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.     

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.     

Cell motility as an entangled quantum coherence.

Cell motility underlying muscle contraction is imputed to a macroscopic quantum mechanical coherence actualized locally in the body of a biological organism. Actin-activated myosin ATPase activity functions as a heat sink operating effectively at an extremely low temperature. Extraction of heat energy from the actin filament can help condensing the atomic degrees of freedom constituting the filament into a macroscopic quantum state carrying a nonvanishing linear momentum. Sliding movement of an actin filament on myosin molecules while hydrolyzing ATP molecules is a consequence of the quantum mechanical coherence due to an extremely slow release of energy stored in an ATP molecule.     

Characterization of single actomyosin rigor bonds: load dependence of lifetime and mechanical properties

Load dependence of the lifetime of the rigor bonds formed between a single myosin molecule (either heavy meromyosin, HMM, or myosin subfragment-1, S1) and actin filament was examined in the absence of nucleotide by pulling the barbed end of the actin filament with optical tweezers. For S1, the relationship between the lifetime (tau) and the externally imposed load (F) at absolute temperature T could be expressed as tau(F) = tau(0).exp(-F.d/k(B)T) with tau(0) of 67 s and an apparent interaction distance d of 2.4 nm (k(B) is the Boltzmann constant). The relationship for HMM was expressed by the sum of two exponentials, with two sets of tau(0) and d being, respectively, 62 s and 2.7 nm, and 950 s and 1.4 nm. The fast component of HMM coincides with tau(F) for S1, suggesting that the fast component corresponds to single-headed binding and the slow component to double-headed binding. These large interaction distances, which may be a common characteristic of motor proteins, are attributed to the geometry for applying an external load. The pulling experiment has also allowed direct estimation of the number of myosin molecules interacting with an actin filament. Actin filaments tethered to a single HMM molecule underwent extensive rotational Brownian motion, indicating a low torsional stiffness for HMM. From these results, we discuss the characteristics of interaction between actin and myosin, with the focus on the manner of binding of myosin.     

A possible mechanism for determining the directionality of myosin molecular motors

There is a large superfamily of myosins, which play various fundamental roles in cellular motility. In this superfamily, most of myosins, including myosins II and V, move to the barbed end of an actin filament, whereas myosin VI was found to move in the opposite direction to the pointed end. Although myosin VI has structural differences compared with the other myosins, the mechanism for the reversal of the directionality has not been satisfactorily explained by conventional theories for myosin motility, including the widely accepted lever-arm hypothesis. In this paper, a simple mechanism for determining the directionality is proposed. The mechanism assumes that the driving force for the power stroke is caused by elastic energy stored within a myosin molecule at the joint between the head and the neck. The elastic energy originates from the attractive force between myosin and actin, and accumulates during the docking process. The energy of ATP is used to reduce the attractive force between myosin and actin and to facilitate the dissociation of these molecules. Therefore, it is not directly engaged in the power stroke. With this mechanism, the directionality of the myosin motility is simply determined by the direction of the neck with respect to the head in the dissociated configuration. This structural difference is actually observed in myosin VI. The same mechanism also explains the behavior of a backward moving engineered myosin. Computer simulations demonstrated the feasibility of this working mechanism.     

Effect of low pH on single skeletal muscle myosin mechanics and kinetics

Acidosis (low pH) is the oldest putative agent of muscular fatigue, but the molecular mechanism underlying its depressive effect on muscular performance remains unresolved. Therefore, the effect of low pH on the molecular mechanics and kinetics of chicken skeletal muscle myosin was studied using in vitro motility (IVM) and single molecule laser trap assays. Decreasing pH from 7.4 to 6.4 at saturating ATP slowed actin filament velocity (V(actin)) in the IVM by 36%. Single molecule experiments, at 1 microM ATP, decreased the average unitary step size of myosin (d) from 10 +/- 2 nm (pH 7.4) to 2 +/- 1 nm (pH 6.4). Individual binding events at low pH were consistent with the presence of a population of both productive (average d = 10 nm) and nonproductive (average d = 0 nm) actomyosin interactions. Raising the ATP concentration from 1 microM to 1 mM at pH 6.4 restored d (9 +/- 3 nm), suggesting that the lifetime of the nonproductive interactions is solely dependent on the [ATP]. V(actin), however, was not restored by raising the [ATP] (1-10 mM) in the IVM assay, suggesting that low pH also prolongs actin strong binding (t(on)). Measurement of t(on) as a function of the [ATP] in the single molecule assay suggested that acidosis prolongs t(on) by slowing the rate of ADP release. Thus, in a detachment limited model of motility (i.e., V(actin) approximately d/t(on)), a slowed rate of ADP release and the presence of nonproductive actomyosin interactions could account for the acidosis-induced decrease in V(actin), suggesting a molecular explanation for this component of muscular fatigue.     

Myosin V exhibits a high duty cycle and large unitary displacement.

Myosin V is a double-headed unconventional myosin that has been implicated in organelle transport. To perform this role, myosin V may have a high duty cycle. To test this hypothesis and understand the properties of this molecule at the molecular level, we used the laser trap and in vitro motility assay to characterize the mechanics of heavy meromyosin-like fragments of myosin V (M5(HMM)) expressed in the Baculovirus system. The relationship between actin filament velocity and the number of interacting M5(HMM) molecules indicates a duty cycle of > or =50%. This high duty cycle would allow actin filament translocation and thus organelle transport by a few M5(HMM) molecules. Single molecule displacement data showed predominantly single step events of 20 nm and an occasional second step to 37 nm. The 20-nm unitary step represents the myosin V working stroke and is independent of the mode of M5(HMM) attachment to the motility surface or light chain content. The large M5(HMM) working stroke is consistent with the myosin V neck acting as a mechanical lever. The second step is characterized by an increased displacement variance, suggesting a model for how the two heads of myosin V function in processive motion.     

Actin-crosslinking protein regulation of filament movement in motility assays: a theoretical model.

The interaction of single actin filaments on a myosin-coated coverslip has been modeled by several authors. One model adds a component of "frictional drag" by myosin heads that oppose movement of the actin filaments. We have extended this concept by including the resistive drag from actin crosslinking proteins to understand better the relationship among crosslinking number, actin-myosin force generation, and motility. The validity of this model is supported by agreement with the experimental results from a previous study in which crosslinking proteins were added with myosin molecules under otherwise standard motility assay conditions. The theoretical relationship provides a means to determine many physical parameters that characterize the interaction between a single actin filament and a single actin-crosslinking molecule (various types). In particular, the force constant of a single filamin molecule is calculated as 1.105 pN, approximately 3 times less than a driving myosin head (3.4 pN). Knowledge of this parameter and others derived from this model allows a better understanding of the interaction between myosin and the actin/actin-binding protein cytoskeleton and the role of actin-binding proteins in the regulation and modulation of motility.     

Motility of myosin V regulated by the dissociation of single calmodulin

Myosin V is a calmodulin-binding motor protein. The dissociation of single calmodulin molecules from individual myosin V molecules at 1 microM Ca(2+) correlates with a reduction in sliding velocity in an in vitro motility assay. The dissociation of two calmodulin molecules at 5 microM Ca(2+) correlates with a detachment of actin filaments from myosin V. To mimic the regulation of myosin V motility by Ca(2+) in a cell, caged Ca(2+) coupled with a UV flash system was used to produce Ca(2+) transients. During the Ca(2+) transient, myosin V goes through the functional cycle of reduced sliding velocity, actin detachment and reattachment followed by the recovery of the sliding velocity. These results indicate that myosin V motility is regulated by Ca(2+) through a reduction in actin-binding affinity resulting from the dissociation of single calmodulin molecules.     

Stochastic properties of actomyosin motor

The epoch-making techniques for manipulating a single myosin molecule have recently been developed, and the unitary mechanical reactions of a single actomyosin, muscle motor molecule, are directly measured. The data show that the unitary mechanical step during sliding along an actin filament of approximately 5.5 nm, but groups of two to five rapid steps in succession produce displacements of approximately 11-30 nm. The instances of multiple stepping are produced by single myosin heads during one biochemical cycle of ATP hydrolysis. Thus, the coupling between ATP hydrolysis cycle and mechanical step is variable, i.e. loose-coupling. Such a unique operation of actomyosin molecules is different from that of man-made machines, and most likely explains the flexible and effective mechanisms of molecular machines in the biosystems.     

Velocity of myosin-based actin sliding depends on attachment and detachment kinetics and reaches a maximum when myosin-binding sites on actin saturate

Molecular motors such as kinesin and myosin often work in groups to generate the directed movements and forces critical for many biological processes. Although much is known about how individual motors generate force and movement, surprisingly, little is known about the mechanisms underlying the macroscopic mechanics generated by multiple motors. For example, the observation that a saturating number, N, of myosin heads move an actin filament at a rate that is influenced by actin–myosin attachment and detachment kinetics is accounted for neither experimentally nor theoretically. To better understand the emergent mechanics of actin–myosin mechanochemistry, we use an in vitro motility assay to measure and correlate the N-dependence of actin sliding velocities, actin-activated ATPase activity, force generation against a mechanical load, and the calcium sensitivity of thin filament velocities. Our results show that both velocity and ATPase activity are strain dependent and that velocity becomes maximized with the saturation of myosin-binding sites on actin at a value that is 40% dependent on attachment kinetics and 60% dependent on detachment kinetics. These results support a chemical thermodynamic model for ensemble motor mechanochemistry and imply molecularly explicit mechanisms within this framework, challenging the assumption of independent force generation.     

The effect of genetically expressed cardiac titin fragments on in vitro actin motility.

Titin is a striated muscle-specific giant protein (M(r) approximately 3,000,000) that consists predominantly of two classes of approximately 100 amino acid motifs, class I and class II, that repeat along the molecule. Titin is found inside the sarcomere, in close proximity to both actin and myosin filaments. Several biochemical studies have found that titin interacts with myosin and actin. In the present work we investigated whether this biochemical interaction is functionally significant by studying the effect of titin on actomyosin interaction in an in vitro motility assay where fluorescently labeled actin filaments are sliding on top of a lawn of myosin molecules. We used genetically expressed titin fragments containing either a single class I motif (Ti I), a single class II motif (Ti II), or the two motifs linked together (Ti I-II). Neither Ti I nor Ti II alone affected actin-filament sliding on either myosin, heavy meromyosin, or myosin subfragment-1. In contrast, the linked fragment (Ti I-II) strongly inhibited actin sliding. Ti I-II-induced inhibition was observed with full-length myosin, heavy meromyosin, and myosin subfragment-1. The degree of inhibition was largest with myosin subfragment-1, intermediate with heavy meromyosin, and smallest with myosin. In vitro binding assays and electrophoretic analyses revealed that the inhibition is most likely caused by interaction between the actin filament and the titin I-II fragment. The physiological relevance of the novel finding of motility inhibition by titin fragments is discussed.     

Dynamic polymorphism of actin as activation mechanism for cell motility

Actin filament dynamics are crucial in cell motility. Actin filaments, and their bundles, networks, and gels assemble and disassemble spontaneously according to thermodynamic rules. These dynamically changing structures of actin are harnessed for some of its functions in cells. The actin systems respond to external signals, forces, or environments by biasing the fluctuation of actin assembly structures. In this study, dynamic conformation of actin molecules was studied by monitoring conformational dynamics of actin molecules at the single molecule level in real time. Actin conformation spontaneously fluctuates between multiple conformational states. Regarding myosin motility, the dynamic equilibrium of actin conformation was interpreted as between states that activates and inhibits the motility. The binding of myosin to actin filaments activates myosin motility by shifting the conformational fluctuation of actin towards the state that activates the motility. Thus, the activation mechanism based on thermal fluctuation is suggested at molecular level as well as at cellular level.     

Phosphorylation of tropomyosin extends cooperative binding of myosin beyond a single regulatory unit

Tropomyosin (Tm) is one of the major phosphoproteins comprising the thin filament of muscle. However, the specific role of Tm phosphorylation in modulating the mechanics of actomyosin interaction has not been determined. Here we show that Tm phosphorylation is necessary for long-range cooperative activation of myosin binding. We used a novel optical trapping assay to measure the isometric stall force of an ensemble of myosin molecules moving actin filaments reconstituted with either natively phosphorylated or dephosphorylated Tm. The data show that the thin filament is cooperatively activated by myosin across regulatory units when Tm is phosphorylated. When Tm is dephosphorylated, this "long-range" cooperative activation is lost and the filament behaves identically to bare actin filaments. However, these effects are not due to dissociation of dephosphorylated Tm from the reconstituted thin filament. The data suggest that end-to-end interactions of adjacent Tm molecules are strengthened when Tm is phosphorylated, and that phosphorylation is thus essential for long range cooperative activation along the thin filament.     

Actin filament dynamics in the actomyosin VI complex is regulated allosterically by calcium-calmodulin light chain

The contractile and enzymatic activities of myosin VI are regulated by calcium binding to associated calmodulin (CaM) light chains. We have used transient phosphorescence anisotropy to monitor the microsecond rotational dynamics of erythrosin-iodoacetamide-labeled actin with strongly bound myosin VI (MVI) and to evaluate the effect of MVI-bound CaM light chain on actin filament dynamics. MVI binding lowers the amplitude but accelerates actin filament microsecond dynamics in a Ca²⁺- and CaM-dependent manner, as indicated from an increase in the final anisotropy and a decrease in the correlation time of transient phosphorescence anisotropy decays. MVI with bound apo-CaM or Ca²⁺-CaM weakly affects actin filament microsecond dynamics, relative to other myosins (e.g., muscle myosin II and myosin Va). CaM dissociation from bound MVI damps filament rotational dynamics (i.e., increases the torsional rigidity), such that the perturbation is comparable to that induced by other characterized myosins. Analysis of individual actin filament shape fluctuations imaged by fluorescence microscopy reveals a correlated effect on filament bending mechanics. These data support a model in which Ca²⁺-dependent CaM binding to the IQ domain of MVI is linked to an allosteric reorganization of the actin binding site(s), which alters the structural dynamics and the mechanical rigidity of actin filaments. Such modulation of filament dynamics may contribute to the Ca²⁺- and CaM-dependent regulation of myosin VI motility and ATP utilization.     

Smooth muscle and skeletal muscle myosins produce similar unitary forces and displacements in the laser trap.

Purified smooth muscle myosin in the in vitro motility assay propels actin filaments at 1/10 the velocity, yet produces 3-4 times more force than skeletal muscle myosin. At the level of a single myosin molecule, these differences in force and actin filament velocity may be reflected in the size and duration of single motion and force-generating events, or in the kinetics of the cross-bridge cycle. Specifically, an increase in either unitary force or duty cycle may explain the enhanced force-generating capacity of smooth muscle myosin. Similarly, an increase in attached time or decrease in unitary displacement may explain the reduced actin filament velocity of smooth muscle myosin. To discriminate between these possibilities, we used a laser trap to measure unitary forces and displacements from single smooth and skeletal muscle myosin molecules. We analyzed our data using mean-variance analysis, which does not rely on scoring individual events by eye, and emphasizes periods in the data with constant properties. Both myosins demonstrated multiple but similar event populations with discrete peaks at approximately +11 and -11 nm in displacement, and 1.5 and 3.5 pN in force. Mean attached times for smooth muscle myosin were longer than for skeletal-muscle myosin. These results explain much of the difference in actin filament velocity between these myosins, and suggest that an increased duty cycle is responsible for the enhanced force-generating capacity of smooth over skeletal-muscle myosin.     

A deterministic mechanism producing the loose coupling phenomenon observed in an actomyosin system

Myosins are molecular motors that convert the chemical energy of ATP into mechanical work called a power stroke. Class II myosin engaged in muscle contraction is reported to show a "loose coupling phenomenon", in which the number of power strokes is greater than the number of ATP hydrolyses. This phenomenon cannot be explained by the lever-arm hypothesis, which is currently accepted as a standard theory for myosin motility. In this paper, a model is proposed to reproduce the loose coupling phenomenon. The model is based on a mechanochemical process called "Driven by Detachment (DbD)" mechanism, which assumes that the energy of the power strokes originates from the potential energy generated by the attractive force between myosin and actin. During the docking process, the potential energy is converted into an intramolecular strain in a myosin molecule, which drives the power stroke after the myosin is firmly attached to an actin filament. The energy of ATP is used to temporarily reduce the attractive force and to increase the potential energy. Therefore, it is not directly linked to the power strokes. When myosin molecules work as an aggregate, the sliding movement of a myosin filament driven by the power strokes of some myosin heads makes other myosin heads that have completed their power strokes detach from the actin without consuming ATP. Under the DbD mechanism, these passively detached myosins can be again engaged in power strokes after the next attachment to actin. As a result, the number of power strokes becomes greater than the number of ATP hydrolyses, and the loose coupling phenomenon will be observed. A theoretical analysis indicates that the efficiency of converting the potential energy into intramolecular elastic energy determines the number of power strokes per each ATP hydrolysis. Computer simulations showed that the DbD mechanism actually produced the loose coupling phenomenon. A critical requirement for this mechanism is that ATP must preferentially facilitate the detachment of myosins that have completed their power strokes, but are still strongly attached to the actin. This requirement may be fulfilled by ATP hydrolysis tightly depending on the conformation of a myosin molecule.     

D-loop of Actin Differently Regulates the Motor Function of Myosins II and V

To gain more information on the manner of actin-myosin interaction, we examined how the motile properties of myosins II and V are affected by the modifications of the DNase I binding loop (D-loop) of actin, performed in two different ways, namely, the proteolytic digestion with subtilisin and the M47A point mutation. In an in vitro motility assay, both modifications significantly decreased the gliding velocity on myosin II-heavy meromyosin due to a weaker generated force but increased it on myosin V. On the other hand, single molecules of myosin V “walked” with the same velocity on both the wild-type and modified actins; however, the run lengths decreased sharply, correlating with a lower affinity of myosin for actin due to the D-loop modifications. The difference between the single-molecule and the ensemble measurements with myosin V indicates that in an in vitro motility assay the non-coordinated multiple myosin V molecules impose internal friction on each other via binding to the same actin filament, which is reduced by the weaker binding to the modified actins. These results show that the D-loop strongly modulates the force generation by myosin II and the processivity of myosin V, presumably affecting actin-myosin interaction in the actomyosin-ADP·P_i state of both myosins.     

The Antiparallel Dimerization of Myosin X Imparts Bundle Selectivity for Processive Motility

Myosin X is an unconventional actin-based molecular motor involved in filopodial formation, microtubule-actin filament interaction, and cell migration. Myosin X is an important component of filopodia regulation, localizing to tips of growing filopodia by an unclear targeting mechanism. The native α-helical dimerization domain of myosin X is thought to associate with antiparallel polarity of the two amino acid chains, making myosin X the only myosin that is currently considered to form antiparallel dimers. This study aims to determine if antiparallel dimerization of myosin X imparts selectivity toward actin bundles by comparing the motility of parallel and antiparallel dimers of myosin X on single and fascin-bundled actin filaments. Antiparallel myosin X dimers exhibit selective processivity on fascin-bundled actin and are only weakly processive on single actin filaments below saturating [ATP]. Artificial forced parallel dimers of myosin X are robustly processive on both single and bundled actin, exhibiting no selectivity. To determine the relationship between gating of the reaction steps and observed differences in motility, a mathematical model was developed to correlate the parameters of motility with the biochemical and mechanical kinetics of the dimer. Results from the model, constrained by experimental data, suggest that the probability of binding forward, toward the barbed end of the actin filament, is lower in antiparallel myosin X on single actin filaments compared to fascin-actin bundles and compared to constructs of myosin X with parallel dimerization.     

Cell motility and thermodynamic fluctuations tailoring quantum mechanics for biology

Cell motility underlying muscle contraction is an instance of thermodynamics tailoring quantum mechanics for biology. Thermodynamics is intrinsically multi-agential in admitting energy consumers in the form of energy-deficient thermodynamic fluctuations. The onset of sliding movement of an actin filament on myosin molecules in the presence of ATP molecules to be hydrolyzed demonstrates that thermodynamic fluctuations transform their nature so as to accommodate themselves to energy transduction subject to the first law of thermodynamics. The transition from transversal to longitudinal fluctuations of an actin filament with the increase of ATP concentration coincides with the change in the nature of energy consumers acting upon thermal energy in the light of the first law, eventually embodying a uniform sliding movement of an actin filament.