Myosin V walks by lever action and Brownian motion

Cargo properties play a critical role in myosin Va-driven cargo transport along actin filaments

High-resolution experiments revealed that a single myosin-Va motor can transport micron-sized cargo on actin filaments in a stepwise manner. However, intracellular cargo transport is mediated through the dense actin meshwork by a team of myosin Va motors. The mechanism of how motors interact mechanically to bring about efficient cargo transport is still poorly understood. This study describes a stochastic model where a quantitative understanding of the collective behaviors of myosin Va motors is developed based on cargo stiffness. To understand how cargo properties affect the overall cargo transport, we have designed a model in which two myosin Va motors were coupled by wormlike chain tethers with persistence length ranging from 10 to 80 nm and contour length from 100 to 200 nm, and predicted distributions of velocity, run length, and tether force. Our analysis showed that these parameters are sensitive to both the contour and persistence length of cargo. While the velocity of two couple motors is decreased compared to a single motor (from 531 ± 251 nm/s to as low as 318 ± 287 nm/s), the run length (716 ± 563 nm for a single motor) decreased for short, rigid tethers (to as low as 377 ± 187 μm) and increased for long, flexible tethers (to as high as 1.74 ± 1.50 μm). The sensitivity of processive properties to tether rigidity (persistence length) was greatest for short tethers, which caused the motors to exhibit close, yet anti-cooperative coordination. Motors coupled by longer tethers stepped more independently regardless of tether rigidity. Therefore, the properties of the cargo or linkage must play an essential role in motor-motor communication and cargo transport.

Myosins and Disease

Myosins constitute a superfamily of actin-based molecular motor proteins that mediates a variety of cellular activities including muscle contraction, cell migration, intracellular transport, the formation of membrane projections, cell adhesion, and cell signaling. The 12 myosin classes that are expressed in humans share sequence similarities especially in the N-terminal motor domain; however, their enzymatic activities, regulation, ability to dimerize, binding partners, and cellular functions differ. It is becoming increasingly apparent that defects in myosins are associated with diseases including cardiomyopathies, colitis, glomerulosclerosis, neurological defects, cancer, blindness, and deafness. Here, we review the current state of knowledge regarding myosins and disease.

High-Speed Atomic Force Microscopy to Study Myosin Motility

High-speed atomic force microscopy (HS-AFM) is a unique tool that enables imaging of protein molecules during their functional activity at sub-100 ms temporal and submolecular spatial resolution. HS-AFM is suited for the study of highly dynamic proteins, including myosin motors. HS-AFM images of myosin V walking on actin filaments provide irrefutable evidence for the swinging lever arm motion propelling the molecule forward. Moreover, molecular behaviors that have not been noticed before are also displayed on the AFM movies. This chapter describes the principle, underlying techniques and performance of HS-AFM, filmed images of myosin V, and mechanistic insights into myosin motility provided from the filmed images.

Myosin V executes steps of variable length via structurally constrained diffusion

The molecular motor myosin V transports cargo by stepping on actin filaments, executing a random diffusive search for actin binding sites at each step. A recent experiment suggests that the joint between the myosin lever arms may not rotate freely, as assumed in earlier studies, but instead has a preferred angle giving rise to structurally constrained diffusion. We address this controversy through comprehensive analytical and numerical modeling of myosin V diffusion and stepping. When the joint is constrained, our model reproduces the experimentally observed diffusion, allowing us to estimate bounds on the constraint energy. We also test the consistency between the constrained diffusion model and previous measurements of step size distributions and the load dependence of various observable quantities. The theory lets us address the biological significance of the constrained joint and provides testable predictions of new myosin behaviors, including the stomp distribution and the run length under off-axis force.

Intra- and intercellular transport of substances: Models and mechanisms

Non-equilibrium-statistical models of intracellular transport are built. The most significant features of these models are microscopic reversibility and the explicit considerations of the driving forces of the process - the ATP-ADP chemical potential difference. In this paper, water transport using contractile vacuoles, the transport and assembly of microtubules and microfilaments, the protein distribution within a cell, the transport of neurotransmitters from the synaptic cleft and the transport of substances between cells using plasmodesmata are discussed. Endocytosis and phagocytosis models are considered, and transport tasks and information transfer mechanisms inside the cell are explored. Based on an analysis of chloroplast movement, it was concluded that they have a complicated method of influencing each other in the course of their movements. The role of quantum effects in sorting and control transport mechanisms is also discussed. It is likely that quantum effects play a large role in these processes, otherwise reliable molecular recognition would be impossible, which would lead to very low intracellular transport efficiency.

Structural basis for power stroke vs. Brownian ratchet mechanisms of motor proteins

Two mechanisms have been proposed for the function of motor proteins: The power stroke and the Brownian ratchet. The former refers to generation of a large downhill free energy gradient over which the motor protein moves nearly irreversibly in making a step, whereas the latter refers to biasing or rectifying the diffusive motion of the motor. Both mechanisms require input of free energy, which generally involves the processing of an ATP (adenosine 5'-triphosphate) molecule. Recent advances in experiments that reveal the details of the stepping motion of motor proteins, together with computer simulations of atomistic structures, have provided greater insights into the mechanisms. Here, we compare the various models of the power stroke and the Brownian ratchet that have been proposed. The 2 mechanisms are not mutually exclusive, and various motor proteins employ them to different extents to perform their biological function. As examples, we discuss linear motor proteins Kinesin-1 and myosin-V, and the rotary motor F₁-ATPase, all of which involve a power stroke as the essential element of their stepping mechanism.

Characteristics of Myosin V Processivity

Myosin V is a processive doubled-headed biomolecular motor involved in many intracellular organelle and vesicle transport. The unidirectional movement is coupled with the adenosine triphosphate (ATP) hydrolysis and product release cycle. With the progress of experimental techniques and the enhancement of measuring directness, detailed knowledge of the motility of myosin V has been obtained. Following the ATPase cycle, the 4-state mechanochemical model of the myosin V's processive movement is used. The transitions between various states take place in a stochastic manner. We can use the master equation to analyze and calculate quantitatively. Meanwhile, the effect of the reverse reaction is taken fully into account. We fit the mean velocity, the mean dwell time, the mean run length, and the ratio of forward/backward steps as a functionof ATP, ADP, and Pi concertration. The theoretical curves are generally in line with the experimental data. This work provides a new insight for the characteristic of myosin V.

Myosin V: Chemomechanical-coupling ratchet with load-induced mechanical slip

A chemomechanical-network model for myosin V is presented on the basis of both the nucleotide-dependent binding affinity of the head to an actin filament (AF) and asymmetries and similarity relations among the chemical transitions due to an intramolecular strain of the leading and trailing heads. The model allows for branched chemomechanical cycles and takes into account not only two different force-generating mechanical transitions between states wherein the leading head is strongly bound and the trailing head is weakly bound to the AF but also load-induced mechanical-slip transitions between states in which both heads are strongly bound. The latter is supported by the fact that ATP-independent high-speed backward stepping has been observed for myosin V, although such motility has never been for kinesin. The network model appears as follows: (1) the high chemomechanical-coupling ratio between forward step and ATP hydrolysis is achieved even at low ATP concentrations by the dual mechanical transitions; (2) the forward stepping at high ATP concentrations is explained by the front head-gating mechanism wherein the power stroke is triggered by the inorganic-phosphate (Pi) release from the leading head; (3) the ATP-binding or hydrolyzed ADP.Pi-binding leading head produces a stable binding to the AF, especially against backward loading.

Single-molecule imaging and manipulation of biomolecular machines and systems

BACKGROUND

Biological molecular machines support various activities and behaviors of cells, such as energy production, signal transduction, growth, differentiation, and migration.

SCOPE OF REVIEW

We provide an overview of single-molecule imaging methods involving both small and large probes used to monitor the dynamic motions of molecular machines in vitro (purified proteins) and in living cells, and single-molecule manipulation methods used to measure the forces, mechanical properties and responses of biomolecules. We also introduce several examples of single-molecule analysis, focusing primarily on motor proteins and signal transduction systems.

MAJOR CONCLUSIONS

Single-molecule analysis is a powerful approach to unveil the operational mechanisms both of individual molecular machines and of systems consisting of many molecular machines.

GENERAL SIGNIFICANCE

Quantitative, high-resolution single-molecule analyses of biomolecular systems at the various hierarchies of life will help to answer our fundamental question: "What is life?" This article is part of a Special Issue entitled "Biophysical Exploration of Dynamical Ordering of Biomolecular Systems" edited by Dr. Koichi Kato.

Run-and-pause dynamics of cytoskeletal motor proteins

Cytoskeletal motor proteins are involved in major intracellular transport processes which are vital for maintaining appropriate cellular function. When attached to cytoskeletal filaments, the motor exhibits distinct states of motility: active motion along the filaments, and pause phase in which it remains stationary for a finite time interval. The transition probabilities between motion and pause phases are asymmetric in general, and considerably affected by changes in environmental conditions which influences the efficiency of cargo delivery to specific targets. By considering the motion of individual non-interacting molecular motors on a single filament as well as a dynamic filamentous network, we present an analytical model for the dynamics of self-propelled particles which undergo frequent pause phases. The interplay between motor processivity, structural properties of filamentous network, and transition probabilities between the two states of motility drastically changes the dynamics: multiple transitions between different types of anomalous diffusive dynamics occur and the crossover time to the asymptotic diffusive or ballistic motion varies by several orders of magnitude. We map out the phase diagrams in the space of transition probabilities, and address the role of initial conditions of motion on the resulting dynamics.

Myosin Vc Is Specialized for Transport on a Secretory Superhighway

A hallmark of the well-studied vertebrate class Va myosin is its ability to take multiple steps on actin as a single molecule without dissociating, a feature called "processivity." Therefore, it was surprising when kinetic and single-molecule assays showed that human myosin Vc (MyoVc) was not processive on single-actin filaments [1-3]. We explored the possibility that MyoVc is processive only under conditions that resemble its biological context. Recently, it was shown that zymogen vesicles are transported on actin "superhighways" composed of parallel actin cables nucleated by formins from the plasma membrane [4]. Loss of these cables compromises orderly apical targeting of vesicles. MyoVc has been implicated in transporting secretory vesicles to the apical membrane [5]. We hypothesized that actin cables regulate the processive properties of MyoVc. We show that MyoVc is unique in taking variable size steps, which are frequently in the backward direction. Results obtained with chimeric constructs implicate the lever arm/rod of MyoVc as being responsible for these properties. Actin bundles allow single MyoVc motors to move processively. Remarkably, even teams of MyoVc motors require actin bundles to move continuously at physiological ionic strength. The irregular stepping pattern of MyoVc, which may result from flexibility in the lever arm/rod of MyoVc, appears to be a unique structural adaptation that allows the actin track to spatially restrict the activity of MyoVc to specialized actin cables in order to co-ordinate and target the final stages of vesicle secretion.

Mechanics and Activation of Unconventional Myosins

Many types of cellular motility are based on the myosin family of motor proteins ranging from muscle contraction to exo- and endocytosis, cytokinesis, cell locomotion or signal transduction in hearing. At the center of this wide range of motile processes lies the adaptation of the myosins for each specific mechanical task and the ability to coordinate the timing of motor protein mobilization and targeting. In recent years, great progress has been made in developing single molecule technology to characterize the diverse mechanical properties of the unconventional myosins. Here, we discuss the basic mechanisms and mechanical adaptations of unconventional myosins, and emerging principles regulating motor mobilization and targeting.

Flexural Stiffness of Myosin Va Subdomains as Measured from Tethered Particle Motion

Myosin Va (MyoVa) is a processive molecular motor involved in intracellular cargo transport on the actin cytoskeleton. The motor's processivity and ability to navigate actin intersections are believed to be governed by the stiffness of various parts of the motor's structure. Specifically, changes in calcium may regulate motor processivity by altering the motor's lever arm stiffness and thus its interhead communication. In order to measure the flexural stiffness of MyoVa subdomains, we use tethered particle microscopy, which relates the Brownian motion of fluorescent quantum dots, which are attached to various single- and double-headed MyoVa constructs bound to actin in rigor, to the motor's flexural stiffness. Based on these measurements, the MyoVa lever arm and coiled-coil rod domain have comparable flexural stiffness (0.034 pN/nm). Upon addition of calcium, the lever arm stiffness is reduced 40% as a result of calmodulins potentially dissociating from the lever arm. In addition, the flexural stiffness of the full-length MyoVa construct is an order of magnitude less stiff than both a single lever arm and the coiled-coil rod. This suggests that the MyoVa lever arm-rod junction provides a flexible hinge that would allow the motor to maneuver cargo through the complex intracellular actin network.

Persistent-random-walk approach to anomalous transport of self-propelled particles

The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walk's displacement. It is shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short-time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.

Structural dynamics of myosin 5 during processive motion revealed by interferometric scattering microscopy

Myosin 5a is a dual-headed molecular motor that transports cargo along actin filaments. By following the motion of individual heads with interferometric scattering microscopy at nm spatial and ms temporal precision we found that the detached head occupies a loosely fixed position to one side of actin from which it rebinds in a controlled manner while executing a step. Improving the spatial precision to the sub-nm regime provided evidence for an ångstrom-level structural transition in the motor domain associated with the power stroke. Simultaneous tracking of both heads revealed that consecutive steps follow identical paths to the same side of actin in a compass-like spinning motion demonstrating a symmetrical walking pattern. These results visualize many of the critical unknown aspects of the stepping mechanism of myosin 5 including head-head coordination, the origin of lever-arm motion and the spatiotemporal dynamics of the translocating head during individual steps.

Structural dynamics of myosin 5 during processive motion revealed by interferometric scattering microscopy

Myosin 5a is a dual-headed molecular motor that transports cargo along actin filaments. By following the motion of individual heads with interferometric scattering microscopy at nm spatial and ms temporal precision we found that the detached head occupies a loosely fixed position to one side of actin from which it rebinds in a controlled manner while executing a step. Improving the spatial precision to the sub-nm regime provided evidence for an ångstrom-level structural transition in the motor domain associated with the power stroke. Simultaneous tracking of both heads revealed that consecutive steps follow identical paths to the same side of actin in a compass-like spinning motion demonstrating a symmetrical walking pattern. These results visualize many of the critical unknown aspects of the stepping mechanism of myosin 5 including head-head coordination, the origin of lever-arm motion and the spatiotemporal dynamics of the translocating head during individual steps.

Anomalous diffusion of self-propelled particles in directed random environments

We theoretically study the transport properties of self-propelled particles on complex structures, such as motor proteins on filament networks. A general master equation formalism is developed to investigate the persistent motion of individual random walkers, which enables us to identify the contributions of key parameters: the motor processivity, and the anisotropy and heterogeneity of the underlying network. We prove the existence of different dynamical regimes of anomalous motion, and that the crossover times between these regimes as well as the asymptotic diffusion coefficient can be increased by several orders of magnitude within biologically relevant control parameter ranges. In terms of motion in continuous space, the interplay between stepping strategy and persistency of the walker is established as a source of anomalous diffusion at short and intermediate time scales.

The path to visualization of walking myosin V by high-speed atomic force microscopy

The quest for understanding the mechanism of myosin-based motility started with studies on muscle contraction. From numerous studies, the basic frameworks for this mechanism were constructed and brilliant hypotheses were put forward. However, the argument about the most crucial issue of how the actin-myosin interaction generates contractile force and shortening has not been definitive. To increase the "directness of measurement", in vitro motility assays and single-molecule optical techniques were created and used. Consequently, detailed knowledge of the motility of muscle myosin evolved, which resulted in provoking more arguments to a higher level. In parallel with technical progress, advances in cell biology led to the discovery of many classes of myosins. Myosin V was discovered to be a processive motor, unlike myosin II. The processivity reduced experimental difficulties because it allowed continuous tracing of the motor action of single myosin V molecules. Extensive studies of myosin V were expected to resolve arguments and build a consensus but did not necessarily do so. The directness of measurement was further enhanced by the recent advent of high-speed atomic force microscopy capable of directly visualizing biological molecules in action at high spatiotemporal resolution. This microscopy clearly visualized myosin V molecules walking on actin filaments and at last provided irrefutable evidence for the swinging lever-arm motion propelling the molecules. However, a peculiar foot stomp behavior also appeared in the AFM movie, raising new questions of the chemo-mechanical coupling in this motor and myosin motors in general. This article reviews these changes in the research of myosin motility and proposes new ideas to resolve the newly raised questions.

Unitary step of gliding machinery in Mycoplasma mobile

Among the bacteria that glide on substrate surfaces, Mycoplasma mobile is one of the fastest, exhibiting smooth movement with a speed of 2.0-4.5 μm⋅s(-1) with a cycle of attachment to and detachment from sialylated oligosaccharides. To study the gliding mechanism at the molecular level, we applied an assay with a fluorescently labeled and membrane-permeabilized ghost model, and investigated the motility by high precision colocalization microscopy. Under conditions designed to reduce the number of motor interactions on a randomly oriented substrate, ghosts took unitary 70-nm steps in the direction of gliding. Although it remains possible that the stepping behavior is produced by multiple interactions, our data suggest that these steps are produced by a unitary gliding machine that need not move between sites arranged on a cytoskeletal lattice.

Interplay between the mechanics of bacteriophage fibers and the strength of virus-host links

Viral fibers play a central role in many virus infection mechanisms since they recognize the corresponding host and establish a mechanical link to its surface. Specifically, bacteriophages have to anchor to bacteria through the fibers surrounding the tail before starting the viral DNA translocation into the host. The protein gene product (gp) 37 from bacteriophage T4 long tail fibers forms a fibrous parallel homotrimer located at the distal end of the long tail fibers. Biochemical data indicate that, at least, three of these fibers are required for initial host cell interaction but do not reveal why three and no other numbers are required. By using atomic force microscopy, we obtained high-resolution images of gp37 fibers adsorbed on a mica substrate in buffer conditions and probed their local mechanical properties. Our experiments of radial indentation at the nanometer scale provided a radial stiffness of ∼ 0.08 N/m and a breaking force of ∼ 120 pN. In addition, we performed finite element analysis and determined a Young's modulus of ∼ 20 MPa. From these mechanical parameters, we hypothesize that three viral fibers provide enough mechanical strength to prevent a T4 virus from being detached from the bacteria by the viral particle Brownian motion, delivering a biophysical justification for the previous biochemical data.

Coupling of lever arm swing and biased Brownian motion in actomyosin

An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (P_i) and ADP weakly binds to actin and that after releasing P_i and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5–11 nm displacement due to the biased Brownian motion and the 3–5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.

Myosin II is a molecular motor that is fueled by ATP hydrolysis and generates mechanical force by interacting with actin filament. Comparison among various myosin structures obtained by X-ray and electron microscope analyses has led to the hypothesis that structural change of myosin in ATP hydrolysis cycle is the driving mechanism of force generation. However, single-molecule experiments have suggested an alternative mechanism in which myosin moves stochastically in a biased direction along actin filament. Computer simulation serves as a platform for assessing these hypotheses by revealing the prominent features of the dynamically changing landscape of actin-myosin interaction. The calculated results show that myosin binds to actin at different locations of actin filament in the weak- and strong-binding states and that the free energy has a global gradient from the weak-binding site to the strong-binding site. Myosin relaxing into the strong-binding state therefore necessarily shows the biased Brownian motion toward the strong-binding site. Lever-arm swing is induced during this relaxation process; therefore, lever-arm swing and the biased Brownian motion are coupled to contribute to the net displacement of myosin. This coupling should affect the dynamical behaviors of muscle and cardiac systems.

Myosin V is a biological Brownian machine

Myosin V is a vesicle transporter that unidirectionally walks along cytoskeletal actin filaments by converting the chemical energy of ATP into mechanical work. Recently, it was found that myosin V force generation is a composition of two processes: a lever-arm swing, which involves a conformational change in the myosin molecule, and a Brownian search-and-catch, which involves a diffusive “search” by the motor domain that is followed by an asymmetric “catch” in the forward actin target such that Brownian motion is rectified. Here we developed a system that combines optical tweezers with DNA nano-material to show that the Brownian search-and-catch mechanism is the energetically dominant process at near stall force, providing 13 k_BT of work compared to just 3 k_BT by the lever-arm swing. Our result significantly reconsiders the lever-arm swinging model, which assumes the swing dominantly produces work (>10 k_BT), and sheds light on the Brownian search-and-catch as a driving process.

Structural insights into the globular tails of the human type v myosins Myo5a, Myo5b, And Myo5c

Vertebrate type V myosins (MyoV) Myo5a, Myo5b, and Myo5c mediate transport of several different cargoes. All MyoV paralogs bind to cargo complexes mainly by their C-terminal globular domains. In absence of cargo, the globular domain of Myo5a inhibits its motor domain. Here, we report low-resolution SAXS models for the globular domains from human Myo5a, Myo5b, and Myo5c, which suggest very similar overall shapes of all three paralogs. We determined the crystal structures of globular domains from Myo5a and Myo5b, and provide a homology model for human Myo5c. When we docked the Myo5a crystal structure into a previously published electron microscopy density of the autoinhibited full-length Myo5a, only one domain orientation resulted in a good fit. This structural arrangement suggests the participation of additional region of the globular domain in autoinhibition. Quantification of the interaction of the Myo5a globular domain with its motor complex revealed a tight binding with dissociation half-life in the order of minutes, suggesting a rather slow transition between the active and inactive states.

Design principles governing the motility of myosin V

The molecular motor myosin V (MyoV) exhibits a wide repertoire of pathways during the stepping process, which is intimately connected to its biological function. The best understood of these is the hand-over-hand stepping by a swinging lever arm movement toward the plus end of actin filaments. Single-molecule experiments have also shown that the motor "foot stomps," with one hand detaching and rebinding to the same site, and back-steps under sufficient load. The complete taxonomy of MyoV's load-dependent stepping pathways, and the extent to which these are constrained by motor structure and mechanochemistry, are not understood. Using a polymer model, we develop an analytical theory to describe the minimal physical properties that govern motor dynamics. We solve the first-passage problem of the head reaching the target-binding site, investigating the competing effects of backward load, strain in the leading head biasing the diffusion in the direction of the target, and the possibility of preferential binding to the forward site due to the recovery stroke. The theory reproduces a variety of experimental data, including the power stroke and slow diffusive search regimes in the mean trajectory of the detached head, and the force dependence of the forward-to-backward step ratio, run length, and velocity. We derive a stall force formula, determined by lever arm compliance and chemical cycle rates. By exploring the MyoV design space, we predict that it is a robust motor whose dynamical behavior is not compromised by reasonable perturbations to the reaction cycle and changes in the architecture of the lever arm.

The load dependence of the physical properties of a molecular motor

The physical properties of a molecular motor with load changing in a wide range will be discussed in this study, in particular the mean velocity, output power and energy efficiency. The main difficulty of this study is that both the states of the molecular motor and the energy barriers between them change with the loading force. Moreover, with the change of load, the number of motor states may also change, so different models should be used to calculate the corresponding physical quantities in different ranges of load. The results show that, in contrast to the usual intuition, the mean velocity and output power of the molecular motor do not change continuously with load.

High-speed AFM and applications to biomolecular systems

Directly observing individual protein molecules in action at high spatiotemporal resolution has long been a holy grail for biological science. This is because we long have had to infer how proteins function from the static snapshots of their structures and dynamic behavior of optical makers attached to the molecules. This limitation has recently been removed to a large extent by the materialization of high-speed atomic force microscopy (HS-AFM). HS-AFM allows us to directly visualize the structure dynamics and dynamic processes of biological molecules in physiological solutions, at subsecond to sub-100-ms temporal resolution, without disturbing their function. In fact, dynamically acting molecules such as myosin V walking on an actin filament and bacteriorhodopsin in response to light are successfully visualized. In this review, we first describe theoretical considerations for the highest possible imaging rate of this new microscope, and then highlight recent imaging studies. Finally, the current limitation and future challenges to explore are described.

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.

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.

A branched kinetic scheme describes the mechanochemical coupling of Myosin Va processivity in response to substrate

Myosin Va is a double-headed cargo-carrying molecular motor that moves processively along cellular actin filaments. Long processive runs are achieved through mechanical coordination between the two heads of myosin Va, which keeps their ATPase cycles out of phase, preventing both heads detaching from actin simultaneously. The biochemical kinetics underlying processivity are still uncertain. Here we attempt to define the biochemical pathways populated by myosin Va by examining the velocity, processive run-length, and individual steps of a Qdot-labeled myosin Va in various substrate conditions (i.e., changes in ATP, ADP, and P(i)) under zero load in the single-molecule total internal reflection fluorescence microscopy assay. These data were used to globally constrain a branched kinetic scheme that was necessary to fit the dependences of velocity and run-length on substrate conditions. Based on this model, myosin Va can be biased along a given pathway by changes in substrate concentrations. This has uncovered states not normally sampled by the motor, and suggests that every transition involving substrate binding and release may be strain-dependent.

Mechanical properties of viruses

Structural biology techniques have greatly contributed to unveil the relationships between structure, properties and functions of viruses. In recent years, classic structural approaches are being complemented by single-molecule techniques such as atomic force microscopy and optical tweezers to study physical properties and functions of viral particles that are not accessible to classic structural techniques. Among these features are mechanical properties such as stiffness, intrinsic elasticity, tensile strength and material fatigue. The field of virus mechanics is contributing to materials science by investigating some physical parameters of "soft" biological matter and biological nano-objects. Virus mechanics studies are also starting to unveil the biological implications of physical properties of viruses. Growing evidence indicate that viruses are subjected to internal and external forces, and that they may have adapted to withstand and even use those forces. This chapter describes what is known on the mechanical properties of virus particles, their structural determinants, and possible biological implications, of which several examples are provided.

Muscle contraction mechanism based on single molecule measurements

Single molecule measurements have shown that a muscle myosin step is driven by biased Brownian movement. Furthermore, they have also demonstrated that in response to strain in the backward direction a detached myosin head preferentially attaches to the forward direction due to an accelerated transition from a weak binding to strong binding state. Because they are consistent with the original Huxley model for muscle contraction, we have built a model that describes macroscopic muscle characteristics based on these single molecule results.

Myosin VI has a one track mind versus myosin Va when moving on actin bundles or at an intersection

Myosin VI (myoVI) and myosin Va (myoVa) serve roles both as intracellular cargo transporters and tethers/anchors. In both capacities, these motors bind to and processively travel along the actin cytoskeleton, a network of intersecting actin filaments and bundles that present directional challenges to these motors. Are myoVI and myoVa inherently different in their abilities to interact and maneuver through the complexities of the actin cytoskeleton? Thus, we created an in vitro model system of intersecting actin filaments and individual unipolar (fascin-actin) or mixed polarity (α-actinin-actin) bundles. The stepping dynamics of individual Qdot-labeled myoVI and myoVa motors were determined on these actin tracks. Interestingly, myoVI prefers to stay on the actin filament it is traveling on, while myoVa switches filaments with higher probability at an intersection or between filaments in a bundle. The structural basis for this maneuverability difference was assessed by expressing a myoVI chimera in which the single myoVI IQ was replaced with the longer, six IQ myoVa lever. The mutant behaved more like myoVI at actin intersections and on bundles, suggesting that a structural element other than the lever arm dictates myoVI's preference to stay on track, which may be critical to its role as an intracellular anchor.

Microfluidic multifunctional probe array dielectrophoretic force spectroscopy with wide loading rates

The simultaneous investigation of a large number of events with different types of intermolecular interactions, from nonequilibrium high-force pulling assays to quasi-equilibrium unbinding events in the same environment, can be very important for fully understanding intermolecular bond-rupture mechanisms. Here, we describe a novel dielectrophoretic force spectroscopy technique that utilizes microsized beads as multifunctional probes for parallel measurement of intermolecular forces with an extremely wide range of force rate (10(-4) to 10(4) pN/s) inside a microfluidic device. In our experiments, various forces, which broadly form the basis of all molecular interactions, were measured across a range of force loading rates by multifunctional probes of various diameters with a throughput of over 600 events per mm(2), simultaneously and in the same environment. Furthermore, the individual bond-rupture forces, the parameters for the characterization of entire energy landscapes, and the effective stiffness of the force spectroscopy were determined on the basis of the measured results. This method of determining intermolecular forces could be very useful for the precise and simultaneous examination of various molecular interactions, as it can be easily and cost-effectively implemented within a microfluidic device for a range of applications including immunoassays, molecular mechanics, chemical and biological screening, and mechanobiology.

Switching of myosin-V motion between the lever-arm swing and brownian search-and-catch

Motor proteins are force-generating nanomachines that are highly adaptable to their ever-changing biological environments and have a high energy conversion efficiency. Here we constructed an imaging system that uses optical tweezers and a DNA handle to visualize elementary mechanical processes of a nanomachine under load. We apply our system to myosin-V, a well-known motor protein that takes 72 nm 'hand-over-hand' steps composed of a 'lever-arm swing' and a 'brownian search-and-catch'. We find that the lever-arm swing generates a large proportion of the force at low load (<0.5 pN), resulting in 3 k(B)T of work. At high load (1.9 pN), however, the contribution of the brownian search-and-catch increases to dominate, reaching 13 k(B)T of work. We believe the ability to switch between these two force-generation modes facilitates myosin-V function at high efficiency while operating in a dynamic intracellular environment.

Orientation and rotational motions of single molecules by polarized total internal reflection fluorescence microscopy (polTIRFM)

In this article, we describe methods to detect the spatial orientation and rotational dynamics of single molecules using polarized total internal reflection fluorescence microscopy (polTIRFM). polTIRFM determines the three-dimensional angular orientation and the extent of wobble of a fluorescent probe bound to the macromolecule of interest. We discuss single-molecule versus ensemble measurements, as well as single-molecule techniques for orientation and rotation, and fluorescent probes for orientation studies. Using calmodulin (CaM) as an example of a target protein, we describe a method for labeling CaM with bifunctional rhodamine (BR). We also describe the physical principles and experimental setup of polTIRFM. We conclude with a brief introduction to assays using polTIRFM to assess the interaction of actin and myosin.

Fluorescence microscopy for simultaneous observation of 3D orientation and movement and its application to quantum rod-tagged myosin V

Single molecule fluorescence polarization techniques have been used for three-dimensional (3D) orientation measurements to observe the dynamic properties of single molecules. However, only few techniques can simultaneously measure 3D orientation and position. Furthermore, these techniques often require complex equipment and cumbersome analysis. We have developed a microscopy system and synthesized highly fluorescent, rod-like shaped quantum dots (Q rods), which have linear polarizations, to simultaneously measure the position and 3D orientation of a single fluorescent probe. The optics splits the fluorescence from the probe into four different spots depending on the polarization angle and projects them onto a CCD camera. These spots are used to determine the 2D position and 3D orientation. Q rod orientations could be determined with better than 10° accuracy at 33 ms time resolution. We applied our microscopy and Q rods to simultaneously measure myosin V movement along an actin filament and rotation around its own axis, finding that myosin V rotates 90° for each step. From this result, we suggest that in the two-headed bound state, myosin V necks are perpendicular to one another, while in the one-headed bound state the detached trailing myosin V head is biased forward in part by rotating its lever arm about its own axis. This microscopy system should be applicable to a wide range of dynamic biological processes that depend on single molecule orientation dynamics.

Tuning the performance of an artificial protein motor

The Tumbleweed (TW) is a concept for an artificial, tri-pedal, protein-based motor designed to move unidirectionally along a linear track by a diffusive tumbling motion. Artificial motors offer the unique opportunity to explore how motor performance depends on design details in a way that is open to experimental investigation. Prior studies have shown that TW's ability to complete many successive steps can be critically dependent on the motor's diffusional step time. Here, we present a simulation study targeted at determining how to minimize the diffusional step time of the TW motor as a function of two particular design choices: nonspecific motor-track interactions and molecular flexibility. We determine an optimal nonspecific interaction strength and establish a set of criteria for optimal molecular flexibility as a function of the nonspecific interaction. We discuss our results in the context of similarities to biological, linear stepping diffusive molecular motors with the aim of identifying general engineering principles for protein motors.

Chemomechanical coupling and motor cycles of myosin V

The molecular motor myosin V has been studied extensively both in bulk and single molecule experiments. Based on the chemical states of the motor, we construct a systematic network theory that includes experimental observations about the stepping behavior of myosin V. We utilize constraints arising from nonequilibrium thermodynamics to determine motor parameters and demonstrate that the motor behavior is governed by three chemomechanical motor cycles. The competition between these cycles can be understood via the influence of external load forces onto the chemical transition rates for the binding of adenosine triphosphate and adenosine diphosphate. In addition, we also investigate the functional dependence of the mechanical stepping rates on these forces. For substall forces, the dominant pathway of the motor network is profoundly different from the one for superstall forces, which leads to a stepping behavior that is in agreement with the experimental observations. Our theory provides a unified description of the experimental data as obtained for myosin V in single motor experiments.

Coarse-grained modeling of conformational transitions underlying the processive stepping of myosin V dimer along filamentous actin

To explore the structural basis of processive stepping of myosin V along filamentous actin, we have performed comprehensive modeling of its key conformational states and transitions with an unprecedented residue level of details. We have built structural models for a myosin V monomer complexed with filamentous actin at four biochemical states [adenosine diphosphate (ATP)-, adenosine diphosphate (ADP)-phosphate-, ADP-bound or nucleotide-free]. Then we have modeled a myosin V dimer (consisting of lead and rear head) at various two-head-bound states with nearly straight lever arms rotated by intramolecular strain. Next, we have performed transition pathway modeling to determine the most favorable sequence of transitions (namely, phosphate release at the lead head followed by ADP release at the rear head, while ADP release at the lead head is inhibited), which underlie the kinetic coordination between the two heads. Finally, we have used transition pathway modeling to reveal the order of structural changes during three key biochemical transitions (phosphate release at the lead head, ADP release and ATP binding at the rear head), which shed lights on the strain-dependence of the allosterically coupled motions at various stages of myosin V's work cycle. Our modeling results are in agreement with and offer structural insights to many results of kinetic, single-molecule and structural studies of myosin V.

Direct observation of the myosin Va recovery stroke that contributes to unidirectional stepping along actin

Myosins are ATP-driven linear molecular motors that work as cellular force generators, transporters, and force sensors. These functions are driven by large-scale nucleotide-dependent conformational changes, termed "strokes"; the "power stroke" is the force-generating swinging of the myosin light chain-binding "neck" domain relative to the motor domain "head" while bound to actin; the "recovery stroke" is the necessary initial motion that primes, or "cocks," myosin while detached from actin. Myosin Va is a processive dimer that steps unidirectionally along actin following a "hand over hand" mechanism in which the trailing head detaches and steps forward ∼72 nm. Despite large rotational Brownian motion of the detached head about a free joint adjoining the two necks, unidirectional stepping is achieved, in part by the power stroke of the attached head that moves the joint forward. However, the power stroke alone cannot fully account for preferential forward site binding since the orientation and angle stability of the detached head, which is determined by the properties of the recovery stroke, dictate actin binding site accessibility. Here, we directly observe the recovery stroke dynamics and fluctuations of myosin Va using a novel, transient caged ATP-controlling system that maintains constant ATP levels through stepwise UV-pulse sequences of varying intensity. We immobilized the neck of monomeric myosin Va on a surface and observed real time motions of bead(s) attached site-specifically to the head. ATP induces a transient swing of the neck to the post-recovery stroke conformation, where it remains for ∼40 s, until ATP hydrolysis products are released. Angle distributions indicate that the post-recovery stroke conformation is stabilized by ≥ 5 k(B)T of energy. The high kinetic and energetic stability of the post-recovery stroke conformation favors preferential binding of the detached head to a forward site 72 nm away. Thus, the recovery stroke contributes to unidirectional stepping of myosin Va.

Kinetics and thermodynamics of the rate-limiting conformational change in the actomyosin V mechanochemical cycle

We used FRET to examine the kinetics and thermodynamics of structural changes associated with ADP release in myosin V, which is thought to be a strain-sensitive step in many muscle and non-muscle myosins. We also explored essential dynamics using FIRST/FRODA starting with three different myosin V X-ray crystal structures to examine intrinsic flexibility and correlated motions. Our steady-state and time-resolved FRET analysis demonstrates a temperature-dependent reversible conformational change in the nucleotide-binding pocket (NBP). Our kinetic results demonstrate that the NBP goes from a closed to an open conformation prior to the release of ADP, while the actin-binding cleft remains closed. Interestingly, we find that the temperature dependence of the maximum actin-activated myosin V ATPase rate is similar to the pocket opening step, demonstrating that this is the rate-limiting structural transition in the ATPase cycle. Thermodynamic analysis demonstrates that the transition from the open to closed NBP conformation is unfavorable because of a decrease in entropy. The intrinsic flexibility analysis is consistent with conformational entropy playing a role in this transition as the MV.ADP structure is highly flexible compared to the MV.APO structure. Our experimental and modeling studies support the conclusion of a novel post-power-stroke actomyosin.ADP state in which the NBP and actin-binding cleft are closed. The novel state may be important for strain sensitivity as the transition from the closed to open NBP conformation may be altered by lever arm position.

Moving into the cell: single-molecule studies of molecular motors in complex environments

Much has been learned in the past decades about molecular force generation. Single-molecule techniques, such as atomic force microscopy, single-molecule fluorescence microscopy and optical tweezers, have been key in resolving the mechanisms behind the power strokes, 'processive' steps and forces of cytoskeletal motors. However, it remains unclear how single force generators are integrated into composite mechanical machines in cells to generate complex functions such as mitosis, locomotion, intracellular transport or mechanical sensory transduction. Using dynamic single-molecule techniques to track, manipulate and probe cytoskeletal motor proteins will be crucial in providing new insights.

Switch between large hand-over-hand and small inchworm-like steps in myosin VI

Many biological motor molecules move within cells using stepsizes predictable from their structures. Myosin VI, however, has much larger and more broadly distributed stepsizes than those predicted from its short lever arms. We explain the discrepancy by monitoring Qdots and gold nanoparticles attached to the myosin-VI motor domains using high-sensitivity nanoimaging. The large stepsizes were attributed to an extended and relatively rigid lever arm; their variability to two stepsizes, one large (72 nm) and one small (44 nm). These results suggest that there exist two tilt angles during myosin-VI stepping, which correspond to the pre- and postpowerstroke states and regulate the leading head. The large steps are consistent with the previously reported hand-over-hand mechanism, while the small steps follow an inchworm-like mechanism and increase in frequency with ADP. Switching between these two mechanisms in a strain-sensitive, ADP-dependent manner allows myosin VI to fulfill its multiple cellular tasks including vesicle transport and membrane anchoring.