Bending-wave propagation by microtubules and flagella

The movement of an elastic filament in a viscous medium can be computed from the fourth-order nonlinear partial differential equation obtained by balancing bending moments at all points along the length of the filament. These bending moments result from active forces, elastic resistance to bending, and viscous resistance to movement through the medium. I have studied numerical solutions obtained for two situations of biological interest: For the movement of individual microtubules, the active force is generated by interaction between the microtubule and the substratum over which it is moving, and is directed along the axis of the microtubule. The computations can reproduce the gliding movement of unrestrained microtubules, and also the periodic bending and bend propagation seen when the leading end of the microtubule is restrained. No modulation of active force is required to generate bending waves. For the movement of flagella, the active forces are generated internally as sliding forces between adjacent members of a cylinder of nine microtubular doublets. Without some additional control assumptions, the forces will be balanced and no bending moments will be generated. The problem faced by investigators of flagellar motility is to determine the control mechanisms that operate to make the system asymmetric, so that active bending moments are generated. Computations with models in which the curvature of the flagellum modulates the active-force generators have indicated that this control specification is sufficient to generate oscillation and bend propagation, but is insufficient to completely determine the movement.     

Organelle, bead, and microtubule translocations promoted by soluble factors from the squid giant axon

A reconstituted system for examining directed organelle movements along purified microtubules has been developed. Axoplasm from the squid giant axon was separated into soluble supernatant and organelle-enriched fractions. Movement of axoplasmic organelles along MAP-free microtubules occurred consistently only after addition of axoplasmic supernatant and ATP. The velocity of such organelle movement (1.6 micron/sec) was the same as in dissociated axoplasm. The axoplasmic supernatant also supported movement of microtubules along a glass surface and movement of carboxylated latex beads along microtubules at 0.5 micron/sec. The direction of microtubule movement on glass was opposite to that of organelle and bead movement on microtubules. The factors supporting movements of microtubules, beads, and organelles were sensitive to heat, trypsin, AMP-PNP and 100 microM vanadate. All of these movements may be driven by a single, soluble ATPase that binds reversibly to organelles, beads, or glass and generates a translocating force on a microtubule.     

Vesikin, a vesicle associated ATPase from squid axoplasm and optic lobe, has characteristics in common with vertebrate brain MAP 1 and MAP 2

Vesikin, a protein that can associate with squid axoplasmic vesicles or optic lobe microtubules, has been implicated as a force-generating molecule involved in microtubule-dependent vesicle transport [Gilbert and Sloboda, 1986, 1988]. Because vesikin crossreacts with an antibody to porcine brain microtubule associated protein 2 (MAP 2), studies were conducted to compare squid vesikin and brain MAPs. When taxol stabilized microtubules containing vesikin as a microtubule associated protein were incubated in the presence of ATP, vesikin dissociated from the microtubule subunit lattice. This behavior would be expected for an ATP-dependent, force generating molecule that serves as a crossbridge between vesicles and microtubules. When chick brain microtubules were treated under the same conditions, MAP 2 remained bound to the microtubules while MAP 1 dissociated in a manner similar to vesikin. One dimensional peptide mapping procedures revealed that, although digestion of vesikin and MAP 2 generated several peptides common to both proteins, vesikin and MAP 2 are clearly not identical. Furthermore, the addition of vesikin or MAPS 1 and 2 to purified tubulin stimulated microtubule assembly in a manner dependent on the concentration of added protein. These findings demonstrate that brain MAPs share characteristics common to squid vesikin and support the suggestion that brain MAPs 1 and 2 might act as a force generating complex for vesicle transport in higher organisms.     

Microtubule organization in three-dimensional confined geometries: evaluating the role of elasticity through a combined in vitro and modeling approach

Microtubules or microtubule bundles in cells often grow longer than the size of the cell, which causes their shape and organization to adapt to constraints imposed by the cell geometry. We test the reciprocal role of elasticity and confinement in the organization of growing microtubules in a confining box-like geometry, in the absence of other (active) microtubule organizing processes. This is inspired, for example, by the cortical microtubule array of elongating plant cells, where microtubules are typically organized in an aligned array transverse to the cell elongation axis. The method we adopt is a combination of analytical calculations, in which the polymers are modeled as inextensible filaments with bending elasticity confined to a two-dimensional surface that defines the limits of a three-dimensional space, and in vitro experiments, in which microtubules are polymerized from nucleation seeds in microfabricated chambers. We show that these features are sufficient to organize the polymers in aligned, coiling configurations as for example observed in plant cells. Though elasticity can account for the regularity of these arrays, it cannot account for a transverse orientation of microtubules to the cell's long axis. We therefore conclude that an additional active, force-generating process is necessary to create a coiling configuration perpendicular to the long axis of the cell.     

Shaping of the sperm nucleus in Marsilea: A distinction between factors responsible for shape generation and shape determination

Spermiogenesis in Marsilea vestita involves the elongation of a roughly spherical nucleus into a spiral that is composed of four to five gyres. A ribbon of microtubules is associated with the outer edge of the nucleus throughout the shaping process. In order to observe nuclear morphogenesis in the absence of microtubules, developing microspores were treated with drugs that are known to affect microtubule assembly. Spermatids cultured in the presence of colchicine from the beginning of spermiogenesis do not form a microtubule ribbon. The nuclei of these cells change from a spherical to an irregular shape with elongate branches or loops. The normal spiral nucleus and elongate rod of condensed chromatin are not formed and the pattern of chromatin condensation is also abnormal. These observations indicate that in Marsilea microtubules do not provide the mechanical force for nuclear shape generation. Bulk chromatin condensation can also be eliminated as the force behind nuclear shaping, because during normal development the chromatin condenses only after nuclear shaping is well advanced. We suggest that a force-generating system is located near or is a part of the nuclear envelope. Microtubules may, however, be important in the determination of the final shape of the nucleus either by organizing or directing the force-generating system or by externally restricting or guiding the shaping nucleus. Microtubules may also function in controlling the pattern of chromatin condensation.     

Gliding movement of and bidirectional transport along single native microtubules from squid axoplasm: evidence for an active role of microtubules in cytoplasmic transport

Native microtubules prepared from extruded and dissociated axoplasm have been observed to transport organelles and vesicles unidirectionally in fresh preparations and more slowly and bidirectionally in older preparations. Both endogenous and exogenous (fluorescent polystyrene) particles in rapid Brownian motion alight on and adhere to microtubules and are transported along them. Particles can switch from one intersecting microtubule to another and move in either direction. Microtubular segments 1 to 30 microns long, produced by gentle homogenization, glide over glass surfaces for hundreds of micrometers in straight lines unless acted upon by obstacles. While gliding they transport particles either in the same (forward) direction and/or in the backward direction. Particle movement and gliding of microtubule segments require ATP and are insensitive to taxol (30 microM). It appears, therefore, that the mechanisms producing the motive force are very closely associated with the native microtubule itself or with its associated proteins. Although these movements appear irreconcilable with several current theories of fast axoplasmic transport, in this article we propose two models that might explain the observed phenomena and, by extension, the process of fast axoplasmic transport itself. The findings presented and the possible mechanisms proposed for fast axoplasmic transport have potential applications across the spectrum of microtubule-based motility processes.     

A torque component in the kinesin-1 power stroke

Kinesin-1 is a twin-headed molecular motor that moves along microtubules in 8-nm steps, using a walking action in which the two heads interact alternately with the microtubule. Constructs with only one head can also produce impulses of force and motion, indicating that the walking action is an amplification strategy that leverages an underlying force-generating event. Recent work suggests that directional force is produced either by directionally biased selection of microtubule binding sites or by a conformational change subsequent to the binding event. We report here that surface-attached rat kinesin-1 monomers drive counterclockwise rotation of sliding microtubules around their axes, and that by manipulating the assay geometry, we could reduce or block the torsional motion with negligible effects on the axial motion. We can account for this behavior on the simple assumption that kinesin heads tend to bind to the closest available tubulin heterodimer in the lattice, but only in the case where an additional biasing process is present that shifts the start position for diffusion-to-capture toward the microtubule plus end by approximately 1 nm.     

Intracellular transport in axonal microtubular domains II. Velocity profile and energetics of circumtubular flow

Summary The microtubule is a highly efficient vectorial structure that could orient a transport force generating mechanism and also absorb the recoil produced by vectorial force generation. We have assumed that a nonspecific shear force is generated in a narrow annulus around the microtubule and have calculated the velocity profiles in the shear flow and drag flow regions that result from such a mechanism. This circumtubular flow of low visocosity cytoplasm is thought to be the basic carrier stream that produces the observed axoplasmic transport phenomena. These carrier streams are devoid of neurofilaments and form the halos or exclusion zones seen around microtubules in electron micrographs. Individual carrier streams may merge hydrodynamically to produce transport domains that are capable of moving large organelles in a saltatory manner. Exchange of material between the low viscosity transport domains and the high macroviscosity neurofilament regions produces mass fluxes akin to those found in chromatographic columns. Calculations of energy required to maintain streaming and of the energy available to the transport system show a close correspondence and demonstrate that a continuous carrier stream activity is energetically feasible.     

Microtubules and axoplasmic transport. Inhibition of transport by podophyllotoxin: an interaction with microtubule protein

Pharmacological evidence is presented for the involvement of microtubules in the process of fast axoplasmic transport. A quantitative measure of the inhibition of axoplasmic transport in an in vitro preparation of rat sciatic nerve is described. The alkaloids colchicine, podophyllotoxin, and vinblastine, which are known both to disrupt microtubules and to bind to the protein subunit of microtubules, are inhibitors of axoplasmic transport. Lumicolchine and picropodophyllin, unlike their respective isomers colchicine and podophyllotoxin, are poor inhibitors of axoplasmic transport. The dissociation constants for the binding of colchicine, lumicolchicine, podophyllotoxin, and picropodophyllin to purified microtubule protein from rat brain have been measured. Inhibition of axoplasmic transport by these drugs correlates favorably with their affinities of microtubule protein.     

A regulatory model for spindle function during mitosis

Structural information on the mitotic spindle of Saccharomyces cerevisiae obtained from isolated whole mount preparations has shown that the spindle undergoes a two-fold increase in length whilst comprising only a single microtubule continuous between the two spindle pole bodies. Further data from immunofluorescence microscopy on the timing of anaphase B has suggested that microtubules do not directly produce the required force, but instead have a more passive role. Here a regulatory function for spindle microtubules during mitosis is explored and the existence of a non-microtubule force-generating system is postulated. Thus it is suggested that the continuous microtubules govern the velocity of anaphase B by providing a resistive force that is itself regulated by the number of microtubules and their rate of polymerization. On this basis a model for the forces acting on a spindle pole body during anaphase is proposed.     

The role of kinesin and other soluble factors in organelle movement along microtubules

Kinesin is a force-generating ATPase that drives the sliding movement of microtubules on glass coverslips and the movement of plastic beads along microtubules. Although kinesin is suspected to participate in microtubule-based organelle transport, the exact role it plays in this process is unclear. To address this question, we have developed a quantitative assay that allows us to determine the ability of soluble factors to promote organelle movement. Salt-washed organelles from squid axoplasm exhibited a nearly undetectable level of movement on purified microtubules. Their frequency of movement could be increased greater than 20-fold by the addition of a high speed axoplasmic supernatant. Immunoadsorption of kinesin from this supernatant decreased the frequency of organelle movement by more than 70%; organelle movements in both directions were markedly reduced. Surprisingly, antibody purified kinesin did not promote organelle movement either by itself or when it was added back to the kinesin-depleted supernatant. This result suggested that other soluble factors necessary for organelle movement were removed along with kinesin during immunoadsorption of the supernatant. A high level of organelle motor activity was recovered in a high salt eluate of the immunoadsorbent that contained only little kinesin. On the basis of these results we propose that organelle movement on microtubules involves other soluble axoplasmic factors in addition to kinesin.     

Transient Pinning and Pulling: A Mechanism for Bending Microtubules

Microtubules have a persistence length of the order of millimeters in vitro, but inside cells they bend over length scales of microns. It has been proposed that polymerization forces bend microtubules in the vicinity of the cell boundary or other obstacles, yet bends develop even when microtubules are polymerizing freely, unaffected by obstacles and cell boundaries. How these bends are formed remains unclear. By tracking the motions of microtubules marked by photobleaching, we found that in LLC-PK1 epithelial cells local bends develop primarily by plus-end directed transport of portions of the microtubule contour towards stationary locations (termed pinning points) along the length of the microtubule. The pinning points were transient in nature, and their eventual release allowed the bends to relax. The directionality of the transport as well as the overall incidence of local bends decreased when dynein was inhibited, while myosin inhibition had no observable effect. This suggests that dynein generates a tangential force that bends microtubules against stationary pinning points. Simulations of microtubule motion and polymerization accounting for filament mechanics and dynein forces predict the development of bends of size and shape similar to those observed in cells. Furthermore, simulations show that dynein-generated bends at a pinning point near the plus end can cause a persistent rotation of the tip consistent with the observation that bend formation near the tip can change the direction of microtubule growth. Collectively, these results suggest a simple physical mechanism for the bending of growing microtubules by dynein forces accumulating at pinning points.     

Cytokinesis in HeLa: Post-telophase delay and microtubule-associated motility

Summary Phase-contrast microcinematography of cultured HeLa cells reveals that cell separation is considerably delayed after telophase. During this period of delay, the daughter cells lose their rounded morphology and become flattened against the substrate, as occurs in interphase. After two or more hours, the cells again become rounded while the thin intercellular bridge connecting them begins to elongate. This active elongation involves the migration of thickenings (waves) along the bridge from the midbody at its center toward either cell. Later, waves occur only on one side of the midbody as this half of the bridge alone continues to elongate. The arrival of waves at the cells is accompanied not only by discrete increases of length in that half of the bridge, but also by blebbing activity in that cell. Rupture of the bridge finally occurs just adjacent to the cell receiving these latter waves.Electron microscopic examination of cells in post-telophase delay has demonstrated a bundle of microtubules passing into either cell from the midbody in the center of the intercellular bridge. These microtubules are of constant length during bridge elongation; the cells are simply forced distally along the surface of the microtubule bundle. The waves themselves are found to contain microtubules just as straight as those in the rest of the bridge, so it is concluded that the force apparently generated here consists of the longitudinal translation of material along the surfaces of the rigid microtubules. It is pointed out that these forces may operate in the earlier phases of mitosis and in other systems of microtubule-associated motility. We also discuss the possible roles of post-telophase delay and of active bridge elongation in the organization of normal tissues.     

Conformation of the myosin motor during force generation in skeletal muscle

Myosin motors drive muscle contraction, cytokinesis and cell locomotion, and members of the myosin superfamily have been implicated in an increasingly diverse range of cell functions. Myosin can displace a bound actin filament several nanometers in a single interaction. Crystallographic studies suggest that this 'working stroke' involves bending of the myosin head between its light chain and catalytic domains. Here we used X-ray fiber diffraction to test the crystallographic model and measure the interdomain bending during force generation in an intact single muscle fiber. The observed bending has two components: an elastic distortion and an active rotation that generates force. The average bend of the force-generating myosin heads in a muscle fiber is intermediate between those in crystal structures with different bound nucleotides, and the C-terminus of the head is displaced by 7 nm along the actin filament axis compared with the in vitro conformation seen in the absence of nucleotide.     

A microtubule-based, dynein-dependent force induces local cell protrusions: Implications for neurite initiation

A key event in neurite initiation is the accumulation of microtubule bundles at the neuron periphery. We hypothesized that such bundled microtubules may generate a force at the plasma membrane that facilitates neurite initiation. To test this idea we observed the behavior of microtubule bundles that were induced by the microtubule-associated protein MAP2c. Endogenous MAP2c contributes to neurite initiation in primary neurons, and exogeneous MAP2c is sufficient to induce neurites in Neuro-2a cells. We performed nocodazol washout experiments in primary neurons, Neuro-2a cells and COS-7 cells to investigate the underlying mechanism. During nocodazol washout, small microtubule bundles formed rapidly in the cytoplasm and immediately began to move toward the cell periphery in a unidirectional manner. In neurons and Neuro-2a cells, neurite-like processes extended within minutes and concurrently accumulated bundles of repolymerized microtubules. Speckle microscopy in COS-7 cells indicated that bundle movement was due to transport, not treadmilling. At the periphery bundles remained under a unidirectional force and induced local cell protrusions that were further enhanced by suppression of Rho kinase activity. Surprisingly, this bundle motility was independent of classical actin- or microtubule-based tracks. It was, however, reversed by function-blocking antibodies against dynein. Suppression of dynein expression in primary neurons by RNA interference severely inhibited the generation of new neurites, but not the elongation of existing neurites formed prior to dynein knockdown. Together, these cell biological data suggest that neuronal microtubule-associated proteins induce microtubule bundles that are pushed outward by dynein and locally override inward contraction to initiate neurite-like cell protrusions. A similar force-generating mechanism might participate in spontaneous initiation of neurites in developing neurons. Electronic Supplementry Materials: Supplementary Materials are available in the online version of this article at     

The motor activity of mammalian axonemal dynein studied in situ on doublet microtubules

Flagellar dynein generates forces that produce relative shearing between doublet microtubules in the axoneme; this drives propagated bending of flagella and cilia. To better understand dynein's role in coordinated flagellar and ciliary motion, we have developed an in situ assay in which polymerized single microtubules glide along doublet microtubules extruded from disintegrated bovine sperm flagella at a pH of 7.8. The exposed, active dynein remain attached to their respective doublet microtubules, allowing gliding of individual microtubules to be observed in an environment that allows direct control of chemical conditions. In the presence of ATP, translocation of microtubules by dynein exhibits Michaelis-Menten type kinetics, with V(max) = 4.7 +/- 0.2 microm/s and K(m) = 124 +/- 11 microM. The character of microtubule translocation is variable, including smooth gliding, stuttered motility, oscillations, buckling, complete dissociation from the doublet microtubule, and occasionally movements reversed from the physiologic direction. The gliding velocity is independent of the number of dynein motors present along the doublet microtubule, and shows no indication of increased activity due to ADP regulation. These results reveal fundamental properties underlying cooperative dynein activity in flagella, differences between mammalian and non-mammalian flagellar dynein, and establish the use of natural tracks of dynein arranged in situ on the doublet microtubules of bovine sperm as a system to explore the mechanics of the dynein-microtubule interactions in mammalian flagella.     

Structural biology of cytoplasmic and axonemal dyneins

Dyneins are microtubule-based, ATP-driven motor proteins with six tandemly linked AAA+ domains, a long N-terminal tail and a coiled-coil stalk. Cytoplasmic dyneins function as individual homodimers and are responsible for minus-end-oriented transport along microtubules. Axonemal dyneins of flagella/cilia are anchored in arrays to peripheral microtubule doublets by their N-terminal tails, and generate sliding motions of adjacent microtubule doublets toward the plus end. The coiled-coil stalk is responsible for communication between the AAA+ domains and the microtubule binding domain. A number of isoforms of axonemal dyneins are integrated to generate bending motion. In this article I will review recent structural studies and address the question as to how dyneins generate force and cause bending in flagella/cilia.     

One-dimensional diffusion of microtubules bound to flagellar dynein

Dynein is a multisubunit ATPase that powers microtubule-based motility. We find that a dissociated dynein particle containing the beta heavy chain subunit translocates microtubules unidirectionally over a glass surface in the presence of ATP. However, after nucleotide hydrolysis is inhibited by vanadate, unidirectional translocation ceases, and microtubules instead undergo irregular back-and-forth motion along their longitudinal axes. Quantitative analysis reveals that this motion is due to thermal-driven diffusion, but, unlike a particle undergoing Brownian motion, the diffusion is restricted to one dimension. The properties of the diffusional movement indicate that dynein can interact with microtubules in a way that permits the latter to diffuse only along their longitudinal axes. This weak binding interaction may constitute an important intermediate state in dynein's force-generating cycle.     

Electric field generated by axial longitudinal vibration modes of microtubule

Microtubules are electrically polar structures fulfilling prerequisites for generation of oscillatory electric field in the kHz to GHz region. Energy supply for excitation of elasto-electrical vibrations in microtubules may be provided from GTP-hydrolysis; motor protein–microtubule interactions; and energy efflux from mitochondria. We calculated electric field generated by axial longitudinal vibration modes of microtubules for random, and coherent excitation. In case of coherent excitation of vibrations, the electric field intensity is highest at the end of microtubule. The dielectrophoretic force exerted by electric field on the surrounding molecules will influence the kinetics of microtubule polymerization via change in the probability of the transport of charge and mass particles. The electric field generated by vibrations of electrically polar cellular structures is expected to play an important role in biological self-organization.     

Structural Aspects of Saltatory Particle Movement

A variety of cells possess particles which show movements statistically different from Brownian movements. They are characterized by discontinuous jumps of 2–30 µ at velocities of 0.5–5 µ/sec or more. A detailed analysis of these saltatory, jumplike movements makes it most likely that they are caused by transmission of force to the particles by a fiber system in the cell outside of the particle itself. Work with isolated droplets of cytoplasm from algae demonstrates a set of fibers involved in both cytoplasmic streaming and saltatory motion, suggesting that both phenomena are related to the same force-generating set of fibers. Analysis of a variety of systems in which streaming and/or saltatory movement occurs reveals two types of fiber systems spatially correlated with the movement, microtubules and 50 A microfilaments. The fibers in Nitella (alga) are of the microfilament type. In other systems (melanocyte processes, mitotic apparatus, nerve axons) microtubules occur. A suggestion is made, based on work on cilia, that a microtubule-microfilament complex may be present in those cases in which only microtubules appear to be present, with the microfilament closely associated with or buried in the microtubule wall. If so, then microfilaments, structurally similar to smooth muscle filaments, may be a force-generating element in a very wide variety of saltatory and streaming phenomena.