In order to explain the molecular mechanism of muscle contraction, it is crucial to know the distribution of the sarcomere compliance of active muscle. Here, we directly measure the stiffness of single actin filaments with and without tropomyosin, using a recently developed technique for nanomanipulation of single actin filaments with microneedles.The results show that the stiffness for 1-,Im-long actin filaments with and without tropomyosin is 65.3 ± 6.3 and 43.7 ± 4.6 pN/nm, respectively. When the distribution of crossbridge forces along the actin ifiament is taken into account, the elongation of a l-,um-long thin rilament during development of isometric contraction is calculated to be -0.23%. The time constant of force in response to a sudden length change is <0.2 ms, indicating that the viscoelasticity is negligible in the millisecond time range. These results suggest that '50% of the sarcomere compliance of active muscle is due to extensibility of the thin riaments.In striated muscles, contraction is due to cyclic interactions of myosin crossbridges with thin filaments in the sarcomere (1, 2). The mechanical properties ofthe interaction have often been studied by analyzing tension transients of contracting muscle fibers. In 1971, Huxley and Simmons (3) deduced an ingenious mechanical model to fit the kinetics of these transients. In this model, the force produced by the crossbridges is transmitted to thick and thin filaments by a series elastic element. The model assumed for simplification that the mechanical compliance (reciprocal of the stiffness) in the sarcomere is mostly localized in the crossbridges and that the thin and thick filaments are rigid to transmit the force produced by the crossbridges to the next sarcomere along the muscle fiber axis. This assumption has allowed us to lump the mechanical behavior of the crossbridges distributed along the thin filaments. Indeed, many subsequent experiments have been interpreted on the basis of this simplifying assumption.The assumption that compliance resides primarily within the crossbridges has been tested by many mechanical and structural studies. Ford et al. (4) measured the instantaneous stiffness of isometrically contracting muscle fibers at various sarcomere lengths and concluded that .80% of the sarcomere compliance is due to the crossbridges. A similar result was obtained from the dependence of the rigor stiffness on the sarcomere length (6). Huxley and coworkers (7,8) showed that the strong 5.9-nm x-ray diffraction peak from actin filaments did not change spacing significantly during contraction. These results suggested that the thin filaments are rigid, but the experiments are not conclusive (see Discussion). On the other hand, measurements of the elastic modulus for bending of actin filaments have suggested that the actin filament is quite flexible and, hence, might contribute significantly to muscle compliance (see ref. 9 for review).Recently, we have developed a nanomanipulation technique for single actin filaments that involves attach...

The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel many species of swimming bacteria. The rotor is a set of rings up to 45 nm in diameter in the cytoplasmic membrane; the stator contains about ten torque-generating units anchored to the cell wall at the perimeter of the rotor. The free-energy source for the motor is an inward-directed electrochemical gradient of ions across the cytoplasmic membrane, the protonmotive force or sodium-motive force for H+-driven and Na+-driven motors, respectively. Here we demonstrate a stepping motion of a Na+-driven chimaeric flagellar motor in Escherichia coli at low sodium-motive force and with controlled expression of a small number of torque-generating units. We observe 26 steps per revolution, which is consistent with the periodicity of the ring of FliG protein, the proposed site of torque generation on the rotor. Backwards steps despite the absence of the flagellar switching protein CheY indicate a small change in free energy per step, similar to that of a single ion transit.

We have developed a technique that allows mechanical and ligand-binding events in a single myosin molecule to be monitored simultaneously. We describe how steps in the ATPase reaction are temporally related to mechanical events at the single molecule level. The results show that the force generation does not always coincide with the release of bound nucleotide, presumably ADP. Instead the myosin head produces force several hundreds of milliseconds after bound nucleotide is released. This finding does not support the widely accepted view that force generation is directly coupled to the release of bound ligands. It suggests that myosin has a hysteresis or memory state, which stores chemical energy from ATP hydrolysis.

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 f luctuations of filaments supplied the torsional rigidity as (8.0 ؎ 1.2) ؋ 10 ؊26 Nm 2 . 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؇, independent of the rotational direction. Our results indicate that an actin filament exhibits comparable f lexibility in the rotational and longitudinal directions, but breaks more easily under torsional load.Actin is a major protein involved in a variety of cellular motile events and in the maintenance of cell shape and form. Determining its elastic properties in the polymeric state is central to an understanding of its function (1, 2). Recently, actin filaments have been measured to be several-fold more flexible longitudinally in vitro (3) and in muscle (4-6) than many models of muscle contraction have assumed (7). This finding would seem to require reconsideration of aspects of such models (8-10). Because of its helical structure, an actin filament should experience not only longitudinal but also torsional loads during interactions with myosin (11). To explain the mechanism of force generation, it is also important to know the elastic behavior of actin filaments during torsion. The torsional rigidity of actin filament can be estimated based on its bending rigidity, assuming the actin filament to be a homogenous rod (12). However, this assumption is not necessarily correct, because the actin filament is a double-helical polymer of globular actin monomers (13,14). Spectroscopic (12,(15)(16)(17) and electron microscopic studies (18) have suggested that the elastic property of an actin filament is largely anisotropic in the directions of twisting, bending, and stretching, i.e., the torsional rigidity is much smaller than the bending and longitudinal ones, assuming the actin filament to be a homogeneous rod, whereas the normal mode analysis based on the atomic structure of actin has shown much larger torsional rigidity than those suggested by these studies (19).Here, we have directly determined the torsional rigidity of actin filaments and the actin-actin bond breaking force under torsion by manipulating single actin filaments with optical tweezers and microneedles, respectively. Developments in video-assist fluorescence microscopy have enabled direct observat...

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.

SummaryThe bacterial flagellar motor is driven by the electrochemical potential of specific ions, H + or Na + . The motor consists of a rotor and stator, and their interaction generates rotation. The stator, which is composed of PomA and PomB in the Na + motor of Vibrio alginolyticus, is thought to be a torque generator converting the energy of ion flux into mechanical power. We found that specific mutations in PomB, including D24N, F33C and S248F, which caused motility defects, affected the assembly of stator complexes into the polar flagellar motor using green fluorescent proteinfused stator proteins. D24 of PomB is the predicted Na + -binding site. Furthermore, we demonstrated that the coupling ion, Na + , is required for stator assembly and that phenamil (an inhibitor of the Na + -driven motor) inhibited the assembly. Carbonyl cyanide m-chlorophenylhydrazone, which is a proton ionophore that collapses the sodium motive force in this organism at neutral pH, also inhibited the assembly. Thus we conclude that the process of Na + influx through the channel, including Na + binding, is essential for the assembly of the stator complex to the flagellar motor as well as for torque generation.

A new system has been developed for measuring the forces produced by a small number (less than 5-150) of myosin molecules interacting with a single actin filament in vitro. The technique can resolve forces of less than a piconewton and has a time resolution in the submillisecond range. It can thus detect fluctuations of force caused by individual molecular interactions. From analysis of these force fluctuations, the coupling between the enzymatic ATPase activity of actomyosin and the resulting mechanical impulses can be elucidated.

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