Mapping the classical cross-bridge theory and backward steps in a three bead laser trap setup

According to the cross-bridge theory (Huxley, 1957) [1], the interaction between myosin and actin is governed by a deterministic process where the myosin molecule pulls the actin filament in one specific direction only. However, studies on single myosin-actin interactions produced displacements of actin not only in the preferred but also in the opposite direction. This phenomenon is typically referred to as backward steps by the myosin head. Molloy et al. (1995) [2] speculated that these backward steps are not caused by the molecular interactions of actin with myosin but are an artifact of the Brownian motion associated with these molecular level experiments. The aim of this study was to investigate, whether a theoretical model can support Molloy’s speculation. We therefore developed a theoretical model of actin-myosin based muscle contraction that was strictly based on Huxley’s assumption of one stepping direction only, but incorporated Brownian motion, as observed in single cross-bridge-actin interactions. The mathematical model is based on Langevin equations describing the classical three-bead laser trap setup and uses a novel semi-analytical approach to study the percentage of backward steps. We analyzed the effects of different initial actin attachment site distribution and laser trap stiffness on the ratio of forward to backward steps. Our results demonstrate that backward steps and the classical cross-bridge theory are perfectly compatible in a three-bead laser trap setup.     

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.     

Differential labeling of myosin V heads with quantum dots allows direct visualization of hand-over-hand processivity

The double-headed myosin V molecular motor carries intracellular cargo processively along actin tracks in a hand-over-hand manner. To test this hypothesis at the molecular level, we observed single myosin V molecules that were differentially labeled with quantum dots having different emission spectra so that the position of each head could be identified with approximately 6-nm resolution in a total internal reflectance microscope. With this approach, the individual heads of a single myosin V molecule were observed taking 72-nm steps as they alternated positions on the actin filament during processive movement. In addition, the heads were separated by 36 nm during pauses in motion, suggesting attachment to actin along its helical repeat. The 36-nm interhead spacing, the 72-nm step size, and the observation that heads alternate between leading and trailing positions on actin are obvious predictions of the hand-over-hand model, thus confirming myosin V's mode of walking along an actin filament.     

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.     

The Stepping Pattern of Myosin X Is Adapted for Processive Motility on Bundled Actin

Myosin X is a molecular motor that is adapted to select bundled actin filaments over single actin filaments for processive motility. Its unique form of motility suggests that myosin X's stepping mechanism takes advantage of the arrangement of actin filaments and the additional target binding sites found within a bundle. Here we use fluorescence imaging with one-nanometer accuracy to show that myosin X takes steps of ∼18 nm along a fascin-actin bundle. This step-size is well short of the 36-nm step-size observed in myosin V and myosin VI that corresponds to the actin pseudohelical repeat distance. Myosin X is able to walk along bundles with this step-size if it straddles two actin filaments, but would be quickly forced to spiral into the constrained interior of the bundle if it were to use only a single actin filament. We also demonstrate that myosin X takes many sideways steps as it walks along a bundle, suggesting that it can switch actin filament pairs within the bundle as it walks. Sideways steps to the left or the right occur on bundles with equal frequency, suggesting a degree of lateral flexibility such that the motor's working stroke does not bias it to the left or to the right. On single actin filaments, we find a broad mixture of 10-20-nm steps, which again falls short of the 36-nm actin repeat. Moreover, the motor leans to the right as it walks along single filaments, which may require myosin X to adopt strained configurations. As a control, we also tracked myosin V stepping along actin filaments and fascin-actin bundles. We find that myosin V follows a narrower path on both structures, walking primarily along one surface of an actin filament and following a single filament within a bundle while occasionally switching to neighboring filaments. Together, these results delineate some of the structural features of the motor and the track that allow myosin X to recognize actin filament bundles.     

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.     

Class VI myosin moves processively along actin filaments backward with large steps.

Among a superfamily of myosin, class VI myosin moves actin filaments backwards. Here we show that myosin VI moves processively on actin filaments backwards with large ( approximately 36 nm) steps, nevertheless it has an extremely short neck domain. Myosin V also moves processively with large ( approximately 36 nm) steps and it is believed that myosin V strides along the actin helical repeat with its elongated neck domain that is critical for its processive movement with large steps. Myosin VI having a short neck cannot take this scenario. We found by electron microscopy that myosin VI cooperatively binds to an actin filament at approximately 36 nm intervals in the presence of ATP, raising a hypothesis that the binding of myosin VI evokes "hot spots" on actin filaments that attract myosin heads. Myosin VI may step on these "hot spots" on actin filaments in every helical pitch, thus producing processive movement with 36 nm steps.     

Functional role of loop 2 in myosin V

Myosin V is molecular motor that is capable of moving processively along actin filaments. The kinetics of monomeric myosin V containing a single IQ domain (MV 1IQ) differ from nonprocessive myosin II in that actin affinity is higher, phosphate release is extremely rapid, and ADP release is rate-limiting. We generated two mutants of myosin V by altering loop 2, a surface loop in the actin-binding region thought to alter actin affinity and phosphate release in myosin II, to determine the role that this loop plays in the kinetic tuning of myosin V. The loop 2 mutants altered the apparent affinity for actin (K(ATPase)) without altering the maximum ATPase rate (V(MAX)). Transient kinetic analysis determined that the rate of binding to actin, as well as the affinity for actin, was dependent on the net positive charge of loop 2, while other steps in the ATPase cycle were unchanged. The maximum rate of phosphate release was unchanged, but the affinity for actin in the M.ADP.Pi-state was dramatically altered by the mutations in loop 2. Thus, loop 2 is important for allowing myosin V to bind to actin with a relatively high affinity in the weak binding states but does not play a direct role in the product release steps. The ability to maintain a high affinity for actin in the weak binding states may prevent diffusion away from the actin filament and increase the degree of processive motion of myosin V.     

Spontaneous Detachment of the Leading Head Contributes to Myosin VI Backward Steps

Myosin VI is an ATP driven molecular motor that normally takes forward and processive steps on actin filaments, but also on occasion stochastic backward steps. While a number of models have attempted to explain the backwards steps, none offer an acceptable mechanism for their existence. We therefore performed single molecule imaging of myosin VI and calculated the stepping rates of forward and backward steps at the single molecule level. The forward stepping rate was proportional to the ATP concentration, whereas the backward stepping rate was independent. Using these data, we proposed that spontaneous detachment of the leading head is uncoupled from ATP binding and is responsible for the backward steps of myosin VI.     

Myosin VI regulates actin dynamics and melanosome biogenesis

Myosin VI has been implicated in various steps of organelle dynamics. However, the molecular mechanism by which this myosin contributes to membrane traffic is poorly understood. Here, we report that myosin VI is associated with a lysosome-related organelle, the melanosome. Using an actin-based motility assay and video microscopy, we observed that myosin VI does not contribute to melanosome movements. Myosin VI expression regulates instead the organization of actin networks in the cytoplasm. Using a cell-free assay, we showed that myosin VI recruited actin at the surface of isolated melanosomes. Myosin VI is involved in the endocytic-recycling pathway, and this pathway contributes to the transport of a melanogenic enzyme to maturing melanosomes. We showed that depletion of myosin VI accumulated a melanogenic enzyme in enlarged melanosomes and increased their melanin content. We confirmed the requirement of myosin VI to regulate melanosome biogenesis by analysing the morphology of melanosomes in choroid cells from of the Snell's waltzer mice that do not express myosin VI. Together, our results provide new evidence that myosin VI regulates the organization of actin dynamics at the surface of a specialized organelle and unravel a novel function of this myosin in regulating the biogenesis of this organelle.     

Chick brain actin and myosin. Isolation and characterization

Brain actin extracted from an acetone powder of chick brains was purified by a cycle of polymerization-depolymerization followed by molecular sieve chromatography. The brain actin had a subunit molecular weight of 42,000 daltons as determined by co-electrophoresis with muscle actin. It underwent salt-dependent g to f transformation to form double helical actin filaments which could be "decorated" by muscle myosin subfragment 1. A critical concentration for polymerization of 1.3 microM was determined by measuring either the change in viscosity or absorbance at 232 nm. Brain actin was also capable of stimulating the ATPase activity of muscle myosin. Brain myosin was isolated from whole chick brain by a procedure involving high salt extraction, ammonium sulfate fractionation and molecular sieve chromatography. The purified myosin was composed of a 200,000-dalton heavy chain and three lower molecular weight light chains. In 0.6 M KCl the brain myosin had ATPase activity which was inhibited by Mg++, stimulated by Ca++, and maximally activated by EDTA. When dialyzed against 0.1 M KCl, the brain myosin self-assembled into short bipolar filaments. The bipolar filaments associated with each other to form long concatamers, and this association was enhanced by high concentrations of Mg++ ion. The brain myosin did not interact with chicken skeletal muscle myosin to form hybrid filaments. Furthermore, antibody recognition studies demonstrated that myosins from chicken brain, skeletal muscle, and smooth muscle were unique.     

Chemical Decoupling of ATPase Activation and Force Production from the Contractile Cycle in Myosin by Steric Hindrance of Lever-Arm Movement

The myosin motor protein generates force in muscle by hydrolyzing Adenosine 5′-triphosphate (ATP) while interacting transiently with actin. Structural evidence suggests the myosin globular head (subfragment 1 or S1) is articulated with semi-rigid catalytic and lever-arm domains joined by a flexible converter domain. According to the prevailing hypothesis for energy transduction, ATP binding and hydrolysis in the catalytic domain drives the relative movement of the lever arm. Actin binding and reversal of the lever-arm movement (power stroke) applies force to actin. These domains interface at the reactive lysine, Lys84, where trinitrophenylation (TNP-Lys84-S1) was observed in this work to block actin activation of myosin ATPase and in vitro sliding of actin over myosin. TNP-Lys84-S1's properties and interactions with actin were examined to determine how trinitrophenylation causes these effects. Weak and strong actin binding, the rate of mantADP release from actomyosin, and actomyosin dissociation by ATP were equivalent in TNP-Lys84-S1 and native S1. Molecular dynamics calculations indicate that lever-arm movement inhibition during ATP hydrolysis and the power stroke is caused by steric clashes between TNP and the converter or lever-arm domains. Together these findings suggest that TNP uncouples actin activation of myosin ATPase and the power stroke from other steps in the contraction cycle by inhibiting the converter and lever-arm domain movements.     

Neck length and processivity of myosin V

Myosin V is an unconventional myosin that transports cargo such as vesicles, melanosomes, or mRNA on actin filaments. It is a two-headed myosin with an unusually long neck that has six IQ motifs complexed with calmodulin. In vitro studies have shown that myosin V moves processively on actin, taking multiple 36-nm steps that coincide with the helical repeat of actin. This allows the molecule to "walk" across the top of an actin filament, a feature necessary for moving large vesicles along an actin filament bound to the cytoskeleton. The extended neck length of the two heads is thought to be critical for taking 36-nm steps for processive movements. To test this hypothesis we have expressed myosin V heavy meromyosin-like fragments containing 6IQ motifs, as well as ones that shorten (2IQ, 4IQ) or lengthen (8IQ) the neck region or alter the spacing between 3rd and 4th IQ motifs. The step size was proportional to neck length for the 2IQ, 4IQ, 6IQ, and 8IQ molecules, but the molecule with the altered spacing took shorter than expected steps. Total internal reflection fluorescence microscopy was used to determine whether the heavy meromyosin IQ molecules were capable of processive movements on actin. At saturating ATP concentrations, all molecules except for the 2IQ mutant moved processively on actin. When the ATP concentration was lowered to 10 microm or less, the 2IQ mutant demonstrated some processive movements but with reduced run lengths compared with the other mutants. Its weak processivity was also confirmed by actin landing assays.     

Adaptability of myosin V studied by simultaneous detection of position and orientation

We studied the structural dynamics of chicken myosin V by combining the localization power of fluorescent imaging with one nanometer accuracy (FIONA) with the ability to detect angular changes of a fluorescent probe. The myosin V was labeled with bifunctional rhodamine on one of its calmodulin light chains. For every 74 nm translocation, the probe exhibited two reorientational motions, associated with alternating smaller and larger translational steps. Molecules previously identified as stepping alternatively 74-0 nm were found to actually step 64-10 nm. Additional tilting often occurred without full steps, possibly indicating flexibility of the attached myosin heads or probing of their vicinity. Processive myosin V molecules sometimes shifted from the top to the side of actin, possibly to avoid an obstacle. The data indicate marked adaptability of this molecular motor to a nonuniform local environment and provide strong support for a straight-neck model of myosin V in which the lever arm of the leading head is tilted backwards at the prepowerstoke angle.     

A kinetic mechanism for the fast movement of Chara myosin

Endoplasmic streaming of characean cells of Nitella or Chara is known to be in the range 30-100 microm/second. The Chara myosin extracted from the cells and fixed onto a glass surface was found to move muscle actin filaments at a velocity of 60 microm/second. This is ten times faster than that of skeletal muscle myosin (myosin II). In this study, the displacement caused by single Chara myosin molecules was measured using optical trapping nanometry. The step size of Chara myosin was approximately 19nm. This step size is longer than that of skeletal muscle myosin but shorter than that of myosin V. The dwell time of the steps was relatively long, and this most likely resulted from two rate-limiting steps, the dissociation of ADP and the binding of ATP. The rate of ADP release from Chara myosin after the completion of the force-generation step was similar to that of myosin V, but was considerably slower than that of skeletal muscle myosin. The 19nm step size and the dwell time obtained could not explain the fast movement. The fast movement could be explained by the load-dependent release of ADP. As the load imposed on the myosin decreased, the rate of ADP release increased. We propose that the interaction of Chara myosin with an actin filament resulted in a negative load being imposed on other myosin molecules interacting with the same actin filament. This resulted in an accelerated release of ADP and the fast sliding movement.     

Effects of ATP and Actin-Filament Binding on the Dynamics of the Myosin II S1 Domain

Actin and myosin interact with one another to perform a variety of cellular functions. Central to understanding the processive motion of myosin on actin is the characterization of the individual states along the mechanochemical cycle. We present an all-atom molecular dynamics simulation of the myosin II S1 domain in the rigor state interacting with an actin filament. We also study actin-free myosin in both rigor and post-rigor conformations. Using all-atom level and coarse-grained analysis methods, we investigate the effects of myosin binding on actin, and of actin binding on myosin. In particular, we determine the domains of actin and myosin that interact strongly with one another at the actomyosin interface using a highly coarse-grained level of resolution, and we identify a number of salt bridges and hydrogen bonds at the interface of myosin and actin. Applying coarse-grained analysis, we identify differences in myosin states dependent on actin-binding, or ATP binding. Our simulations also indicate that the actin propeller twist-angle and nucleotide cleft-angles are influenced by myosin at the actomyosin interface. The torsional rigidity of the myosin-bound filament is also calculated, and is found to be increased compared to previous simulations of the free filament.     

Magnesium regulates ADP dissociation from myosin V

Processivity in myosin V is mediated through the mechanical strain that results when both heads bind strongly to an actin filament, and this strain regulates the timing of ADP release. However, what is not known is which steps that lead to ADP release are affected by this mechanical strain. Answering this question will require determining which of the several potential pathways myosin V takes in the process of ADP release and how actin influences the kinetics of these pathways. We have addressed this issue by examining how magnesium regulates the kinetics of ADP release from myosin V and actomyosin V. Our data support a model in which actin accelerates the release of ADP from myosin V by reducing the magnesium affinity of a myosin V-MgADP intermediate. This is likely a consequence of the structural changes that actin induces in myosin to release phosphate. This effect on magnesium affinity provides a plausible explanation for how mechanical strain can alter this actin-induced acceleration. For actomyosin V, magnesium release follows phosphate release and precedes ADP release. Increasing magnesium concentration to within the physiological range would thus slow both the ATPase activity and the velocity of movement of this motor.     

Effects of ATP and Actin-Filament Binding on the Dynamics of the Myosin II S1 Domain

Actin and myosin interact with one another to perform a variety of cellular functions. Central to understanding the processive motion of myosin on actin is the characterization of the individual states along the mechanochemical cycle. We present an all-atom molecular dynamics simulation of the myosin II S1 domain in the rigor state interacting with an actin filament. We also study actin-free myosin in both rigor and post-rigor conformations. Using all-atom level and coarse-grained analysis methods, we investigate the effects of myosin binding on actin, and of actin binding on myosin. In particular, we determine the domains of actin and myosin that interact strongly with one another at the actomyosin interface using a highly coarse-grained level of resolution, and we identify a number of salt bridges and hydrogen bonds at the interface of myosin and actin. Applying coarse-grained analysis, we identify differences in myosin states dependent on actin-binding, or ATP binding. Our simulations also indicate that the actin propeller twist-angle and nucleotide cleft-angles are influenced by myosin at the actomyosin interface. The torsional rigidity of the myosin-bound filament is also calculated, and is found to be increased compared to previous simulations of the free filament.     

Kinetic mechanism and regulation of myosin VI.

Myosin VI is the only pointed end-directed myosin identified and is likely regulated by heavy chain phosphorylation (HCP) at the actin-binding site in vivo. We undertook a detailed kinetic analysis of the actomyosin VI ATPase cycle to determine whether there are unique adaptations to support reverse directionality and to determine the molecular basis of regulation by HCP. ADP release is the rate-limiting step in the cycle. ATP binds slowly and with low affinity. At physiological nucleotide concentrations, myosin VI is strongly bound to actin and populates the nucleotide-free (rigor) and ADP-bound states. Therefore, myosin VI is a high duty ratio motor adapted for maintaining tension and has potential to be processive. A mutant mimicking HCP increases the rate of P(i) release, which lowers the K(ATPase) but does not affect ADP release. These measurements are the first to directly measure the steps regulated by HCP for any myosin. Measurements with double-headed myosin VI demonstrate that the heads are not independent, and the native dimer hydrolyzes multiple ATPs per diffusional encounter with an actin filament. We propose an alternating site model for the stepping and processivity of two-headed high duty ratio myosins.