Mechanism of muscle contraction based on stochastic properties of single actomyosin motors observed in vitro

Landscape-Based View on the Stepping Movement of Myosin VI

Myosin VI dimer walks toward the minus end of the actin filament with a large and variable step size of 25–36 nm. Two competing models have been put forward to explain this large step size. The Spudich model assumes that the myosin VI dimer associates at a distal tail near the cargo-binding domain, which makes two full-length single α-helix (SAH) domains serve as long legs. In contrast, the Houdusse–Sweeney model assumes that the association occurs in the middle (between residues 913 and 940) of the SAH domain and that the three-helix bundles unfold to ensure the large step size. Their consistency with the observation of stepping motion with a large and variable step size has not been examined in detail. To compare the two proposed models of myosin VI, we computationally characterized the free energy landscape experienced by the leading head during the stepping movement along the actin filament using the elastic network model of two heads and an implicit model of the SAH domains. Our results showed that the Spudich model is more consistent with the 25–36 nm step size than the Houdusse–Sweeney model. The unfolding of the three-helix bundles gives rise to the free energy bias toward a shorter distance between two heads. Besides, the stiffness of the SAH domain is a key factor for giving strong energetic bias toward the longer distance of stepping. Free energy analysis of the stepping motion complements the visual inspection of static structures and enables a deeper understanding of underlying mechanisms of molecular motors.

Cross-bridge mechanism of residual force enhancement after stretching in a skeletal muscle

A muscle model that uses a modified Langevin equation with actomyosin potentials was used to describe the residual force enhancement after active stretching. Considering that the new model uses cross-bridge theory to describe the residual force enhancement, it is different from other models that use passive stretching elements. Residual force enhancement was simulated using a half sarcomere comprising 100 myosin molecules. In this paper, impulse is defined as the integral of an excess force from the steady isometric force over the time interval for which a stretch is applied. The impulse was calculated from the force response due to fast and slow muscle stretches to demonstrate the viscoelastic property of the cross-bridges. A cross-bridge mechanism was proposed as a way to describe the residual force enhancement on the basis of the impulse results with reference to the compliance of the actin filament. It was assumed that the period of the actin potential increased by 0.5% and the amplitude of the potential decreased by 0.5% when the half sarcomere was stretched by 10%. The residual force enhancement after 21.0% sarcomere stretching was 6.9% of the maximum isometric force of the muscle; this value was due to the increase in the number of cross-bridges.

Single molecule detection, thermal fluctuation and life

Single molecule detection has contributed to our understanding of the unique mechanisms of life. Unlike artificial man-made machines, biological molecular machines integrate thermal noises rather than avoid them. For example, single molecule detection has demonstrated that myosin motors undergo biased Brownian motion for stepwise movement and that single protein molecules spontaneously change their conformation, for switching to interactions with other proteins, in response to thermal fluctuation. Thus, molecular machines have flexibility and efficiency not seen in artificial machines.

Modulation of Skeletal Muscle Contraction by Myosin Phosphorylation

The striated muscle sarcomere is a highly organized and complex enzymatic and structural organelle. Evolutionary pressures have played a vital role in determining the structure-function relationship of each protein within the sarcomere. A key part of this multimeric assembly is the light chain-binding domain (LCBD) of the myosin II motor molecule. This elongated "beam" functions as a biological lever, amplifying small interdomain movements within the myosin head into piconewton forces and nanometer displacements against the thin filament during the cross-bridge cycle. The LCBD contains two subunits known as the essential and regulatory myosin light chains (ELC and RLC, respectively). Isoformic differences in these respective species provide molecular diversity and, in addition, sites for phosphorylation of serine residues, a highly conserved feature of striated muscle systems. Work on permeabilized skeletal fibers and thick filament systems shows that the skeletal myosin light chain kinase catalyzed phosphorylation of the RLC alters the "interacting head motif" of myosin motor heads on the thick filament surface, with myriad consequences for muscle biology. At rest, structure-function changes may upregulate actomyosin ATPase activity of phosphorylated cross-bridges. During activation, these same changes may increase the Ca2+ sensitivity of force development to enhance force, work, and power output, outcomes known as "potentiation." Thus, although other mechanisms may contribute, RLC phosphorylation may represent a form of thick filament activation that provides a "molecular memory" of contraction. The clinical significance of these RLC phosphorylation mediated alterations to contractile performance of various striated muscle systems are just beginning to be understood. © 2017 American Physiological Society. Compr Physiol 7:171-212, 2017.

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

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

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.

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.

Output-input ratio in thermally fluctuating biomolecular machines

Biological molecular machines are proteins that operate under isothermal conditions and hence are referred to as free energy transducers. They can be formally considered as enzymes that simultaneously catalyze two chemical reactions: the free energy-donating (input) reaction and the free energy-accepting (output) one. Most if not all biologically active proteins display a slow stochastic dynamics of transitions between a variety of conformational substates composing their native state. This makes the description of the enzymatic reaction kinetics in terms of conventional rate constants insufficient. In the steady state, upon taking advantage of the assumption that each reaction proceeds through a single pair (the gate) of transition conformational substates of the enzyme-substrates complex, the degree of coupling between the output and the input reaction fluxes has been expressed in terms of the mean first-passage times on a conformational transition network between the distinguished substates. The theory is confronted with the results of random-walk simulations on the five-dimensional hypercube. The formal proof is given that, for single input and output gates, the output-input degree of coupling cannot exceed unity. As some experiments suggest such exceeding, looking for the conditions for increasing the degree of coupling value over unity challenges the theory. Performed simulations of random walks on several model networks involving more extended gates indicate that the case of the degree of coupling value higher than 1 is realized in a natural way on critical branching trees extended by long-range shortcuts. Such networks are scale-free and display the property of the small world. For short-range shortcuts, the networks are scale-free and fractal, representing a reasonable model for biomolecular machines displaying tight coupling, i.e., the degree of coupling equal exactly to unity. A hypothesis is stated that the protein conformational transition networks, as just as higher-level biological networks, the protein interaction network, and the metabolic network, have evolved in the process of self-organized criticality.

Attached molecular motor in a trapped single molecule assay as a bidimensional Brownian multistable system

To elucidate the physical properties of the force generation mechanism in molecular motors, we have obtained an analytical solution of the bidimensional Fokker-Plank equation which describes a common setup used in single molecule experiments. As a first application of this general result, we have shown that the size of the trapping system affects the dwell time of a multistable particle linearly. A quantitative application to skeletal actomyosin complex, using direct observation of force generation dynamics in the literature, shows that the size of the trapping system used was important for increasing the dwell time of the myosin head stable states to an observable time scale.

Muscle contraction and the elasticity-mediated crosstalk effect

Cooperative action of molecular motors is essential for many cellular processes. One possible regulator of motor coordination is the elasticity-mediated crosstalk (EMC) coupling between myosin II motors whose origin is the tensile stress that they collectively generate in actin filaments. Here, we use a statistical mechanical analysis to investigate the influence of the EMC effect on the sarcomere -- the basic contractile unit of skeletal muscles. We demonstrate that the EMC effect leads to an increase in the attachment probability of motors located near the end of the sarcomere while simultaneously decreasing the attachment probability of the motors in the central part. Such a polarized attachment probability would impair the motors' ability to cooperate efficiently. Interestingly, this undesired phenomenon becomes significant only when the system size exceeds that of the sarcomere in skeletal muscles, which provides an explanation for the remarkable lack of sarcomere variability in vertebrates. Another phenomenon that we investigate is the recently observed increase in the duty ratio of the motors with the tension in muscle. We reveal that the celebrated Hill's equation for muscle contraction is very closely related to this observation.

Distinct Conformation of ATP Molecule in Solution and on Protein

Adenosine triphosphate (ATP) is a versatile molecule used mainly for energy and a phosphate source. The hydrolysis of γ phosphate initiates the reactions and these reactions almost always start when ATP binds to protein. Therefore, there should be a mechanism to prevent spontaneous hydrolysis reaction and a mechanism to lead ATP to a pure energy source or to a phosphate source. To address these questions, we extensively analyzed the effect of protein to ATP conformation based on the sampling of the ATP solution conformations obtained from molecular dynamics simulation and the sampling of ATP structures bound to protein found in a protein structure database. The comparison revealed mainly the following three points; 1) The ribose ring in ATP molecule, which puckers in many ways in solution, tends to assume either C2′ exo or C2′ endo when it binds to protein. 2) The adenine ring in ATP molecule, which takes open-book motion with the two ring structures, has two distinct structures when ATP binds to protein. 3) The glycosyl-bond and the bond between phosphate and the ribose have unique torsion angles, when ATP binds to protein. The combination of torsion angles found in protein-bound forms is under-represented in ATP molecule in water. These findings suggest that ATP-binding protein exerts forces on ATP molecule to assume a conformation that is rarely found in solution, and that this conformation change should be a trigger for the reactions on ATP molecule.

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.

Fluctuation-mediated optical screening of nanoparticles

Inspired by biological motors, we propose a guiding principle for selectively separating nanoparticles (NPs) by efficiently using the light-induced force (LIF) and thermal fluctuations. We demonstrate the possibility of transporting metallic NPs of different sizes with a size-selection accuracy of less than 10 nm even at room temperature by designing asymmetric spatiotemporal light fields. This technique will lead to unconventional nanoextraction processes based on light and fluctuations.

From single molecule fluctuations to muscle contraction: a Brownian model of A.F. Huxley's hypotheses

Muscular force generation in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion. However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations reported in the literature. We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios.

Single-molecule measurements using microneedles

Myosin is both an enzyme and a molecular motor that hydrolyzes ATP and interacts with actin filaments for force generation. Manipulation techniques with microneedles and laser traps have recently been developed to capture and manipulate the actomyosin interaction for the purpose of revealing the mechanics of this system. Combined with single-molecule imaging techniques, the coupling between chemical processes (ATP hydrolysis) and mechanical processes (myosin force generation) has been directly determined. In this chapter, we describe these two manipulation techniques, especially microneedle method, in detail.

Entropic potential field formed for a linear-motor protein near a filament: Statistical-mechanical analyses using simple models

We report a new progress in elucidating the mechanism of the unidirectional movement of a linear-motor protein (e.g., myosin) along a filament (e.g., F-actin). The basic concept emphasized here is that a potential field is entropically formed for the protein on the filament immersed in solvent due to the effect of the translational displacement of solvent molecules. The entropic potential field is strongly dependent on geometric features of the protein and the filament, their overall shapes as well as details of the polyatomic structures. The features and the corresponding field are judiciously adjusted by the binding of adenosine triphosphate (ATP) to the protein, hydrolysis of ATP into adenosine diphosphate (ADP)+Pi, and release of Pi and ADP. As the first step, we propose the following physical picture: The potential field formed along the filament for the protein without the binding of ATP or ADP+Pi to it is largely different from that for the protein with the binding, and the directed movement is realized by repeated switches from one of the fields to the other. To illustrate the picture, we analyze the spatial distribution of the entropic potential between a large solute and a large body using the three-dimensional integral equation theory. The solute is modeled as a large hard sphere. Two model filaments are considered as the body: model 1 is a set of one-dimensionally connected large hard spheres and model 2 is a double helical structure formed by two sets of connected large hard spheres. The solute and the filament are immersed in small hard spheres forming the solvent. The major findings are as follows. The solute is strongly confined within a narrow space in contact with the filament. Within the space there are locations with sharply deep local potential minima along the filament, and the distance between two adjacent locations is equal to the diameter of the large spheres constituting the filament. The potential minima form a ringlike domain in model 1 while they form a pointlike one in model 2. We then examine the effects of geometric features of the solute on the amplitudes and asymmetry of the entropic potential field acting on the solute along the filament. A large aspherical solute with a cleft near the solute-filament interface, which mimics the myosin motor domain, is considered in the examination. Thus, the two fields in our physical picture described above are qualitatively reproduced. The factors to be taken into account in further studies are also discussed.

Mechanical characterization of one-headed myosin-V using optical tweezers

Class V myosin (myosin-V) is a cargo transporter that moves along an actin filament with large (approximately 36-nm) successive steps. It consists of two heads that each includes a motor domain and a long (23 nm) neck domain. One of the more popular models describing these steps, the hand-over-hand model, assumes the two-headed structure is imperative. However, we previously succeeded in observing successive large steps by one-headed myosin-V upon optimizing the angle of the acto-myosin interaction. In addition, it was reported that wild type myosin-VI and myosin-IX, both one-headed myosins, can also generate successive large steps. Here, we describe the mechanical properties (stepsize and stepping kinetics) of successive large steps by one-headed and two-headed myosin-Vs. This study shows that the stepsize and stepping kinetics of one-headed myosin-V are very similar to those of the two-headed one. However, there was a difference with regards to stability against load and the number of multisteps. One-headed myosin-V also showed unidirectional movement that like two-headed myosin-V required 3.5 k(B)T from ATP hydrolysis. This value is also similar to that of smooth muscle myosin-II, a non-processive motor, suggesting the myosin family uses a common mechanism for stepping regardless of the steps being processive or non-processive. In this present paper, we conclude that one-headed myosin-V can produce successive large steps without following the hand-over-hand mechanism.

Load-dependent sliding direction change of a myosin head on an actin molecule and its energetic aspects: Energy borrowing model of a cross-bridge cycle

A model of muscle contraction is proposed, assuming loose coupling between power strokes and ATP hydrolysis of a myosin head. The energy borrowing mechanism is introduced in a cross-bridge cycle that borrows energy from the environment to cover the necessary energy for enthalpy production during sliding movement. Important premises for modeling are as follows: 1) the interaction area where a myosin head slides is supposed to be on an actin molecule; 2) the actomyosin complex is assumed to generate force F(θ), which slides the myosin head M* in the interaction area; 3) the direction of the force F(θ) varies in proportion to the load P; 4) the energy supplied by ATP hydrolysis is used to retain the myosin head in the high-energy state M*, and is not used for enthalpy production; 5) the myosin head enters a hydration state and dehydration state repeatedly during the cross-bridge cycle. The dehydrated myosin head recovers its hydrated state by hydration in the surrounding medium; 6) the energy source for work and heat production liberated by the AM* complex is of external origin. On the basis of these premises, the model adequately explains the experimental results observed at various levels in muscular samples: 1) twist in actin filaments observed in shortening muscle fibers; 2) the load-velocity relationship in single muscle fiber; 3) energy balance among enthalpy production, the borrowed energy and the energy supplied by ATP hydrolysis during muscle contraction. Force F(θ) acting on the myosin head is depicted.

Recombinant alpha-actin for specific fluorescent labeling

Until recently, actin was thought to act merely as a passive track for its motility partner, myosin, during actomyosin interactions. Yet a recent report having observed dynamical conformational changes in labeled skeletal muscle alpha-actin suggests that actin has a more active role. Because the labeling technique was still immature, however, conclusions regarding the significance of the different conformations are difficult to make. Here, we describe the preparation of fully active alpha-actin obtained from a baculovirus expression system. We developed alpha-actin recombinants, of which subdomains 1 and 2 have specific sites for fluorescent probes. This specific labeling technique offers to significantly expand the information acquired from actin studies.

Single molecule measurements and molecular motors

Single molecule imaging and manipulation are powerful tools in describing the operations of molecular machines like molecular motors. The single molecule measurements allow a dynamic behaviour of individual biomolecules to be measured. In this paper, we describe how we have developed single molecule measurements to understand the mechanism of molecular motors. The step movement of molecular motors associated with a single cycle of ATP hydrolysis has been identified. The single molecule measurements that have sensitivity to monitor thermal fluctuation have revealed that thermal Brownian motion is involved in the step movement of molecular motors. Several mechanisms have been suggested in different motors to bias random thermal motion to directional movement.

Statistical properties of the dichotomous noise generated in biochemical processes

Dichotomous noise detected with the help of various single-molecule techniques convincingly reveals the actual occurrence of a multitude of conformational substates composing the native state of proteins. The nature of the stochastic dynamics of transitions between these substates is determined by the particular statistical properties of the noise observed. These involve nonexponential and possibly oscillatory time decay of the second order autocorrelation function, its relation to the third order autocorrelation function, and a relationship to dwell-time distribution densities and their correlations. Processes gated by specific conformational substates are distinguished from those with fluctuating barriers. This study throws light on the intriguing matter of the possibility of multiple stepping of the myosin motor along the actin filament per ATP molecule hydrolyzed.

F1-ATPase rotates by an asymmetric, sequential mechanism using all three catalytic subunits

F1-ATPase, the catalytic part of FoF1-ATP synthase, rotates the central gamma subunit within the alpha3beta3 cylinder in 120 degrees steps, each step consuming a single ATP molecule. However, how the catalytic activity of each beta subunit is coordinated with the other two beta subunits to drive rotation remains unknown. Here we show that hybrid F1 containing one or two mutant beta subunits with altered catalytic kinetics rotates in an asymmetric stepwise fashion. Analysis of the rotations reveals that for any given beta subunit, the subunit binds ATP at 0 degrees, cleaves ATP at approximately 200 degrees and carries out a third catalytic event at approximately 320 degrees. This demonstrates the concerted nature of the F1 complex activity, where all three beta subunits participate to drive each 120 degrees rotation of the gamma subunit with a 120 degrees phase difference, a process we describe as a 'sequential three-site mechanism'.

Structural change and nucleotide dissociation of Myosin motor domain: dual go model simulation

We investigated the structural relaxation of myosin motor domain from the pre-power stroke state to the near-rigor state using molecular dynamics simulation of a coarse-grained protein model. To describe the spontaneous structural change, we propose a dual Gō-model-a variant of the Gō-like model that has two reference structures. The nucleotide dissociation process is also studied by introducing a coarse-grained nucleotide in the simulation. We found that the myosin structural relaxation toward the near-rigor conformation cannot be completed before the nucleotide dissociation. Moreover, the relaxation and the dissociation occurred cooperatively when the nucleotide was tightly bound to the myosin head. The result suggested that the primary role of the nucleotide is to suppress the structural relaxation.

Nonlinear relaxation dynamics in elastic networks and design principles of molecular machines

Analyzing nonlinear conformational relaxation dynamics in elastic networks corresponding to two classical motor proteins, we find that they respond by well defined internal mechanical motions to various initial deformations and that these motions are robust against external perturbations. We show that this behavior is not characteristic for random elastic networks. However, special network architectures with such properties can be designed by evolutionary optimization methods. Using them, an example of an artificial elastic network, operating as a cyclic machine powered by ligand binding, is constructed.

Cooperative actions between myosin heads bring effective functions

A recent study with single molecule measurements has reported that muscle myosin, a molecular motor, stochastically generates multiple steps along an actin filament associated with the hydrolysis of a single ATP molecule [Kitamura, K., Tokunaga, M., Esaki, S., Iwane, A.H., Yanagida, T., 2005. Mechanism of muscle contraction based on stochastic properties of single actomyosin motors observed in vitro. Biophysics 1, 1-19]. We have built a model reproducing such a stochastic movement of a myosin molecule incorporated with ATPase reaction cycles and demonstrated that the thermal fluctuation was a key for the function of myosin molecules [Esaki, S., Ishii, Y., Yanagida, T., 2003. Model describing the biased Brownian movement of myosin. Proc. Jpn. Acad. 79 (Ser B), 9-14]. The size of the displacement generated during the hydrolysis of single ATP molecules was limited within a half pitch of an actin filament when a single myosin molecules work separately. However, in muscle the size of the displacement has been reported to be greater than 60 nm [Yanagida, T., Arata, T., Oosawa, F., 1985. Sliding distance of actin filament induced by a myosin crossbridge during one ATP hydrolysis cycle. Nature 316, 366-369; Higuchi et al., 1991]. The difference suggests cooperative action between myosin heads in muscle. Here we extended the model built for an isolated myosin head to a system in which myosin heads are aligned in muscle arrangement to understand the cooperativity between heads. The simulation showed that the rotation of the actin filament [Takezawa, Y., Sugimoto, Y., Wakabayashi, K., 1998. Extensibility of the actin and myosin filaments in various states of skeletal muscles as studied by X-ray diffraction. Adv. Exp. Med. Biol. 453, 309-317; Wakabayashi, K., Ueno, Y., Takezawa, Y., Sugimoto, Y., 2001. Muscle contraction mechanism: use of X-ray synchrotron radiation. Nat. Enc. Life Sci. 1-11] associated with the release of ATPase products and binding of ATP as well as interaction between myosin heads allowed the myosin filament to move greater than a half pitch of the actin filament while a single ATP molecule is hydrolyzed. Our model demonstrated that the movement is loosely coupled to the ATPase cycle as observed in muscle.

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.

Role of multiple bonds between the single cell adhesion molecules, nectin and cadherin, revealed by high sensitive force measurements

Nectins and cadherins, members of cell adhesion molecules (CAMs), are the primary mediators for various types of cell-cell junctions. Here, intermolecular force microscopy (IFM) with force sensitivity at sub-picoNewtons is used to characterize the extracellular trans-interactions between paired nectins and paired cadherins at the single molecule level. Three and four different bound states between paired nectins and paired cadherins are, respectively, identified and characterized based on bond strength distributions where each bound state has a unique lifetime and bond length. The results indicate that multiple domains of nectins act uncooperatively, as a zipper-like multiply bonded system whereas those of cadherins act cooperatively, as a parallel-like multiply bonded system, consistent with a "fork initiation and zipper" hypothesis for the formation of cell-cell adhesion. The observed dynamic properties among multiple bonds are expected to be advantageous such that nectins search adaptively in the cell-cell exploratory recognition process while cadherins slowly stabilize in the cell-cell zippering process.

Unidirectional movement of an actin filament taking advantage of temperature gradients

An actin filament with heat acceptors attached to its Cys374 residue in each actin monomer could move unidirectionally even under heat pulsation alone, while in the total absence of both ATP and myosin. The prime driver for the movement was temperature gradients operating between locally heated portions on an actin filament and its cooler surroundings. In this report, we investigated how the mitigation of the temperature gradients induces a unidirectional movement of an actin filament. We then observed the transversal fluctuations of the filament in response to heat pulsation and their transition into longitudinally unidirectional movement. The transition was significantly accelerated when Cys374 and Lys336 were simultaneously excited within an actin monomer. These results suggest that the mitigation of the temperature gradients within each actin monomer first went through the energy transformation to transversal fluctuations of the filament, and then followed by the transformation further down to longitudinal movements of the filament. The faster mitigation of temperature gradients within actin monomer helps build up the transition from the transversal to longitudinal movements of the filament by coordinating the interaction between the neighboring monomers.

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.

Cargo-binding makes a wild-type single-headed myosin-VI move processively

Class VI myosin is an intracellular vesicle and organelle transporter that moves along actin filaments in a direction opposite to most other known myosin classes. The myosin-VI was expected to form a dimer to move processively along actin filaments with a hand-over-hand mechanism like other myosin organelle transporters. Recently, however, wild-type myosin-VI was demonstrated to be monomer and single-headed, casting a doubt on its processivity. By using single molecule techniques, we show that green-fluorescent-protein-tagged single-headed, wild-type myosin-VI does not move processively. However, when coupled to 200-nm polystyrene beads (comparable to intracellular vesicles in size) at a ratio of one head per bead, single-headed myosin-VI moves processively with large (40-nm) steps. The characteristics of this monomer-driven movement were different to that of artificial dimer-driven movement: Compared to the artificial dimer, the monomer-bead complex had a reduced stall force (1 pN compared to 2 pN), an average run length 2.5-fold shorter (91 nm compared to 220 nm) and load-dependent step size. Furthermore, we found that a monomer-bead complex moved more processively in a high viscous solution (40-fold higher than water) similar to cellular environment. Because the diffusion constant of the bead is 60-fold lower than myosin-VI heads alone in water, we propose a model in which the bead acts as a diffusional anchor for the myosin-VI, enhancing its rebinding following detachment and supporting processive movement of the bead-monomer complexes. Although a single-headed myosin-VI was able to move processively with a large cargo, the travel distance was rather short. Multiple molecules may be involved in the cargo transport for a long travel distance in cells.

Entropy rectifies the Brownian steps of kinesin

Kinesin is a stepping motor that successively produces forward and backward 8-nm steps along microtubules. Under physiological conditions, the steps powering kinesin's motility are biased in one direction and drive various biological motile processes. The physical mechanism underlying the unidirectional bias of the kinesin steps is not fully understood. Here we explored the mechanical kinetics and thermodynamics of forward and backward kinesin steps by analyzing their temperature and load dependence. Results show that the frequency asymmetry between forward and backward steps is produced by entropy. Furthermore, the magnitude of the entropic asymmetry is 6 k(B)T, more than three times greater than expected from a current model, in which a mechanical conformational change within the kinesin molecular structure directly biases the kinesin steps forward. We propose that the stepping direction of kinesin is preferably caused by an entropy asymmetry resulting from the compatibility between the kinesin and microtubule interaction based on their polar structures.

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.