Nonlinear elasticity and an 8-nm working stroke of single myosin molecules in myofilaments

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.

The kinetics of mechanically coupled myosins exhibit group size-dependent regimes

Naturally occurring groups of muscle myosin behave differently from individual myosins or small groups commonly assayed in vitro. Here, we investigate the emergence of myosin group behavior with increasing myosin group size. Assuming the number of myosin binding sites (N) is proportional to actin length (L) (N = L/35.5 nm), we resolve in vitro motility of actin propelled by skeletal muscle myosin for L = 0.2-3 μm. Three distinct regimes were found: L < 0.3 μm, sliding arrest; 0.3 μm ≤ L ≤ 1 μm, alternation between arrest and continuous sliding; L > 1 μm, continuous sliding. We theoretically investigated the myosin group kinetics with mechanical coupling via actin. We find rapid actin sliding steps driven by power-stroke cascades supported by postpower-stroke myosins, and phases without actin sliding caused by prepower-stroke myosin buildup. The three regimes are explained: N = 8, rare cascades; N = 15, cascade bursts; N = 35, continuous cascading. Two saddle-node bifurcations occur for increasing N (mono → bi → mono-stability), with steady states corresponding to arrest and continuous cascading. The experimentally measured dependence of actin sliding statistics on L and myosin concentration is correctly predicted.

Sarcomere length nanometry in rat neonatal cardiomyocytes expressed with α-actinin-AcGFP in Z discs

Nanometry is widely used in biological sciences to analyze the movement of molecules or molecular assemblies in cells and in vivo. In cardiac muscle, a change in sarcomere length (SL) by a mere ∼100 nm causes a substantial change in contractility, indicating the need for the simultaneous measurement of SL and intracellular Ca(2+) concentration ([Ca(2+)]i) in cardiomyocytes at high spatial and temporal resolution. To accurately analyze the motion of individual sarcomeres with nanometer precision during excitation-contraction coupling, we applied nanometry techniques to primary-cultured rat neonatal cardiomyocytes. First, we developed an experimental system for simultaneous nanoscale analysis of single sarcomere dynamics and [Ca(2+)]i changes via the expression of AcGFP in Z discs. We found that the averaging of the lengths of sarcomeres along the myocyte, a method generally used in today's myocardial research, caused marked underestimation of sarcomere lengthening speed because of the superpositioning of different timings for lengthening between sequentially connected sarcomeres. Then, we found that after treatment with ionomycin, neonatal myocytes exhibited spontaneous sarcomeric oscillations (cell-SPOCs) at partial activation with blockage of sarcoplasmic reticulum functions, and the waveform properties were indistinguishable from those obtained in electric field stimulation. The myosin activator omecamtiv mecarbil markedly enhanced Z-disc displacement during cell-SPOC. Finally, we interpreted the present experimental findings in the framework of our mathematical model of SPOCs. The present experimental system has a broad range of application possibilities for unveiling single sarcomere dynamics during excitation-contraction coupling in cardiomyocytes under various settings.

Dynamic coupling of regulated binding sites and cycling myosin heads in striated muscle

Myosim, a computer model of muscle contraction, includes molecular-level effects and incorporates dynamic coupling of myosin heads and binding sites.

In an activated muscle, binding sites on the thin filament and myosin heads switch frequently between different states. Because the status of the binding sites influences the status of the heads, and vice versa, the binding sites and myosin heads are dynamically coupled. The functional consequences of this coupling were investigated using MyoSim, a new computer model of muscle. MyoSim extends existing models based on Huxley-type distribution techniques by incorporating Ca²⁺ activation and cooperative effects. It can also simulate arbitrary cross-bridge schemes set by the researcher. Initial calculations investigated the effects of altering the relative speeds of binding-site and cross-bridge kinetics, and of manipulating cooperative processes. Subsequent tests fitted simulated force records to experimental data recorded using permeabilized myocardial preparations. These calculations suggest that the rate of force development at maximum activation is limited by myosin cycling kinetics, whereas the rate at lower levels of activation is limited by how quickly binding sites become available. Additional tests investigated the behavior of transiently activated cells by driving simulations with experimentally recorded Ca²⁺ signals. The unloaded shortening profile of a twitching myocyte could be reproduced using a model with two myosin states, cooperative activation, and strain-dependent kinetics. Collectively, these results demonstrate that dynamic coupling of binding sites and myosin heads is important for contractile function.

The non-linear elasticity of the muscle sarcomere and the compliance of myosin motors

Force in striated muscle is due to attachment of the heads of the myosin, the molecular motors extending from the myosin filament, to the actin filament in each half-sarcomere, the functional unit where myosin motors act in parallel. Mechanical and X-ray structural evidence indicates that at the plateau of isometric contraction (force T0), less than half of the elastic strain of the half-sarcomere is due to the strain in the array of myosin motors (s), with the remainder being accounted for by the compliance of filaments acting as linear elastic elements in series with the motor array. Early during the development of isometric force, however, the half-sarcomere compliance has been found to be less than that expected from the linear elastic model assumed above, and this non-linearity may affect the estimate of s. This question is investigated here by applying nanometre-microsecond-resolution mechanics to single intact fibres from frog skeletal muscle at 4 °C, to record the mechanical properties of the half-sarcomere throughout the development of force in isometric contraction. The results are interpreted with mechanical models to estimate the compliance of the myosin motors. Our conclusions are as follows: (i) early during the development of an isometric tetanus, an elastic element is present in parallel with the myosin motors, with a compliance of ∼200 nm MPa(-1) (∼20 times larger than the compliance of the motor array at T0); and (ii) during isometric contraction, s is 1.66 ± 0.05 nm, which is not significantly different from the value estimated with the linear elastic model.

Flexibility within the heads of muscle myosin-2 molecules

We show that negative-stain electron microscopy and image processing of nucleotide-free (apo) striated muscle myosin-2 subfragment-1 (S1), possessing one light chain or both light chains, is capable of resolving significant amounts of structural detail. The overall appearance of the motor and the lever is similar in rabbit, scallop and chicken S1. Projection matching of class averages of the different S1 types to projection views of two different crystal structures of apo S1 shows that all types most commonly closely resemble the appearance of the scallop S1 structure rather than the methylated chicken S1 structure. Methylation of chicken S1 has no effect on the structure of the molecule at this resolution: it too resembles the scallop S1 crystal structure. The lever is found to vary in its angle of attachment to the motor domain, with a hinge point located in the so-called pliant region between the converter and the essential light chain. The chicken S1 crystal structure lies near one end of the range of flexion observed. The Gaussian spread of angles of flexion suggests that flexibility is driven thermally, from which a torsional spring constant of ~ 23 pN·nm/rad² is estimated on average for all S1 types, similar to myosin-5. This translates to apparent cantilever-type stiffness at the tip of the lever of 0.37 pN/nm. Because this stiffness is lower than recent estimates from myosin-2 heads attached to actin, we suggest that binding to actin leads to an allosteric stiffening of the motor–lever junction.

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Elasticity of muscle crossbridges is important, but its structural basis is obscure.

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Muscle myosin heads from rabbit, scallop and chicken share a common structure.

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The lever domain hinges about its connection with the motor domain.

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The stiffness of the motor–lever hinge is lower than estimates for crossbridges.

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Flexibility within the myosin head can be the basis of crossbridge stiffness.

Stiffness, working stroke, and force of single-myosin molecules in skeletal muscle: elucidation of these mechanical properties via nonlinear elasticity evaluation

In muscles, the arrays of skeletal myosin molecules interact with actin filaments and continuously generate force at various contraction speeds. Therefore, it is crucial for myosin molecules to generate force collectively and minimize the interference between individual myosin molecules. Knowledge of the elasticity of myosin molecules is crucial for understanding the molecular mechanisms of muscle contractions because elasticity directly affects the working and drag (resistance) force generation when myosin molecules are positively or negatively strained. The working stroke distance is also an important mechanical property necessary for elucidation of the thermodynamic efficiency of muscle contractions at the molecular level. In this review, we focus on these mechanical properties obtained from single-fiber and single-molecule studies and discuss recent findings associated with these mechanical properties. We also discuss the potential molecular mechanisms associated with reduction of the drag effect caused by negatively strained myosin molecules.

Nonlinear cross-bridge elasticity and post-power-stroke events in fast skeletal muscle actomyosin

Generation of force and movement by actomyosin cross-bridges is the molecular basis of muscle contraction, but generally accepted ideas about cross-bridge properties have recently been questioned. Of the utmost significance, evidence for nonlinear cross-bridge elasticity has been presented. We here investigate how this and other newly discovered or postulated phenomena would modify cross-bridge operation, with focus on post-power-stroke events. First, as an experimental basis, we present evidence for a hyperbolic [MgATP]-velocity relationship of heavy-meromyosin-propelled actin filaments in the in vitro motility assay using fast rabbit skeletal muscle myosin (28-29°C). As the hyperbolic [MgATP]-velocity relationship was not consistent with interhead cooperativity, we developed a cross-bridge model with independent myosin heads and strain-dependent interstate transition rates. The model, implemented with inclusion of MgATP-independent detachment from the rigor state, as suggested by previous single-molecule mechanics experiments, accounts well for the [MgATP]-velocity relationship if nonlinear cross-bridge elasticity is assumed, but not if linear cross-bridge elasticity is assumed. In addition, a better fit is obtained with load-independent than with load-dependent MgATP-induced detachment rate. We discuss our results in relation to previous data showing a nonhyperbolic [MgATP]-velocity relationship when actin filaments are propelled by myosin subfragment 1 or full-length myosin. We also consider the implications of our results for characterization of the cross-bridge elasticity in the filament lattice of muscle.

A cross-bridge cycle with two tension-generating steps simulates skeletal muscle mechanics

We examined whether cross-bridge cycle models with one or two tension-generating steps can account for the force-velocity relation of and tension response to length steps of frog skeletal muscle. Transition-state theory defined the strain dependence of the rate constants. The filament stiffness was non-Hookean. Models were refined against experimental data by simulated annealing and downhill simplex runs. Models with one tension-generating step were rejected, as they had a low efficiency and fitted the experimental data relatively poorly. The best model with two tension-generating steps (stroke distances 5.6 and 4.6 nm) and a cross-bridge stiffness of 1.7 pN/nm gave a good account of the experimental data. The two tensing steps allow an efficiency of up to 38% during shortening. In an isometric contraction, 54.7% of the attached heads were in a pre-tension-generating state, 44.5% of the attached heads had undergone the first tension-generating step, and only 0.8% had undergone both tension-generating steps; they bore 34%, 64%, and 2%, respectively, of the isometric tension. During slow shortening, the second tensing step made a greater contribution. During lengthening, up to 93% of the attached heads were in a pre-tension-generating state yet bore elevated tension by being dragged to high strains before detaching.

Actin Sliding Velocities are Influenced by the Driving Forces of Actin-Myosin Binding

Unloaded shortening speeds, V, of muscle are thought to be limited by actin-bound myosin heads that resist shortening, or V = a·d·τon-1 where τon-1 is the rate at which myosin detaches from actin and d is myosin's step size. The a-term describes the efficiency of force transmission between myosin heads, and has been shown to become less than one at low myosin densities in a motility assay. Molecules such as inorganic phosphate, Pi, and blebbistatin inhibit both V and actin-myosin strong binding kinetics suggesting a link between V and attachment kinetics. To determine whether these small molecules slow V by increasing resistance to actin sliding or by decreasing the efficiency of force transmission, a, we determine how inhibition of V by Pi and blebbistatin changes the force exerted on actin filaments during an in vitro sliding assay, measured from changes in the rate, τbreak-1, at which actin filaments break. Upon addition of 30 mM Pi to a low (30 μM) [ATP] motility buffer V decreased from 1.8 to 1.3 μm·sec-1 and τbreak-1 from 0.029 to 0.018 sec-1. Upon addition of 50 μM blebbistatin to a low [ATP] motility buffer, V decreased from 1.0 to 0.7 μm·sec-1 and τbreak-1 from 0.059 to 0.022 sec-1. These results imply that blebbistatin and Pi slow V by decreasing force transmission, a, not by increasing resistive forces, implying that actin-myosin attachment kinetics influence V.

Transportation of nanoscale cargoes by myosin propelled actin filaments

Myosin II propelled actin filaments move ten times faster than kinesin driven microtubules and are thus attractive candidates as cargo-transporting shuttles in motor driven lab-on-a-chip devices. In addition, actomyosin-based transportation of nanoparticles is useful in various fundamental studies. However, it is poorly understood how actomyosin function is affected by different number of nanoscale cargoes, by cargo size, and by the mode of cargo-attachment to the actin filament. This is studied here using biotin/fluorophores, streptavidin, streptavidin-coated quantum dots, and liposomes as model cargoes attached to monomers along the actin filaments (“side-attached”) or to the trailing filament end via the plus end capping protein CapZ. Long-distance transportation (>100 µm) could be seen for all cargoes independently of attachment mode but the fraction of motile filaments decreased with increasing number of side-attached cargoes, a reduction that occurred within a range of 10–50 streptavidin molecules, 1–10 quantum dots or with just 1 liposome. However, as observed by monitoring these motile filaments with the attached cargo, the velocity was little affected. This also applied for end-attached cargoes where the attachment was mediated by CapZ. The results with side-attached cargoes argue against certain models for chemomechanical energy transduction in actomyosin and give important insights of relevance for effective exploitation of actomyosin-based cargo-transportation in molecular diagnostics and other nanotechnological applications. The attachment of quantum dots via CapZ, without appreciable modulation of actomyosin function, is useful in fundamental studies as exemplified here by tracking with nanometer accuracy.

Myosin motors fragment and compact membrane-bound actin filaments

Cell cortex remodeling during cell division is a result of myofilament-driven contractility of the cortical membrane-bound actin meshwork. Little is known about the interaction between individual myofilaments and membrane-bound actin filaments. Here we reconstituted a minimal actin cortex to directly visualize the action of individual myofilaments on membrane-bound actin filaments using TIRF microscopy. We show that synthetic myofilaments fragment and compact membrane-bound actin while processively moving along actin filaments. We propose a mechanism by which tension builds up between the ends of myofilaments, resulting in compressive stress exerted to single actin filaments, causing their buckling and breakage. Modeling of this mechanism revealed that sufficient force (∼20 pN) can be generated by single myofilaments to buckle and break actin filaments. This mechanism of filament fragmentation and compaction may contribute to actin turnover and cortex reorganization during cytokinesis.

DOI:http://dx.doi.org/10.7554/eLife.00116.001

Actin is a multi-functional protein that is found in almost all eukaryotic cells. When polymerized, it forms robust filaments that participate in a variety of cellular processes. For example, actin filaments are involved in the contraction of muscles, and they are also a major component in the various structures that maintain and control the shape of cells as they move and divide. These structures include the cell cortex, a meshwork of actin filaments that is bound to the inner surface of the plasma membrane by anchor proteins. However, both the cell cortex and the plasma membrane must undergo dramatic changes when a cell divides, and the forces that drive these changes are generated by another protein, myosin II.

Myosin II contains three domains: a head domain, also known as the motor domain, that binds to actin; a neck domain; and a tail domain. Like actin, myosin II proteins also form filaments, but these myofilaments have a distinctive structure: the tail domains of two Myosin II proteins join together, with the motor domains being found at both ends of the filament. When activated, the motor domains grab actin filaments and pull against them in a ‘powerstroke’. However, the details of the interactions between the myofilament motor domains and the actin filaments in the cell cortex, which are bound to the plasma membrane, are not fully understood.

Studying these processes in living cells is extremely challenging, so Vogel et al. have built an in vitro model of the cell cortex, and then used single-molecule imaging to watch the interactions between the myofilaments and the actin filaments in this model. They show that the myofilaments move along the actin in the cortex, breaking up the filaments and compressing them in the process. They propose that tension builds up between the ends of the myofilaments, leading to compressive stress being exerted on the actin filaments. Computer simulations confirm that the forces generated are high enough to cause the actin filaments to buckle and break. The in vitro model developed by Vogel et al. should allow researchers to clarify the basic biophysical principles that underpin the structure and function of the cell cortex.

DOI:http://dx.doi.org/10.7554/eLife.00116.002

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.

Ultrafast force-clamp spectroscopy of single molecules reveals load dependence of myosin working stroke

We describe a dual-trap force-clamp configuration that applies constant loads between a binding protein and an intermittently interacting biological polymer. The method has a measurement delay of only ∼10 μs, allows detection of interactions as brief as ∼100 μs and probes sub-nanometer conformational changes with a time resolution of tens of microseconds. We tested our method on molecular motors and DNA-binding proteins. We could apply constant loads to a single motor domain of myosin before its working stroke was initiated (0.2-1 ms), thus directly measuring its load dependence. We found that, depending on the applied load, myosin weakly interacted (<1 ms) with actin without production of movement, fully developed its working stroke or prematurely detached (<5 ms), thus reducing the working stroke size with load. Our technique extends single-molecule force-clamp spectroscopy and opens new avenues for investigating the effects of forces on biological processes.

Molecular mechanics of cardiac myosin-binding protein C in native thick filaments

The heart's pumping capacity results from highly regulated interactions of actomyosin molecular motors. Mutations in the gene for a potential regulator of these motors, cardiac myosin-binding protein C (cMyBP-C), cause hypertrophic cardiomyopathy. However, cMyBP-C's ability to modulate cardiac contractility is not well understood. Using single-particle fluorescence imaging techniques, transgenic protein expression, proteomics, and modeling, we found that cMyBP-C slowed actomyosin motion generation in native cardiac thick filaments. This mechanical effect was localized to where cMyBP-C resides within the thick filament (i.e., the C-zones) and was modulated by phosphorylation and site-specific proteolytic degradation. These results provide molecular insight into why cMyBP-C should be considered a member of a tripartite complex with actin and myosin that allows fine tuning of cardiac muscle contraction.

Mechanical coupling between myosin molecules causes differences between ensemble and single-molecule measurements

In contracting muscle, individual myosin molecules function as part of a large ensemble, hydrolyzing ATP to power the relative sliding of actin filaments. The technological advances that have enabled direct observation and manipulation of single molecules, including recent experiments that have explored myosin's force-dependent properties, provide detailed insight into the kinetics of myosin's mechanochemical interaction with actin. However, it has been difficult to reconcile these single-molecule observations with the behavior of myosin in an ensemble. Here, using a combination of simulations and theory, we show that the kinetic mechanism derived from single-molecule experiments describes ensemble behavior; but the connection between single molecule and ensemble is complex. In particular, even in the absence of external force, internal forces generated between myosin molecules in a large ensemble accelerate ADP release and increase how far actin moves during a single myosin attachment. These myosin-induced changes in strong binding lifetime and attachment distance cause measurable properties, such as actin speed in the motility assay, to vary depending on the number of myosin molecules interacting with an actin filament. This ensemble-size effect challenges the simple detachment limited model of motility, because even when motility speed is limited by ADP release, increasing attachment rate can increase motility speed.

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.

Translational actomyosin research: fundamental insights and applications hand in hand

This review describes the development towards actomyosin based nanodevices taking a starting point in pioneering studies in the 1990s based on conventional in vitro motility assays. References are given to parallel developments using the kinesin–microtubule motor system. The early developments focused on achieving cargo-transportation using actin filaments as cargo-loaded shuttles propelled by surface-adsorbed heavy meromyosin along micro- and nanofabricated channels. These efforts prompted extensive studies of surface–motor interactions contributing with new insights of general relevance in surface and colloid chemistry. As a result of these early efforts, a range of complex devices have now emerged, spanning applications in medical diagnostics, biocomputation and formation of complex nanostructures by self-organization. In addition to giving a comprehensive account of the developments towards real-world applications an important goal of the present review is to demonstrate important connections between the applied studies and fundamental biophysical studies of actomyosin and muscle function. Thus the manipulation of the motor proteins towards applications has resulted in new insights into methodological aspects of the in vitro motiliy assay. Other developments have advanced the understanding of the dynamic materials properties of actin filaments.

Quasiperiodic distribution of rigor cross-bridges along a reconstituted thin filament in a skeletal myofibril

Electron microscopy has shown that cross-bridges (CBs) are formed at the target zone that is periodically distributed on the thin filament in striated muscle. Here, by manipulating a single bead-tailed actin filament with optical tweezers, we measured the unbinding events of rigor CBs one by one on the surface of the A-band in rabbit skeletal myofibrils. We found that the spacings between adjacent CBs were not always the same, and instead were 36, 72, or 108 nm. Tropomyosin and troponin did not affect the CB spacing except for a relative increase in the appearance of longer spacing in the presence of Ca(2+). In addition, in an in vitro assay where myosin molecules were randomly distributed, were obtained the same spacing, i.e., a multiple of 36 nm. These results indicate that the one-dimensional distribution of CBs matches with the 36-nm half pitch of a long helical structure of actin filaments. A stereospecific model composed of three actin protomers per target zone was shown to explain the experimental results. Additionally, the unbinding force (i.e., the binding affinity) of CBs for the reconstituted thin filaments was found to be larger and smaller relative to that for actin filaments with and without Ca(2+), respectively.

Rotational model for actin filament alignment by myosin

Dynamics of the actomyosin cytoskeleton regulate cellular processes such as secretion, cell division, cell motility, and shape change. Actomyosin dynamics are themselves regulated by proteins that control actin filament polymerization and depolymerization, and myosin motor contractility. Previous theoretical work has focused on translational movement of actin filaments but has not considered the role of filament rotation. Since filament rotational movements are likely sources of forces that direct cell shape change and movement we explicitly model the dynamics of actin filament rotation as myosin II motors traverse filament pairs, drawing them into alignment. Using Monte Carlo simulations we find an optimal motor velocity for alignment of actin filaments. In addition, when we introduce polymerization and depolymerization of actin filaments, we find that alignment is reduced and the filament arrays exist in a stable, asynchronous state. Further analysis with continuum models allows us to investigate factors contributing to the stability of filament arrays and their ability to generate force. Interestingly, we find that two different morphologies of F-actin arrays generate the same amount of force. We also identify a phase transition to alignment which occurs when either polymerization rates are reduced or motor velocities are optimized. We have extended our analysis to include a maximum allowed stretch of the myosin motors, and a non-uniform length for filaments leading to little change in the qualitative results. Through the integration of simulations and continuum analysis, we are able to approach the problem of understanding rotational alignment of actin filaments by myosin II motors.

Theory of muscle contraction mechanism with cooperative interaction among crossbridges

The power stroke model was criticized and a model was proposed for muscle contraction mechanism (Mitsui, 1999). The proposed model was further developed and calculations based on the model well reproduced major experimental data on the steady filament sliding (Mitsui and Ohshima, 2008) and on the transient phenomena (Mitsui, Takai and Ohshima, 2011). In this review more weight is put on explanation of the basic ideas of the model, especially logical necessity of the model, leaving mathematical details to the above-mentioned papers. A thermodynamic relationship that any models based upon the sliding filament theory should fulfill is derived. The model which fulfills the thermodynamic relationship is constructed on the assumption that a myosin head bound to an actin filament forms a complex with three actin molecules. In shortening muscles, the complex moves along the actin filament changing the partner actin molecules with steps of about 5.5 nm. This process is made possible through cooperative interaction among cross-bridges. The ATP hydrolysis energy is liberated by fraction at each step through chemical reactions between myosin and actin molecules. The cooperativity among crossbridges disappears in length-clamped muscles, in agreement with experimental observations that the cross-bridge produces force independently in the isometric tetanus state. The distance of the head movement per ATP hydrolysis cycle is expected to be about 5.5 nm or a few times of it under the condition of the in vitro single head experiments. Calculation results are surveyed illustrating that they are in good agreement with major experimental observations.

Beyond-limit light focusing in the intermediate zone

We experimentally verify that a new nanolens of a designed plasmonic aperture can focus visible light to a single line with its width smaller than the limit of half the wavelength in the intermediate zone. The experimental measurement indicates that while the near field plays a role to increase the spot size in the near zone, it is negligible at the beyond-limit focused region; i.e., the focused light is dominated by the radiative fields. The image taken by the optical microscope shows that the fields focused have propagated to the far zone. Besides being of academic interest, the nanolens capable in achieving a lower diffraction limit in the intermediate zone is important for application possibilities.

Thin filament-reconstituted skinned muscle fibers for the study of muscle physiology

We review the use of thin filament-reconstituted muscle fibers in the study of muscle physiology. Thin filament extraction and reconstitution protocol is a powerful technique to study the role of each component of the thin filament. It is also useful for studying the properties of genetically modified molecules such as actin and tropomyosin. We also review the combination of this protocol with sinusoidal analysis, which will provide a solid technique for determining the effect of regulatory proteins on actomyosin interaction and concomitant cross-bridge kinetics. We suggest that thin filament-reconstituted muscle fibers are an ideal system for studying muscle physiology especially when gene modifications of actin or tropomyosin are involved.

Survey on indirect optical manipulation of cells, nucleic acids, and motor proteins

Optical tweezers have emerged as a promising technique for manipulating biological objects. Instead of direct laser exposure, more often than not, optically-trapped beads are attached to the ends or boundaries of the objects for translation, rotation, and stretching. This is referred to as indirect optical manipulation. In this paper, we utilize the concept of robotic gripping to explain the different experimental setups which are commonly used for indirect manipulation of cells, nucleic acids, and motor proteins. We also give an overview of the kind of biological insights provided by this technique. We conclude by highlighting the trends across the experimental studies, and discuss challenges and promising directions in this domain of active current research.

Modeling myosin-dependent rearrangement and force generation in an actomyosin network

Actomyosin contractility is a major force-generating mechanism that drives rearrangement of actomyosin networks; it is fundamental to cellular functions such as cellular reshaping and movement. Thus, to clarify the mechanochemical foundation of the emergence of cellular functions, understanding the relationship between actomyosin contractility and rearrangement of actomyosin networks is crucial. For this purpose, in this study, we present a new particulate-based model for simulating the motions of actin, non-muscle myosin II, and α-actinin. To confirm the model's validity, we successfully simulated sliding and bending motions of actomyosin filaments, which are observed as fundamental behaviors in dynamic rearrangement of actomyosin networks in migrating keratocytes. Next, we simulated the dynamic rearrangement of actomyosin networks. Our simulation results indicate that an increase in the density fraction of myosin induces a higher-order structural transition of actomyosin filaments from networks to bundles, in addition to increasing the force generated by actomyosin filaments in the network. We compare our simulation results with experimental results and confirm that actomyosin bundles bridging focal adhesions and the characteristics of myosin-dependent rearrangement of actomyosin networks agree qualitatively with those observed experimentally.