Fluctuation in the microtubule sliding movement driven by kinesin in vitro.

We studied the fluctuation in the translational sliding movement of microtubules driven by kinesin in a motility assay in vitro. By calculating the mean-square displacement deviation from the average as a function of time, we obtained motional diffusion coefficients for microtubules and analyzed the dependence of the coefficients on microtubule length. Our analyses suggest that 1) the motional diffusion coefficient consists of the sum of two terms, one that is proportional to the inverse of the microtubule length (as the longitudinal diffusion coefficient of a filament in Brownian movement is) and another that is independent of the length, and 2) the length-dependent term decreases with increasing kinesin concentration. This latter term almost vanishes within the length range we studied at high kinesin concentrations. From the length-dependence relationship, we evaluated the friction coefficient for sliding microtubules. This value is much larger than the solvent friction and thus consistent with protein friction. The length independence of the motional diffusion coefficient observed at sufficiently high kinesin concentrations indicates the presence of correlation in the sliding movement fluctuation. This places significant constraint on the possible mechanisms of the sliding movement generation by kinesin motors in vitro.     

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

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

Enhancing the staggered fluctuations of an actin filament sliding on Chara myosin

We examined both longitudinal and transversal fluctuations of displacements of an actin filament sliding upon Chara myosin molecules. Although the magnitude of transversal fluctuations remained rather independent of ATP concentration, the longitudinal ones were found to increase their magnitude as the concentration increased. In addition, the longitudinal fluctuations gradually increased as the sliding velocity of the filament increased.     

Mitotic motors and chromosome segregation: the mechanism of anaphase B

Anaphase B spindle elongation plays an important role in chromosome segregation. In the present paper, we discuss our model for anaphase B in Drosophila syncytial embryos, in which spindle elongation depends on an ip (interpolar) MT (microtubule) sliding filament mechanism generated by homotetrameric kinesin-5 motors acting in concert with poleward ipMT flux, which acts as an 'on/off' switch. Specifically, the pre-anaphase B spindle is maintained at a steady-state length by the balance between ipMT sliding and ipMT depolymerization at spindle poles, producing poleward flux. Cyclin B degradation at anaphase B onset triggers: (i) an MT catastrophe gradient causing ipMT plus ends to invade the overlap zone where ipMT sliding forces are generated; and (ii) the inhibition of ipMT minus-end depolymerization so flux is turned 'off', tipping the balance of forces to allow outward ipMT sliding to push apart the spindle poles. We briefly comment on the relationship of this model to anaphase B in other systems.     

Myosin-IXb is a single-headed and processive motor.

Class IX myosins are unique among the many classes of known actin-based motors in that the tail region of these myosins contains a GTPase-activating protein domain for the small GTP-binding protein, Rho. Previous studies on human myosin-IXb indicate that this myosin is mechanochemically active and exhibits actin-binding properties similar to the processive motor, myosin-Va. Motility analysis of antibody-tethered myosin-IXb performed using the sliding actin filament assay indicates that this myosin does exhibit properties characteristic of a processive motor. Like myosin-Va, the velocity of myosin-IXb remains constant (38.2 +/- 1.2 nm/s) even at single motor/filament densities. At low motor densities, filaments can be seen passing through and pivoting about single points on the motility surface. Analysis of filament landing rates as a function of motor density also indicates that a single motor is sufficient for filament movement. However, in contrast to myosin-Va, which uses coordinated motion of its two heads to move processively along the filament, hydrodynamic and chemical cross-linking studies indicate that under the conditions tested, myosin-IXb is a single-headed motor consisting of a single heavy chain and associated light chains.     

Filament-Filament Switching Can Be Regulated by Separation Between Filaments Together with Cargo Motor Number

How intracellular transport controls the probability that cargos switch at intersections between filaments is not well understood. In one hypothesis some motors on the cargo attach to one filament while others attach to the intersecting filament, and the ensuing tug-of-war determines which filament is chosen. We investigate this hypothesis using 3D computer simulations, and discover that switching at intersections increases with the number of motors on the cargo, but is not strongly dependent on motor number when the filaments touch. Thus, simply controlling the number of active motors on the cargo cannot account for in vivo observations that found reduced switching with increasing motor number, suggesting additional mechanisms of regulation. We use simulations to show that one possible way to regulate switching is by simultaneously adjusting the separation between planes containing the crossing filaments and the total number of active motors on the cargo. Heretofore, the effect of filament-filament separation on switching has been unexplored. We find that the switching probability decreases with increasing filament separation. This effect is particularly strong for cargos with only a modest number of motors. As the filament separation increases past the maximum head-to-head distance of the motor, individual motors walking along a filament will be unable to reach the intersecting filament. Thus, any switching requires that other motors on the cargo attach to the intersecting filament and haul the cargo along it, while motor(s) engaged on the original filament detach. Further, if the filament separation is large enough, the cargo can have difficulty proceeding along the initial filament because the engaged motors can walk underneath the intersecting filament, but the cargo itself cannot fit between the filaments. Thus, the cargo either detaches entirely from the original filament, or must dip to the side of the initial filament and then pass below the crossing filament.     

The microtubule cross-linker Feo controls the midzone stability,motor composition,and elongation of the anaphase B spindle in Drosophila embryos

Chromosome segregation during anaphase depends on chromosome-to-pole motility and pole-to-pole separation. We propose that in Drosophila embryos, the latter process (anaphase B) depends on a persistent kinesin-5–generated interpolar (ip) microtubule (MT) sliding filament mechanism that “engages” to push apart the spindle poles when poleward flux is turned off. Here we investigated the contribution of the midzonal, antiparallel MT-cross-linking nonmotor MAP, Feo, to this “slide-and-flux-or-elongate” mechanism. Whereas Feo homologues in other systems enhance the midzone localization of the MT-MT cross-linking motors kinesin-4, -5 and -6, the midzone localization of these motors is respectively enhanced, reduced, and unaffected by Feo. Strikingly, kinesin-5 localizes all along ipMTs of the anaphase B spindle in the presence of Feo, including at the midzone, but the antibody-induced dissociation of Feo increases kinesin-5 association with the midzone, which becomes abnormally narrow, leading to impaired anaphase B and incomplete chromosome segregation. Thus, although Feo and kinesin-5 both preferentially cross-link MTs into antiparallel polarity patterns, kinesin-5 cannot substitute for loss of Feo function. We propose that Feo controls the organization, stability, and motor composition of antiparallel ipMTs at the midzone, thereby facilitating the kinesin-5–driven sliding filament mechanism underlying proper anaphase B spindle elongation and chromosome segregation.     

Slowly modulating fluctuations as mesoscopic distortions occurring on an actin filament

An actin filament sliding on myosin molecules exhibits fluctuating or staggered movements as responding to changes in the ATP concentration. We previously observed that fluctuations in the sliding velocity enhanced in a manner being independent of the magnitude of the velocity. The present study focused upon a single actin filament bound to a glass surface through avidin–biotin bonding to examine those fluctuations inherent to the filament in the presence of heavy meromyosin. The auto-correlation analysis revealed that the relaxation time of fluctuations in the filamental displacement obtains its maximum value at about 100 μM of the ATP concentration in the ambient, while the magnitude of the fluctuations gradually increased with an increase of the concentration. Furthermore, the measurement of the fluorescence intensity from the markers fixed on the filament demonstrated an enhancement of the negative correlation between the measured peak intensity and the spatial spreading of its intensity over the range of 0–200 μM of the ATP concentration, as indicating both development and mitigation of local distortions occurring within the filament.     

Superresolution Imaging of Dynamic MreB Filaments in B. subtilis—A Multiple-Motor-Driven Transport?

The cytoskeletal protein MreB is an essential component of the bacterial cell-shape generation system. Using a superresolution variant of total internal reflection microscopy with structured illumination, as well as three-dimensional stacks of deconvolved epifluorescence microscopy, we found that inside living Bacillus subtilis cells, MreB forms filamentous structures of variable lengths, typically not longer than 1 μm. These filaments move along their orientation and mainly perpendicular to the long bacterial axis, revealing a maximal velocity at an intermediate length and a decreasing velocity with increasing filament length. Filaments move along straight trajectories but can reverse or alter their direction of propagation. Based on our measurements, we provide a mechanistic model that is consistent with all observations. In this model, MreB filaments mechanically couple several motors that putatively synthesize the cell wall, whereas the filaments’ traces mirror the trajectories of the motors. On the basis of our mechanistic model, we developed a mathematical model that can explain the nonlinear velocity length dependence. We deduce that the coupling of cell wall synthesis motors determines the MreB filament transport velocity, and the filament mechanically controls a concerted synthesis of parallel peptidoglycan strands to improve cell wall stability.     

Super helix formation of actin filaments in an in vitro motile system.

Muscle contraction results from relative sliding of actin and myosin filaments. However, the possibility that actin filaments twist or rotate during sliding has not yet been experimentally investigated. We found that a super helix of an actin filament is formed in an in vitro motile system. This fact suggests that an actin filament twists and rotates due to a torque component of a sliding force generated at cross-bridges.     

Assessment of the mechanical activity of cardiac isomyosins V1 and V3 by the in vitro motility assay with regulated thin filament

The dependences of thin filament sliding velocity on the calcium concentration in solution (pCa 5 to 8) for rabbit cardiac myosin isoforms V1 and V3 were determined in a set of experiments using an in vitro motility assay with a reconstructed thin filament. The constructed pCa-versus-velocity curves had a sigmoid shape. It was demonstrated that the sliding velocity of regulated thin filament at the saturating calcium concentration (pCa 5) did not differ from the actin sliding velocity for each isoform. The determined values of Hill’s cooperativity coefficient for isomyosins V1 and V3 were 1.04 and 0.75, respectively. It was demonstrated that isomyosin V3 was more sensitive to calcium as compared with isomyosin V1. Using the same assay, the dependence of thin filament sliding velocity on the concentration of the actin-binding protein α-actinin (analog of a force-velocity dependence) was determined at the saturating calcium concentration for each myosin isoform (V1 and V3). The results suggest that the calcium regulation of V1 and V3 contractile activity follows different mechanisms.     

Direct observation of molecular motility by light microscopy

We used video-fluorescence microscopy to directly observe the sliding movement of single fluorescently labeled actin filaments along myosin fixed on a glass surface. Single actin filaments labeled with phalloidin-tetramethyl-rhodamine, which stabilizes the filament structure of actin, could be seen very clearly and continuously for at least 60 min in 02-free solution, and the sensitivity was high enough to see very short actin filaments less than 40 nm long that contained less than eight dye molecules. The actin filaments were observed to move along double-headed and, similarly, single-headed myosin filaments on which the density of the heads varied widely in the presence of ATP, showing that the cooperative interaction between the two heads of the myosin molecule is not essential to produce the sliding movement. The velocity of actin filament independent of filament length (greater than 1 micron) was almost unchanged until the density of myosin heads along the thick filament was decreased from six heads/14.3 nm to 1 head/34 nm. This result suggests that five to ten heads are sufficient to support the maximum sliding velocity of actin filaments (5 micron/s) under unloaded conditions. In order for five to ten myosin heads to achieve the observed maximum velocity, the sliding distance of actin filaments during one ATP cycle must be more than 60 nm.     

Superresolution Imaging of Dynamic MreB Filaments in B.?subtilis—A Multiple-Motor-Driven Transport?

The cytoskeletal protein MreB is an essential component of the bacterial cell-shape generation system. Using a superresolution variant of total internal reflection microscopy with structured illumination, as well as three-dimensional stacks of deconvolved epifluorescence microscopy, we found that inside living Bacillus subtilis cells, MreB forms filamentous structures of variable lengths, typically not longer than 1 μm. These filaments move along their orientation and mainly perpendicular to the long bacterial axis, revealing a maximal velocity at an intermediate length and a decreasing velocity with increasing filament length. Filaments move along straight trajectories but can reverse or alter their direction of propagation. Based on our measurements, we provide a mechanistic model that is consistent with all observations. In this model, MreB filaments mechanically couple several motors that putatively synthesize the cell wall, whereas the filaments’ traces mirror the trajectories of the motors. On the basis of our mechanistic model, we developed a mathematical model that can explain the nonlinear velocity length dependence. We deduce that the coupling of cell wall synthesis motors determines the MreB filament transport velocity, and the filament mechanically controls a concerted synthesis of parallel peptidoglycan strands to improve cell wall stability.     

Up-and-down movement of a sliding actin filament in the in vitro motility assay

We observed a three-dimensional up-and-down movement of an actin filament sliding on heavy mero-myosin (HMM) molecules in an in vitro motility assay. The up-and-down movement occurred along the direction perpendicular to the planar glass plane on which the filament demonstrated a sliding movement. The height length of the up-and-down movement was measured by monitoring the extent of diminishing fluorescent emission from the marker attached to the filament in the evanescent field of attenuation. The height lengths whose distribution exhibits a local maximum were found around the two values, 150 nm and 90 nm, separately. This undulating three-dimensional movement of an actin filament suggests that the interactions between myosin (HMM) molecules and the actin filament may temporally be modulated during its sliding movement.     

Direct Measurements of Local Coupling between Myosin Molecules Are Consistent with a Model of Muscle Activation

Muscle contracts due to ATP-dependent interactions of myosin motors with thin filaments composed of the proteins actin, troponin, and tropomyosin. Contraction is initiated when calcium binds to troponin, which changes conformation and displaces tropomyosin, a filamentous protein that wraps around the actin filament, thereby exposing myosin binding sites on actin. Myosin motors interact with each other indirectly via tropomyosin, since myosin binding to actin locally displaces tropomyosin and thereby facilitates binding of nearby myosin. Defining and modeling this local coupling between myosin motors is an open problem in muscle modeling and, more broadly, a requirement to understanding the connection between muscle contraction at the molecular and macro scale. It is challenging to directly observe this coupling, and such measurements have only recently been made. Analysis of these data suggests that two myosin heads are required to activate the thin filament. This result contrasts with a theoretical model, which reproduces several indirect measurements of coupling between myosin, that assumes a single myosin head can activate the thin filament. To understand this apparent discrepancy, we incorporated the model into stochastic simulations of the experiments, which generated simulated data that were then analyzed identically to the experimental measurements. By varying a single parameter, good agreement between simulation and experiment was established. The conclusion that two myosin molecules are required to activate the thin filament arises from an assumption, made during data analysis, that the intensity of the fluorescent tags attached to myosin varies depending on experimental condition. We provide an alternative explanation that reconciles theory and experiment without assuming that the intensity of the fluorescent tags varies.     

Skeletal muscle performance determined by modulation of number of myosin motors rather than motor force or stroke size

Skeletal muscle can bear a high load at constant length, or shorten rapidly when the load is low. This force-velocity relationship is the primary determinant of muscle performance in vivo. Here we exploited the quasi-crystalline order of myosin II motors in muscle filaments to determine the molecular basis of this relationship by X-ray interference and mechanical measurements on intact single cells. We found that, during muscle shortening at a wide range of velocities, individual myosin motors maintain a force of about 6 pN while pulling an actin filament through a 6 nm stroke, then quickly detach when the motor reaches a critical conformation. Thus we show that the force-velocity relationship is primarily a result of a reduction in the number of motors attached to actin in each filament in proportion to the filament load. These results explain muscle performance and efficiency in terms of the molecular mechanism of the myosin motor.     

Actin polymerization or myosin contraction: two ways to build up cortical tension for symmetry breaking

Cells use complex biochemical pathways to drive shape changes for polarization and movement. One of these pathways is the self-assembly of actin filaments and myosin motors that together produce the forces and tensions that drive cell shape changes. Whereas the role of actin and myosin motors in cell polarization is clear, the exact mechanism of how the cortex, a thin shell of actin that is underneath the plasma membrane, can drive cell shape changes is still an open question. Here, we address this issue using biomimetic systems: the actin cortex is reconstituted on liposome membranes, in an ‘outside geometry’. The actin shell is either grown from an activator of actin polymerization immobilized at the membrane by a biotin–streptavidin link, or built by simple adsorption of biotinylated actin filaments to the membrane, in the presence or absence of myosin motors. We show that tension in the actin network can be induced either by active actin polymerization on the membrane via the Arp2/3 complex or by myosin II filament pulling activity. Symmetry breaking and spontaneous polarization occur above a critical tension that opens up a crack in the actin shell. We show that this critical tension is reached by growing branched networks, nucleated by the Arp2/3 complex, in a concentration window of capping protein that limits actin filament growth and by a sufficient number of motors that pull on actin filaments. Our study provides the groundwork to understanding the physical mechanisms at work during polarization prior to cell shape modifications.     

Longitudinal Distortions and Transversal Fluctuations of an Actin Filament Sliding on Myosin Molecules

An actin filament sliding on myosin moleculesdemonstrates both longitudinal distortions and transversal fluctuationswith the linear dimension far exceeding the diameter of an actinmonomer. Local swaying of a single actin filament was identified byreading speckled fluorescent markers attached on the filament. Theaccuracy of reading each speckled marker was about 10.4 nm (r.m.s.).Longitudinal distortions of an actin filament at a low ATP concentrationof 20 M were as much as 0.5 m for the average filament lengthof 5.4 m. The magnitude of transversal fluctuations was as much as60 nm, that was independent of the filament length. Both longitudinaldistortions and transversal fluctuations are suggested to play a pivotalrole for facilitating a smooth sliding movement of an actin filament.     

Twirling Motion of Actin Filaments in Gliding Assays with Nonprocessive Myosin Motors

We present a model study of gliding assays in which actin filaments are moved by nonprocessive myosin motors. We show that even if the power stroke of the motor protein has no lateral component, the filaments will rotate around their axis while moving over the surface. Notably, the handedness of this twirling motion is opposite from that of the actin filament structure. It stems from the fact that the gliding actin filament has target zones, where its subunits point toward the surface and are therefore more accessible for myosin heads. Each myosin head has a higher binding probability before it reaches the center of the target zone than afterwards, which results in a left-handed twirling. We present a stochastic simulation and an approximative analytical solution. The calculated pitch of the twirling motion depends on the filament velocity (ATP concentration). It reaches ∼400 nm for low speeds and increases with higher speeds.     

Critical motor number for fractional steps of cytoskeletal filaments in gliding assays

In gliding assays, filaments are pulled by molecular motors that are immobilized on a solid surface. By varying the motor density on the surface, one can control the number [Formula: see text] of motors that pull simultaneously on a single filament. Here, such gliding assays are studied theoretically using Brownian (or Langevin) dynamics simulations and taking the local force balance between motors and filaments as well as the force-dependent velocity of the motors into account. We focus on the filament stepping dynamics and investigate how single motor properties such as stalk elasticity and step size determine the presence or absence of fractional steps of the filaments. We show that each gliding assay can be characterized by a critical motor number, [Formula: see text]. Because of thermal fluctuations, fractional filament steps are only detectable as long as [Formula: see text]. The corresponding fractional filament step size is [Formula: see text] where [Formula: see text] is the step size of a single motor. We first apply our computational approach to microtubules pulled by kinesin-1 motors. For elastic motor stalks that behave as linear springs with a zero rest length, the critical motor number is found to be [Formula: see text], and the corresponding distributions of the filament step sizes are in good agreement with the available experimental data. In general, the critical motor number [Formula: see text] depends on the elastic stalk properties and is reduced to [Formula: see text] for linear springs with a nonzero rest length. Furthermore, [Formula: see text] is shown to depend quadratically on the motor step size [Formula: see text]. Therefore, gliding assays consisting of actin filaments and myosin-V are predicted to exhibit fractional filament steps up to motor number [Formula: see text]. Finally, we show that fractional filament steps are also detectable for a fixed average motor number [Formula: see text] as determined by the surface density (or coverage) of the motors on the substrate surface.