unphosphorylated to approximate in vivo conditions. The slope of nu(max) versus [MgADP] was significantly greater for tonic (-0.51 +/- 0.04) than phasic muscle myosin (-0.15 +/- 0.04), demonstrating the greater MgADP affinity of myosin from tonic muscle. We then used a laser trap assay to measure the unbinding force from actin of populations of unphosphorylated tonic and phasic muscle myosin. Both myosin types attached to actin, and their unbinding force (0.092 +/- 0.022 pN for phasic muscle and 0.084 +/- 0.017 pN for tonic muscle) was not statistically different. We conclude that the greater affinity for MgADP of tonic muscle myosin and the reattachment of dephosphorylated myosin to actin may both contribute to the latch state.