Steady-state force-velocity relation in the ATP-dependent sliding movement of myosin-coated beads on actin cables in vitro studied with a centrifuge microscope

The role of mechanics in axonal stability and development

Much of the focus of neuronal cell biology has been devoted to growth cone guidance, synaptogenesis, synaptic activity, plasticity, etc. The axonal shaft too has received much attention, mainly for its astounding ability to transmit action potentials and the transport of material over long distances. For these functions, the axonal cytoskeleton and membrane have been often assumed to play static structural roles. Recent experiments have changed this view by revealing an ultrastructure much richer in features than previously perceived and one that seems to be maintained at a dynamic steady state. The role of mechanics in this is only beginning to be broadly appreciated and appears to involve passive and active modes of coupling different biopolymer filaments, filament turnover dynamics and membrane biophysics. Axons, being unique cellular processes in terms of high aspect ratios and often extreme lengths, also exhibit unique passive mechanical properties that might have evolved to stabilize them under mechanical stress. In this review, we summarize the experiments that have exposed some of these features. It is our view that axonal mechanics deserves much more attention not only due to its significance in the development and maintenance of the nervous system but also due to the susceptibility of axons to injury and neurodegeneration.

Force-Regulated State Transitions of Growing Axons

Growing axons are one-dimensional active structures that are important for wiring the brain and repairing nerves. However, the biophysical mechanisms underlying the complex kinetics of growing axons remain elusive. Here, we develop a theoretical framework to recapitulate force-regulated states and their transitions in growing axons. We demonstrate a unique negative feedback mechanism that defines four distinct kinetic states in a growing axon, whose transitional boundaries depend on the interplay between cytoskeletal dynamics and axon-substrate adhesion. A phase diagram for axonal growth is formulated based on two dimensionless numbers.

Actin Stress Fibers Response and Adaptation under Stretch

One of the many effects of soft tissues under mechanical solicitation in the cellular damage produced by highly localized strain. Here, we study the response of peripheral stress fibers (SFs) to external stretch in mammalian cells, plated onto deformable micropatterned substrates. A local fluorescence analysis reveals that an adaptation response is observed at the vicinity of the focal adhesion sites (FAs) due to its mechanosensor function. The response depends on the type of mechanical stress, from a Maxwell-type material in compression to a complex scenario in extension, where a mechanotransduction and a self-healing process takes place in order to prevent the induced severing of the SF. A model is proposed to take into account the effect of the applied stretch on the mechanics of the SF, from which relevant parameters of the healing process are obtained. In contrast, the repair of the actin bundle occurs at the weak point of the SF and depends on the amount of applied strain. As a result, the SFs display strain-softening features due to the incorporation of new actin material into the bundle. In contrast, the response under compression shows a reorganization with a constant actin material suggesting a gliding process of the SFs by the myosin II motors.

A Myosin II-Based Nanomachine Devised for the Study of Ca2+-Dependent Mechanisms of Muscle Regulation

The emergent properties of the array arrangement of the molecular motor myosin II in the sarcomere of the striated muscle, the generation of steady force and shortening, can be studied in vitro with a synthetic nanomachine made of an ensemble of eight heavy-meromyosin (HMM) fragments of myosin from rabbit psoas muscle, carried on a piezoelectric nanopositioner and brought to interact with a properly oriented actin filament attached via gelsolin (a Ca²⁺-regulated actin binding protein) to a bead trapped by dual laser optical tweezers. However, the application of the original version of the nanomachine to investigate the Ca²⁺-dependent regulation mechanisms of the other sarcomeric (regulatory or cytoskeleton) proteins, adding them one at a time, was prevented by the impossibility to preserve [Ca²⁺] as a free parameter. Here, the nanomachine is implemented by assembling the bead-attached actin filament with the Ca²⁺-insensitive gelsolin fragment TL40. The performance of the nanomachine is determined both in the absence and in the presence of Ca²⁺ (0.1 mM, the concentration required for actin attachment to the bead with gelsolin). The nanomachine exhibits a maximum power output of 5.4 aW, independently of [Ca²⁺], opening the possibility for future studies of the Ca²⁺-dependent function/dysfunction of regulatory and cytoskeletal proteins.

On the Shape of the Force-Velocity Relationship in Skeletal Muscles: The Linear, the Hyperbolic, and the Double-Hyperbolic

The shape of the force-velocity (F-V) relationship has important implications for different aspects of muscle physiology, such as muscle efficiency and fatigue, the understanding of the pathophysiology of several myopathies or the mechanisms of muscle contraction per se, and may be of relevance for other fields, such as the development of robotics and prosthetic applications featuring natural muscle-like properties. However, different opinions regarding the shape of the F-V relationship and the underlying mechanisms exist in the literature. In this review, we summarize relevant evidence on the shape of the F-V relationship obtained over the last century. Studies performed at multiple scales ranging from the sarcomere to the organism level have described the concentric F-V relationship as linear, hyperbolic or double-hyperbolic. While the F-V relationship has most frequently been described as a rectangular hyperbola, a large number of studies have found deviations from the hyperbolic function at both ends of the F-V relation. Indeed, current evidence suggests that the F-V relation in skeletal muscles follows a double-hyperbolic pattern, with a breakpoint located at very high forces/low velocities, which may be a direct consequence of the kinetic properties of myofilament cross-bridge formation. Deviations at low forces/high velocities, by contrast, may be related to a recently discovered, calcium-independent regulatory mechanism of muscle contraction, which may also explain the low metabolic cost of very fast muscle shortening contractions. Controversial results have also been reported regarding the eccentric F-V relationship, with studies in prepared muscle specimens suggesting that maximum eccentric force is substantially greater than isometric force, whereas in vivo studies in humans show only a modest increase, no change, or even a decrease in force in lengthening contractions. This review discusses possible reasons reported in the literature for these discrepant findings, including the testing procedures (familiarization, pre-load condition, and temperature) and a potential neural inhibition at higher lengthening velocities. Finally, some unresolved questions and recommendations for F-V testing in humans are reported at the end of this document.

Morphological and dynamical properties of semiflexible filaments driven by molecular motors

We consider an explicit model of a semiflexible filament moving in two dimensions on a gliding assay of motor proteins, which attach to and detach from filament segments stochastically, with a detachment rate that depends on the local load experienced. Attached motor proteins move along the filament to one of its ends with a velocity that varies nonlinearly with the motor protein extension. The resultant force on the filament drives it out of equilibrium. The distance from equilibrium is reflected in the end-to-end distribution, modified bending stiffness, and a transition to spiral morphology of the polymer. The local stress dependence of activity results in correlated fluctuations in the speed and direction of the center of mass leading to a series of ballistic-diffusive crossovers in its dynamics.

Multiplexed single-molecule force spectroscopy using a centrifuge

We present a miniature centrifuge force microscope (CFM) that repurposes a benchtop centrifuge for high-throughput single-molecule experiments with high-resolution particle tracking, a large force range, temperature control and simple push-button operation. Incorporating DNA nanoswitches to enable repeated interrogation by force of single molecular pairs, we demonstrate increased throughput, reliability and the ability to characterize population heterogeneity. We perform spatiotemporally multiplexed experiments to collect 1,863 bond rupture statistics from 538 traceable molecular pairs in a single experiment, and show that 2 populations of DNA zippers can be distinguished using per-molecule statistics to reduce noise.

Single molecule force spectroscopy (SMFS) has limitations in throughput and the ability to repeatedly interrogate single bonds. Here the authors repurpose a benchtop centrifuge and use DNA nanoswitches to enable high throughput SMFS capable of repeatedly measuring forces of single molecular pairs.

Forced desorption of semiflexible polymers, adsorbed and driven by molecular motors

We formulate and characterize a model to describe the dynamics of semiflexible polymers in the presence of activity due to motor proteins attached irreversibly to a substrate, and a transverse pulling force acting on one end of the filament. The stochastic binding-unbinding of the motor proteins and their ability to move along the polymer generate active forces. As the pulling force reaches a threshold value, the polymer eventually desorbs from the substrate. Performing underdamped Langevin dynamics simulation of the polymer, and with stochastic motor activity, we obtain desorption phase diagrams. The correlation time for fluctuations in the desorbed fraction increases as one approaches complete desorption, captured quantitatively by a power law spectral density. We present theoretical analysis of the phase diagram using mean field approximations in the weakly bending limit of the polymer and performing linear stability analysis. This predicts an increase in the desorption force with the polymer bending rigidity, active velocity and processivity of the motor proteins to capture the main features of the simulation results.

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

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

Geometrical conditions indispensable for muscle contraction

Computer simulation has uncovered the geometrical conditions under which the vertebrate striated muscle sarcomere can contract. First, all thick filaments should have identical structure, namely: three myosin cross-bridges, building a crown, should be aligned at angles of 0°, 120°, 180°, and the successive crowns and the two filament halves should be turned around 120°. Second, all thick filaments should act simultaneously. Third, coordination in action of the myosin cross-bridges should exist, namely: the three cross-bridges of a crown should act simultaneously and the cross-bridge crowns axially 43 and 14.333 nm apart should act, respectively, simultaneously and with a phase shift. Fifth, six thin filaments surrounding the thick filament should be turned around 180° to each other in each sarcomere half. Sixth, thin filaments should be oppositely oriented in relation to the sarcomere middle. Finally, the structure of each of the thin filaments should change in consequence of strong interaction with myosin heads, namely: the axial distance and the angular alignment between neighboring actin monomers should be, respectively, 2.867 nm and 168° instead of 2.75 nm and 166.15°. These conditions ensure the stereo-specific interaction between actin and myosin and good agreement with the data gathered by electron microscopy and X-ray diffraction methods. The results suggest that the force is generated not only by the myosin cross-bridges but also by the thin filaments; the former acts by cyclical unwrapping and wrapping the thick filament backbone, and the latter byelongation.

The molecular basis of frictional loads in the in vitro motility assay with applications to the study of the loaded mechanochemistry of molecular motors

Molecular motors convert chemical energy into mechanical movement, generating forces necessary to accomplish an array of cellular functions. Since molecular motors generate force, they typically work under loaded conditions where the motor mechanochemistry is altered by the presence of a load. Several biophysical techniques have been developed to study the loaded behavior and force generating capabilities of molecular motors yet most of these techniques require specialized equipment. The frictional loading assay is a modification to the in vitro motility assay that can be performed on a standard epifluorescence microscope, permitting the high-throughput measurement of the loaded mechanochemistry of molecular motors. Here, we describe a model for the molecular basis of the frictional loading assay by modeling the load as a series of either elastic or viscoelastic elements. The model, which calculates the frictional loads imposed by different binding proteins, permits the measurement of isotonic kinetics, force-velocity relationships, and power curves in the motility assay. We show computationally and experimentally that the frictional load imposed by alpha-actinin, the most widely employed actin binding protein in frictional loading experiments, behaves as a viscoelastic rather than purely elastic load. As a test of the model, we examined the frictional loading behavior of rabbit skeletal muscle myosin under normal and fatigue-like conditions using alpha-actinin as a load. We found that, consistent with fiber studies, fatigue-like conditions cause reductions in myosin isometric force, unloaded sliding velocity, maximal power output, and shift the load at which peak power output occurs.

Ratchetlike properties of in vitro microtubule translocation by a Chlamydomonas inner-arm dynein species c in the presence of flow

To investigate the force generation properties of Chlamydomonas axonemal inner-arm dyneins in response to external force, we analyzed microtubule gliding on dynein-coated surfaces under shear flow. When inner-arm dynein c was used, microtubule translocation in the downstream direction accelerated with increasing flow speed in a manner that depended on the dynein density and ATP concentration. In contrast, the microtubule translocation velocity in the upstream direction was unaffected by the flow speed. The number of microtubules on the glass surface was almost constant with and without flow, suggesting that gliding acceleration was not simply caused by weakened dynein-microtubule binding. With other inner-arm dynein species, the microtubule gliding velocity was unaffected by the flow regardless of the flow direction or nucleotide concentration. The flow-generated force acting on a single dynein was estimated to be as small as approximately 0.03 pN/dynein. These results indicate that dynein c possesses a ratchetlike property that allows acceleration only in one direction by a very small external force. This property should be important for slow- and fast-moving dyneins to function simultaneously within the axoneme.

The receptor deformation model of TCR triggering

Through T cell receptors (TCRs), T cells can detect and respond to very small numbers of foreign peptides among a huge number of self-peptides presented by major histocompatibility complexes (pMHCs) on the surface of antigen-presenting cells (APCs). How T cells achieve such remarkable sensitivity and specificity through pMHC-TCR binding is an intensively pursued issue in immunology today; the key question is how pMHC-TCR binding initiates, or triggers, a signal from TCRs. Multiple competing models have been proposed, none of which fully explains the sensitivity and specificity of TCR triggering. What has been omitted from existing theories is that the pMHC-TCR interaction at the T cell/APC interface must be under constant mechanical stress, due to the dynamic nature of cell-cell interaction. Taking this condition into consideration, we propose the receptor deformation model of TCR triggering. In this model, TCR signaling is initiated by conformational changes of the TCR/CD3 complex, induced by a pulling force originating from the cytoskeleton and transmitted through pMHC-TCR binding interactions with enough strength to resist rupture. By introducing mechanical force into a model of T cell signal initiation, the receptor deformation model provides potential mechanistic solutions to the sensitivity and specificity of TCR triggering.

Mechanical properties of axons

The mechanical response of PC12 neurites under tension is investigated using a microneedle technique. Elastic response, viscoelastic relaxation, and active contraction are observed. The mechanical model proposed by Dennerll et al. [J. Cell Biol. 109, 3073 (1989).10.1083/jcb.109.6.3073], which involves three mechanical devices--a stiff spring kappa coupled with a Voigt element that includes a less stiff spring k and a dashpot gamma--has been improved by adding a new element to describe the main features of the contraction of axons. This element, which represents the action of molecular motors, acts in parallel with viscous forces defining a global tension response of axons T against elongation rates delta(k). Under certain conditions, axons show a transition from a viscoelastic elongation to active contraction, suggesting the presence of a negative elongation rate sensitivity in the curve T vs delta(k).

The biphasic force-velocity relationship in whole rat skeletal muscle in situ

Edman has reported that the force-velocity relationship (FVR) departs from Hill's classic hyperbola near 0.80 of measured isometric force (J Physiol 404: 301-321, 1988). The purpose of this study was to investigate the biphasic nature of the FVR in the rested state and after some recovery from fatigue in the rat medial gastrocnemius muscle in situ. Force-velocity characteristics were determined before and during recovery from fatigue induced by intermittent stimulation at 170 Hz for 100 ms each second for 6 min. Force-velocity data were obtained for isotonic contractions with 100 ms of 200-Hz stimulation, including several measurements with loads above 0.80 of measured isometric force. The force-velocity data obtained in this study were fit well by a double-hyperbolic equation. A departure from Hill's classic hyperbola was found at 0.88+/-0.01 of measured isometric force, which is higher than the approximately 0.80 reported by Edman et al. for isolated frog fibers. After 45 min of recovery, maximum shortening velocity was 86+/-2% of prefatigue, but neither curvature nor predicted isometric force was significantly different from prefatigue. The location of the departure from Hill's classic hyperbola was not different after this recovery from the fatiguing contractions. Including an isometric point in the data set will not yield the same values for maximal velocity and the degree of curvature as would be obtained using the double hyperbola approach. Data up to 0.88 of measured isometric force can be used to fit data to the Hill equation.

A quantitative analysis of cardiac myocyte relaxation: a simulation study

The determinants of relaxation in cardiac muscle are poorly understood, yet compromised relaxation accompanies various pathologies and impaired pump function. In this study, we develop a model of active contraction to elucidate the relative importance of the [Ca2+]i transient magnitude, the unbinding of Ca2+ from troponin C (TnC), and the length-dependence of tension and Ca2+ sensitivity on relaxation. Using the framework proposed by one of our researchers, we extensively reviewed experimental literature, to quantitatively characterize the binding of Ca2+ to TnC, the kinetics of tropomyosin, the availability of binding sites, and the kinetics of crossbridge binding after perturbations in sarcomere length. Model parameters were determined from multiple experimental results and modalities (skinned and intact preparations) and model results were validated against data from length step, caged Ca2+, isometric twitches, and the half-time to relaxation with increasing sarcomere length experiments. A factorial analysis found that the [Ca2+]i transient and the unbinding of Ca2+ from TnC were the primary determinants of relaxation, with a fivefold greater effect than that of length-dependent maximum tension and twice the effect of tension-dependent binding of Ca2+ to TnC and length-dependent Ca2+ sensitivity. The affects of the [Ca2+]i transient and the unbinding rate of Ca2+ from TnC were tightly coupled with the effect of increasing either factor, depending on the reference [Ca2+]i transient and unbinding rate.

Slip sliding away: load-dependence of velocity generated by skeletal muscle myosin molecules in the laser trap

Skeletal muscle's ability to shorten and lengthen against a load is a fundamental property, presumably reflecting the inherent load-dependence of the myosin molecular motor. Here we report the velocity of a single actin filament translocated by a mini-ensemble of skeletal myosin approximately 8 heads under constant loads up to 15 pN in a laser trap assay. Actin filament velocity decreased with increasing load hyberbolically, with unloaded velocity and stall force differing by a factor of 2 with [ATP] (30 vs. 100 muM). Analysis of actin filament movement revealed that forward motion was punctuated with rapid backward 60-nm slips, with the slip frequency increasing with resistive load. At stall force, myosin-generated forward movement was balanced by backward slips, whereas at loads greater than stall, myosin could no longer sustain forward motion, resulting in negative velocities as in eccentric contractions of whole muscle. Thus, the force-velocity relationship of muscle reflects both the inherent load-dependence of the actomyosin interaction and the balance between forward and reverse motion observed at the molecular level.

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

We have previously measured the process of displacement generation by a single head of muscle myosin (S1) using scanning probe nanometry. Given that the myosin head was rigidly attached to a fairly large scanning probe, it was assumed to stably interact with an underlying actin filament without diffusing away as would be the case in muscle. The myosin head has been shown to step back and forth stochastically along an actin filament with actin monomer repeats of 5.5 nm and to produce a net movement in the forward direction. The myosin head underwent 5 forward steps to produce a maximum displacement of 30 nm per ATP at low load (<1 pN). Here, we measured the steps over a wide range of forces up to 4 pN. The size of the steps (∼5.5 nm) did not change as the load increased whereas the number of steps per displacement and the stepping rate both decreased. The rate of the 5.5-nm steps at various force levels produced a force-velocity curve of individual actomyosin motors. The force-velocity curve from the individual myosin heads was comparable to that reported in muscle, suggesting that the fundamental mechanical properties in muscle are basically due to the intrinsic stochastic nature of individual actomyosin motors. In order to explain multiple stochastic steps, we propose a model arguing that the thermally-driven step of a myosin head is biased in the forward direction by a potential slope along the actin helical pitch resulting from steric compatibility between the binding sites of actin and a myosin head. Furthermore, computer simulations show that multiple cooperating heads undergoing stochastic steps generate a long (>60 nm) sliding distance per ATP between actin and myosin filaments, i.e., the movement is loosely coupled to the ATPase cycle as observed in muscle.

Force-velocity relationships in actin-myosin interactions causing cytoplasmic streaming in algal cells

Cytoplasmic streaming in giant internodal cells of green algae is caused by ATP-dependent sliding between actin cables fixed on chloroplast rows and cytoplasmic myosin molecules attached to cytoplasmic organelles. Its velocity (>/=50 micro m s(-1)) is many times larger than the maximum velocity of actin-myosin sliding in muscle. We studied kinetic properties of actin-myosin sliding causing cytoplasmic streaming in internodal cell preparations of Chara corallina, into which polystyrene beads, coated with cytoplasmic myosin molecules, were introduced. Constant centrifugal forces directed opposite to the bead movement were applied as external loads. The steady-state force-velocity (P-V) curves obtained were nearly straight, irrespective of the maximum isometric force generated by cytoplasmic myosin molecules, indicating a large duty ratio of cytoplasmic myosin head. The large velocity of cytoplasmic streaming can be accounted for, at least qualitatively, by assuming a mechanically coupled interaction between cytoplasmic myosin heads as well as a large distance of unitary actin-myosin sliding.

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.

Myosin cross-bridge mechanics: geometrical determinants for continuous sliding

Advances in experimental techniques have provided new details on the molecular mechanisms governing the cross-bridge kinetics. Nevertheless, the issue of micromechanics of sliding is still debated. In particular, uncertainty exists regarding the myosin filament arrangement and structure and the mechanics of the myosin head with respect to the working stroke distance (WS) and the duty ratio (r), i.e. the fraction of the ATPase cycle time the myosin head is attached to the actin filament. The object of the present work is to provide a theoretical framework to correlate different features of cross-bridge mechanics; the main hypothesis is that the attachment between the actin filament and the surrounding myosin filaments has to be continuous through the sliding (continuous sliding hypothesis) in order to maximise the effect of the myosin head performance. A 3-D model of the sliding mechanism based on a geometrical approach is presented, which is able to identify the architectures that accomplish the continuous sliding under unloaded conditions. About 200 different configurations have been simulated by changing the myosin head binding range, i.e. its ability to reach an actin binding site from its rest position, WS, the myosin head orientation and the actin filament orientation. Only few configurations were consistent with the continuous sliding hypothesis. Depending on the parameter set adopted, the percentage of attached heads (%AH) calculated ranges between 4% and 28%, r between 0.08 and 0.02s(-1), and the sliding velocity between 0.7 and 10.6 microm/s. In all the cases, results were not affected by the WS value.

Analysis of single-molecule mechanical recordings: application to acto-myosin interactions

Several laboratories have now developed methods to make single-molecule mechanical recordings from interacting pairs of biological molecules. The mechanical work done (product of force and distance) by a single biomolecular interaction is usually of the same order as thermal energy. Recordings made from non-processive, intermittently interacting, molecular motors such as acto-myosin therefore contain a large background of thermal noise. We have applied Page's test to analyse mechanical interactions between muscle myosin II's and F-actin recorded using an optical tweezers based single-molecule mechanical transducer. We compare Page's test with other variance-based methods and find it to be a robust method for analysing both simulated and real data sets. We discuss some of the problems associated with automatic detection of transient mechanical events in noisy data signals, and show that if the start and end points of individual events are known accurately then the events may be synchronised and combined to give more detailed information about different mechanical states.

Evidence for the essential role of myosin subfragment-2 in the ATP-dependent actin-myosin sliding in muscle contraction

The role of myosin subfragment-2 (myosin S-2) in muscle contraction was studied by using an in vitro motility assay system in which the ATP-dependent sliding between myosin-coated polystyrene beads and actin filament arrays (actin cables) of giant algal cells were recorded under constant external loads provided with a centrifuge microscope. With antibody to myosin S-2 below 0.3 mg/ml, the maximum "isometric" force generated by myosin molecules on the bead decreased markedly, but the unloaded bead-sliding velocity along actin cables did not change appreciably, indicating a decrease in the number of myosin molecules interacting with actin cables. The antibody at 0.3-1.5 mg/ml decreased not only the maximum isometric force, but also the unloaded bead-sliding velocity in a dose-dependent manner. With the antibody at 1.5-3 mg/ml, the beads eventually stopped moving to remain attached to actin cables. These beads could be readily detached from actin cables with very small centrifugal forces, indicating very weak actin-myosin linkages. The antibody had no effect on rigor actin-myosin linkages formed before the antibody application. These results are consistent with the view that myosin S-2 plays an essential role in muscle contraction.

Force-velocity relation of sliding of skeletal muscle myosin, arranged on a paramyosin filament, on actin cables

To investigate in vitro ATP-dependent sliding of regularly arranged myosin molecules on actin filaments, we prepared thick hybrid filaments in which myosin molecules isolated from rabbit skeletal muscle were arranged around the paramyosin core (length, 10-20 micron; diameter, </=0.2 micron) obtained from a molluscan smooth muscle. A single to a few thick hybrid filaments were attached to a polystyrene bead (diameter, 4.5 micron; specific gravity, 1.5) and made to slide on actin filament arrays (actin cables) in the internodal cell of an alga, mounted on the rotor of a centrifuge microscope. The bead was subjected to centrifugal forces serving as external loads to the ATP-dependent actin-myosin sliding. The maximum unloaded sliding velocity of the thick filament attached-bead (mean, 3.4 micron/s; 20-23 degrees C) was significantly higher than that of the bead coated with randomly oriented myosin molecules reported previously. The steady-state force-velocity (P-V) relations obtained were qualitatively similar to those in intact skeletal muscle fibers. These results indicate that this in vitro motility assay system retains the basic characteristics of contracting skeletal muscle fibers, and that it may be effectively used to study mechanisms underlying the steady-state P-V characteristics of ATP-dependent actin-myosin sliding using various recombinant myosins produced in nonmuscle cells.

The behavior of chick gastrula mesodermal cells under the unidirectional tractive force parallel to the substrata

Advancement of leading lamellae of a migratory cell inevitably causes a strain inside the cell body. We investigated the effect of the tension arisen inside a mesodermal cell on its behavior by pulling the cell body unidirectionally along the substratum. Chick gastrula mesodermal cells, known as highly migratory, were dissociated into single cells in sodium citrate buffer, conjugated with paramagnetic beads activated by tosyl-residue (4.5 microns in diameter) and seeded onto coverglasses coated with fibronectin. After the cells spread on the substratum and protruded cellular processes in all directions, they were exposed to a non-uniform magnetic field by a magnet. Thus the cells bearing the beads were pulled with a force in the order of 10(−10) N. The behavior of such cells was recorded with a time-lapse video taperecorder and assessed quantitatively. Shortly after the magnetic force was applied, the beads stuck to the cells were aligned in tandem along the line of magnetic force at the site for the magnet. Subsequently, they frequently came to extend their leading lamella precisely counter to the traction on the line of the beads. Observation with scanning electron microscope revealed that a large part of the beads attached to the cells were wrapped in the cell membrane. In this condition, the cells were stretched locally between the attachment site of the beads and adhesion plaques beneath the leading edge, which was formed in a direction away from the traction. It was proved statistically that such cells tended to locomote away from the magnet at the 0.1% significance level with Hotelling's T2-test. In contrast, the mesodermal cells free of the artificial traction in three kinds of control experiments did not show such a preference in the direction of locomotion. These results proved that migratory cells tended to move in the direction away from the tractive force parallel to the substratum, suggesting that advancement of a leading lamella is accelerated when it is stretched along the direction of projection by a mechanical force of sufficient strength. Implication of this finding to the mechanism of cell locomotion will be discussed.

Centrifuge microscope as a tool in the study of cell motility

The centrifuge microscope (CM) is composed of a centrifuge and a microscope optical system designed to observe minute objects, especially living cells, during the application of centrifugal acceleration. Structures and characteristics of various types of CM designed and constructed up to the present and studies done with the CM on cell biology, especially cell motility, are reviewed. These studies include observations of the behavior of cells and cell components in a centrifugal field, determination of the mechanical properties of the cell surface and cytoplasm, microsurgical operations on cells with centrifugal force, and determination of the magnitude and the site of generation of motive force for cell motility.

The force exerted by a single kinesin molecule against a viscous load

Kinesin is a motor protein that uses the energy derived from the hydrolysis of ATP to power the transport of organelles along microtubules. To probe the mechanism of this chemical-to-mechanical energy transduction reaction, the movement of microtubules across glass surfaces coated with kinesin was perturbed by raising the viscosity of the buffer solution. When the viscosity of the solution used in the low density motility assay was increased approximately 100-fold through addition of polysaccharides and polypeptides, the longer microtubules, which experienced a larger drag force from the fluid, moved more slowly than the shorter ones. The speed of movement of a microtubule depended linearly on the drag force loading the motor. At the lowest kinesin density, where dilution experiments indicated that the movement was caused by a single kinesin molecule, extrapolation of the linear relationship yielded a maximum time-averaged drag force of 4.2 +/- 0.5 pN per motor (mean +/- experimental SE). The magnitude of the force argues against one type of "ratchet" model in which the motor is hypothesized to rectify the diffusion of the microtubule; at high viscosity, diffusion is too slow to account for the observed speeds. On the other hand, our data are consistent with models in which force is a consequence of strain developed in an elastic element within the motor; these models include a different "ratchet" model (of the type proposed by A. F. Huxley in 1957) as well as "power-stroke" models.

Smooth, cardiac and skeletal muscle myosin force and motion generation assessed by cross-bridge mechanical interactions in vitro

Differences in the mechanical properties of mammalian smooth, skeletal, and cardiac muscle have led to the proposal that the myosin isozymes expressed by these tissues may differ in their molecular mechanics. To test this hypothesis, mixtures of fast skeletal, V1 cardiac, V3 cardiac and smooth muscle (phosphorylated and unphosphorylated) myosin were studied in an in vitro motility assay in which fluorescently-labelled actin filaments are observed moving over a myosin coated surface. Pure populations of each myosin produced actin filament velocities proportional to their actin-activated ATPase rates. Mixtures of two myosin species produced actin filament velocities between those of the faster and slower myosin alone. However, the shapes of the myosin mixture curves depended upon the types of myosins present. Analysis of myosin mixtures data suggest that: (1) the two myosins in the mixture interact mechanically and (2) the same force-velocity relationship describes a myosin's ability to operate over both positive and negative forces. These data also allow us to rank order the myosins by their average force per cross-bridge and ability to resist motion (phosphorylated smooth > skeletal = V3 cardiac > V1 cardiac). The results of our study may reflect the mechanical consequence of multiple myosin isozyme expression in a single muscle cell.

Relation between magnetically-applied force and velocity in beads coated with rabbit myosin, sliding on actin cables in Nitellopsis cells

We have succeeded in controlling the sliding movement of myosin-coated magnetizable beads on actin cables in Nitellopsis cells by the inhomogeneous magnetic field adjacent to a small, strong permanent magnet. The relation between magnetic force acting on the bead and the bead velocity was, in many respects, similar to that obtained from the same system by the use of centrifugal force (Oiwa et al., 1990). In particular, force favouring the motion (negative load) had little effect on the velocity until it was sufficient to pull the bead off the actin, whereas a relatively small positive load caused a reduction in velocity to a plateau value. Although the present method does not allow a good control of force direction, it demonstrates the promise of magnetic force in studying in vitro motility.

Force-velocity relationships in kinesin-driven motility

Kinesin is a microtubule-based motor protein that uses energy released from Mg-ATP hydrolysis to generate force for the movement of intracellular membranes towards the fast-growing (plus) ends of microtubule tracks in cells. Kinesin-driven microtubule movement can be visualized and quantified using light microscope motility assays but our understanding of how kinesin generates force and motion is incomplete. Here we report the use of a centrifuge microscope to obtain force-velocity curves for kinesin-driven motility and to estimate that the maximal isometric force generated per kinesin is 0.12 +/- 0.03 pN per molecule.

Kinetic properties of the ATP-dependent actin-myosin sliding as revealed by the force-movement assay system with a centrifuge microscope

To study the kinetic properties of the ATP-dependent actin-myosin sliding responsible for muscle contraction, we developed an in vitro force-movement assay system, in which centrifugal forces were applied to myosin-coated polystyrene beads sliding along actin cables of giant algal cells in the presence of ATP. Under constant centrifugal forces directed opposite to the bead movement ("positive" loads), the beads moved with constant velocities. The steady-state force-velocity (P-V) curve thus obtained was double-hyperbolic in shape, being analogous to the P-V curve of single muscle fibers. Under constant centrifugal forces in the direction of the bead movement ("negative" loads), on the other hand, the beads also moved with constant velocities. Unexpectedly, the velocity of bead movement did not increase with increasing negative loads, but decreased markedly (by 20-60%). We also studied the effect of centrifugal forces at right angles with actin cables on the bead movement.

Further studies of the self-induced translation model of myosin head motion along the actin filament

We have extended and refined the model of myosin head motion along the actin filament which we proposed in 1988 (J. Muscle Res. Cell Motility 9, 248-260), and obtained the following results. (1) We assumed that the height of the induced potential depends upon tension with a maximum around the isometric tension, and got a force-velocity relation similar to the observation by Oiwa et al. (1990) that the velocity of the myosin-coated beads along the actin cables decreases with increasing centrifugal force applied in the direction of bead movement and then the velocity tends to increase when the force increases in the same direction beyond a certain value. (2) We introduced a correction factor in the relation between the measured tension and the microscopic tension produced by myosin head, and got a feature in force-velocity relation similar to the observation by Edman (1988) that the velocity drops sharply as the tension approaches to about 80% of the isometric tension. (3) We assumed that binding of an ATP-activated myosin head to an actin filament causes a local structural change extended roughly 20nm long along the filament, which provides a potential well spread over about 16nm for the myosin head, with three shallow potential wells in it. We studied kinetics of the myosin head in the potential well of about 16nm in order to explain the early tension recovery after the sudden change of muscle length observed by Ford, Huxley and Simmons (1977), with results in good agreement with their experimental data.

Mechanism underlying double-hyperbolic force-velocity relation in vertebrate skeletal muscle

The force-velocity relation of frog striated muscle exhibits two distinct curvatures located on either side of a breakpoint that occurs near 80% of maximum isometric force (Po) where the shortening velocity is approximately 1/10 of Vmax. The present experiments have been performed to further elucidate the high-force deviation of the force-velocity curve in frog single muscle fibres. The biphasic shape of the force-velocity curve appears at the same relative values of Po and Vmax also after depressing the isometric force to 80% of the control value by dantrolene, a substance known to reduce the release of activator calcium from the sarcoplasmic reticulum. This finding suggests that the breakpoint of the force-velocity curve is not related to the force level per se but rather to the speed of shortening of the contractile system. Thus as the speed of shortening goes below 1/10 of Vmax, the performance of the myofilament system is changed such that less force and less motion are produced than expected from the main part of the force-velocity curve. In a series of experiments active force and fibre stiffness were simultaneously recorded while the fibre shortened at various speeds during tetanus. Stiffness was measured as the change in force that occurred in response to a 4 kHz sinusoidal length oscillation of the fibre. A plotting of stiffness against force recorded under these conditions provides a biphasic relationship with a distinct transition between the two phases near 80% of Po, i.e. at the same relative force at which the breakpoint occurs in the force-velocity curve. Above 0.8 Po stiffness increases more steeply with force than below this point. This means that while more crossbridges than expected attach to the thin filaments when the load is raised above 0.8 Po, the force output and the speed of shortening become lower than predicted from measurements at low and intermediate loads. The results suggest that the kinetics of crossbridge function is changed as the speed of filament sliding is reduced below a critical level, 1/10 of Vmax. Beyond this point a greater portion of myosin crossbridges would seem to accumulate in a state where less force is being produced. Data are also presented to further elucidate the force-velocity relation at negative loads. In these experiments the passive tension at long sarcomere lengths has been utilized to produce a longitudinal compressive force on the sarcomeres during unloaded shortening (force-clamp recording).(ABSTRACT TRUNCATED AT 400 WORDS)

Dependence of the work done by ATP-induced actin-myosin sliding on the initial baseline force: its implications for kinetic properties of myosin heads in muscle contraction

The properties of the ATP-dependent actin-myosin sliding responsible for muscle contraction was studied using an in vitro force-movement assay system, in which a myosin-coated glass microneedle was made to slide on actin filament arrays (actin cables) in the giant algal cell with iontophoretic application of ATP. With a constant amount of ATP application, the amount of work done by the actin-myosin sliding increased with increasing baseline force from zero to 0.4-0.6 Po, and then decreased with further increasing baseline force, thus giving a bell-shaped work versus baseline force relation. The result that the maximum actin-myosin sliding velocity did not change appreciably with increasing baseline force up to 0.4-0.6 Po implies, together with the limited number of myosin heads involved, that (1) the rate of power output of actin-myosin sliding is determined primarily by the amount of external load rather than the velocity of actin-myosin sliding, and (2) the bell shaped work versus baseline force relation (and also the hyperbolic force-velocity relation) results from the kinetic properties of individual myosin head rather than the change in the number of myosin heads involved.

Measurement of work done by ATP-induced sliding between rabbit muscle myosin and algal cell actin cables in vitro

1. The basic properties of the ATP-dependent actin-myosin interaction responsible for muscle contraction were studied using an in vitro force-movement assay system, in which a glass microneedle coated with rabbit skeletal muscle myosin was made to slide on the actin filament arrays (actin cables) in the internodal cell of an alga Nitellopsis obtusa with ionophoretic application of ATP. 2. In response to an ATP current pulse (intensity, 5-85 nA; duration, 0.5-10 s), the myosin-coated needle moved for a distance and eventually stopped, indicating reformation of rigor actin-myosin linkages to prevent elastic recoil of the bent needle. A subsequent ATP current pulse again produced the needle movement starting from the baseline force attained by the preceding needle movement. 3. With a constant amount of ATP application, the amount of work done by the ATP-induced actin-myosin sliding first increased with increasing baseline force from zero to 0.4-0.6P0, and then decreased with further increasing baseline force, thus giving a bell-shaped work versus baseline force relation. 4. With increasing amount of ATP application, the amount of work done by the actin-myosin sliding increased more steeply as the baseline force was increased from zero to 0.4-0.6P0. 5. These results are discussed in connection with the basic properties of the actin-myosin sliding in muscle contraction.