Purified kinesin promotes vesicle motility and induces active sliding between microtubules in vitro

Direct detection of deformation modes on varying length scales in active biopolymer networks

Correlated flows and forces that emerge from active matter orchestrate complex processes such as shape regulation and deformations in biological cells and tissues. The active materials central to cellular mechanics are cytoskeletal networks, where molecular motor activity drives deformations and remodeling. Here, we investigate deformation modes in actin networks driven by the molecular motor myosin II through quantitative fluorescence microscopy. We examine the deformation anisotropy at different length scales in networks of entangled, cross-linked, and bundled actin. In sparsely cross-linked networks, we find myosin-dependent biaxial buckling modes across length scales. In cross-linked bundled networks, uniaxial contraction is predominate on long length scales, while the uniaxial or biaxial nature of the deformation depends on bundle microstructure at shorter length scales. The anisotropy of deformations may provide insight to regulation of collective behavior in a variety of active materials.

Effects of confinement on the dynamics and correlation scales in kinesin-microtubule active fluids

We study the influence of solid boundaries on dynamics and structure of kinesin-driven microtubule active fluids as the height of the container, H, increases from hundreds of micrometers to several millimeters. By three-dimensional tracking of passive tracers dispersed in the active fluid, we observe that the activity level, characterized by velocity fluctuations, increases as system size increases and retains a small-scale isotropy. Concomitantly, as the confinement level decreases, the velocity-velocity temporal correlation develops a strong positive correlation at longer times, suggesting the establishment of a "memory". We estimate the characteristic size of the flow structures from the spatial correlation function and find that, as the confinement becomes weaker, the correlation length, l_{c}, saturates at approximately 400 microns. This saturation suggests an intrinsic length scale which, along with the small-scale isotropy, demonstrates the multiscale nature of this kinesin-driven bundled microtubule active system.

A small-molecule activator of kinesin-1 drives remodeling of the microtubule network

The microtubule motor kinesin-1 interacts via its cargo-binding domain with both microtubules and organelles, and hence plays an important role in controlling organelle transport and microtubule dynamics. In the absence of cargo, kinesin-1 is found in an autoinhibited conformation. The molecular basis of how cargo engagement affects the balance between kinesin-1's active and inactive conformations and roles in microtubule dynamics and organelle transport is not well understood. Here we describe the discovery of kinesore, a small molecule that in vitro inhibits kinesin-1 interactions with short linear peptide motifs found in organelle-specific cargo adaptors, yet activates kinesin-1's function of controlling microtubule dynamics in cells, demonstrating that these functions are mechanistically coupled. We establish a proof-of-concept that a microtubule motor-cargo interface and associated autoregulatory mechanism can be manipulated using a small molecule, and define a target for the modulation of microtubule dynamics.

Enhanced Dynamics of Confined Cytoskeletal Filaments Driven by Asymmetric Motors

Cytoskeletal filaments and molecular motors facilitate the micron-scale force generation necessary for the distribution of organelles and the restructuring of the cytoskeleton within eukaryotic cells. Although the mesoscopic structure and the dynamics of such filaments have been studied in vitro and in vivo, their connection with filament polarity-dependent motor-mediated force generation is not well understood. Using 2D Brownian dynamics simulations, we study a dense, confined mixture of rigid microtubules (MTs) and active springs that have arms that cross-link neighboring MT pairs and move unidirectionally on the attached MT. We simulate depletion interactions between MTs using an attractive potential. We show that dimeric motors, with a motile arm on only one of the two MTs, produce large polarity-sorted MT clusters, whereas tetrameric motors, with motile arms on both microtubules, produce bundles. Furthermore, dimeric motors induce, on average, higher velocities between antialigned MTs than tetrameric motors. Our results, where MTs move faster near the confining wall, are consistent with experimental observations in Drosophila oocytes where enhanced microtubule activity is found close to the confining plasma membrane.

Filament rigidity and connectivity tune the deformation modes of active biopolymer networks

Molecular motors embedded within collections of actin and microtubule filaments underlie the dynamics of cytoskeletal assemblies. Understanding the physics of such motor-filament materials is critical to developing a physical model of the cytoskeleton and designing biomimetic active materials. Here, we demonstrate through experiments and simulations that the rigidity and connectivity of filaments in active biopolymer networks regulates the anisotropy and the length scale of the underlying deformations, yielding materials with variable contractility. We find that semiflexible filaments can be compressed and bent by motor stresses, yielding materials that undergo predominantly biaxial deformations. By contrast, rigid filament bundles slide without bending under motor stress, yielding materials that undergo predominantly uniaxial deformations. Networks dominated by biaxial deformations are robustly contractile over a wide range of connectivities, while networks dominated by uniaxial deformations can be tuned from extensile to contractile through cross-linking. These results identify physical parameters that control the forces generated within motor-filament arrays and provide insight into the self-organization and mechanics of cytoskeletal assemblies.

A single-headed fission yeast myosin V transports actin in a tropomyosin-dependent manner

Myo51, a class V myosin in fission yeast, localizes to and assists in the assembly of the contractile ring, a conserved eukaryotic actomyosin structure that facilitates cytokinesis. Rng8 and Rng9 are binding partners that dictate the cellular localization and function of Myo51. Myo51 was expressed in insect cells in the presence or absence of Rng8/9. Surprisingly, electron microscopy of negatively stained images and hydrodynamic measurements showed that Myo51 is single headed, unlike most class V myosins. When Myo51-Rng8/9 was bound to actin-tropomyosin, two attachment sites were observed: the typical ATP-dependent motor domain attachment and a novel ATP-independent binding of the tail mediated by Rng8/9. A modified motility assay showed that this additional binding site anchors Myo51-Rng8/9 so that it can cross-link and slide actin-tropomyosin filaments relative to one another, functions that may explain the role of this motor in contractile ring assembly.

Active contraction of microtubule networks

Many cellular processes are driven by cytoskeletal assemblies. It remains unclear how cytoskeletal filaments and motor proteins organize into cellular scale structures and how molecular properties of cytoskeletal components affect the large-scale behaviors of these systems. Here, we investigate the self-organization of stabilized microtubules in Xenopus oocyte extracts and find that they can form macroscopic networks that spontaneously contract. We propose that these contractions are driven by the clustering of microtubule minus ends by dynein. Based on this idea, we construct an active fluid theory of network contractions, which predicts a dependence of the timescale of contraction on initial network geometry, a development of density inhomogeneities during contraction, a constant final network density, and a strong influence of dynein inhibition on the rate of contraction, all in quantitative agreement with experiments. These results demonstrate that the motor-driven clustering of filament ends is a generic mechanism leading to contraction.

Emergent complexity of the cytoskeleton: from single filaments to tissue

Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.

Charcot-Marie-Tooth disease and intracellular traffic

Mutations of genes whose primary function is the regulation of membrane traffic are increasingly being identified as the underlying causes of various important human disorders. Intriguingly, mutations in ubiquitously expressed membrane traffic genes often lead to cell type- or organ-specific disorders. This is particularly true for neuronal diseases, identifying the nervous system as the most sensitive tissue to alterations of membrane traffic. Charcot-Marie-Tooth (CMT) disease is one of the most common inherited peripheral neuropathies. It is also known as hereditary motor and sensory neuropathy (HMSN), which comprises a group of disorders specifically affecting peripheral nerves. This peripheral neuropathy, highly heterogeneous both clinically and genetically, is characterized by a slowly progressive degeneration of the muscle of the foot, lower leg, hand and forearm, accompanied by sensory loss in the toes, fingers and limbs. More than 30 genes have been identified as targets of mutations that cause CMT neuropathy. A number of these genes encode proteins directly or indirectly involved in the regulation of intracellular traffic. Indeed, the list of genes linked to CMT disease includes genes important for vesicle formation, phosphoinositide metabolism, lysosomal degradation, mitochondrial fission and fusion, and also genes encoding endosomal and cytoskeletal proteins. This review focuses on the link between intracellular transport and CMT disease, highlighting the molecular mechanisms that underlie the different forms of this peripheral neuropathy and discussing the pathophysiological impact of membrane transport genetic defects as well as possible future ways to counteract these defects.

Biophysics of mitosis

Mitosis is the process by which eukaryotic cells organize and segregate their chromosomes in preparation for cell division. It is accomplished by a cellular machine composed largely of microtubules (MTs) and their associated proteins. This article reviews literature on mitosis from a biophysical point of view, drawing attention to the assembly and motility processes required to do this complex job with precision. Work from both the recent and the older literature is integrated into a description of relevant biological events and the experiments that probe their mechanisms. Theoretical work on specific subprocesses is also reviewed. Our goal is to provide a document that will expose biophysicists to the fascination of this quite amazing process and provide them with a good background from which they can pursue their own research interests in the subject.

Shaping microtubules into diverse patterns: molecular connections for setting up both ends

Microtubules serve as rails for intracellular trafficking and their appropriate organization is critical for the generation of cell polarity, which is a foundation of cell differentiation, tissue morphogenesis, ontogenesis and the maintenance of homeostasis. The microtubule array is not just a static railway network; it undergoes repeated collapse and reassembly in diverse patterns during cell morphogenesis. In the last decade much progress has been made toward understanding the molecular mechanisms governing complex microtubule patterning. This review first revisits the basic principle of microtubule dynamics, and then provides an overview of how microtubules are arranged in highly shaped and functional patterns in cells changing their morphology by factors controlling the fate of microtubule ends.

Loop formation of microtubules during gliding at high density

The microtubule cytoskeleton, including the associated proteins, forms a complex network essential to multiple cellular processes. Microtubule-associated motor proteins, such as kinesin-1, travel on microtubules to transport membrane bound vesicles across the crowded cell. Other motors, such as cytoplasmic dynein and kinesin-5, are used to organize the cytoskeleton during mitosis. In order to understand the self-organization processes of motors on microtubules, we performed filament-gliding assays with kinesin-1 motors bound to the cover glass with a high density of microtubules on the surface. To observe microtubule organization, 3% of the microtubules were fluorescently labeled to serve as tracers. We find that microtubules in these assays are not confined to two dimensions and can cross one other. This causes microtubules to align locally with a relatively short correlation length. At high density, this local alignment is enough to create 'intersections' of perpendicularly oriented groups of microtubules. These intersections create vortices that cause microtubules to form loops. We characterize the radius of curvature and time duration of the loops. These different behaviors give insight into how crowded conditions, such as those in the cell, might affect motor behavior and cytoskeleton organization.

Active multistage coarsening of actin networks driven by myosin motors

In cells, many vital processes involve myosin-driven motility that actively remodels the actin cytoskeleton and changes cell shape. Here we study how the collective action of myosin motors organizes actin filaments into contractile structures in a simplified model system devoid of biochemical regulation. We show that this self-organization occurs through an active multistage coarsening process. First, motors form dense foci by moving along the actin network structure followed by coalescence. Then the foci accumulate actin filaments in a shell around them. These actomyosin condensates eventually cluster due to motor-driven coalescence. We propose that the physical origin of this multistage aggregation is the highly asymmetric load response of actin filaments: they can support large tensions but buckle easily under piconewton compressive loads. Because the motor-generated forces well exceed this threshold, buckling is induced on the connected actin network that resists motor-driven filament sliding. We show how this buckling can give rise to the accumulation of actin shells around myosin foci and subsequent coalescence of foci into superaggregates. This new physical mechanism provides an explanation for the formation and contractile dynamics of disordered condensed actomyosin states observed in vivo.

Cytoplasmic microtubule sliding: An unconventional function of conventional kinesin

There are well known examples in nature of microtubules dramatically changing their function by re-organizing their structure. Most interphase animal cells rely on the radial organization of the microtubule network for precise cargo delivery. Dividing cells re-organize microtubules with the help of motor proteins to form the spindle and drive the segregation of chromosomes into daughter cells. These examples present a kind of dichotomy: microtubules can be utilized as stationary tracks along which motor proteins move, or they can perform work themselves by utilizing the power of motor proteins. While both occur during mitosis, our recent findings demonstrate that both functions may occur simultaneously in interphase cells as well. We find that kinesin-1 (a motor known for its role in transporting cargo along microtubule tracks) powers microtubule sliding in non-dividing cells and this mechanism is used to form cellular protrusions.

Kinesin-1 heavy chain mediates microtubule sliding to drive changes in cell shape

Microtubules are typically observed to buckle and loop during interphase in cultured cells by an unknown mechanism. We show that lateral microtubule movement and looping is a result of microtubules sliding against one another in interphase Drosophila S2 cells. RNAi of the kinesin-1 heavy chain (KHC), but not dynein or the kinesin-1 light chain, eliminates these movements. KHC-dependent microtubule sliding powers the formation of cellular processes filled with parallel microtubule bundles. The growth of these cellular processes is independent of the actin cytoskeleton. We further observe cytoplasmic microtubule sliding in Xenopus and Ptk2 cells, and show that antibody inhibition of KHC in mammalian cells prevents sliding. We therefore propose that, in addition to its well established role in organelle transport, an important universal function of kinesin-1 is to mediate cytoplasmic microtubule-microtubule sliding. This provides the cell with a dedicated mechanism to transport long and short microtubule filaments and drive changes in cell shape.

Kinesin's light chains inhibit the head- and microtubule-binding activity of its tail

Kinesin-1 is a microtubule-based motor comprising two heavy chains (KHCs) and two light chains (KLCs). Motor activity is precisely regulated to avoid futile ATP consumption and to ensure proper intracellular localization of kinesin-1 and its cargoes. The KHC tail inhibits ATPase activity by interacting with the enzymatic KHC heads, and the tail also binds microtubules. Here, we present a role for the KLCs in regulating both the head- and microtubule-binding activities of the kinesin-1 tail. We show that KLCs reduce the affinity of the head-tail interaction over tenfold and concomitantly repress the tail's regulatory activity. We also show that KLCs inhibit tail-microtubule binding by a separate mechanism. Inhibition of head-tail binding requires steric and electrostatic factors. Inhibition of tail-microtubule binding is largely electrostatic, pH dependent, and mediated partly by a highly negatively charged linker region between the KHC-interacting and cargo-binding domains of the KLCs. Our data support a model wherein KLCs promote activation of kinesin-1 for cargo transport by simultaneously suppressing tail-head and tail-microtubule interactions. KLC-mediated inhibition of tail-microtubule binding may also influence diffusional movement of kinesin-1 on microtubules, and kinesin-1's role in microtubule transport/sliding.

Collective alignment of polar filaments by molecular motors

We study the alignment of polar biofilaments, such as microtubules and actin, subject to the action of multiple molecular motors attached simultaneously to more than one filament. Focusing on a paradigm model of only two filaments interacting with multiple motors, we were able to investigate in detail the alignment dynamics. While almost no alignment occurs in the case of a single motor, the filaments become rapidly aligned due to the collective action of the motors. Our analysis shows that the alignment time is governed by the number of bound motors and the magnitude of the motors' stepping fluctuations. We predict that the time scale of alignment is in the order of seconds, much faster than that reported for passive crosslink-induced bundling. In vitro experiments on the alignment of microtubules by multiple-motor covered beads are in qualitative agreement. We also discuss another mode of fast alignment of filaments, namely the cooperation between motors and passive crosslinks.

Motor-mediated alignment of microtubules in semidilute mixtures

We propose and study a model of molecular motor-induced ordering in a cytoskeletal filament solution for the semidilute case. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. In the semidilute regime multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. The motors, on the one hand, cause closer filament alignment, and, on the other hand, induce fluctuations that are dependent on the relative orientation of the filaments to which the motors are attached. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. This model considers each filament to be in motor contact with all other filaments in the solution. We show that the transition to the oriented state changes from second order to first order when the force-dependent detachment becomes important.

Instabilities in a two-dimensional polar-filament--motor system

The dynamical interaction between filaments and motor proteins is known for their propensity to self-organize into spatio-temporal patterns. Since the filaments are polar in the sense that motors define a direction of motion on them, the system can display a spatially homogeneous polar-filament orientation. We show that the latter anisotropic state itself may become unstable with respect to inhomogeneous fluctuations. This scenario shares similarities with instabilities in planarly aligned nematic liquid crystals: in both cases the wave vector of the instability may be oriented either parallel or oblique to the polarity axis. However, the encountered instabilities here are long-wave instead of short-wave and the destabilizing modes are drifting ones due to the polar symmetry. Additionally a nonpropagating transverse instability is possible. The stability diagrams related to the various wave vector orientations relative to the polarity axis are determined and discussed for a specific model of motor-filament interactions.

Ustilago maydis, a new fungal model system for cell biology

The use of fungal model systems, such as Saccharomyces cerevisisae and Schizosaccharomyces pombe, has contributed enormously to our understanding of essential cellular processes in animals. Here, we introduce the corn smut fungus Ustilago maydis as a new model organism for studying cell biological processes. Genome-wide analysis demonstrates that U. maydis is more closely related to humans than to budding yeast, and numerous proteins are shared only by U. maydis and Homo sapiens. Growing evidence suggests that basic principles of long-distance transport, mitosis and motor-based microtubule organization are conserved between U. maydis and humans. The fungus U. maydis, therefore, offers a unique system for the study of certain mammalian processes.

Directing the polar organization of microtubules

Microtubules (MTs) are polar protein filaments that participate in critical biological functions ranging from motor protein direction to coordination of chromosome separation during cell division. The effective facilitation of these processes, however, requires careful regulation of the polar orientation and spatial organization of the assembled MTs. We describe here an artificial approach to polar MT assembly that enables us to create three-dimensional polar-oriented synthetic microtubule organizing centers (POSMOCs). Utilizing engineered MT polymerization in concert with functionalized micro- and nanoscale particles, we demonstrate the controllable polar assembly of MTs into asters and the variations in aster structure determined by the interactions between the MTs and the functionalized organizing particles. Inspired by the aster-like form of biological structures such as centrosomes, these POSMOCs represent a key step toward replicating biology's complex materials assembly machinery.

Bundle dynamics of interacting polar rods

We use a probabilistic model of microtubule interaction via molecular motors to study microtubule bundle interaction. Our model indicates that initially disordered systems of interacting polar rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results show a long term attraction and coalescing of bundles indicating a clear coarsening in the system; Microtubule bundles concentrate into fewer orientations on a slow logarithmic time scale.

Simulation studies of self-organization of microtubules and molecular motors

We perform Monte Carlo type simulation studies of self-organization of microtubules interacting with molecular motors. We model microtubules as stiff polar rods of equal length exhibiting anisotropic diffusion in the plane. The molecular motors are implicitly introduced by specifying certain probabilistic collision rules resulting in realignment of the rods. This approximation of the complicated microtubule-motor interaction by a simple instant collision allows us to bypass the "computational bottlenecks" associated with the details of the diffusion and the dynamics of motors and the reorientation of microtubules. Consequently, we are able to perform simulations of large ensembles of microtubules and motors on a very large time scale. This simple model reproduces all important phenomenology observed in in vitro experiments: Formation of vortices for low motor density and raylike asters and bundles for higher motor density.

Taxol crystals can masquerade as stabilized microtubules

Taxol is a potent anti-mitotic drug used in chemotherapy, angioplastic stents, and cell biology research. By binding and stabilizing microtubules, Taxol inhibits their dynamics, crucial for cell division, motility, and survival. The drug has also been reported to induce formation of asters and bundles composed of stabilized microtubules. Surprisingly, at commonly used concentrations, Taxol forms crystals that rapidly bind fluorescent tubulin subunits, generating structures with an uncanny resemblance to microtubule asters and bundles. Kinetic and topological considerations suggest that tubulin subunits, rather than microtubules, bind the crystals. This sequestration of tubulin from the subunit pool would be expected to shift the equilibrium of free to polymerized tubulin to disfavor assembly. Our results imply that some previously reported Taxol-induced asters or bundles could include or be composed of tubulin-decorated Taxol crystals. Thus, reevaluation of certain morphological, chemical, and physical properties of Taxol-treated microtubules may be necessary. Moreover, our findings suggest a novel mechanism for chemotherapy-induced cytotoxicity in non-dividing cells, with far-reaching medical implications.

Interactions of semiflexible filaments and molecular motors

This paper summarizes the results of numerical simulations of the interaction of a pair of biofilaments mediated by a molecular motor. The filaments are modeled as flexible rods, and the results are applicable to microtubules, which are relatively stiff, as well as to much softer filaments, such as actin. The results provide insight into the effects of flexibility on cytoskeleton formation and the rheology of semiflexible filament networks. The simulations are based on a nonlinear elasticity equation. The results show that flexibility enhances the tendency of filaments to align. The enhancement in turn favors the formation of large-scale structures in multifilament systems. Simulations for soft filaments show that the action of the motor can result in the formation of multiple loops of the filaments as a result of buckling, which can affect the structure of a cross-linked network and thereby its rheology. The estimate for the minimal buckling length as a function of the motor speed, the viscosity of the solvent, and the bending stiffness of the filament is derived analytically.

Cargo Transport: Two Motors Are Sometimes Better Than One

Molecular motor proteins are crucial for the proper distribution of organelles and vesicles in cells. Much of our current understanding of how motors function stems from studies of single motors moving cargos in vitro. More recently, however, there has been mounting evidence that the cooperation of multiple motors in moving cargos and the regulation of motor-filament affinity could be key mechanisms that cells utilize to regulate cargo transport. Here, we review these recent advances and present a picture of how the different mechanisms of regulating the number of motors moving a cargo could facilitate cellular functions.

Rheology of active filament solutions

We study the viscoelasticity of an active solution of polar biofilaments and motor proteins. Using a molecular model, we derive the constitutive equations for the stress tensor in the isotropic phase and in phases with liquid crystalline order. The stress relaxation in the various phases is discussed. Contractile activity is responsible for a spectacular difference in the viscoelastic properties on opposite sides of the order-disorder transition.

Active gels: where polymer physics meets cytoskeletal dynamics

The cytoskeleton provides eukaryotic cells with mechanical support and helps them to perform their biological functions. It is predominantly composed of a network of semiflexible polar protein filaments. In addition, there are many accessory proteins that bind to these filaments, regulate their assembly, link them to organelles and provide the motors that either move the organelles along the filaments or move the filaments themselves. A natural approach to such a multiple particle system is the study of its collective excitations. I review some recent work on the theoretical description of the emergence of a number of particular collective motile behaviours from the interactions between different elements of the cytoskeleton. In order to do this, close analogies have been made to the study of driven soft condensed matter systems. However, it emerges naturally that a description of these soft active motile systems gives rise to new types of collective phenomena not seen in conventional soft systems. I discuss the implications of these results and perspectives for the future.

Modelling microtubule patterns

The cellular cytoskeleton is well studied in terms of its biological and physical properties, making it an attractive subject for systems approaches. Here, we describe the experimental and theoretical strategies used to study the collective behaviour of microtubules and motors. We illustrate how this led to the beginning of an understanding of dynamic cellular patterns that have precise functions.

Hydrodynamics of isotropic and liquid crystalline active polymer solutions

We describe the large-scale collective behavior of solutions of polar biofilaments and stationary and mobile crosslinkers. Both mobile and stationary crosslinkers induce filament alignment promoting either polar or nematic order. In addition, mobile crosslinkers, such as clusters of motor proteins, exchange forces and torques among the filaments and render the homogeneous states unstable via filament bundling. We start from a Smoluchowski equation for rigid filaments in solutions, where pairwise crosslink-mediated interactions among the filaments yield translational and rotational currents. The large-scale properties of the system are described in terms of continuum equations for filament and motor densities, polarization, and alignment tensor obtained by coarse-graining the Smoluchovski equation. The possible homogeneous and inhomogeneous states of the systems are obtained as stable solutions of the dynamical equations and are characterized in terms of experimentally accessible parameters. We make contact with work by other authors and show that our model allows for an estimate of the various parameters in the hydrodynamic equations in terms of physical properties of the crosslinkers.

Theory of self-assembly of microtubules and motors

We derive a model describing spatiotemporal organization of an array of microtubules interacting via molecular motors. Starting from a stochastic model of inelastic polar rods with a generic anisotropic interaction kernel, we obtain a set of equations for the local rods concentration and orientation. At large enough mean density of rods and concentration of motors, the model describes an orientational instability. We demonstrate that the orientational instability leads to the formation of vortices and (for large density and/or kernel anisotropy) asters seen in recent experiments. We derive the specific form of the interaction kernel from the detailed analysis of microscopic interaction of two filaments mediated by a moving molecular motor and extend our results to include variable motor density and motor attachment to the substrate.

Alignment of rods and partition of integers

We study dynamical ordering of rods. In this process, rod alignment via pairwise interactions competes with diffusive wiggling. Under strong diffusion, the system is disordered, but at weak diffusion, the system is ordered. We present an exact steady-state solution for the nonlinear and nonlocal kinetic theory of this process. We find the Fourier transform as a function of the order parameter, and show that Fourier modes decay exponentially with the wave number. We also obtain the order parameter in terms of the diffusion constant. This solution is obtained using iterated partitions of the integer numbers.

Conventional kinesin mediates microtubule-microtubule interactions in vivo

Conventional kinesin is a ubiquitous organelle transporter that moves cargo toward the plus-ends of microtubules. In addition, several in vitro studies indicated a role of conventional kinesin in cross-bridging and sliding microtubules, but in vivo evidence for such a role is missing. In this study, we show that conventional kinesin mediates microtubule-microtubule interactions in the model fungus Ustilago maydis. Live cell imaging and ultrastructural analysis of various mutants in Kin1 revealed that this kinesin-1 motor is required for efficient microtubule bundling and participates in microtubule bending in vivo. High levels of Kin1 led to increased microtubule bending, whereas a rigor-mutation in the motor head suppressed all microtubule motility and promoted strong microtubule bundling, indicating that kinesin can form cross-bridges between microtubules in living cells. This effect required a conserved region in the C terminus of Kin1, which was shown to bind microtubules in vitro. In addition, a fusion protein of yellow fluorescent protein and the Kin1tail localized to microtubule bundles, further supporting the idea that a conserved microtubule binding activity in the tail of conventional kinesins mediates microtubule-microtubule interactions in vivo.

Nematic and polar order in active filament solutions

Using a microscopic model of interacting polar biofilaments and motor proteins, we characterize the phase diagram of both homogeneous and inhomogeneous states in terms of experimental parameters. The polarity of motor clusters is key in determining the organization of the filaments in homogeneous isotropic, polarized, and nematic states, while motor-induced bundling yields spatially inhomogeneous structures.

Nonlinear competition between asters and stripes in filament-motor systems

A model for polar filaments interacting via molecular motor complexes is investigated which exhibits bifurcations to spatial patterns. It is shown that the homogeneous distribution of filaments, such as actin or microtubules, may become either unstable with respect to an orientational instability of a finite wave number or with respect to modulations of the filament density, where long-wavelength modes are amplified as well. Above threshold nonlinear interactions select either stripe patterns or periodic asters. The existence and stability ranges of each pattern close to threshold are predicted in terms of a weakly nonlinear perturbation analysis, which is confirmed by numerical simulations of the basic model equations. The two relevant parameters determining the bifurcation scenario of the model can be related to the concentrations of the active molecular motors and of the filaments, respectively, which both could be easily regulated by the cell.

Self-organized density patterns of molecular motors in arrays of cytoskeletal filaments

The stationary states of systems with many molecular motors are studied theoretically for uniaxial and centered (asterlike) arrangements of cytoskeletal filaments using Monte Carlo simulations and a two-state model. Mutual exclusion of motors from binding sites of the filaments is taken into account. For small overall motor concentration, the density profiles are exponential and algebraic in uniaxial and centered filament systems, respectively. For uniaxial systems, exclusion leads to the coexistence of regions of high and low densities of bound motors corresponding to motor traffic jams, which grow upon increasing the overall motor concentration. These jams are insensitive to the motor behavior at the end of the filament. In centered systems, traffic jams remain small and an increase in the motor concentration leads to a flattening of the profile if the motors move inwards, and to the buildup of a concentration maximum in the center of the aster if motors move outwards. In addition to motor density patterns, we also determine the corresponding patterns of the motor current.

Dynamics of inextensible semiflexible filaments

We address the problem of the fluctuating dynamics of an isolated inextensible and semiflexible filament of length L . By focusing explicitly on two key properties of the filaments--their connectivity and inextensibility--we obtain insights into their dynamics. We calculate the dynamics, and we calculate the correlation functions for chains of finite length taking into account the boundary conditions at the chain ends. We obtain closed-form expressions that separate the internal bending modes from the global rotation modes.

Pattern formation of microtubules and motors: inelastic interaction of polar rods

We derive a model describing spatiotemporal organization of an array of microtubules interacting via molecular motors. Starting from a stochastic model of inelastic polar rods with a generic anisotropic interaction kernel we obtain a set of equations for the local rods concentration and orientation. At large enough mean density of rods and concentration of motors, the model describes orientational instability. We demonstrate that the orientational instability leads to the formation of vortices and (for large density and/or kernel anisotropy) asters seen in recent experiments.

The elongation and contraction of actin bundles are induced by double-headed myosins in a motor concentration-dependent manner

Many types of myosin have been found and characterized to date, and already nearly 20 classes have been identified. However, these myosin motors can be classified more simply into two groups according to their head-structure, i.e. double- or single-headed myosins. Why do some myosin motors possess a double-headed structure? One obvious possible reason would be that the two heads improve the motor's processivity and sliding performance. Previously, to investigate the possibility that the double-headed myosins simultaneously interact with parallel arrayed two actin filaments in the presence of Mg-ATP, we developed an in vitro assay system using actin bundles formed by inert polymers. Using that system, we show here that skeletal muscle heavy meromyosin (HMM), a double-headed myosin derivative, but not subfragment-1 (S-1), a single-headed one, was able to contract or elongate actin bundles in a concentration-dependent manner. Similar elongation or contraction of actin bundles can also be induced by other double-headed myosin species isolated in the native state from Dictyostelium, from green algae Chara or from chicken brain. The results of this study confirm that double-headed myosin motors can induce sliding movements among neighboring actin filaments. The double-headed structure of myosins may also be important for generating tension or elongation in actin bundles or gels, and for organizing polarity-sorted actin networks, not just for improving their motor processivity or activity.

Cell and molecular biology of spindle poles and NuMA

Mitotic and meiotic cells contain a bipolar spindle apparatus of microtubules and associated proteins. To arrange microtubules into focused spindle poles, different mechanisms are used by various organisms. Principally, two major pathways have been characterized: nucleation and anchorage of microtubules at preexisting centers such as centrosomes or spindle pole bodies, or microtubule growth off the surface of chromosomes, followed by sorting and focusing into spindle poles. These two mechanisms can even be found in cells of the same organism: whereas most somatic animal cells utilize the centrosome as an organizing center for spindle microtubules, female meiotic cells build an acentriolar spindle apparatus. Most interestingly, the molecular components that drive acentriolar spindle pole formation are also present in cells containing centrosomes. They include microtubule-dependent motor proteins and a variety of structural proteins that regulate microtubule orientation, anchoring, and stability. The first of these spindle pole proteins, NuMA, had already been identified more than 20 years ago. In addition, several new proteins have been characterized more recently. This review discusses their role during spindle formation and their regulation in the cell cycle.

The minus end in sight

Microtubules are intrinsically polar structures. A consequence of this polarity is that the two ends of the microtubule polymer exhibit different properties. The more dynamic plus ends and the mechanisms that regulate their behavior have been the focus of much recent attention. Here, we concentrate on the dynamics and regulation of minus ends, which play distinct but equally critical roles in microtubule function. In the first part of this review, we compare the in vitro and in vivo behavior of microtubules from a minus end perspective. This comparison suggests that cells possess conserved mechanisms to specifically inhibit minus end polymerization, and perhaps also to actively promote depolymerization. In the second part, we focus on the spatial positioning of minus ends, which is achieved by localized microtubule nucleation, minus end capping and minus end anchoring as well as by motor-dependent sorting. These mechanisms are used in different biological contexts to generate the diversity of organized microtubule arrays in cells.

Self-organization and mechanical properties of active filament bundles

A general framework for the description of active bundles of polar filaments is presented. The activity of the bundle results from mobile cross-links that induce relative displacements between the aligned filaments. Our generic description is based on momentum conservation within the bundle. By specifying the internal forces, a simple minimal model for the bundle dynamics can be derived, capturing a rich variety of dynamic behaviors. In particular, contracted states as well as solitary and oscillatory waves appear through dynamic instabilities. We present the full bifurcation diagram of this model and study the effects of a dynamic motor distribution on the bundle dynamics. Furthermore, we discuss the mechanical properties of the bundle in the presence of externally applied forces. Our description is motivated by dynamic phenomena in the cytoskeleton and could apply to in vitro experiments as well as to stress fibers and to self-organization phenomena during cell locomotion.

Instabilities of isotropic solutions of active polar filaments

We study the dynamics of an isotropic solution of polar filaments coupled by molecular motors which generate relative motion of the filaments in two and three dimensions. We investigate the stability of the homogeneous state for constant motor concentration taking into account excluded volume and an estimate of entanglement. At low filament density the system develops a density instability, while at high density entanglement drives the instability of orientational fluctuations.

In vitro assays demonstrate that pollen tube organelles use kinesin-related motor proteins to move along microtubules

The movement of pollen tube organelles relies on cytoskeletal elements. Although the movement of organelles along actin filaments in the pollen tube has been studied widely and is becoming progressively clear, it remains unclear what role microtubules play. Many uncertainties about the role of microtubules in the active transport of pollen tube organelles and/or in the control of this process remain to be resolved. In an effort to determine if organelles are capable of moving along microtubules in the absence of actin, we extracted organelles from tobacco pollen tubes and analyzed their ability to move along in vitro-polymerized microtubules under different experimental conditions. Regardless of their size, the organelles moved at different rates along microtubules in the presence of ATP. Cytochalasin D did not inhibit organelle movement, indicating that actin filaments are not required for organelle transport in our assay. The movement of organelles was cytosol independent, which suggests that soluble factors are not necessary for the organelle movement to occur and that microtubule-based motor proteins are present on the organelle surface. By washing organelles with KI, it was possible to release proteins capable of gliding carboxylated beads along microtubules. Several membrane fractions, which were separated by Suc density gradient centrifugation, showed microtubule-based movement. Proteins were extracted by KI treatment from the most active organelle fraction and then analyzed with an ATP-sensitive microtubule binding assay. Proteins isolated by the selective binding to microtubules were tested for the ability to glide microtubules in the in vitro motility assay, for the presence of microtubule-stimulated ATPase activity, and for cross-reactivity with anti-kinesin antibodies. We identified and characterized a 105-kD organelle-associated motor protein that is functionally, biochemically, and immunologically related to kinesin. This work provides clear evidence that the movement of pollen tube organelles is not just actin based; rather, they show a microtubule-based motion as well. This unexpected finding suggests new insights into the use of pollen tube microtubules, which could be used for short-range transport, as actin filaments are in animal cells.

Macroscopic equations for pattern formation in mixtures of microtubules and molecular motors

Inspired by patterns observed in mixtures of microtubules and molecular motors, we propose continuum equations for the evolution of motor density and microtubule orientation. The chief ingredients are the transport of motors along tubules, and the alignment of tubules in the process. The macroscopic equations lead to aster and vortex patterns in qualitative agreement with experiments. While the early stages of evolution of tubules are similar to coarsening of spins following a quench, the rearrangement of motors leads to arrested coarsening at low densities. Even in one dimension, the equations exhibit a variety of interesting behaviors, such as symmetry breaking, moving fronts, and motor localization.