Movement of single myosin filaments and myosin step size on an actin filament suspended in solution by a laser trap

One must reconstitute the functions of interest from purified proteins

I am often asked by students and younger colleagues and now by the editors of this issue to tell the history of the development of the in vitro motility assay and the dual-beam single-molecule laser trap assay for myosin-driven actin filament movement, used widely as key assays for understanding how both muscle and nonmuscle myosin molecular motors work. As for all discoveries, the history of the development of the myosin assays involves many people who are not authors of the final publications, but without whom the assays would not have been developed as they are. Also, early experiences shape how one develops ideas and experiments, and influence future discoveries in major ways. I am pleased here to trace my own path and acknowledge the many individuals involved and my early science experiences that led to the work I and my students, postdoctoral fellows, and sabbatical visitors did to develop these assays. Mentors are too often overlooked in historical descriptions of discoveries, and my story starts with those who mentored me.

Materials for Smart Soft Actuator Systems

In contrast to conventional hard actuators, soft actuators offer many vivid advantages, such as improved flexibility, adaptability, and reconfigurability, which are intrinsic to living systems. These properties make them particularly promising for different applications, including soft electronics, surgery, drug delivery, artificial organs, or prosthesis. The additional degree of freedom for soft actuatoric devices can be provided through the use of intelligent materials, which are able to change their structure, macroscopic properties, and shape under the influence of external signals. The use of such intelligent materials allows a substantial reduction of a device's size, which enables a number of applications that cannot be realized by externally powered systems. This review aims to provide an overview of the properties of intelligent synthetic and living/natural materials used for the fabrication of soft robotic devices. We discuss basic physical/chemical properties of the main kinds of materials (elastomers, gels, shape memory polymers and gels, liquid crystalline elastomers, semicrystalline ferroelectric polymers, gels and hydrogels, other swelling polymers, materials with volume change during melting/crystallization, materials with tunable mechanical properties, and living and naturally derived materials), how they are related to actuation and soft robotic application, and effects of micro/macro structures on shape transformation, fabrication methods, and we highlight selected applications.

Force-velocity and tension transient measurements from Drosophila jump muscle reveal the necessity of both weakly-bound cross-bridges and series elasticity in models of muscle contraction

Muscle contraction is a fundamental biological process where molecular interactions between the myosin molecular motor and actin filaments result in contraction of a whole muscle, a process spanning size scales differing in eight orders of magnitude. Since unique behavior is observed at every scale in between these two extremes, to fully understand muscle function it is vital to develop multi-scale models. Based on simulations of classic measurements of muscle heat generation as a function of work, and shortening rate as a function of applied force, we hypothesize that a model based on molecular measurements must be modified to include a weakly-bound interaction between myosin and actin in order to fit measurements at the muscle fiber or whole muscle scales. This hypothesis is further supported by the model's need for a weakly-bound state in order to qualitatively reproduce the force response that occurs when a muscle fiber is rapidly stretched a small distance. We tested this hypothesis by measuring steady-state force as a function of shortening velocity, and the force transient caused by a rapid length step in Drosophila jump muscle fibers. Then, by performing global parameter optimization, we quantitatively compared the predictions of two mathematical models, one lacking a weakly-bound state and one with a weakly-bound state, to these measurements. Both models could reproduce our force-velocity measurements, but only the model with a weakly-bound state could reproduce our force transient measurements. However, neither model could concurrently fit both measurements. We find that only a model that includes weakly-bound cross-bridges with force-dependent detachment and an elastic element in series with the cross-bridges is able to fit both of our measurements. This result suggests that the force response after stretch is not a reflection of distinct steps in the cross-bridge cycle, but rather arises from the interaction of cross-bridges with a series elastic element. Additionally, the model suggests that the curvature of the force-velocity relationship arises from a combination of the force-dependence of weakly- and strongly-bound cross-bridges. Overall, this work presents a minimal cross-bridge model that has predictive power at the fiber level.

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.

Recent Advances in Biological Single-Molecule Applications of Optical Tweezers and Fluorescence Microscopy

Over the past two decades, single-molecule techniques have evolved into robust tools to study many fundamental biological processes. The combination of optical tweezers with fluorescence microscopy and microfluidics provides a powerful single-molecule manipulation and visualization technique that has found widespread application in biology. In this combined approach, the spatial (~nm) and temporal (~ms) resolution, as well as the force scale (~pN) accessible to optical tweezers is complemented with the power of fluorescence microscopy. Thereby, it provides information on the local presence, identity, spatial dynamics, and conformational dynamics of single biomolecules. Together, these techniques allow comprehensive studies of, among others, molecular motors, protein-protein and protein-DNA interactions, biomolecular conformational changes, and mechanotransduction pathways. In this chapter, recent applications of fluorescence microscopy in combination with optical trapping are discussed. After an introductory section, we provide a description of instrumentation together with the current capabilities and limitations of the approaches. Next we summarize recent studies that applied this combination of techniques in biological systems and highlight some representative biological assays to mark the exquisite opportunities that optical tweezers combined with fluorescence microscopy provide.

Rotation of large asymmetrical absorbing objects by Laguerre-Gauss beams

In this Letter, we show the manipulation and rotation of opaque graphite through adhesion with optically trapped polystyrene spheres. The absorbing graphite is rotated by the orbital angular momentum transfer from a Laguerre-Gauss laser mode and is trapped due to the presence of refracting spheres. This technique is effective for trapping and rotating absorbing objects of all sizes, including those larger than the laser mode.

Definite differences between in vitro actin-myosin sliding and muscle contraction as revealed using antibodies to myosin head

Muscle contraction results from attachment-detachment cycles between myosin heads extending from myosin filaments and actin filaments. It is generally believed that a myosin head first attaches to actin, undergoes conformational changes to produce force and motion in muscle, and then detaches from actin. Despite extensive studies, the molecular mechanism of myosin head conformational changes still remains to be a matter for debate and speculation. The myosin head consists of catalytic (CAD), converter (CVD) and lever arm (LD) domains. To give information about the role of these domains in the myosin head performance, we have examined the effect of three site-directed antibodies to the myosin head on in vitro ATP-dependent actin-myosin sliding and Ca2+-activated contraction of muscle fibers. Antibody 1, attaching to junctional peptide between 50K and 20K heavy chain segments in the CAD, exhibited appreciable effects neither on in vitro actin-myosin sliding nor muscle fiber contraction. Since antibody 1 covers actin-binding sites of the CAD, one interpretation of this result is that rigor actin-myosin linkage is absent or at most a transient intermediate in physiological actin-myosin cycling. Antibody 2, attaching to reactive lysine residue in the CVD, showed a marked inhibitory effect on in vitro actin-myosin sliding without changing actin-activated myosin head (S1) ATPase activity, while it showed no appreciable effect on muscle contraction. Antibody 3, attaching to two peptides of regulatory light chains in the LD, had no significant effect on in vitro actin-myosin sliding, while it reduced force development in muscle fibers without changing MgATPase activity. The above definite differences in the effect of antibodies 2 and 3 between in vitro actin-myosin sliding and muscle contraction can be explained by difference in experimental conditions; in the former, myosin heads are randomly oriented on a glass surface, while in the latter myosin heads are regularly arranged within filament-lattice structures.

Joining forces: integrating the mechanical and optical single molecule toolkits

Combining single molecule force measurements with fluorescence detection opens up exciting new possibilities for the characterization of mechanoresponsive molecules in Biology and Materials Science.

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.

STEP SIZE IN ACTIVATED RABBIT SARCOMERES IS INDEPENDENT OF FILAMENT OVERLAP

Investigations carried out on single cardiac and bumblebee myofibrils have shown stepwise sarcomere-length change of ~2.7 nm.1 We have carried out parallel measurements on single myofibrils from rabbit psoas muscle. Activated specimens were released or stretched using a motor-imposed ramp. With a high-resolution algorithm, we found that step sizes were always integer multiples of 2.7 nm, whether the length change was positive or negative, and independent of ramp velocity. Also, the influence of initial sarcomere length was studied, and found to be negligible. The value 2.7 nm, seen consistently, is equal to the linear repeat of actin monomers along the thin filament, a result that ties dynamical events to molecular structure, and places narrow constraints on any proposed molecular mechanism.

Cell and molecular biology of the fastest myosins

Chara myosin is a class XI plant myosin in green algae Chara corallina and responsible for fast cytoplasmic streaming. The Chara myosin exhibits the fastest sliding movement of F-actin at 60 mum/s as observed so far, 10-fold of the shortening speed of muscle. It has some distinct properties differing from those of muscle myosin. Although knowledge about Chara myosin is very limited at present, we have tried to elucidate functional bases of its characteristics by comparing with those of other myosins. In particular, we have built the putative atomic model of Chara myosin by using the homology-based modeling system and databases. Based on the putative structure of Chara myosin obtained, we have analyzed the relationship between structure and function of Chara myosin to understand its distinct properties from various aspects by referring to the accumulated knowledge on mechanochemical and structural properties of other classes of myosin, particularly animal and fungal myosin V. We will also discuss the functional significance of Chara myosin in a living cell.

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.

New techniques in linear and non-linear laser optics in muscle research

This review proposes a brief summary of two applications of lasers to muscle research. The first application (laser tweezers), is now a well-established technique in the field, adopted by several laboratories in the world and producing a constant stream of original data, fundamental for our improved understanding of muscle contraction at the level of detail that only single molecule measurements can provide. As an example of the power of this technique, here we focus on some recent results, revealing the performance of the working stroke in at least two distinct steps also in skeletal muscle myosin. A second laser-based technique described here is second-harmonic generation; the application of this technique to muscle research is very recent. We describe the main results obtained thus far in this area and the potentially remarkable impact that this technology may have in muscle research.

Geometrical correspondence identified and a new interaction unit suggested in striated muscle

It has long been believed that the periodic structure of the myosin helix is a consequence only of compressing the actin-myosin interaction sites. Here, we identify a length correspondence between the smallest helical unit on the thick filament and the helical pitch of the actin filaments in two different contractile muscles. This suggests a rotation/swing of the filaments that creates a new interaction unit in addition to the single interaction between an actin filament and a myosin head. Numerical characteristics of the single interaction are estimated from discussion about an in vivo interaction utilizing the new unit. The estimated twisted angle of the actin filaments is consistent with that calculated from its torsion rigidity and the evaluated step sizes per cross-bridge can be performed by a single bend of a myosin head. By comparing our evaluated step sizes with experimental results, we conclude that the most plausible mechanism at the force-recovery stage involves swings or rotations of both filaments in the same direction (clockwise).

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.

Effect of sarcomere length on step size in relaxed rabbit psoas muscle

Recent experiments have shown that shortening and stretching of sarcomeres in single activated and unactivated myofibrils occur in stepwise fashion (Yang et al. (1998) Biophys J 74: 1473-1483; Blyakhman et al. (2001) Biophys J 81: 1093-1100; Yakovenko et al. (2002) Am J Physiol Cell Physiol 283: 735-742). Here, we carried out measurements on single myofibrils from rabbit psoas muscle to investigate steps in unactivated specimens in more detail. Activated and unactivated myofibrils were released and stretched in ramp-like fashion. The time course of length change in the single sarcomere was consistently stepwise. We found that in the unactivated myofibrils, step size depended on initial sarcomere length, diminishing progressively with increase of initial sarcomere length, whereas in the case of activated sarcomeres, step size was consistently 2.7 nm.

Correlation between mechanical and enzymatic events in contracting skeletal muscle fiber

The conventional hypothesis of muscle contraction postulates that the interaction between actin and myosin involves tight coupling between the power stroke and hydrolysis of ATP. However, some in vitro experiments suggested that hydrolysis of a single molecule of ATP caused multiple mechanical cycles. To test whether the tight coupling is present in contracting muscle, we simultaneously followed mechanical and enzymatic events in a small population of cross-bridges of glycerinated rabbit psoas fibers. Such small population behaves as a single cross-bridge when muscle contraction is initiated by a sudden release of caged ATP. Mechanical events were measured by changes of orientation of probes bound to the regulatory domain of myosin. Enzymatic events were simultaneously measured from the same cross-bridge population by the release of fluorescent ADP from the active site. If the conventional view were true, ADP desorption would occur simultaneously with dissociation of cross-bridges from thin filaments and would be followed by cross-bridge rebinding to thin filaments. Such sequence of events was indeed observed in contracting muscle fibers, suggesting that mechanical and enzymatic events are tightly coupled in vivo.

Dynamic axial-position control of a laser-trapped particle by wave-front modification

The axial position of a laser-trapped particle has been controlled by modification of the wave front by means of a membrane deformable mirror. The mirror gives wave-front modulation in terms of Zernike polynomials. By modulation of the Zernike defocus term we can modulate the particle position under conditions of laser trapping. A polystyrene particle of 1-microm diameter was moved along the optical axis direction for a distance of 2370 nm in minimum steps of 55.4 nm. We also demonstrated particle oscillation along the optical axis by changing the focal position in a sinusoidal manner. From the frequency dependency of the amplitude of particle oscillation we determined the spring constant as 91.7 nN/m.

Resource Letter: LBOT-1: Laser-based optical tweezers

This Resource Letter provides a guide to the literature on optical tweezers, also known as laser-based, gradient-force optical traps. Journal articles and books are cited for the following main topics: general papers on optical tweezers, trapping instrument design, optical detection methods, optical trapping theory, mechanical measurements, single molecule studies, and sections on biological motors, cellular measurements and additional applications of optical tweezers.

Zigzag motions of the myosin-coated beads actively sliding along actin filaments suspended between immobilized beads

The motions of myosin filaments actively sliding along suspended actin filaments were studied. By manipulating a double-beam laser tweezers, single actin filaments were suspended between immobilized microbeads. When another beads coated with myosin filaments were dragged to suspended actin filaments, the beads instantly and unidirectionally slid along the actin filaments. The video image analysis showed that the beads slid at a velocity of ca. 3-5 microm/s accompanied with zigzag motions. When beads were densely coated with myosin filaments, the sliding motions became straight and smooth. The obtained results indicate that (1) during the sliding motions, the interaction between myosin heads and actin filaments is weak and susceptible to random thermal agitations, (2) the effects of thermal agitations to the sliding motions of myofilaments are readily suppressed by mechanical constraints imposed to the filaments, and (3) the active sliding force is produced almost in parallel to the filaments axis.

Fundamental step size in single cardiac and skeletal sarcomeres

In attempting to deduce the size of the elementary molecular translation step, recent experiments using single myosin molecules translating over actin filaments have shown a consistent step size of 5.4 nm (10, 21). We have carried out parallel measurements on single myofibrils from rabbit cardiac muscle and bumblebee flight muscle. Activated specimens were released or stretched with a motor-imposed ramp, and the time course of length of individual sarcomeres was measured by projecting the image of the striations onto a linear photodiode array and tracking the spacing between A-band centroids. We confirmed the 5.4-nm step. With subnanometer precision, however, we find that this value is two times that of a more fundamental step size of 2.7 nm. Step sizes were always integer multiples of 2.7 nm, whether the length change was positive or negative. This value is equal to the linear repeat of actin monomers along the thin filament, a result that ties dynamic events to molecular structure and places narrow constraints on any proposed molecular mechanism.

Conformational change of the actomyosin complex drives the multiple stepping movement

Actin-myosin (actomyosin) generates mechanical force by consuming ATP molecules. We apply the energy landscape perspective to address a controversial issue as to whether the myosin head moves with multiple steps after a single ATP hydrolysis or only a single mechanical event of the lever-arm swinging follows a single ATP hydrolysis. Here we propose a theoretical model in which the refolding of the partially unfolded actomyosin complex and the movement of the myosin head along the actin filament are coupled. A single ATP hydrolysis is followed by the formation of a high free-energy partially unfolded actomyosin complex, which then gradually refolds with a concomitant multiple stepping movement on the way to the lowest free-energy rigor state. The model quantitatively explains the single-molecular observation of the multiple stepping movement and is consistent with structural observations of the disorder in the actomyosin-binding process. The model also explains the observed variety in dwell time before each step, which is not accounted for by previous models, such as the lever-arm or ratchet models.

Twisting and stretching single DNA molecules

The elastic properties of DNA are essential for its biological function. They control its bending and twisting as well as the induction of structural modifications in the molecule. These can affect its interaction with the cell machinery. The response of a single DNA molecule to a mechanical stress can be precisely determined in single-molecule experiments which give access to an accurate measurement of the elastic parameters of DNA.

Link between the enzymatic kinetics and mechanical behavior in an actomyosin motor

We have attempted to link the solution actomyosin ATPase with the mechanical properties of in vitro actin filament sliding over heavy meromyosin. To accomplish this we perturbed the system by altering the substrate with various NTPs and divalent cations, and by altering ionic strength. A wide variety of enzymatic and mechanical measurements were made under very similar solution conditions. Excellent correlations between the mechanical and enzymatic quantities were revealed. Analysis of these correlations based on a force-balance model led us to two fundamental equations, which can be described approximately as follows: the maximum sliding velocity is proportional to square root of V(max)K(m)(A), where K(m)(A) is the actin concentration at which the substrate turnover rate is half of its maximum (V(max)). The active force generated by a cross-bridge under no external load or under a small external load is proportional to square root of V(max)/K(m)(A). The equations successfully accounted for the correlations observed in the present study and observations in other laboratories.

The myosin motor: muscle contraction and in vitro movement

The molecular mechanism of in vitro movement is assumed, by most investigators, to be identical to that of muscle contraction. We discuss this view, which raises various problems. We believe there are mechanisms for muscle contraction (in this case considerable forces are developed, with small displacements) and other mechanisms for in vitro movement (giving large displacements, without necessarily generating substantial forces). Hybrid models may explain muscle contraction. The traditional swinging-crossbridge model may explain in vitro movement. For muscle contraction, movement may result partly from the swinging-crossbridge mechanism and partly from other factors. Comparisons of different fibres at different moments of the Mg-ATPase cycle suggest that both the value of the isometric force in muscle and in vitro and that of the Mg-ATPase activity used in vitro need to be reconsidered. The recently reported dependence of the isometric active tension of smooth skinned fibres on temperature appears to be weaker than predicted by the swinging-crossbridge theory alone. This recent observation is compatible with the existence of other forces (electrostatic repulsions) decreasing with temperature as has been known for some years. From recent experimental data, we think the biochemistry of myosin and actomyosin should be reassessed, to try to find new details of the mechanisms of muscle contraction and in vitro motility.

Cross-bridge attachment during high-speed active shortening of skinned fibers of the rabbit psoas muscle: implications for cross-bridge action during maximum velocity of filament sliding

To characterize the kinetics of cross-bridge attachment to actin during unloaded contraction (maximum velocity of filament sliding), ramp-shaped stretches with different stretch-velocities (2-40,000 nm per half-sarcomere per s) were applied to actively contracting skinned fibers of the rabbit psoas muscle. Apparent fiber stiffness observed during such stretches was plotted versus the speed of the imposed stretch (stiffness-speed relation) to derive the rate constants for cross-bridge dissociation from actin. The stiffness-speed relation obtained for unloaded shortening conditions was shifted by about two orders of magnitude to faster stretch velocities compared to isometric conditions and was almost identical to the stiffness-speed relation observed in the presence of MgATPgammaS at high Ca(2+) concentrations, i.e., under conditions where cross-bridges are weakly attached to the fully Ca(2+) activated thin filaments. These data together with several control experiments suggest that, in contrast to previous assumptions, most of the fiber stiffness observed during high-speed shortening results from weak cross-bridge attachment to actin. The fraction of strongly attached cross-bridges during unloaded shortening appears to be as low as some 1-5% of the fraction present during isometric contraction. This is about an order of magnitude less than previous estimates in which contribution of weak cross-bridge attachment to observed fiber stiffness was not considered. Our findings imply that 1) the interaction distance of strongly attached cross-bridges during high-speed shortening is well within the range consistent with conventional cross-bridge models, i.e., that no repetitive power strokes need to be assumed, and 2) that a significant part of the negative forces that limit the maximum speed of filament sliding might originate from weak cross-bridge interactions with actin.

Quantal length changes in single contracting sarcomeres

The time course of shortening was investigated in the single sarcomere, the smallest contractile unit that retains natural structure. We projected the striation patterns of single bumblebee flight-muscle myofibrils onto a linear photodiode array, which was scanned periodically to produce repetitive traces of intensity vs. position along the array. Sarcomere length was taken as the span between adjacent A-band or Z-line centroids. When myofibrils were ramp-released by a motor, individual sarcomeres shortened in steps punctuated by pauses. The single sarcomere-shortening trace was consistently stepwise both in activated and relaxed specimens. Although step size was variable, the size distribution showed a signature-like feature: the histogram comprised distinct peaks that were spaced quasi-regularly. In the activated myofibrils the interpeak separation corresponded to 2.71 nm per half-sarcomere. This value is equal to the linear advance of actin subunits along the thin filament. Thus, actin filaments translate over thick filaments by steps that may be integer multiples of the actin-subunit spacing.

Implications of quantal motor action in biological systems

We demonstrate in this paper that quantal behavior is a central feature of biological motile and contractile systems. Step-like behavior has been demonstrated in the interaction between single molecules and filaments both in the kinesin-microtubule system and in the myosin-actin filament system. We show here that the step-like molecular features appear also in the single intact sarcomere. We studied single sarcomeres of single bumble-bee myofibrils, both in the unactivated and activated states. Myofibril-length changes induced by a motor-imposed ramp were accompanied by corresponding sarcomere-length changes. However, the sarcomere-length changes were stepwise. Computer analysis of the stepwise shortening patterns revealed a step-size distribution containing multiple peaks. In the activated state, the peaks were separated by 2.7 nm per half-sarcomere which is the linear actin-subunit spacing. Thus, translation steps are an integer multiple of the actin-subunit spacing. This result parallels the one observed in the kinesin-tubulin spacing, where step size is a multiple of the tubulin-subunit spacing. In the muscle system, however, the steps are preserved on a macroscopic scale, implying high synchrony. The quantal steps are easily explained by a model in which the actin filament propels itself over stationary cross-bridges: if actin binds to the cross-bridges between steps, then the observed quantal result is inevitable. As probes of contractile phenomena approach the molecular level, the discrete unitary events underlying contraction begin to emerge. Thus, step-like behavior is observed as the single kinesin molecule translates along the microtubule, as the single myosin molecule translates over the actin filament, and as the single isolated titin molecule is stretched.

The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer

Muscle contraction is brought about by the cyclical interaction of myosin with actin coupled to the breakdown of ATP. The current view of the mechanism is that the bound actomyosin complex (or "cross-bridge") produces force and movement by a change in conformation. This process is known as the "working stroke." We have measured the stiffness and working stroke of a single cross-bridge (kappa xb, dxb, respectively) with an optical tweezers transducer. Measurements were made with the "three bead" geometry devised by Finer et al. (1994), in which two beads, supported in optical traps, are used to hold an actin filament in the vicinity of a myosin molecule, which is immobilized on the surface of a third bead. The movements and forces produced by actomyosin interactions were measured by detecting the position of both trapped beads. We measured, and corrected for, series compliance in the system, which otherwise introduces large errors. First, we used video image analysis to measure the long-range, force-extension property of the actin-to-bead connection (kappa con), which is the main source of "end compliance." We found that force-extension diagrams were nonlinear and rather variable between preparations, i.e., end compliance depended not only upon the starting tension, but also upon the F-actin-bead pair used. Second, we measured kappa xb and kappa con during a single cross-bridge attachment by driving one optical tweezer with a sinusoidal oscillation while measuring the position of both beads. In this way, the bead held in the driven optical tweezer applied force to the cross-bridge, and the motion of the other bead measured cross-bridge movement. Under our experimental conditions (at approximately 2 pN of pretension), connection stiffness (kappa con) was 0.26 +/- 0.16 pN nm-1. We found that rabbit heavy meromyosin produced a working stroke of 5.5 nm, and cross-bridge stiffness (kappa xb) was 0.69 +/- 0.47 pN nm-1.

Elastic properties of isolated thick filaments measured by nanofabricated cantilevers

Using newly developed nanofabricated cantilever force transducers, we have measured the mechanical properties of isolated thick filaments from the anterior byssus retractor muscle of the blue mussel Mytilus edulis and the telson levator muscle of the horseshoe crab Limulus polyphemus. The single thick filament specimen was suspended between the tip of a flexible cantilever and the tip of a stiff reference beam. Axial stress was placed on the filament, which bent the flexible cantilever. Cantilever tips were microscopically imaged onto a photodiode array to extract tip positions, which could be converted into force by using the cantilever stiffness value. Length changes up to 23% initial length (Mytilus) and 66% initial length (Limulus) were fully reversible and took place within the physiological force range. When stretch exceeded two to three times initial length (Mytilus) or five to six times initial length (Limulus), at forces approximately 18 nN and approximately 7 nN, respectively, the filaments broke. Appreciable and reversible strain within the physiological force range implies that thick-filament length changes could play a significant physiological role, at least in invertebrate muscles.

Muscle contraction as a Markov process. I: Energetics of the process

Force generation during muscle contraction can be understood in terms of cyclical length changes in segments of actin thin filaments moving through the three-dimensional lattice of myosin thick filaments. Recent anomalies discovered in connection with analysis of myosin step sizes in in vitro motility assays and with skinned fibres can be rationalized by assuming that ATP hydrolysis on actin accompanies these length changes. The paradoxically rapid regeneration of tension in quick release experiments, as well as classical energetic relationships, such as Hill's force-velocity curve, the Fenn effect, and the unexplained enthalpy of shortening, can be given mutually self-consistent explanations with this model. When muscle is viewed as a Markov process, the vectorial process of chemomechanical transduction can be understood in terms of lattice dependent transitions, wherein the phosphate release steps of the myosin and actin ATPases depend only on occurrence of allosteric changes in neighbouring molecules. Tropomyosin has a central role in coordinating the steady progression of these cooperative transitions along actin filaments and in gearing up the system in response to higher imposed loads.

Tension/stiffness ratio of skinned rat skeletal muscle fibre types at various temperatures

It is well known that shortening velocity and maximal tension of muscle preparations are strongly dependent on experimental temperature. Conversely, studies about temperature effects on muscle fibre stiffness are scarce. In the present study, we measured tension and stiffness of maximally Ca2+-activated skinned rat skeletal muscle fibres of different types over a wide temperature range. All fibre types exhibited a similar tension/stiffness ratio at each experimental temperature. This ratio increased almost linearly from 6 to 18 nm when the temperature was raised from 6 to 34 degrees C. Our results are discussed in the light of the drastic discrepancies reported for the amount of compliance inside and outside the attached myosin cross-bridges of activated muscle fibres (Ford et al. 1981, Huxley et al. 1994, Kojima et al. 1994, Wakabayashi et al. 1994, Higuchi et al. 1995). The relation between these compliances had been deduced from various experimental approaches executed at different temperatures. The large temperature sensitivity of the tension/stiffness ratio found in this study provides evidence for the assumption that the compliance outside the cross-bridges increases with rising temperature. This view would reconcile the contrasting results reported for the relation of compliances inside and outside the attached cross-bridges.

Accelerative sliding of myosin-coated glass-beads under suspended condition from actin paracrystal

The maximum sliding velocity of rabbit skeletal-muscle myosin is about 10 micron/sec under zero load and physiological conditions. We have found, however, that a large glass-bead (diameter, 65 micron) coated by rabbit skeletal myosin slides at 338 +/- 47 micron/sec under a condition suspended from an actin paracrystal surface. Also the sliding velocity increases exponentially as the size of myosin-coated glass-beads increases. We report here that the sliding velocity of myosin can be controlled by the adhesion force and the external normal force acting between actin and myosin.

Single molecule imaging of fluorophores and enzymatic reactions achieved by objective-type total internal reflection fluorescence microscopy

Imaging of single fluorescent molecules has been achieved in a relatively simple manner using objective-type total internal reflection fluorescence microscopy (TIRFM). Switching from epi-fluorescence microscopy to objective-type TIRFM was achieved by translation of a single mirror in the system. Clear images of single molecules of an orange fluorescent dye, Cy3, were obtained with a fluorescence-to-background ratio of 12, using a conventional high aperture objective (PlanApo, 100 x, NA 1.4) with ordinary coverslips and immersion oil. This method allowed visualization of single molecules under scanning probe microscopes. Taking advantage of the technique of single molecule imaging, individual ATP turnovers have been visualized with a fluorescent ATP analogue, Cy3-ATP, using a simple experimental strategy. Clear on/off signals were obtained that correspond to the association and dissociation of single Cy3-ATP/ADP molecules with a single myosin head molecule. This method will allow a variety of single-molecular assays of biomolecular functions to be performed using fluorescently labeled substrates, ligands, messengers, and biologically active molecules. Thus, the present technique provides a simple yet powerful and universal tool for researchers to probe the events of single molecules.

Torsional rigidity of single actin filaments and actin-actin bond breaking force under torsion measured directly by in vitro micromanipulation

Knowledge of the elastic properties of actin filaments is crucial for considering its role in muscle contraction, cellular motile events, and formation of cell shape. The stiffness of actin filaments in the directions of stretching and bending has been determined. In this study, we have directly determined the torsional rigidity and breaking force of single actin filaments by measuring the rotational Brownian motion and tensile strength using optical tweezers and microneedles, respectively. Rotational angular fluctuations of filaments supplied the torsional rigidity as (8.0 +/- 1.2) x 10(-26) Nm2. This value is similar to that deduced from the longitudinal rigidity, assuming the actin filament to be a homogeneous rod. The breaking force of the actin-actin bond was measured while twisting a filament through various angles using microneedles. The breaking force decreased greatly under twist, e.g., from 600-320 pN when filaments were turned through 90 degrees, independent of the rotational direction. Our results indicate that an actin filament exhibits comparable flexibility in the rotational and longitudinal directions, but breaks more easily under torsional load.

Direct inhibition of the actomyosin motility by local anesthetics in vitro

Using a recently developed in vitro motility assay, we have demonstrated that local anesthetics directly inhibit myosin-based movement of single actin filaments in a reversible dose-dependent manner. This is the first reported account of the actions of local anesthetics on purified proteins at the molecular level. In this study, two tertiary amine local anesthetics, lidocaine and tetracaine, were used. The inhibitory action of the local anesthetics on actomyosin sliding movement was pH dependent; the anesthetics were more potent at higher pH values, and this reaction was accompanied by an increased proportion of the uncharged form of the anesthetics. QX-314, a permanently charged derivative of lidocaine, had no effect on actomyosin sliding movement. These results indicate that the uncharged form of local anesthetics is predominantly responsible for the inhibition of actomyosin sliding movement. The local anesthetics inhibited sliding movement but hardly interfered with the binding of actin filaments to myosin on the surface or with actomyosin ATPase activity at low ionic strength. To characterize the actomyosin interaction in the presence of anesthetics, we measured the binding and breaking force of the actomyosin complex. The binding of actin filaments to myosin on the surface was not affected by lidocaine at low ionic strength. The breaking force, measured using optical tweezers, was approximately 1.5 pN per micron of an actin filament, which was much smaller than in rigor and isometric force. The binding and breaking force greatly decreased with increasing ionic strength, indicating that the remaining interaction is ionic in nature. The result suggests that the binding and ATPase of actomyosin are governed predominantly by ionic interaction, which is hardly affected by anesthetics; whereas the force generation requires hydrophobic interaction, which plays a major part of the strong binding and is blocked by anesthetics, in addition to the ionic interaction.

Mutual sensitization of ATP and GTP in driving F-actin on the surface-fixed H-meromyosin

Using an in vitro motility assay on acto-H-meromyosin, we studied the sliding velocity of an actin filament driven by two kinds of H-meromyosin heads: H-meromyosin head with ATP bound (fast motor) and with GTP bound (slow motor). We found a significant increase in the sliding velocity owing to the coexistence of the fast motor and the slow motor. This phenomenon may give an important suggestion with regard to the integration over multiple interactions of H-meromyosin heads along the actin filament.

Conservation within the myosin motor domain: implications for structure and function

BACKGROUND

Myosins are motors that use energy supplied by ATP to travel along actin filaments. The structure of myosin is known, but the actin-binding site is not well defined, and the mechanisms by which actin activates ATP hydrolysis by myosin, and myosin moves relative to the actin filament, developing force, are not fully understood. Previous phylogenetic analyses of the motor domain of myosins have identified up to twelve classes. We set out to analyse the positions of conserved residues within this domain in detail, and relate the conserved residues to the myosin structure.

RESULTS

Our analysis indicates that there are at least thirteen myosin classes. Conserved residues in the motor domain have been positioned within the framework provided by the recent crystal structures, thus helping to define those residues involved in actin and ATP binding, in hydrolysis and in conformational change. This has revealed remarkably poor overall conservation at the site thought to be involved in actin binding, but several highly conserved residues have been identified that may be functionally important.

CONCLUSIONS

Information from such a sequence analysis is a useful tool in the further interpretation of X-ray structures. It allows the position of crucial residues from other members of a superfamily to be determined within the framework provided by the known structures and the functional significance of conserved or mutated residues to be assessed.

Force responses following stepwise length changes of rat skeletal muscle fibre types

1. Force responses following stepwise length changes of Ca(2+)-activated skinned leg muscle fibres (6 degrees C) of the rat were correlated with their myosin heavy chain (HC) isoforms (myosin HC I, fibre type I; myosin HC IIA, type IIA; myosin HC IID (HC IIX), type IID (type IIX); myosin HC IIB, type IIB) in order to study the mechanical properties of these molecules. 2. Marked differences in the time behaviour of force transients following quick releases of fibre length existed between various muscle fibres, and a conspicuous correlation with their myosin HC complement was noticed (order of velocity: IIB > IID > IIA > > I). No differences were found in the relationship between the applied length step and the resulting force (T1, T2 curves). 3. Our results suggest that the heads of various myosin heavy chain isoforms exhibit different kinetic properties. The differences concern the kinetics of the myosin head movements and the duration of cyclic interactions between myosin heads and thin filaments. The extent of force-generating movements and the mean elongation of attached heads in the isometric state seem to be independent of the isoform.

Detection of sub-8-nm movements of kinesin by high-resolution optical-trap microscopy

Kinesin is a molecular motor that transports organelles along microtubules. This enzyme has two identical 7-nm-long motor domains, which it uses to move between consecutive tubulin binding sites spaced 8 nm apart along a microtubular protofilament. The molecular mechanism of this movement, which remains to be elucidated, may be common to all families of motor proteins. In this study, a high-resolution optical-trap microscope was used to measure directly the magnitude of abrupt displacements produced by a single kinesin molecule transporting a microscopic bead. The distribution of magnitudes reveals that kinesin not only undergoes discrete 8-nm movements, in agreement with previous work [Svoboda, K., Schmidt, C. F., Schnapp, B. J. & Block, S.M. (1993) Nature (London) 365, 721-727], but also frequently exhibits smaller movements of about 5 nm. A possible explanation for these unexpected smaller movements is that kinesin's movement from one dimer to the next along a protofilament involves at least two distinct events in the mechanical cycle.

Multiple- and single-molecule analysis of the actomyosin motor by nanometer-piconewton manipulation with a microneedle: unitary steps and forces

We have developed a new technique for measurements of piconewton forces and nanometer displacements in the millisecond time range caused by actin-myosin interaction in vitro by manipulating single actin filaments with a glass microneedle. Here, we describe in full the details of this method. Using this method, the elementary events in energy transduction by the actomyosin motor, driven by ATP hydrolysis, were directly recorded from multiple and single molecules. We found that not only the velocity but also the force greatly depended on the orientations of myosin relative to the actin filament axis. Therefore, to avoid the effects of random orientation of myosin and association of myosin with an artificial substrate in the surface motility assay, we measured forces and displacements by myosin molecules correctly oriented in single synthetic myosin rod cofilaments. At a high myosin-to-rod ratio, large force fluctuations were observed when the actin filament interacted in the correct orientation with a cofilament. The noise analysis of the force fluctuations caused by a small number of heads showed that the myosin head generated a force of 5.9 +/- 0.8 pN at peak and 2.1 +/- 0.4 pN on average over the whole ATPase cycle. The rate constants for transitions into (k+) and out of (k-) the force generation state and the duty ratio were 12 +/- 2 s-1, and 22 +/- 4 s-1, and 0.36 +/- 0.07, respectively. The stiffness was 0.14 pN nm-1 head-1 for slow length change (100 Hz), which would be approximately 0.28 pN nm-1 head-1 for rapid length change or in rigor. At a very low myosin-to-rod ratio, distinct actomyosin attachment, force generation (the power stroke), and detachment events were directly detected. At high load, one power stroke generated a force spike with a peak value of 5-6 pN and a duration of 50 ms (k(-)-1), which were compatible with those of individual myosin heads deduced from the force fluctuations. As the load was reduced, the force of the power stroke decreased and the needle displacement increased. At near zero load, the mean size of single displacement spikes, i.e., the unitary steps caused by correctly oriented myosin, which were corrected for the stiffness of the needle-to-myosin linkage and the randomizing effect by the thermal vibration of the needle, was approximately 20 nm.