How Cytoplasmic Dynein Couples ATP Hydrolysis Cycle to Diverse Stepping Motions: Kinetic Modeling

Cytoplasmic dynein is a two-headed molecular motor that moves to the minus end of a microtubule by ATP hydrolysis free energy. By employing its two heads (motor domains), cytoplasmic dynein exhibits various bipedal stepping motions: inchworm and hand-over-hand motions, as well as nonalternating steps of one head. However, the molecular basis to achieve such diverse stepping manners remains unclear because of the lack of an experimental method to observe stepping and the ATPase reaction of dynein simultaneously. Here, we propose a kinetic model for bipedal motions of cytoplasmic dynein and perform Gillespie Monte Carlo simulations that qualitatively reproduce most experimental data obtained to date. The model represents the status of each motor domain as five states according to conformation and nucleotide- and microtubule-binding conditions of the domain. In addition, the relative positions of the two domains were approximated by three discrete states. Accompanied by ATP hydrolysis cycles, the model dynein stochastically and processively moved forward in multiple steps via diverse pathways, including inchworm and hand-over-hand motions, similarly to experimental data. The model reproduced key experimental motility-related properties, including velocity and run length, as functions of the ATP concentration and external force, therefore providing a plausible explanation of how dynein achieves various stepping manners with explicit characterization of nucleotide states. Our model highlights the uniqueness of dynein in the coupling of ATPase with its movement during both inchworm and hand-over-hand stepping.     

Myosin VI walks hand-over-hand along actin

Myosin VI is a molecular motor that can walk processively on actin filaments with a 36-nm step size. The walking mechanism of myosin VI is controversial because it takes very large steps without an apparent lever arm of required length. Therefore, myosin VI is argued to be the first exception to the widely established lever arm theory. It is therefore critical to directly demonstrate whether this motor walks hand-over-hand along actin despite its short lever arm. Here, we follow the displacement of a single myosin VI head during the stepping process. A single head is displaced 72 nm during stepping, whereas the center of mass previously has been shown to move 36 nm. The most likely explanation for this result is a hand-over-hand walking mechanism. We hypothesize the existence of a flexible element that would allow the motor to bridge the observed 72-nm distance.     

The diffusive search mechanism of processive myosin class-V motor involves directional steps along actin subunits

It is widely accepted that the vesicle-transporter myosin-V moves processively along F-actin with large steps of approximately 36 nm using a hand-over-hand mechanism. A key question is how does the rear head of two-headed myosin-V search for the forward actin target in the forward direction. Scanning probe nanometry was used to resolve this underlying search process, which was made possible by attaching the head to a relatively large probe. One-headed myosin-V undergoes directional diffusion with approximately 5.5 nm substeps to develop an average displacement of approximately 20 nm, which was independent of the neck length (2IQ and 6IQ motifs). Two-headed myosin-V showed several approximately 5.5 nm substeps within each processive approximately 36 nm step. These results suggest that the myosin-V head searches in the forward direction for the actin target using directional diffusion on the actin subunits according to a potential slope created along the actin helix.     

Dwell Time Distributions of the Molecular Motor Myosin V

The dwell times between two successive steps of the two-headed molecular motor myosin V are governed by non-exponential distributions. These distributions have been determined experimentally for various control parameters such as nucleotide concentrations and external load force. First, we use a simplified network representation to determine the dwell time distributions of myosin V, with the associated dynamics described by a Markov process on networks with absorbing boundaries. Our approach provides a direct relation between the motor’s chemical kinetics and its stepping properties. In the absence of an external load, the theoretical distributions quantitatively agree with experimental findings for various nucleotide concentrations. Second, using a more complex branched network, which includes ADP release from the leading head, we are able to elucidate the motor’s gating effect. This effect is caused by an asymmetry in the chemical properties of the leading and the trailing head of the motor molecule. In the case of an external load acting on the motor, the corresponding dwell time distributions reveal details about the motor’s backsteps.     

Processivity and Velocity for Motors Stepping on Periodic Tracks

Processive molecular motors enable cargo transportation by assembling into dimers capable of taking several consecutive steps along a cytoskeletal filament. In the well-accepted hand-over-hand stepping mechanism, the trailing motor detaches from the track and binds the filament again in the leading position. This requires fuel consumption in the form of ATP hydrolysis and coordination of the catalytic cycles between the leading and the trailing heads. Alternate stepping pathways also exist, including inchworm-like movements, backward steps, and foot stomps. Whether all the pathways are coupled to ATP hydrolysis remains to be determined. Here, to establish the principles governing the dynamics of processive movement, we present a theoretical framework that includes all of the alternative stepping mechanisms. Our theory bridges the gap between the elemental rates describing the biochemical and structural transitions in each head and the experimentally measurable quantities such as velocity, processivity, and probability of backward stepping. Our results, obtained under the assumption that the track is periodic and infinite, provide expressions that hold regardless of the topology of the network connecting the intermediate states, and are therefore capable of describing the function of any molecular motor. We apply the theory to myosin VI, a motor that takes frequent backward steps and moves forward with a combination of hand-over-hand and inchworm-like steps. Our model quantitatively reproduces various observables of myosin VI motility reported by four experimental groups. The theory is used to predict the gating mechanism, the pathway for backward stepping, and the energy consumption as a function of ATP concentration.     

The Lever Arm Effects a Mechanical Asymmetry of the Myosin-V-Actin Bond

Myosin-V is a two-headed molecular motor taking multiple ATP-dependent steps toward the plus end (forward) of actin filaments. At high mechanical loads, the motor processively steps toward the minus end (backward) even in the absence of ATP, whereas analogous forward steps cannot be induced. The detailed mechanism underlying this mechanical asymmetry is not known. We investigate the effect of force on individual single headed myosin-V constructs bound to actin in the absence of ATP. If pulled forward, the myosin-V head dissociates at forces twice as high than if pulled backward. Moreover, backward but not forward distances to the unbinding barrier are dependent on the lever arm length. This asymmetry of unbinding force distributions in a single headed myosin forms the basis of the two-headed asymmetry. Under load, the lever arm functions as a true lever in a mechanical sense.     

Flexible light-chain and helical structure of F-actin explain the movement and step size of myosin-VI

Myosin-VI is a dimeric isoform of unconventional myosins. Single molecule experiments indicate that myosin-VI and myosin-V are processive molecular motors, but travel toward opposite ends of filamentous actin. Structural studies show several differences between myosin-V and VI, including a significant difference in the light-chain domain connecting the motor domains. Combining the measured kinetics of myosin-VI with the elasticity of the light chains, and the helical structure of F-actin, we compare and contrast the motility of myosin-VI with myosin-V. We show that the elastic properties of the light-chain domain control the stepping behavior of these motors. Simple models incorporating the motor elastic energy can quantitatively capture most of the observed data. Implications of our result for other processive motors are discussed.     

Step-size is determined by neck length in myosin V

The highly processive motor, myosin V, has an extremely long neck containing six calmodulin-binding IQ motifs that allows it to take multiple 36 nm steps corresponding to the pseudo-repeat of actin. To further investigate how myosin V moves processively on actin filaments, we altered the length of the neck by adding or deleting IQ motifs in myosin constructs lacking the globular tail domain. These myosin V IQ mutants were fluorescently labeled by exchange of a single Cy3-labeled calmodulin into the neck region of one head. We measured the step-size of these individual IQ mutants with nanometer precision and subsecond resolution using FIONA. The step-size was proportional to neck length for constructs containing 2, 4, 6, and 8 IQ motifs, providing strong support for the swinging lever-arm model of myosin motility. In addition, the kinetics of stepping provided additional support for the hand-over-hand model whereby the two heads alternately assume the leading position. Interestingly, the 8IQ myosin V mutant gave a broad distribution of step-sizes with multiple peaks, suggesting that this mutant has many choices of binding sites on an actin filament. These data demonstrate that the step-size of myosin V is affected by the length of its neck and is not solely determined by the pseudo-repeat of the actin filament.     

Dynamics of myosin-V processivity

Myosin-V is an actin-associated processive molecular motor. Single molecule experiments revealed that myosin-V walks in a stepwise fashion with occasional backward steps. By combining the mechanical structure of the motor with the ATP hydrolysis kinetics, we construct a dynamical model that accounts for the stepwise processivity. The molecular properties of the protein chains connecting the myosin heads are important. A simple elastic model demonstrates that the stress transmitted from the leading head to the trailing head leads to net forward motion. The step-sizes are non-uniform. We also predict there are several substeps. The translational speed and step-size distributions are computed for several different conditions. The computed force-versus-velocity curve shows that under an external load, myosin-V slows down. However, the sizes of the steps remain the same.     

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.     

Orientation dependence of displacements by a single one-headed myosin relative to the actin filament.

Displacements of single one-headed myosin molecules in a sparse myosin-rod cofilament were measured from bead displacements at various angles relative to an actin filament by dual optical trapping nanometry. The sparse myosin-rod cofilaments, 5-8 micron long, were synthesized by slowly mixing one-headed myosin prepared by papain digestion with myosin rods at molar ratios of 1:400 to 1:1500, so that one to four one-headed myosin molecules were on average scattered along the cofilament. The bead displacement was approximately 10 nm at low loads ( approximately 0.5 pN) and at angles of 5-10 degrees between the actin and myosin filaments (near physiologically correct orientation). The bead displacement decreased with an increase in the angle. The bead displacement at nearly 90 degrees was approximately 0 nm. When the angle was increased to approximately 150 degrees-170 degrees, the bead displacements increased to 5 nm. A native two-headed myosin showed similar size and orientation dependence of bead displacements as a one-headed myosin.     

Dissection of Kinesin's Processivity

The protein family of kinesins contains processive motor proteins that move stepwise along microtubules. This mechanism requires the precise coupling of the catalytic steps in the two heads, and their precise mechanical coordination. Here we show that these functionalities can be uncoupled in chimera of processive and non-processive kinesins. A chimera with the motor domain of Kinesin-1 and the dimerization domain of a non-processive Kinesin-3 motor behaves qualitatively as conventional kinesin and moves processively in TIRF and bead motility assays, suggesting that spatial proximity of two Kinein-1 motor domains is sufficient for processive behavior. In the reverse chimera, the non-processive motor domains are unable to step along microtubules, despite the presence of the Kinesin-1 neck coiled coil. Still, ATP-binding to one head of these chimera induces ADP-release from the partner head, a characteristic feature of alternating site catalysis. These results show that processive movement of kinesin dimers requires elements in the motor head that respond to ADP-release and induce stepping, in addition to a proper spacing of the motor heads via the neck coiled coil.     

Interhead distance measurements in myosin VI via SHRImP support a simplified hand-over-hand model

Myosin VI walks in a hand-over-hand fashion with an average step size of 30 nm, which is much larger than its 10 nm lever arm. Recent experiments suggest that the myosin VI structure has an unfolded and flexible region in the proximal tail which makes such a large step possible. In addition, cryoelectron microscopy images of actomyosin VI show the two heads bound to the actin monomers with a broad distribution of distances, including some as close as a few nanometers. This observation, when combined with the existence of a flexible region in the structure, which takes part in stepping, challenged the hand-over-hand model. In the hand-over-hand model, the lever arm is considered to be rigid and the interhead separation should not be very different from 30 nm. We considered an alternative model in which myosin VI heads sequentially take 60 nm steps whereas the interhead separation alternates between a large and small value (x and 60 - x, where x < 30). To clarify these issues, we used a new technique, SHRImP, to measure the interhead distance of nearly rigor myosin VI molecules. Our data show a single peak at 29.3 +/- 0.7 nm, in agreement with the straightforward hand-over-hand model.     

Rapid double 8-nm steps by a kinesin mutant

The mechanism by which conventional kinesin walks along microtubules is poorly understood, but may involve alternate binding to the microtubule and hydrolysis of ATP by the two heads. Here we report a single amino-acid change that affects stepping by the motor. Under low force or low ATP concentration, the motor moves by successive 8-nm steps in single-motor laser-trap assays, indicating that the mutation does not alter the basic mechanism of kinesin walking. Remarkably, under high force, the mutant motor takes successive 16-nm displacements that can be resolved into rapid double 8-nm steps with a short dwell between steps, followed by a longer dwell. The alternating short and long dwells under high force demonstrate that the motor stepping mechanism is inherently asymmetric, revealing an asymmetric phase in the kinesin walking cycle. Our findings support an asymmetric two-headed walking model for kinesin, with cooperative interactions between the two heads. The sensitivity of the 16-nm displacements to nucleotide and load raises the possibility that ADP release is a force-producing event of the kinesin cycle.     

The neck domain of myosin II primarily regulates the actomyosin kinetics, not the stepsize

In order to study the role of the neck domain of myosin in muscle contraction, we measured the steps of individual myosin II molecules engineered to have no neck domain (light chain-binding domain) by optical trapping nanometry. The actin filament and myosin cofilaments interacted on a glass surface to minimize the angle between them, and to minimize the interaction between myosin and the glass surface. The results showed that the average myosin stepsize did not change much when the neck domain was removed, but the sliding velocity decreased approximately fivefold. Furthermore, the duration of steps for neckless myosin was several times longer at saturated ATP concentration, indicating that the slower velocity was due to a slower dissociation rate of myosin heads from actin. From these data, we conclude that the neck domain of myosin-II primarily regulates the actomyosin kinetics, not the mechanics.     

A unique mechanism for the processive movement of single-headed myosin-IX

It has been puzzled that in spite of its single-headed structure, myosin-IX shows the typical character of processive motor in multi-molecule in vitro motility assay, because this cannot be explained by hand-over-hand mechanism of the two-headed processive myosins. Here, we show direct evidence of the processive movement of myosin-IX using two different single molecule techniques. Using optical trap nanometry, we found that myosin-IX takes several large ( approximately 20nm) steps before detaching from an actin filament. Furthermore, we directly visualized the single myosin-IX molecules moving on actin filaments for several hundred nanometers without dissociating from actin filament. Since myosin-IX processively moves without anchoring the neck domain, the result suggests that the neck tilting is not involved for the processive movement of myosin-IX. We propose that the myosin-IX head moves processively along an actin filament like an inchworm via a unique long and positively charged insertion in the loop 2 region of the head.     

Force-dependent stepping kinetics of myosin-V

Myosin-V is a processive two-headed actin-based motor protein involved in many intracellular transport processes. A key question for understanding myosin-V function and the communication between its two heads is its behavior under load. Since in vivo myosin-V colocalizes with other much stronger motors like kinesins, its behavior under superstall forces is especially relevant. We used optical tweezers with a long-range force feedback to study myosin-V motion under controlled external forward and backward loads over its full run length. We find the mean step size remains constant at approximately 36 nm over a wide range of forces from 5 pN forward to 1.5 pN backward load. We also find two force-dependent transitions in the chemomechanical cycle. The slower ADP-release is rate limiting at low loads and depends only weakly on force. The faster rate depends more strongly on force. The stronger force dependence suggests this rate represents the diffusive search of the leading head for its binding site. In contrast to kinesin motors, myosin-V's run length is essentially independent of force between 5 pN of forward to 1.5 pN of backward load. At superstall forces of 5 pN, we observe continuous backward stepping of myosin-V, indicating that a force-driven reversal of the power stroke is possible.     

Myosin VI walks "wiggly" on actin with large and variable tilting

Myosin VI is an unconventional motor protein with unusual motility properties such as its direction of motion and path on actin and a large stride relative to its short lever arms. To understand these features, the rotational dynamics of the lever arm were studied by single-molecule polarized total internal reflection fluorescence (polTIRF) microscopy during processive motility of myosin VI along actin. The axial angle is distributed in two peaks, consistent with the hand-over-hand model. The changes in lever arm angles during discrete steps suggest that it exhibits large and variable tilting in the plane of actin and to the sides. These motions imply that, in addition to the previously suggested flexible tail domain, there is a compliant region between the motor domain and lever arm that allows myosin VI to accommodate the helical position of binding sites while taking variable step sizes along the actin filament.     

Model for kinetics of myosin-V molecular motors

A hand-over-hand model is presented for the processive movement of myosin-V based on previous biochemical experimental results and structural observations of nucleotide-dependent conformational changes of single-headed myosins. The model shows that the ADP-release rate of the trailing head is much higher than that of the leading head, thus giving a 1 : 1 mechanochemical coupling for the processive movement of the motor. It explains well the previous finding that some 36-nm steps consist of two substeps, while other 36-nm steps consist of no substeps. Using the model, the calculated kinetic behaviors of myosin-V such as the main and intermediate dwell time distributions, the load dependence of the average main and intermediate dwell time and the load dependence of occurrence frequency of the intermediate state under various nucleotide conditions show good quantitative agreement with previous experimental results.     

Tilting and Wobble of Myosin V by High-Speed Single-Molecule Polarized Fluorescence Microscopy

Myosin V is biomolecular motor with two actin-binding domains (heads) that take multiple steps along actin by a hand-over-hand mechanism. We used high-speed polarized total internal reflection fluorescence (polTIRF) microscopy to study the structural dynamics of single myosin V molecules that had been labeled with bifunctional rhodamine linked to one of the calmodulins along the lever arm. With the use of time-correlated single-photon counting technology, the temporal resolution of the polTIRF microscope was improved ∼50-fold relative to earlier studies, and a maximum-likelihood, multitrace change-point algorithm was used to objectively determine the times when structural changes occurred. Short-lived substeps that displayed an abrupt increase in rotational mobility were detected during stepping, likely corresponding to random thermal fluctuations of the stepping head while it searched for its next actin-binding site. Thus, myosin V harnesses its fluctuating environment to extend its reach. Additional, less frequent angle changes, probably not directly associated with steps, were detected in both leading and trailing heads. The high-speed polTIRF method and change-point analysis may be applicable to single-molecule studies of other biological systems.